question
stringlengths 37
38.8k
| group_id
int64 0
74.5k
| sentence_embeddings
listlengths 1.02k
1.02k
|
|---|---|---|
<p>Ok, so on Science channel was a special about Hawking/Susskind debating black holes, which can somehow remove information from the universe.</p>
<p>A) In stars, fusion converts 4 hydrogen into 1 helium, with a small fraction of the mass being converted to energy. </p>
<p>This happens all the time, and nobody is that amazed about it anymore. So, I have to assume that science is ok with the idea of fusion happening, and so, converting matter into energy doesn't destroy the information of the matter.</p>
<p>Let's take that as Assuption 1:<br>
** 1: Converting matter to energy is OK.</p>
<p>B) In empty space, quantum fluctuations of the energy levels are presumed to allow "pair creation" where a particle and its anti-particle can be created out of the really tiny amounts of energy that exist in empty space. For quantum fluctutations, if I understand it, the uncertaincy principle actually dictates that the amount of energy can fluctuate, allowing a pair to be created even if there "shouldn't be enough energy", because the amount of energy in a small space is uncertain.</p>
<p>The tiny amount of energy becomes a particle + anti-particle, for a tiny instant, and then they fall back into each other, and are converted back to the same tiny amount of energy.</p>
<p>Anyways, ignoring the fact that I'm fuzzy on all the requirements for pair creation -- it is generally accepted as part of quantum physics that it can happen. </p>
<p>So, again, I have to assume that science is ok with the idea of pair creation. And so, converting energy into matter, must also not destroy the information value of the energy, and that information value must remain even after the 2 particles annihilate and go back to being energy.</p>
<p>Let's take that as Assumptions 2 + 3:
** 2: Converting energy into matter is OK.
** 3: Pair creation, doesn't mess up anything.</p>
<p>C) Ok, now black holes. My (weak) understanding of Hawking's idea on how black holes emit energy is that pair creation can happen close to the black hole. Since the position of energy is uncertain at the quantum level, some of the energy that "should be" inside the black hole's event horizon, can be treated as uncertainly outside the black hole, and then that extra energy can cause pair creation. If the black hole then pulls in both particles, then nothing special happens -- the mass/energy stays inside the black hole. </p>
<p>But if one or both of the particles moves away from the black hole, and somehow escapes, that can cause the energy to leave the black hole. This is assumed to be a very unlikely event, but still within possibility.</p>
<p>Anyways, that's my (very rough) understanding of Hawking's theory on how black holes can loose mass over time, when in theory "nothing can escape a black hole". Let's assume Hawking's correct...</p>
<p>If a black hole continues to loose mass over cosmic time, it will eventually disappear, and the problem is stated that when it vanishes: All of the information which the black hole had formerly consumned, will be lost. </p>
<p>Which contradicts the Law of Conservation of Information. At least, that's how the Science channel presented it.</p>
<p>So, my idea/question:</p>
<p>** Every time the black hole looses mass, it's through the processes of energy->matter, or matter->energy->matter, involved in pair creation. Based on assumptions 1, 2 + 3 above, none of these should violate the Law of Conservation of Information. It seems that the very slow process of loosing mass, should also be a very slow process of "leaking" information back into the rest of the universe.</p>
<pre><code>*** So, WHAT's the problem? ***
</code></pre>
<p>By my understanding: By the time the black hole vanishes, it's OK -- because all of it's information should also have leaked back into the rest of the universe, and no information will be lost.</p>
<p>OK, so please tell me why this is wrong. It seems intuituve to me, but really smart people have spent years looking into this. So, am I missing something?</p>
<p>Thanks!
-Chuck</p>
<p>ps. Also, if my statement of fusion, pair creation, and/or hawking radition is wrong -- BUT NOT IN A WAY THAT MATERIALLY AFFECTS THE QUESITON -- please overlook that and just focus on the question.</p>
| 9,544 |
[
-0.006727488711476326,
-0.02680419199168682,
0.013969726860523224,
-0.06191987544298172,
0.012515272945165634,
-0.024759262800216675,
-0.05124704912304878,
-0.03247640281915665,
-0.019891921430826187,
0.00445083761587739,
-0.016961030662059784,
-0.014442681334912777,
0.04291292279958725,
0.03496025502681732,
-0.0037559897173196077,
0.01771468110382557,
0.034660253673791885,
-0.03455877676606178,
-0.013897622004151344,
-0.0231162216514349,
0.016786882653832436,
0.014731190167367458,
-0.008162994869053364,
-0.02418947033584118,
-0.056137096136808395,
0.023781873285770416,
0.016275599598884583,
-0.0053765675984323025,
0.01032404787838459,
0.08930379897356033,
-0.025478187948465347,
-0.04129573702812195,
0.03955301269888878,
0.029486678540706635,
0.023002929985523224,
0.00005485575456987135,
-0.010763302445411682,
-0.037670016288757324,
-0.006109224632382393,
0.021631114184856415,
-0.019485898315906525,
-0.0020488696172833443,
-0.006668627727776766,
0.025654418393969536,
-0.051882654428482056,
-0.0019288792973384261,
0.024110842496156693,
-0.0014398872153833508,
0.04374228045344353,
-0.05140969157218933,
0.030164048075675964,
0.011415635235607624,
0.005938511807471514,
0.0031005500350147486,
-0.010810588486492634,
0.0252953190356493,
0.08372512459754944,
0.07812772691249847,
0.011301489546895027,
-0.04982445389032364,
-0.025716343894600868,
-0.01726710796356201,
-0.0117154186591506,
0.02450207993388176,
-0.007331755943596363,
0.03855406120419502,
0.009884855709969997,
0.0039743343368172646,
0.009047061204910278,
-0.004315503407269716,
0.024426540359854698,
-0.006161813158541918,
-0.024518335238099098,
0.021093204617500305,
0.04965047538280487,
-0.01660178229212761,
0.040690720081329346,
-0.025356849655508995,
0.029703227803111076,
0.0995742604136467,
-0.016827953979372978,
0.01431596651673317,
0.043877825140953064,
0.033303916454315186,
0.03958490490913391,
0.002930206712335348,
0.08272476494312286,
-0.015385664068162441,
0.016652995720505714,
0.03497195243835449,
0.005514033138751984,
0.00666334293782711,
0.020545294508337975,
-0.008631267584860325,
-0.021931402385234833,
0.05306828394532204,
0.001945767435245216,
0.041485145688056946,
-0.030120307579636574,
-0.012699084356427193,
-0.015526678413152695,
0.012798415496945381,
0.06230320781469345,
0.06997451931238174,
0.008392374031245708,
-0.0551820807158947,
-0.05146678537130356,
0.030041445046663284,
-0.014439956285059452,
-0.00866872537881136,
-0.028557799756526947,
0.00828884169459343,
-0.030257467180490494,
-0.029811928048729897,
0.026266710832715034,
-0.05112291872501373,
0.00417611189186573,
-0.014472316019237041,
0.09036903083324432,
0.06962589174509048,
0.05205904692411423,
-0.017179297283291817,
-0.006104635074734688,
-0.01767619140446186,
-0.028939127922058105,
0.003279896918684244,
0.029509665444493294,
-0.004344457760453224,
-0.027188122272491455,
0.022535890340805054,
-0.01754980906844139,
-0.0002957299875561148,
0.03514329716563225,
0.01538659818470478,
-0.013280357234179974,
-0.01708899438381195,
-0.08864043653011322,
-0.03763183206319809,
0.05050237476825714,
-0.03581342473626137,
-0.05306343361735344,
-0.0784381851553917,
0.009660251438617706,
0.03321303427219391,
0.07668018341064453,
-0.03335089981555939,
-0.033710651099681854,
-0.01731261797249317,
0.03674810007214546,
0.012145769782364368,
-0.03678146377205849,
-0.03723003715276718,
-0.010323217138648033,
-0.03677117079496384,
-0.02578166499733925,
-0.030554326251149178,
0.027951281517744064,
0.04223262146115303,
0.0069625903852283955,
0.015805071219801903,
0.06728606671094894,
-0.006662890315055847,
-0.0015189767582342029,
0.019478052854537964,
-0.014835398644208908,
-0.00769803998991847,
0.06398060917854309,
0.03640718758106232,
-0.01484790351241827,
0.02371922880411148,
0.011746286414563656,
-0.007447302341461182,
0.002806833479553461,
0.0027462586294859648,
0.018550744280219078,
-0.02703963592648506,
-0.01616826467216015,
-0.07045265287160873,
0.025236625224351883,
-0.014238572679460049,
-0.02421276457607746,
-0.01747523993253708,
-0.02901380881667137,
-0.02542329952120781,
0.017353501170873642,
0.04081988334655762,
-0.00006811865750933066,
0.024342810735106468,
0.01601324789226055,
-0.033582523465156555,
-0.04250842705368996,
-0.056535471230745316,
0.0003053848340641707,
0.013630853965878487,
0.01379634439945221,
0.0008600400178693235,
0.03140845149755478,
0.005999716930091381,
-0.039348211139440536,
-0.05863958224654198,
0.013306256383657455,
0.04209677502512932,
-0.004948373418301344,
-0.004749946296215057,
0.025239065289497375,
0.0648631826043129,
0.020546993240714073,
0.010133719071745872,
0.01395566388964653,
0.01948358863592148,
-0.020439332351088524,
0.008493531495332718,
0.016479365527629852,
0.009768793359398842,
0.0019445433281362057,
-0.025915047153830528,
0.05251118913292885,
-0.010234431363642216,
-0.018080903217196465,
-0.006013564299792051,
-0.04124210774898529,
0.06877073645591736,
0.008357765153050423,
0.00016790590598247945,
-0.026462707668542862,
0.04431892931461334,
0.01584712043404579,
0.011746951378881931,
-0.019268987700343132,
-0.03498899191617966,
-0.06052754819393158,
0.02895617112517357,
0.008731730282306671,
0.037764765322208405,
0.01352755632251501,
0.013632994145154953,
0.031680796295404434,
0.004623363260179758,
0.012315806932747364,
0.004091598559170961,
-0.009695213288068771,
-0.034005969762802124,
0.02011469565331936,
-0.0035724316257983446,
0.004835980478674173,
0.0046052695252001286,
0.03051477111876011,
0.004370342008769512,
-0.025900885462760925,
-0.004352292977273464,
-0.021795237436890602,
-0.014036992564797401,
-0.004187475889921188,
0.01517549715936184,
-0.025051014497876167,
-0.019622044637799263,
0.0039228470996022224,
0.015143143944442272,
0.03326559439301491,
0.003374214982613921,
0.002762169810011983,
-0.01056444551795721,
-0.04261656105518341,
-0.016871586441993713,
-0.006587783340364695,
0.023636499419808388,
-0.0036753425374627113,
0.0032078977674245834,
0.012255281209945679,
-0.018939541652798653,
-0.032394036650657654,
-0.01923847198486328,
-0.004522050730884075,
-0.04014220088720322,
-0.00711735337972641,
0.014850100502371788,
-0.0022470795083791018,
0.04630720987915993,
-0.05588444322347641,
-0.019605698063969612,
-0.00950276106595993,
-0.00718551455065608,
0.02912997268140316,
0.04759754613041878,
-0.058774299919605255,
0.011106027290225029,
-0.06180540472269058,
-0.026670431718230247,
0.04995327070355415,
-0.04782294109463692,
0.045325540006160736,
0.003851388581097126,
-0.0024982099421322346,
-0.05126006901264191,
0.020896660163998604,
-0.03903413936495781,
-0.03728558123111725,
-0.030661949887871742,
0.018641645088791847,
0.04208661988377571,
-0.011883380822837353,
-0.07315639406442642,
0.021901369094848633,
-0.009714747779071331,
-0.03330996632575989,
-0.005720940884202719,
-0.001332149375230074,
0.019765717908740044,
-0.01607835665345192,
0.03934333845973015,
0.03380943089723587,
-0.034732282161712646,
-0.015285017900168896,
-0.06402713805437088,
-0.056975387036800385,
0.02956939861178398,
-0.012101609259843826,
0.007729472126811743,
-0.0338178426027298,
-0.07480773329734802,
0.03334435820579529,
-0.005323705263435841,
-0.010108990594744682,
0.006195066496729851,
0.0027217722963541746,
0.022145655006170273,
-0.004716163035482168,
0.024351026862859726,
0.031375616788864136,
0.02472555823624134,
0.02546410821378231,
0.004785851575434208,
0.051142290234565735,
-0.022631829604506493,
0.002550384495407343,
-0.03842698782682419,
0.015119599178433418,
0.000922266102861613,
0.010865965858101845,
0.04067949950695038,
0.0066942693665623665,
-0.0322929210960865,
0.027103204280138016,
-0.02094135992228985,
0.02055981010198593,
0.008426938205957413,
-0.05012119561433792,
0.0630987212061882,
0.02798980288207531,
0.030955636873841286,
-0.03206295520067215,
0.03475048393011093,
-0.022447777912020683,
-0.03504692390561104,
0.03863704204559326,
-0.01714932546019554,
0.0547620914876461,
0.0014466941356658936,
0.022365253418684006,
0.014185721054673195,
0.062409866601228714,
-0.007421111688017845,
-0.024483734741806984,
-0.011355375871062279,
-0.002138865180313587,
0.011854652315378189,
-0.01967480592429638,
0.0043474058620631695,
0.04236987978219986,
0.038975074887275696,
0.006229712162166834,
0.0021783693227916956,
-0.00872565247118473,
-0.030276397243142128,
-0.050704874098300934,
-0.007736853323876858,
-0.027019256725907326,
0.0545312874019146,
0.017337720841169357,
0.04202215000987053,
0.040889788419008255,
0.0140217375010252,
-0.003731443313881755,
-0.03920209780335426,
-0.06777983158826828,
-0.005942259915173054,
-0.00816364586353302,
-0.014397119171917439,
0.013824481517076492,
-0.0017301171319559216,
-0.018449800089001656,
-0.028589773923158646,
-0.035105250775814056,
-0.04903452470898628,
0.021773194894194603,
-0.06554247438907623,
0.01779090240597725,
-0.03431900590658188,
-0.04684129357337952,
-0.012434335425496101,
0.046337466686964035,
0.08703967183828354,
0.005636070854961872,
0.020639736205339432,
0.017089081928133965,
-0.058269619941711426,
0.005162728950381279,
0.01211174950003624,
0.01762496307492256,
-0.008024667389690876,
0.03930893540382385,
0.030267756432294846,
-0.0036047366447746754,
-0.03509383276104927,
-0.0030426837038248777,
0.05952522158622742,
0.02742116153240204,
-0.010387898422777653,
0.009343362413346767,
-0.01746664009988308,
0.010457498952746391,
-0.023792365565896034,
0.011152978055179119,
0.0765087753534317,
-0.0063462890684604645,
0.014590831473469734,
-0.02623100019991398,
0.032253094017505646,
-0.0011411086888983846,
0.01905209757387638,
0.08679947257041931,
-0.023782890290021896,
-0.024916745722293854,
-0.043668121099472046,
-0.02569468691945076,
-0.023620540276169777,
-0.026377510279417038,
0.006315093021839857,
0.023924682289361954,
-0.03419509157538414,
-0.01966308243572712,
-0.010958649218082428,
0.02368093654513359,
-0.028000157326459885,
-0.012692754156887531,
-0.05951425060629845,
0.01956465095281601,
-0.007319227792322636,
0.01882767677307129,
0.020515182986855507,
0.03234501928091049,
0.03457261994481087,
0.01877109706401825,
0.015092005021870136,
-0.057151131331920624,
-0.011291655711829662,
0.03220215439796448,
0.09138001501560211,
-0.007236924022436142,
-0.013413574546575546,
-0.07056427001953125,
-0.004630121868103743,
0.036053676158189774,
-0.0425073504447937,
0.01767873205244541,
-0.01851191371679306,
0.009609196335077286,
0.0013770883670076728,
-0.018579743802547455,
0.021357199177145958,
0.060218773782253265,
-0.03462290018796921,
0.016315964981913567,
-0.020182907581329346,
-0.02004336006939411,
-0.006977671757340431,
0.01452802773565054,
0.04621689394116402,
0.07200627028942108,
-0.009237830527126789,
-0.03830626979470253,
0.028940340504050255,
-0.011651908978819847,
-0.03313365951180458,
-0.08350380510091782,
0.015396594069898129,
-0.004806856624782085,
-0.04855231195688248,
0.05994421988725662,
-0.018460100516676903,
-0.05443599075078964,
-0.028039267286658287,
0.002116970717906952,
-0.027721982449293137,
-0.00906379148364067,
-0.05229081213474274,
0.028884097933769226,
0.030833899974822998,
0.011732030659914017,
0.03845396637916565,
0.04712757468223572,
-0.05374632775783539,
0.019344180822372437,
-0.027408568188548088,
0.023285776376724243,
0.0019454520661383867,
0.035426851361989975,
-0.03937428072094917,
-0.007990000769495964,
-0.060917023569345474,
-0.0004934529424645007,
-0.0011337080504745245,
0.00965094193816185,
0.03445202112197876,
-0.030567336827516556,
0.000667071552015841,
-0.014248305931687355,
-0.009388224221765995,
0.01606578193604946,
-0.04408956691622734,
0.028733378276228905,
-0.0028830973897129297,
0.000056375458370894194,
0.012350269593298435,
0.011535627767443657,
-0.021182622760534286,
0.02955673448741436,
-0.013512494042515755,
0.02341688796877861,
-0.02526174485683441,
-0.031858645379543304,
0.032022830098867416,
-0.039383042603731155,
0.006618458777666092,
-0.016074219718575478,
-0.013971757143735886,
0.01864585280418396,
-0.011429212987422943,
-0.04482419788837433,
-0.025960983708500862,
-0.014122307300567627,
0.020284568890929222,
-0.031004920601844788,
0.02882472239434719,
0.004133298061788082,
0.013853772543370724,
-0.0665547251701355,
-0.007959938608109951,
0.024005386978387833,
0.00017588853370398283,
-0.008999962359666824,
0.0029273906257003546,
0.032865360379219055,
-0.043209683150053024,
-0.017771443352103233,
-0.010454143397510052,
0.00249777315184474,
-0.06986643373966217,
-0.02125631831586361,
0.0010749294888228178,
0.013430394232273102,
0.00937174167484045,
0.010427136905491352,
-0.0117459362372756,
-0.001029621227644384,
0.016398156061768532,
-0.0025421862956136465,
0.02182147093117237,
0.028333835303783417,
-0.01892554573714733,
-0.05951967090368271,
-0.00408267742022872,
-0.011316465213894844,
-0.006104236468672752,
-0.03333013877272606,
-0.009869853965938091,
0.03099444881081581,
0.01856825314462185,
0.006640342064201832,
0.022452985867857933,
0.023059383034706116,
-0.04836191609501839,
0.024788904935121536,
0.004416555631905794,
0.025228222832083702,
0.010080426931381226,
-0.019400522112846375,
0.011592498980462551,
0.00017051375471055508,
0.006915845908224583,
-0.008197471499443054,
0.03015238605439663,
0.03309930860996246,
-0.03984185680747032,
0.011480373330414295,
-0.062296319752931595,
0.01777815632522106,
-0.01832045055925846,
0.030972782522439957,
0.0014433951582759619,
-0.008507042191922665,
-0.005711974576115608,
-0.015580074861645699,
-0.04148855805397034,
-0.0021469551138579845,
0.03922777995467186,
-0.013689965941011906,
0.027966467663645744,
0.008884175680577755,
0.028448959812521935,
0.009807047434151173,
-0.0617845393717289,
0.004735248163342476,
0.013924610801041126,
0.005430441349744797,
-0.001069011283107102,
-0.006615063175559044,
-0.04277142882347107,
0.06499640643596649,
0.04157361015677452,
-0.011128994636237621,
0.010530717670917511,
0.04657454788684845,
0.03716476634144783,
0.025707384571433067,
-0.021419737488031387,
-0.07111570239067078,
0.008768877014517784,
-0.04133163392543793,
0.014901300892233849,
0.016060158610343933,
-0.008768967352807522,
0.02472744695842266,
0.005541564896702766,
0.01142721064388752,
-0.02969677373766899,
-0.04685717448592186,
-0.051214370876550674,
0.006659206468611956,
-0.044830791652202606,
-0.022765018045902252,
-0.009767044335603714,
0.02142993174493313,
-0.0025910157710313797,
0.006281146313995123,
-0.02031194604933262,
0.011372239328920841,
-0.08426331728696823,
-0.015703603625297546,
0.0036997897550463676,
-0.043144043534994125,
0.05519548058509827,
-0.03084718994796276,
-0.06370670348405838,
0.03414919227361679,
-0.01070981752127409,
0.027337178587913513,
0.012681839987635612,
0.019160525873303413,
-0.04880443215370178,
0.030645590275526047,
-0.0039697629399597645,
0.026825694367289543,
-0.07143844664096832,
0.019884776324033737,
0.1516595333814621,
0.024333635345101357,
-0.01496910024434328,
-0.03758671507239342,
-0.024421006441116333,
-0.012607252225279808,
0.005830663722008467,
-0.00037961988709867,
0.04844237491488457,
-0.007176738698035479,
0.019560489803552628,
0.024461654946208,
0.031177327036857605,
0.05002373084425926,
-0.04575365036725998,
0.04277893528342247,
-0.022429175674915314,
-0.0036680386401712894,
-0.005960498936474323,
0.015287380665540695,
-0.004600693937391043,
-0.0037452748510986567,
-0.032301221042871475,
-0.003189870622009039,
-0.012424936518073082,
0.016306638717651367,
-0.00940028578042984,
-0.017800865694880486,
0.00764297042042017,
0.029883425682783127,
-0.051318418234586716,
0.015166891738772392,
0.007714633364230394,
0.011562595143914223,
0.0070210895501077175,
0.001757888589054346,
0.01728614792227745,
-0.02970816195011139,
-0.007817711681127548,
0.04036113992333412,
0.012100365944206715,
-0.013371780514717102,
0.026533709838986397,
0.022285908460617065,
-0.05940084531903267,
-0.034287065267562866,
-0.03149789199233055,
0.07634460926055908,
-0.031659018248319626,
-0.0015939895529299974,
-0.0071493047289550304,
0.015726380050182343,
0.05582370609045029,
-0.028796419501304626,
-0.005211976356804371,
0.013829102739691734,
-0.007265961728990078,
0.015265128575265408,
-0.005442066118121147,
0.01081128604710102,
0.04467415437102318,
-0.014371613040566444,
0.02464601956307888,
0.006977902725338936,
0.01874101720750332,
-0.02621927484869957,
0.023854520171880722,
0.02632283791899681,
0.015217889100313187,
0.003825180698186159,
-0.03674640133976936,
-0.00006080811726860702,
-0.040311627089977264,
-0.03663996607065201,
0.019297413527965546,
0.022969739511609077,
0.051033686846494675,
0.007602513302117586,
0.03424862399697304,
-0.007720591966062784,
-0.03501458466053009,
0.030494745820760727,
-0.03067675232887268,
0.00036050728522241116,
-0.012258879840373993,
0.011788984760642052,
-0.0018206146778538823,
0.0129865612834692,
-0.043570488691329956,
-0.006904307287186384,
0.016337843611836433,
0.038496945053339005,
0.0019838660955429077,
-0.03574555739760399,
-0.01408472005277872,
0.012775150127708912,
-0.02131616324186325,
-0.01273641362786293,
-0.011969199404120445,
0.014118949882686138,
0.03590572625398636,
0.0071971239522099495,
0.03054615668952465,
0.019615497440099716,
0.0074447751976549625,
0.0008726859232410789,
0.03135346248745918,
-0.020180437713861465,
0.007225534413009882,
0.027086222544312477,
0.03973258659243584,
-0.0007022637291811407,
-0.024772487580776215,
0.010623619891703129,
0.011296442709863186,
-0.041432637721300125,
0.036760155111551285,
-0.026691140606999397,
0.03346836194396019,
0.005575156304985285,
0.03278632089495659,
-0.010164591483771801,
0.020558703690767288,
-0.04802059382200241,
0.030240386724472046,
0.005108040291815996,
0.012606065720319748,
0.00021236069733276963,
0.04510790854692459,
0.0118486899882555,
-0.01943720132112503,
0.03336280956864357,
-0.017935777083039284,
-0.03165552765130997,
-0.01688413694500923,
0.02438795194029808,
0.017480114474892616,
0.007550880778580904,
0.030474498867988586,
-0.023905355483293533,
0.02809528075158596,
-0.049121301621198654,
-0.05693459138274193,
0.013464230112731457,
0.006161141209304333,
0.0010390362003818154,
0.03697962686419487,
-0.03852234035730362,
-0.011189893819391727,
0.07207588851451874,
0.0030100999865680933,
-0.0041835736483335495,
0.034536659717559814,
-0.017322933301329613,
-0.02495579421520233,
0.024047277867794037,
0.028151312842965126,
-0.011097116395831108,
0.014282670803368092,
0.03950941935181618,
0.029552066698670387,
-0.008435028605163097,
0.013601761311292648,
-0.02037682570517063,
-0.028223520144820213,
0.021986456587910652,
-0.00962133426219225,
-0.013677692040801048,
-0.027465004473924637,
0.036431796848773956,
-0.010529961436986923,
0.037272948771715164,
0.04023554548621178,
0.045785244554281235,
-0.1321112960577011,
-0.04074917361140251,
0.012874983251094818,
-0.003550610039383173,
0.009931448847055435,
-0.05254930257797241,
0.03603450208902359,
0.022145604714751244,
-0.05150879546999931,
0.04037557914853096,
-0.035750389099121094,
-0.037925392389297485,
-0.006004517897963524,
0.024238573387265205,
-0.04487442225217819,
0.004799795337021351,
0.025212803855538368,
0.02957148477435112,
-0.022980235517024994,
-0.003910896833986044,
-0.03463596850633621,
-0.005269583780318499,
-0.04030692204833031,
0.007428228855133057,
-0.006245956290513277,
0.0034231829922646284,
0.0751417800784111,
-0.03647790849208832,
-0.005839695688337088,
0.02485523372888565,
-0.004879092797636986,
-0.012672466225922108,
-0.048355188220739365,
0.009314779192209244,
0.018698982894420624,
0.017177918925881386,
0.023223429918289185,
0.013813258148729801,
0.047786079347133636,
0.024167221039533615,
0.016220444813370705,
0.017367102205753326,
0.006242664530873299,
0.005466170608997345,
0.008052700199186802,
-0.04963274672627449,
-0.014753220602869987,
0.02674116939306259,
-0.012029960751533508,
0.006079397164285183,
-0.010801825672388077,
0.0270179845392704,
-0.01777735911309719,
-0.004685241263359785,
-0.03569018095731735,
-0.02627156488597393,
-0.03481408208608627,
0.019407562911510468,
0.03427552059292793,
0.009061471559107304,
0.01996167004108429,
-0.01853920891880989,
-0.0012956061400473118,
0.024775516241788864,
-0.02133730798959732,
-0.0014862779062241316,
-0.04380140081048012,
-0.027395272627472878,
-0.005098343826830387,
0.061235591769218445,
0.036794234067201614,
-0.07586876302957535,
-0.03462255746126175,
0.037482716143131256,
-0.008868547156453133,
0.05459049716591835,
-0.05571505054831505,
-0.047068726271390915,
-0.0340312235057354,
-0.08235974609851837,
0.017490945756435394,
-0.0108192702755332,
0.05583474040031433,
-0.059172146022319794,
-0.04233776777982712,
0.00826390739530325,
0.00027113239048048854,
0.03752412274479866,
0.014221010729670525,
-0.02606736309826374,
0.02463357150554657,
-0.04891099035739899,
0.029642220586538315,
-0.014749068766832352,
0.04270137473940849,
0.00806975644081831,
0.01319653820246458,
0.01611192896962166,
0.001913654850795865,
0.012448274530470371,
0.022690441459417343,
0.04091263189911842,
-0.03770983964204788,
0.023430414497852325,
-0.003947446588426828,
-0.03653967007994652,
0.028675757348537445,
0.0067365579307079315,
0.013898059725761414,
0.02771630883216858,
0.005925299599766731,
0.034688904881477356,
0.04525329917669296,
-0.016348645091056824,
-0.023118939250707626,
0.02673058584332466,
-0.01999027281999588,
0.012926634401082993,
-0.012151375412940979,
-0.004751570988446474,
0.03507357835769653,
-0.039670009166002274,
-0.008999133482575417,
0.06919696182012558,
-0.026915373280644417,
-0.00964533630758524,
0.05913986265659332,
-0.0008213358814828098,
0.06293757259845734,
-0.011652871035039425,
0.028873413801193237,
-0.01697043888270855,
0.03983978554606438,
-0.01829918660223484,
0.04837736487388611,
0.025178613141179085,
0.014474747702479362,
-0.007899463176727295,
0.015796111896634102,
-0.0026513393968343735,
-0.011883864179253578,
0.0011153859086334705,
0.03595816716551781,
-0.012221846729516983,
-0.02207794226706028,
0.026315506547689438,
-0.00882844626903534,
-0.0029293105471879244,
0.04029451310634613,
-0.012371663935482502,
0.07251393049955368,
0.017257899045944214,
0.010026934556663036,
-0.03183739259839058,
0.005016201641410589,
-0.018002314493060112,
0.017937367781996727,
0.008910072036087513,
0.08532676100730896,
-0.0019662906415760517,
-0.025230569764971733,
-0.019276028499007225,
0.035249944776296616,
0.013289875350892544,
-0.07525332272052765,
0.012787366285920143,
-0.014577691443264484,
0.019289379939436913,
-0.023037990555167198,
-0.007624202407896519,
-0.012389080598950386,
-0.045669857412576675,
0.04376882687211037,
0.019703129306435585,
-0.005183771252632141,
0.02097826823592186,
-0.036434419453144073,
-0.017014125362038612,
0.02799813449382782,
-0.018900811672210693,
-0.004104385152459145,
-0.03217410296201706,
0.05228237807750702,
-0.012350320816040039,
-0.035509828478097916
] |
<p>In an infinite plane elastic plate of thickness $d$, it is shown that the modes of oscillation corresponding to a fixed time-frequency $\omega$ have wave-numbers given by solutions of the Rayleigh-Lamb equations</p>
<p>$$\frac{\tan (pd)}{\tan (qd)}=-\left[\frac{4k^2pq}{\left(k^2-q^2\right)^2}\right]^{\pm 1}$$</p>
<p>where the +1 exponent corresponds to symmetric modes and the -1 exponent to antisymmetric modes, and</p>
<p>$$p^2=\frac{\omega ^2}{c_L^2}-k^2$$</p>
<p>$$q^2=\frac{\omega ^2}{c_T^2}-k^2$$</p>
<p>where $c_L^2=\frac{2\mu +\lambda }{\rho }$ is the longitudinal wave-speed and $c_T^2=\frac{\mu }{\rho }$ is the transverse wave-speed ($\mu$ and $\lambda$ being the Lame constants). From this equation one obtains certain dispersion curves, relating the wave-number of each mode to the frequency. My question is: For each value of the frequency, the Rayliegh-Lamb equations give a discrete number of wave-numbers. How do you decide which wave-number belongs to which mode? That is, if I have a set of wave-numbers corresponding to one value of the frequency, say $\omega_1$, and then I get a new set of wave-numbers corresponding to a different frequency, say $\omega_2$, then how do I identify wave-numbers corresponding to different frequencies as belonging to the same mode?</p>
<p>I hope I've explained myself adequately. You can see that my question can also be framed for many other trascendental equations with multiple roots that show up in mathematical physics. I chose this particular problem to make my point. One might think that it is just a matter of ordering the wave-numbers in increasing order. But I've seen dispersion curves in which the curves for different modes intersect, so an ordering criterion is not applicable (not sure if this happens for the Rayleigh-Lamb modes, though)</p>
<p>Thanks. And sorry for the brick of text.</p>
| 9,545 |
[
0.0037058519665151834,
-0.01703045144677162,
0.018633374944329262,
-0.05658847838640213,
0.01940501108765602,
0.003934518434107304,
-0.022945890203118324,
-0.026936441659927368,
-0.003962240181863308,
-0.02552439272403717,
0.04535476490855217,
0.00978389848023653,
0.022494129836559296,
-0.010336633771657944,
0.033723462373018265,
0.03393826261162758,
-0.031604256480932236,
0.011374005116522312,
-0.025457803159952164,
-0.06330493092536926,
0.004824775271117687,
-0.0241461843252182,
-0.035097893327474594,
-0.006808087229728699,
-0.036113183945417404,
0.02923683077096939,
0.03702378273010254,
0.006631160154938698,
0.036348115652799606,
0.012694370932877064,
0.029058048501610756,
-0.015350906178355217,
0.014367553405463696,
0.024761473760008812,
-0.0018062647432088852,
-0.013432886451482773,
-0.03310740366578102,
0.014838652685284615,
-0.010662549175322056,
0.0251200832426548,
-0.0156668983399868,
-0.029278641566634178,
-0.00559024466201663,
0.008048993535339832,
0.010586333461105824,
0.020045753568410873,
0.05258483439683914,
-0.03434116765856743,
0.0036952595692127943,
-0.04562671482563019,
0.08876856416463852,
-0.001282603945583105,
0.03499086573719978,
0.005349671468138695,
-0.003328376915305853,
-0.002253914950415492,
0.05766671150922775,
0.03273831680417061,
-0.0029083590488880873,
-0.07209444046020508,
-0.022624123841524124,
0.026670172810554504,
0.012642265297472477,
-0.0004992266185581684,
-0.047514960169792175,
0.030915169045329094,
-0.014587672427296638,
0.002993321977555752,
-0.010906598530709743,
-0.027835505083203316,
-0.001242289668880403,
-0.0004909937852062285,
0.042307257652282715,
-0.05340631306171417,
-0.01351000927388668,
-0.020611824467778206,
-0.009080975316464901,
0.05556340515613556,
0.016112055629491806,
-0.0048459479585289955,
0.02949349582195282,
0.03623118996620178,
-0.02682468481361866,
0.033865801990032196,
0.003620611736550927,
-0.013606542721390724,
0.05106620490550995,
0.019622251391410828,
0.013312115333974361,
0.011448446661233902,
0.01223317626863718,
0.01646287553012371,
-0.00549459969624877,
-0.019401423633098602,
0.030821580439805984,
-0.007567337714135647,
0.007599685341119766,
-0.007344454992562532,
0.0036207817029207945,
-0.031830910593271255,
0.01909925602376461,
-0.06491012871265411,
-0.010904033668339252,
0.06224186718463898,
-0.003306418424472213,
0.00245895073749125,
-0.02941548451781273,
0.03224843367934227,
0.01319811213761568,
-0.011561037041246891,
-0.009080096147954464,
0.04247598350048065,
-0.01564980112016201,
-0.007558980491012335,
-0.01327216625213623,
0.004110034089535475,
0.01302125584334135,
-0.04753834381699562,
0.03131240978837013,
0.07925199717283249,
0.07043112814426422,
-0.039394207298755646,
0.030143681913614273,
-0.02165001817047596,
-0.08819080889225006,
-0.03375545144081116,
0.0003836546966340393,
-0.0026711991522461176,
-0.01730327121913433,
0.019617756828665733,
0.060713157057762146,
-0.0295484010130167,
0.01992257498204708,
-0.02331257238984108,
0.047482773661613464,
-0.004728822968900204,
-0.09140977263450623,
-0.06747362017631531,
0.048211243003606796,
-0.011829381808638573,
-0.017132341861724854,
-0.05290898680686951,
-0.019411688670516014,
0.04276713356375694,
0.05048783868551254,
-0.013814633712172508,
0.005265828687697649,
0.0024293921887874603,
0.025802548974752426,
0.025242546573281288,
0.013972611166536808,
-0.0010657249949872494,
-0.03098972700536251,
-0.03551449254155159,
0.028284551575779915,
-0.01288849301636219,
0.0005798257188871503,
0.019083065912127495,
-0.005151723977178335,
-0.009078140370547771,
0.055797286331653595,
-0.020082669332623482,
-0.020557422190904617,
0.03054625354707241,
-0.018775174394249916,
-0.024782303720712662,
0.04748337343335152,
0.021922117099165916,
-0.023624012246727943,
0.05020485445857048,
0.0171993225812912,
-0.017569955438375473,
-0.015265287831425667,
0.04582345858216286,
-0.0006664073443971574,
-0.019311893731355667,
-0.008673724718391895,
-0.03447766974568367,
-0.011618400923907757,
0.00424965238198638,
-0.006978907622396946,
-0.04359637200832367,
0.0393686480820179,
0.011830052360892296,
0.025290731340646744,
0.05508020147681236,
-0.004181684926152229,
0.051305193454027176,
0.04290234297513962,
-0.06352870166301727,
-0.010034318082034588,
-0.013233238831162453,
0.02823658473789692,
0.0019906789530068636,
-0.006312415469437838,
0.04751412197947502,
0.0034990310668945312,
-0.01699935272336006,
-0.019382696598768234,
-0.01030912809073925,
-0.022890441119670868,
0.039208319038152695,
0.03279123455286026,
-0.015001272782683372,
0.04017408937215805,
0.0301711093634367,
0.014582117088139057,
-0.006222927011549473,
0.05637529119849205,
-0.013889926485717297,
0.020921891555190086,
0.03614741191267967,
-0.03863007202744484,
0.029330115765333176,
-0.02551402896642685,
-0.04522687941789627,
-0.006563290487974882,
-0.0601077638566494,
-0.028721969574689865,
0.046459078788757324,
-0.061511751264333725,
0.030774882063269615,
0.06614699214696884,
-0.016910839825868607,
0.00920136645436287,
0.049392346292734146,
-0.0280618779361248,
0.07843442261219025,
-0.020739644765853882,
-0.0020945314317941666,
-0.05270911008119583,
-0.015240470878779888,
0.03124075196683407,
0.05694454908370972,
-0.01867717318236828,
0.006391171831637621,
0.013780100271105766,
0.045507512986660004,
0.04268765076994896,
-0.02243044413626194,
-0.03223337233066559,
-0.0379628911614418,
0.02315872348845005,
0.024250540882349014,
-0.0316610261797905,
0.005163226742297411,
0.017686180770397186,
0.018260078504681587,
0.0348488911986351,
-0.06176324188709259,
0.004319734405726194,
0.043946098536252975,
-0.003327874466776848,
-0.0006166421226225793,
0.009356488473713398,
0.004851986188441515,
0.014910222962498665,
-0.015306109562516212,
0.034390971064567566,
0.03271074220538139,
-0.03950236365199089,
0.004344302695244551,
0.005155849736183882,
0.009686958976089954,
0.04154741391539574,
-0.012354080565273762,
-0.03188265487551689,
-0.011298036202788353,
0.02933588996529579,
-0.030948970466852188,
-0.024611275643110275,
-0.02182801626622677,
-0.03929688408970833,
0.0067871203646063805,
-0.011970092542469501,
0.03688070550560951,
0.024942317977547646,
0.0439499132335186,
-0.02727055922150612,
-0.01408845279365778,
0.018182048574090004,
-0.03110508620738983,
0.016972864046692848,
0.012822285294532776,
-0.008626973256468773,
0.0007683310541324317,
-0.026953428983688354,
-0.015850145369768143,
0.02164158783853054,
0.0077956970781087875,
-0.022905461490154266,
0.03192884474992752,
-0.004691219888627529,
-0.06386962532997131,
-0.030258581042289734,
-0.07610198855400085,
0.003861559322103858,
-0.04664558544754982,
0.026932736858725548,
0.04983019456267357,
-0.0030718029011040926,
0.0022523589432239532,
-0.022699804976582527,
-0.029668189585208893,
-0.045289039611816406,
0.005317962262779474,
-0.022564219310879707,
0.028546186164021492,
-0.014820033684372902,
0.008910802192986012,
0.03313446789979935,
-0.03532607853412628,
0.029079614207148552,
-0.011930271983146667,
-0.050979726016521454,
0.023460526019334793,
-0.01867137849330902,
0.07485074549913406,
0.000046477041905745864,
-0.004931090399622917,
0.09688163548707962,
0.0294658113270998,
-0.03624806925654411,
-0.0057528382167220116,
0.02324327453970909,
0.019090192392468452,
-0.031128546223044395,
-0.0001708160270936787,
0.04819365218281746,
-0.01723242737352848,
0.053204044699668884,
0.020604409277439117,
0.04531621187925339,
0.025934435427188873,
0.007130742538720369,
-0.013570334762334824,
-0.0039537213742733,
0.007933813147246838,
0.03702876716852188,
0.032891251146793365,
0.02336736023426056,
0.01756817288696766,
0.03870778903365135,
-0.01944238506257534,
0.003596049267798662,
0.019881466403603554,
-0.05649261176586151,
0.04847082868218422,
0.028958596289157867,
-0.01224016584455967,
-0.035752225667238235,
0.011651181615889072,
0.02475009672343731,
-0.016752608120441437,
-0.011156988330185413,
0.04037916660308838,
0.027262328192591667,
-0.014675908721983433,
-0.013252024538815022,
0.05550716817378998,
0.01968996785581112,
0.020836712792515755,
0.019443640485405922,
-0.01769663766026497,
-0.018428392708301544,
0.04140733182430267,
-0.049322567880153656,
-0.010703286156058311,
0.02413969300687313,
0.04673416540026665,
0.028391201049089432,
0.005048139486461878,
-0.019755622372031212,
0.013682303950190544,
-0.033811215311288834,
-0.06193500757217407,
-0.01362878829240799,
0.04845366254448891,
0.0150007838383317,
0.07018990814685822,
0.036947913467884064,
-0.024381736293435097,
0.03254936262965202,
-0.020280232653021812,
-0.05596870183944702,
0.030945496633648872,
-0.006457917857915163,
0.0073183802887797356,
-0.01671021245419979,
-0.032218966633081436,
0.012268790043890476,
-0.038442932069301605,
-0.030556676909327507,
0.013621838763356209,
-0.003239025827497244,
-0.06257300823926926,
0.03667452931404114,
-0.04848892241716385,
-0.06558970361948013,
-0.004343277309089899,
0.04914795979857445,
0.028839046135544777,
-0.020205629989504814,
-0.012898553162813187,
0.07818061113357544,
-0.01613665372133255,
0.030288580805063248,
-0.029182441532611847,
-0.024379584938287735,
0.011158411391079426,
0.025611940771341324,
0.005086645018309355,
0.02626013569533825,
-0.019486574456095695,
-0.020310504361987114,
0.022872598841786385,
0.04059598222374916,
0.02584163472056389,
-0.026567034423351288,
-0.022435234859585762,
-0.02909262478351593,
0.049335163086652756,
0.0038369649555534124,
0.06192314624786377,
-0.0058318632654845715,
-0.024246301501989365,
0.05280938372015953,
-0.01882510632276535,
-0.027070043608546257,
0.049003589898347855,
0.01781877502799034,
0.00596237787976861,
0.005627680569887161,
-0.05904034525156021,
-0.018582316115498543,
-0.03507249429821968,
-0.01772766187787056,
-0.014784818515181541,
0.011557123623788357,
0.01900847814977169,
0.041427988559007645,
0.03841153159737587,
-0.006312559358775616,
0.01378929615020752,
-0.001422207336872816,
-0.00638617342337966,
-0.01739191636443138,
0.003567397128790617,
-0.0331251434981823,
0.01672663912177086,
0.0411841906607151,
0.0283451396971941,
-0.010976416990160942,
0.007673820946365595,
-0.08796419203281403,
-0.04032105579972267,
0.01170970406383276,
0.037902843207120895,
0.012291220016777515,
0.006507241167128086,
-0.042483482509851456,
-0.04612506181001663,
0.016324736177921295,
-0.02431323193013668,
0.011976802721619606,
-0.020719995722174644,
0.007262742146849632,
-0.020916897803544998,
0.0011659420561045408,
-0.010416876524686813,
0.03118744306266308,
0.07349589467048645,
-0.0432836189866066,
-0.08246468752622604,
0.03657972812652588,
-0.022269723936915398,
0.015582401305437088,
-0.008011240512132645,
0.01841285638511181,
-0.03621403127908707,
-0.018592236563563347,
-0.010867476463317871,
0.016704704612493515,
-0.002946417545899749,
-0.045213352888822556,
-0.0027345363050699234,
0.042609233409166336,
0.03746411204338074,
0.021755561232566833,
-0.012519602663815022,
-0.04192977771162987,
0.058226801455020905,
0.008831534534692764,
0.005100607872009277,
0.04555121436715126,
-0.003903978271409869,
0.06498626619577408,
0.003523434279486537,
0.01564124785363674,
0.03341579809784889,
0.05714336037635803,
-0.0213658157736063,
-0.030299900099635124,
-0.009632519446313381,
0.0072879791259765625,
-0.026263009756803513,
-0.006943104322999716,
-0.007473845034837723,
0.04571541026234627,
-0.020202752202749252,
0.05004461482167244,
-0.00282848859205842,
0.025871211662888527,
-0.00020764258806593716,
-0.017353186383843422,
-0.0052930209785699844,
0.02634141594171524,
0.02383342944085598,
0.0018492764793336391,
0.01816030591726303,
0.03985019773244858,
0.004196972120553255,
-0.0020086790900677443,
0.010757445357739925,
-0.00629157992079854,
0.015988126397132874,
0.02015850879251957,
0.025142287835478783,
0.023670384660363197,
-0.05715915188193321,
-0.003189181676134467,
-0.0023801694624125957,
-0.040546443313360214,
0.018029266968369484,
0.012323825620114803,
-0.0006972400587983429,
0.014806908555328846,
-0.06607002019882202,
-0.02395964227616787,
0.029700133949518204,
0.035521965473890305,
0.04057083651423454,
0.008358445949852467,
0.005333913955837488,
0.07149004191160202,
-0.01848902553319931,
-0.07568664103746414,
0.014152312651276588,
0.011178644374012947,
0.01589818485081196,
-0.052091311663389206,
-0.004850058816373348,
0.01732943207025528,
0.02149827405810356,
-0.041235074400901794,
0.03509072586894035,
0.04845566302537918,
0.001049404963850975,
-0.013983283191919327,
0.005872360896319151,
0.0463503859937191,
0.06337759643793106,
-0.03835465759038925,
-0.018022770062088966,
0.0028290951158851385,
-0.01687021180987358,
-0.024567697197198868,
0.013383258134126663,
0.019777018576860428,
-0.019018320366740227,
-0.006853081285953522,
-0.01856132596731186,
-0.021222904324531555,
0.02632186748087406,
-0.02881244383752346,
-0.03043857216835022,
-0.010319123044610023,
0.011761942878365517,
-0.020093997940421104,
-0.009239655919373035,
0.003268531756475568,
-0.010491603054106236,
0.02863151766359806,
0.022838743403553963,
0.012756966054439545,
-0.05445336923003197,
-0.05092135816812515,
-0.010265841148793697,
-0.03131815418601036,
0.015821153298020363,
0.005159460473805666,
0.03535294905304909,
-0.023708472028374672,
0.004307472612708807,
-0.03373776376247406,
-0.0211934931576252,
0.04633240029215813,
-0.01339003536850214,
0.01491170097142458,
-0.022241825237870216,
0.0013988001737743616,
-0.030312564224004745,
-0.04175758361816406,
-0.04083717241883278,
0.007552854251116514,
0.07708702236413956,
-0.005525919608771801,
0.038400109857320786,
0.007119381800293922,
-0.04023691266775131,
0.012624241411685944,
0.0035898967180401087,
-0.012567361816763878,
-0.0064413840882480145,
0.0018605267396196723,
0.04002225771546364,
-0.07991720736026764,
-0.05088527500629425,
-0.004242124035954475,
0.024611517786979675,
0.031173963099718094,
-0.020323341712355614,
-0.011136122979223728,
0.038964271545410156,
-0.035195913165807724,
-0.040393318980932236,
-0.036929670721292496,
0.05123733729124069,
0.009464861825108528,
0.018286561593413353,
-0.0060364059172570705,
-0.02180176042020321,
0.041211698204278946,
0.04258877411484718,
0.0237436406314373,
-0.016964979469776154,
0.020845938473939896,
-0.05400197580456734,
0.06091179698705673,
0.015031707473099232,
0.011057572439312935,
0.0331561304628849,
0.013103149831295013,
0.0007416579755954444,
0.022183600813150406,
0.037399400025606155,
-0.006119797006249428,
-0.005952615290880203,
-0.006103592924773693,
-0.013918484561145306,
-0.055170923471450806,
0.03712499886751175,
-0.010180553421378136,
-0.03331071883440018,
0.012682176195085049,
-0.03017657995223999,
0.0292599368840456,
0.022577697411179543,
0.0029453143943101168,
-0.06805483996868134,
0.06425167620182037,
-0.019505491480231285,
0.014133735559880733,
0.007149761542677879,
-0.011987642385065556,
0.12701952457427979,
0.0799906849861145,
0.016498230397701263,
-0.01883307658135891,
0.013455718755722046,
-0.0054759737104177475,
0.00017552313511259854,
-0.04603774473071098,
0.024895600974559784,
-0.0023623346351087093,
0.0013557333732023835,
0.024123547598719597,
0.051848236471414566,
-0.03932471200823784,
0.01855061762034893,
0.036295946687459946,
-0.017382316291332245,
-0.0207209475338459,
-0.011111652478575706,
0.00648432457819581,
-0.006795504130423069,
0.013732561841607094,
0.006399370729923248,
0.00984279066324234,
-0.019448325037956238,
-0.0033726405818015337,
-0.019025346264243126,
-0.03951408714056015,
0.02177027240395546,
-0.017958518117666245,
-0.05772151052951813,
-0.004326186142861843,
0.01567011885344982,
-0.038483746349811554,
-0.020745357498526573,
0.03275315836071968,
-0.004825678188353777,
-0.03871062770485878,
0.05545128881931305,
0.01479275617748499,
-0.010610952042043209,
-0.017729556187987328,
-0.0009043904137797654,
0.012930475175380707,
-0.02240179479122162,
-0.003584272926673293,
-0.03223252296447754,
0.018955115228891373,
-0.012874146923422813,
-0.014056939631700516,
-0.009702431969344616,
0.01659589633345604,
0.0014043954433873296,
-0.04066632688045502,
-0.029127413406968117,
-0.034103378653526306,
0.04181821271777153,
-0.023580556735396385,
0.009319913573563099,
-0.035532087087631226,
0.010267219506204128,
-0.0011788381962105632,
0.022517306730151176,
-0.004822266288101673,
-0.03910006955265999,
-0.02340814657509327,
-0.004295005463063717,
0.02800324186682701,
0.006577544845640659,
0.005676680244505405,
-0.04056733474135399,
-0.011386477388441563,
-0.02709725685417652,
-0.013309096917510033,
-0.007396328262984753,
0.02456817589700222,
0.046231869608163834,
0.00962221808731556,
-0.025197651237249374,
-0.08216062933206558,
-0.08380241692066193,
0.0010530726285651326,
0.005984495859593153,
-0.0010097876656800508,
-0.023353243246674538,
-0.027370333671569824,
-0.010273830965161324,
0.0636184886097908,
-0.0510089248418808,
0.04677928239107132,
0.014794215559959412,
0.010522485710680485,
0.030917786061763763,
-0.04916924238204956,
-0.04354085400700569,
0.017853638157248497,
-0.013533109799027443,
0.025998922064900398,
-0.007027564104646444,
0.013931783847510815,
0.0018794448114931583,
0.022158019244670868,
-0.016298415139317513,
0.058446042239665985,
-0.02576219104230404,
-0.01781226322054863,
-0.002967311069369316,
-0.023973636329174042,
0.021531932055950165,
0.011410756036639214,
0.040166955441236496,
-0.05459960177540779,
-0.042426347732543945,
0.0021325601264834404,
-0.004458802752196789,
-0.002633210737258196,
0.0203719362616539,
-0.0005164036410860717,
-0.011318228207528591,
-0.04687924310564995,
-0.025975627824664116,
-0.05040659010410309,
-0.01690012402832508,
-0.019862279295921326,
0.017077045515179634,
-0.018899690359830856,
0.01852569542825222,
-0.014941316097974777,
0.03990492969751358,
-0.016845496371388435,
-0.021966444328427315,
0.0015271318843588233,
0.032860759645700455,
0.01935356669127941,
-0.018550513312220573,
0.04033147543668747,
-0.021228622645139694,
0.038272425532341,
0.020390672609210014,
-0.035128962248563766,
0.02161344885826111,
-0.03846032917499542,
-0.031059056520462036,
0.04127105697989464,
-0.011309737339615822,
0.026557736098766327,
0.05151749029755592,
0.023516470566391945,
-0.03244045749306679,
0.022435063496232033,
-0.04062463343143463,
0.0056473929435014725,
-0.034411512315273285,
0.00844530388712883,
-0.013788365758955479,
-0.0443151518702507,
-0.00033626327058300376,
-0.017180711030960083,
-0.013256513513624668,
0.010550344362854958,
0.034626107662916183,
-0.03005059063434601,
0.0028356711845844984,
0.016550378873944283,
-0.02652384527027607,
0.016568917781114578,
0.004353048279881477,
0.0529269278049469,
0.008698327466845512,
0.043636880815029144,
-0.00315737072378397,
0.0652601420879364,
0.05798590928316116,
-0.0023580400738865137,
-0.07272571325302124,
-0.01659633219242096,
0.007689665071666241,
0.0513407327234745,
0.029157571494579315,
-0.007063363678753376,
0.020686563104391098,
-0.004352974239736795,
-0.041153017431497574,
0.06092231348156929,
-0.05695771798491478,
0.014928216114640236,
-0.05685996636748314,
-0.020892295986413956,
-0.046106670051813126,
0.04666813462972641,
0.05051419883966446,
0.021815910935401917,
0.03658963367342949,
0.03545114025473595,
-0.029894139617681503,
-0.018411686643958092,
0.011707869358360767,
0.0240020751953125,
0.037995222955942154,
-0.035192959010601044,
0.03141607344150543,
-0.01602385938167572,
-0.043721698224544525,
0.019787780940532684,
-0.00162819167599082,
0.015907397493720055,
0.005388427525758743,
0.030762048438191414,
0.0004967063432559371,
0.01691691018640995,
-0.0008156935800798237,
-0.0025965715758502483,
-0.044254738837480545,
0.03472794219851494,
0.0068619102239608765,
-0.026401212438941002,
-0.02210964635014534,
0.0045270901173353195,
0.032700955867767334,
-0.0450846366584301,
-0.03253736346960068,
0.01483925711363554,
-0.0635763555765152,
0.00994474533945322,
0.011574759148061275,
-0.012702448293566704,
-0.0013312366791069508,
0.003082182025536895,
0.011674784123897552,
-0.027430422604084015,
-0.022559979930520058,
0.012392762117087841,
0.006881789304316044,
-0.006158479489386082,
0.03285376727581024,
-0.019048301503062248,
-0.06432240456342697,
0.0393502302467823,
0.03410698473453522,
-0.012461147271096706,
-0.060435228049755096,
-0.01879947818815708,
0.009772217832505703,
0.00003693422695505433,
-0.0014252450782805681,
-0.012901765294373035,
-0.0160604789853096,
0.02878737263381481,
-0.0012738395016640425,
0.015055869705975056,
-0.06855693459510803,
-0.05802588164806366,
0.005799677688628435,
-0.049937471747398376,
0.02278042398393154,
0.03276435658335686,
-0.04825930669903755,
-0.01389233022928238,
-0.04328102245926857,
-0.004903205204755068,
0.04470884054899216,
0.05863971635699272,
-0.0005128923803567886,
0.0002250133256893605,
-0.010906017385423183,
-0.0005315610906109214,
0.04950934275984764,
-0.03818298131227493,
-0.014947258867323399,
-0.02372327260673046,
0.003381911898031831,
-0.04388684779405594,
0.01936402916908264,
-0.019119873642921448,
0.01427463162690401,
0.05981200933456421,
-0.01593264378607273,
0.0154446791857481,
0.005974991712719202,
-0.07236895710229874,
0.024059485644102097,
-0.01902245357632637,
-0.020213602110743523,
0.066494420170784,
-0.04670073091983795,
-0.013241635635495186,
0.014627720229327679,
-0.06449317187070847,
-0.04598396271467209,
0.011980179697275162,
-0.05349041149020195,
0.017618782818317413,
0.02274698205292225,
0.04847662150859833,
0.0403592512011528,
-0.04087694361805916,
0.00022649686434306204,
0.04582232981920242,
-0.015308553352952003,
-0.053860221058130264,
0.02582971192896366,
0.023385189473628998,
0.009047778323292732,
0.012765983119606972,
0.024677768349647522,
-0.006482323165982962,
-0.03265479952096939,
0.026451347395777702,
0.004601395223289728,
-0.016487617045640945,
0.0036132752429693937,
-0.006169795989990234,
0.0015118239680305123,
-0.04863296449184418,
0.01595459133386612,
-0.019052525982260704,
0.024233384057879448,
-0.02656223624944687,
-0.017045602202415466,
-0.004753999412059784,
-0.006244578864425421,
-0.03853534907102585,
0.015636343508958817,
-0.03790163993835449,
0.08865215629339218,
0.010312382131814957,
0.0371895469725132,
-0.018011538311839104,
0.004215922672301531,
0.004623450804501772,
0.01468551717698574,
-0.00980502087622881,
-0.0008292766869999468,
-0.05249345675110817,
0.029726959764957428,
-0.02074313536286354,
-0.020730311051011086,
0.02569875679910183,
-0.046641722321510315,
0.006303505506366491,
0.025927044451236725,
-0.01719103939831257,
0.04245685040950775,
-0.017530884593725204,
-0.0445348396897316,
0.03565974906086922,
0.0520167201757431,
0.0273536816239357,
-0.0135313356295228,
0.017142251133918762,
0.011646927334368229,
-0.011206360533833504,
0.008425524458289146,
-0.042824722826480865,
-0.01096414029598236,
-0.015032067894935608,
0.02004421129822731,
0.007724250666797161,
0.002033014316111803
] |
<p>I'm trying to understand how the <a href="http://en.wikipedia.org/wiki/Gell-Mann%E2%80%93Nishijima_formula" rel="nofollow">Gell-Mann–Nishijima relation</a> has been derived:
\begin{equation}
Q = I_3 + \frac{Y}{2}
\end{equation}
where $Q$ is the electric charge of the quarks, $I_3$ is the isospin quantum number and $Y$ is the hypercharge given by:
\begin{equation}
Y = B + S
\end{equation}
where $B$ is the baryon number and $S$ is the strangeness number. </p>
<p>Most books (I have looked at) discuss the Gell-Mann–Nishijima in relation to the approximate global $\mathrm{SU(3)}$ flavour symmetry that is associated with the up-,down- and strange-quark at high enough energies. But I have yet to fully understand the connection between the Gell-Mann–Nishijima and the $\mathrm{SU(3)}$ flavour symmetry. </p>
<p>Can the Gell-Mann–Nishijima relation somehow been derived or has it simply been postulated by noticing the relation between $Q$, $I_3$ and $Y$? If it can be derived, then I would be very grateful if someone can give a brief outline of how it is derived.</p>
| 9,546 |
[
-0.017186827957630157,
-0.03298289701342583,
0.017260799184441566,
-0.011340286582708359,
0.024464387446641922,
0.04938000813126564,
-0.04173947870731354,
0.006031302269548178,
0.023261472582817078,
-0.0402185395359993,
0.032115042209625244,
0.024818982928991318,
0.07257380336523056,
0.035232413560152054,
0.003717841347679496,
0.04527623578906059,
0.0007918322226032615,
0.021110858768224716,
-0.019053446128964424,
-0.05681163817644119,
0.02080276422202587,
0.030946027487516403,
-0.012903926894068718,
0.006909497547894716,
0.00028716144151985645,
0.023955505341291428,
0.06315047293901443,
0.03901715949177742,
0.033034633845090866,
0.05774664133787155,
0.03481524810194969,
-0.05607670545578003,
0.027231507003307343,
-0.024804377928376198,
0.01155488658696413,
0.017460377886891365,
0.0000027377977858122904,
-0.039816707372665405,
0.0007807399379089475,
0.02183808758854866,
-0.06179341673851013,
-0.00110279256477952,
-0.016700504347682,
0.04824887961149216,
-0.03217606246471405,
0.02201479859650135,
-0.0523071363568306,
-0.0055355289950966835,
0.03414110466837883,
-0.05996120721101761,
0.07620777934789658,
0.03758680447936058,
0.01979476399719715,
0.02190474607050419,
-0.006782027892768383,
0.0016752071678638458,
0.07926277816295624,
0.0368998683989048,
-0.004743281286209822,
-0.06466145813465118,
-0.03982485458254814,
-0.04216184467077255,
0.01073999423533678,
-0.03166130557656288,
0.0036119893193244934,
0.022236261516809464,
-0.025603799149394035,
-0.006334979552775621,
-0.006847748067229986,
-0.03704569861292839,
0.023891685530543327,
0.032170698046684265,
0.020431993529200554,
-0.03882959112524986,
0.02574075199663639,
0.0056063346564769745,
-0.012926477007567883,
-0.01396797876805067,
0.02893352508544922,
0.025379732251167297,
-0.033038798719644547,
0.037638433277606964,
0.006730030756443739,
0.018638839945197105,
-0.005504198372364044,
-0.008565224707126617,
0.07487062364816666,
-0.03655983507633209,
-0.003475850448012352,
0.022507665678858757,
-0.010698620229959488,
0.003837146097794175,
0.041452229022979736,
-0.004515767563134432,
-0.018869757652282715,
0.03275071084499359,
0.022519048303365707,
0.0404408760368824,
0.01072384137660265,
0.007541163358837366,
-0.007981431670486927,
-0.018503284081816673,
0.0009052630048245192,
0.10761168599128723,
-0.009922211989760399,
-0.035246413201093674,
-0.02772732824087143,
-0.008589211851358414,
-0.013852668926119804,
-0.002235843800008297,
-0.0024096104316413403,
-0.015912530943751335,
-0.04346076026558876,
-0.02263251319527626,
-0.014407986775040627,
-0.006691094022244215,
0.042892731726169586,
-0.008927704766392708,
0.05044640600681305,
0.025480300188064575,
0.027622103691101074,
0.016520392149686813,
0.0009153382270596921,
-0.03502008318901062,
-0.059519361704587936,
0.025190068408846855,
0.03425048291683197,
-0.007652945816516876,
-0.020893946290016174,
0.037742480635643005,
-0.008899789303541183,
-0.020159076899290085,
-0.01407779660075903,
0.009707772172987461,
0.025898775085806847,
-0.00011242504115216434,
-0.06811534613370895,
-0.06596069782972336,
0.042090144008398056,
-0.004861851222813129,
-0.009995301254093647,
-0.07066500186920166,
-0.019224751740694046,
0.03308270499110222,
0.07258328795433044,
-0.004294770769774914,
0.0006985955405980349,
-0.03384224325418472,
-0.0036511849611997604,
0.032458364963531494,
-0.0048674666322767735,
-0.033309292048215866,
0.0005742473877035081,
-0.041291818022727966,
-0.021183988079428673,
-0.048540666699409485,
0.04421902820467949,
0.01325192116200924,
0.0003292313194833696,
0.0018674598541110754,
0.09483186900615692,
-0.024472016841173172,
-0.005553307011723518,
0.02896083891391754,
-0.01789705827832222,
0.001969175413250923,
0.08538740128278732,
-0.007209923584014177,
0.006894655525684357,
0.04231913760304451,
-0.026043210178613663,
0.016817376017570496,
0.02602662891149521,
0.04057931527495384,
0.06060076877474785,
-0.06225741282105446,
-0.02572839893400669,
-0.05114065483212471,
-0.03172007575631142,
-0.020143620669841766,
-0.051136232912540436,
-0.020993495360016823,
0.003528706729412079,
-0.0006498818984255195,
0.009326505474746227,
0.007201205939054489,
-0.05143008381128311,
-0.0215541310608387,
0.029125453904271126,
-0.059923991560935974,
-0.06294012069702148,
-0.0491841621696949,
-0.02717846818268299,
-0.007273248862475157,
-0.04917909950017929,
0.017787430435419083,
-0.004426754545420408,
0.009743176400661469,
0.01138813141733408,
-0.008054465986788273,
0.02209111675620079,
0.03833232447504997,
0.03137720376253128,
0.0004665438609663397,
0.0334274061024189,
0.018277248367667198,
0.0214744433760643,
-0.01364675909280777,
0.05244564265012741,
-0.05937131121754646,
-0.034807924181222916,
0.007597684394568205,
-0.03472452238202095,
0.04743770882487297,
-0.012707460671663284,
-0.009126844815909863,
0.01639743521809578,
0.017688648775219917,
-0.03360021859407425,
-0.002477450529113412,
-0.02431926131248474,
0.07388633489608765,
0.029497841373085976,
0.021773122251033783,
-0.004565269686281681,
0.040307532995939255,
0.022995389997959137,
0.05443112924695015,
0.00339689664542675,
-0.05397908389568329,
-0.05017087608575821,
-0.042571600526571274,
-0.003041944233700633,
0.02566128596663475,
-0.019315987825393677,
-0.000117455143481493,
0.03409145399928093,
0.021534539759159088,
-0.0008690799004398286,
0.009148911572992802,
-0.031834736466407776,
-0.00006460751319536939,
-0.001207615016028285,
0.031408585608005524,
-0.04686562716960907,
0.02429804392158985,
-0.009937952272593975,
0.007373799104243517,
0.01374043244868517,
-0.037076082080602646,
-0.05445157736539841,
0.014170512557029724,
0.014337291941046715,
-0.028677042573690414,
0.005920883268117905,
-0.033778656274080276,
0.05578821152448654,
-0.045864541083574295,
0.044544145464897156,
0.030284840613603592,
-0.003205927088856697,
0.011577368713915348,
-0.009642372839152813,
-0.016926931217312813,
0.014906481839716434,
0.013271982781589031,
-0.033893465995788574,
0.012598819099366665,
0.006428741384297609,
-0.009188770316541195,
0.028757262974977493,
-0.007227704394608736,
-0.007467953488230705,
-0.01976933516561985,
-0.024735966697335243,
-0.00959286279976368,
0.020899280905723572,
0.01800941489636898,
-0.04307350143790245,
-0.03979329392313957,
0.020329207181930542,
0.012425803579390049,
0.009516560472548008,
-0.038560900837183,
-0.03371116518974304,
0.0010781817836686969,
-0.07171902060508728,
-0.01898372545838356,
0.0058182962238788605,
-0.018858527764678,
0.008813104592263699,
0.0023304845672100782,
-0.006593678612262011,
-0.022313371300697327,
-0.018098797649145126,
-0.002256381791085005,
0.026998862624168396,
-0.018467381596565247,
-0.00018794920470099896,
0.029371382668614388,
0.011571891605854034,
-0.01860128715634346,
0.03251904621720314,
-0.040192924439907074,
-0.017276927828788757,
-0.013572855852544308,
0.0376436822116375,
-0.023567553609609604,
-0.03178166598081589,
0.014321960508823395,
0.0438985750079155,
-0.021157892420887947,
-0.019254816696047783,
-0.03420654311776161,
-0.059083860367536545,
0.02885272540152073,
0.018460355699062347,
0.01548328623175621,
-0.009901611134409904,
-0.08203086256980896,
0.1001376286149025,
0.027517322450876236,
-0.04995150864124298,
-0.02328723855316639,
-0.013169519603252411,
0.009996491484344006,
-0.007127037271857262,
0.022526923567056656,
0.03385185822844505,
-0.009844934567809105,
0.02078634686768055,
0.020161930471658707,
0.05602804198861122,
0.023591255769133568,
0.01646919548511505,
-0.05592437461018562,
0.0024005481973290443,
0.018934940919280052,
0.016246642917394638,
0.050808653235435486,
0.0006256109336391091,
-0.0707935020327568,
-0.025150613859295845,
0.02118120901286602,
0.009394990280270576,
-0.014740228652954102,
-0.03877480328083038,
0.0658353865146637,
0.018259776756167412,
0.008875113911926746,
0.007995807565748692,
0.026349317282438278,
-0.026664501056075096,
-0.024996060878038406,
0.02225131168961525,
0.04388578608632088,
0.037501122802495956,
-0.018516359850764275,
-0.0008154154638759792,
0.02614901214838028,
0.03841501101851463,
-0.03933088853955269,
-0.014853283762931824,
-0.03033747524023056,
-0.054742492735385895,
0.00825573317706585,
-0.0068527464754879475,
-0.033333972096443176,
0.025001510977745056,
0.02987619675695896,
0.008778962306678295,
-0.012962139211595058,
-0.030469611287117004,
0.0012827740283682942,
-0.056486278772354126,
-0.0374300517141819,
0.01933877542614937,
0.01587871089577675,
-0.01582730934023857,
0.08982924371957779,
0.02409287542104721,
-0.013763205148279667,
0.03955177962779999,
-0.003176495898514986,
-0.07672809809446335,
0.031178703531622887,
-0.036706648766994476,
0.014536871574819088,
-0.03731504827737808,
-0.008280269801616669,
0.02126486599445343,
-0.005694433115422726,
-0.049403123557567596,
-0.01698225364089012,
-0.002630598610267043,
-0.02486972138285637,
0.012127961032092571,
-0.03670009970664978,
-0.0013893769355490804,
-0.02888648211956024,
0.03122972697019577,
0.04943009465932846,
-0.04102534055709839,
-0.041970569640398026,
0.03501870483160019,
-0.0664382055401802,
-0.03419436514377594,
-0.01334387343376875,
0.047610487788915634,
0.02246786095201969,
0.014028039760887623,
-0.013187726959586143,
0.028965935111045837,
-0.020899783819913864,
-0.01791323348879814,
-0.009518420323729515,
0.05048208683729172,
0.014712183736264706,
-0.03673793748021126,
-0.03311806544661522,
-0.026556257158517838,
0.020227616652846336,
0.04453691840171814,
0.04324348643422127,
0.025513768196105957,
0.026787057518959045,
0.04230010509490967,
0.023803604766726494,
-0.039365872740745544,
0.02005852572619915,
0.09740234911441803,
0.01521403156220913,
-0.022344570606946945,
-0.05749763548374176,
0.01264274213463068,
-0.0002503131399862468,
-0.01767546869814396,
-0.01098563987761736,
0.001387225347571075,
-0.024251233786344528,
0.019162528216838837,
0.03198482096195221,
0.0036128684878349304,
0.00595612358301878,
-0.05103412643074989,
0.01576167345046997,
0.006904718931764364,
0.0050349123775959015,
0.0021922681480646133,
0.014238342642784119,
0.011597787030041218,
0.05007530003786087,
0.006653692107647657,
-0.021288210526108742,
-0.021047182381153107,
-0.006165069527924061,
0.028164705261588097,
0.03479121997952461,
-0.046383392065763474,
-0.018747998401522636,
-0.08125986903905869,
0.00354852550663054,
0.03755912184715271,
-0.009927716106176376,
0.026319529861211777,
0.0002481358824297786,
-0.024425959214568138,
-0.006678386125713587,
-0.02110063098371029,
-0.013637838885188103,
0.046352140605449677,
0.006983256433159113,
0.013973191380500793,
-0.056781183928251266,
0.006555653177201748,
-0.047060027718544006,
0.030680758878588676,
0.017456943169236183,
0.0363604836165905,
0.012483171187341213,
0.03072322905063629,
0.007027945481240749,
0.0054715825244784355,
-0.009888323955237865,
-0.08632350713014603,
0.015270720236003399,
-0.006217234302312136,
0.043292395770549774,
0.0439617820084095,
-0.027181463316082954,
-0.020874477922916412,
0.010773067362606525,
0.019979380071163177,
0.03561593219637871,
0.01008773222565651,
-0.0689510703086853,
0.036221038550138474,
0.03362902253866196,
0.009455455467104912,
0.028733307495713234,
0.027841689065098763,
-0.015723975375294685,
-0.01332746259868145,
-0.020619617775082588,
0.03648993745446205,
0.0026293375995010138,
-0.0199457835406065,
-0.018498249351978302,
0.02575208805501461,
-0.033348310738801956,
0.0599239282310009,
-0.020324582234025,
0.004688870161771774,
-0.03756212070584297,
-0.01715041883289814,
-0.02632736787199974,
0.013954146765172482,
0.01150406152009964,
-0.026985563337802887,
0.0055860248394310474,
0.04269443824887276,
0.04014219716191292,
0.009524052031338215,
0.034677159041166306,
-0.026177000254392624,
-0.00963056180626154,
0.004734212066978216,
0.0037897611036896706,
0.013814229518175125,
-0.014457235112786293,
-0.025127293542027473,
0.025442125275731087,
-0.010281182825565338,
0.041927989572286606,
-0.06711392104625702,
-0.010949576273560524,
-0.0106054013594985,
-0.03331746906042099,
-0.023683011531829834,
0.004613685421645641,
0.004995438270270824,
0.012516656890511513,
-0.004014823120087385,
0.007087080739438534,
0.011099890805780888,
-0.000044049953430658206,
-0.09585649520158768,
-0.0029288772493600845,
0.03888238966464996,
0.014121679589152336,
-0.05919990688562393,
-0.027938006445765495,
-0.0302085243165493,
-0.0354393906891346,
-0.05561633035540581,
0.04755247011780739,
0.08506107330322266,
-0.043058812618255615,
-0.04874377325177193,
0.0020534894429147243,
0.03760118782520294,
0.0019050824921578169,
-0.007284428458660841,
-0.006276319269090891,
0.007387671619653702,
-0.00036539905704557896,
0.02454027347266674,
0.0027140090242028236,
0.07111166417598724,
-0.0009987285593524575,
-0.010097148828208447,
-0.007301095873117447,
-0.023377800360322,
0.010845436714589596,
-0.054400328546762466,
-0.028431620448827744,
0.024347996339201927,
0.03704191744327545,
0.01505129411816597,
-0.005926478188484907,
0.045974284410476685,
-0.010430210269987583,
0.0014590234495699406,
-0.021234527230262756,
-0.017206186428666115,
-0.043008096516132355,
0.03081592731177807,
0.04641939327120781,
-0.0059087323024868965,
-0.005873469170182943,
-0.0017668051877990365,
0.012786084786057472,
0.005182311404496431,
-0.03678644075989723,
0.0392020009458065,
-0.010554244741797447,
0.019301733002066612,
-0.009112785570323467,
0.03185229375958443,
0.032356638461351395,
0.015857642516493797,
0.023699374869465828,
-0.02606971189379692,
-0.05311507359147072,
0.0749952495098114,
0.07921542227268219,
-0.04450919106602669,
0.03694624826312065,
-0.007709047291427851,
-0.010562768206000328,
0.004956638440489769,
0.011447971686720848,
-0.0444803424179554,
0.011829374358057976,
0.01201976090669632,
0.007771781645715237,
-0.06658709794282913,
0.0015741760144010186,
0.02919609472155571,
0.05543386563658714,
-0.0371890664100647,
0.004109179135411978,
0.03155350685119629,
0.018834039568901062,
0.01630472019314766,
-0.015730857849121094,
-0.03357355296611786,
0.10078750550746918,
-0.004557242151349783,
0.03164725750684738,
0.016412947326898575,
-0.015224847011268139,
0.024788208305835724,
0.051950518041849136,
0.004887052811682224,
0.0025272993370890617,
-0.03766530379652977,
-0.029546750709414482,
0.037236206233501434,
0.07612347602844238,
0.013729996047914028,
0.036008112132549286,
0.01339415181428194,
-0.001625239267013967,
-0.022979917004704475,
0.021264929324388504,
-0.0007857987657189369,
-0.0671238973736763,
-0.0018858875846490264,
-0.004909238778054714,
-0.03635652735829353,
0.02016337215900421,
-0.021377205848693848,
-0.04133271425962448,
-0.010187212377786636,
-0.0016680677654221654,
0.045366037636995316,
0.015923889353871346,
0.0496247224509716,
-0.005387336481362581,
0.05124840512871742,
-0.02127176895737648,
0.008937260136008263,
-0.009132680483162403,
0.0181596502661705,
0.10572201013565063,
0.06045915558934212,
0.015588069334626198,
-0.08078189939260483,
0.012536964379251003,
0.0076897842809557915,
0.01729786954820156,
0.013903186656534672,
0.008806281723082066,
0.03451289236545563,
0.0038881597574800253,
-0.02274606190621853,
0.0512908473610878,
-0.0072480458766222,
-0.009547103196382523,
0.043440669775009155,
-0.03311440721154213,
-0.06434141844511032,
0.00854793656617403,
0.028593938797712326,
0.016261611133813858,
-0.025833893567323685,
-0.029482275247573853,
0.0014812196604907513,
0.011756540276110172,
-0.006128573324531317,
-0.016133194789290428,
-0.02372180111706257,
-0.01905413530766964,
0.0111501170322299,
-0.025492770597338676,
-0.0016732843359932303,
-0.0013481522910296917,
-0.0002513486542738974,
-0.021946212276816368,
0.023671651259064674,
-0.0030554537661373615,
-0.011495586484670639,
0.05246039479970932,
0.01583213545382023,
0.04883197695016861,
-0.006377648562192917,
0.027227485552430153,
0.02843388170003891,
-0.043578293174505234,
-0.01907924748957157,
0.030140172690153122,
0.019830599427223206,
-0.04254309833049774,
-0.01113387756049633,
-0.029089290648698807,
-0.011356158182024956,
0.02316746674478054,
-0.026122992858290672,
-0.006970922462642193,
-0.004632365889847279,
0.02576284110546112,
-0.07216158509254456,
-0.016359563916921616,
-0.0024390986654907465,
0.03353993222117424,
-0.015662573277950287,
0.024435698986053467,
-0.0037452038377523422,
-0.01398339495062828,
-0.014574996195733547,
0.012581638991832733,
0.011554365046322346,
-0.019882194697856903,
-0.021307120099663734,
-0.02622278593480587,
-0.0035562440752983093,
-0.03151649236679077,
-0.049151595681905746,
-0.01461526658385992,
0.04053692892193794,
0.05542042851448059,
0.02903502807021141,
-0.03543729707598686,
-0.0022233433555811644,
-0.03940686210989952,
0.03505938500165939,
0.003984346520155668,
0.01336733065545559,
-0.025180581957101822,
-0.006612658035010099,
0.01320936344563961,
0.030990421772003174,
-0.032107334583997726,
0.02374580316245556,
0.0011451522586867213,
0.03414367511868477,
0.008363672532141209,
-0.020597156137228012,
-0.03134651109576225,
0.0037848742213100195,
-0.02896856516599655,
-0.018764067441225052,
-0.01822545751929283,
-0.005940861999988556,
-0.011215291917324066,
0.04393642023205757,
0.01065770536661148,
0.02572508528828621,
-0.019100675359368324,
-0.015520492568612099,
0.013262602500617504,
-0.02214411273598671,
0.016272973269224167,
0.03197602555155754,
0.012873819097876549,
-0.01339196041226387,
-0.023812439292669296,
0.05533977225422859,
-0.005661404691636562,
0.027706323191523552,
-0.003616295289248228,
-0.03839700296521187,
-0.03741661459207535,
-0.004754657857120037,
-0.006592169404029846,
-0.03839632123708725,
-0.026415865868330002,
-0.02354568801820278,
0.03536195680499077,
-0.061232078820466995,
0.03563563898205757,
0.006195932626724243,
0.033051908016204834,
-0.010655217804014683,
-0.018926307559013367,
-0.029290998354554176,
0.0008798628696240485,
-0.026417294517159462,
-0.032912805676460266,
-0.005085523705929518,
-0.0012912657111883163,
0.012530594132840633,
-0.02296966314315796,
-0.03683583810925484,
0.020425189286470413,
-0.055731210857629776,
-0.05683267489075661,
0.016135644167661667,
-0.012936260551214218,
0.008523952215909958,
0.03732352331280708,
-0.01888875477015972,
-0.03801744431257248,
0.05964960902929306,
0.012117852456867695,
0.0035972315818071365,
-0.010098010301589966,
-0.01280889566987753,
-0.00247279554605484,
-0.026496700942516327,
-0.04522089287638664,
-0.010139960795640945,
-0.015916533768177032,
0.04396316781640053,
0.033372458070516586,
-0.04250774532556534,
0.015910256654024124,
0.00759118003770709,
-0.014535529538989067,
0.024931715801358223,
0.013915871270000935,
0.013179510831832886,
0.008504791185259819,
0.01687237247824669,
-0.021962033584713936,
0.028490636497735977,
-0.0128715168684721,
-0.012820914387702942,
-0.05133036896586418,
-0.015300804749131203,
0.021025661379098892,
0.02172139659523964,
0.05096205696463585,
-0.07782866060733795,
0.027025587856769562,
-0.0077519724145531654,
-0.021914033219218254,
0.02015082538127899,
-0.0314185693860054,
-0.03012446127831936,
0.0006351789925247431,
-0.012425429187715054,
0.014297038316726685,
0.017627691850066185,
0.0353349968791008,
0.036884844303131104,
0.029618412256240845,
0.022317061200737953,
0.007783741690218449,
-0.028585420921444893,
-0.02904556319117546,
-0.0020982851274311543,
0.02020890638232231,
-0.03980429843068123,
0.06635268777608871,
-0.013462425209581852,
-0.01666921004652977,
0.06371821463108063,
-0.05244903638958931,
-0.011927255429327488,
0.014762265607714653,
0.04319208115339279,
-0.02989133633673191,
0.02074611932039261,
0.017350858077406883,
-0.008001592010259628,
0.003774057375267148,
-0.011961211450397968,
0.027616320177912712,
0.043798889964818954,
-0.00550856813788414,
0.005209804512560368,
-0.0019588307477533817,
-0.018002824857831,
-0.032791681587696075,
0.017847178503870964,
-0.028568042442202568,
-0.01590968482196331,
0.025539344176650047,
-0.012001029215753078,
0.018472444266080856,
-0.018501533195376396,
0.045330725610256195,
-0.05175231024622917,
0.024937590584158897,
0.009501013904809952,
0.033141281455755234,
0.027803337201476097,
0.03226283937692642,
0.011519791558384895,
-0.033914439380168915,
0.025912925601005554,
0.028207292780280113,
-0.016799548640847206,
-0.04875551164150238,
0.007874715141952038,
0.015510616824030876,
0.04252073913812637,
0.012098281644284725,
-0.04240522161126137,
-0.05152677372097969,
0.03165552392601967,
0.014754325151443481,
0.0069196405820548534,
0.010623377747833729,
-0.019656717777252197,
0.00005383714596973732,
-0.050263911485672,
0.054087504744529724,
0.020307675004005432,
0.001310790074057877,
-0.018407000228762627,
-0.011307765729725361,
-0.016428302973508835,
0.010625774972140789,
0.0733783096075058,
-0.026578348129987717,
-0.02773025445640087,
0.012961718253791332,
0.01564326137304306,
-0.006442361045628786,
0.005838672164827585,
0.016026629135012627,
0.013073548674583435,
-0.004179602023214102,
-0.01957343891263008,
0.018345961347222328,
-0.03515584394335747,
0.0240155179053545,
0.0381443165242672,
-0.017520133405923843,
0.0028731219936162233,
0.011874998919665813,
-0.039310310035943985,
0.014563633129000664,
-0.02021264098584652,
0.008585674688220024,
0.06801215559244156,
-0.015046273358166218,
-0.01465020701289177,
0.038284316658973694,
-0.032377395778894424,
-0.03881300240755081,
0.017620615661144257,
-0.01228695921599865,
-0.009620925411581993,
0.011442531831562519,
-0.04418784752488136,
0.04079139232635498,
-0.041985806077718735,
0.006929733324795961,
0.03866855427622795,
-0.025594331324100494,
-0.020031128078699112,
0.04538390412926674,
0.03067842870950699,
0.01714276149868965,
0.02627132087945938,
-0.03043505735695362,
0.02475476823747158,
0.0029182019643485546,
0.0216625165194273,
0.053685106337070465,
0.03245846554636955,
0.019432976841926575,
-0.009241773746907711,
-0.006544250063598156,
0.022506242617964745,
-0.00028778932755813,
0.005343031138181686,
0.01113375648856163,
-0.030999017879366875,
-0.01422535628080368,
0.051395710557699203,
-0.009039311669766903,
-0.0037052303086966276,
0.006177265662699938,
-0.04775616154074669,
0.09483222663402557,
-0.03509989753365517,
0.01834472082555294,
-0.052344612777233124,
0.005655078217387199,
-0.016669224947690964,
0.025954628363251686,
-0.00205888319760561,
-0.02755558490753174,
0.0016071312129497528,
0.0037050156388431787,
-0.01811044290661812,
-0.0004992892500013113,
0.018478861078619957,
-0.02731352113187313,
-0.029446693137288094,
0.015452777966856956,
0.0026247997302562,
0.033941373229026794,
-0.023264357820153236,
0.007263322826474905,
-0.0011429579462856054,
0.031340088695287704,
0.02720402553677559,
0.010937700979411602,
0.03290710970759392,
0.010289971716701984,
0.015281625092029572,
0.05228192359209061,
-0.04750903323292732,
-0.057170264422893524,
-0.03349065035581589,
0.0025164063554257154,
-0.03222322836518288,
-0.02648741751909256
] |
<p>I am trying to recreate the results of an article (membrane simulation) and I have the following line:</p>
<blockquote>
<p>Both particles have the same soft radius,</p>
<p>$U_{rep} (r)/\epsilon = \text{exp}\left\{ -20 (r/\sigma -1 )\right \}$</p>
</blockquote>
<p>With $\epsilon$ being the energy scale, $\sigma$ being the length scale, and $r$ is the distance between two particles. This is a two body interactions. If I calculate the interactions between two particles, should I put $U_{rep}$ or half of it into each particle? </p>
| 9,547 |
[
0.046331170946359634,
-0.022217439487576485,
-0.016062743961811066,
0.0000527220981894061,
-0.02367638237774372,
0.03532249853014946,
0.00720618199557066,
-0.029569903388619423,
0.0024821388069540262,
-0.006046636495739222,
0.042721278965473175,
0.002226804383099079,
0.07854705303907394,
0.003180085914209485,
0.006250408478081226,
-0.004698844626545906,
0.004590757191181183,
-0.008660364896059036,
0.007486134301871061,
-0.026526611298322678,
0.025122417137026787,
-0.000284948677290231,
0.016174359247088432,
-0.01689240150153637,
-0.016999894753098488,
0.06380139291286469,
0.01385481096804142,
-0.02011263743042946,
-0.005807559937238693,
0.029669150710105896,
-0.023016350343823433,
-0.02672281675040722,
0.03298909217119217,
-0.03766929358243942,
0.028826167806982994,
0.018095586448907852,
-0.060014281421899796,
-0.025491800159215927,
-0.027125783264636993,
0.01364865805953741,
-0.02953832782804966,
0.03168859705328941,
0.025381000712513924,
0.005410804878920317,
0.006715257186442614,
0.018228966742753983,
-0.0033658030442893505,
-0.015696894377470016,
0.03675686568021774,
-0.04742515832185745,
0.05201765149831772,
0.038666848093271255,
0.048235904425382614,
-0.004459749441593885,
0.018194660544395447,
0.014455156400799751,
0.04408172518014908,
0.06541493535041809,
0.003323177108541131,
-0.03664875030517578,
-0.008687256835401058,
-0.009329715743660927,
-0.01796684041619301,
0.007678505498915911,
0.008819797076284885,
0.008629657328128815,
-0.025498002767562866,
0.0016755785327404737,
0.039918962866067886,
0.018463533371686935,
0.03927164524793625,
0.0008390144794248044,
0.06952746957540512,
-0.014805438928306103,
0.03598704934120178,
0.024183427914977074,
0.006702893413603306,
0.01321863941848278,
0.004323593340814114,
0.059035252779722214,
-0.03831121325492859,
0.005380451213568449,
0.04772068187594414,
0.06067471578717232,
-0.013647723011672497,
-0.019589591771364212,
0.05372597649693489,
-0.028680535033345222,
0.0063765812665224075,
0.02197769470512867,
-0.015344268642365932,
0.002556437626481056,
0.064069002866745,
-0.006409334484487772,
-0.03341781347990036,
-0.003526316024363041,
0.017556985840201378,
0.04413232579827309,
-0.020470382645726204,
-0.04290121793746948,
-0.054792895913124084,
-0.03801052272319794,
0.01182272657752037,
0.0733812004327774,
0.006797706242650747,
-0.037543099373579025,
-0.0395735464990139,
-0.020082741975784302,
-0.00002310398849658668,
-0.03348391875624657,
-0.03292467072606087,
-0.006150812841951847,
-0.03756529465317726,
0.022202691063284874,
0.053674645721912384,
-0.005382292438298464,
0.013632732443511486,
0.01976950094103813,
0.06165573000907898,
0.053630173206329346,
0.0502948984503746,
-0.026053989306092262,
0.00036245258525013924,
0.004128003027290106,
-0.04959532245993614,
0.03242078050971031,
0.07103224843740463,
0.007929503917694092,
-0.04248260334134102,
0.06040239706635475,
-0.0025141097139567137,
0.021153267472982407,
-0.022905834019184113,
0.01720885932445526,
0.03086063079535961,
0.007298600859940052,
-0.08285258710384369,
-0.032471541315317154,
0.011040444485843182,
0.016999412328004837,
0.0035541276447474957,
-0.06908788532018661,
-0.02734312415122986,
0.04313269257545471,
0.06647646427154541,
0.0225610863417387,
0.003530915128067136,
0.016397099941968918,
0.05877534672617912,
-0.003496409161016345,
0.016288528218865395,
-0.01180920097976923,
-0.04973496496677399,
-0.0005388636491261423,
-0.03392978385090828,
-0.053716327995061874,
-0.0069936285726726055,
0.04152093082666397,
-0.0010508211562409997,
0.005159846041351557,
0.06692640483379364,
-0.05561855062842369,
0.010117682628333569,
0.017630940303206444,
-0.03238145262002945,
-0.05088880658149719,
0.07426153123378754,
0.006815494503825903,
0.01858074776828289,
-0.0021600904874503613,
0.012980401515960693,
-0.00430027162656188,
0.002924947766587138,
0.01679493859410286,
0.04523354396224022,
-0.0030616973526775837,
0.01225348375737667,
-0.04553811997175217,
-0.03802989795804024,
0.04165870323777199,
-0.05761332809925079,
-0.06771921366453171,
-0.032192379236221313,
0.021140137687325478,
-0.013699007220566273,
-0.021991660818457603,
-0.005776168778538704,
-0.022548630833625793,
-0.02392038330435753,
-0.053042128682136536,
-0.04538867250084877,
-0.029816702008247375,
-0.001576696988195181,
0.0024231092538684607,
-0.02062317542731762,
0.018114561215043068,
0.005476559977978468,
0.010955982841551304,
0.016410328447818756,
-0.030800405889749527,
-0.03302837163209915,
0.005925862118601799,
0.030651861801743507,
0.006065268535166979,
0.02950979955494404,
0.05940256640315056,
0.059935569763183594,
-0.0019318319391459227,
0.020703446120023727,
-0.019979776814579964,
-0.05860687419772148,
-0.02057988941669464,
-0.028283903375267982,
0.019121387973427773,
-0.00020491183386184275,
-0.03262777626514435,
0.016514010727405548,
0.003221903694793582,
-0.0017739447066560388,
-0.004623951856046915,
-0.02066136710345745,
0.07688318938016891,
0.05766672268509865,
0.034034550189971924,
-0.0072336927987635136,
0.028003040701150894,
0.04625599831342697,
0.06126679107546806,
0.007754550315439701,
-0.04549967870116234,
-0.029541317373514175,
-0.01253852155059576,
0.029056847095489502,
0.006722297519445419,
-0.04401779547333717,
-0.0135811697691679,
0.04716288670897484,
0.013689232058823109,
0.02294567972421646,
0.02666967734694481,
-0.026360508054494858,
-0.03804086521267891,
0.06057961285114288,
0.03315563499927521,
0.011090432293713093,
-0.03377330303192139,
-0.001319480943493545,
0.014181159436702728,
0.02069929428398609,
-0.011752303689718246,
0.018117716535925865,
0.014242592267692089,
0.00744054839015007,
0.026048770174384117,
-0.016634086146950722,
-0.02480039745569229,
0.04440372437238693,
-0.01899600215256214,
0.042512573301792145,
0.038012534379959106,
-0.0015335767529904842,
-0.01618325337767601,
-0.0012169803958386183,
-0.015987591817975044,
-0.009204959496855736,
0.04994109272956848,
-0.019744737073779106,
-0.013652551919221878,
0.021089298650622368,
-0.05777185037732124,
0.007040075026452541,
-0.007061208598315716,
0.0005898067029193044,
-0.024442827329039574,
-0.007870658300817013,
0.05549998581409454,
0.018021561205387115,
0.009347718209028244,
-0.044484928250312805,
-0.0003237251075915992,
-0.01932314969599247,
-0.0004526328411884606,
-0.004701424855738878,
0.004874867852777243,
-0.05967249721288681,
0.02957238256931305,
-0.018553823232650757,
-0.017299871891736984,
-0.012363175861537457,
0.011505084112286568,
0.012712867930531502,
-0.007559244055300951,
0.004647710360586643,
-0.02572925016283989,
-0.03377893194556236,
-0.0014900154201313853,
0.02108348160982132,
0.008986884728074074,
-0.021209094673395157,
0.05217968672513962,
0.0071917083114385605,
-0.03064948134124279,
0.02626444771885872,
-0.026622328907251358,
-0.008108487352728844,
-0.012129946611821651,
0.004982016980648041,
0.00997807364910841,
0.01660308614373207,
0.021920328959822655,
0.020581794902682304,
-0.013046630658209324,
-0.03362355753779411,
-0.07123839110136032,
-0.07093363255262375,
0.030282413586974144,
-0.005490816663950682,
0.028741221874952316,
-0.013394738547503948,
-0.028142575174570084,
0.06188684701919556,
-0.060860712081193924,
-0.013629043474793434,
-0.012091650627553463,
0.0007385999779216945,
-0.02370580844581127,
0.0032693082466721535,
-0.013908089138567448,
0.007106289267539978,
0.0026383500080555677,
0.0035644618328660727,
-0.007624009158462286,
0.0485386848449707,
0.016739213839173317,
0.029321985319256783,
-0.02751273475587368,
-0.0045026009902358055,
-0.015302485786378384,
-0.049559179693460464,
0.07136396318674088,
-0.013234619982540607,
-0.0031981731299310923,
0.03939659893512726,
-0.010667528957128525,
0.05016442388296127,
0.04474802315235138,
-0.06183500960469246,
0.027073493227362633,
0.0025590278673917055,
-0.007638365961611271,
0.010953295975923538,
0.021921560168266296,
0.00124383345246315,
-0.03059053234755993,
-0.014670861884951591,
0.029243404045701027,
0.08617788553237915,
-0.034677937626838684,
-0.017863493412733078,
0.08373658359050751,
0.0736783817410469,
-0.016473717987537384,
-0.04966957867145538,
-0.029960373416543007,
-0.021420210599899292,
0.013581612147390842,
0.002643159357830882,
-0.06862542033195496,
0.044295407831668854,
0.013202566653490067,
0.04159020259976387,
-0.04050856828689575,
-0.05675813928246498,
-0.021385112777352333,
-0.06750103831291199,
-0.02727869339287281,
-0.046168409287929535,
0.0434998981654644,
0.004885088186711073,
0.02423134818673134,
-0.012756969779729843,
-0.001916459179483354,
-0.01672077551484108,
-0.00476476177573204,
-0.06198791414499283,
0.03915160894393921,
-0.03827211633324623,
-0.0005807495908811688,
-0.0006415823008865118,
-0.015210676938295364,
0.0060869064182043076,
-0.028569992631673813,
-0.021682072430849075,
0.018048053607344627,
-0.016755323857069016,
-0.01976005919277668,
-0.008254104293882847,
-0.0510440357029438,
-0.05702010914683342,
-0.022875165566802025,
0.03350130841135979,
0.006342307198792696,
-0.02977036125957966,
0.023667611181735992,
0.05644328147172928,
-0.025234753265976906,
-0.0025652481708675623,
-0.0279938206076622,
0.030469851568341255,
0.019523415714502335,
0.0645088329911232,
0.03006683848798275,
0.02857569046318531,
0.0029459940269589424,
0.011752762831747532,
0.04228854924440384,
0.04512694478034973,
-0.04113740101456642,
-0.042906373739242554,
-0.027934277430176735,
-0.027553945779800415,
-0.0172872431576252,
-0.03628864139318466,
0.04894629120826721,
-0.015178661793470383,
0.025535108521580696,
0.0277884379029274,
-0.015539891086518764,
-0.0074308342300355434,
0.03733387216925621,
0.0729713886976242,
0.013549922965466976,
-0.029101848602294922,
-0.0614735372364521,
0.0015052247326821089,
0.0078749880194664,
0.009549010545015335,
0.0035434304736554623,
0.024584587663412094,
-0.004853154998272657,
-0.02414620667695999,
0.022579126060009003,
-0.0021202447824180126,
-0.06026105210185051,
-0.016920041292905807,
-0.03540415316820145,
0.002892794320359826,
-0.03653920814394951,
-0.04057475924491882,
0.015777597203850746,
0.028304653242230415,
0.02571781352162361,
0.004748648032546043,
0.008927184157073498,
-0.023596709594130516,
0.009376411326229572,
0.018784329295158386,
0.024526041001081467,
0.011791116558015347,
-0.0017006321577355266,
-0.03547307848930359,
-0.0000747920130379498,
0.04191378504037857,
-0.04431421682238579,
0.009830771014094353,
-0.0029026411939412355,
0.005687282886356115,
0.03424587845802307,
0.014519520103931427,
-0.0612264908850193,
-0.0011307280510663986,
-0.007917078211903572,
0.026124097406864166,
-0.03104206547141075,
-0.04419887065887451,
-0.026988204568624496,
0.02334001660346985,
0.021809838712215424,
0.029611334204673767,
-0.048270173370838165,
-0.029136283323168755,
-0.012263862416148186,
0.0012505128979682922,
-0.02706257253885269,
-0.09267077594995499,
0.005465177819132805,
0.011439287103712559,
0.033820945769548416,
0.05280042067170143,
-0.029408276081085205,
-0.013286730274558067,
0.0660908967256546,
0.013457883149385452,
0.0060467845760285854,
-0.062442898750305176,
-0.036124337464571,
0.07798558473587036,
0.048721689730882645,
-0.029090257361531258,
0.05994894728064537,
0.04571922495961189,
-0.006428130902349949,
-0.035079944878816605,
-0.05250844359397888,
0.01697787083685398,
-0.03773513808846474,
0.017537139356136322,
-0.04385725036263466,
-0.012990725226700306,
-0.010712397284805775,
0.013503625988960266,
-0.013600808568298817,
0.0489656925201416,
-0.015772802755236626,
-0.03366241604089737,
-0.0052974633872509,
0.00954638421535492,
-0.02583491802215576,
0.010931531898677349,
0.022578109055757523,
-0.004740590695291758,
0.012099948711693287,
0.008807689882814884,
-0.011189003475010395,
-0.01943896897137165,
-0.013348551467061043,
0.03744560107588768,
-0.02622484788298607,
0.024749988690018654,
0.016868699342012405,
-0.026289349421858788,
0.002494421089068055,
-0.08366113156080246,
0.010731653310358524,
-0.02538263611495495,
-0.008177680894732475,
0.007814020849764347,
-0.024531936272978783,
0.026698900386691093,
0.009281309321522713,
-0.0020983857102692127,
0.011993895284831524,
-0.08463582396507263,
0.04311390593647957,
0.018231280148029327,
0.022144967690110207,
-0.07382374256849289,
-0.043834906071424484,
0.008480806834995747,
-0.019887693226337433,
-0.040385305881500244,
-0.03872061148285866,
-0.008412905968725681,
-0.014121470041573048,
-0.03586909547448158,
-0.013641576282680035,
0.019727077335119247,
0.0012141830520704389,
-0.021930858492851257,
0.003286820836365223,
0.025836754590272903,
0.054406166076660156,
0.01588483899831772,
0.015319915488362312,
0.0169815756380558,
-0.015120293945074081,
-0.004958471283316612,
-0.002113644964993,
0.062266215682029724,
-0.04151414707303047,
-0.010273907333612442,
-0.04191173240542412,
-0.001977278385311365,
0.03605622425675392,
-0.0014169897185638547,
0.009525371715426445,
0.03554678335785866,
0.017912941053509712,
0.01684746891260147,
0.019016079604625702,
-0.010301720350980759,
-0.014102686196565628,
-0.02658950351178646,
0.020625248551368713,
0.011031612753868103,
-0.038493812084198,
0.00441767880693078,
0.01908472552895546,
-0.013839703053236008,
-0.020266812294721603,
-0.0075155035592615604,
0.08884407579898834,
-0.006298436317592859,
-0.039188433438539505,
0.022591607645154,
-0.0391785204410553,
0.028539879247546196,
-0.030200479552149773,
-0.022938692942261696,
0.023722082376480103,
0.014317929744720459,
-0.01297255139797926,
-0.038225091993808746,
-0.02535325661301613,
0.020681994035840034,
0.06477008014917374,
-0.03231263533234596,
0.034675776958465576,
0.023769473657011986,
-0.013324526138603687,
0.016711218282580376,
-0.0337611548602581,
-0.03771586716175079,
-0.013625693507492542,
-0.014937611296772957,
0.03291361778974533,
-0.07781343907117844,
-0.00855682510882616,
-0.027560928836464882,
0.030424991622567177,
-0.01614752970635891,
0.0033799023367464542,
0.0036541286390274763,
0.029706768691539764,
0.027563704177737236,
-0.00687129283323884,
0.027966231107711792,
0.016776401549577713,
-0.028196431696414948,
0.04214910417795181,
-0.00585137540474534,
0.021030539646744728,
0.04011618345975876,
0.04222304746508598,
0.03616838902235031,
-0.041382405906915665,
0.005514817778021097,
-0.0003996147424913943,
-0.0027951954398304224,
-0.0027898524422198534,
-0.004853895865380764,
0.01790248043835163,
0.028106197714805603,
0.037735555320978165,
0.022309379652142525,
0.027163997292518616,
-0.03172404319047928,
-0.09171441942453384,
-0.02316616103053093,
-0.030510714277625084,
-0.05294778570532799,
0.042466919869184494,
-0.000798567314632237,
-0.04860657826066017,
0.05461658537387848,
-0.014482085593044758,
0.022409019991755486,
0.02282058075070381,
0.0010816972935572267,
-0.0165228471159935,
0.07648148387670517,
0.02078733779489994,
0.027244677767157555,
-0.020862020552158356,
0.004931943491101265,
0.11824242025613785,
0.038226913660764694,
0.01747705042362213,
-0.04602517932653427,
0.04628538712859154,
-0.036138974130153656,
-0.02009047567844391,
0.007339967880398035,
0.006663444451987743,
0.019997144117951393,
-0.030652184039354324,
-0.0096145523712039,
0.03677185997366905,
0.03002532199025154,
-0.010252435691654682,
0.05371040478348732,
-0.050419289618730545,
-0.05907293036580086,
-0.002325459849089384,
-0.012357753701508045,
-0.01705675572156906,
0.0034453850239515305,
-0.005722781643271446,
0.013808690942823887,
-0.0097319595515728,
0.011425080709159374,
-0.039915986359119415,
-0.02590935491025448,
0.041381753981113434,
-0.002461017342284322,
-0.008207311853766441,
0.009750123135745525,
-0.04898455739021301,
0.005775798577815294,
-0.006327664479613304,
0.02693113684654236,
0.07133420556783676,
-0.007244540378451347,
-0.01241396926343441,
0.00869805458933115,
-0.01619575545191765,
0.06321027874946594,
0.004403074271976948,
0.023878907784819603,
-0.0365840382874012,
-0.020511699840426445,
-0.010571313090622425,
0.040369559079408646,
0.011219240725040436,
-0.03411010652780533,
0.00798382144421339,
0.01007993333041668,
0.02529548481106758,
-0.054600123316049576,
-0.03414062783122063,
0.02838154509663582,
-0.00618985528126359,
0.017113905400037766,
0.008764762431383133,
-0.015134942717850208,
0.057956796139478683,
-0.027046676725149155,
0.04268922284245491,
0.02940264157950878,
-0.03527035191655159,
-0.030969174578785896,
-0.001128247706219554,
0.030208902433514595,
0.002250347286462784,
-0.013098451308906078,
-0.05556469410657883,
0.024509795010089874,
-0.04877175763249397,
0.005966530181467533,
-0.027851883322000504,
0.03461238741874695,
0.047179318964481354,
-0.026321595534682274,
0.013499066233634949,
-0.03364257514476776,
-0.05667232722043991,
0.0851845070719719,
-0.033791039139032364,
-0.0348038487136364,
-0.02814268320798874,
-0.030369779095053673,
-0.02317187748849392,
0.03580596670508385,
-0.04085598140954971,
-0.016075458377599716,
0.023145655170083046,
0.054345693439245224,
0.015312228351831436,
-0.035290107131004333,
-0.04787037894129753,
-0.004312160424888134,
-0.05566806346178055,
0.002970360917970538,
0.01083436980843544,
0.004261357709765434,
-0.0031227050349116325,
0.007664122618734837,
0.009068969637155533,
0.04443937540054321,
-0.04753653332591057,
-0.0028781360015273094,
-0.004849972669035196,
-0.008807049132883549,
-0.0004680741112679243,
0.019018927589058876,
-0.04135523736476898,
-0.025304783135652542,
0.035241421312093735,
0.023186391219496727,
-0.03573272377252579,
-0.0026071297470480204,
0.0007589951273985207,
-0.012834243476390839,
0.011140457354485989,
-0.03995297849178314,
0.004098036326467991,
-0.00940765906125307,
-0.020032189786434174,
-0.06259962916374207,
-0.0061122518964111805,
0.003921689931303263,
0.015539596788585186,
-0.033117592334747314,
0.010065469890832901,
-0.01799323782324791,
0.0016666840529069304,
0.0021608942188322544,
0.00864957831799984,
-0.0013519690837711096,
-0.015388905070722103,
0.04258660227060318,
0.0065903980284929276,
0.03911339491605759,
-0.04124629124999046,
0.0036987720523029566,
0.03750506788492203,
-0.04899407923221588,
-0.034647781401872635,
0.009581862017512321,
-0.023218533024191856,
0.03419632837176323,
-0.013855795376002789,
0.01193954423069954,
-0.0025945103261619806,
0.06446197628974915,
-0.016292566433548927,
0.008394233882427216,
-0.026427365839481354,
-0.0454903319478035,
0.005822406150400639,
-0.039742663502693176,
-0.019635766744613647,
0.010569171980023384,
0.009710264392197132,
0.028794899582862854,
-0.017867108806967735,
-0.05399201065301895,
0.009223535656929016,
-0.00004780096060130745,
0.02629733271896839,
0.03005320206284523,
-0.009118309244513512,
-0.004645925480872393,
-0.0011179266730323434,
0.02454058639705181,
-0.010923424735665321,
0.019117284566164017,
0.019710751250386238,
-0.016615672037005424,
-0.04539806768298149,
-0.029537901282310486,
-0.009785659611225128,
-0.01427236944437027,
0.01833493821322918,
-0.01858435571193695,
0.021227803081274033,
-0.007159516680985689,
-0.01731332205235958,
0.016900843009352684,
-0.043572213500738144,
-0.002199257258325815,
-0.024832090362906456,
0.004787815269082785,
-0.027516618371009827,
0.021679271012544632,
0.023463139310479164,
0.055521342903375626,
0.014638561755418777,
-0.029806621372699738,
-0.003068208694458008,
-0.034644052386283875,
-0.00282087130472064,
0.019115835428237915,
0.014024395495653152,
-0.018585387617349625,
0.06733548641204834,
-0.004297578241676092,
-0.05729895457625389,
0.003316168673336506,
-0.014925633557140827,
0.009046724997460842,
-0.007673788815736771,
-0.003048272104933858,
0.003312538843601942,
0.048749446868896484,
0.030802370980381966,
-0.012922856025397778,
0.02507590502500534,
-0.018839705735445023,
0.005830641370266676,
0.01641087606549263,
-0.02274503745138645,
0.0054358672350645065,
0.02253912016749382,
-0.010049507021903992,
-0.017019595950841904,
0.044264987111091614,
0.011077053844928741,
-0.013668791390955448,
-0.032904502004384995,
0.0017103235004469752,
0.007820670492947102,
-0.04645421728491783,
0.01060324814170599,
-0.030867116525769234,
0.03680518642067909,
0.04865880310535431,
0.005019247531890869,
-0.009492148645222187,
0.030798885971307755,
-0.011861401610076427,
0.006319212727248669,
-0.03215790167450905,
0.00021264026872813702,
-0.03779730945825577,
-0.013647881336510181,
0.0031825473997741938,
-0.0008889614837244153,
0.014765903353691101,
-0.02890101447701454,
-0.053943805396556854,
-0.047977592796087265,
0.02192097343504429,
0.03244113177061081,
0.040554966777563095,
-0.004428474232554436,
0.006744627375155687,
0.019075904041528702,
-0.04732568934559822,
0.028455443680286407,
0.029688339680433273,
-0.006561471614986658,
-0.02393524907529354,
-0.035660240799188614,
-0.014217473566532135,
0.03280944749712944,
0.032043829560279846,
0.05040279030799866,
-0.03211439773440361,
-0.028476934880018234,
0.04475986957550049,
0.013256517238914967,
-0.03444388508796692,
-0.005743476562201977,
0.0025608623400330544,
0.01668083667755127,
0.009006510488688946,
0.0021477648988366127,
-0.009501304477453232,
0.048451829701662064,
0.012946845032274723,
-0.015385582111775875,
0.0022511212155222893,
-0.005973713472485542,
-0.037915222346782684,
0.010598457418382168,
-0.003714031772688031,
0.02251906506717205,
0.04471948370337486,
0.0274016335606575,
0.06525836139917374,
-0.013103400357067585,
0.016220051795244217,
-0.009641289710998535,
0.03834129869937897,
-0.03252553194761276,
-0.0063912332989275455,
-0.002466324483975768,
0.008157898671925068,
0.02910781465470791,
-0.08606190979480743,
-0.017393166199326515,
0.03335980325937271,
-0.02604588493704796,
0.00887490063905716,
0.010225318372249603,
0.025859523564577103,
-0.008551346138119698,
0.014720473438501358,
0.025745758786797523,
0.04204130545258522,
-0.01580222323536873,
-0.007805907167494297,
0.04015238955616951,
0.04428697004914284,
0.016196949407458305,
0.018360452726483345,
0.05319194495677948,
0.0036902744323015213,
0.010427373461425304,
0.0033316179178655148,
-0.004191117361187935,
0.00518391327932477,
0.0018190834671258926,
0.049786217510700226,
-0.0077591207809746265,
-0.0105509664863348,
0.01852872595191002,
-0.009280191734433174,
0.0729447603225708,
-0.029140688478946686,
0.039043840020895004,
-0.026707686483860016,
-0.012498420663177967,
0.01542859897017479,
0.026581687852740288,
0.03876454010605812,
0.0025545156095176935,
0.004443064797669649,
-0.015280725434422493,
-0.053986407816410065,
-0.00234472774900496,
0.008914733305573463,
-0.05202518031001091,
-0.0018925777403637767,
0.010278304107487202,
0.05234401673078537,
-0.03709965571761131,
0.0009728268487378955,
0.01588616333901882,
-0.030147554352879524,
0.06601126492023468,
0.030152279883623123,
0.002209777943789959,
-0.012747460976243019,
-0.001049370621331036,
0.03409164398908615,
0.07154053449630737,
-0.052166327834129333,
-0.02916247770190239,
0.010947490110993385,
-0.002042576903477311,
-0.003366617253050208,
0.01926041953265667
] |
<p>I want to have a general solution for calculating orbits. Wikipedia says how to put object on circle orbit. We must give it speed $v_1 = \sqrt{g(h_o +R)} $ Where $h_o$ - is the orbit height, and $R$ - Earth radius.</p>
<p>But how to calculate the speed that the object must have, if we want to place it in an elliptical orbit?</p>
<p>For example: </p>
<p>Having massive massive spherical object with mass $M$ and radius $R$. </p>
<p>which speed $V$ we must to give to this object to put it on elliptical orbit with eccentricity $\epsilon = E$ , and perihelium $P$?</p>
| 311 |
[
-0.0075206030160188675,
-0.023629721254110336,
-0.009149059653282166,
-0.010119452141225338,
0.043608810752630234,
-0.005203224718570709,
-0.029978642240166664,
-0.01459767296910286,
0.041903432458639145,
-0.026531361043453217,
0.00798187404870987,
0.020213330164551735,
0.05823136493563652,
0.0025809549260884523,
0.030593400821089745,
-0.019421793520450592,
-0.017376190051436424,
0.020740855485200882,
0.011285154148936272,
-0.03549680486321449,
0.015006673522293568,
-0.03391271457076073,
0.056072257459163666,
-0.004334292374551296,
-0.005226971581578255,
0.033970851451158524,
0.0468747615814209,
0.002291248645633459,
-0.00031744822626933455,
0.06205885857343674,
-0.005455718841403723,
0.0057653868570923805,
0.0360516756772995,
0.03654465451836586,
-0.005629411898553371,
0.013873301446437836,
-0.040301062166690826,
0.008672120980918407,
0.007233461365103722,
0.041183918714523315,
-0.03389328718185425,
-0.020943349227309227,
0.0024529541842639446,
0.02774367853999138,
-0.0014262706972658634,
0.01822751946747303,
-0.010047076269984245,
-0.020537007600069046,
0.060828156769275665,
-0.05887402594089508,
0.06608983874320984,
0.008398259989917278,
0.0487632118165493,
0.031022926792502403,
0.012717261910438538,
0.013076186180114746,
0.08089794218540192,
0.06823941320180893,
-0.01698981411755085,
-0.016293495893478394,
-0.02947445958852768,
-0.03681595250964165,
0.008833113126456738,
-0.05800143629312515,
0.006926410831511021,
0.02541741356253624,
-0.03984564542770386,
0.011793731711804867,
0.007921264506876469,
0.042336393147706985,
0.052020084112882614,
0.005433403421193361,
-0.0021168426610529423,
-0.05194665491580963,
0.007618074305355549,
-0.035324133932590485,
0.019723376259207726,
-0.01506736222654581,
0.01986331306397915,
0.030871570110321045,
-0.035990096628665924,
0.003271988360211253,
0.01748274825513363,
0.011874843388795853,
-0.01157657615840435,
0.0373106487095356,
0.03281676769256592,
0.028015369549393654,
-0.01598537154495716,
0.014819295145571232,
-0.01593867316842079,
-0.01685495860874653,
0.03977070748806,
-0.0537884347140789,
-0.002338602440431714,
0.04232822358608246,
-0.018701011314988136,
0.04641054570674896,
-0.0066211712546646595,
-0.025134626775979996,
0.00005810729635413736,
-0.03826232999563217,
0.00495896628126502,
0.09920462220907211,
-0.009198708459734917,
-0.023183457553386688,
-0.033251043409109116,
0.004999754950404167,
-0.003969060722738504,
-0.019544176757335663,
0.01955319568514824,
0.015630407258868217,
-0.004612741060554981,
-0.023236893117427826,
0.0071918112225830555,
-0.002714071422815323,
-0.01438894309103489,
-0.03753053769469261,
0.04783017560839653,
0.011840584687888622,
0.0577179491519928,
-0.0007181301480159163,
0.020530007779598236,
-0.039721474051475525,
-0.03206148371100426,
0.020500745624303818,
0.04137016087770462,
-0.016089359298348427,
-0.013854870572686195,
-0.009299279190599918,
0.02394028753042221,
-0.052070483565330505,
0.03000873699784279,
0.0010731953661888838,
0.01620590314269066,
-0.027064397931098938,
-0.10183069854974747,
-0.06266660243272781,
0.014791697263717651,
0.006225262302905321,
-0.016342611983418465,
-0.06515590846538544,
0.017225174233317375,
0.03296446055173874,
0.08949360996484756,
0.00646365387365222,
-0.019800538197159767,
0.03856896236538887,
0.0635383278131485,
0.011376825161278248,
-0.03879602998495102,
-0.019621292129158974,
0.009388883598148823,
-0.034409407526254654,
0.016681380569934845,
-0.10221263766288757,
-0.01613198220729828,
0.009526719339191914,
0.00012178251927252859,
-0.015156684443354607,
0.08893822878599167,
-0.051496632397174835,
0.018607456237077713,
-0.028772924095392227,
0.018553322181105614,
-0.02316124550998211,
0.07474847137928009,
0.05039314180612564,
-0.006638645194470882,
0.04013131186366081,
0.0542842335999012,
0.041284725069999695,
0.016807619482278824,
-0.005501533858478069,
0.06260032206773758,
-0.03398288041353226,
0.012885426171123981,
-0.0304777380079031,
0.005997152533382177,
0.00733773922547698,
-0.012522486969828606,
-0.05920010060071945,
0.029974116012454033,
-0.013728121295571327,
0.03425460681319237,
0.060754917562007904,
0.0005103616858832538,
0.057000741362571716,
0.01710684224963188,
-0.04499293863773346,
0.009763787500560284,
-0.06822004169225693,
0.0298817977309227,
0.02290470525622368,
-0.01067530270665884,
0.008600149303674698,
0.0012733971234411001,
0.011984613724052906,
0.017960913479328156,
0.015234539285302162,
-0.014469421468675137,
0.050976794213056564,
0.013053649105131626,
-0.02648666687309742,
0.007012380287051201,
0.058464497327804565,
0.02309405617415905,
-0.005231834482401609,
-0.005118034780025482,
0.007606391329318285,
0.007348367478698492,
-0.024866998195648193,
-0.0046186503022909164,
0.014808793552219868,
-0.009669016115367413,
-0.010079978965222836,
-0.007873913273215294,
0.023541733622550964,
0.019288791343569756,
0.04333668202161789,
-0.032084871083498,
0.11473081260919571,
0.05953631177544594,
0.048624470829963684,
0.01002926379442215,
0.02828088589012623,
0.02672448754310608,
0.008630036376416683,
-0.013584908097982407,
-0.016667598858475685,
-0.02526474930346012,
-0.012122712098062038,
0.01868392340838909,
0.0036585398484021425,
-0.054735273122787476,
0.01721150428056717,
0.07287278026342392,
0.030581699684262276,
0.05524811893701553,
0.03147557005286217,
-0.037237927317619324,
-0.034874096512794495,
0.015683326870203018,
0.032279592007398605,
0.011408866383135319,
0.010521352291107178,
-0.0009878468699753284,
0.033057864755392075,
0.02146797440946102,
0.016943471506237984,
-0.03718991205096245,
0.06634051352739334,
0.031254902482032776,
-0.0011095864465460181,
0.0028089070692658424,
-0.001705910894088447,
0.03470659628510475,
-0.04588034749031067,
0.01872885599732399,
0.03229714184999466,
-0.017183218151330948,
0.01834825426340103,
-0.026702752336859703,
0.021667899563908577,
0.0017688655061647296,
0.020806094631552696,
-0.02517424337565899,
-0.0016220812685787678,
0.018139377236366272,
-0.04975990578532219,
0.008254236541688442,
-0.01634165458381176,
-0.015828976407647133,
-0.04457160830497742,
0.013899954035878181,
0.010905700735747814,
0.00894248392432928,
0.005037091206759214,
0.016654163599014282,
-0.020270956680178642,
-0.009468760341405869,
-0.0408303327858448,
-0.01854640059173107,
-0.008411622606217861,
-0.05360613018274307,
0.0033882095012813807,
-0.04431336373090744,
-0.027872184291481972,
0.037468090653419495,
0.00911091547459364,
-0.020383603870868683,
0.017866790294647217,
0.0024339526426047087,
-0.05222388729453087,
-0.011984314769506454,
-0.058079421520233154,
-0.008047456853091717,
-0.03976830095052719,
0.006706935353577137,
0.03530220687389374,
-0.011965413577854633,
-0.020554037764668465,
-0.011648094281554222,
-0.051427505910396576,
-0.03142383322119713,
-0.025510115548968315,
-0.011085881851613522,
0.007799145299941301,
-0.05372219532728195,
0.04120548814535141,
-0.029500797390937805,
-0.010310489684343338,
-0.004040846601128578,
-0.02380085363984108,
-0.032326482236385345,
0.025961436331272125,
-0.002825693227350712,
0.021340452134609222,
0.004564911592751741,
-0.0664069876074791,
0.09277282655239105,
0.00837598368525505,
-0.0002492415951564908,
-0.047796644270420074,
0.014264681376516819,
0.0005959487752988935,
-0.024016058072447777,
0.0002702231868170202,
0.028628814965486526,
-0.014924797229468822,
-0.025794144719839096,
0.02863558754324913,
-0.016832895576953888,
0.02884102240204811,
0.012835483998060226,
-0.032546266913414,
-0.0112781235948205,
0.018160730600357056,
-0.00042339556966908276,
0.042754076421260834,
0.020733973011374474,
-0.009446642361581326,
0.0633288323879242,
-0.007564269471913576,
0.04383813217282295,
0.007104261312633753,
-0.0887441486120224,
0.026780080050230026,
-0.014473390765488148,
-0.020623231306672096,
0.024744227528572083,
0.021934840828180313,
0.019470026716589928,
0.004777102265506983,
0.008613770827651024,
0.044230666011571884,
0.03483087196946144,
0.011564689688384533,
-0.035914886742830276,
0.027629734948277473,
0.032307546585798264,
-0.020346684381365776,
-0.03384598717093468,
-0.013199258595705032,
-0.0239262655377388,
0.03714708238840103,
0.012978867627680302,
-0.01836857572197914,
0.025844257324934006,
0.022579550743103027,
0.0017146661411970854,
-0.015070846304297447,
-0.02375367097556591,
0.014027625322341919,
-0.08955120295286179,
-0.014765475876629353,
-0.003869391046464443,
0.042152538895606995,
-0.01345057226717472,
0.046094074845314026,
-0.0029681359883397818,
-0.024908725172281265,
0.020712384954094887,
0.007004882674664259,
-0.0430123545229435,
0.0611252523958683,
-0.044987186789512634,
-0.05949955806136131,
0.0015705551486462355,
-0.007908864878118038,
-0.03055437095463276,
-0.04696252569556236,
-0.009330518543720245,
-0.041418105363845825,
-0.019505763426423073,
-0.015732884407043457,
0.027065807953476906,
-0.007899961434304714,
-0.01777459681034088,
-0.0008117344113998115,
0.05858753249049187,
0.006895757745951414,
-0.02660050243139267,
0.03206155076622963,
0.039088357239961624,
-0.035591550171375275,
-0.013072138652205467,
-0.018830766901373863,
-0.010295000858604908,
-0.020946364849805832,
0.019968131557106972,
-0.0006528531084768474,
0.02597464621067047,
-0.023659992963075638,
0.029011663049459457,
-0.01804330199956894,
0.05863200128078461,
0.01387124415487051,
0.012503785081207752,
-0.019478704780340195,
-0.02767554298043251,
0.007031312212347984,
0.00112832710146904,
0.04208758473396301,
-0.024551324546337128,
0.001385818817652762,
0.0484660267829895,
-0.01542118564248085,
0.00983255822211504,
0.006231500301510096,
0.06255623698234558,
0.0021928849164396524,
0.006604025140404701,
-0.06735456734895706,
-0.03807929530739784,
-0.01777307689189911,
0.0027700888458639383,
0.018241556361317635,
-0.017784100025892258,
-0.03254787251353264,
-0.017426548525691032,
-0.004072702024132013,
-0.011027493514120579,
-0.0022558565251529217,
-0.016063274815678596,
0.008604011498391628,
0.04148705676198006,
-0.03790470212697983,
-0.016956422477960587,
0.021959926933050156,
0.019243551418185234,
0.04933106526732445,
-0.0207844115793705,
0.031217677518725395,
-0.06705751270055771,
-0.003094428451731801,
0.0325201153755188,
0.024424217641353607,
-0.006645949557423592,
-0.0013433753047138453,
-0.0725015178322792,
-0.027666231617331505,
0.05956443399190903,
-0.020967300981283188,
0.0389532707631588,
-0.029141906648874283,
-0.0030825866851955652,
0.018775537610054016,
-0.020028308033943176,
-0.03552590310573578,
0.032485801726579666,
-0.0021271314471960068,
-0.008470308966934681,
-0.04145340994000435,
0.039137620478868484,
-0.005480010993778706,
-0.017692675814032555,
0.03370975703001022,
0.046265676617622375,
0.033814191818237305,
0.006638204213231802,
0.005343764089047909,
0.005090010818094015,
-0.0037631988525390625,
-0.0662526860833168,
-0.025738071650266647,
0.0017903090920299292,
-0.001506915083155036,
0.016072556376457214,
-0.06101566180586815,
-0.026827314868569374,
0.06345713883638382,
-0.004748276900500059,
-0.031074535101652145,
-0.006753501482307911,
-0.05551256239414215,
0.03299863636493683,
0.02336188592016697,
0.003913389053195715,
0.030929164960980415,
0.01882159896194935,
-0.026640761643648148,
-0.03333407640457153,
-0.04534470662474632,
-0.008621281944215298,
-0.026027875021100044,
-0.034284502267837524,
-0.00996559951454401,
0.009307615458965302,
-0.040805067867040634,
0.03844679147005081,
0.016127953305840492,
0.03190690651535988,
0.0005732572171837091,
-0.03367627412080765,
-0.024228079244494438,
0.04278077557682991,
-0.009386434219777584,
0.015488267876207829,
0.0011486641597002745,
-0.01809494011104107,
0.022120893001556396,
-0.020547855645418167,
0.012694994919002056,
0.015072373673319817,
0.015738362446427345,
0.024243028834462166,
-0.008421490900218487,
0.01183344330638647,
-0.018211720511317253,
-0.019984446465969086,
-0.0030493629164993763,
-0.04867380112409592,
0.054354872554540634,
-0.014186680316925049,
-0.026767263188958168,
0.05276362597942352,
-0.09031274169683456,
-0.04913858324289322,
-0.0021914595272392035,
-0.007487010210752487,
0.008461401797831059,
-0.02213599905371666,
-0.013581069186329842,
0.021322136744856834,
0.011872529052197933,
-0.0640874058008194,
-0.03374027833342552,
0.039987895637750626,
-0.022904520854353905,
-0.0182826928794384,
-0.0270855575799942,
0.023140737786889076,
-0.02402442879974842,
-0.03938500955700874,
-0.004917780868709087,
0.050227098166942596,
-0.022306187078356743,
-0.00601087836548686,
-0.003695510793477297,
0.01212590467184782,
0.057876843959093094,
-0.0009480301523581147,
0.016542630270123482,
0.03243958577513695,
0.004010514821857214,
0.005581870675086975,
0.0035341486800462008,
0.09112494438886642,
-0.035629753023386,
-0.03852897137403488,
-0.05423278361558914,
-0.0167232733219862,
0.018314437940716743,
0.004797821398824453,
0.005266319494694471,
0.03533114492893219,
0.011656008660793304,
-0.021512772887945175,
0.003714177291840315,
0.04887881129980087,
-0.010665715672075748,
0.029372597113251686,
-0.007576047908514738,
-0.00046399570419453084,
-0.029648112133145332,
-0.026750557124614716,
0.015968281775712967,
-0.017119644209742546,
0.03683549910783768,
-0.03897185996174812,
0.04572334513068199,
-0.018763646483421326,
-0.014280606061220169,
0.006668012123554945,
0.005537412595003843,
-0.005905409809201956,
-0.012622219510376453,
-0.022717313840985298,
0.010089846327900887,
0.0031942438799887896,
-0.005108734127134085,
-0.01493847742676735,
-0.025658641010522842,
-0.008680016733705997,
0.09640270471572876,
-0.041567325592041016,
0.041547324508428574,
0.004645796958357096,
0.02061655931174755,
-0.01858208142220974,
-0.010939176194369793,
-0.0088784946128726,
-0.0034145007375627756,
0.02620805613696575,
0.05119837448000908,
-0.02042003720998764,
0.005150703713297844,
0.01879672147333622,
0.06662656366825104,
-0.030200472101569176,
0.024416469037532806,
0.021499810740351677,
0.0058951727114617825,
-0.012504362501204014,
-0.004625382833182812,
-0.007910426706075668,
0.026296133175492287,
0.019131410866975784,
0.06918548047542572,
-0.028037941083312035,
-0.0011018149089068174,
0.05887699872255325,
0.030378861352801323,
0.025323977693915367,
-0.01977158896625042,
-0.03592156618833542,
-0.030182350426912308,
0.009610374458134174,
0.03572716563940048,
-0.03513000160455704,
-0.01302014198154211,
0.007870600558817387,
0.028947681188583374,
0.0036810478195548058,
0.03329820930957794,
-0.028869086876511574,
-0.07285425812005997,
-0.04043256491422653,
-0.019939647987484932,
-0.08765307813882828,
0.023089881986379623,
0.03248913958668709,
-0.011906294152140617,
-0.004150075372308493,
0.012090248055756092,
0.0004271076468285173,
0.036465998739004135,
0.02498071826994419,
-0.018040841445326805,
0.0929785817861557,
-0.021265489980578423,
-0.030979448929429054,
0.006176472175866365,
0.0281659122556448,
0.10401016473770142,
0.046400465071201324,
0.00482782069593668,
-0.07149716466665268,
0.029695773497223854,
-0.0341029055416584,
0.0015531857497990131,
-0.06516673415899277,
0.03574150428175926,
-0.011558896861970425,
-0.01668751798570156,
0.004548471886664629,
0.051406752318143845,
-0.0116062480956316,
-0.025089304894208908,
0.056167121976614,
-0.01145006064325571,
-0.04337054491043091,
-0.013228031806647778,
0.02515922300517559,
-0.02923581376671791,
0.01593167707324028,
-0.015518703497946262,
0.028158433735370636,
-0.04203534871339798,
-0.013853070326149464,
-0.052276622503995895,
-0.026378020644187927,
0.0445164330303669,
0.0026428154669702053,
-0.06029734015464783,
0.01991821639239788,
-0.005708534736186266,
-0.044950854033231735,
-0.012461736798286438,
0.03660990297794342,
0.010354778729379177,
-0.029201440513134003,
0.014552095904946327,
0.040597282350063324,
-0.002949981251731515,
0.030801422894001007,
0.008834012784063816,
-0.020469825714826584,
-0.03522118553519249,
0.013528089039027691,
-0.037922538816928864,
0.04295412451028824,
-0.020614903420209885,
0.021675709635019302,
0.017833059653639793,
0.0022856825962662697,
-0.0173569954931736,
-0.07311906665563583,
0.017311904579401016,
0.004160288255661726,
0.010118393227458,
-0.010509859770536423,
-0.011435549706220627,
-0.005266320426017046,
0.006722498219460249,
-0.017729884013533592,
0.03903500735759735,
-0.008959666825830936,
0.000565909780561924,
-0.004127776715904474,
-0.03257109969854355,
0.04142574965953827,
0.004534213803708553,
-0.03903099521994591,
-0.008965419605374336,
-0.009625080041587353,
-0.03501726686954498,
0.008874774910509586,
0.030710186809301376,
0.01702243834733963,
-0.017248278483748436,
0.011715279892086983,
-0.01627657376229763,
0.0013817992294207215,
-0.055868979543447495,
0.01635570079088211,
-0.017478128895163536,
-0.03605429828166962,
-0.040707167237997055,
-0.01983517035841942,
0.049346160143613815,
0.021726908162236214,
0.019433271139860153,
0.015033986419439316,
-0.044860027730464935,
0.03540439158678055,
0.016493769362568855,
-0.02864435501396656,
-0.015410755760967731,
0.032362546771764755,
-0.01166192814707756,
0.007616664282977581,
-0.039135221391916275,
0.03811582177877426,
0.02280683070421219,
-0.01557748019695282,
-0.014119873754680157,
0.01274837926030159,
-0.016608113422989845,
0.015956388786435127,
0.0021996856667101383,
0.00846684630960226,
0.014203405939042568,
0.01218704879283905,
0.029003983363509178,
-0.022007210180163383,
-0.007562865968793631,
-0.03392428159713745,
-0.03214180842041969,
-0.014543096534907818,
0.009682653471827507,
-0.015219937078654766,
0.06488341093063354,
-0.04004784673452377,
0.028147602453827858,
-0.037966083735227585,
0.028305048123002052,
-0.002443289617076516,
0.03164009749889374,
0.016976136714220047,
-0.009335187263786793,
-0.027592306956648827,
0.018204152584075928,
-0.009431209415197372,
-0.010165938176214695,
-0.015491875819861889,
-0.005747491028159857,
0.02315438725054264,
0.004056131467223167,
0.020939314737915993,
-0.04404609277844429,
0.07008805871009827,
0.00019542021618690342,
-0.013276186771690845,
0.0031618557404726744,
-0.04889858886599541,
-0.05440272390842438,
0.044547174125909805,
-0.024139121174812317,
0.05713783577084541,
-0.022120743989944458,
-0.03459654375910759,
-0.01797431893646717,
0.06139786168932915,
-0.04352172836661339,
-0.004499195143580437,
0.024707427248358727,
-0.0018582125194370747,
-0.020837146788835526,
-0.001359497313387692,
0.03727369010448456,
-0.023519277572631836,
0.002215079264715314,
0.03026699833571911,
-0.011892584152519703,
-0.035897284746170044,
0.026311492547392845,
0.019475651904940605,
-0.012168209999799728,
0.03386906161904335,
0.011464494280517101,
0.022942423820495605,
0.04647769033908844,
0.021036986261606216,
-0.02748134918510914,
0.024973345920443535,
0.03624074533581734,
-0.006705509964376688,
-0.06267175823450089,
0.007047800347208977,
-0.024992313235998154,
0.009242668747901917,
0.0763464868068695,
-0.07667433470487595,
-0.006103467661887407,
0.026415619999170303,
-0.03490736335515976,
0.012831028550863266,
-0.03581736609339714,
-0.008283862844109535,
-0.014011581428349018,
-0.03395308554172516,
0.009614496491849422,
0.03700442239642143,
0.041930560022592545,
-0.004874553997069597,
0.026006843894720078,
-0.005264848005026579,
-0.009898076765239239,
-0.025001641362905502,
0.036565151065588,
0.012635061517357826,
-0.004537730943411589,
-0.004974048584699631,
0.06500376015901566,
-0.01897665672004223,
-0.0038099964149296284,
0.025928834453225136,
0.009973901323974133,
0.03562571108341217,
-0.0033294809982180595,
0.004040217958390713,
-0.029224639758467674,
0.033184632658958435,
0.028878582641482353,
0.013710645027458668,
-0.05383111536502838,
0.001525860046967864,
0.009334572590887547,
0.040019676089286804,
-0.031003113836050034,
-0.015928486362099648,
0.029146818444132805,
0.00412847800180316,
-0.03320714458823204,
0.05146360397338867,
-0.006539667025208473,
-0.022395463660359383,
0.01914159581065178,
0.006561197806149721,
0.0015510404482483864,
-0.04213665798306465,
0.021775517612695694,
-0.03274635598063469,
0.01754022017121315,
0.02633196860551834,
-0.046920046210289,
-0.0009018402197398245,
-0.0063742040656507015,
-0.006651925854384899,
-0.03458551689982414,
0.0250129085034132,
-0.017214326187968254,
-0.016975929960608482,
-0.043491072952747345,
0.005238768644630909,
0.011645468883216381,
-0.04731700196862221,
-0.012571360915899277,
-0.04601188749074936,
-0.036124806851148605,
0.051632143557071686,
0.011890632100403309,
-0.011689725331962109,
-0.030660847201943398,
-0.0013511463766917586,
-0.01869579218327999,
-0.00938031729310751,
0.007623882498592138,
0.008457965217530727,
-0.026038696989417076,
0.0034485217183828354,
-0.03503160551190376,
0.0005115272360853851,
-0.01194985955953598,
0.05497141554951668,
-0.001206091372296214,
-0.0008537438116036355,
0.01001141406595707,
-0.01886775717139244,
-0.002153548877686262,
-0.05316377431154251,
0.004245552234351635,
-0.01266666129231453,
-0.03319341316819191,
-0.016376134008169174,
-0.018957244232296944,
0.004249562509357929,
0.015244639478623867,
0.0013355639530345798,
0.011094984598457813,
0.025518951937556267,
0.026898035779595375,
-0.016171490773558617,
0.04150879383087158,
0.003881123848259449,
0.019373802468180656,
0.07421435415744781,
0.010735724121332169,
-0.010849065147340298,
0.03156871348619461,
-0.012300034984946251,
-0.03024817444384098,
-0.013890421949326992,
-0.04787501320242882,
-0.03283321484923363,
-0.01346403919160366,
-0.006179526448249817,
0.0006968739908188581,
-0.08702950924634933,
0.0036959804128855467,
0.0477650947868824,
-0.0360276959836483,
-0.014600160531699657,
0.03166557848453522,
0.012134775519371033,
0.03407445549964905,
-0.009959729388356209,
0.009451442398130894,
0.02713790535926819,
-0.04367182403802872,
-0.008643134497106075,
0.010072793811559677,
0.029876498505473137,
0.04675701633095741,
0.015206219628453255,
0.03937201946973801,
0.051574040204286575,
0.03282879665493965,
-0.013983291573822498,
0.03744026646018028,
-0.0013832601252943277,
-0.0217493437230587,
-0.01087314821779728,
-0.02819049544632435,
0.023002151399850845,
0.003492903895676136,
-0.022623620927333832,
0.044829536229372025,
-0.04418187588453293,
-0.012696289457380772,
0.009417926892638206,
-0.016113879159092903,
-0.04953724890947342,
0.0030711034778505564,
-0.019895965233445168,
0.02873402275145054,
0.0029495172202587128,
0.02271278388798237,
0.006062917876988649,
-0.004661179147660732,
0.06512521952390671,
-0.02519076131284237,
0.0006248988211154938,
0.03604280203580856,
-0.023667052388191223,
-0.03124595433473587,
-0.028899818658828735,
-0.014403607696294785,
-0.017617158591747284,
0.000805032963398844,
0.07145413011312485,
0.0402061901986599,
-0.0006179741467349231,
-0.002499430673196912,
-0.01960770972073078,
0.04357147961854935,
-0.08370303362607956,
-0.014036064967513084,
-0.026489004492759705,
0.02220091037452221,
-0.017963554710149765,
-0.0030916344840079546
] |
<p>In a Young’s double slit experiment 10 fringes are observed in a given segment of the screen when light of wavelength 500.0 nm is used. When the experiment is performed in a medium of refractive index 1.2, the number of fringes observed in the same segment remains 10. The wavelength of light used in this case is? </p>
<p>(Also provide some explanations)</p>
<p>(But do look at my Answer & say whether it is correct or not.)</p>
<p>My Explanations: </p>
<p>Number and position of fringes formed in young’s double slit experiment is only dependant on the frequency of light used. Here, the number of fringes in both cases remains same because light of same frequency is used in two different mediums. To compare the wavelengths, we should only look at the change in speed and wavelength caused by the new medium, as compared to vacuum.
As given in the question, the number of fringes in a particular segment doesn’t change, so fringe width (β) remains same.
Therefore,</p>
<p><img src="http://i.stack.imgur.com/Dh1NJ.jpg" alt="enter image description here"></p>
<p>Where β = fringe width</p>
<p>When a ray of light passing through vacuum with wavelength λ1 is passed through a medium of refractive index µ, the new wavelength λ2 is given by:</p>
<p><img src="http://i.stack.imgur.com/o5Zmp.jpg" alt="enter image description here"></p>
<p>(which can be proved by the fact that velocity of light in a medium is inversely proportional to refractive index. Since frequency of light is constant (depends on the source only), refractive index is also inversely proportional to wavelength.)
In the question, µ = 1.2, λ1 = 500nm. </p>
<p>Hence, λ2 = (500) / (1.2) = 416.6667 nm.</p>
| 9,548 |
[
-0.004783164709806442,
-0.037797752767801285,
-0.01415215153247118,
-0.022291095927357674,
0.042137809097766876,
-0.01082698442041874,
-0.015248470939695835,
-0.054501067847013474,
-0.015497948043048382,
0.009421812370419502,
0.0609525702893734,
0.02983810193836689,
0.06819675862789154,
0.02701716497540474,
0.003793366951867938,
0.046557631343603134,
0.013293644413352013,
-0.01769484020769596,
-0.04789550602436066,
-0.03863385319709778,
-0.03018227592110634,
0.011765207163989544,
0.006378105841577053,
-0.010208778083324432,
-0.05939221754670143,
0.04005255177617073,
0.04270683601498604,
0.009579946286976337,
0.016849346458911896,
0.021039757877588272,
0.026906784623861313,
0.006183896213769913,
0.027636514976620674,
0.03234856203198433,
-0.017952008172869682,
-0.01713087409734726,
-0.05452835559844971,
-0.026677986606955528,
0.006381799932569265,
0.008863741531968117,
0.00038819870678707957,
0.04887083172798157,
-0.024924609810113907,
0.061904314905405045,
0.014080588705837727,
0.004615148063749075,
0.016391178593039513,
0.018038231879472733,
0.06698958575725555,
-0.03326082602143288,
0.05108806863427162,
0.0019995856564491987,
0.04616759717464447,
-0.007971826940774918,
-0.04171016439795494,
-0.040361616760492325,
0.08783044666051865,
0.06784678250551224,
-0.018346820026636124,
-0.047837719321250916,
-0.022841941565275192,
-0.0029943499248474836,
-0.010590286925435066,
0.018852680921554565,
-0.009295818395912647,
-0.0029867677949368954,
-0.027391448616981506,
-0.0021255281753838062,
-0.0013416948495432734,
0.005326786078512669,
0.00602754158899188,
0.009590969420969486,
0.041119158267974854,
-0.02103998512029648,
-0.001915416563861072,
-0.052288178354501724,
-0.0035967060830444098,
0.05536825209856033,
0.022357884794473648,
0.06838816404342651,
-0.014176959171891212,
-0.010160750709474087,
0.025527670979499817,
0.017001429572701454,
0.023794634267687798,
-0.06565562635660172,
0.09259020537137985,
-0.0052475654520094395,
0.003246031701564789,
0.028147321194410324,
-0.008923925459384918,
0.010094193741679192,
0.028311727568507195,
0.02546689659357071,
-0.0006349259638227522,
0.04739844799041748,
-0.015825027599930763,
0.044315457344055176,
0.01612194813787937,
-0.013203970156610012,
-0.025842947885394096,
-0.024077992886304855,
0.059960030019283295,
0.07229877263307571,
-0.004830518271774054,
-0.04064447805285454,
-0.045978937298059464,
0.03880297765135765,
-0.03663414716720581,
-0.007237636484205723,
-0.006648445036262274,
0.03592552989721298,
-0.008600790984928608,
0.04102562740445137,
0.02282530441880226,
-0.022222047671675682,
0.030927928164601326,
-0.03687620908021927,
0.07104285061359406,
0.08421792834997177,
0.025777222588658333,
-0.025107378140091896,
0.0010206979932263494,
-0.0043886397033929825,
-0.0475846529006958,
0.028153372928500175,
0.027529682964086533,
-0.0021476331166923046,
0.00637370441108942,
0.015902018174529076,
0.019059468060731888,
-0.0035293169785290956,
0.018302779644727707,
0.005910808686167002,
-0.0038882605731487274,
0.036097120493650436,
-0.07183186709880829,
-0.07746895402669907,
0.05422068387269974,
0.024107616394758224,
0.0006796166417188942,
-0.06172846630215645,
0.04471373185515404,
0.02614070475101471,
0.08702896535396576,
0.012491519562900066,
0.014591964893043041,
-0.04746086150407791,
0.028653951361775398,
-0.018583117052912712,
-0.018453825265169144,
0.00970432534813881,
0.002085120650008321,
-0.03682117536664009,
0.01228545606136322,
-0.050627563148736954,
0.0033100128639489412,
0.039361584931612015,
-0.02044971100986004,
-0.025075577199459076,
0.040087662637233734,
0.00206729001365602,
0.003270441433414817,
0.028536750003695488,
0.03195560351014137,
-0.04441676661372185,
0.06164458021521568,
0.014982628636062145,
-0.023621900007128716,
-0.002286839997395873,
-0.06505972892045975,
0.028679130598902702,
-0.03259151801466942,
-0.01062696147710085,
0.028089072555303574,
-0.004413009621202946,
-0.01329129096120596,
-0.02319219708442688,
0.019220180809497833,
0.020392218604683876,
-0.016811344772577286,
-0.037951771169900894,
-0.04107952490448952,
0.0036620066966861486,
0.012888174504041672,
0.04293058067560196,
-0.016471991315484047,
-0.009361909702420235,
0.003963482566177845,
-0.051905255764722824,
-0.045000601559877396,
-0.009067771956324577,
0.005975918844342232,
0.010374506004154682,
-0.0596686452627182,
0.008853230625391006,
0.0007517542107962072,
-0.000055646320106461644,
0.007293789181858301,
-0.017912769690155983,
-0.0334068164229393,
0.009463324211537838,
0.016789548099040985,
-0.010568785481154919,
0.006152759771794081,
0.04536120593547821,
0.048957131803035736,
-0.03928108885884285,
0.007598515134304762,
-0.044564180076122284,
-0.00708753289654851,
-0.002834893064573407,
-0.002852548146620393,
0.02791561558842659,
-0.012567413039505482,
-0.008807605132460594,
0.013430893421173096,
0.004968715365976095,
-0.04402769356966019,
0.0161488875746727,
-0.0373292900621891,
0.05813789740204811,
0.06368745863437653,
0.005169890355318785,
-0.012856454588472843,
0.02239176072180271,
0.006128993816673756,
0.03538573533296585,
-0.005143667105585337,
-0.037457119673490524,
-0.056001145392656326,
-0.025197643786668777,
-0.009223408065736294,
0.029133914038538933,
-0.018299652263522148,
0.030461527407169342,
-0.006506131961941719,
0.017906760796904564,
0.02810296043753624,
0.013502339832484722,
0.02702094428241253,
-0.07039163261651993,
0.018049292266368866,
-0.014639372937381268,
0.024419542402029037,
0.01552903838455677,
0.0323832668364048,
-0.009862959384918213,
0.014306357130408287,
-0.011498358100652695,
0.009682237170636654,
0.025194570422172546,
0.0038241823203861713,
0.01230436097830534,
-0.01626906730234623,
0.037862006574869156,
0.010809240862727165,
0.021944643929600716,
0.001622397219762206,
0.04013865441083908,
-0.006219374481588602,
-0.0063006458804011345,
-0.03376816585659981,
0.01338163111358881,
0.019154826179146767,
-0.0026402936782687902,
-0.04067947342991829,
0.007745412178337574,
0.03181410953402519,
-0.031396858394145966,
0.009670190513134003,
-0.006981870159506798,
-0.00447470648214221,
-0.03550960496068001,
-0.012747541069984436,
0.015806052833795547,
0.04279903322458267,
0.011009368114173412,
-0.05620235577225685,
-0.033891286700963974,
0.032919738441705704,
-0.03252006322145462,
0.005165108945220709,
-0.00029710406670346856,
-0.02788868173956871,
0.014350767247378826,
-0.013500177301466465,
-0.027386460453271866,
0.026727866381406784,
-0.015520005486905575,
-0.028302408754825592,
0.0048046172596514225,
-0.006380185950547457,
-0.09711407124996185,
-0.02076711505651474,
-0.017668548971414566,
-0.012220448814332485,
-0.009207410737872124,
0.00034903534105978906,
0.016004152595996857,
0.018514787778258324,
-0.05572893097996712,
0.04152894765138626,
-0.026894401758909225,
-0.0457330085337162,
-0.01543298177421093,
-0.01275801844894886,
0.022555232048034668,
-0.016644412651658058,
-0.02662619948387146,
0.010164288803935051,
0.0038226821925491095,
0.026722317561507225,
-0.024249278008937836,
-0.06006702408194542,
0.0451631136238575,
-0.004619992803782225,
0.05498359724879265,
-0.045879628509283066,
-0.004119035787880421,
0.04768674820661545,
0.04670020192861557,
-0.005619433242827654,
-0.04615915194153786,
0.04331094026565552,
0.023059429600834846,
-0.03701509162783623,
-0.0060358671471476555,
0.024479806423187256,
-0.0064476775005459785,
0.050019461661577225,
0.02484622783958912,
0.04518190026283264,
0.05927806720137596,
0.034743938595056534,
0.00805291160941124,
-0.005049108061939478,
-0.00319510605186224,
-0.039721619337797165,
0.024648062884807587,
0.04183864966034889,
0.001208654372021556,
0.009098860435187817,
0.0045526702888309956,
0.05690493434667587,
0.007438263390213251,
-0.05886031314730644,
0.04783112555742264,
0.01288563571870327,
-0.000986849656328559,
-0.00398890720680356,
0.019775623455643654,
0.031534723937511444,
-0.0018412312492728233,
-0.0003749613824766129,
-0.004297940991818905,
0.04270174354314804,
0.022866401821374893,
-0.05228782817721367,
0.029109759256243706,
-0.00674816407263279,
0.03536186367273331,
0.007431831210851669,
-0.00814208947122097,
-0.03967604041099548,
0.056240927428007126,
-0.05868653208017349,
-0.026494313031435013,
0.04321768879890442,
0.050151653587818146,
0.01997068151831627,
-0.026122376322746277,
-0.029312878847122192,
-0.013377075083553791,
-0.032983794808387756,
-0.02027919702231884,
-0.03943479433655739,
0.053591977804899216,
0.010396062396466732,
0.043304745107889175,
0.02992691472172737,
0.03838556632399559,
0.01231627818197012,
-0.007535072043538094,
-0.060812704265117645,
0.0362074039876461,
0.007229663897305727,
-0.039627376943826675,
-0.04076053574681282,
-0.006311492528766394,
-0.012559695169329643,
-0.025415536016225815,
0.0018620711052790284,
-0.0030786350835114717,
0.01566922478377819,
-0.05910991504788399,
0.003018359886482358,
-0.028115566819906235,
-0.02050015889108181,
-0.04379943758249283,
0.05947161093354225,
0.026624931022524834,
-0.0009944039629772305,
0.014436603523790836,
0.0448857843875885,
-0.03169112652540207,
0.004083436448127031,
0.0003107990196440369,
-0.018391530960798264,
0.017908204346895218,
0.04969509318470955,
0.03898882493376732,
-0.00031383242458105087,
-0.03843209147453308,
0.037546463310718536,
0.013691360130906105,
0.04353255033493042,
0.015914084389805794,
0.001324406242929399,
-0.03444274514913559,
-0.015445857308804989,
-0.004745421931147575,
-0.037912800908088684,
0.07957979291677475,
-0.007977503351867199,
-0.01635795645415783,
0.02109508402645588,
-0.01279947068542242,
-0.004177546594291925,
0.052938345819711685,
0.02524973824620247,
-0.018984105437994003,
-0.012660476379096508,
-0.045491885393857956,
-0.02127673290669918,
-0.021395934745669365,
-0.014922866597771645,
0.03712873533368111,
0.030787719413638115,
0.01239506434649229,
-0.015397290699183941,
0.033555928617715836,
-0.00474443007260561,
-0.0005825810949318111,
0.03581314906477928,
-0.06628450006246567,
-0.006299508735537529,
-0.006243814714252949,
-0.02599027007818222,
0.004796264227479696,
0.015975208953022957,
0.006864431779831648,
-0.011950093321502209,
-0.03995982185006142,
-0.07837469130754471,
-0.03238147124648094,
-0.008666078560054302,
0.041569288820028305,
-0.033265113830566406,
0.01828392781317234,
-0.05053164064884186,
-0.03594093769788742,
0.04331531375646591,
-0.031035752967000008,
0.02150649018585682,
0.0030230931006371975,
-0.0059127286076545715,
-0.007160970009863377,
-0.016286781057715416,
-0.023241957649588585,
-0.002863585948944092,
-0.001988969510421157,
0.0019407564541324973,
-0.05502906069159508,
-0.012192970141768456,
0.0074618225917220116,
-0.021527549251914024,
0.024532290175557137,
0.03711805120110512,
-0.006265575066208839,
-0.0012697058264166117,
-0.005442088469862938,
-0.033858172595500946,
-0.04277661070227623,
-0.041249923408031464,
0.04793410748243332,
-0.0006558369495905936,
0.03493645042181015,
0.05299312621355057,
-0.025047671049833298,
-0.024235397577285767,
0.03245934098958969,
0.023921353742480278,
0.0067208921536803246,
0.020445503294467926,
-0.0001997407671296969,
0.03985128179192543,
0.021236935630440712,
0.013679072260856628,
0.032441917806863785,
0.03198075294494629,
-0.007073169574141502,
0.026765644550323486,
-0.0322449691593647,
0.055274590849876404,
-0.040419526398181915,
0.0003435242979321629,
0.0016315056709572673,
0.008966467343270779,
-0.0327022485435009,
0.08718279749155045,
0.002671124180778861,
0.03287466615438461,
0.01799064129590988,
-0.029096290469169617,
-0.023354558274149895,
-0.004952715244144201,
-0.010474964044988155,
0.0412261001765728,
-0.028111768886446953,
-0.005887927021831274,
0.029939325526356697,
-0.040405452251434326,
-0.00022753329540137202,
0.0007679248228669167,
-0.009202987886965275,
0.014865006320178509,
0.005050539970397949,
0.03363586962223053,
-0.0237698033452034,
0.004199318587779999,
-0.01376077439635992,
-0.05066470801830292,
0.03120085783302784,
-0.005904864985495806,
0.03446799889206886,
0.03898448497056961,
-0.03136390075087547,
-0.04048565402626991,
0.02317848615348339,
-0.023211374878883362,
0.014322560280561447,
-0.04985254630446434,
0.0363406166434288,
0.038265716284513474,
0.006691474001854658,
-0.057317741215229034,
-0.03296787664294243,
0.008163869380950928,
0.048335961997509,
0.019987035542726517,
0.008219371549785137,
-0.016401903703808784,
-0.023083331063389778,
-0.012147701345384121,
-0.01731168106198311,
0.03592025488615036,
-0.015157962217926979,
-0.02643418498337269,
0.034108906984329224,
0.008914033882319927,
0.05262741073966026,
-0.01736912876367569,
0.008265407755970955,
-0.0316883809864521,
0.010421455837786198,
-0.00588651280850172,
0.020534293726086617,
0.053270380944013596,
-0.013326406478881836,
-0.04571620002388954,
-0.006339397747069597,
-0.009929647669196129,
0.01812038943171501,
-0.0074034095741808414,
-0.006695448886603117,
0.006744515150785446,
0.010489723645150661,
-0.003588546998798847,
-0.022381827235221863,
-0.034552738070487976,
-0.008028672076761723,
0.01194276288151741,
0.021292151883244514,
0.006136284675449133,
-0.043255891650915146,
-0.03832250460982323,
-0.0181556548923254,
0.006116168573498726,
0.006379596423357725,
0.005211427807807922,
0.0736854150891304,
-0.026905743405222893,
0.02384244091808796,
0.013835910707712173,
-0.03144223615527153,
-0.014939948916435242,
-0.01471693441271782,
-0.023474175482988358,
0.014888808131217957,
0.019486697390675545,
-0.007073568645864725,
-0.04184545949101448,
-0.031276267021894455,
0.002061696955934167,
0.05829755216836929,
-0.01976187713444233,
0.027638457715511322,
-0.011226991191506386,
-0.026012038812041283,
0.009800334461033344,
-0.009341610595583916,
0.0202316977083683,
-0.00788169912993908,
-0.009039829485118389,
0.01650484837591648,
-0.03226492181420326,
-0.05163067951798439,
0.0291278213262558,
0.043136127293109894,
0.01675146073102951,
-0.011769112199544907,
0.021961042657494545,
0.01412628497928381,
-0.01507643237709999,
-0.04740937799215317,
-0.020726464688777924,
0.02513771690428257,
-0.03567729890346527,
0.04267013818025589,
0.004266948439180851,
-0.00665957760065794,
0.04877028241753578,
-0.009646966122090816,
0.013523641973733902,
-0.017376301810145378,
-0.012684649787843227,
-0.04356013610959053,
0.011061079800128937,
0.017330635339021683,
0.03171941265463829,
-0.006666197907179594,
-0.044975947588682175,
0.04267590865492821,
0.012083922512829304,
-0.007904105819761753,
-0.061617713421583176,
-0.06175384670495987,
-0.06186740845441818,
-0.05226542055606842,
-0.02986755780875683,
0.05654530227184296,
-0.008242976851761341,
-0.031501732766628265,
0.03411174565553665,
-0.02011478878557682,
0.026381470263004303,
0.014972224831581116,
0.04142781347036362,
-0.034090373665094376,
0.062380921095609665,
0.010807356797158718,
0.05987318605184555,
-0.03611450269818306,
0.03065011091530323,
0.12389448285102844,
0.05476531386375427,
0.013361665420234203,
-0.007406860124319792,
0.03051082417368889,
-0.010991627350449562,
0.04124889150261879,
-0.017278317362070084,
0.03432704508304596,
-0.020346451550722122,
0.0022708310279995203,
0.019056411460042,
0.0563037283718586,
-0.011559754610061646,
0.022853735834360123,
0.0002705800288822502,
-0.025762826204299927,
-0.008595271036028862,
0.0009209706331603229,
-0.01063317060470581,
0.017876531928777695,
0.018945420160889626,
-0.009611598215997219,
-0.000916621123906225,
-0.03148023784160614,
-0.010861619375646114,
-0.03174281492829323,
-0.01760490983724594,
0.01982858218252659,
-0.0060851736925542355,
-0.01439729519188404,
-0.003630114020779729,
0.01007818803191185,
-0.028857391327619553,
-0.04764020815491676,
0.0094524547457695,
0.022106807678937912,
-0.008152706548571587,
0.025471629574894905,
0.05252920091152191,
0.008508885279297829,
0.020183894783258438,
0.0026567173190414906,
0.03514137491583824,
-0.02963837794959545,
0.0026829554699361324,
-0.008193778805434704,
0.030697984620928764,
0.0002783370728138834,
-0.03219100087881088,
-0.015813937410712242,
-0.01984352432191372,
-0.009762152098119259,
-0.05922425538301468,
-0.005893962923437357,
0.02907431870698929,
0.01484665460884571,
0.0016933747101575136,
0.0015747614670544863,
-0.02710343338549137,
0.014478380791842937,
-0.002072736853733659,
0.023188427090644836,
-0.013709750026464462,
0.015979059040546417,
-0.08332694321870804,
0.03943813219666481,
0.04359044134616852,
0.007755620405077934,
-0.03346102312207222,
-0.021090228110551834,
-0.02122781239449978,
-0.01669565588235855,
0.000942444778047502,
-0.01417443435639143,
0.038420941680669785,
0.029064061120152473,
-0.03991587460041046,
-0.024923915043473244,
-0.03583551198244095,
-0.06813905388116837,
0.0028755106031894684,
0.017539091408252716,
-0.005432930309325457,
0.013149499893188477,
-0.004113102797418833,
0.005629536230117083,
0.029761526733636856,
-0.0488869771361351,
-0.0317678228020668,
-0.0001479589263908565,
0.023751525208353996,
0.042937103658914566,
-0.022154971957206726,
-0.030514607205986977,
-0.012157980352640152,
-0.004808816127479076,
-0.022099211812019348,
-0.028280504047870636,
0.021285638213157654,
0.017863638699054718,
0.01028944831341505,
0.04622635245323181,
0.026432333514094353,
-0.04299692437052727,
0.04009696841239929,
-0.03392421454191208,
-0.02503041736781597,
0.007672618608921766,
0.03745553269982338,
0.039752475917339325,
-0.03171098604798317,
-0.003028514562174678,
0.010029477067291737,
-0.030404094606637955,
0.017296133562922478,
0.009610604494810104,
-0.016732940450310707,
0.012909616343677044,
-0.018660221248865128,
-0.01917685940861702,
-0.06087394058704376,
-0.009109817445278168,
-0.03239581361413002,
0.019331788644194603,
0.006125483196228743,
-0.026827335357666016,
-0.0012476191623136401,
0.03857976943254471,
-0.008264875039458275,
-0.07283839583396912,
0.03959637135267258,
0.0392017737030983,
0.02183089777827263,
0.0018665905809029937,
0.02025378867983818,
-0.00832171831279993,
-0.012729905545711517,
-0.022560179233551025,
-0.07500475645065308,
0.02035897597670555,
-0.022786028683185577,
-0.019725093618035316,
0.0491555780172348,
0.005474820267409086,
0.01283995620906353,
0.04568065330386162,
0.0016532872105017304,
0.024756694212555885,
0.07477603852748871,
-0.02716728299856186,
-0.025018176063895226,
-0.003298617899417877,
-0.06102756783366203,
0.03086346760392189,
-0.06843038648366928,
-0.012490061111748219,
-0.0273367278277874,
0.003390165977180004,
0.055429644882678986,
0.018236834555864334,
-0.0025004532653838396,
-0.026832347735762596,
0.0169873908162117,
-0.015793416649103165,
-0.010684128850698471,
0.00898643210530281,
0.012353791855275631,
0.014295960776507854,
0.041534990072250366,
-0.014715835452079773,
0.06335007399320602,
0.0271099004894495,
-0.019788799807429314,
-0.11427808552980423,
-0.021032126620411873,
0.011067520827054977,
0.03697025403380394,
0.03454015776515007,
-0.00551698449999094,
0.019123705103993416,
0.025732925161719322,
-0.08937220275402069,
0.008646744303405285,
-0.017013421282172203,
0.017105193808674812,
-0.05263629928231239,
-0.01063243392854929,
-0.02170068956911564,
0.0025475728325545788,
0.03257336840033531,
0.029390309005975723,
0.035183995962142944,
0.03513110801577568,
-0.04245232045650482,
-0.04992157220840454,
0.01215266715735197,
0.012143977917730808,
-0.0069288271479308605,
-0.01938691735267639,
0.0465364046394825,
0.007343293633311987,
0.004453698638826609,
0.032321177423000336,
-0.018748067319393158,
-0.0027185154613107443,
-0.005034284666180611,
0.0032330674584954977,
-0.0031751971691846848,
0.03385929390788078,
-0.015351695008575916,
0.038052961230278015,
0.017477773129940033,
0.013050517067313194,
0.02414427511394024,
-0.049323294311761856,
0.014024519361555576,
-0.02480047196149826,
0.04372143745422363,
-0.04952610284090042,
0.007371768821030855,
0.001304096425883472,
-0.0012411325005814433,
0.017654933035373688,
0.029175596311688423,
0.012531465850770473,
0.008541970513761044,
-0.01813722588121891,
-0.020107127726078033,
-0.05751056224107742,
-0.024922046810388565,
0.030201902613043785,
0.024509670212864876,
-0.06366629153490067,
-0.003296743845567107,
-0.020193463191390038,
-0.04069513827562332,
0.026265747845172882,
-0.025601273402571678,
-0.005781313870102167,
-0.022115418687462807,
-0.004114803392440081,
0.02052990533411503,
0.028564123436808586,
0.037422433495521545,
-0.0022844828199595213,
-0.04750392585992813,
0.015682034194469452,
-0.03684072569012642,
0.006156450137495995,
-0.015965154394507408,
-0.004084707237780094,
-0.03426629304885864,
-0.03361646085977554,
-0.011049660854041576,
0.030229143798351288,
-0.0197831392288208,
-0.05309314653277397,
0.0032223861198872328,
-0.05019611865282059,
0.04775277152657509,
0.07254807651042938,
0.021230624988675117,
-0.014690344221889973,
-0.006501961033791304,
-0.01831131801009178,
0.041525084525346756,
-0.059472665190696716,
-0.009272249415516853,
-0.015052082017064095,
-0.025100039318203926,
-0.024126116186380386,
0.005992574617266655,
-0.025321101769804955,
0.03035949543118477,
0.023597445338964462,
-0.012712531723082066,
0.029750028625130653,
-0.0035130346659570932,
-0.018517594784498215,
-0.02812023274600506,
-0.0012931812088936567,
0.020663166418671608,
0.07711657881736755,
-0.0025887221563607454,
0.019229235127568245,
0.00509850587695837,
-0.014830881729722023,
-0.05240578204393387,
-0.00408144062384963,
-0.060887303203344345,
-0.02274785004556179,
-0.002318083541467786,
-0.01986457034945488,
0.03276073932647705,
-0.07011837512254715,
-0.00622900202870369,
0.003653091611340642,
-0.03442282974720001,
-0.06888648867607117,
0.04242410510778427,
-0.005522879771888256,
-0.007036434952169657,
0.01649332046508789,
0.055264804512262344,
0.030436858534812927,
0.0015763218980282545,
-0.02504463493824005,
0.06129198521375656,
-0.012985634617507458,
0.0024585528299212456,
0.020948387682437897,
0.05187847465276718,
0.008887766860425472,
0.027761181816458702,
0.007980354130268097,
0.05124540627002716,
0.011299572885036469,
-0.04314164072275162,
-0.004015659913420677,
-0.03167424350976944,
-0.04496164247393608,
0.07804317772388458,
-0.010503765195608139,
0.020103570073843002,
-0.03013237938284874,
0.06028593331575394,
-0.008618493564426899,
0.00568625470623374,
-0.033601339906454086,
0.04215094447135925,
0.0523722842335701,
0.026810606941580772,
0.007884216494858265,
-0.03445979580283165,
0.007173139601945877,
-0.01019992120563984,
0.009450272656977177,
-0.05912404507398605,
0.0034610657021403313,
0.0025416638236492872,
-0.04226185753941536,
0.011318068020045757,
0.012242782860994339,
-0.026395097374916077,
-0.007749931421130896,
0.04567389190196991,
-0.004653577227145433,
-0.011427685618400574,
0.010995167307555676,
0.012239028699696064,
-0.028468472883105278,
0.07298312336206436,
-0.0283806212246418,
-0.029768606647849083,
0.015756232663989067,
0.01078945491462946,
0.007687275763601065,
-0.0015963880578055978
] |
<p>If <strong>yes</strong>, then how does this accord with relativity: the laws of physics are the same in all reference frames? We can move from a reference frame in which the photon has near zero energy density, to a reference frame where it has near infinite energy density.</p>
<p>If <strong>no</strong>, why are there no gravitational effects for a photon with an arbitrarily high energy density? For some reference frames, a photon can have more energy that the mass of the sun. How are these reference frames consistent with each other?</p>
| 9,549 |
[
-0.03628963977098465,
-0.041370801627635956,
0.002335532568395138,
-0.03150928020477295,
0.0564369261264801,
0.026364706456661224,
-0.038591209799051285,
-0.04397335276007652,
0.0056889294646680355,
-0.03710242360830307,
0.05092988908290863,
0.023658502846956253,
0.035155512392520905,
0.019613346084952354,
0.0533122718334198,
-0.015779290348291397,
0.018452512100338936,
0.02200130932033062,
-0.032029613852500916,
-0.04725538194179535,
-0.022825265303254128,
0.019585005939006805,
-0.006847019772976637,
0.0037431803066283464,
-0.046874891966581345,
0.011665207333862782,
0.00993913784623146,
-0.018186165019869804,
0.016370423138141632,
0.05206144228577614,
-0.017517738044261932,
0.01382021326571703,
-0.007329889107495546,
0.05846896395087242,
0.0606522336602211,
0.005148665513843298,
-0.022613277658820152,
-0.02492859959602356,
0.009252026677131653,
-0.008554410189390182,
-0.027394946664571762,
-0.013477188535034657,
0.008062807843089104,
0.03720853477716446,
-0.02720574475824833,
-0.0085729556158185,
0.01602056808769703,
0.009649687446653843,
0.03884982317686081,
-0.04642544686794281,
0.08121798932552338,
-0.024630064144730568,
0.030877312645316124,
0.045683249831199646,
-0.024616368114948273,
-0.020091114565730095,
0.07012221962213516,
0.06305621564388275,
-0.023658527061343193,
-0.04084086790680885,
-0.020908858627080917,
0.012750298716127872,
-0.011168205179274082,
-0.014894924126565456,
0.008575843647122383,
0.024479437619447708,
-0.018779683858156204,
-0.001455685356631875,
0.018466267734766006,
-0.01628928817808628,
0.0028037135489284992,
0.03396176919341087,
0.02139660157263279,
-0.0007490525022149086,
0.007573426701128483,
-0.0332014337182045,
0.044972386211156845,
0.0035958364605903625,
0.021144025027751923,
0.0846160426735878,
-0.020347371697425842,
-0.0032452649902552366,
0.020595872774720192,
0.02948862314224243,
0.04682931303977966,
0.012410654686391354,
0.06782572716474533,
0.01861531473696232,
0.025264576077461243,
0.05411532148718834,
0.018028700724244118,
-0.00470793666318059,
0.006864747032523155,
0.01187418308109045,
-0.017659300938248634,
0.04688410460948944,
0.0004083847161382437,
0.045156948268413544,
-0.008871338330209255,
-0.01214663591235876,
0.013536789454519749,
0.0019338753772899508,
0.04355723783373833,
0.04822005704045296,
-0.010368389077484608,
-0.06388016790151596,
-0.0442001111805439,
0.03183882310986519,
-0.03711477294564247,
0.02204008400440216,
-0.018198294565081596,
0.004451053682714701,
-0.01639462262392044,
-0.016508424654603004,
0.03741445764899254,
-0.018108299002051353,
0.02590039372444153,
-0.009941717609763145,
0.06188206374645233,
0.06128053367137909,
0.05039497837424278,
-0.026823626831173897,
-0.00382431223988533,
-0.010899471119046211,
-0.018131034448742867,
0.03337576240301132,
0.045691538602113724,
0.0065130447037518024,
-0.04248422011733055,
0.010347560979425907,
-0.031694091856479645,
0.0015195203013718128,
-0.03244183212518692,
-0.005470521282404661,
0.041750162839889526,
-0.013325067237019539,
-0.13798359036445618,
-0.07945536822080612,
0.04890791326761246,
0.00867357850074768,
-0.044147200882434845,
-0.04909729212522507,
0.0208982415497303,
0.041277386248111725,
0.07036881148815155,
-0.038524460047483444,
-0.013867056928575039,
-0.0055198888294398785,
0.029094431549310684,
-0.02063407003879547,
-0.0028770880308002234,
0.0020288776140660048,
0.00817968137562275,
-0.06553322076797485,
0.020067187026143074,
-0.08001408725976944,
-0.00510888546705246,
0.03209049999713898,
0.025774424895644188,
-0.008306639268994331,
0.05892037972807884,
-0.03824581578373909,
0.025362316519021988,
-0.00043863384053111076,
0.0017457695212215185,
-0.01834164373576641,
0.08176042139530182,
0.013656556606292725,
-0.013253087177872658,
0.047878775745630264,
-0.01164685282856226,
0.013329362496733665,
-0.013051127083599567,
0.00869768112897873,
0.008722363971173763,
-0.03364090994000435,
-0.011314785107970238,
-0.04270417243242264,
0.028032496571540833,
0.006216747220605612,
-0.04544879123568535,
-0.025827549397945404,
-0.01180501189082861,
-0.022204922512173653,
0.011010861955583096,
0.046594008803367615,
-0.00990440882742405,
-0.00783375184983015,
-0.01661437377333641,
-0.016356300562620163,
0.01556509267538786,
-0.05435760319232941,
0.03125952556729317,
-0.01831059344112873,
-0.008681097067892551,
0.020588643848896027,
0.01412112358957529,
0.010913219302892685,
-0.04671582952141762,
0.0046195173636078835,
-0.009678352624177933,
0.040325459092855453,
-0.006366249639540911,
-0.009268246591091156,
0.0312952920794487,
0.051876600831747055,
0.03930508345365524,
0.0005707554519176483,
-0.007114461623132229,
0.0015652503352612257,
-0.05328283831477165,
0.027658753097057343,
-0.014153165742754936,
0.042688366025686264,
0.0061781080439686775,
0.023350002244114876,
0.001793695380911231,
0.015519151464104652,
-0.033086147159338,
0.03457173332571983,
-0.016322731971740723,
0.05828914791345596,
0.021639995276927948,
-0.035721469670534134,
0.007960996590554714,
0.03491135314106941,
-0.005613301414996386,
0.025430062785744667,
-0.027055781334638596,
-0.04192863032221794,
-0.03975660726428032,
-0.01500244252383709,
0.010341486893594265,
0.022202150896191597,
-0.03695443645119667,
0.02767609804868698,
0.03853141888976097,
0.06770242750644684,
-0.01875951513648033,
0.023881418630480766,
-0.04127419739961624,
-0.06356877088546753,
0.03621382266283035,
0.010697654448449612,
0.036957867443561554,
0.017259778454899788,
0.014327256940305233,
0.042022883892059326,
0.014133078046143055,
-0.004407057072967291,
0.033283330500125885,
0.014677542261779308,
-0.006289576180279255,
-0.01151992380619049,
0.007712358143180609,
-0.05849939212203026,
0.029918164014816284,
-0.03397471085190773,
0.0269856508821249,
0.03707766905426979,
-0.044312670826911926,
-0.01967627741396427,
-0.025472896173596382,
-0.05389934778213501,
-0.029431715607643127,
0.026104915887117386,
-0.014510028064250946,
0.010334441438317299,
0.02938523143529892,
-0.061162617057561874,
-0.0008214850095100701,
-0.0273186843842268,
-0.0215758066624403,
-0.022768307477235794,
-0.010165897198021412,
0.057352520525455475,
0.010688570328056812,
0.02723124995827675,
-0.043278928846120834,
-0.03162393346428871,
-0.018918074667453766,
-0.03364267200231552,
-0.04532041773200035,
-0.01677507907152176,
-0.05094139277935028,
0.018147960305213928,
-0.019951147958636284,
-0.041176795959472656,
0.024087917059659958,
0.013606863096356392,
0.04703782498836517,
0.05062444135546684,
-0.01583203859627247,
-0.03996269032359123,
-0.002490214304998517,
-0.036239102482795715,
-0.006339076906442642,
0.01313418336212635,
-0.003229632508009672,
0.08730480819940567,
-0.0494537390768528,
-0.06919579952955246,
-0.03379758819937706,
-0.049052268266677856,
-0.04334664344787598,
-0.004902231507003307,
0.022165557369589806,
0.012463393621146679,
-0.03131487965583801,
0.036390271037817,
0.022009918466210365,
-0.0699034333229065,
-0.00013447942910715938,
-0.06369627267122269,
-0.033590059727430344,
0.038766779005527496,
0.020344266667962074,
0.039634041488170624,
0.018189582973718643,
-0.012977860867977142,
0.07070066779851913,
0.07987503707408905,
-0.009365588426589966,
-0.04317096620798111,
-0.021483689546585083,
0.008198991417884827,
-0.023341447114944458,
0.00812245812267065,
0.011848579160869122,
-0.019083887338638306,
-0.01743614301085472,
0.03601403161883354,
0.03663036972284317,
0.002534753642976284,
0.02410309575498104,
-0.0023760132025927305,
-0.01893470250070095,
0.013288852758705616,
-0.02021532505750656,
0.03301076591014862,
0.0383511520922184,
-0.012829635292291641,
-0.013929475098848343,
0.024584652855992317,
0.03128569573163986,
-0.02696889080107212,
-0.023040831089019775,
0.09339449554681778,
0.05226106196641922,
0.020812872797250748,
-0.04835886135697365,
0.058071624487638474,
0.015210932120680809,
-0.013304576277732849,
-0.01161872036755085,
0.005231835879385471,
0.04767746850848198,
0.006743195932358503,
0.004024706780910492,
0.004143510479480028,
0.046770207583904266,
-0.0435054637491703,
-0.023432986810803413,
0.019585968926548958,
0.001815520809032023,
-0.0006751873879693449,
-0.02549690008163452,
-0.016328660771250725,
0.05783770605921745,
0.023378519341349602,
0.03440277650952339,
0.01317377295345068,
-0.038389623165130615,
-0.012178965844213963,
-0.04885831102728844,
0.0065645743161439896,
0.0027335386257618666,
0.02328881248831749,
0.024061348289251328,
0.06483809649944305,
0.032061610370874405,
0.0429060161113739,
0.03406033664941788,
-0.006867112126201391,
-0.076290063560009,
0.00978933647274971,
-0.038472503423690796,
-0.006332969758659601,
0.008190193213522434,
-0.009101285599172115,
-0.05679123476147652,
-0.019510116428136826,
0.007608168292790651,
-0.03771187737584114,
-0.03344333916902542,
-0.05659879744052887,
-0.012629291974008083,
-0.0483965240418911,
-0.06109960377216339,
-0.014232386834919453,
0.01151296403259039,
0.02019307017326355,
-0.023509720340371132,
0.013902516104280949,
0.0091104032471776,
-0.044166043400764465,
0.009580535814166069,
0.00009084554039873183,
0.032025232911109924,
0.006876180414110422,
0.0433591790497303,
0.013786861672997475,
0.012699836865067482,
0.008107520639896393,
0.018875885754823685,
0.033379003405570984,
0.027160881087183952,
0.03305324912071228,
-0.03983549401164055,
-0.025619493797421455,
-0.007580050267279148,
-0.01389453373849392,
-0.008205605670809746,
0.05322329327464104,
0.0047579193487763405,
-0.012644341215491295,
-0.0010472706053406,
0.011750719510018826,
0.009207389317452908,
0.05283360183238983,
0.03296439349651337,
-0.005248729605227709,
0.0007601304678246379,
-0.03986552357673645,
0.0061163282953202724,
-0.023844370618462563,
0.013433237560093403,
0.023992322385311127,
-0.014519941993057728,
-0.045077886432409286,
-0.020602094009518623,
-0.03352833166718483,
0.023967750370502472,
-0.035937704145908356,
-0.013834016397595406,
0.0008427033899351954,
-0.0054036639630794525,
-0.016944386065006256,
-0.00042745372047647834,
-0.02560524456202984,
0.004171246197074652,
0.036539871245622635,
0.0055165160447359085,
-0.007873844355344772,
-0.06685273349285126,
0.026156550273299217,
0.03676922619342804,
0.05580003932118416,
0.014443782158195972,
0.019106082618236542,
-0.05959254875779152,
-0.02750065177679062,
0.024663789197802544,
-0.023055920377373695,
0.026807302609086037,
-0.013210022822022438,
0.014614260755479336,
0.012940695509314537,
-0.03612799942493439,
-0.005020245909690857,
0.013497944921255112,
-0.03186235949397087,
0.00006506200588773936,
-0.013314425013959408,
0.0075241276063025,
-0.0056433905847370625,
0.01802043803036213,
0.012058688327670097,
0.0547059066593647,
0.019989553838968277,
0.014584937132894993,
0.0011020724195986986,
-0.011450868099927902,
-0.03277653828263283,
-0.08018729090690613,
-0.020639879629015923,
0.0270916149020195,
-0.019059034064412117,
0.03903394192457199,
-0.028574267402291298,
-0.07473250478506088,
0.029991406947374344,
-0.0033423425629734993,
-0.03522448241710663,
-0.007536774966865778,
-0.05084368586540222,
0.018413398414850235,
0.03131193295121193,
-0.020900147035717964,
0.02919474057853222,
0.03411656245589256,
-0.03466183692216873,
0.008691692724823952,
-0.0350322425365448,
0.03819559887051582,
-0.03265421465039253,
-0.0019416753202676773,
-0.048604078590869904,
-0.007637195289134979,
-0.01675308123230934,
0.038018159568309784,
-0.007315205875784159,
-0.0023726921062916517,
0.05761222168803215,
-0.020114069804549217,
-0.018820255994796753,
0.029636666178703308,
0.010535390116274357,
-0.003592162625864148,
-0.05338661000132561,
-0.00546727841719985,
-0.015568285249173641,
-0.023585129529237747,
0.025077776983380318,
0.01582150161266327,
0.022169748321175575,
0.032119035720825195,
0.025211088359355927,
0.048295143991708755,
-0.006658898200839758,
0.010879027657210827,
-0.013732606545090675,
-0.017196830362081528,
0.03463991358876228,
0.00017995623056776822,
-0.005072592757642269,
0.04016859829425812,
-0.023381805047392845,
-0.0434374138712883,
0.002789613325148821,
-0.047248758375644684,
0.040785644203424454,
-0.03157273679971695,
0.0377948060631752,
-0.004795210435986519,
-0.006861995905637741,
-0.0918797105550766,
-0.026057081297039986,
-0.00845042522996664,
0.02500765770673752,
0.01896878518164158,
-0.007826941087841988,
0.03027845360338688,
-0.04765360802412033,
0.0007632856140844524,
-0.04686085879802704,
0.021756242960691452,
0.009862484410405159,
-0.014723745174705982,
0.024655142799019814,
-0.008800587616860867,
0.047273583710193634,
-0.014161450788378716,
-0.03165065124630928,
0.012559430673718452,
0.008915266953408718,
-0.020270684733986855,
-0.03194344416260719,
0.05667535960674286,
-0.01526548434048891,
-0.05988967418670654,
-0.0022797530982643366,
0.003719603642821312,
-0.006341550033539534,
-0.007278783712536097,
-0.009899280034005642,
0.05951772630214691,
-0.005618487484753132,
-0.02119617909193039,
-0.03273405134677887,
0.019841236993670464,
-0.023838995024561882,
0.03055432438850403,
0.013721832074224949,
-0.00959384348243475,
-0.022447161376476288,
-0.046348605304956436,
0.028101857751607895,
-0.00654205959290266,
0.026438143104314804,
-0.003979643806815147,
0.06583388894796371,
-0.008078739047050476,
0.006568341050297022,
0.008221864700317383,
-0.001132927369326353,
0.008344456553459167,
-0.032024770975112915,
-0.0002784151874948293,
-0.010709007270634174,
-0.019529012963175774,
-0.033642373979091644,
-0.0019641078542917967,
-0.020740624517202377,
-0.024048883467912674,
0.060588132590055466,
-0.0014728046953678131,
0.04283497482538223,
0.0012376592494547367,
-0.008700101636350155,
0.029260100796818733,
-0.04308519884943962,
-0.0051949177868664265,
-0.003730376251041889,
0.009213036857545376,
0.009494203142821789,
0.014106208458542824,
0.003472515381872654,
0.07434358447790146,
0.07168160378932953,
0.018377499654889107,
0.02938184142112732,
0.02625136449933052,
0.024523010477423668,
0.03302086889743805,
0.00074141746154055,
-0.05062464624643326,
0.02225656248629093,
-0.03698648884892464,
0.0023910931777209044,
0.0019740608986467123,
-0.018828637897968292,
0.022981949150562286,
-0.01763392798602581,
0.019129537045955658,
0.0051634348928928375,
-0.025042321532964706,
-0.03410503268241882,
0.02553480491042137,
-0.0011692140251398087,
0.039351705461740494,
-0.01561860740184784,
0.0037097232416272163,
0.03275240585207939,
0.015651967376470566,
-0.0033634393475949764,
-0.01643039658665657,
-0.07046689838171005,
-0.04186154156923294,
-0.04335872083902359,
-0.02307518757879734,
0.052485041320323944,
-0.012116306461393833,
-0.06516335904598236,
0.011879676952958107,
-0.03319802135229111,
0.014560234732925892,
0.05484643206000328,
0.04966626316308975,
0.012792950496077538,
0.026395708322525024,
-0.010261313989758492,
0.02183237113058567,
-0.009046428836882114,
-0.0030021118000149727,
0.08483950048685074,
0.062286850064992905,
0.004687364213168621,
-0.017319122329354286,
0.009562964551150799,
-0.01361083984375,
0.015119177289307117,
-0.04091108217835426,
0.016348088160157204,
-0.04612385854125023,
0.021789848804473877,
0.027695205062627792,
0.036575205624103546,
-0.02357112057507038,
-0.03203301504254341,
0.028522642329335213,
-0.032244760543107986,
-0.028838275000452995,
0.03020625375211239,
0.042915694415569305,
0.02661045640707016,
0.011341005563735962,
-0.01366726029664278,
-0.024785161018371582,
-0.04231274873018265,
-0.011495400220155716,
0.0066482448019087315,
-0.04032670333981514,
0.00229567289352417,
0.0030639595352113247,
-0.034251619130373,
-0.0189477801322937,
0.017256516963243484,
-0.01981414295732975,
-0.04652899131178856,
-0.014487714506685734,
0.037126898765563965,
0.0018912238301709294,
0.00203300011344254,
0.04218266159296036,
0.010414974763989449,
0.006166687700897455,
0.00920052919536829,
0.03168083354830742,
-0.030601786449551582,
0.01189147774130106,
-0.013486122712492943,
0.01924949698150158,
-0.017977077513933182,
0.015507763251662254,
0.01809910126030445,
0.008208032697439194,
-0.011640951037406921,
-0.05544187128543854,
-0.00039218668825924397,
0.006179544609040022,
-0.004444400779902935,
0.015430431813001633,
-0.014580832794308662,
-0.01532003004103899,
0.016356930136680603,
0.013709803111851215,
0.02825242467224598,
-0.03893987089395523,
0.005792108364403248,
0.011164240539073944,
-0.00963523518294096,
0.032807089388370514,
-0.04585162550210953,
-0.0072146812453866005,
-0.009448735974729061,
-0.042901795357465744,
-0.051412273198366165,
-0.04774586483836174,
0.03482361510396004,
0.035113412886857986,
0.009026098996400833,
0.018150651827454567,
-0.000253790058195591,
-0.031251851469278336,
-0.08237960934638977,
0.029444364830851555,
-0.020738430321216583,
-0.03764325752854347,
-0.00394590524956584,
0.016332920640707016,
0.026738693937659264,
0.03870677202939987,
0.0027756355702877045,
0.010395520366728306,
-0.014117579907178879,
0.01731221005320549,
0.018879109993577003,
-0.024196945130825043,
-0.008634956553578377,
-0.006796426605433226,
0.006186238490045071,
-0.0023172800429165363,
-0.019659457728266716,
-0.00459110364317894,
0.026536358520388603,
-0.006407011300325394,
0.016937803477048874,
0.011760605499148369,
-0.011313718743622303,
-0.01624756120145321,
0.006118374411016703,
0.008130085654556751,
-0.009926809929311275,
0.04303053766489029,
0.04001016542315483,
-0.03018534742295742,
-0.045199472457170486,
-0.05105889216065407,
-0.01106071937829256,
-0.009056015871465206,
0.014491544105112553,
-0.007354794070124626,
0.009738068096339703,
0.002152516972273588,
0.03053748421370983,
-0.03821729123592377,
-0.02512269839644432,
-0.016826169565320015,
0.03062662109732628,
0.000158093505888246,
-0.035793863236904144,
0.004751084838062525,
0.019816754385828972,
-0.04334447532892227,
-0.03480176627635956,
0.032682303339242935,
0.01987568847835064,
-0.019129445776343346,
0.022406602278351784,
0.011780132539570332,
-0.019706010818481445,
0.04887338727712631,
-0.0006173159927129745,
-0.025747381150722504,
0.02326895482838154,
-0.03783402591943741,
-0.015368535183370113,
0.053123775869607925,
-0.04843968152999878,
0.018140770494937897,
0.024477090686559677,
-0.020475056022405624,
0.015135536901652813,
0.045101430267095566,
-0.004957006778568029,
0.002924270462244749,
0.008734090253710747,
-0.06412629783153534,
-0.00019083764345850796,
0.02163768745958805,
0.03934738039970398,
0.013110066764056683,
-0.04344244301319122,
0.059570327401161194,
0.0295685064047575,
0.03614325076341629,
0.01510942354798317,
-0.007181855384260416,
-0.022603671997785568,
-0.03868463262915611,
-0.006810242310166359,
0.0064908829517662525,
0.032884467393159866,
0.0304911769926548,
-0.025410624220967293,
0.04342439025640488,
0.005347759462893009,
0.008714721538126469,
-0.1055474802851677,
-0.017958270385861397,
-0.011944402940571308,
0.0028873328119516373,
0.03165890648961067,
-0.037980273365974426,
0.056399453431367874,
0.006635100115090609,
-0.09811559319496155,
0.04483509436249733,
0.02446419931948185,
-0.0014654753031209111,
0.0006726837018504739,
0.04569394886493683,
-0.020759042352437973,
0.06123856082558632,
0.03416813910007477,
0.06497656553983688,
-0.029061483219265938,
0.009641085751354694,
0.020596472546458244,
-0.000964048900641501,
-0.02712976559996605,
0.025337934494018555,
-0.023591307923197746,
0.012619591318070889,
0.06236371397972107,
0.0057211690582334995,
-0.013140819035470486,
0.03078608214855194,
-0.01259428821504116,
0.03475832939147949,
0.010341058485209942,
-0.0020619796123355627,
0.009756180457770824,
0.024268409237265587,
-0.00019003722991328686,
-0.01144091784954071,
-0.06950302422046661,
0.028409196063876152,
0.008349752984941006,
0.04316987097263336,
-0.021151140332221985,
-0.0017244472401216626,
0.013098730705678463,
-0.0580197349190712,
-0.05161087587475777,
0.042868517339229584,
0.003076449502259493,
0.01468745432794094,
0.0051927086897194386,
0.041703127324581146,
-0.0036788249853998423,
-0.007706635165959597,
-0.017423324286937714,
-0.06519386172294617,
-0.01337583176791668,
0.0028881889302283525,
-0.014216303825378418,
0.004167144652456045,
0.0180563572794199,
0.006243499461561441,
-0.017975442111492157,
0.016085926443338394,
-0.0035369994584470987,
-0.0043496014550328255,
-0.02009909227490425,
0.018579017370939255,
0.008177774958312511,
-0.004714248701930046,
0.019170982763171196,
-0.045784078538417816,
-0.04652881249785423,
0.02622206136584282,
-0.0003793894429691136,
0.006762107368558645,
0.015453887172043324,
-0.01156566757708788,
-0.06665246188640594,
-0.07079131156206131,
0.007271252106875181,
0.015178760513663292,
0.012395461089909077,
-0.056525975465774536,
-0.011609386652708054,
-0.020528653636574745,
0.037288155406713486,
0.024212097749114037,
0.008119995705783367,
-0.009102731011807919,
0.04374145716428757,
-0.03084738552570343,
-0.008971819654107094,
-0.08067955076694489,
0.014036642387509346,
0.0074539026245474815,
-0.04681099206209183,
-0.01600424200296402,
0.024634908884763718,
-0.04938394948840141,
-0.00938674621284008,
-0.007137867622077465,
-0.03252468630671501,
0.041072405874729156,
0.018576180562376976,
-0.04138187691569328,
0.07203850895166397,
0.026366326957941055,
-0.015093352645635605,
0.07048187404870987,
-0.0011637822026386857,
0.03323464095592499,
0.03838126361370087,
-0.03648154065012932,
-0.040253881365060806,
0.006503815297037363,
-0.023622948676347733,
-0.012247784063220024,
-0.01904558762907982,
0.023221924901008606,
0.03151468187570572,
-0.02214411087334156,
0.011081377975642681,
0.0628332570195198,
-0.03501094505190849,
-0.010431195609271526,
0.05196201428771019,
-0.012878323905169964,
0.05153663456439972,
0.013326041400432587,
0.033531129360198975,
-0.007624390535056591,
-0.008323095738887787,
-0.0036401995457708836,
0.05170297250151634,
0.012736077420413494,
-0.004558940418064594,
0.019205404445528984,
0.030964815989136696,
0.01876935549080372,
-0.011811943724751472,
0.0008313525468111038,
0.0467076450586319,
-0.03407050296664238,
-0.0046944092027843,
0.016101496294140816,
0.023002218455076218,
-0.0026671597734093666,
0.02500811219215393,
-0.02932649292051792,
0.04950942099094391,
-0.025095609948039055,
-0.012192824855446815,
0.0131112951785326,
-0.012886840850114822,
-0.0074439384043216705,
0.029605410993099213,
0.012038606218993664,
0.057214729487895966,
0.01725616678595543,
0.004488272592425346,
-0.024274811148643494,
-0.014970934018492699,
0.01260368898510933,
-0.043103694915771484,
-0.02295101247727871,
0.003327044192701578,
-0.021932566538453102,
0.005245349835604429,
0.015269575640559196,
-0.015235744416713715,
-0.02161414735019207,
0.00746318232268095,
0.023905524984002113,
0.011447696015238762,
-0.03037724271416664,
0.0003422707668505609,
-0.013017810881137848,
0.04962873086333275,
-0.031462498009204865,
0.005536314565688372,
-0.02220948040485382,
0.003872566157951951,
-0.003751634620130062,
-0.04975007101893425
] |
<p>I am working on the Hydrogen atom and I was trying to calculate $\frac{d<r>}{dt}$ using $$\frac{d<r>}{dt} = \frac{i}{\hbar} <[\hat{H} , \hat{r}]>.$$ Here $r = \sqrt(x^2 + y^2 + z^2)$ and $H = \frac{p^2}{2m} + V$ where $p^2 = -\hbar^2 \nabla^2 $. Now according to Ehrenfest's theorem should behave classically and give me some equivalent of velocity, and indeed I do get something but it does't resemble velocity: $\frac{-\hbar^2}{2m} (2\nabla r \nabla f + f \nabla^2 r)$ </p>
<p>where $f$ is a test function.</p>
<p>Steps:
$[H ,r]f = [\frac{p^2}{2m} + V , r]f = \frac{p^2(rf)}{2m} + Vrf - \frac{rp^2(f)}{2m} - rVf = \frac{1}{2m}[p^2 ,r]f = \frac{1}{2m}[-\hbar^2\nabla^2 , r]f = \frac{-\hbar^2}{2m}[\nabla^2 , r]f $$= \frac{-\hbar^2}{2m} (\nabla^2(rf) - r\nabla^2(f)) = \frac{-\hbar^2}{2m} (\nabla r\nabla f + r\nabla^2f + \nabla f \nabla r + f\nabla^2 r - r\nabla^2f) = \frac{-\hbar^2}{2m} (2\nabla r \nabla f + f \nabla^2 r) $</p>
<p>Am I doing something wrong?</p>
| 9,550 |
[
-0.0019535417668521404,
0.012417826801538467,
-0.0011623995378613472,
-0.03168603405356407,
0.04247771576046944,
-0.020506318658590317,
-0.04587193578481674,
-0.014597631059587002,
0.012594947591423988,
-0.007867418229579926,
0.05825554206967354,
0.025706905871629715,
0.07755818963050842,
-0.031242735683918,
0.008329752832651138,
0.05323488637804985,
-0.004170131869614124,
0.00614062137901783,
0.0038552593905478716,
-0.02473589777946472,
-0.007998478598892689,
0.022118298336863518,
0.051264699548482895,
-0.02141481079161167,
-0.006226964294910431,
-0.004514862783253193,
-0.007174307946115732,
-0.01261693611741066,
-0.043370988219976425,
0.042193468660116196,
-0.0038579890970140696,
-0.018730677664279938,
0.02546180598437786,
-0.007647355552762747,
-0.03148472309112549,
0.05239107832312584,
-0.043073780834674835,
-0.03141042962670326,
-0.041030194610357285,
0.03421519324183464,
-0.01586710475385189,
-0.0028011046815663576,
-0.01366129145026207,
0.05895918607711792,
0.02733748033642769,
0.006961022969335318,
0.008734863251447678,
0.011639973148703575,
0.05737820640206337,
-0.04745104908943176,
0.07049907743930817,
0.006653442978858948,
0.0289345383644104,
0.008889930322766304,
-0.042596783488988876,
-0.0384608693420887,
0.03937810659408569,
0.0894344300031662,
0.04078511521220207,
-0.0473087877035141,
-0.01470092311501503,
-0.03217819705605507,
-0.030021140351891518,
-0.023078495636582375,
-0.013898073695600033,
0.017244063317775726,
0.0007036479655653238,
-0.026194069534540176,
-0.010766216553747654,
0.0046097515150904655,
0.03833416849374771,
-0.024202561005949974,
0.014702562242746353,
-0.035101499408483505,
0.023203160613775253,
0.0027959507424384356,
-0.007924909703433514,
0.005633027292788029,
0.022209765389561653,
0.02148113213479519,
-0.0013528349809348583,
0.014591120183467865,
0.024965403601527214,
0.03488730639219284,
0.0030157838482409716,
-0.025695577263832092,
0.038512520492076874,
-0.00048431303002871573,
0.02072526514530182,
0.0334618017077446,
-0.014789136126637459,
0.00930635817348957,
0.033002641052007675,
-0.0053435638546943665,
0.00960545800626278,
0.003642047755420208,
-0.018796183168888092,
0.01918751932680607,
0.0036254520528018475,
-0.02370467223227024,
-0.03578132763504982,
-0.041126370429992676,
0.004740697797387838,
0.07514984160661697,
0.010260598734021187,
-0.019772712141275406,
0.003293468151241541,
-0.016105415299534798,
-0.014177254401147366,
-0.017453553155064583,
-0.036522917449474335,
0.044232528656721115,
-0.002333632204681635,
-0.017149347811937332,
0.0011623699683696032,
-0.044119905680418015,
-0.005156633909791708,
-0.019443701952695847,
0.06864304095506668,
0.046887513250112534,
0.014331283047795296,
-0.02394682727754116,
-0.0000036752535379491746,
0.007873345166444778,
-0.029092613607645035,
0.018316218629479408,
0.01718761771917343,
0.032335832715034485,
0.011393933556973934,
-0.005910544190555811,
0.015641942620277405,
-0.021658139303326607,
-0.004253907594829798,
0.02029483951628208,
-0.010506028309464455,
-0.005998887121677399,
-0.09625129401683807,
-0.049722809344530106,
0.02685735374689102,
-0.0019125586841255426,
0.013932943344116211,
-0.08475390821695328,
0.01352518331259489,
0.015826744958758354,
0.08625828474760056,
0.03372117877006531,
-0.0006128106615506113,
0.018314506858587265,
0.06925452500581741,
-0.010902774520218372,
-0.010080101899802685,
-0.02849901281297207,
-0.04379172995686531,
-0.029240822419524193,
-0.021339552477002144,
-0.03961765021085739,
0.01786084845662117,
0.007525147870182991,
0.026692848652601242,
0.0293907318264246,
0.06778282672166824,
-0.0007448124815709889,
0.004341233056038618,
0.011799300089478493,
-0.008776252157986164,
0.008868257515132427,
0.0609649196267128,
0.007728228345513344,
0.002607422647997737,
0.021017828956246376,
0.01765596866607666,
0.009821238927543163,
-0.016618311405181885,
-0.00022894851281307638,
0.03716851398348808,
-0.043802473694086075,
0.0010405766079202294,
-0.007800749968737364,
0.004105806350708008,
-0.01156943291425705,
-0.036682721227407455,
-0.027553893625736237,
-0.0051920791156589985,
-0.012932530604302883,
0.001791121787391603,
0.04766176640987396,
0.044722869992256165,
0.0010496759787201881,
0.0006024875328876078,
-0.04784625396132469,
0.025938773527741432,
-0.03029949776828289,
-0.013660556636750698,
-0.0017668119398877025,
-0.03224622830748558,
0.04161468893289566,
-0.0018014009110629559,
0.0064095305278897285,
-0.00720165204256773,
-0.044464897364377975,
-0.010562760755419731,
0.01417341735213995,
0.022973110899329185,
0.011709245853126049,
0.05014685541391373,
0.03632275387644768,
0.042598459869623184,
0.02346109226346016,
0.02837294526398182,
-0.028847236186265945,
0.007700697053223848,
-0.007192178629338741,
-0.035638049244880676,
-0.0015249602729454637,
0.038485050201416016,
-0.021930115297436714,
0.020914629101753235,
-0.01497784536331892,
-0.002047567628324032,
0.005987240932881832,
-0.029576944187283516,
0.03252631053328514,
0.037311628460884094,
0.03364337235689163,
0.0042806146666407585,
0.03174562752246857,
0.0018812445923686028,
0.007484640926122665,
-0.012851487845182419,
-0.027625948190689087,
-0.004046138375997543,
0.004379610996693373,
0.06839341670274734,
0.04798123612999916,
-0.08976585417985916,
0.034458547830581665,
0.032837994396686554,
0.03885257989168167,
0.042772192507982254,
0.028779515996575356,
-0.016674596816301346,
-0.06776728481054306,
0.037561945617198944,
-0.0026373155415058136,
0.014637712389230728,
-0.008734882809221745,
0.013793648220598698,
0.02640569768846035,
0.021370256319642067,
-0.029355652630329132,
-0.02016771398484707,
0.03816169127821922,
-0.009343250654637814,
-0.04539409652352333,
0.007686483673751354,
-0.020293837413191795,
0.0211623664945364,
0.007114027161151171,
0.005357304122298956,
0.0781034603714943,
-0.01413023192435503,
0.03447585180401802,
-0.04299004748463631,
0.0004300781583879143,
0.027818752452731133,
0.01737631857395172,
0.006385101471096277,
0.008976251818239689,
0.01347699947655201,
-0.028484666720032692,
-0.01076713390648365,
-0.03776226565241814,
-0.02060353010892868,
-0.009293222799897194,
-0.027457842603325844,
-0.003643524134531617,
0.05477995052933693,
-0.03163803368806839,
-0.007561631966382265,
-0.005939646624028683,
0.01575879193842411,
-0.00892188772559166,
0.011998243629932404,
-0.010077574290335178,
-0.010801143012940884,
-0.011667992919683456,
-0.04634213447570801,
-0.00954482052475214,
0.08700435608625412,
0.024370193481445312,
-0.02454437129199505,
-0.05106198787689209,
-0.004396482836455107,
-0.04933755472302437,
-0.02887129969894886,
-0.028457168489694595,
0.015759507194161415,
-0.06760910898447037,
0.01126093976199627,
0.02692948654294014,
-0.028605692088603973,
-0.00459862407296896,
0.03508637845516205,
0.008468284271657467,
-0.03507748618721962,
-0.036536622792482376,
-0.01893262192606926,
0.011791924014687538,
-0.00045625821803696454,
0.0227969940751791,
0.04085996374487877,
-0.003684353781864047,
0.004289631266146898,
-0.04179168492555618,
-0.043351516127586365,
-0.00465421425178647,
0.017447812482714653,
0.018494781106710434,
0.00892904307693243,
-0.014808597043156624,
0.07620285451412201,
-0.006107998546212912,
-0.019454658031463623,
-0.013698088005185127,
0.024078551679849625,
-0.006926258094608784,
-0.025006573647260666,
0.0030678159091621637,
0.062180474400520325,
0.012072531506419182,
0.02084779553115368,
-0.030477797612547874,
0.02791581302881241,
0.03369147703051567,
-0.010752544738352299,
0.010912865400314331,
0.041986096650362015,
-0.0096316272392869,
0.004333876073360443,
0.10317444801330566,
0.025950049981474876,
-0.01980944536626339,
0.013665257953107357,
-0.004883359652012587,
0.016181163489818573,
0.03099190443754196,
-0.052179571241140366,
0.056539665907621384,
-0.02280401438474655,
0.007915052585303783,
-0.02413587085902691,
0.015185981057584286,
0.00007012126297922805,
-0.044302307069301605,
-0.02580268494784832,
-0.029722299426794052,
0.060552824288606644,
0.007655832916498184,
0.0029331643600016832,
0.04411430284380913,
-0.002459942828863859,
-0.014517495408654213,
0.004227564670145512,
-0.027692105621099472,
0.0009997922461479902,
0.050912149250507355,
0.003232356160879135,
-0.04015190899372101,
0.04373616725206375,
0.02723020128905773,
0.004182427655905485,
-0.00894878152757883,
-0.024676285684108734,
-0.0075770472176373005,
-0.03070717118680477,
-0.018642349168658257,
-0.06691999733448029,
0.06661181896924973,
-0.036889802664518356,
0.07679000496864319,
0.02759966067969799,
0.02757405862212181,
0.02220379188656807,
-0.009098600596189499,
-0.04600325971841812,
0.017491910606622696,
-0.019881999120116234,
-0.057679589837789536,
-0.048158831894397736,
-0.010143188759684563,
0.003261854872107506,
-0.050704825669527054,
0.008854915387928486,
-0.020242836326360703,
-0.017146939411759377,
-0.024299394339323044,
0.014708596281707287,
-0.014366883784532547,
-0.05232042446732521,
-0.03633072227239609,
0.03897066414356232,
0.07171650975942612,
-0.019023282453417778,
0.023636598140001297,
0.06289301067590714,
-0.05848785489797592,
-0.021537210792303085,
-0.050920769572257996,
0.00913210865110159,
0.019771045073866844,
0.022770950570702553,
-0.007931175641715527,
-0.02284897118806839,
0.0011784941889345646,
0.025305476039648056,
-0.005501620937138796,
0.033508382737636566,
0.018811305984854698,
-0.013992699794471264,
-0.01797463744878769,
-0.012214857153594494,
0.03677993267774582,
-0.007302701473236084,
0.08958196640014648,
-0.018774325028061867,
0.002566501498222351,
0.022956542670726776,
-0.006994175259023905,
0.027266360819339752,
0.015774143859744072,
0.026778094470500946,
-0.011346458457410336,
-0.0010790297528728843,
-0.09922978281974792,
-0.01202530786395073,
-0.02330121211707592,
-0.0227940883487463,
0.005531806033104658,
-0.028797289356589317,
-0.04018787667155266,
-0.031347520649433136,
0.022088849917054176,
0.06580138206481934,
0.01789974793791771,
0.0032556126825511456,
-0.025774512439966202,
0.0033727572299540043,
0.018907425925135612,
0.015264099463820457,
0.012709512375295162,
0.030967455357313156,
0.04645209014415741,
-0.019984843209385872,
-0.003954483196139336,
-0.06403873860836029,
0.03699428588151932,
-0.006948804948478937,
0.03637446090579033,
-0.051071759313344955,
0.035854585468769073,
-0.03657475858926773,
-0.046567901968955994,
0.040111709386110306,
-0.009544456377625465,
0.025828683748841286,
-0.007056619971990585,
-0.021376963704824448,
-0.002021058462560177,
-0.03976031020283699,
-0.043055400252342224,
-0.011096890084445477,
-0.003825597930699587,
-0.03153952956199646,
-0.06244756281375885,
-0.001252699294127524,
-0.0014830109430477023,
-0.010160261765122414,
0.016417117789387703,
0.0586884543299675,
0.005885383579879999,
-0.0009493583929724991,
0.013065768405795097,
0.0035990141332149506,
-0.03671165555715561,
-0.05261343717575073,
0.017311982810497284,
0.0052233184687793255,
0.024637116119265556,
0.02932305447757244,
-0.07945422828197479,
-0.0454091913998127,
0.09205851703882217,
-0.00858865212649107,
0.014357107691466808,
0.04179426282644272,
-0.005124103743582964,
0.053993307054042816,
0.033120084553956985,
-0.013238503597676754,
0.046557120978832245,
0.01942765712738037,
-0.013289974071085453,
-0.02666505239903927,
-0.014820845797657967,
-0.009533504955470562,
-0.01068404596298933,
-0.021031996235251427,
-0.04449276253581047,
0.001202553161419928,
0.002825766569003463,
0.04086671769618988,
-0.00504756486043334,
0.03650115057826042,
-0.05058416724205017,
-0.04972168803215027,
0.03531116619706154,
-0.015154610387980938,
-0.030349083244800568,
-0.03862554579973221,
-0.013543087057769299,
0.011441132985055447,
-0.0005637385183945298,
-0.01956813968718052,
0.012559237889945507,
0.004650493152439594,
0.014046594500541687,
0.03646007925271988,
-0.006345896981656551,
-0.00013300534919835627,
-0.02457134611904621,
-0.03227704390883446,
-0.0064559439197182655,
-0.07825654745101929,
-0.009243356995284557,
-0.005596434231847525,
-0.04090382531285286,
0.003381642047315836,
-0.005128280259668827,
-0.018612533807754517,
0.057154424488544464,
-0.010404220782220364,
0.014262707903981209,
-0.01904604211449623,
-0.023782214149832726,
0.01477422472089529,
-0.013771139085292816,
-0.03822276368737221,
-0.01893320307135582,
0.017388811334967613,
0.006685895845293999,
-0.03253709897398949,
-0.05086749792098999,
-0.0076963165774941444,
-0.013470449484884739,
-0.0016625919379293919,
0.013246901333332062,
0.04816311597824097,
-0.008279687725007534,
0.00016160904488060623,
0.007696537766605616,
0.007718284148722887,
0.03564656525850296,
-0.02399272657930851,
-0.003271960886195302,
0.016488343477249146,
0.010223496705293655,
-0.015374626964330673,
0.02865816466510296,
0.010462775826454163,
-0.007247759494930506,
0.0009761663968674839,
0.005385627504438162,
-0.020470282062888145,
0.022676393389701843,
-0.006729861255735159,
-0.0003607646794989705,
0.009774904698133469,
-0.010015464387834072,
-0.03032750077545643,
-0.032869599759578705,
-0.02926059253513813,
0.01841377466917038,
0.026122238487005234,
-0.009091324172914028,
0.00971705187112093,
-0.03233786299824715,
-0.04592694714665413,
0.02021958865225315,
-0.036634527146816254,
-0.006641138345003128,
-0.023561054840683937,
0.04265017807483673,
-0.04101746529340744,
0.029029730707406998,
0.020258251577615738,
-0.009069591760635376,
-0.03829114884138107,
0.009769261814653873,
0.019922854378819466,
-0.013180846348404884,
0.0107524823397398,
-0.037691354751586914,
-0.0473337396979332,
-0.07086792588233948,
0.009956817142665386,
0.08879896253347397,
-0.013839642517268658,
0.0530722439289093,
-0.0315764956176281,
0.0037545703817158937,
-0.024368366226553917,
-0.040164630860090256,
0.011143437586724758,
0.011057845316827297,
0.0064573283307254314,
0.04505500942468643,
0.0016707913018763065,
0.01432151161134243,
0.043355245143175125,
0.025948811322450638,
-0.015536734834313393,
-0.01860702596604824,
0.00007016040763119236,
0.030542831867933273,
0.013115004636347294,
-0.004917064215987921,
0.0038278596475720406,
0.013255885802209377,
-0.014594749547541142,
0.03897932544350624,
-0.020700108259916306,
0.031955838203430176,
0.057843707501888275,
0.05767582356929779,
0.013619842007756233,
-0.03508635237812996,
-0.003796100616455078,
0.0038717342540621758,
0.04753830283880234,
0.019646240398287773,
-0.022664519026875496,
-0.008255337364971638,
0.024028118699789047,
0.032459110021591187,
-0.0017812849255278707,
0.029446154832839966,
-0.0028763555455952883,
-0.008901642635464668,
0.005919309798628092,
-0.04932054877281189,
-0.034746985882520676,
0.0615355558693409,
0.0043996418826282024,
-0.036700524389743805,
-0.011748804710805416,
0.015335558913648129,
0.011640068143606186,
0.04100878909230232,
0.016913071274757385,
-0.015377750620245934,
0.0722334012389183,
-0.0014577378751710057,
-0.016583893448114395,
-0.010593391954898834,
-0.0008624771144241095,
0.1457216888666153,
0.0229366272687912,
0.031996119767427444,
-0.006771659478545189,
-0.002758893184363842,
-0.015259030275046825,
0.02562701515853405,
-0.020088592544198036,
0.00514556560665369,
-0.0032240240834653378,
-0.02776377834379673,
0.04146545007824898,
0.0748363733291626,
0.02580704540014267,
0.018845856189727783,
0.009897674433887005,
-0.023265354335308075,
0.00784038845449686,
-0.03972773626446724,
-0.0030157510191202164,
-0.009499586187303066,
0.04306955263018608,
-0.018148550763726234,
0.04116985574364662,
-0.08123547583818436,
0.04818904399871826,
-0.04209648072719574,
-0.02027570828795433,
0.011814563535153866,
-0.009936288930475712,
-0.07382477074861526,
0.015252145007252693,
-0.01389302033931017,
-0.012442080304026604,
0.009090119041502476,
0.016696840524673462,
0.03411131352186203,
-0.021264102309942245,
0.01629885472357273,
0.007177623454481363,
0.007166326977312565,
0.024504896253347397,
-0.025841601192951202,
-0.014970039017498493,
-0.018768999725580215,
0.022728554904460907,
-0.030146334320306778,
0.053756967186927795,
-0.010988861322402954,
-0.001968852709978819,
0.006082023959606886,
-0.022833989933133125,
-0.00589707912877202,
-0.07764282822608948,
0.02299509383738041,
-0.004489687271416187,
-0.019672058522701263,
0.01748381182551384,
0.029826458543539047,
-0.025290291756391525,
0.04718004912137985,
0.024285942316055298,
-0.036518413573503494,
-0.015670018270611763,
0.0007818687008693814,
-0.0157761350274086,
0.02267530933022499,
0.02346254140138626,
-0.03274242579936981,
-0.014152687974274158,
-0.03137188032269478,
-0.019751064479351044,
-0.05012546107172966,
-0.026746302843093872,
0.01854783482849598,
0.02257966808974743,
0.06383036822080612,
0.0064863902516663074,
-0.03216671571135521,
-0.05999499186873436,
-0.07420537620782852,
0.0149619709700346,
0.03050524741411209,
-0.05011191964149475,
-0.010319867171347141,
-0.001031931140460074,
0.021943246945738792,
0.02229006588459015,
-0.035297028720378876,
-0.0020414963364601135,
-0.02205878309905529,
0.07147840410470963,
0.02508639171719551,
-0.0009141915361396968,
-0.029625777155160904,
0.011860806494951248,
0.014821055345237255,
0.012696652673184872,
0.014873860403895378,
-0.02080867439508438,
0.06243157759308815,
0.03515627607703209,
-0.03311317414045334,
0.002532806247472763,
-0.02347797155380249,
0.014578884467482567,
0.027935709804296494,
-0.02188824862241745,
-0.000034627457353053614,
0.010132827796041965,
-0.003910869359970093,
-0.04996802657842636,
0.022166503593325615,
-0.03064330667257309,
-0.02605188824236393,
0.0039909821934998035,
0.016890309751033783,
0.005131767597049475,
0.019187547266483307,
-0.0299050472676754,
0.006589536089450121,
-0.03905436024069786,
-0.013623948208987713,
-0.047602809965610504,
0.02729107066988945,
-0.022504594177007675,
0.013086164370179176,
-0.019457820802927017,
0.041339971125125885,
-0.03303847834467888,
0.008877749554812908,
0.046552326530218124,
0.039961077272892,
-0.01826629973948002,
0.0150771364569664,
0.027420267462730408,
0.0036929110065102577,
0.04397928714752197,
0.007526277564466,
0.01268137339502573,
0.004989663138985634,
-0.036626171320676804,
-0.051136650145053864,
0.011691401712596416,
0.0450216680765152,
0.03626491501927376,
0.012701095081865788,
-0.012029548175632954,
-0.03283196687698364,
0.06352125853300095,
-0.028085604310035706,
-0.001955185318365693,
-0.010260993614792824,
-0.04929162189364433,
-0.03101404570043087,
-0.0443110391497612,
0.029304418712854385,
-0.03350251168012619,
0.01213857252150774,
0.054401155561208725,
0.002280856017023325,
-0.07175585627555847,
0.03093799203634262,
0.020765554159879684,
-0.03813710808753967,
0.024985499680042267,
0.02118567004799843,
0.024654105305671692,
0.05615491047501564,
0.04259362816810608,
-0.02427506633102894,
0.024296099320054054,
0.01913333125412464,
0.0016489073168486357,
-0.08642660826444626,
-0.004722475539892912,
0.0010272176004946232,
0.013799886219203472,
0.00987002719193697,
-0.03615425154566765,
0.008716056123375893,
0.021916430443525314,
-0.07980708032846451,
0.01850789226591587,
-0.03519665449857712,
-0.007701850961893797,
-0.015993524342775345,
-0.057118698954582214,
-0.01865570619702339,
0.03207526355981827,
0.008869032375514507,
0.06775075197219849,
0.030260540544986725,
0.053424540907144547,
-0.019756954163312912,
0.0011639873264357448,
-0.020858658477663994,
0.04391171783208847,
-0.0437275655567646,
-0.021707167848944664,
0.04173243045806885,
0.022604724392294884,
0.027543097734451294,
0.004671155009418726,
-0.026950959116220474,
0.0176464281976223,
-0.01875586062669754,
0.02606707625091076,
0.03515248745679855,
0.01030984241515398,
-0.01609453186392784,
0.004206656478345394,
-0.057625118643045425,
-0.015683701261878014,
0.01719007082283497,
0.013813729397952557,
-0.016284432262182236,
0.009880349971354008,
-0.006356735248118639,
-0.01583709940314293,
-0.049470722675323486,
0.0604030080139637,
-0.014815950766205788,
-0.014791855588555336,
0.028696099296212196,
0.01113948505371809,
0.006899976171553135,
-0.02576283924281597,
0.03155617043375969,
0.0007079190108925104,
0.019704850390553474,
0.01830267906188965,
-0.02295815758407116,
0.00591832771897316,
0.03373187035322189,
-0.03145414963364601,
-0.04836362600326538,
0.020120317116379738,
0.011535377241671085,
-0.019400594756007195,
-0.07181046158075333,
-0.015463697724044323,
0.0224436204880476,
-0.03684769198298454,
0.013442098163068295,
-0.04377540573477745,
-0.03271354362368584,
0.013661938719451427,
0.006694636773318052,
-0.00636215228587389,
-0.031220443546772003,
-0.015158482827246189,
-0.025778694078326225,
-0.09063789248466492,
0.015979304909706116,
-0.014703525230288506,
-0.036982785910367966,
0.01361023262143135,
-0.014730357564985752,
0.01970030553638935,
0.0007543161045759916,
0.06952979415655136,
-0.013950356282293797,
0.0018055317923426628,
-0.010403078980743885,
-0.009080816991627216,
0.005366480443626642,
-0.0803317278623581,
-0.028401296585798264,
0.005995403043925762,
0.009609021246433258,
0.014836466871201992,
0.015828123316168785,
-0.005429037380963564,
0.018010875210165977,
0.0029324274510145187,
0.03160880506038666,
0.039240092039108276,
0.022858187556266785,
-0.05762664973735809,
0.03481568023562431,
0.0006855085375718772,
-0.020072994753718376,
0.04222732409834862,
0.01503046229481697,
0.010752754285931587,
0.029207948595285416,
-0.03554517403244972,
-0.03869165852665901,
-0.021064655855298042,
-0.017899099737405777,
-0.06008347123861313,
0.018193520605564117,
-0.007928865030407906,
0.02077287621796131,
-0.038850538432598114,
0.028337720781564713,
0.042868372052907944,
-0.0364571139216423,
-0.02029282972216606,
0.04618828743696213,
0.01780633255839348,
0.016751350834965706,
0.014434312470257282,
0.02845262736082077,
-0.005548751447349787,
-0.03140304610133171,
0.05835038796067238,
0.00941351056098938,
0.007834807969629765,
0.01795385219156742,
0.034651171416044235,
0.038140490651130676,
-0.053750645369291306,
-0.015960702672600746,
0.04293540492653847,
0.005992142483592033,
-0.028459465131163597,
-0.019040236249566078,
0.03773090988397598,
-0.03416471555829048,
0.027126960456371307,
0.022037290036678314,
0.003041989402845502,
0.0827217623591423,
-0.030786219984292984,
0.02355201356112957,
0.02149292826652527,
0.030431831255555153,
-0.03808720409870148,
0.04037029296159744,
-0.013388092629611492,
-0.0005616859998553991,
-0.009520318359136581,
-0.007492728065699339,
-0.023766737431287766,
-0.008548918180167675,
0.011105652898550034,
-0.014866398647427559,
0.013534835539758205,
0.01940048113465309,
-0.037157610058784485,
0.004020116291940212,
-0.019063176587224007,
0.0008565046591684222,
-0.03225952386856079,
-0.00032946685678325593,
0.03220929205417633,
0.009747135452926159,
-0.02921769581735134,
0.05644356459379196,
0.011868800036609173,
0.010952223092317581,
-0.08253823965787888,
-0.000533335842192173,
-0.0007227743626572192,
0.02018245868384838,
-0.0007058092160150409,
-0.010273580439388752
] |
<p>Firstly I think shades of this question have appeared elsewhere (like <a href="http://physics.stackexchange.com/questions/10088/why-does-gravity-need-to-be-quantised">here</a>, or <a href="http://physics.stackexchange.com/questions/57228/why-is-gravity-such-a-unique-force">here</a>). Hopefully mine is a slightly different take on it. If I'm just being thick please correct me.</p>
<p>We always hear about the force of gravity being the odd-one-out of the four forces. And this argument, whenever it's presented in popular science at least, always hinges on the relative strength of the forces. Or for a more in depth picture <a href="http://physics.stackexchange.com/questions/57228/why-is-gravity-such-a-unique-force">this excellent thread</a>. But, having had a single, brief semester studying general relativity, I'm struggling to see how it is viewed as a force at all.</p>
<p>A force, as I understand it, involves the interaction of matter particles with each other via a field. An energy quantisation of the field is the force carrying particle of the field.</p>
<p>In the case of gravity though, particles don't interact with one another in this way. General relativity describes how space-time is distorted by energy. So what looked to everyone before Einstein like two orbiting celestial bodies, bound by some long distance force was actually two lumps of energy distorting space-time enough to make their paths through 3D space elliptical. </p>
<p>Yet theorists are still very concerned with "uniting the 4 forces". Even though that pesky 4<sup>th</sup> force has been well described by distortions in space time. Is there a reason for this that is understandable to a recent physics graduate like myself? </p>
<p>My main points of confusion:</p>
<ul>
<li>Why is gravity still viewed as a force?</li>
<li>Is the interaction of particles with space time the force-like interaction?</li>
<li>Is space-time <em>the</em> force field?</li>
<li>If particles not experiencing EM/weak/strong forces merely follow straight lines in higher-dimensional space (what I understand geodesics to be) then how can there be a 4<sup>th</sup> force acting on them? </li>
</ul>
<p>Thanks to anyone who can help shed some light on this for me!</p>
| 9,551 |
[
-0.03138856962323189,
-0.010552502237260342,
0.031862713396549225,
-0.024008672684431076,
0.04581606760621071,
0.026526201516389847,
-0.005984800402075052,
-0.025571461766958237,
-0.011345669627189636,
-0.024587102234363556,
0.03367205709218979,
0.015116546303033829,
0.057470086961984634,
0.017831748351454735,
0.0030236360616981983,
-0.0028050229884684086,
0.025578398257493973,
-0.015340096317231655,
-0.010111073963344097,
-0.06407614797353745,
-0.0050800577737390995,
0.027291012927889824,
-0.03585510328412056,
0.0015983087942004204,
-0.01961049810051918,
0.01794964261353016,
0.03545433655381203,
0.015590636990964413,
0.011477700434625149,
0.08626928180456161,
-0.00542672723531723,
-0.03319349139928818,
0.011572923511266708,
0.014698107726871967,
0.03228047862648964,
0.01515250001102686,
-0.017859378829598427,
-0.006652325391769409,
0.01145154144614935,
0.030975105240941048,
-0.05972769111394882,
-0.010533243417739868,
-0.032484348863363266,
0.050677936524152756,
-0.05553817376494408,
0.05248865485191345,
0.03093084692955017,
0.047151871025562286,
0.07637413591146469,
-0.03170095011591911,
0.05538708344101906,
-0.004392552189528942,
0.04357567057013512,
0.007468624971807003,
-0.015065197832882404,
-0.02798346057534218,
0.060603659600019455,
0.05828450620174408,
-0.02871718257665634,
-0.0446278415620327,
-0.03717545047402382,
0.012385623529553413,
-0.016962556168437004,
-0.02059333212673664,
-0.0019387333886697888,
0.0400073304772377,
-0.007132864557206631,
-0.014279034920036793,
0.023718418553471565,
-0.012982146814465523,
0.00170181377325207,
0.017037399113178253,
0.016873672604560852,
0.019548632204532623,
-0.028675410896539688,
-0.008656115271151066,
0.010329053737223148,
-0.0020798654295504093,
0.054261464625597,
0.02833634242415428,
-0.0464392714202404,
-0.0013761348091065884,
0.028876733034849167,
0.0158994123339653,
0.038452617824077606,
0.002542270580306649,
0.07646776735782623,
-0.0351419672369957,
-0.010143361985683441,
0.030877675861120224,
-0.03335650637745857,
0.03048563003540039,
0.04058355838060379,
0.0034473645500838757,
-0.0187319777905941,
0.040387678891420364,
0.002109430730342865,
0.013319876044988632,
0.0033840781543403864,
0.004223891533911228,
0.0039513385854661465,
-0.027828438207507133,
0.0061522964388132095,
0.07594271004199982,
-0.009349973872303963,
-0.02581014111638069,
-0.05630619823932648,
0.026419637724757195,
-0.02384212426841259,
-0.01344297919422388,
-0.005590979475528002,
0.00711544556543231,
0.006766609847545624,
-0.04323907569050789,
0.009052618406713009,
-0.017717130482196808,
0.04264165833592415,
0.009429726749658585,
0.06132638826966286,
0.08119085431098938,
0.02090349793434143,
-0.06421959400177002,
0.0075711836107075214,
-0.022474806755781174,
-0.0480072945356369,
-0.00630869809538126,
0.05376047641038895,
-0.008184200152754784,
0.023748302832245827,
0.011565543711185455,
0.013459865935146809,
-0.0044823274947702885,
-0.03129313886165619,
0.025698835030198097,
0.044074393808841705,
0.0012974049896001816,
-0.12135379016399384,
-0.06853729486465454,
0.06664203107357025,
-0.013536835089325905,
-0.02756316028535366,
-0.062154620885849,
0.016605405136942863,
-0.001581861055456102,
0.08114882558584213,
-0.011778000742197037,
0.0017905384302139282,
-0.012657718732953072,
0.039899084717035294,
0.0059878029860556126,
-0.021820630878210068,
0.014191125519573689,
-0.011877374723553658,
-0.022501958534121513,
-0.007705858908593655,
-0.04283847659826279,
0.004044141620397568,
0.025412939488887787,
0.0011759138433262706,
-0.018363013863563538,
0.09843973070383072,
0.013054482638835907,
0.015096379444003105,
0.03176072984933853,
0.022544369101524353,
-0.02852654829621315,
0.06272006034851074,
0.00927671231329441,
-0.0002868596639018506,
0.044478800147771835,
-0.009111222811043262,
0.019609922543168068,
-0.021098380908370018,
0.000013993337233841885,
0.003702402114868164,
-0.0632370337843895,
-0.029018307104706764,
-0.030043743550777435,
-0.03450372442603111,
-0.02858288772404194,
-0.051370903849601746,
-0.03031892143189907,
0.005887315142899752,
-0.011240607127547264,
0.0006956419674679637,
0.026492031291127205,
0.0182478167116642,
-0.013866758905351162,
-0.012495473027229309,
-0.017820075154304504,
-0.015332497656345367,
-0.05372707545757294,
-0.0016683118883520365,
-0.00812140665948391,
-0.017501860857009888,
0.007672293111681938,
0.0017495839856564999,
-0.01772373542189598,
-0.017422577366232872,
-0.005788647569715977,
-0.001949697034433484,
0.06585677713155746,
-0.006031996104866266,
0.017077283933758736,
0.03625732287764549,
0.07582270354032516,
0.04185939207673073,
0.002645659726113081,
-0.0021048011258244514,
0.030268415808677673,
-0.03581569343805313,
0.03821493312716484,
-0.008918950334191322,
0.03835728392004967,
-0.005693771876394749,
0.010266846977174282,
0.00988144800066948,
0.020012574270367622,
-0.022979876026511192,
0.04524834826588631,
-0.037851620465517044,
0.0863737016916275,
0.003068571211770177,
-0.0349813736975193,
-0.013201922178268433,
0.08371732383966446,
0.01613556779921055,
0.043876998126506805,
-0.00021712479065172374,
-0.006716995965689421,
-0.07300574332475662,
-0.02019706554710865,
0.043536532670259476,
0.04641259089112282,
-0.007573842536658049,
0.011354641057550907,
0.021313076838850975,
0.05413828417658806,
-0.01485062949359417,
0.0013159108348190784,
-0.025507478043437004,
-0.05886788293719292,
0.04957333207130432,
-0.014104646630585194,
0.006083889864385128,
0.02316790074110031,
0.009981581009924412,
-0.007911608554422855,
0.006379907950758934,
0.006875638850033283,
-0.023827189579606056,
0.04889732971787453,
-0.0002592956880107522,
0.034777361899614334,
0.01790403388440609,
-0.012112138792872429,
0.05268856883049011,
0.0021407892927527428,
0.02793937362730503,
0.03228050470352173,
-0.008570465259253979,
-0.031876739114522934,
-0.03138282895088196,
-0.012707922607660294,
0.008142548613250256,
0.019268227741122246,
-0.03685500845313072,
-0.025320976972579956,
0.013461939059197903,
-0.03921188414096832,
-0.006553203798830509,
0.0041859690099954605,
-0.043293096125125885,
-0.010887177661061287,
0.005512489937245846,
-0.00866281520575285,
0.02594124712049961,
0.059316571801900864,
-0.026798618957400322,
-0.003939673770219088,
0.011261023581027985,
-0.022821715101599693,
-0.013770456425845623,
-0.0017663263715803623,
-0.03485414385795593,
-0.0039812433533370495,
-0.052234746515750885,
-0.0014729039976373315,
0.04245550185441971,
-0.028772108256816864,
0.02676960825920105,
-0.011790456250309944,
-0.007389923091977835,
-0.04822975769639015,
-0.011136661283671856,
-0.05870482325553894,
0.019615376368165016,
-0.034184493124485016,
-0.015704993158578873,
0.08013339340686798,
-0.03150831162929535,
-0.05326511338353157,
0.006091980263590813,
-0.022503023967146873,
-0.04854743555188179,
0.003164991270750761,
0.02892209216952324,
0.023529231548309326,
-0.01522854808717966,
0.00284122908487916,
0.026813309639692307,
-0.05015968531370163,
-0.012319027446210384,
-0.05152497813105583,
-0.015313379466533661,
0.028707068413496017,
-0.013939451426267624,
0.04131646454334259,
-0.02461835741996765,
-0.034454748034477234,
0.06548800319433212,
0.040644560009241104,
-0.0016729561612010002,
-0.02086198329925537,
-0.024049242958426476,
0.0029073168989270926,
0.0012769773602485657,
0.03930569067597389,
-0.0010637188097462058,
0.02571728080511093,
0.02404545620083809,
0.018012842163443565,
0.05154922232031822,
-0.012690111994743347,
0.017120052129030228,
-0.017136001959443092,
-0.02223336696624756,
0.01606239750981331,
-0.02092094160616398,
0.057921357452869415,
0.04909462481737137,
-0.04909496754407883,
0.01103923935443163,
-0.0077160983346402645,
0.005761075299233198,
0.010330744087696075,
-0.048639483749866486,
0.059942878782749176,
0.009279420599341393,
0.011757535859942436,
-0.0309908427298069,
0.022469570860266685,
-0.004785246215760708,
-0.04017280414700508,
0.04306626692414284,
0.0022254446521401405,
0.05485633388161659,
-0.0008146287873387337,
0.0018045639153569937,
0.025293901562690735,
0.04794885963201523,
-0.039837855845689774,
-0.004517736379057169,
-0.008801845833659172,
-0.010289317928254604,
0.004123848397284746,
-0.016166197136044502,
-0.015387787483632565,
0.042915914207696915,
0.034731458872556686,
0.0322234183549881,
0.0035032315645366907,
-0.046806562691926956,
-0.05239611864089966,
-0.06924525648355484,
-0.003791430499404669,
-0.0024428656324744225,
0.045254938304424286,
0.019473660737276077,
0.043735552579164505,
0.03467791527509689,
0.004889227449893951,
-0.019469216465950012,
0.021570712327957153,
-0.10391996800899506,
0.021536443382501602,
-0.04484013468027115,
-0.006054670549929142,
-0.018459511920809746,
-0.0019313482334837317,
-0.021569030359387398,
-0.038656335324048996,
-0.02269635535776615,
-0.01795397326350212,
-0.01175973191857338,
-0.040848564356565475,
0.031239403411746025,
-0.026058055460453033,
-0.03069690242409706,
0.0031487871892750263,
0.04271715506911278,
0.04850924015045166,
-0.015464890748262405,
-0.013725449331104755,
0.0446360744535923,
-0.027919143438339233,
-0.025075377896428108,
0.022434812039136887,
0.0029570204205811024,
0.028023790568113327,
-0.003000465454533696,
-0.035270363092422485,
-0.004851356614381075,
-0.009502898901700974,
-0.009612498804926872,
0.0508401058614254,
0.009662596508860588,
0.0094091622158885,
-0.011181829497218132,
-0.03240984305739403,
-0.05360418185591698,
-0.015587051399052143,
-0.010616916231811047,
0.06152445077896118,
-0.016862457618117332,
0.002318492392078042,
0.009713732637465,
0.009803925640881062,
-0.02303355000913143,
0.051082681864500046,
0.061583083122968674,
-0.004592076875269413,
-0.04153812304139137,
-0.033881425857543945,
-0.008024327456951141,
-0.022052649408578873,
0.0005645458004437387,
0.01662650890648365,
0.006109730340540409,
-0.04840359091758728,
0.019208155572414398,
0.011444403789937496,
0.015855617821216583,
-0.03394205868244171,
-0.025992028415203094,
-0.03042013570666313,
-0.007425438612699509,
-0.022586749866604805,
0.012529609724879265,
-0.02363092266023159,
0.03307227045297623,
0.07147891819477081,
0.010278530418872833,
-0.0038335847202688456,
-0.08757809549570084,
-0.0063812704756855965,
0.05061192810535431,
0.04096256569027901,
-0.008914315141737461,
-0.01845799945294857,
-0.016382263973355293,
-0.024083655327558517,
0.014619280584156513,
-0.06186966970562935,
0.018277671188116074,
-0.027323303744196892,
0.02978440187871456,
0.00699322996661067,
-0.04567265138030052,
-0.021054578945040703,
0.041721031069755554,
-0.018914801999926567,
-0.004997327923774719,
-0.009240086190402508,
0.017640842124819756,
-0.006382616236805916,
0.03658097982406616,
0.020206967368721962,
0.02902567945420742,
0.013911408372223377,
-0.010718580335378647,
-0.017345217987895012,
0.003609448904171586,
-0.07205792516469955,
-0.08266985416412354,
-0.009353704750537872,
0.017537320032715797,
-0.03732633590698242,
0.029956568032503128,
-0.06206658110022545,
-0.05050261691212654,
-0.012107948772609234,
-0.003667151555418968,
0.03135501220822334,
0.002758511807769537,
-0.07409805059432983,
0.04777758941054344,
0.027435487136244774,
0.013660411350429058,
0.03876573592424393,
0.049604032188653946,
-0.04745694249868393,
-0.012555348686873913,
-0.02364007942378521,
0.01227378100156784,
-0.041860345751047134,
0.005373697262257338,
0.006777636241167784,
0.028004875406622887,
-0.0681958794593811,
0.04228314012289047,
-0.01588571071624756,
-0.008506416343152523,
-0.01471476349979639,
-0.05724421516060829,
-0.04237499088048935,
0.014214533381164074,
0.027283309027552605,
0.0065931277349591255,
-0.0068518128246068954,
0.0018589303363114595,
-0.007168653421103954,
-0.016050204634666443,
0.016634564846754074,
0.037539876997470856,
-0.04096721485257149,
0.024790925905108452,
0.03536344692111015,
-0.0009897280251607299,
0.007084548473358154,
0.0030399549286812544,
0.02099638804793358,
-0.04463372752070427,
0.04379463940858841,
-0.00908250454813242,
0.006568534299731255,
0.031637098640203476,
-0.04216282442212105,
-0.05510088428854942,
-0.0018132023978978395,
0.0025216401554644108,
0.02120288833975792,
0.012738652527332306,
-0.004495588596910238,
0.0001069636782631278,
0.01122345495969057,
-0.07247196137905121,
-0.02057899907231331,
0.026355836540460587,
-0.010914165526628494,
-0.007724246475845575,
-0.023459427058696747,
-0.001485561835579574,
-0.06535515934228897,
-0.015003508888185024,
-0.000010263800504617393,
0.05112496763467789,
-0.048583757132291794,
0.03165026754140854,
0.014434030279517174,
0.03193347156047821,
0.009584754705429077,
-0.012417980469763279,
-0.0046709743328392506,
0.010986304841935635,
0.0075890799053013325,
0.0065124486573040485,
-0.015800490975379944,
0.043421532958745956,
-0.03328973054885864,
-0.0375235415995121,
-0.0072649745270609856,
-0.021593065932393074,
-0.024332154542207718,
-0.022971011698246002,
0.020327266305685043,
0.054539766162633896,
-0.01023131888359785,
-0.034762248396873474,
-0.022092662751674652,
0.0482945553958416,
-0.007827223278582096,
0.032356906682252884,
-0.029321596026420593,
0.015974925830960274,
-0.012531033717095852,
-0.047100067138671875,
0.04674849286675453,
-0.023317953571677208,
-0.0038281576707959175,
0.0027499638963490725,
0.057972680777311325,
0.0018656306201592088,
-0.008911347016692162,
0.011511669494211674,
-0.027216849848628044,
0.02515975944697857,
-0.016302812844514847,
-0.0034568393602967262,
0.010861481539905071,
0.004790802951902151,
-0.008848415687680244,
-0.007860928773880005,
-0.0035989456810057163,
0.0034341379068791866,
0.05373590812087059,
-0.005750988610088825,
0.04765520244836807,
0.035780712962150574,
-0.03133577108383179,
-0.03357495740056038,
-0.013344625942409039,
0.015858307480812073,
-0.009780227206647396,
0.008063355460762978,
0.008377778343856335,
-0.04222438856959343,
-0.0066683427430689335,
0.03245513141155243,
0.04437417909502983,
-0.013489512726664543,
0.004700652323663235,
0.03224492073059082,
0.03917005658149719,
0.01956985518336296,
-0.015505357645452023,
-0.03729261830449104,
0.029384387657046318,
-0.0038439384661614895,
0.0042632874101400375,
0.03715714067220688,
-0.027228472754359245,
0.03127221018075943,
0.023593375459313393,
0.020575830712914467,
-0.022312482818961143,
-0.011782134883105755,
-0.04346726834774017,
0.012897803448140621,
0.012034637853503227,
-0.0017358589684590697,
0.002863638335838914,
0.008721204474568367,
-0.00477706640958786,
0.011751879006624222,
0.00480209244415164,
-0.004943691194057465,
-0.06892091035842896,
0.006817415822297335,
-0.0417199544608593,
-0.05357274413108826,
0.03166075050830841,
-0.00640115374699235,
-0.07135479152202606,
-0.005191747099161148,
-0.03100482001900673,
0.02668440341949463,
0.027959102764725685,
0.017129771411418915,
-0.043068233877420425,
0.03694132715463638,
-0.014597233384847641,
-0.0023658096324652433,
-0.02918822318315506,
-0.0009263379615731537,
0.1335074007511139,
0.04339854046702385,
-0.01351021695882082,
-0.039917148649692535,
-0.01459568552672863,
-0.010903551243245602,
0.004019902087748051,
-0.03472724184393883,
0.012010027654469013,
-0.04465528577566147,
-0.00879189558327198,
-0.011185756884515285,
0.05311897024512291,
0.02114803157746792,
-0.03125426545739174,
0.07010618597269058,
-0.03178730234503746,
-0.011172018945217133,
-0.02336850017309189,
0.04752534255385399,
-0.0028825150802731514,
-0.006696856115013361,
-0.034746646881103516,
0.03517327457666397,
-0.03173406794667244,
0.032699376344680786,
-0.05101470649242401,
-0.045550256967544556,
0.00435903063043952,
0.0038099060766398907,
-0.06918270140886307,
0.020320376381278038,
-0.0001315975096076727,
-0.053836043924093246,
-0.05033207684755325,
0.026502061635255814,
0.03853496164083481,
-0.02330588921904564,
0.019806697964668274,
0.008226029574871063,
-0.02430586889386177,
0.003397489432245493,
0.02279939502477646,
0.00904178712517023,
-0.020106660202145576,
-0.03936905413866043,
-0.035106584429740906,
0.06789495795965195,
-0.014112195931375027,
-0.00889374315738678,
0.02397925592958927,
-0.028893684968352318,
0.015595054253935814,
-0.06272467225790024,
-0.003992774523794651,
-0.030423838645219803,
0.041060663759708405,
-0.009678144939243793,
-0.039615415036678314,
-0.0009241542429663241,
0.05590111017227173,
-0.0033650377299636602,
0.04866447299718857,
0.00211038114503026,
0.019287778064608574,
-0.0058565279468894005,
-0.03439284861087799,
0.02929200790822506,
0.0040156044997274876,
0.0007573546608909965,
-0.009835394099354744,
-0.037469882518053055,
-0.05353860557079315,
-0.010094662196934223,
0.02494574710726738,
0.0728016048669815,
0.03705519810318947,
0.005668144207447767,
0.017890509217977524,
-0.023004181683063507,
-0.03199627250432968,
0.04093707725405693,
-0.01475005503743887,
-0.01266908086836338,
-0.016109680756926537,
0.015060054138302803,
-0.008939847350120544,
0.036990243941545486,
0.018991103395819664,
0.017998602241277695,
-0.005842758808284998,
-0.02733004093170166,
0.003991231322288513,
-0.018469536677002907,
-0.01350786630064249,
0.028190853074193,
-0.011761955916881561,
-0.03406575322151184,
-0.012097937986254692,
-0.013851366937160492,
-0.005739079788327217,
0.011673073284327984,
0.014026536606252193,
0.0418316014111042,
-0.0327666737139225,
0.005137257743626833,
0.04678576439619064,
0.0036424873396754265,
-0.013624189421534538,
0.012100223451852798,
-0.014620469883084297,
-0.03943628445267677,
-0.02146320417523384,
-0.006096983328461647,
-0.008246327750384808,
-0.01940467581152916,
0.02786816656589508,
-0.04396504536271095,
0.005857824347913265,
-0.013254625722765923,
0.022387629374861717,
-0.057817839086055756,
-0.00036480085691437125,
-0.06080593913793564,
0.017974574118852615,
-0.007552121300250292,
-0.027927881106734276,
-0.015876339748501778,
0.020270507782697678,
0.0005744833033531904,
-0.02209971472620964,
-0.0034418085124343634,
0.018070673570036888,
-0.028271576389670372,
0.002748665167018771,
0.024844128638505936,
-0.018234645947813988,
0.044901102781295776,
0.027631642296910286,
-0.04380394518375397,
0.030520789325237274,
-0.019406624138355255,
-0.047871481627225876,
0.02374209649860859,
-0.02038540504872799,
0.013145693577826023,
0.04160996526479721,
-0.021908089518547058,
-0.017079558223485947,
0.0612998902797699,
-0.000058172474382445216,
0.030589845031499863,
-0.013004164211452007,
-0.02605513669550419,
0.005320046562701464,
-0.012952184304594994,
-0.009971950203180313,
-0.011199031956493855,
-0.005242314655333757,
0.00969937164336443,
-0.019970256835222244,
0.016254611313343048,
0.005669108126312494,
0.02490902692079544,
-0.005406784359365702,
-0.018617097288370132,
0.013623819686472416,
0.01348922774195671,
0.01360933668911457,
0.054539743810892105,
-0.03732962906360626,
0.03252338618040085,
0.044508449733257294,
0.044805847108364105,
-0.09165487438440323,
0.0008467333973385394,
0.0059043653309345245,
0.00981803797185421,
0.03398476168513298,
-0.04446423426270485,
0.017685942351818085,
0.018386078998446465,
-0.059644341468811035,
0.04346761852502823,
-0.007078764960169792,
-0.005990057252347469,
-0.00922766700387001,
0.022345079109072685,
-0.009565258398652077,
0.04188252240419388,
0.025927795097231865,
0.033883579075336456,
-0.009512409567832947,
0.009285437874495983,
0.007984588854014874,
-0.02046102285385132,
-0.01396072655916214,
0.03361915796995163,
-0.04215420410037041,
0.053044393658638,
0.08253876119852066,
0.02677471563220024,
-0.0028317414689809084,
0.04883607104420662,
0.002706137951463461,
-0.009981431998312473,
-0.029802830889821053,
0.0010848930105566978,
0.025162048637866974,
0.04741677641868591,
0.015895599499344826,
-0.02484930120408535,
-0.008921235799789429,
0.03096788562834263,
0.008985129185020924,
0.044950030744075775,
0.03845424950122833,
-0.0052823652513325214,
0.023286886513233185,
-0.03690222650766373,
-0.022176645696163177,
0.033934395760297775,
-0.019135095179080963,
0.02556084468960762,
-0.005256713833659887,
0.01737947389483452,
0.019600244238972664,
-0.0014393465826287866,
-0.003713802667334676,
-0.07164580374956131,
-0.004922551102936268,
0.020471809431910515,
-0.01963362656533718,
-0.020139480009675026,
0.030632371082901955,
-0.017477141693234444,
-0.0025320290587842464,
-0.011310987174510956,
-0.024468740448355675,
0.01788044348359108,
-0.013947834260761738,
0.0076144482009112835,
0.012539589777588844,
0.02328164502978325,
0.007313141133636236,
-0.05366774648427963,
-0.02887870743870735,
0.0247952900826931,
0.030346708372235298,
0.003731405595317483,
-0.026089536026120186,
-0.026888985186815262,
0.002411424880847335,
-0.08967018872499466,
0.011500971391797066,
0.017643440514802933,
-0.007369346916675568,
-0.04908888414502144,
-0.03696855530142784,
-0.024902118369936943,
0.01853342540562153,
0.04872523248195648,
-0.023981625214219093,
-0.0032999145332723856,
0.04058282449841499,
0.0023106876760721207,
0.008990666829049587,
-0.025507748126983643,
-0.01141083799302578,
0.018718844279646873,
0.000168752929312177,
0.00043705309508368373,
0.008482689969241619,
-0.029166480526328087,
0.027915414422750473,
0.03185959905385971,
-0.03819674998521805,
0.03944336622953415,
-0.0038219031412154436,
-0.0542818084359169,
0.06113029643893242,
0.009725826792418957,
-0.0018982387846335769,
0.021922271698713303,
0.0009896942647174,
-0.006904506590217352,
0.03609755262732506,
-0.007637109141796827,
0.003529219189658761,
0.022281017154455185,
-0.034738700836896896,
-0.024239949882030487,
-0.02672392874956131,
0.0002723197394516319,
0.04572366550564766,
-0.04460839554667473,
-0.020111868157982826,
0.062203299254179,
-0.008787059225142002,
0.0019674859941005707,
0.03102775290608406,
0.027594739571213722,
0.03526841849088669,
0.016568176448345184,
0.011858663521707058,
-0.00707234488800168,
-0.007042549550533295,
0.021506497636437416,
0.015198396518826485,
0.04125218838453293,
0.04471350088715553,
-0.018084567040205002,
0.041914552450180054,
0.027171172201633453,
-0.009132652543485165,
-0.0038150381296873093,
0.005284325685352087,
-0.04778171330690384,
-0.007151452824473381,
0.027794577181339264,
0.01030766312032938,
0.0034488672390580177,
0.05678679421544075,
-0.0058161430060863495,
0.0861680880188942,
-0.013890828937292099,
0.0032023123931139708,
0.00748484069481492,
0.029323281720280647,
-0.006508137099444866,
0.04149673134088516,
0.008212247863411903,
0.04122383892536163,
0.0003993057180196047,
-0.014197050593793392,
-0.009587457403540611,
-0.009048341773450375,
0.014043772593140602,
-0.01573438011109829,
-0.014852250926196575,
0.020902199670672417,
0.0021684220992028713,
-0.009352981112897396,
0.0007203368586488068,
-0.03322359547019005,
-0.032075874507427216,
0.04191703721880913,
0.007520534098148346,
0.02094925381243229,
-0.04395516589283943,
0.03471482917666435,
-0.03465308994054794,
0.050890155136585236,
-0.06114477291703224,
-0.035467155277729034,
-0.00896897166967392,
0.04021058976650238,
-0.02107893116772175,
-0.011841032654047012
] |
<p>There is a large disk of glass sitting outside, it is pretty thick and wide. Via different sensors hooked up to a controller, I can measure the air temperature, glass temperature (on the surface), and air humidity. Since the disk is fairly large, the temperature difference between it and the air could reach a few degrees-- due to thermal inertia and the fact that air temperature can change rapidly after sunset and sunrise.</p>
<p>Is there a formula or some empirical data that will tell me when the conditions are right for the disk to start getting covered in dew?</p>
<p>Would air flow across the glass surface matter? If it does, assume the air is nearly static (except for convection) - there's no wind. Also, humidity such as fog or rain drops falling from the sky can't reach the disk. All I care about is humidity in the air around the disk condensing on the glass surface.</p>
| 9,552 |
[
-0.015557128936052322,
-0.037236493080854416,
0.029621202498674393,
0.04788798466324806,
0.033470116555690765,
-0.015611957758665085,
-0.018873754888772964,
0.0024861725978553295,
-0.01595606841146946,
-0.020059088245034218,
0.027044277638196945,
0.02270684577524662,
0.029376573860645294,
0.03457380086183548,
0.02851036563515663,
-0.0017037984216585755,
0.009360468946397305,
-0.029491320252418518,
-0.0006513021653518081,
0.0010779908625409007,
-0.05745415762066841,
0.013997776433825493,
0.004399118013679981,
-0.02620597556233406,
-0.0342709943652153,
0.004523327108472586,
-0.004815290216356516,
-0.02706281654536724,
-0.012878856621682644,
0.027437949553132057,
-0.03514361381530762,
-0.00531257688999176,
0.017000645399093628,
0.017545685172080994,
0.044349491596221924,
-0.003969088662415743,
-0.04505103826522827,
-0.003093068255111575,
-0.045143067836761475,
0.006261470261961222,
-0.023119144141674042,
0.007470216602087021,
0.01798802986741066,
0.006101407576352358,
-0.006102771498262882,
0.007650621235370636,
0.012849291786551476,
0.00870219711214304,
0.04417301341891289,
-0.09394437074661255,
0.051768504083156586,
-0.021421393379569054,
0.06743098050355911,
0.03618399798870087,
-0.012890428304672241,
-0.01846182532608509,
0.05399353429675102,
0.04076266288757324,
-0.018423914909362793,
-0.015830792486667633,
-0.02401743084192276,
-0.01929464563727379,
-0.045163754373788834,
-0.04693868011236191,
0.006651648320257664,
-0.006479621399194002,
-0.03035055287182331,
-0.04480399936437607,
0.006211672909557819,
0.04755210503935814,
0.01139773242175579,
0.0020457080099731684,
0.037469565868377686,
0.021742040291428566,
0.004523752257227898,
-0.0002403187390882522,
0.013171966187655926,
0.04628017172217369,
0.0481058731675148,
0.02136279083788395,
-0.012272988446056843,
0.019566824659705162,
0.021653687581419945,
0.020467745140194893,
0.02604764513671398,
-0.03361443430185318,
0.09544812142848969,
-0.028630895540118217,
-0.006033765152096748,
0.026551412418484688,
0.01981646940112114,
0.02011292800307274,
0.020467063412070274,
0.011505245231091976,
-0.017860116437077522,
0.009271848015487194,
-0.005025271791964769,
0.05088154599070549,
-0.034434810280799866,
-0.02562553994357586,
0.005211306270211935,
0.021227829158306122,
0.03015078790485859,
0.0669812485575676,
-0.016065767034888268,
-0.035356149077415466,
-0.025811083614826202,
0.00972412247210741,
0.013037572614848614,
-0.025152020156383514,
-0.0678594782948494,
0.028822237625718117,
-0.02767951972782612,
-0.038077469915151596,
0.004676000215113163,
-0.007579010911285877,
0.028022252023220062,
-0.0040265293791890144,
0.008678996935486794,
0.04385273903608322,
0.059886131435632706,
-0.02671283856034279,
-0.008425596170127392,
-0.03312835097312927,
-0.09066029638051987,
0.04728737473487854,
0.009061845019459724,
-0.006684434600174427,
-0.028453011065721512,
-0.0006119065801613033,
-0.01353379525244236,
-0.010238847695291042,
0.014844701625406742,
-0.04262036830186844,
-0.023244192823767662,
-0.021408822387456894,
-0.08402035385370255,
-0.05083681643009186,
0.03843554109334946,
0.025785833597183228,
-0.03002539463341236,
-0.0652279481291771,
0.024724870920181274,
0.007420843932777643,
0.06712399423122406,
-0.004009282682090998,
0.0334840752184391,
-0.03653321787714958,
0.03604584187269211,
-0.028633974492549896,
-0.031041016802191734,
-0.006267797201871872,
0.035947564989328384,
-0.026568125933408737,
-0.036632850766181946,
-0.06637690961360931,
0.031914204359054565,
0.09750320017337799,
0.004064006730914116,
-0.008606381714344025,
0.048785027116537094,
-0.003915054257959127,
0.012704084627330303,
0.011192022822797298,
0.014943487010896206,
-0.05496273934841156,
0.026093896478414536,
0.010097851045429707,
0.02174101024866104,
-0.008210829459130764,
0.030729545280337334,
0.024058423936367035,
-0.00783039815723896,
0.025553423911333084,
0.10562000423669815,
0.027819085866212845,
0.01611454412341118,
-0.004195458721369505,
0.004683734383434057,
0.010944193229079247,
-0.01357179693877697,
-0.004966943059116602,
-0.016645297408103943,
-0.013459555804729462,
-0.025366205722093582,
0.05276431888341904,
-0.007939517498016357,
-0.0026629737112671137,
0.00888886209577322,
-0.07557288557291031,
-0.06846161186695099,
-0.048054225742816925,
0.003773254109546542,
-0.02917792834341526,
-0.005932391621172428,
0.018365539610385895,
0.009851469658315182,
0.021188315004110336,
-0.0054012988694012165,
-0.06223766878247261,
-0.026346078142523766,
0.009625979699194431,
0.05384761840105057,
-0.017354145646095276,
0.01731218583881855,
0.021272283047437668,
0.03914455324411392,
-0.019126757979393005,
0.021115584298968315,
-0.08172184973955154,
-0.028242390602827072,
-0.02717420645058155,
-0.0412633940577507,
-0.014878442510962486,
0.023223591968417168,
0.007188695017248392,
0.02195732481777668,
0.01806822419166565,
0.03868738189339638,
-0.008366363123059273,
-0.03003515861928463,
0.059291623532772064,
0.06213634833693504,
0.03213203698396683,
0.015075688250362873,
0.02435184270143509,
0.014901349321007729,
-0.058736447244882584,
-0.02603887766599655,
-0.0323423370718956,
-0.028972381725907326,
-0.0032902504317462444,
0.03877616673707962,
0.02506139501929283,
-0.015315188094973564,
-0.00428093271329999,
0.007179480977356434,
0.06570681184530258,
0.02816884033381939,
0.04168372601270676,
0.018511079251766205,
0.013310190290212631,
0.028955385088920593,
0.003200697246938944,
0.01839171163737774,
0.009530799463391304,
0.03729008138179779,
0.034457407891750336,
0.02081243321299553,
-0.025206519290804863,
-0.014367420226335526,
0.028718218207359314,
0.025254152715206146,
0.0373324379324913,
-0.012524486519396305,
-0.01975756511092186,
0.040059592574834824,
-0.038301628082990646,
-0.037356432527303696,
0.0027277180925011635,
0.01399060059338808,
0.04497194662690163,
-0.021032076328992844,
-0.03045307658612728,
0.03569726645946503,
0.028614141047000885,
-0.0034043847117573023,
-0.03171306475996971,
0.020109931007027626,
-0.048518676310777664,
0.0464913584291935,
-0.020812857896089554,
-0.029470421373844147,
-0.012941116467118263,
-0.029103172942996025,
0.04313302040100098,
0.0169950183480978,
0.02594425342977047,
-0.018540315330028534,
-0.058283425867557526,
-0.042768582701683044,
-0.0249217189848423,
-0.012014761567115784,
0.020819248631596565,
-0.03247290104627609,
-0.011064749211072922,
0.0034022554755210876,
-0.01488504745066166,
0.03967655450105667,
-0.00945443008095026,
-0.020850567147135735,
-0.011746667325496674,
0.0150642404332757,
-0.025225955992937088,
0.0007539825746789575,
-0.02048029750585556,
-0.03976579010486603,
-0.04610884189605713,
0.0038792190607637167,
0.005439752712845802,
-0.03075321577489376,
-0.02955048717558384,
-0.000643478415440768,
-0.04403414577245712,
-0.06716694682836533,
-0.02824905700981617,
-0.03513869270682335,
-0.013515531085431576,
-0.026488106697797775,
0.01697101816534996,
0.010424591600894928,
-0.029364848509430885,
0.0029795574955642223,
-0.04731065779924393,
-0.08350515365600586,
0.04721440374851227,
-0.008924643509089947,
0.043783873319625854,
-0.008523429743945599,
-0.02514640800654888,
0.06236942484974861,
-0.0027340142987668514,
-0.03747472167015076,
0.011608606204390526,
-0.01804332621395588,
-0.03433140367269516,
-0.03274970129132271,
-0.024491673335433006,
0.014034157618880272,
-0.0012982888147234917,
0.02508809044957161,
0.0369521863758564,
-0.0036635759752243757,
-0.00463876174762845,
0.027928827330470085,
0.014352582395076752,
-0.011686884798109531,
0.03249841928482056,
-0.0029909226577728987,
0.0372098945081234,
0.05775836482644081,
0.01811392232775688,
-0.010370668023824692,
-0.03203257918357849,
0.029140697792172432,
0.026899946853518486,
-0.05152474343776703,
0.022611359134316444,
-0.0043741026893258095,
0.0050884741358459,
-0.039220236241817474,
0.04481704905629158,
-0.03898041695356369,
-0.020010946318507195,
0.010135114192962646,
-0.000862539280205965,
0.04784540459513664,
0.030787987634539604,
0.003473537741228938,
0.05603991076350212,
0.049976520240306854,
-0.026264550164341927,
-0.015722714364528656,
-0.005406810902059078,
-0.020697906613349915,
0.006910478696227074,
-0.023558061569929123,
0.026662729680538177,
0.04577132686972618,
0.031586840748786926,
0.0535958968102932,
-0.005051469895988703,
-0.054975543171167374,
-0.010280809365212917,
-0.05996275320649147,
-0.006876638624817133,
-0.017291327938437462,
0.044438447803258896,
-0.012328715063631535,
0.044949568808078766,
0.013639827258884907,
0.028784479945898056,
0.06232813745737076,
-0.021597091108560562,
-0.07242941856384277,
0.030924415215849876,
-0.020351842045783997,
-0.0210059005767107,
-0.018621310591697693,
-0.020262151956558228,
0.04059434309601784,
-0.02350020781159401,
-0.008338840678334236,
0.01809484139084816,
0.027946989983320236,
-0.018008701503276825,
0.0009479040163569152,
-0.06182058900594711,
-0.03730642795562744,
-0.04184393212199211,
0.01981331780552864,
0.05039734020829201,
-0.036300431936979294,
0.03720630332827568,
0.058251116424798965,
0.01035166997462511,
-0.019540080800652504,
-0.01576780527830124,
-0.010106941685080528,
-0.003159663872793317,
0.01288129948079586,
0.0012010828359052539,
-0.016516132280230522,
-0.03121113032102585,
0.0204759668558836,
0.027904875576496124,
0.04736494645476341,
0.011796887032687664,
0.01094573549926281,
-0.026425663381814957,
-0.025216126814484596,
-0.028201425448060036,
0.010724780149757862,
0.036581069231033325,
-0.01551387645304203,
0.0268538985401392,
0.01662781462073326,
-0.0245553869754076,
-0.03132142126560211,
0.04985221475362778,
0.05846475064754486,
0.014211688190698624,
0.012497157789766788,
-0.05424916371703148,
-0.00874574575573206,
-0.035398416221141815,
0.02181568741798401,
0.017627526074647903,
0.03555160015821457,
-0.027213456109166145,
-0.026264196261763573,
0.013028746470808983,
-0.027514562010765076,
-0.005820296239107847,
0.011836650781333447,
0.0012429752387106419,
0.06695349514484406,
0.013180128298699856,
-0.018946364521980286,
0.009495637379586697,
0.0493156760931015,
0.022720282897353172,
0.0035645493771880865,
-0.0036832261830568314,
-0.10451056808233261,
-0.008183476515114307,
0.04572617635130882,
0.03739628940820694,
-0.003728611394762993,
-0.006657016463577747,
-0.04826493188738823,
-0.017307983711361885,
0.05877082049846649,
0.002906719921156764,
0.03319492191076279,
-0.03204629570245743,
0.003073285100981593,
-0.018969643861055374,
-0.03767738491296768,
-0.01544660422950983,
0.004656862933188677,
-0.007643986027687788,
0.025655219331383705,
-0.016140924766659737,
-0.051223061978816986,
-0.002568585565313697,
0.04185214638710022,
0.033143289387226105,
-0.00015469711797777563,
-0.01842385344207287,
0.03380914404988289,
-0.011826809495687485,
-0.04232574254274368,
-0.028339244425296783,
-0.06592541188001633,
0.029230112209916115,
-0.020970074459910393,
-0.011624639853835106,
0.024311142042279243,
0.0093074981123209,
-0.0012384337605908513,
0.04014098644256592,
0.0007905064849182963,
-0.030931217595934868,
-0.009080548770725727,
-0.030063962563872337,
0.007690843194723129,
-0.0029554693028330803,
0.00780625781044364,
0.03481768071651459,
0.03167925775051117,
0.010807327926158905,
0.02861003391444683,
-0.00027630754630081356,
0.03299158066511154,
-0.004510285798460245,
-0.002466359408572316,
-0.033022161573171616,
-0.02478988654911518,
-0.04935625568032265,
0.051352135837078094,
0.001362589537166059,
0.05976945906877518,
-0.021852346137166023,
-0.022850895300507545,
0.0005351583822630346,
-0.023322872817516327,
-0.013506419956684113,
-0.017527036368846893,
0.011276676319539547,
0.0495467483997345,
-0.00214940938167274,
-0.0381624735891819,
0.01752910576760769,
-0.0069147334434092045,
0.03864816203713417,
0.041232287883758545,
0.03045370616018772,
0.022215066477656364,
-0.038745734840631485,
-0.04295714199542999,
0.012124206870794296,
-0.030499570071697235,
0.08370231091976166,
-0.026650458574295044,
0.01765270344913006,
0.04670657962560654,
-0.047915440052747726,
0.04508354887366295,
0.01439756155014038,
0.005953668616712093,
0.05300993099808693,
-0.05078593268990517,
0.0026955401990562677,
0.005266856402158737,
-0.004173015709966421,
-0.055510085076093674,
-0.01966118812561035,
0.06849775463342667,
0.009430757723748684,
-0.023524010553956032,
-0.07046127319335938,
-0.000046934768761275336,
-0.05353337526321411,
-0.0500638447701931,
-0.003167241346091032,
0.011266856454312801,
-0.05855034291744232,
-0.007045798934996128,
0.038680534809827805,
-0.022506168112158775,
0.06568684428930283,
-0.01940847374498844,
0.009525506757199764,
0.009793484583497047,
-0.025983275845646858,
-0.03915982320904732,
0.012045016512274742,
0.030803130939602852,
-0.030864078551530838,
-0.01964588090777397,
0.010944980196654797,
0.014983287081122398,
0.0693814679980278,
-0.00521610863506794,
0.013327962718904018,
0.035421013832092285,
0.0022350444924086332,
-0.011407067999243736,
0.014503546990454197,
0.04612826183438301,
0.011687538586556911,
-0.026518691331148148,
-0.030456379055976868,
-0.0035757783334702253,
-0.02160324715077877,
-0.011724796146154404,
-0.01169632375240326,
0.02019760198891163,
0.020146159455180168,
0.01623222604393959,
0.07653523981571198,
-0.04406123608350754,
-0.019188344478607178,
0.024566305801272392,
-0.014926440082490444,
0.019191177561879158,
0.013764025643467903,
-0.017142444849014282,
-0.0229436457157135,
0.01810765266418457,
-0.020028861239552498,
-0.03839593008160591,
-0.008730698376893997,
-0.03357532620429993,
0.07549651712179184,
-0.005096775013953447,
0.04321957379579544,
0.03192426636815071,
0.007422207854688168,
0.0019654282368719578,
0.03010033443570137,
-0.02346290461719036,
0.04909241572022438,
-0.003810269758105278,
0.005420697387307882,
-0.0038521643728017807,
0.023205894976854324,
-0.02379709854722023,
0.012767120264470577,
-0.00829047616571188,
0.022572733461856842,
0.01500088069587946,
-0.015146823599934578,
0.05041605979204178,
-0.05340470001101494,
-0.03313146531581879,
0.034288469702005386,
-0.06143931671977043,
0.04058028757572174,
0.004839851055294275,
-0.010844466276466846,
0.03474878892302513,
0.019390910863876343,
0.015234402380883694,
-0.03301464393734932,
-0.01071204338222742,
-0.05565737932920456,
0.029074065387248993,
0.02764170616865158,
-0.005466942209750414,
0.02019757218658924,
0.04697803035378456,
0.02516806498169899,
-0.0025753735098987818,
-0.015662232413887978,
-0.01689496636390686,
-0.04254697263240814,
0.002408927073702216,
-0.015431016683578491,
-0.03622021898627281,
0.05058227479457855,
0.0018790510948747396,
-0.023465590551495552,
0.006367884110659361,
-0.014788448810577393,
0.023759542033076286,
0.030639322474598885,
0.0300016887485981,
0.031038908287882805,
0.061810847371816635,
-0.0031310096383094788,
0.014673983678221703,
-0.035719987004995346,
0.06493303179740906,
0.10848180204629898,
0.01856549270451069,
-0.010539526119828224,
-0.012376345694065094,
0.0055168261751532555,
-0.016671573743224144,
-0.0029453716706484556,
-0.023565039038658142,
0.006826884113252163,
-0.048176903277635574,
0.03681536763906479,
0.05321216955780983,
0.031049564480781555,
-0.027132121846079826,
0.003559968201443553,
0.03960530087351799,
-0.04470853880047798,
-0.0012113630073145032,
0.03665536642074585,
0.02356725186109543,
-0.009166362695395947,
0.017291396856307983,
-0.013863311149179935,
0.04225289449095726,
-0.021138938143849373,
-0.01310710795223713,
0.003353619948029518,
-0.029767896980047226,
0.012222223915159702,
0.02123948372900486,
-0.038069166243076324,
0.010707089677453041,
0.0192524753510952,
-0.008389565162360668,
-0.059723637998104095,
-0.004758537281304598,
0.03466387465596199,
-0.01398950070142746,
0.006152702029794455,
0.05006950721144676,
0.025155121460556984,
-0.00240988377481699,
-0.001148986630141735,
0.05360965430736542,
-0.04021969065070152,
0.010689087212085724,
-0.007012736517935991,
0.03148777782917023,
-0.02275664545595646,
0.0049821739085018635,
0.01336977630853653,
0.014411152340471745,
-0.0007590525783598423,
-0.01979850046336651,
0.0028265637811273336,
0.014411087147891521,
0.027882108464837074,
-0.05044322833418846,
-0.038559235632419586,
0.015309843234717846,
0.03820366412401199,
0.012038960121572018,
-0.00973652396351099,
0.017100103199481964,
-0.00381361972540617,
-0.02568267285823822,
-0.008311287499964237,
0.041858769953250885,
-0.036803487688302994,
-0.027615226805210114,
-0.06683401763439178,
-0.02533404715359211,
0.0006228229613043368,
-0.015119549818336964,
-0.004187104292213917,
-0.009876968339085579,
0.0032966220751404762,
-0.0038170863408595324,
0.003598536364734173,
0.0030958279967308044,
-0.034088730812072754,
-0.021222852170467377,
-0.02266010083258152,
-0.008075246587395668,
-0.03726423904299736,
-0.013381551951169968,
0.005214481148868799,
0.01673085056245327,
-0.011495150625705719,
-0.025337591767311096,
0.032701145857572556,
0.06452944129705429,
0.027168771252036095,
-0.00425654835999012,
-0.002546388655900955,
-0.006110844202339649,
-0.009583966806530952,
0.01499930676072836,
0.012447108514606953,
0.0702018290758133,
0.03331651911139488,
0.018084276467561722,
0.00800327304750681,
0.0015289988368749619,
-0.053110767155885696,
0.02274397574365139,
0.009672324173152447,
-0.010164984501898289,
-0.02292836643755436,
-0.015571908093988895,
-0.03765999525785446,
-0.03435799479484558,
-0.03183802217245102,
-0.030594924464821815,
-0.00819997675716877,
-0.045871756970882416,
0.01342150941491127,
0.001798524521291256,
0.012586245313286781,
0.0019599301740527153,
0.012407803907990456,
-0.029373230412602425,
-0.017109602689743042,
-0.05526980385184288,
-0.018214061856269836,
0.01842442713677883,
0.02534090168774128,
0.023312916979193687,
0.027577394619584084,
-0.047385040670633316,
-0.05633171647787094,
-0.0005183026078157127,
0.004386343527585268,
-0.004720652010291815,
0.0014545728918164968,
0.00875361543148756,
-0.024247217923402786,
0.04202292859554291,
-0.013881630264222622,
-0.04189998283982277,
0.035075053572654724,
-0.052206654101610184,
-0.02889379858970642,
0.0170566588640213,
0.013572240248322487,
0.017508165910840034,
-0.0057694013230502605,
-0.05038180202245712,
0.011582798324525356,
0.03763769567012787,
-0.0034858135040849447,
-0.006773374043405056,
-0.008610797114670277,
-0.0318855382502079,
0.01921953819692135,
-0.009056758135557175,
0.03888086602091789,
-0.02556520886719227,
-0.01979217492043972,
0.06157585233449936,
0.007755540311336517,
-0.021007651463150978,
0.021754059940576553,
0.01287531666457653,
-0.03591533005237579,
-0.027239518240094185,
-0.02872190810739994,
0.00846621859818697,
0.03542374074459076,
0.04399897903203964,
-0.04578421637415886,
0.007716530002653599,
0.002739610383287072,
-0.009745930321514606,
-0.093706414103508,
0.012700099498033524,
0.04011453315615654,
0.022297881543636322,
0.011374762281775475,
-0.07503408193588257,
-0.0041774786077439785,
0.029231077060103416,
-0.05450299009680748,
-0.008729366585612297,
0.0021716677583754063,
-0.008372313342988491,
-0.0685754120349884,
0.013648292981088161,
0.0033932116348296404,
-0.007323159836232662,
0.021192172542214394,
0.021996695548295975,
-0.010016389191150665,
0.034748926758766174,
-0.016378965228796005,
-0.054429613053798676,
-0.019073862582445145,
0.03769303485751152,
0.016262508928775787,
-0.028525909408926964,
0.018340671434998512,
-0.024619558826088905,
0.030393870547413826,
-0.008838359266519547,
-0.06858406960964203,
0.033438023179769516,
-0.030165735632181168,
-0.019978603348135948,
0.009850830771028996,
0.028479987755417824,
0.013079063035547733,
-0.007224604487419128,
0.000756015011575073,
0.04018101096153259,
0.011306357569992542,
0.012922050431370735,
0.013061299920082092,
0.026372075080871582,
0.03467101231217384,
-0.043560322374105453,
-0.033658307045698166,
0.023863403126597404,
-0.004179920069873333,
0.006767557933926582,
0.011647290550172329,
0.012625711970031261,
0.037552811205387115,
-0.023190317675471306,
-0.036704711616039276,
-0.04121651500463486,
-0.0004333068791311234,
0.011705886572599411,
0.03036336787045002,
-0.02727906033396721,
-0.008152725175023079,
0.006054738536477089,
-0.03528829291462898,
0.034549444913864136,
0.020450420677661896,
-0.0004944932879880071,
-0.04377580061554909,
-0.05073227360844612,
-0.014791524969041348,
-0.0027628757525235415,
-0.004019295796751976,
-0.004030915442854166,
-0.03887104615569115,
0.013461858965456486,
-0.00023953134950716048,
0.017470041289925575,
0.038264572620391846,
-0.048771221190690994,
-0.015219360589981079,
-0.017993515357375145,
0.05170653387904167,
-0.004928457550704479,
0.03097207471728325,
-0.02030099369585514,
-0.005570532288402319,
-0.03130102530121803,
-0.021864309906959534,
0.043618205934762955,
0.005723459646105766,
-0.01672196015715599,
-0.0016781947342678905,
0.018488053232431412,
0.006849278695881367,
-0.04154371842741966,
0.00985098909586668,
-0.010673356242477894,
-0.015557542443275452,
-0.017980264499783516,
-0.004084387794137001,
-0.005432996433228254,
-0.02799360826611519,
0.04553784057497978,
-0.010332769714295864,
0.038453608751297,
0.03034409135580063,
-0.04103602096438408,
0.053576331585645676,
0.013595711439847946,
0.006764063611626625,
0.07183118164539337,
-0.013983238488435745,
-0.01834922283887863,
0.03895602375268936,
-0.016701767221093178,
-0.05335071682929993,
0.03986993059515953,
-0.056407392024993896,
0.02466011419892311,
-0.006853720638900995,
0.0008032016339711845,
0.012028628028929234,
-0.031870488077402115,
0.0024866878520697355,
0.018389225006103516,
-0.0358269028365612,
0.00594307528808713,
0.023238344117999077,
0.0038359989412128925,
0.04110550880432129,
-0.03964885696768761,
0.011660139076411724,
0.05949370563030243,
0.009257987141609192,
-0.0542190782725811,
0.06882163137197495,
0.06592805683612823,
-0.010824647732079029,
0.026863884180784225,
0.0328202061355114,
0.011603191494941711,
0.016591470688581467,
-0.01628808118402958,
0.032865531742572784,
0.009598477743566036,
-0.04013127088546753,
0.05182688310742378,
0.0317952036857605,
-0.02532103843986988,
0.031439680606126785,
-0.03183688968420029,
0.07946953922510147,
0.01766025833785534,
-0.020254481583833694,
-0.017345936968922615,
0.007742552552372217,
-0.00671033188700676,
0.05425123870372772,
0.02670329250395298,
0.05471279099583626,
0.021181683987379074,
-0.000168163503985852,
-0.01857704482972622,
-0.0054682898335158825,
-0.01634366065263748,
-0.03126802667975426,
0.04676922410726547,
-0.030152466148138046,
0.02477174997329712,
-0.005100629758089781,
-0.026696491986513138,
-0.011368532665073872,
-0.010333932936191559,
0.025736559182405472,
0.005673063453286886,
0.012534666806459427,
0.03855124115943909,
0.012846626341342926,
0.013977622613310814,
0.0673447921872139,
-0.06476457417011261,
-0.006390808150172234,
-0.007373237516731024,
0.022820748388767242,
-0.0113265635445714,
-0.032176341861486435
] |
<p>Let us define a 4D rotation by using two unit quaternions: $$\mathring{q}_l=\frac{a+ib+jc+kd}{\left|a+ib+jc+kd\right|}$$ and $$\mathring{q}_r=\frac{e+ib+jc+kd}{\left|e+ib+jc+kd\right|}.$$ They differ only by the real term (the denominators are only for normalization). And let us consider two cases: the $a,b,c,d,e \in \mathbb{R}$ in the first case and $a,b,c,d,e \in \mathbb{C}$ in the second case - that would be biquaternions. Now let us consider a rotation of an arbitrary (non-unit) quaternion $\mathring{q}$ so that: </p>
<p>$$\mathring{q}_{rotated}=\mathring{q}_l\,\mathring{q}\,\mathring{q}_r^* $$ </p>
<p>(note the conjugate of $\mathring{q}_r$). I can represent this 4D rotation using a $4 \times 4$ rotation matrix, and thus I can find eigenvalues and eigenvectors of this matrix. The question is - what is the interpretation of eigenvectors of such rotation?</p>
<p>In 3D rotations the invariant vector (a vector that is not being rotated) is the rotation axis, and the eigenvalue has to be 1 (because it is a rotation, so no particular interpretation here). In 4D rotations I know that there are two planes around which the rotation occurs, but are those planes the invariant of the rotation? If yes, then how can I describe this plane as an eigenvector quaternion - would such quaternion be a "normal vector" of this plane, analogous to 3D space where normal vector of a plane is just a 3D vector?</p>
<p>How is that different between <a href="http://en.wikipedia.org/wiki/Quaternion" rel="nofollow">quaternions</a> and <a href="http://en.wikipedia.org/wiki/Biquaternion" rel="nofollow">biquaternions</a>?</p>
<p>Please note that since $e \neq a$ the normalized quaternion $\mathring{q}_r$ will be very different from $\mathring{q}_l$ - all the imaginary components of unit quaternion (those created by $b,c,d$) will be in fact different, thanks to normalization.</p>
| 9,553 |
[
-0.009833564050495625,
0.02449909597635269,
-0.02871004305779934,
0.004944695625454187,
0.07979989051818848,
0.054022643715143204,
-0.03266376629471779,
-0.03822801262140274,
-0.004797210916876793,
-0.061244916170835495,
0.02118413709104061,
-0.015338870696723461,
0.027573145925998688,
0.025933464989066124,
-0.004333895165473223,
0.01631726697087288,
-0.04396149888634682,
-0.032132815569639206,
-0.02684168517589569,
-0.015591073781251907,
0.019369155168533325,
0.008620667271316051,
0.01323994155973196,
0.0018045271281152964,
-0.001901412382721901,
0.04231536388397217,
0.029735812917351723,
-0.004487327300012112,
0.017878981307148933,
0.03405928239226341,
0.006790751591324806,
-0.025559093803167343,
0.025831051170825958,
0.028493117541074753,
-0.03390597552061081,
0.001544647617265582,
-0.017192304134368896,
0.016744427382946014,
0.012093497440218925,
0.027124840766191483,
-0.05340581014752388,
-0.009016893804073334,
-0.029150335118174553,
0.04735364392399788,
0.0008305609808303416,
0.016937097534537315,
-0.00005379309368436225,
-0.009390989318490028,
0.021233096718788147,
-0.07179197669029236,
0.11781046539545059,
-0.009431671351194382,
0.010380435734987259,
-0.01890774630010128,
0.008590561337769032,
-0.020293548703193665,
0.05421285703778267,
0.051146894693374634,
0.0015016321558505297,
-0.078663669526577,
-0.04394807294011116,
-0.033386074006557465,
0.015555627644062042,
-0.0030297625344246626,
-0.024377411231398582,
-0.025885384529829025,
0.01179234404116869,
-0.01148500107228756,
0.020168844610452652,
-0.01751452125608921,
-0.018727077171206474,
0.060092199593782425,
0.027642913162708282,
-0.06479784846305847,
0.006533134263008833,
-0.02019699662923813,
0.01737578958272934,
0.02621876262128353,
0.0500810369849205,
-0.013454965315759182,
-0.00010640260734362528,
-0.010062070563435555,
-0.003703498048707843,
-0.021158359944820404,
0.021807830780744553,
0.013437189161777496,
0.05610600486397743,
-0.003716865321621299,
0.02242288738489151,
0.02434481866657734,
0.003683895105496049,
0.035187967121601105,
0.0005879740347154438,
-0.00996911060065031,
-0.010994906537234783,
0.017735514789819717,
0.017656628042459488,
0.018026456236839294,
0.01079574879258871,
-0.02848264016211033,
0.0017576051177456975,
-0.03084232099354267,
-0.017275456339120865,
0.07881622761487961,
0.022095557302236557,
0.03221301734447479,
-0.03170435130596161,
0.03369828686118126,
-0.0009639959898777306,
-0.046255648136138916,
-0.03744674101471901,
0.02198777347803116,
-0.03385598212480545,
0.018167171627283096,
0.004922627471387386,
-0.034388139843940735,
0.019367225468158722,
-0.011426991783082485,
0.04343069717288017,
0.08104518055915833,
0.03308819979429245,
-0.047098226845264435,
-0.019099656492471695,
-0.020069945603609085,
-0.035817280411720276,
0.005920252297073603,
0.03485332056879997,
0.011710685677826405,
-0.012464352883398533,
0.005702928639948368,
0.010822315700352192,
-0.024004114791750908,
0.0009666560217738152,
-0.018087632954120636,
0.018053995445370674,
0.008828765712678432,
-0.10782479494810104,
-0.0418187640607357,
0.0764068141579628,
-0.011363041587173939,
-0.01027781330049038,
-0.08857301622629166,
0.01038431841880083,
0.010209380649030209,
0.05811389908194542,
-0.01437141839414835,
0.03924046456813812,
0.031039027497172356,
0.009421948343515396,
0.018052922561764717,
-0.003436283441260457,
0.006230444181710482,
-0.031008420512080193,
-0.047631531953811646,
0.004917847458273172,
-0.03879641368985176,
0.019164353609085083,
0.011880993843078613,
0.020671099424362183,
-0.012306185439229012,
0.02942703478038311,
-0.012635821476578712,
-0.009243549779057503,
0.06346087902784348,
-0.0021532783284783363,
-0.008621144108474255,
0.02396758459508419,
0.02686990424990654,
0.021613668650388718,
0.01307421363890171,
-0.021146951243281364,
0.012325320392847061,
-0.013829478062689304,
0.062106601893901825,
0.03521544113755226,
-0.01882794313132763,
-0.006690080743283033,
-0.039983879774808884,
0.025550514459609985,
-0.024898111820220947,
-0.06375183910131454,
-0.056336622685194016,
0.02298012562096119,
-0.0004821921174880117,
-0.020486237481236458,
0.04771123081445694,
0.014501157216727734,
0.027358295395970345,
0.012593918479979038,
-0.023771578446030617,
0.01927877962589264,
-0.05182405933737755,
0.022147702053189278,
0.022289413958787918,
-0.04973975941538811,
0.015998054295778275,
0.017058929428458214,
0.031388018280267715,
-0.015368524007499218,
-0.008480195887386799,
-0.020116794854402542,
0.032708458602428436,
0.016330257058143616,
-0.025684736669063568,
0.03320653364062309,
0.0073857088573277,
0.03672310337424278,
0.02133653126657009,
0.02695167437195778,
-0.00564329931512475,
-0.0031783385202288628,
-0.015257050283253193,
-0.01636439748108387,
0.0055177900940179825,
-0.0011473055928945541,
-0.019938195124268532,
0.0014805670361965895,
0.019805558025836945,
-0.029365047812461853,
0.020273108035326004,
-0.033263836055994034,
0.02934728004038334,
0.0339982695877552,
-0.03285332769155502,
-0.017900757491588593,
0.05013316497206688,
0.009877296164631844,
0.013416546396911144,
-0.016801362857222557,
-0.010857821442186832,
-0.03131278231739998,
0.015493492595851421,
0.015184247866272926,
0.05696658790111542,
-0.07286512106657028,
0.001525186002254486,
-0.0009936292190104723,
0.04855494573712349,
0.038152385503053665,
-0.00749266566708684,
-0.022885659709572792,
-0.028038902208209038,
0.010220649652183056,
-0.0032557176891714334,
0.025504177436232567,
0.018170932307839394,
-0.0045448350720107555,
-0.022033143788576126,
0.040395136922597885,
-0.01950441673398018,
-0.056168001145124435,
0.05457870662212372,
-0.033069074153900146,
0.002384789055213332,
0.023101935163140297,
0.008316049352288246,
0.025038983672857285,
0.006662262137979269,
0.018816189840435982,
0.019929710775613785,
-0.016700156033039093,
-0.009627300314605236,
-0.010018057189881802,
0.010473689995706081,
0.011222368106245995,
-0.01088798325508833,
-0.0010737045668065548,
-0.012195991352200508,
0.011815928854048252,
0.0008905437425710261,
0.03552918881177902,
-0.038464274257421494,
-0.039840176701545715,
0.023343725129961967,
-0.022743791341781616,
0.02263803407549858,
-0.004440718330442905,
-0.008123272098600864,
-0.02098088152706623,
-0.04235176369547844,
0.035677116364240646,
-0.0032182433642446995,
0.01969321258366108,
0.035162948071956635,
-0.045840125530958176,
-0.005662951152771711,
-0.07440096139907837,
-0.01740538515150547,
0.015145812183618546,
-0.016938043758273125,
0.01745845191180706,
0.033842071890830994,
-0.032157160341739655,
-0.018865449354052544,
-0.017811182886362076,
-0.02219122275710106,
0.018346711993217468,
-0.06189480423927307,
-0.011257576756179333,
0.035592202097177505,
-0.043301843106746674,
-0.013739857822656631,
-0.00933055393397808,
-0.01292723324149847,
-0.036473341286182404,
-0.006482465658336878,
-0.03464190289378166,
0.027610911056399345,
-0.013420289382338524,
0.019367117434740067,
0.004182785749435425,
-0.0005129895289428532,
0.00698319124057889,
-0.02854824997484684,
-0.018080182373523712,
0.0018921641167253256,
-0.035809338092803955,
0.06315749883651733,
-0.0011812510201707482,
-0.008166659623384476,
0.10021694749593735,
0.019743086770176888,
-0.019681615754961967,
-0.021204805001616478,
0.0071153221651911736,
-0.0090365344658494,
-0.028237683698534966,
0.00901762768626213,
0.022157272323966026,
0.001917861052788794,
0.012398581020534039,
0.007410830352455378,
-0.02441415749490261,
0.030839694663882256,
-0.006668001879006624,
-0.03567175194621086,
0.04305543377995491,
0.0047918641939759254,
0.01814967952668667,
0.050521884113550186,
0.0032187378965318203,
-0.006552460137754679,
0.015457317233085632,
0.027608400210738182,
-0.0025059508625417948,
0.03280014917254448,
-0.06982587277889252,
0.047546353191137314,
0.0018957986030727625,
0.017391839995980263,
-0.01374457124620676,
0.0664774477481842,
0.007775723934173584,
-0.03469962254166603,
-0.010616977699100971,
0.026201259344816208,
0.007561343256384134,
-0.016847409307956696,
0.04059988632798195,
0.020010700449347496,
-0.009467195719480515,
-0.008926070295274258,
0.01780209131538868,
-0.00965148489922285,
-0.03185064345598221,
0.04321307688951492,
-0.03697282075881958,
-0.026722129434347153,
0.039760250598192215,
0.02361968159675598,
0.02146046794950962,
-0.002748999511823058,
-0.03522947430610657,
-0.012994811870157719,
-0.008241834118962288,
-0.004561715759336948,
-0.009896060451865196,
0.024762684479355812,
0.007285175379365683,
0.06100177392363548,
-0.0029353478457778692,
0.005866109859198332,
0.0017392606241628528,
-0.0021745488047599792,
-0.05925379693508148,
-0.014062555506825447,
-0.008395272307097912,
0.002803165465593338,
0.0021923554595559835,
-0.007650745566934347,
0.04491185024380684,
0.013691374100744724,
-0.053012438118457794,
-0.028713423758745193,
-0.03483910486102104,
-0.05805649235844612,
0.020505474880337715,
-0.02442188560962677,
-0.037785958498716354,
-0.029220866039395332,
0.031096255406737328,
0.07274358719587326,
-0.02249727211892605,
0.01757865399122238,
0.03887275233864784,
-0.04746329411864281,
0.02384035289287567,
-0.0051710475236177444,
-0.001142224413342774,
0.009951798245310783,
-0.0015462097944691777,
0.00606555724516511,
0.014809067361056805,
0.04059278964996338,
-0.048468124121427536,
-0.018261242657899857,
0.032321080565452576,
0.012859989888966084,
-0.003345542587339878,
-0.0031153380405157804,
-0.04617631062865257,
0.031120486557483673,
-0.028814231976866722,
0.09057248383760452,
-0.04414450749754906,
0.0024681922513991594,
0.05091969296336174,
0.024866711348295212,
-0.008234376087784767,
0.0004956345073878765,
0.037498898804187775,
0.05665380135178566,
-0.019297759979963303,
-0.05591186136007309,
-0.018117664381861687,
-0.012450825423002243,
-0.02676176279783249,
0.018839525058865547,
-0.022772110998630524,
-0.05224243924021721,
0.0006779481191188097,
0.02023185044527054,
-0.024419955909252167,
-0.010396869853138924,
0.039892297238111496,
-0.005490243434906006,
0.011499316431581974,
0.009019982069730759,
0.010084523819386959,
-0.004476427566260099,
0.04477782920002937,
0.03608008474111557,
-0.0026187810581177473,
-0.00366236106492579,
-0.06701985746622086,
-0.002944273641332984,
0.011035580188035965,
0.02119593136012554,
0.0111478790640831,
0.004380318336188793,
-0.005076415371149778,
-0.03143634647130966,
0.02061043120920658,
-0.020880160853266716,
0.04600675776600838,
0.009072486311197281,
0.000986222643405199,
-0.03351375833153725,
0.009487827308475971,
-0.010314724408090115,
0.01532141026109457,
-0.0003059260197915137,
-0.009927129372954369,
-0.02796306647360325,
0.015893639996647835,
-0.034548476338386536,
-0.015545686706900597,
-0.004177417606115341,
0.01696622185409069,
0.020639196038246155,
0.02468358725309372,
0.023928599432110786,
0.03535931184887886,
-0.006392395123839378,
-0.05165819078683853,
0.018827298656105995,
0.06872344762086868,
-0.009952434338629246,
0.018366876989603043,
-0.057411469519138336,
-0.03911936655640602,
0.015776921063661575,
-0.010280963033437729,
0.005460348445922136,
0.061615239828825,
-0.02019410952925682,
0.023891951888799667,
0.010498016141355038,
-0.002309718169271946,
0.01957090198993683,
-0.0057404232211411,
-0.004903531167656183,
-0.027119992300868034,
-0.023439552634954453,
0.042961761355400085,
-0.024020465090870857,
-0.028004024177789688,
0.007585367187857628,
0.01929837092757225,
-0.00032346483203582466,
0.03892209753394127,
-0.045317746698856354,
0.018168404698371887,
-0.020724784582853317,
-0.010380364954471588,
-0.030228380113840103,
0.03952158987522125,
-0.014499302953481674,
-0.007930312305688858,
-0.01740691438317299,
0.011452676728367805,
0.0024117438588291407,
-0.03554004430770874,
0.02861981838941574,
-0.009844738058745861,
-0.019972113892436028,
0.04472858086228371,
0.012809418141841888,
-0.009756429120898247,
-0.04834814369678497,
0.024314342066645622,
-0.0015965515049174428,
-0.025244316086173058,
0.02375372312963009,
0.000018683447706280276,
-0.016328390687704086,
0.013524015434086323,
-0.05671042948961258,
-0.02339017018675804,
-0.0023687270004302263,
-0.021762827411293983,
0.014557644724845886,
0.008719668723642826,
0.02127547562122345,
0.03511083126068115,
0.03145615756511688,
-0.06387486308813095,
-0.033365994691848755,
0.020444782450795174,
0.010489394888281822,
-0.015075743198394775,
-0.025991275906562805,
-0.02297985926270485,
0.004493418615311384,
-0.06745774298906326,
0.012729956768453121,
0.05086953938007355,
-0.060005053877830505,
-0.0033132240641862154,
0.03151891753077507,
0.025850357487797737,
0.05000804364681244,
-0.026189642027020454,
-0.008552455343306065,
0.008787468075752258,
-0.01106616947799921,
0.024406369775533676,
0.03646845370531082,
0.04380830377340317,
-0.020373763516545296,
-0.003083188086748123,
-0.04757872596383095,
-0.02215644158422947,
0.00979817844927311,
-0.029148530215024948,
-0.0071163238026201725,
0.026372835040092468,
0.029882296919822693,
-0.009892523288726807,
-0.04506993666291237,
-0.011038379743695259,
0.020801931619644165,
0.01654820889234543,
-0.0329422652721405,
-0.0021248452831059694,
0.013369269669055939,
-0.06350097805261612,
0.015962127596139908,
-0.01682366617023945,
0.008757340721786022,
-0.020271416753530502,
0.04996746778488159,
-0.012149261310696602,
0.007602552883327007,
-0.01156831718981266,
-0.017307154834270477,
0.01672419346868992,
-0.018652165308594704,
0.013628577813506126,
0.03273073211312294,
0.006522378418594599,
-0.02286641299724579,
-0.06565065681934357,
-0.05690401792526245,
0.012736440636217594,
0.04910142719745636,
-0.010283947922289371,
0.06715049594640732,
0.07451735436916351,
0.001647618249990046,
-0.007910878397524357,
-0.010230802930891514,
0.009116792120039463,
0.05043264478445053,
-0.0055608018301427364,
0.011609488166868687,
-0.021649381145834923,
-0.022145219147205353,
-0.0012238851049914956,
0.03908843547105789,
-0.057753972709178925,
0.012301528826355934,
0.01644190214574337,
0.034354161471128464,
-0.015370567329227924,
0.013190224766731262,
-0.06476686894893646,
0.07007075846195221,
-0.025053944438695908,
0.049953311681747437,
0.004830542951822281,
-0.03803226724267006,
0.046769220381975174,
0.034939996898174286,
0.012651568278670311,
-0.05023843050003052,
-0.02777354046702385,
-0.05288105458021164,
0.04179735854268074,
0.028585949912667274,
0.005482545122504234,
-0.04125010967254639,
0.012296538800001144,
0.052357591688632965,
-0.02010190300643444,
0.03676038607954979,
-0.005363085772842169,
-0.02362678200006485,
-0.011911880224943161,
-0.015786122530698776,
-0.03750564530491829,
0.05033651739358902,
-0.0003455776022747159,
-0.020089101046323776,
-0.04037421941757202,
-0.036040131002664566,
0.019667478278279305,
0.036016177386045456,
0.0628272071480751,
-0.07397250086069107,
0.028056208044290543,
-0.007123499643057585,
-0.00768475653603673,
0.0017820606008172035,
-0.024442709982395172,
0.11556876450777054,
0.04970284551382065,
-0.008804052136838436,
-0.05222657322883606,
0.010104755870997906,
0.01646614819765091,
0.018954969942569733,
-0.025547809898853302,
0.01791314035654068,
-0.0063810101710259914,
0.027856824919581413,
-0.005494671408087015,
0.04559529945254326,
-0.008385851047933102,
-0.02980654686689377,
0.03910936787724495,
-0.008178620599210262,
-0.057094182819128036,
-0.030261600390076637,
0.045728206634521484,
-0.02973121963441372,
0.024538416415452957,
-0.07392455637454987,
0.017584890127182007,
-0.03827208653092384,
0.006423457991331816,
-0.06549520045518875,
-0.011812125332653522,
-0.005774226505309343,
-0.02973463013768196,
-0.027541127055883408,
0.007368486374616623,
0.01990063302218914,
-0.03264721482992172,
-0.035623665899038315,
0.04400916025042534,
-0.001580628682859242,
-0.03304076939821243,
0.05375376343727112,
0.020607709884643555,
-0.0008048443705774844,
-0.01983383111655712,
0.05171532183885574,
0.006038656458258629,
-0.0429178811609745,
-0.02507890947163105,
-0.06386802345514297,
0.057239752262830734,
-0.02040010131895542,
0.025308536365628242,
-0.0261007621884346,
-0.006273040547966957,
0.008225679397583008,
-0.07059865444898605,
0.0058147115632891655,
-0.03420824185013771,
0.028438139706850052,
0.008638528175652027,
0.028189226984977722,
-0.026824744418263435,
0.014090890064835548,
0.03716080263257027,
0.007061702664941549,
-0.01711100898683071,
-0.011057387106120586,
0.0236602034419775,
-0.0213322676718235,
0.044500309973955154,
-0.016797106713056564,
0.012044570408761501,
-0.014073763974010944,
-0.013842461630702019,
-0.007831460796296597,
-0.02256539836525917,
-0.03515251353383064,
0.0314672589302063,
0.055201586335897446,
0.0253768227994442,
-0.03496742993593216,
-0.009433790110051632,
-0.05891643092036247,
-0.017759911715984344,
-0.0065000709146261215,
-0.020380690693855286,
-0.03242432698607445,
0.007989729754626751,
0.050361134111881256,
0.0524001382291317,
-0.049523163586854935,
0.021821213886141777,
0.0018506365595385432,
0.018627289682626724,
0.037685099989175797,
-0.005423245020210743,
-0.014579971320927143,
0.03401060402393341,
-0.032971132546663284,
-0.013393857516348362,
-0.02901141531765461,
0.02315669320523739,
0.044669993221759796,
0.0259205661714077,
-0.03465395048260689,
0.05609280616044998,
-0.046022504568099976,
-0.015905356034636497,
0.005555284675210714,
-0.04519803076982498,
0.03987808898091316,
0.03156423568725586,
0.03772667422890663,
-0.09035737067461014,
-0.00658295676112175,
-0.014621316455304623,
-0.022213611751794815,
0.0002592506352812052,
-0.01910855621099472,
-0.016005152836441994,
-0.025137195363640785,
-0.037700291723012924,
0.04356219619512558,
-0.04825056344270706,
-0.01939355954527855,
-0.012019563466310501,
0.03852280601859093,
0.031073860824108124,
0.016437340527772903,
-0.03118067793548107,
-0.01003654021769762,
0.03232482820749283,
0.0001527510758023709,
0.017400750890374184,
0.022470032796263695,
-0.02879205346107483,
0.0064605469815433025,
-0.014638133347034454,
0.0037195412442088127,
0.02234007976949215,
0.020461225882172585,
-0.02253522165119648,
0.016844367608428,
-0.02286667935550213,
-0.021047376096248627,
0.035761941224336624,
-0.01138538308441639,
0.0009547807858325541,
0.04670961573719978,
0.0005475918296724558,
-0.03701178729534149,
0.022018833085894585,
-0.006216738373041153,
-0.008466929197311401,
-0.006413210649043322,
-0.021306239068508148,
-0.018060628324747086,
-0.03128060698509216,
0.0055571384727954865,
0.0021827418822795153,
0.011440110392868519,
0.012515030801296234,
0.02116415649652481,
-0.03214913606643677,
-0.006427411455661058,
0.020887643098831177,
0.015220840461552143,
0.014420163817703724,
0.03749198839068413,
0.004223007708787918,
0.04583314433693886,
0.027488913387060165,
-0.03288684040307999,
0.025075625628232956,
0.03976859152317047,
0.031447164714336395,
-0.09333395212888718,
-0.029960619285702705,
0.04084043577313423,
0.0363711379468441,
0.05105554684996605,
-0.06226411834359169,
0.010267850011587143,
0.05515788495540619,
-0.11670278012752533,
0.019990503787994385,
-0.026228776201605797,
-0.02814582921564579,
-0.02023465186357498,
0.008333303965628147,
0.010006467811763287,
0.030057841911911964,
0.022916069254279137,
0.01050126925110817,
0.011917723342776299,
0.03515128046274185,
-0.01993253454566002,
0.0071568735875189304,
0.008372205309569836,
-0.0014375055907294154,
0.03541473299264908,
-0.007851546630263329,
0.04760094732046127,
-0.01286365371197462,
-0.030373018234968185,
0.013852051459252834,
0.024548014625906944,
0.03555477410554886,
-0.005677907727658749,
0.02801850065588951,
0.014653416350483894,
-0.0003975418221671134,
-0.0005160586442798376,
-0.017859306186437607,
-0.026040418073534966,
-0.019441775977611542,
0.03869258984923363,
0.04268069192767143,
-0.002657486591488123,
-0.005358228925615549,
0.02078666165471077,
-0.058689262717962265,
0.0029849500861018896,
0.02470189332962036,
-0.027818651869893074,
-0.008614793419837952,
-0.020836427807807922,
-0.021414505317807198,
-0.016435956582427025,
-0.029138442128896713,
0.031131062656641006,
-0.04039963707327843,
-0.009949869476258755,
0.00777871860191226,
-0.011978094466030598,
0.043718282133340836,
0.01826370880007744,
-0.013160890899598598,
-0.02783728763461113,
0.06552834808826447,
0.002998444251716137,
-0.020539719611406326,
-0.1186838448047638,
0.003833492286503315,
0.01132622268050909,
-0.018353892490267754,
-0.001529559725895524,
-0.023382026702165604,
-0.024977536872029305,
0.0029581671115010977,
0.023764628916978836,
0.03187292814254761,
-0.03128260746598244,
-0.04771674424409866,
-0.03897405043244362,
-0.0674288272857666,
0.03918328136205673,
0.033860135823488235,
-0.07503852993249893,
-0.012770909816026688,
0.0034094967413693666,
0.007627672981470823,
0.038438908755779266,
0.06423555314540863,
0.02311321720480919,
0.009027879685163498,
0.005470082629472017,
0.02490844763815403,
0.04311812296509743,
-0.034409139305353165,
-0.03088037483394146,
-0.009755894541740417,
-0.0008186700288206339,
0.015328223817050457,
0.02669753134250641,
-0.0458073727786541,
-0.014518811367452145,
0.028568165376782417,
0.00015300995437428355,
0.02166472002863884,
0.027700571343302727,
-0.046857234090566635,
0.06462384015321732,
0.010160699486732483,
-0.027581090107560158,
0.05895894020795822,
0.010821050964295864,
-0.012972231954336166,
0.06253276765346527,
-0.048742204904556274,
-0.004410753026604652,
0.004617213271558285,
-0.018655629828572273,
-0.01238325983285904,
0.0074775489047169685,
0.005272869020700455,
0.07589501887559891,
-0.05740996450185776,
0.02807508409023285,
0.06910745799541473,
-0.04553036764264107,
0.014038358815014362,
0.06158877909183502,
0.02148391678929329,
0.028964487835764885,
-0.012266306206583977,
0.06053847447037697,
0.017437875270843506,
-0.053760554641485214,
0.07061374187469482,
-0.006241267547011375,
0.010493221692740917,
-0.016717731952667236,
-0.029434140771627426,
0.03342854231595993,
0.0008304051589220762,
0.02946036122739315,
-0.014028403908014297,
0.01868405006825924,
-0.026997731998562813,
0.02612834796309471,
0.014643090777099133,
-0.024111364036798477,
0.004834067542105913,
0.04201596975326538,
-0.017184948548674583,
0.07126428186893463,
-0.023801393806934357,
-0.00907373707741499,
-0.022675087675452232,
-0.0005029859021306038,
-0.019471975043416023,
0.005604942329227924,
0.02039588987827301,
0.021259885281324387,
0.012301099486649036,
-0.012094208039343357,
-0.027009181678295135,
-0.020606057718396187,
0.02578488551080227,
-0.00196585850790143,
0.005687758792191744,
0.024000832810997963,
0.021010655909776688,
0.009757722727954388,
-0.0428626574575901,
-0.02007225714623928,
-0.004327261820435524,
0.01702032797038555,
0.012249804101884365,
0.03885051980614662,
0.008542785421013832,
-0.03632340952754021,
-0.02588265761733055,
0.031832486391067505,
-0.05207027494907379,
-0.031794801354408264,
-0.0007377256988547742,
0.03429434075951576,
0.03250069171190262,
0.002974196569994092
] |
<p>In physics total energy is extremal for the static solutions of equation of motions.</p>
<p>Can anyone explain this sentence to me?</p>
| 9,554 |
[
-0.016996372491121292,
-0.04562835022807121,
-0.0017467730212956667,
-0.002545201452448964,
0.029159601777791977,
0.0404621846973896,
0.0012382296845316887,
-0.00455965381115675,
-0.02808201126754284,
-0.047223448753356934,
0.02883431874215603,
0.021455079317092896,
0.02349969744682312,
0.058695584535598755,
0.04018377512693405,
-0.014321472495794296,
-0.006325496360659599,
-0.006847722455859184,
-0.003986143507063389,
-0.019811229780316353,
-0.01185531821101904,
-0.015478083863854408,
0.002520328387618065,
0.03148242458701134,
0.001329344930127263,
0.030105505138635635,
0.02520737051963806,
-0.014246976003050804,
0.008375703357160091,
0.05789068713784218,
-0.012219000607728958,
-0.016043098643422127,
-0.02597672864794731,
0.004985487088561058,
0.03436970338225365,
0.02610020525753498,
-0.02994363382458687,
0.011754048056900501,
0.013594536110758781,
0.007548606023192406,
-0.05293785408139229,
-0.03783314675092697,
-0.0011080042459070683,
0.0401252917945385,
-0.051514141261577606,
0.052734971046447754,
0.030474688857793808,
-0.010646804235875607,
0.04923950508236885,
-0.04010985046625137,
0.10766475647687912,
-0.002371820155531168,
0.03817691653966904,
-0.004206666257232428,
-0.005799578502774239,
0.03588773310184479,
0.049384571611881256,
0.04313167929649353,
-0.0268593467772007,
-0.0714733824133873,
-0.02085251919925213,
-0.018489180132746696,
-0.008113820105791092,
0.002676881616935134,
-0.010699387639760971,
0.01725573092699051,
0.029906712472438812,
-0.050586823374032974,
0.04452527314424515,
-0.00414619967341423,
-0.034206733107566833,
0.025470636785030365,
0.05769698694348335,
-0.030743295326828957,
0.014588192105293274,
-0.03390079364180565,
0.022838499397039413,
-0.0002556406252551824,
-0.0026148471515625715,
0.047778524458408356,
0.00974525697529316,
-0.004466261714696884,
0.02369071915745735,
0.07023153454065323,
-0.058283064514398575,
0.00807978119701147,
0.06880397349596024,
0.009858030825853348,
0.033375732600688934,
0.05537792667746544,
-0.000054106483730720356,
-0.0021217558532953262,
0.03414063900709152,
0.010633605532348156,
-0.060524310916662216,
0.010191130451858044,
0.02506575733423233,
0.05407271161675453,
0.006001011934131384,
-0.007978958077728748,
0.03841334208846092,
-0.031009608879685402,
0.004776696674525738,
0.04517034813761711,
0.018588824197649956,
-0.012881469912827015,
-0.08389837294816971,
0.04117982089519501,
-0.0051319049671292305,
0.02062416449189186,
-0.030972467735409737,
-0.017409225925803185,
-0.008296863175928593,
0.004011604003608227,
-0.017346981912851334,
-0.015972398221492767,
-0.0004144227132201195,
-0.011249355971813202,
0.03545200079679489,
0.026807934045791626,
0.040587179362773895,
-0.024795768782496452,
0.02854786440730095,
-0.00804074201732874,
-0.07337747514247894,
0.0245597492903471,
0.056245576590299606,
-0.02523970790207386,
-0.05476132035255432,
-0.023170458152890205,
-0.013937671668827534,
0.017349079251289368,
-0.0158194862306118,
0.004642182495445013,
0.02406492456793785,
-0.0389329195022583,
-0.11143062263727188,
-0.05822369083762169,
0.03410239890217781,
0.00016737938858568668,
-0.02235051430761814,
-0.07856425642967224,
0.004480790812522173,
0.030224502086639404,
0.050013136118650436,
-0.029867080971598625,
-0.0018574115820229053,
0.025460708886384964,
0.009320360608398914,
-0.009999909438192844,
-0.014693173579871655,
-0.0361071415245533,
0.009122608229517937,
-0.02794981561601162,
0.005039740353822708,
-0.08543872833251953,
-0.005276578012853861,
0.025425106287002563,
-0.007318894378840923,
-0.01780952326953411,
0.025479819625616074,
-0.02845848724246025,
-0.028915885835886,
-0.003908084239810705,
-0.006374043878167868,
-0.031486328691244125,
0.06195022910833359,
0.021323658525943756,
0.012473367154598236,
0.047291070222854614,
0.028428668156266212,
0.03979642316699028,
-0.023321451619267464,
0.038016896694898605,
0.010641539469361305,
-0.030489280819892883,
-0.010012645274400711,
-0.024399731308221817,
-0.009479308500885963,
0.015129974111914635,
-0.042901411652565,
-0.06274204701185226,
0.031900595873594284,
0.031359706073999405,
0.011259496212005615,
0.0334189347922802,
-0.036043208092451096,
0.02460484579205513,
0.009650740772485733,
-0.025927184149622917,
-0.016317663714289665,
-0.08346808701753616,
0.03532306104898453,
0.01099615078419447,
-0.023884369060397148,
0.011323184706270695,
0.03818908706307411,
0.0156424418091774,
-0.06341776251792908,
0.026761271059513092,
0.007468265946954489,
-0.011030864901840687,
-0.0034856945276260376,
-0.019065048545598984,
0.035789698362350464,
0.07088901102542877,
0.052659209817647934,
0.039811503142118454,
-0.004545694682747126,
0.0185170266777277,
-0.0281673651188612,
0.02942505106329918,
-0.029628120362758636,
0.04132900387048721,
0.010667867958545685,
0.014309687539935112,
0.009633324109017849,
-0.020408228039741516,
-0.005021046381443739,
0.03132525086402893,
-0.028855372220277786,
0.05585591122508049,
0.03643298149108887,
0.011498774401843548,
-0.0052786399610340595,
0.03676476329565048,
-0.01763293333351612,
0.023216338828206062,
0.013502989895641804,
-0.005182257387787104,
-0.03227478265762329,
-0.022569017484784126,
0.008958619087934494,
0.04316655173897743,
-0.07317651808261871,
-0.001822438556700945,
0.06371321529150009,
0.02186513878405094,
0.05191940814256668,
0.030762795358896255,
-0.01392429880797863,
-0.04630850628018379,
0.02864953875541687,
0.032390084117650986,
0.003325333120301366,
0.05586031451821327,
0.024232596158981323,
0.032440148293972015,
-0.004406752064824104,
-0.00017251691315323114,
-0.02067968249320984,
0.07071185111999512,
0.030751891434192657,
0.028052665293216705,
0.038830436766147614,
-0.040034715086221695,
0.020795447751879692,
-0.04296109080314636,
0.04268628731369972,
0.024039989337325096,
-0.004406863357871771,
0.02587386965751648,
-0.04358387738466263,
-0.010129512287676334,
0.03055347315967083,
0.02229793556034565,
-0.006276174448430538,
-0.023434726521372795,
0.036555007100105286,
-0.02581578679382801,
-0.015315815806388855,
0.004988761618733406,
-0.037905704230070114,
-0.013297435827553272,
-0.03183282911777496,
0.07214047014713287,
-0.007038745563477278,
0.035608600825071335,
-0.007917669601738453,
-0.008216091431677341,
-0.006486536934971809,
-0.03502890467643738,
-0.023552248254418373,
-0.000009079645678866655,
-0.0387762188911438,
0.00491842208430171,
-0.01227365992963314,
-0.04447602853178978,
0.05382794514298439,
-0.020189767703413963,
0.018507586792111397,
0.062156934291124344,
-0.022170979529619217,
-0.024997297674417496,
-0.00256211101077497,
-0.043986331671476364,
0.023151064291596413,
-0.04086470976471901,
0.0018970731180161238,
0.06396087259054184,
-0.007487087976187468,
-0.021496841683983803,
0.009048518724739552,
-0.029443642124533653,
-0.027951998636126518,
-0.033306024968624115,
-0.01244097575545311,
0.04318814352154732,
-0.007323346100747585,
0.045029282569885254,
0.0006959429010748863,
-0.04244288057088852,
0.019863547757267952,
-0.08085238933563232,
-0.027964718639850616,
0.014687387272715569,
-0.00327474856749177,
0.0627502053976059,
-0.020316073670983315,
-0.033616598695516586,
0.09076710045337677,
0.012028224766254425,
-0.03631184622645378,
-0.009206408634781837,
-0.014911430887877941,
0.0031760549172759056,
0.0030148373916745186,
0.029335707426071167,
0.02411140687763691,
0.0018414822407066822,
0.03765324875712395,
0.009483858942985535,
0.05460461974143982,
0.012477547861635685,
-0.029257882386446,
-0.021302705630660057,
-0.013389050029218197,
-0.02091684564948082,
0.027892954647541046,
0.015088430605828762,
0.018061082810163498,
-0.04405030235648155,
0.059270791709423065,
0.014423253946006298,
0.03499988093972206,
-0.0004893199075013399,
-0.058479685336351395,
0.07256487011909485,
-0.014542780816555023,
0.0022995658218860626,
-0.03487232327461243,
0.04568886011838913,
0.0008406517445109785,
-0.021736696362495422,
0.007735694758594036,
0.0500669963657856,
0.028763314709067345,
0.0011318052420392632,
-0.0031665796414017677,
0.0036390689201653004,
0.07216349244117737,
-0.0460846908390522,
-0.031337641179561615,
0.024361107498407364,
-0.002322173910215497,
0.008329233154654503,
-0.0033358014188706875,
-0.026356786489486694,
0.021447420120239258,
0.029005298390984535,
0.025518862530589104,
0.011493477039039135,
-0.040773048996925354,
0.009711884893476963,
-0.052977271378040314,
0.01764470525085926,
-0.013878916390240192,
0.04457583278417587,
-0.01228154357522726,
0.05339222773909569,
0.041988734155893326,
0.04510807991027832,
0.026592304930090904,
0.014487722888588905,
-0.10510523617267609,
0.03439576178789139,
-0.02579132840037346,
0.008511003106832504,
0.020068565383553505,
-0.004277091473340988,
0.016936050727963448,
-0.0334530808031559,
-0.03277554735541344,
-0.003594249254092574,
-0.0051498254761099815,
-0.0623781755566597,
0.0019498952897265553,
-0.05544276908040047,
-0.013471180573105812,
0.011390157043933868,
0.016014495864510536,
0.019826918840408325,
-0.030284326523542404,
0.015744071453809738,
0.0540693961083889,
-0.045833636075258255,
-0.01380639337003231,
-0.007211453281342983,
-0.0020425908733159304,
0.015183987095952034,
0.03406408429145813,
0.004619762767106295,
0.02023899368941784,
0.007750651333481073,
0.006028466392308474,
-0.031828854233026505,
0.050232838839292526,
0.018814466893672943,
-0.02523873560130596,
-0.04771117866039276,
-0.0046373712830245495,
0.008734182454645634,
0.025518914684653282,
0.008143513463437557,
0.0068507413379848,
0.005002401303499937,
0.004615929443389177,
0.03994966298341751,
-0.042387887835502625,
0.06891440600156784,
0.04163379222154617,
0.030605046078562737,
-0.024351783096790314,
-0.036647628992795944,
-0.009521879255771637,
-0.03421242535114288,
-0.015683673322200775,
0.010008673183619976,
-0.01661643758416176,
-0.03495822474360466,
0.0035334439016878605,
0.016055332496762276,
0.009469648823142052,
-0.05019605532288551,
-0.020594056695699692,
-0.02182924933731556,
0.003974036313593388,
-0.02672664076089859,
-0.029069453477859497,
-0.020208999514579773,
0.00921587087213993,
0.03787299618124962,
-0.017331790179014206,
0.01727503351867199,
-0.04530816897749901,
-0.0132077531889081,
0.03950218856334686,
0.031246637925505638,
0.005155988037586212,
-0.00202657631598413,
-0.046169862151145935,
0.02033698558807373,
-0.0020709747914224863,
-0.03058788739144802,
0.03937355801463127,
-0.038058556616306305,
0.003592967987060547,
-0.02523723617196083,
-0.03001456707715988,
-0.01928408443927765,
0.0018490416696295142,
0.0006288414006121457,
0.043466366827487946,
-0.006493010092526674,
0.0021678691264241934,
-0.041266802698373795,
-0.020752757787704468,
0.00653470354154706,
0.020363450050354004,
0.04758128151297569,
-0.026450596749782562,
-0.004594518803060055,
0.0410919152200222,
-0.02059876173734665,
-0.06533463299274445,
-0.00407344289124012,
-0.009924682788550854,
0.023832036182284355,
-0.009544040076434612,
-0.048248376697301865,
-0.04181748628616333,
0.014810232445597649,
-0.02711368538439274,
-0.02630973421037197,
-0.01268080249428749,
-0.027071623131632805,
0.018447408452630043,
0.0649094358086586,
-0.014740332961082458,
0.025845035910606384,
0.04015050828456879,
-0.04259778559207916,
-0.005296547897160053,
-0.01746365800499916,
0.023710500448942184,
-0.0017216859851032495,
-0.012077531777322292,
-0.06060763821005821,
0.0018274107715114951,
-0.030394529923796654,
0.005293231923133135,
-0.03752080723643303,
0.01851678267121315,
0.002024861052632332,
-0.0488569401204586,
-0.03797192499041557,
0.043368253856897354,
0.0470476895570755,
-0.030915511772036552,
-0.0149665093049407,
0.011095662601292133,
0.010559669695794582,
-0.03720290586352348,
0.009575704112648964,
0.005193017888814211,
-0.009786832146346569,
0.061465825885534286,
0.012641248293220997,
0.029607538133859634,
-0.03203953057527542,
-0.021822696551680565,
0.00823146291077137,
-0.04873155057430267,
0.0029905217234045267,
-0.027256865054368973,
-0.03008340857923031,
0.026900848373770714,
-0.044518958777189255,
-0.0576094426214695,
0.011932737194001675,
-0.004613532684743404,
0.029952852055430412,
-0.009899642318487167,
-0.000888949609361589,
0.022223377600312233,
0.012536432594060898,
-0.060318730771541595,
-0.0487004853785038,
0.02119843102991581,
0.003662072354927659,
-0.02371072769165039,
-0.030774353072047234,
-0.009825478307902813,
-0.03895167261362076,
-0.019471893087029457,
0.00320298969745636,
0.023238977417349815,
-0.0061035738326609135,
-0.008315162733197212,
0.0087613919749856,
0.011890202760696411,
0.029991336166858673,
0.02717941254377365,
-0.024750256910920143,
0.0413174033164978,
-0.01072534080594778,
-0.015302044339478016,
-0.03689257800579071,
0.06954506039619446,
-0.016033023595809937,
-0.007236834615468979,
0.04142877459526062,
-0.006212527863681316,
0.04441673681139946,
0.006505664438009262,
0.005212767515331507,
0.019689271226525307,
-0.004079004283994436,
0.00863599218428135,
0.01169167086482048,
0.02060522884130478,
-0.032667048275470734,
0.05839608237147331,
0.016330312937498093,
0.0015525065828114748,
0.010623387061059475,
-0.06639878451824188,
0.03551604598760605,
-0.0009419652633368969,
0.015299123711884022,
0.02060464210808277,
0.08975014835596085,
0.006773209199309349,
0.003739840816706419,
-0.004653572104871273,
-0.009481457993388176,
0.034551769495010376,
0.015246394090354443,
0.01004115305840969,
-0.011072768829762936,
0.01095567550510168,
0.005403979681432247,
-0.0011346980463713408,
-0.02868550270795822,
0.030922332778573036,
0.023274434730410576,
-0.017298568040132523,
0.04587573558092117,
0.02028018608689308,
-0.007564944680780172,
0.0067835780791938305,
-0.018337994813919067,
0.01698913425207138,
0.005217882338911295,
0.014391574077308178,
0.04378708079457283,
-0.025306139141321182,
-0.005176318809390068,
0.057900503277778625,
0.05142031982541084,
-0.03557879850268364,
0.010655483230948448,
0.025293124839663506,
0.026062512770295143,
-0.05328894406557083,
-0.011734314262866974,
-0.042524345219135284,
0.02664327807724476,
-0.03951212763786316,
0.058338385075330734,
0.01111017819494009,
-0.005744137801229954,
0.010708292946219444,
0.006526860874146223,
-0.012744070962071419,
-0.020649706944823265,
0.016559207811951637,
-0.040244366973638535,
0.021184947341680527,
-0.01508351881057024,
-0.019044235348701477,
-0.010292471386492252,
0.008213549852371216,
0.03176819533109665,
0.011052549816668034,
0.01449601724743843,
-0.019101640209555626,
-0.02183677814900875,
-0.012864012271165848,
-0.03139922767877579,
-0.04764807969331741,
-0.007813296280801296,
-0.005693848244845867,
-0.02117355912923813,
0.028097040951251984,
-0.017621709033846855,
-0.005803849548101425,
0.01087665930390358,
0.02791786752641201,
0.0004298064159229398,
0.04937182739377022,
0.03098987229168415,
0.017740091308951378,
-0.0013479702174663544,
0.00975615531206131,
0.11764825880527496,
0.06966312974691391,
0.029176106676459312,
-0.03669494763016701,
-0.002354404889047146,
-0.0474071279168129,
0.00016919155314099044,
-0.010639003477990627,
-0.011046193540096283,
-0.003912529442459345,
-0.025437861680984497,
0.021654115989804268,
0.0033310656435787678,
-0.006089242175221443,
-0.004810173064470291,
0.04089898616075516,
-0.10047238320112228,
-0.030754027888178825,
0.026347342878580093,
0.005741437431424856,
0.00038522377144545317,
-0.02117232419550419,
-0.013002418912947178,
0.012876215390861034,
-0.03622806817293167,
-0.00877193920314312,
0.00551593815907836,
-0.06953565776348114,
0.013685926795005798,
0.010555500164628029,
-0.030760034918785095,
0.02691231109201908,
0.013787924312055111,
0.002556138439103961,
-0.04079004004597664,
-0.0009116721921600401,
0.018520798534154892,
-0.012145566754043102,
0.001891588093712926,
0.04509976506233215,
0.018816089257597923,
0.0037694135680794716,
0.013532930053770542,
0.015953755006194115,
-0.034618526697158813,
0.002276131184771657,
-0.02891593798995018,
0.01568102091550827,
0.008295097388327122,
0.03280283510684967,
-0.014789368957281113,
0.006950982380658388,
-0.044363681226968765,
-0.02019740641117096,
-0.01791108399629593,
-0.009336274117231369,
0.03187721595168114,
-0.005471952725201845,
-0.0496782585978508,
-0.04548770561814308,
-0.0236507561057806,
0.008665131404995918,
0.030704090371727943,
0.003090695245191455,
0.008304446004331112,
0.04872632026672363,
-0.021702894940972328,
0.01377105712890625,
-0.0330331027507782,
-0.03207322955131531,
0.0376480296254158,
-0.04056656360626221,
-0.042839258909225464,
-0.020667068660259247,
0.0005172746023163199,
-0.007555007003247738,
0.0013529635034501553,
0.024553468450903893,
0.002903362037613988,
-0.04211961850523949,
-0.01872701570391655,
0.01897609233856201,
-0.02944854460656643,
-0.023724770173430443,
-0.02535541169345379,
0.01289235521107912,
-0.005065807607024908,
0.0397537499666214,
-0.02991027757525444,
0.005769470240920782,
-0.009868369437754154,
0.039314839988946915,
0.009427248500287533,
0.01209163386374712,
-0.0405719056725502,
0.003529531182721257,
-0.043316829949617386,
0.02473238855600357,
0.028259973973035812,
-0.0005041847471147776,
0.024839108809828758,
0.0019838616717606783,
0.04112915322184563,
0.020889099687337875,
-0.03331552818417549,
-0.010987985879182816,
0.04667317122220993,
-0.0012526940554380417,
-0.015321386978030205,
0.060285840183496475,
0.013172752223908901,
-0.031399935483932495,
-0.0064556049183011055,
-0.025094827637076378,
0.014655615203082561,
0.011403917334973812,
0.06351269036531448,
-0.0011249243980273604,
0.027095435187220573,
-0.023968426510691643,
0.039357636123895645,
-0.02017463743686676,
-0.013414218090474606,
-0.07452128827571869,
0.05168447270989418,
0.030079802498221397,
-0.011105610989034176,
-0.04166121780872345,
0.022307466715574265,
0.011126772500574589,
-0.021214542910456657,
0.016550378873944283,
0.016084205359220505,
-0.012571661733090878,
-0.02028203196823597,
0.03524436429142952,
-0.03608500212430954,
0.06936284154653549,
-0.003237953642383218,
-0.02338160015642643,
0.045129526406526566,
-0.05263844504952431,
-0.03189991042017937,
0.015546668320894241,
-0.024126466363668442,
0.009617805480957031,
0.03681032359600067,
-0.011769269593060017,
-0.03007887862622738,
0.04224489629268646,
-0.029794037342071533,
0.005998572800308466,
0.017785942181944847,
0.01023833453655243,
-0.041197676211595535,
-0.019291624426841736,
0.005152036435902119,
-0.024522222578525543,
-0.005001014564186335,
-0.003488319693133235,
0.024043451994657516,
-0.021730249747633934,
-0.034070808440446854,
0.011384507641196251,
-0.01710444875061512,
-0.027473347261548042,
0.019427374005317688,
0.03289038687944412,
0.027808669954538345,
0.042386431246995926,
-0.04122857004404068,
0.011218810454010963,
-0.017995279282331467,
0.024902377277612686,
-0.08079278469085693,
-0.009044451639056206,
-0.028020620346069336,
-0.022470489144325256,
0.039122309535741806,
-0.02712339162826538,
0.031779926270246506,
0.04103710129857063,
-0.05145309492945671,
0.02455178089439869,
-0.018764566630125046,
0.025324761867523193,
-0.04900725930929184,
-0.009785576723515987,
-0.02966693416237831,
0.07857629656791687,
0.026742596179246902,
0.04020347073674202,
0.03294657915830612,
0.004427365027368069,
-0.027746528387069702,
-0.039285190403461456,
0.019722193479537964,
0.04427604004740715,
-0.031194452196359634,
-0.01366083137691021,
0.06498920917510986,
-0.0019215180072933435,
-0.052633676677942276,
0.036011952906847,
-0.01918150670826435,
-0.016797464340925217,
0.004098531790077686,
0.05462571233510971,
0.0060871439054608345,
0.01434357836842537,
0.03403891995549202,
0.005024568643420935,
-0.023256104439496994,
0.000876481703016907,
-0.012004239484667778,
0.018160318955779076,
-0.015612234361469746,
0.0018443629378452897,
0.018159059807658195,
-0.04432003200054169,
-0.07517495006322861,
0.012164660729467869,
-0.011493001133203506,
-0.03083750046789646,
-0.006227122154086828,
0.03216655179858208,
0.006400120444595814,
-0.05054811015725136,
0.0004981058882549405,
-0.022278428077697754,
-0.0031460917089134455,
0.03648804873228073,
-0.006070944480597973,
0.009203142486512661,
0.0017655134433880448,
0.011442850343883038,
-0.03722365200519562,
0.0032036970369517803,
0.02718772366642952,
-0.005431371740996838,
-0.05392078310251236,
0.008612050674855709,
0.0003468630602583289,
-0.013049362227320671,
-0.04400766268372536,
-0.030529020354151726,
-0.04821070283651352,
0.020907606929540634,
0.08397619426250458,
0.040943894535303116,
-0.0067235990427434444,
-0.023089181631803513,
-0.02663411758840084,
-0.07940202951431274,
0.013268609531223774,
-0.023428313434123993,
0.0008197169518098235,
-0.017293833196163177,
-0.016012517735362053,
0.006406312808394432,
0.016926439478993416,
0.024940526112914085,
-0.025000665336847305,
-0.038983460515737534,
0.013018811121582985,
0.010732394643127918,
0.0055683269165456295,
-0.02591809257864952,
-0.005524503067135811,
-0.024122683331370354,
-0.049353569746017456,
0.02271665818989277,
-0.017938800156116486,
-0.024253761395812035,
-0.0038784178905189037,
0.006080822553485632,
-0.027648158371448517,
0.0396759919822216,
-0.020211517810821533,
0.0007110504666343331,
0.03204599767923355,
0.016329651698470116,
-0.032577887177467346,
0.06935327500104904,
-0.022606464102864265,
0.033431656658649445,
0.030539166182279587,
-0.0222251508384943,
-0.05741645395755768,
0.025810454040765762,
-0.05326984077692032,
0.006118211429566145,
-0.022630544379353523,
-0.020694177597761154,
0.023863034322857857,
-0.011093627661466599,
0.003961732145398855,
0.0635220855474472,
-0.051965054124593735,
-0.010467760264873505,
0.02635149098932743,
0.07660416513681412,
0.04585340619087219,
0.014909655787050724,
0.026489708572626114,
0.00009965979552362114,
-0.02958548814058304,
0.011838934384286404,
0.07663574814796448,
0.05664714053273201,
0.0052958037704229355,
0.012437363155186176,
0.0015551612013950944,
0.004918437451124191,
0.028996065258979797,
0.01169918105006218,
0.013995092362165451,
-0.028590615838766098,
-0.057614441961050034,
-0.024287747219204903,
0.007495183497667313,
-0.0054346295073628426,
0.009149407036602497,
0.004739067051559687,
0.06242561340332031,
-0.02683158777654171,
0.0022251750342547894,
0.020369097590446472,
0.011464981362223625,
-0.023386534303426743,
-0.024532508105039597,
-0.004971969407051802,
0.015886550769209862,
-0.01215154118835926,
0.014008277095854282,
-0.020617535337805748,
0.03232070058584213,
-0.004153176676481962,
-0.013977459631860256,
-0.00941308680921793,
0.02208748273551464,
0.011186748743057251,
-0.016198700293898582,
0.0003238117496948689,
-0.01190140750259161,
-0.0180610790848732,
0.011478642001748085,
0.04584667086601257,
-0.011031994596123695,
0.028177160769701004,
-0.02929661236703396,
-0.024068351835012436,
0.01919315755367279,
-0.04248124361038208,
-0.013043232262134552,
-0.036321960389614105,
0.043308794498443604,
-0.044476013630628586,
-0.002535411389544606
] |
<p>The short story is, that I have to calculate some transport coefficients, but using the the MB distribution as my distribution function.
What I currently need to solve is:</p>
<p>${{\mathcal{L}}^{\,\left( \alpha \right)}}=\frac{1}{2}\frac{{\bar{N}}}{V}{{\left( \frac{{{h}^{2}}}{2\pi m{{k}_{B}}T} \right)}^{3/2}}\frac{1}{{{k}_{B}}T}\int{{{e}^{-\varepsilon /{{k}_{B}}T}}}{{\left( \varepsilon -\mu \right)}^{\alpha }}{{\varepsilon }^{3/2}}d\varepsilon$</p>
<p>As it shows, it's not that the integral is hard, it's more what I use for $\mu$ that is my concern. According to my teacher I need to use:</p>
<p>${{e}^{-\mu /{{k}_{B}}T}}=\frac{1}{2}\frac{V}{{\bar{N}}}{{\left( \frac{2\pi m{{k}_{B}}T}{{{h}^{2}}} \right)}^{3/2}}$</p>
<p>But I can't see how I can use this instead of $\mu$ without solving for $\mu$. And then I would just end up with a ln() term, which I really can't imagine doing anything good for me. But maybe I'm mistaken ?</p>
<p>Any hint would be appreciated :)</p>
| 9,555 |
[
-0.001076549757272005,
-0.011507643386721611,
0.004306693561375141,
-0.0045947302132844925,
0.04555627331137657,
0.018972134217619896,
-0.02284744381904602,
-0.00810268148779869,
0.021427098661661148,
-0.031446151435375214,
0.022208817303180695,
0.046574875712394714,
0.07962410151958466,
0.032262686640024185,
0.013079507276415825,
0.00247897207736969,
-0.002661819104105234,
-0.01607559248805046,
-0.016428496688604355,
-0.047086089849472046,
0.002272011712193489,
0.02608930878341198,
0.023302258923649788,
-0.010379492305219173,
-0.0400182381272316,
0.050691526383161545,
0.0005118112312629819,
0.002724369987845421,
0.0024208545219153166,
0.028720475733280182,
-0.03560653701424599,
-0.015510780736804008,
0.03233735263347626,
0.0019716781098395586,
-0.00895153172314167,
0.06352580338716507,
-0.03677448257803917,
-0.04945936053991318,
-0.02943485789000988,
0.027996188029646873,
-0.05156366899609566,
-0.010167589411139488,
0.02124500274658203,
0.016344916075468063,
-0.01028217002749443,
0.006251918617635965,
0.033551499247550964,
-0.024843141436576843,
0.005953480955213308,
-0.06051109731197357,
0.05210648477077484,
0.03734481334686279,
0.04791984334588051,
0.03262365236878395,
-0.024946454912424088,
-0.06398729234933853,
0.03676895797252655,
0.08596286922693253,
0.025974536314606667,
-0.023307139053940773,
0.025452053174376488,
-0.02261163294315338,
-0.024138376116752625,
-0.009753047488629818,
0.0073043121956288815,
-0.0022708652541041374,
0.03497607260942459,
-0.0009195402963086963,
0.05302504077553749,
-0.001143969246186316,
0.04363861680030823,
-0.009692246094346046,
0.03306987136602402,
-0.016274932771921158,
0.03129968047142029,
0.00944934319704771,
0.01236806157976389,
-0.021120348945260048,
0.02840997837483883,
0.029480790719389915,
-0.021992625668644905,
0.038862504065036774,
0.04128681868314743,
0.019142499193549156,
-0.0021462005097419024,
-0.022641293704509735,
0.08514643460512161,
-0.006403300445526838,
0.009588123299181461,
0.00021529122022911906,
-0.06619759649038315,
0.05151401087641716,
0.04137550666928291,
0.004893144126981497,
-0.046615585684776306,
0.040508933365345,
-0.00520991301164031,
0.036845944821834564,
0.016507858410477638,
-0.027413243427872658,
-0.024531876668334007,
-0.009008887223899364,
0.04653703048825264,
0.08290593326091766,
0.018285954371094704,
0.008487509563565254,
-0.02536170184612274,
-0.02674877643585205,
-0.02428898587822914,
-0.03617193177342415,
-0.04994700476527214,
0.035708166658878326,
-0.023344872519373894,
0.01347433589398861,
0.001208815141580999,
-0.02937713824212551,
-0.014850794337689877,
-0.0069986749440431595,
0.03583511337637901,
0.05560014769434929,
0.023246312513947487,
0.009168284013867378,
0.01825382374227047,
-0.025703871622681618,
-0.09350559115409851,
0.0388057604432106,
0.03493297100067139,
0.022798137739300728,
-0.03350101411342621,
0.047426965087652206,
0.021057656034827232,
0.010457058437168598,
-0.0004232150095049292,
-0.0162216704338789,
0.030265415087342262,
-0.058733247220516205,
-0.06050846353173256,
-0.08355813473463058,
0.04020416736602783,
-0.006257433444261551,
-0.02121049351990223,
-0.045696619898080826,
-0.034995440393686295,
0.046426303684711456,
0.05032957345247269,
0.014198740012943745,
0.014186350628733635,
-0.009267611429095268,
0.02617373690009117,
0.008864857256412506,
-0.049957968294620514,
-0.04113493487238884,
-0.006372788920998573,
0.016049981117248535,
0.009253141470253468,
-0.07294737547636032,
0.03983789309859276,
0.01679607853293419,
-0.002609266433864832,
-0.013199817389249802,
0.09036456048488617,
0.006593044847249985,
-0.019088217988610268,
0.0048274206928908825,
0.0009746357100084424,
-0.04336283355951309,
0.06430289149284363,
0.017649760469794273,
0.018043821677565575,
-0.005326511804014444,
0.06643888354301453,
0.021898431703448296,
-0.04958360269665718,
0.020185405388474464,
0.038818541914224625,
-0.03504865616559982,
0.019796786829829216,
-0.01396933849900961,
0.030143560841679573,
0.0480944998562336,
-0.005824373569339514,
-0.025068538263440132,
-0.03821096569299698,
-0.012785013765096664,
0.01446352805942297,
0.020619619637727737,
0.03356573358178139,
0.007758220657706261,
0.03253980353474617,
-0.04556424170732498,
-0.04666728526353836,
-0.042624812573194504,
0.024675002321600914,
0.015893280506134033,
-0.037093568593263626,
0.017598243430256844,
-0.04640737920999527,
-0.0028861616738140583,
0.02948945201933384,
-0.03444940969347954,
0.026331784203648567,
-0.03800604119896889,
0.008397219702601433,
-0.022361645475029945,
0.0015536423306912184,
0.04030238837003708,
0.015625832602381706,
-0.01563829742372036,
0.03055635280907154,
-0.01939570903778076,
-0.011542079038918018,
-0.019113676622509956,
-0.04062242433428764,
0.041791293770074844,
-0.010082314722239971,
-0.023453211411833763,
-0.0017802042420953512,
-0.01729200780391693,
0.013737481087446213,
0.0004208491591271013,
-0.05484691634774208,
0.05666593834757805,
0.05795452371239662,
0.03946204110980034,
-0.009529385715723038,
0.02287564054131508,
0.00799654982984066,
0.012529999949038029,
-0.023057952523231506,
-0.029993019998073578,
-0.041962165385484695,
-0.0051119462586939335,
0.039411094039678574,
-0.014992905780673027,
-0.032243240624666214,
0.011048187501728535,
0.0021472435910254717,
-0.01940855011343956,
0.06633514165878296,
-0.00585705041885376,
0.01165272481739521,
0.0038120788522064686,
0.026248043403029442,
-0.011116879992187023,
-0.018954897299408913,
0.010828303173184395,
0.0374479703605175,
0.0019817904103547335,
0.022245978936553,
-0.035411082208156586,
-0.03987612575292587,
0.021495824679732323,
0.00459884712472558,
-0.005554397124797106,
-0.01481716614216566,
0.010855818167328835,
0.05430929362773895,
-0.0488068051636219,
0.05167200043797493,
0.0884707123041153,
-0.015734268352389336,
0.009424920193850994,
0.0023342440836131573,
-0.035443637520074844,
-0.00581735372543335,
0.0335703119635582,
-0.00010320362343918532,
-0.029778696596622467,
0.018078535795211792,
-0.016327839344739914,
0.006499629933387041,
-0.008616577833890915,
-0.0068465848453342915,
0.011030346155166626,
0.010692056268453598,
0.020820384845137596,
0.0037674589548259974,
0.02257372811436653,
-0.02371121384203434,
-0.009162700735032558,
0.031726960092782974,
0.034867387264966965,
0.024937206879258156,
0.0011653699912130833,
-0.04345706105232239,
-0.003499062033370137,
-0.007420657202601433,
-0.014615505933761597,
0.038641899824142456,
0.014029153622686863,
-0.04889313876628876,
0.012482255697250366,
-0.017221525311470032,
-0.07880166918039322,
-0.011188740842044353,
0.017937973141670227,
-0.027127670124173164,
-0.011333339847624302,
0.01832759566605091,
0.02704734168946743,
0.02835429087281227,
-0.034313641488552094,
0.018606388941407204,
-0.05384558439254761,
-0.04861174523830414,
-0.04089363291859627,
-0.016251809895038605,
-0.0019050026312470436,
-0.0039383950643241405,
0.031609274446964264,
0.018818844109773636,
-0.0036929070483893156,
-0.04666001349687576,
-0.029764428734779358,
-0.007617393974214792,
0.03075365349650383,
0.016673710197210312,
0.008177557960152626,
0.0007814124110154808,
-0.03410112112760544,
0.06734856218099594,
0.043970588594675064,
-0.014370624907314777,
0.010223634541034698,
-0.02615422010421753,
-0.029337527230381966,
-0.052221398800611496,
0.030529513955116272,
0.02822962962090969,
-0.017221599817276,
0.03200441971421242,
-0.025171546265482903,
0.03754834458231926,
0.049792323261499405,
0.0010062387445941567,
-0.02222581021487713,
0.04869590327143669,
-0.021164005622267723,
0.01656321808695793,
0.05530571937561035,
-0.005060641095042229,
-0.03085981495678425,
0.0321802943944931,
-0.0205728467553854,
0.0009930032538250089,
0.046550143510103226,
-0.03793779015541077,
0.03820991516113281,
0.0015131139662116766,
0.01438132394105196,
-0.06492532044649124,
0.013192031532526016,
-0.01005513221025467,
-0.025271929800510406,
-0.004771312698721886,
0.014193641021847725,
0.014136197045445442,
-0.003918806090950966,
0.017346587032079697,
0.058033183217048645,
0.06546945124864578,
0.007696093525737524,
-0.05062834918498993,
-0.0016855299472808838,
-0.0031928708776831627,
-0.008735237643122673,
-0.018192226067185402,
-0.005711963865906,
0.0169842466711998,
0.05571216717362404,
-0.007601416669785976,
-0.041219014674425125,
-0.048761870712041855,
-0.0389828197658062,
-0.054707370698451996,
-0.009899900294840336,
-0.03909013792872429,
0.06019822135567665,
0.002912945579737425,
0.029101723805069923,
0.011102299205958843,
0.002027320908382535,
0.023678826168179512,
0.03391332924365997,
-0.07976813614368439,
0.050604481250047684,
0.03535272926092148,
-0.04369211941957474,
0.0006109036039561033,
-0.015167014673352242,
0.03195912018418312,
-0.0422588475048542,
-0.025221969932317734,
0.020642034709453583,
0.006334873382002115,
-0.023167286068201065,
0.011292441748082638,
-0.03118235059082508,
-0.01668519899249077,
-0.013976097106933594,
0.015190273523330688,
0.03367535024881363,
-0.0013474916340783238,
-0.002488569123670459,
0.029874255880713463,
-0.032238926738500595,
-0.019025277346372604,
-0.04702128469944,
0.00600205035880208,
-0.0034638741053640842,
0.02994646318256855,
0.00484310369938612,
0.0012405297020450234,
-0.03677684813737869,
0.018660414963960648,
0.038491539657115936,
0.03343101590871811,
0.030491042882204056,
0.005286036990582943,
-0.028378847986459732,
-0.03439603000879288,
0.005734215956181288,
0.009214460849761963,
0.024021677672863007,
0.024730775505304337,
0.021504394710063934,
0.028173400089144707,
-0.01467569638043642,
-0.018385333940386772,
-0.0020296722650527954,
0.02301250398159027,
-0.0032712051179260015,
-0.0002362249797442928,
-0.04973451793193817,
0.009714380837976933,
0.021293848752975464,
-0.011432317085564137,
0.012051926925778389,
-0.008042664267122746,
-0.030114224180579185,
-0.00940615963190794,
0.02640470303595066,
0.05253313109278679,
0.031006675213575363,
0.0006997200543992221,
0.03636986389756203,
0.0012529421364888549,
0.03101605921983719,
-0.014832193031907082,
0.012386202812194824,
0.04163804277777672,
0.024187341332435608,
0.026003915816545486,
0.004341119900345802,
-0.08326573669910431,
-0.01804349012672901,
0.024605387821793556,
0.02387298457324505,
-0.030230648815631866,
-0.016788959503173828,
-0.07845566421747208,
-0.0186795461922884,
0.05120610073208809,
-0.019402023404836655,
0.01593799889087677,
-0.011981590650975704,
0.00904513243585825,
0.027398057281970978,
-0.044803984463214874,
-0.06826284527778625,
0.01949533447623253,
-0.019853945821523666,
-0.001050863298587501,
-0.058073434978723526,
0.014925392344594002,
0.007573488634079695,
0.0361558236181736,
0.04576418548822403,
0.05354207009077072,
-0.018808472901582718,
-0.04913904145359993,
0.011586823500692844,
0.014820249751210213,
-0.029141169041395187,
-0.06927615404129028,
-0.025060035288333893,
-0.005479023326188326,
0.021216971799731255,
-0.009815691038966179,
-0.03306620568037033,
-0.04589522257447243,
0.06372565031051636,
0.014201660640537739,
-0.006361315026879311,
-0.02022654004395008,
-0.028147565200924873,
0.05883076414465904,
0.020399220287799835,
0.014630785211920738,
0.07861331850290298,
0.06241768226027489,
0.03917350992560387,
0.03321843966841698,
-0.05152392387390137,
0.017959078773856163,
-0.015340995974838734,
-0.005512254778295755,
-0.029751228168606758,
-0.03368239849805832,
0.0009844793239608407,
0.055722925812006,
-0.006257851608097553,
0.0258469320833683,
-0.0004939613863825798,
-0.02027292735874653,
0.028478514403104782,
0.011873094365000725,
-0.014935779385268688,
-0.015840010717511177,
0.013374706730246544,
0.0218881294131279,
0.041664205491542816,
-0.028936903923749924,
0.012975072488188744,
0.018135305494070053,
0.011601211503148079,
0.02554601989686489,
-0.03888211399316788,
-0.001950971782207489,
-0.013423954136669636,
-0.017489727586507797,
0.00577634247019887,
-0.023598751053214073,
0.039411503821611404,
-0.005766661372035742,
0.0007732496596872807,
0.02557583712041378,
-0.03502881899476051,
-0.025854716077446938,
-0.009918595664203167,
-0.02701241336762905,
0.014428173191845417,
-0.03627202287316322,
-0.0015763496048748493,
-0.00011765867384383455,
0.015378162264823914,
-0.087978295981884,
-0.02126813866198063,
0.01065141148865223,
0.0043210056610405445,
0.001900085131637752,
-0.03607786074280739,
-0.03168835863471031,
0.022574881091713905,
-0.05478719621896744,
0.04026741907000542,
0.07815942168235779,
0.013562665320932865,
-0.006785016972571611,
-0.023862864822149277,
0.04080760478973389,
0.06243332475423813,
0.01645675115287304,
-0.010874774307012558,
0.038452401757240295,
-0.023207489401102066,
-0.051254115998744965,
0.0057966457679867744,
0.041160549968481064,
0.00018754109623841941,
-0.008706311695277691,
-0.005299597978591919,
0.006291745696216822,
0.06001884490251541,
-0.0028359033167362213,
-0.035682015120983124,
0.04432719200849533,
0.035747360438108444,
-0.00881736259907484,
-0.0032246671617031097,
0.010520798154175282,
0.019843323156237602,
0.038503970950841904,
-0.048635467886924744,
0.01693936623632908,
-0.05413975194096565,
0.019311117008328438,
0.03922346234321594,
-0.010682355612516403,
0.0026299040764570236,
-0.01789330132305622,
0.05852604657411575,
-0.01816650480031967,
0.018825531005859375,
0.016217375174164772,
0.01537339761853218,
0.03394559770822525,
-0.03201233968138695,
0.006590466480702162,
0.011140452697873116,
0.01967192441225052,
-0.03517400845885277,
-0.017717687413096428,
-0.061780259013175964,
-0.010356517508625984,
0.04699110612273216,
-0.014883782714605331,
0.0366436243057251,
-0.018255669623613358,
0.014255101792514324,
0.01718459092080593,
-0.012832419015467167,
-0.02019825018942356,
0.018606513738632202,
-0.022266628220677376,
0.024242740124464035,
-0.03073839843273163,
-0.016260849311947823,
0.0014931889018043876,
0.02285948023200035,
-0.0098988963291049,
0.007171380799263716,
0.014468097127974033,
0.025029005482792854,
0.009651528671383858,
0.001151000615209341,
-0.026219412684440613,
0.054150715470314026,
-0.0319814570248127,
0.031330741941928864,
-0.02797451615333557,
-0.03865371271967888,
0.06107068434357643,
0.03279738500714302,
-0.012657023966312408,
-0.020486023277044296,
-0.006765461061149836,
-0.026271138340234756,
0.01943584717810154,
0.038836218416690826,
-0.04466542229056358,
0.03899841383099556,
-0.01715877838432789,
0.063136026263237,
-0.01406015269458294,
0.011949697509407997,
-0.02220018208026886,
-0.06892964988946915,
0.01642690971493721,
-0.04270428419113159,
-0.052030984312295914,
0.0379093699157238,
-0.00199745106510818,
-0.01524188183248043,
0.044185783714056015,
-0.0279025137424469,
0.03280515596270561,
0.0040661548264324665,
0.001214396208524704,
0.004925668239593506,
0.10484617203474045,
-0.014335962943732738,
0.00754761416465044,
-0.02863343060016632,
0.00970535259693861,
0.10724329203367233,
0.05039699003100395,
0.03756040334701538,
-0.0726400837302208,
-0.013663616962730885,
-0.03842555359005928,
0.0213067214936018,
-0.04626813530921936,
0.0031650697346776724,
0.0033799775410443544,
-0.021985793486237526,
-0.028254827484488487,
0.05276939272880554,
-0.003660547314211726,
0.0064795957878232,
0.019842281937599182,
-0.004417121410369873,
-0.038482602685689926,
0.028728628531098366,
0.002419029828161001,
-0.008338207378983498,
-0.003241932252421975,
-0.044368378818035126,
0.03296239674091339,
0.003303817007690668,
0.0037921492476016283,
-0.040764689445495605,
-0.03037351556122303,
0.03833093121647835,
-0.022499218583106995,
-0.06703715771436691,
0.004882001783698797,
0.020655406638979912,
-0.017705285921692848,
0.06590362638235092,
-0.010900110937654972,
0.03281189128756523,
-0.006094668060541153,
0.06054777279496193,
0.025906328111886978,
-0.004316821228712797,
0.020831020548939705,
0.028287529945373535,
0.012797301635146141,
-0.022811632603406906,
-0.026056934148073196,
-0.023960668593645096,
0.06963353604078293,
-0.019374186173081398,
-0.006766151171177626,
0.004481120500713587,
-0.018908560276031494,
-0.004013367462903261,
-0.039000824093818665,
0.009613335132598877,
-0.03014468401670456,
0.0009220002102665603,
-0.033607471734285355,
0.009651022031903267,
-0.041678253561258316,
0.010589315555989742,
0.01746964082121849,
0.003764081746339798,
0.0033011275809258223,
-0.0054270122200250626,
0.000540599983651191,
0.017476893961429596,
0.05062655732035637,
-0.023129651322960854,
-0.013430510647594929,
-0.032919082790613174,
0.008082461543381214,
-0.03982606902718544,
0.0007119086221791804,
0.003997015301138163,
-0.002771994797512889,
0.034868691116571426,
-0.036100342869758606,
0.00780594814568758,
-0.032901689410209656,
-0.04926960542798042,
0.0011433784384280443,
0.00813746266067028,
-0.0006983905914239585,
0.0020502544939517975,
-0.028640057891607285,
-0.021047204732894897,
0.061577003449201584,
0.017348680645227432,
-0.02459125779569149,
0.016466371715068817,
0.02093108557164669,
0.009170991368591785,
-0.07283592224121094,
-0.06313581764698029,
0.007708709686994553,
-0.030857792124152184,
0.012996893376111984,
-0.015478251501917839,
0.010951973497867584,
-0.031723085790872574,
0.04035084694623947,
-0.02478007785975933,
0.02835146337747574,
0.01097011100500822,
0.005308796186000109,
-0.029956303536891937,
-0.02233911119401455,
-0.012565999291837215,
0.028670862317085266,
0.026970015838742256,
-0.021050795912742615,
0.007493972312659025,
-0.037116095423698425,
0.0058628772385418415,
-0.015175065957009792,
0.0013286133762449026,
-0.049640167504549026,
-0.011342445388436317,
-0.0030117318965494633,
0.015122007578611374,
-0.01733262650668621,
0.06231465935707092,
-0.003485743422061205,
-0.011561639606952667,
-0.050881531089544296,
0.00342725426889956,
-0.025251980870962143,
0.04091711714863777,
-0.029288284480571747,
0.013705522753298283,
0.010607493110001087,
0.03518575429916382,
0.01668953150510788,
-0.02474473975598812,
-0.03348718211054802,
0.008140906691551208,
0.0579175166785717,
-0.007785202004015446,
-0.009029760025441647,
0.04756884649395943,
-0.005872390232980251,
-0.03229959309101105,
0.011912570334970951,
0.039915453642606735,
0.019419142976403236,
0.025589333847165108,
-0.010005796328186989,
-0.02363550290465355,
0.06537740677595139,
-0.018281202763319016,
-0.0002458984963595867,
-0.02067561261355877,
-0.05490335077047348,
0.0024700339417904615,
-0.02903810702264309,
-0.0057504731230437756,
0.01946134679019451,
0.036676075309515,
0.04046927019953728,
-0.0007730526267550886,
-0.03270881623029709,
0.03746279701590538,
-0.006693786475807428,
0.011655815877020359,
-0.0004860965709667653,
-0.004164137877523899,
-0.009585123509168625,
-0.006328541785478592,
0.09231949597597122,
-0.023973248898983,
0.017744529992341995,
-0.021420210599899292,
0.005574377719312906,
-0.06979681551456451,
-0.02317262999713421,
0.0038659304846078157,
-0.018092090263962746,
0.07477577030658722,
-0.08330809324979782,
0.0015801667468622327,
0.019080275669693947,
-0.05319305509328842,
-0.010192391462624073,
-0.03509660065174103,
-0.011927538551390171,
-0.03717943653464317,
-0.021365514025092125,
-0.019678683951497078,
0.024706555530428886,
0.03188508376479149,
0.013389921747148037,
0.015506070107221603,
0.036250315606594086,
0.028678875416517258,
-0.047070104628801346,
0.005103436764329672,
0.0035422504879534245,
0.01585862599313259,
-0.03324098140001297,
0.05981997773051262,
-0.006247645244002342,
-0.019507022574543953,
0.009671276435256004,
-0.045313380658626556,
0.002381335012614727,
-0.0221476461738348,
0.026522129774093628,
0.0021400228142738342,
0.05314482003450394,
0.04240342974662781,
0.016830559819936752,
0.03976697102189064,
-0.015648778527975082,
0.047707926481962204,
-0.027326276525855064,
-0.02989068627357483,
0.007261753547936678,
-0.00013937344192527235,
-0.010665854439139366,
-0.02510092407464981,
0.01803082786500454,
-0.013162748888134956,
-0.04012767970561981,
0.00601887796074152,
-0.01849050633609295,
0.015687385573983192,
-0.023992395028471947,
0.03026057779788971,
-0.06592485308647156,
-0.0029757528100162745,
0.03633797541260719,
0.0022812422830611467,
-0.0105201480910182,
-0.03371614217758179,
-0.035628776997327805,
-0.03002472035586834,
0.01777331531047821,
0.01168539933860302,
-0.040477145463228226,
-0.04088461399078369,
-0.03834410756826401,
-0.01845194213092327,
0.027217896655201912,
-0.03724765405058861,
-0.04311486706137657,
-0.047258585691452026,
0.02241172455251217,
-0.0007304103928618133,
0.03464076295495033,
0.005762992426753044,
-0.020517364144325256,
-0.003843731712549925,
-0.045209623873233795,
0.006805723533034325,
-0.0032695613335818052,
-0.03577194735407829,
-0.01335122250020504,
-0.042729463428258896,
-0.009255819022655487,
0.035751357674598694,
0.06639657914638519,
0.023485222831368446,
-0.008170557208359241,
0.021660344675183296,
-0.01859060488641262,
0.016250301152467728,
-0.07673536241054535,
0.013569221831858158,
0.022323576733469963,
-0.02860672026872635,
0.0059049795381724834,
0.04725360870361328,
0.00007300028664758429,
0.019680539146065712,
0.013131204061210155,
0.018163273110985756,
-0.001891233492642641,
0.005394626874476671,
0.007897878997027874,
0.0036536792758852243,
-0.024332135915756226,
-0.01839432306587696,
0.026330944150686264,
0.0023805382661521435,
0.0077194892801344395,
0.020108550786972046,
0.003180835396051407,
-0.04848781228065491,
0.025103311985731125,
0.002801695140078664,
-0.027517002075910568,
-0.005589979700744152,
0.0023309967946261168,
0.0018448083428665996,
-0.049906130880117416,
-0.004086352419108152,
-0.0035411969292908907,
-0.0428142175078392,
-0.02729005739092827,
0.012196514755487442,
0.019549379125237465,
0.06056569144129753,
0.024417828768491745,
0.01994231529533863,
0.015074126422405243,
0.0069317808374762535,
0.006493899505585432,
0.0196362417191267,
0.021624870598316193,
-0.04704150930047035,
0.020872902125120163,
0.0344715341925621,
-0.04858668893575668,
-0.033831365406513214,
0.0166276004165411,
-0.009665035642683506,
-0.023694686591625214,
-0.02360335923731327,
0.004365493543446064,
-0.003720734966918826,
0.024593647569417953,
-0.008593819104135036,
-0.0012363488785922527,
0.07101862877607346,
-0.03032109886407852,
0.02568225748836994,
0.004173476714640856,
-0.003965129144489765,
0.0015403705183416605,
0.06390143930912018,
0.01103122252970934,
0.005213927011936903,
0.030381454154849052,
-0.025393540039658546,
-0.05177987739443779,
-0.010730762034654617,
0.020417142659425735,
-0.04479359835386276,
-0.023845253512263298,
-0.013787662610411644,
-0.031164975836873055,
-0.019171347841620445,
-0.023925209417939186,
0.0025058011524379253,
-0.04696251079440117,
0.00513681722804904,
0.04545045271515846,
-0.0014324828516691923,
-0.010588479228317738,
-0.01412722747772932,
-0.011426846496760845,
0.06743883341550827,
-0.041823916137218475,
0.0010447578970342875,
-0.028422830626368523,
0.013044322840869427,
0.008768687024712563,
0.00188956328202039
] |
<p>I am trying to reproduce a calculation by <a href="http://dx.doi.org/10.1080/00218469508014354" rel="nofollow">Carre et al. (1995)</a> in which they calculate the shape of a droplet on an incline.</p>
<p>My issue is in the derivation of the potential energy (essentially the center of mass) of the droplet. The droplet is defined in the coordinate system as shown below, with the droplet base being circular. The function for $z$ is known, but not important for now.</p>
<blockquote>
<p><img src="http://i.stack.imgur.com/18JOI.png" alt="coordinate system for droplet on an incline"></p>
</blockquote>
<p>The potential energy is defined with respect to the origin of the coordinate system. </p>
<p>The function given in the paper (in Eq. 5) is
$$E_p=\int_{-\pi}^{\pi}\int_0^{r_0} \rho g z r \left(\frac{z}{2}\cos\alpha-r\sin\alpha\cos\phi\right) dr\,d\phi$$</p>
<p>I cannot figure out how they get to this. I understand that there should be a $\cos\alpha$ in there due to the inclination. Moreover, I would say the potential energy should be $$E_p=\int_{-\pi}^{\pi}\int_0^{r_0}\int \rho g z dz\,rdr\,d\phi $$ and since I am going to apply the equation in an euler-lagrange like scheme I only need to integrate the $z$ component. However, I am having some doubts here, because the height of the center of mass above the origin would be $h=z \cos\alpha$.</p>
<p>Apart from those 'vague' statements above I can't get to the answer. Could someone please explain (i) whether my equation for the potential energy is correct (or whether I need something in terms of $h$?) and (ii) how I could go about doing the integration.</p>
| 9,556 |
[
-0.018415268510580063,
-0.02107677422463894,
0.006288270931690931,
0.0036015023943036795,
0.028570104390382767,
-0.016575433313846588,
-0.052704617381095886,
-0.04112968593835831,
-0.016509052366018295,
-0.029638081789016724,
0.012982746586203575,
0.03561369702219963,
0.046137526631355286,
0.03911846503615379,
0.04455949366092682,
0.014975011348724365,
-0.012612140737473965,
0.018675005063414574,
0.007722975220531225,
-0.01128324307501316,
-0.012941707856953144,
-0.00748083833605051,
-0.003358018584549427,
-0.010280397720634937,
0.009598435834050179,
-0.0018358464585617185,
0.021362638100981712,
-0.035506006330251694,
-0.017013993114233017,
0.035472046583890915,
-0.03273741155862808,
-0.020776769146323204,
0.0006558591267094016,
0.01854422129690647,
-0.005021767690777779,
0.018226258456707,
-0.02136676199734211,
-0.012695087119936943,
-0.05471652001142502,
0.0538882315158844,
-0.03204503655433655,
-0.004151859786361456,
-0.012271114625036716,
0.0571306049823761,
-0.058752115815877914,
0.010788987390697002,
0.004946214612573385,
0.005332034081220627,
0.06318271160125732,
-0.07007725536823273,
0.0193443913012743,
0.0008869839948602021,
0.006432432681322098,
0.023140693083405495,
-0.00208763824775815,
-0.029150603339076042,
0.054950375109910965,
0.045357245951890945,
-0.014661455526947975,
-0.04605118930339813,
-0.037848614156246185,
-0.020755385980010033,
-0.04496089741587639,
-0.04375509172677994,
0.004695874638855457,
-0.026755092665553093,
0.041846442967653275,
-0.016441544517874718,
0.000020911600586259738,
0.012987961061298847,
0.022089794278144836,
-0.002592136152088642,
-0.007934648543596268,
-0.03839828446507454,
0.03340425714850426,
-0.020561521872878075,
0.0023475755006074905,
0.0016969592543318868,
-0.004216267727315426,
0.020002514123916626,
0.022490119561553,
0.025502512231469154,
0.05966835096478462,
0.04042282700538635,
-0.01795705407857895,
0.00021047808695584536,
0.08004117012023926,
0.028503065928816795,
0.02181890793144703,
0.03255043551325798,
-0.01785624958574772,
0.033467840403318405,
0.014388488605618477,
-0.0067092678509652615,
0.01954098977148533,
0.011982410214841366,
0.009837417863309383,
0.03172370046377182,
-0.026915645226836205,
-0.03840486705303192,
-0.004279259592294693,
0.0015871917130425572,
-0.012359101325273514,
0.11123432219028473,
0.029136518016457558,
-0.012405618093907833,
-0.02956989035010338,
-0.015454635955393314,
-0.03362594172358513,
-0.06503554433584213,
-0.038365401327610016,
0.0405990332365036,
-0.03410922363400459,
-0.03146538883447647,
-0.014570389874279499,
0.023744897916913033,
-0.010819069109857082,
-0.01678253710269928,
0.05449961870908737,
-0.020319968461990356,
0.032724570482969284,
-0.0008658907609060407,
0.017300289124250412,
-0.04694950953125954,
-0.06344013661146164,
0.008760911412537098,
0.024939624592661858,
-0.002794075757265091,
-0.04821023717522621,
-0.00026368742692284286,
0.01842215470969677,
0.030591147020459175,
-0.0007123462273739278,
0.021688373759388924,
-0.0013867736561223865,
-0.017118848860263824,
-0.04201100021600723,
-0.017654050141572952,
0.03044588305056095,
-0.000558973231818527,
-0.015838623046875,
-0.04569064453244209,
-0.020972613245248795,
0.04262204095721245,
0.06572782248258591,
-0.00120124826207757,
0.016636718064546585,
0.02780950255692005,
0.05607352405786514,
-0.013904762454330921,
0.025148602202534676,
-0.013743754476308823,
-0.01647300459444523,
-0.02738022431731224,
-0.038454074412584305,
-0.05239154025912285,
0.04399287700653076,
0.005609846208244562,
-0.008126987144351006,
-0.03919333592057228,
0.036086536943912506,
-0.00923179928213358,
0.019150393083691597,
-0.008584324270486832,
0.007006112486124039,
-0.03872852399945259,
0.054689258337020874,
0.009218303486704826,
0.011356831528246403,
0.037512607872486115,
-0.01536570955067873,
0.036316946148872375,
-0.04247504472732544,
0.018383625894784927,
0.07137390226125717,
-0.02796744555234909,
-0.016013603657484055,
-0.04540831968188286,
0.021537233144044876,
0.013362111523747444,
-0.03566870838403702,
-0.05736599117517471,
0.003384097246453166,
-0.00415333267301321,
-0.03186196833848953,
0.04610953480005264,
0.0017282611224800348,
-0.046668410301208496,
-0.016114141792058945,
-0.022716134786605835,
-0.011288892477750778,
-0.034981463104486465,
0.040244054049253464,
0.0018980385502800345,
0.005570443347096443,
0.04939143732190132,
0.01320644561201334,
0.02630593627691269,
-0.033458516001701355,
-0.021336102858185768,
0.013234621845185757,
0.008052929304540157,
0.026996908709406853,
0.007384553551673889,
0.03842988237738609,
0.04196758195757866,
0.005169771611690521,
0.018313251435756683,
0.008146610110998154,
0.019613994285464287,
0.006746493745595217,
-0.041880052536726,
-0.012775073759257793,
0.03482281416654587,
0.0077929748222231865,
0.032908953726291656,
0.01697554439306259,
0.026163557544350624,
0.018933091312646866,
0.015434026718139648,
-0.050045013427734375,
0.035170409828424454,
0.0657794401049614,
0.03899351879954338,
0.015021600760519505,
0.025286687538027763,
0.00808610301464796,
0.045695044100284576,
0.022151818498969078,
-0.02856503427028656,
-0.01219104416668415,
-0.011886968277394772,
0.06436002999544144,
0.030265795066952705,
-0.04431045800447464,
-0.03307504206895828,
0.038314804434776306,
0.039021074771881104,
0.023146500810980797,
0.026949625462293625,
0.01093987561762333,
-0.04854629188776016,
0.0438900850713253,
0.041628364473581314,
-0.024672958999872208,
0.02254660241305828,
0.016376234591007233,
-0.02768428809940815,
0.02451264299452305,
-0.018804851919412613,
-0.04458475485444069,
0.029274310916662216,
0.004702656529843807,
0.01848798617720604,
-0.006617295555770397,
0.034501101821660995,
0.04018817096948624,
-0.043917763978242874,
0.021648775786161423,
0.0580301359295845,
-0.014396061189472675,
-0.013232888653874397,
-0.035368502140045166,
-0.027852362021803856,
0.03578861057758331,
0.053306300193071365,
-0.0039681377820670605,
-0.009000727906823158,
0.018113860860466957,
-0.019244328141212463,
0.020870391279459,
-0.033402737230062485,
-0.03284939378499985,
0.004335204139351845,
-0.020660635083913803,
0.015722081065177917,
0.02686702460050583,
-0.04790316894650459,
-0.00313750421628356,
-0.011057482101023197,
0.011021475307643414,
0.022807469591498375,
-0.015252896584570408,
0.0655733272433281,
-0.05632059648633003,
-0.02322608418762684,
-0.043796151876449585,
0.014773163013160229,
0.06697952747344971,
0.035963963717222214,
-0.012531321495771408,
-0.019890347495675087,
-0.00203071185387671,
-0.04817292466759682,
-0.01776355691254139,
0.0008938140235841274,
0.010731366463005543,
-0.07261543720960617,
0.017422612756490707,
0.009462973102927208,
0.022679297253489494,
-0.036582835018634796,
0.051076166331768036,
-0.017665265128016472,
-0.038034357130527496,
-0.00019394353148527443,
0.008956843055784702,
0.014205544255673885,
-0.013857299461960793,
0.020707974210381508,
0.005629148334264755,
0.010283841751515865,
-0.0031570931896567345,
-0.08583272248506546,
-0.0543924942612648,
-0.004747435450553894,
-0.055227722972631454,
0.004826026502996683,
-0.0001313262910116464,
-0.0008632129756733775,
0.08001372963190079,
-0.00392772164195776,
-0.050642095506191254,
0.0000010421449587738607,
0.027240168303251266,
-0.01203000545501709,
0.02166811376810074,
-0.009679269045591354,
0.04227191209793091,
-0.017439037561416626,
0.001795508316718042,
-0.026012413203716278,
-0.02172696590423584,
0.05097241327166557,
0.0025574862957000732,
0.035912226885557175,
0.024640217423439026,
0.017026662826538086,
0.009626938961446285,
0.037090200930833817,
-0.013960429467260838,
0.020301787182688713,
0.010854977183043957,
-0.00542147783562541,
0.054193165153265,
0.014711778610944748,
-0.10301917046308517,
0.04284370690584183,
-0.0010785587364807725,
-0.005289497319608927,
-0.003434057580307126,
0.04288262128829956,
0.022885624319314957,
-0.07074015587568283,
-0.001436984515748918,
0.018565787002444267,
0.07976587116718292,
-0.02534407749772072,
-0.015785332769155502,
0.050664108246564865,
0.030816100537776947,
-0.024570904672145844,
-0.021001016721129417,
-0.0379047654569149,
-0.0026686065830290318,
0.04947352781891823,
-0.030592750757932663,
-0.011357070878148079,
0.02082683891057968,
0.04664049670100212,
0.0014094577636569738,
-0.023581726476550102,
-0.0567370168864727,
-0.0006599339540116489,
-0.07342635095119476,
0.012995229102671146,
0.0013438975438475609,
0.03483312949538231,
-0.008870584890246391,
0.0848175659775734,
0.012874254025518894,
0.02943684160709381,
0.00923870038241148,
-0.0009442379814572632,
-0.08657900243997574,
0.005539167672395706,
-0.050713568925857544,
-0.015933921560645103,
-0.01802864857017994,
-0.01509207021445036,
0.00897843949496746,
-0.013856225647032261,
0.00847863219678402,
0.014147891663014889,
-0.0067139193415641785,
-0.020531989634037018,
0.04783020168542862,
-0.030774129554629326,
-0.008848682977259159,
-0.00380270485766232,
0.0585206001996994,
0.010568263940513134,
-0.040577229112386703,
0.01654455065727234,
0.045740511268377304,
-0.017978431656956673,
0.0023836097680032253,
-0.029913686215877533,
0.016040915623307228,
0.01182475220412016,
0.004477330483496189,
0.011559410020709038,
0.012313119135797024,
0.05249966308474541,
-0.0033022635616362095,
-0.01585562527179718,
0.06993233412504196,
0.00675144512206316,
-0.011367728002369404,
-0.035125695168972015,
-0.04692273586988449,
-0.00007423479110002518,
0.0056051090359687805,
0.037381820380687714,
-0.030120963230729103,
0.03688916563987732,
0.012301120907068253,
-0.019146546721458435,
0.0009738137596286833,
0.03238137438893318,
0.026847265660762787,
0.05270184949040413,
-0.013046038337051868,
-0.05960896983742714,
0.007867868058383465,
-0.012732788920402527,
-0.010291818529367447,
0.038731783628463745,
-0.0013865515356883407,
-0.04925365373492241,
-0.02326437644660473,
0.036119185388088226,
0.026156414300203323,
-0.015050007961690426,
-0.01014658808708191,
-0.012669467367231846,
0.027189716696739197,
-0.02199907787144184,
-0.011608782224357128,
-0.003902237396687269,
0.03336797282099724,
0.032827362418174744,
0.0014251167885959148,
0.013711977750062943,
-0.05121246352791786,
-0.05373271182179451,
0.02604438178241253,
0.05379404127597809,
-0.030439184978604317,
0.02119426056742668,
-0.0803002342581749,
-0.04864855855703354,
0.05740303173661232,
-0.026643071323633194,
0.044299304485321045,
-0.0455147884786129,
0.03647778183221817,
-0.002640895312651992,
-0.018802588805556297,
-0.04929852485656738,
-0.013464529067277908,
-0.009301336482167244,
-0.011599172838032246,
-0.04051343351602554,
-0.02257009781897068,
0.008490788750350475,
0.040356043726205826,
0.006285525858402252,
0.03767863288521767,
0.02350701205432415,
-0.01541799958795309,
-0.012798409909009933,
0.0006150439148768783,
-0.022682413458824158,
-0.07147793471813202,
-0.03159760311245918,
-0.0037409658543765545,
0.039794400334358215,
0.018913859501481056,
-0.03217475116252899,
-0.05099445953965187,
0.06654411554336548,
0.03839236497879028,
0.013187432661652565,
0.004273463971912861,
-0.033477623015642166,
0.027554824948310852,
0.08203338086605072,
-0.030426397919654846,
0.048380400985479355,
0.031024858355522156,
-0.03924061357975006,
-0.028425388038158417,
-0.04150949791073799,
-0.007100428454577923,
-0.024904627352952957,
-0.04159344360232353,
-0.05681493878364563,
0.007787112612277269,
-0.014563409611582756,
0.010068445466458797,
0.0010463909711688757,
0.00030886539025232196,
-0.033502642065286636,
-0.0028764866292476654,
0.007636719848960638,
-0.013020395301282406,
-0.007548860274255276,
0.0009361074771732092,
0.008634500205516815,
0.02947225235402584,
0.02147642895579338,
-0.0022924006916582584,
-0.02007986046373844,
-0.03291498124599457,
0.0003388617478776723,
0.02097279205918312,
-0.03809795901179314,
0.0072184475138783455,
-0.02814950793981552,
-0.009941193275153637,
0.012409664690494537,
-0.03415876626968384,
0.04419595003128052,
-0.013945148326456547,
0.0239210594445467,
0.04620831087231636,
-0.04548729956150055,
-0.04466905817389488,
0.015613244846463203,
0.005738229490816593,
0.03003794699907303,
-0.060248106718063354,
-0.018047913908958435,
0.023362716659903526,
0.017882954329252243,
-0.03452400863170624,
-0.019348664209246635,
0.05521310865879059,
0.0024129075463861227,
-0.038516294211149216,
-0.029944075271487236,
-0.018499057739973068,
0.010388379916548729,
-0.007761267013847828,
0.004862628411501646,
-0.017804281786084175,
-0.04189201444387436,
0.016011489555239677,
0.014615071937441826,
0.018632415682077408,
0.04176037386059761,
-0.027095569297671318,
-0.0013961605727672577,
0.05845087021589279,
0.005464124493300915,
0.0036820562090724707,
-0.023569976910948753,
0.025755567476153374,
-0.004291595425456762,
-0.031375762075185776,
-0.005462003871798515,
-0.0068390038795769215,
0.046927712857723236,
-0.009919799864292145,
-0.02102375403046608,
-0.010944548062980175,
0.02099565789103508,
0.02338317781686783,
0.019978100433945656,
-0.03468295559287071,
0.01179658342152834,
0.03421474248170853,
-0.03455197811126709,
-0.0229024700820446,
0.0062712556682527065,
0.005450189579278231,
0.0044782436452806,
-0.03487696126103401,
-0.00002649613634275738,
0.0035328816156834364,
0.08086676895618439,
-0.0328436903655529,
0.0010796117130666971,
0.003262253012508154,
-0.012665136717259884,
0.016305850818753242,
-0.012453388422727585,
-0.005097935441881418,
0.027117284014821053,
0.0032649864442646503,
-0.027904212474822998,
-0.008858561515808105,
-0.0489792637526989,
0.03864523023366928,
0.0686340257525444,
0.04694755747914314,
0.017145035788416862,
0.008796697482466698,
0.005329080391675234,
-0.021566802635788918,
-0.01678594760596752,
0.004396222531795502,
0.018293945118784904,
-0.007078123744577169,
0.015823354944586754,
-0.018085163086652756,
-0.0030954445246607065,
0.02999984845519066,
0.002960043493658304,
-0.05518964305520058,
0.042667411267757416,
-0.0010489122942090034,
0.0008646373171359301,
-0.007794419769197702,
0.004770920146256685,
-0.05327697843313217,
0.057998642325401306,
0.009975966066122055,
0.06546113640069962,
-0.01394077017903328,
-0.0833093523979187,
0.03743492439389229,
0.025362567976117134,
0.06806619465351105,
-0.046023301780223846,
0.028294824063777924,
-0.03826319798827171,
0.031200414523482323,
-0.001008385675959289,
-0.005414750427007675,
-0.018675092607736588,
0.009960738942027092,
0.027546383440494537,
0.011021183803677559,
-0.00321704288944602,
-0.023858189582824707,
-0.024511119350790977,
0.026611777022480965,
-0.02685696631669998,
-0.08179660141468048,
0.05106988921761513,
0.03248078003525734,
-0.008806233294308186,
0.030058516189455986,
-0.04025322198867798,
0.010589626617729664,
0.022977126762270927,
0.0008082574349828064,
0.01931523159146309,
0.09585785865783691,
0.0030845392029732466,
0.03573966771364212,
-0.04351446032524109,
-0.028857635334134102,
0.13752460479736328,
0.05121724307537079,
0.003757590427994728,
-0.04106341674923897,
-0.007861069403588772,
-0.02986925095319748,
0.0011766270035877824,
-0.05110304430127144,
0.011173336766660213,
-0.028621133416891098,
-0.03608661890029907,
0.006010379176586866,
0.07018287479877472,
-0.03476518765091896,
-0.019597161561250687,
0.026298752054572105,
-0.03944525867700577,
-0.04405183717608452,
-0.005882874596863985,
0.019639628008008003,
-0.031392842531204224,
-0.0031046324875205755,
-0.021965911611914635,
0.03786131739616394,
-0.02694942057132721,
-0.03471696004271507,
-0.05194629728794098,
-0.007736185099929571,
-0.006488088984042406,
-0.010375667363405228,
-0.0467824786901474,
-0.003922829870134592,
-0.0015929723158478737,
-0.014670101925730705,
0.004531228914856911,
0.03943343088030815,
-0.011873678304255009,
-0.02730472758412361,
0.0341266430914402,
0.048105016350746155,
-0.009736240841448307,
0.011359569616615772,
0.02660560794174671,
-0.002487059449777007,
-0.032745346426963806,
-0.02807779051363468,
-0.047868624329566956,
0.057746436446905136,
-0.054253075271844864,
0.0038009497802704573,
-0.005640584044158459,
-0.009317523799836636,
0.007740267552435398,
-0.027175378054380417,
0.014385916292667389,
-0.029708750545978546,
0.007617294788360596,
0.0001756525452947244,
0.006737650837749243,
0.037081245332956314,
-0.0006306165014393628,
0.017964022234082222,
0.03809276968240738,
-0.009229657240211964,
-0.03356984630227089,
-0.014822898432612419,
-0.008006908930838108,
0.058486323803663254,
-0.028122678399086,
-0.011872694827616215,
-0.029768051579594612,
0.008991282433271408,
-0.040736403316259384,
-0.0027125042397528887,
-0.006352421827614307,
0.00017794613086152822,
0.02848603017628193,
0.03521420806646347,
0.025205213576555252,
-0.018921703100204468,
-0.04604245349764824,
0.021684544160962105,
-0.0017675025155767798,
-0.015192157588899136,
-0.02966937981545925,
-0.003956182394176722,
0.010812973603606224,
0.044981829822063446,
0.013384159654378891,
0.01037465501576662,
-0.01722731627523899,
0.03707720711827278,
0.012648970820009708,
-0.007906838320195675,
-0.049492303282022476,
-0.013064449653029442,
-0.014756624586880207,
-0.018741125240921974,
-0.014376966282725334,
-0.009415993466973305,
0.015638457611203194,
0.03558316454291344,
0.006613449193537235,
0.039230599999427795,
-0.044304974377155304,
-0.013031359761953354,
-0.02750067412853241,
0.019802570343017578,
-0.012095944955945015,
0.014101733453571796,
0.012036405503749847,
-0.07106545567512512,
0.010662433691322803,
-0.002760360948741436,
-0.035356808453798294,
-0.021677887067198753,
0.0064897481352090836,
-0.012524520047008991,
-0.00991369504481554,
-0.033787794411182404,
0.02252986840903759,
0.00598871661350131,
0.0027458530385047197,
-0.04056716710329056,
0.02583211101591587,
-0.020424099639058113,
0.03818979486823082,
-0.03152850270271301,
0.041055940091609955,
-0.007714003790169954,
-0.013574364595115185,
0.008108374662697315,
0.01968231424689293,
0.0045362976379692554,
-0.03821238875389099,
0.03936664015054703,
0.004205677192658186,
0.03602121025323868,
-0.0053177340887486935,
-0.013132586143910885,
0.010929781943559647,
0.006605188362300396,
-0.01982302777469158,
-0.002556051593273878,
0.003147473558783531,
-0.022904548794031143,
0.01851203665137291,
-0.039820682257413864,
-0.00010350123920943588,
0.009394025430083275,
0.02416350319981575,
-0.040409788489341736,
-0.02749796025454998,
-0.03171880543231964,
-0.02964894287288189,
-0.00865843053907156,
0.019751500338315964,
-0.006357603706419468,
0.03097330778837204,
0.03079841285943985,
0.007984306663274765,
-0.04336798936128616,
0.015398155897855759,
0.02640162780880928,
-0.041331697255373,
0.009222149848937988,
0.004976383876055479,
0.013064844533801079,
0.0208144411444664,
0.039683662354946136,
-0.03982957452535629,
0.0027481031138449907,
0.030969757586717606,
0.004621667321771383,
-0.08480622619390488,
-0.012261390686035156,
0.017698124051094055,
0.012159626930952072,
0.04556352645158768,
-0.06485731899738312,
0.02260461077094078,
-0.0014505863655358553,
-0.08716538548469543,
0.018338603898882866,
-0.028056861832737923,
0.0350777842104435,
-0.0013686997117474675,
-0.023911036550998688,
0.0027045500464737415,
0.03909745439887047,
-0.00041091241291724145,
0.04951564222574234,
0.028650831431150436,
0.022210149094462395,
-0.04392612352967262,
-0.023673001676797867,
0.019561100751161575,
0.05953602120280266,
-0.008958427235484123,
-0.018120527267456055,
0.08932681381702423,
-0.009063166566193104,
-0.006217113696038723,
-0.019710198044776917,
-0.0015998703893274069,
0.018110379576683044,
0.008901036344468594,
0.01220407523214817,
0.010286103934049606,
0.06561383605003357,
0.0028644308913499117,
0.025472352281212807,
-0.01380211766809225,
-0.011096855625510216,
0.02749425545334816,
-0.006387834437191486,
-0.006596751511096954,
-0.01817135699093342,
0.00048267701640725136,
0.004945341031998396,
-0.04012106731534004,
0.04286395385861397,
-0.04114383086562157,
-0.014337703585624695,
0.004014739766716957,
-0.018433433026075363,
0.007224269211292267,
-0.028442269191145897,
0.011919059790670872,
-0.06009881943464279,
0.002097330056130886,
0.02242511324584484,
0.0030794558115303516,
-0.006461279932409525,
0.009192260913550854,
0.0019327541813254356,
-0.016861427575349808,
0.022617336362600327,
-0.005658307578414679,
-0.022228263318538666,
-0.06656329333782196,
0.029413843527436256,
-0.06150050461292267,
-0.03782067820429802,
0.007584185339510441,
0.002943943487480283,
-0.05448376387357712,
-0.00153244542889297,
0.020863618701696396,
0.0010654504876583815,
0.019063841551542282,
-0.02490580454468727,
-0.01485749613493681,
-0.07316882908344269,
-0.004756753332912922,
-0.0012764367274940014,
-0.05866425484418869,
0.007691652048379183,
-0.025369681417942047,
0.031596940010786057,
0.008859258145093918,
0.03726603835821152,
0.015318789519369602,
-0.018937230110168457,
0.018947580829262733,
-0.0018406996969133615,
0.033086858689785004,
0.01981090009212494,
0.03379590064287186,
0.009870408102869987,
-0.008684792555868626,
0.049122702330350876,
0.00315505126491189,
0.0036568862851709127,
0.01984284073114395,
0.03831973299384117,
-0.044789403676986694,
0.008826801553368568,
0.00717720203101635,
-0.0386582612991333,
0.0002301935019204393,
0.004785597790032625,
-0.034929268062114716,
0.09160712361335754,
0.00349642476066947,
0.010367907583713531,
-0.009226101450622082,
0.0019102308433502913,
-0.0448964424431324,
0.00845274142920971,
-0.02654244750738144,
-0.01064294669777155,
-0.03221352398395538,
0.00406803609803319,
0.04250117391347885,
-0.0511007234454155,
0.020957674831151962,
0.01734492927789688,
-0.024740975350141525,
-0.02913638949394226,
0.06514672935009003,
0.00455815251916647,
0.03727935254573822,
0.023394251242280006,
0.051381006836891174,
0.01070973090827465,
-0.004221877083182335,
0.015322243794798851,
0.020806318148970604,
0.059444136917591095,
-0.0029166138265281916,
-0.004565020091831684,
0.039255548268556595,
-0.01319457869976759,
0.02326422929763794,
0.02783149480819702,
-0.00405411422252655,
0.006869823206216097,
-0.019890334457159042,
0.04460645094513893,
-0.028943046927452087,
0.0005886857397854328,
0.040369801223278046,
0.021176716312766075,
0.08987389504909515,
0.017712442204356194,
0.024123813956975937,
-0.0156770721077919,
-0.014046529307961464,
-0.00638195127248764,
0.0223536416888237,
0.02251575142145157,
0.04199926182627678,
0.0186698567122221,
0.0044291201047599316,
-0.04294006526470184,
-0.013293285854160786,
-0.0013804015470668674,
0.022136691957712173,
0.01046556606888771,
0.0140481973066926,
-0.003922564443200827,
-0.0009193996083922684,
-0.05040919408202171,
-0.019373761489987373,
-0.02320653200149536,
0.007715555373579264,
0.04808225482702255,
0.032052747905254364,
0.037397660315036774,
0.006884692702442408,
-0.028551314026117325,
0.05394911766052246,
-0.055922847241163254,
-0.045156266540288925,
0.00984545424580574,
-0.000036913126677973196,
0.008147526532411575,
-0.017336364835500717
] |
<p>There is something I don't really understand about flashes of lightning.</p>
<p>When a flash occurs, how come electricity be transferred at the speed of light since electricity's displacement is very slow ?</p>
<p>It is not that I don't understand anything about that. I've read wikipedia and the others. But on that particular point there's something I really don't get ...</p>
<p>But the question could be for lighting as for any charge strike between two points of course.</p>
| 9,557 |
[
-0.04802405461668968,
-0.008223236538469791,
0.030368275940418243,
-0.03382585942745209,
0.03396455943584442,
-0.03173436224460602,
-0.0251881442964077,
-0.014207183383405209,
-0.011656307615339756,
0.04146949201822281,
0.025479471310973167,
0.04397040233016014,
0.05574799329042435,
0.015958305448293686,
-0.0005577701376751065,
-0.016720134764909744,
0.032482679933309555,
-0.011924135498702526,
-0.016067108139395714,
-0.05678318068385124,
-0.02421324886381626,
0.008292842656373978,
0.011473176069557667,
0.028954358771443367,
-0.02129741944372654,
0.014000273309648037,
0.01816318742930889,
0.020687639713287354,
0.023828590288758278,
0.013514110818505287,
0.00035907988785766065,
-0.03148115798830986,
-0.005850305315107107,
0.03337234631180763,
0.017108919098973274,
0.01103982049971819,
-0.04308346286416054,
-0.05664800852537155,
0.020607540383934975,
-0.0005679882597178221,
-0.01277151983231306,
-0.016006965190172195,
-0.004011668264865875,
0.022924836724996567,
-0.038952138274908066,
0.013155747205018997,
0.006962982937693596,
-0.008086233399808407,
0.04879036918282509,
-0.06529588252305984,
0.021534249186515808,
-0.01628825068473816,
0.02661891281604767,
0.025423415005207062,
-0.012269515544176102,
0.042452335357666016,
0.09570514410734177,
0.07866444438695908,
-0.03839605301618576,
-0.024519700556993484,
0.013086647726595402,
-0.01727132685482502,
0.0005676127038896084,
-0.03987007960677147,
0.005088334903120995,
0.04444024711847305,
-0.005565048661082983,
-0.02766350470483303,
0.015339124016463757,
0.008709038607776165,
0.008348450064659119,
-0.026279626414179802,
0.015028581954538822,
0.013502457179129124,
0.00989531259983778,
-0.033233121037483215,
0.028389742597937584,
0.0011458240915089846,
0.05077908933162689,
0.07649436593055725,
-0.03607915714383125,
0.004225116688758135,
0.023625485599040985,
0.0037435744889080524,
-0.01488154660910368,
-0.04970724508166313,
0.07037592679262161,
0.010117053985595703,
0.01773151196539402,
-0.0028181360103189945,
-0.016446346417069435,
0.0014646191848441958,
-0.010225430130958557,
0.014907722361385822,
0.014547272585332394,
0.017697377130389214,
0.006218211725354195,
0.02811993844807148,
0.03286081552505493,
-0.019287584349513054,
0.009680786170065403,
0.021584367379546165,
0.05431013181805611,
0.031705357134342194,
-0.0034402920864522457,
-0.03769540414214134,
-0.015075650997459888,
0.014802079647779465,
-0.007954658940434456,
-0.0010321703739464283,
-0.05423019826412201,
0.012220690958201885,
0.004631099756807089,
0.01315256953239441,
0.020290324464440346,
-0.04264817014336586,
0.04293914511799812,
-0.008746583014726639,
0.06473103165626526,
0.03323898836970329,
-0.006638471968472004,
-0.053360503166913986,
0.014039862900972366,
-0.0014123631408438087,
-0.04386245086789131,
0.019466392695903778,
0.0352996364235878,
-0.003325449535623193,
-0.010015140287578106,
0.04257979616522789,
-0.009516899473965168,
-0.021652549505233765,
0.009811880998313427,
-0.006536519154906273,
0.03308849781751633,
0.0009471035446040332,
-0.1222294345498085,
-0.03702641651034355,
0.027666550129652023,
0.04048267751932144,
-0.03422128036618233,
-0.0946616604924202,
0.015609553083777428,
0.014870801940560341,
0.07226046174764633,
-0.017116019502282143,
0.0029829731211066246,
-0.028183020651340485,
0.018404889851808548,
0.014250291511416435,
0.0027704648673534393,
-0.038543701171875,
0.046995390206575394,
-0.012472025118768215,
0.019624335691332817,
-0.0368528887629509,
-0.0019338572164997458,
0.049033716320991516,
-0.0262900423258543,
0.007596858777105808,
0.03171781823039055,
0.0003859375137835741,
0.0056761931627988815,
0.016943857073783875,
0.0009962946642190218,
-0.0068031661212444305,
0.09449796378612518,
0.02535572461783886,
-0.005695277359336615,
0.05165281891822815,
0.0117783909663558,
0.0430392362177372,
-0.02001887746155262,
0.021388793364167213,
0.026611575856804848,
-0.05141912028193474,
-0.022031011059880257,
-0.010846351273357868,
-0.01778366044163704,
-0.021765392273664474,
-0.0319838784635067,
-0.03559507057070732,
-0.0006314589409157634,
-0.012011183425784111,
0.03972772881388664,
0.07592956721782684,
-0.0125892898067832,
0.018885329365730286,
-0.025893671438097954,
-0.016809411346912384,
-0.03621423617005348,
-0.044643584638834,
0.040584880858659744,
-0.0009909890359267592,
0.012474273331463337,
0.008914507925510406,
-0.01991025172173977,
0.01995900832116604,
0.013796297833323479,
-0.0012074637925252318,
-0.013262782245874405,
0.016799654811620712,
-0.02680901251733303,
-0.039617203176021576,
0.02637542225420475,
0.04928302764892578,
0.010605830699205399,
0.03163734823465347,
0.005951401777565479,
0.008600937202572823,
-0.021281041204929352,
0.02579827606678009,
-0.006029701791703701,
0.04878677427768707,
0.03394465520977974,
-0.0042374213226139545,
0.015401222743093967,
0.005249788053333759,
0.0007726798648945987,
0.01715323142707348,
0.021909596398472786,
0.07220672070980072,
0.04787399619817734,
-0.038221582770347595,
-0.025474021211266518,
0.06725804507732391,
-0.016878260299563408,
-0.0005193634424358606,
0.028916802257299423,
-0.011712945997714996,
-0.03209611400961876,
0.005382828880101442,
0.010714014992117882,
0.013239750638604164,
-0.018945863470435143,
-0.0026540125254541636,
0.03930102661252022,
0.05745929107069969,
0.031952619552612305,
0.0033443209249526262,
-0.02744966372847557,
-0.06647065281867981,
-0.0012223352678120136,
0.003380132606253028,
-0.017878267914056778,
0.001364244963042438,
0.0385570153594017,
0.0015163031639531255,
0.012813284061849117,
-0.024744275957345963,
0.0024118218570947647,
0.04048609733581543,
-0.0052767121233046055,
-0.002777440007776022,
0.0018834004877135158,
-0.029074886813759804,
0.04598325118422508,
-0.015039511024951935,
0.05826013162732124,
0.016604045405983925,
0.03804336488246918,
0.0624140128493309,
-0.015291152521967888,
0.011540662497282028,
0.04187628626823425,
-0.014862672425806522,
-0.011492645367980003,
-0.024190008640289307,
0.023765532299876213,
-0.05326666310429573,
0.04664313793182373,
-0.020177768543362617,
-0.011014233343303204,
-0.03603123500943184,
-0.023207351565361023,
0.020376285538077354,
0.04721755534410477,
0.03058251552283764,
-0.041036684066057205,
-0.04130278900265694,
-0.021552307531237602,
-0.026472782716155052,
0.03783208876848221,
-0.014222178608179092,
-0.038876332342624664,
0.0226570013910532,
-0.021932698786258698,
-0.026632672175765038,
0.05307072773575783,
-0.008430052548646927,
0.015613929368555546,
0.017081856727600098,
-0.012023930437862873,
-0.056206732988357544,
0.009948511607944965,
-0.021771274507045746,
0.00806941743940115,
-0.0234066229313612,
-0.010743820108473301,
0.08724839240312576,
-0.05805911496281624,
-0.03829412907361984,
0.010553990490734577,
-0.043141115456819534,
-0.028347734361886978,
0.003573655616492033,
-0.026350444182753563,
0.036992624402046204,
-0.03276264667510986,
0.02794451080262661,
-0.008687213994562626,
-0.06272353231906891,
0.0053004315122962,
-0.01283769030123949,
-0.03404800221323967,
0.01948983035981655,
0.0041336603462696075,
0.06579452008008957,
-0.029407089576125145,
-0.0512288436293602,
0.03619956225156784,
0.031415265053510666,
-0.020812634378671646,
-0.0026082892436534166,
-0.00012626373791135848,
-0.03295367956161499,
-0.0076668038964271545,
0.009773613885045052,
0.06905006617307663,
-0.02163827419281006,
-0.0038805666845291853,
0.009620225988328457,
0.04486546665430069,
0.04381474480032921,
0.0035860438365489244,
0.0022310770582407713,
-0.009867372922599316,
-0.012047337368130684,
0.021058320999145508,
0.006577559281140566,
0.018470704555511475,
-0.036529868841171265,
0.013732113875448704,
-0.014708309434354305,
0.023475876078009605,
0.023055624216794968,
-0.026586657389998436,
0.05058036744594574,
0.009528366848826408,
-0.00297488528303802,
-0.02869516611099243,
0.03539110720157623,
-0.013333846814930439,
0.0027301893569529057,
-0.013694925233721733,
0.029503803700208664,
0.04618426784873009,
-0.0044545941054821014,
0.0024012925568968058,
0.014512717723846436,
0.05111732706427574,
-0.03790442273020744,
-0.031691789627075195,
-0.0006060798186808825,
-0.03443801775574684,
0.02861158549785614,
-0.006846381817013025,
-0.007608749903738499,
0.041540004312992096,
0.0007174677448347211,
-0.005570085719227791,
-0.0003087715886067599,
-0.013701589778065681,
-0.02257154881954193,
-0.04545855149626732,
0.018399178981781006,
0.0320831835269928,
0.039924394339323044,
0.017616329714655876,
0.1135542020201683,
0.0488719716668129,
0.03649888187646866,
0.008311497047543526,
0.010284800082445145,
-0.06817273050546646,
0.007314329035580158,
-0.03655508905649185,
-0.018751248717308044,
-0.058491311967372894,
0.0038867895491421223,
-0.03756992891430855,
-0.024227749556303024,
-0.028023164719343185,
-0.05126118287444115,
-0.008510996587574482,
-0.05536353215575218,
-0.01834193244576454,
-0.007109598256647587,
-0.031289052218198776,
-0.036920055747032166,
0.014363784343004227,
0.022757776081562042,
-0.01865156553685665,
0.030890030786395073,
0.06593301892280579,
-0.03345777466893196,
-0.015604863874614239,
-0.025653883814811707,
-0.014155667275190353,
0.015122071839869022,
0.011464797891676426,
0.02401343174278736,
-0.02850446291267872,
-0.03722349554300308,
0.02647988125681877,
0.008063447661697865,
0.00825484935194254,
0.04721827059984207,
-0.019291512668132782,
-0.04068876802921295,
-0.0045201475732028484,
-0.013604078441858292,
-0.003250701818615198,
0.06821984052658081,
-0.009875972755253315,
-0.008289421908557415,
0.013497321866452694,
0.01600372977554798,
0.019758403301239014,
0.026285404339432716,
0.024659227579832077,
-0.010313828475773335,
-0.00440984359011054,
-0.08292216807603836,
-0.011094671674072742,
-0.022916311398148537,
0.009962731972336769,
0.019619863480329514,
-0.00153992953710258,
0.0029329012613743544,
-0.002817174419760704,
0.037812963128089905,
-0.004564160946756601,
0.026056978851556778,
-0.013046493753790855,
0.0036471488419920206,
-0.027797168120741844,
0.02559925615787506,
0.02905557118356228,
0.021226296201348305,
-0.016946006566286087,
0.03395756334066391,
0.00020108257012907416,
0.01563768833875656,
-0.08223269879817963,
-0.0169092807918787,
0.021793091669678688,
0.031356848776340485,
-0.032256659120321274,
-0.008902068249881268,
-0.052264463156461716,
0.011811879463493824,
0.0244137030094862,
-0.03294533118605614,
0.02779584750533104,
0.0009872775990515947,
-0.033024970442056656,
-0.03390326350927353,
-0.046330682933330536,
-0.004413235932588577,
0.009707881137728691,
-0.0009713945910334587,
0.01737108640372753,
0.0019795382395386696,
-0.01909397915005684,
0.0036322087980806828,
-0.014701386913657188,
0.02431350015103817,
0.08101587742567062,
0.010905873961746693,
0.010442927479743958,
-0.018552161753177643,
-0.002291353652253747,
-0.02465767227113247,
-0.07544685155153275,
0.006835231091827154,
-0.0108690420165658,
-0.03224397078156471,
0.03266531974077225,
-0.02035682648420334,
-0.05381617322564125,
0.027587665244936943,
0.005695606116205454,
-0.007747169118374586,
-0.004455142188817263,
-0.04756057262420654,
0.023711953312158585,
0.03382839262485504,
0.02222650870680809,
0.08020622283220291,
0.025522436946630478,
-0.06341680139303207,
0.006223638076335192,
0.022795822471380234,
0.05699937045574188,
0.004540173336863518,
0.024349186569452286,
0.0035936275962740183,
0.04235575720667839,
-0.026945849880576134,
0.08656366169452667,
-0.024456003680825233,
0.027352143079042435,
-0.008612164296209812,
-0.03027535229921341,
-0.016788536682724953,
0.020131386816501617,
0.006481704767793417,
0.007457707542926073,
-0.04466011002659798,
-0.00024727461277507246,
-0.014525793492794037,
0.004166897851973772,
0.04054480791091919,
0.010718894191086292,
0.01466120220720768,
0.03222808241844177,
0.021738041192293167,
-0.009106412529945374,
-0.06365983188152313,
-0.012397494167089462,
0.009577031247317791,
-0.04359782114624977,
0.058374810963869095,
0.02186994068324566,
-0.020741065964102745,
0.03209094703197479,
-0.044937122613191605,
-0.05903894826769829,
0.006509990897029638,
-0.009912294335663319,
0.0520632341504097,
-0.0834202840924263,
-0.002645853441208601,
0.000563997367862612,
-0.021857693791389465,
-0.0620361864566803,
-0.08253782987594604,
0.03800738975405693,
0.038981180638074875,
-0.02415572479367256,
-0.036569226533174515,
0.01788468286395073,
-0.022502725943922997,
-0.03271651268005371,
0.01592298410832882,
0.008857336826622486,
-0.022568045184016228,
0.008460992947220802,
0.03906024619936943,
-0.03142039477825165,
0.044668301939964294,
-0.025286126881837845,
-0.0137811079621315,
0.01732494868338108,
-0.037552595138549805,
-0.02579692006111145,
-0.03871532902121544,
0.07620056718587875,
-0.029018839821219444,
-0.048138462007045746,
-0.016493653878569603,
-0.026712339371442795,
0.020841894671320915,
-0.015566070564091206,
0.015379474498331547,
0.014202541671693325,
0.01626518927514553,
-0.018670164048671722,
-0.014431037940084934,
0.038465969264507294,
0.03956419974565506,
0.0052490681409835815,
-0.01095650065690279,
-0.006195523776113987,
-0.04712443798780441,
-0.030652277171611786,
0.014504630118608475,
0.04927254468202591,
0.025019405409693718,
-0.027954839169979095,
0.026997113600373268,
-0.05831390619277954,
0.0027504556346684694,
0.08425012230873108,
-0.0053659845143556595,
0.05102071911096573,
-0.006017661187797785,
-0.0028902047779411077,
0.003695817431434989,
-0.02785688266158104,
0.0015392843633890152,
-0.006379492115229368,
0.012961172498762608,
-0.02328544110059738,
0.07259999960660934,
-0.03230810910463333,
0.047554899007081985,
0.009996172972023487,
-0.03576073423027992,
-0.001901180250570178,
-0.002677960554137826,
-0.018078025430440903,
0.031123774126172066,
0.0028201823588460684,
-0.0006220951327122748,
-0.033418286591768265,
0.009964319877326488,
0.017464688047766685,
0.04816693440079689,
-0.016054902225732803,
-0.005484908353537321,
0.02510535903275013,
0.00044611896737478673,
0.028850415721535683,
0.011611567810177803,
-0.029519004747271538,
0.013179020024836063,
-0.022316059097647667,
0.030065521597862244,
0.02262907288968563,
-0.013103308156132698,
0.07150541245937347,
-0.03186177834868431,
-0.0074266609735786915,
-0.024978945031762123,
-0.010128908790647984,
-0.026039443910121918,
-0.014272887259721756,
-0.01991310343146324,
0.025083504617214203,
0.0036390889436006546,
0.0078222481533885,
0.013409961014986038,
-0.01431985478848219,
0.028959067538380623,
-0.001424105721525848,
-0.034577567130327225,
-0.05051801726222038,
-0.021834764629602432,
-0.03274576738476753,
0.03967318683862686,
-0.005197806283831596,
-0.011542792432010174,
0.005384692456573248,
-0.04021833837032318,
0.03548517823219299,
0.006657930091023445,
0.02056918665766716,
-0.013481906615197659,
0.08806871622800827,
0.04048701748251915,
-0.0037465596105903387,
-0.0052963607013225555,
-0.002071977127343416,
0.09929559379816055,
0.014710759744048119,
0.0340898223221302,
-0.049523286521434784,
0.007075347006320953,
-0.033476799726486206,
0.0019097685581073165,
-0.047234855592250824,
0.007126946002244949,
-0.04086854308843613,
0.03926384076476097,
0.04012833163142204,
0.04440459981560707,
0.025410005822777748,
0.006540287286043167,
0.005324199330061674,
-0.027217283844947815,
-0.004260693676769733,
0.025889618322253227,
0.03181762620806694,
0.0011930117616429925,
0.06996586918830872,
-0.05353531986474991,
0.0010689421324059367,
-0.026899443939328194,
-0.013940369710326195,
-0.027299566194415092,
-0.033501483500003815,
0.02584526315331459,
-0.0038140546530485153,
-0.04556403309106827,
0.0045481291599571705,
0.052525319159030914,
-0.0903855636715889,
-0.05104043334722519,
0.0346679724752903,
0.0485287569463253,
0.001795270130969584,
0.019676044583320618,
0.019046135246753693,
0.004210921004414558,
0.01718672551214695,
0.015689976513385773,
0.02060871571302414,
-0.048225998878479004,
-0.015770643949508667,
-0.03263785317540169,
0.014613771811127663,
-0.005904388148337603,
0.01705373264849186,
0.0031443273182958364,
0.0009784518042579293,
0.010540052317082882,
-0.05759986490011215,
-0.026917828246951103,
0.021010486409068108,
0.013711025938391685,
-0.0025547335390001535,
0.001223855186253786,
-0.055077530443668365,
-0.01303928904235363,
-0.010210446082055569,
0.007830544374883175,
-0.024975784122943878,
0.013310988433659077,
-0.001738367835059762,
0.0108016487210989,
-0.011162964627146721,
-0.014415489509701729,
-0.018998347222805023,
0.009025001898407936,
0.02957523986697197,
-0.02839590050280094,
-0.017132272943854332,
0.023758014664053917,
0.03950033709406853,
-0.016747230663895607,
-0.003103944705799222,
-0.005784495268017054,
-0.026972651481628418,
-0.07231409847736359,
0.03276650980114937,
0.022846005856990814,
-0.03290730342268944,
-0.03611573949456215,
-0.003862533951178193,
0.05138995870947838,
0.009938032366335392,
0.013676980510354042,
0.026636246591806412,
-0.04049690440297127,
0.04342545196413994,
0.02540469542145729,
-0.06645018607378006,
-0.000385865947464481,
0.018793078139424324,
0.013559053651988506,
-0.0034885527566075325,
-0.0025047077797353268,
0.025407914072275162,
0.030252238735556602,
-0.0037421686574816704,
0.023539725691080093,
0.005296939983963966,
-0.026199540123343468,
0.00011910043394891545,
0.032245561480522156,
-0.024583792313933372,
0.0007293820381164551,
0.010077038779854774,
0.011231976561248302,
0.025632398203015327,
-0.021485313773155212,
-0.0167124941945076,
0.0012109394883736968,
-0.02015097439289093,
0.006887983530759811,
-0.00911156740039587,
-0.010250473394989967,
-0.006931723561137915,
0.027551041916012764,
-0.035893380641937256,
-0.016324693337082863,
-0.03941666707396507,
0.015636727213859558,
-0.029171094298362732,
-0.0007612181361764669,
-0.03294845670461655,
0.03532819822430611,
-0.058797579258680344,
0.009010766632854939,
0.0339101180434227,
0.012614070437848568,
0.008090387098491192,
0.009256825782358646,
-0.00302457669749856,
-0.02390175685286522,
0.07644664496183395,
-0.02164677530527115,
-0.019852718338370323,
0.040818292647600174,
-0.009402228519320488,
-0.037766169756650925,
0.0416550375521183,
-0.02700793743133545,
0.01896682009100914,
0.0091061657294631,
0.0013451548293232918,
-0.01886959746479988,
0.09562499821186066,
-0.0017118281684815884,
-0.0025035461876541376,
0.004491948056966066,
-0.028176026418805122,
0.008748074062168598,
0.0009034837130457163,
-0.003909386228770018,
-0.05106024071574211,
0.013356819748878479,
0.03407956287264824,
-0.0010216401424258947,
-0.027064984664320946,
0.021050989627838135,
0.005908231716603041,
-0.024893254041671753,
-0.00328592280857265,
0.045022524893283844,
0.018023693934082985,
0.009799265302717686,
0.04636299982666969,
0.0003566017549019307,
0.04336293414235115,
-0.02980281226336956,
0.006038966588675976,
-0.11640637367963791,
0.009410209953784943,
-0.010174116119742393,
0.016564184799790382,
0.03688862919807434,
-0.02993743307888508,
-0.008914236910641193,
0.019768036901950836,
-0.07998423278331757,
0.023694897070527077,
-0.01564357988536358,
-0.03519822284579277,
-0.016252903267741203,
0.006254406645894051,
-0.008351718075573444,
0.04875100776553154,
0.03965440019965172,
0.0486452542245388,
0.014762637205421925,
0.02038215473294258,
-0.008361389860510826,
-0.014143968932330608,
-0.03057534247636795,
0.04582071304321289,
0.006931039970368147,
0.02288529835641384,
0.05880341678857803,
-0.038073133677244186,
0.00772922532632947,
0.026076901704072952,
0.004179772455245256,
0.010240014642477036,
0.01190469041466713,
0.014172093011438847,
0.020372191444039345,
0.00754722161218524,
-0.01129379402846098,
-0.018848085775971413,
0.009179002605378628,
0.021939214318990707,
0.012126118876039982,
0.01200835220515728,
-0.02690587379038334,
-0.019129859283566475,
0.015765009447932243,
-0.03697657585144043,
-0.05483735725283623,
0.02445807494223118,
-0.0151786794885993,
-0.004635365214198828,
0.028003022074699402,
0.056009441614151,
0.0358993336558342,
-0.01898530125617981,
-0.03648057207465172,
-0.023582788184285164,
-0.02514639124274254,
0.030051574110984802,
-0.02232070453464985,
-0.010012385435402393,
0.0223299041390419,
-0.032961685210466385,
-0.029162535443902016,
-0.020829154178500175,
-0.013668419793248177,
0.005407681688666344,
-0.06604510545730591,
-0.01757459156215191,
0.049272604286670685,
-0.023334771394729614,
-0.0028186070267111063,
-0.008605956099927425,
-0.016841141507029533,
-0.0076162791810929775,
0.02128094807267189,
0.01731528341770172,
0.02087513357400894,
-0.04630741477012634,
-0.030843406915664673,
-0.07253094762563705,
-0.0019348328933119774,
-0.029992733150720596,
-0.014768393710255623,
-0.040643349289894104,
-0.06237335503101349,
-0.009950248524546623,
0.06374090909957886,
0.06566815823316574,
-0.03471868485212326,
-0.0252746120095253,
0.04597293585538864,
-0.045055702328681946,
0.06501765549182892,
-0.04064447060227394,
-0.0356682687997818,
0.00941089354455471,
-0.021226845681667328,
0.00433477433398366,
-0.019105147570371628,
-0.02662571147084236,
0.015749646350741386,
0.0153010543435812,
-0.002865138463675976,
0.029227783903479576,
-0.056380495429039,
-0.05769634246826172,
0.007996185682713985,
0.02079751528799534,
-0.03417046368122101,
0.03773926571011543,
-0.015258638188242912,
0.0036248131655156612,
0.019419802352786064,
-0.020782388746738434,
-0.0496380552649498,
0.01420945767313242,
-0.02968917228281498,
0.013565157540142536,
-0.005053553264588118,
-0.02389015443623066,
0.022842127829790115,
-0.052940886467695236,
0.02873077616095543,
0.010146409273147583,
-0.01374097540974617,
-0.00984564982354641,
0.06940113008022308,
-0.02405443787574768,
0.032396093010902405,
0.011716539040207863,
0.029818348586559296,
-0.016184037551283836,
-0.015468944795429707,
-0.018528293818235397,
0.01563963107764721,
0.015843557193875313,
-0.02388649620115757,
0.02834099903702736,
0.01749747432768345,
0.024895362555980682,
0.005763544235378504,
-0.013436013832688332,
0.01272333413362503,
-0.021184701472520828,
-0.02995435521006584,
0.002915182849392295,
-0.01761213317513466,
0.005450422875583172,
0.026312101632356644,
-0.024423185735940933,
0.06784020364284515,
-0.02110135927796364,
0.032600175589323044,
0.023970190435647964,
0.03879236429929733,
-0.013476521708071232,
0.011481757275760174,
-0.014452878385782242,
0.01416832022368908,
-0.02665434405207634,
0.014829848892986774,
-0.007483126129955053,
0.0033047443721443415,
0.03401613608002663,
-0.04061327874660492,
0.008420529775321484,
-0.00836511142551899,
-0.03942807763814926,
0.005312218330800533,
0.03053768165409565,
-0.0246114581823349,
0.0023148139007389545,
0.007324324920773506,
0.002786328550428152,
-0.021107926964759827,
0.021314000710844994,
0.018657682463526726,
-0.00664568180218339,
0.04291275516152382,
-0.07033523917198181,
0.01084684394299984,
-0.05150091275572777,
0.03141649067401886,
-0.01052983570843935,
0.0005607044440694153
] |
<p>I am trying to understand the workings of a CMOS image sensor. I understand that increasing wavelength results in an increased penetration depth in the silicon often used in <a href="http://en.wikipedia.org/wiki/CMOS" rel="nofollow">CMOS</a> image sensors. What I am in need of assistance in understanding is how the wavelengths (corresponding to the primary colours, red green and blue) relate to the vertical structure of the CMOS sensor.</p>
<p>After reading several articles and performing some experiments, I am aware that CMOS sensors are indeed sensitive to UV wavelengths, but I am trying to understand how I was able to get a reddish-pink response using an incident UV source.</p>
| 9,558 |
[
0.0024993042461574078,
-0.049336519092321396,
0.015399080701172352,
0.0023186763282865286,
0.0025510089471936226,
-0.0003149322292301804,
0.0027808998711407185,
-0.0060835108160972595,
0.003932376857846975,
-0.0837240219116211,
0.007146823685616255,
0.03190208971500397,
0.02046724408864975,
0.026559241116046906,
0.018525607883930206,
-0.026213306933641434,
0.0039032665081322193,
-0.02584051340818405,
-0.005711736157536507,
-0.033184848725795746,
-0.01395491324365139,
0.0222887322306633,
0.00958220474421978,
0.007162776775658131,
-0.07336625456809998,
0.0012072823010385036,
0.035153940320014954,
0.027336249127984047,
0.02312132529914379,
0.03408137336373329,
-0.03389883413910866,
-0.03322570025920868,
-0.05503212288022041,
0.011260025203227997,
-0.015738073736429214,
-0.006045679561793804,
-0.0012348853051662445,
-0.05407861992716789,
-0.027907120063900948,
0.029697339981794357,
0.025787215679883957,
0.00968747679144144,
0.008622079156339169,
0.010205858387053013,
-0.00024255736207123846,
-0.0344473272562027,
-0.031408533453941345,
-0.00805977825075388,
0.02543589286506176,
-0.0670042410492897,
0.06739698350429535,
-0.01601039618253708,
0.04636263847351074,
0.03541151434183121,
-0.007278440520167351,
-0.005936101544648409,
0.07017152011394501,
0.09411360323429108,
-0.038106344640254974,
-0.011427382007241249,
0.018602577969431877,
-0.0090632950887084,
-0.01690327748656273,
0.0019367182394489646,
-0.016908150166273117,
-0.004093850962817669,
0.017010193318128586,
-0.06977293640375137,
0.04261462017893791,
0.03907214105129242,
0.05131133273243904,
-0.0107652572914958,
0.015769030898809433,
-0.015423648990690708,
-0.014858337119221687,
-0.04848431423306465,
0.013989415019750595,
0.05614721402525902,
-0.012298336252570152,
-0.00047553901094943285,
-0.004250215832144022,
0.01891421712934971,
-0.04943158105015755,
0.01881352625787258,
-0.010162497870624065,
-0.02314494363963604,
0.08276194334030151,
-0.00704362615942955,
-0.01998411864042282,
0.021108699962496758,
-0.02048523724079132,
0.019459418952465057,
-0.0012499552685767412,
0.002173556014895439,
-0.06642075628042221,
0.022430382668972015,
0.00256249587982893,
0.04952632263302803,
0.006173811387270689,
0.012242593802511692,
0.00930790789425373,
0.0055700307711958885,
0.008607352152466774,
0.07574839890003204,
-0.03104039840400219,
-0.0028340930584818125,
0.01655462197959423,
0.03600086644291878,
0.012020629830658436,
0.020963583141565323,
-0.05436708778142929,
-0.02398858033120632,
0.007383223623037338,
0.0013102705124765635,
0.04474489763379097,
-0.014305546879768372,
-0.01364471111446619,
-0.014127353206276894,
0.0468413345515728,
0.03477053344249725,
-0.004745905287563801,
-0.03667968139052391,
0.008822008036077023,
0.01152478251606226,
-0.056977201253175735,
0.043949514627456665,
0.026754168793559074,
-0.009189805947244167,
-0.0006929612718522549,
0.00808875821530819,
0.0013780887238681316,
-0.004489489831030369,
0.0027089552022516727,
-0.029805831611156464,
-0.005361140239983797,
-0.009807021357119083,
-0.11443683505058289,
-0.05811586603522301,
0.024967234581708908,
0.017278851941227913,
-0.008957150392234325,
-0.08450775593519211,
0.0033259137999266386,
0.046107031404972076,
0.05604206770658493,
-0.016937952488660812,
0.008706971071660519,
0.0034751647617667913,
0.022502195090055466,
-0.00007735239341855049,
-0.0018959956942126155,
-0.0167528223246336,
0.008464636281132698,
0.0025579428765922785,
0.023890111595392227,
-0.06288059800863266,
0.044573646038770676,
-0.0006044345791451633,
0.03427838534116745,
-0.04432668164372444,
0.07724253088235855,
0.0023124716244637966,
-0.0024351547472178936,
0.03274092823266983,
0.015176940709352493,
-0.036781467497348785,
0.05636009946465492,
-0.01726519502699375,
0.0210740827023983,
0.06741621345281601,
-0.018140485510230064,
0.005464132409542799,
-0.00910924468189478,
0.015010183677077293,
0.01953686960041523,
-0.0072240158915519714,
-0.028200604021549225,
-0.015094690956175327,
0.041820790618658066,
-0.012572715990245342,
-0.05495835095643997,
-0.042314376682043076,
-0.016121530905365944,
0.035769183188676834,
0.024749377742409706,
0.034540168941020966,
0.004418151918798685,
-0.05786699801683426,
0.015185752883553505,
-0.022500189021229744,
-0.00009257533383788541,
-0.03429029509425163,
-0.006719495635479689,
0.008787418715655804,
-0.013120374642312527,
0.0031348448246717453,
-0.02916380949318409,
0.003602628130465746,
0.0078432597219944,
-0.039460260421037674,
-0.03140414506196976,
-0.04579930007457733,
0.006752758286893368,
0.0016152445459738374,
0.002192310756072402,
0.04259507358074188,
0.0014252887340262532,
0.0287375058978796,
0.041042499244213104,
-0.03554214909672737,
0.013806981965899467,
0.02303348295390606,
-0.008807212114334106,
0.04303031042218208,
-0.00949649978429079,
0.005940972361713648,
0.007952984422445297,
-0.008208861574530602,
-0.008326131850481033,
0.028361691161990166,
0.005470232106745243,
0.09258177131414413,
0.056660253554582596,
0.011910511180758476,
0.015245010145008564,
0.04058472812175751,
-0.015117754228413105,
0.00001579949639562983,
-0.005937865935266018,
-0.022941241040825844,
-0.05343891307711601,
-0.0344979390501976,
0.03948277235031128,
-0.012603417970240116,
-0.05267747491598129,
0.009396449662744999,
-0.0046540130861103535,
0.04871256649494171,
0.040573716163635254,
0.05330624431371689,
-0.007909695617854595,
0.004925747402012348,
0.006725863087922335,
0.018083900213241577,
-0.013156336732208729,
-0.007944720797240734,
0.00577331380918622,
0.007393408101052046,
0.04186045378446579,
-0.016521280631422997,
0.004189782310277224,
0.03075403720140457,
0.016621412709355354,
0.035506993532180786,
-0.008710759691894054,
-0.026975786313414574,
0.0022481640335172415,
-0.027701007202267647,
0.01880999654531479,
0.017472969368100166,
-0.028627749532461166,
-0.003354353830218315,
-0.02117656171321869,
-0.04334773123264313,
-0.0022217317018657923,
0.03255185857415199,
-0.05034225061535835,
-0.019405679777264595,
0.01591867208480835,
-0.0300303902477026,
-0.009914319030940533,
-0.015023652464151382,
-0.004237412009388208,
-0.038808029145002365,
-0.006324087735265493,
0.010617188178002834,
0.014516162686049938,
0.023812109604477882,
-0.05239314213395119,
-0.043851353228092194,
-0.008406922221183777,
-0.002591661410406232,
0.018356163054704666,
-0.0005300487973727286,
-0.02022971585392952,
-0.006703967694193125,
-0.022233737632632256,
-0.014525924809277058,
0.012466734275221825,
0.007035794202238321,
-0.0016004283679649234,
-0.056812793016433716,
-0.0028046094812452793,
-0.029897646978497505,
-0.007662245072424412,
0.012464332394301891,
0.018740838393568993,
0.015291072428226471,
-0.03448435664176941,
0.021061815321445465,
-0.006510082166641951,
-0.02718101628124714,
0.05428747460246086,
-0.05261728912591934,
-0.03592531755566597,
-0.027910836040973663,
0.015264158137142658,
-0.007251940201967955,
-0.026141589507460594,
0.0449417345225811,
0.015223067253828049,
-0.05028696358203888,
0.01882617548108101,
-0.03236773610115051,
-0.03716655448079109,
0.01500957552343607,
0.014638282358646393,
0.04771081730723381,
-0.030058477073907852,
0.031328313052654266,
0.03876727819442749,
0.025445541366934776,
-0.01699252612888813,
-0.017698608338832855,
-0.02676263451576233,
-0.03110836260020733,
-0.029069654643535614,
0.06192346289753914,
0.044989485293626785,
-0.005075587425380945,
0.025047581642866135,
0.002369145629927516,
0.04852782562375069,
0.08659623563289642,
0.014803587459027767,
0.0039857784286141396,
-0.02441038005053997,
0.008012237958610058,
-0.017592983320355415,
0.034268058836460114,
0.05375472083687782,
0.005236819386482239,
0.033744484186172485,
0.0027270254213362932,
0.023541759699583054,
0.033714719116687775,
-0.03786226734519005,
0.04198545962572098,
-0.02253984473645687,
-0.01030818372964859,
-0.044597554951906204,
-0.006653391290456057,
0.00492399837821722,
-0.002101697027683258,
0.0022304910235106945,
0.027611052617430687,
0.05092208832502365,
-0.027324337512254715,
-0.029345650225877762,
0.02230874076485634,
0.04146492853760719,
-0.004973041359335184,
-0.01342250220477581,
0.045859195291996,
-0.04164940118789673,
0.03692241758108139,
-0.018676798790693283,
0.05033864825963974,
0.04835441708564758,
0.023671073839068413,
0.024057060480117798,
0.02538640797138214,
-0.0532296821475029,
-0.009939800016582012,
-0.036928147077560425,
-0.00010502931399969384,
-0.001430258620530367,
0.05950835347175598,
0.006473992485553026,
0.08721208572387695,
0.045030735433101654,
0.027124295011162758,
0.022362906485795975,
0.023736432194709778,
-0.09410353004932404,
-0.014243495650589466,
0.018139954656362534,
-0.005296408664435148,
-0.036536674946546555,
-0.023302102461457253,
0.017030254006385803,
-0.01458256971091032,
-0.04145006090402603,
-0.010000593960285187,
0.02403312548995018,
-0.013707448728382587,
0.02958361804485321,
-0.019895678386092186,
-0.030328430235385895,
-0.03806878253817558,
0.029300451278686523,
-0.002759308321401477,
-0.012472892180085182,
0.007972244173288345,
0.02099332958459854,
-0.009759481996297836,
-0.01703643426299095,
-0.024628223851323128,
0.00912583526223898,
0.0013764299219474196,
0.02360101230442524,
0.023386484012007713,
0.016467709094285965,
-0.011841910891234875,
-0.014307227917015553,
0.004163592588156462,
0.05648190528154373,
0.023984866216778755,
-0.016690058633685112,
-0.01274071540683508,
-0.06856294721364975,
-0.02355816587805748,
0.003226162865757942,
0.03639962524175644,
-0.04470906779170036,
-0.011777402833104134,
0.06983507424592972,
-0.010415524244308472,
-0.026640910655260086,
0.04303743317723274,
0.027224723249673843,
-0.015148761682212353,
-0.013083996251225471,
-0.021578647196292877,
-0.013255709782242775,
-0.05332235246896744,
0.009283394552767277,
0.0301061999052763,
0.03408128395676613,
-0.028198599815368652,
0.006074636708945036,
0.06909260898828506,
0.0023347975220531225,
-0.04458775743842125,
0.002360272454097867,
0.00027323796530254185,
0.031551800668239594,
-0.027031155303120613,
0.004545708652585745,
-0.025547662749886513,
0.03926306217908859,
0.04637641832232475,
-0.00392152089625597,
-0.014456224627792835,
-0.10665491223335266,
-0.04593276232481003,
0.03529758006334305,
0.05397263541817665,
-0.007803003769367933,
-0.02588592655956745,
-0.0668153166770935,
-0.020671259611845016,
0.0043533192947506905,
-0.010447872802615166,
0.03171810880303383,
-0.036970335990190506,
0.0006340243853628635,
-0.020234879106283188,
-0.022161006927490234,
-0.018964240327477455,
0.005053470376878977,
0.006898874416947365,
-0.0028477634768933058,
-0.016192546114325523,
-0.026688897982239723,
-0.07009654492139816,
-0.005907346028834581,
0.012192150577902794,
0.04233252629637718,
-0.015263580717146397,
0.03057069145143032,
-0.010761202313005924,
0.025962622836232185,
-0.00514041306450963,
-0.09876761585474014,
-0.006575221195816994,
0.02082260698080063,
0.032800402492284775,
0.07193714380264282,
-0.002036112127825618,
0.029312865808606148,
0.07561212033033371,
0.041522443294525146,
-0.020207373425364494,
-0.006708146538585424,
-0.046742647886276245,
0.041332047432661057,
0.04745087772607803,
-0.021091366186738014,
0.06440815329551697,
0.018493911251425743,
-0.02450389601290226,
0.009629108011722565,
-0.017375130206346512,
0.0625477209687233,
-0.025167308747768402,
-0.021002603694796562,
0.00479896878823638,
0.0300996545702219,
0.00842306949198246,
0.058448951691389084,
0.010620929300785065,
0.025829996913671494,
0.001200715429149568,
-0.08801910281181335,
0.015522671863436699,
0.0044974531047046185,
-0.0034226318821310997,
0.02356504276394844,
0.0013851625844836235,
0.02454286813735962,
0.008070078678429127,
-0.0031734774820506573,
-0.007397480774670839,
0.0019125546095892787,
-0.026431957259774208,
-0.02080513723194599,
-0.0026932440232485533,
-0.006092740222811699,
-0.042375676333904266,
0.001958932727575302,
-0.011794114485383034,
-0.016249995678663254,
0.0745306983590126,
-0.014703154563903809,
0.01110852975398302,
-0.014232799410820007,
-0.047836754471063614,
0.013143578544259071,
0.016487091779708862,
-0.030117571353912354,
0.05058852955698967,
-0.0395868755877018,
0.06309366226196289,
-0.0066924202255904675,
0.031350016593933105,
-0.07414133101701736,
-0.03472862020134926,
-0.0037299059331417084,
0.036920979619026184,
-0.022194266319274902,
-0.021570928394794464,
0.010095701552927494,
0.004132016096264124,
-0.037527959793806076,
0.042430371046066284,
0.029544418677687645,
-0.005952024832367897,
-0.017907049506902695,
0.016603117808699608,
0.04063492640852928,
0.04983964562416077,
-0.019460458308458328,
0.015422716736793518,
0.02763250097632408,
0.006400786340236664,
-0.029796713963150978,
-0.007493089884519577,
0.03268393501639366,
-0.024638758972287178,
-0.018947772681713104,
0.004542007111012936,
-0.001185599248856306,
0.05368485674262047,
-0.05341501533985138,
-0.041589029133319855,
0.026788603514432907,
0.05441008880734444,
-0.00041071249870583415,
-0.03882591426372528,
0.03073158673942089,
-0.008836819790303707,
0.022071320563554764,
0.019833048805594444,
-0.03940776735544205,
-0.05625152587890625,
-0.006149470340460539,
0.006317370571196079,
-0.005885726306587458,
0.042612142860889435,
0.03539690002799034,
0.06339049339294434,
-0.005602019373327494,
0.020523404702544212,
0.01877768151462078,
-0.029777230694890022,
0.029188325628638268,
-0.025836192071437836,
0.008991317823529243,
0.017819756641983986,
0.040956754237413406,
-0.003304474288597703,
-0.002648565685376525,
-0.029856499284505844,
-0.01843937113881111,
0.06908322125673294,
-0.02287173643708229,
0.04726970195770264,
-0.016249096021056175,
-0.012325930409133434,
-0.00787037331610918,
-0.04723091423511505,
-0.009710161946713924,
0.008173834532499313,
-0.015758447349071503,
0.0556362085044384,
-0.039179857820272446,
0.004878401290625334,
-0.019015301018953323,
0.028207765892148018,
0.015058143995702267,
-0.0011314073344692588,
0.0626620277762413,
0.010776740498840809,
0.024981006979942322,
-0.024610469117760658,
-0.04109596088528633,
0.02962428517639637,
-0.016453595831990242,
0.014623759314417839,
0.030740592628717422,
-0.02672227844595909,
0.05205472186207771,
-0.01785513013601303,
0.010426548309624195,
-0.04422828182578087,
-0.05353746935725212,
-0.03372699394822121,
0.018178660422563553,
-0.008717198856174946,
0.005363241769373417,
-0.010790199041366577,
0.009112817235291004,
0.02160959504544735,
0.02226022444665432,
-0.010825035162270069,
0.00598142808303237,
-0.03735771402716637,
-0.054022807627916336,
-0.043741341680288315,
-0.023639511317014694,
0.03741991147398949,
-0.020908959209918976,
-0.03628980740904808,
0.003041897900402546,
-0.08088970929384232,
0.029799271374940872,
0.0054890913888812065,
0.059908732771873474,
0.008966709487140179,
0.04972982779145241,
0.0004889940028078854,
0.03339553624391556,
0.00691229198127985,
0.01041928306221962,
0.11238833516836166,
0.09551505744457245,
-0.01240503042936325,
-0.05813539773225784,
0.016522526741027832,
-0.04395955428481102,
0.028483405709266663,
-0.02425166592001915,
0.024544140323996544,
-0.00499653909355402,
0.0016114049358293414,
-0.01246271375566721,
0.0266755111515522,
-0.005677747540175915,
0.01930631883442402,
0.031126512214541435,
-0.01590181700885296,
-0.024694178253412247,
0.033875662833452225,
-0.0012179962359368801,
-0.00044707334018312395,
0.045448482036590576,
-0.03884368762373924,
0.018143726512789726,
-0.04149487614631653,
-0.038801029324531555,
-0.011844075284898281,
-0.03536389768123627,
0.05187723785638809,
0.0011961181880906224,
-0.02914777770638466,
0.012750555761158466,
0.015445341356098652,
0.00344075751490891,
-0.03073778748512268,
0.00610478688031435,
0.011342853307723999,
-0.014259613119065762,
0.029972681775689125,
-0.004252602346241474,
0.027944937348365784,
-0.009942506439983845,
-0.007651218678802252,
0.02108364924788475,
-0.01812778227031231,
0.00252696149982512,
-0.034821853041648865,
0.016874779015779495,
-0.004519603680819273,
-0.0018384258728474379,
-0.026654597371816635,
0.0018309189472347498,
-0.032435763627290726,
-0.04741786792874336,
-0.041863493621349335,
0.04558645933866501,
0.03711865097284317,
-0.005537716206163168,
-0.050226110965013504,
0.012423769570887089,
0.02347656711935997,
0.02332591637969017,
0.020203083753585815,
0.016759729012846947,
0.004747751168906689,
-0.00715592410415411,
-0.030292512848973274,
0.04027164354920387,
-0.014209417626261711,
-0.04048134759068489,
0.0021001265849918127,
0.004591731354594231,
-0.019470002502202988,
-0.017011666670441628,
-0.010816199705004692,
0.015677835792303085,
0.008443430997431278,
0.01213352382183075,
-0.03048018552362919,
0.008210803382098675,
-0.0717228427529335,
0.031732071191072464,
0.014828759245574474,
0.0019006269285455346,
-0.02719719149172306,
0.0008637121063657105,
0.05257493630051613,
0.029392680153250694,
-0.005588872823864222,
0.0052935415878891945,
-0.01943982020020485,
-0.0013810766395181417,
0.03319982811808586,
-0.019612273201346397,
-0.03058101236820221,
0.04466995224356651,
-0.018157700076699257,
-0.012241088785231113,
-0.03624974191188812,
0.03776064142584801,
-0.016290711238980293,
0.044854529201984406,
0.041462674736976624,
0.002256074221804738,
-0.061284031718969345,
-0.024422816932201385,
-0.00032559738610871136,
0.013354571536183357,
0.01457144133746624,
-0.05101369321346283,
0.05158998817205429,
-0.00519199064001441,
-0.025031547993421555,
-0.01438998058438301,
-0.055578067898750305,
0.015121820382773876,
-0.0019086675019934773,
0.010389250703155994,
0.00915593933314085,
-0.06268171221017838,
0.016249842941761017,
-0.026542816311120987,
-0.031657762825489044,
-0.019596904516220093,
0.029350390657782555,
-0.019590144976973534,
-0.02145858108997345,
-0.006362811662256718,
0.02657083049416542,
-0.027666926383972168,
-0.04773162677884102,
0.03103247471153736,
0.049210164695978165,
0.027057906612753868,
0.017804667353630066,
0.006663341540843248,
-0.0075685749761760235,
0.03493816405534744,
-0.013727599754929543,
-0.005741294473409653,
0.05440474674105644,
-0.02090027555823326,
-0.040801141411066055,
0.049758631736040115,
-0.039903149008750916,
0.027021141722798347,
0.02444593422114849,
-0.007291105110198259,
-0.011047517880797386,
0.04127654433250427,
-0.009564224630594254,
-0.01332605816423893,
-0.027619535103440285,
-0.023611241951584816,
0.03525330498814583,
0.016891274601221085,
-0.01360346470028162,
-0.015381086617708206,
0.010566203854978085,
0.022810742259025574,
-0.01762591488659382,
-0.007463503163307905,
-0.014322015456855297,
0.0008058536914177239,
-0.03112458437681198,
0.015744660049676895,
-0.006173288449645042,
-0.004128371365368366,
0.025118350982666016,
0.03143607825040817,
-0.02419717237353325,
0.06210557743906975,
0.001739637809805572,
-0.019079916179180145,
-0.06590951234102249,
0.0017255751881748438,
0.01523500680923462,
0.03378497436642647,
0.026808306574821472,
-0.05590037256479263,
-0.012776462361216545,
0.03791835159063339,
-0.06594815850257874,
0.007969474419951439,
-0.01590845361351967,
-0.022999484091997147,
-0.04399635270237923,
0.02366475947201252,
0.010094501078128815,
0.007566574029624462,
-0.0059191398322582245,
0.030653372406959534,
0.03501878306269646,
0.016032196581363678,
-0.01923639327287674,
-0.023359326645731926,
0.01231024507433176,
0.023808078840374947,
-0.0023803506046533585,
-0.033268459141254425,
0.06350602954626083,
-0.022076120600104332,
-0.009847274981439114,
-0.0014927963493391871,
-0.0035439543426036835,
0.0038774865679442883,
0.01771923154592514,
0.0015755491331219673,
0.010592524893581867,
0.011065489612519741,
-0.000609596841968596,
0.002946596359834075,
-0.024955270811915398,
-0.007426377851516008,
0.04005800932645798,
0.00690004276111722,
0.03476403281092644,
0.005758804269134998,
0.02992561087012291,
-0.010248968377709389,
-0.012616921216249466,
0.02156401053071022,
-0.00007708270277362317,
-0.007891838438808918,
0.041645683348178864,
0.0038427452091127634,
0.06078055873513222,
-0.049627695232629776,
0.026489663869142532,
-0.057016123086214066,
-0.024664640426635742,
-0.024149198085069656,
0.01369633898139,
0.015561960637569427,
-0.00509735057130456,
0.017977163195610046,
-0.01301622949540615,
-0.01062344666570425,
0.016494927927851677,
0.008667497895658016,
-0.012554445303976536,
0.026602838188409805,
0.0147948507219553,
-0.02637839876115322,
0.011188688687980175,
-0.0037489724345505238,
-0.03491256386041641,
0.03556167706847191,
-0.029819201678037643,
0.024356963112950325,
-0.002502172254025936,
-0.04789155721664429,
-0.023477694019675255,
-0.06566080451011658,
0.02918822318315506,
-0.0011068512685596943,
0.00043015286792069674,
-0.05970845744013786,
-0.020302504301071167,
-0.024753812700510025,
0.04221934452652931,
0.05559041351079941,
-0.0012773646740242839,
-0.027285488322377205,
-0.0010836998699232936,
0.03178142383694649,
0.005884603597223759,
-0.05269181728363037,
0.010448438115417957,
0.01721283048391342,
-0.04466473311185837,
-0.03920498490333557,
-0.03075827658176422,
-0.024453436955809593,
0.011977066285908222,
0.008650457486510277,
0.01372970174998045,
0.001391569385305047,
-0.014530712738633156,
-0.0008037890656851232,
0.0506892167031765,
-0.006107509136199951,
0.0018833541544154286,
0.08914279192686081,
0.014803201891481876,
-0.017127100378274918,
0.022547559812664986,
0.02475111186504364,
-0.05314527451992035,
0.0028266904409974813,
-0.028799960389733315,
-0.018143221735954285,
-0.016541052609682083,
-0.0027003337163478136,
0.040104806423187256,
-0.06399843841791153,
-0.0024369913153350353,
0.021122002974152565,
-0.016705863177776337,
-0.031390439718961716,
0.09030072391033173,
-0.028847383335232735,
0.018963700160384178,
0.018664700910449028,
0.01951979473233223,
0.03159766644239426,
-0.000557317805942148,
-0.023008815944194794,
0.024184145033359528,
0.001440044492483139,
-0.02156694605946541,
0.031091351062059402,
0.03693808615207672,
0.010263991542160511,
-0.00012896604312118143,
0.014111925847828388,
0.01314005721360445,
-0.019899873062968254,
-0.003655415028333664,
-0.02545214258134365,
-0.014175718650221825,
-0.0012870744103565812,
0.014359045773744583,
-0.0322551466524601,
0.09757187217473984,
-0.04236585274338722,
-0.0011782991932705045,
-0.017216401174664497,
-0.010429554618895054,
-0.007954603992402554,
0.0142577039077878,
0.024137131869792938,
0.04520094394683838,
-0.021178511902689934,
-0.004011370241641998,
0.0035584524739533663,
0.028073228895664215,
0.016824569553136826,
-0.06965423375368118,
0.06426209211349487,
0.0016404255293309689,
-0.034307245165109634,
0.04975884035229683,
-0.009916717186570168,
-0.03112664818763733,
0.01307763159275055,
0.009337040595710278,
0.029040705412626266,
-0.011374510824680328,
0.027805274352431297,
0.010040482506155968,
-0.030671361833810806,
0.006489528343081474,
-0.08427096158266068,
0.008004231378436089,
-0.017531605437397957,
-0.01886563189327717,
-0.051247574388980865,
-0.02546008490025997
] |
<p>When we use the quantum fourier transform, for a function, the output is entangled, so if a measurement is made on the output, the result may not be that of the function that one wanted in the first place. For a trivial example, consider addition of two polynomials, using DFT, or
even FFT, this is straight forward, but if we consider the same setting in the quantum case, where FFT, or DFTs are subsituted with Quantum gates, how can the result of the addition two
polynomials be accomplished. </p>
| 9,559 |
[
0.0209345743060112,
-0.002373996190726757,
-0.04560655355453491,
-0.01954701729118824,
0.044179804623126984,
0.026880843564867973,
-0.041125472635030746,
-0.012026761658489704,
0.05373107269406319,
-0.02163466438651085,
0.01883748173713684,
0.03889597952365875,
0.05040198937058449,
0.005994576960802078,
-0.01228594221174717,
0.0031664168927818537,
-0.023691674694418907,
-0.030338816344738007,
-0.021440407261252403,
-0.001350119709968567,
-0.017460843548178673,
0.08209067583084106,
0.01110558956861496,
0.0027171762194484472,
-0.0030417018570005894,
0.02582884579896927,
0.008153662085533142,
-0.02525799535214901,
0.05883834511041641,
0.07107032835483551,
-0.00045781274093315005,
-0.05187512934207916,
0.00413282448425889,
0.03728344291448593,
-0.0005170710501261055,
-0.017775779590010643,
-0.049390558153390884,
-0.012734383344650269,
0.02225174568593502,
0.0041350689716637135,
-0.053615570068359375,
-0.024270690977573395,
-0.00415336899459362,
0.02416124753654003,
-0.011929173022508621,
0.007599981501698494,
0.0033779738005250692,
-0.009072401560842991,
0.04458891972899437,
-0.05922591686248779,
0.04282647371292114,
0.01681624911725521,
-0.000665204890538007,
0.013260658830404282,
-0.013015213422477245,
0.04208991304039955,
0.06919386237859726,
0.09970072656869888,
-0.001077899243682623,
-0.027900638058781624,
-0.027852162718772888,
-0.012853537686169147,
0.030987154692411423,
-0.011875449679791927,
-0.04593175649642944,
-0.0013754256069660187,
-0.007840982638299465,
-0.006075224373489618,
-0.027569079771637917,
-0.02061271294951439,
0.004159817472100258,
0.057246118783950806,
0.04405108094215393,
-0.02129795402288437,
0.029562339186668396,
-0.013116976246237755,
0.020252134650945663,
0.029244977980852127,
0.05447835475206375,
0.014801045879721642,
0.002135055372491479,
0.008859670720994473,
0.035376597195863724,
0.022792700678110123,
0.019839894026517868,
0.006949316244572401,
0.03994229435920715,
-0.02654898539185524,
0.006539611611515284,
0.03599444404244423,
0.001997631508857012,
-0.004113723523914814,
0.04994814842939377,
-0.022781645879149437,
-0.022567739710211754,
0.015822727233171463,
-0.014795823954045773,
0.020400790497660637,
-0.0009012387017719448,
-0.05202498659491539,
0.016375642269849777,
-0.019346371293067932,
0.017441507428884506,
0.08290062099695206,
-0.013683225028216839,
0.012674529105424881,
0.013040635734796524,
0.05094274878501892,
-0.002518479712307453,
-0.0016925066011026502,
-0.003012110013514757,
0.019995128735899925,
-0.003040553070604801,
-0.014119132421910763,
-0.024719450622797012,
0.00416404427960515,
-0.008184708654880524,
-0.015515122562646866,
0.07861332595348358,
0.07745365053415298,
0.03379673883318901,
-0.029014164581894875,
0.0038557997904717922,
-0.020610971376299858,
-0.030953049659729004,
0.03407008945941925,
0.011585848405957222,
-0.012955747544765472,
-0.0615912489593029,
0.03877910599112511,
0.0009480724111199379,
-0.05093005299568176,
0.021835722029209137,
-0.005038454197347164,
0.013597752898931503,
-0.04181571677327156,
-0.13488361239433289,
-0.06267519295215607,
0.02847455069422722,
-0.016947366297245026,
0.0023132264614105225,
-0.06133105233311653,
0.03913737088441849,
0.04639463871717453,
0.08534485846757889,
-0.005312036722898483,
0.016768889501690865,
-0.017892608419060707,
-0.0004057283222209662,
0.015971774235367775,
0.012210299260914326,
-0.013986182399094105,
0.016736112534999847,
-0.0305920522660017,
-0.018160611391067505,
-0.007292378693819046,
0.029675187543034554,
0.04542187973856926,
-0.030533328652381897,
-0.0208057202398777,
0.047392766922712326,
0.021478528156876564,
-0.006467950064688921,
0.0020517793018370867,
-0.011812636628746986,
-0.04511581361293793,
0.06733238697052002,
0.039568204432725906,
0.0115992845967412,
0.04886138439178467,
-0.0009940806776285172,
0.011729729361832142,
0.012022254057228565,
0.013380165211856365,
0.020317383110523224,
-0.04402847960591316,
-0.035966165363788605,
-0.02234756574034691,
0.04001934453845024,
-0.03414224088191986,
-0.0033836939837783575,
-0.011142319068312645,
-0.010202347300946712,
0.03424805775284767,
0.024352876469492912,
0.014921610243618488,
0.0002653443953022361,
-0.004857851192355156,
0.0022431903053075075,
-0.041368015110492706,
0.0004975928459316492,
-0.061653900891542435,
0.03029937855899334,
0.03444619104266167,
-0.025698985904455185,
0.024324528872966766,
0.015772415325045586,
0.03477388620376587,
-0.011722425930202007,
-0.05959102883934975,
-0.01433782372623682,
0.01497030258178711,
0.03364148363471031,
-0.004647831432521343,
0.015091336332261562,
0.07007431238889694,
0.07431373745203018,
0.010532911866903305,
0.03219606354832649,
-0.028155792504549026,
-0.03145289793610573,
0.011611377820372581,
-0.007832823321223259,
-0.006899015046656132,
0.006538940593600273,
-0.011835681274533272,
0.01451612077653408,
-0.00540905399248004,
-0.015458505600690842,
0.008541563525795937,
-0.05358589068055153,
0.05981015786528587,
0.028860341757535934,
0.014378940686583519,
-0.001589432475157082,
0.045957300812006,
0.022963635623455048,
0.0062483069486916065,
-0.0018812328344210982,
-0.07449866086244583,
-0.053383003920316696,
0.008772972971200943,
0.01703588105738163,
0.0539139099419117,
-0.03276979178190231,
0.004922729451209307,
0.04088063910603523,
0.0016213390044867992,
0.007026903331279755,
0.02691733092069626,
-0.020790603011846542,
0.04122950881719589,
0.010940773412585258,
-0.0011368696577847004,
0.0476493239402771,
-0.004054637625813484,
-0.005249552428722382,
-0.013770893216133118,
-0.02320033125579357,
0.010196859017014503,
-0.03500281646847725,
0.04185087978839874,
-0.02601717598736286,
0.04432152211666107,
-0.020503314211964607,
-0.027235087007284164,
-0.01553799957036972,
-0.03690515458583832,
-0.012756320647895336,
-0.03140147030353546,
-0.03196229040622711,
-0.013916642405092716,
0.02151412144303322,
-0.01685742847621441,
0.03280511125922203,
-0.02155454084277153,
-0.04827404394745827,
-0.0030789957381784916,
0.03303055092692375,
-0.027140676975250244,
0.008080748841166496,
-0.032106056809425354,
0.01999691314995289,
0.006905416026711464,
0.022821029648184776,
0.04700088128447533,
-0.04238990694284439,
0.05403798818588257,
-0.0478929802775383,
-0.053139474242925644,
-0.014077253639698029,
-0.056861892342567444,
0.035840071737766266,
0.012172593735158443,
-0.04711655527353287,
0.01742413453757763,
-0.03441004455089569,
-0.030913516879081726,
0.032776013016700745,
-0.04374097287654877,
0.028965871781110764,
-0.024714745581150055,
-0.024762272834777832,
-0.02984381653368473,
-0.028143661096692085,
-0.0362822450697422,
-0.011642754077911377,
-0.006461767014116049,
-0.00326713640242815,
0.01847999542951584,
-0.02063879184424877,
-0.014891408383846283,
0.03321387246251106,
-0.00768760871142149,
0.001962427981197834,
-0.006063105072826147,
-0.021844446659088135,
0.026357926428318024,
-0.040750905871391296,
0.0252258088439703,
-0.026182493194937706,
-0.06339547783136368,
-0.014885501004755497,
-0.060367900878190994,
-0.054146427661180496,
0.02563588134944439,
0.008231938816606998,
0.0483698770403862,
-0.01190260797739029,
-0.00947301834821701,
0.052701905369758606,
-0.001067441888153553,
-0.02797490544617176,
0.007429021876305342,
-0.005490264389663935,
0.00770086282864213,
-0.022675421088933945,
0.005661408416926861,
0.03314146026968956,
-0.021818004548549652,
0.09726884216070175,
0.011838582344353199,
-0.02961462363600731,
0.05722324550151825,
0.011583632789552212,
-0.06294052302837372,
0.023790741339325905,
0.03679049760103226,
0.03100431337952614,
0.042258281260728836,
0.017598414793610573,
-0.02000632882118225,
0.00942540168762207,
0.02576342411339283,
-0.021985545754432678,
-0.004677772521972656,
0.007849925197660923,
0.0332794114947319,
0.019440975040197372,
0.013696554116904736,
-0.06123695150017738,
0.05250868573784828,
0.008696204051375389,
0.007970960810780525,
-0.0066440817900002,
0.009211335331201553,
0.01149214431643486,
-0.024612292647361755,
0.03597600758075714,
0.017218362540006638,
0.029771186411380768,
-0.02481766790151596,
-0.019769364967942238,
-0.018808143213391304,
-0.0024306888226419687,
0.047006286680698395,
-0.045256081968545914,
-0.037613555788993835,
0.053097907453775406,
0.012293427251279354,
0.012437180615961552,
0.0019571653101593256,
0.0023093982599675655,
-0.004279229324311018,
-0.03836110234260559,
-0.019893990829586983,
0.004472740925848484,
0.05666571855545044,
0.03230496868491173,
0.03422706946730614,
0.055777665227651596,
0.02231445722281933,
-0.03707261011004448,
-0.003346386132761836,
-0.08388514816761017,
0.0044570970349013805,
0.005472996737807989,
-0.006700876634567976,
-0.0030672671273350716,
-0.028030287474393845,
-0.02063979022204876,
-0.05789586529135704,
-0.07337762415409088,
-0.040270645171403885,
-0.015356257557868958,
-0.0462007150053978,
0.008205600082874298,
0.034576911479234695,
-0.01936877891421318,
-0.007216437719762325,
0.03450976684689522,
0.03365582972764969,
-0.03265979886054993,
-0.0034839760046452284,
0.033786896616220474,
-0.04516275227069855,
0.014986257068812847,
0.010827934369444847,
0.011944676749408245,
-0.014531489461660385,
0.029531627893447876,
0.03841624781489372,
0.06463506817817688,
-0.01584869623184204,
0.02683662436902523,
0.0035503427498042583,
0.07424888759851456,
0.027474433183670044,
-0.051316291093826294,
0.00572632672265172,
-0.028085652738809586,
-0.0012592491693794727,
-0.001163021195679903,
0.04392537474632263,
-0.004638273268938065,
0.005356427747756243,
0.022031353786587715,
0.013339726254343987,
-0.003781822044402361,
0.008658435195684433,
0.05323454365134239,
0.014556041918694973,
-0.009804979898035526,
-0.040211066603660583,
-0.01351223699748516,
-0.0020117147359997034,
-0.021482277661561966,
0.02089289389550686,
-0.013064408674836159,
-0.0016180045204237103,
0.013557912781834602,
0.03583264723420143,
0.022601433098316193,
-0.02105930633842945,
-0.002963137114420533,
0.004493992310017347,
0.0004821255279239267,
0.00483551062643528,
0.02617061883211136,
-0.007336433511227369,
0.0300305038690567,
0.006793218199163675,
0.011338666081428528,
-0.010045968927443027,
-0.10019219666719437,
-0.0031888908706605434,
0.039147134870290756,
0.032716620713472366,
0.020167140290141106,
0.011429972015321255,
-0.02651144191622734,
-0.014566553756594658,
0.03538116067647934,
-0.00934891402721405,
0.062435343861579895,
-0.005351165309548378,
0.001701856730505824,
-0.02239709347486496,
-0.003670634003356099,
0.009394748136401176,
0.022784072905778885,
0.0048818509094417095,
0.008544553071260452,
-0.01475780550390482,
-0.02990654483437538,
-0.02103598043322563,
-0.01469375193119049,
0.04459483176469803,
0.05326365306973457,
-0.0006853541708551347,
-0.013710812665522099,
-0.011161846108734608,
0.033600758761167526,
-0.0159864854067564,
-0.07005540281534195,
0.02963954024016857,
-0.01475257147103548,
0.01480080746114254,
0.0644136294722557,
-0.0441233366727829,
-0.045256853103637695,
-0.0033115441910922527,
-0.03135232627391815,
-0.007503022439777851,
0.03336139768362045,
-0.011882618069648743,
0.04631822928786278,
0.01952582225203514,
0.027887500822544098,
0.0659785345196724,
0.0496583990752697,
-0.021322637796401978,
0.019534185528755188,
0.0032806771341711283,
0.030907906591892242,
-0.028100498020648956,
0.03990427404642105,
-0.03520982712507248,
0.006749324966222048,
-0.02043866366147995,
0.02882927469909191,
-0.024857906624674797,
0.02520068548619747,
0.005921825300902128,
0.007236476056277752,
-0.022023556753993034,
-0.008699027821421623,
-0.013292822055518627,
0.02206733636558056,
-0.013888473622500896,
0.022008134052157402,
-0.021559499204158783,
-0.020157182589173317,
0.005635623354464769,
0.013541923835873604,
0.008844535797834396,
0.015769246965646744,
0.007992868311703205,
0.03411552309989929,
-0.011005462147295475,
-0.014073834754526615,
0.04673432558774948,
-0.02033049799501896,
0.02253718674182892,
-0.019634420052170753,
0.003810472320765257,
0.0193827785551548,
-0.06498268991708755,
-0.009099493734538555,
-0.01229097694158554,
-0.01886572875082493,
-0.008686346933245659,
-0.032525818794965744,
0.03826053440570831,
0.00012023612362099811,
-0.01420951820909977,
-0.04469682276248932,
-0.036677904427051544,
-0.0016804757760837674,
0.006556370295584202,
0.025045329704880714,
-0.024782437831163406,
0.016813036054372787,
-0.02467404678463936,
-0.006487064994871616,
-0.036939382553100586,
0.03374960646033287,
-0.005473712924867868,
-0.00859181210398674,
0.02920992113649845,
-0.024061720818281174,
0.03957878425717354,
-0.023441221565008163,
0.0072066751308739185,
0.013508826494216919,
-0.03503387048840523,
-0.025108855217695236,
-0.020266732200980186,
0.002560690278187394,
-0.033245157450437546,
-0.027205809950828552,
-0.013479070737957954,
-0.004439331591129303,
0.003125353017821908,
-0.024880114942789078,
-0.015878411009907722,
-0.0006033231038600206,
0.008932683616876602,
0.013575919903814793,
-0.0012885580072179437,
-0.011323759332299232,
0.012678169645369053,
0.06794645637273788,
-0.0001668902114033699,
-0.008100874722003937,
-0.011623878963291645,
-0.032754357904195786,
0.00669212406501174,
0.007751870434731245,
-0.01631345972418785,
-0.006088834721595049,
0.07008078694343567,
-0.0080720828846097,
-0.0007907490944489837,
0.02623695693910122,
-0.01581444963812828,
0.021597575396299362,
-0.009423392824828625,
0.020010055974125862,
-0.010568869300186634,
0.022182535380125046,
-0.03900139406323433,
-0.0425875298678875,
-0.03577044978737831,
-0.045978039503097534,
0.05841963365674019,
-0.012812424451112747,
0.050000183284282684,
0.030303211882710457,
-0.02467712201178074,
-0.012699943035840988,
-0.011572567746043205,
-0.024721931666135788,
-0.0009135861764661968,
-0.004883885383605957,
0.020866191014647484,
0.00017259657033719122,
0.012382912449538708,
0.012716210447251797,
0.015608099289238453,
0.010708296671509743,
0.012531394138932228,
0.01830356754362583,
0.03198956698179245,
0.018214529380202293,
-0.02963254787027836,
-0.04347294196486473,
0.023314449936151505,
-0.07553178817033768,
-0.007389307953417301,
0.000700351083651185,
0.007013754453510046,
0.03668860346078873,
0.00019331132352817804,
0.004127313382923603,
-0.05012919381260872,
-0.009704690426588058,
-0.039342984557151794,
0.0020574748050421476,
-0.000025971614377340302,
-0.0036498894914984703,
0.011076895520091057,
-0.01537600439041853,
0.03301621973514557,
0.012417776510119438,
0.0109070660546422,
0.00010105963156092912,
-0.046035055071115494,
-0.029642589390277863,
-0.03725630044937134,
-0.026739362627267838,
0.055786117911338806,
0.008276375941932201,
-0.03364497423171997,
0.04574427008628845,
0.01311799231916666,
0.08009149134159088,
-0.0000891858508111909,
0.02191627211868763,
-0.03675570711493492,
0.050430409610271454,
-0.028789538890123367,
0.027642633765935898,
-0.013189459219574928,
0.02656693197786808,
0.09483736753463745,
0.04435182735323906,
0.020379187539219856,
-0.08958832174539566,
-0.014560803771018982,
-0.01948702149093151,
0.026570700109004974,
-0.006227778736501932,
0.031237853690981865,
-0.014529221691191196,
0.01935688592493534,
-0.011186715215444565,
0.02531127631664276,
0.017668351531028748,
-0.013098267838358879,
0.027924079447984695,
-0.047828275710344315,
-0.037330519407987595,
0.01762242428958416,
0.041793279349803925,
0.013178877532482147,
0.01861949823796749,
-0.04449722543358803,
-0.05092495679855347,
-0.04893358424305916,
-0.015285837464034557,
-0.024225251749157906,
-0.02723313309252262,
0.01286749541759491,
0.04858171567320824,
-0.044573258608579636,
0.010558131150901318,
0.04944264143705368,
-0.010481506586074829,
-0.021518362686038017,
0.022883567959070206,
0.01266791857779026,
-0.017140669748187065,
-0.006586405448615551,
0.03662886470556259,
0.04944838583469391,
-0.01255256962031126,
-0.03878810629248619,
0.02226060815155506,
-0.07029010355472565,
0.007925939746201038,
-0.036832742393016815,
0.013994114473462105,
-0.038846760988235474,
-0.03178698197007179,
-0.04925532266497612,
-0.027115346863865852,
0.008989588357508183,
-0.05932078883051872,
-0.020272603258490562,
0.014405619353055954,
0.02664639987051487,
-0.01163569837808609,
-0.03325073421001434,
-0.0007203063578344882,
0.041765984147787094,
-0.010816994123160839,
0.025765255093574524,
-0.006627632305026054,
-0.04448617622256279,
0.012747105211019516,
0.016817590221762657,
0.021772611886262894,
-0.038539133965969086,
-0.01796584017574787,
-0.026000769808888435,
0.020021216943860054,
0.004423136822879314,
-0.04367116466164589,
0.04750211164355278,
0.0199358519166708,
0.07589610666036606,
-0.02209492400288582,
0.0006813691579736769,
-0.007910323329269886,
-0.06708075851202011,
0.009582472033798695,
-0.03369628265500069,
-0.013406533747911453,
0.0028251083567738533,
-0.005844954866915941,
0.06397439539432526,
0.04035036265850067,
-0.029954837635159492,
-0.02545834891498089,
0.01312799472361803,
-0.0192282572388649,
0.06909548491239548,
-0.01645001769065857,
0.004352249670773745,
0.013103821314871311,
0.007839230820536613,
-0.024263376370072365,
-0.05623793974518776,
0.04690368473529816,
0.046599533408880234,
-0.004462189041078091,
-0.0408003106713295,
0.038750842213630676,
-0.040140338242053986,
-0.003917299211025238,
0.003975540399551392,
0.006018233019858599,
-0.03036959283053875,
-0.03165692836046219,
0.02741370163857937,
-0.04258231818675995,
-0.0318070650100708,
-0.04147346317768097,
-0.006110365502536297,
0.004355971701443195,
0.005034943111240864,
-0.04051939770579338,
-0.013569011352956295,
0.021191662177443504,
0.04776163026690483,
-0.007890158332884312,
-0.022348938509821892,
-0.017581913620233536,
0.001845474005676806,
0.01113069336861372,
-0.02678573504090309,
0.003356119617819786,
0.0052512213587760925,
-0.059977687895298004,
-0.019216949120163918,
0.03479885682463646,
0.03759589046239853,
-0.013202990405261517,
-0.009429286234080791,
0.010083131492137909,
-0.0023611129727214575,
0.007756381761282682,
-0.012525057420134544,
-0.0019255896331742406,
0.04950285330414772,
-0.06004546210169792,
-0.005516897886991501,
0.04810544475913048,
-0.03383950889110565,
0.0004072815936524421,
0.05169404298067093,
-0.0053589134477078915,
-0.04020553082227707,
0.004556085914373398,
-0.010762087069451809,
-0.00857362151145935,
0.04218106344342232,
0.01582186482846737,
-0.028612839058041573,
0.0016953264130279422,
0.0006833867519162595,
-0.05123022571206093,
0.0020050937309861183,
0.022549035027623177,
0.03675924241542816,
0.04078279063105583,
0.008159542456269264,
0.020031295716762543,
-0.004906483925879002,
0.034336160868406296,
0.02892819605767727,
-0.03633905574679375,
-0.0010894887382164598,
0.03570151701569557,
-0.0022436364088207483,
0.021649518981575966,
0.0059136999770998955,
-0.009088520891964436,
-0.09711688756942749,
-0.0066329361870884895,
0.013309633359313011,
-0.035327572375535965,
0.036143429577350616,
-0.013771696016192436,
-0.0024699801579117775,
0.0287154670804739,
-0.08286847919225693,
0.046135686337947845,
-0.05905652418732643,
-0.03936126455664635,
-0.024449989199638367,
0.027001451700925827,
-0.0335317887365818,
0.03222734481096268,
0.02063070237636566,
0.03016144596040249,
0.03612525761127472,
-0.0008817602647468448,
-0.002046342007815838,
-0.010820131748914719,
-0.031485579907894135,
-0.02424452267587185,
-0.013691350817680359,
-0.0015987226506695151,
0.07171092927455902,
-0.030128251761198044,
-0.0056904819793999195,
0.008984246291220188,
-0.021117959171533585,
-0.006341471336781979,
-0.03135748952627182,
0.017177704721689224,
0.052430786192417145,
0.04796554520726204,
-0.004795809276401997,
-0.023756008595228195,
0.0036181164905428886,
0.03177963197231293,
0.01630566082894802,
0.02903931960463524,
-0.030333759263157845,
0.013394605368375778,
0.02945750206708908,
-0.008160082623362541,
-0.0035973552148789167,
0.031151166185736656,
0.01901472732424736,
-0.017429865896701813,
-0.013362317346036434,
0.010014859959483147,
0.03469238430261612,
-0.04091689735651016,
0.025247862562537193,
-0.016864165663719177,
-0.01267827209085226,
0.011166580952703953,
0.017411047592759132,
-0.03699757158756256,
-0.009871249087154865,
-0.02259647287428379,
-0.04945753142237663,
0.07019199430942535,
0.002060945611447096,
-0.012851131148636341,
-0.04559418186545372,
-0.04261530563235283,
0.015612167306244373,
-0.006797317881137133,
0.021673381328582764,
-0.05520879104733467,
0.002578285988420248,
0.043547406792640686,
-0.01749495044350624,
0.013742875307798386,
-0.04367399215698242,
-0.0349804125726223,
-0.04938448965549469,
-0.05045337602496147,
0.04596639424562454,
0.02378733642399311,
0.02565995417535305,
-0.01751836948096752,
-0.01462172158062458,
-0.01224265806376934,
-0.0030769496224820614,
0.03605946525931358,
-0.003078562207520008,
-0.03040017932653427,
-0.03223124146461487,
0.009746581315994263,
0.02906802110373974,
0.003990354016423225,
0.010058237239718437,
-0.026101423427462578,
-0.010559841990470886,
-0.036281511187553406,
-0.030293621122837067,
-0.008555413223803043,
0.0403035469353199,
0.026266105473041534,
0.009348079562187195,
0.006562262773513794,
-0.01885141432285309,
-0.04003371670842171,
0.08059858530759811,
0.0012617870233953,
0.0424455888569355,
0.03238767385482788,
-0.03226499632000923,
0.052999347448349,
0.024551084265112877,
-0.0032483062241226435,
-0.06783084571361542,
0.012747352942824364,
-0.013080567121505737,
-0.01399682741612196,
-0.021261276677250862,
0.031661272048950195,
0.03919339179992676,
-0.007248044013977051,
-0.0072502875700592995,
0.03638649359345436,
-0.06417174637317657,
-0.006714677903801203,
0.07790035754442215,
-0.010717133060097694,
0.020437905564904213,
-0.00492072245106101,
0.04254186525940895,
0.024101493880152702,
-0.009221798740327358,
0.01049346849322319,
0.030530592426657677,
0.03272738680243492,
0.02750125154852867,
0.04730842635035515,
0.046554647386074066,
-0.037725336849689484,
0.021780099719762802,
0.014384130947291851,
0.05123193562030792,
-0.04047458991408348,
-0.023969940841197968,
0.0034047099761664867,
-0.03281271830201149,
-0.013672607950866222,
0.003905021585524082,
-0.018614165484905243,
0.07492099702358246,
-0.015197491273283958,
-0.0017221977468580008,
-0.03449606895446777,
0.0018932176753878593,
-0.018602989614009857,
-0.004853490740060806,
0.015681549906730652,
0.06871025264263153,
-0.02342088520526886,
-0.016034036874771118,
-0.021668093279004097,
-0.003681519301608205,
-0.0074832020327448845,
-0.00855912733823061,
0.016146428883075714,
-0.030313102528452873,
-0.03252467140555382,
-0.005880216136574745,
-0.03660817816853523,
-0.044349554926157,
-0.03524937108159065,
0.02732839435338974,
0.04089893400669098,
0.02317754365503788,
-0.007630991283804178,
-0.00757612893357873,
-0.008815696462988853,
0.03326806426048279,
-0.06811893731355667,
0.03031933307647705,
0.004384864587336779,
0.06291653215885162,
0.021894918754696846,
-0.0288226455450058
] |
<p>Given a fixed shell with the mass of $M$ and a radius $R$ ,
what would be the metric tensor for $r<R$?
I do know that using Birkhoff Theorem the metric for $r>R$ should be schwarzschild.
I'm not sure how to solve $G_{\mu\nu}=0$ for the inner part, and I'm not sure if I can demand continuity at $r=R$.</p>
| 50 |
[
-0.043796926736831665,
0.0033213424030691385,
-0.019400322809815407,
-0.031140198931097984,
-0.013540671207010746,
0.012452756054699421,
-0.005543286446481943,
-0.03448563069105148,
-0.02686871960759163,
-0.0389668345451355,
0.05152799189090729,
0.037859879434108734,
0.09243809431791306,
-0.006328101735562086,
0.017459021881222725,
-0.02106456458568573,
-0.035328201949596405,
-0.017644306644797325,
-0.019367380067706108,
-0.043472837656736374,
0.023126225918531418,
-0.006455576047301292,
0.015335646457970142,
-0.03168303519487381,
-0.008738839998841286,
0.03995253145694733,
-0.0062341089360415936,
-0.03113269992172718,
-0.00012501674063969404,
0.038532789796590805,
-0.03442632406949997,
-0.01771608367562294,
0.011799506843090057,
0.032977331429719925,
0.009367696940898895,
-0.0014450334711000323,
-0.050859056413173676,
-0.00823232438415289,
-0.040702398866415024,
0.025907134637236595,
-0.030399609357118607,
-0.020700272172689438,
-0.011839897371828556,
0.04540005698800087,
0.0071626091375947,
-0.000053927855333313346,
0.028593381866812706,
0.0037287892773747444,
0.04018135741353035,
-0.02209630236029625,
0.07886937260627747,
0.017143340781331062,
0.03466799855232239,
0.008990578353404999,
-0.01247493177652359,
-0.01948845386505127,
0.07523933798074722,
0.07509946823120117,
0.01118692196905613,
-0.033468712121248245,
-0.041002918034791946,
-0.03580448776483536,
-0.017294635996222496,
-0.02589457668364048,
-0.00046953302808105946,
0.0661928728222847,
-0.03559670224785805,
0.015478172339498997,
0.02506854571402073,
-0.007440666202455759,
0.025485146790742874,
0.01696483977138996,
0.014343850314617157,
-0.029055386781692505,
0.003024846548214555,
-0.027649804949760437,
0.013257472775876522,
0.01018096785992384,
0.009042037650942802,
0.010515378788113594,
-0.039637401700019836,
0.007842355407774448,
0.03752738982439041,
0.05373045802116394,
-0.006238950882107019,
0.0040297480300068855,
0.042068514972925186,
0.010524713434278965,
0.029265809804201126,
0.019611885771155357,
0.0073041063733398914,
-0.0466022826731205,
0.04135593771934509,
0.011140315793454647,
-0.009896320290863514,
0.044830240309238434,
-0.030887676402926445,
0.05628594011068344,
-0.007526759058237076,
-0.025217320770025253,
-0.008913490921258926,
-0.022478025406599045,
-0.005290613975375891,
0.08810526132583618,
0.02834557369351387,
-0.006607003044337034,
-0.027036933228373528,
-0.005953262094408274,
-0.01754106767475605,
-0.006149298511445522,
-0.0600549653172493,
0.010036175139248371,
-0.0152133135125041,
-0.04108148813247681,
0.04764038324356079,
-0.0388985350728035,
0.012674066238105297,
-0.037345029413700104,
0.01193712092936039,
0.05973164737224579,
0.053519684821367264,
0.018445614725351334,
0.04342062771320343,
-0.08134179562330246,
-0.07366029173135757,
0.01203196682035923,
0.05544452369213104,
-0.014978944323956966,
-0.027736466377973557,
-0.019935989752411842,
0.023508591577410698,
-0.019373813644051552,
-0.016335677355527878,
-0.012311401776969433,
0.03897622600197792,
-0.04182940721511841,
-0.09489168226718903,
-0.06721857935190201,
0.02479405887424946,
0.015138281509280205,
-0.03235771134495735,
-0.03296341001987457,
0.008490079082548618,
0.038397204130887985,
0.068138487637043,
0.06408336013555527,
0.005392460618168116,
0.024275116622447968,
0.06036103516817093,
-0.01631474494934082,
0.0009106682264246047,
-0.004799827001988888,
-0.013082274235785007,
-0.031552139669656754,
0.0016670572804287076,
-0.07015606015920639,
-0.0033969625364989042,
0.01268172450363636,
0.025753142312169075,
-0.015486727468669415,
0.057078342884778976,
0.00006242108065634966,
0.037126243114471436,
-0.00857581291347742,
-0.006906251888722181,
-0.0036448154132813215,
0.029328785836696625,
0.03438073396682739,
-0.020458701997995377,
0.022877350449562073,
0.032321907579898834,
0.009055950678884983,
0.05373835563659668,
0.04554019495844841,
0.045980509370565414,
-0.07104532420635223,
0.020297424867749214,
-0.02015761472284794,
0.01254974864423275,
0.04991269111633301,
-0.0267009437084198,
-0.03513822332024574,
0.027144838124513626,
-0.02020716294646263,
0.018636755645275116,
0.012078521773219109,
-0.01643923483788967,
-0.008940077386796474,
0.031122636049985886,
-0.0399896539747715,
0.022670892998576164,
-0.023107752203941345,
0.03541938215494156,
0.02732061594724655,
-0.031310927122831345,
-0.009464624337852001,
0.01852893829345703,
0.021532244980335236,
-0.002294895937666297,
-0.0031959256157279015,
-0.0065903733484447,
0.02768127992749214,
-0.020345188677310944,
0.00964672677218914,
-0.02274359203875065,
0.026193633675575256,
0.01000298373401165,
0.02392396330833435,
0.051153529435396194,
-0.0017473665066063404,
-0.012954694218933582,
0.024710722267627716,
0.04390968754887581,
0.026333773508667946,
-0.03403583914041519,
0.005591916851699352,
0.007969867438077927,
0.005266144406050444,
-0.005183121655136347,
0.01810416392982006,
-0.05141826719045639,
0.07945758104324341,
0.036546360701322556,
-0.002750150626525283,
0.023024633526802063,
-0.00397228728979826,
0.01625731959939003,
0.02733420394361019,
0.011979456059634686,
-0.03707880526781082,
-0.0191746037453413,
0.002292039804160595,
0.0035769615788012743,
0.031916916370391846,
-0.05439536273479462,
0.03804432228207588,
0.025260379537940025,
0.02866317331790924,
0.0029174520168453455,
0.00030008910107426345,
-0.03743236884474754,
-0.048665933310985565,
0.005821670405566692,
0.0023564558941870928,
-0.031856875866651535,
-0.011643684469163418,
-0.020221324637532234,
0.017449479550123215,
0.03301190584897995,
0.010203738696873188,
0.012775055132806301,
0.039613980799913406,
-0.01737787388265133,
-0.03295111283659935,
-0.016900360584259033,
-0.03079232946038246,
0.07354100793600082,
-0.004637938924133778,
0.02054918371140957,
0.07514369487762451,
-0.008568225428462029,
-0.025304114446043968,
-0.04815094918012619,
-0.004694793839007616,
0.02831375226378441,
0.01190146803855896,
0.00702239153906703,
-0.022183777764439583,
0.028789762407541275,
-0.04468556493520737,
0.0013069970300421119,
-0.003959098365157843,
-0.0025091867428272963,
-0.0270986370742321,
-0.017504464834928513,
0.007791379000991583,
0.029956653714179993,
0.004704324062913656,
0.016180137172341347,
-0.028405234217643738,
0.007123027928173542,
0.009940705262124538,
0.014310567639768124,
0.02683349698781967,
-0.06058402359485626,
0.00774254510179162,
-0.021083833649754524,
0.0035733880940824747,
0.022926315665245056,
0.009595413692295551,
-0.01918731816112995,
0.012950003147125244,
0.00022582603560294956,
-0.052556589245796204,
0.009309514425694942,
-0.020119786262512207,
-0.009997167624533176,
-0.021340299397706985,
0.033541008830070496,
0.057383738458156586,
0.002240333938971162,
-0.03684533014893532,
0.0012928341748192906,
-0.04507914185523987,
-0.0514523908495903,
-0.016416890546679497,
0.007513964548707008,
0.03795398026704788,
-0.01312471367418766,
0.03214946761727333,
0.06718206405639648,
0.010394690558314323,
-0.0013280019629746675,
-0.0395987294614315,
-0.041230544447898865,
0.054620709270238876,
0.0017723555210977793,
0.012485531158745289,
-0.0017615723190829158,
-0.04817437380552292,
0.08971691876649857,
0.009453905746340752,
-0.017793020233511925,
-0.011046742089092731,
0.026206757873296738,
0.017627529799938202,
-0.043437957763671875,
-0.009106523357331753,
-0.005872885696589947,
0.009594127535820007,
-0.01264242734760046,
0.06671970337629318,
0.02907012589275837,
0.014183496125042439,
0.028089605271816254,
-0.007407062686979771,
0.029428942129015923,
0.008630878292024136,
-0.0001178972379420884,
0.04993734881281853,
0.004513694904744625,
0.024705160409212112,
0.031242510303854942,
-0.014973049983382225,
0.016569187864661217,
-0.002690692665055394,
-0.0746212899684906,
0.0245960745960474,
-0.0056109968572855,
-0.002534208819270134,
0.006777886301279068,
0.01847829297184944,
-0.017916547134518623,
-0.011968675069510937,
0.020637670531868935,
0.04260632395744324,
0.015478869900107384,
-0.03578553721308708,
-0.001061460468918085,
0.049845222383737564,
-0.005573953501880169,
-0.019527101889252663,
0.014813607558608055,
0.01343810185790062,
-0.03045336715877056,
0.02472831681370735,
-0.006752459332346916,
-0.03462103009223938,
0.013354087248444557,
0.05112621188163757,
0.040394581854343414,
-0.029420698061585426,
-0.024030735716223717,
0.0035680767614394426,
-0.06365872174501419,
-0.007729187607765198,
-0.0014389898860827088,
0.03613545745611191,
-0.005584095139056444,
0.03141938894987106,
0.06386927515268326,
0.020158421248197556,
0.03351752460002899,
-0.0001990601740544662,
-0.058373238891363144,
0.027839161455631256,
-0.03362957760691643,
-0.022809147834777832,
0.0020159368868917227,
-0.0344848670065403,
-0.03967341035604477,
-0.03215404227375984,
-0.028914928436279297,
-0.012773831374943256,
-0.01916949637234211,
-0.08548051863908768,
0.02239156886935234,
-0.04154009744524956,
-0.04522799327969551,
0.005325194448232651,
0.025501303374767303,
0.018902532756328583,
-0.022261492908000946,
-0.015381470322608948,
0.03029036521911621,
-0.050243787467479706,
-0.0018272583838552237,
-0.005776179023087025,
0.02873784303665161,
-0.014192862436175346,
0.05245587229728699,
0.022601790726184845,
0.047183554619550705,
0.0028870704118162394,
-0.009652758948504925,
0.029620755463838577,
0.06853931397199631,
-0.0047020078636705875,
-0.030815904960036278,
0.002306723967194557,
-0.04825928807258606,
-0.04112909361720085,
0.02942053973674774,
0.07597780227661133,
-0.02670910768210888,
-0.007999409921467304,
0.040967997163534164,
-0.006518075242638588,
-0.008199185132980347,
-0.005817845929414034,
0.0806068629026413,
0.02535545639693737,
-0.06032373383641243,
-0.05244578421115875,
-0.03346853330731392,
-0.02063038945198059,
0.005471318960189819,
0.010964666493237019,
-0.017241165041923523,
-0.035709548741579056,
-0.020865051075816154,
0.00007710986392339692,
-0.0004447161918506026,
-0.011016287840902805,
-0.011065857484936714,
-0.010854363441467285,
0.01833988167345524,
-0.005856730043888092,
-0.035021837800741196,
0.006695847027003765,
0.04709767922759056,
0.07170233875513077,
0.027611950412392616,
0.0039767129346728325,
-0.04251930117607117,
-0.006413409020751715,
0.03846263512969017,
0.0029660891741514206,
-0.009228669106960297,
-0.0018806001171469688,
-0.06333454698324203,
-0.02298177406191826,
0.061016522347927094,
0.0013373212423175573,
0.03219433128833771,
0.001555686816573143,
0.0036401294637471437,
0.00017368870612699538,
0.00806618481874466,
-0.019417624920606613,
0.013790453784167767,
-0.01953129470348358,
-0.02408670075237751,
-0.04101184755563736,
0.03997016325592995,
-0.02546997368335724,
0.02847324311733246,
0.030327098444104195,
0.022365864366292953,
0.03907931596040726,
-0.010393036529421806,
0.022783389315009117,
0.03360624611377716,
0.009816102683544159,
-0.0750398263335228,
-0.023579856380820274,
0.028394725173711777,
-0.05010262504220009,
0.0008656163117848337,
-0.03569529205560684,
-0.023495139554142952,
0.030586332082748413,
0.020729852840304375,
-0.0003085790085606277,
0.06912337243556976,
-0.029903383925557137,
0.029287219047546387,
0.012196526862680912,
-0.000028660806492553093,
0.011473879218101501,
-0.021756211295723915,
0.04927268624305725,
0.0004548613796941936,
-0.03555271402001381,
0.012726197950541973,
-0.026433546096086502,
-0.020318210124969482,
-0.000990425469353795,
0.001354701234959066,
-0.05066310614347458,
0.05400379002094269,
-0.004585002548992634,
0.03461645171046257,
0.0027472046203911304,
-0.03245237097144127,
0.002401804318651557,
0.049967601895332336,
-0.0377175472676754,
-0.003608244238421321,
0.03567839413881302,
-0.00857006385922432,
-0.00019461936608422548,
-0.02211248315870762,
0.005937756970524788,
-0.0029139560647308826,
-0.015183699317276478,
0.01738939993083477,
-0.002679054858162999,
0.03548882529139519,
-0.006636835169047117,
-0.00719889160245657,
0.029653554782271385,
-0.027564657852053642,
0.05088851600885391,
-0.03333161771297455,
-0.026778312399983406,
0.02523689717054367,
-0.002228823956102133,
-0.03691898286342621,
-0.0008245885255746543,
0.011014224030077457,
0.0391790047287941,
-0.018732735887169838,
-0.01745722070336342,
0.033775195479393005,
0.011828519403934479,
-0.0858398899435997,
-0.016958195716142654,
0.037358589470386505,
-0.008946960791945457,
-0.027802033349871635,
-0.020497795194387436,
0.014868450351059437,
-0.028313037008047104,
-0.022134985774755478,
0.00811332743614912,
0.05057898163795471,
-0.0358651727437973,
-0.0001624834694666788,
-0.03584342077374458,
0.003840734949335456,
0.04324079304933548,
-0.017127498984336853,
0.023867568001151085,
0.005398487206548452,
0.018127068877220154,
0.019106360152363777,
0.011230021715164185,
0.06347774714231491,
-0.01742776297032833,
-0.018725885078310966,
-0.053256213665008545,
-0.03089001029729843,
0.04585404694080353,
-0.01464703120291233,
-0.003258706768974662,
0.04446125030517578,
0.02792922593653202,
-0.02220156416296959,
-0.014342856593430042,
0.050869934260845184,
-0.040055811405181885,
0.010354270227253437,
-0.03104792907834053,
-0.009561188519001007,
-0.009100857190787792,
-0.06676401197910309,
0.03430423140525818,
-0.018743010237812996,
0.019840478897094727,
-0.017453160136938095,
0.09920313209295273,
0.007114287465810776,
-0.0005875278729945421,
0.009757583029568195,
-0.006433837115764618,
0.008427873253822327,
-0.0011633678805083036,
-0.022580457851290703,
0.02346501685678959,
-0.0014603041345253587,
-0.0012481457088142633,
-0.029951272532343864,
-0.02996239997446537,
0.011161478236317635,
0.07549473643302917,
-0.023089779540896416,
0.026144016534090042,
0.018805498257279396,
-0.02016720362007618,
0.021996894851326942,
-0.024289678782224655,
-0.005243782885372639,
-0.007756066042929888,
0.017814043909311295,
0.033328913152217865,
-0.017579376697540283,
0.0019973632879555225,
0.029143307358026505,
0.056651994585990906,
-0.05243870988488197,
0.01154959574341774,
-0.0111240828409791,
0.050607696175575256,
0.0010477342875674367,
-0.024928290396928787,
-0.04289182275533676,
0.03457440808415413,
-0.012591864913702011,
0.0570245087146759,
0.003419959219172597,
0.03648458048701286,
0.007457685191184282,
0.015135849826037884,
0.019279681146144867,
0.007330019026994705,
-0.03769669309258461,
-0.04200572893023491,
0.04675420746207237,
0.04106593132019043,
-0.0010708129266276956,
-0.05953436717391014,
0.04786008596420288,
0.033578112721443176,
-0.016917657107114792,
0.03852832317352295,
-0.01303969044238329,
-0.032850828021764755,
-0.003023226745426655,
-0.05113713815808296,
-0.0789131224155426,
0.032173771411180496,
-0.00875608529895544,
-0.016464034095406532,
0.019993344321846962,
-0.0250236876308918,
-0.0009006390464492142,
0.019653471186757088,
0.04289009049534798,
-0.010835668072104454,
0.09482415020465851,
-0.017211463302373886,
-0.011408240534365177,
-0.008808251470327377,
-0.005793397780507803,
0.1057976633310318,
0.0629277229309082,
0.008054351434111595,
-0.03400639072060585,
-0.01240080688148737,
0.01610814779996872,
-0.05139406397938728,
-0.009843140840530396,
0.05444455146789551,
-0.019000343978405,
-0.011449437588453293,
0.010356606915593147,
0.0476028136909008,
-0.011204701848328114,
0.009828245267271996,
0.07358652353286743,
-0.004870329052209854,
0.0042729671113193035,
-0.001071868697181344,
0.014268298633396626,
-0.003421436995267868,
0.0038359612226486206,
-0.014182589948177338,
0.04926157742738724,
-0.017915017902851105,
0.021976470947265625,
-0.06988269090652466,
-0.02429862692952156,
0.009394382126629353,
0.012984458357095718,
-0.02348366193473339,
0.024762066081166267,
-0.02452079765498638,
0.00013324059545993805,
-0.013807951472699642,
-0.010921532288193703,
0.0191436056047678,
-0.008253036998212337,
0.025664959102869034,
0.014691764488816261,
-0.005883109290152788,
0.020781509578227997,
0.008509643375873566,
-0.014458799734711647,
-0.044038183987140656,
0.019416891038417816,
-0.02165537141263485,
0.056375209242105484,
-0.03341701999306679,
-0.016763124614953995,
0.018103716894984245,
-0.009931501001119614,
-0.018270883709192276,
-0.0283508338034153,
0.022493857890367508,
-0.009520342573523521,
0.012510761618614197,
0.012403232976794243,
0.0027037274558097124,
0.0009089744999073446,
0.06949328631162643,
0.017754610627889633,
-0.00022781411826144904,
-0.05196566507220268,
0.006903111934661865,
-0.0038173338398337364,
-0.020209187641739845,
0.0402909591794014,
-0.031660810112953186,
-0.040009405463933945,
-0.03954320773482323,
-0.041357073932886124,
-0.012988965958356857,
-0.009525678120553493,
0.021113529801368713,
0.008157444186508656,
0.05415576323866844,
0.03806079179048538,
0.006114105693995953,
0.00847713090479374,
-0.06640447676181793,
0.006568132899701595,
-0.02949775755405426,
-0.03431205078959465,
-0.023271841928362846,
-0.04782574996352196,
-0.0015448819613084197,
0.044562891125679016,
-0.028176916763186455,
0.003568683983758092,
-0.015611140988767147,
0.00037254419294185936,
-0.01301359198987484,
-0.043188389390707016,
0.013715137727558613,
0.023716658353805542,
-0.03404727205634117,
0.04017847403883934,
-0.05693889409303665,
-0.037669360637664795,
0.0395943820476532,
0.014731169678270817,
-0.0011796950129792094,
0.03312460705637932,
-0.03235404193401337,
0.011408766731619835,
0.011730421334505081,
-0.021713687106966972,
0.019852517172694206,
0.013235678896307945,
-0.004874317906796932,
-0.06167959049344063,
-0.0029472389724105597,
-0.033716484904289246,
-0.043769076466560364,
-0.0007316689006984234,
0.014012770727276802,
0.003953713923692703,
-0.006543798837810755,
-0.012259607203304768,
-0.019973071292042732,
-0.020401116460561752,
-0.006475992500782013,
-0.02287694811820984,
0.026609480381011963,
0.034943655133247375,
-0.03331204876303673,
-0.026060622185468674,
-0.005038728471845388,
-0.008682540617883205,
-0.013862148858606815,
-0.012074317783117294,
-0.02741776779294014,
-0.0434124656021595,
0.0416971780359745,
0.03488902747631073,
-0.015511282719671726,
0.0683680847287178,
0.023039594292640686,
-0.00022100721253082156,
0.001373450388200581,
-0.030586587265133858,
-0.037377309054136276,
0.03361618518829346,
-0.0002756045723799616,
0.05216745659708977,
-0.017427993938326836,
-0.04291882738471031,
0.008694572374224663,
0.09567493200302124,
-0.02381417341530323,
0.006435546092689037,
-0.013748769648373127,
-0.003852383466437459,
-0.011698702350258827,
-0.015314273536205292,
0.012524076737463474,
-0.03517317399382591,
0.002625856315717101,
0.0023996643722057343,
0.0018640935886651278,
-0.04692985117435455,
0.006437703035771847,
0.004303415305912495,
-0.031977105885744095,
0.009547864086925983,
-0.005784756038337946,
0.018793020397424698,
0.0459943488240242,
0.06464903056621552,
-0.0337735116481781,
-0.006053868681192398,
0.030623452737927437,
0.0009533233824186027,
-0.0979485958814621,
-0.015874993056058884,
0.01229582354426384,
-0.003911138977855444,
0.046014897525310516,
-0.0736842155456543,
0.024669339880347252,
0.021088937297463417,
-0.040404774248600006,
0.023189503699541092,
-0.01876744255423546,
-0.03841951861977577,
-0.012812500819563866,
-0.029507171362638474,
-0.0306476429104805,
0.0295769814401865,
0.02876390889286995,
0.07306675612926483,
0.021842703223228455,
0.025693384930491447,
-0.03686588630080223,
-0.014904656447470188,
-0.01808231510221958,
0.029580118134617805,
-0.0005986951873637736,
-0.019580796360969543,
0.06766431778669357,
0.01066677737981081,
-0.005710703786462545,
0.018668537959456444,
-0.040079619735479355,
-0.004604422487318516,
-0.005916271824389696,
0.02781384252011776,
0.001940794987604022,
0.02741336263716221,
0.03196002542972565,
0.004396284464746714,
-0.010478375479578972,
0.011172841303050518,
0.020228907465934753,
0.006266805808991194,
-0.01790555566549301,
0.012875608168542385,
0.027072472497820854,
-0.05779992416501045,
-0.03464630991220474,
0.046334899961948395,
-0.042758263647556305,
-0.03287121653556824,
0.007880031131207943,
-0.03649871051311493,
0.0007432629354298115,
-0.03911294415593147,
-0.020684944465756416,
-0.03771304339170456,
0.025047045201063156,
0.009261997416615486,
0.02139309048652649,
-0.0115814208984375,
0.021560819819569588,
0.009823893196880817,
-0.030500689521431923,
-0.013179799541831017,
-0.002776480047032237,
-0.023378372192382812,
-0.0575832761824131,
0.004587752278894186,
-0.003478690516203642,
-0.016611628234386444,
0.0035833909641951323,
-0.010498522780835629,
-0.024727627635002136,
0.03944326192140579,
0.04894813895225525,
0.03269275650382042,
-0.018272995948791504,
-0.015504241921007633,
-0.010238932445645332,
-0.061662714928388596,
-0.01648101396858692,
-0.0024772014003247023,
-0.019941724836826324,
0.017940375953912735,
-0.003574650501832366,
0.01882854290306568,
-0.024542581290006638,
0.06545300781726837,
-0.030233528465032578,
-0.00856067519634962,
0.04007067158818245,
0.0012132823467254639,
0.004424157086759806,
-0.05413062870502472,
0.008452112786471844,
-0.000803321017883718,
-0.025593357160687447,
-0.014570296742022038,
-0.025200780481100082,
-0.0023862679954618216,
0.036624688655138016,
0.0119225038215518,
0.024292228743433952,
-0.02334609068930149,
0.011709730140864849,
-0.010044478811323643,
0.06536149978637695,
0.008081052452325821,
0.0064708273857831955,
0.05378109961748123,
0.013756898231804371,
-0.03457101061940193,
0.01446856465190649,
-0.02752446010708809,
-0.02038002759218216,
0.020431773737072945,
-0.02330155111849308,
-0.04667259007692337,
0.002386032836511731,
-0.00951654464006424,
0.002957120770588517,
-0.032901011407375336,
-0.005104781594127417,
0.07387250661849976,
-0.05966303125023842,
-0.005435593891888857,
0.010689690709114075,
0.014042537659406662,
0.05892214551568031,
0.012651011347770691,
-0.016485320404171944,
0.0325780026614666,
-0.028785310685634613,
0.0331539623439312,
0.015292559750378132,
0.023343384265899658,
-0.007055325899273157,
-0.03458607941865921,
0.01537405513226986,
-0.06139230355620384,
-0.00558848399668932,
0.003941312897950411,
0.01797683909535408,
-0.046433355659246445,
-0.03547421097755432,
0.022313257679343224,
-0.03465379402041435,
-0.0015722463140264153,
0.0025810629595071077,
-0.010923689231276512,
0.049746084958314896,
0.0015785840805619955,
-0.01999637857079506,
-0.03495005518198013,
0.0018634521402418613,
-0.023753276094794273,
0.05585544928908348,
0.009009086526930332,
-0.0002326222456758842,
-0.005313339177519083,
0.01849788799881935,
-0.014223442412912846,
0.006376438308507204,
0.05147993192076683,
-0.01829308085143566,
0.0018247680272907019,
0.030541613698005676,
0.02406056597828865,
-0.019828278571367264,
-0.03492104634642601,
-0.01335915643721819,
-0.014253147877752781,
0.058407850563526154,
0.025741420686244965,
0.008703102357685566,
-0.0057494500651955605,
0.025610296055674553,
-0.04936601594090462,
0.038967642933130264,
-0.06764392554759979,
0.0006130129913799465,
-0.027036210522055626,
-0.005288441199809313,
-0.03491486981511116,
-0.013130689971148968
] |
<p>Inspired by a similar post, I wanted to know what video games, past or present, most accurately employ the laws of physics. </p>
<p>I believe this is an appropriate question for this site, since the users are far more qualified to answer it than anyone on typical gaming sites, who think they know a lot more about physics than they really do. In my limited experience, most games claiming "realistic physics" are anything but.</p>
| 9,560 |
[
-0.006522220093756914,
-0.0856623724102974,
-0.02583928406238556,
-0.01793104037642479,
0.033678218722343445,
0.01376516092568636,
-0.004850080702453852,
0.0038395889569073915,
-0.006702926009893417,
0.006249523721635342,
0.020098790526390076,
0.03480341657996178,
0.0014047158183529973,
0.04975622147321701,
0.0018388396129012108,
0.0025964858941733837,
0.00776482792571187,
-0.009585191495716572,
-0.0006710817106068134,
-0.025328537449240685,
-0.01664208248257637,
-0.011488485150039196,
0.0013221361441537738,
-0.004732985515147448,
-0.048588864505290985,
-0.0009504916379228234,
0.0016270109917968512,
-0.012985414825379848,
0.020102033391594887,
0.01736586168408394,
-0.03427409380674362,
-0.013703308068215847,
0.0031916736625134945,
0.024849867448210716,
0.019262097775936127,
0.005365253891795874,
-0.01261595543473959,
-0.026565302163362503,
-0.0039815036579966545,
0.015878142789006233,
-0.015150691382586956,
-0.006124566774815321,
-0.019872741773724556,
0.04780460149049759,
-0.00407256418839097,
0.062416646629571915,
-0.029925774782896042,
-0.014867988415062428,
0.048354316502809525,
-0.04483209177851677,
0.05452970787882805,
-0.010326610878109932,
0.06531532853841782,
0.033400144428014755,
0.013030433095991611,
-0.03750986605882645,
0.07175794988870621,
0.04533027857542038,
-0.03787145018577576,
-0.06883309781551361,
-0.014936977997422218,
-0.003851077752187848,
-0.031310439109802246,
0.002417820505797863,
-0.0023308536037802696,
0.05881718918681145,
0.009187129326164722,
-0.03011144883930683,
0.03042191080749035,
0.017823373898863792,
-0.03810122609138489,
0.0231107696890831,
0.008880694396793842,
0.03797071427106857,
0.021493075415492058,
-0.007181013002991676,
0.02201084792613983,
0.007125280797481537,
0.017070135101675987,
0.027852792292833328,
-0.023502981290221214,
-0.02285720780491829,
0.040537603199481964,
0.04236023128032684,
0.0206880085170269,
-0.04317089542746544,
0.08268249779939651,
0.01683075726032257,
-0.012034522369503975,
0.009292596019804478,
-0.01689220406115055,
-0.010839620605111122,
0.01073815580457449,
0.0011853530304506421,
-0.02475455217063427,
-0.014998285099864006,
0.029688280075788498,
0.05936121568083763,
0.037654146552085876,
-0.02892703004181385,
0.007917049340903759,
-0.012012775056064129,
0.0254780612885952,
0.0529048927128315,
0.009657623246312141,
-0.043478649109601974,
-0.027033209800720215,
0.009268492460250854,
-0.03597726300358772,
0.03064342588186264,
-0.001420740270987153,
0.05124090239405632,
0.013094139285385609,
-0.012665260583162308,
0.015491564758121967,
-0.01427608635276556,
0.007213519886136055,
-0.024857424199581146,
0.07678298652172089,
0.03661593794822693,
0.060902711004018784,
-0.019989054650068283,
0.032772697508335114,
0.0058939396403729916,
-0.0269872285425663,
0.00444700475782156,
0.021474219858646393,
-0.005442335736006498,
-0.04729653149843216,
-0.004220856353640556,
0.00003687552089104429,
-0.030163461342453957,
-0.002595811150968075,
-0.013415828347206116,
0.05854096636176109,
0.0016246753511950374,
-0.061708804219961166,
-0.06127866730093956,
0.04493296891450882,
-0.012894412502646446,
-0.03079979121685028,
-0.040720708668231964,
0.010415428318083286,
0.041341882199048996,
0.06869886070489883,
0.038745928555727005,
0.02357344515621662,
0.012966390699148178,
0.04836243391036987,
-0.06782680004835129,
-0.005201392341405153,
-0.0028734118677675724,
0.008451505564153194,
-0.011353551410138607,
0.015296787023544312,
-0.06876472383737564,
0.0109763965010643,
0.037355393171310425,
0.023463420569896698,
-0.02438553422689438,
0.06549849361181259,
-0.021679500117897987,
-0.0005504889413714409,
0.01264574658125639,
-0.012785936705768108,
-0.02100176177918911,
0.041191644966602325,
0.0011607265332713723,
0.015399646013975143,
0.001722492859698832,
-0.024111498147249222,
0.017572548240423203,
0.037796761840581894,
-0.004885011352598667,
0.08078047633171082,
-0.013421555981040001,
-0.002978692762553692,
-0.002989052329212427,
-0.01644277200102806,
-0.000874513469170779,
-0.056779924780130386,
-0.02191287651658058,
0.03614135831594467,
-0.00921402033418417,
-0.011333640664815903,
0.05257454514503479,
0.005112739279866219,
-0.0013758662389591336,
0.04399329051375389,
0.009435498155653477,
-0.019546853378415108,
-0.02601560950279236,
0.05466112494468689,
-0.0022491919808089733,
-0.0013848822563886642,
0.0334668904542923,
0.02968895062804222,
0.037540774792432785,
-0.06252116709947586,
0.00992708932608366,
-0.018915753811597824,
0.0353226363658905,
0.004843569826334715,
-0.025294285267591476,
-0.02817915380001068,
0.07437039166688919,
0.018085869029164314,
-0.0195729061961174,
0.013102484866976738,
0.01541793905198574,
-0.05707802250981331,
-0.047651346772909164,
-0.016884494572877884,
0.01749224215745926,
-0.005845197942107916,
-0.011245176196098328,
0.050603557378053665,
-0.04293428733944893,
0.006011858582496643,
0.01762685552239418,
-0.018385279923677444,
0.05553833395242691,
0.0011267121881246567,
-0.008221624419093132,
0.0032694018445909023,
0.03584196791052818,
-0.05398977920413017,
-0.02775389887392521,
0.030917704105377197,
-0.02898462302982807,
-0.02932751737535,
-0.03499726578593254,
0.0474126860499382,
0.040145259350538254,
-0.028019366785883904,
0.0050412751734256744,
0.01952311024069786,
0.04332945868372917,
0.02605452761054039,
0.021064480766654015,
-0.06943541020154953,
-0.04571782797574997,
0.03851212188601494,
-0.007479853928089142,
0.023021774366497993,
0.012771503068506718,
-0.0011411752784624696,
0.06482893973588943,
-0.055125169456005096,
0.0012174812145531178,
-0.018914660438895226,
0.024902669712901115,
0.029612921178340912,
0.04123504459857941,
0.013146217912435532,
-0.09203950315713882,
0.025438595563173294,
0.006662588566541672,
-0.01521345041692257,
0.005934316199272871,
-0.00502299889922142,
-0.004630886949598789,
-0.04106493666768074,
-0.01995551586151123,
0.014741920866072178,
0.014286846853792667,
-0.016963578760623932,
-0.013875989243388176,
0.05081462860107422,
-0.0006162392091937363,
0.013376380316913128,
-0.02775919996201992,
-0.0012850979110226035,
0.002133244415745139,
0.021299397572875023,
0.023381251841783524,
0.024030642583966255,
0.04436217620968819,
-0.011844548396766186,
0.006578024011105299,
-0.01783604919910431,
-0.04429033026099205,
0.0008361181244254112,
0.029992878437042236,
-0.06019139289855957,
0.02509228140115738,
-0.054230011999607086,
-0.033336091786623,
0.06750065088272095,
0.0028625461272895336,
-0.020151326432824135,
0.05650239810347557,
0.0014546678867191076,
-0.03255952522158623,
0.010416857898235321,
-0.026712872087955475,
-0.04540858045220375,
0.001679719309322536,
-0.012060177512466908,
0.01719941757619381,
-0.013123910874128342,
-0.024730682373046875,
0.02137327566742897,
-0.024105291813611984,
-0.05002063885331154,
0.00875291507691145,
0.025607159361243248,
0.0006121589685790241,
0.008542253635823727,
0.0032091462053358555,
0.056363195180892944,
-0.05079265311360359,
-0.0002513993822503835,
-0.023436972871422768,
-0.036276452243328094,
0.024424200877547264,
-0.010377119295299053,
0.01065706554800272,
-0.00303906318731606,
-0.026248205453157425,
0.043835826218128204,
0.008053689263761044,
-0.020240917801856995,
0.014909084886312485,
0.00097715575248003,
0.012604819610714912,
0.014890785329043865,
-0.017903773114085197,
0.009666787460446358,
-0.007918168790638447,
0.017110152170062065,
0.0027627490926533937,
0.02115948498249054,
-0.009469090029597282,
-0.01877410337328911,
0.033908661454916,
-0.005780619569122791,
0.02325540781021118,
-0.02892649918794632,
0.02311374433338642,
0.029236480593681335,
-0.05318789184093475,
0.010985747911036015,
0.011809831485152245,
0.005421069450676441,
0.007687872741371393,
-0.058223359286785126,
0.05097871646285057,
-0.011869048699736595,
0.02330521121621132,
0.031860459595918655,
0.009250424802303314,
-0.01938610151410103,
-0.00652230903506279,
-0.026862014085054398,
0.0849313884973526,
0.0028644262347370386,
-0.006167120300233364,
0.009805912151932716,
-0.01771480217576027,
-0.0020499685779213905,
-0.013121500611305237,
-0.0013105965917930007,
0.03981434926390648,
-0.0038406141102313995,
0.011130684055387974,
0.00705717084929347,
-0.01596352644264698,
0.06264355033636093,
-0.017527928575873375,
0.05967790260910988,
0.0029999420512467623,
-0.01529630646109581,
-0.019754132255911827,
-0.08108611404895782,
0.008123685605823994,
-0.058160923421382904,
0.025886714458465576,
-0.016697511076927185,
0.02590000629425049,
0.01639835350215435,
0.03384821489453316,
0.0036376910284161568,
-0.007839041762053967,
-0.08628100156784058,
0.06555602699518204,
-0.0427190400660038,
-0.023786870762705803,
-0.030302779749035835,
0.013409619219601154,
-0.013033694587647915,
-0.01819382794201374,
0.0013662276323884726,
-0.02953488379716873,
-0.017634978517889977,
-0.035037871450185776,
-0.023325392976403236,
-0.050733212381601334,
-0.09859860688447952,
0.013816585764288902,
-0.024467701092362404,
-0.013859170489013195,
-0.017054680734872818,
-0.005265606101602316,
0.035135168582201004,
0.005868904292583466,
-0.050832875072956085,
-0.000056970511650433764,
0.055407408624887466,
-0.017024194821715355,
0.04129631817340851,
0.023718025535345078,
0.019674891605973244,
-0.0004472624568734318,
-0.006521714851260185,
0.0059335301630198956,
0.03882542997598648,
-0.03406241908669472,
-0.029738347977399826,
-0.027550281956791878,
-0.04056215658783913,
-0.01137570384889841,
-0.0018314812332391739,
0.04693185165524483,
0.02051706612110138,
0.027663985267281532,
0.0032975543290376663,
0.018950557336211205,
-0.014857488684356213,
0.01957050897181034,
0.05139634758234024,
0.0022960095666348934,
-0.00476002087816596,
-0.04051903635263443,
-0.008140253834426403,
0.013426197692751884,
0.02501087449491024,
0.03907383233308792,
0.0008561118156649172,
0.013205204159021378,
0.0373346246778965,
0.016503429040312767,
-0.008195544593036175,
-0.027955222874879837,
0.02202755957841873,
0.030005276203155518,
0.03130115941166878,
-0.008741207420825958,
0.005985508672893047,
-0.0014675261918455362,
0.012615280225872993,
0.043300092220306396,
-0.004118472337722778,
-0.011645268648862839,
-0.04561780020594597,
0.0393097847700119,
0.04138398915529251,
-0.02095666341483593,
-0.029316391795873642,
-0.012437171302735806,
-0.0353875495493412,
-0.039202731102705,
0.05545591190457344,
0.007524099666625261,
0.025631889700889587,
-0.0220546405762434,
0.01916566677391529,
-0.03546471148729324,
0.01054203137755394,
0.005063971038907766,
-0.0012303062248975039,
0.0018098549917340279,
0.0031465827487409115,
-0.014219172298908234,
-0.017779240384697914,
-0.009376262314617634,
0.028994204476475716,
0.04430714249610901,
0.04503859952092171,
0.011834277771413326,
-0.022638102993369102,
-0.02580849640071392,
0.030160345137119293,
-0.07699164748191833,
-0.034712377935647964,
0.0045898729003965855,
0.029427068307995796,
-0.04052281379699707,
0.002762207295745611,
0.01737603358924389,
-0.019122349098324776,
0.02314208634197712,
-0.05443843454122543,
0.032198112457990646,
-0.01952025294303894,
0.005042084492743015,
-0.0008914523059502244,
0.009049679152667522,
0.040139224380254745,
0.005917120259255171,
0.05107782781124115,
-0.009916570968925953,
-0.0386008620262146,
0.02213776670396328,
0.03417130187153816,
-0.003120984649285674,
-0.014156423509120941,
-0.036855533719062805,
-0.024100972339510918,
-0.07976851612329483,
0.03698580339550972,
-0.014349706470966339,
0.03281636908650398,
-0.009972085244953632,
0.006109765265136957,
-0.0429595448076725,
0.032707393169403076,
-0.03379356116056442,
-0.0386466421186924,
-0.006466966588050127,
-0.005307948216795921,
-0.03735482692718506,
-0.01869572512805462,
0.0012340121902525425,
0.03738110885024071,
-0.027862615883350372,
0.0463259182870388,
-0.031000133603811264,
0.047786515206098557,
-0.03567487373948097,
0.026001540943980217,
-0.04168814420700073,
-0.03972190245985985,
0.04941101744771004,
0.022170180454850197,
0.01646500639617443,
0.011408708989620209,
-0.05646677315235138,
-0.02002800814807415,
-0.00004983057078788988,
0.0175568088889122,
0.052124056965112686,
-0.05280076339840889,
0.03126845508813858,
-0.03347848728299141,
0.00804051011800766,
-0.05595593526959419,
-0.031725719571113586,
0.00427089212462306,
0.03214861825108528,
0.003947401884943247,
-0.03975358232855797,
0.042395178228616714,
-0.048538874834775925,
-0.039434727281332016,
0.007721965666860342,
0.012519790790975094,
0.011732006445527077,
0.01679840311408043,
0.0025738650001585484,
-0.05231994763016701,
0.023552700877189636,
0.013850013725459576,
0.01680000126361847,
0.002263420494273305,
-0.029301896691322327,
0.03325490280985832,
-0.010701782070100307,
0.05748260021209717,
0.0013736082473769784,
0.04903548210859299,
-0.019645672291517258,
0.002277711173519492,
0.049224331974983215,
-0.005737734958529472,
0.06710703670978546,
0.05122463032603264,
-0.027824874967336655,
-0.029948437586426735,
-0.023208830505609512,
-0.00250197178684175,
-0.01874038577079773,
0.02283434383571148,
-0.011678971350193024,
-0.03734034299850464,
0.01494673639535904,
-0.020742222666740417,
0.0305817648768425,
-0.01441649068146944,
0.024035150185227394,
-0.022554902359843254,
0.06193898618221283,
-0.009464210830628872,
-0.03958753123879433,
-0.004566892981529236,
-0.007296406198292971,
0.038895994424819946,
-0.07387447357177734,
-0.02404562383890152,
0.030809326097369194,
0.03888441622257233,
-0.01749570667743683,
-0.03130995109677315,
-0.01431853324174881,
0.053933706134557724,
0.0767589882016182,
-0.02550731599330902,
0.06717590242624283,
0.030941711738705635,
0.017075076699256897,
0.008242660202085972,
0.005112244747579098,
-0.040346115827560425,
0.016864323988556862,
-0.0005510736955329776,
0.0063715106807649136,
-0.03713377192616463,
0.009789470583200455,
0.012980853207409382,
-0.004452112130820751,
-0.014961318112909794,
-0.020122213289141655,
-0.018344806507229805,
-0.0020259800367057323,
-0.00819140300154686,
-0.03655518218874931,
-0.013130069710314274,
0.046595700085163116,
-0.06124400347471237,
0.05171513557434082,
0.011296785436570644,
0.007467883173376322,
0.03274349495768547,
-0.011760884895920753,
-0.01884191855788231,
-0.0009039987926371396,
-0.0001757796126184985,
-0.006788283586502075,
0.008405477739870548,
-0.011231863871216774,
0.03716167435050011,
-0.016531506553292274,
-0.016837041825056076,
0.02436703070998192,
0.011055340059101582,
-0.0005555220413953066,
-0.01666809804737568,
-0.09419350326061249,
-0.028025522828102112,
-0.016192413866519928,
-0.018135203048586845,
0.037027955055236816,
0.04619994014501572,
0.0003797857207246125,
0.009458609856665134,
-0.035610076040029526,
0.0034118485637009144,
0.010764560662209988,
0.034249626100063324,
0.0013206774601712823,
0.03712029755115509,
-0.04250200465321541,
-0.013045938685536385,
-0.012360962107777596,
-0.005545404739677906,
0.11204983294010162,
0.048897355794906616,
-0.009374523535370827,
-0.022362180054187775,
-0.00705548282712698,
-0.048959847539663315,
-0.005562096368521452,
-0.011655854992568493,
0.02918406017124653,
0.02442549355328083,
0.03572174906730652,
-0.0010017530294135213,
0.022978778928518295,
0.06649811565876007,
-0.009296572767198086,
0.03438735753297806,
-0.030737679451704025,
-0.022711483761668205,
-0.017475491389632225,
-0.010378452949225903,
-0.005679253488779068,
0.021230224519968033,
-0.014513332396745682,
-0.02521778643131256,
-0.017599720507860184,
0.012281741015613079,
0.015184729360044003,
-0.02188582718372345,
0.01620381511747837,
0.0564471036195755,
-0.005126936826854944,
0.013634772039949894,
0.015085389837622643,
-0.015302452258765697,
-0.05945553258061409,
-0.0019104655366390944,
0.003765283152461052,
-0.021652935072779655,
0.0067104073241353035,
0.001492228708229959,
0.025221556425094604,
-0.005862981081008911,
-0.016222570091485977,
-0.004114372190088034,
-0.04956517368555069,
0.012392492033541203,
-0.05168413370847702,
-0.006338335108011961,
-0.01136999111622572,
0.051019731909036636,
0.011602602899074554,
-0.02776535227894783,
-0.00014946848386898637,
-0.03630189970135689,
-0.015345167368650436,
-0.018834933638572693,
0.05182233452796936,
-0.05259811878204346,
-0.0008503747521899641,
-0.004134771879762411,
0.021839290857315063,
-0.026063455268740654,
0.04902299866080284,
0.025428876280784607,
0.02132425084710121,
-0.003413301892578602,
-0.003304602112621069,
0.050372857600450516,
-0.060004256665706635,
-0.010823061689734459,
0.016939004883170128,
0.003915197215974331,
-0.04856092482805252,
-0.005617600400000811,
0.03372528776526451,
0.052755068987607956,
-0.007652416359633207,
0.04337402805685997,
-0.013920236378908157,
-0.05089419335126877,
-0.07539364695549011,
0.03970003128051758,
-0.006792421452701092,
0.026516111567616463,
-0.06736242026090622,
-0.03618201985955238,
0.03390507400035858,
-0.01033165492117405,
-0.016928648576140404,
-0.0025463420897722244,
-0.06108089163899422,
-0.017446761950850487,
-0.0014199576107785106,
-0.025095051154494286,
-0.04947274550795555,
0.004324962850660086,
-0.0358659029006958,
0.028007863089442253,
-0.03027503937482834,
0.05601091682910919,
0.016317646950483322,
-0.023638151586055756,
0.02488352730870247,
0.04196585714817047,
-0.049943406134843826,
0.013688914477825165,
-0.0024448009207844734,
-0.05814475193619728,
-0.04732902720570564,
-0.013605489395558834,
0.035988133400678635,
-0.008027258329093456,
-0.034224070608615875,
-0.03132997825741768,
0.003910810686647892,
-0.03854919597506523,
0.013916125521063805,
0.010579761117696762,
0.01887332648038864,
-0.0063986945897340775,
0.010417272336781025,
-0.02866281010210514,
-0.02353597618639469,
-0.026815591380000114,
0.029357533901929855,
0.02510918863117695,
-0.026735810562968254,
-0.010350939817726612,
-0.0009380587725900114,
-0.0211412962526083,
-0.010956618934869766,
0.046114109456539154,
0.004222009796649218,
-0.014190517365932465,
-0.026249095797538757,
-0.0035223255399614573,
-0.004549985285848379,
-0.006398677825927734,
-0.007942316122353077,
0.0050596436485648155,
0.03210026025772095,
-0.03233429044485092,
-0.03311529383063316,
0.025221943855285645,
-0.015189393423497677,
-0.00614338181912899,
-0.00413808599114418,
-0.020764105021953583,
0.022975148633122444,
0.06779945641756058,
-0.01902763731777668,
0.010797934606671333,
0.03676609694957733,
-0.014104988425970078,
0.00003841789657599293,
0.002849087817594409,
0.02310350351035595,
-0.049845512956380844,
-0.03972393646836281,
0.024866364896297455,
0.043345559388399124,
0.019279280677437782,
0.018927795812487602,
0.017698409035801888,
-0.0074886782094836235,
-0.0022522485814988613,
0.06473293900489807,
0.022231247276067734,
0.034189630299806595,
0.029877018183469772,
-0.026492051780223846,
0.03301136940717697,
0.03908855468034744,
0.012402720749378204,
-0.0730646401643753,
-0.012472503818571568,
0.016043422743678093,
0.008500919677317142,
0.04351259022951126,
-0.08398875594139099,
0.03423597663640976,
0.02078874409198761,
-0.09176244586706161,
0.0070369672030210495,
-0.02468479610979557,
-0.014484881423413754,
-0.01731206104159355,
-0.035513993352651596,
0.012163921259343624,
0.01164889894425869,
0.00006936854333616793,
0.008404843509197235,
0.027163784950971603,
0.02585245668888092,
-0.02964971214532852,
-0.0071919700130820274,
-0.009040256962180138,
0.05292709544301033,
-0.03423328325152397,
0.017782896757125854,
-0.01381726935505867,
-0.0089497622102499,
-0.0425606332719326,
0.020517747849225998,
0.03970571234822273,
0.056825388222932816,
-0.016627777367830276,
0.03185388445854187,
-0.01904999651014805,
0.029096029698848724,
0.04020674154162407,
-0.017653491348028183,
-0.025332245975732803,
0.0026348333340138197,
-0.00042414985364302993,
0.04461593180894852,
-0.015185141935944557,
0.008642170578241348,
0.019818566739559174,
-0.0421711802482605,
-0.03601144999265671,
-0.012905092909932137,
0.051191408187150955,
-0.013955656439065933,
-0.03376847878098488,
-0.0068019418977200985,
0.013831314630806446,
-0.01068359799683094,
-0.010224463418126106,
-0.020560845732688904,
0.025915803387761116,
0.03651310130953789,
-0.015632158145308495,
0.01377531886100769,
0.036786146461963654,
-0.010221478529274464,
-0.0018434616504237056,
-0.04738307371735573,
-0.009466374292969704,
0.016019923612475395,
-0.052635494619607925,
0.004554770886898041,
0.05044779181480408,
0.032702043652534485,
0.015660841017961502,
-0.053289078176021576,
-0.04265507683157921,
0.04073813185095787,
0.010846405290067196,
-0.00595464650541544,
0.026139790192246437,
-0.01861502230167389,
-0.002555862534791231,
-0.054198358207941055,
0.05841981992125511,
-0.026472633704543114,
0.016162965446710587,
-0.04746879264712334,
0.004421398509293795,
0.04031936079263687,
-0.000986869796179235,
0.031924981623888016,
-0.040397826582193375,
0.006933397147804499,
-0.022377626970410347,
-0.0016019289614632726,
-0.020391592755913734,
-0.037078678607940674,
-0.01606827788054943,
-0.017032334581017494,
-0.07159378379583359,
-0.03270827606320381,
0.02786051295697689,
-0.011711613275110722,
-0.03184978663921356,
0.01670181378722191,
-0.015651891008019447,
0.007660372648388147,
-0.00692344643175602,
-0.018333675339818,
0.04702674224972725,
0.07765652239322662,
-0.01319743599742651,
0.036441560834646225,
-0.01631353236734867,
0.00849235337227583,
0.02835140936076641,
-0.053152166306972504,
0.005700825247913599,
0.045785412192344666,
-0.00548236770555377,
-0.037403665482997894,
-0.036605190485715866,
-0.015465517528355122,
-0.02188541181385517,
-0.05693286657333374,
0.004147784318774939,
0.022614585235714912,
-0.008342222310602665,
0.012197778560221195,
0.02846994251012802,
-0.016687534749507904,
0.04388999938964844,
0.013974171131849289,
0.05411244183778763,
0.050611771643161774,
0.002320351079106331,
0.0046281530521810055,
0.029864734038710594,
0.07133244723081589,
0.009385889396071434,
-0.0063196634873747826,
0.05609374865889549,
-0.005929226521402597,
0.0443849079310894,
0.0023709023371338844,
0.0326499305665493,
-0.029839731752872467,
-0.013671522960066795,
0.029917223379015923,
-0.031791962683200836,
-0.0072469026781618595,
0.02941090241074562,
-0.02951364405453205,
0.05550835281610489,
-0.039450205862522125,
-0.0027137696743011475,
-0.02639324776828289,
0.011553380638360977,
0.018424997106194496,
-0.039108797907829285,
-0.01706014573574066,
0.05395545810461044,
-0.015393397770822048,
-0.013722012750804424,
0.003003054764121771,
0.01794930174946785,
0.026485301554203033,
-0.0034616761840879917,
0.05345506966114044,
-0.015061375685036182,
0.0030152343679219484,
0.0042205131612718105,
-0.010313247330486774,
-0.03886672854423523,
-0.012122484855353832,
0.008719385601580143,
0.04222893714904785,
0.010590900667011738,
-0.03892187774181366,
0.008951720781624317,
-0.06576710939407349,
0.04880820959806442,
-0.08629905432462692,
0.019139530137181282,
-0.00911654531955719,
0.04443212226033211,
0.0225527361035347,
0.030237087979912758
] |
<p>Let us consider the functional integral:
\begin{equation}
\int \mathcal{D} A e^{iS[A]}
\end{equation}
where $S[A]$ is the action for $U(1)$ gauge field and
\begin{equation}
\mathcal{D}A\equiv \mathcal{D}A_0 \mathcal{D}A_1 \mathcal{D}A_2 \mathcal{D}A_3; \\
\mathcal{D}A_i = \prod_x dA_i(x).
\end{equation}</p>
<p>Now I have two questions:</p>
<p><strong>1. How to show that the integration measure $\mathcal{D} A $ is invariant under the gauge transformation:</strong>
\begin{equation}
A_\mu (x) \to A_\mu (x) + \frac{1}{e}\partial_\mu \alpha(x)
\end{equation}
<strong>2. How to show that the integration measure $\mathcal{D} A $ is invariant under the Lorentz transformation?</strong></p>
| 9,561 |
[
-0.010647627525031567,
0.01066126860678196,
-0.0027706644032150507,
-0.009609432891011238,
0.05538487061858177,
0.027935506775975227,
-0.016820041462779045,
-0.057068973779678345,
-0.007515914738178253,
-0.0072184968739748,
0.055199768394231796,
-0.022848818451166153,
0.10324300080537796,
0.012912241742014885,
0.0148563077673316,
-0.001865794532932341,
0.002823257353156805,
-0.013350830413401127,
-0.014370383694767952,
-0.03191503882408142,
-0.02825465425848961,
0.04101479426026344,
-0.00940908957272768,
-0.018802504986524582,
-0.01588246412575245,
0.024411899968981743,
-0.02959858626127243,
0.003853041213005781,
-0.01374385692179203,
0.06765689700841904,
-0.01074012741446495,
-0.045372121036052704,
0.02784375101327896,
0.019617781043052673,
-0.001996120437979698,
0.0022042058408260345,
-0.04513540118932724,
-0.0328894779086113,
0.00594070041552186,
0.0024638979230076075,
-0.03623934090137482,
-0.03202905133366585,
-0.02767813950777054,
0.04635316878557205,
-0.008781877346336842,
0.028494616970419884,
-0.0010040454799309373,
0.018183693289756775,
0.04748711735010147,
-0.03171516954898834,
0.06289835274219513,
0.03870350867509842,
0.03373809903860092,
0.049422625452280045,
-0.022337447851896286,
-0.06999751180410385,
0.020542306825518608,
0.061930324882268906,
-0.012341233901679516,
-0.021637508645653725,
-0.05202745646238327,
-0.04228852316737175,
0.03637869283556938,
-0.007033111527562141,
-0.01899171993136406,
0.045522622764110565,
-0.012217200361192226,
0.0013626712607219815,
0.033304765820503235,
-0.04233712702989578,
0.005133397411555052,
-0.000622967432718724,
-0.012870087288320065,
-0.017817853018641472,
-0.016550421714782715,
0.0033977157436311245,
-0.00982438214123249,
0.0225338377058506,
0.06097577139735222,
0.04383758455514908,
-0.002009710995480418,
0.051027026027441025,
0.06712561100721359,
0.006180889438837767,
0.02223932556807995,
-0.02919967845082283,
0.07163066416978836,
0.04098880663514137,
0.008213420398533344,
0.009904731996357441,
0.007296750787645578,
-0.026467427611351013,
0.02345784194767475,
-0.025967661291360855,
-0.03047775663435459,
0.03017473593354225,
0.015147889032959938,
0.057144828140735626,
0.0032415848691016436,
-0.030902141705155373,
-0.03134785592556,
-0.015637099742889404,
0.0301376786082983,
0.050301939249038696,
0.036677177995443344,
0.017579879611730576,
-0.02392338030040264,
-0.015434503555297852,
-0.01841762103140354,
-0.01582360826432705,
-0.03469717875123024,
0.023483753204345703,
-0.045383624732494354,
-0.00781695544719696,
0.019603561609983444,
-0.02096751146018505,
-0.011783364228904247,
-0.013696971349418163,
0.031764037907123566,
0.07371923327445984,
0.04378509894013405,
-0.0032461832743138075,
0.006584955845028162,
0.025691911578178406,
-0.08237427473068237,
0.022446321323513985,
0.0179922915995121,
0.006136015523225069,
-0.06763140112161636,
0.05567091703414917,
-0.004314733203500509,
-0.007919607684016228,
-0.030710984021425247,
0.019644493237137794,
-0.0020571351051330566,
-0.03928538039326668,
-0.10196058452129364,
-0.06469456106424332,
0.03467252850532532,
-0.035445939749479294,
-0.0008878977387212217,
-0.05490750074386597,
-0.007281531114131212,
0.03828461840748787,
0.09695296734571457,
-0.010026073083281517,
0.010595238767564297,
0.0004971116431988776,
0.03659331053495407,
0.012644429691135883,
-0.017846325412392616,
-0.035260703414678574,
-0.017528891563415527,
-0.022664247080683708,
-0.004983716644346714,
-0.032360225915908813,
0.018389027565717697,
0.003347068326547742,
-0.04650944843888283,
-0.04558532312512398,
0.11100031435489655,
0.024000734090805054,
0.04402156174182892,
0.021611085161566734,
-0.006337266881018877,
0.004148945678025484,
0.06095439940690994,
0.017320863902568817,
-0.009233586490154266,
0.009087271057069302,
-0.01548007968813181,
0.03084462694823742,
-0.04352238029241562,
0.04865249991416931,
0.05074513331055641,
-0.045504938811063766,
-0.02352765016257763,
-0.008873898535966873,
0.001664662384428084,
0.028973614796996117,
0.002572534140199423,
-0.04273482412099838,
-0.05761580169200897,
-0.003952420316636562,
-0.013687467202544212,
0.0195789597928524,
-0.010651499032974243,
0.004682854283601046,
-0.018399912863969803,
-0.0419757217168808,
-0.0543724000453949,
-0.08798837661743164,
0.048431165516376495,
0.02267116867005825,
-0.047375332564115524,
0.04462982714176178,
-0.017421016469597816,
0.01157678198069334,
0.011584034189581871,
-0.013340097852051258,
0.0047827851958572865,
-0.0001576300128363073,
0.0037077104207128286,
-0.006326261907815933,
0.0346791036427021,
0.04288944974541664,
0.05994509160518646,
-0.017284750938415527,
0.04152965918183327,
-0.002573988866060972,
0.0031801732257008553,
0.011439496651291847,
-0.006941520608961582,
0.011019590310752392,
-0.020063966512680054,
0.009363921359181404,
-0.0007973458850756288,
-0.011927898973226547,
-0.021910348907113075,
0.018182963132858276,
-0.021951520815491676,
0.046916041523218155,
0.07816042751073837,
-0.022620409727096558,
0.005611953791230917,
0.048698265105485916,
-0.011904655955731869,
0.0628562867641449,
0.002886619418859482,
-0.04811275750398636,
-0.043263789266347885,
0.017918696627020836,
0.02528497204184532,
0.03743103891611099,
-0.020861804485321045,
0.007034082431346178,
0.03438987955451012,
0.004670516587793827,
0.01897181011736393,
0.02469942718744278,
0.013570238836109638,
-0.03790636360645294,
-0.0012418009573593736,
0.0061534796841442585,
0.008358573541045189,
-0.010268136858940125,
0.000004398925284476718,
-0.028038738295435905,
0.018248872831463814,
0.030922584235668182,
-0.008776750415563583,
0.008211513049900532,
-0.03627908229827881,
0.01772150956094265,
0.0009843871230259538,
0.019087156280875206,
0.03356863930821419,
0.006849146913737059,
0.04949519410729408,
0.024329842999577522,
-0.005827942863106728,
-0.014814185909926891,
-0.0167818795889616,
-0.007185505703091621,
0.035989947617053986,
-0.02763448655605316,
0.015767883509397507,
-0.052360374480485916,
0.009990788996219635,
-0.017544638365507126,
-0.007336732931435108,
-0.009290204383432865,
0.0027135086711496115,
-0.03498341143131256,
-0.013474717736244202,
0.026906384155154228,
0.008573342114686966,
-0.0219386275857687,
-0.04693162441253662,
-0.02211916446685791,
0.034797556698322296,
0.016634617000818253,
0.056276798248291016,
0.07272551208734512,
-0.04190652444958687,
0.0094749191775918,
-0.05201542750000954,
0.01100555807352066,
0.06297396868467331,
-0.02924443781375885,
0.032557714730501175,
0.042156875133514404,
-0.0025021883193403482,
-0.08529821783304214,
-0.010282107628881931,
-0.006863121874630451,
0.019317885860800743,
-0.0021730754524469376,
-0.033816903829574585,
0.032211627811193466,
0.014408514834940434,
-0.04726637527346611,
-0.005493463482707739,
-0.029311999678611755,
-0.018833979964256287,
-0.02567698061466217,
0.007857045158743858,
0.01336093619465828,
-0.027511266991496086,
0.07603225111961365,
0.025015726685523987,
-0.06715978682041168,
-0.017795799300074577,
-0.04675719141960144,
-0.02124893106520176,
-0.013344798237085342,
0.021451350301504135,
0.01044593658298254,
-0.011940100230276585,
-0.06949079781770706,
0.04175980016589165,
0.0407898873090744,
-0.07599586248397827,
-0.020961005240678787,
0.008536440320312977,
-0.014329155907034874,
-0.05546994507312775,
0.015205636620521545,
0.0098201809450984,
-0.017120109871029854,
0.034047193825244904,
0.02556699886918068,
0.05523208528757095,
-0.008720208890736103,
0.008669775910675526,
-0.041029904037714005,
0.028692351654171944,
-0.007431541569530964,
0.029035648331046104,
0.008009090088307858,
0.017120974138379097,
0.030914193019270897,
-0.002879808424040675,
0.006840849760919809,
0.005087801720947027,
0.008394664153456688,
-0.03233412653207779,
0.054365288466215134,
0.0011480598477646708,
-0.010830200277268887,
-0.05355820432305336,
0.04838494583964348,
0.03362919017672539,
-0.029078898951411247,
0.006485996767878532,
0.002845323644578457,
0.004360327497124672,
-0.020005598664283752,
-0.004631302785128355,
0.021388685330748558,
0.028056476265192032,
-0.018822574988007545,
-0.025805935263633728,
-0.05804231017827988,
-0.002062118612229824,
0.03900286182761192,
-0.044790856540203094,
-0.04131411015987396,
0.0411287359893322,
0.05866179242730141,
0.017444433644413948,
-0.02442816086113453,
-0.04286544397473335,
-0.010269985534250736,
-0.0676032230257988,
0.00017452264728490263,
0.006236710585653782,
0.029209427535533905,
0.0350591316819191,
0.010645662434399128,
0.044757477939128876,
0.018580136820673943,
-0.01741090789437294,
-0.0008910184260457754,
-0.07144010066986084,
0.045622024685144424,
-0.0042161764577031136,
-0.007938012480735779,
-0.023197628557682037,
0.0007453102734871209,
-0.0102957459166646,
-0.02091883309185505,
-0.029501672834157944,
-0.034969791769981384,
-0.03119657374918461,
-0.02517940104007721,
-0.0056022112257778645,
-0.05192888528108597,
-0.04676153510808945,
-0.04310929775238037,
0.06724055856466293,
0.02318105846643448,
-0.04907074570655823,
-0.007538531441241503,
0.015704594552516937,
-0.04522678256034851,
-0.011773360893130302,
-0.002458274131640792,
0.0034493969287723303,
-0.0011619515717029572,
0.02874154970049858,
0.04009529948234558,
-0.021054284647107124,
0.015641968697309494,
0.019351474940776825,
0.04422274976968765,
0.05667346715927124,
-0.008310381323099136,
-0.008552169427275658,
-0.04502293840050697,
-0.038819435983896255,
-0.023774772882461548,
0.011832226067781448,
0.07160279154777527,
0.03246401250362396,
-0.014207347296178341,
0.0378926582634449,
0.033138591796159744,
-0.03712783381342888,
0.04945657402276993,
0.04251105338335037,
-0.0006774437497369945,
-0.0008006124990060925,
-0.04031822830438614,
-0.007213183678686619,
-0.016199937090277672,
-0.017772292718291283,
0.01999390497803688,
-0.013997257687151432,
-0.0075560202822089195,
-0.008740585297346115,
-0.002935311058536172,
0.01285158284008503,
-0.0041932035237550735,
-0.00701874541118741,
0.04171265661716461,
0.005733417347073555,
0.06103498488664627,
-0.035281870514154434,
-0.004378406796604395,
0.0569373294711113,
0.04192810133099556,
0.013750836253166199,
0.009618166834115982,
-0.04094625264406204,
-0.022785943001508713,
0.023095250129699707,
0.04142238199710846,
0.007996412925422192,
0.0018094562692567706,
-0.03339352086186409,
-0.007049045991152525,
0.04568871110677719,
-0.023212425410747528,
0.013848826289176941,
0.0062299310229718685,
-0.0036221491172909737,
0.004890750627964735,
-0.03455105423927307,
-0.041588194668293,
0.01818583346903324,
0.029785921797156334,
0.002222473965957761,
-0.04086701199412346,
-0.002725962782278657,
0.00988798588514328,
0.006226118188351393,
-0.011267479509115219,
0.04901052266359329,
-0.0004393976996652782,
0.028877874836325645,
-0.0035544331185519695,
0.056958165019750595,
-0.03919325768947601,
-0.0859399065375328,
0.0005013663903810084,
0.024783078581094742,
-0.01185761857777834,
0.049535784870386124,
-0.04449015110731125,
-0.026343505829572678,
0.016787193715572357,
0.020363690331578255,
0.009420806542038918,
0.030754704028367996,
-0.03678298369050026,
0.022803014144301414,
0.02794310264289379,
0.01656370982527733,
0.03542335703969002,
0.015998445451259613,
0.005881382152438164,
0.004899823106825352,
0.025845518335700035,
0.03792477771639824,
-0.030722562223672867,
-0.0014257333241403103,
-0.02180800586938858,
0.001167316222563386,
-0.03039506822824478,
0.06587632745504379,
-0.018692634999752045,
0.0055544497445225716,
0.0142206447198987,
0.004656464327126741,
-0.0032077396754175425,
0.03218905255198479,
-0.002984737977385521,
-0.021172480657696724,
-0.010580231435596943,
0.04032386839389801,
0.009120171889662743,
-0.020657263696193695,
0.029114989563822746,
-0.01362780574709177,
-0.0035910808946937323,
0.01702107861638069,
0.0004275380342733115,
0.033561207354068756,
0.01076195202767849,
-0.03201470151543617,
-0.042044300585985184,
-0.040624771267175674,
0.0008352951845154166,
-0.0037988435942679644,
0.010090650990605354,
0.017903584986925125,
-0.035688616335392,
-0.014882626943290234,
-0.01867714896798134,
0.015773186460137367,
0.041746482253074646,
-0.04646206647157669,
0.021451056003570557,
0.03916171193122864,
0.0222188588231802,
-0.08285584300756454,
-0.027654211968183517,
-0.010892017744481564,
0.0263832937926054,
-0.00008335578604601324,
-0.03785712271928787,
0.019624752923846245,
-0.03269373998045921,
-0.030735963955521584,
-0.03034486249089241,
0.03404439613223076,
-0.025747645646333694,
0.020802540704607964,
0.01615525782108307,
0.0360417403280735,
0.06257062405347824,
-0.04025553911924362,
0.02757188491523266,
0.014058973640203476,
-0.018144682049751282,
-0.02026868239045143,
-0.0161257516592741,
0.029678115621209145,
-0.010692557319998741,
-0.0060086799785494804,
0.00006374513759510592,
-0.02146276831626892,
0.012768328189849854,
-0.001350506441667676,
-0.024579904973506927,
0.0017519909888505936,
0.007511528208851814,
0.01123958732932806,
-0.00316457636654377,
-0.038868360221385956,
-0.006654447875916958,
0.02293502911925316,
-0.001380380941554904,
0.017449989914894104,
-0.032336410135030746,
-0.02733946032822132,
0.05246720835566521,
-0.01975012570619583,
0.010470499284565449,
0.008876889012753963,
0.05190455913543701,
0.00402061315253377,
0.009175647981464863,
0.020912431180477142,
0.009505999274551868,
0.024826450273394585,
-0.032138172537088394,
0.03267122060060501,
0.019186193123459816,
-0.022442098706960678,
-0.05051884427666664,
-0.04622828587889671,
-0.028757642954587936,
0.027470238506793976,
0.04602143540978432,
-0.005631222389638424,
0.038723792880773544,
0.046085044741630554,
0.010944545269012451,
-0.04131770133972168,
-0.009622281417250633,
-0.027601605281233788,
0.0026567638851702213,
-0.0034113244619220495,
0.019157974049448967,
-0.005620755720883608,
-0.005875196307897568,
0.017426665872335434,
0.006938075181096792,
0.0008775955648161471,
0.005128059070557356,
0.011958369985222816,
0.046265050768852234,
-0.0022404782939702272,
0.007171371020376682,
-0.06104413792490959,
0.027420319616794586,
-0.028451979160308838,
0.013282790780067444,
0.009463295340538025,
0.004885382950305939,
0.018944231793284416,
0.014237754046916962,
0.012740690261125565,
-0.003660600632429123,
-0.03877151012420654,
-0.07738450914621353,
0.0339990071952343,
0.028157532215118408,
0.018924647942185402,
0.053633179515600204,
-0.005428513046354055,
0.07283423095941544,
-0.03532867506146431,
-0.02520311065018177,
-0.03423306718468666,
-0.04689884930849075,
-0.0013055969029664993,
-0.06455706804990768,
-0.03271317481994629,
0.05374263599514961,
-0.021500935778021812,
0.0030816602520644665,
-0.0225489754229784,
-0.01587134599685669,
-0.02237756922841072,
0.025173747912049294,
0.020628144964575768,
-0.010259550996124744,
0.07366812974214554,
-0.0018196292221546173,
0.03309579938650131,
-0.0039839968085289,
-0.03455106541514397,
0.10086224228143692,
0.05247167870402336,
0.003885457990691066,
-0.08244181424379349,
-0.0005865696584805846,
-0.019218947738409042,
0.007690850179642439,
-0.041223056614398956,
0.030527524650096893,
-0.010868306271731853,
-0.011842024512588978,
-0.009021059609949589,
0.07834991812705994,
0.023455876857042313,
-0.012432701885700226,
0.06217359006404877,
-0.03792080283164978,
-0.016987403854727745,
0.04892776533961296,
0.004096261691302061,
-0.03945877403020859,
0.015799205750226974,
-0.073880136013031,
0.023219147697091103,
-0.015713317319750786,
0.03246165066957474,
-0.022668372839689255,
-0.020419156178832054,
0.014852144755423069,
0.0018724097171798348,
0.017689824104309082,
0.004950451198965311,
-0.01930009387433529,
0.0016601437237113714,
-0.01994662918150425,
0.004965113941580057,
0.02027115598320961,
-0.01934817247092724,
0.04550185799598694,
0.03727773204445839,
-0.0032782263588160276,
0.0032027496490627527,
0.013928363099694252,
0.03931373357772827,
-0.036021169275045395,
-0.02318146452307701,
-0.0217983890324831,
0.058460962027311325,
-0.011012007482349873,
-0.01988144777715206,
0.008821293711662292,
-0.011976456269621849,
-0.03638715669512749,
-0.05182266980409622,
-0.036935944110155106,
-0.027115311473608017,
0.008534951135516167,
-0.006036267150193453,
0.013257070444524288,
-0.020599061623215675,
0.026734858751296997,
-0.015642663463950157,
0.035844095051288605,
-0.020144706591963768,
-0.031108533963561058,
0.004572571720927954,
-0.0009676986956037581,
0.01960299164056778,
0.016843339428305626,
-0.016316847875714302,
-0.002973295981064439,
-0.024524495005607605,
-0.02462696097791195,
0.007788667920976877,
0.008425688371062279,
-0.023092737421393394,
0.04113757237792015,
0.025855472311377525,
0.023876776918768883,
0.000436766364146024,
-0.06959297508001328,
-0.0053360047750175,
-0.04283029958605766,
0.0007913507870398462,
-0.03864969313144684,
-0.00769855035468936,
0.01910250633955002,
0.05130666494369507,
0.002455290639773011,
-0.04223869368433952,
0.013156266883015633,
0.03652495518326759,
0.02533908374607563,
-0.011910507455468178,
-0.0008512926287949085,
-0.020524926483631134,
-0.02637496218085289,
-0.0014335321029648185,
-0.023964790627360344,
0.016481030732393265,
0.015314653515815735,
-0.009068743325769901,
-0.022670427337288857,
0.018411455675959587,
-0.0037868760991841555,
0.0030028624460101128,
-0.0002931495546363294,
0.01383750420063734,
0.006033929064869881,
0.05591732636094093,
0.010731762275099754,
-0.037668369710445404,
-0.017579710111021996,
-0.028309185057878494,
0.0008273487910628319,
0.01485240925103426,
0.018740832805633545,
-0.03488117456436157,
0.01818968914449215,
0.007726093754172325,
0.0226889718323946,
-0.044240549206733704,
0.013717261143028736,
-0.01934306137263775,
0.004913128912448883,
-0.004539187066257,
-0.030513858422636986,
0.006175529211759567,
0.0440949909389019,
-0.008948233909904957,
-0.04708108305931091,
0.014919247478246689,
0.010066160000860691,
-0.01570257917046547,
-0.008633258752524853,
0.007108732126653194,
0.0031497625168412924,
0.04872579872608185,
0.011345785111188889,
-0.050368282943964005,
0.04000746086239815,
-0.04361547529697418,
0.00462934747338295,
0.05824248492717743,
-0.013285398483276367,
0.02150586061179638,
0.02845012955367565,
-0.03531486541032791,
0.015696676447987556,
0.01869773305952549,
0.01478091161698103,
-0.027623841539025307,
-0.03704652935266495,
-0.07119113206863403,
-0.020702548325061798,
-0.027950379997491837,
0.03869442269206047,
0.013132376596331596,
0.006831429898738861,
0.01972837932407856,
0.02828490547835827,
-0.03246021643280983,
-0.03942219913005829,
0.010066669434309006,
0.010032000951468945,
0.029812702909111977,
0.016208821907639503,
-0.005521650891751051,
0.03495825082063675,
0.09090203046798706,
-0.025578847154974937,
0.0021394831128418446,
-0.02850687876343727,
-0.01725178211927414,
-0.09045354276895523,
-0.007007026579231024,
0.014928692020475864,
0.021590961143374443,
0.03903547674417496,
-0.04839140176773071,
0.014135647565126419,
0.0475534051656723,
-0.029373085126280785,
0.0004888337571173906,
-0.041710712015628815,
-0.02127864398062229,
-0.004827921744436026,
-0.01491779275238514,
-0.0072424141690135,
0.07608050107955933,
0.02865014597773552,
0.01755322329699993,
-0.009828989394009113,
0.019758103415369987,
0.003910721279680729,
-0.04894211143255234,
-0.03359227254986763,
0.012539702467620373,
0.02755901962518692,
-0.03438453748822212,
0.06679800897836685,
-0.010061414912343025,
-0.04203829914331436,
0.045267894864082336,
-0.016776133328676224,
-0.028935370966792107,
-0.0024117566645145416,
0.019678637385368347,
0.0220672357827425,
0.016706399619579315,
0.01950356550514698,
0.04723471403121948,
0.02638017013669014,
-0.0019037508172914386,
0.031647760421037674,
-0.03276122733950615,
-0.03049194999039173,
0.004746276419609785,
0.026645036414265633,
0.019094591960310936,
-0.01686587743461132,
0.022438134998083115,
-0.01329768169671297,
-0.046859294176101685,
0.0007998972432687879,
-0.055280111730098724,
0.005128596909344196,
-0.015750307589769363,
-0.017253391444683075,
0.0016511110588908195,
0.008409133180975914,
0.018703224137425423,
0.01503029651939869,
-0.01625293307006359,
-0.016322018578648567,
0.0006063969922251999,
-0.030186975374817848,
0.06613876670598984,
0.01015434693545103,
-0.01597311906516552,
-0.06708600372076035,
-0.005156857427209616,
-0.029351448640227318,
-0.00655559916049242,
-0.01337379589676857,
-0.04210406541824341,
-0.011134466156363487,
0.004059650935232639,
0.008224127814173698,
0.003319345647469163,
-0.026501048356294632,
-0.03297087177634239,
-0.010216415859758854,
-0.036981429904699326,
0.011533922515809536,
0.034084100276231766,
-0.018998216837644577,
-0.03325902670621872,
0.011699400842189789,
-0.02970989979803562,
0.028576480224728584,
0.030539479106664658,
0.004189623519778252,
-0.02878059819340706,
0.0310750100761652,
0.005244743544608355,
0.03179045021533966,
-0.022779051214456558,
0.0073508210480213165,
-0.005472760647535324,
0.002864591311663389,
0.007199388928711414,
0.023286480456590652,
0.03387515991926193,
0.04061657562851906,
-0.026474464684724808,
-0.00025194211048074067,
0.0018433014629408717,
0.002541719935834408,
-0.06159258261322975,
0.0039600711315870285,
0.005476164165884256,
0.012947757728397846,
0.06695924699306488,
-0.025134252384305,
0.020506637170910835,
0.0025108184199780226,
-0.030154330655932426,
-0.005257857497781515,
0.02889091894030571,
-0.036092184484004974,
0.009830678813159466,
-0.0010544494725763798,
0.017269210889935493,
0.019826294854283333,
-0.05590781196951866,
-0.027698202058672905,
0.038222163915634155,
-0.027776585891842842,
-0.018740328028798103,
0.06593449413776398,
0.02072468400001526,
0.027998287230730057,
0.045053668320178986,
-0.0039155674166977406,
0.027371587231755257,
0.02931426465511322,
0.01137921679764986,
0.046450525522232056,
0.048838697373867035,
-0.01488281786441803,
-0.003933384083211422,
0.032395776361227036,
-0.04454931989312172,
-0.025826694443821907,
-0.011003764346241951,
0.027617566287517548,
-0.0301835834980011,
0.005308191291987896,
0.0022234239149838686,
-0.02691105753183365,
0.009799044579267502,
0.0053438348695635796,
-0.025913754478096962,
0.04959230124950409,
-0.06897846609354019,
0.028009900823235512,
-0.008566740900278091,
-0.0089956633746624,
-0.024914417415857315,
0.04065356403589249,
0.06455560028553009,
0.07934735715389252,
-0.006785915233194828,
-0.010684533976018429,
-0.021561838686466217,
-0.017616895958781242,
-0.010622094385325909,
-0.015188442543148994,
0.02202025055885315,
0.0028778505511581898,
-0.0059971679002046585,
-0.004641748033463955,
-0.010427863337099552,
-0.01621379517018795,
-0.01050138846039772,
-0.008555184118449688,
0.018129680305719376,
0.04015647992491722,
-0.014665747061371803,
-0.035510823130607605,
-0.0406450591981411,
0.0645432248711586,
-0.0345289409160614,
-0.04303702712059021,
-0.020858321338891983,
-0.028878463432192802,
-0.0038860365748405457,
0.03039419651031494
] |
<p>This is a question motivated by <a href="http://en.wikipedia.org/wiki/Angry_Birds" rel="nofollow">Angry Birds</a>. </p>
<p>When playing the game, I notice that if the initial velocity is constant, the way to land a bird furthest away from the launching point is by launching the bird at 45 degrees from the ground. </p>
<p>Is it possible to obtain a derivation and a proof of this?</p>
| 9,562 |
[
-0.026211630553007126,
-0.02652157098054886,
0.009823834523558617,
0.05749097093939781,
0.029901595786213875,
-0.022129451856017113,
-0.03389409929513931,
0.012316538952291012,
-0.00795780774205923,
-0.03861471265554428,
-0.012578785419464111,
0.0567728690803051,
0.04039955511689186,
0.05043119564652443,
0.0030410639010369778,
-0.03303975611925125,
-0.058462172746658325,
-0.013127232901751995,
0.014140931889414787,
-0.027640625834465027,
0.004944940563291311,
0.01643345318734646,
0.019770702347159386,
-0.022825749590992928,
-0.01818682625889778,
0.00812277477234602,
0.019294623285531998,
-0.00020331129780970514,
-0.0380866713821888,
0.06018777936697006,
-0.01890833117067814,
0.01272995863109827,
0.03136787563562393,
0.027534184977412224,
0.04036739096045494,
0.03324192017316818,
-0.0026725882198661566,
0.024427540600299835,
-0.03121235780417919,
-0.01163006667047739,
0.003937574569135904,
-0.0020040813833475113,
-0.027094967663288116,
0.0620257593691349,
0.015447224490344524,
0.0417698509991169,
-0.04010786488652229,
-0.012536664493381977,
0.04844944551587105,
-0.048173967748880386,
0.10372258722782135,
0.013940460048615932,
0.0073751057498157024,
0.03153621032834053,
0.02439991571009159,
-0.0173506923019886,
0.08335140347480774,
0.0258868969976902,
-0.03297792747616768,
-0.023068133741617203,
0.002845369977876544,
-0.07985054701566696,
-0.004209097009152174,
-0.010636434890329838,
-0.01569218374788761,
0.04079001396894455,
-0.0295109823346138,
-0.00352381425909698,
0.023842910304665565,
-0.0422021709382534,
-0.025467269122600555,
0.05474928393959999,
0.04808532074093819,
0.009789062663912773,
0.034843917936086655,
-0.02936614118516445,
0.02927166037261486,
0.01912735588848591,
0.028691884130239487,
0.012280183844268322,
-0.03936994820833206,
0.041818343102931976,
0.06600192189216614,
0.04380333796143532,
0.042363204061985016,
-0.008534649387001991,
0.03905167803168297,
-0.006120712496340275,
0.030960094183683395,
0.06063934043049812,
0.03476421535015106,
-0.0280944611877203,
0.03506266698241234,
-0.0374443419277668,
-0.03554440662264824,
0.051066987216472626,
0.005817290395498276,
0.054873138666152954,
0.005038238130509853,
-0.0389101579785347,
-0.026076771318912506,
-0.0545266829431057,
-0.01264174748212099,
0.045829907059669495,
-0.0003640350478235632,
-0.01719716191291809,
-0.046284548938274384,
0.020869014784693718,
-0.027545377612113953,
0.004197230562567711,
-0.043678805232048035,
0.05423571914434433,
-0.01394821610301733,
-0.010009851306676865,
0.018682541325688362,
-0.014508913271129131,
-0.015061592683196068,
0.009763216599822044,
0.024592308327555656,
0.016278669238090515,
0.0297336895018816,
-0.005338113289326429,
0.033456310629844666,
-0.019751494750380516,
-0.03536853566765785,
0.01735428161919117,
-0.02235996350646019,
-0.037183649837970734,
-0.015143195167183876,
0.034720733761787415,
-0.007320693228393793,
-0.012232557870447636,
-0.008271767757833004,
0.024879463016986847,
0.021684778854250908,
0.00004333863398642279,
-0.08890705555677414,
-0.0711495503783226,
0.0663655698299408,
-0.018945733085274696,
0.011171004734933376,
-0.07743387669324875,
-0.006315062288194895,
0.04018144682049751,
0.06424357742071152,
-0.003916529007256031,
0.03899393975734711,
-0.018259413540363312,
-0.00274904677644372,
0.006151048932224512,
0.00858055055141449,
-0.028068825602531433,
0.005998041946440935,
-0.07876093685626984,
0.0005285098450258374,
-0.03477853909134865,
0.015503093600273132,
0.024853721261024475,
-0.00034818515996448696,
-0.036870796233415604,
0.06291970610618591,
-0.041414353996515274,
-0.02366643026471138,
-0.03295213729143143,
0.0032558992970734835,
-0.01161222904920578,
0.09416501224040985,
0.0620102733373642,
-0.06200239434838295,
-0.01297153253108263,
-0.010598042979836464,
0.03842172399163246,
-0.025264743715524673,
0.023490654304623604,
0.08359556645154953,
-0.04678957909345627,
-0.03630300611257553,
-0.008508380502462387,
0.02438276819884777,
-0.01809903420507908,
-0.042177535593509674,
-0.015668364241719246,
-0.025371070951223373,
0.031522560864686966,
0.018794668838381767,
0.06051037088036537,
-0.03881724551320076,
0.03851844370365143,
0.022956229746341705,
-0.01998610608279705,
0.0007094863103702664,
-0.08935347199440002,
0.0514044426381588,
0.0011488235322758555,
-0.015546071343123913,
0.03515380248427391,
0.005971328355371952,
0.04512067884206772,
-0.05275164917111397,
0.015295957215130329,
-0.01293197926133871,
0.0032738051377236843,
0.04650284722447395,
-0.01812523417174816,
0.006975197233259678,
0.06585592776536942,
0.03803355619311333,
0.02732333540916443,
0.01756851002573967,
-0.021983677521348,
-0.017432596534490585,
-0.008558139204978943,
-0.0446770042181015,
-0.0165784303098917,
0.008799123577773571,
0.025333385914564133,
0.016104407608509064,
0.004365116823464632,
-0.013581778854131699,
0.020413341000676155,
-0.05078808218240738,
0.05557578057050705,
0.05171824246644974,
0.01668868027627468,
0.05404280498623848,
0.04607977345585823,
-0.01322278194129467,
-0.00201065163128078,
0.019680531695485115,
-0.04279020428657532,
-0.022197984158992767,
-0.05205151066184044,
0.01909218728542328,
0.003821359947323799,
-0.029536401852965355,
0.0027693796437233686,
0.047253262251615524,
0.017872098833322525,
0.019237490370869637,
0.06951051950454712,
0.00027277375920675695,
-0.0016845478676259518,
-0.010103555396199226,
-0.0054890974424779415,
-0.006198763381689787,
0.015184573829174042,
0.0007152656326070428,
0.012981615960597992,
-0.03137961030006409,
-0.0009536537108942866,
-0.03348319232463837,
0.006939761806279421,
0.027488376945257187,
-0.026516081765294075,
0.025755461305379868,
-0.04188690334558487,
0.018094368278980255,
-0.01977541856467724,
0.013560391031205654,
0.017014918848872185,
0.024498596787452698,
0.012334075756371021,
-0.016059510409832,
0.02293000929057598,
0.024460388347506523,
0.0033664756920188665,
0.018002986907958984,
0.02849261276423931,
0.04695241525769234,
-0.027019444853067398,
-0.016872018575668335,
-0.038775522261857986,
-0.034072283655405045,
0.02012917585670948,
0.0009098502341657877,
0.02702942118048668,
0.00694913137704134,
-0.00732575124129653,
-0.011147025972604752,
-0.008993787690997124,
-0.024457260966300964,
0.0036589798983186483,
0.0032679797150194645,
-0.008493580855429173,
-0.02429165318608284,
0.04666750505566597,
-0.019765092059969902,
-0.01062031276524067,
0.01472159568220377,
0.02262733317911625,
0.029390953481197357,
0.025494588539004326,
-0.017022261396050453,
-0.01531465258449316,
-0.0016028092941269279,
-0.04025951400399208,
-0.027899298816919327,
0.002805290510877967,
0.0016645914874970913,
0.03315933421254158,
0.02074436843395233,
-0.026685994118452072,
0.024105049669742584,
-0.04286976903676987,
-0.04639136418700218,
-0.04142805188894272,
0.01714460179209709,
0.03819720819592476,
-0.0077834660187363625,
0.010037856176495552,
0.008159595541656017,
-0.01195271871984005,
-0.020127883180975914,
-0.059356044977903366,
-0.0511530339717865,
-0.00633660051971674,
0.017383240163326263,
0.038167793303728104,
0.008679844439029694,
-0.029629595577716827,
0.05514080449938774,
0.02834710106253624,
-0.017552731558680534,
-0.03631734475493431,
-0.009039117954671383,
0.03820819407701492,
0.015568532049655914,
-0.017257431522011757,
0.021063849329948425,
-0.04955064132809639,
0.03973224014043808,
0.004818245768547058,
-0.015506896190345287,
0.049482423812150955,
-0.021596072241663933,
0.00790933333337307,
-0.036180540919303894,
0.01750079356133938,
0.02141406573355198,
0.006304486654698849,
0.025409044697880745,
-0.06759082525968552,
0.0026131724007427692,
0.02183801494538784,
0.050601258873939514,
0.002864288166165352,
-0.04670247435569763,
0.013339064083993435,
-0.028655225411057472,
-0.0237765833735466,
-0.004808696452528238,
0.03387865051627159,
0.01014784537255764,
-0.012890651822090149,
-0.011200741864740849,
0.018685363233089447,
0.04661526903510094,
-0.0027056457474827766,
-0.013930870220065117,
0.016910744830965996,
-0.020292019471526146,
-0.035621125251054764,
-0.06655897945165634,
-0.006986300926655531,
0.012909910641610622,
0.02095567062497139,
0.01833643577992916,
-0.010939355939626694,
0.02717513218522072,
0.01884489692747593,
0.010036187246441841,
0.0450860820710659,
-0.03848462179303169,
0.020422251895070076,
-0.07227515429258347,
0.00530243618413806,
0.014308324083685875,
0.013447105884552002,
-0.009016653522849083,
0.02741851843893528,
0.007188828662037849,
0.021369852125644684,
0.0014737657038494945,
0.007254846394062042,
-0.09691516309976578,
0.01246737502515316,
-0.026178594678640366,
-0.04128692299127579,
-0.015569922514259815,
-0.014429548755288124,
0.006970072630792856,
-0.02762557938694954,
-0.0229243915528059,
-0.011257047764956951,
-0.04196172580122948,
-0.04444178193807602,
0.048230551183223724,
-0.05863581597805023,
-0.04782332852482796,
0.008290695026516914,
0.0038759808521717787,
0.054589997977018356,
-0.06334470212459564,
0.06300677359104156,
0.04075394943356514,
-0.02881474606692791,
-0.011213455349206924,
-0.030825793743133545,
-0.014679023064672947,
-0.03809715434908867,
0.018186306580901146,
0.0226270891726017,
0.03765532374382019,
0.04037224128842354,
0.01570293679833412,
-0.04885632172226906,
0.008209374733269215,
0.002365690656006336,
-0.013530631549656391,
-0.04602733999490738,
-0.07578527182340622,
-0.0158829465508461,
0.03272626921534538,
0.023511650040745735,
-0.02864897809922695,
0.01254598144441843,
0.058945950120687485,
0.03731553256511688,
-0.012522736564278603,
-0.021951112896203995,
0.037360530346632004,
0.0349854938685894,
0.007573062554001808,
-0.031125042587518692,
0.0032886324916034937,
0.0020202966406941414,
-0.01650257594883442,
0.012435785494744778,
-0.020787805318832397,
-0.00808890350162983,
0.016223303973674774,
0.057280056178569794,
-0.009903308004140854,
-0.016455696895718575,
0.00021987012587487698,
-0.020496048033237457,
0.034613609313964844,
-0.03351808711886406,
-0.006861458998173475,
-0.019788948819041252,
0.024094315245747566,
0.028766842558979988,
-0.0053894054144620895,
-0.015288213267922401,
-0.05664584040641785,
-0.01264756266027689,
0.012452572584152222,
0.02402416057884693,
-0.018224572762846947,
0.025494858622550964,
-0.032778386026620865,
-0.019881945103406906,
0.016071539372205734,
0.018963221460580826,
0.04361412301659584,
-0.024847356602549553,
-0.019099954515695572,
0.0049943579360842705,
-0.021386589854955673,
-0.05475877970457077,
0.009217692539095879,
-0.008273561485111713,
0.028957711532711983,
0.012335305102169514,
-0.0007127809221856296,
-0.004477132111787796,
0.01148996315896511,
0.039550602436065674,
0.06805670261383057,
0.0446622297167778,
0.0005679872701875865,
-0.009869907982647419,
0.01297406293451786,
-0.049094308167696,
-0.0225532129406929,
0.0121367909014225,
0.014960618689656258,
0.0077316961251199245,
0.01922927238047123,
0.010357756167650223,
0.014524435624480247,
0.03593647480010986,
0.012942032888531685,
0.006754667032510042,
0.0007578575750812888,
-0.03530704230070114,
-0.02376183494925499,
0.0299886055290699,
0.012060408480465412,
-0.009694044478237629,
0.026432665064930916,
0.011572347022593021,
-0.0171698909252882,
0.014212117530405521,
0.03241307660937309,
-0.006276385858654976,
-0.02468586526811123,
-0.02542208880186081,
0.01594097539782524,
-0.02583216316998005,
0.00912361778318882,
0.014413407072424889,
0.018809983506798744,
-0.028239741921424866,
0.014547232538461685,
-0.029016932472586632,
0.020753176882863045,
-0.0005024707061238587,
0.018629861995577812,
-0.013322153128683567,
0.04270080104470253,
0.015590023249387741,
-0.009664313867688179,
-0.011049850843846798,
-0.0012455645482987165,
0.03151251748204231,
0.01088325958698988,
-0.0013242033310234547,
0.018273066729307175,
-0.013521125540137291,
-0.025830384343862534,
-0.004117801785469055,
-0.03357720747590065,
0.022793903946876526,
-0.020258253440260887,
-0.025055447593331337,
0.03532300516963005,
-0.06520669907331467,
-0.03171903267502785,
0.0001527546701254323,
-0.005605531390756369,
-0.006587618496268988,
-0.05324803665280342,
0.0090872123837471,
0.017939714714884758,
0.02639649249613285,
-0.04185912758111954,
-0.029653120785951614,
0.02427057921886444,
0.010593706741929054,
-0.007248030975461006,
-0.057968128472566605,
-0.013925367966294289,
-0.02644064649939537,
-0.03947395086288452,
0.003621378680691123,
0.01499433908611536,
-0.00427950918674469,
-0.03755403310060501,
-0.007026053033769131,
-0.03919919207692146,
0.059861958026885986,
-0.004343406762927771,
0.006097109522670507,
0.024837428703904152,
-0.02731238678097725,
0.013561252504587173,
0.028317492455244064,
0.07147379219532013,
-0.02216675505042076,
-0.009303555823862553,
-0.00702066021040082,
0.003336444031447172,
0.008600269444286823,
-0.03993915766477585,
-0.0008667939691804349,
0.009371653199195862,
0.01677032746374607,
-0.012579631991684437,
-0.003470916533842683,
0.018389059230685234,
0.004520811606198549,
-0.03614543378353119,
-0.008823384530842304,
0.025263648480176926,
-0.0013990647858008742,
-0.007581942714750767,
0.03633879870176315,
0.02817291021347046,
0.04041183739900589,
-0.00891190953552723,
0.0635678842663765,
-0.07497908174991608,
-0.055717360228300095,
0.03825293108820915,
0.05436521768569946,
0.019549041986465454,
-0.006556415464729071,
-0.003806459251791239,
-0.007268880493938923,
0.007863247767090797,
-0.02870880626142025,
0.01175608579069376,
-0.0467551089823246,
0.05767589807510376,
0.06303229182958603,
-0.038155943155288696,
0.08518212288618088,
0.047385238111019135,
0.04867715761065483,
-0.012182577513158321,
0.021996047347784042,
-0.00442324997857213,
-0.04292338714003563,
-0.004138085059821606,
0.032686904072761536,
-0.02249792031943798,
0.004638174548745155,
0.015665875747799873,
0.02401995286345482,
0.011737540364265442,
-0.002811272395774722,
0.004086531698703766,
-0.018956702202558517,
0.0603691041469574,
0.0066671292297542095,
-0.012002639472484589,
0.0114585030823946,
0.0045197149738669395,
0.014695660211145878,
-0.03393535688519478,
-0.021970363333821297,
0.030610138550400734,
0.020559975877404213,
-0.004234188236296177,
-0.0431121364235878,
-0.01822226122021675,
-0.005750394891947508,
0.0048988740891218185,
-0.003907901234924793,
0.07541920989751816,
0.029076462611556053,
0.020758934319019318,
0.040545716881752014,
-0.02358490414917469,
0.018556347116827965,
-0.03400943800806999,
-0.004376415628939867,
-0.04783954843878746,
-0.027191011235117912,
0.0004577600338961929,
0.04238826036453247,
-0.005235795397311449,
-0.033983003348112106,
0.020062241703271866,
-0.046528834849596024,
-0.014939623884856701,
0.04052305966615677,
0.02434934675693512,
0.01877046562731266,
0.12335148453712463,
0.02816597931087017,
-0.03167884796857834,
0.0012796876253560185,
0.00721885496750474,
0.103220134973526,
0.04439660906791687,
-0.007273337338119745,
-0.04099320247769356,
0.004361052066087723,
-0.022298414260149002,
-0.02464183419942856,
-0.03663593530654907,
0.0019375430420041084,
0.006447930820286274,
-0.012887810356914997,
0.02458527870476246,
-0.0017494671046733856,
0.018416935577988625,
-0.03903123736381531,
0.0401138961315155,
-0.040313590317964554,
-0.02993401512503624,
0.0014254370471462607,
-0.025729862973093987,
0.017136288806796074,
0.0027748574502766132,
-0.02421576902270317,
0.006445753388106823,
0.0065278057008981705,
-0.006753061898052692,
0.0025318360421806574,
-0.0534968376159668,
-0.0026302600745111704,
0.010931337252259254,
-0.050515688955783844,
0.014395412988960743,
0.06661354750394821,
-0.007963969372212887,
-0.04606335237622261,
0.04099547117948532,
0.0066823153756558895,
-0.008120168931782246,
0.008628854528069496,
0.03254380449652672,
0.041699934750795364,
0.01107715629041195,
0.013431469909846783,
0.03019464947283268,
-0.02805851399898529,
-0.018614891916513443,
-0.06580334901809692,
0.006570698227733374,
-0.016123123466968536,
0.01944832131266594,
-0.011905619874596596,
0.00991413276642561,
0.014366887509822845,
-0.07152533531188965,
0.001718025770969689,
0.02027180604636669,
0.04332653433084488,
0.000468437880044803,
-0.014275052584707737,
0.00022276300296653062,
0.008542426861822605,
0.013411145657300949,
-0.02071838080883026,
-0.012980101630091667,
-0.000892656622454524,
-0.013627310283482075,
-0.02872755192220211,
0.07968366146087646,
-0.038588445633649826,
-0.06976994127035141,
-0.0423324815928936,
0.00007532724703196436,
-0.04843343794345856,
0.032085418701171875,
0.02345219999551773,
0.013273327611386776,
-0.016010191291570663,
0.03255871310830116,
-0.04560352861881256,
-0.0005385138792917132,
-0.03035108931362629,
0.02165146917104721,
-0.03373149409890175,
0.0022339129354804754,
-0.05594858154654503,
-0.018911276012659073,
-0.0038823531940579414,
0.057615987956523895,
-0.018976569175720215,
0.018257448449730873,
-0.06325458735227585,
0.028190886601805687,
0.0029806934762746096,
-0.03380656614899635,
-0.05592621862888336,
0.006631277501583099,
-0.04509536176919937,
-0.010626643896102905,
-0.03678445518016815,
0.08686703443527222,
0.05317367613315582,
0.02725859172642231,
0.0020435755141079426,
-0.0055158245377242565,
-0.02967044897377491,
0.05265578255057335,
0.025615153834223747,
-0.03317411616444588,
-0.017546044662594795,
0.0020831525325775146,
-0.018059322610497475,
-0.05186798423528671,
-0.01573397032916546,
-0.004231921397149563,
-0.003488532267510891,
-0.03613544628024101,
-0.0006026432383805513,
-0.017960695549845695,
-0.005910226609557867,
-0.01729152351617813,
0.008028277195990086,
-0.048398565500974655,
0.015941686928272247,
-0.036826249212026596,
-0.0008900649263523519,
-0.03275791183114052,
-0.006065514404326677,
-0.008062920533120632,
0.010787148959934711,
-0.027751704677939415,
0.01767144165933132,
0.02556796930730343,
0.027047162875533104,
0.02706092596054077,
-0.03538807854056358,
0.031679362058639526,
-0.01195296086370945,
0.047922272235155106,
-0.04548931121826172,
-0.019275490194559097,
-0.010440262965857983,
-0.06052678823471069,
-0.030708516016602516,
-0.008621638640761375,
-0.00046164001105353236,
0.047793980687856674,
0.009603857062757015,
0.02111171931028366,
-0.013791370205581188,
0.05927738919854164,
0.024723900482058525,
-0.013433512300252914,
0.021269474178552628,
0.005268624983727932,
0.0032108949963003397,
0.0012705473927780986,
0.005331422667950392,
-0.055892203003168106,
-0.0008514024666510522,
0.015352940186858177,
0.02412986382842064,
-0.015703564509749413,
0.03134042024612427,
0.05245494470000267,
-0.007885015569627285,
-0.01845698617398739,
0.025484981015324593,
-0.000842948560602963,
0.02858639508485794,
0.030294407159090042,
-0.007389918435364962,
0.025300469249486923,
0.03384148329496384,
0.01953885145485401,
-0.07163367420434952,
0.03353280574083328,
0.00981444027274847,
-0.018221911042928696,
0.05512107163667679,
-0.07343459874391556,
0.007221730891615152,
0.05316390469670296,
-0.09416473656892776,
-0.010994981974363327,
-0.00512834545224905,
0.006281914189457893,
-0.06323248147964478,
-0.01667148806154728,
0.014237937517464161,
0.04848405718803406,
0.03494827076792717,
0.03798070549964905,
0.020762505009770393,
-0.0007749958313070238,
-0.008071450516581535,
-0.00758565217256546,
0.022382019087672234,
-0.001014884328469634,
-0.009462892077863216,
-0.00842486321926117,
0.027032513171434402,
-0.007531481795012951,
-0.04111588001251221,
0.036667436361312866,
-0.014880198054015636,
0.027253834530711174,
0.005404939409345388,
0.020467760041356087,
0.011830895207822323,
0.01644338108599186,
0.006308653391897678,
0.016655387356877327,
0.023831939324736595,
0.022302130237221718,
-0.01307669747620821,
0.02019253931939602,
-0.01913309283554554,
-0.023090694099664688,
0.02613687701523304,
-0.04561760649085045,
-0.03140704333782196,
0.016258100047707558,
-0.012254555709660053,
-0.025090977549552917,
-0.003659055335447192,
0.0003093829727731645,
0.0020864105317741632,
0.005409921985119581,
-0.020352018997073174,
-0.03159252926707268,
0.006928544025868177,
0.015389470383524895,
-0.03199607878923416,
-0.014493034221231937,
-0.009181196801364422,
-0.023911770433187485,
-0.027256350964307785,
-0.033137280493974686,
-0.014126510359346867,
0.011264929547905922,
-0.05535950884222984,
-0.022181466221809387,
0.005413646809756756,
-0.01565161906182766,
-0.004644483327865601,
-0.00046358208055607975,
-0.025405531749129295,
0.02887078747153282,
0.01827729307115078,
0.015016504563391209,
0.0011665110941976309,
0.0051842606626451015,
-0.0051520527340471745,
-0.05956973880529404,
0.06333327293395996,
0.01867038570344448,
-0.00709694204851985,
-0.04038139060139656,
-0.04543223977088928,
0.03574378415942192,
-0.0018462507287040353,
0.028613394126296043,
-0.051678307354450226,
-0.01713339425623417,
0.001929295132867992,
0.007439039647579193,
0.00341798341833055,
-0.019844040274620056,
0.007057955022901297,
0.001707955147139728,
-0.03558634966611862,
0.0166699830442667,
-0.019220832735300064,
-0.026516014710068703,
0.000540380657184869,
-0.016410360112786293,
0.0280280951410532,
-0.0030942566227167845,
-0.007271468173712492,
-0.042916081845760345,
0.019947828724980354,
0.05083104223012924,
0.011811425909399986,
0.08824172616004944,
0.023091688752174377,
-0.05137917399406433,
0.03629951551556587,
-0.01776244305074215,
-0.0501626618206501,
0.041473470628261566,
-0.034381620585918427,
-0.04426044970750809,
-0.00879515241831541,
-0.013093123212456703,
0.012074893340468407,
-0.04418919235467911,
-0.040702998638153076,
0.05471404641866684,
-0.012342403642833233,
-0.03340823948383331,
0.014543524943292141,
-0.009495263919234276,
0.030507642775774002,
-0.003972753416746855,
-0.008509519509971142,
0.023308992385864258,
-0.0180156659334898,
-0.01975121721625328,
-0.0031216272618621588,
0.03269432857632637,
-0.000447563681518659,
0.014989005401730537,
0.012324068695306778,
0.019508754834532738,
0.06430859863758087,
0.01447450090199709,
0.029586566612124443,
0.013127872720360756,
-0.01214874442666769,
-0.007512811105698347,
-0.023402860388159752,
0.001032601692713797,
0.0027361188549548388,
-0.053173139691352844,
0.04287272319197655,
-0.003431284101679921,
0.00444786436855793,
-0.0002667096850927919,
0.045777566730976105,
-0.02463698200881481,
-0.010184209793806076,
0.03334305062890053,
0.029539117589592934,
0.0013712083455175161,
-0.014395147562026978,
0.04157170653343201,
-0.009261145256459713,
0.02541871927678585,
0.018252871930599213,
0.02391902729868889,
0.024612244218587875,
-0.007096831686794758,
-0.014330280013382435,
-0.02772149071097374,
-0.040687091648578644,
0.005260320845991373,
0.04328380897641182,
0.06187167391180992,
0.01535269245505333,
-0.021237539127469063,
-0.009272600524127483,
-0.05250644311308861,
0.09438051283359528,
-0.056183990091085434,
-0.023193372413516045,
-0.015891509130597115,
0.009636376984417439,
-0.006433926057070494,
0.019221803173422813
] |
<p>I know a lot about Theoretical Physicists from <a href="http://en.wikipedia.org/wiki/Sheldon_Cooper" rel="nofollow">Sheldon Cooper</a> of <a href="http://en.wikipedia.org/wiki/The_Big_Bang_Theory" rel="nofollow">Big Bang Theory</a>. I know about parallel universes (and I wonder if one codingtales in one of the parallel universes believes if parallel universes do not exist).</p>
<p>I'm sorry, but this is just for fun.
But I've real questions:</p>
<ul>
<li>Are all the equations that appear on the board and Sheldon tries to solve true?</li>
<li>How is a Rocket Scientist different from a Theoretical Physicist?</li>
<li>I figure out some errors in the definition of a "Screw" that Sheldon gives. He says he is on an inclined plane wrapped helically around its axis. As far as I know there are no inclined planes with axes. Can you please explain it to me?</li>
<li>Any other suggestion that would help me understand Big Bang Theory better would be appreciated.</li>
</ul>
<p>(And please forgive the tags. I didn't find "Theoretical-Physics" tag. I have to bluntly use some other alternative.)</p>
| 9,563 |
[
-0.0006395989912562072,
-0.050362810492515564,
-0.01906351000070572,
-0.02443593554198742,
0.05935736373066902,
-0.012152692303061485,
0.014161665923893452,
-0.007898173294961452,
-0.01667734421789646,
-0.03666676953434944,
0.025474855676293373,
0.020251590758562088,
0.02839840203523636,
0.03932179510593414,
0.03190810605883598,
0.009978425689041615,
0.0013046434614807367,
0.0011133713414892554,
-0.042364221066236496,
-0.0016340356087312102,
0.026978114619851112,
0.007900414057075977,
-0.0077868676744401455,
0.015789521858096123,
0.014077737927436829,
0.022745663300156593,
0.03548099473118782,
0.007153199519962072,
0.008740240707993507,
0.020232677459716797,
0.023747898638248444,
-0.04437168315052986,
0.020050419494509697,
-0.002906810026615858,
-0.01455643493682146,
-0.006092261988669634,
-0.018092544749379158,
0.007916633039712906,
0.014414920471608639,
-0.005759108811616898,
-0.03475315123796463,
-0.004684069659560919,
-0.029023928567767143,
0.04987932741641998,
-0.03180538862943649,
0.022902317345142365,
-0.0054742987267673016,
-0.0020838326308876276,
0.08998523652553558,
-0.04270168021321297,
0.061332784593105316,
0.005510011687874794,
0.011560073122382164,
0.02596104145050049,
-0.012925340794026852,
-0.006051152478903532,
0.08784805983304977,
0.06665419787168503,
-0.018344378098845482,
-0.08268396556377411,
-0.010237588547170162,
0.004857800435274839,
0.0037191235460340977,
0.014340085908770561,
-0.02316041849553585,
0.03224964067339897,
-0.020670942962169647,
-0.02317109704017639,
0.021576806902885437,
-0.018108196556568146,
-0.01284116879105568,
0.043888043612241745,
0.020147107541561127,
-0.01424542348831892,
-0.0038758106529712677,
-0.04047060012817383,
-0.0036927880719304085,
0.0281430222094059,
0.0019760318100452423,
0.03982876241207123,
-0.02401091903448105,
0.025399548932909966,
0.046760544180870056,
0.06625398993492126,
0.004667432513087988,
-0.021982643753290176,
0.060900818556547165,
-0.01995236985385418,
-0.0024951647501438856,
0.034101519733667374,
0.006982062943279743,
0.034413840621709824,
0.03600708022713661,
0.02506358176469803,
-0.024392027407884598,
0.06616616249084473,
0.006762329954653978,
0.04068676382303238,
0.007000288926064968,
-0.026368550956249237,
-0.0031473604030907154,
-0.010419382713735104,
0.019922299310564995,
0.04180898517370224,
-0.017197854816913605,
-0.024837462231516838,
-0.02860734984278679,
0.03165950998663902,
-0.03157325088977814,
-0.008303382433950901,
-0.03449453413486481,
0.030190108343958855,
-0.020650863647460938,
0.007704842835664749,
0.03644074499607086,
-0.05613422021269798,
0.002020324347540736,
-0.02902790904045105,
0.0676826760172844,
0.057241521775722504,
0.05009317025542259,
-0.01105513982474804,
0.048185888677835464,
-0.015366630628705025,
-0.08640135824680328,
-0.0033449509646743536,
0.027747923508286476,
-0.020018354058265686,
-0.034747932106256485,
0.04772958159446716,
0.00957228522747755,
0.02415025606751442,
-0.0024369924794882536,
0.002994328970089555,
0.05417842045426369,
0.023743808269500732,
-0.0968233197927475,
-0.05636211112141609,
0.033999331295490265,
0.02785632014274597,
-0.003513845382258296,
-0.07839687168598175,
0.010331377387046814,
-0.001921924646012485,
0.06803367286920547,
-0.024559879675507545,
-0.019381443038582802,
-0.011758506298065186,
0.039485957473516464,
-0.017088647931814194,
-0.05096643045544624,
-0.0017694372218102217,
-0.023435305804014206,
-0.059201788157224655,
0.008325968869030476,
-0.06325123459100723,
0.004286516923457384,
0.009638626128435135,
-0.014475537464022636,
-0.03619232401251793,
0.07464578747749329,
-0.01698172464966774,
-0.002175322500988841,
-0.007137453183531761,
-0.03318101912736893,
-0.029605194926261902,
0.08094478398561478,
0.03598695993423462,
0.0038201152347028255,
0.06148473545908928,
-0.006754917558282614,
0.0039673009887337685,
-0.038065794855356216,
-0.01112073753029108,
0.028973525390028954,
-0.03967134654521942,
-0.02848965860903263,
-0.010444632731378078,
0.0040091583505272865,
-0.009883460588753223,
-0.060930658131837845,
-0.01864836923778057,
-0.0037422801833599806,
-0.002221814589574933,
-0.022402973845601082,
0.023041287437081337,
-0.011035132221877575,
0.008232848718762398,
0.0021442759316414595,
-0.024661019444465637,
-0.0018860052805393934,
-0.09145287424325943,
0.015733769163489342,
-0.019618479534983635,
0.01226383913308382,
-0.0021732954774051905,
0.012119428254663944,
0.017947249114513397,
-0.05855698138475418,
-0.01770796999335289,
0.0030810406897217035,
0.05194193869829178,
0.027867954224348068,
0.059811703860759735,
0.00031644408591091633,
0.05978304147720337,
0.052806440740823746,
-0.01128874346613884,
0.0169900581240654,
-0.0025092412251979113,
0.011492240242660046,
0.025140201672911644,
-0.021232161670923233,
0.03606810048222542,
0.013177228160202503,
-0.007531573064625263,
0.017885485664010048,
-0.0015850436175242066,
-0.009866082109510899,
0.03119179978966713,
-0.009700489230453968,
0.03747794032096863,
-0.0034880749881267548,
0.00674360990524292,
0.0010773192625492811,
0.02335588075220585,
-0.0031569513957947493,
0.010315178893506527,
0.01905713602900505,
-0.019922327250242233,
-0.06162705272436142,
-0.008400918915867805,
0.028693564236164093,
0.029684558510780334,
-0.028841529041528702,
0.02554313838481903,
0.003258325392380357,
0.05552815645933151,
-0.007588354405015707,
0.015136972069740295,
-0.05873532593250275,
-0.042668018490076065,
0.023015694692730904,
-0.0026162005960941315,
-0.005182344000786543,
0.026320500299334526,
0.013488415628671646,
0.0155900027602911,
-0.0034919208846986294,
-0.030891742557287216,
-0.018604330718517303,
0.014863476157188416,
-0.010679660364985466,
-0.005960648879408836,
0.0615113265812397,
-0.007910579442977905,
0.03410107642412186,
-0.00050819554599002,
0.00816724169999361,
0.03670775890350342,
-0.009123476222157478,
-0.02078813686966896,
-0.03496584668755531,
0.02175736427307129,
-0.042102959007024765,
0.04494209960103035,
-0.033556245267391205,
-0.040658190846443176,
0.04503563418984413,
-0.058955393731594086,
-0.028532179072499275,
-0.015613097697496414,
0.0233952384442091,
-0.02046002447605133,
0.007586262654513121,
0.01623694784939289,
0.024601232260465622,
0.04811178147792816,
-0.03263315558433533,
-0.03961114212870598,
0.014301974326372147,
-0.040135350078344345,
0.022122390568256378,
0.010037180036306381,
-0.05624549463391304,
0.03585539013147354,
-0.0433318056166172,
-0.012585383839905262,
0.014747913926839828,
-0.01568022556602955,
0.02817419543862343,
0.00781933218240738,
-0.02970784157514572,
-0.014354350045323372,
-0.02291998267173767,
-0.039614949375391006,
0.05504050478339195,
-0.02364073134958744,
-0.02218720130622387,
0.07130224257707596,
0.007056704722344875,
0.007983965799212456,
0.026768270879983902,
-0.08020314574241638,
-0.034661803394556046,
0.006010638549923897,
0.0042826454155147076,
0.03624558448791504,
0.033032242208719254,
0.015180050395429134,
0.019451456144452095,
-0.06311985105276108,
-0.010968773625791073,
-0.04612283408641815,
-0.04305117204785347,
0.0004016530292574316,
-0.0037359632551670074,
0.04845084995031357,
-0.007609997875988483,
-0.01779896579682827,
0.036911558359861374,
0.03120255097746849,
-0.07026926428079605,
-0.00929507426917553,
-0.0154455890879035,
-0.014381860382854939,
-0.029960162937641144,
0.01717090606689453,
0.028974231332540512,
-0.01608203537762165,
0.034590382128953934,
0.029297037050127983,
0.04394920915365219,
0.020968982949852943,
0.033958252519369125,
0.005294147413223982,
-0.030077241361141205,
-0.0006952397525310516,
-0.017108019441366196,
0.04845929890871048,
-0.0009387620375491679,
-0.04033773019909859,
0.017829028889536858,
-0.021408289670944214,
0.009081482887268066,
0.012059811502695084,
-0.06432710587978363,
0.055847667157649994,
0.008430183865129948,
-0.005868765525519848,
-0.029162662103772163,
0.04753098636865616,
-0.016056055203080177,
-0.019372565671801567,
-0.0038326983340084553,
0.007188248913735151,
0.03369783237576485,
-0.007444090209901333,
0.012385569512844086,
0.011766418814659119,
0.054863784462213516,
-0.03003196232020855,
-0.007506023161113262,
-0.015338174067437649,
-0.028612971305847168,
-0.004075551405549049,
-0.03901086002588272,
-0.033729325979948044,
0.07561101764440536,
0.06486572325229645,
0.05178483575582504,
0.025600861757993698,
-0.0249681007117033,
0.02289881929755211,
-0.05385631322860718,
0.00690909568220377,
-0.02061876282095909,
0.06038841977715492,
0.0017463420517742634,
0.06116489693522453,
0.015063763596117496,
0.006840522401034832,
0.017022058367729187,
0.014236547984182835,
-0.059092842042446136,
0.027883095666766167,
0.005537054967135191,
-0.011780320666730404,
-0.00021084531908854842,
0.015750039368867874,
0.030072679743170738,
-0.02140318788588047,
-0.022584907710552216,
-0.0025819302536547184,
0.009595689363777637,
-0.037524014711380005,
0.015947388485074043,
-0.05788743123412132,
-0.045818936079740524,
-0.005910953972488642,
0.023144768550992012,
0.05137816071510315,
-0.029221100732684135,
0.0390789732336998,
0.046277888119220734,
-0.026149971410632133,
-0.009802023880183697,
-0.017379503697156906,
-0.004123142920434475,
0.013351297937333584,
0.030076492577791214,
0.02009977586567402,
0.00455044349655509,
0.019485486671328545,
0.03248215839266777,
0.010048048570752144,
0.03571392968297005,
0.033722877502441406,
0.00533945532515645,
-0.019105060026049614,
-0.03373877704143524,
0.004737218376249075,
-0.03064563311636448,
0.01800381951034069,
-0.02834746055305004,
0.01294183824211359,
0.039012644439935684,
0.04594172164797783,
-0.001209284644573927,
0.03534988686442375,
0.0579560287296772,
-0.027462733909487724,
0.005699504166841507,
-0.009320098906755447,
-0.027912721037864685,
-0.012166749686002731,
0.00818539410829544,
0.014522057957947254,
0.017557520419359207,
-0.05407155677676201,
0.04377202317118645,
0.022122519090771675,
0.0020756328012794256,
-0.02674119733273983,
0.0604754276573658,
-0.03905652090907097,
0.03682290017604828,
-0.015140514820814133,
-0.0009607776300981641,
-0.023557502776384354,
0.04127564653754234,
0.053561508655548096,
-0.011062389239668846,
-0.012993323616683483,
-0.06745768338441849,
-0.009059018455445766,
0.02312217280268669,
0.06529500335454941,
-0.003792103147134185,
-0.005029090214520693,
-0.07516952604055405,
-0.0003469731018412858,
0.04172617942094803,
-0.055976737290620804,
0.030477374792099,
-0.026028092950582504,
0.035258907824754715,
-0.0065469564869999886,
-0.017955904826521873,
-0.0015397100942209363,
-0.014001624658703804,
-0.022094935178756714,
0.024706527590751648,
0.00009693763422546908,
0.017412342131137848,
-0.02526121959090233,
-0.013321664184331894,
0.04014969617128372,
0.02663474902510643,
0.0013382375473156571,
0.03190217912197113,
0.007118957582861185,
-0.002776122884824872,
-0.01322969514876604,
-0.05358083173632622,
-0.018339302390813828,
0.012897753156721592,
-0.028540002182126045,
0.045339539647102356,
-0.0007528967689722776,
-0.04311274737119675,
-0.0019397756550461054,
-0.019086085259914398,
-0.01446701493114233,
0.009412052109837532,
-0.03582027181982994,
0.022433094680309296,
0.031105922535061836,
0.014635086059570312,
0.008241032250225544,
0.06679704040288925,
-0.05183696746826172,
0.021236257627606392,
-0.023110855370759964,
-0.0151658421382308,
0.030099228024482727,
0.047361377626657486,
-0.03296821191906929,
-0.001610956504009664,
-0.020447183400392532,
0.009611408226191998,
-0.01577642932534218,
-0.01513025164604187,
-0.03975866362452507,
-0.03139986842870712,
-0.014966826885938644,
0.0251119676977396,
-0.02229454182088375,
-0.004236967768520117,
-0.008307372219860554,
-0.005408317781984806,
0.011067320592701435,
-0.04259471222758293,
-0.0008133251103572547,
0.021540872752666473,
0.0066270893439650536,
0.0038202241994440556,
0.0485733300447464,
0.04043789580464363,
-0.03471249341964722,
0.020758436992764473,
0.008279779925942421,
-0.045651379972696304,
0.039600007236003876,
-0.007021385245025158,
-0.02882203459739685,
0.003055474255234003,
-0.02972932904958725,
-0.05053979903459549,
-0.03605214133858681,
-0.0141100799664855,
-0.027351204305887222,
0.00509165832772851,
0.018054792657494545,
-0.005307622253894806,
0.03169027343392372,
-0.014786322601139545,
-0.02381293661892414,
0.046818897128105164,
0.0323312021791935,
0.002095568925142288,
-0.006231037899851799,
0.002560903551056981,
-0.027710745111107826,
-0.03735676035284996,
0.010221750475466251,
0.0317998081445694,
-0.041552867740392685,
-0.026876945048570633,
0.010006840340793133,
0.003598725190386176,
0.06763286888599396,
0.01858353242278099,
-0.05018074810504913,
0.020705191418528557,
-0.009354175999760628,
-0.01563846506178379,
0.016168037429451942,
0.05330855771899223,
-0.02373083308339119,
-0.06575848907232285,
0.003658873029053211,
0.014758259989321232,
0.02533005364239216,
-0.03742951154708862,
0.026511821895837784,
0.007931454107165337,
0.01677839830517769,
-0.035561174154281616,
-0.002028924413025379,
0.01744660921394825,
0.007813464850187302,
0.021255750209093094,
-0.015477657318115234,
0.015345646999776363,
0.01843353919684887,
-0.06145334988832474,
0.01110807154327631,
-0.0030170343816280365,
0.015867512673139572,
0.026961233466863632,
0.05770820006728172,
-0.01351574994623661,
-0.02302912436425686,
0.05518794432282448,
-0.036750201135873795,
0.0196499302983284,
0.0023226886987686157,
0.01368006318807602,
0.0071379076689481735,
-0.0007465022499673069,
0.00465221656486392,
-0.01833389699459076,
-0.03118167631328106,
0.009729070588946342,
0.030870536342263222,
0.005340051371604204,
0.05215565860271454,
0.011279064230620861,
-0.05013087019324303,
-0.030410615727305412,
-0.01764114573597908,
0.0017654252005741,
0.013619637116789818,
-0.013257271610200405,
-0.0060333251021802425,
-0.02769584208726883,
-0.018047232180833817,
0.04672224447131157,
0.059633880853652954,
-0.01980743370950222,
-0.027581829577684402,
0.05558369681239128,
0.033716898411512375,
-0.02746155485510826,
-0.004365857690572739,
-0.038719721138477325,
0.07177598029375076,
-0.019145231693983078,
0.07662545144557953,
0.017204122617840767,
-0.013247250579297543,
0.04521559178829193,
0.00949901808053255,
-0.01981501281261444,
-0.030658874660730362,
-0.013613395392894745,
-0.06295055896043777,
0.019839376211166382,
0.01201589498668909,
0.026675747707486153,
0.012893467210233212,
-0.04761423170566559,
0.0342811681330204,
-0.011705227196216583,
0.019292140379548073,
-0.007656056433916092,
-0.057426027953624725,
0.010126679204404354,
-0.019116505980491638,
-0.059467680752277374,
0.04022084176540375,
-0.014521780423820019,
-0.01138822827488184,
0.03266441449522972,
-0.02702839858829975,
0.02612367644906044,
0.027625378221273422,
0.047481968998909,
-0.0456932969391346,
0.03610829636454582,
-0.015249880962073803,
-0.0076088751666247845,
-0.04361587017774582,
-0.02665885165333748,
0.1193423643708229,
0.05919213965535164,
0.002495952881872654,
-0.05756497383117676,
-0.0010350844822824001,
-0.04144952446222305,
0.03365176171064377,
-0.04121535271406174,
0.010325365699827671,
-0.017586158588528633,
0.021829454228281975,
-0.009002615697681904,
0.04933512583374977,
0.015544561669230461,
0.009180012159049511,
0.041717249900102615,
-0.05636655539274216,
-0.07340972125530243,
-0.0060016135685145855,
0.03703344985842705,
-0.009315919131040573,
-0.019923271611332893,
-0.0397605299949646,
0.009639361873269081,
-0.033719658851623535,
0.018064165487885475,
-0.05267157405614853,
-0.06178499385714531,
0.03161759302020073,
0.0018457717960700393,
-0.009563497267663479,
0.02902844175696373,
-0.0012932384852319956,
-0.044399064034223557,
-0.003514582756906748,
0.023147881031036377,
0.05448087304830551,
-0.044413935393095016,
0.030350981280207634,
0.0461714044213295,
0.0060678101144731045,
0.007382166106253862,
0.02983846887946129,
0.01252465508878231,
-0.04122038558125496,
0.021666400134563446,
-0.01750870794057846,
0.013837012462317944,
-0.018838591873645782,
-0.04666601121425629,
-0.015873372554779053,
0.015935374423861504,
-0.008970236405730247,
-0.03651631996035576,
-0.00036600889870896935,
0.009446686133742332,
0.05662030354142189,
-0.004888819996267557,
-0.04562718793749809,
-0.020428283140063286,
0.02435595728456974,
-0.01474426593631506,
0.024727102369070053,
0.024668756872415543,
0.013792067766189575,
0.01213369145989418,
-0.033638566732406616,
0.03395824134349823,
-0.00452517531812191,
0.011664227582514286,
-0.0776204764842987,
0.0009417811525054276,
-0.05719694867730141,
-0.005972323473542929,
0.017862480133771896,
0.031829603016376495,
0.0012883490417152643,
-0.0003635771572589874,
0.013667114078998566,
-0.013356541283428669,
-0.018500326201319695,
0.012413869611918926,
0.0024922089651226997,
-0.03061261773109436,
-0.018836913630366325,
0.026783207431435585,
0.04191230610013008,
0.039682310074567795,
0.0022435944993048906,
0.008307482115924358,
-0.03499038890004158,
0.01681620441377163,
0.04652896523475647,
-0.025772079825401306,
-0.040277786552906036,
-0.0038687705527991056,
-0.016982611268758774,
-0.022384194657206535,
-0.03352753445506096,
0.02865329384803772,
0.03456694260239601,
-0.003954372834414244,
0.008731400594115257,
-0.002749186707660556,
0.011867566965520382,
-0.022241760045289993,
0.037935078144073486,
-0.03064083307981491,
-0.014444137923419476,
0.0324416346848011,
0.019774269312620163,
-0.043586354702711105,
-0.059332672506570816,
0.0027679293416440487,
-0.015590251423418522,
-0.007764325477182865,
0.04020296037197113,
-0.038368888199329376,
-0.03982028365135193,
-0.018730882555246353,
0.001844615675508976,
-0.04471678286790848,
0.018692143261432648,
-0.03689151629805565,
0.008167212828993797,
0.0007237325189635158,
0.040223605930805206,
-0.039032213389873505,
0.04489057883620262,
-0.014453000389039516,
-0.046691857278347015,
0.024129686877131462,
0.0006334779900498688,
-0.03343630209565163,
-0.03947756439447403,
0.008384094573557377,
0.009486082009971142,
0.02662656642496586,
-0.03448591008782387,
-0.010127232410013676,
0.024112064391374588,
-0.006224178243428469,
-0.0639825239777565,
0.019215576350688934,
-0.020870395004749298,
0.0020385512616485357,
0.006752008572220802,
-0.045256465673446655,
-0.0382373109459877,
0.05180566757917404,
-0.01805858500301838,
0.00537503557279706,
0.01502069178968668,
-0.011053048074245453,
0.005578476004302502,
-0.018116706982254982,
0.02993673086166382,
-0.00956434104591608,
-0.004887085873633623,
0.008823820389807224,
0.024320639669895172,
0.008730612695217133,
-0.008999085053801537,
-0.016866663470864296,
-0.0012096533318981528,
-0.03852251172065735,
-0.018996933475136757,
0.015410604886710644,
0.007586160209029913,
0.0653916522860527,
-0.03813624382019043,
0.04171556606888771,
-0.013834751211106777,
0.03572537750005722,
-0.08864638209342957,
0.0090711060911417,
0.009630165062844753,
-0.02387411892414093,
0.028939370065927505,
-0.019606200978159904,
0.01598837412893772,
-0.0015343028353527188,
-0.025614220649003983,
0.01812097430229187,
0.011511726304888725,
-0.026821082457900047,
-0.024552570655941963,
-0.03568720445036888,
-0.01635361649096012,
0.05701721832156181,
0.02119968831539154,
0.06393181532621384,
-0.003243879647925496,
0.01770477183163166,
-0.0074196066707372665,
-0.01757383719086647,
0.01960303634405136,
0.04857436940073967,
-0.016056180000305176,
-0.008467542938888073,
0.06850525736808777,
-0.020768703892827034,
-0.02663392387330532,
0.027616269886493683,
0.042657699435949326,
0.0044447085820138454,
-0.015969401225447655,
0.018866052851080894,
0.020638685673475266,
0.04809248819947243,
0.018803810700774193,
-0.011572069488465786,
0.016250180080533028,
0.06301882117986679,
-0.016065800562500954,
0.020801177248358727,
0.015721380710601807,
-0.011037863790988922,
-0.003240004414692521,
-0.06423003226518631,
-0.024803446605801582,
0.03464280813932419,
-0.02491919882595539,
0.012720081023871899,
-0.026150451973080635,
0.0045159864239394665,
0.02401410974562168,
-0.028056858107447624,
0.007036210037767887,
-0.040096718817949295,
-0.00519817927852273,
0.03685823455452919,
-0.011861791834235191,
-0.019523657858371735,
-0.0021185637451708317,
0.025701113045215607,
-0.003817921970039606,
0.034834373742341995,
-0.005848622880876064,
-0.04032247141003609,
-0.022243693470954895,
-0.02340405248105526,
-0.0013802300672978163,
0.027726823464035988,
0.007623712532222271,
-0.03427806869149208,
-0.013490557670593262,
0.04074329882860184,
0.00922304019331932,
0.016456957906484604,
0.010914734564721584,
-0.024593301117420197,
-0.02327033504843712,
-0.07834792137145996,
0.010175565257668495,
0.03487932309508324,
0.00022076594177633524,
-0.05590282008051872,
-0.02239038050174713,
0.04086057096719742,
0.006955689284950495,
0.04696332663297653,
-0.0023750849068164825,
0.014045629650354385,
0.002012737561017275,
-0.02450532279908657,
0.01627662032842636,
-0.0701141431927681,
0.0192022155970335,
0.028155028820037842,
-0.03134188801050186,
-0.019789159297943115,
-0.0032393834553658962,
-0.04098520800471306,
0.027455288916826248,
0.060146525502204895,
0.013788480311632156,
0.036677028983831406,
-0.015422110445797443,
-0.03952554985880852,
-0.000054967465985100716,
-0.007989143952727318,
0.017380543053150177,
0.05832437798380852,
-0.01836737059056759,
0.02448830008506775,
0.052021365612745285,
-0.03601936623454094,
-0.019444361329078674,
0.0309451874345541,
-0.04222163185477257,
-0.018320918083190918,
-0.010559641756117344,
-0.051516663283109665,
0.018088793382048607,
-0.01782265119254589,
-0.0008317364263348281,
0.0394454263150692,
-0.013947886414825916,
-0.011826482601463795,
0.029667260125279427,
0.021900499239563942,
0.04037461429834366,
-0.04702271148562431,
0.010930401273071766,
0.015328419394791126,
-0.05380572751164436,
0.0020525504369288683,
0.05230676010251045,
0.03937724977731705,
-0.007072861306369305,
0.01363061461597681,
0.038734517991542816,
0.009090173058211803,
0.02456420101225376,
-0.0043420023284852505,
0.026219354942440987,
-0.04756352677941322,
-0.0035813210997730494,
0.006124804262071848,
-0.03403354063630104,
-0.0015421363059431314,
0.04885444790124893,
-0.01904546469449997,
0.05629882216453552,
-0.026475830003619194,
0.026741573587059975,
0.015916714444756508,
-0.011308373883366585,
-0.0012484068283811212,
-0.012301682494580746,
-0.011427654884755611,
0.02266620472073555,
-0.031017255038022995,
-0.059266284108161926,
-0.04883244261145592,
0.024621179327368736,
0.04527159780263901,
-0.01887827180325985,
-0.005441129207611084,
-0.004246801603585482,
-0.013301517814397812,
0.04039387404918671,
0.012162079103291035,
-0.03073478862643242,
-0.020832426846027374,
0.027230488136410713,
0.034747179597616196,
-0.022261779755353928,
-0.028191639110445976,
0.011953131295740604,
-0.017224928364157677,
0.03702810779213905,
-0.06855621933937073,
-0.004385203123092651,
-0.021837303414940834,
0.03309975937008858,
-0.031197676435112953,
-0.017363950610160828
] |
<p>Related: <a href="http://physics.stackexchange.com/questions/18117/is-a-white-object-always-white">Is a white object always white?</a></p>
<p>If you are standing in front of a glass window during the day, you can see your dim white t-shirt’s reflection in the window. The reflection is dim because only 4% of the light is reflected (assuming you’re perpendicular to the window) while the rest is transmitted through the glass. If a white object is placed in front of this glass pane, it’s obvious that white light is reflected as white and not colored. Why is this? </p>
<p>I vaguely remember that visible light that is reflected penetrates glass about λ/2, so that means that blue light penetrates the least while red light penetrates more. If I shine white light onto a glass window (assume RGB color model), I have to account for all three colored scatterers in roughly equal amounts of intensity to produce white. Here is what I think.</p>
<p>• Blue light penetrates shorter distances into the glass window’s atomic layers and recruits less atomic scatterers that back scatter more intensity blue light. I assume Rayleigh scattering is valid since wavelengths of light are much greater than the atomic spacing’s in glass, therefore $I ∝ 1/λ^4$.</p>
<p>• Green light penetrates deeper into the glass window’s atomic layers and recruits more atomic scatterers that back scatter more “less intensity” green light according to $I ∝ 1/λ^4$?. So the larger number of green atomic scatterers scattered less intense green light but there are more green atomic scatterers.</p>
<p>• In a similar fashion, red light would recruit an even larger number of red atomic scatterers (but less intense than green or blue), however, the increased number of red atomic scatterers compensates for a more overall intense red intensity. </p>
<p>In summary, there are roughly equal amounts of blue, green and red light reflected such that a glass window reflects white objects white. Here is what I am asking: is this correct way to view this? I was unable to find this anywhere online or on . I would greatly appreciate feedback, especially if this is not correct. </p>
| 9,564 |
[
-0.03850235044956207,
-0.03191082924604416,
0.01696036569774151,
-0.03143433853983879,
0.022840017452836037,
0.029566025361418724,
-0.02246103435754776,
-0.03199393302202225,
0.009820769540965557,
-0.028678912669420242,
0.050625257194042206,
0.05438057333230972,
0.02987099066376686,
0.03180398792028427,
0.03452064469456673,
-0.005055835470557213,
-0.000005332215096132131,
-0.006760862655937672,
-0.015996212139725685,
-0.0259777270257473,
-0.002842961112037301,
-0.0019456177251413465,
0.02282886952161789,
-0.005569582339376211,
-0.028986051678657532,
0.02281123213469982,
-0.006162385921925306,
-0.006682560313493013,
0.0055455407127738,
0.012988132424652576,
0.016097234562039375,
0.01732313632965088,
0.00563516840338707,
0.038628336042165756,
0.0035405319649726152,
0.013635179959237576,
0.01067474577575922,
-0.0007105187396518886,
-0.03496736288070679,
0.02402004972100258,
-0.008696028962731361,
-0.006035722326487303,
-0.01572393625974655,
0.023863721638917923,
0.0023743235506117344,
-0.026008959859609604,
-0.0162254199385643,
-0.04535531625151634,
0.023013247177004814,
-0.07575903832912445,
0.05247064307332039,
-0.017129581421613693,
0.03989799693226814,
0.03351325914263725,
-0.005010589025914669,
-0.02299976348876953,
0.05653208866715431,
0.051744621247053146,
-0.03087015077471733,
-0.05225278064608574,
0.005085978657007217,
0.0049897488206624985,
-0.04018035903573036,
0.013725589029490948,
-0.027602551504969597,
0.007102387025952339,
-0.01148759201169014,
-0.03594674542546272,
0.008713002316653728,
0.018941771239042282,
0.02799408882856369,
0.035293933004140854,
0.03189445659518242,
-0.020967314019799232,
0.01249193586409092,
0.008645042777061462,
0.009594859555363655,
0.046564385294914246,
0.050898198038339615,
0.003617600305005908,
0.01074844691902399,
-0.01969427615404129,
0.0050054071471095085,
0.029724301770329475,
0.001980279805138707,
-0.00894453376531601,
0.10523026436567307,
-0.020449867472052574,
-0.03465348482131958,
0.03487112745642662,
0.01886441372334957,
0.03372236341238022,
0.010826307348906994,
0.03809116780757904,
0.005380604416131973,
0.028659863397479057,
-0.01238742284476757,
0.047124363481998444,
-0.019729236140847206,
0.005602707155048847,
-0.03682968392968178,
-0.02099495939910412,
0.021482547745108604,
0.07817273586988449,
-0.018689345568418503,
-0.037893619388341904,
-0.029516277834773064,
0.01879049465060234,
0.012365099973976612,
0.013975432142615318,
-0.039768584072589874,
0.030572935938835144,
0.005454600788652897,
-0.013464853167533875,
-0.022043030709028244,
-0.04995856061577797,
0.030640345066785812,
-0.010519600473344326,
0.07234226912260056,
0.07303029298782349,
-0.0012694756733253598,
-0.019894184544682503,
0.007539074402302504,
-0.012068112380802631,
-0.049336254596710205,
0.04172743111848831,
0.03147808462381363,
-0.002975338138639927,
-0.022281495854258537,
0.03798895329236984,
0.03538378328084946,
-0.018349407240748405,
0.017029453068971634,
-0.013311164453625679,
-0.004728734493255615,
-0.016902394592761993,
-0.09791432321071625,
-0.03494011610746384,
0.04665695130825043,
0.03168909251689911,
-0.0366976335644722,
-0.07765734940767288,
0.025006556883454323,
0.013513052836060524,
0.047280583530664444,
0.0035088579170405865,
0.015004425309598446,
0.0276959128677845,
0.026308994740247726,
-0.008880354464054108,
-0.012760845012962818,
-0.008340544998645782,
0.0026827433612197638,
-0.025761088356375694,
0.010715238749980927,
-0.02575390413403511,
0.02860744297504425,
0.01778988167643547,
-0.005855937954038382,
-0.029165197163820267,
0.05654832348227501,
0.009609906934201717,
-0.011388726532459259,
0.03250185027718544,
0.04130488261580467,
-0.04070311784744263,
0.023953760042786598,
0.011144682765007019,
0.04928452521562576,
-0.010859009809792042,
-0.030803874135017395,
-0.004636680707335472,
-0.03674184903502464,
0.024078236892819405,
0.0032067380379885435,
0.0016602386021986604,
0.0222142543643713,
-0.019523516297340393,
0.00905622635036707,
0.02643747813999653,
-0.03303144499659538,
-0.024380428716540337,
0.0027014189399778843,
0.010820373892784119,
0.02879311516880989,
0.043901316821575165,
0.01886601373553276,
-0.027410117909312248,
0.026992252096533775,
-0.04394090175628662,
-0.0244668647646904,
-0.010578819550573826,
-0.005065651144832373,
0.013895868323743343,
-0.015433860942721367,
0.036290332674980164,
-0.0037176557816565037,
0.006866898387670517,
0.031097643077373505,
-0.018734389916062355,
-0.014021039009094238,
0.030216556042432785,
0.022771378979086876,
0.0015984524507075548,
0.027570310980081558,
0.05753112956881523,
0.02331424690783024,
-0.006854288745671511,
0.011153796687722206,
-0.04398098215460777,
-0.01829812303185463,
0.017370713874697685,
-0.023686885833740234,
0.039492685347795486,
-0.023914916440844536,
-0.01442183367908001,
0.04129220172762871,
0.034674059599637985,
-0.02399696782231331,
0.025668110698461533,
-0.0074911219999194145,
0.011736620217561722,
0.020066190510988235,
-0.0023045605048537254,
0.010395980440080166,
0.0016635848442092538,
-0.00776186166331172,
0.028358308598399162,
0.0035300643648952246,
-0.010017843917012215,
-0.032637108117341995,
0.001504046842455864,
0.028932685032486916,
0.0029424901586025953,
-0.04329686984419823,
0.024166429415345192,
-0.017350129783153534,
0.05317506194114685,
0.03104509599506855,
0.015532238408923149,
-0.013303878717124462,
-0.05778989568352699,
-0.00398228969424963,
0.02333214320242405,
0.007189578842371702,
0.020563790574669838,
-0.008795267902314663,
-0.028476685285568237,
0.02842346765100956,
-0.027882909402251244,
-0.015006259083747864,
0.01634685881435871,
-0.0003404157469049096,
0.007410505320876837,
-0.04389765486121178,
-0.014663447625935078,
0.039465099573135376,
-0.016531966626644135,
0.019456835463643074,
0.046219564974308014,
-0.0070043704472482204,
0.033465676009655,
-0.027838844805955887,
-0.04051155596971512,
-0.005283229053020477,
0.032317981123924255,
-0.047633618116378784,
0.0015825486043468118,
0.02038556896150112,
-0.03150911256670952,
0.03436334431171417,
-0.018336763605475426,
0.020099947229027748,
-0.04844963178038597,
-0.01782119832932949,
-0.00015098942094482481,
0.011626821011304855,
-0.0017436903435736895,
-0.07587132602930069,
-0.030240967869758606,
0.005924746859818697,
-0.017629997804760933,
-0.0004697481926996261,
-0.013506964780390263,
-0.032473109662532806,
0.003334559267386794,
-0.047528594732284546,
-0.03228659927845001,
0.017795555293560028,
-0.008027558214962482,
-0.02995382808148861,
0.017834851518273354,
0.009498737752437592,
-0.04604601860046387,
-0.022923648357391357,
-0.023613683879375458,
0.001562521792948246,
-0.040862418711185455,
-0.015534119680523872,
0.028224842622876167,
0.006149863824248314,
-0.06178004667162895,
0.009570618160068989,
-0.05445701628923416,
-0.05766374245285988,
-0.02200094610452652,
-0.048444196581840515,
0.002792182145640254,
-0.0019573464524000883,
0.0012853601947426796,
0.01019527018070221,
-0.01772768795490265,
-0.008621319197118282,
-0.04795550927519798,
-0.039246972650289536,
0.006350926589220762,
-0.014797545969486237,
0.052387505769729614,
-0.018611880019307137,
0.00003760663093999028,
0.05962233617901802,
0.04565892368555069,
-0.019052492454648018,
-0.029019400477409363,
-0.005250376649200916,
-0.037166811525821686,
-0.05448893830180168,
0.02514292486011982,
0.04323015734553337,
-0.010331262834370136,
0.05340341478586197,
-0.014406980946660042,
0.052652083337306976,
0.055015988647937775,
0.033520929515361786,
-0.017765771597623825,
0.06787752360105515,
0.010887393727898598,
-0.01906270906329155,
0.052003853023052216,
0.00697995675727725,
-0.008255675435066223,
0.015230249613523483,
-0.014872360043227673,
0.016494043171405792,
0.02099377103149891,
-0.06844569742679596,
0.05739396810531616,
-0.004561480600386858,
0.020305251702666283,
-0.036099422723054886,
0.014537178911268711,
0.027592666447162628,
-0.011714925058186054,
-0.017839934676885605,
0.013840209692716599,
0.04051247984170914,
-0.007880667224526405,
-0.0050508491694927216,
0.04541731998324394,
0.027183089405298233,
0.010352435521781445,
-0.00770556228235364,
-0.013535388745367527,
-0.003885448444634676,
0.05538240820169449,
-0.016629686579108238,
-0.012265549972653389,
0.049632199108600616,
0.0644134134054184,
0.041728172451257706,
-0.007276540622115135,
-0.045373305678367615,
-0.045176390558481216,
-0.047579072415828705,
-0.020110882818698883,
-0.04105101898312569,
0.028617793694138527,
-0.029778819531202316,
0.039040643721818924,
0.028053399175405502,
0.02240978367626667,
0.00201021833345294,
-0.01730169728398323,
-0.061498064547777176,
0.013341917656362057,
0.0015464217867702246,
-0.014642470516264439,
-0.028323668986558914,
-0.04078871011734009,
-0.022288309410214424,
-0.03066985122859478,
-0.023141341283917427,
-0.001934893662109971,
0.002795625012367964,
-0.03769874945282936,
0.009299686178565025,
0.0025569575373083353,
-0.027088221162557602,
-0.013193834573030472,
0.06532476842403412,
0.00518778758123517,
0.0025710740592330694,
0.001338469097390771,
0.037611089646816254,
-0.01415687333792448,
0.012755808420479298,
-0.03043784201145172,
0.023755265399813652,
0.030089640989899635,
0.023825978860259056,
0.039725519716739655,
0.03736940026283264,
-0.014915850013494492,
-0.004112196620553732,
0.03139135614037514,
-0.0015542927430942655,
-0.009754959493875504,
-0.02264791540801525,
-0.009869283065199852,
-0.03379160165786743,
-0.052932750433683395,
-0.03833485394716263,
0.037763986736536026,
-0.03971559554338455,
0.020580986514687538,
0.01815919391810894,
-0.011795098893344402,
-0.013385898433625698,
0.03356181085109711,
-0.00792291946709156,
-0.009375671856105328,
-0.015405640937387943,
-0.05370592698454857,
0.010439416393637657,
-0.005536007694900036,
0.043023884296417236,
0.03861933574080467,
0.006597310304641724,
0.01754625141620636,
-0.019081491976976395,
0.02170817367732525,
-0.006797846406698227,
-0.039834633469581604,
0.005837100557982922,
-0.056892070919275284,
-0.019425800070166588,
-0.004988395143300295,
-0.02657320722937584,
-0.0330120325088501,
0.055619560182094574,
0.02818419598042965,
-0.002346570137888193,
0.0010766304330900311,
-0.07198190689086914,
-0.0310769472271204,
0.018432289361953735,
0.04745839163661003,
-0.005019569303840399,
0.039412856101989746,
-0.059879083186388016,
-0.008523472584784031,
-0.0009408489568158984,
-0.0044185444712638855,
0.05816075578331947,
-0.016234174370765686,
0.014942805282771587,
-0.018404649570584297,
-0.015721537172794342,
-0.006379882805049419,
-0.021023660898208618,
0.008626912720501423,
-0.014517318457365036,
-0.005138247273862362,
0.010841473005712032,
-0.01748463697731495,
0.02066740021109581,
0.01975630410015583,
0.012039616703987122,
-0.04986469820141792,
-0.0005822691600769758,
-0.04274134337902069,
-0.006158757489174604,
-0.026318684220314026,
-0.04550853744149208,
0.014315983280539513,
0.017180711030960083,
-0.010269095189869404,
0.061778489500284195,
-0.03988597169518471,
-0.001766688423231244,
0.06853717565536499,
0.05156648904085159,
-0.009420506656169891,
0.006958920508623123,
-0.044144514948129654,
0.0752050057053566,
0.0218709297478199,
-0.008877616375684738,
0.05988580733537674,
0.048580579459667206,
-0.011113512329757214,
0.04271303862333298,
-0.013359683565795422,
0.04871739447116852,
-0.04728485271334648,
-0.03180302307009697,
0.016200317069888115,
-0.04765072464942932,
-0.018281515687704086,
0.05452100560069084,
0.007482257671654224,
0.010364736430346966,
-0.01478820014744997,
-0.07316769659519196,
0.014009245671331882,
0.0031437764409929514,
-0.007492924574762583,
0.02911924012005329,
-0.027955440804362297,
0.038310568779706955,
0.012121482752263546,
-0.012748886831104755,
0.007792961318045855,
-0.008888065814971924,
0.008852600120007992,
0.0028982062358409166,
0.003729210002347827,
0.05665729194879532,
-0.043907687067985535,
0.00221828231588006,
-0.011946944519877434,
-0.025670403614640236,
0.04083213582634926,
-0.006130903493613005,
0.009479621425271034,
0.014245168305933475,
-0.05395206809043884,
-0.008200087584555149,
0.021344292908906937,
-0.040762998163700104,
0.03681720420718193,
0.004381874576210976,
0.030871950089931488,
0.006532993167638779,
0.004813899286091328,
-0.05898111313581467,
0.012025658041238785,
-0.02304774522781372,
0.030177203938364983,
-0.03438585251569748,
-0.004565023351460695,
-0.011515160091221333,
-0.01724972575902939,
-0.047310564666986465,
-0.009129771962761879,
0.014277012087404728,
-0.02072237990796566,
-0.022827230393886566,
0.010736752301454544,
0.009972622618079185,
0.029811255633831024,
-0.012618359178304672,
-0.005245944019407034,
-0.020449504256248474,
-0.033920709043741226,
-0.024260755628347397,
0.013235109858214855,
0.02083257958292961,
-0.03304189443588257,
-0.028712540864944458,
0.022843608632683754,
-0.021030085161328316,
0.023507339879870415,
-0.024617251008749008,
-0.03830788657069206,
0.030118733644485474,
0.02471170574426651,
-0.023244671523571014,
-0.024866744875907898,
0.01896882802248001,
0.026187831535935402,
0.024572746828198433,
0.01008116640150547,
0.002671149093657732,
-0.040954381227493286,
-0.04947821795940399,
0.0206677857786417,
0.019436419010162354,
-0.01871039904654026,
0.026421550661325455,
0.10627280920743942,
-0.02909301035106182,
0.02529555931687355,
0.023530324921011925,
0.0040826452895998955,
0.003015275811776519,
-0.04097995162010193,
0.03355340287089348,
0.010425875894725323,
0.003454521531239152,
-0.017161866649985313,
-0.016344472765922546,
-0.06132340058684349,
0.0010731583461165428,
0.07361891865730286,
-0.016613144427537918,
0.07101774215698242,
0.0011743070790544152,
-0.028181418776512146,
-0.004094552714377642,
-0.04821033775806427,
0.007412038743495941,
-0.0024620424956083298,
-0.024797555059194565,
0.03232709318399429,
-0.05245590955018997,
-0.03180364891886711,
0.003062199568375945,
0.036202508956193924,
-0.004412977024912834,
0.03027534671127796,
0.03603887930512428,
0.006600345019251108,
0.007359216921031475,
-0.0735068991780281,
-0.02332744374871254,
0.04184185713529587,
-0.04309028387069702,
0.0036424421705305576,
0.0355798676609993,
-0.03576330095529556,
0.04204503074288368,
0.009807114489376545,
-0.005645706318318844,
-0.06211018189787865,
-0.02411218173801899,
-0.04122326523065567,
0.017062382772564888,
0.014648349024355412,
0.012663441710174084,
-0.010015270672738552,
-0.013698793016374111,
-0.005075042601674795,
-0.010357019491493702,
0.05547204241156578,
-0.04007351025938988,
-0.05277905985713005,
-0.02754802815616131,
-0.04364543408155441,
-0.03460662066936493,
0.04986600950360298,
0.0023730441462248564,
-0.03676660731434822,
-0.019763002172112465,
-0.06378022581338882,
0.03359135612845421,
0.03911789879202843,
0.0075894128531217575,
0.00982982013374567,
0.03435319662094116,
-0.0034665195271372795,
0.06463676691055298,
0.009086662903428078,
0.0047607747837901115,
0.13848958909511566,
0.10218542814254761,
-0.01611323654651642,
-0.004886893089860678,
-0.012941035442054272,
0.00033949906355701387,
-0.01070116925984621,
-0.03225279226899147,
0.006115695461630821,
-0.05833271145820618,
0.02108772099018097,
0.016764122992753983,
0.07864062488079071,
0.00981786847114563,
0.00051786849508062,
0.013208112679421902,
-0.03711770847439766,
-0.03104129619896412,
0.017896320670843124,
-0.008836815133690834,
-0.00023458103532902896,
0.037578001618385315,
-0.03027474693953991,
0.02514301799237728,
-0.0237659253180027,
0.010462705977261066,
-0.018118644133210182,
-0.0024628713726997375,
0.0039656455628573895,
-0.015400509350001812,
-0.025580521672964096,
-0.009051617234945297,
-0.010663681663572788,
0.004614547360688448,
-0.04541581869125366,
-0.012573600746691227,
0.056765537708997726,
-0.01732644997537136,
0.03545910492539406,
0.02932921051979065,
0.027228428050875664,
0.0013585265260189772,
0.013552339747548103,
0.06173969432711601,
-0.05085233598947525,
-0.002087858971208334,
-0.017579585313796997,
0.05407494679093361,
-0.04847067967057228,
-0.01482829824090004,
-0.010169291868805885,
-0.007198622450232506,
-0.006413548719137907,
-0.030803412199020386,
0.013192180544137955,
0.007398501038551331,
0.05140002444386482,
-0.035323891788721085,
-0.0174857284873724,
0.004862403031438589,
0.050395309925079346,
0.0049827746115624905,
0.015515580773353577,
0.0018485469045117497,
-0.013619743287563324,
-0.07143261283636093,
0.01424133125692606,
0.018541285768151283,
0.027117634192109108,
-0.0009161204216070473,
-0.057726096361875534,
-0.002852710196748376,
0.013881704770028591,
-0.056724514812231064,
0.017742931842803955,
0.03426237404346466,
0.05006243661046028,
-0.00986190140247345,
-0.007503550499677658,
-0.025168070569634438,
-0.07952217757701874,
-0.014356620609760284,
-0.011008627712726593,
0.02431463450193405,
-0.03831850737333298,
-0.040158625692129135,
0.02103070728480816,
0.028100384399294853,
0.004784802906215191,
-0.0012614447623491287,
0.022814182564616203,
0.05599037557840347,
0.051202982664108276,
-0.022629300132393837,
-0.02112303487956524,
0.014023988507688046,
0.008975609205663204,
0.01607794687151909,
0.009273575618863106,
0.02018601819872856,
0.02474113181233406,
0.02528182789683342,
0.050240203738212585,
0.006709911860525608,
-0.03358099237084389,
-0.014850913546979427,
-0.02580886334180832,
-0.054016225039958954,
-0.013841099105775356,
0.012674194760620594,
-0.002430825959891081,
-0.024201462045311928,
-0.04048250988125801,
0.0022971907164901495,
-0.0188736729323864,
0.008795982226729393,
-0.007240187842398882,
0.02271355129778385,
-0.022166382521390915,
-0.017037570476531982,
0.018444061279296875,
-0.022511528804898262,
-0.03567812219262123,
-0.014135736040771008,
-0.005999929737299681,
-0.03199244663119316,
-0.008761441335082054,
-0.00972286332398653,
0.03473003953695297,
0.00885647814720869,
-0.005942595656961203,
0.03971331566572189,
0.0033101195003837347,
0.009808623231947422,
0.008206512778997421,
0.01670488342642784,
-0.0031307812314480543,
0.0032480014488101006,
0.013485319912433624,
-0.03331945464015007,
0.054728418588638306,
-0.007547091227024794,
-0.04202745854854584,
0.02611931972205639,
-0.03975337743759155,
0.04182087630033493,
0.013193825259804726,
0.015896838158369064,
-0.02499491348862648,
0.04788852110505104,
-0.019715210422873497,
-0.01123473234474659,
-0.011023239232599735,
-0.012103941291570663,
0.058650217950344086,
-0.028797568753361702,
0.003135438309982419,
0.009295836091041565,
0.026255808770656586,
0.03953137621283531,
0.002891869517043233,
-0.025275899097323418,
0.005519564729183912,
-0.01912567764520645,
-0.05476952716708183,
-0.03252319619059563,
0.012186620384454727,
0.0414455346763134,
-0.020548153668642044,
0.013218266889452934,
-0.018081361427903175,
0.07624287158250809,
0.03888174518942833,
-0.04936610162258148,
-0.05685460940003395,
0.014234199188649654,
0.036617670208215714,
0.004572369158267975,
0.011487085372209549,
-0.036193836480379105,
0.03428569436073303,
0.031158365309238434,
-0.11932563781738281,
0.007148731034249067,
-0.008673085831105709,
-0.023171577602624893,
-0.07707784324884415,
0.02000243030488491,
-0.03687949851155281,
-0.0054051014594733715,
-0.012934563681483269,
0.0494508221745491,
0.04524654150009155,
0.07512161135673523,
-0.008889129385352135,
-0.019077058881521225,
0.005193585995584726,
0.05897049233317375,
-0.00786632765084505,
-0.0026210590731352568,
0.07033958286046982,
-0.011022089049220085,
-0.0037031909450888634,
-0.010961959138512611,
0.0658695325255394,
0.0252575371414423,
-0.027563439682126045,
-0.039938658475875854,
0.005152049008756876,
-0.008330659940838814,
-0.014874875545501709,
-0.004807202145457268,
0.015545633621513844,
0.0064260088838636875,
0.06384889781475067,
0.014502907171845436,
0.01651948131620884,
-0.009580706246197224,
0.027221020311117172,
-0.05309854447841644,
-0.05294954776763916,
0.013590318150818348,
0.028736738488078117,
-0.020768266171216965,
0.02557438239455223,
0.020739763975143433,
0.002888546558097005,
-0.03983991593122482,
0.010088127106428146,
-0.07688497006893158,
0.003076190361753106,
-0.00026003358652815223,
0.024614136666059494,
-0.02843940630555153,
0.02247946709394455,
-0.0344107449054718,
-0.015387925319373608,
-0.0013296072138473392,
0.01009602751582861,
0.0039088004268705845,
-0.01562739908695221,
-0.013221973553299904,
-0.016359936445951462,
0.008008619770407677,
-0.00743135018274188,
0.03485047072172165,
-0.06680157035589218,
0.02213832177221775,
-0.008007013238966465,
-0.0071097686886787415,
-0.007501245941966772,
-0.035588573664426804,
-0.04865562170743942,
-0.07300803810358047,
0.029956845566630363,
0.018747473135590553,
-0.055558837950229645,
-0.05073825269937515,
-0.00938022043555975,
-0.024433011189103127,
0.04815700650215149,
0.05190518870949745,
0.00658732233569026,
-0.02287384308874607,
-0.02589501067996025,
0.02378637157380581,
0.03392785042524338,
-0.05995798110961914,
0.013872082345187664,
-0.009552881121635437,
-0.008915518410503864,
-0.043072476983070374,
0.011470191180706024,
0.017306821420788765,
0.04771042242646217,
0.028889168053865433,
0.01291415560990572,
0.00972804892808199,
0.010119697079062462,
-0.030244918540120125,
0.04811813309788704,
-0.0377940870821476,
-0.03838000446557999,
0.08457884192466736,
0.0002589052019175142,
0.016899149864912033,
0.007088993676006794,
-0.027826867997646332,
-0.05015669763088226,
-0.0017914986237883568,
-0.01974555477499962,
-0.01697278395295143,
0.0006942698964849114,
0.04591817036271095,
0.05004800483584404,
-0.028460826724767685,
0.011855832301080227,
0.016977714374661446,
-0.019681252539157867,
-0.04817432537674904,
0.03151649236679077,
-0.00539789954200387,
0.04529256001114845,
0.030294377356767654,
0.04104470834136009,
0.008296859450638294,
0.02943822182714939,
-0.021070994436740875,
0.06256920844316483,
0.00271396292373538,
-0.009338484145700932,
0.03951824828982353,
0.03185528889298439,
0.03318500891327858,
0.016550924628973007,
0.006718119140714407,
0.03051823563873768,
-0.01845112070441246,
0.013480487279593945,
0.045918259769678116,
0.015707936137914658,
-0.0077517093159258366,
0.03969552740454674,
0.012069880031049252,
0.07243421673774719,
-0.03362521901726723,
0.023917902261018753,
-0.022396421059966087,
0.002692212350666523,
-0.04326300695538521,
0.023227093741297722,
0.038220152258872986,
0.01667766645550728,
-0.0032324246130883694,
-0.007771157193928957,
-0.049991220235824585,
0.013502822257578373,
0.01787809282541275,
-0.05460314452648163,
0.02768261358141899,
0.015083735808730125,
-0.011039864271879196,
0.011633618734776974,
-0.013937109149992466,
-0.009731918573379517,
-0.009493343532085419,
0.011310668662190437,
0.02917434275150299,
0.0156339630484581,
-0.015993503853678703,
0.02009597048163414,
0.01025956217199564,
0.07129067927598953,
-0.05535249412059784,
-0.002426055260002613,
0.006882882211357355,
-0.007945111952722073,
-0.046522244811058044,
-0.0014501615660265088
] |
<p>Suppose we have a container divided into equal halves. Right half is fixed at temperature $T$, volume $\frac{V}{2}$. </p>
<p>Initially it has pressure $P_0$, a hole of area $A$ is opened between them. I have to show that the pressure in the right half is:</p>
<p>$$ p = \frac{p_0}{2} \left[ 1 + exp \left(-\langle v \rangle\frac{A}{V}t \right) \right] $$ where $\langle v \rangle$ is average speed of molecules in right half.</p>
<p>I got an answer that's very very close, but off by a factor of $2$ in the exponential!</p>
<p><strong>Attempt</strong></p>
<p>$$ dN = -A\phi_{(t)} dt $$</p>
<p>Using flux $\phi = \frac{1}{4} n\langle v \rangle $,</p>
<p>$$dN = - \frac{A}{4} n \langle v \rangle dt = -\frac{A}{4}\left( \frac{N}{V/2} \right) \langle v \rangle dt = -\frac{NA}{2V} \langle v \rangle dt $$</p>
<p>The graph looks something like this: <img src="http://i.stack.imgur.com/KisWM.png" alt="enter image description here"></p>
<p>We solve for the dotted graph, then translate upwards by $\frac{N_0}{2}$.</p>
<p>Integrating, and translating upwards i get: $ p = \frac{p_0}{2} \left[ 1 + exp \left(-\langle v \rangle\frac{A}{2V}t \right) \right] $</p>
<p>Not sure why I'm missing a factor of $2$..</p>
| 9,565 |
[
0.02604695037007332,
-0.013978937640786171,
-0.047447558492422104,
-0.020575225353240967,
0.04584184288978577,
-0.03832712769508362,
-0.044076137244701385,
0.000689737091306597,
0.00988096185028553,
0.006311415694653988,
0.06660570204257965,
0.00885707139968872,
0.04911384359002113,
0.0014092823257669806,
-0.018968991935253143,
0.025434643030166626,
-0.024563593789935112,
-0.018502984195947647,
0.012254844419658184,
-0.04132762551307678,
0.028496144339442253,
0.019781431183218956,
-0.009683925658464432,
-0.009660953655838966,
-0.03545699641108513,
0.038431040942668915,
0.01310783438384533,
-0.047339729964733124,
-0.011189602315425873,
0.06143610551953316,
-0.01150812953710556,
-0.02023054100573063,
0.04498516395688057,
0.004675990901887417,
0.036576367914676666,
0.03558661416172981,
0.00013509539712686092,
-0.015715211629867554,
0.02642681635916233,
0.044993333518505096,
0.008253301493823528,
0.02483551576733589,
0.0002604169712867588,
0.00951117742806673,
0.0041162315756082535,
0.037585943937301636,
0.06428644806146622,
-0.007333811838179827,
0.0763826072216034,
-0.07359913736581802,
0.03460624814033508,
-0.007251087576150894,
0.05001409351825714,
0.02296341024339199,
-0.027114305645227432,
-0.024361563846468925,
0.04806595295667648,
0.09204967319965363,
-0.004268957301974297,
-0.041554566472768784,
-0.004723906982690096,
0.014145043678581715,
-0.03233860805630684,
-0.015880830585956573,
-0.0037190059665590525,
-0.022822918370366096,
-0.014600374735891819,
-0.041964877396821976,
0.03135586902499199,
0.007904975675046444,
-0.0026107195299118757,
-0.04240564629435539,
0.06916311383247375,
-0.013733390718698502,
0.02357061579823494,
0.009213565848767757,
0.0123569555580616,
0.016243597492575645,
-0.010176488198339939,
0.05849168449640274,
-0.028147650882601738,
-0.001409061485901475,
0.045625630766153336,
0.01823871023952961,
0.00426512910053134,
0.023472052067518234,
0.06869803369045258,
-0.011951536871492863,
-0.010497386567294598,
0.04431456699967384,
0.0035031633451581,
0.007009305525571108,
0.027124818414449692,
-0.022624421864748,
0.018644453957676888,
-0.0014109991025179625,
0.011904174461960793,
0.02503737062215805,
0.029836900532245636,
-0.028866581618785858,
-0.015274596400558949,
-0.0005814466276206076,
-0.0006261491216719151,
0.08771368116140366,
-0.0010718151461333036,
-0.03314101696014404,
-0.0484875813126564,
-0.0027411330956965685,
-0.018404994159936905,
0.0004251990467309952,
-0.06087566912174225,
0.03680349141359329,
-0.011251399293541908,
0.002612453419715166,
-0.04185190796852112,
-0.02431195043027401,
0.008444218896329403,
-0.02082752250134945,
-0.007875465787947178,
0.0273191649466753,
0.05441055819392204,
-0.022272229194641113,
0.0142109589651227,
0.011615851894021034,
-0.07416743040084839,
0.01542856078594923,
0.026768969371914864,
-0.008812970481812954,
-0.002066301414743066,
0.00019216278451494873,
0.004703568294644356,
0.012248724699020386,
0.023671867325901985,
0.006985514424741268,
0.04457137733697891,
0.008021889254450798,
-0.06875825673341751,
-0.07141030579805374,
0.0559297651052475,
-0.028299860656261444,
-0.020256884396076202,
-0.08803178369998932,
0.0014117024838924408,
0.03912557289004326,
0.04552188515663147,
-0.017109045758843422,
-0.02680961787700653,
-0.027322689071297646,
0.014994749799370766,
-0.008992374874651432,
0.015280788764357567,
0.009033659473061562,
-0.04488043859601021,
-0.057297900319099426,
-0.008897628635168076,
-0.011649815365672112,
0.03694823756814003,
0.025917042046785355,
-0.007328689098358154,
-0.01962512731552124,
0.05734703689813614,
-0.02630729414522648,
-0.010787329636514187,
-0.006796673405915499,
-0.0019886374939233065,
-0.03290727734565735,
0.060374077409505844,
-0.0005792347365058959,
-0.002437818795442581,
0.00871330127120018,
-0.000907955807633698,
0.014857335016131401,
-0.045985929667949677,
-0.028655841946601868,
0.036128781735897064,
0.0021104433108121157,
-0.005208417773246765,
-0.019686833024024963,
-0.000595595280174166,
-0.00748814083635807,
-0.002951947273686528,
-0.03526369109749794,
-0.03543957322835922,
0.01960046961903572,
0.028837380930781364,
-0.01041234191507101,
0.03444325178861618,
-0.00019341055303812027,
-0.03477278724312782,
-0.04133663326501846,
-0.0484224371612072,
-0.031644001603126526,
0.004768827464431524,
0.006843856535851955,
-0.03951340913772583,
0.030974481254816055,
-0.004232849460095167,
0.03189487010240555,
-0.014100983738899231,
-0.02364184707403183,
-0.005347981117665768,
0.010325196199119091,
0.021462928503751755,
-0.03144055977463722,
0.013076724484562874,
0.051670901477336884,
0.051261596381664276,
-0.02065744437277317,
0.009752446785569191,
-0.02084367722272873,
0.02314666286110878,
-0.0023785720113664865,
-0.03691207244992256,
-0.0002684063510969281,
-0.0013096118345856667,
-0.031493764370679855,
0.04336591437458992,
0.02073482610285282,
0.022708209231495857,
0.02023867703974247,
-0.03161235153675079,
0.06866712123155594,
0.0507051907479763,
0.004903311841189861,
0.004774580243974924,
0.0011926069855690002,
0.0033669655676931143,
0.04225298762321472,
0.013346889987587929,
-0.04831402748823166,
-0.04264470934867859,
-0.02405736595392227,
0.004809353966265917,
0.017376378178596497,
-0.032127417623996735,
0.000351027149008587,
0.04053414613008499,
-0.005188640672713518,
0.03711726889014244,
0.009969978593289852,
0.008688411675393581,
-0.026987846940755844,
0.036225318908691406,
0.04367022216320038,
-0.016622554510831833,
0.026947326958179474,
0.007486323360353708,
0.010613247752189636,
0.03710688650608063,
0.007475593127310276,
-0.02449273131787777,
-0.0004897582111880183,
-0.00003351881605340168,
0.017061220481991768,
0.004645573906600475,
0.014995227567851543,
0.03471295163035393,
-0.00984252616763115,
0.017707835882902145,
0.06787203997373581,
0.013697104528546333,
0.029132740572094917,
-0.056123457849025726,
-0.0328005775809288,
0.033509958535432816,
-0.0011691770050674677,
0.012744362466037273,
-0.025848152115941048,
0.031138792634010315,
-0.004786607343703508,
0.029062384739518166,
-0.04113144427537918,
0.018518507480621338,
-0.000474640546599403,
-0.018134454265236855,
0.019468778744339943,
0.035538624972105026,
-0.0075731645338237286,
-0.036757130175828934,
-0.009182211011648178,
0.0031451936811208725,
0.003698870074003935,
0.0006325796130113304,
0.020710185170173645,
-0.013576666824519634,
0.005253004375845194,
-0.030512766912579536,
-0.032902833074331284,
0.02126704528927803,
0.0016311693470925093,
-0.030459094792604446,
0.005232364404946566,
-0.007705553434789181,
-0.06521973013877869,
-0.018817009404301643,
-0.016644207760691643,
0.00947939045727253,
-0.10022102296352386,
-0.003095026593655348,
0.042949777096509933,
-0.008476955816149712,
-0.03630761429667473,
0.009712397120893002,
-0.018745645880699158,
-0.033120207488536835,
-0.004622825887054205,
-0.040770966559648514,
0.016865605488419533,
0.010821600444614887,
0.01869858242571354,
0.00805414654314518,
0.010895405896008015,
-0.025172675028443336,
-0.07542264461517334,
-0.02401771955192089,
0.00737373111769557,
0.01083762850612402,
0.03740482032299042,
-0.006715060211718082,
-0.02475103549659252,
0.05612422153353691,
0.01797427237033844,
-0.02319752238690853,
0.006155483890324831,
-0.023122111335396767,
-0.009018742479383945,
-0.07052924484014511,
0.027806155383586884,
0.023814167827367783,
-0.04564385861158371,
0.01431649923324585,
-0.04306140914559364,
0.07675875723361969,
0.023513324558734894,
-0.012083868496119976,
0.026145311072468758,
0.07094846665859222,
0.02191656082868576,
0.015751047059893608,
0.07776257395744324,
0.008637306280434132,
0.027084095403552055,
0.037703875452280045,
-0.028519755229353905,
0.017426716163754463,
0.019038215279579163,
-0.07168072462081909,
0.05364576354622841,
-0.008900403045117855,
0.010521894320845604,
-0.03975256532430649,
0.010080703534185886,
0.004296415485441685,
-0.010428192093968391,
-0.016307471320033073,
0.047010261565446854,
0.04759126901626587,
0.011502684094011784,
0.02771107107400894,
0.042411018162965775,
0.023268861696124077,
-0.0019319455605000257,
-0.062356121838092804,
0.021604381501674652,
-0.010769299231469631,
0.020941605791449547,
-0.011773491278290749,
-0.011717736721038818,
0.03685974329710007,
0.04948120564222336,
0.0045254952274262905,
0.00009535384742775932,
0.00008285776857519522,
0.013173652812838554,
-0.02983337827026844,
-0.0212967898696661,
-0.028475793078541756,
0.05392178148031235,
0.002616714918985963,
0.05465603992342949,
-0.020887339487671852,
0.03737802058458328,
0.013214781880378723,
0.021509572863578796,
-0.10310210287570953,
-0.013582063838839531,
0.04218071699142456,
-0.03236538544297218,
0.006548007950186729,
-0.040010716766119,
0.021798554807901382,
-0.043891943991184235,
-0.024678897112607956,
-0.0032435827888548374,
0.01622919738292694,
-0.07568567246198654,
0.034586016088724136,
0.021250547841191292,
-0.003116696374490857,
-0.0274614579975605,
0.02752714604139328,
0.0377245731651783,
-0.019076867029070854,
-0.015369451604783535,
0.07948632538318634,
0.0006432222435250878,
0.0023728865198791027,
-0.042105451226234436,
-0.00440496951341629,
0.05882908031344414,
0.07443082332611084,
0.012664358131587505,
-0.022110972553491592,
0.006716177798807621,
-0.028176534920930862,
-0.010191891342401505,
0.03602183237671852,
-0.04605304077267647,
-0.012202800251543522,
-0.01325489953160286,
-0.0023768662940710783,
-0.011495091952383518,
-0.01552996039390564,
0.053153183311223984,
0.0029297329019755125,
0.029612330719828606,
-0.015790939331054688,
0.023020068183541298,
-0.0020037591457366943,
0.04422874376177788,
0.03323759511113167,
-0.04277290776371956,
0.010033788159489632,
-0.0441834032535553,
-0.02630087360739708,
-0.039841149002313614,
0.016274021938443184,
0.006166713312268257,
-0.022652503103017807,
-0.021282659843564034,
0.008828162215650082,
-0.007073939777910709,
0.012713365256786346,
0.01758519560098648,
0.022057386115193367,
-0.019469574093818665,
-0.009179198183119297,
-0.024203844368457794,
0.0022220597602427006,
0.0024862277787178755,
-0.00030705539393238723,
0.009744787588715553,
-0.026912575587630272,
-0.026525398716330528,
-0.10412769764661789,
-0.0386047437787056,
0.015695679932832718,
0.06943020224571228,
0.0024315002374351025,
0.004804976284503937,
-0.04511846974492073,
-0.03356286510825157,
0.02269178070127964,
-0.0041622743010520935,
0.012992613017559052,
-0.004589458461850882,
-0.007965432479977608,
0.0012935276608914137,
-0.08891094475984573,
-0.032451678067445755,
-0.003893657121807337,
-0.018682774156332016,
0.00859012920409441,
-0.022191030904650688,
-0.017572350800037384,
0.002259298227727413,
0.00994885340332985,
0.03875665366649628,
0.03903115540742874,
-0.02068491466343403,
-0.048923250287771225,
-0.011079627089202404,
0.002368784276768565,
-0.03406272828578949,
-0.0718836560845375,
0.03967180848121643,
-0.02160416543483734,
0.004063196014612913,
-0.013850988820195198,
-0.05285285785794258,
-0.055919598788022995,
0.06454446911811829,
0.0018863434670493007,
-0.022377101704478264,
0.001648366916924715,
-0.011704860255122185,
0.07591594755649567,
0.030800066888332367,
-0.03356633335351944,
0.06599343568086624,
0.047146786004304886,
0.012251188978552818,
-0.020902244374155998,
-0.05019751936197281,
0.045698683708906174,
-0.0232129767537117,
0.008783131837844849,
-0.030977588146924973,
-0.018772456794977188,
-0.011239094659686089,
0.02631922997534275,
-0.036952707916498184,
0.019650468602776527,
0.0060002245008945465,
-0.03485863283276558,
0.042866580188274384,
-0.008180998265743256,
0.011023014783859253,
0.003124190028756857,
-0.0005032983026467264,
-0.0033809675369411707,
0.051789283752441406,
-0.032491814345121384,
0.014672845602035522,
-0.0030809652525931597,
0.020227033644914627,
0.0181228406727314,
-0.02788912132382393,
0.017426330596208572,
-0.012859465554356575,
-0.03162692114710808,
-0.0026563662104308605,
-0.07948951423168182,
0.04573871195316315,
-0.010030941106379032,
0.01598895899951458,
0.02103874832391739,
-0.008826923556625843,
-0.03875789791345596,
0.011188682168722153,
0.02221517451107502,
-0.011509682983160019,
-0.02686581388115883,
-0.012040512636303902,
-0.005542782600969076,
0.01414118055254221,
-0.05959787964820862,
-0.017825765535235405,
-0.0065580131486058235,
-0.011365793645381927,
-0.042380254715681076,
-0.03753675892949104,
-0.02768847346305847,
0.0037105598021298647,
-0.03875952214002609,
0.039773356169462204,
0.041106004267930984,
-0.037943318486213684,
-0.013063591904938221,
0.04111422225832939,
0.03967122733592987,
0.04511392116546631,
0.022243646904826164,
0.0070289745926856995,
-0.005575059447437525,
-0.010075192898511887,
-0.03681277856230736,
-0.014905284158885479,
0.01857423223555088,
-0.034764718264341354,
0.0034305432345718145,
0.014346866868436337,
-0.015571726486086845,
0.047757040709257126,
-0.009497592225670815,
0.011354003101587296,
0.02533581294119358,
0.015252337791025639,
-0.011096845380961895,
-0.02144111692905426,
-0.001827001222409308,
0.021745653823018074,
0.019358990713953972,
0.0020977058447897434,
0.003271447028964758,
-0.008835317566990852,
-0.021210456266999245,
-0.023727629333734512,
-0.02409464120864868,
0.007592593785375357,
-0.01675833761692047,
0.07726062089204788,
-0.006401132792234421,
0.01040875818580389,
0.02114705555140972,
-0.032295554876327515,
0.032124608755111694,
0.0038873611483722925,
-0.028136899694800377,
0.0014755446463823318,
-0.04485398158431053,
-0.07162900269031525,
-0.04658079147338867,
-0.06845112144947052,
0.0011685109930112958,
0.05547152832150459,
0.004310027230530977,
0.04258822277188301,
-0.02173110656440258,
0.016922125592827797,
0.00703839585185051,
-0.03478534147143364,
-0.012415285222232342,
0.0269604604691267,
-0.019061651080846786,
0.021444732323288918,
-0.025937816128134727,
0.007082914002239704,
0.033334292471408844,
0.02781371772289276,
-0.030907446518540382,
0.018477443605661392,
0.0069725546054542065,
-0.010237578302621841,
-0.011973735876381397,
-0.0026642659213393927,
-0.004084783140569925,
0.049319956451654434,
-0.005501843988895416,
0.0719146654009819,
-0.015107783488929272,
-0.020147128030657768,
0.04126402735710144,
0.022680269554257393,
-0.019684508442878723,
-0.05701475590467453,
0.0024886252358555794,
-0.04417455941438675,
-0.006148659624159336,
-0.0037264376878738403,
-0.003134215949103236,
0.0076566170901060104,
0.027499310672283173,
0.022223761305212975,
-0.031249316409230232,
0.02453438751399517,
-0.029557960107922554,
0.0035419645719230175,
-0.008011947385966778,
-0.014524897560477257,
-0.023805642500519753,
0.04995165765285492,
-0.018516885116696358,
-0.02703520469367504,
0.026313114911317825,
-0.047491125762462616,
0.02674213983118534,
-0.0008764620288275182,
0.020145757123827934,
-0.011219979263842106,
0.050929442048072815,
0.010902219451963902,
0.0177963487803936,
-0.04219365119934082,
0.02816936746239662,
0.1470841020345688,
0.025659196078777313,
0.01668497733771801,
-0.013406578451395035,
-0.021222669631242752,
-0.01612185128033161,
0.026381921023130417,
-0.0325738824903965,
-0.005353712011128664,
-0.016663845628499985,
-0.0270332433283329,
0.0005232284893281758,
0.08675534278154373,
-0.015645097941160202,
0.033554285764694214,
0.004647820722311735,
-0.017839135602116585,
-0.0033116096165031195,
-0.007165637798607349,
0.029093647375702858,
-0.02497774362564087,
0.029878556728363037,
-0.0001489974238211289,
0.028171876445412636,
-0.042757682502269745,
0.012165110558271408,
-0.058358993381261826,
-0.005668438971042633,
0.0361764132976532,
-0.018662262707948685,
-0.04543847590684891,
0.03690209239721298,
0.0233604833483696,
-0.034484174102544785,
-0.0012164710788056254,
0.006000690162181854,
-0.0035622911527752876,
0.009404839016497135,
-0.00907568633556366,
0.021274112164974213,
0.0325586311519146,
0.010121806524693966,
0.029727626591920853,
-0.004246256779879332,
-0.04724077507853508,
-0.0058014304377138615,
-0.017758717760443687,
0.04069280996918678,
0.009009359404444695,
-0.01666579395532608,
0.02692209556698799,
-0.0080298762768507,
-0.011427110992372036,
-0.02343553863465786,
-0.03347029536962509,
0.01859244331717491,
0.0269403588026762,
0.0048783826641738415,
-0.0016371194506064057,
0.016263622790575027,
0.02095966413617134,
0.01998847909271717,
0.0074650682508945465,
-0.008422923274338245,
0.033440832048654556,
-0.00046690955059602857,
-0.005396388936787844,
0.03435342013835907,
-0.014187791384756565,
-0.01698324829339981,
-0.013587680645287037,
0.02522088959813118,
-0.04387703910470009,
-0.004317173734307289,
-0.017999064177274704,
0.017730897292494774,
0.04869654402136803,
0.03220941871404648,
-0.010048847645521164,
-0.02284477837383747,
-0.08358142524957657,
0.019267374649643898,
-0.022408057004213333,
-0.014537508599460125,
-0.009446307085454464,
-0.011983426287770271,
-0.0016591757303103805,
0.0378853939473629,
-0.013813728466629982,
-0.01081926841288805,
0.04559369757771492,
0.07954245805740356,
0.07287762314081192,
-0.023786475881934166,
-0.05459383502602577,
-0.040886759757995605,
-0.012845772318542004,
0.02574450522661209,
0.0411466509103775,
0.044053029268980026,
0.006016481202095747,
-0.0013438453897833824,
0.005316759459674358,
-0.005315345246344805,
-0.048160530626773834,
-0.007931905798614025,
-0.014783770777285099,
-0.05623353645205498,
0.019899098202586174,
0.032265566289424896,
0.02175072580575943,
-0.03581474348902702,
0.021324507892131805,
-0.03272626921534538,
0.006406288128346205,
-0.028987150639295578,
0.014728114008903503,
0.0055945441126823425,
0.03291875496506691,
-0.026886366307735443,
0.020611347630620003,
-0.03014908730983734,
-0.017306728288531303,
-0.03412659838795662,
-0.02644054777920246,
-0.018362177535891533,
0.02109609730541706,
-0.00635991245508194,
0.037549905478954315,
-0.025388525798916817,
0.005361795425415039,
0.04393152892589569,
0.05134391784667969,
0.016402577981352806,
-0.0271694865077734,
0.03249010816216469,
0.036975111812353134,
0.023504668846726418,
-0.008206029422581196,
-0.026361554861068726,
-0.00481185968965292,
0.011205666698515415,
-0.06876974552869797,
0.016210194677114487,
0.02822563424706459,
0.01984909363090992,
-0.009880604222416878,
-0.0003584147780202329,
-0.02614944986999035,
0.04869936779141426,
-0.03895033895969391,
-0.010540395975112915,
-0.01868433877825737,
-0.08822046965360641,
0.006003614980727434,
-0.03944888710975647,
0.034977808594703674,
0.028463413938879967,
0.03824470937252045,
0.01772806979715824,
-0.007048779632896185,
-0.005773044656962156,
0.0025985119864344597,
-0.005136063788086176,
-0.03246414661407471,
0.03754296898841858,
0.00303774350322783,
0.008529757149517536,
0.03409324586391449,
0.014054853469133377,
0.026351191103458405,
-0.012544515542685986,
-0.01037154532968998,
0.028854280710220337,
-0.0754677951335907,
-0.050676651298999786,
-0.00951559841632843,
0.018291814252734184,
0.026713663712143898,
-0.07813820242881775,
0.024570701643824577,
0.0593467578291893,
-0.07352278381586075,
0.033671580255031586,
-0.03468718007206917,
-0.0049308910965919495,
-0.04922375828027725,
-0.03377740457653999,
-0.022168826311826706,
0.022432509809732437,
0.04884786903858185,
0.037119295448064804,
-0.022692395374178886,
0.04626530781388283,
-0.006434157490730286,
-0.013848935253918171,
0.002576107159256935,
0.029136257246136665,
0.011861245147883892,
-0.040808022022247314,
0.019960768520832062,
-0.0037831265944987535,
0.019893350079655647,
0.029107263311743736,
-0.05756250396370888,
0.008827351965010166,
-0.03845491260290146,
0.0037503514904528856,
0.017204223200678825,
0.027380909770727158,
-0.007565109990537167,
0.034600045531988144,
0.0059623150154948235,
-0.036226529628038406,
0.013326823711395264,
-0.012639843858778477,
0.0018672141013666987,
-0.010351073928177357,
0.03650175780057907,
-0.011007013730704784,
-0.05508273094892502,
0.014945534989237785,
0.009237692691385746,
0.0072624837048351765,
0.04242683947086334,
-0.03436066582798958,
0.023734062910079956,
-0.03429753705859184,
0.016385791823267937,
-0.01719771884381771,
0.006077959667891264,
0.025382056832313538,
0.015705833211541176,
-0.04663778841495514,
0.006594170816242695,
0.009747220203280449,
-0.0076879276894032955,
0.03861827775835991,
0.012176290154457092,
-0.012713732197880745,
-0.048590000718832016,
-0.01947016827762127,
-0.037409089505672455,
-0.009244986809790134,
0.018810955807566643,
-0.030073614791035652,
-0.03291672095656395,
0.02944146655499935,
0.0548119992017746,
0.03574143350124359,
-0.021437613293528557,
-0.010196632705628872,
-0.025491395965218544,
-0.06903352588415146,
0.01647566631436348,
0.0036540329456329346,
-0.01104418933391571,
-0.04512033239006996,
-0.014128895476460457,
0.020719945430755615,
0.06218043342232704,
0.06516546756029129,
0.040831439197063446,
-0.010137023404240608,
-0.014336995780467987,
-0.020219959318637848,
-0.006080062128603458,
-0.05240941420197487,
0.007498550694435835,
-0.03313999995589256,
0.007285764906555414,
0.05744294822216034,
0.015096855349838734,
-0.010389848612248898,
0.026024915277957916,
0.012285406701266766,
-0.028705094009637833,
0.00784134492278099,
-0.004743556957691908,
0.0006553758285008371,
-0.00905327033251524,
-0.017313949763774872,
-0.006017417646944523,
0.055612120777368546,
-0.0045394692569971085,
0.020071247592568398,
0.0063665141351521015,
-0.0049701835960149765,
-0.04003753140568733,
-0.010482925921678543,
-0.0374128632247448,
-0.009265498258173466,
-0.04192405194044113,
-0.033940818160772324,
0.019162679091095924,
-0.05986148118972778,
-0.004515590611845255,
0.06157434731721878,
-0.03251461684703827,
0.009711145423352718,
0.0352320522069931,
0.01396769005805254,
0.03946210443973541,
-0.018218155950307846,
0.061294615268707275,
0.0112567488104105,
0.028528688475489616,
0.02482002228498459,
0.02714937925338745,
0.03669152408838272,
-0.021624429151415825,
0.029965097084641457,
0.028206704184412956,
-0.034205447882413864,
-0.00016853462147992104,
0.019434068351984024,
-0.020152125507593155,
-0.0009595035226084292,
0.023044198751449585,
0.027239130809903145,
-0.01792433299124241,
-0.0038905476685613394,
0.041653066873550415,
0.027811503037810326,
0.06409718841314316,
0.011429817415773869,
0.02053377404808998,
-0.023891296237707138,
0.025213314220309258,
-0.024969063699245453,
0.047552090138196945,
-0.012821413576602936,
0.005733692552894354,
-0.061262425035238266,
0.007882336154580116,
-0.00491173192858696,
-0.009025467559695244,
-0.0343611016869545,
-0.01809842512011528,
0.001583082601428032,
0.015890011563897133,
0.005814692471176386,
-0.0032200899440795183,
-0.00851744506508112,
0.003281182609498501,
-0.054891373962163925,
0.0406656377017498,
0.034991972148418427,
-0.02020133100450039,
0.02209295704960823,
0.009856456890702248,
0.023935966193675995,
0.07742632180452347,
-0.04196954891085625,
-0.039396338164806366,
0.014522385783493519,
-0.00699332682415843,
0.0020365749951452017,
-0.0366220697760582
] |
<p>OK, so $\ce{Fe}$ is the most 'stable element'. As such, why do all elements above it not decay into $\ce{Fe}$? In all cases, would it not lead to an increase in binding energy and therefore energy been released, meaning it is energetically feasible, and should happen spontaneously (given enough time)? </p>
| 9,566 |
[
-0.05865015462040901,
-0.026233594864606857,
-0.010419279336929321,
-0.01281068753451109,
-0.001683440525084734,
0.01841258630156517,
-0.0649179145693779,
-0.06521137058734894,
0.012503690086305141,
-0.0611884631216526,
0.019348904490470886,
0.003901928663253784,
0.04403163865208626,
0.012244739569723606,
0.018053488805890083,
0.032893985509872437,
0.007202780339866877,
-0.02468762919306755,
-0.01141003891825676,
-0.0016637714579701424,
0.009532099589705467,
0.023912932723760605,
0.0016845676582306623,
0.003086236072704196,
-0.021259116008877754,
-0.00720168137922883,
0.0039227972738444805,
0.0066322810016572475,
0.06803194433450699,
0.05990755558013916,
-0.01046764012426138,
-0.04746190458536148,
0.030220791697502136,
0.03228483349084854,
0.04244768247008324,
-0.005768447648733854,
0.0030160679016262293,
-0.03431756794452667,
-0.026520421728491783,
0.06241845712065697,
-0.061882682144641876,
-0.047106485813856125,
-0.012528618797659874,
0.06860888749361038,
-0.0113667668774724,
0.00298401084728539,
0.0013463717186823487,
-0.029760941863059998,
0.06593310087919235,
-0.016939975321292877,
0.033973753452301025,
-0.031161364167928696,
0.04351276904344559,
0.014135061763226986,
0.012934313155710697,
-0.02137036994099617,
0.09598897397518158,
0.06402425467967987,
-0.003890726948156953,
-0.003457764396443963,
-0.033539362251758575,
-0.046113576740026474,
-0.012361125089228153,
0.008460840210318565,
-0.019747965037822723,
0.037283431738615036,
-0.00907720997929573,
-0.015098681673407555,
0.031922437250614166,
0.037677861750125885,
0.023815477266907692,
0.006453734822571278,
0.012184888124465942,
-0.023553339764475822,
0.0003249244182370603,
-0.002087865024805069,
0.058356333523988724,
0.01934393122792244,
0.06161769852042198,
0.07157352566719055,
-0.011675266548991203,
0.009868421591818333,
0.042563360184431076,
0.051605064421892166,
-0.017896592617034912,
0.005829205736517906,
0.04743194580078125,
-0.004459720570594072,
0.020517122000455856,
0.03360708802938461,
0.00730208121240139,
-0.0002377427590545267,
0.03282606229186058,
-0.006024287082254887,
-0.03204752132296562,
0.013301730155944824,
-0.006926155183464289,
0.0469495952129364,
0.007385505363345146,
0.0038206889294087887,
0.057490553706884384,
-0.01341171283274889,
0.025393567979335785,
0.054450150579214096,
0.02961714379489422,
-0.025411158800125122,
-0.07084133476018906,
-0.010529614984989166,
-0.0210054162889719,
0.0030955204274505377,
0.02086685784161091,
-0.007429866120219231,
-0.0010843673953786492,
0.019613223150372505,
0.006215143948793411,
-0.01851540245115757,
-0.017006907612085342,
-0.044889844954013824,
0.03613933175802231,
0.051427192986011505,
0.02334175631403923,
-0.026855412870645523,
0.012094291858375072,
-0.025939250364899635,
-0.054139502346515656,
0.00742689985781908,
0.01170870941132307,
-0.004741516895592213,
-0.01798565685749054,
-0.0003569181135389954,
-0.023538047447800636,
-0.03324347734451294,
0.024991970509290695,
-0.017199454829096794,
0.05156940966844559,
-0.02543020248413086,
-0.1255704164505005,
-0.042469464242458344,
0.023956380784511566,
-0.04452783986926079,
-0.038332004100084305,
-0.09305664151906967,
-0.0012903620954602957,
0.03500586375594139,
0.05748865380883217,
-0.015980908647179604,
-0.03507087007164955,
0.00797522533684969,
0.037879180163145065,
-0.0039519513957202435,
-0.030724236741662025,
-0.01708764024078846,
0.02968277409672737,
-0.031370118260383606,
0.011800008825957775,
-0.04953576251864433,
0.006335850339382887,
-0.02516791969537735,
0.017418960109353065,
-0.02488364465534687,
0.05031527578830719,
-0.050389450043439865,
0.0370231457054615,
-0.013558538630604744,
0.04813562333583832,
0.0059509919956326485,
0.06843703985214233,
0.03532031551003456,
0.02590588480234146,
0.0349043570458889,
0.02695547603070736,
0.007969250902533531,
0.036735691130161285,
0.056727781891822815,
0.04683956503868103,
-0.04514338821172714,
-0.04768829792737961,
-0.07048207521438599,
0.006207102444022894,
0.0064567686058580875,
-0.06177926063537598,
0.0028511607088148594,
0.015277184545993805,
0.03073791041970253,
0.030815256759524345,
0.04927570000290871,
-0.01725790463387966,
-0.02311914600431919,
-0.011948511004447937,
-0.06546809524297714,
-0.009636678732931614,
-0.06637565791606903,
0.01239739265292883,
0.02557101845741272,
-0.005041502881795168,
0.01391148753464222,
0.006288373842835426,
0.012151051312685013,
-0.032421428710222244,
-0.009113315492868423,
-0.009193616919219494,
0.025333592668175697,
0.007403501775115728,
-0.001715467544272542,
0.056687530130147934,
0.07779865711927414,
0.03359903767704964,
0.019876986742019653,
0.026781156659126282,
-0.006517625413835049,
-0.046889692544937134,
0.006086221430450678,
0.005008114036172628,
-0.004671895410865545,
0.03746046498417854,
-0.04280593991279602,
-0.005333692766726017,
-0.018639691174030304,
-0.011325542815029621,
0.03778411075472832,
-0.010133241303265095,
0.1060522124171257,
0.022510100156068802,
0.007502929773181677,
-0.006087340880185366,
0.02553260698914528,
0.011688852682709694,
0.029295481741428375,
-0.044877417385578156,
-0.03256431967020035,
-0.05007854849100113,
-0.01752389781177044,
0.021916428580880165,
0.04791641607880592,
-0.07951389253139496,
0.03526022285223007,
-0.0019077196484431624,
0.016933118924498558,
0.0181971937417984,
0.04314497858285904,
-0.0133162010461092,
-0.031864043325185776,
0.01568944752216339,
0.027653461322188377,
0.041697531938552856,
0.036066051572561264,
-0.0007022094214335084,
0.025580814108252525,
0.0025200729724019766,
-0.0046633402816951275,
0.01839543506503105,
0.031992338597774506,
0.0011004862608388066,
-0.011737472377717495,
-0.0018610237166285515,
-0.050109896808862686,
0.02438219077885151,
-0.03346800059080124,
0.01062628161162138,
0.00686597777530551,
0.01832260563969612,
0.006618366576731205,
-0.024187056347727776,
-0.030336283147335052,
0.037733595818281174,
0.01141357421875,
-0.02328549325466156,
0.0021263770759105682,
0.023157335817813873,
-0.00735463947057724,
0.010918224230408669,
-0.039419617503881454,
-0.024980489164590836,
0.007177233230322599,
-0.025175517424941063,
0.03886578604578972,
-0.013348630629479885,
0.027565795928239822,
-0.03833705186843872,
-0.030114462599158287,
-0.0245556328445673,
-0.04989348724484444,
0.0004537370114121586,
0.013062512502074242,
-0.04363679140806198,
0.01331767626106739,
0.011353645473718643,
-0.052425745874643326,
0.06810373067855835,
-0.011365720070898533,
0.023093512281775475,
0.040812503546476364,
0.014685272239148617,
-0.04318351298570633,
-0.008066215552389622,
0.0006002517184242606,
-0.04382999241352081,
0.00252413097769022,
-0.003197290701791644,
0.08336862176656723,
-0.03004862740635872,
-0.029743099585175514,
0.03306422755122185,
-0.038735296577215195,
-0.022954178974032402,
0.0012933860998600721,
-0.017236031591892242,
-0.019497625529766083,
-0.013096524402499199,
0.036252398043870926,
0.02437167428433895,
-0.06861390918493271,
0.004134384449571371,
-0.04361617565155029,
-0.021575482562184334,
-0.013348469510674477,
-0.04688004404306412,
0.03142126649618149,
-0.01865258999168873,
-0.04131793603301048,
0.061932552605867386,
0.03850182890892029,
-0.03443372994661331,
-0.008331410586833954,
-0.022919120267033577,
-0.00035059641231782734,
-0.04408256709575653,
-0.009065776132047176,
-0.0011677753645926714,
0.02064060978591442,
0.021303335204720497,
-0.003096800995990634,
0.03656831383705139,
-0.008114433847367764,
0.0019660587422549725,
-0.02738400734961033,
0.021247074007987976,
0.04105749353766441,
0.010413449257612228,
0.02170991152524948,
0.004506764467805624,
-0.03071863017976284,
0.0138812605291605,
0.028809264302253723,
0.05846733599901199,
0.028898058459162712,
-0.06631547212600708,
0.05135856196284294,
0.013383022509515285,
0.0063552213832736015,
-0.05320441722869873,
0.042873725295066833,
-0.005319565534591675,
-0.047016289085149765,
0.010666834190487862,
-0.0025771143846213818,
0.05825081840157509,
-0.031752198934555054,
0.015819435939192772,
0.0000034720328585535754,
0.019043345004320145,
-0.015389244072139263,
-0.026915911585092545,
0.0005576605326496065,
-0.012051102705299854,
-0.007620081305503845,
0.02984149567782879,
-0.014384090900421143,
0.031418945640325546,
0.02950103208422661,
0.053142745047807693,
-0.016676727682352066,
-0.017985699698328972,
-0.023704366758465767,
-0.06263238191604614,
-0.016311107203364372,
0.005028062965720892,
0.028297126293182373,
-0.017474984750151634,
0.05272958055138588,
0.03959653899073601,
0.0254896841943264,
-0.008655653335154057,
-0.020884264260530472,
-0.08331894874572754,
0.027299242094159126,
-0.04163398966193199,
0.015051954425871372,
-0.014402106404304504,
-0.008138987235724926,
-0.01876852475106716,
-0.015208077616989613,
-0.007766406517475843,
-0.029940862208604813,
-0.03809506446123123,
-0.015841756016016006,
-0.024717265740036964,
-0.05366387963294983,
-0.03277831897139549,
-0.019695701077580452,
0.026985257863998413,
0.034237951040267944,
-0.023831335827708244,
-0.004058466758579016,
0.019656090065836906,
-0.04892770200967789,
-0.00717503996565938,
-0.017043860629200935,
0.009062773548066616,
0.004523822572082281,
-0.011317012831568718,
0.06153089925646782,
0.020591195672750473,
-0.030141295865178108,
-0.03213538974523544,
0.0328034870326519,
0.05916498601436615,
0.012084187008440495,
0.005759572610259056,
-0.03788510710000992,
-0.024693675339221954,
-0.011869348585605621,
0.02866472862660885,
0.012806793674826622,
0.0008643248584121466,
0.04004255682229996,
0.0148817403241992,
-0.000028345786631689407,
-0.023175036534667015,
0.06526319682598114,
0.0240828488022089,
0.010380320250988007,
-0.055163249373435974,
-0.0035588997416198254,
-0.011749377474188805,
-0.01859002560377121,
-0.027853654697537422,
-0.001122716348618269,
-0.014413033612072468,
-0.013529099524021149,
-0.005810640286654234,
0.005627543665468693,
0.009325484745204449,
-0.017052607610821724,
-0.00831903237849474,
0.02824876829981804,
0.03764073923230171,
0.008230175822973251,
-0.011826794594526291,
-0.0015741866081953049,
-0.009512768127024174,
0.03441882133483887,
-0.028120730072259903,
0.0117275919765234,
-0.07871538400650024,
0.020220503211021423,
0.014274385757744312,
0.08008205890655518,
-0.032089173793792725,
-0.019345227628946304,
-0.04461843892931938,
-0.033888742327690125,
0.0309478510171175,
-0.04702227935194969,
0.018384607508778572,
-0.029489897191524506,
-0.01926017366349697,
-0.0186640452593565,
-0.05113951861858368,
-0.00027242364012636244,
-0.024266798049211502,
0.007357895374298096,
0.0017237981082871556,
-0.024402962997555733,
-0.003585374914109707,
-0.02229420468211174,
0.027281494811177254,
0.007695381063967943,
0.05830155685544014,
0.004312749952077866,
0.03406348451972008,
0.009259924292564392,
0.03564225137233734,
-0.014997434802353382,
-0.05954622104763985,
-0.02012394368648529,
0.010534075088799,
0.0004479828930925578,
0.040901683270931244,
-0.03647731989622116,
-0.1191641241312027,
0.016249248757958412,
0.022629765793681145,
-0.008013838902115822,
-0.02464926801621914,
-0.04918789863586426,
0.053044531494379044,
0.026979997754096985,
-0.013644096441566944,
0.04127991199493408,
0.053914397954940796,
-0.03201479837298393,
-0.00290787685662508,
-0.011643664911389351,
0.01457337848842144,
-0.04071676358580589,
0.009689796715974808,
-0.03715468943119049,
0.04261760413646698,
0.023104961961507797,
0.0211194921284914,
-0.00856728944927454,
-0.012970777228474617,
0.007534757722169161,
-0.014053240418434143,
0.003647555597126484,
0.03230654448270798,
0.01777946949005127,
-0.00007533274037996307,
-0.022367537021636963,
0.005753695964813232,
-0.010684571228921413,
-0.02053867280483246,
0.006826661992818117,
-0.008585702627897263,
-0.0056682308204472065,
0.021705811843276024,
-0.013590123504400253,
0.017925241962075233,
-0.039287179708480835,
0.006560925859957933,
0.04641508683562279,
-0.031742118299007416,
0.031542349606752396,
0.004911016207188368,
0.018649287521839142,
0.018459707498550415,
-0.06862933188676834,
-0.0068855672143399715,
0.007933828048408031,
-0.018208492547273636,
0.032222677022218704,
0.001779884216375649,
0.05171258747577667,
0.02390323393046856,
-0.007202077656984329,
-0.09955907613039017,
-0.04212924838066101,
-0.00968119502067566,
0.0030532795935869217,
-0.02662113681435585,
-0.006751332897692919,
-0.01675688475370407,
-0.03869917243719101,
-0.016416452825069427,
0.0048013911582529545,
0.014131195843219757,
-0.016415605321526527,
0.01961340568959713,
0.035164110362529755,
0.009563261643052101,
0.03581807389855385,
-0.0016108761774376035,
-0.028910089284181595,
0.025958329439163208,
-0.004778160247951746,
-0.00010732776718214154,
-0.028042078018188477,
0.03899858146905899,
-0.01932010054588318,
-0.011478492058813572,
0.03398597240447998,
-0.004180856980383396,
0.03757791966199875,
-0.0049949996173381805,
-0.0034781002905219793,
0.05245555564761162,
0.00000733504066374735,
0.015002242289483547,
-0.010513119399547577,
0.05128469690680504,
-0.008342023938894272,
0.04742277413606644,
0.0362517349421978,
0.009055177681148052,
-0.022183123975992203,
-0.05628034472465515,
0.03676742687821388,
-0.015507090836763382,
0.04980798810720444,
0.019517259672284126,
0.06109226495027542,
-0.00012532103573903441,
-0.0016182513209059834,
0.012561419978737831,
-0.0016536037437617779,
0.00402971962466836,
0.007349501363933086,
0.012480729259550571,
0.02913598157465458,
-0.017294103279709816,
-0.023556392639875412,
-0.04006168618798256,
-0.013894008472561836,
0.04015003517270088,
0.040841393172740936,
-0.03991144523024559,
0.015027284622192383,
-0.01567624881863594,
0.012807306833565235,
0.03061935305595398,
-0.02561955899000168,
-0.01316489651799202,
-0.004635364282876253,
-0.008271731436252594,
0.025140954181551933,
0.024028025567531586,
0.0207903403788805,
0.04220909625291824,
0.03739936649799347,
-0.0159586351364851,
0.02796577848494053,
0.017773615196347237,
0.015649501234292984,
-0.0005993414670228958,
-0.011808414943516254,
-0.053942035883665085,
0.05147692933678627,
-0.02882419526576996,
0.025719840079545975,
-0.01508869044482708,
-0.04219045117497444,
0.03161703050136566,
-0.029147367924451828,
0.02371860295534134,
-0.03930259123444557,
-0.04417527839541435,
-0.022140925750136375,
0.0372605063021183,
0.017941677942872047,
0.011867888271808624,
0.011779979802668095,
0.017402872443199158,
0.02412731572985649,
0.021141070872545242,
-0.001953601138666272,
-0.003163871355354786,
-0.09488581866025925,
-0.021511128172278404,
-0.02431945502758026,
-0.04831516370177269,
0.03403128311038017,
-0.018046915531158447,
-0.027510961517691612,
-0.03570205345749855,
-0.017522035166621208,
-0.001845035352744162,
-0.032801125198602676,
0.04882822185754776,
-0.004825778771191835,
0.02026313729584217,
-0.003977748099714518,
0.04245574772357941,
0.02077888511121273,
0.007851757109165192,
0.115296371281147,
0.05304691568017006,
0.025427162647247314,
-0.027400536462664604,
0.005987185053527355,
-0.0409909263253212,
-0.004318322520703077,
0.008259669877588749,
0.01578456535935402,
0.003779591992497444,
0.028632991015911102,
-0.00976238027215004,
0.04546623304486275,
-0.017080672085285187,
0.0273432657122612,
0.06630373001098633,
-0.04335278272628784,
-0.019324298948049545,
-0.0054828692227602005,
0.038120709359645844,
0.004173469264060259,
0.004494904074817896,
-0.0186168160289526,
0.010002451948821545,
-0.025872085243463516,
-0.01874018833041191,
-0.01167876087129116,
-0.01627994328737259,
0.013919929042458534,
0.017761433497071266,
-0.03609108179807663,
-0.03652793541550636,
0.0067662885412573814,
-0.008464905433356762,
-0.04303845390677452,
0.018245184794068336,
0.013779890723526478,
-0.01227792538702488,
0.03008699230849743,
0.032300323247909546,
0.03116774559020996,
0.038329292088747025,
-0.01991214044392109,
0.01862914487719536,
-0.033221133053302765,
-0.019423101097345352,
-0.03071500174701214,
0.038023579865694046,
-0.05859283730387688,
0.02385684661567211,
0.0034230821765959263,
0.012498700059950352,
0.007869765162467957,
0.004953999072313309,
-0.01683381386101246,
-0.04698400944471359,
0.023693475872278214,
-0.023173481225967407,
-0.02574804611504078,
-0.05787511542439461,
0.02998274564743042,
-0.014721931889653206,
0.012082460336387157,
0.006399533245712519,
-0.04862205684185028,
0.007705647964030504,
-0.022755198180675507,
-0.01486905012279749,
0.015562925487756729,
0.018340764567255974,
-0.005299991928040981,
-0.012495283968746662,
-0.01339142769575119,
-0.014869360253214836,
0.028843309730291367,
0.032831624150276184,
0.061629168689250946,
0.036084506660699844,
-0.015291728079319,
-0.02143164910376072,
-0.03909032419323921,
0.06883390992879868,
-0.028797844424843788,
-0.013667725957930088,
-0.03424030542373657,
-0.008522176183760166,
-0.014081668108701706,
0.026344794780015945,
-0.04653574153780937,
0.02032763697206974,
-0.02400892600417137,
-0.021955037489533424,
-0.0010688860202208161,
-0.04399143531918526,
-0.03188889101147652,
-0.016231875866651535,
-0.008705788291990757,
0.027194852009415627,
0.006467896047979593,
0.03953273594379425,
0.019261011853814125,
-0.02134738117456436,
0.05726061388850212,
0.018540125340223312,
-0.016764014959335327,
0.02158922329545021,
0.024715673178434372,
-0.013218559324741364,
0.03117738664150238,
0.003926275297999382,
-0.019415568560361862,
-0.013216075487434864,
-0.02652943693101406,
-0.0224961806088686,
0.001713826903142035,
0.025716600939631462,
0.005936710629612207,
-0.01310657523572445,
0.02909022569656372,
-0.046025488525629044,
0.011125299148261547,
-0.04703652858734131,
-0.025688190013170242,
-0.04895718768239021,
0.016351960599422455,
0.025600789114832878,
-0.03464619442820549,
-0.02468651346862316,
0.029139598831534386,
0.020866967737674713,
-0.02232307754456997,
0.04295318201184273,
0.016017714515328407,
-0.020362958312034607,
-0.022936135530471802,
0.03447233885526657,
-0.0173668023198843,
0.031957875937223434,
-0.018920807167887688,
-0.0025844036135822535,
0.05337817594408989,
-0.021204087883234024,
-0.03189124912023544,
0.02899983525276184,
-0.00017581749125383794,
0.009284766390919685,
0.005389098078012466,
0.011686218902468681,
-0.023989016190171242,
0.07723095268011093,
-0.04185207933187485,
0.009800980798900127,
0.03240121155977249,
0.02544664405286312,
-0.023196475580334663,
-0.005501266103237867,
0.00040560326306149364,
0.01281209010630846,
0.01607191376388073,
0.017938554286956787,
0.020882532000541687,
0.006209313403815031,
-0.00006139359174994752,
-0.02568170614540577,
-0.012691282667219639,
0.009117568843066692,
0.04958546906709671,
0.036695320159196854,
-0.0036224755458533764,
0.04899786040186882,
-0.02663544937968254,
0.03160315006971359,
0.01281768549233675,
-0.01436496153473854,
-0.05751606076955795,
0.022091327235102654,
-0.015547347255051136,
-0.01629802957177162,
-0.010985922999680042,
-0.03245255723595619,
-0.0004027907853014767,
0.03777164965867996,
-0.08246121555566788,
0.0014063100097700953,
-0.03517937660217285,
-0.04015718027949333,
-0.04061070457100868,
-0.03740192577242851,
-0.030067311599850655,
0.055971309542655945,
0.05190236493945122,
0.08017373085021973,
0.04034963995218277,
-0.0066911326721310616,
-0.030313963070511818,
-0.006285846699029207,
-0.03861522674560547,
0.022683914750814438,
-0.014188396744430065,
0.01471859309822321,
0.04850071668624878,
0.012415658682584763,
-0.022434717044234276,
0.0033687357790768147,
0.017565296962857246,
0.001958240056410432,
0.01711326092481613,
0.017061714082956314,
-0.023937255144119263,
0.008025174960494041,
-0.006318059284240007,
-0.00960049033164978,
-0.00522217620164156,
0.02828044444322586,
0.015508642420172691,
0.04266015812754631,
0.005888520739972591,
-0.005841671489179134,
0.00843649823218584,
-0.024253780022263527,
-0.03140830248594284,
0.01582801342010498,
-0.011852176859974861,
0.0037624870892614126,
0.032830610871315,
0.03010159358382225,
0.006024075206369162,
-0.03009125217795372,
-0.05774473771452904,
0.0019942675717175007,
-0.033770304173231125,
0.001992887584492564,
0.018948962911963463,
0.040102727711200714,
0.01645856536924839,
-0.022550325840711594,
-0.007660058792680502,
-0.016638755798339844,
0.031198950484395027,
-0.020869433879852295,
-0.023290840908885002,
0.0014758121687918901,
0.021578215062618256,
-0.008229479193687439,
-0.021367477253079414,
-0.02414117567241192,
-0.06893064081668854,
0.03707771748304367,
0.02821747399866581,
0.040853578597307205,
-0.03116024099290371,
-0.05107253044843674,
-0.016571637243032455,
-0.03661787509918213,
0.03882463276386261,
-0.05357128009200096,
0.012904683127999306,
-0.06443822383880615,
-0.021094588562846184,
0.02421734668314457,
-0.0125923166051507,
0.04929288476705551,
-0.0025526005774736404,
-0.00486797746270895,
0.04829087108373642,
-0.006523546762764454,
0.00038031121948733926,
-0.023756390437483788,
0.026440711691975594,
-0.012270799838006496,
-0.02808470092713833,
0.0036138661671429873,
-0.02451436221599579,
0.012002803385257721,
0.02618035301566124,
0.030212512239813805,
-0.024753747507929802,
-0.01731894351541996,
-0.01241177599877119,
0.02290518768131733,
0.04553277790546417,
-0.03455403447151184,
-0.05154632776975632,
0.08490952104330063,
-0.0025468773674219847,
-0.0007477502804249525,
0.015422699972987175,
-0.007362545933574438,
-0.025274507701396942,
0.047465842217206955,
-0.02341906912624836,
0.02190791629254818,
-0.021278491243720055,
-0.013005148619413376,
-0.00021774349443148822,
-0.03815343603491783,
0.013275844976305962,
0.050380807369947433,
-0.030062127858400345,
0.008865784853696823,
0.03895566985011101,
0.008436858654022217,
0.02602612040936947,
0.01520103495568037,
0.005931542720645666,
0.006106019485741854,
0.0373571515083313,
0.022013699635863304,
0.057184848934412,
0.013805834576487541,
-0.01052889320999384,
0.029191285371780396,
-0.010038992390036583,
-0.0034641253296285868,
-0.023875366896390915,
0.03687940537929535,
0.01893424056470394,
-0.05110564082860947,
-0.01877947524189949,
0.009359356947243214,
-0.004947262816131115,
0.033663369715213776,
-0.0039001265540719032,
-0.03993099555373192,
0.0783989205956459,
-0.03935124725103378,
0.017629770562052727,
0.007569562178105116,
0.0063079041428864,
0.004316913895308971,
0.025473471730947495,
-0.004984508268535137,
0.03410312905907631,
-0.03428923711180687,
0.005046418402343988,
-0.02252064272761345,
0.05089157447218895,
0.03164590150117874,
-0.028249362483620644,
0.01271664910018444,
-0.020598897710442543,
-0.017631441354751587,
-0.04791444540023804,
0.01995273306965828,
-0.0346439965069294,
-0.035862796008586884,
-0.0040025487542152405,
0.03513375669717789,
0.034557413309812546,
0.004927701782435179,
-0.03309972584247589,
-0.015429016202688217,
0.03353922814130783,
-0.02074270322918892,
0.009062708355486393,
-0.050410185009241104,
0.014767378568649292,
-0.04982241988182068,
-0.0060525392182171345
] |
<p><strong>Disclaimer</strong>: I am not asking whether or not the events that occur in Anathem are possible. I understand that this book is a work of speculative science fiction and this site has no interest in it as such. I'm asking about the physics of a <strong>particular</strong> plot device.</p>
<p>In Anathem, Neal Stephenson states that the configuration of hadrons within atomic nuclei created during (stellar) nucleosynthesis is dependent on the fundamental constants of the universe (non derivable constants such as the speed of light and the cosmological constant), and that this configuration affects the electrical properties of the elements, and thus their chemistry.</p>
<p>In the book, physicists have created machines that can generate energy densities on the order of the big bang (or so). The idea is, in the beginning of the universe, the fundamental constants were unfixed and ambiguous. As the universe cooled down, the constants became fixed, the forces separated, and the universe was born. By creating high energy densities, the values of the constants can be fudged, allowing nucleosynthesis that generates nuclei with hadronic configuration different from ordinary matter. With that different configuration comes different electrical properties and thus different chemistry. This last feature prevents (or interferes with) 'newmatter' or matter from parallel universes with different constants from interacting chemically with matter of the universe the book is set in. These physicists tweaked the constants until they generated 'newmatter' with desirable chemical properties.</p>
<p>I have two questions. First, do the constants of nature affect nucleosynthesis in any way that measurably changes the electrical properties of the orbitals? Second, is there any veracity to the claim that the fundamental physical constants were 'unfixed' during the first instants of the big bang and that they can be locally unfixed by high enough energy densities?</p>
| 9,567 |
[
-0.0216747485101223,
-0.011795704253017902,
0.026268869638442993,
-0.023160003125667572,
0.04756341129541397,
0.012126700021326542,
-0.01168535090982914,
-0.041516270488500595,
0.010437543503940105,
-0.036612603813409805,
0.01745135709643364,
0.035484716296195984,
0.027300192043185234,
0.05129440873861313,
0.008626146242022514,
-0.030220946297049522,
0.02139829471707344,
-0.005969969090074301,
0.013238301500678062,
-0.033976320177316666,
0.0214379969984293,
0.02465999312698841,
-0.0016058679902926087,
-0.000019400889868848026,
0.0038242896553128958,
0.028572697192430496,
-0.024445202201604843,
-0.023640809580683708,
-0.015976551920175552,
0.03361601382493973,
0.026523714885115623,
-0.04365938901901245,
0.03171011805534363,
0.0006078763399273157,
0.03651948645710945,
0.026927918195724487,
0.0001442698121536523,
-0.040476009249687195,
-0.020496973767876625,
0.033406488597393036,
-0.04336118698120117,
0.025757772848010063,
-0.0442582443356514,
0.053455378860235214,
-0.018786432221531868,
0.029144732281565666,
0.015243172645568848,
0.0069939615204930305,
0.034435976296663284,
-0.028424106538295746,
0.005983468610793352,
0.03581780567765236,
0.033677563071250916,
0.05442936345934868,
-0.05481340363621712,
-0.014683999121189117,
0.09098560363054276,
0.039932023733854294,
-0.0019101302605122328,
-0.03287053853273392,
-0.012504705227911472,
-0.012566521763801575,
0.04415413364768028,
0.003683070419356227,
-0.029946405440568924,
0.04109867289662361,
0.013823099434375763,
-0.053346917033195496,
0.006041259039193392,
0.012476851232349873,
0.0508316308259964,
0.057660676538944244,
-0.0093305055052042,
0.006307125091552734,
0.007912085391581059,
-0.049763306975364685,
0.032596997916698456,
-0.013218056410551071,
0.02485017105937004,
0.02641647681593895,
-0.011409730650484562,
-0.010954586789011955,
0.023245586082339287,
0.03819090873003006,
-0.0011103961151093245,
0.03019561804831028,
0.015555334277451038,
-0.04267249256372452,
0.018113242462277412,
0.039742011576890945,
0.0011321675265207887,
0.028037451207637787,
0.0482807420194149,
0.012872771359980106,
-0.05097116902470589,
0.0309176966547966,
-0.0027691898867487907,
0.04926009476184845,
-0.02027217112481594,
-0.009845477528870106,
0.013720473274588585,
-0.0032313810661435127,
0.006136596202850342,
0.03814811632037163,
0.03028813563287258,
-0.07699181139469147,
-0.020918652415275574,
0.009195813909173012,
0.004459815099835396,
0.02690156362950802,
-0.0359259732067585,
-0.01032956037670374,
-0.015051250346004963,
-0.01193196140229702,
0.020515786483883858,
-0.020218463614583015,
0.010320963338017464,
-0.04004261642694473,
0.0698818489909172,
0.03419128432869911,
0.04482671990990639,
0.0004244499432388693,
0.01136443018913269,
-0.0119376415386796,
-0.03580785170197487,
-0.02341727912425995,
-0.007411519065499306,
-0.0003087832883466035,
-0.024442149326205254,
0.02067134901881218,
-0.013016262091696262,
0.010518895462155342,
-0.027886826545000076,
-0.02155248634517193,
0.03672860190272331,
0.02478688955307007,
-0.05925992876291275,
-0.062056876718997955,
0.026576604694128036,
-0.008905619382858276,
-0.010198005475103855,
-0.08716846257448196,
0.007921126671135426,
0.014827198348939419,
0.06153964623808861,
0.008908850140869617,
-0.07550065219402313,
-0.025858625769615173,
0.035425443202257156,
0.02549292892217636,
-0.04405844211578369,
0.01425290945917368,
0.004947699140757322,
-0.06565672904253006,
-0.027836808934807777,
-0.07299661636352539,
0.033108893781900406,
0.02518976479768753,
0.018882159143686295,
0.0015944096958264709,
0.03399757668375969,
-0.0592552125453949,
0.005773728247731924,
0.001342114876024425,
-0.01253621093928814,
-0.02073127217590809,
0.07066487520933151,
0.075142502784729,
-0.00543884327635169,
0.015950744971632957,
0.003697176929563284,
0.0733523741364479,
0.03489048033952713,
0.010984942317008972,
0.04509260877966881,
-0.036282215267419815,
-0.007134276442229748,
-0.03719041496515274,
0.03297902271151543,
0.026194551959633827,
-0.0549301840364933,
0.0022202201653271914,
-0.01792757585644722,
0.011197454296052456,
0.011965801008045673,
0.018424464389681816,
-0.035152241587638855,
0.01907847635447979,
-0.0059109460562467575,
-0.019087420776486397,
0.02696743793785572,
-0.08747316151857376,
-0.01245212834328413,
-0.012082556262612343,
-0.046975310891866684,
0.03489365801215172,
-0.02370493672788143,
0.039474502205848694,
-0.04026786610484123,
-0.0548870824277401,
0.015643546357750893,
0.04535399749875069,
0.06121223792433739,
-0.0029864092357456684,
0.02357211895287037,
0.05432352423667908,
0.018807141110301018,
-0.012201087549328804,
0.013843461871147156,
-0.014357360079884529,
-0.0651073083281517,
0.0328451506793499,
-0.016611481085419655,
0.02548299729824066,
0.0044800289906561375,
-0.014310664497315884,
0.0041837431490421295,
-0.006163821555674076,
0.018480589613318443,
0.04699360206723213,
-0.016800373792648315,
0.07207740098237991,
0.02301819995045662,
-0.003021392272785306,
0.03274865075945854,
0.08563531935214996,
0.002281269058585167,
0.010000386275351048,
-0.016727276146411896,
-0.03810311108827591,
-0.10155002772808075,
-0.03454805910587311,
0.02014312520623207,
0.03535810858011246,
-0.01023509819060564,
0.04672171175479889,
0.012811052612960339,
0.05414648354053497,
0.032922375947237015,
-0.019086988642811775,
-0.05896410346031189,
-0.05378283932805061,
0.018569881096482277,
0.02226843871176243,
0.040790218859910965,
0.03455815464258194,
-0.00023377359320875257,
0.03992754966020584,
-0.007044561672955751,
-0.034820012748241425,
0.005240896716713905,
0.009622163139283657,
-0.0176609568297863,
-0.018331043422222137,
-0.005602728575468063,
-0.03634662553668022,
-0.02031642384827137,
-0.0042417594231665134,
0.021892156451940536,
0.005462033674120903,
0.00925269816070795,
0.0011773668229579926,
-0.05313077196478844,
0.002207790967077017,
0.008855014108121395,
0.03031705878674984,
-0.034048713743686676,
-0.008699790574610233,
0.02442566677927971,
-0.058465152978897095,
-0.00594510231167078,
0.01425262726843357,
0.008161586709320545,
0.009309741668403149,
-0.02787761017680168,
-0.002504331525415182,
0.022449946030974388,
0.004439876414835453,
-0.004172084853053093,
-0.014193319715559483,
-0.019789326936006546,
-0.02410256303846836,
-0.022042909637093544,
0.032345980405807495,
-0.06425691395998001,
0.004490961786359549,
-0.03271312639117241,
-0.016293084248900414,
0.009089586324989796,
-0.04058805853128433,
0.015212956815958023,
0.03593597188591957,
-0.019178662449121475,
-0.05283471941947937,
0.02106841281056404,
-0.037713900208473206,
-0.006032848730683327,
0.0006575782899744809,
-0.026788296177983284,
0.054309554398059845,
0.00682450458407402,
-0.02288660779595375,
-0.011711341328918934,
-0.03228389844298363,
-0.0075998008251190186,
-0.0066232942044734955,
-0.0018564530182629824,
0.015431225299835205,
-0.01741519384086132,
0.0375223346054554,
0.06738084554672241,
-0.04983621835708618,
-0.002945981454104185,
-0.06272535771131516,
-0.012085292488336563,
0.010023863054811954,
-0.037420500069856644,
0.045282457023859024,
0.007896214723587036,
-0.04182347282767296,
0.0601450651884079,
0.04762496426701546,
-0.0647476315498352,
-0.031908340752124786,
0.015545430593192577,
0.025248773396015167,
-0.03560643270611763,
-0.009343210607767105,
0.028676679357886314,
0.03571673482656479,
0.002688186476007104,
0.03678968921303749,
0.023143351078033447,
0.0506681427359581,
-0.017195500433444977,
-0.021362489089369774,
0.03966359794139862,
-0.011323593556880951,
0.023454109206795692,
0.06011830270290375,
0.0313098207116127,
0.005118785426020622,
0.028545143082737923,
-0.011193321086466312,
0.03380337357521057,
-0.002157954964786768,
-0.0492141991853714,
0.047341134399175644,
0.04520310461521149,
0.009798781014978886,
-0.020150385797023773,
0.016121357679367065,
-0.029901789501309395,
-0.06971269100904465,
-0.024815650656819344,
0.04015691578388214,
0.03897102549672127,
-0.012581643648445606,
0.022903326898813248,
0.005699801724404097,
0.03600713238120079,
-0.02950218692421913,
-0.009806668385863304,
0.04349600896239281,
-0.0060476334765553474,
0.0340920016169548,
-0.03030664101243019,
0.023268647491931915,
0.05614231899380684,
0.012023012153804302,
0.03739594668149948,
0.005789488088339567,
-0.04749364033341408,
0.02227570116519928,
-0.05835740640759468,
-0.02434602379798889,
0.025896677747368813,
0.008620083332061768,
0.019665049389004707,
0.051153793931007385,
-0.01498475018888712,
0.015034588985145092,
-0.033346403390169144,
-0.03218622878193855,
-0.09417910873889923,
0.028827359899878502,
-0.037253789603710175,
-0.016238555312156677,
-0.007104367017745972,
-0.002555272774770856,
-0.0384460911154747,
0.00409713527187705,
-0.003829656168818474,
-0.027434106916189194,
-0.03717198595404625,
-0.056244466453790665,
0.0428810752928257,
-0.04278988018631935,
-0.03296852856874466,
-0.04198750853538513,
0.06628650426864624,
0.05777660757303238,
-0.03929722681641579,
0.028940200805664062,
-0.022986939176917076,
-0.06949514150619507,
-0.013610269874334335,
-0.03887400031089783,
0.0022303047589957714,
0.012530419044196606,
0.03855418413877487,
0.022924963384866714,
0.016883332282304764,
-0.002514416119083762,
-0.020749984309077263,
0.06907980889081955,
0.04141596332192421,
0.007407027296721935,
-0.008672249503433704,
-0.04627998173236847,
-0.01950906030833721,
-0.023151611909270287,
0.027379414066672325,
0.021795520558953285,
0.012671070173382759,
0.01164120901376009,
0.025430090725421906,
0.030709167942404747,
-0.029715389013290405,
0.0362989567220211,
0.05878250673413277,
0.010575405322015285,
-0.00954270176589489,
-0.0030032184440642595,
0.004147363360971212,
-0.012370087206363678,
0.008713937364518642,
0.020763132721185684,
0.0020634843967854977,
-0.022162171080708504,
-0.0006890365621075034,
0.015368870459496975,
0.018314866349101067,
-0.09255944192409515,
0.015406220220029354,
-0.012128619477152824,
0.004297015722841024,
-0.05098811909556389,
0.018994474783539772,
-0.0038423535879701376,
0.021470021456480026,
0.029614204540848732,
-0.03676337003707886,
-0.022790562361478806,
-0.05477726832032204,
0.008600750006735325,
0.026178251951932907,
0.05823525786399841,
-0.0016887100646272302,
0.018088707700371742,
-0.06742651015520096,
-0.006786565762013197,
0.011769445613026619,
-0.03571592643857002,
0.029299959540367126,
-0.00017486524302512407,
-0.028079692274332047,
0.022027870640158653,
-0.04481701925396919,
-0.001961795147508383,
-0.013109353370964527,
-0.00499008409678936,
0.018401212990283966,
-0.028020702302455902,
-0.012487305328249931,
0.013919990509748459,
0.01904410310089588,
-0.0013313015224412084,
0.020083067938685417,
-0.03879199177026749,
-0.03411703556776047,
0.015315083786845207,
0.004854209255427122,
0.021828923374414444,
-0.0721510723233223,
0.029775941744446754,
-0.01675480604171753,
0.01323084719479084,
0.039631687104701996,
-0.014731472358107567,
-0.04811542108654976,
-0.005330868065357208,
-0.004563033115118742,
0.004886133596301079,
-0.0330343022942543,
-0.0022788671776652336,
0.06776367127895355,
0.029980480670928955,
0.0012386733433231711,
0.022733770310878754,
0.033308204263448715,
-0.02565140649676323,
0.00960568804293871,
-0.07504091411828995,
0.0063692121766507626,
-0.014701524749398232,
0.014013632200658321,
-0.03750184178352356,
-0.0008987282635644078,
-0.002184937708079815,
0.006923351902514696,
0.0025935012381523848,
-0.013406727463006973,
0.01799853891134262,
-0.027730245143175125,
0.03307701274752617,
0.026388144120573997,
-0.027415893971920013,
0.01206208299845457,
-0.026974864304065704,
0.02227652072906494,
0.010817740112543106,
0.00947059877216816,
-0.007762157823890448,
-0.02735423482954502,
0.043788403272628784,
0.019481103867292404,
-0.031386371701955795,
0.03497755527496338,
-0.02786886878311634,
-0.011986353434622288,
0.018706349655985832,
-0.02732107974588871,
0.017941325902938843,
0.02681230939924717,
0.03481151908636093,
0.022733036428689957,
-0.054217379540205,
-0.04029345512390137,
-0.008819127455353737,
-0.05884706228971481,
0.016842825338244438,
-0.021892549470067024,
0.04167073592543602,
-0.009611048735678196,
0.020362304523587227,
-0.04218494892120361,
-0.011067317798733711,
0.024887418374419212,
0.004350048955529928,
-0.01273051742464304,
-0.017029447481036186,
0.001776510733179748,
0.016316421329975128,
0.0033470087219029665,
0.027793655171990395,
0.04546314850449562,
-0.01988266408443451,
-0.026211462914943695,
0.00871345680207014,
0.01233163382858038,
0.07265203446149826,
-0.017242299392819405,
-0.014298375695943832,
0.023616958409547806,
-0.007261688821017742,
0.039000462740659714,
0.005993003491312265,
0.014906392432749271,
-0.010857689194381237,
-0.05616951361298561,
0.006798987276852131,
0.07186711579561234,
0.04407224431633949,
-0.048902612179517746,
-0.012518143281340599,
0.043080057948827744,
-0.0069846236146986485,
0.021215073764324188,
0.0023036557249724865,
-0.00047176971565932035,
-0.038401246070861816,
0.011256006546318531,
0.024635806679725647,
-0.0037473354022949934,
0.003971996251493692,
-0.0636197179555893,
0.018013769760727882,
-0.0026004204992204905,
0.015913495793938637,
0.0032154195941984653,
0.05520401522517204,
0.020100673660635948,
-0.03136097267270088,
0.049578599631786346,
-0.029614847153425217,
0.041671380400657654,
0.015754448249936104,
0.01924697682261467,
-0.0014614022802561522,
-0.015653446316719055,
-0.01969864033162594,
-0.02993244118988514,
-0.04303283616900444,
0.047003597021102905,
0.021238718181848526,
0.017670104280114174,
0.032801441848278046,
0.003289710031822324,
-0.009355920366942883,
-0.015895692631602287,
-0.0037712566554546356,
-0.03648697957396507,
-0.00672417227178812,
-0.04829004406929016,
0.013741406612098217,
-0.006737996824085712,
0.011245439760386944,
0.04068044200539589,
0.05651567876338959,
-0.04984532296657562,
-0.0005308125400915742,
0.04583122208714485,
0.022497037425637245,
0.02785305678844452,
-0.007901772856712341,
-0.021870795637369156,
0.03978947177529335,
-0.038000352680683136,
0.042670682072639465,
0.0035133231431245804,
-0.022984851151704788,
-0.007154096849262714,
-0.00799959059804678,
0.028148338198661804,
0.012515773996710777,
-0.086995430290699,
-0.009385139681398869,
0.005610751919448376,
0.043263740837574005,
0.012008813209831715,
-0.03414854407310486,
0.035243257880210876,
0.04272621124982834,
-0.017797071486711502,
-0.026673559099435806,
0.020250800997018814,
-0.07557247579097748,
-0.017704244703054428,
-0.028319725766777992,
-0.00453974911943078,
0.06895438581705093,
-0.05876866355538368,
-0.062135543674230576,
0.03932884335517883,
-0.04236337170004845,
0.02682824432849884,
0.03254755958914757,
0.03755904361605644,
-0.013009077869355679,
0.06506440788507462,
-0.0495595820248127,
-0.007567341439425945,
-0.014709352515637875,
0.012721596285700798,
0.1295487880706787,
0.03914808854460716,
0.0006176657625474036,
-0.05747528374195099,
0.0013046418316662312,
-0.032877057790756226,
0.00958484411239624,
0.02388041280210018,
-0.00622028112411499,
-0.007625849451869726,
0.001069805701263249,
-0.010518519207835197,
0.009008348919451237,
0.04262813180685043,
0.013429475948214531,
0.03147822618484497,
-0.03039734996855259,
-0.003983331378549337,
0.014055902138352394,
0.005949015263468027,
-0.011548834852874279,
-0.0192975252866745,
-0.06805359572172165,
-0.03288247808814049,
0.024028489366173744,
0.026302525773644447,
-0.02009076438844204,
-0.01599332131445408,
0.03600596264004707,
0.05427023768424988,
-0.01921985112130642,
0.009126238524913788,
0.00832164566963911,
-0.014109286479651928,
0.00934574007987976,
0.01091006863862276,
0.031164906919002533,
0.0076486459001898766,
-0.0067521315068006516,
0.03555942326784134,
0.03538084402680397,
-0.015010067261755466,
0.016378600150346756,
0.032307349145412445,
-0.01753649301826954,
-0.023131441324949265,
-0.006542267743498087,
0.0003221783263143152,
0.007368700113147497,
-0.031034449115395546,
0.03037184663116932,
0.0023680487647652626,
0.03889195993542671,
-0.008775844238698483,
-0.014064363203942776,
-0.031115103513002396,
0.01717718318104744,
-0.00912938266992569,
-0.02569766901433468,
-0.0032454542815685272,
0.03261355683207512,
-0.023420248180627823,
0.025422604754567146,
0.03208552300930023,
-0.009961995296180248,
0.025505011901259422,
-0.022245733067393303,
-0.004783896263688803,
0.010498789139091969,
-0.020311998203396797,
-0.05774747207760811,
-0.014471147209405899,
-0.07745391875505447,
-0.043898433446884155,
0.0228554829955101,
0.05398198962211609,
0.05025307089090347,
0.010525880381464958,
0.014156990684568882,
0.0053565120324492455,
0.00013026449596509337,
0.002036032732576132,
-0.011241395026445389,
-0.013083859346807003,
-0.017267266288399696,
0.009047328494489193,
0.01654839888215065,
0.003922862000763416,
-0.015939978882670403,
0.015203922055661678,
-0.005326367914676666,
0.03599517047405243,
0.028126711025834084,
-0.022687336429953575,
-0.019887804985046387,
-0.016513759270310402,
-0.03690928593277931,
-0.005528376437723637,
0.007658033631742001,
0.01775660552084446,
0.015061353333294392,
-0.03587222844362259,
0.0369645319879055,
0.009774293750524521,
0.011665514670312405,
0.008736729621887207,
0.036183226853609085,
-0.027231134474277496,
-0.0011661805910989642,
0.021906115114688873,
0.024044718593358994,
-0.005401443690061569,
-0.016666477546095848,
-0.034472785890102386,
0.0005476819933392107,
0.007265572901815176,
0.04082050919532776,
-0.03616171330213547,
-0.000802190275862813,
-0.02325480990111828,
-0.024027887731790543,
0.010737935081124306,
0.0009931201348081231,
-0.009536778554320335,
-0.021080370992422104,
-0.0004341091262176633,
-0.007666447199881077,
0.03218790888786316,
0.06151613965630531,
-0.02280876412987709,
-0.057426560670137405,
0.024124126881361008,
0.019710134714841843,
-0.025098532438278198,
-0.0025207363069057465,
0.0018490939401090145,
0.027766607701778412,
0.024273734539747238,
-0.06626548618078232,
-0.03628141060471535,
0.027928313240408897,
-0.034049324691295624,
-0.051841408014297485,
0.023909755051136017,
-0.0545961819589138,
0.0068397545255720615,
0.018498415127396584,
-0.010544935241341591,
-0.028398070484399796,
0.07081824541091919,
-0.027405817061662674,
0.04811850190162659,
0.031071990728378296,
-0.010074899531900883,
-0.031317733228206635,
0.01595882885158062,
0.014347134158015251,
0.012778767384588718,
-0.00958167389035225,
0.0288438368588686,
0.028867274522781372,
0.004591390024870634,
0.013441751711070538,
0.008316772989928722,
-0.006727186031639576,
-0.019317185506224632,
0.02565997838973999,
0.03742431849241257,
0.015019194222986698,
0.003985666669905186,
-0.03496434912085533,
0.020282916724681854,
0.029842602089047432,
-0.013298243284225464,
-0.10729576647281647,
-0.01257808692753315,
-0.018937528133392334,
0.006584525108337402,
0.0008154489332810044,
0.000051251467084512115,
0.01364473719149828,
0.014206397347152233,
-0.06331124156713486,
-0.02363063581287861,
-0.030136633664369583,
-0.024150243028998375,
-0.03409583494067192,
-0.032825443893671036,
-0.00836210884153843,
0.01284053549170494,
0.009268469177186489,
0.03969627991318703,
0.0007579404045827687,
0.04636242240667343,
-0.02955271676182747,
-0.007323303259909153,
-0.03505607694387436,
-0.011565408669412136,
-0.046040721237659454,
-0.014556865207850933,
0.050597064197063446,
-0.009074248373508453,
-0.034416913986206055,
0.009059980511665344,
-0.014125233516097069,
-0.000645737920422107,
-0.0076045808382332325,
-0.008466853760182858,
0.011521035805344582,
0.018995242193341255,
0.005833243951201439,
0.017317786812782288,
-0.0067929597571492195,
0.008105996064841747,
-0.0014872122555971146,
0.0346764512360096,
0.025745701044797897,
0.003943841438740492,
0.022193653509020805,
-0.012070352211594582,
-0.02137846313416958,
0.0044015455059707165,
-0.010284323245286942,
0.02728530950844288,
0.023845961317420006,
0.06440316140651703,
0.02942465990781784,
-0.025461755692958832,
-0.030423561111092567,
-0.04527217149734497,
-0.006938667967915535,
0.008564978837966919,
0.014236428774893284,
0.03560034558176994,
0.02210412546992302,
-0.03614763915538788,
0.008938230574131012,
0.006471557542681694,
0.01087347511202097,
-0.03485241159796715,
-0.035752516239881516,
0.010759974829852581,
0.0416581928730011,
0.04266616329550743,
0.033207714557647705,
-0.03514518216252327,
-0.03237605467438698,
0.05436920374631882,
0.012837106361985207,
0.021699635311961174,
-0.05412130430340767,
-0.034568559378385544,
0.022502459585666656,
-0.026712724938988686,
0.011091252788901329,
-0.03250138834118843,
0.04475318267941475,
-0.049096401780843735,
-0.03963962197303772,
-0.025119567289948463,
0.011999807320535183,
0.034195080399513245,
-0.007659745868295431,
-0.03034382127225399,
-0.0015559110324829817,
-0.000745061261113733,
0.015834452584385872,
-0.05465998873114586,
-0.0054629091173410416,
0.036373235285282135,
-0.024358656257390976,
0.013552135787904263,
-0.016176730394363403,
-0.035217829048633575,
0.0316140279173851,
-0.005652070976793766,
-0.026952335610985756,
-0.015115553513169289,
-0.004762849770486355,
-0.039744626730680466,
0.03125070035457611,
-0.020312068983912468,
0.03523259609937668,
0.06695251911878586,
0.014000163413584232,
0.014235882088541985,
0.033958226442337036,
-0.008886699564754963,
-0.04732003062963486,
0.036752402782440186,
-0.03558441251516342,
-0.008861316367983818,
-0.01191173866391182,
-0.04607544466853142,
0.02362716943025589,
-0.025000616908073425,
-0.01909342221915722,
0.06965886801481247,
0.025053473189473152,
0.001220191246829927,
0.004697710741311312,
0.01693875715136528,
0.03437742218375206,
0.018447112292051315,
-0.026584075763821602,
-0.0009208358824253082,
-0.0073292795568704605,
-0.013865607790648937,
0.019996384158730507,
0.047800734639167786,
0.06035661697387695,
-0.0024152009282261133,
0.01697402261197567,
-0.014512676745653152,
0.012137697078287601,
0.06143658980727196,
-0.0062546380795538425,
-0.010225747711956501,
-0.01928817853331566,
0.032188694924116135,
-0.01482071541249752,
-0.011234198696911335,
0.029224181547760963,
-0.009127956815063953,
0.06632699072360992,
-0.017977293580770493,
0.048198066651821136,
-0.006015388295054436,
0.020842766389250755,
-0.028752632439136505,
0.005020109470933676,
-0.02509230561554432,
0.028654353693127632,
-0.032214000821113586,
-0.02117791771888733,
-0.020805103704333305,
0.010184315033257008,
0.02536012977361679,
-0.054022856056690216,
-0.009232096374034882,
-0.0013372560497373343,
-0.022511519491672516,
-0.009972979314625263,
0.030879858881235123,
-0.02370746247470379,
-0.06083187460899353,
0.02170960046350956,
0.013318531215190887,
0.011343740858137608,
-0.03134806454181671,
-0.046251069754362106,
-0.02551286108791828,
0.03215224668383598,
-0.0240207239985466,
-0.020672833546996117,
-0.0070266579277813435,
-0.013113756664097309,
-0.03995922580361366,
-0.033257219940423965
] |
<p>I'm revisiting the elementary algorithms of renormalization that are taught in a classroom setting and find that the procedure taught to students is as follows:</p>
<ol>
<li>Write down the bare Lagrangian: $\mathcal{L}_0$</li>
<li>Renormalize the field strengths: $\phi_0\rightarrow Z^{1/2}\phi_r$</li>
<li>Renormalize coupling constants: <em>e.g.</em> $Z^2\lambda_0\rightarrow Z_\lambda \mu^{2\epsilon}\lambda_R$</li>
<li>For perturbation theory rewrite $Z=1+\delta$, where $\delta$'s are counterterms.</li>
</ol>
<p>I have thought long and hard about steps 2 and 3 (especially in the context of operator renormalization), and have come to the following conclusions which I would like verified.</p>
<p>In <strong>step 3</strong>, the renormalization of coupling constants is actually the renormalization of the operator product multiplying the coupling constant. And, in <strong>step 2</strong>, when they renormalize the field strength, it is not the renormalization of a single operator; they are actually renormalizing another composite operator: the kinetic term $\partial_\mu\phi\,\partial^\mu\phi$. The renormalization of a single operator $\phi$ actually corresponds to tadpoles, the one-point function.</p>
<p>Am I interpreting this correctly?</p>
| 9,568 |
[
0.00709000276401639,
0.003933224827051163,
0.020358076319098473,
-0.002445030491799116,
0.020486915484070778,
0.02176470309495926,
0.013229124248027802,
-0.05114584043622017,
-0.00004138264193898067,
-0.018654610961675644,
0.035886116325855255,
0.012894682586193085,
0.07667271792888641,
0.0012124743079766631,
0.044639263302087784,
-0.008127679117023945,
0.02647191844880581,
-0.002673135371878743,
0.005801153369247913,
0.004549777135252953,
0.002790531376376748,
0.027541767805814743,
-0.015199092216789722,
0.0045852200128138065,
-0.004959504585713148,
-0.001992142293602228,
-0.004870277363806963,
0.06154653802514076,
-0.021058423444628716,
0.04813919961452484,
-0.009252655319869518,
-0.047667246311903,
0.04124261066317558,
-0.02042941190302372,
-0.001707339775748551,
0.027698226273059845,
-0.034141454845666885,
-0.03496351093053818,
-0.002571873366832733,
0.012908900156617165,
-0.04525976628065109,
-0.01124909520149231,
-0.0011615511029958725,
0.016733162105083466,
-0.032331038266420364,
0.012240144424140453,
-0.024855704978108406,
0.0003955448919441551,
0.0806746631860733,
-0.03205772116780281,
-0.00021006555471103638,
0.06286422908306122,
0.03502384573221207,
0.03583056852221489,
-0.031141290441155434,
0.01813567616045475,
0.054703641682863235,
0.03929292783141136,
0.009288501925766468,
-0.025884678587317467,
-0.012876134365797043,
-0.05586128309369087,
0.0036893205251544714,
0.020021604374051094,
-0.003599131479859352,
0.029224412515759468,
-0.020458629354834557,
0.006927957758307457,
0.029484441503882408,
-0.016400262713432312,
0.022851893678307533,
0.003807809203863144,
0.05200321972370148,
0.0016865934012457728,
0.008417146280407906,
0.0203325767070055,
0.002660498721525073,
-0.01218018215149641,
0.03946638107299805,
0.061778031289577484,
-0.017138469964265823,
0.0069918567314744,
0.04336247593164444,
0.05339858680963516,
0.001032288302667439,
-0.023733559995889664,
0.061129163950681686,
0.0022787374909967184,
-0.0068479073233902454,
0.03947991505265236,
0.010323958471417427,
-0.026409806683659554,
0.03437131270766258,
0.002794540487229824,
-0.04640719294548035,
0.04436635971069336,
-0.0021397718228399754,
0.027941588312387466,
0.004231482744216919,
0.020191941410303116,
-0.04000765457749367,
0.01987481117248535,
0.01435926090925932,
0.034120943397283554,
-0.011956542730331421,
-0.030167963355779648,
-0.0406133271753788,
-0.016797346994280815,
-0.03555125370621681,
-0.0365886464715004,
-0.07321487367153168,
-0.00931482296437025,
-0.03380275145173073,
0.0032290127128362656,
-0.018117111176252365,
-0.03049856424331665,
-0.04274338483810425,
-0.02873723953962326,
0.08284251391887665,
0.0600254200398922,
0.044711433351039886,
-0.026697224006056786,
0.0037409793585538864,
-0.04648793488740921,
-0.05605745315551758,
0.03817445784807205,
0.04935406520962715,
-0.02874927408993244,
-0.06263817846775055,
0.01751362718641758,
0.042345911264419556,
0.04497514292597771,
-0.012372312135994434,
0.02967706136405468,
0.024080010131001472,
-0.01016880664974451,
-0.05282925069332123,
-0.07283638417720795,
0.025402486324310303,
-0.01821836642920971,
-0.029689794406294823,
-0.0704762265086174,
-0.04422132298350334,
0.024429116398096085,
0.08305710554122925,
-0.0064076827839016914,
0.00972101092338562,
-0.002632555551826954,
0.024058064445853233,
0.013412087224423885,
-0.021406471729278564,
-0.008654504083096981,
-0.0168569628149271,
-0.036238931119441986,
-0.038923297077417374,
-0.06592242419719696,
0.024163395166397095,
0.0013946708058938384,
-0.020110802724957466,
-0.010224277153611183,
0.11860427260398865,
-0.04888733848929405,
0.006695231422781944,
-0.0008675094577483833,
-0.0017384345410391688,
-0.020586976781487465,
0.06431218236684799,
0.02952943556010723,
0.03245685622096062,
0.033389367163181305,
0.0017703884514048696,
-0.005465049762278795,
0.004512918181717396,
0.007459421642124653,
0.0379197932779789,
-0.024271471425890923,
-0.02998584881424904,
-0.03247041255235672,
-0.010492194443941116,
-0.004388007335364819,
-0.03723696619272232,
-0.04591013118624687,
-0.03361988440155983,
0.015017676167190075,
-0.038636304438114166,
0.03568274900317192,
-0.006456398870795965,
0.022856511175632477,
0.009284880943596363,
-0.06543628126382828,
-0.012521679513156414,
-0.07594853639602661,
0.001158126280643046,
0.02804221771657467,
-0.007963543757796288,
0.02798805758357048,
-0.02597098983824253,
0.013157973997294903,
-0.00566840311512351,
-0.05596029385924339,
-0.020215727388858795,
0.021989166736602783,
0.04104537516832352,
0.037362240254879,
0.031997211277484894,
0.03958183526992798,
0.04142051935195923,
0.008501047268509865,
0.03993930295109749,
-0.015274721197783947,
-0.007220751605927944,
0.0042676725424826145,
-0.02160157449543476,
0.020419228821992874,
0.004662500694394112,
-0.012663002125918865,
0.004242779687047005,
-0.024863827973604202,
0.001079015783034265,
0.04151560366153717,
-0.07178264856338501,
0.0559488870203495,
0.04015417397022247,
0.026712022721767426,
0.009815102443099022,
0.03754337131977081,
-0.015265374444425106,
0.0016934981103986502,
-0.012921037152409554,
0.003301147138699889,
-0.010651538148522377,
-0.031663015484809875,
0.07054317742586136,
0.027487892657518387,
-0.04134874790906906,
0.02708897367119789,
0.024088554084300995,
0.02019314467906952,
0.04098215326666832,
0.0561835840344429,
-0.027372652664780617,
-0.03186997026205063,
0.034555014222860336,
0.023993385955691338,
0.007661625277251005,
0.017704861238598824,
0.004125641193240881,
0.01896720752120018,
0.014337045140564442,
-0.014334508217871189,
-0.00875193439424038,
0.022277558222413063,
-0.020288044586777687,
-0.0008721628692001104,
-0.016836488619446754,
-0.027714360505342484,
0.028101610019803047,
-0.022915450856089592,
0.048228200525045395,
0.035519298166036606,
-0.0187012180685997,
0.001068674959242344,
-0.031240392476320267,
-0.010243584401905537,
0.020351750776171684,
-0.017297467216849327,
-0.04119343310594559,
0.0019676832016557455,
0.004266148898750544,
-0.04246731847524643,
-0.016522061079740524,
-0.013789156451821327,
0.0025960560888051987,
0.0031515464652329683,
-0.006764056161046028,
0.036317113786935806,
-0.012025263160467148,
0.013915002346038818,
-0.029631102457642555,
-0.018713776022195816,
0.03247654065489769,
0.004418244585394859,
0.040998946875333786,
0.06013679504394531,
-0.03807110711932182,
-0.024114256724715233,
-0.07245932519435883,
-0.03895583376288414,
0.01999199576675892,
0.009973322972655296,
0.026057397946715355,
-0.02235523797571659,
-0.0021184231154620647,
-0.05218140780925751,
-0.04179588705301285,
-0.006514072883874178,
0.0127864396199584,
0.009318984113633633,
0.014988028444349766,
0.09106912463903427,
0.008893725462257862,
-0.05514673516154289,
0.005742005538195372,
0.01068936102092266,
-0.016920004040002823,
-0.0022514143493026495,
0.011156397871673107,
0.020213184878230095,
-0.02556731551885605,
0.012401479296386242,
0.06004754826426506,
-0.015163668431341648,
0.010173932649195194,
-0.04516385868191719,
-0.018982023000717163,
-0.006189703941345215,
0.021519474685192108,
0.048131175339221954,
0.008865251205861568,
-0.03795834258198738,
0.07078231871128082,
0.01875436119735241,
-0.050996918231248856,
-0.03234810754656792,
0.028617503121495247,
-0.012772544287145138,
-0.0323779322206974,
0.001845114747993648,
0.003975067753344774,
-0.03772677108645439,
0.031112033873796463,
0.0004014454607386142,
0.0204275194555521,
0.04978758469223976,
0.03100632131099701,
-0.002764735370874405,
-0.0050784084014594555,
-0.006008621770888567,
-0.05140062794089317,
0.05997326970100403,
-0.04069322347640991,
-0.004401012323796749,
0.016688242554664612,
0.00008704498031875119,
0.013603512197732925,
-0.00014961000124458224,
-0.051548346877098083,
0.06293974816799164,
0.040481287986040115,
0.001167995622381568,
-0.029349979013204575,
0.03352903202176094,
0.021091172471642494,
-0.05657299607992172,
0.005071321036666632,
0.0004649560432881117,
-0.010830871760845184,
-0.06838829815387726,
0.03497506305575371,
-0.0019420509925112128,
0.06497067213058472,
-0.018923241645097733,
-0.0427461601793766,
-0.012826965190470219,
0.00757479015737772,
0.029014894738793373,
-0.03274298459291458,
-0.006834978237748146,
0.03925827518105507,
0.034614626318216324,
-0.004319800995290279,
-0.05490010604262352,
-0.04197002574801445,
0.019959770143032074,
-0.07648065686225891,
-0.004385034553706646,
-0.02991853654384613,
0.05203285813331604,
-0.03045882284641266,
0.05103163793683052,
-0.017080070450901985,
-0.012043772265315056,
0.03396514430642128,
0.021207790821790695,
-0.09223148971796036,
0.026430003345012665,
-0.004831317812204361,
-0.04416005685925484,
0.019590601325035095,
0.00776203628629446,
0.013327046297490597,
-0.01098168920725584,
-0.036591704934835434,
-0.03675960376858711,
-0.03300974518060684,
-0.034794580191373825,
0.03213748708367348,
-0.043698251247406006,
-0.030818210914731026,
-0.014802929945290089,
0.019623402506113052,
0.04663775488734245,
-0.02266523241996765,
-0.02139876037836075,
0.006800270173698664,
-0.02463027834892273,
-0.007648116908967495,
-0.03662664443254471,
0.026375416666269302,
0.04775400832295418,
0.05292285233736038,
0.05686634033918381,
0.040595974773168564,
-0.029764119535684586,
0.029109477996826172,
0.04039957374334335,
0.06404585391283035,
0.011347685940563679,
0.0032289065420627594,
-0.023022182285785675,
-0.03667580708861351,
-0.03987663984298706,
0.034812405705451965,
0.055538360029459,
0.006178232375532389,
-0.011663922108709812,
0.05617045238614082,
0.04923752322793007,
-0.022420402616262436,
0.02977795898914337,
0.04524530470371246,
-0.0232162494212389,
-0.038050875067710876,
-0.03470223397016525,
0.039054907858371735,
0.02761133201420307,
-0.011728170327842236,
-0.0184775423258543,
0.00047021888894960284,
-0.0013053723378106952,
-0.017047403380274773,
0.059619009494781494,
0.025414470583200455,
-0.04635399580001831,
0.021934567019343376,
-0.011153606697916985,
0.02947532758116722,
-0.026366451755166054,
-0.013560780324041843,
0.004743626341223717,
0.056975845247507095,
0.03605501353740692,
0.007802302483469248,
-0.02727413736283779,
-0.0346093587577343,
0.0009413767256774008,
0.010696051642298698,
0.03849124535918236,
0.0061335996724665165,
0.022169996052980423,
-0.018791204318404198,
-0.03704463690519333,
0.05503853037953377,
-0.013098138384521008,
0.034643933176994324,
-0.010336370207369328,
-0.010831441730260849,
0.0019999449141323566,
-0.036417607218027115,
-0.042541176080703735,
0.04374944418668747,
-0.009321173653006554,
0.018852747976779938,
-0.04916322976350784,
0.022962873801589012,
-0.031306907534599304,
0.02876000665128231,
-0.01168710459023714,
0.05307465046644211,
0.012824193574488163,
-0.011895907111465931,
0.04610623046755791,
-0.019187387079000473,
0.008926406502723694,
-0.0846702978014946,
0.008949666284024715,
0.0036355324555188417,
-0.006894911173731089,
0.047281987965106964,
-0.03057790733873844,
-0.045014768838882446,
0.021542707458138466,
0.03623603656888008,
-0.03084252029657364,
0.003056058194488287,
-0.05753498896956444,
0.051040880382061005,
0.03083488903939724,
0.0019116749754175544,
0.08210793882608414,
0.05617523193359375,
-0.025919223204255104,
0.004122662357985973,
-0.007532299961894751,
-0.021859005093574524,
0.04333704337477684,
0.047586698085069656,
-0.028714660555124283,
0.022003930062055588,
-0.026384299620985985,
0.04687515273690224,
-0.01347227580845356,
0.015492028556764126,
-0.04104888066649437,
-0.01925947330892086,
-0.010359060950577259,
0.007605157792568207,
-0.057515449821949005,
-0.0534471794962883,
0.033611148595809937,
0.026075128465890884,
-0.014935052953660488,
-0.028355127200484276,
-0.006653108634054661,
-0.0018496604170650244,
0.0043543921783566475,
0.019818872213363647,
-0.009066634811460972,
0.034076027572155,
-0.027490021660923958,
0.0009135442669503391,
0.027167273685336113,
-0.0687175765633583,
0.03561674803495407,
-0.01654803194105625,
0.03299738094210625,
-0.026728453114628792,
-0.028724102303385735,
-0.049078524112701416,
-0.007407877128571272,
0.015595963224768639,
-0.0028498112224042416,
0.004302310757339001,
-0.006567283999174833,
0.03452955558896065,
-0.01135173998773098,
-0.047929827123880386,
-0.03142473101615906,
-0.014226828701794147,
0.026820354163646698,
-0.008449011482298374,
0.015420147217810154,
-0.015142950229346752,
-0.025343962013721466,
-0.044756025075912476,
0.007171612232923508,
0.05202912539243698,
-0.04922565445303917,
0.004022387322038412,
0.02726803347468376,
0.04635705426335335,
0.04585207998752594,
0.007639216259121895,
-0.0020872182212769985,
0.003114726161584258,
-0.00758685078471899,
-0.012751370668411255,
0.035027433186769485,
0.05413790047168732,
-0.009286770597100258,
-0.04616525024175644,
-0.00854635238647461,
0.0016435290453955531,
0.028055381029844284,
-0.012505872175097466,
-0.0008627706556580961,
0.0325990691781044,
-0.01046904269605875,
-0.00316350138746202,
-0.026357557624578476,
-0.004037201404571533,
-0.018811382353305817,
0.04240082949399948,
0.019177572801709175,
0.016871850937604904,
0.002319426741451025,
0.0028406872879713774,
0.027698377147316933,
0.026926454156637192,
0.010029167868196964,
-0.007971850223839283,
0.04209401085972786,
-0.02120876871049404,
-0.0204355139285326,
0.001525125582702458,
-0.04047961160540581,
-0.012245002202689648,
0.024204188957810402,
0.04207883030176163,
0.032979290932416916,
0.01621767319738865,
-0.02140885218977928,
0.0122825987637043,
-0.01836482621729374,
0.02662641927599907,
0.04389313980937004,
-0.01295954268425703,
0.01706434041261673,
0.015342212282121181,
-0.03241248056292534,
0.016428697854280472,
-0.004828761797398329,
-0.02641267329454422,
0.0070684319362044334,
-0.024854818359017372,
0.0550839938223362,
-0.06558343023061752,
-0.00886279996484518,
0.019536523148417473,
0.010776563547551632,
-0.017231466248631477,
-0.010364845395088196,
0.013792590238153934,
0.02801651507616043,
-0.010431163012981415,
-0.01990092545747757,
-0.0012950177770107985,
0.030215300619602203,
-0.004334097262471914,
0.04804190248250961,
0.0016169421141967177,
0.013228537514805794,
0.051938217133283615,
-0.011305443942546844,
0.03805655613541603,
0.006052081473171711,
-0.01942436397075653,
-0.06971686333417892,
-0.0097350487485528,
-0.030800573527812958,
0.010733308270573616,
0.018733156844973564,
-0.009286523796617985,
0.07268832623958588,
0.013988267630338669,
0.033295512199401855,
-0.012834647670388222,
-0.03348548337817192,
-0.014780213125050068,
-0.024520162492990494,
-0.040228527039289474,
0.057850971817970276,
-0.026289992034435272,
-0.08644252270460129,
0.022042496129870415,
-0.011872918345034122,
0.04446946084499359,
0.009690025821328163,
0.03128322586417198,
-0.041176505386829376,
0.05387912318110466,
-0.00445949099957943,
0.002213364699855447,
-0.0007125159609131515,
-0.026712611317634583,
0.14631696045398712,
0.08522676676511765,
0.0003650160215329379,
-0.08184316009283066,
0.03420460596680641,
-0.02955116331577301,
0.0023136346135288477,
-0.025016676634550095,
0.040423519909381866,
-0.01453467644751072,
0.000048373880417784676,
-0.005937382113188505,
0.07050318270921707,
0.013647036626935005,
-0.021032512187957764,
0.03131286799907684,
-0.024309247732162476,
-0.05589054897427559,
0.011917310766875744,
0.03388303890824318,
0.005976070649921894,
-0.02771941013634205,
-0.027082519605755806,
-0.005619786214083433,
-0.003928816877305508,
0.03307952359318733,
0.007505098357796669,
-0.03151845559477806,
0.017439380288124084,
-0.025219766423106194,
-0.026796340942382812,
-0.005707525182515383,
0.007758770603686571,
0.00564760435372591,
0.016239041462540627,
0.02366247959434986,
0.027610179036855698,
-0.026833098381757736,
0.05136445164680481,
0.04678996652364731,
0.016162598505616188,
0.027335934340953827,
0.019821226596832275,
0.019007625058293343,
-0.006544196512550116,
-0.036756739020347595,
-0.0003855536342598498,
0.06242384761571884,
0.001476956531405449,
0.012444817461073399,
0.012540796771645546,
-0.024862810969352722,
0.01700015738606453,
-0.029669178649783134,
-0.022869352251291275,
0.012971941381692886,
0.033749617636203766,
-0.03734660521149635,
0.041131481528282166,
-0.04761487618088722,
0.008598603308200836,
-0.03519965335726738,
0.030100656673312187,
-0.010609909892082214,
-0.03441423922777176,
-0.031051037833094597,
-0.03743387386202812,
0.0074900793842971325,
0.004500820301473141,
-0.027465706691145897,
-0.0494239442050457,
-0.014433294534683228,
-0.03709030896425247,
-0.0033444007858633995,
-0.01403028704226017,
-0.014293530024588108,
0.0616525374352932,
-0.009394051507115364,
0.024957429617643356,
-0.004765153396874666,
-0.05785592645406723,
0.03161270543932915,
-0.0013933751033619046,
-0.001706938841380179,
0.011768292635679245,
-0.05337109416723251,
-0.025824537500739098,
0.044344138354063034,
0.006495549343526363,
-0.03311839699745178,
-0.006758596748113632,
0.01876024715602398,
0.017694681882858276,
-0.040349289774894714,
-0.03852177411317825,
-0.029970867559313774,
-0.01447075791656971,
-0.04178789258003235,
-0.03824843466281891,
0.005780259612947702,
-0.010671673342585564,
0.019948281347751617,
0.005451901350170374,
0.02802778221666813,
0.001788830035366118,
0.0052635506726801395,
0.015551084652543068,
-0.011529280804097652,
0.011809004470705986,
0.01785500906407833,
0.0032817211467772722,
-0.050501808524131775,
-0.039711084216833115,
-0.0065269796177744865,
-0.004863548092544079,
-0.0017748066456988454,
-0.007114435080438852,
-0.057187821716070175,
-0.040898118168115616,
-0.05172453075647354,
0.003525859210640192,
-0.036140669137239456,
-0.0155613012611866,
-0.03472958505153656,
0.020693790167570114,
0.005341840907931328,
-0.00398290017619729,
0.017057953402400017,
0.042648669332265854,
0.004986361134797335,
-0.019113168120384216,
0.025890866294503212,
0.0018813393544405699,
-0.0021002995781600475,
-0.027262572199106216,
0.012125796638429165,
0.015529398806393147,
0.0030369835440069437,
-0.008669129572808743,
-0.04677733778953552,
0.026872729882597923,
-0.035463545471429825,
-0.05906287953257561,
0.01942368969321251,
-0.012096866965293884,
0.013576429337263107,
0.00160317774862051,
-0.019781315699219704,
-0.04834643378853798,
0.006098206155002117,
-0.022699207067489624,
-0.00006868643686175346,
-0.03875615447759628,
-0.01774466224014759,
-0.001882712123915553,
-0.03540606051683426,
0.030785301700234413,
0.03074348345398903,
0.021791620180010796,
0.03028404898941517,
0.0007832119008526206,
-0.036787934601306915,
-0.0060902857221663,
-0.011423931457102299,
-0.03033270128071308,
0.04946251958608627,
-0.003248827066272497,
0.03871924430131912,
-0.011977397836744785,
0.050564173609018326,
-0.021875102072954178,
0.012873717583715916,
-0.0020721834152936935,
0.015505649149417877,
-0.08395228534936905,
-0.02540242299437523,
-0.004516212269663811,
-0.005639031995087862,
-0.013685503974556923,
-0.05533067137002945,
0.037359293550252914,
0.013701795600354671,
-0.037796057760715485,
-0.006112349219620228,
-0.02083548717200756,
-0.012019982561469078,
-0.03041406348347664,
-0.008750617504119873,
-0.004736708011478186,
0.006576151587069035,
0.02550007961690426,
0.03278382867574692,
-0.010676626116037369,
0.005958519410341978,
0.002338468562811613,
-0.0088206697255373,
-0.025342639535665512,
0.0022775086108595133,
0.0018467518966645002,
-0.03791667893528938,
0.060508400201797485,
0.005175201687961817,
-0.018443293869495392,
0.00891144946217537,
-0.006887272000312805,
-0.010065917856991291,
-0.00023019322543404996,
0.007523251697421074,
0.007916971109807491,
0.0027580023743212223,
0.03598877415060997,
-0.02080119587481022,
-0.00743072247132659,
0.006340184714645147,
0.03338715434074402,
0.04785630479454994,
-0.011753213591873646,
-0.0002636442077346146,
0.04480304569005966,
-0.006990241352468729,
-0.022448720410466194,
0.06310969591140747,
-0.027158398181200027,
-0.017338696867227554,
-0.005659953225404024,
0.021379606798291206,
-0.008214864879846573,
-0.0035711699165403843,
0.036905527114868164,
-0.03458068147301674,
-0.004074394702911377,
0.031031275168061256,
0.04237246885895729,
-0.013234158046543598,
0.017615925520658493,
0.018455086275935173,
-0.0022595615591853857,
0.010552802123129368,
-0.007277281489223242,
0.011066775768995285,
-0.050789546221494675,
-0.01255441177636385,
0.016582760959863663,
-0.007186925038695335,
0.00261125061661005,
-0.038625359535217285,
-0.03912137821316719,
0.004776544403284788,
-0.010486895218491554,
0.020890509709715843,
-0.053574927151203156,
-0.006091285962611437,
-0.0028478712774813175,
-0.029485730454325676,
0.002426191931590438,
0.040205445140600204,
-0.009018023498356342,
-0.018895667046308517,
-0.027889441698789597,
-0.004772616550326347,
0.016690609976649284,
0.04074550047516823,
0.030350277200341225,
-0.03766912966966629,
-0.007845679298043251,
0.04974156245589256,
0.017191337421536446,
-0.03374382108449936,
-0.010241004638373852,
-0.0015265446854755282,
0.0040209596045315266,
-0.0350429005920887,
0.0026818951591849327,
0.0033147530630230904,
0.06712796539068222,
0.03784617409110069,
0.0076077841222286224,
0.010493247769773006,
0.010596917010843754,
-0.010911526158452034,
0.029924463480710983,
-0.03671706095337868,
-0.02713925950229168,
0.064786896109581,
0.005789839196950197,
0.022005220875144005,
0.03462740033864975,
-0.01966058649122715,
-0.028745297342538834,
0.023354142904281616,
-0.02451399900019169,
-0.024320241063833237,
0.00404655234888196,
-0.0058384910225868225,
0.001833236776292324,
-0.055432289838790894,
-0.026103420183062553,
0.037466052919626236,
-0.027561603114008904,
-0.030339315533638,
0.046291645616292953,
0.028515949845314026,
0.004440467804670334,
0.015383217483758926,
-0.016033219173550606,
0.050564754754304886,
0.025517389178276062,
-0.011389648541808128,
0.048185043036937714,
0.042290568351745605,
0.01687563955783844,
0.014417815022170544,
0.020143602043390274,
-0.03508738800883293,
0.035668522119522095,
0.00048597107524983585,
0.008722248487174511,
-0.01617083139717579,
-0.007665176875889301,
0.025775913149118423,
-0.04958204925060272,
-0.019583923742175102,
-0.0024486638139933348,
-0.0033742841333150864,
0.07512161135673523,
-0.0585586354136467,
0.011647563427686691,
-0.033774733543395996,
0.001374658546410501,
0.017115239053964615,
0.027803977951407433,
0.024675287306308746,
0.051876697689294815,
-0.02357529290020466,
0.019812822341918945,
-0.02708262950181961,
-0.004341782536357641,
0.0025899941101670265,
-0.044569794088602066,
-0.010397454723715782,
0.015195799991488457,
-0.012837565504014492,
-0.001525812316685915,
-0.026457231491804123,
-0.020878151059150696,
-0.04364226013422012,
0.024452820420265198,
0.009403511881828308,
0.00013419617607723922,
-0.0018542124889791012,
-0.05315197631716728,
-0.01467706449329853,
0.06561804562807083,
-0.027655890211462975,
-0.02382815256714821,
-0.006580118089914322,
0.002962468657642603,
-0.029232952743768692,
-0.007570615503937006
] |
<p>Can some one please explain to me why electricity flowing though a copper coil generates a magnetic field or where I could possibly find that information? Are there other materials that produce a magnetic field when a current is run through them in a different shape? Thanks!</p>
| 9,569 |
[
-0.05328163877129555,
-0.014989328570663929,
-0.0019335270626470447,
-0.05529054254293442,
0.017560793086886406,
0.014484429731965065,
-0.029194284230470657,
-0.020761432126164436,
0.000562670233193785,
-0.04906998947262764,
0.03213176876306534,
0.03475411608815193,
0.0587814562022686,
0.021608976647257805,
0.018578501418232918,
-0.0005792925367131829,
0.03078223578631878,
-0.01589573360979557,
-0.01332116313278675,
-0.018943674862384796,
0.0030352245084941387,
0.002922228304669261,
-0.03484700992703438,
0.026710323989391327,
-0.009016613475978374,
0.030735991895198822,
0.052162859588861465,
0.037223394960165024,
0.053457241505384445,
0.014535174705088139,
0.02018241584300995,
-0.04829809069633484,
-0.016009444370865822,
0.007453261408954859,
0.03367013856768608,
-0.017209403216838837,
-0.006941671017557383,
-0.03682319447398186,
-0.0027270964346826077,
0.020005429163575172,
-0.01511032972484827,
-0.01846158318221569,
0.00623045489192009,
0.0687348023056984,
-0.01602468080818653,
-0.005734988488256931,
0.0014245330821722746,
-0.047268159687519073,
0.017248980700969696,
-0.07535713911056519,
0.055015917867422104,
-0.04213552176952362,
0.033498287200927734,
0.014782611280679703,
0.015226875431835651,
0.009923461824655533,
0.0824294462800026,
0.04195990040898323,
0.007955128327012062,
-0.06048886477947235,
-0.017435071989893913,
-0.017919374629855156,
-0.02906370535492897,
-0.06532866507768631,
-0.04969791695475578,
0.0554007962346077,
-0.020595211535692215,
-0.02777169831097126,
0.037873774766922,
0.0014759503537788987,
0.033026035875082016,
0.014586602337658405,
0.0075142341665923595,
-0.004331995267421007,
-0.018032774329185486,
-0.023693475872278214,
0.011426049284636974,
-0.00004742649616673589,
0.041022252291440964,
0.029595037922263145,
-0.026416806504130363,
0.013429032638669014,
0.01645294763147831,
0.013473965227603912,
0.019865965470671654,
0.029208824038505554,
0.06388919800519943,
-0.007375430315732956,
0.02904769405722618,
0.011529491282999516,
0.01202127430588007,
0.0030806632712483406,
0.03494994714856148,
-0.02204323746263981,
-0.020575912669301033,
0.021532617509365082,
-0.003289266722276807,
0.055498577654361725,
0.023573923856019974,
-0.013185358606278896,
0.028329085558652878,
0.005168029107153416,
0.03423504903912544,
0.0672949030995369,
0.036032047122716904,
-0.030828826129436493,
-0.003233768278732896,
0.020947134122252464,
0.0011967342579737306,
0.022710705175995827,
-0.005333221051841974,
0.015157320536673069,
0.01859578862786293,
-0.01667345128953457,
-0.00506336335092783,
-0.017706429585814476,
0.02756326273083687,
-0.02987612411379814,
0.018610283732414246,
0.08648122847080231,
0.0013924211962148547,
-0.05002099648118019,
0.044303927570581436,
-0.01697620190680027,
-0.057959672063589096,
-0.013001056388020515,
0.022668736055493355,
0.012870736420154572,
-0.012850582599639893,
0.04253707081079483,
-0.02122919075191021,
-0.037349432706832886,
-0.01752712018787861,
0.012098755687475204,
0.05398687347769737,
0.004060696344822645,
-0.12719972431659698,
-0.08059336990118027,
0.019000504165887833,
-0.031770285218954086,
-0.012049403972923756,
-0.06877271831035614,
0.008800601586699486,
0.030892977491021156,
0.06593703478574753,
-0.016568036749958992,
-0.021460097283124924,
-0.006529712583869696,
0.04944515600800514,
-0.0022910337429493666,
-0.012555635534226894,
-0.03630368411540985,
0.023273762315511703,
-0.026441870257258415,
0.00760324252769351,
-0.03597874194383621,
0.017128216102719307,
0.0028924578800797462,
-0.008572760969400406,
-0.02673872746527195,
0.053996529430150986,
-0.030679859220981598,
0.003599097253754735,
0.014639471657574177,
-0.019950775429606438,
0.0003554187132976949,
0.08679760247468948,
0.006136198062449694,
0.01285320334136486,
0.041428398340940475,
0.0004639798717107624,
0.031040923669934273,
0.045776862651109695,
0.04380562901496887,
0.022052956745028496,
-0.06677232682704926,
-0.03374842181801796,
0.011257948353886604,
0.055435068905353546,
-0.016691163182258606,
-0.06325552612543106,
-0.006041782442480326,
0.02415771223604679,
0.0022835610434412956,
0.0029366621747612953,
0.05914199724793434,
-0.009629120118916035,
-0.040683288127183914,
-0.005488638300448656,
-0.05984026938676834,
-0.004916592035442591,
-0.01873970590531826,
0.040434613823890686,
-0.03995078429579735,
-0.040907979011535645,
0.0156315378844738,
0.020163634791970253,
0.03219086304306984,
-0.041876617819070816,
-0.029987825080752373,
-0.005892044864594936,
0.02027793787419796,
-0.00753027806058526,
-0.015671933069825172,
0.0038264067843556404,
0.023321375250816345,
0.0006985724321566522,
-0.005328234750777483,
0.05397798866033554,
-0.0199816282838583,
-0.01559378020465374,
-0.007917176000773907,
-0.03440257906913757,
0.006648941896855831,
-0.0002485969744157046,
-0.017733048647642136,
0.012820436619222164,
0.0028416807763278484,
0.010679926723241806,
0.05573910102248192,
0.00272592855617404,
0.08179869502782822,
0.02440384216606617,
0.013973788358271122,
0.004096112214028835,
0.032678261399269104,
-0.00843061413615942,
-0.019477246329188347,
-0.019840966910123825,
-0.03673360124230385,
-0.05851024016737938,
0.032662298530340195,
0.046915289014577866,
0.02086113765835762,
-0.06143231689929962,
0.007585523650050163,
-0.01659575290977955,
0.04314897581934929,
0.024251360446214676,
0.038057856261730194,
-0.0279204361140728,
-0.04228958487510681,
-0.006928025279194117,
0.018535973504185677,
-0.015001228079199791,
0.014825547114014626,
0.04092700406908989,
0.028533179312944412,
0.0160825178027153,
0.023627787828445435,
-0.048734888434410095,
0.07917546480894089,
-0.03635492920875549,
-0.00439079524949193,
0.006216181442141533,
-0.05297263339161873,
0.03408869355916977,
-0.048500485718250275,
0.020391065627336502,
-0.01332914363592863,
0.0037341041024774313,
0.01685551181435585,
-0.0006150623667053878,
-0.01333193201571703,
0.006027075462043285,
-0.006280166562646627,
-0.019974619150161743,
-0.011445184238255024,
0.026475567370653152,
-0.035327184945344925,
-0.00011317581811454147,
0.021382207050919533,
-0.016284724697470665,
-0.028987104073166847,
0.009481131099164486,
0.01946178264915943,
0.012494117021560669,
0.03916051983833313,
-0.011845665983855724,
-0.039825815707445145,
-0.034618228673934937,
-0.03256189450621605,
0.011814868077635765,
-0.009875742718577385,
-0.04915151372551918,
0.03506491333246231,
-0.014449979178607464,
-0.02079513855278492,
0.047425780445337296,
0.012706962414085865,
0.00835348293185234,
0.02364843711256981,
-0.0064177182503044605,
-0.050353385508060455,
0.012850511819124222,
-0.02374812215566635,
0.02878842130303383,
-0.006025591865181923,
0.0017217446584254503,
0.03623654693365097,
-0.013320407830178738,
-0.015145830810070038,
0.038821540772914886,
-0.04542090743780136,
-0.0197224710136652,
0.008819909766316414,
-0.0020872289314866066,
0.029006319120526314,
-0.019058560952544212,
0.03951624408364296,
0.0038491892628371716,
-0.06607011705636978,
-0.002129080006852746,
-0.0009145705262199044,
-0.022026007995009422,
-0.002987414365634322,
-0.025531191378831863,
0.026923323050141335,
-0.02016930840909481,
-0.04816991835832596,
0.05795060098171234,
0.029923954978585243,
-0.07612815499305725,
-0.02439361810684204,
-0.037035297602415085,
-0.01785798743367195,
-0.07533369958400726,
0.023880142718553543,
0.068483367562294,
-0.02605496533215046,
0.02278820052742958,
0.030335213989019394,
0.01205842662602663,
0.0002596247650217265,
-0.004369613714516163,
-0.004165437538176775,
0.019418125972151756,
-0.0013105031102895737,
-0.02188168652355671,
0.04444827884435654,
-0.0038693516980856657,
-0.05729641392827034,
0.0035716805141419172,
0.005094396416097879,
0.0497368723154068,
0.021876756101846695,
-0.021275222301483154,
0.034896474331617355,
-0.012252015061676502,
0.004273899830877781,
-0.0627295970916748,
0.03921851888298988,
-0.03021952323615551,
0.006081555504351854,
-0.00865937676280737,
0.025327453389763832,
0.0049308473244309425,
-0.021653005853295326,
0.002038490492850542,
0.03488592430949211,
-0.0021075045224279165,
-0.044121790677309036,
-0.03165958821773529,
-0.04496303200721741,
-0.003658440662547946,
0.029481805860996246,
-0.016357576474547386,
-0.0011390846921131015,
0.050338756293058395,
0.039804574102163315,
0.04296395927667618,
0.0032138351816684008,
-0.030277281999588013,
-0.0022141251247376204,
-0.054769814014434814,
0.005684285424649715,
-0.007392663974314928,
0.02707020193338394,
-0.013326994143426418,
0.07731664180755615,
0.03642187640070915,
-0.008132719434797764,
0.01119406707584858,
-0.02345150150358677,
-0.08611233532428741,
0.04552524909377098,
-0.038707632571458817,
0.007848764769732952,
-0.026171032339334488,
-0.02244848944246769,
-0.0029637205880135298,
-0.0014147169422358274,
-0.021853994578123093,
-0.0013742605224251747,
-0.04249998554587364,
-0.06687643378973007,
0.008987539447844028,
0.008430537767708302,
-0.039517201483249664,
-0.02775433100759983,
0.049104221165180206,
0.017845993861556053,
-0.020304447039961815,
0.011362051591277122,
-0.014595131389796734,
-0.01558675616979599,
0.009112445637583733,
0.002104723360389471,
-0.00298451934941113,
0.00947500765323639,
0.023257378488779068,
0.03360074386000633,
-0.048118866980075836,
-0.038651783019304276,
0.0007602886762470007,
0.016665607690811157,
0.07268821448087692,
0.023064246401190758,
0.008975578472018242,
-0.047741517424583435,
-0.05894055217504501,
-0.0266120582818985,
-0.01955089531838894,
0.04740973934531212,
0.008669554255902767,
0.037189893424510956,
0.016690732911229134,
0.0008067458402365446,
-0.025366540998220444,
0.02008715644478798,
0.04148932918906212,
0.014102725312113762,
-0.026229990646243095,
-0.04594322666525841,
-0.009075954556465149,
-0.04707574471831322,
-0.027336953207850456,
-0.0014812690205872059,
-0.02061961218714714,
-0.020775673910975456,
0.005365514662116766,
0.024595461785793304,
-0.020431917160749435,
0.008824044838547707,
-0.015372089110314846,
0.019345231354236603,
0.028301579877734184,
0.00044431176502257586,
-0.01800764538347721,
0.024761365726590157,
0.02449975721538067,
0.06200399622321129,
0.01858438178896904,
-0.04969986900687218,
-0.09127996116876602,
-0.0036512534134089947,
0.04360669106245041,
0.041330572217702866,
-0.037209879606962204,
-0.020222008228302002,
-0.04250932112336159,
0.015278114005923271,
0.052471425384283066,
-0.02784896269440651,
0.03418978676199913,
-0.029492437839508057,
-0.012511778622865677,
-0.02717718668282032,
-0.002122282749041915,
-0.02358129248023033,
0.04543616622686386,
-0.0031443906482309103,
0.054401546716690063,
-0.03897310420870781,
-0.007648288272321224,
0.011466392315924168,
0.021043945103883743,
0.0463709756731987,
0.021711602807044983,
0.011709772981703281,
0.037371277809143066,
0.008156822994351387,
0.03687916323542595,
-0.016079507768154144,
-0.0736500471830368,
0.006230365484952927,
-0.007450126577168703,
-0.0335315577685833,
0.0506163164973259,
0.0005409090081229806,
-0.05057628080248833,
-0.01442793756723404,
-0.009762352332472801,
0.030820472165942192,
-0.01358151063323021,
-0.028757160529494286,
0.02368423342704773,
0.01698988862335682,
-0.0014600694412365556,
0.054005272686481476,
0.01938265934586525,
-0.017766600474715233,
-0.007932372391223907,
-0.002541180234402418,
0.062258753925561905,
-0.005461798515170813,
-0.00549447862431407,
-0.014355414547026157,
0.02138395607471466,
-0.013918658718466759,
0.06266846507787704,
-0.037301503121852875,
0.004681417718529701,
-0.0302343238145113,
-0.009406396187841892,
-0.015486021526157856,
0.017315851524472237,
0.016926342621445656,
-0.033454496413469315,
0.0020626415498554707,
0.00198750919662416,
0.010235540568828583,
-0.03170143812894821,
0.022833170369267464,
-0.010375362820923328,
0.011314833536744118,
0.010354144498705864,
-0.010978998616337776,
-0.01988588459789753,
-0.042103320360183716,
-0.0024827413726598024,
0.02734842710196972,
-0.04856066405773163,
0.05728362873196602,
-0.02389523759484291,
-0.008304119110107422,
-0.0006624478846788406,
-0.09353455156087875,
-0.019184084609150887,
0.02964586764574051,
-0.013632048852741718,
0.04690540209412575,
-0.04354272037744522,
0.030411208048462868,
-0.0018428137991577387,
-0.00002988773849210702,
-0.075703926384449,
-0.08584300428628922,
0.013478082604706287,
0.021012306213378906,
-0.0023042026441544294,
0.012138561345636845,
-0.0032452053856104612,
-0.021068144589662552,
-0.06657197326421738,
0.019503504037857056,
0.03879823163151741,
-0.03982479125261307,
0.01908358559012413,
0.03740564361214638,
-0.002565057249739766,
0.06916404515504837,
0.017346199601888657,
-0.05146941915154457,
0.010808534920215607,
-0.023251373320817947,
-0.00019728936604224145,
-0.004734336864203215,
0.0385281965136528,
-0.01684609055519104,
0.0019146818667650223,
0.03543838858604431,
0.03695056214928627,
0.04392298683524132,
-0.025370942428708076,
0.003942146431654692,
0.026640502735972404,
0.025037433952093124,
-0.013051518239080906,
-0.048374250531196594,
0.015629667788743973,
0.012900582514703274,
0.01542302593588829,
-0.004384161438792944,
-0.008058656938374043,
-0.06815508008003235,
-0.041471775621175766,
0.008204597979784012,
0.010706202127039433,
0.014789935201406479,
0.004690398462116718,
0.0627078041434288,
-0.009436573833227158,
-0.028170088306069374,
-0.0016131820157170296,
-0.013660387136042118,
0.010797479189932346,
0.006500808522105217,
0.03857295215129852,
0.013170276768505573,
0.004861639346927404,
-0.0016045584343373775,
-0.009719624184072018,
0.013832444325089455,
0.0028574324678629637,
0.06195014715194702,
-0.03035839833319187,
0.07298950105905533,
0.03134075179696083,
0.004601765424013138,
-0.007604352664202452,
-0.014939936809241772,
-0.02438599430024624,
0.011783137917518616,
-0.016374727711081505,
0.03137603774666786,
0.02365126647055149,
0.029893914237618446,
0.012767571955919266,
0.03681014105677605,
-0.020252598449587822,
0.019621388986706734,
0.0459265261888504,
0.03699350357055664,
0.04503549635410309,
0.04155819118022919,
-0.047658439725637436,
0.02876504883170128,
-0.023357650265097618,
0.044196825474500656,
0.007119437213987112,
0.007401240989565849,
0.02572297304868698,
-0.027776502072811127,
0.0038371719419956207,
-0.014126164838671684,
-0.017751358449459076,
-0.030724581331014633,
0.026600003242492676,
0.017471687868237495,
0.013354014605283737,
-0.008849519304931164,
0.038454025983810425,
0.024243440479040146,
-0.017930256202816963,
-0.013058498501777649,
0.011363163590431213,
-0.07809507101774216,
-0.024524284526705742,
-0.025244804099202156,
-0.03100902959704399,
0.04321729391813278,
0.0202291551977396,
-0.03969927877187729,
0.01038844883441925,
-0.00973073672503233,
0.03397246450185776,
0.011539088562130928,
0.026339808478951454,
-0.0026120611000806093,
0.07993468642234802,
-0.012791585177183151,
0.014581738039851189,
-0.03644997626543045,
0.025710010901093483,
0.10168513655662537,
0.02645384892821312,
0.00529457489028573,
-0.05736025795340538,
0.0021304020192474127,
-0.0409940741956234,
0.012354542501270771,
-0.02294091321527958,
0.0496312752366066,
-0.027978789061307907,
0.03355375677347183,
0.020670317113399506,
0.04883906617760658,
0.01670854166150093,
0.03165731206536293,
0.06134828180074692,
-0.011667957529425621,
-0.014920931309461594,
-0.02891969308257103,
0.01308352593332529,
-0.02107991650700569,
0.00948413647711277,
-0.06193067505955696,
0.02578364498913288,
-0.048195865005254745,
-0.022981323301792145,
-0.015306125394999981,
-0.02897070348262787,
0.04860212281346321,
0.015681473538279533,
-0.021290462464094162,
-0.00010507425031391904,
-0.010361654683947563,
0.00034967801184393466,
-0.05000055953860283,
0.0032045720145106316,
0.05595625936985016,
0.02322123758494854,
0.003416033461689949,
0.010966441594064236,
0.023071393370628357,
0.0015070810914039612,
0.01199850719422102,
0.06541838496923447,
-0.016461240127682686,
0.0020662248134613037,
-0.048338524997234344,
0.016302166506648064,
-0.013527746312320232,
0.030794082209467888,
-0.0029963599517941475,
0.06517300754785538,
0.004972266964614391,
0.0033169679809361696,
-0.0625622496008873,
-0.03147132694721222,
-0.012372954748570919,
-0.057770874351263046,
0.0019101114012300968,
-0.040663182735443115,
0.02951647713780403,
-0.03268211707472801,
0.025448737666010857,
-0.004425997845828533,
-0.00576427998021245,
0.01627855934202671,
-0.012124561704695225,
0.02635996788740158,
-0.018115730956196785,
-0.027151549234986305,
-0.014194941148161888,
-0.03598099201917648,
-0.02752436138689518,
0.022313596680760384,
0.03088723123073578,
0.013163745403289795,
0.02803601324558258,
0.001914388034492731,
-0.03253170847892761,
0.041874829679727554,
-0.04533245041966438,
0.04543893411755562,
0.017962558194994926,
-0.012463588267564774,
-0.027265969663858414,
0.022802772000432014,
0.036257702857255936,
0.00867076963186264,
-0.0011872842442244291,
0.033878766000270844,
-0.007084547076374292,
-0.024138638749718666,
0.017509080469608307,
-0.029147053137421608,
-0.03234975039958954,
-0.0021001831628382206,
-0.006436015944927931,
-0.002539663342759013,
-0.022229207679629326,
0.024507004767656326,
0.048203013837337494,
-0.0020511436741799116,
0.010141330771148205,
0.032202329486608505,
-0.02355721965432167,
0.00959192868322134,
0.008652906864881516,
-0.034154098480939865,
0.01542168203741312,
-0.009820109233260155,
-0.0018828368047252297,
-0.014093701727688313,
-0.05088399350643158,
0.00140911596827209,
-0.00664410600438714,
0.02369241788983345,
0.04517288878560066,
-0.029530012980103493,
-0.0035333666019141674,
-0.02827277034521103,
0.02445390820503235,
-0.04469968006014824,
-0.010575796477496624,
-0.05866356939077377,
0.0006527299410663545,
0.047216787934303284,
-0.013625293038785458,
-0.00023866356059443206,
0.03486887365579605,
0.0038981635589152575,
0.0028200168162584305,
0.03905325010418892,
0.016740068793296814,
0.008959208615124226,
0.015679262578487396,
0.0010544904507696629,
-0.014393593184649944,
0.03792615234851837,
-0.0016436832956969738,
-0.04026411101222038,
0.04962659627199173,
-0.05398653447628021,
-0.02974194660782814,
-0.0018407717579975724,
-0.02582554891705513,
0.007137950509786606,
0.04530224949121475,
0.005636857822537422,
0.016262196004390717,
0.045422717928886414,
-0.010564702562987804,
-0.010255738161504269,
-0.013777664862573147,
0.012226204387843609,
0.028385011479258537,
-0.006453523878008127,
0.015973588451743126,
-0.020260069519281387,
-0.006351055111736059,
0.017551805824041367,
0.02004009485244751,
0.034780848771333694,
-0.03351028263568878,
0.004579049535095692,
-0.00029379769694060087,
-0.023333212360739708,
0.0475311279296875,
0.01891286112368107,
0.03002275340259075,
0.03851393982768059,
-0.022167999297380447,
0.03577094525098801,
-0.01936407946050167,
0.015090735629200935,
-0.0840398296713829,
-0.016330519691109657,
0.001213572919368744,
-0.043050434440374374,
0.015197989530861378,
-0.040096599608659744,
0.007725433446466923,
0.03247300907969475,
-0.06664504110813141,
0.020519990473985672,
0.003619423368945718,
-0.03909026458859444,
0.0009400073904544115,
-0.04337155073881149,
-0.002110373927280307,
0.03826458752155304,
0.05818820744752884,
0.04475267231464386,
0.006950530223548412,
-0.009314893744885921,
-0.022575223818421364,
0.00828574039041996,
-0.03852901607751846,
0.04172864556312561,
0.02258905954658985,
-0.015624819323420525,
0.0456484779715538,
-0.023420266807079315,
-0.022304590791463852,
0.01830904744565487,
-0.026841284707188606,
-0.0029233135282993317,
0.01411918830126524,
-0.0017932103946805,
-0.0014185778563842177,
0.025498436763882637,
-0.010370234958827496,
-0.014248790219426155,
-0.003163105109706521,
0.009621795266866684,
0.03030877187848091,
0.01229480467736721,
-0.0031948527321219444,
-0.0007187942392192781,
0.02339349314570427,
-0.03821701556444168,
-0.00419635372236371,
0.010335852392017841,
-0.04816767945885658,
-0.015622040256857872,
-0.00695030065253377,
0.02595975063741207,
0.04551393911242485,
-0.01933932676911354,
-0.007583804428577423,
-0.035632431507110596,
-0.048516105860471725,
0.0030606018844991922,
0.001684357994236052,
0.02064705453813076,
0.03493392467498779,
-0.008358175866305828,
-0.015389765612781048,
0.02551141381263733,
0.01483470480889082,
-0.01562392245978117,
-0.02968616969883442,
0.017771519720554352,
0.02470032311975956,
0.0003671855665743351,
0.0109444260597229,
-0.047014083713293076,
-0.006818125024437904,
0.018498234450817108,
0.0024714376777410507,
0.010945367626845837,
-0.004857617896050215,
-0.07064717262983322,
-0.019831255078315735,
-0.028318069875240326,
0.057886265218257904,
-0.042018868029117584,
-0.04365089535713196,
-0.05431804433465004,
-0.029128821566700935,
0.007833749987185001,
0.033429570496082306,
0.04440273344516754,
-0.014843732118606567,
-0.0033396263606846333,
0.013358847238123417,
-0.009162305854260921,
0.03364759311079979,
-0.049117740243673325,
0.03469088301062584,
0.006211470812559128,
-0.03250586614012718,
0.005305661354213953,
-0.012261993251740932,
-0.012861419469118118,
0.046437207609415054,
0.007348024286329746,
0.0033781654201447964,
0.010571599937975407,
-0.03940783813595772,
0.000857039587572217,
0.025798311457037926,
0.0026302083861082792,
-0.020090986043214798,
0.06140023097395897,
-0.032105453312397,
0.0010491561843082309,
-0.025132043287158012,
0.008459478616714478,
-0.04261615872383118,
0.03011753410100937,
-0.02250622771680355,
0.016441619023680687,
-0.03296510502696037,
-0.01499874982982874,
0.06317451596260071,
-0.017397908493876457,
0.001616243040189147,
0.026802852749824524,
-0.033499300479888916,
-0.01224883459508419,
0.06237452104687691,
-0.002475177403539419,
0.006460702512413263,
-0.052381664514541626,
0.027026355266571045,
-0.014692760072648525,
-0.002463783835992217,
-0.023443836718797684,
0.042584650218486786,
0.021255681291222572,
0.009435665793716908,
-0.004864121787250042,
0.04248686879873276,
-0.019942695274949074,
0.005301023367792368,
0.0007602455443702638,
0.01890302635729313,
-0.054835934191942215,
-0.013678934425115585,
0.0026764150243252516,
-0.03718578442931175,
0.022358175367116928,
0.027079766616225243,
-0.05172545835375786,
0.0833834707736969,
-0.03156250715255737,
-0.004628589376807213,
-0.014700991101562977,
0.03878453001379967,
0.02193901129066944,
-0.011625304818153381,
0.026259714737534523,
0.040937695652246475,
0.015699787065386772,
0.0017952255439013243,
0.000394844711991027,
-0.016180379316210747,
0.07443812489509583,
-0.02928810380399227,
0.034011222422122955,
-0.023103488609194756,
-0.00999739021062851,
-0.039038144052028656,
-0.0007728172931820154,
-0.0533115528523922,
-0.04435976594686508,
0.04492150992155075,
0.04142320901155472,
0.005144251976162195,
-0.004152072127908468,
-0.0337124727666378,
-0.027711674571037292,
0.04008884355425835,
-0.06768997758626938,
0.009675285778939724,
-0.0330769419670105,
0.006206729914993048,
0.0025325396563857794,
0.01919170841574669
] |
<p>Consider the typical problem, "You have a conducting sphere of charge $Q$ and a point charge q a certain distance away, what is the force on the point charge?". The solution is a simple application of the method of images, but in Griffiths part of the argument relies on saying
$$Q_{conductor} = \sum_i q_{image}$$
Or, that the image charges in the conductor add to the total charge. I don't really see how this is a mathematically valid statement. I was thinking it may come from the Neumann boundary conditions and integrating Poisson's eq, but I am not sure.</p>
<p>For reference consider Griffiths Problem 3.8 which deals with the $Q=0$ case.</p>
<p>An explanation would really be helpful.</p>
| 9,570 |
[
-0.017294468358159065,
-0.009179276414215565,
0.022141415625810623,
-0.03829623758792877,
0.009034400805830956,
0.029702402651309967,
-0.04289833828806877,
0.022492628544569016,
-0.0014988543698564172,
-0.022797470912337303,
0.04813823476433754,
0.03069431148469448,
0.1145869567990303,
0.030375029891729355,
0.006992052774876356,
0.004883470945060253,
-0.0009070495143532753,
-0.04721531644463539,
-0.010233871638774872,
-0.023932937532663345,
0.014621355570852757,
0.06162883713841438,
0.008749027736485004,
-0.015231640078127384,
0.019603906199336052,
0.023471197113394737,
-0.005711110774427652,
-0.0439341776072979,
0.029791776090860367,
0.06286032497882843,
-0.021004237234592438,
-0.031616102904081345,
-0.000981244957074523,
-0.017862051725387573,
0.030488301068544388,
0.013239759020507336,
-0.02672906219959259,
-0.02894463948905468,
0.02327398769557476,
0.002458950038999319,
0.014653876423835754,
0.020965255796909332,
0.036299943923950195,
0.020067693665623665,
-0.03350842371582985,
0.039109159260988235,
0.03915126621723175,
-0.02484729513525963,
0.0004124503757338971,
-0.06920183449983597,
0.062014009803533554,
0.009093888103961945,
0.05365472659468651,
0.027582503855228424,
-0.006136576645076275,
-0.018811799585819244,
0.047107044607400894,
0.03408700227737427,
0.006978638470172882,
-0.030972439795732498,
-0.04136596992611885,
-0.003070945618674159,
-0.02085704170167446,
-0.04450559988617897,
-0.010809763334691525,
0.03905145078897476,
0.013228798285126686,
-0.02092653140425682,
0.02570798248052597,
-0.018335465341806412,
-0.024978064000606537,
0.025284675881266594,
0.027566667646169662,
-0.026361437514424324,
-0.024951860308647156,
0.013978535309433937,
0.015901707112789154,
0.01793092116713524,
0.01485851127654314,
0.0024665617384016514,
-0.024695634841918945,
0.004698544275015593,
0.026503605768084526,
0.03396345674991608,
0.024452155455946922,
-0.024924255907535553,
0.05859828367829323,
0.0032342500053346157,
0.009274347685277462,
-0.006886850576847792,
-0.011635481379926205,
0.011933187954127789,
0.030936410650610924,
-0.02766263671219349,
0.012269485741853714,
0.020976606756448746,
-0.010406658984720707,
0.0362275056540966,
-0.0017356625758111477,
-0.006392226088792086,
-0.012007134035229683,
-0.013967877253890038,
-0.0050033084116876125,
0.08791092783212662,
0.0077573987655341625,
-0.015243569388985634,
-0.028200441971421242,
0.023159468546509743,
-0.018554627895355225,
-0.005956265144050121,
-0.03555452078580856,
0.0253082737326622,
0.009429571218788624,
0.00043355245725251734,
-0.02474326454102993,
0.0007284774910658598,
0.008893498219549656,
-0.016665706411004066,
0.035504478961229324,
0.05813859403133392,
-0.0034220062661916018,
-0.0328427329659462,
0.01438381988555193,
-0.049933597445487976,
-0.06783470511436462,
0.06568962335586548,
0.04830017685890198,
-0.04328421130776405,
0.007279224693775177,
0.0217752605676651,
0.04241282120347023,
-0.008701547980308533,
-0.023555489256978035,
0.0443907305598259,
0.026827296242117882,
-0.012384261004626751,
-0.08558020740747452,
-0.03561340272426605,
0.008571007288992405,
-0.029269777238368988,
0.01369175873696804,
-0.04868413880467415,
-0.0124890748411417,
0.06175466254353523,
0.06155773997306824,
0.002124382648617029,
-0.014529149979352951,
0.004357487428933382,
0.0594945065677166,
-0.01546197198331356,
-0.024938512593507767,
-0.03965869918465614,
0.0018114217091351748,
0.00676904758438468,
-0.03087965026497841,
-0.08473333716392517,
0.04073569178581238,
0.03890702500939369,
0.0010184284765273333,
-0.036573007702827454,
0.05497772991657257,
-0.0035977705847471952,
0.010438223369419575,
0.016482558101415634,
-0.01975608803331852,
-0.02401183918118477,
0.03340449184179306,
-0.005146477837115526,
0.03711285442113876,
0.02731236442923546,
0.022267984226346016,
0.03091246820986271,
0.002315802499651909,
0.0018299974035471678,
0.030529651790857315,
-0.029248535633087158,
0.0011980278650298715,
-0.05511350557208061,
0.033395253121852875,
0.00882868841290474,
-0.018210848793387413,
-0.05826273933053017,
0.005496286321431398,
0.03275677561759949,
0.01871602237224579,
0.020419249311089516,
-0.00804902333766222,
-0.029860449954867363,
-0.013400268740952015,
-0.0021420882549136877,
-0.025108810514211655,
-0.03904508799314499,
0.07633138447999954,
0.0015031248331069946,
-0.028245113790035248,
0.009887403808534145,
-0.018845468759536743,
-0.04323318228125572,
0.010172574780881405,
-0.006047648377716541,
0.008315177634358406,
-0.0012389529729261994,
-0.02809988707304001,
-0.043070610612630844,
0.021461838856339455,
0.03444455564022064,
0.049116965383291245,
0.04116931930184364,
0.05659763142466545,
-0.017900394275784492,
-0.0030666282400488853,
-0.035843320190906525,
-0.010312559083104134,
0.02413851208984852,
0.029927421361207962,
-0.008009529672563076,
0.032590433955192566,
-0.010327287949621677,
-0.006684384774416685,
0.014692358672618866,
-0.014860760420560837,
0.061426110565662384,
0.059375252574682236,
0.03365931287407875,
0.003897125134244561,
0.02993408963084221,
0.023325059562921524,
0.0025207765866070986,
0.003929195459932089,
-0.045007091015577316,
-0.0380907766520977,
0.011238626204431057,
0.03332548588514328,
0.04907095059752464,
-0.031819745898246765,
-0.004458140581846237,
0.0502953976392746,
0.03924703598022461,
-0.004785452038049698,
-0.009454447776079178,
-0.018886417150497437,
-0.04917602986097336,
0.02991683967411518,
0.009701100178062916,
-0.01706407591700554,
-0.01723392866551876,
0.042691562324762344,
-0.040701910853385925,
0.027278678491711617,
-0.01586166024208069,
-0.014515593647956848,
0.006306237541139126,
-0.06261368840932846,
0.025626350194215775,
-0.0197603702545166,
-0.011555837467312813,
0.04397323355078697,
-0.03185025230050087,
0.03694732114672661,
0.011080069467425346,
0.02682543359696865,
-0.019017061218619347,
-0.04476754739880562,
0.01145534310489893,
0.03472417965531349,
-0.02216145023703575,
-0.029215477406978607,
0.019172590225934982,
0.03096657432615757,
-0.06706439703702927,
0.007986809127032757,
-0.026972513645887375,
-0.04409312829375267,
-0.02295907773077488,
-0.009677868336439133,
0.01365218497812748,
0.05558491498231888,
0.04371968284249306,
-0.02706247754395008,
0.0014944870490580797,
-0.040233079344034195,
-0.026144325733184814,
0.01909024640917778,
0.06393841654062271,
-0.05485963076353073,
0.00697744358330965,
-0.02388845384120941,
0.002142072655260563,
0.05654020234942436,
-0.006094660144299269,
-0.0030233904253691435,
0.017800455912947655,
0.007437319494783878,
-0.020035797730088234,
0.008978433907032013,
-0.03518368676304817,
0.003778595943003893,
-0.0468558743596077,
0.02614463120698929,
0.03983497619628906,
-0.009760267101228237,
-0.030245034024119377,
0.02531183324754238,
-0.03691328316926956,
-0.055632334202528,
-0.004752058070152998,
-0.021417725831270218,
0.023869210854172707,
-0.027287479490041733,
0.010991827584803104,
0.037107452750205994,
-0.04142605513334274,
-0.006418232340365648,
-0.06512895971536636,
-0.06476572901010513,
0.046674247831106186,
-0.039507415145635605,
0.048375293612480164,
-0.02778683975338936,
-0.051506154239177704,
0.09461931139230728,
0.003484802320599556,
-0.014393815770745277,
-0.02286091074347496,
0.008009645156562328,
-0.019921865314245224,
0.0002215626445831731,
0.01004057191312313,
0.0369403176009655,
-0.020300954580307007,
0.00882861390709877,
-0.010249198414385319,
0.007903171703219414,
-0.004411548376083374,
0.006387935020029545,
0.0032151963096112013,
-0.007806358393281698,
0.03430856019258499,
-0.013473576866090298,
0.04597388207912445,
0.012833419255912304,
-0.023847756907343864,
0.021487906575202942,
-0.020245801657438278,
0.03371860459446907,
0.03488486260175705,
-0.030520908534526825,
0.028697170317173004,
-0.005308973602950573,
0.0030241943895816803,
-0.019619258120656013,
0.07953048497438431,
-0.028639644384384155,
-0.02437969669699669,
-0.0012986732181161642,
0.03699643537402153,
0.047153010964393616,
-0.06204415112733841,
-0.008921357803046703,
0.029009008780121803,
0.0539235919713974,
-0.03165046125650406,
-0.028382960706949234,
-0.006915641017258167,
-0.03900563344359398,
0.03565457463264465,
-0.04710177332162857,
-0.023659154772758484,
0.02649591863155365,
0.02251839078962803,
0.033882878720760345,
0.02349761687219143,
-0.01632855087518692,
-0.01520571205765009,
-0.0902465209364891,
-0.029221616685390472,
-0.013042892329394817,
0.06589043885469437,
0.029830574989318848,
0.025637932121753693,
0.03479127213358879,
0.001885575708001852,
0.013305598869919777,
0.02942788414657116,
-0.09719721227884293,
-0.003671812592074275,
0.026034124195575714,
-0.012181668542325497,
0.00436421250924468,
-0.04181545227766037,
0.0036389664746820927,
-0.02362557128071785,
0.003783043008297682,
-0.011260985396802425,
0.004731729160994291,
-0.031350575387477875,
0.020738836377859116,
-0.015643317252397537,
-0.032162442803382874,
0.0035761587787419558,
0.04137343540787697,
-0.0024330969899892807,
-0.03885801509022713,
-0.036354921758174896,
0.0024745704140514135,
-0.049396611750125885,
-0.014576626941561699,
-0.019194843247532845,
-0.007722722366452217,
0.00711351353675127,
0.005139623302966356,
-0.015616425313055515,
0.017108751460909843,
-0.05176214873790741,
0.023161431774497032,
0.0361517034471035,
0.0701429545879364,
0.028490740805864334,
-0.047578115016222,
-0.024413147941231728,
-0.050940003246068954,
-0.055081550031900406,
-0.02041604369878769,
0.07430388778448105,
-0.02485591545701027,
-0.0241929329931736,
0.010827597230672836,
-0.002059947932139039,
0.021672740578651428,
0.028488140553236008,
0.05016494542360306,
0.03406522050499916,
-0.006618849467486143,
-0.04130881652235985,
0.01464164163917303,
-0.01845639757812023,
0.014842481352388859,
0.051896121352910995,
-0.004089787136763334,
-0.006511840969324112,
0.011155511252582073,
0.022168884053826332,
0.009969276376068592,
-0.005392615683376789,
0.007704775780439377,
0.011089077219367027,
0.0033602104522287846,
0.00456995889544487,
-0.011153794825077057,
0.03487497195601463,
0.01696716621518135,
0.07993730157613754,
0.034033581614494324,
-0.05218350887298584,
-0.06742893159389496,
-0.03615543246269226,
0.061417073011398315,
0.01716616190969944,
0.003045816905796528,
-0.00797475129365921,
-0.04120291396975517,
0.0010350925149396062,
0.01643540896475315,
-0.019926555454730988,
0.007695940788835287,
0.01240098848938942,
0.013416698202490807,
0.0050396849401295185,
-0.05642884224653244,
-0.03917957469820976,
0.017823051661252975,
0.00540622603148222,
0.05517953634262085,
-0.047814272344112396,
0.017501283437013626,
0.024231866002082825,
0.04195642098784447,
0.02483302913606167,
0.06820254027843475,
0.02159123867750168,
0.00043394413660280406,
0.006409636698663235,
-0.010939479805529118,
-0.045538026839494705,
-0.06800929456949234,
0.02194059267640114,
0.020694483071565628,
0.016242889687418938,
0.007466288283467293,
-0.019777556881308556,
-0.03842713683843613,
-0.011306209489703178,
0.01691359654068947,
-0.01694868691265583,
0.010116069577634335,
-0.049966566264629364,
0.0407114140689373,
0.027874497696757317,
-0.002832186408340931,
0.04837131127715111,
0.009064270183444023,
-0.032564807683229446,
-0.014334903098642826,
-0.02454768307507038,
0.05034463480114937,
0.003096924861893058,
-0.004295358434319496,
-0.02600322663784027,
0.04618118703365326,
-0.012065392918884754,
0.05043159797787666,
0.02508579194545746,
0.020537305623292923,
-0.018482234328985214,
-0.010657441802322865,
-0.021374981850385666,
0.012789192609488964,
0.018986688926815987,
0.00012292985047679394,
-0.01305640023201704,
0.02496829256415367,
0.026700852438807487,
-0.033173371106386185,
0.03267956152558327,
-0.017971480265259743,
-0.01883442886173725,
0.05176452174782753,
0.0022759016137570143,
-0.008673453703522682,
-0.03140776604413986,
0.00026691865059547126,
0.012710090726613998,
-0.0465310662984848,
0.035461947321891785,
-0.026704633608460426,
-0.013443530537188053,
0.022570310160517693,
-0.016201237216591835,
-0.025463195517659187,
0.011061311699450016,
-0.04130170866847038,
0.03029892034828663,
-0.059138223528862,
-0.0001270566281164065,
0.05909908562898636,
0.007055345922708511,
-0.04895242676138878,
-0.032964251935482025,
0.03188340738415718,
0.0024973927065730095,
0.0042673819698393345,
-0.0430438332259655,
-0.02021951973438263,
0.007814597338438034,
-0.041338834911584854,
0.013984509743750095,
0.04351355880498886,
-0.0376383513212204,
0.020268144086003304,
0.0015812705969437957,
0.021279793232679367,
0.04567698761820793,
-0.0022470392286777496,
-0.019725661724805832,
0.031487081199884415,
-0.033808015286922455,
0.011199073866009712,
-0.0023158262483775616,
0.018471788614988327,
-0.008598484098911285,
-0.0031187483109533787,
-0.03131071850657463,
-0.00615404499694705,
0.0036666253581643105,
-0.01930595003068447,
-0.0387277826666832,
0.000016016607332858257,
0.020368920639157295,
-0.02006516046822071,
-0.011753263883292675,
0.0015215604798868299,
0.03933925926685333,
0.026191724464297295,
-0.03564092144370079,
0.022877853363752365,
-0.030927058309316635,
-0.039907895028591156,
0.026314612478017807,
0.015624570660293102,
-0.011525552719831467,
0.007492384873330593,
0.05637914314866066,
-0.01993810199201107,
-0.006727440282702446,
0.034750353544950485,
0.010305517353117466,
0.01462682243436575,
-0.016698069870471954,
-0.011852873489260674,
0.010034468956291676,
0.013130687177181244,
-0.026572151109576225,
0.006589692551642656,
-0.03979407250881195,
0.04746202751994133,
0.05128380283713341,
-0.01876627653837204,
0.07928717881441116,
0.02126910910010338,
0.0013858997263014317,
-0.033682018518447876,
0.017361298203468323,
-0.022875601425766945,
-0.0035497823264449835,
-0.004911213181912899,
0.017115050926804543,
-0.03661720082163811,
-0.01061323657631874,
0.011283337138593197,
0.06056501716375351,
-0.05150827020406723,
-0.03256646543741226,
-0.00896380003541708,
0.03709997236728668,
0.002035910729318857,
-0.03868599608540535,
-0.043004848062992096,
0.043053727596998215,
-0.0365435965359211,
0.03114505484700203,
0.01052230503410101,
-0.028304455801844597,
0.06662242859601974,
0.029575461521744728,
0.015000082552433014,
-0.03273424133658409,
-0.038692373782396317,
-0.01707843877375126,
-0.0024242799263447523,
0.018561309203505516,
0.01671789586544037,
-0.005715315695852041,
-0.026001552119851112,
0.0022438080050051212,
-0.008499237708747387,
0.01945962943136692,
-0.018153810873627663,
-0.07114280760288239,
-0.004307745490223169,
-0.0396442674100399,
-0.023399583995342255,
-0.003069983795285225,
-0.003466562833636999,
0.009497455321252346,
0.01050859596580267,
-0.04125087335705757,
0.03956839069724083,
0.041736241430044174,
0.007461833767592907,
-0.014130203984677792,
0.041371461004018784,
-0.005507748108357191,
0.0049887727946043015,
-0.015546057373285294,
0.008215358480811119,
0.12288694083690643,
0.03159270063042641,
0.011317485012114048,
-0.07517113536596298,
-0.02871720865368843,
0.00047630409244447947,
-0.0267417561262846,
-0.029216084629297256,
0.028652232140302658,
-0.021568521857261658,
-0.006818649359047413,
0.01281531061977148,
0.03466019406914711,
-0.027126340195536613,
-0.03432152047753334,
0.05986179783940315,
-0.03569206967949867,
-0.03759279474616051,
0.014290050603449345,
0.024354618042707443,
-0.005528684705495834,
0.01451942976564169,
-0.061352938413619995,
0.030542420223355293,
-0.010630709119141102,
-0.017725486308336258,
0.01578322798013687,
0.01253685262054205,
0.0160966869443655,
0.042902469635009766,
-0.0714978352189064,
-0.01099682692438364,
0.015053718350827694,
-0.05162994936108589,
-0.030556073412299156,
0.027609916403889656,
0.012029817327857018,
-0.025694232434034348,
0.009908858686685562,
-0.006708391010761261,
0.023300180211663246,
0.021816987544298172,
0.005093005020171404,
0.033869415521621704,
-0.02007892355322838,
0.033770374953746796,
-0.05225531756877899,
0.0628175139427185,
-0.008042358793318272,
0.032976310700178146,
0.006747725885361433,
-0.0160635095089674,
0.01206186506897211,
-0.05615949258208275,
-0.0024901265278458595,
-0.0047272490337491035,
0.003044953104108572,
0.004555054474622011,
-0.015583961270749569,
-0.02328641340136528,
0.03816136717796326,
0.020012669265270233,
0.02225188910961151,
0.03373703360557556,
-0.0368766188621521,
-0.014484193176031113,
-0.0063854712061584,
0.04718933627009392,
0.012617375701665878,
-0.01739576645195484,
-0.006743068806827068,
-0.04721037298440933,
0.0008785038371570408,
-0.04869946464896202,
-0.048317234963178635,
0.031081166118383408,
0.040499843657016754,
-0.012040319852530956,
-0.0038159138057380915,
-0.019459063187241554,
-0.06870657950639725,
0.009078695438802242,
-0.019051266834139824,
-0.017301369458436966,
-0.03377104550600052,
-0.015268543735146523,
-0.0007757112616673112,
0.03174344450235367,
-0.013571741059422493,
-0.026289690285921097,
0.03351971134543419,
0.02482287958264351,
0.013718410395085812,
-0.01813730038702488,
-0.040927816182374954,
0.011475936509668827,
-0.03514329716563225,
0.007421294692903757,
-0.008304129354655743,
-0.03831879049539566,
-0.011052533984184265,
0.009621022269129753,
0.024738822132349014,
0.05766900256276131,
0.006301220040768385,
0.0281174685806036,
-0.01007944904267788,
0.01775956153869629,
0.00965567585080862,
-0.005958036053925753,
0.008779555559158325,
-0.040697816759347916,
0.013908462598919868,
-0.03403359651565552,
-0.011374014429748058,
0.022383004426956177,
0.004015016369521618,
-0.034475069493055344,
-0.004428723361343145,
0.005301059689372778,
0.010549835860729218,
0.019770532846450806,
-0.00688509875908494,
-0.03785373270511627,
-0.003989013843238354,
0.008702193386852741,
-0.01334280427545309,
-0.018688766285777092,
0.005454422906041145,
-0.0284653902053833,
-0.0318947471678257,
0.052722398191690445,
-0.005860254634171724,
0.0058830976486206055,
0.017890162765979767,
-0.014198385179042816,
-0.005633579567074776,
0.04081618785858154,
0.008413483388721943,
-0.01256607286632061,
0.042518250644207,
-0.015449337661266327,
-0.04141632840037346,
0.018797114491462708,
-0.007090706843882799,
-0.01321652065962553,
0.0722929835319519,
0.004356602672487497,
-0.06388843059539795,
0.02383437007665634,
-0.01297388318926096,
-0.023184161633253098,
0.010097339749336243,
-0.011413306929171085,
-0.013333979994058609,
-0.06561626493930817,
-0.010760029777884483,
0.00638140132650733,
0.016815373674035072,
-0.0021653762087225914,
-0.020135657861828804,
-0.02542322501540184,
-0.024246657267212868,
0.011902505531907082,
-0.01160119567066431,
-0.036814119666814804,
0.03246331214904785,
0.008881249465048313,
0.009611403569579124,
0.05393975228071213,
-0.03587140887975693,
0.0005981471622362733,
-0.011019501835107803,
0.022884702309966087,
-0.11865998059511185,
-0.0336960144340992,
0.0016300198622047901,
0.01717628538608551,
0.04040289297699928,
-0.053942374885082245,
0.03655533120036125,
-0.024393076077103615,
-0.10240819305181503,
0.0399429015815258,
-0.012015587650239468,
-0.01933981478214264,
-0.038054805248975754,
-0.01111781969666481,
0.013449852354824543,
0.011000854894518852,
0.016851501539349556,
0.039532337337732315,
0.008521595038473606,
0.023305902257561684,
-0.0008264927892014384,
-0.0398392453789711,
-0.003536395961418748,
0.036773912608623505,
-0.017778828740119934,
-0.0210972111672163,
0.06376190483570099,
0.005503503140062094,
-0.019653789699077606,
0.013722861185669899,
-0.03041326068341732,
-0.030992725864052773,
0.01927885413169861,
0.03577088192105293,
-0.011156557127833366,
0.08015409111976624,
-0.005102739669382572,
0.0007157285581342876,
-0.005219114478677511,
-0.004160810727626085,
0.020226197317242622,
0.01825999841094017,
-0.0369696281850338,
-0.022006679326295853,
0.044407546520233154,
-0.0010010709520429373,
-0.057042196393013,
0.04902809113264084,
0.0012076215352863073,
-0.004957002121955156,
0.00755477836355567,
0.02936949022114277,
0.0013733810046687722,
-0.007910782471299171,
0.015069693326950073,
-0.05341481417417526,
0.0014832554152235389,
0.011097400449216366,
0.009901249781250954,
0.00029170216294005513,
-0.00003958983870688826,
-0.00036701347562484443,
-0.03499684855341911,
-0.03192298114299774,
0.009161651134490967,
0.016170289367437363,
-0.050860386341810226,
0.02032984048128128,
0.03399072214961052,
0.03183751553297043,
0.005425170063972473,
-0.026896214112639427,
-0.024224411696195602,
0.03598658740520477,
0.029883109033107758,
0.018039846792817116,
-0.005002842750400305,
-0.0526537261903286,
-0.014163394458591938,
-0.058318234980106354,
0.02307531237602234,
0.007576036266982555,
-0.026469511911273003,
0.01844773069024086,
-0.045082394033670425,
-0.010831708088517189,
0.021775424480438232,
0.08570900559425354,
-0.015025295317173004,
-0.03924646973609924,
0.01980401761829853,
-0.04663250967860222,
0.012217399664223194,
-0.031219085678458214,
-0.038535259664058685,
-0.015428784303367138,
0.031632304191589355,
0.014748580753803253,
0.021984579041600227,
-0.00441741431131959,
0.013797922991216183,
0.03326550871133804,
0.020697299391031265,
0.044674430042505264,
-0.032311975955963135,
-0.06109499931335449,
0.035784102976322174,
0.03570710867643356,
0.017663873732089996,
0.06358220428228378,
-0.009954063221812248,
0.001451835036277771,
-0.01925123855471611,
-0.04997275024652481,
-0.037796445190906525,
0.026206551119685173,
-0.01510671153664589,
-0.0014028807636350393,
-0.011416062712669373,
0.005602408200502396,
0.04642853885889053,
-0.03417046740651131,
0.001441089785657823,
-0.00360748334787786,
-0.03700434789061546,
-0.012153406627476215,
0.03338952735066414,
0.03238057345151901,
0.017646126449108124,
-0.018509378656744957,
0.025047125294804573,
0.022971659898757935,
-0.01636420376598835,
-0.004579155705869198,
0.022689538076519966,
0.012885450385510921,
0.006295412313193083,
-0.017038803547620773,
0.06785588711500168,
0.04376783221960068,
0.0032507271971553564,
0.01042236853390932,
0.012330837547779083,
-0.01888534240424633,
-0.025934701785445213,
0.015434532426297665,
-0.02107105404138565,
0.018780723214149475,
0.025270549580454826,
0.0023002016823738813,
0.11035620421171188,
-0.0187914427369833,
-0.007493316195905209,
-0.001577800139784813,
0.023079868406057358,
-0.005112400744110346,
0.04582890123128891,
0.011339553631842136,
0.06507277488708496,
-0.024714946746826172,
-0.043204501271247864,
-0.022136667743325233,
-0.018895627930760384,
-0.02756042592227459,
-0.010304181836545467,
0.00660473108291626,
0.03643224015831947,
0.02057661861181259,
-0.002828585682436824,
-0.0016075077001005411,
-0.006105558481067419,
0.03808758407831192,
0.029153019189834595,
0.0318986251950264,
0.007401243783533573,
0.011097263544797897,
0.010772106237709522,
-0.036520592868328094,
0.03626502677798271,
-0.0711480975151062,
-0.0135753583163023,
-0.021202487871050835,
0.03724672272801399,
0.035725172609090805,
0.0003927674551960081
] |
<p>Hydrogen is the lightest element, so it's cable of lifting the most weight in out atmosphere (probably not the best terminology there, but you get the picture)</p>
<p>Would hot hydrogen (in the same sense as hot air) be able to lift even more mass?
Would a higher or lower density of hydrogen in a ballon lift more?
If you could have a balloon which had nothing in it (it was a vacuum inside) would that lift more than a hydrogen balloon?</p>
<p>Basically what are the physics to balloons and lifting?</p>
<p>(really not sure what to tag this, so if someone else could that'd be great)</p>
| 978 |
[
-0.04494093358516693,
-0.03914675861597061,
-0.011175631545484066,
-0.007886558771133423,
0.048174332827329636,
0.01872093789279461,
-0.03196128085255623,
-0.03262756019830704,
0.0016293261433020234,
-0.02721524052321911,
0.04910958930850029,
0.036508020013570786,
0.035367365926504135,
-0.008313138037919998,
0.010635465383529663,
0.01195511594414711,
0.01964731514453888,
-0.03763173148036003,
0.020828697830438614,
0.006663563661277294,
-0.026113124564290047,
-0.005049166735261679,
0.014897104352712631,
0.035840749740600586,
-0.011282505467534065,
0.033175427466630936,
0.03758871927857399,
0.0031612601596862078,
0.04056904837489128,
0.02471894398331642,
-0.00022475648438557982,
-0.006229273043572903,
0.015710774809122086,
0.021003782749176025,
0.054014693945646286,
0.014913327060639858,
-0.014617384411394596,
-0.013762731105089188,
-0.035533178597688675,
-0.00027683243388310075,
-0.018682366237044334,
-0.03901272639632225,
-0.013983381912112236,
0.03619799017906189,
-0.02340199425816536,
0.03684685006737709,
-0.0039791446179151535,
-0.010718796402215958,
0.0743323415517807,
-0.08547735959291458,
0.022433308884501457,
0.03779906406998634,
0.02792574092745781,
0.0634225383400917,
0.006408417597413063,
-0.011617598123848438,
0.06143965944647789,
0.041846178472042084,
-0.00047321213060058653,
-0.05476388707756996,
-0.014488153159618378,
-0.0021146179642528296,
-0.06281320005655289,
-0.023643914610147476,
0.011655311100184917,
0.04406028613448143,
-0.0654299408197403,
-0.029274867847561836,
0.031457625329494476,
0.023636313155293465,
0.03531979024410248,
-0.01713648810982704,
0.04918674752116203,
-0.025344591587781906,
0.0445457361638546,
-0.0031594212632626295,
-0.002374892355874181,
-0.019440919160842896,
0.04144483059644699,
0.07954683154821396,
-0.02630540542304516,
0.008922507986426353,
0.03141121566295624,
0.04244983568787575,
0.003738359548151493,
-0.02232782542705536,
0.04889398068189621,
-0.015060256235301495,
0.021644923835992813,
0.02044788934290409,
0.0005852283211424947,
-0.044852036982774734,
0.02248380333185196,
-0.002886373084038496,
-0.024416014552116394,
-0.006230093538761139,
-0.004833143204450607,
0.03222030773758888,
0.03489286080002785,
0.014705873094499111,
-0.024311158806085587,
0.015335118398070335,
0.046155840158462524,
0.09081845730543137,
0.02132836915552616,
-0.0275072380900383,
-0.03820885717868805,
-0.010989083908498287,
0.008417061530053616,
0.02272011712193489,
-0.025569899007678032,
0.006429722066968679,
-0.01635020785033703,
-0.06735377013683319,
0.017348231747746468,
-0.03427628427743912,
0.04226720333099365,
-0.03650248423218727,
0.03348580002784729,
0.0417744480073452,
0.041981350630521774,
0.0021772037725895643,
0.04353497177362442,
-0.038243845105171204,
-0.0036836147774010897,
0.0010490871500223875,
0.03436044976115227,
0.027499308809638023,
0.006132324226200581,
0.06381106376647949,
-0.016870345920324326,
0.0066538965329527855,
-0.022458769381046295,
0.007811139803379774,
0.047437846660614014,
-0.01131700724363327,
-0.08914694935083389,
-0.038237083703279495,
0.0231384988874197,
-0.007075413595885038,
-0.023743635043501854,
-0.02857917733490467,
0.014820811338722706,
0.014799905009567738,
0.06072431802749634,
0.0010485592065379024,
0.007756446022540331,
-0.04359477385878563,
0.02788008749485016,
0.013688649982213974,
-0.009854297153651714,
-0.016092339530587196,
-0.005223240703344345,
-0.05730070173740387,
-0.01007828675210476,
-0.06371200829744339,
-0.013368118554353714,
0.010966400615870953,
0.006549908313900232,
-0.04177223518490791,
0.07345031201839447,
-0.013717643916606903,
0.018535085022449493,
-0.011249938979744911,
-0.015276271849870682,
-0.027210798114538193,
0.035470232367515564,
-0.001553461654111743,
0.0030288612470030785,
0.06389275938272476,
-0.010603082366287708,
0.032693736255168915,
0.02095743454992771,
0.021297434344887733,
0.04575888812541962,
-0.040189143270254135,
-0.023760700598359108,
-0.06895894557237625,
0.02827502228319645,
0.00891139730811119,
-0.04336734861135483,
-0.018167853355407715,
-0.014565736055374146,
0.019776279106736183,
0.002097554737702012,
0.056625399738550186,
0.0253857783973217,
-0.034749895334243774,
0.04091782495379448,
-0.046860214322805405,
-0.010719290934503078,
-0.061541665345430374,
0.017920752987265587,
0.00018888406339101493,
0.010400775820016861,
0.024398742243647575,
0.05732265114784241,
0.02517886273562908,
-0.04070262983441353,
0.00043195398757234216,
-0.0332149937748909,
0.046062301844358444,
0.002004677429795265,
0.03973967209458351,
0.028694607317447662,
0.04196133837103844,
0.0004965239786542952,
0.02814645878970623,
0.006840248592197895,
-0.00969635508954525,
-0.05196152999997139,
-0.017751049250364304,
-0.03349680081009865,
-0.009473515674471855,
0.0057441191747784615,
-0.0013071736320853233,
0.044570259749889374,
-0.041025206446647644,
-0.024518894031643867,
0.040936220437288284,
-0.005871901288628578,
0.09981383383274078,
0.017630483955144882,
0.0017150152707472444,
0.01313875149935484,
0.03370283171534538,
0.01763319782912731,
0.010250366292893887,
0.015322781167924404,
-0.0005304282531142235,
-0.05836404860019684,
0.012863174080848694,
0.04523594304919243,
0.039391856640577316,
-0.03001474402844906,
-0.006756482645869255,
-0.004202944226562977,
0.03909587487578392,
0.026896536350250244,
0.03567534312605858,
-0.023849038407206535,
-0.047896821051836014,
0.0025671350304037333,
0.03240594267845154,
0.014048952609300613,
0.03137066215276718,
0.02871282584965229,
0.031002407893538475,
0.037751346826553345,
-0.025238150730729103,
-0.00030085991602391005,
0.04523348808288574,
0.014699861407279968,
-0.010728760622441769,
-0.02793080173432827,
-0.03286081552505493,
0.03810890018939972,
-0.023514894768595695,
0.02220974862575531,
0.015028302557766438,
-0.006720131728798151,
0.02677542343735695,
-0.033615391701459885,
-0.028300000354647636,
0.01389121264219284,
0.009236468933522701,
0.004463959019631147,
-0.008496351540088654,
0.040034323930740356,
-0.06057587265968323,
0.024827677756547928,
-0.025805281475186348,
0.05094457045197487,
-0.041863396763801575,
-0.012359684333205223,
-0.018851181492209435,
-0.016449548304080963,
0.05721015855669975,
-0.00024544092593714595,
-0.045057035982608795,
-0.007378814741969109,
-0.04779629409313202,
0.009328342042863369,
-0.01932191103696823,
-0.03648316115140915,
0.0001366976066492498,
-0.018491754308342934,
-0.03297156095504761,
0.05748878791928291,
0.0205454733222723,
-0.042522452771663666,
0.00942482240498066,
-0.00552463810890913,
-0.019712364301085472,
0.03797580674290657,
-0.016882391646504402,
0.0222209133207798,
-0.011249516159296036,
-0.0024134379345923662,
0.04809751361608505,
-0.04257793352007866,
0.00905054435133934,
0.04339200630784035,
-0.057115521281957626,
-0.05699986219406128,
-0.04415315389633179,
0.016385674476623535,
-0.01710359752178192,
-0.024254409596323967,
0.015712667256593704,
0.045387085527181625,
-0.013219096697866917,
-0.017712557688355446,
-0.032787058502435684,
-0.011021099053323269,
0.009670928120613098,
-0.01982562243938446,
0.006047826260328293,
-0.02467070333659649,
-0.03892243281006813,
0.08697070181369781,
0.03524080663919449,
-0.03939628601074219,
-0.009980419650673866,
-0.03654539957642555,
-0.027675285935401917,
-0.006463601719588041,
0.04257290065288544,
0.0421052910387516,
-0.005963589064776897,
0.001954021630808711,
0.08239459991455078,
0.009768521413207054,
-0.007189941592514515,
0.022907769307494164,
-0.006963718682527542,
0.003258089767768979,
0.034567561000585556,
-0.026376940310001373,
0.12398769706487656,
0.002440160373225808,
-0.0033828835003077984,
0.005783209577202797,
0.004726465791463852,
0.044391147792339325,
-0.014940374530851841,
-0.04144805669784546,
0.06615906208753586,
0.0412907749414444,
0.011976342648267746,
-0.01407158188521862,
0.025927821174263954,
0.0024357144720852375,
-0.05641590431332588,
0.008017010055482388,
0.024536261335015297,
0.040221426635980606,
0.01272597722709179,
-0.04861607030034065,
0.021397408097982407,
0.07210855931043625,
-0.04343017563223839,
-0.019942719489336014,
0.009791736491024494,
0.02536097541451454,
0.013746376149356365,
-0.021262669935822487,
-0.009485321119427681,
0.044254470616579056,
0.00443145539611578,
0.007482276763767004,
0.018720125779509544,
-0.037281543016433716,
-0.005836219526827335,
-0.07831498980522156,
-0.013537595048546791,
-0.011890826746821404,
0.054961688816547394,
-0.023236991837620735,
0.051296889781951904,
0.010875525884330273,
0.05771472677588463,
0.014574162662029266,
-0.03170458599925041,
-0.07667987048625946,
0.014809617772698402,
-0.024353599175810814,
0.004793623927980661,
-0.02627021260559559,
-0.011415941640734673,
-0.021020714193582535,
-0.061064667999744415,
-0.002651527523994446,
-0.02812948077917099,
-0.007357425056397915,
-0.036321595311164856,
0.037772368639707565,
-0.03993552178144455,
-0.040709007531404495,
0.009947001934051514,
0.003407498588785529,
0.047898970544338226,
-0.02175779826939106,
0.045164018869400024,
0.02218928001821041,
-0.053361743688583374,
-0.008553571999073029,
-0.029812583699822426,
0.0195640716701746,
-0.00923227984458208,
0.011253580451011658,
-0.008221038617193699,
0.027948912233114243,
-0.004703958053141832,
-0.022755015641450882,
0.019445154815912247,
0.01160422619432211,
-0.02067345194518566,
0.008778586983680725,
-0.012300878763198853,
-0.04312713071703911,
-0.032107774168252945,
0.00031894471612758934,
0.03152039647102356,
-0.02512158267199993,
0.0015425195451825857,
-0.01758686825633049,
-0.02140447497367859,
-0.008999453857541084,
0.03813464567065239,
0.03427138552069664,
-0.010549644008278847,
-0.02291468158364296,
-0.046872578561306,
0.004301370587199926,
-0.02255985513329506,
-0.0018117957515642047,
0.038347914814949036,
0.0064779240638017654,
-0.04967770352959633,
-0.01194054540246725,
0.01080985926091671,
-0.011385473422706127,
-0.021273858845233917,
0.021382031962275505,
-0.003621743991971016,
0.03468560427427292,
-0.035264138132333755,
-0.002985613187775016,
-0.005762703716754913,
0.03971673175692558,
0.0487402118742466,
-0.0021421012934297323,
-0.001202692394144833,
-0.10525748878717422,
-0.024722490459680557,
0.02319158986210823,
0.030972642824053764,
-0.03949793055653572,
-0.01771995611488819,
-0.05980755016207695,
0.02700810134410858,
0.0496554896235466,
-0.03364194184541702,
0.0020809415727853775,
-0.03348109498620033,
-0.006722589954733849,
0.010819676332175732,
0.004627194255590439,
-0.020795349031686783,
-0.00118971336632967,
-0.012543522752821445,
0.0006304801790975034,
-0.03729940950870514,
0.031319938600063324,
0.002661954378709197,
0.03298606351017952,
0.04650525376200676,
0.0033453917130827904,
0.032588981091976166,
0.036926768720149994,
0.00214644568040967,
0.03678780794143677,
-0.020336473360657692,
-0.10004056990146637,
-0.017225749790668488,
0.02943619340658188,
-0.01060989499092102,
0.0412735752761364,
-0.015602747909724712,
-0.05625375360250473,
0.006939465180039406,
0.01737263984978199,
-0.017776519060134888,
-0.016181860119104385,
-0.050275448709726334,
0.015347061678767204,
0.04814455658197403,
0.018773524090647697,
0.011855916120111942,
0.05291992425918579,
-0.0042785839177668095,
0.004274048376828432,
-0.015849508345127106,
0.019525060430169106,
-0.011647442355751991,
0.0038559609092772007,
-0.03481599688529968,
-0.013026906177401543,
-0.03316785767674446,
0.03023342601954937,
0.02129160426557064,
0.03987223654985428,
0.007987018674612045,
-0.06869251281023026,
-0.013329125009477139,
0.02806159108877182,
0.015683142468333244,
-0.032831821590662,
-0.012431475333869457,
0.00961821898818016,
0.0021563577465713024,
-0.02532307431101799,
0.010244895704090595,
0.02095961943268776,
0.010765607468783855,
-0.017186854034662247,
-0.03648357093334198,
0.006652564741671085,
-0.0010156367206946015,
0.00023785533267073333,
0.02179599367082119,
-0.08043918013572693,
0.06961116939783096,
-0.01321882288902998,
-0.018577218055725098,
0.009780538268387318,
-0.03729884326457977,
-0.00551885599270463,
0.009852293878793716,
-0.0072166998870670795,
0.011088420636951923,
-0.02564210258424282,
0.00717664510011673,
-0.0311855711042881,
-0.02675735205411911,
-0.03949659690260887,
-0.021744731813669205,
0.03401359170675278,
0.01703425869345665,
-0.004459407180547714,
-0.04917685687541962,
0.010003319941461086,
-0.0448879599571228,
-0.048570871353149414,
0.004082133062183857,
0.03316207230091095,
-0.030855365097522736,
0.012565572746098042,
0.045248065143823624,
-0.01330607384443283,
0.05581412836909294,
0.01940169185400009,
-0.052701186388731,
-0.012775261886417866,
0.02567490190267563,
-0.008632151409983635,
-0.034303929656744,
0.03819522261619568,
-0.02120782621204853,
-0.024391165003180504,
0.02615865133702755,
-0.01409299485385418,
-0.0038053635507822037,
-0.03033030405640602,
-0.004369514063000679,
0.0636148527264595,
0.01251031830906868,
-0.022617924958467484,
-0.023641744628548622,
0.007426668424159288,
0.00711615988984704,
0.030611859634518623,
0.010420835576951504,
0.022068016231060028,
-0.029745087027549744,
-0.04477042332291603,
0.02326110750436783,
0.012149942107498646,
0.028026500716805458,
-0.003787736175581813,
0.044871412217617035,
-0.005046692676842213,
0.007463713642209768,
0.025949204340577126,
0.003209058428183198,
0.03126619756221771,
-0.01637398637831211,
-0.009658033028244972,
0.025639623403549194,
0.009619022719562054,
-0.006900289095938206,
-0.00181323301512748,
-0.016013070940971375,
-0.007600381504744291,
0.05891489237546921,
-0.020916739478707314,
0.02508736401796341,
-0.016610514372587204,
-0.030631741508841515,
0.014320185407996178,
-0.01792619377374649,
-0.018892178311944008,
-0.002942974679172039,
-0.012865714728832245,
0.013015884906053543,
0.002970797475427389,
0.0037277594674378633,
0.04925357550382614,
0.0366230271756649,
0.00108516204636544,
-0.006589659955352545,
0.04548856243491173,
0.033984120935201645,
0.014433193020522594,
-0.03832489624619484,
-0.040985070168972015,
0.018071062862873077,
-0.02351541258394718,
0.04426107183098793,
-0.030877280980348587,
0.005361150484532118,
0.042836930602788925,
-0.003461620304733515,
0.0164254792034626,
-0.03553444519639015,
-0.02970229648053646,
-0.03593209385871887,
0.01531991083174944,
0.04585149884223938,
0.012611384503543377,
-0.017444681376218796,
-0.015520300716161728,
0.038537610322237015,
-0.013815334066748619,
0.03431890532374382,
-0.02280653826892376,
-0.024309175089001656,
-0.03615603968501091,
-0.010895699262619019,
-0.042224038392305374,
0.04768763855099678,
0.007460346911102533,
-0.05140553042292595,
0.02014750801026821,
-0.005764665547758341,
-0.007547818124294281,
0.011858934536576271,
0.03890671208500862,
-0.03230896219611168,
0.06757846474647522,
-0.04625452682375908,
0.01120840571820736,
0.012076803483068943,
0.040075525641441345,
0.10388867557048798,
0.051059357821941376,
0.020197002217173576,
-0.01782512292265892,
-0.012100364081561565,
-0.031792908906936646,
0.01966061256825924,
-0.05016365274786949,
0.0029108652379363775,
-0.02769627794623375,
0.03390909358859062,
-0.011821896769106388,
0.07439140230417252,
-0.013760285452008247,
0.01111836638301611,
0.047401294112205505,
-0.04048830643296242,
-0.004163922742009163,
-0.021908849477767944,
0.033301543444395065,
-0.028397612273693085,
0.0326240248978138,
-0.06639572232961655,
0.048150964081287384,
-0.035997990518808365,
0.008997052907943726,
-0.026779308915138245,
-0.030538763850927353,
0.023182405158877373,
-0.026831623166799545,
-0.07091726362705231,
0.008152760565280914,
-0.017420616000890732,
-0.03224625810980797,
-0.038285210728645325,
0.023235423490405083,
-0.003164416179060936,
-0.018112067133188248,
0.0016724744345992804,
0.012804169207811356,
0.011521794833242893,
0.008239427581429482,
-0.005374947562813759,
0.03412541002035141,
-0.04520608112215996,
0.011017778888344765,
-0.02135515958070755,
0.030548980459570885,
-0.022479161620140076,
0.013074951246380806,
0.0254408847540617,
0.014519991353154182,
0.010242622345685959,
-0.03917878121137619,
-0.028038639575242996,
-0.03704826533794403,
0.021937627345323563,
-0.001514421310275793,
-0.04229806363582611,
-0.03682911396026611,
0.03585876524448395,
0.01886860467493534,
0.029766777530312538,
-0.02503940276801586,
0.023371698334813118,
0.006133892107754946,
-0.025971779599785805,
0.0641363263130188,
-0.03256739303469658,
-0.024842364713549614,
-0.027037540450692177,
-0.0007434749859385192,
-0.02673228085041046,
-0.00765646155923605,
0.01800386793911457,
0.03926791250705719,
0.05106500908732414,
-0.005467584356665611,
0.009922530502080917,
-0.025724545121192932,
-0.018186256289482117,
0.04772578924894333,
0.0009290110319852829,
-0.01755436509847641,
-0.0169055312871933,
-0.039328448474407196,
0.004298038315027952,
0.03938652202486992,
0.020489603281021118,
0.002217319328337908,
-0.008316131308674812,
-0.0007520075305365026,
-0.0006100009777583182,
-0.05964341759681702,
-0.02769852802157402,
0.03988967463374138,
-0.048098478466272354,
-0.003657112829387188,
0.016703635454177856,
0.022952977567911148,
0.05067988485097885,
-0.034633323550224304,
-0.03739439323544502,
0.012027759104967117,
-0.009757870808243752,
0.006449730601161718,
0.014114944264292717,
-0.030934615060687065,
-0.0047541349194943905,
0.010480571538209915,
-0.018781602382659912,
-0.041561514139175415,
-0.025637079030275345,
-0.03789843991398811,
-0.0015415444504469633,
-0.003563354955986142,
0.029149405658245087,
0.020015813410282135,
0.01055847480893135,
-0.028201254084706306,
0.05016984045505524,
-0.011257421225309372,
0.0028132074512541294,
-0.08785676956176758,
-0.014629913493990898,
0.018962588161230087,
-0.028431018814444542,
-0.026404457166790962,
0.03659215569496155,
-0.055686697363853455,
-0.0011586187174543738,
-0.013246974907815456,
-0.029537569731473923,
-0.015127292834222317,
-0.04180990532040596,
-0.01819589175283909,
-0.039634574204683304,
0.04016486182808876,
-0.02600657008588314,
-0.014794014394283295,
0.007344473153352737,
-0.01911846734583378,
-0.03345765173435211,
0.014853687025606632,
0.0030476306565105915,
0.03494269773364067,
0.05794728919863701,
-0.01759880967438221,
-0.009092902764678001,
0.06963720917701721,
-0.027757320553064346,
-0.007967405021190643,
-0.002181079937145114,
-0.03222517669200897,
-0.01874936930835247,
-0.0033860886469483376,
0.015597482211887836,
-0.016234539449214935,
-0.037880782037973404,
0.028480686247348785,
0.010130765847861767,
0.000027348336516297422,
0.019720925018191338,
0.011907973326742649,
0.0013700707349926233,
0.0038053584285080433,
0.023261038586497307,
0.02614537626504898,
0.015048330649733543,
0.03407515957951546,
-0.05105109512805939,
0.03009043075144291,
0.04489728435873985,
0.03338754177093506,
-0.10098567605018616,
-0.0022374738473445177,
0.007730438373982906,
-0.03762563318014145,
0.021291086450219154,
-0.04257884994149208,
0.02887495793402195,
-0.009479384869337082,
-0.08790843933820724,
0.036654628813266754,
-0.02274140901863575,
0.0037362989969551563,
-0.03366260603070259,
-0.030868608504533768,
-0.003217083867639303,
0.0587908960878849,
0.013942350633442402,
0.05546164512634277,
0.008999616838991642,
0.016534749418497086,
-0.003277706215158105,
0.012624275870621204,
-0.01408728864043951,
0.03186691924929619,
0.0103762773796916,
-0.007245497312396765,
0.0455811470746994,
-0.041310954838991165,
-0.030638813972473145,
0.016801241785287857,
0.011019274592399597,
0.011609052307903767,
-0.019783305004239082,
-0.03758073225617409,
0.01914817839860916,
0.017183292657136917,
0.014510099776089191,
0.016375618055462837,
-0.01646430976688862,
0.06572441756725311,
0.02837691642343998,
0.024741156026721,
-0.0012912447564303875,
-0.01175166666507721,
0.025119882076978683,
-0.060630813241004944,
-0.01516232080757618,
0.0265783853828907,
-0.014882686547935009,
0.004705595783889294,
0.0008868848090060055,
-0.0044228858314454556,
0.018634483218193054,
0.00891370140016079,
-0.011633184738457203,
-0.041398994624614716,
0.02002151682972908,
0.02674981765449047,
-0.041771285235881805,
-0.015893857926130295,
0.026567326858639717,
-0.014423844404518604,
0.015569389797747135,
-0.01580066978931427,
-0.012109742499887943,
-0.012914595194160938,
-0.022860530763864517,
-0.0016909897094592452,
0.06079569458961487,
0.015291844494640827,
0.005074992310255766,
-0.016263887286186218,
-0.021537939086556435,
0.048575252294540405,
0.04247059300541878,
0.0457046777009964,
0.008699479512870312,
-0.07560822367668152,
0.0009185546659864485,
-0.06562430411577225,
0.01553040836006403,
-0.012020152993500233,
0.010380037128925323,
-0.0189206600189209,
-0.022776346653699875,
0.02282791957259178,
0.015836205333471298,
0.04415220767259598,
-0.015028727240860462,
-0.009963109157979488,
0.013334075920283794,
-0.027549296617507935,
0.011527560651302338,
-0.05011388659477234,
-0.005757778882980347,
0.023264732211828232,
-0.03722083196043968,
0.007180781103670597,
-0.018656225875020027,
-0.01823369413614273,
0.003533479990437627,
0.045135922729969025,
-0.0005534614901989698,
0.033585257828235626,
-0.012989327311515808,
-0.015618274919688702,
0.04549003764986992,
0.023476827889680862,
-0.040163442492485046,
0.07238615304231644,
-0.014341579750180244,
0.013666920363903046,
-0.010369171388447285,
-0.01795251853764057,
-0.028459783643484116,
0.03882984444499016,
-0.007536545395851135,
-0.00620332732796669,
-0.03191366791725159,
-0.04935922101140022,
-0.008971178904175758,
-0.0284484401345253,
0.03823589161038399,
0.04251042380928993,
-0.04788830131292343,
-0.010288701392710209,
0.05692615360021591,
0.03614572808146477,
0.033633917570114136,
-0.046154431998729706,
0.002371888840571046,
0.017407024279236794,
-0.013999038375914097,
-0.009565397165715694,
0.0672503337264061,
0.02666524611413479,
-0.024144185706973076,
-0.0015743318945169449,
0.009624582715332508,
0.04013298824429512,
0.013246002607047558,
0.04088667035102844,
0.004834415391087532,
-0.04669167101383209,
-0.023629236966371536,
-0.01862558349967003,
-0.004868569318205118,
0.016514059156179428,
0.02961554005742073,
0.013678341172635555,
0.04680866375565529,
-0.011330680921673775,
0.011326463893055916,
0.006506441626697779,
0.014468248933553696,
0.05042966827750206,
0.023405231535434723,
-0.00911876279860735,
0.0393868163228035,
0.00048244729987345636,
-0.02788880467414856,
-0.02118120901286602,
-0.0032106300350278616,
0.024652116000652313,
-0.013741012662649155,
0.023264022544026375,
0.002232210710644722,
0.009651701897382736,
-0.013671685941517353,
-0.040700506418943405,
-0.010569809935986996,
0.003158405190333724,
0.03600581735372543,
0.014513670466840267,
-0.014864064753055573,
0.01216190867125988,
-0.02294033393263817,
-0.015486023388803005,
0.010276093147695065,
-0.036297157406806946,
0.020371751859784126,
-0.04894280806183815,
0.031751733273267746,
-0.02313871867954731,
0.002399900695309043
] |
<p>The change of entropy is defined $$\Delta S = \int \frac{dQ_\mathrm{rev}}{T}.$$ If a system is isolated the heat transfer between the system and the surroundings is zero ($dQ = 0$), thus $\Delta S = 0$.</p>
<p>However, it is commonly stated that the entropy of an isolated system can increase. How is this possible, given the above definition of entropy?</p>
| 9,571 |
[
-0.009515533223748207,
-0.02055283449590206,
0.01036105863749981,
0.02359859086573124,
0.03268016129732132,
0.014768446795642376,
-0.043350089341402054,
-0.0008121048449538648,
-0.002120247343555093,
-0.0599861815571785,
-0.013226857408881187,
0.016532637178897858,
-0.00403548264876008,
0.010161438956856728,
0.006602379027754068,
-0.0007617437513545156,
-0.010735019110143185,
0.017938924953341484,
0.0003559751494321972,
0.00048313551815226674,
-0.02248425781726837,
0.07075122743844986,
0.009499389678239822,
-0.016216371208429337,
-0.040190428495407104,
0.025957051664590836,
-0.02967592515051365,
-0.011583256535232067,
0.020482374355196953,
0.03477500006556511,
0.005139804910868406,
0.0059894113801419735,
0.0029752955306321383,
0.017634062096476555,
0.012011431157588959,
-0.055668722838163376,
-0.036931782960891724,
-0.014288966543972492,
0.013852412812411785,
-0.0000048671327022020705,
-0.06097203865647316,
-0.027331436052918434,
0.004998925141990185,
0.04589555785059929,
-0.04426751285791397,
-0.016810588538646698,
0.004178435541689396,
-0.033715877681970596,
0.04591470956802368,
-0.037843745201826096,
0.02571146748960018,
-0.024618756026029587,
0.05971016362309456,
0.0352146215736866,
0.02755574695765972,
0.042967721819877625,
0.031279753893613815,
0.031450510025024414,
-0.03156644478440285,
-0.021172398701310158,
-0.02550637163221836,
-0.008228138089179993,
-0.01934506930410862,
-0.02129543013870716,
0.010579248890280724,
0.025770176202058792,
0.010861321352422237,
-0.011649218387901783,
0.0388232097029686,
0.003930981736630201,
-0.007403039373457432,
0.02912215143442154,
0.027563076466321945,
-0.0041467733681201935,
0.04639540612697601,
-0.037069205194711685,
-0.004288297146558762,
-0.00478507112711668,
0.016722137108445168,
0.05111398920416832,
0.04862719774246216,
0.0032239023130387068,
0.05678735673427582,
0.003007130231708288,
0.030506150797009468,
-0.03681548684835434,
0.07932580262422562,
0.0024524908512830734,
0.05066826939582825,
0.029757777228951454,
0.020121771842241287,
0.031480852514505386,
0.009434757754206657,
-0.019254008308053017,
-0.009444360621273518,
0.016919516026973724,
-0.01390845887362957,
0.06304055452346802,
0.0009972220286726952,
-0.04504045844078064,
-0.01041093934327364,
-0.011878622695803642,
0.07417237758636475,
0.04741959273815155,
0.015490055084228516,
-0.022247392684221268,
-0.044524770230054855,
-0.005555265583097935,
0.006181481759995222,
-0.026812659576535225,
-0.04376981034874916,
0.007357653696089983,
0.041272953152656555,
-0.013959947973489761,
0.006586277857422829,
-0.011946833692491055,
-0.03405499830842018,
-0.04206758737564087,
0.024967242032289505,
0.04534900560975075,
0.027302417904138565,
-0.04114368185400963,
0.006313789170235395,
-0.014036855660378933,
-0.04867636784911156,
0.06133227422833443,
0.00041443773079663515,
-0.003875743830576539,
-0.03444497659802437,
-0.005943555384874344,
-0.01995902694761753,
0.013141123577952385,
-0.012478748336434364,
0.012951746582984924,
0.03696329891681671,
-0.011393757537007332,
-0.10552594810724258,
-0.07505730539560318,
0.06374811381101608,
-0.007016249932348728,
-0.0002690553665161133,
-0.057430971413850784,
-0.0006732434849254787,
0.05672665312886238,
0.061483632773160934,
0.0073715257458388805,
-0.011145517230033875,
0.00457360316067934,
0.011830640956759453,
0.029504884034395218,
-0.0053069801069796085,
-0.04455046355724335,
0.012543066404759884,
-0.01953248679637909,
-0.007720824331045151,
-0.08694864809513092,
0.07381808012723923,
0.056625619530677795,
-0.028810376301407814,
-0.02598302811384201,
0.014680885709822178,
-0.04430326074361801,
-0.00921616330742836,
0.0015754972118884325,
-0.003082831157371402,
-0.047135014086961746,
0.10061703622341156,
-0.022381532937288284,
0.0350971519947052,
0.023989206179976463,
0.05239982157945633,
0.04091893136501312,
-0.015479067340493202,
0.04736855998635292,
0.009819178842008114,
-0.01801084354519844,
-0.036503784358501434,
-0.013210155069828033,
-0.008656839840114117,
0.027626996859908104,
-0.029660243541002274,
-0.021727237850427628,
-0.016056425869464874,
0.009891475550830364,
0.015653256326913834,
0.01795734278857708,
0.007734368089586496,
0.013771998696029186,
0.0005212680553086102,
-0.03125571459531784,
-0.016811372712254524,
-0.09996292740106583,
0.034463491290807724,
0.014653272926807404,
0.004029174335300922,
0.03266479820013046,
0.024826783686876297,
0.06806642562150955,
-0.013170440681278706,
0.003693311009556055,
-0.011209444142878056,
0.006010863464325666,
0.0059242551214993,
-0.04087323322892189,
0.04316987097263336,
0.04347417503595352,
0.06742621958255768,
0.026921093463897705,
0.02885415218770504,
0.009716009721159935,
-0.05070346221327782,
0.003319176845252514,
-0.02872241660952568,
-0.005288979969918728,
-0.016352098435163498,
-0.018871504813432693,
0.020037464797496796,
-0.00907253660261631,
-0.008703438565135002,
0.029013890773057938,
-0.0048128156922757626,
0.06173965707421303,
0.032229285687208176,
0.030164165422320366,
-0.0013305455213412642,
0.03347288444638252,
0.0239349864423275,
-0.000555554055608809,
-0.024546455591917038,
-0.06182773783802986,
-0.056382060050964355,
0.004057074431329966,
0.029061276465654373,
0.06314510107040405,
-0.052361682057380676,
0.004246185068041086,
0.019990788772702217,
0.008219792507588863,
0.017330646514892578,
-0.0017451774328947067,
-0.009173835627734661,
-0.007227669935673475,
0.05181414261460304,
-0.013073242269456387,
0.04089038446545601,
0.013386743143200874,
0.01497346255928278,
-0.02951381541788578,
0.022778639569878578,
-0.006797607988119125,
0.03173359856009483,
0.04044806584715843,
0.014430945739150047,
0.020455272868275642,
-0.016814181581139565,
-0.0014084638096392155,
0.020470181480050087,
-0.017707563936710358,
0.000523786002304405,
-0.010767101310193539,
0.009783835150301456,
0.036475758999586105,
-0.020714914426207542,
-0.011213240213692188,
0.008741985075175762,
-0.026541469618678093,
-0.008406874723732471,
-0.005581612698733807,
0.018659457564353943,
-0.045503709465265274,
0.013581523671746254,
-0.00455903448164463,
0.023223182186484337,
-0.004116323310881853,
-0.028249457478523254,
0.018553409725427628,
0.009460271336138248,
0.026396330446004868,
-0.056052472442388535,
-0.007248655427247286,
0.009833311662077904,
-0.022163379937410355,
-0.005694888066500425,
0.01697605848312378,
-0.004640662111341953,
0.03321738541126251,
-0.01439819484949112,
-0.039116643369197845,
0.024799887090921402,
-0.04013998433947563,
0.014315849170088768,
-0.015713291242718697,
-0.02891658991575241,
-0.05240281671285629,
0.0003038958238903433,
-0.01822204701602459,
-0.00003940121678169817,
-0.024299858137965202,
-0.011544243432581425,
0.04829184710979462,
-0.03235429525375366,
-0.015685198828577995,
0.03921886160969734,
-0.07138398289680481,
-0.038922760635614395,
-0.0071852803230285645,
-0.017160896211862564,
0.034744758158922195,
-0.030407335609197617,
0.04204293340444565,
0.025063736364245415,
-0.03755195811390877,
-0.02958875149488449,
-0.04528876766562462,
-0.05666155368089676,
0.007317782379686832,
-0.013064347207546234,
0.02719280868768692,
-0.03125004842877388,
-0.031783074140548706,
0.0701286792755127,
0.021588636562228203,
-0.036724042147397995,
0.01680312119424343,
-0.03071773424744606,
-0.03245200589299202,
-0.028901617974042892,
-0.03384220600128174,
0.02122013457119465,
-0.004281856585294008,
0.02841128222644329,
0.02902459353208542,
0.05283055827021599,
0.02542167529463768,
-0.01565699093043804,
-0.045086465775966644,
0.02033211477100849,
0.0320037417113781,
0.02310713566839695,
0.025860749185085297,
-0.0029728885274380445,
0.002108108950778842,
0.011606443673372269,
0.017864352092146873,
0.048338595777750015,
0.0105630187317729,
-0.04386092722415924,
0.07252531498670578,
0.04031544178724289,
0.05610894784331322,
-0.06797076761722565,
0.05312817543745041,
-0.026087243109941483,
0.008984875865280628,
0.004567153286188841,
0.012811249122023582,
0.03214553743600845,
-0.017094412818551064,
0.0002162700257031247,
-0.026525333523750305,
0.044642332941293716,
-0.01410573162138462,
-0.025882991030812263,
-0.012050720863044262,
-0.0010114568285644054,
0.02148149348795414,
0.0024908750783652067,
0.031007353216409683,
0.030918056145310402,
0.038725949823856354,
0.018970858305692673,
-0.024118572473526,
-0.0127443578094244,
-0.008097471669316292,
-0.0511457584798336,
-0.015393276698887348,
-0.01019273791462183,
0.04028114676475525,
0.00394285237416625,
0.059538859874010086,
0.012179642915725708,
0.007851259782910347,
0.0222452562302351,
-0.037303440272808075,
-0.07392042130231857,
0.06476710736751556,
-0.05158236250281334,
-0.02478405460715294,
0.015920624136924744,
0.008262690156698227,
0.034244656562805176,
-0.0092681385576725,
-0.044051289558410645,
-0.022366421297192574,
0.011370101012289524,
-0.06829068809747696,
-0.012451021932065487,
-0.013903717510402203,
-0.04543733969330788,
-0.011556859128177166,
0.03645505756139755,
0.04216373711824417,
-0.039860352873802185,
-0.01386351604014635,
0.020849984139204025,
-0.009536607190966606,
0.013888195157051086,
-0.018526511266827583,
-0.011574558913707733,
0.01592707447707653,
0.007821201346814632,
0.04314105585217476,
0.01428313460201025,
0.010185928083956242,
0.029603417962789536,
0.020328518003225327,
0.013544675894081593,
-0.010917297564446926,
-0.010589794255793095,
-0.014289715327322483,
-0.05980134382843971,
-0.0177680104970932,
-0.009127238765358925,
0.012492403388023376,
-0.007958241738379002,
0.062326837331056595,
-0.0007305312319658697,
-0.0019746876787394285,
-0.03812456876039505,
-0.0021305521950125694,
0.019442884251475334,
0.016759783029556274,
-0.04388032108545303,
-0.019640544429421425,
-0.025278931483626366,
-0.017334744334220886,
-0.03157917037606239,
0.022894103080034256,
-0.007469623815268278,
-0.024276386946439743,
0.021354811266064644,
-0.030652716755867004,
-0.0007781913736835122,
0.01147510390728712,
-0.023987744003534317,
0.019041672348976135,
0.04843228682875633,
0.013734889216721058,
0.02353384532034397,
0.0023328079842031,
0.019999580457806587,
0.0156693235039711,
-0.0069829137064516544,
-0.006855433341115713,
-0.0673580914735794,
-0.01883671246469021,
0.0156774390488863,
0.03507915139198303,
-0.006006036885082722,
0.030469469726085663,
-0.03582232818007469,
-0.002083565341308713,
0.03326671943068504,
0.0018917875131592155,
0.04489029571413994,
-0.017106568440794945,
-0.03794333338737488,
-0.01031377911567688,
-0.003598600858822465,
-0.010078907012939453,
0.013312348164618015,
0.0065775066614151,
0.050633225589990616,
-0.010563120245933533,
-0.024649079889059067,
-0.01839136704802513,
0.015679579228162766,
-0.012530953623354435,
0.05590576305985451,
-0.034335050731897354,
0.013439820148050785,
-0.016721174120903015,
0.011818857863545418,
-0.0006208322010934353,
-0.07292206585407257,
0.026662558317184448,
0.008375127799808979,
-0.0006172017310746014,
-0.015013855881989002,
-0.026647664606571198,
-0.04560251161456108,
0.0028854357078671455,
0.019867314025759697,
-0.018953192979097366,
-0.004004692658782005,
-0.014179042540490627,
0.05015324801206589,
0.03858393803238869,
-0.01613876409828663,
0.05961029231548309,
0.0659809485077858,
-0.011968012899160385,
0.0030479240231215954,
-0.022140195593237877,
0.048787809908390045,
-0.05936658754944801,
-0.0056471326388418674,
-0.04638837277889252,
0.04252896457910538,
-0.020406123250722885,
0.0802471935749054,
0.0023391193244606256,
0.020989231765270233,
0.0032715294510126114,
-0.014581874012947083,
0.006246700417250395,
0.04101071506738663,
-0.01789059117436409,
0.004420408979058266,
-0.02088824100792408,
0.03940236195921898,
0.014390955679118633,
-0.022906435653567314,
-0.016264157369732857,
-0.008732487447559834,
0.004315884783864021,
0.01605694554746151,
-0.03060869313776493,
0.03704189136624336,
-0.013251146301627159,
-0.03181922063231468,
0.013877629302442074,
-0.04519675299525261,
0.04869804531335831,
-0.014197288081049919,
-0.009709075093269348,
0.033707767724990845,
-0.06843160092830658,
0.0057617309503257275,
-0.015915514901280403,
-0.006114010699093342,
-0.004092596936970949,
-0.0727204978466034,
0.042302072048187256,
0.01573992893099785,
0.005223450250923634,
-0.08247604966163635,
-0.04258101060986519,
0.01729155145585537,
-0.0020755226723849773,
-0.00033875982626341283,
-0.06370096653699875,
-0.02035120315849781,
-0.015309968031942844,
-0.03976129740476608,
-0.02260538749396801,
0.04320138320326805,
0.005349029321223497,
-0.00011454673222033307,
0.031495172530412674,
0.044253814965486526,
0.017863735556602478,
-0.018779762089252472,
-0.01948677748441696,
0.022908994928002357,
-0.031082412227988243,
0.0012772131012752652,
0.028938619419932365,
0.032430361956357956,
-0.032332971692085266,
-0.01156491506844759,
0.02142845280468464,
0.0006695684278383851,
0.03930952399969101,
0.011172158643603325,
-0.03324731066823006,
0.011159583926200867,
0.010115372948348522,
0.00000956202347879298,
0.006610209587961435,
0.010059728287160397,
0.034000929445028305,
0.031670790165662766,
0.035831350833177567,
-0.007139634806662798,
0.0005931477644480765,
-0.04623686149716377,
0.01985919289290905,
-0.007626920938491821,
-0.019249310716986656,
-0.007890108972787857,
0.07074176520109177,
-0.009338120929896832,
-0.03566285967826843,
-0.004039081744849682,
0.0017089471220970154,
0.036721013486385345,
-0.0021251726429909468,
0.02293531969189644,
-0.011862751096487045,
-0.012302049435675144,
-0.035216446965932846,
-0.03287544474005699,
-0.04320414736866951,
-0.012410732917487621,
0.05165058374404907,
-0.022897860035300255,
0.05107634887099266,
0.012786280363798141,
0.0014887219294905663,
0.006224023178219795,
-0.023441078141331673,
0.0037138962652534246,
0.013103939592838287,
-0.005900267045944929,
0.02739408239722252,
-0.006148679181933403,
-0.016722794622182846,
0.023465381935238838,
0.05430378392338753,
-0.05119919404387474,
0.014091604389250278,
0.019210275262594223,
-0.0017275934806093574,
-0.017626119777560234,
-0.05988098308444023,
-0.01813972368836403,
0.02576184831559658,
-0.035279180854558945,
0.03985437750816345,
-0.0007777445716783404,
-0.004160859156399965,
0.04885120317339897,
-0.037600986659526825,
0.0326479934155941,
-0.08282306790351868,
-0.00954652763903141,
-0.022101834416389465,
0.022358544170856476,
0.012156719341874123,
0.019046491011977196,
0.041954223066568375,
-0.019893886521458626,
0.0006958332378417253,
-0.0004677155229728669,
-0.01852521114051342,
0.003624745411798358,
-0.057513125240802765,
-0.011113228276371956,
-0.024207929149270058,
-0.042325299233198166,
0.0336495004594326,
0.0026565715670585632,
-0.03869037330150604,
0.022433767095208168,
-0.014837775379419327,
0.030600043013691902,
0.02964606322348118,
0.01431907806545496,
0.002243075519800186,
0.08624902367591858,
0.004700193647295237,
0.04205779358744621,
-0.014512443915009499,
0.020129190757870674,
0.10742559283971786,
0.045277051627635956,
-0.016466977074742317,
-0.062059637159109116,
-0.019449951127171516,
0.007781137712299824,
0.03218044713139534,
-0.010710478760302067,
0.02587052248418331,
0.012428916059434414,
-0.00753448810428381,
-0.004795765969902277,
0.05006450414657593,
0.011779982596635818,
-0.009454791434109211,
0.045569635927677155,
-0.054375406354665756,
-0.02390301413834095,
-0.01312379539012909,
0.010055556893348694,
-0.040881406515836716,
0.011144403368234634,
-0.023741692304611206,
-0.006339430809020996,
-0.000991107546724379,
0.012941303662955761,
-0.027983283624053,
-0.05239364504814148,
0.0132523812353611,
-0.009885011240839958,
-0.0279256422072649,
-0.012648177333176136,
0.03059461899101734,
-0.010530163533985615,
-0.035254232585430145,
0.025100227445364,
0.01452886126935482,
0.019172726199030876,
-0.011441760696470737,
0.04087948426604271,
0.0011129630729556084,
-0.006397856865078211,
0.023049429059028625,
0.01168826874345541,
-0.05958729609847069,
-0.02552860975265503,
-0.0201122984290123,
0.0239028949290514,
-0.003484416054561734,
0.021162929013371468,
-0.024429040029644966,
-0.0011744187213480473,
-0.011724848300218582,
-0.02365191839635372,
-0.03775721788406372,
0.0031885637436062098,
0.0030563774053007364,
-0.013298084028065205,
-0.047642312943935394,
-0.016222424805164337,
0.030419809743762016,
-0.00019386633357498795,
0.03980410844087601,
0.009805710054934025,
-0.01658988557755947,
0.029960306361317635,
-0.0021695562172681093,
0.034093137830495834,
-0.020822586491703987,
0.014114555902779102,
-0.04971281439065933,
-0.014108187519013882,
-0.036717113107442856,
-0.00802004337310791,
-0.00420027319341898,
-0.01731385849416256,
0.037101104855537415,
0.03223414719104767,
0.012818899936974049,
-0.02261050045490265,
-0.048701267689466476,
0.003865198465064168,
0.01932198368012905,
0.003993692342191935,
-0.03779805079102516,
0.013339368626475334,
-0.0022979523055255413,
0.07524576783180237,
0.018458541482686996,
-0.028421957045793533,
0.03359825164079666,
0.0004517026536632329,
0.022342203184962273,
0.0009335239301435649,
-0.01297821942716837,
0.014639808796346188,
-0.03641844913363457,
0.004333095159381628,
0.006334880366921425,
0.01743149757385254,
0.03283454105257988,
-0.003163538407534361,
-0.016333337873220444,
0.03546113893389702,
-0.03003576770424843,
0.03787620738148689,
0.00918692909181118,
0.0058248708955943584,
-0.0466463528573513,
0.01812703162431717,
-0.0067084478214383125,
0.009115572087466717,
-0.06773870438337326,
0.012207898311316967,
-0.014868143945932388,
-0.024497205391526222,
0.03594476357102394,
-0.030825303867459297,
-0.0035776381846517324,
-0.04170030727982521,
0.056674886494874954,
-0.03934178501367569,
-0.03900088742375374,
-0.030347488820552826,
-0.016958918422460556,
0.04572886973619461,
0.03593956306576729,
0.006201812531799078,
0.014216608367860317,
0.005060405004769564,
-0.002676228992640972,
0.01837264932692051,
0.044297151267528534,
0.005482941400259733,
-0.042806223034858704,
-0.007573123089969158,
-0.010301806963980198,
0.02812355011701584,
-0.04344913735985756,
-0.04323175176978111,
0.05653003975749016,
-0.052559055387973785,
-0.016763288527727127,
-0.0073073264211416245,
0.03068637102842331,
0.038869794458150864,
0.02245582453906536,
-0.032227739691734314,
-0.02739597298204899,
0.02554362267255783,
-0.022656060755252838,
-0.0037827054038643837,
-0.011174939572811127,
-0.031081698834896088,
-0.032995764166116714,
-0.003795106429606676,
-0.0051992810331285,
-0.0002706892555579543,
0.001966545358300209,
0.030274543911218643,
0.026977937668561935,
0.014388377778232098,
-0.013148397207260132,
0.022897934541106224,
0.011567827314138412,
0.009125870652496815,
0.025289153680205345,
0.011359716765582561,
0.04070230945944786,
0.04228739067912102,
-0.0044191330671310425,
0.03463395684957504,
0.03680591657757759,
-0.0028541150968521833,
-0.09786820411682129,
0.03938112035393715,
0.006226771045476198,
-0.05072956159710884,
0.02652730606496334,
-0.03401714190840721,
0.026951424777507782,
0.03520338237285614,
-0.08427748829126358,
0.016190970316529274,
-0.059395600110292435,
-0.008988909423351288,
-0.016374830156564713,
-0.006604469381272793,
-0.033499546349048615,
0.07310277223587036,
0.08201536536216736,
0.013286055065691471,
0.0008318393956869841,
0.0026137453969568014,
-0.0018253858434036374,
-0.0004272234800737351,
-0.015299010090529919,
0.02747691050171852,
0.007137490436434746,
0.008420745842158794,
0.042252473533153534,
-0.03221003711223602,
-0.034760117530822754,
-0.00765469204634428,
-0.03445422276854515,
-0.04635467007756233,
0.006504357326775789,
0.027512066066265106,
0.01827065274119377,
0.043693020939826965,
0.013519790023565292,
-0.009932063519954681,
-0.025687217712402344,
0.011011290363967419,
0.02501637302339077,
0.036840133368968964,
0.001659971196204424,
-0.06349404901266098,
0.002127992222085595,
-0.02050452120602131,
-0.020931696519255638,
0.03300142660737038,
-0.0244097001850605,
-0.01677865721285343,
0.03960525617003441,
-0.007566750515252352,
0.001978743588551879,
-0.018304573372006416,
0.026409035548567772,
-0.04285687580704689,
-0.020442694425582886,
0.030048202723264694,
0.03270699083805084,
-0.015610617585480213,
-0.009713075123727322,
0.010773621499538422,
-0.029459448531270027,
0.027320489287376404,
-0.014718426391482353,
-0.035179413855075836,
-0.09037090092897415,
-0.009650906547904015,
-0.010323364287614822,
0.018964044749736786,
-0.02638978138566017,
-0.018579259514808655,
-0.03726380690932274,
0.03824666887521744,
0.0027117179706692696,
0.026232730597257614,
-0.023471606895327568,
-0.08349078893661499,
-0.03999070078134537,
-0.05033480003476143,
0.07463523745536804,
-0.008188530802726746,
-0.021253231912851334,
-0.0866646096110344,
-0.029065484181046486,
-0.03206378221511841,
0.01499913353472948,
0.09320810437202454,
0.010064512491226196,
-0.0293357502669096,
0.02411489561200142,
0.02653462626039982,
0.04408692941069603,
-0.010548905469477177,
0.018692201003432274,
-0.02798144891858101,
-0.008435839787125587,
0.011271952651441097,
-0.01555912010371685,
-0.011873245239257812,
0.037248626351356506,
0.019783498719334602,
-0.039301175624132156,
0.015654025599360466,
0.009663618169724941,
-0.022582372650504112,
0.04503891244530678,
0.007211014628410339,
-0.03391749784350395,
0.04107166826725006,
-0.040478263050317764,
0.03536340594291687,
-0.0014966456219553947,
0.006953176110982895,
-0.043320853263139725,
0.01921158656477928,
-0.0006618937477469444,
0.00235935440286994,
-0.0061119296588003635,
-0.039823275059461594,
0.009068865329027176,
-0.014100884087383747,
-0.012042705900967121,
0.027405934408307076,
-0.049267228692770004,
0.017186645418405533,
0.026312895119190216,
0.015093809925019741,
0.03633004426956177,
0.0032723681069910526,
0.02318011410534382,
-0.003996085841208696,
0.045439865440130234,
-0.008480277843773365,
0.07800433784723282,
0.04618322104215622,
-0.02354351431131363,
0.01839345507323742,
0.023087643086910248,
-0.020494267344474792,
0.011842296458780766,
0.03015149012207985,
-0.017813285812735558,
-0.00768246129155159,
-0.03125808760523796,
0.006838740780949593,
-0.01117346715182066,
0.011507079936563969,
0.03180159628391266,
-0.002640506951138377,
0.06716039776802063,
0.0101495161652565,
0.029376285150647163,
-0.019237641245126724,
-0.004997325129806995,
-0.035158149898052216,
-0.027774106711149216,
0.029023831710219383,
0.056114986538887024,
-0.011713053099811077,
-0.009450461715459824,
-0.005178432911634445,
-0.03195173665881157,
0.0013298646081238985,
-0.029464708641171455,
0.05973121523857117,
0.020048972219228745,
0.006986198015511036,
-0.027316942811012268,
-0.005279159639030695,
-0.017497221007943153,
-0.033141136169433594,
0.028637174516916275,
0.056883811950683594,
0.053694259375333786,
0.04291795566678047,
-0.06051809340715408,
-0.009294858202338219,
0.08250229805707932,
-0.034696318209171295,
-0.014257499948143959,
0.004049269948154688,
0.03548194840550423,
-0.02783665992319584,
-0.03365887701511383
] |
<p>I was in Solid State Physics lecture yesterday and we BRIEFLY went over what causes phonons to collide with one another. Things such as crystal imperfections, boundaries, Temperature, but I was wondering:</p>
<p>Do Optical mode phonons interact differently than acoustic ones? Also, is there a way I can quantify this?</p>
| 9,572 |
[
-0.00786840170621872,
-0.041875943541526794,
-0.03969661518931389,
-0.05203687399625778,
0.0160246379673481,
0.04395432397723198,
-0.010367144830524921,
-0.03989946469664574,
0.03353046253323555,
0.008766786195337772,
0.061032406985759735,
0.0182168111205101,
0.03975515067577362,
-0.004992715083062649,
0.010003562085330486,
0.0015230784192681313,
-0.018928783014416695,
-0.023411191999912262,
-0.00886031799018383,
-0.015666425228118896,
-0.02084086649119854,
0.032739464193582535,
0.005772344768047333,
-0.002999283839017153,
-0.018397292122244835,
0.024133263155817986,
-0.0075118448585271835,
-0.0049088322557508945,
0.06543032824993134,
-0.013768097385764122,
0.018015211448073387,
-0.01202964037656784,
0.013029004447162151,
0.05865643545985222,
0.013470867648720741,
0.0016037392197176814,
-0.010760143399238586,
-0.01762610487639904,
-0.05662761256098747,
0.03124978020787239,
-0.02695464715361595,
-0.013746856711804867,
0.0019445625366643071,
0.03510741516947746,
0.014246267266571522,
0.0006163623766042292,
0.007245650514960289,
-0.017322387546300888,
0.03158745914697647,
-0.0741472840309143,
0.03115461766719818,
-0.0035173373762518167,
0.03543509915471077,
0.03489185497164726,
0.020126251503825188,
-0.0050607421435415745,
0.07739301025867462,
0.08924854546785355,
0.013639005832374096,
-0.055173538625240326,
0.03305571526288986,
0.020599815994501114,
-0.028825290501117706,
-0.008599664084613323,
-0.051974616944789886,
0.010186982341110706,
0.014437885023653507,
-0.053475234657526016,
0.05284357815980911,
0.015232919715344906,
-0.015670353546738625,
0.008693228475749493,
0.07042383402585983,
-0.0036051147617399693,
0.018224984407424927,
-0.028496814891695976,
0.030727269127964973,
0.02408897504210472,
0.033202435821294785,
0.01851155050098896,
-0.022005973383784294,
0.0011058843228965998,
-0.006842645816504955,
0.010579777881503105,
-0.018953733146190643,
-0.034088652580976486,
0.06609772145748138,
-0.031695276498794556,
-0.029966970905661583,
0.009463092312216759,
0.004340778104960918,
0.002120835240930319,
0.032206472009420395,
0.019350947812199593,
-0.02101108990609646,
-0.03400780260562897,
0.016549700871109962,
0.030981427058577538,
0.010427712462842464,
-0.03760774806141853,
0.002366569358855486,
0.002716974588111043,
0.03099408932030201,
0.07912113517522812,
-0.009814449585974216,
-0.04012373089790344,
-0.017533963546156883,
0.021914903074502945,
-0.02114630863070488,
-0.006979715079069138,
-0.04780949279665947,
-0.008452904410660267,
-0.03191832825541496,
0.007932750508189201,
0.015991758555173874,
-0.01098613627254963,
0.015235668048262596,
-0.008235562592744827,
0.03805222362279892,
0.09063231199979782,
0.030201971530914307,
-0.027968883514404297,
-0.0016372366808354855,
-0.05687008798122406,
-0.0714937299489975,
-0.014137452468276024,
0.019491687417030334,
-0.0040647611021995544,
-0.045214831829071045,
0.03874553367495537,
-0.006108931265771389,
-0.0033442776184529066,
-0.030482502654194832,
-0.057327792048454285,
0.023252835497260094,
-0.030990881845355034,
-0.08923815935850143,
-0.041963521391153336,
0.054636914283037186,
-0.022225089371204376,
-0.04994809255003929,
-0.04393906518816948,
0.0032708996441215277,
0.02240644581615925,
0.061041977256536484,
0.029408108443021774,
0.04670248553156853,
-0.004177554044872522,
0.040707383304834366,
0.021363144740462303,
-0.011900908313691616,
-0.012059852480888367,
-0.0017034324118867517,
-0.015021647326648235,
0.051043156534433365,
-0.046221617609262466,
0.021852999925613403,
0.033189620822668076,
-0.015445238910615444,
-0.019284984096884727,
0.029804151505231857,
-0.015613707713782787,
-0.01188263762742281,
0.05370808392763138,
0.03508083522319794,
-0.05963578820228577,
0.05067824199795723,
-0.0017805981915444136,
-0.0008108210749924183,
0.059234652668237686,
0.004800640977919102,
0.01803802326321602,
0.0014096361119300127,
0.015794403851032257,
0.001032783417031169,
0.001169452560134232,
-0.0026661341544240713,
-0.054896846413612366,
-0.006451939698308706,
0.0009909049840644002,
-0.04023810103535652,
-0.054516326636075974,
-0.004070099908858538,
0.021609675139188766,
-0.04349241778254509,
0.041704192757606506,
0.020844697952270508,
-0.007095706649124622,
0.009758030995726585,
-0.034596607089042664,
-0.02765231765806675,
-0.023588446900248528,
0.06056930124759674,
-0.017878208309412003,
-0.02433188073337078,
0.023613115772604942,
0.029960252344608307,
0.02293984219431877,
-0.027203300967812538,
-0.012750670313835144,
-0.01936301216483116,
0.02046452835202217,
-0.005995100364089012,
-0.045502856373786926,
0.041738662868738174,
0.012281829491257668,
0.03436455875635147,
-0.003951572347432375,
0.02912631817162037,
-0.033362340182065964,
-0.017608003690838814,
0.017732324078679085,
-0.03560616075992584,
0.0003467965580057353,
-0.006036089733242989,
-0.019005319103598595,
0.022095689550042152,
-0.030754800885915756,
-0.034880030900239944,
0.03354039043188095,
0.000417147675761953,
0.04614943638443947,
0.06057675927877426,
0.004645994398742914,
-0.03384993597865105,
0.027509981766343117,
0.010373653843998909,
0.013775922358036041,
-0.0325898677110672,
-0.007412572856992483,
-0.04744672030210495,
-0.02596203051507473,
0.07018537819385529,
0.0033976263366639614,
-0.03622376173734665,
0.034739162772893906,
0.05414619296789169,
0.017274506390094757,
0.030947476625442505,
0.0036421811673790216,
-0.050206512212753296,
-0.007557368371635675,
0.022085251286625862,
0.028909973800182343,
0.027980785816907883,
0.02355847880244255,
0.0322662815451622,
0.0010278532281517982,
0.03363475576043129,
-0.03742991015315056,
-0.024564340710639954,
0.030412284657359123,
-0.006813603453338146,
0.04371187835931778,
-0.013388202525675297,
-0.04416234791278839,
0.01809193752706051,
-0.010335005819797516,
0.027686143293976784,
0.012228114530444145,
-0.017658906057476997,
-0.007272509392350912,
0.002290761563926935,
0.0025849638041108847,
0.022071242332458496,
-0.020320706069469452,
-0.03873305022716522,
-0.026599852368235588,
0.030267849564552307,
-0.051787130534648895,
-0.006576719228178263,
-0.004952600225806236,
0.025536352768540382,
-0.01688576489686966,
0.012693124823272228,
0.06983750313520432,
0.01795799471437931,
0.06213789060711861,
-0.06454889476299286,
-0.06440597772598267,
0.009434718638658524,
-0.05230674147605896,
-0.013733345083892345,
0.03226304426789284,
-0.034697916358709335,
0.04204186797142029,
-0.028269661590456963,
-0.022280098870396614,
-0.016092369332909584,
-0.033364638686180115,
0.025606218725442886,
0.011948708444833755,
-0.02039509452879429,
-0.0625229999423027,
-0.015507150441408157,
0.008047901093959808,
-0.01988639310002327,
-0.02829376608133316,
0.036908067762851715,
0.013016024604439735,
-0.029079148545861244,
-0.017777111381292343,
-0.0013237609528005123,
-0.007161566987633705,
-0.019326211884617805,
-0.010394061915576458,
-0.03595396503806114,
0.02005193941295147,
-0.05955859273672104,
0.005558062810450792,
0.0367034450173378,
-0.02401862107217312,
-0.0022901876363903284,
-0.06121520698070526,
0.003288902807980776,
0.04805173724889755,
0.0077980575151741505,
0.053012508898973465,
-0.01075683068484068,
0.014562892727553844,
0.06329955905675888,
0.014476414769887924,
-0.053793031722307205,
0.0011872532777488232,
0.0040390100330114365,
-0.02278520166873932,
-0.006195983849465847,
0.02004150114953518,
0.034641265869140625,
-0.013494868762791157,
0.0336165577173233,
0.03850419446825981,
0.030908972024917603,
0.030122539028525352,
0.02128954418003559,
-0.03371277451515198,
-0.010122300125658512,
-0.01017096359282732,
0.013460271991789341,
0.03120529279112816,
0.004670158494263887,
-0.027213169261813164,
-0.008011349476873875,
0.01326723676174879,
0.011446778662502766,
0.0005428273580037057,
-0.06591085344552994,
0.045087698847055435,
-0.01251667458564043,
0.0015215461608022451,
-0.05887043848633766,
0.03339507058262825,
-0.0013190330937504768,
0.047961026430130005,
-0.009016868658363819,
0.05402934178709984,
0.03889031708240509,
-0.0134803531691432,
-0.0028859188314527273,
0.015618543140590191,
0.024714024737477303,
0.014572993852198124,
-0.019880833104252815,
-0.001723859109915793,
-0.00029154703952372074,
0.006707340478897095,
0.009045924060046673,
-0.015889860689640045,
0.02727563865482807,
0.010583064518868923,
0.03030671551823616,
-0.023857194930315018,
-0.033048663288354874,
-0.003988071344792843,
-0.04841027036309242,
-0.018264438956975937,
-0.002574001904577017,
0.043689582496881485,
0.017149267718195915,
0.07555513083934784,
0.0383780337870121,
0.008924413472414017,
0.04206172376871109,
-0.038929082453250885,
-0.09622543305158615,
0.025863630697131157,
-0.02875211276113987,
-0.0408041849732399,
-0.027395715937018394,
-0.02127889357507229,
-0.015010906383395195,
-0.01376907154917717,
-0.04414006695151329,
-0.050136957317590714,
-0.010360372252762318,
-0.05662776902318001,
-0.010954691097140312,
-0.03212331607937813,
-0.003743641311302781,
-0.021769950166344643,
-0.0034583089873194695,
0.0014518648386001587,
-0.019742675125598907,
0.0011308131506666541,
0.048440415412187576,
-0.03551159054040909,
-0.005211803130805492,
-0.02993103675544262,
0.015896925702691078,
-0.021513856947422028,
0.05375921353697777,
0.033754028379917145,
0.03176069259643555,
-0.01151853147894144,
0.0015056978445500135,
0.026060674339532852,
0.0629395991563797,
0.03715556487441063,
-0.015530669130384922,
-0.021643342450261116,
-0.011310416273772717,
0.000648714485578239,
0.0010555458720773458,
0.06178244203329086,
-0.03298047557473183,
-0.024763254448771477,
0.022497616708278656,
0.022834880277514458,
-0.036283425986766815,
0.05020975321531296,
0.0027061444707214832,
0.01331757940351963,
-0.025595732033252716,
-0.08896702527999878,
-0.023652566596865654,
-0.024098163470625877,
-0.010742159560322762,
0.01642949879169464,
0.017874183133244514,
-0.007162211928516626,
0.028215816244482994,
0.0016803203616291285,
0.030781755223870277,
0.0034099933691322803,
0.011234846897423267,
-0.005591846536844969,
-0.024602539837360382,
0.004141658078879118,
-0.016973961144685745,
-0.01976187154650688,
0.05998172238469124,
0.032891590148210526,
-0.00275199837051332,
-0.00896294042468071,
-0.07218942791223526,
0.025322964414954185,
0.04286724701523781,
0.01982872746884823,
-0.0027111221570521593,
-0.004707701038569212,
-0.0010828978847712278,
-0.008394659496843815,
0.0205985177308321,
0.00026020550285466015,
0.04063475504517555,
-0.011154687963426113,
-0.0341213196516037,
-0.03229357302188873,
-0.010676641948521137,
-0.0024248359259217978,
0.03734505921602249,
0.025274237617850304,
0.009759684093296528,
-0.04658280313014984,
-0.038580261170864105,
-0.02074885554611683,
0.029932869598269463,
0.044357962906360626,
0.06136808171868324,
-0.05121378228068352,
0.003949064761400223,
0.01874888315796852,
0.018204132094979286,
-0.03878328204154968,
-0.08466994762420654,
0.00528759928420186,
0.0022848842199891806,
-0.0059491414576768875,
0.04436296224594116,
-0.014702185057103634,
-0.05686749890446663,
0.05250808596611023,
0.021901331841945648,
0.0302155539393425,
-0.021955858916044235,
-0.0023754481226205826,
0.04673722758889198,
0.00851566530764103,
-0.010787364095449448,
0.03315749019384384,
0.05833953246474266,
-0.007159586995840073,
-0.039110906422138214,
-0.00521476287394762,
0.07641306519508362,
-0.04542452469468117,
0.002614466240629554,
0.012776254676282406,
0.021330872550606728,
-0.010228991508483887,
0.04723629727959633,
-0.01432847697287798,
0.037720937281847,
0.009415028616786003,
-0.031570881605148315,
-0.0009936054702848196,
-0.008583633229136467,
-0.00659762741997838,
-0.013641845434904099,
-0.012462889775633812,
0.036141131073236465,
-0.024176444858312607,
0.007023168262094259,
0.01294270996004343,
-0.006157637108117342,
-0.011749322526156902,
0.02510758303105831,
-0.011132030747830868,
0.04601934179663658,
-0.07058566808700562,
-0.02876328118145466,
-0.007809984963387251,
-0.060497283935546875,
0.03848739713430405,
-0.03587103262543678,
0.039439547806978226,
0.02536492608487606,
-0.045306019484996796,
-0.007662000600248575,
0.0230232123285532,
-0.01817081868648529,
0.04900577291846275,
-0.03419148921966553,
0.04098404571413994,
0.0030663495417684317,
-0.02988242544233799,
-0.068463534116745,
-0.07982435077428818,
0.023916028439998627,
0.02640690840780735,
0.0006488026701845229,
-0.001639311434701085,
0.027358418330550194,
-0.006732908543199301,
-0.017344683408737183,
0.04459824413061142,
0.010692008771002293,
-0.010953961871564388,
-0.009666248224675655,
0.012442518956959248,
0.012708301655948162,
0.04613080620765686,
0.019633285701274872,
-0.06978077441453934,
0.011892592534422874,
0.0008286425727419555,
-0.03733047842979431,
0.015207033604383469,
0.053613271564245224,
-0.030927203595638275,
-0.033036969602108,
-0.02190978266298771,
-0.0014759184559807181,
0.038900818675756454,
-0.011083228513598442,
0.024042349308729172,
-0.003981214947998524,
-0.009122398681938648,
0.021061532199382782,
-0.020825659856200218,
0.023503189906477928,
0.033063363283872604,
-0.008893897756934166,
-0.010505350306630135,
-0.007442974951118231,
-0.015088675543665886,
-0.05574270337820053,
0.0052086045034229755,
0.011506742797791958,
0.038367338478565216,
0.024974267929792404,
0.06949374824762344,
-0.005678072106093168,
0.00921073742210865,
0.008537217043340206,
-0.007730640005320311,
0.017528044059872627,
-0.04877503961324692,
0.03857313469052315,
-0.01570056565105915,
0.017291085794568062,
-0.018257716670632362,
-0.05620892718434334,
-0.020139606669545174,
-0.026864347979426384,
0.07277099043130875,
-0.027585964649915695,
0.05470516160130501,
0.02129669301211834,
-0.026390142738819122,
-0.0014960257103666663,
-0.008178846910595894,
0.006900651380419731,
0.05518481507897377,
-0.026051485911011696,
0.04973164200782776,
-0.03979892656207085,
-0.0336097851395607,
0.01838412694633007,
0.04692254215478897,
-0.003343841526657343,
0.008263027295470238,
0.023637449368834496,
0.025776540860533714,
0.03738153353333473,
0.0028213495388627052,
-0.027600573375821114,
0.04067878797650337,
-0.048447225242853165,
0.019560672342777252,
-0.0019109437707811594,
0.0306700449436903,
0.04596000164747238,
0.0374385230243206,
0.021346651017665863,
-0.006760332267731428,
-0.022899232804775238,
-0.02073099836707115,
0.043666303157806396,
0.00006497236608993262,
0.032965224236249924,
0.019712012261152267,
0.02428583614528179,
0.04596838727593422,
0.0384056493639946,
0.03170132637023926,
0.022166399285197258,
-0.067535400390625,
-0.030077822506427765,
0.016743673011660576,
-0.014294812455773354,
0.03927101939916611,
-0.02911527082324028,
-0.023355567827820778,
0.026377664878964424,
-0.03634963929653168,
0.027987349778413773,
0.016609787940979004,
0.011564258486032486,
-0.009872876107692719,
0.02941843308508396,
0.0030653271824121475,
0.06322922557592392,
-0.011695235967636108,
0.025856949388980865,
0.09802351891994476,
0.03696132078766823,
0.0440211184322834,
-0.05731337517499924,
-0.005990233272314072,
-0.006107765715569258,
0.016982104629278183,
-0.04745398089289665,
-0.001452761352993548,
0.012141857296228409,
0.04107392206788063,
-0.009090658277273178,
0.058246731758117676,
-0.013000117614865303,
-0.0455828420817852,
0.01407206617295742,
-0.030739063397049904,
-0.023962894454598427,
0.03721795231103897,
0.0010838450398296118,
-0.006253228522837162,
0.02758372388780117,
-0.03023732639849186,
-0.006160686258226633,
-0.0460808090865612,
-0.030045805498957634,
-0.043552421033382416,
-0.04510891065001488,
0.04737170413136482,
0.005289882887154818,
-0.016720134764909744,
0.00016979167412500829,
0.04544922709465027,
0.003819067729637027,
-0.008869885466992855,
0.026291247457265854,
-0.016473324969410896,
0.02442138083279133,
0.013658415526151657,
-0.013000927865505219,
-0.00792577676475048,
-0.005238933954387903,
-0.00020758765458595008,
-0.00961348321288824,
-0.03393616899847984,
-0.022835012525320053,
0.005972566083073616,
0.021814469248056412,
-0.0009407435427419841,
-0.012867061421275139,
-0.014984655193984509,
0.0173228457570076,
0.033612608909606934,
-0.05465590953826904,
-0.04085862264037132,
-0.009440138004720211,
0.027908312156796455,
-0.042755503207445145,
0.0008333061705343425,
-0.00554191879928112,
-0.009810191579163074,
0.006400547455996275,
0.005566428881138563,
-0.02693041041493416,
0.023685360327363014,
0.024891909211874008,
-0.01368843112140894,
0.007381095550954342,
-0.03618969768285751,
-0.04249650239944458,
-0.01701020449399948,
0.011355380527675152,
-0.046667519956827164,
-0.0269191674888134,
-0.00023820959904696792,
0.0593283586204052,
0.04544505476951599,
0.022612664848566055,
-0.02166958898305893,
-0.041407495737075806,
-0.05563517287373543,
0.012744487263262272,
-0.009929071180522442,
-0.049118246883153915,
-0.00015300774248316884,
-0.011854197829961777,
0.0510704442858696,
0.019322402775287628,
-0.037717305123806,
0.00565327238291502,
-0.009329580701887608,
0.013245553709566593,
0.03142871707677841,
-0.007295943796634674,
-0.023687494918704033,
0.027117544785141945,
-0.01944580301642418,
0.004541214555501938,
0.027609944343566895,
0.006665411870926619,
0.024726955220103264,
-0.023916391655802727,
0.027588389813899994,
0.035599563270807266,
-0.04197445511817932,
0.02212560921907425,
0.007268351502716541,
-0.041030824184417725,
0.000990288332104683,
0.00416181143373251,
-0.0017536466475576162,
-0.046799615025520325,
-0.06507039815187454,
-0.004952354822307825,
-0.0028689142782241106,
-0.0067066107876598835,
0.011536743491888046,
-0.018096977844834328,
0.0030822500120848417,
-0.014215076342225075,
0.011824695393443108,
-0.044968657195568085,
-0.03741731122136116,
-0.054130278527736664,
-0.0315113328397274,
0.003415969666093588,
0.019582929089665413,
-0.006030162330716848,
0.03258311375975609,
-0.005632483400404453,
-0.038202349096536636,
0.016379760578274727,
0.07922276109457016,
0.018471447750926018,
-0.03327988460659981,
0.023760143667459488,
-0.019910475239157677,
0.05365807190537453,
-0.028960993513464928,
-0.04391847923398018,
0.04436871036887169,
-0.029865706339478493,
-0.04939332231879234,
0.024312699213624,
-0.013241441920399666,
-0.00715896300971508,
0.014601637609302998,
0.021304402500391006,
-0.005345569457858801,
0.058825571089982986,
-0.040867675095796585,
0.006097805220633745,
0.010132486000657082,
-0.030472444370388985,
-0.030294422060251236,
0.009500261396169662,
0.005397038068622351,
-0.021674225106835365,
-0.02135660871863365,
0.03149792551994324,
0.00616896478459239,
-0.007961461320519447,
0.004336186684668064,
-0.027598734945058823,
-0.023959513753652573,
0.0346762053668499,
0.011915531009435654,
0.01257413998246193,
0.012287884019315243,
0.03647571802139282,
0.018678152933716774,
0.06823230534791946,
0.06054716184735298,
0.010912296362221241,
-0.09263324737548828,
0.0015673702582716942,
-0.004937137942761183,
-0.0017995649250224233,
0.02287987619638443,
-0.025769390165805817,
0.0708874836564064,
-0.004027035553008318,
-0.06968200206756592,
-0.0031931723933666945,
-0.019445927813649178,
-0.04456760361790657,
-0.08355047553777695,
0.02934522181749344,
0.009459709748625755,
0.03424297645688057,
0.016265645623207092,
0.025066358968615532,
-0.00584504846483469,
0.022280758246779442,
-0.03308530151844025,
0.032017674297094345,
-0.0164395272731781,
0.016997572034597397,
0.0019090516725555062,
0.018345320597290993,
0.03335409238934517,
-0.0162840336561203,
-0.030353717505931854,
0.000258100830251351,
-0.012392142787575722,
-0.006376312114298344,
0.010440385900437832,
0.005580128636211157,
-0.001966155134141445,
0.01700511947274208,
-0.00828870851546526,
-0.023404771462082863,
0.004213974345475435,
0.022689830511808395,
0.02550373040139675,
0.01011850405484438,
-0.02041592262685299,
-0.0038448942359536886,
0.006547012832015753,
-0.05922229588031769,
-0.01610969938337803,
0.0021976232528686523,
0.011409571394324303,
-0.007457515690475702,
-0.02165316790342331,
-0.017801031470298767,
0.0338444709777832,
-0.03140638396143913,
0.00043306589941494167,
-0.0552939772605896,
-0.014213713817298412,
-0.0007242693682201207,
0.04131616652011871,
-0.02449038252234459,
0.0011062431149184704,
-0.001230602734722197,
0.0015806962037459016,
0.0031691871117800474,
0.02527395822107792,
-0.015770841389894485,
-0.048853036016225815,
-0.016440492123365402,
0.02466721273958683,
-0.013331511057913303,
0.013793610036373138,
-0.027307935059070587,
-0.030005676671862602,
0.048446591943502426,
-0.013954429887235165,
0.04445664957165718,
0.0033041846472769976,
-0.051329370588064194,
-0.029210984706878662,
-0.06100926920771599,
0.02049557864665985,
-0.026547834277153015,
0.024896714836359024,
-0.038792338222265244,
0.002954755211248994,
-0.0025353834498673677,
0.006863934453576803,
0.03432389348745346,
0.00893449317663908,
-0.005101646296679974,
-0.005583035293966532,
-0.0348501019179821,
0.014701073989272118,
-0.013466577976942062,
-0.018562771379947662,
-0.04393937438726425,
0.008164814673364162,
-0.023685354739427567,
-0.01583568938076496,
-0.038518477231264114,
0.024271253496408463,
0.051802508533000946,
-0.03998697176575661,
0.02310887724161148,
0.003933418542146683,
-0.01793268322944641,
0.07248850166797638,
-0.004613206721842289,
0.01949109509587288,
0.05377139151096344,
-0.006585960742086172,
0.015744920819997787,
0.05043668672442436,
-0.03395078331232071,
-0.05124543979763985,
0.03843811899423599,
-0.04243925213813782,
-0.010385413654148579,
0.008084535598754883,
0.021745195612311363,
0.054813116788864136,
0.006215833593159914,
0.01263807900249958,
0.011154504492878914,
-0.01635751500725746,
-0.01064995862543583,
0.001326130935922265,
0.012572535313665867,
0.016294894739985466,
0.010784409008920193,
0.04129816219210625,
0.009943230077624321,
0.002471962245181203,
-0.032107047736644745,
0.02767198719084263,
0.03182494640350342,
0.017343273386359215,
0.024969588965177536,
0.01101324800401926,
-0.001859318814240396,
-0.018256334587931633,
0.006733368616551161,
0.014528660103678703,
-0.00914920773357153,
-0.025694379583001137,
0.0496959425508976,
0.003540622303262353,
-0.009352854453027248,
0.015014329925179482,
-0.0008128996705636382,
0.06754475831985474,
-0.056561216711997986,
0.03397490456700325,
-0.04319807142019272,
0.00030331272864714265,
0.004581372253596783,
0.015428148210048676,
0.04239150509238243,
0.02769089862704277,
-0.01774062030017376,
-0.004057436715811491,
-0.03390998765826225,
0.019145330414175987,
0.001420981832779944,
-0.09912698715925217,
0.02930636517703533,
-0.014052228070795536,
-0.00892116129398346,
0.006867186166346073,
0.0007758918218314648,
-0.05243201553821564,
-0.002155730500817299,
0.05665216222405434,
0.03338940814137459,
-0.02694578841328621,
0.0525212362408638,
-0.0012618671171367168,
-0.0033144031185656786,
0.058206118643283844,
-0.047837261110544205,
0.0047773998230695724,
-0.028778402134776115,
0.05626488849520683,
-0.006143515929579735,
0.028887176886200905
] |
<p>As I see it, as light comes through approximately same angular area of the lens, it should have less aberrations, and at the same time, it should still have high θ -> diffraction limit should stay as without this diaphragm.</p>
<p>What am I missing?</p>
| 9,573 |
[
-0.03731187433004379,
-0.0015921486774459481,
0.00841293204575777,
-0.029995692893862724,
0.059575051069259644,
0.02059146761894226,
-0.009629344567656517,
-0.02728753536939621,
-0.028937140479683876,
-0.028101900592446327,
0.04432286322116852,
0.026264816522598267,
0.056972358375787735,
0.0174125786870718,
-0.0007190449396148324,
-0.031686194241046906,
-0.01634705439209938,
-0.010140487924218178,
0.0012896397383883595,
-0.021001409739255905,
-0.04402688518166542,
0.06564781069755554,
-0.0069356635212898254,
0.001241335878148675,
-0.033304132521152496,
-0.004736893344670534,
0.035832587629556656,
-0.01678812876343727,
0.020284369587898254,
0.05642049014568329,
-0.023253368213772774,
0.022822249680757523,
0.02285475842654705,
0.035358428955078125,
-0.013537687249481678,
-0.013355080969631672,
-0.021991968154907227,
-0.02097298577427864,
-0.0014430740848183632,
0.025970468297600746,
-0.014921127818524837,
0.002178084570914507,
-0.02721528522670269,
0.07286976277828217,
-0.02148866094648838,
0.018541233614087105,
-0.044840093702077866,
-0.006888503674417734,
0.036074403673410416,
-0.06777619570493698,
0.058949064463377,
0.013442928902804852,
0.05838954821228981,
0.054220251739025116,
0.019754141569137573,
-0.011253799311816692,
0.08030004054307938,
0.056546974927186966,
-0.04180074855685234,
-0.038211576640605927,
-0.02911553531885147,
-0.01044843252748251,
0.02208324894309044,
-0.01248791255056858,
-0.007825162261724472,
0.013623416423797607,
0.0011129087070003152,
-0.02537049911916256,
0.02221410721540451,
-0.000013229558135208208,
0.02551119402050972,
0.03445896878838539,
0.029428953304886818,
-0.02231152169406414,
-0.004841207526624203,
-0.05103641748428345,
0.011040767654776573,
0.032106008380651474,
0.012962172739207745,
0.030082322657108307,
0.012433847412467003,
0.012447593733668327,
0.025739319622516632,
0.042910944670438766,
0.002050944371148944,
0.00545860081911087,
0.08028600364923477,
-0.02174558863043785,
0.004040970467031002,
0.0039720297791063786,
-0.00997393112629652,
0.01977834850549698,
0.027871012687683105,
0.0006906770286150277,
-0.020960869267582893,
0.025719311088323593,
-0.013617413118481636,
0.060192301869392395,
0.01260716374963522,
-0.023506853729486465,
-0.000015744670236017555,
-0.009512487798929214,
0.028364058583974838,
0.04760737717151642,
0.029484620317816734,
-0.015715884044766426,
-0.05755181238055229,
0.028308263048529625,
-0.0006905571790412068,
0.010643779300153255,
-0.05161255598068237,
0.026304425671696663,
-0.02003697119653225,
0.02925656922161579,
0.012772534042596817,
0.002942190272733569,
-0.02578280121088028,
-0.0018786544678732753,
0.038282789289951324,
0.11764351278543472,
0.04601775109767914,
0.0029992754571139812,
0.010459406301379204,
-0.027291512116789818,
-0.07691209018230438,
0.03206811472773552,
0.010038550943136215,
-0.020861957222223282,
-0.032693035900592804,
0.010094479657709599,
0.0277725663036108,
0.004172510001808405,
0.004887755494564772,
-0.007598519325256348,
0.01533673144876957,
-0.008834776468575,
-0.05796828493475914,
-0.069425567984581,
0.0659780204296112,
0.010904268361628056,
-0.010098440572619438,
-0.06420177966356277,
0.031872596591711044,
0.012351421639323235,
0.0882413238286972,
0.020778711885213852,
0.010017605498433113,
0.01607254333794117,
0.03873139247298241,
-0.023510606959462166,
-0.04725541174411774,
0.037459250539541245,
0.014137872494757175,
-0.015527835115790367,
-0.0023410844150930643,
-0.06136655807495117,
0.028162507340312004,
0.017920460551977158,
0.020574763417243958,
-0.02469012513756752,
0.049706656485795975,
-0.04186044633388519,
0.012379749678075314,
-0.033127617090940475,
-0.008624064736068249,
-0.05211322382092476,
0.037774182856082916,
0.012864957563579082,
0.01959538459777832,
-0.006169980391860008,
-0.012728358618915081,
0.026255590841174126,
-0.0314490869641304,
-0.005640086252242327,
0.044699400663375854,
-0.03201877325773239,
0.020026467740535736,
-0.06607811152935028,
0.023869836702942848,
0.0433562695980072,
-0.02103782817721367,
-0.03221281245350838,
-0.012675458565354347,
0.06351795792579651,
-0.001707453397102654,
0.06066501513123512,
0.003055821405723691,
-0.009680773131549358,
0.011378522031009197,
-0.07162533700466156,
-0.014869455248117447,
-0.05441682040691376,
0.00221478589810431,
0.026498278602957726,
-0.005856792908161879,
-0.004698571749031544,
-0.003938158508390188,
0.020530473440885544,
0.024241439998149872,
0.00727291963994503,
-0.017365358769893646,
0.028441615402698517,
0.012667840346693993,
0.0059649040922522545,
0.05758402869105339,
0.07722550630569458,
0.04651033878326416,
0.028400558978319168,
0.028752001002430916,
-0.0046256110072135925,
0.013957935385406017,
0.019671572372317314,
-0.021956048905849457,
-0.0010771858505904675,
0.00663771340623498,
-0.019605033099651337,
0.0213451087474823,
0.03509481996297836,
0.00884733721613884,
0.025456489995121956,
-0.03434940427541733,
0.09082475304603577,
0.028543518856167793,
0.005709363613277674,
0.014491906389594078,
0.060817476361989975,
0.0162217877805233,
0.02365683950483799,
-0.03032935969531536,
-0.0052452292293310165,
-0.023221077397465706,
0.03306346386671066,
0.03400811180472374,
0.005507409572601318,
-0.065044105052948,
0.034929562360048294,
0.012974392622709274,
-0.0027913390658795834,
0.03716529533267021,
0.03364165499806404,
-0.019251635298132896,
-0.02966400608420372,
-0.010825716890394688,
0.05670640245079994,
-0.0036344530526548624,
0.007561421953141689,
-0.019096460193395615,
-0.011169832199811935,
-0.005229058209806681,
-0.01000984851270914,
-0.000151922125951387,
0.031265899538993835,
-0.019797561690211296,
0.014100599102675915,
-0.012763215228915215,
0.023126034066081047,
0.04956188425421715,
-0.001044520060531795,
-0.009192433208227158,
0.04090190306305885,
-0.028591295704245567,
0.01458210963755846,
-0.05259912461042404,
-0.034482065588235855,
0.041225969791412354,
0.012103679589927197,
-0.025059791281819344,
-0.019384264945983887,
0.04060222581028938,
-0.029780419543385506,
-0.015588965266942978,
-0.06127044931054115,
-0.011901021003723145,
-0.006801136303693056,
0.0007329829386435449,
0.03766709193587303,
0.035650335252285004,
0.05627760663628578,
-0.03790438547730446,
-0.038387518376111984,
-0.017967233434319496,
-0.0011383930686861277,
0.002792628249153495,
0.005378806497901678,
-0.0356677807867527,
-0.03301634639501572,
0.0127830496057868,
-0.032051391899585724,
0.026146497577428818,
0.015237977728247643,
0.023564347997307777,
-0.049036599695682526,
0.007048152852803469,
-0.030948784202337265,
-0.005929966457188129,
-0.01898469775915146,
-0.0361044742166996,
-0.028665605932474136,
-0.038467440754175186,
0.0296085886657238,
-0.011446231044828892,
-0.026391897350549698,
-0.0005770672578364611,
-0.040421999990940094,
-0.04042630270123482,
-0.0019881490152329206,
0.030157366767525673,
0.04435603320598602,
-0.059703268110752106,
-0.01331871747970581,
0.02773624286055565,
-0.042785242199897766,
0.0063737528398633,
-0.04801105707883835,
-0.049862612038850784,
0.013158640824258327,
-0.02745479717850685,
0.03229684755206108,
-0.029344357550144196,
-0.0236007422208786,
0.07343300431966782,
0.013321898877620697,
-0.019203640520572662,
-0.03098236955702305,
-0.026200564578175545,
-0.012417989782989025,
-0.05834660679101944,
-0.026702044531702995,
0.018926791846752167,
0.008101488463580608,
0.07089249044656754,
0.020617203786969185,
0.010452959686517715,
0.0408448651432991,
0.018540997058153152,
-0.0156747717410326,
-0.00031831272644922137,
0.004144595004618168,
-0.03132737800478935,
0.04104888066649437,
0.004524868912994862,
-0.013948221690952778,
0.006791441701352596,
0.0021918744314461946,
0.05185936391353607,
-0.004970699083060026,
-0.05590483918786049,
0.003744425717741251,
-0.002574844053015113,
0.001490165712311864,
0.014572336338460445,
0.020428096875548363,
0.008256183005869389,
0.014434480108320713,
-0.0037920016329735518,
0.025824567303061485,
0.0563436858355999,
-0.0209017563611269,
-0.03404697775840759,
0.00655721640214324,
0.009433699771761894,
0.009021701291203499,
-0.0018367896554991603,
-0.008430483750998974,
0.033327195793390274,
0.010476258583366871,
0.003394327824935317,
-0.03326253965497017,
0.03292052447795868,
0.029032232239842415,
0.017108209431171417,
0.0030288861598819494,
-0.02358192764222622,
0.018870258703827858,
-0.03909609094262123,
0.009289664216339588,
-0.022612925618886948,
0.041357289999723434,
0.01576007902622223,
0.020611878484487534,
0.0443841852247715,
0.03229300305247307,
0.02373415231704712,
-0.0049116662703454494,
-0.08763819187879562,
-0.01343301497399807,
-0.027778854593634605,
-0.05611824244260788,
-0.032907407730817795,
-0.011489758267998695,
-0.0005679379682987928,
-0.01423982996493578,
-0.017278557643294334,
-0.040941692888736725,
-0.012274447828531265,
-0.04186667501926422,
0.033218808472156525,
-0.0026738226879388094,
-0.0014161732979118824,
-0.04909617453813553,
0.028358634561300278,
0.020137444138526917,
-0.007649633567780256,
0.028764421120285988,
0.051723409444093704,
-0.044571224600076675,
0.01727272756397724,
-0.0030580635648220778,
0.0608159601688385,
-0.008259567432105541,
0.02081872522830963,
0.030840575695037842,
0.041482340544462204,
-0.01333467848598957,
-0.014617077074944973,
0.011807648465037346,
0.022076377645134926,
0.029376743361353874,
-0.014546123333275318,
-0.054091677069664,
-0.03637875244021416,
-0.050480734556913376,
-0.0156610906124115,
0.03681305795907974,
-0.003460697364062071,
-0.022833354771137238,
0.051789913326501846,
-0.0205228291451931,
-0.03794049844145775,
0.014879628084599972,
-0.028474977239966393,
-0.008858753368258476,
-0.010234854184091091,
-0.07867412269115448,
0.003152339719235897,
-0.020363572984933853,
-0.014780649915337563,
0.036349643021821976,
0.022910863161087036,
-0.0322442390024662,
-0.004597458057105541,
0.0322401337325573,
-0.048040375113487244,
-0.04403948783874512,
0.05236978083848953,
-0.019218137487769127,
-0.010699285194277763,
0.016469018533825874,
0.035952161997556686,
0.02814166247844696,
0.042551178485155106,
0.04140389338135719,
0.05753856152296066,
-0.003269093343988061,
-0.06547395884990692,
-0.044527750462293625,
0.03533582016825676,
0.026384321972727776,
0.02239520661532879,
-0.0375947542488575,
-0.055046986788511276,
-0.03670402616262436,
0.043833259493112564,
-0.07082259654998779,
0.058472029864788055,
-0.028544574975967407,
-0.020355703309178352,
-0.04525517299771309,
-0.03266800940036774,
-0.05388297140598297,
0.011874169111251831,
0.016748137772083282,
-0.013448992744088173,
-0.02410864271223545,
-0.027592843398451805,
-0.0014191860100254416,
-0.010142200626432896,
0.004991309717297554,
0.015942424535751343,
0.03059208206832409,
-0.03242297098040581,
-0.014365396462380886,
0.02726864442229271,
-0.0005361096700653434,
-0.05972086265683174,
0.008247601799666882,
0.008437198586761951,
-0.0010289421770721674,
0.018620453774929047,
-0.03517528250813484,
0.009861983358860016,
0.02940172702074051,
0.022084755823016167,
-0.02188054658472538,
0.0019559389911592007,
-0.045286182314157486,
0.01355026662349701,
0.04607852175831795,
-0.005299139302223921,
0.06884478777647018,
0.03885664790868759,
-0.01068632397800684,
-0.007328774780035019,
-0.06322323530912399,
0.02202332392334938,
-0.024844679981470108,
-0.0040887948125600815,
-0.024598166346549988,
0.009835654869675636,
-0.046873390674591064,
0.06743375957012177,
-0.008311708457767963,
0.046883001923561096,
0.001801545382477343,
-0.04255777969956398,
0.021641919389367104,
-0.0049436576664447784,
-0.001456966856494546,
-0.00264106341637671,
0.01285179890692234,
0.020980743691325188,
0.01124133262783289,
0.004387551452964544,
-0.000896371784619987,
-0.01947569102048874,
-0.011188671924173832,
0.03684278577566147,
0.018482446670532227,
-0.008618008345365524,
-0.04395139217376709,
-0.03880203142762184,
-0.03207693248987198,
-0.057120680809020996,
0.07576820254325867,
-0.04534408822655678,
0.02864743582904339,
0.025062402710318565,
-0.05833376571536064,
-0.01709907129406929,
0.0263883825391531,
-0.027579456567764282,
0.052376639097929,
-0.05563289299607277,
0.02995673008263111,
0.004127549007534981,
0.0010135704651474953,
-0.056216783821582794,
-0.014056755229830742,
-0.0014578728005290031,
-0.003060081508010626,
-0.007721497677266598,
0.0018230436835438013,
-0.001883809920400381,
0.01227001566439867,
-0.057289138436317444,
0.011127771809697151,
0.025932710617780685,
-0.02580874413251877,
-0.008712450042366982,
-0.00255900458432734,
-0.02180243469774723,
0.06554781645536423,
-0.025478888303041458,
-0.043952517211437225,
0.016974082216620445,
-0.02752116322517395,
-0.010304953902959824,
-0.009158380329608917,
0.06849125027656555,
-0.04989860579371452,
-0.027887674048542976,
-0.029506895691156387,
-0.018794171512126923,
0.03249261528253555,
-0.021730922162532806,
-0.01088046282529831,
0.00544762471690774,
0.010837261565029621,
-0.00019423980847932398,
-0.03653924539685249,
-0.002742394804954529,
-0.017188388854265213,
0.02863622084259987,
-0.009177829138934612,
-0.007445414550602436,
-0.013688270933926105,
-0.06037294864654541,
0.03917017579078674,
0.025648027658462524,
0.04715866595506668,
-0.02859426476061344,
0.08786729723215103,
-0.01956796646118164,
0.03886498883366585,
-0.016279885545372963,
-0.005238162353634834,
0.008468671701848507,
0.025481419637799263,
0.02579323574900627,
0.031654831022024155,
0.022672336548566818,
-0.014968790113925934,
-0.03190521150827408,
-0.04528327286243439,
0.0007723397575318813,
0.08430856466293335,
-0.017746685072779655,
0.039753638207912445,
-0.004953477531671524,
-0.01115812361240387,
-0.011901779100298882,
-0.015607393346726894,
0.018638789653778076,
0.001456892816349864,
-0.017023732885718346,
0.04540800303220749,
-0.027653226628899574,
-0.006961666978895664,
0.02406657487154007,
0.0491674542427063,
-0.004684635903686285,
0.0013157749781385064,
0.022734040394425392,
0.029003003612160683,
0.007061885669827461,
-0.003621896496042609,
-0.038746170699596405,
0.014106960035860538,
-0.03535765781998634,
0.03588880971074104,
0.012061164714396,
-0.013758617453277111,
0.0463750921189785,
-0.03094455599784851,
0.02618868462741375,
-0.03321494534611702,
0.012647543102502823,
-0.02478085644543171,
-0.009082860313355923,
0.005229835864156485,
0.011161532253026962,
-0.028518779203295708,
-0.008667386136949062,
0.03730633854866028,
0.029782751575112343,
0.01084648072719574,
-0.03349153324961662,
-0.06158413738012314,
-0.03733030706644058,
-0.060848284512758255,
-0.04296598583459854,
0.0603349544107914,
-0.002724017482250929,
-0.018770745024085045,
-0.01018451526761055,
-0.02680022083222866,
0.013595922850072384,
0.016210854053497314,
0.0030805214773863554,
-0.014331298880279064,
0.020997101441025734,
0.019794180989265442,
0.07069124281406403,
0.0109836021438241,
-0.01793358288705349,
0.11605254560709,
0.05420643463730812,
0.00396348349750042,
-0.04774816706776619,
0.025949900969862938,
-0.02995770424604416,
-0.019169187173247337,
-0.030352381989359856,
0.04001237824559212,
0.002960922196507454,
0.0010375832207500935,
-0.010859550908207893,
0.02716987207531929,
0.015945350751280785,
0.01499724481254816,
0.04782295972108841,
-0.03909192234277725,
-0.04372342303395271,
0.018374744802713394,
0.010879993438720703,
0.020704610273241997,
0.018784629181027412,
-0.01328282244503498,
0.011513136327266693,
-0.03520534560084343,
-0.011491844430565834,
-0.019920609891414642,
-0.05016988143324852,
0.014078675769269466,
-0.0027686459943652153,
-0.013439616188406944,
-0.036629609763622284,
-0.022402940317988396,
-0.016282495111227036,
-0.03844515606760979,
0.04139295592904091,
-0.009338743053376675,
0.014406247064471245,
0.011174308136105537,
0.008719690144062042,
0.02386251650750637,
0.001984786009415984,
0.052905160933732986,
-0.006598294712603092,
-0.014398063533008099,
0.01037629321217537,
0.0027371824253350496,
0.04802979156374931,
-0.022805342450737953,
0.014345759525895119,
0.012564525008201599,
0.004500139970332384,
-0.008668368682265282,
-0.0797460600733757,
-0.002875641454011202,
0.011676367372274399,
-0.014031601138412952,
-0.0030210167169570923,
-0.03799963742494583,
0.035269517451524734,
0.031019050627946854,
0.008559554815292358,
0.044586196541786194,
-0.03592205047607422,
0.012333224527537823,
-0.017813989892601967,
0.003477753372862935,
0.058750856667757034,
-0.025483228266239166,
-0.052111461758613586,
-0.04363594576716423,
0.015949247404932976,
-0.03475688770413399,
0.00877560768276453,
-0.0018259495263919234,
0.019116977229714394,
0.050427161157131195,
-0.018986722454428673,
-0.0075366259552538395,
-0.03275660052895546,
-0.06327928602695465,
0.020367784425616264,
0.004064076114445925,
-0.04757777974009514,
-0.037880394607782364,
0.006844910327345133,
0.02380864880979061,
0.02179477922618389,
-0.01595953293144703,
-0.006676288787275553,
-0.025501424446702003,
0.04347032308578491,
0.029926475137472153,
-0.0033247077371925116,
-0.06607789546251297,
0.016947666183114052,
-0.0013110662112012506,
0.0005206362693570554,
0.009767839685082436,
0.016818402335047722,
0.032898835837841034,
0.013143692165613174,
0.03342139720916748,
0.032158948481082916,
-0.02559160441160202,
0.013991693034768105,
-0.017835885286331177,
-0.02798321656882763,
0.007989531382918358,
0.028108088299632072,
0.02096002921462059,
-0.0234321728348732,
0.005832240451127291,
-0.031199974939227104,
-0.03414519876241684,
0.05048396810889244,
0.02259296365082264,
0.02424938604235649,
-0.020964641124010086,
-0.043666232377290726,
-0.007402483839541674,
-0.007986101321876049,
-0.03415795788168907,
-0.030792761594057083,
0.002848584670573473,
-0.014587835408747196,
0.012744443491101265,
-0.01409448403865099,
0.04098216071724892,
0.015144947916269302,
-0.03176712989807129,
0.00030512281227856874,
-0.011988824233412743,
-0.02211000770330429,
0.005016148556023836,
-0.01711496151983738,
0.011041674762964249,
0.056525807827711105,
-0.02439071796834469,
0.016417263075709343,
0.0355752669274807,
0.00491138594225049,
-0.02403874695301056,
0.027138207107782364,
0.005926558747887611,
0.005267000291496515,
0.0195700041949749,
-0.03837573900818825,
0.015288104303181171,
0.051356952637434006,
-0.01141032762825489,
-0.05103679001331329,
0.0028577949851751328,
-0.03828350082039833,
0.027812624350190163,
-0.013232983648777008,
-0.016499118879437447,
-0.029458800330758095,
0.01787496916949749,
0.054764583706855774,
0.03169472888112068,
0.020992044359445572,
-0.023743411526083946,
0.03886013105511665,
-0.01113620400428772,
0.020959675312042236,
-0.028431333601474762,
0.012060296721756458,
0.020097725093364716,
0.001997379818931222,
-0.042528778314590454,
0.006923729553818703,
0.03501961752772331,
0.008405523374676704,
-0.07279686629772186,
0.013268345966935158,
0.006152232643216848,
0.018365250900387764,
0.03453972563147545,
-0.03106400929391384,
0.028651781380176544,
0.01166707556694746,
-0.0411267913877964,
-0.011327694170176983,
-0.0126621900126338,
-0.033766165375709534,
-0.09031806886196136,
0.01221843808889389,
-0.0136526208370924,
0.027727339416742325,
0.02639945223927498,
0.04116563871502876,
0.047321055084466934,
-0.016438962891697884,
-0.04765031486749649,
-0.016050411388278008,
-0.016424546018242836,
0.014109992422163486,
-0.038705550134181976,
0.012036947533488274,
0.06156297028064728,
0.005173954647034407,
-0.039879996329545975,
0.0008491808548569679,
0.013918953016400337,
0.0031121668871492147,
0.027850493788719177,
0.014163356274366379,
0.015703799203038216,
0.02128699980676174,
0.03304320201277733,
-0.0168541818857193,
-0.040332019329071045,
-0.012909756042063236,
0.030892161652445793,
0.015112971886992455,
-0.018231350928544998,
0.03874338045716286,
0.03007308393716812,
-0.03203551843762398,
-0.027737341821193695,
0.021107951179146767,
-0.001144333160482347,
-0.021250907331705093,
-0.0027588331140577793,
0.006442137528210878,
0.0011176584521308541,
-0.05023106187582016,
0.01549589540809393,
-0.010083556175231934,
-0.014294110238552094,
0.03296682983636856,
0.00178966810926795,
-0.012965572066605091,
0.01347155962139368,
-0.03852391988039017,
-0.05506381765007973,
-0.00030191391124390066,
0.011632503010332584,
0.016114134341478348,
-0.027987942099571228,
0.03702392056584358,
0.02701646089553833,
0.0005672000115737319,
0.02406640164554119,
-0.0002550864010117948,
-0.06133605167269707,
0.03879034146666527,
-0.017121395096182823,
0.004399322438985109,
0.025847578421235085,
-0.01029006764292717,
-0.03682948648929596,
-0.08151742070913315,
0.04789547622203827,
-0.02302480675280094,
-0.03825778141617775,
-0.0174721572548151,
-0.0074995290488004684,
-0.00450238399207592,
0.06258678436279297,
0.05968266725540161,
0.013552962802350521,
-0.032922402024269104,
0.015733012929558754,
0.03614307567477226,
0.010240666568279266,
-0.028412729501724243,
0.00648723216727376,
-0.0009027199703268707,
-0.0058939517475664616,
-0.025883950293064117,
-0.04448863863945007,
-0.03247053921222687,
0.0281993318349123,
-0.001718695042654872,
0.005321706645190716,
0.0499165803194046,
0.012038111686706543,
-0.030622417107224464,
0.022478559985756874,
-0.02098493091762066,
-0.034780800342559814,
0.08043164014816284,
0.01426092442125082,
0.0015934375114738941,
0.030291832983493805,
-0.02768608368933201,
-0.04069038853049278,
0.03276079148054123,
-0.04122442007064819,
-0.006607296410948038,
-0.043254390358924866,
-0.006536663975566626,
0.06560733169317245,
-0.0431411936879158,
0.004049300216138363,
0.03858064115047455,
-0.049169328063726425,
-0.0021062493324279785,
0.039774198085069656,
0.0002453412744216621,
0.02037908136844635,
-0.020348988473415375,
0.030115336179733276,
0.008288608863949776,
-0.024591106921434402,
0.009941386990249157,
0.045903392136096954,
0.0073951175436377525,
-0.0040065087378025055,
0.0338280014693737,
0.012421809136867523,
-0.017872095108032227,
0.012495677918195724,
-0.016674863174557686,
0.030726071447134018,
-0.03298984095454216,
-0.04561614245176315,
-0.02211141027510166,
-0.005473623052239418,
0.0030839191749691963,
0.04672028496861458,
0.024316107854247093,
0.052983153611421585,
-0.016685044392943382,
0.03074996918439865,
-0.020774206146597862,
-0.01858769915997982,
-0.040096014738082886,
0.008234310895204544,
0.03391072899103165,
0.05067594349384308,
-0.0064302291721105576,
-0.03540344908833504,
-0.012806260958313942,
0.0023970669135451317,
0.011594603769481182,
-0.020101308822631836,
0.030929891392588615,
0.005271192640066147,
-0.0064322869293391705,
0.018274599686264992,
-0.011189407669007778,
-0.015211659483611584,
-0.015969574451446533,
0.03310228884220123,
0.021384121850132942,
0.030476221814751625,
0.01748960092663765,
-0.03377493843436241,
-0.02625974640250206,
0.011615272611379623,
-0.08578649908304214,
0.03914748504757881,
0.00397002836689353,
-0.005796578247100115,
-0.013109629042446613,
-0.014185850508511066
] |
<p>I'm looking for a list of immiscible (and miscible) liquids.</p>
<p>I currently developing a game that will use the property of differents liquid, some of them will mix, other will not (positioning in the recipient is important so density is).</p>
<p>I'm searching but not found anything very relevant.</p>
<p>Of course I know water, oil (and mercury). But I'm looking for more than two (at least 8 differents elements in three or four groups).</p>
<p>I can always invent them but I'd like to keep things real as far as I can. </p>
<p>The elements must be at the liquid state in normal conditions.</p>
| 9,574 |
[
0.00611618859693408,
-0.002107648877426982,
-0.016817208379507065,
0.00255789328366518,
0.014039174653589725,
-0.021381128579378128,
-0.0414075069129467,
-0.022494763135910034,
0.009615038521587849,
0.0036390016321092844,
0.034406714141368866,
0.041356828063726425,
0.008705281652510166,
0.01784774288535118,
-0.024619827046990395,
-0.01753426529467106,
0.02912924624979496,
-0.01965927518904209,
0.03286338225007057,
-0.028573593124747276,
0.023104453459382057,
-0.014226982370018959,
0.024724284186959267,
0.012418260797858238,
0.0035490477457642555,
0.03980805724859238,
0.01130167581140995,
-0.032983943819999695,
0.03691884130239487,
0.022878633812069893,
-0.02075197920203209,
-0.0586843341588974,
-0.012926395982503891,
-0.0015070624649524689,
0.0037755132652819157,
-0.0007349055958911777,
-0.02649519592523575,
-0.0008555049425922334,
-0.021589552983641624,
0.016901817172765732,
-0.06888191401958466,
-0.015562761574983597,
0.003867330029606819,
0.05048533156514168,
0.006157465744763613,
0.023230882361531258,
0.008827190846204758,
-0.04324623569846153,
0.007729186210781336,
-0.06748723983764648,
0.02547495812177658,
0.01656232215464115,
0.04165276885032654,
0.03949715197086334,
-0.008581522852182388,
0.03002026304602623,
0.04847121611237526,
0.07993914932012558,
0.025673920288681984,
-0.05184600129723549,
0.02869509719312191,
0.011328631080687046,
-0.0011510023614391685,
-0.029416559264063835,
-0.05395117029547691,
0.03123963251709938,
-0.009197920560836792,
0.005992161110043526,
-0.008642678149044514,
0.009049845859408379,
-0.019991612061858177,
0.013980775140225887,
0.03983818367123604,
0.016409870237112045,
0.029277455061674118,
-0.024532778188586235,
0.011179127730429173,
0.03112311288714409,
0.02460342086851597,
0.04020101949572563,
-0.02362111210823059,
-0.00553697207942605,
-0.028774555772542953,
0.0066229309886693954,
-0.01846357248723507,
-0.019362492486834526,
0.08160112798213959,
-0.01647127978503704,
0.021490704268217087,
0.038760002702474594,
-0.011545076034963131,
-0.002635194454342127,
0.019787857308983803,
0.02654455415904522,
-0.015447625890374184,
-0.04731813073158264,
-0.02323237806558609,
0.03309628739953041,
0.002235921798273921,
-0.013353778049349785,
0.010226933285593987,
-0.03435170277953148,
0.02371576614677906,
0.1070341169834137,
0.008261408656835556,
-0.031088607385754585,
-0.052846066653728485,
-0.036062926054000854,
0.030646439641714096,
0.011022542603313923,
0.046241141855716705,
-0.008981217630207539,
0.024304965510964394,
-0.0028169273864477873,
-0.044035520404577255,
-0.041750457137823105,
0.008335045538842678,
-0.019910253584384918,
0.044183045625686646,
0.06507854163646698,
0.03663353621959686,
-0.039225850254297256,
0.06764116138219833,
0.012434368021786213,
-0.0811648964881897,
0.025201352313160896,
-0.025142384693026543,
0.01760716177523136,
-0.03227598965167999,
0.030775900930166245,
-0.002819516696035862,
0.008974638767540455,
0.012686043046414852,
-0.004726266488432884,
0.05359023064374924,
-0.04905321076512337,
-0.06314808875322342,
-0.08158551156520844,
0.037425510585308075,
-0.041010621935129166,
-0.06363192945718765,
-0.056854091584682465,
0.02798604406416416,
0.03229834511876106,
0.046172380447387695,
0.0027450688648968935,
0.006007726304233074,
-0.015233543701469898,
0.041841279715299606,
0.017328068614006042,
-0.02748306468129158,
-0.00696302717551589,
-0.0014657301362603903,
-0.02187185548245907,
0.0283425971865654,
-0.024411959573626518,
0.019892049953341484,
0.0821692943572998,
0.011494598351418972,
0.007146961521357298,
0.01792318932712078,
-0.06825138628482819,
0.021290486678481102,
0.03165021166205406,
0.013867950066924095,
-0.052063118666410446,
0.06871581077575684,
0.007312467321753502,
0.046218063682317734,
-0.0013544806279242039,
0.00041636990499682724,
0.027832690626382828,
0.034322094172239304,
-0.0012141605839133263,
0.055235352367162704,
-0.017076710239052773,
-0.017635058611631393,
0.013010538183152676,
0.028238236904144287,
0.0025017436128109694,
-0.03380835801362991,
-0.015188944526016712,
-0.021115276962518692,
0.02604348585009575,
0.005530066788196564,
0.0056676859967410564,
0.022084074094891548,
-0.02869504876434803,
0.03887011110782623,
-0.03863847628235817,
0.026695629581809044,
-0.0405663326382637,
0.024812323972582817,
-0.02349848300218582,
0.002719527343288064,
0.03322669491171837,
0.03571457043290138,
0.030599115416407585,
-0.0636279433965683,
-0.024340957403182983,
-0.02948114275932312,
-0.020847776904702187,
0.02270229160785675,
0.01720229722559452,
-0.002676122123375535,
0.0788666307926178,
0.018613219261169434,
-0.03829118236899376,
0.004564930219203234,
-0.004524377174675465,
-0.01778402552008629,
-0.020802222192287445,
-0.018276527523994446,
0.04396705701947212,
-0.024476736783981323,
-0.016514571383595467,
0.035699356347322464,
0.0019793708343058825,
0.03360128775238991,
0.017705244943499565,
-0.04272156208753586,
0.08423555642366409,
0.05191395431756973,
0.0049496423453092575,
0.004321136511862278,
0.018018200993537903,
-0.000026736874133348465,
0.02838791348040104,
0.024638475850224495,
0.002968881279230118,
-0.06817008554935455,
-0.027197340503335,
0.028070416301488876,
0.05828751623630524,
-0.030998779460787773,
0.029494328424334526,
0.01928684115409851,
0.03365083038806915,
0.03883914276957512,
0.014225456863641739,
-0.012960288673639297,
-0.016013044863939285,
-0.004896451719105244,
0.015295358374714851,
0.030271099880337715,
0.03333072364330292,
-0.0071265436708927155,
0.04589400812983513,
0.04217179864645004,
-0.019108669832348824,
-0.036102890968322754,
0.005766287911683321,
0.0007541717495769262,
0.024711262434720993,
-0.022100958973169327,
-0.04600847139954567,
0.0061170794069767,
-0.02718552015721798,
-0.014432408846914768,
-0.0009990900289267302,
0.01223617885261774,
-0.02046784944832325,
-0.01309452299028635,
-0.025405049324035645,
0.01537267118692398,
0.017328720539808273,
-0.02917211875319481,
-0.00004737520794151351,
0.02288266457617283,
-0.05367739126086235,
-0.013058565557003021,
0.010481460019946098,
0.025470668449997902,
-0.028496336191892624,
0.025002535432577133,
0.010020654648542404,
-0.02661774680018425,
0.01240245345979929,
-0.019914552569389343,
-0.0056172385811805725,
-0.03237288072705269,
-0.031871773302555084,
-0.004179148469120264,
-0.02159304916858673,
-0.0547342374920845,
0.01551256887614727,
-0.01466596219688654,
-0.038120072335004807,
0.01917939819395542,
0.014084615744650364,
-0.009447677060961723,
0.03450755402445793,
-0.03138737007975578,
-0.030304625630378723,
0.001290600746870041,
-0.01616879738867283,
0.035740144550800323,
-0.02648373320698738,
0.02712215669453144,
0.006053864490240812,
-0.0046716961078345776,
-0.05131332576274872,
-0.0079830102622509,
-0.04031166806817055,
-0.04691562429070473,
-0.011289927177131176,
-0.010954555124044418,
0.028733164072036743,
-0.022758129984140396,
-0.021662544459104538,
0.049017999321222305,
-0.04291534051299095,
0.009061607532203197,
-0.05025455355644226,
-0.08318840712308884,
0.00958747137337923,
0.026509076356887817,
0.04374207183718681,
0.024965627118945122,
-0.026432590559124947,
0.04038974270224571,
-0.006599510088562965,
-0.07962619513273239,
-0.016871780157089233,
-0.009085603058338165,
-0.02236543782055378,
-0.01624828763306141,
0.05612665042281151,
0.02237316407263279,
-0.014546516351401806,
0.02064225822687149,
0.030908972024917603,
0.016117043793201447,
0.020208559930324554,
0.02102130465209484,
0.03264440596103668,
0.027027444913983345,
0.05245869979262352,
-0.01211968157440424,
0.07011476159095764,
0.027842659503221512,
-0.04555882513523102,
0.00899890810251236,
0.014765321277081966,
0.039479974657297134,
0.03917321562767029,
-0.037262920290231705,
0.004772115498781204,
0.025026559829711914,
0.011208491399884224,
-0.014326435513794422,
0.02446250431239605,
0.013932759873569012,
-0.0235958993434906,
-0.010403402149677277,
0.0341765321791172,
0.015972964465618134,
0.0067190323024988174,
0.009118734858930111,
0.06523805111646652,
-0.018189210444688797,
-0.05110926553606987,
-0.00833536684513092,
0.0180917177349329,
0.01178654283285141,
0.015309283509850502,
-0.024065615609288216,
0.00047964401892386377,
0.06977405399084091,
-0.02076605148613453,
0.01828131452202797,
-0.00006733424379490316,
-0.016154667362570763,
-0.00020004718680866063,
-0.09829216450452805,
-0.0026876493357121944,
-0.04038915038108826,
0.023678390309214592,
0.005997452884912491,
0.08166027069091797,
0.02061540260910988,
0.0022320449352264404,
-0.006167588289827108,
0.017098544165492058,
-0.04916704073548317,
0.02916872128844261,
-0.030989067628979683,
0.034056153148412704,
-0.0036300348583608866,
-0.010235062800347805,
-0.02874574437737465,
-0.056222084909677505,
-0.05274840071797371,
0.01584639586508274,
0.018560044467449188,
-0.03746558353304863,
0.005106450989842415,
-0.028978778049349785,
-0.03308549523353577,
0.0036960209254175425,
0.013799850828945637,
-0.010329978540539742,
0.03753337264060974,
0.06229660287499428,
0.015677064657211304,
0.007920163683593273,
-0.03470052033662796,
-0.011819916777312756,
0.022097615525126457,
0.014730842784047127,
0.05377780646085739,
0.032897401601076126,
0.018767688423395157,
0.010173098184168339,
-0.016514334827661514,
-0.014176055788993835,
0.05381932109594345,
-0.032014574855566025,
0.02221502922475338,
-0.0313691720366478,
-0.057030223309993744,
0.0021277472842484713,
0.022337857633829117,
0.012091037817299366,
0.005509966053068638,
0.027749134227633476,
-0.010387685149908066,
-0.007428861688822508,
-0.048420581966638565,
0.04376779496669769,
0.08418219536542892,
0.030007055029273033,
-0.010582911781966686,
0.01560201682150364,
-0.036504827439785004,
-0.017926083877682686,
0.039303213357925415,
0.010251207277178764,
0.040045369416475296,
0.015986213460564613,
-0.019241657108068466,
0.00948311947286129,
0.012427554465830326,
-0.0485081821680069,
-0.009956913068890572,
0.0025341957807540894,
-0.003623352153226733,
-0.03269052505493164,
-0.0006276664789766073,
-0.00978735089302063,
0.015456758439540863,
0.01677253656089306,
-0.011814379133284092,
-0.013550824485719204,
-0.07879717648029327,
0.04526112228631973,
0.06128455325961113,
0.057732876390218735,
-0.005929667502641678,
-0.015581957995891571,
-0.057367268949747086,
-0.030557041987776756,
0.015279511921107769,
-0.01842883601784706,
0.0036152524407953024,
-0.05961821600794792,
-0.008035046979784966,
-0.026753569021821022,
-0.045802418142557144,
0.006462601013481617,
0.013707997277379036,
-0.003982929978519678,
0.013341275975108147,
-0.002824334427714348,
-0.011766796931624413,
-0.0056463624350726604,
0.026537040248513222,
0.04276585951447487,
0.0390327051281929,
0.026755087077617645,
-0.014664134941995144,
0.0020514335483312607,
0.0055535221472382545,
-0.027509260922670364,
-0.0644209235906601,
0.010015151463449001,
0.005626906640827656,
0.00328364921733737,
0.04850442335009575,
-0.024671101942658424,
-0.05592798814177513,
0.03247532248497009,
0.0225167628377676,
-0.0016326081240549684,
0.0028188920114189386,
-0.02118239365518093,
0.05645643547177315,
0.03494884818792343,
0.02139565534889698,
0.03367253765463829,
0.02729356661438942,
-0.02171589434146881,
-0.04810585081577301,
-0.024308571591973305,
0.030010905116796494,
-0.03535180911421776,
0.0347130224108696,
-0.029160939157009125,
0.020551951602101326,
-0.047209806740283966,
0.0253214742988348,
0.010335292667150497,
-0.012734098359942436,
-0.01078424509614706,
-0.024144664406776428,
-0.025939442217350006,
0.020751573145389557,
0.022245517000555992,
-0.035284578800201416,
0.011433243751525879,
0.005717955995351076,
-0.020920051261782646,
0.029771341010928154,
0.058845460414886475,
-0.005433057900518179,
-0.02413172833621502,
0.01597592420876026,
-0.010180346667766571,
0.05371217802166939,
-0.03367219120264053,
0.01345430500805378,
-0.027811994776129723,
-0.014005794189870358,
0.03129592537879944,
0.029941217973828316,
0.05642242357134819,
0.012114794924855232,
-0.04522211104631424,
0.00501302070915699,
0.026015805080533028,
0.023965924978256226,
0.026454264298081398,
-0.02643035538494587,
0.01722276210784912,
-0.024748217314481735,
0.010396239347755909,
-0.050853412598371506,
-0.0816149115562439,
0.04758821055293083,
0.035049423575401306,
-0.011288891546428204,
-0.05074132978916168,
-0.005057182163000107,
-0.007129085715860128,
-0.011144706979393959,
0.0394827276468277,
0.011812989600002766,
-0.009328216314315796,
-0.021168658509850502,
0.026541471481323242,
0.015369752421975136,
0.039888449013233185,
0.017265604808926582,
-0.015366887673735619,
0.026325775310397148,
-0.0010827109217643738,
0.029172677546739578,
-0.02553843893110752,
0.02472558245062828,
-0.013528983108699322,
-0.025948714464902878,
-0.0202777162194252,
-0.00039643648779019713,
0.06361430883407593,
-0.030808430165052414,
0.03080924227833748,
-0.014031626284122467,
-0.016258923336863518,
-0.058471936732530594,
-0.011043274775147438,
0.031229456886649132,
-0.028226865455508232,
-0.0048082186840474606,
-0.014454275369644165,
0.024535005912184715,
-0.004232749808579683,
-0.04996731877326965,
0.0019396780990064144,
-0.040195267647504807,
-0.004239432979375124,
-0.005591950379312038,
0.07787708193063736,
-0.007233699318021536,
-0.015977654606103897,
0.037252649664878845,
-0.021777451038360596,
0.054213207215070724,
-0.025938818231225014,
-0.030199386179447174,
0.009381447918713093,
0.03723718971014023,
-0.06731458753347397,
-0.06667616963386536,
-0.023564545437693596,
0.01848672889173031,
-0.00016059492190834135,
-0.03873664513230324,
0.043616145849227905,
0.06472545117139816,
0.006506128702312708,
0.013854493387043476,
0.03746252879500389,
-0.025744009763002396,
0.03811148926615715,
-0.05099470540881157,
0.04038489982485771,
-0.008820989169180393,
-0.0198030024766922,
0.0034474735148251057,
0.04440339654684067,
0.0072737946175038815,
-0.00993313454091549,
0.04669458046555519,
-0.015516011975705624,
0.00021855637896806002,
-0.02808929793536663,
-0.05789477750658989,
0.008991978131234646,
-0.06461784988641739,
0.028306983411312103,
0.009300747886300087,
-0.031334903091192245,
0.021685859188437462,
-0.006670298520475626,
0.027835886925458908,
-0.024226447567343712,
-0.011705922894179821,
-0.011567770503461361,
0.06526355445384979,
0.015235277824103832,
-0.001533903181552887,
0.00032848140108399093,
0.03200392797589302,
0.01999039202928543,
0.009298830293118954,
-0.01626678742468357,
-0.016006305813789368,
-0.08930554240942001,
-0.0012744623236358166,
-0.02593914419412613,
-0.0355944000184536,
0.005376868415623903,
0.004614419769495726,
-0.00014666517381556332,
0.004321185406297445,
0.008055134676396847,
-0.002994249342009425,
-0.01133029256016016,
0.001072544138878584,
-0.00873363297432661,
0.029067782685160637,
-0.027145516127347946,
0.029293222352862358,
-0.0344938300549984,
-0.0028415098786354065,
0.1315654218196869,
0.0352630577981472,
0.008738664910197258,
-0.0526004433631897,
-0.013312039896845818,
0.00783398188650608,
-0.021149447187781334,
-0.030265625566244125,
0.013690494000911713,
-0.021901991218328476,
0.026659151539206505,
-0.009154326282441616,
0.035599470138549805,
0.015823006629943848,
0.028382794931530952,
0.02584538422524929,
-0.060336798429489136,
-0.007207544986158609,
-0.018403466790914536,
0.0034561590291559696,
-0.04277500510215759,
0.03224993497133255,
-0.06210402026772499,
0.027784176170825958,
-0.010205804370343685,
-0.0005252867704257369,
-0.019161522388458252,
-0.015732385218143463,
0.07179619371891022,
0.02040775865316391,
-0.014841051772236824,
-0.01406094804406166,
0.004255891311913729,
0.002259219530969858,
-0.024120962247252464,
0.022197477519512177,
0.02757064439356327,
-0.044494934380054474,
-0.0024309204891324043,
-0.003781226696446538,
0.018979083746671677,
-0.0213661789894104,
-0.007246450055390596,
0.009346948936581612,
-0.03775063157081604,
-0.015875179320573807,
-0.024969246238470078,
0.01191770751029253,
-0.027957532554864883,
-0.03009880520403385,
-0.0015776149230077863,
-0.006764734163880348,
0.009687026031315327,
-0.023054001852869987,
-0.050161853432655334,
-0.012302011251449585,
0.04856341704726219,
-0.030032670125365257,
0.0007088265847414732,
-0.02803558111190796,
0.029400987550616264,
-0.025651412084698677,
0.0012763731647282839,
-0.02277725748717785,
0.0043548960238695145,
0.018902597948908806,
-0.033370256423950195,
0.03245849162340164,
0.012901952490210533,
-0.01304344180971384,
-0.0319732129573822,
-0.012137566693127155,
-0.03404351696372032,
0.001044581993483007,
0.0038874137680977583,
0.043028198182582855,
0.02237188071012497,
0.011652939021587372,
-0.027765240520238876,
-0.007928108796477318,
-0.016072263941168785,
0.08303844928741455,
-0.02253136597573757,
0.0016504836967214942,
-0.020140981301665306,
-0.007305041421204805,
0.026086481288075447,
0.0324581041932106,
-0.03659133240580559,
0.006426146253943443,
-0.0131961889564991,
0.006220771465450525,
0.03233129531145096,
0.0019381651654839516,
-0.04393379017710686,
0.02968158759176731,
-0.04447552561759949,
0.012331081554293633,
0.01583673804998398,
0.0816156417131424,
0.025638900697231293,
-0.03161301091313362,
0.02279919758439064,
0.0018157890299335122,
-0.023534368723630905,
0.0004428486281540245,
0.0009711944148875773,
-0.021067269146442413,
-0.06514620035886765,
-0.0162664707750082,
0.02423281967639923,
0.04206738620996475,
-0.043150920420885086,
-0.04341341555118561,
0.0012675834586843848,
-0.012364263646304607,
0.011379227973520756,
-0.020406002178788185,
-0.003035289701074362,
0.011351142078638077,
-0.00014438960351981223,
-0.0034207147546112537,
0.018016377463936806,
-0.0530121736228466,
-0.03528090938925743,
0.0246859323233366,
0.00926562212407589,
-0.0018786481814458966,
-0.004096405580639839,
-0.027010714635252953,
0.013237983919680119,
0.04419456794857979,
0.03354698419570923,
0.0010516749462112784,
-0.03420212119817734,
0.028429986909031868,
0.003969443030655384,
0.052420005202293396,
-0.06446288526058197,
-0.034792523831129074,
0.001062859082594514,
-0.025347551330924034,
-0.01013121660798788,
0.0042808479629457,
-0.041247449815273285,
0.02801330015063286,
0.03641141578555107,
-0.004593016114085913,
-0.029690071940422058,
0.11152318120002747,
0.015865188091993332,
0.01613793708384037,
-0.004938758909702301,
0.004102372098714113,
0.009371565654873848,
-0.0036795600317418575,
0.005353272892534733,
-0.013829589821398258,
-0.0006470491643995047,
0.026638183742761612,
0.05392798036336899,
0.08354858309030533,
-0.01704869605600834,
-0.020189205184578896,
0.022397201508283615,
0.030872894451022148,
0.06815478950738907,
-0.03187323734164238,
0.02343599870800972,
0.016222810372710228,
-0.021361004561185837,
0.04421617090702057,
0.05848566070199013,
-0.01195614319294691,
-0.1029207855463028,
0.010643739253282547,
0.0012581594055518508,
0.01330536138266325,
0.01676899567246437,
-0.04949573054909706,
-0.005900910124182701,
0.02468801662325859,
-0.05863427743315697,
0.0030308403074741364,
-0.026227323338389397,
-0.026653427630662918,
-0.011415570974349976,
0.0016520563513040543,
-0.04643479362130165,
0.05223475769162178,
-0.0024087554775178432,
0.03707370534539223,
0.016160184517502785,
0.013155162334442139,
-0.04747665300965309,
-0.007932781241834164,
-0.012537531554698944,
0.029827378690242767,
-0.02201618067920208,
-0.013244262896478176,
0.00994447898119688,
-0.029694169759750366,
-0.03386871516704559,
0.001235332922078669,
0.003397977212443948,
0.010963400825858116,
-0.014545725658535957,
0.0063118478283286095,
-0.04866599291563034,
0.034846656024456024,
0.012461457401514053,
0.033758752048015594,
-0.01652391254901886,
0.019609475508332253,
-0.0038625237066298723,
0.049889225512742996,
-0.007684516254812479,
-0.004637322388589382,
0.01596841961145401,
-0.021411268040537834,
-0.04136331006884575,
0.04957035928964615,
-0.045374222099781036,
0.003089869860559702,
-0.01821271888911724,
0.008980832993984222,
0.03854794800281525,
0.0029898700304329395,
-0.020665062591433525,
-0.004579119849950075,
-0.005416193511337042,
0.01910272426903248,
0.005769283976405859,
0.012301144190132618,
0.03029169887304306,
-0.012233519926667213,
0.004139765165746212,
-0.03144577145576477,
0.03254438564181328,
-0.014427301473915577,
-0.04578183591365814,
-0.004238956142216921,
-0.014883915893733501,
-0.007237401325255632,
0.01528872735798359,
-0.0007106263656169176,
-0.05577252805233002,
0.03898950666189194,
0.011420716531574726,
0.014756038784980774,
-0.007130250800400972,
-0.019973358139395714,
0.01529718842357397,
-0.028018275275826454,
0.03681519627571106,
-0.030158385634422302,
0.029874905943870544,
-0.03337612748146057,
-0.022921616211533546,
0.020599769428372383,
0.01775256171822548,
0.04080769419670105,
-0.02359345182776451,
-0.0063563124276697636,
-0.026928238570690155,
0.01762467436492443,
0.040978554636240005,
-0.01578168012201786,
0.012278294190764427,
-0.006500206422060728,
-0.06402914971113205,
0.01901187002658844,
0.008014746941626072,
0.04954487085342407,
-0.03603462502360344,
0.030436163768172264,
-0.04411667212843895,
-0.02986966446042061,
-0.011700591072440147,
-0.029673054814338684,
0.029950877651572227,
-0.014131705276668072,
-0.023548215627670288,
0.07326288521289825,
-0.0480780154466629,
0.008932141587138176,
-0.006359083577990532,
0.010390781797468662,
-0.02687869779765606,
0.05667759105563164,
-0.01923150196671486,
-0.026767391711473465,
-0.03127717599272728,
-0.005519736558198929,
0.01205331552773714,
-0.0657309964299202,
0.04608647897839546,
-0.0216642115265131,
-0.026431817561388016,
0.00035179886617697775,
0.08493376523256302,
-0.0011587321059778333,
0.06311848014593124,
-0.015090987086296082,
0.03428314998745918,
-0.002293621888384223,
-0.009481080807745457,
0.02543184906244278,
-0.0020209182985126972,
0.046730250120162964,
-0.00021573767298832536,
-0.031697917729616165,
-0.0032996847294270992,
0.022966355085372925,
0.019491195678710938,
0.030817048624157906,
-0.015268445014953613,
-0.0160880908370018,
-0.01727050542831421,
0.020594514906406403,
0.0014226367929950356,
0.031996287405490875,
0.016268029808998108,
-0.010112045332789421,
0.054107945412397385,
-0.03082411363720894,
0.014345006085932255,
-0.06715366989374161,
0.03744275122880936,
-0.02782057225704193,
-0.0035182181745767593,
-0.027010971680283546,
0.009591806679964066,
-0.006356524303555489,
-0.006634480319917202,
0.009178797714412212,
-0.01287643052637577,
0.015251914970576763,
-0.04336528852581978,
0.03259142488241196,
-0.0082724429666996,
0.003630280029028654,
-0.01127858366817236,
-0.022997252643108368,
-0.008539442904293537,
-0.0058860271237790585,
-0.003746784059330821,
0.016193509101867676,
-0.002466203412041068,
-0.029717830941081047,
-0.015582581982016563,
-0.026670126244425774,
0.038826365023851395,
-0.03995870053768158,
-0.007986695505678654,
-0.0548449382185936,
0.040415406227111816,
-0.008973469026386738,
0.016905317083001137
] |
<p>This may sound as a mathematical question, but it should be very familiar to physicists. I am trying to perform an expansion of the function $$f(x) = \sum_{n=1}^{\infty} \frac{K_2(nx)}{n^2 x^2},$$ for $x \ll 1$. Here, $K_2(x)$ is the modified Bessel function of the second kind. This series is a result of solving the integral $$f(x) = \frac{1}{3}\int_1^\infty \frac{(t^2-1)^{3/2}}{\mathrm{e}^{xt}-1}\mathrm{d}t.$$ The result should be $$f(x) \approx \frac{\pi^4}{45 x^4} - \frac{\pi^2}{12 x^2}+\frac{\pi}{6x}-\frac{1}{32}\left( \frac{3}{2}-2\gamma+2\ln4\pi-\ln x^2\right)+\mathcal{O}(x^2),$$ where $\gamma$ is the Euler-Mascheroni constant. It agrees numerically with $f(x)$ for small $x$. However, by using the series expansion of the Bessel function $$K_2(nx) = \frac{2}{n^2x^2}-\frac{1}{2}+\frac{1}{2}\sum_{k=0}^\infty \left[\psi(k+1)+\psi(k+3)-\ln\frac{n^2x^2}{4}\right]\frac{\left(\frac{n^2 x^2}{4}\right)^{k+1}}{k!(k+2)!},$$ with $\psi(x)$ being the digamma function and using the zeta regularization for summation over $n$, I am able to reproduce all the terms except $\frac{\pi}{6x}$. I.e., my result is $$f(x) = \frac{2\zeta(4)}{x^4} - \frac{\zeta(2)}{2x^2} + \frac{1}{8}\sum_{k=0}^\infty \left[\left(\psi(k+1)+\psi(k+3)-\ln\frac{x^2}{4}\right)\zeta(-2k) + 2 \zeta'(-2k)\right]\frac{\left(\frac{x^2}{4}\right)^{k}}{k!(k+2)!}.$$ It seems very strange that the $\frac{\pi}{6x}$ term should appear in the expansion since only even powers of $x$ appear in $K_2(nx)$. But, numerically, it is certainly there. How did I miss it?</p>
<p>I think that the missing term indicates that the zeta regularization isn't used properly. The term $\frac{\pi}{6x}$ appears right in the middle, separating the convergent sums $\zeta(4)$ and $\zeta(2)$ from the (regularized) divergent sums $\zeta(-2k)$ and $\zeta'(-2k)$. So, the missing term may be the price to pay for using the zeta regularization. Unfortunately, I don't know enough formal math to, so to speak, "repair the damage". Any help on the subject is more than welcome.</p>
| 9,575 |
[
0.030059555545449257,
-0.02940606139600277,
0.008977950550615788,
-0.010341857559978962,
0.019462699070572853,
-0.007660171948373318,
-0.028988538309931755,
-0.081519216299057,
-0.007679654750972986,
-0.051649827510118484,
0.06134350225329399,
0.027737393975257874,
0.06670323759317398,
0.0282478928565979,
-0.003824247745797038,
0.022526634857058525,
-0.048411451280117035,
0.0016169697046279907,
0.01367996633052826,
-0.046676766127347946,
0.017720375210046768,
0.03842654451727867,
-0.03434891998767853,
-0.006383686326444149,
-0.03106989711523056,
0.02874048799276352,
0.020179102197289467,
0.008815456181764603,
-0.03206245228648186,
0.07892971485853195,
-0.004034453071653843,
-0.02493015117943287,
0.041782647371292114,
0.03045681118965149,
0.0027041311841458082,
0.026669951155781746,
-0.025902925059199333,
-0.023565033450722694,
0.018692191690206528,
0.04280241206288338,
-0.049001216888427734,
-0.031158167868852615,
0.0019166577840223908,
0.010020270943641663,
0.0312923863530159,
-0.008769306354224682,
-0.009443962015211582,
-0.06089917942881584,
0.04473288357257843,
-0.03319014608860016,
0.057270221412181854,
0.03235085308551788,
0.023021306842565536,
0.014248944818973541,
-0.009170272387564182,
-0.036411359906196594,
0.021379513666033745,
0.06945986300706863,
0.02913524955511093,
-0.04505940154194832,
-0.02117992378771305,
-0.03757207468152046,
0.011987138539552689,
-0.01498020626604557,
-0.014045397751033306,
-0.003770336974412203,
-0.0016877891030162573,
-0.01840936206281185,
-0.05297846719622612,
-0.028543079271912575,
0.04604692757129669,
0.05622171238064766,
0.048000793904066086,
0.002927863970398903,
0.00011552434443728998,
0.03022964857518673,
-0.03545702248811722,
-0.008300538174808025,
0.028952017426490784,
-0.002477440983057022,
0.002558742417022586,
0.0001174618664663285,
0.04007567837834358,
0.009439866989850998,
0.007710921578109264,
0.03399863839149475,
0.057781826704740524,
-0.005548116751015186,
-0.0005427391151897609,
0.008647673763334751,
0.00833398662507534,
0.04474180191755295,
0.048273079097270966,
-0.0500902384519577,
0.020463740453124046,
0.034484025090932846,
-0.01779002882540226,
0.018445583060383797,
0.0023857736960053444,
0.006406112108379602,
0.0177585631608963,
-0.03333146125078201,
-0.009147386066615582,
0.0994778499007225,
0.025847861543297768,
-0.01650926284492016,
-0.014788927510380745,
0.021371060982346535,
-0.009413649328052998,
-0.05050266906619072,
-0.002577538136392832,
0.02483292669057846,
-0.016932614147663116,
0.010733219794929028,
-0.005509738344699144,
0.009416218847036362,
-0.050510331988334656,
-0.011012657545506954,
0.01710120216012001,
0.047775380313396454,
0.021362895146012306,
-0.0384802371263504,
0.03156377375125885,
-0.046000655740499496,
-0.04359271749854088,
0.05009927228093147,
0.033956509083509445,
-0.01181289553642273,
-0.053716227412223816,
0.02658071741461754,
0.023447426036000252,
-0.0163742583245039,
-0.011568484827876091,
0.038001082837581635,
0.018149567767977715,
-0.026765674352645874,
-0.06618285179138184,
-0.043254755437374115,
0.06480785459280014,
0.012620174326002598,
0.008345462381839752,
-0.08234596252441406,
-0.02326994761824608,
0.06219660863280296,
0.07249727100133896,
-0.004907099064439535,
-0.01143765076994896,
-0.00045344032696448267,
0.06682312488555908,
0.005990713834762573,
-0.04483723267912865,
-0.016438592225313187,
-0.01765764318406582,
-0.037832457572221756,
0.0030356531497091055,
-0.007092274725437164,
0.02477213367819786,
0.04543156921863556,
-0.0015837062383070588,
-0.013347447849810123,
0.07137693464756012,
0.013975687325000763,
-0.015237540937960148,
0.01521387416869402,
0.02888878434896469,
-0.0026118166279047728,
0.08836396038532257,
0.050096020102500916,
-0.018671507015824318,
0.006330309901386499,
-0.018622135743498802,
-0.006421527825295925,
-0.009883496910333633,
-0.005050954408943653,
0.03880304470658302,
-0.046273939311504364,
-0.020807763561606407,
-0.03891425207257271,
0.031919609755277634,
0.00684485724195838,
-0.023181824013590813,
0.007489180192351341,
0.002532681915909052,
-0.010254600085318089,
0.0364002026617527,
0.03508147969841957,
0.015619605779647827,
0.003671468934044242,
-0.0020048110745847225,
-0.04584230110049248,
-0.03363794833421707,
-0.011259352788329124,
0.0036678374744951725,
0.020610205829143524,
-0.020704621449112892,
0.014835993759334087,
-0.054711658507585526,
0.012973303906619549,
0.033167093992233276,
-0.016698097810149193,
-0.008585568517446518,
0.018451426178216934,
0.028425762429833412,
-0.0136878015473485,
0.03632330894470215,
0.018081549555063248,
0.033347904682159424,
0.001246701693162322,
0.05489286780357361,
-0.05415815860033035,
-0.010314232669770718,
-0.010059532709419727,
-0.03238411992788315,
0.03427647799253464,
-0.02921249158680439,
-0.00893611740320921,
0.02857869677245617,
-0.03699859604239464,
-0.023364201188087463,
0.027886154130101204,
-0.026097001507878304,
0.05693475157022476,
0.03730638325214386,
0.02425244078040123,
0.004108342807739973,
0.01809634454548359,
-0.0013759495923295617,
0.027741190046072006,
-0.04275188222527504,
-0.06632357835769653,
-0.043461382389068604,
-0.03151528909802437,
0.05935877934098244,
0.06709223985671997,
-0.022007234394550323,
-0.00730249285697937,
0.04987996444106102,
0.012128783389925957,
0.04140131548047066,
0.00047250589705072343,
-0.01202104240655899,
-0.035099007189273834,
0.01482351589947939,
0.01784554123878479,
-0.005356141831725836,
0.046148303896188736,
0.028998956084251404,
-0.0016219234094023705,
0.021125150844454765,
0.007638187613338232,
-0.05215621367096901,
-0.014378145337104797,
0.005452997982501984,
-0.012742227874696255,
-0.039962038397789,
-0.009697158820927143,
0.04069897159934044,
-0.006829738616943359,
0.016017066314816475,
0.017051344737410545,
0.005185575690120459,
0.027971815317869186,
-0.019302578642964363,
-0.01922496408224106,
0.06544617563486099,
-0.002647582907229662,
-0.022960355505347252,
-0.04146953299641609,
0.015790611505508423,
-0.0304128248244524,
0.0021846352610737085,
-0.023986898362636566,
-0.047470543533563614,
-0.006302377674728632,
-0.006106887478381395,
-0.027087176218628883,
-0.006165246944874525,
-0.005910329520702362,
-0.024528296664357185,
-0.02669174037873745,
-0.005065645556896925,
0.03562033548951149,
-0.012498622760176659,
0.028608836233615875,
-0.04388659447431564,
-0.0017702026525512338,
-0.00694548012688756,
0.020769814029335976,
0.042641520500183105,
0.015904175117611885,
0.041081756353378296,
0.04079972580075264,
-0.02291986532509327,
-0.02767203561961651,
-0.019805140793323517,
-0.01788979396224022,
-0.012820322997868061,
-0.057061273604631424,
0.0005484613939188421,
0.04836539924144745,
0.012049232609570026,
-0.05631157010793686,
0.03751904517412186,
-0.021024271845817566,
-0.029254579916596413,
-0.037981364876031876,
0.009012624621391296,
0.03526062145829201,
-0.021001027897000313,
0.009111065417528152,
-0.05545678362250328,
-0.03048895299434662,
0.010102808475494385,
-0.06643019616603851,
-0.032927028834819794,
0.011328491382300854,
-0.013409440405666828,
0.04652521014213562,
0.026926929131150246,
-0.05133570358157158,
0.08206673711538315,
-0.00012403217260725796,
0.011256708763539791,
-0.033366262912750244,
0.02199571393430233,
0.018143950030207634,
-0.023161232471466064,
0.004832696169614792,
0.034652844071388245,
-0.041843872517347336,
0.0163316261023283,
-0.0681472197175026,
-0.013701333664357662,
0.026654427871108055,
-0.03092055954039097,
-0.013597297482192516,
0.07172135263681412,
0.02881481871008873,
0.013963060453534126,
0.03740939870476723,
0.0035125287249684334,
-0.01890501379966736,
-0.006710269022732973,
0.009491310454905033,
-0.03481416776776314,
0.024594414979219437,
-0.03896760195493698,
0.03553302586078644,
0.0013291150098666549,
-0.0178716778755188,
-0.021237611770629883,
0.04919147491455078,
0.0012337007792666554,
-0.053392935544252396,
-0.04537670314311981,
0.004486920777708292,
0.04066023603081703,
-0.0008460920653305948,
0.03879016265273094,
0.0351431667804718,
0.029386963695287704,
0.015045341104269028,
0.01546989195048809,
-0.009562326595187187,
-0.010252942331135273,
0.03529488667845726,
-0.07292401790618896,
0.0037843813188374043,
0.036019906401634216,
0.04660548269748688,
0.017892036586999893,
-0.028835391625761986,
-0.007777150254696608,
-0.012210382148623466,
-0.04328645020723343,
-0.029842358082532883,
-0.043508194386959076,
0.04660235345363617,
0.003954758867621422,
-0.014703668653964996,
0.056858375668525696,
0.009004141204059124,
-0.036247167736291885,
0.06013688072562218,
-0.08208779990673065,
0.031202176585793495,
-0.02859063446521759,
-0.011991728097200394,
-0.02538096345961094,
0.0007852921262383461,
0.008349668234586716,
0.016123395413160324,
-0.027101313695311546,
-0.02963215857744217,
-0.010649905540049076,
-0.012128781527280807,
0.023261139169335365,
-0.0031311067286878824,
0.016732394695281982,
-0.04878793656826019,
0.04601255804300308,
0.05178799480199814,
-0.0028136982582509518,
-0.033519163727760315,
0.03363830968737602,
-0.03918970748782158,
0.00018345077114645392,
-0.02668464370071888,
0.009030045941472054,
0.00935276784002781,
-0.01598038524389267,
-0.004534685984253883,
-0.012295038439333439,
-0.017333367839455605,
-0.0033941029105335474,
0.002413203241303563,
0.05312257632613182,
0.018596384674310684,
0.024504119530320168,
0.00909046083688736,
-0.018530404195189476,
0.034963518381118774,
0.028977779671549797,
0.06343136727809906,
0.005418960936367512,
0.024340806528925896,
0.02365599013864994,
0.008879409171640873,
0.019677361473441124,
0.0041913376189768314,
0.0352914072573185,
-0.03926762565970421,
0.001754728495143354,
-0.05832638964056969,
-0.01234934851527214,
-0.019045324996113777,
0.006132689770311117,
-0.007216950878500938,
0.007414813619107008,
-0.021342381834983826,
-0.018787479028105736,
0.018767131492495537,
0.0249306783080101,
-0.00800714734941721,
-0.010476155206561089,
0.02269311062991619,
0.016657302156090736,
-0.0009157209424301982,
-0.021702028810977936,
0.006547955330461264,
-0.03248262032866478,
0.031832512468099594,
-0.012636625207960606,
-0.014438162557780743,
-0.07646907866001129,
-0.04126160591840744,
0.02717459946870804,
0.04828959330916405,
0.0070601641200482845,
0.015258986502885818,
-0.05085071176290512,
-0.0007760845473967493,
0.011113354004919529,
-0.002998039126396179,
0.005292897112667561,
-0.0031486565712839365,
0.01154718454927206,
0.004202474839985371,
-0.06135986000299454,
-0.032024040818214417,
0.02538420259952545,
-0.026080815121531487,
0.009036309085786343,
-0.05491683632135391,
-0.011047177016735077,
-0.01825779117643833,
0.010992479510605335,
0.006324563641101122,
0.09282305836677551,
0.02613689750432968,
-0.06251047551631927,
0.031054140999913216,
-0.0145627586171031,
-0.04333709925413132,
-0.05239110812544823,
0.021811818704009056,
-0.015489628538489342,
-0.016868360340595245,
0.023346025496721268,
-0.02862982451915741,
-0.04717845842242241,
0.0006297104991972446,
-0.016896136105060577,
-0.005589951295405626,
0.040855202823877335,
-0.06305962800979614,
0.02878718264400959,
0.04540266841650009,
0.04110221564769745,
0.07158294320106506,
0.07399721443653107,
-0.028257757425308228,
0.02103080041706562,
-0.027601420879364014,
0.009683401323854923,
-0.04156985878944397,
-0.023526644334197044,
-0.026278499513864517,
-0.03240903094410896,
-0.021980276331305504,
0.0452565923333168,
-0.0515771247446537,
0.02328362688422203,
0.003232999239116907,
-0.005869951099157333,
0.006436499767005444,
0.01903761550784111,
-0.02783540077507496,
0.043738339096307755,
-0.010346216149628162,
0.02264256216585636,
0.04501412436366081,
-0.04715645685791969,
0.03307001292705536,
-0.01300092414021492,
0.02972964569926262,
0.03296462073922157,
0.006119256839156151,
-0.017830247059464455,
-0.0032445951364934444,
-0.01798955351114273,
0.026735572144389153,
0.005273754708468914,
0.02452239766716957,
0.02018096297979355,
-0.01581537164747715,
-0.01348796021193266,
-0.042311470955610275,
-0.04379691183567047,
-0.003819535719230771,
-0.026149488985538483,
0.05101362243294716,
-0.023867996409535408,
0.006185533478856087,
0.025972047820687294,
-0.01693050190806389,
-0.0835375115275383,
0.008679237216711044,
0.03939060494303703,
-0.014840184710919857,
0.014735924080014229,
-0.04832872375845909,
-0.042509131133556366,
-0.030262760818004608,
-0.022680822759866714,
0.008626117371022701,
0.0505988672375679,
-0.00010607341391732916,
-0.003999148495495319,
-0.010392433032393456,
0.01128969807177782,
0.059351690113544464,
-0.030070161446928978,
-0.0027080215513706207,
-0.006086688954383135,
-0.03455360606312752,
-0.036297161132097244,
0.0051185451447963715,
0.020346414297819138,
-0.013064171187579632,
-0.005914789158850908,
0.0002627556386869401,
-0.0067134276032447815,
0.005195168778300285,
-0.06324376165866852,
-0.041409336030483246,
0.0572519488632679,
0.013486209325492382,
0.042970914393663406,
-0.043087832629680634,
-0.02489553764462471,
0.022120509296655655,
0.02788414992392063,
-0.013002711348235607,
-0.027454981580376625,
-0.025866972282528877,
-0.03238315135240555,
-0.020309191197156906,
-0.002210580511018634,
-0.019723931327462196,
-0.007350841537117958,
0.04343342036008835,
-0.05163617059588432,
-0.038720354437828064,
0.008220701478421688,
0.020715998485684395,
0.02587767131626606,
0.044574569910764694,
0.004158730152994394,
0.010785158723592758,
0.01468355767428875,
-0.028151649981737137,
-0.03221133351325989,
-0.04316948354244232,
-0.0004646733868867159,
0.05246395990252495,
-0.021861372515559196,
-0.011736725457012653,
-0.006571556441485882,
0.016869472339749336,
0.0394887700676918,
0.024332985281944275,
-0.0017751975683495402,
0.019969278946518898,
-0.04889370873570442,
-0.0011272593401372433,
-0.02929920144379139,
0.005740068387240171,
0.005906278267502785,
-0.012463065795600414,
-0.008412419818341732,
0.036030616611242294,
-0.0021298974752426147,
0.03020559437572956,
-0.012831401079893112,
-0.03708743676543236,
-0.02322552353143692,
0.051990438252687454,
-0.01187001820653677,
0.03522076830267906,
-0.03141997009515762,
-0.015793127939105034,
0.017375051975250244,
0.02289057895541191,
-0.008349437266588211,
-0.018484510481357574,
0.007781035266816616,
-0.01715235225856304,
-0.012740766629576683,
0.015822190791368484,
-0.03383569419384003,
0.06784035265445709,
0.005496543366461992,
-0.02865041047334671,
0.039732642471790314,
0.002301532309502363,
-0.00933352392166853,
-0.032730210572481155,
0.014192088507115841,
0.011501180939376354,
-0.07139790058135986,
0.03373109921813011,
-0.006630091927945614,
-0.029118608683347702,
0.01724623329937458,
-0.00035763232153840363,
0.022359199821949005,
0.056563764810562134,
0.011260895989835262,
-0.018251968547701836,
0.015026775188744068,
-0.008989970199763775,
-0.006528062745928764,
-0.01710284873843193,
0.02495613321661949,
0.141292542219162,
0.04307025671005249,
0.0012538929004222155,
-0.053209464997053146,
0.006385805085301399,
-0.026024777442216873,
0.02451017126441002,
-0.036571916192770004,
-0.03926081955432892,
-0.016379591077566147,
-0.06293736398220062,
-0.007982367649674416,
0.02900904044508934,
-0.023987894877791405,
0.0016126139089465141,
0.011720120906829834,
-0.01324414648115635,
-0.017420804128050804,
0.04131065309047699,
-0.025971809402108192,
0.012480548582971096,
0.020474961027503014,
-0.026184281334280968,
0.006429840344935656,
-0.04737241566181183,
0.012621995061635971,
-0.048982828855514526,
0.006623172666877508,
0.01524150837212801,
0.016169605776667595,
-0.047290753573179245,
-0.010107120499014854,
0.04846761375665665,
-0.03988725319504738,
0.02435787208378315,
0.010808332823216915,
0.031838078051805496,
-0.033121258020401,
0.041455481201410294,
0.028245270252227783,
0.021255724132061005,
0.0025935948360711336,
0.03375053405761719,
0.03952646628022194,
-0.03173701837658882,
-0.032753873616456985,
-0.03307495638728142,
0.0476006455719471,
0.006503231357783079,
0.001285967300646007,
0.01156889833509922,
-0.010461841709911823,
-0.018150635063648224,
-0.009647919796407223,
0.029994282871484756,
-0.0071170516312122345,
0.023772316053509712,
-0.06284177303314209,
-0.02950483374297619,
0.017362257465720177,
0.05129266157746315,
0.03482453152537346,
0.03316399082541466,
0.003980984445661306,
-0.03006589226424694,
0.005229341797530651,
0.004967651329934597,
0.036605674773454666,
-0.00760282389819622,
-0.011542155407369137,
0.0011912946356460452,
-0.0004534587205853313,
-0.017763014882802963,
-0.030444523319602013,
0.0009241995867341757,
-0.0005147783667780459,
0.046026166528463364,
0.018039213493466377,
-0.03234900161623955,
-0.04786190018057823,
-0.06703674048185349,
0.011157015338540077,
0.004982755985110998,
0.0014373880112543702,
-0.003306337632238865,
-0.019985876977443695,
0.008310927078127861,
-0.00387720949947834,
-0.0177569929510355,
0.02881840616464615,
0.027661122381687164,
0.02989625558257103,
0.023769529536366463,
-0.0429515577852726,
-0.052625756710767746,
-0.03972800076007843,
0.01243002712726593,
-0.00622553238645196,
-0.04821787029504776,
0.04159297049045563,
0.023595187813043594,
0.014817588031291962,
0.026171356439590454,
0.013302004896104336,
-0.06150588393211365,
-0.003972336649894714,
-0.024690022692084312,
-0.0032993853092193604,
0.0028044141363352537,
-0.0022205053828656673,
0.005488620605319738,
-0.027554690837860107,
-0.006469701416790485,
-0.04401309788227081,
-0.0031050138641148806,
-0.009936267510056496,
0.018269434571266174,
-0.02240718901157379,
-0.027055947110056877,
0.012151246890425682,
-0.04158947616815567,
0.040545519441366196,
-0.015344402752816677,
0.004254527855664492,
-0.011936670169234276,
-0.033951885998249054,
0.014358973130583763,
-0.016568206250667572,
0.0561700202524662,
0.010651754215359688,
0.0037337462417781353,
0.05596313998103142,
0.06404481828212738,
-0.009503747336566448,
-0.04175698384642601,
-0.006268841680139303,
-0.02344435825943947,
0.026602046564221382,
-0.005427398718893528,
-0.02181936800479889,
0.02869802713394165,
-0.05173034965991974,
-0.06411749869585037,
0.0346052311360836,
-0.02283339761197567,
-0.013632663525640965,
0.0538250170648098,
0.03518874570727348,
-0.040201179683208466,
0.06849323958158493,
-0.014255057089030743,
-0.01042608916759491,
-0.0223771370947361,
-0.01783093251287937,
0.01718372292816639,
-0.036763276904821396,
0.0035517222713679075,
0.013806736096739769,
-0.002506560180336237,
-0.003404280636459589,
0.039584796875715256,
-0.006585862021893263,
0.017875347286462784,
0.020219668745994568,
-0.008085720241069794,
-0.00018276531773153692,
0.004963290877640247,
0.00656806118786335,
0.05984685570001602,
0.05155937373638153,
-0.007471858523786068,
0.03236033767461777,
-0.037841226905584335,
-0.005139866378158331,
-0.08688650280237198,
-0.019129501655697823,
-0.02327348291873932,
0.0407213494181633,
0.051837339997291565,
-0.043133288621902466,
0.017212506383657455,
0.01212473213672638,
-0.0034687547013163567,
0.014080582186579704,
-0.01991427317261696,
-0.038616642355918884,
-0.012203508988022804,
-0.04400009661912918,
0.022899121046066284,
0.0058046565391123295,
0.05574248358607292,
0.06602779030799866,
0.02285102568566799,
0.008794957771897316,
0.0030934554524719715,
0.010182335041463375,
0.032746411859989166,
0.016387758776545525,
-0.016697991639375687,
-0.03953149542212486,
0.037623532116413116,
-0.03331905975937843,
-0.012947779148817062,
0.03028327412903309,
0.009752320125699043,
0.016060706228017807,
-0.036150284111499786,
0.0012940230080857873,
0.01681365631520748,
0.05886707454919815,
0.0062828934751451015,
0.0020430583972483873,
0.04398398473858833,
-0.016409721225500107,
0.023914985358715057,
-0.023018591105937958,
-0.045471906661987305,
-0.004139491822570562,
0.010852706618607044,
-0.014572057873010635,
-0.06423264741897583,
0.03184190019965172,
0.013016586191952229,
-0.0038678415585309267,
-0.026475796476006508,
-0.021819600835442543,
0.026492463424801826,
-0.027942126616835594,
0.002222159644588828,
-0.023780012503266335,
0.0025881680194288492,
-0.012085238471627235,
0.019896741956472397,
0.01079817209392786,
0.026941321790218353,
0.0134178651496768,
-0.03278760612010956,
0.004157640039920807,
0.007065226323902607,
0.006027085706591606,
-0.03620152920484543,
-0.027036301791667938,
-0.0075831166468560696,
0.039346400648355484,
0.023060591891407967,
0.0007249266491271555,
-0.04295032471418381,
0.010339842177927494,
0.0024459976702928543,
0.0299573615193367,
-0.03074108436703682,
-0.005613699555397034,
0.00943660642951727,
-0.07454898953437805,
0.021344507113099098,
0.011006185784935951,
-0.02484849840402603,
0.0035808715038001537,
0.009412563405930996,
0.012126109562814236,
0.03272796794772148,
0.05528932437300682,
0.004850434605032206,
-0.02081798017024994,
0.018518399447202682,
0.007407305762171745,
0.03637385740876198,
-0.031072476878762245,
-0.011077257804572582,
0.020812319591641426,
-0.0016485940432175994,
-0.019951555877923965,
0.020579485222697258,
-0.04412323236465454,
0.02570877969264984,
-0.009814714081585407,
0.02112625353038311,
0.009358670562505722,
0.00827653706073761,
-0.015683108940720558,
0.047416575253009796,
-0.011323140002787113,
-0.03378945216536522,
0.04577196016907692,
0.003621280426159501,
-0.0009521184838376939,
0.011988794431090355,
-0.031631503254175186,
-0.05132894217967987,
0.01794031634926796,
-0.03571813926100731,
-0.05140367150306702,
-0.010218510404229164,
-0.005327131133526564,
0.041821565479040146,
-0.010554473847150803,
0.003562162397429347,
0.06406877189874649,
-0.0013452903367578983,
-0.04483616724610329,
0.06229235604405403,
0.006290205288678408,
0.02483523078262806,
0.04518422111868858,
0.03398805111646652,
0.01959594525396824,
-0.013723686337471008,
0.029120564460754395,
-0.023418979719281197,
-0.01044809352606535,
-0.019848424941301346,
-0.0017913134070113301,
-0.014367194846272469,
0.0038082487881183624,
-0.014126424677670002,
0.0033141786698251963,
-0.018030140548944473,
-0.021457448601722717,
-0.021035300567746162,
0.027832411229610443,
-0.044229649007320404,
0.0036946202162653208,
0.021827952936291695,
-0.015371250919997692,
0.10450253635644913,
-0.011065698228776455,
0.05557847395539284,
-0.015797359868884087,
0.019288016483187675,
0.023321107029914856,
0.03466849401593208,
0.03700433298945427,
0.041729871183633804,
-0.004994531627744436,
0.023366916924715042,
0.0009884502505883574,
-0.04272020608186722,
0.02751799114048481,
-0.03885782137513161,
-0.022787801921367645,
-0.029629753902554512,
0.008054859936237335,
-0.023738816380500793,
-0.031871020793914795,
-0.03290732577443123,
-0.048218004405498505,
0.0138250095769763,
0.05353531986474991,
0.043983060866594315,
0.02247568592429161,
-0.0002525186282582581,
-0.0014346621464937925,
0.07864837348461151,
-0.024785537272691727,
0.01687689684331417,
0.037496086210012436,
0.0017830819124355912,
0.030078068375587463,
0.00692571047693491
] |
<p>The dynamic viscosity of air is $1.78\cdot 10^{-5}Pas = 1.78\cdot 10^{-5}\frac{kg}{ms}$. How do I convert this to the minute scale? I see a reason for multiplying the value with 60 (because of the $\frac{kg}{ms}$) or dividing it by 60 (because of the $Pa s$).</p>
<p>Background: I need the value in a numerical CFD simulation, where I have all my timesteps in the minute scale.</p>
| 9,576 |
[
0.02122526802122593,
-0.01767141744494438,
-0.03930586948990822,
0.02839788608253002,
0.027517979964613914,
-0.015189060941338539,
-0.027701154351234436,
-0.016551421955227852,
-0.004505647346377373,
0.028380637988448143,
0.06131312996149063,
0.051674842834472656,
0.029226837679743767,
0.015253754332661629,
0.0013598253717646003,
-0.014932042919099331,
-0.04761124402284622,
0.022364206612110138,
0.037563174962997437,
-0.005625616759061813,
0.008423836901783943,
-0.03279111534357071,
0.014328529126942158,
-0.045401327311992645,
-0.015744825825095177,
0.04536530002951622,
0.012613306753337383,
0.010874174535274506,
-0.035447195172309875,
0.021388575434684753,
-0.023847881704568863,
-0.020928023383021355,
0.02497556060552597,
0.023635705932974815,
0.027313461527228355,
0.007097420282661915,
-0.03297775983810425,
-0.014252772554755211,
-0.04081978648900986,
0.05389054864645004,
-0.019009985029697418,
-0.0095932362601161,
0.010726158507168293,
0.008324503898620605,
0.009338397532701492,
0.016274016350507736,
0.03530839830636978,
-0.004567790310829878,
0.04109152406454086,
-0.07637730985879898,
0.08599799871444702,
0.008721076883375645,
0.039682675153017044,
0.03665367141366005,
-0.015933778136968613,
-0.021315623074769974,
0.03868149220943451,
0.05942126363515854,
-0.018645191565155983,
-0.024042930454015732,
0.01575935259461403,
0.01574081927537918,
-0.01650908775627613,
-0.02573300153017044,
0.0005158593994565308,
0.014811010099947453,
-0.01776576042175293,
-0.0009931758977472782,
0.041669849306344986,
-0.027342239394783974,
0.017806457355618477,
0.002466659527271986,
0.06077251955866814,
-0.0023810819257050753,
0.024260656908154488,
-0.018832331523299217,
0.017620110884308815,
0.029262438416481018,
0.06718489527702332,
0.07272813469171524,
-0.021961750462651253,
0.010550231672823429,
0.019045574590563774,
0.005297818221151829,
0.0025386596098542213,
-0.004098924808204174,
0.06709562242031097,
0.009640587493777275,
0.02766593173146248,
0.027827603742480278,
-0.014032791368663311,
0.010697129182517529,
0.03847444802522659,
-0.013500590808689594,
0.015391787514090538,
0.00791656132787466,
-0.011936461552977562,
0.02742236852645874,
-0.012278796173632145,
0.0006319436361081898,
-0.018559787422418594,
-0.05048683285713196,
0.029068881645798683,
0.072374626994133,
0.01160016842186451,
-0.009710383601486683,
-0.012202035635709763,
-0.00983161386102438,
0.012095591984689236,
-0.053021688014268875,
-0.023168431594967842,
-0.01995745114982128,
-0.0058179739862680435,
-0.0005363636300899088,
0.003238441189751029,
-0.030959635972976685,
0.0008520298870280385,
-0.0011564356973394752,
0.04490344598889351,
0.05196203663945198,
0.07972028106451035,
-0.026226986199617386,
0.016488337889313698,
-0.021399587392807007,
-0.05945320054888725,
0.006808084435760975,
-0.005057758651673794,
-0.004880866967141628,
-0.03017774410545826,
0.00004398843157105148,
-0.03610621765255928,
-0.03735032305121422,
0.024109460413455963,
-0.03251473605632782,
0.011919023469090462,
-0.013470846228301525,
-0.06720180064439774,
-0.057531971484422684,
0.017296206206083298,
0.0004568199801724404,
0.012300378642976284,
-0.0768214613199234,
-0.015747476369142532,
0.006555323954671621,
0.03309906646609306,
0.03380749747157097,
0.014378336258232594,
-0.005182724446058273,
0.04181139916181564,
-0.015260156244039536,
-0.050461698323488235,
-0.00006803744327044114,
0.000976645271293819,
-0.027258308604359627,
-0.0021633466240018606,
-0.021448735147714615,
0.0007125656120479107,
0.0713195949792862,
0.01943662390112877,
0.006734748370945454,
0.026045748963952065,
-0.027519546449184418,
-0.032758090645074844,
-0.01153184287250042,
0.01051744632422924,
-0.049743782728910446,
0.038322027772665024,
0.0032838291954249144,
-0.012930094264447689,
-0.008031473495066166,
0.027376344427466393,
-0.03288455307483673,
0.010820076800882816,
0.015197599306702614,
0.09739107638597488,
0.0320187546312809,
-0.000543330330401659,
-0.01030778232961893,
-0.0031685675494372845,
0.019823690876364708,
-0.04533681273460388,
-0.03577115014195442,
-0.04415133595466614,
0.01195572130382061,
0.04197821393609047,
0.020236359909176826,
-0.018974866718053818,
0.031704939901828766,
0.010257900692522526,
-0.06079946458339691,
-0.06936962157487869,
-0.05621209740638733,
0.022888578474521637,
-0.014883407391607761,
0.02172425203025341,
0.017453886568546295,
-0.03167034313082695,
0.0329374335706234,
-0.0037149940617382526,
-0.033330146223306656,
0.005567009560763836,
-0.007061847019940615,
0.06859993934631348,
-0.019720107316970825,
-0.011119642294943333,
-0.003481857245787978,
0.04475873336195946,
-0.013372517190873623,
0.008854617364704609,
-0.006565788760781288,
-0.008281867019832134,
-0.019633429124951363,
-0.03430884703993797,
0.047970689833164215,
-0.034606631845235825,
-0.017637502402067184,
0.019244074821472168,
0.009979607537388802,
0.018578078597784042,
0.005509541369974613,
0.007373738568276167,
0.05621612071990967,
0.10562140494585037,
0.004978497978299856,
0.011641040444374084,
0.03977299481630325,
0.014949291944503784,
-0.015730135142803192,
0.01676500216126442,
-0.041573625057935715,
-0.03990985080599785,
-0.016238374635577202,
0.037111733108758926,
0.03956231847405434,
-0.02256917394697666,
0.0071891541592776775,
0.06644610315561295,
0.01936260797083378,
0.10394047945737839,
0.02893843874335289,
0.000999347073957324,
-0.056653961539268494,
0.006478391587734222,
0.0253716092556715,
0.0040138643234968185,
-0.00046471907990053296,
0.03634199872612953,
0.05216237157583237,
0.05199680104851723,
0.02301156520843506,
0.012598497793078423,
-0.01669858768582344,
0.02917899191379547,
0.029039571061730385,
-0.004357161931693554,
-0.02709735371172428,
0.0549699105322361,
-0.03401051461696625,
0.008846870623528957,
0.03811907768249512,
0.008467980660498142,
0.014191321097314358,
0.002043717075139284,
-0.031962063163518906,
0.015148742124438286,
0.01788918860256672,
-0.0005596926785074174,
-0.019375070929527283,
-0.0011497868690639734,
-0.012092694640159607,
0.02093501389026642,
-0.013910419307649136,
0.03504212200641632,
-0.048646192997694016,
-0.015842845663428307,
0.04780013859272003,
0.030990315601229668,
0.006083319894969463,
-0.01226363517343998,
-0.028207119554281235,
0.009251691401004791,
-0.01023811288177967,
0.004253457300364971,
0.023676330223679543,
-0.04670053347945213,
0.025759747251868248,
0.009046953171491623,
-0.047598037868738174,
0.0224775280803442,
-0.010797793976962566,
-0.026665998622775078,
0.003276997013017535,
-0.0278026033192873,
-0.05073223263025284,
0.02416352555155754,
-0.04626033082604408,
0.027577044442296028,
-0.03966054320335388,
-0.02602086402475834,
0.06966637074947357,
-0.019747018814086914,
-0.0411078967154026,
0.01938662678003311,
-0.044753801077604294,
-0.01998424343764782,
-0.0358542799949646,
0.0167839452624321,
0.011977016925811768,
-0.059473954141139984,
0.001444422174245119,
0.035197798162698746,
-0.01237491425126791,
0.0036770456936210394,
-0.002088257111608982,
-0.06571564823389053,
0.0049483501352369785,
0.0023601865395903587,
0.03918016329407692,
0.01726684346795082,
-0.048912301659584045,
0.04793713614344597,
0.002191589679569006,
-0.007758273743093014,
0.00014875362103339285,
0.02242233045399189,
-0.005770581308752298,
-0.06315634399652481,
-0.028127377852797508,
0.04050391912460327,
-0.010130850598216057,
-0.0194555651396513,
0.0025262946728616953,
0.023013848811388016,
0.09209206700325012,
0.014952159486711025,
-0.014842568896710873,
-0.018919862806797028,
-0.03631521016359329,
-0.0005111157661303878,
0.028448667377233505,
-0.007050045765936375,
-0.06366575509309769,
0.020489798858761787,
-0.040691718459129333,
0.017957355827093124,
0.03393984213471413,
-0.028400374576449394,
0.04467860236763954,
-0.0032117695081979036,
-0.02704627253115177,
-0.04707745090126991,
-0.010381622239947319,
-0.01659734733402729,
-0.019024742767214775,
-0.025009872391819954,
0.050502143800258636,
0.05601280555129051,
-0.01006900705397129,
-0.008111611008644104,
0.04888465255498886,
0.05054955929517746,
0.019488569349050522,
-0.03903733938932419,
-0.022763334214687347,
-0.024213530123233795,
0.027352945879101753,
-0.011881466023623943,
-0.009746339172124863,
0.027034059166908264,
0.02499331720173359,
0.0494450107216835,
-0.024314267560839653,
-0.06160978972911835,
0.033564161509275436,
-0.043183334171772,
-0.015172489918768406,
-0.005139767192304134,
0.05051792412996292,
0.02380048669874668,
0.051057908684015274,
0.037012483924627304,
0.01291247271001339,
0.009035482071340084,
-0.005675411783158779,
-0.06024570018053055,
0.09209095686674118,
-0.013755643740296364,
-0.02037988044321537,
0.0014267395017668605,
0.01344523299485445,
0.011765366420149803,
-0.030482470989227295,
-0.00889641884714365,
0.029264120385050774,
0.003682138863950968,
-0.03385114669799805,
0.008164094761013985,
-0.027544567361474037,
-0.005028819665312767,
-0.005845671985298395,
0.026693070307374,
0.042159274220466614,
-0.02463192492723465,
0.03986736387014389,
0.045703690499067307,
-0.003282687393948436,
-0.04780655726790428,
-0.04597224295139313,
0.0006953878910280764,
-0.019551102072000504,
-0.011623777449131012,
0.026748603209853172,
0.0025723876897245646,
-0.021880703046917915,
0.027017300948500633,
0.02019757218658924,
0.03312970697879791,
-0.047899845987558365,
0.0016910608392208815,
-0.04519280791282654,
-0.05277739092707634,
0.012440766207873821,
0.057734113186597824,
-0.007631134707480669,
0.015469815582036972,
0.04159596189856529,
0.0196253452450037,
-0.01616724394261837,
-0.024451052770018578,
0.05352718010544777,
0.04058978706598282,
-0.03456463664770126,
-0.005790595430880785,
-0.06981716305017471,
0.00948353298008442,
0.0010092247975990176,
-0.01598108746111393,
0.001292998087592423,
0.0625307559967041,
0.006838356610387564,
0.010610101744532585,
0.025946037843823433,
0.00006075175406294875,
0.033545561134815216,
0.0015552464174106717,
-0.0038229587953537703,
0.0462241992354393,
0.009794380515813828,
-0.0024920061696320772,
0.0026719465386122465,
0.024852508679032326,
0.003294819500297308,
0.023887263610959053,
0.011944940313696861,
-0.1097182035446167,
-0.0059865848161280155,
-0.00008532749052392319,
0.03611263632774353,
-0.028849944472312927,
0.00951642356812954,
-0.05769844725728035,
-0.029115157201886177,
0.05791785195469856,
-0.024797676131129265,
0.04797026142477989,
0.02491496503353119,
0.035746559500694275,
0.013283039443194866,
0.024200035259127617,
-0.04059828072786331,
0.023438217118382454,
-0.006621780339628458,
0.024365248158574104,
-0.048963554203510284,
-0.001584398909471929,
-0.019744040444493294,
0.04654223099350929,
0.001776907709427178,
0.08800112456083298,
-0.004412360955029726,
-0.02672354318201542,
-0.02909117564558983,
-0.03487604111433029,
-0.0767098143696785,
-0.04457014054059982,
-0.0005993901868350804,
-0.0120818130671978,
0.012217637151479721,
-0.006622753106057644,
0.006609961856156588,
-0.04283438250422478,
0.020444143563508987,
0.004720317665487528,
0.0029971094336360693,
0.007678227499127388,
-0.03173041716217995,
0.07758447527885437,
0.024533424526453018,
-0.008867640979588032,
0.030391495674848557,
0.030977049842476845,
0.0039617023430764675,
0.02523099258542061,
-0.027247678488492966,
0.03189942240715027,
-0.013732293620705605,
0.008637125603854656,
-0.006951525341719389,
0.03046869859099388,
-0.016453681513667107,
0.04559580981731415,
-0.03709894418716431,
0.04576173052191734,
0.002741909120231867,
-0.02181699313223362,
0.002083140192553401,
0.03761684149503708,
0.020872898399829865,
-0.017414698377251625,
0.025237688794732094,
0.018203314393758774,
0.003084916155785322,
-0.021478965878486633,
-0.006062145810574293,
0.008144652470946312,
-0.0006321098771877587,
0.02428276836872101,
-0.032263755798339844,
0.01620103232562542,
-0.0013798261061310768,
-0.0038395957089960575,
-0.0007668184698559344,
-0.02878793329000473,
0.022345352917909622,
-0.028338149189949036,
-0.011820316314697266,
-0.003860212629660964,
-0.05388662591576576,
-0.019299471750855446,
0.02238346077501774,
0.005185762885957956,
0.007068853825330734,
-0.10383929312229156,
0.02108355425298214,
-0.02180396392941475,
0.009696493856608868,
-0.05928152799606323,
-0.041323114186525345,
0.029428279027342796,
0.030420798808336258,
-0.029297644272446632,
-0.04007002338767052,
-0.03351781889796257,
-0.02350413240492344,
-0.04773040488362312,
0.020395586267113686,
0.04672503471374512,
-0.027916504070162773,
-0.046565983444452286,
-0.0251708272844553,
0.021782180294394493,
0.03868021443486214,
-0.016941674053668976,
0.02975747361779213,
-0.02254578098654747,
0.01144517119973898,
-0.048808690160512924,
0.019265923649072647,
0.041736356914043427,
-0.030477803200483322,
0.011885584332048893,
0.0005609578802250326,
-0.024098895490169525,
0.0686800628900528,
0.009374505840241909,
0.01668298989534378,
-0.015452812425792217,
-0.006295985542237759,
0.02404184825718403,
0.0017341033089905977,
0.03774157539010048,
-0.033572372049093246,
0.020717259496450424,
-0.014885613694787025,
-0.011726862750947475,
-0.04348185285925865,
0.026809222996234894,
0.02259952761232853,
0.027524471282958984,
0.003026306629180908,
-0.018633436411619186,
0.06477486342191696,
-0.03989917412400246,
0.011545246466994286,
0.03472479432821274,
0.00965927168726921,
0.039052218198776245,
0.0264300387352705,
-0.013960383832454681,
0.016063496470451355,
0.010501460172235966,
-0.02509899064898491,
-0.020027391612529755,
-0.03584373742341995,
0.007759968750178814,
0.04344583675265312,
-0.01606094092130661,
0.031195836141705513,
0.01808016560971737,
0.01714995503425598,
0.01738189533352852,
-0.012727806344628334,
-0.028781529515981674,
0.017460176721215248,
0.007006410975009203,
0.031319957226514816,
-0.004504431504756212,
-0.0029160822741687298,
-0.030856620520353317,
0.028623303398489952,
0.028565706685185432,
0.016290828585624695,
0.04066414758563042,
0.02205684408545494,
-0.01358699332922697,
-0.028980130329728127,
-0.0316149964928627,
0.014032794162631035,
-0.0028320166748017073,
0.05180652067065239,
-0.012796042487025261,
-0.0016831152606755495,
0.04726746678352356,
-0.0018047804478555918,
-0.0066733043640851974,
-0.03401951119303703,
0.02696390636265278,
-0.010790768079459667,
0.0002706589293666184,
0.002601006766781211,
-0.037480078637599945,
0.0258062444627285,
0.006722097285091877,
0.05398888885974884,
-0.0003285080019850284,
0.03288419172167778,
-0.016163216903805733,
0.006144525948911905,
-0.012311839498579502,
-0.02133847028017044,
-0.05779857933521271,
0.04008691757917404,
-0.001127654337324202,
-0.04601586237549782,
0.025954850018024445,
-0.005208901595324278,
0.02837810106575489,
-0.013377165421843529,
0.02202722057700157,
0.004674203228205442,
0.07904938608407974,
0.026839883998036385,
-0.009265396744012833,
-0.030857764184474945,
0.03720949590206146,
0.12558242678642273,
0.04780588671565056,
0.0023039747029542923,
-0.032508499920368195,
-0.011462295427918434,
0.006732390262186527,
0.033372290432453156,
-0.02545977011322975,
0.02094639092683792,
-0.0016403582412749529,
-0.05288027599453926,
0.03278974071145058,
0.05662029609084129,
0.014443888328969479,
0.0027062101289629936,
0.021223168820142746,
-0.03995824605226517,
-0.01792469620704651,
-0.015124021098017693,
-0.02004404179751873,
-0.02248571440577507,
-0.00048557936679571867,
-0.04143717512488365,
0.07340185344219208,
-0.026449067518115044,
-0.009715750813484192,
0.00012168212560936809,
-0.028795333579182625,
-0.004230877850204706,
-0.0037499868776649237,
-0.05357521027326584,
0.018391625955700874,
0.03239358961582184,
-0.005353053566068411,
-0.008886730298399925,
0.014778227545320988,
0.024770738556981087,
-0.0035993477795273066,
0.0010240674018859863,
0.045222941786050797,
-0.01816347986459732,
0.018220124766230583,
-0.02372634969651699,
0.02394738607108593,
-0.03747402876615524,
-0.03352322429418564,
-0.0482465997338295,
-0.009719405323266983,
0.003315662732347846,
0.02306399494409561,
0.010205456055700779,
-0.005673282314091921,
-0.02309516631066799,
-0.05556521937251091,
0.003603758290410042,
0.0026595275849103928,
0.029570506885647774,
-0.01288872491568327,
-0.02646491304039955,
-0.05808383226394653,
0.01023989636451006,
0.023725062608718872,
0.013344106264412403,
-0.007222311571240425,
0.014936672523617744,
0.010054236277937889,
-0.005052400752902031,
0.03346136584877968,
-0.04404008388519287,
-0.013769564218819141,
0.006264024414122105,
0.024357525631785393,
-0.04000001773238182,
0.0034790479112416506,
0.028555529192090034,
0.017639901489019394,
0.012555084191262722,
-0.007138218265026808,
0.0070375557988882065,
-0.06472224742174149,
-0.040618326514959335,
0.027356846258044243,
0.010286565870046616,
-0.01293923333287239,
-0.021100010722875595,
-0.05146240070462227,
-0.014107485301792622,
0.03988290950655937,
-0.02614905685186386,
0.004046405199915171,
-0.03182617574930191,
0.05105028674006462,
0.009535156190395355,
-0.027610259130597115,
-0.01271913107484579,
0.031984176486730576,
-0.03907628729939461,
0.027080511674284935,
0.01555115357041359,
0.06054539605975151,
0.023991955444216728,
-0.013140525668859482,
-0.01484853308647871,
0.01703404262661934,
-0.039080195128917694,
0.006218854337930679,
0.0036076020915061235,
-0.02348632737994194,
-0.006368620786815882,
0.007920166477560997,
-0.005837705451995134,
-0.03560877591371536,
-0.0236496664583683,
-0.07057024538516998,
0.0132828950881958,
-0.013690115883946419,
0.005894686095416546,
0.022710593417286873,
0.0656593069434166,
-0.023923048749566078,
0.013644465245306492,
-0.04074815288186073,
-0.01962468773126602,
-0.06311511993408203,
0.01748066395521164,
-0.008230668492615223,
0.014498192816972733,
-0.0036499632988125086,
0.0033989406656473875,
-0.018290134146809578,
0.040463440120220184,
0.026418955996632576,
0.028505396097898483,
0.044178713113069534,
-0.056193120777606964,
-0.02042553760111332,
-0.0029843593947589397,
0.06825215369462967,
-0.027160964906215668,
-0.018963880836963654,
0.05934940651059151,
-0.03858182951807976,
-0.03477172553539276,
0.05743904784321785,
0.02359418012201786,
0.03063751757144928,
0.021027907729148865,
-0.007009848952293396,
-0.01834031566977501,
0.07105612009763718,
-0.02795821614563465,
-0.015286899171769619,
-0.006244909018278122,
-0.007736212573945522,
-0.027561048045754433,
-0.0117237139493227,
-0.020981011912226677,
-0.01792253367602825,
0.023008132353425026,
0.032415200024843216,
-0.007402313873171806,
-0.011802583932876587,
-0.006099509075284004,
0.013200148940086365,
0.0062530613504350185,
-0.016772305592894554,
0.02852318249642849,
-0.026920555159449577,
0.011082591488957405,
0.022100236266851425,
-0.04192524030804634,
-0.02922780252993107,
-0.024780992418527603,
-0.011126014403998852,
-0.09862324595451355,
0.019508875906467438,
-0.01648862101137638,
0.0119529590010643,
0.05860477685928345,
-0.05984443426132202,
-0.017276115715503693,
0.029814159497618675,
-0.027597738429903984,
-0.023798195645213127,
-0.07309477031230927,
0.003457722021266818,
-0.0034423379693180323,
-0.011519573628902435,
-0.01154239010065794,
0.05404970422387123,
0.03203360363841057,
0.010244403034448624,
0.005245226435363293,
-0.029138712212443352,
0.007460162043571472,
-0.033474043011665344,
0.03540784493088722,
-0.007178839296102524,
0.03035401552915573,
-0.06010134890675545,
0.0333123616874218,
-0.03287213668227196,
-0.03604345768690109,
0.05446767807006836,
-0.03948529437184334,
0.044002383947372437,
-0.03544256463646889,
0.02885274775326252,
-0.03388266637921333,
0.04016811400651932,
0.03277180343866348,
-0.0016887601232156157,
-0.011865168809890747,
0.022581079974770546,
-0.021627288311719894,
0.001538806245662272,
0.003616953268647194,
0.0032750708051025867,
0.033594436943531036,
0.001945394673384726,
-0.034904055297374725,
0.006045110989362001,
-0.042953845113515854,
-0.021636998280882835,
-0.0021850643679499626,
-0.019126856699585915,
0.006427645683288574,
-0.023057343438267708,
0.010563626885414124,
0.014696343801915646,
0.002274854341521859,
0.03504409268498421,
-0.01769358478486538,
-0.0200615543872118,
0.0023706266656517982,
-0.016414115205407143,
-0.03641476109623909,
-0.0038829150144010782,
-0.009835606440901756,
-0.006646322086453438,
-0.03764483332633972,
-0.04624322056770325,
0.004029856063425541,
-0.020384568721055984,
-0.025233227759599686,
0.016018854454159737,
-0.0033062424045056105,
0.03382633253931999,
0.010370808653533459,
0.019773581996560097,
-0.015329203568398952,
-0.033413805067539215,
-0.0078009264543652534,
-0.07152816653251648,
-0.010730202309787273,
0.036581117659807205,
-0.04443523660302162,
-0.012551453895866871,
-0.022959239780902863,
0.0275571309030056,
0.03383442014455795,
0.04376577213406563,
0.0024903188459575176,
-0.04409300535917282,
-0.0010838432935997844,
0.011003912426531315,
0.027756093069911003,
-0.03492024913430214,
-0.012918475084006786,
-0.012508759275078773,
-0.028759581968188286,
0.031767163425683975,
-0.01293555460870266,
-0.006828076206147671,
0.021602991968393326,
0.011469407938420773,
0.012728150933980942,
-0.022409794852137566,
-0.017797870561480522,
-0.0483066700398922,
0.03570661321282387,
0.01981624960899353,
-0.01578749157488346,
0.024505935609340668,
-0.0005284265498630702,
-0.009646670892834663,
0.051012370735406876,
0.00305555434897542,
-0.03139603137969971,
0.006503753364086151,
-0.045824240893125534,
-0.0023738166783005,
0.005362970754504204,
-0.015682406723499298,
-0.008230781182646751,
-0.08372189104557037,
0.0031795164104551077,
0.010320900939404964,
-0.033536434173583984,
0.010476630181074142,
0.023722313344478607,
0.03747549280524254,
0.018637754023075104,
0.038481488823890686,
-0.014037853106856346,
0.026046698912978172,
0.04013323783874512,
-0.008938664570450783,
0.01910383440554142,
0.07054160535335541,
-0.016685277223587036,
0.02262495830655098,
-0.00679357536137104,
-0.019945260137319565,
0.01905819959938526,
0.007081415504217148,
0.001451200107112527,
0.016010606661438942,
-0.046004049479961395,
-0.01072720717638731,
-0.012280975468456745,
-0.005271460395306349,
0.03367104381322861,
-0.014253494329750538,
0.05753491446375847,
0.009471158497035503,
0.022953059524297714,
-0.034318096935749054,
0.00638224370777607,
-0.04238545894622803,
0.04218222573399544,
0.0031947644893079996,
0.0027173294220119715,
-0.007827838882803917,
0.00405249185860157,
-0.02573975920677185,
-0.031617578119039536,
-0.011312934570014477,
-0.061969656497240067,
-0.024029944092035294,
0.030062681064009666,
0.01520723570138216,
-0.009980102069675922,
-0.05640573427081108,
-0.07365186512470245,
-0.015234589576721191,
0.0002950630441773683,
0.018701590597629547,
0.004301792476326227,
0.012767871841788292,
-0.05762645974755287,
0.02012367732822895,
0.050879333168268204,
-0.08634733408689499,
-0.01536440197378397,
0.03298488259315491,
0.027132002636790276,
0.0018210993148386478,
0.007001681253314018
] |
<p>What do the supercharges in <a href="http://en.wikipedia.org/wiki/Supersymmetry_algebra">extended supersymmetry</a> do?</p>
<p>In $N=1$ supersymmetry there are a certain number of fermions and and equal number of bosons. You can transform all fermions to the bosons (and vice versa) in a 1 to 1 fashion using a single supercharge, $Q$.</p>
<p>So what happens when you have, for example, $N=2$ supersymmetry with 8 supercharges? Since $Q$ is a generator of supersymmetry transformations, is it a linear combination of these supercharges that act on the particles? In which case could one particle be acted on by two separate linear combinations of $Q$? Or is it strictly one linear combination of $Q$ per fermion/boson?</p>
<p>Also, what does $N$ mean physically? What difference does $N=2$ have to $N=1$ other than more supercharges? Or is that the only difference between the two theories?</p>
| 9,577 |
[
-0.023348158225417137,
0.005398751236498356,
-0.010216113179922104,
-0.036893852055072784,
0.030039256438612938,
0.012787907384335995,
-0.0305069237947464,
-0.06367605924606323,
0.006692074239253998,
-0.03366431966423988,
0.02045373059809208,
0.017795292660593987,
0.05471448227763176,
0.008645260706543922,
-0.0038000091444700956,
0.03208666294813156,
0.005786411929875612,
-0.03204912319779396,
-0.020094584673643112,
-0.010763869620859623,
0.016284730285406113,
0.0479121208190918,
-0.0008710549445822835,
0.016085799783468246,
-0.002923671854659915,
0.0337962731719017,
0.013788304291665554,
0.0012646535178646445,
0.043044090270996094,
0.04888973385095596,
0.04460474103689194,
-0.0635499581694603,
0.01971372775733471,
0.058445293456315994,
-0.014991147443652153,
-0.03579728305339813,
-0.004072248004376888,
-0.046672213822603226,
0.003999326843768358,
0.007368286605924368,
-0.04526734724640846,
-0.03967488929629326,
-0.03923911228775978,
0.024138672277331352,
-0.011416643857955933,
-0.00007484546222258359,
-0.02470347099006176,
-0.03654500097036362,
0.05207137018442154,
-0.07446539402008057,
0.06787175685167313,
0.05199157074093819,
-0.0009214077144861221,
0.011737803928554058,
0.009984591044485569,
0.0036407667212188244,
0.05491650477051735,
0.07669773697853088,
-0.002586473012343049,
-0.0844493880867958,
-0.06729048490524292,
-0.06027641519904137,
0.0079062944278121,
-0.01385502703487873,
-0.03832629323005676,
0.030222604051232338,
0.03848196566104889,
0.013167665340006351,
0.013001288287341595,
-0.0029549901373684406,
0.017876727506518364,
0.029803214594721794,
0.012542418204247952,
-0.013140583410859108,
0.011687872931361198,
-0.036770135164260864,
0.006168824154883623,
-0.004081842955201864,
0.06297473609447479,
0.050096381455659866,
0.001114578335545957,
0.03500744327902794,
0.02173478715121746,
0.015406163409352303,
0.020104411989450455,
-0.02234959602355957,
0.07670337706804276,
0.014926348812878132,
0.007266715168952942,
0.007623766083270311,
-0.022211337462067604,
0.01527951005846262,
0.04712486267089844,
-0.02587137743830681,
-0.020776791498064995,
0.04262787476181984,
0.03384264558553696,
0.03917722404003143,
-0.0032854361925274134,
-0.0323963426053524,
-0.01116428803652525,
-0.023738684132695198,
0.0013177221408113837,
0.0747564360499382,
0.021588092669844627,
-0.013548210263252258,
-0.01303455512970686,
0.021589362993836403,
-0.052378829568624496,
-0.005950947292149067,
-0.016510050743818283,
0.019478240981698036,
-0.013370485045015812,
0.0015919074648991227,
-0.016775712370872498,
-0.02202438749372959,
0.002594984835013747,
-0.006430877838283777,
0.054785750806331635,
0.08601617813110352,
0.047556884586811066,
-0.01960751600563526,
-0.013902552425861359,
-0.01984616555273533,
-0.057305630296468735,
-0.005466508213430643,
0.03498078137636185,
0.014142029918730259,
-0.048152778297662735,
0.004460938274860382,
0.01595587283372879,
-0.008678535930812359,
0.0025413085240870714,
-0.013863722793757915,
0.021212473511695862,
-0.0037852763198316097,
-0.07232557237148285,
-0.05978310853242874,
0.03214172646403313,
-0.011204591020941734,
-0.01235344260931015,
-0.040396105498075485,
-0.00320559274405241,
0.05098160356283188,
0.10248608142137527,
0.006427227519452572,
0.014090857468545437,
0.01343614049255848,
0.008872773498296738,
0.01973237469792366,
-0.010825120843946934,
0.013310149312019348,
0.01306831929832697,
-0.04719993844628334,
-0.025084033608436584,
-0.06039910763502121,
0.04563416540622711,
0.06028681993484497,
0.017429320141673088,
0.005638903006911278,
0.11676707118749619,
-0.030703136697411537,
0.012811524793505669,
0.027007274329662323,
0.016606634482741356,
0.007834075950086117,
0.03528401628136635,
0.003127671778202057,
0.020849211141467094,
0.053232189267873764,
-0.03064698353409767,
0.0275659691542387,
0.028133656829595566,
0.06770102679729462,
0.026419973000884056,
-0.0018955185078084469,
-0.0384117029607296,
-0.0012112545082345605,
-0.009003548882901669,
0.006822850089520216,
-0.023580139502882957,
-0.03873659297823906,
0.0036195653956383467,
0.020911993458867073,
0.006474604830145836,
0.013891244307160378,
-0.021635854616761208,
-0.024975797161459923,
-0.03000415675342083,
-0.04666168987751007,
-0.05599745735526085,
-0.060599781572818756,
0.0018730093725025654,
0.00742495758458972,
-0.0061513762921094894,
0.04659709706902504,
0.008014366962015629,
0.014119427651166916,
-0.03316668048501015,
-0.03715583682060242,
0.008524457924067974,
0.07109562307596207,
-0.025487570092082024,
0.012823095545172691,
0.010664133355021477,
0.028562257066369057,
0.02644221857190132,
-0.022952640429139137,
0.029916629195213318,
-0.0205799899995327,
-0.03331688418984413,
0.01953810453414917,
-0.015596969984471798,
0.014559007249772549,
-0.01670633628964424,
0.003405708819627762,
0.007153327576816082,
-0.0006951953400857747,
-0.03771935775876045,
0.05598917603492737,
-0.029708728194236755,
0.0715814158320427,
0.03443034365773201,
-0.004633296746760607,
-0.0085924556478858,
0.02082771807909012,
-0.0019560002256184816,
0.01270714495331049,
-0.014574811793863773,
-0.019021114334464073,
-0.04134952649474144,
-0.006074435543268919,
0.015497743152081966,
0.050699517130851746,
-0.003935174085199833,
0.0369165763258934,
0.03135000169277191,
0.0195329487323761,
0.014948840253055096,
-0.01187298633158207,
-0.04586533084511757,
-0.017382146790623665,
0.01258269976824522,
0.005740039050579071,
-0.006059085484594107,
0.003032814245671034,
0.014986786060035229,
0.001550421235151589,
0.011395038105547428,
0.010821541771292686,
-0.03740489482879639,
0.04725045710802078,
-0.023416738957166672,
-0.0002216234424849972,
0.013067302294075489,
-0.036254048347473145,
0.028852498158812523,
-0.025462644174695015,
0.039507973939180374,
0.03396211192011833,
-0.010396081954240799,
0.006584469228982925,
-0.012982703745365143,
0.006425774656236172,
0.03081091120839119,
-0.0006386631284840405,
-0.004789456725120544,
-0.030602803453803062,
-0.003067658981308341,
-0.03868364542722702,
0.014371070079505444,
-0.018702883273363113,
0.004001872148364782,
-0.01892166957259178,
0.03957248479127884,
0.007046396378427744,
-0.011099199764430523,
0.07057354599237442,
-0.05338488891720772,
-0.010678011924028397,
0.04952185973525047,
-0.01809976063668728,
0.038586534559726715,
0.01777576468884945,
-0.06400290876626968,
-0.013602516613900661,
-0.11028850823640823,
-0.006344662047922611,
0.05579414963722229,
0.004740113392472267,
0.0251083392649889,
0.018014488741755486,
-0.027221551164984703,
-0.03229670226573944,
-0.03595559671521187,
-0.009119333699345589,
0.03259517252445221,
-0.02200070396065712,
-0.042116064578294754,
0.054773759096860886,
0.01964753493666649,
-0.03465629369020462,
0.011771009303629398,
-0.02868659421801567,
-0.010345515795052052,
-0.013927949592471123,
0.03924175724387169,
0.018826209008693695,
-0.055279165506362915,
0.05258685722947121,
0.0009782240958884358,
-0.03895096853375435,
0.01936592534184456,
-0.02674952708184719,
-0.05524563416838646,
0.0070073106326162815,
-0.017255190759897232,
0.026367440819740295,
-0.004604636691510677,
-0.07029969990253448,
0.10268522799015045,
0.03585337847471237,
-0.03233196213841438,
-0.009067573584616184,
0.020534640178084373,
-0.0046470859088003635,
0.002269347198307514,
-0.00012263038661330938,
0.024285603314638138,
0.0046778228133916855,
0.0001968177530216053,
0.03941060230135918,
0.06877246499061584,
0.026931721717119217,
-0.006464991252869368,
-0.04387255385518074,
-0.009906112216413021,
0.006550334859639406,
-0.01544598862528801,
0.03001205064356327,
-0.0167545173317194,
0.004335599951446056,
-0.013807331211864948,
0.011385690420866013,
0.0047575123608112335,
0.023108363151550293,
-0.019603556022047997,
0.06104068458080292,
0.01723710261285305,
0.021791433915495872,
-0.00873992033302784,
0.035290107131004333,
-0.015320142731070518,
-0.04641317203640938,
-0.0025336365215480328,
0.055167026817798615,
0.02486119605600834,
-0.06755952537059784,
-0.008661828935146332,
-0.0005592138622887433,
0.058707427233457565,
-0.07599367201328278,
-0.03620780631899834,
0.002257126849144697,
0.016405325382947922,
0.0019461261108517647,
-0.018967872485518456,
-0.01338739413768053,
0.027891134843230247,
0.029280886054039,
0.028400346636772156,
0.0010019594337791204,
-0.0027338946238160133,
0.024036934599280357,
-0.01801365055143833,
-0.007321885321289301,
0.007071852218359709,
0.04462900012731552,
0.005963817238807678,
0.042236436158418655,
-0.0050657144747674465,
-0.0027047395706176758,
0.03973118215799332,
-0.013720797374844551,
-0.0764627531170845,
0.001806051703169942,
-0.030398104339838028,
-0.006951989606022835,
-0.0006930498057045043,
-0.027669083327054977,
0.007561208680272102,
-0.00951375626027584,
-0.04345918819308281,
-0.04287067428231239,
-0.010018027387559414,
-0.037413086742162704,
0.016068564727902412,
-0.06739369034767151,
-0.03132912144064903,
-0.0019796472042798996,
0.0320529043674469,
0.04014315828680992,
-0.04541928693652153,
-0.01390116848051548,
0.03377866744995117,
-0.050862547010183334,
-0.021146496757864952,
0.011002677492797375,
0.043296679854393005,
0.02406175062060356,
0.032375577837228775,
0.050575464963912964,
0.0031260426621884108,
-0.029977688565850258,
-0.008456887677311897,
0.03059752658009529,
0.061724212020635605,
0.004891599528491497,
0.0072454833425581455,
0.004754090681672096,
-0.042061276733875275,
0.006022108718752861,
-0.0036396074574440718,
0.0901007428765297,
0.013203968293964863,
-0.01119102444499731,
0.03665943816304207,
0.020459560677409172,
-0.011884205043315887,
0.04433675855398178,
0.041478488594293594,
-0.012217302806675434,
-0.05425911024212837,
-0.030493218451738358,
0.004401490557938814,
-0.006670313887298107,
-0.022355033084750175,
-0.026665106415748596,
-0.0075902147218585014,
-0.03362084925174713,
0.02661670185625553,
0.01099535170942545,
-0.016558771952986717,
-0.04226628690958023,
-0.021004779264330864,
0.014105458743870258,
-0.008913562633097172,
0.016457585617899895,
0.0032758598681539297,
-0.014299971982836723,
0.03734589368104935,
0.03674740344285965,
-0.010119440965354443,
-0.005921015981584787,
-0.05266201123595238,
0.0016940389759838581,
0.05017158016562462,
0.007931359112262726,
-0.006471824366599321,
-0.02112117037177086,
-0.028459947556257248,
0.015241310000419617,
0.039705172181129456,
-0.04544096440076828,
0.023716937750577927,
0.011284657754004002,
-0.009014959447085857,
-0.0288042314350605,
-0.016185002401471138,
0.008745359256863594,
0.05683424323797226,
0.0182490311563015,
0.04722778871655464,
0.005468216724693775,
0.0013891637790948153,
-0.003595101647078991,
0.022289317101240158,
0.04555117338895798,
0.028154252097010612,
-0.003897902090102434,
0.03366570174694061,
-0.008789492771029472,
0.0165182426571846,
-0.022959228605031967,
-0.047868311405181885,
-0.00004542813258012757,
-0.00346369412727654,
-0.05279375985264778,
0.05030476674437523,
-0.03960366174578667,
-0.027662793174386024,
-0.018013393506407738,
-0.01511186733841896,
-0.01355200819671154,
-0.023640859872102737,
-0.05942722409963608,
0.065080925822258,
0.033065974712371826,
0.01597914658486843,
0.011940104886889458,
0.020278573036193848,
-0.02204764261841774,
0.007932226173579693,
-0.03547479957342148,
0.014236549846827984,
-0.003842409932985902,
-0.0061591072008013725,
-0.016093198210000992,
0.008841688744723797,
-0.03987959772348404,
0.0792909637093544,
-0.00823673140257597,
0.009563276544213295,
0.0029573997016996145,
-0.0422939658164978,
-0.02289443276822567,
0.046304862946271896,
0.022839803248643875,
0.02298293262720108,
-0.0199186559766531,
0.010272293351590633,
0.011671063490211964,
-0.00018911420193035156,
0.037530895322561264,
-0.011483459733426571,
0.018224842846393585,
-0.0011347481049597263,
-0.0032030984293669462,
0.017644735053181648,
-0.00005427765063359402,
0.0033063108567148447,
0.05031743273139,
-0.04970143362879753,
0.053033195436000824,
0.03289944306015968,
-0.01819450780749321,
-0.015490898862481117,
-0.04383893311023712,
-0.032407838851213455,
-0.0023458257783204317,
-0.016072336584329605,
-0.008477033115923405,
-0.02437387965619564,
0.04114890471100807,
0.020519211888313293,
0.01406378485262394,
-0.03699811175465584,
-0.06486821174621582,
-0.008620461449027061,
-0.012898634187877178,
0.023777438327670097,
-0.003626619465649128,
-0.000562190602067858,
-0.008643199689686298,
-0.022514719516038895,
-0.011222035624086857,
0.06990966200828552,
-0.04637790098786354,
0.001969281816855073,
0.024217337369918823,
0.03039821982383728,
0.03143130615353584,
0.019138552248477936,
-0.025026729330420494,
-0.03469229117035866,
0.0032593056093901396,
0.036792028695344925,
-0.014188811182975769,
0.03816652670502663,
-0.0044454168528318405,
-0.03418350964784622,
-0.011749091558158398,
-0.006210926454514265,
0.0389760322868824,
-0.033780649304389954,
0.006562783848494291,
0.029072988778352737,
0.04790879413485527,
0.007742910645902157,
-0.026344245299696922,
-0.00607497151941061,
-0.015149924904108047,
0.017045535147190094,
-0.01852855086326599,
0.01343616098165512,
0.007967974059283733,
-0.030058564618229866,
0.01965523697435856,
0.008386495523154736,
-0.020926380529999733,
0.012628679163753986,
0.06388969719409943,
0.008847742341458797,
-0.002596799051389098,
0.009827293455600739,
-0.04605487361550331,
0.01113311480730772,
0.016883745789527893,
0.02029402181506157,
0.001718049985356629,
-0.019398855045437813,
0.033612195402383804,
-0.062320247292518616,
-0.028164256364107132,
-0.013575410470366478,
0.0584285594522953,
-0.019670935347676277,
0.03044191189110279,
0.017062800005078316,
-0.029206296429038048,
0.019684558734297752,
-0.05047781765460968,
0.015574951656162739,
0.009894019924104214,
-0.00874438975006342,
0.023019302636384964,
-0.04052231088280678,
-0.016726283356547356,
0.03413062542676926,
0.06335058808326721,
0.0024870827328413725,
-0.0009411507635377347,
0.04164605587720871,
0.0289827398955822,
0.027157872915267944,
-0.035077691078186035,
-0.04638151451945305,
0.05317351222038269,
-0.04115183651447296,
0.027866290882229805,
0.010861446149647236,
0.017624789848923683,
0.04165688902139664,
0.016801616176962852,
-0.013901090249419212,
-0.005092583131045103,
-0.01303181517869234,
-0.05026700720191002,
0.014356585219502449,
0.03025050461292267,
0.023672016337513924,
0.027312345802783966,
0.00011349708074703813,
0.043891631066799164,
-0.022892780601978302,
0.009353294037282467,
0.01322891190648079,
-0.07246864587068558,
-0.046379271894693375,
-0.006168222986161709,
-0.03805644437670708,
0.0493638850748539,
-0.031353943049907684,
-0.03490395098924637,
-0.0068352739326655865,
-0.03550891950726509,
0.0436173751950264,
0.003639685921370983,
0.009021159261465073,
-0.013657772913575172,
0.033141735941171646,
-0.05679553374648094,
0.015006201341748238,
0.0008306775707751513,
0.019763031974434853,
0.10372884571552277,
0.07010287046432495,
-0.0035861902870237827,
-0.09256959706544876,
0.013910501264035702,
0.0016924735391512513,
-0.009449933655560017,
-0.01908804476261139,
-0.0028280664701014757,
0.013462137430906296,
0.006701192352920771,
-0.025154387578368187,
0.05147058144211769,
-0.01453475747257471,
-0.028893351554870605,
0.05482054129242897,
-0.020929589867591858,
-0.03516651690006256,
-0.0009165157098323107,
0.023403190076351166,
-0.009353437460958958,
0.04335847124457359,
-0.053456928580999374,
0.010938887484371662,
0.0057146139442920685,
0.028772611171007156,
-0.025795521214604378,
-0.04330182820558548,
0.01476935762912035,
0.017108162865042686,
0.01712757907807827,
-0.008014819584786892,
-0.001477508689276874,
-0.027460237964987755,
-0.023536374792456627,
0.026571497321128845,
-0.019261015579104424,
-0.03241119161248207,
0.02047019824385643,
0.04346310719847679,
0.018255503848195076,
-0.008560813032090664,
0.03868035972118378,
0.027203287929296494,
-0.047864776104688644,
-0.019180938601493835,
-0.009411041624844074,
0.019739685580134392,
0.0006047768983989954,
-0.02674364671111107,
0.004796423949301243,
0.027846552431583405,
0.0064107016660273075,
-0.04568302258849144,
-0.04495090991258621,
-0.0038399922195822,
0.030463002622127533,
-0.032477010041475296,
-0.016632407903671265,
-0.013469097204506397,
0.019330885261297226,
-0.011264793574810028,
0.014929023571312428,
-0.01960586942732334,
-0.013851187191903591,
0.028679534792900085,
0.0034557050094008446,
0.0019277887186035514,
0.014077612198889256,
0.007878370583057404,
-0.047685153782367706,
0.014571627601981163,
-0.035598527640104294,
0.007503603119403124,
0.03755776956677437,
0.04005298763513565,
0.03750259801745415,
0.021739937365055084,
-0.016550421714782715,
-0.025975301861763,
-0.020260628312826157,
0.003631375730037689,
0.009256635792553425,
-0.02775307558476925,
0.005080500617623329,
-0.020098380744457245,
0.018490254878997803,
0.02780717797577381,
-0.007105445954948664,
0.021875642240047455,
-0.007534464821219444,
0.011030013673007488,
0.007158820517361164,
-0.016971707344055176,
-0.013226957991719246,
-0.02466357871890068,
-0.052871908992528915,
-0.01109071634709835,
-0.028119370341300964,
0.039207685738801956,
0.007575142662972212,
-0.015951916575431824,
-0.00460935989394784,
0.06604787707328796,
0.005855097901076078,
-0.026065852493047714,
0.02940472960472107,
-0.031042804941534996,
0.036528803408145905,
0.036299798637628555,
0.03913527727127075,
-0.027192702516913414,
-0.037019629031419754,
0.011908875778317451,
-0.007383202202618122,
0.03848778456449509,
0.017109517008066177,
-0.05683932825922966,
-0.01987432688474655,
-0.021845214068889618,
-0.005562665872275829,
-0.03659982606768608,
-0.01731783151626587,
-0.013557273894548416,
0.058449551463127136,
-0.015622601844370365,
0.005569548811763525,
0.022903231903910637,
0.015337962657213211,
-0.00964729767292738,
-0.037300799041986465,
0.010672026313841343,
0.01855049468576908,
-0.030598081648349762,
-0.027997620403766632,
0.002214923268184066,
-0.023447727784514427,
0.004228151403367519,
-0.032512638717889786,
-0.030922723934054375,
0.028461430221796036,
-0.022964712232351303,
-0.03510923311114311,
0.027661645784974098,
-0.0008325974340550601,
0.01125321164727211,
0.06995009630918503,
-0.02649422362446785,
-0.06859127432107925,
0.036574721336364746,
-0.05966658517718315,
-0.019611960276961327,
-0.025805439800024033,
-0.033236414194107056,
-0.053706035017967224,
-0.02493869699537754,
-0.025134271010756493,
0.010526604019105434,
-0.03191675245761871,
0.005273713730275631,
0.05589962750673294,
-0.022405141964554787,
-0.030316481366753578,
-0.015193798579275608,
-0.0016767767956480384,
0.04277985915541649,
-0.007799017708748579,
0.0031002219766378403,
-0.010502738878130913,
0.023705143481492996,
-0.03695524483919144,
0.039213236421346664,
-0.0059621077962219715,
-0.03314215689897537,
-0.07375115156173706,
-0.012387039139866829,
0.015697646886110306,
-0.0032690453808754683,
0.02159499190747738,
-0.04651501029729843,
0.009143861941993237,
0.023381981998682022,
-0.05523970350623131,
0.06648971885442734,
0.004458040464669466,
-0.02451005019247532,
-0.01479345839470625,
0.013305463828146458,
0.002138391137123108,
0.06422197818756104,
0.030673012137413025,
0.024807777255773544,
-0.0014427973655983806,
-0.02571079693734646,
0.002604756271466613,
0.0005102713475935161,
-0.04411990940570831,
0.013654261827468872,
0.037050336599349976,
-0.022369515150785446,
0.05464468523859978,
-0.027942746877670288,
-0.041272856295108795,
0.043277934193611145,
0.002255429048091173,
-0.029914535582065582,
0.028342386707663536,
0.018492059782147408,
-0.012314914725720882,
0.032517801970243454,
0.005538862198591232,
-0.011143811047077179,
-0.012610451318323612,
0.014292871579527855,
0.04234572872519493,
0.01787290722131729,
0.0012667449191212654,
-0.0071802022866904736,
-0.0009127080556936562,
-0.01947288028895855,
-0.020528635010123253,
0.004155947361141443,
-0.005686963442713022,
-0.04937335103750229,
0.0005649775848723948,
-0.0059922789223492146,
0.00890888087451458,
0.012880881316959858,
0.012906518764793873,
-0.0017126776510849595,
0.024145005270838737,
0.022982265800237656,
0.013727765530347824,
0.00897184293717146,
0.0547964908182621,
0.019451208412647247,
-0.026898309588432312,
0.011792298406362534,
0.03603193536400795,
-0.017987769097089767,
-0.061928585171699524,
0.00319449370726943,
0.02070152387022972,
0.029634250327944756,
0.012028125114738941,
-0.04471895471215248,
-0.03555399551987648,
0.02125205099582672,
0.0022446943912655115,
0.018391985446214676,
-0.019842220470309258,
-0.0483541414141655,
-0.0020857651252299547,
-0.047650568187236786,
0.045349638909101486,
0.00472454447299242,
0.007490966003388166,
-0.06326131522655487,
0.011227639392018318,
-0.021093690767884254,
-0.008853226900100708,
0.06572951376438141,
-0.014331432059407234,
-0.040247030556201935,
0.020499348640441895,
0.0034804304596036673,
0.028621185570955276,
0.002048503840342164,
-0.0069454265758395195,
0.009613593108952045,
-0.04176269471645355,
-0.06013878062367439,
0.01580692268908024,
-0.05642544850707054,
0.06030813604593277,
0.03351082652807236,
-0.03142361342906952,
0.02983427606523037,
-0.00273003033362329,
-0.018237914890050888,
0.04123852774500847,
-0.02218237705528736,
-0.019368784502148628,
0.04725045710802078,
-0.02634686790406704,
0.029817795380949974,
-0.0004819609166588634,
-0.018404686823487282,
-0.02086642012000084,
-0.012973107397556305,
-0.028114357963204384,
0.01558824721723795,
0.0011875602649524808,
-0.04803616181015968,
0.04124656319618225,
-0.056539665907621384,
0.002390702487900853,
0.043093666434288025,
-0.03452303260564804,
-0.030575180426239967,
0.055221933871507645,
0.010488118976354599,
0.0018386989831924438,
0.020105035975575447,
-0.007100945804268122,
-0.01677074283361435,
-0.002484048716723919,
0.026825450360774994,
0.05170140415430069,
0.02297654002904892,
0.006090524140745401,
0.02484738640487194,
0.030077872797846794,
-0.0023121521808207035,
0.02328568510711193,
-0.0036410570610314608,
0.026561126112937927,
-0.02143699862062931,
-0.012206035666167736,
0.04165097326040268,
-0.022110307589173317,
0.029635900631546974,
-0.006746518891304731,
-0.04987687990069389,
0.08909006416797638,
-0.05022333934903145,
0.030161598697304726,
-0.022039595991373062,
-0.013993716798722744,
-0.009740707464516163,
-0.037057820707559586,
-0.023876173421740532,
0.07458426058292389,
-0.020546210929751396,
-0.023531032726168633,
-0.04858790338039398,
0.01410976704210043,
0.01877237670123577,
-0.07191688567399979,
0.023699885234236717,
-0.008967041969299316,
0.0022114054299890995,
-0.01669899746775627,
-0.00630527688190341,
-0.02172860875725746,
0.0010033316211774945,
0.031393054872751236,
0.021129664033651352,
0.006415573414415121,
-0.0017323156353086233,
-0.02736254595220089,
0.01615210808813572,
0.020730089396238327,
-0.030785566195845604,
-0.039660755544900894,
-0.009459193795919418,
-0.003418021136894822,
-0.03154323622584343,
-0.02124202810227871
] |
<p>The other day we derived Kepler's third law.</p>
<p>$$
\left( \frac{T_1}{T_2} \right)^2 = \left( \frac{r_1}{r_2} \right) ^3
$$</p>
<p>In order to derive this, you can look at a given planet that revolves around the sun. If you assume that the sun is way heavier than the planet and that the planet moves on a circle, you can simply state the force on the Planet by the sun:</p>
<p>$$
F_G = G \frac{mM}{r^2}
$$</p>
<p>Where $F_G$ is the force on the planet, $G$ is the gravitational constant, $m$ is the mass of the planet, $M$ the mass of the sun and $r$ the distance of the planet to the sun.</p>
<p>Our tutor said that you now have to have a centrifugal force $F_c$ that is equal in absolute value to $F_G$, but opposite in direction so that the sum of the forces would be zero. The absolute value of this $F_c$ would then be equal to $F_G$:</p>
<p><img src="http://wstaw.org/m/2011/11/15/m9.png" alt=""></p>
<p>Then you plug in the formulas for the respective forces:</p>
<p>$$ |\vec{F_c}| = |\vec{F_G}| $$
$$ m \frac{v^2}{r} = G \frac{mM}{r^2} $$
$$ \frac{v^2}{r} = G \frac{M}{r^2} $$
$$ v^2 = G \frac{M}{r} $$
$$ v = \sqrt{G \frac{M}{r}} $$</p>
<p>Where $v$ is the tangential velocity of the planet.</p>
<p>Together with $v=\frac{2\pi r}{T}$, where $T$ is the revolution period, you get:</p>
<p>$$ \frac{2\pi r}{T} = \sqrt{G \frac{M}{r}} $$
$$ \frac{4\pi^2 r^2}{T^2} = G \frac{M}{r} $$
$$ \frac{r^3}{T^2} = G \frac{M}{4\pi^2} $$</p>
<p>Since the right part is constant for each solar system, you can form a ratio and optain Kepler's law. So this approach does work.</p>
<hr>
<p>I think that this view is only valid if you construct it from a rotating observation point, i. e. standing on the planet and facing the sun at all times. Our tutor said that this is from a static (with respect to the sun) observation point.</p>
<p>In the rotating system, you do have the centrifugal force, but it is not a real force in this sense. So by saying that you have a centrifugal force, I think that you are in this rotating reference frame. And in the rotating frame, the planet is not moving at all. And by not moving in this rotating frame, it does revolve around the sun in the static frame. Since the planet is not moving, there must not be any force on it. Constructing a force equilibrium is the way to achieve this.</p>
<p>But our tutor told me that there is a force equilibrium in the static reference frame as well. I say that if you have an equilibrium there, there is no net force, therefore the planet does only move along a straight line in a static frame. I was then told that although there is no net force, the forces are still there.</p>
<p>At that point, I think that this is converting dynamics into statics by adding opposing forces so that everything cancels out.</p>
<p>Say we <em>do</em> have a net force (gravity) on the planet.</p>
<p><img src="http://wstaw.org/m/2011/11/15/m10.png" alt=""></p>
<p>This force is something like this, if the planet has rotated $\theta$ around the sun:</p>
<p>$$
\vec{F_G} \propto
\left(
\begin{matrix}
-\cos(\theta) \\
-\sin(\theta)
\end{matrix}
\right)
$$</p>
<p>If you integrate this, you will get the velocity and the position of the planet.</p>
<p>$$
\int \vec{F_G} \, \mathrm d\theta \propto
\left(
\begin{matrix}
-\sin(\theta) \\
\cos(\theta)
\end{matrix}
\right)
$$</p>
<p>This seems very good, since it goes along the circle, so this is the tangential velocity.</p>
<p>$$
\iint \vec{F_G} \, \mathrm d\theta \propto
\left(
\begin{matrix}
\cos(\theta) \\
\sin(\theta)
\end{matrix}
\right)
$$</p>
<p>And that is simply the position around the unit circle.</p>
<p>You can substitute $\theta$ with $\omega t$ if you wish to express the angle with time.</p>
<p>So I claim that you need a net force in order for the circular trajectory to appear at all. My tutor told me that if the force is too high (too weak), the planet will spiral into (away from) the sun, and therefore the equilibrium has to be there. That makes no sense to me. What makes sense to me is that if the trajectory is deflected too much (not enough) to form a circle, there is no circle.</p>
<hr>
<p>If you have no force, integration turns out quite different:</p>
<p>$$
F = 0
$$</p>
<p>$$
\int F \, \mathrm dt = \underbrace{0t}_{a=0} + \underbrace{c_1}_{v_0}
$$</p>
<p>$$
\iint F \, \mathrm dt = \underbrace{0t^2}_{a=0} + \underbrace{c_1t}_{v_0} + \underbrace{c_2}_{d_0}
$$</p>
<p>The latter is your $d = v_0 t + d_0$, which models a linear, unaccelerated movement. In the rotating system, $v_0$ is just zero, and it works out. In the static system, that would mean that the planet either remains still or moves on a straight line -- which is not what is really happening.</p>
<hr>
<p>So I claim that you must <em>not</em> have a force equilibrium for the earth to rotate -- that is the basic disagreement we have.</p>
<p>Who is right? Or are we both right, just looking differently at the same problem?</p>
| 9,578 |
[
-0.012784389778971672,
-0.02299894206225872,
-0.029175015166401863,
0.026049740612506866,
0.06894456595182419,
-0.0050529595464468,
-0.05026009678840637,
0.018697673454880714,
0.012039285153150558,
0.015754058957099915,
-0.0006439486751332879,
0.05847600847482681,
0.036622319370508194,
0.017218463122844696,
0.02932761423289776,
-0.013392530381679535,
0.011957688257098198,
-0.04400894418358803,
-0.00766712473705411,
-0.02510904334485531,
-0.016084838658571243,
-0.009364976547658443,
-0.00003484623084659688,
0.003493489930406213,
0.002850947668775916,
0.025365933775901794,
0.05481797084212303,
-0.03966107591986656,
-0.010415876284241676,
0.0480196587741375,
0.02373950183391571,
0.012708581984043121,
-0.006776527501642704,
0.018818899989128113,
0.04157572612166405,
0.060568228363990784,
-0.01999676413834095,
-0.02540634386241436,
-0.0018899940187111497,
0.05811255797743797,
-0.04977792128920555,
0.008361863903701305,
-0.018392931669950485,
0.01988736167550087,
-0.05077916756272316,
0.028017565608024597,
0.01674502156674862,
-0.014282869175076485,
0.06585577875375748,
-0.05886685103178024,
0.06741911917924881,
0.021081892773509026,
0.04224811866879463,
0.009679635986685753,
-0.004919699393212795,
-0.01771821267902851,
0.06549912691116333,
0.06541023403406143,
0.019552243873476982,
-0.04101813584566116,
-0.012456855736672878,
-0.0208261851221323,
-0.05628211423754692,
-0.03608066961169243,
0.0038434769958257675,
0.014717482030391693,
-0.01931079290807247,
-0.010732543654739857,
0.012061113491654396,
0.04041885584592819,
0.015576012432575226,
0.000011673713743221015,
0.0171932652592659,
0.0008748550899326801,
-0.02630716934800148,
-0.0358574204146862,
0.01181579940021038,
0.010778800584375858,
0.021456506103277206,
0.02122037298977375,
-0.011526087298989296,
0.022386718541383743,
0.021500905975699425,
0.07129242271184921,
0.023853685706853867,
0.016352849081158638,
0.029842285439372063,
0.02513466402888298,
-0.005321679171174765,
0.028103837743401527,
0.017115116119384766,
0.035113874822854996,
0.014369246549904346,
-0.019340185448527336,
0.013124087825417519,
0.05461693927645683,
-0.0029394293669611216,
-0.012050801888108253,
0.0029355150181800127,
0.018048329278826714,
-0.0006365636363625526,
-0.02358018234372139,
0.021501122042536736,
0.06705938279628754,
0.02519378252327442,
-0.024008965119719505,
-0.021823005750775337,
0.009563738480210304,
-0.009539003483951092,
-0.012825383804738522,
-0.05360720679163933,
0.022708730772137642,
0.0094867292791605,
-0.020068472251296043,
0.0027341435197740793,
0.016780255362391472,
0.008686274290084839,
-0.028051940724253654,
0.04863131791353226,
0.02560284733772278,
0.014984590001404285,
-0.010470096953213215,
0.029812024906277657,
-0.0722690001130104,
-0.02504228986799717,
0.033723365515470505,
0.008472505956888199,
-0.009642858989536762,
0.0010424212086945772,
0.006674242205917835,
-0.006395433098077774,
-0.010127229616045952,
-0.061772070825099945,
0.0021322283428162336,
-0.004671117290854454,
-0.005422487389296293,
-0.08146240562200546,
-0.05558218061923981,
0.03494800254702568,
0.019243355840444565,
-0.009735011495649815,
-0.04161856696009636,
0.028245730325579643,
0.02873721905052662,
0.08424971997737885,
0.018114624544978142,
-0.02735026925802231,
-0.019907986745238304,
0.030719302594661713,
-0.02800569497048855,
-0.005552323069423437,
0.00869717076420784,
0.012371651828289032,
-0.02963625267148018,
-0.018538514152169228,
-0.08000942319631577,
0.010907747782766819,
0.028001153841614723,
0.03888406231999397,
-0.011780220083892345,
0.06948763877153397,
-0.017496483400464058,
-0.02077445201575756,
0.02766447141766548,
-0.014472467824816704,
-0.013132563792169094,
0.06224824860692024,
0.015242611058056355,
-0.04558204859495163,
0.04541458562016487,
0.00341134169138968,
0.021346822381019592,
-0.010763020254671574,
-0.013302428647875786,
0.035752374678850174,
-0.014300785027444363,
-0.010485841892659664,
-0.0399203784763813,
0.015150642953813076,
0.00805998221039772,
-0.03392214700579643,
-0.051549382507801056,
0.009969147853553295,
0.01554249506443739,
0.02173175849020481,
0.0511888787150383,
0.013764385133981705,
0.019684482365846634,
0.025864891707897186,
-0.01353209838271141,
0.006517205387353897,
-0.025808360427618027,
0.04106110706925392,
-0.004938589874655008,
-0.042064256966114044,
-0.010211372748017311,
0.03180677443742752,
0.010801728814840317,
-0.003119435627013445,
0.0000373989823856391,
0.011529159732162952,
0.058334410190582275,
0.004077377263456583,
0.024795014411211014,
0.019455907866358757,
0.06381142884492874,
0.03306996449828148,
0.004205555189400911,
-0.01924324594438076,
-0.012563597410917282,
0.007622802630066872,
-0.02243267558515072,
-0.021605897694826126,
0.03808276355266571,
0.008579918183386326,
0.027156924828886986,
0.005199079401791096,
0.020584391430020332,
-0.0030942284502089024,
0.008117825724184513,
-0.046998679637908936,
0.06516315788030624,
0.035723138600587845,
0.015599875710904598,
0.0319502018392086,
-0.002028605667874217,
-0.0023942976258695126,
0.011419986374676228,
0.0275976974517107,
-0.01896570436656475,
-0.07056288421154022,
-0.029748445376753807,
0.011262736283242702,
0.022105855867266655,
0.00039212836418300867,
0.00861124787479639,
0.07478291541337967,
0.04229217395186424,
0.024034840986132622,
-0.003247238928452134,
-0.0050217630341649055,
-0.04438559338450432,
0.02555776946246624,
0.004834432154893875,
0.016542114317417145,
0.031327761709690094,
0.021161682903766632,
0.034782808274030685,
-0.021896321326494217,
0.008177432231605053,
-0.03425632044672966,
0.01161408144980669,
0.03286213055253029,
0.031283456832170486,
0.051516078412532806,
-0.00997384637594223,
0.03678474202752113,
-0.028531327843666077,
-0.0010699372505769134,
0.03345554322004318,
-0.012724237516522408,
0.0040987711399793625,
-0.03549838438630104,
0.004100566264241934,
-0.021951675415039062,
-0.0022259496618062258,
-0.027261322364211082,
0.030573198571801186,
0.02651110291481018,
-0.06576775014400482,
-0.03081229329109192,
-0.014014344662427902,
-0.03197900205850601,
-0.03752361610531807,
-0.008546198718249798,
-0.0050150733441114426,
0.016628839075565338,
0.021307675167918205,
0.0014721937477588654,
0.013730091042816639,
-0.000054270840337267146,
-0.01852717623114586,
-0.035118162631988525,
0.0075516849756240845,
-0.02752452716231346,
0.06484591215848923,
-0.00574445677921176,
-0.022427543997764587,
0.02848377637565136,
0.03903091698884964,
-0.006344167981296778,
0.0197773240506649,
0.012851500883698463,
-0.054889000952243805,
0.010630051605403423,
-0.007506996858865023,
-0.007476281374692917,
-0.04237063601613045,
0.011151562444865704,
0.02185673452913761,
-0.005923939403146505,
-0.028696035966277122,
0.008065667003393173,
-0.07064184546470642,
-0.04880324378609657,
-0.01850350759923458,
0.01697942055761814,
-0.016811322420835495,
-0.04478844627737999,
0.0055780233815312386,
0.011573470197618008,
-0.00024026927712839097,
-0.029095567762851715,
-0.05311436206102371,
-0.021014897152781487,
-0.004774594679474831,
0.02284407801926136,
0.059662893414497375,
-0.053608573973178864,
-0.051381248980760574,
0.08637037873268127,
0.03665870800614357,
-0.0018012310611084104,
-0.02736816741526127,
0.015482514165341854,
0.0051385099068284035,
-0.031242232769727707,
0.0364292748272419,
0.033188823610544205,
-0.011464975774288177,
-0.03045162372291088,
-0.007561251521110535,
0.009044049307703972,
0.0506620854139328,
0.004873004741966724,
0.019570400938391685,
0.012516527436673641,
-0.009285626001656055,
-0.014589137397706509,
0.0838172659277916,
0.019628485664725304,
0.007115275599062443,
0.00917003396898508,
0.010361316613852978,
0.061971016228199005,
0.020867617800831795,
-0.08624739944934845,
0.02145615592598915,
0.00595439737662673,
0.0012478171847760677,
-0.028672274202108383,
0.052270058542490005,
0.010152427479624748,
0.014318296685814857,
0.03654260188341141,
-0.004550943151116371,
0.05985996499657631,
-0.0025610311422497034,
-0.040117114782333374,
0.038508135825395584,
0.0379975363612175,
-0.016133490949869156,
-0.03324362263083458,
-0.007932694628834724,
-0.007927578873932362,
0.027661088854074478,
-0.052840329706668854,
0.006151222623884678,
0.034409020096063614,
0.014045706018805504,
0.011192651465535164,
0.022574642673134804,
-0.0337819866836071,
0.011847683228552341,
-0.03913000226020813,
-0.04480132833123207,
-0.014570923522114754,
0.03720332309603691,
0.032200589776039124,
0.05850791558623314,
-0.012837343849241734,
0.006976197473704815,
0.051850177347660065,
0.0005823211977258325,
-0.0703093558549881,
0.03144143149256706,
0.0035703997127711773,
-0.04211551696062088,
0.01715187169611454,
-0.008276400156319141,
-0.010155751369893551,
-0.03680459409952164,
0.006567688193172216,
-0.05241095647215843,
-0.028557248413562775,
-0.027513602748513222,
-0.028310419991612434,
0.00042776449117809534,
-0.03916914016008377,
-0.014282303862273693,
0.013435181230306625,
0.04964412376284599,
-0.009488371200859547,
0.038477230817079544,
0.06880445778369904,
0.003772769123315811,
-0.007050120737403631,
-0.02562600187957287,
-0.04140440747141838,
0.01644470915198326,
0.003261166624724865,
0.000057537105021765456,
0.022689413279294968,
0.01672237366437912,
0.0028735697269439697,
-0.023297198116779327,
0.00795635487884283,
0.04564541205763817,
0.014618800953030586,
-0.0009303942788392305,
-0.04037316516041756,
0.011172712780535221,
0.02896673046052456,
0.043287187814712524,
-0.04807964339852333,
-0.00824329536408186,
0.01388594601303339,
-0.008830655366182327,
0.007783414330333471,
0.02556643821299076,
0.013260306790471077,
-0.011470459401607513,
-0.0024231714196503162,
-0.05009191855788231,
0.016735222190618515,
-0.03487516939640045,
-0.014188953675329685,
0.018024712800979614,
0.012287836521863937,
-0.026573164388537407,
-0.033118776977062225,
0.009370765648782253,
0.014732206240296364,
0.012577035464346409,
0.0206743236631155,
-0.06983427703380585,
0.021281791850924492,
-0.028830906376242638,
0.0034649313893169165,
0.00817449763417244,
0.0401480458676815,
0.019522953778505325,
-0.01950686424970627,
-0.02655748277902603,
-0.06435296684503555,
-0.03767543286085129,
0.02182643488049507,
0.0332271009683609,
-0.025586217641830444,
-0.009347920306026936,
-0.04417845979332924,
-0.04187363386154175,
0.050550904124975204,
-0.02567603997886181,
0.0705854520201683,
-0.015507366508245468,
0.004387285560369492,
-0.031093589961528778,
-0.06402143836021423,
-0.0391400083899498,
0.013030600734055042,
-0.05443675071001053,
-0.0009149208781309426,
-0.014606370590627193,
0.026946699246764183,
-0.004992585629224777,
0.03490938991308212,
0.019962728023529053,
0.031963448971509933,
0.018480323255062103,
-0.03141624480485916,
-0.003764169290661812,
-0.02423972636461258,
-0.049704570323228836,
-0.057632897049188614,
-0.018708398565649986,
-0.011492909863591194,
-0.01438992004841566,
0.013849056325852871,
-0.055784326046705246,
-0.055325549095869064,
0.006232507526874542,
0.0021195164881646633,
-0.010310032404959202,
0.020409589633345604,
-0.03606656193733215,
0.00515092583373189,
0.02861214242875576,
-0.036292776465415955,
0.03975021094083786,
0.046592604368925095,
-0.023250801488757133,
0.00809044111520052,
-0.03335757181048393,
-0.017597567290067673,
-0.009807457216084003,
-0.028762327507138252,
-0.006943859625607729,
-0.009424739517271519,
-0.006998825818300247,
0.00015090721717569977,
0.017346495762467384,
0.018615830689668655,
-0.028813473880290985,
-0.03623225539922714,
-0.009709923528134823,
-0.008511940017342567,
0.02366061881184578,
0.02522345446050167,
-0.0019187545403838158,
-0.027895871549844742,
0.011021877638995647,
-0.010623322799801826,
0.02483542636036873,
-0.02207106538116932,
0.014647074043750763,
0.013694518245756626,
0.014246947132050991,
0.010891268961131573,
-0.05890367180109024,
-0.005046037025749683,
-0.02725651115179062,
-0.046339381486177444,
0.0725042074918747,
-0.022244879975914955,
0.02150498703122139,
0.0162748321890831,
0.018663618713617325,
-0.05525343865156174,
-0.007508554495871067,
-0.0037818248383700848,
-0.00842755101621151,
-0.01502446923404932,
-0.018745236098766327,
0.020387208089232445,
0.015082571655511856,
-0.024626005440950394,
-0.022774456068873405,
0.028227003291249275,
0.018758315593004227,
-0.018269319087266922,
0.011932590045034885,
-0.028121156617999077,
-0.00804322212934494,
-0.04145001620054245,
0.020384401082992554,
0.0513179786503315,
-0.03993313014507294,
-0.009259345941245556,
-0.034854624420404434,
-0.0018878537230193615,
0.054301824420690536,
-0.029170503839850426,
-0.019538862630724907,
0.006664795335382223,
-0.006387370638549328,
0.007578506600111723,
0.009248009882867336,
0.06123068183660507,
-0.019916629418730736,
-0.025192834436893463,
-0.024249205365777016,
-0.007808325812220573,
0.00838068313896656,
-0.006265580188483,
-0.02427198551595211,
0.03863496333360672,
0.003404393093660474,
-0.0392901711165905,
-0.05396256595849991,
0.03592951223254204,
0.014799082651734352,
0.031860288232564926,
-0.042221058160066605,
0.003737279213964939,
0.0009857359109446406,
-0.028322318568825722,
0.014008705504238605,
-0.014374234713613987,
-0.009099066257476807,
-0.05603252351284027,
0.09655848145484924,
-0.024638570845127106,
0.013376958668231964,
0.03400545194745064,
-0.0025539922062307596,
0.007246245164424181,
-0.025811070576310158,
0.0019707409664988518,
0.010136758908629417,
0.008042286150157452,
-0.03800635039806366,
0.030619537457823753,
-0.06995318830013275,
0.013710078783333302,
0.07868374139070511,
-0.03142794221639633,
0.06272078305482864,
0.028544064611196518,
0.016143647953867912,
0.004734732676297426,
-0.041999511420726776,
-0.022473284974694252,
-0.013398708775639534,
0.019987057894468307,
0.020869819447398186,
-0.021765276789665222,
-0.0034016058780252934,
0.07521316409111023,
0.037778425961732864,
-0.040318671613931656,
-0.011183459311723709,
0.03245941549539566,
-0.015681611374020576,
0.00801450852304697,
-0.01942746713757515,
-0.020860962569713593,
0.018500247970223427,
-0.033263590186834335,
0.037000108510255814,
0.0009474419057369232,
0.009309106506407261,
0.05679602175951004,
0.0023805468808859587,
-0.035389360040426254,
-0.053682759404182434,
-0.028975892812013626,
-0.024759341031312943,
0.026478052139282227,
0.0639273151755333,
-0.017714163288474083,
0.00918152742087841,
-0.00037434863043017685,
0.04308208450675011,
-0.00470232218503952,
0.009963265620172024,
-0.0291596669703722,
-0.04423856735229492,
0.008746013045310974,
-0.0012950306991115212,
-0.047748956829309464,
0.010130343027412891,
0.0021932851523160934,
-0.04138301685452461,
0.017991261556744576,
-0.00040763552533462644,
0.014262918382883072,
0.035178929567337036,
0.02224794402718544,
-0.03321179375052452,
0.06850824505090714,
-0.022923581302165985,
0.0004454829031601548,
-0.019686086103320122,
0.0008762939251028001,
0.14604733884334564,
0.004656211007386446,
0.010288209654390812,
0.018451619893312454,
0.05627918615937233,
0.014740947633981705,
-0.033118244260549545,
-0.032679662108421326,
0.0008290328551083803,
-0.043511077761650085,
0.005965071730315685,
0.011802930384874344,
0.06479982286691666,
-0.04084952175617218,
-0.024967312812805176,
0.05966364964842796,
0.0018550241366028786,
-0.00897896382957697,
-0.012891143560409546,
0.034804683178663254,
-0.03286653012037277,
0.024094510823488235,
-0.029814917594194412,
0.0373685397207737,
-0.03428873419761658,
-0.02681642398238182,
-0.030750300735235214,
-0.01657927967607975,
0.0415804460644722,
0.030943309888243675,
-0.07594413310289383,
0.042614880949258804,
0.013716097921133041,
-0.030211813747882843,
-0.024212345480918884,
0.03715217858552933,
0.03087579645216465,
-0.03643409162759781,
-0.0025622863322496414,
0.02388901636004448,
-0.03717450425028801,
0.0285173486918211,
-0.020936841145157814,
-0.012862234376370907,
-0.03251732885837555,
0.02492564544081688,
-0.05017485469579697,
0.048237331211566925,
-0.013171613216400146,
0.011962110176682472,
-0.010818603448569775,
0.04404833912849426,
-0.012811016291379929,
-0.06804639846086502,
0.005213209893554449,
-0.003673994680866599,
0.029112454503774643,
-0.059311628341674805,
-0.023236941546201706,
0.025262147188186646,
0.0031127172987908125,
0.03732186555862427,
-0.0070898281410336494,
-0.033132996410131454,
0.025852195918560028,
0.00006805422162869945,
0.011169764213263988,
0.05713224783539772,
-0.006224433425813913,
-0.02060909941792488,
-0.016308311372995377,
-0.016972895711660385,
-0.008501570671796799,
-0.012345033697783947,
0.01307019405066967,
0.05686792731285095,
-0.004213990177959204,
-0.001786768320016563,
-0.019023429602384567,
-0.0549146831035614,
-0.031277310103178024,
0.030079402029514313,
-0.012346724979579449,
-0.02621661126613617,
0.004830661229789257,
-0.032851506024599075,
-0.004952152259647846,
0.03094146028161049,
-0.01235183235257864,
0.016109028831124306,
0.017941083759069443,
0.01928403601050377,
0.008531373925507069,
0.00020263147598598152,
-0.007912909612059593,
0.0429704487323761,
-0.018493643030524254,
-0.0004998671356588602,
-0.0000018128390593119548,
0.021810799837112427,
0.06732607632875443,
0.019652381539344788,
-0.01735975220799446,
0.02694660983979702,
0.0005023329867981374,
0.028675029054284096,
0.04085882008075714,
-0.012106158770620823,
-0.002428546082228422,
0.030505266040563583,
0.007536709774285555,
-0.04213358834385872,
0.015430744737386703,
-0.01611422374844551,
-0.00009886954649118707,
-0.035843826830387115,
0.021757598966360092,
-0.01918998546898365,
0.039492495357990265,
-0.03382277116179466,
0.030823998153209686,
-0.07835789024829865,
0.00040565599920228124,
-0.0425058975815773,
-0.009735442698001862,
-0.008181166835129261,
-0.026303134858608246,
-0.04648720473051071,
0.031119151040911674,
-0.006044906564056873,
0.024306215345859528,
0.023061804473400116,
-0.016064459457993507,
0.038141392171382904,
-0.04612636938691139,
0.022267797961831093,
-0.050974808633327484,
0.043573036789894104,
-0.015894588083028793,
-0.026494858786463737,
0.026724662631750107,
-0.0155296316370368,
-0.04622114822268486,
-0.0034582384396344423,
0.030958306044340134,
0.028593726456165314,
-0.010679030790925026,
-0.032865654677152634,
0.016161728650331497,
0.03517623618245125,
0.0014826878905296326,
-0.012626687996089458,
-0.010039189830422401,
-0.02693682350218296,
0.01920146867632866,
0.012167696841061115,
0.025420865043997765,
-0.05252843350172043,
0.010308577679097652,
0.042414143681526184,
-0.025608902797102928,
-0.026966365054249763,
0.013582860119640827,
-0.002260867739096284,
-0.01108420267701149,
-0.023629626259207726,
-0.003141628811135888,
0.02440362051129341,
0.045218516141176224,
0.002902646316215396,
-0.006597717292606831,
0.045367103070020676,
0.029008937999606133,
0.0071159848012030125,
-0.0841631293296814,
-0.008905756287276745,
-0.005882570520043373,
-0.009448534809052944,
0.03352508693933487,
-0.07020294666290283,
-0.016355497762560844,
0.02969781868159771,
-0.08784586191177368,
0.011026237159967422,
-0.02742220088839531,
-0.00045629622763954103,
0.01746373251080513,
-0.016810735687613487,
0.015199017710983753,
0.028356485068798065,
-0.02921893633902073,
0.017732974141836166,
0.001928391633555293,
0.03695530816912651,
-0.021978076547384262,
-0.024544864892959595,
0.019847413524985313,
0.05495038256049156,
-0.011851415038108826,
0.040703482925891876,
0.021104203537106514,
0.0018262353260070086,
0.020359398797154427,
0.047600723803043365,
-0.02332397922873497,
0.05572746321558952,
-0.07220479846000671,
0.010522332042455673,
-0.03456538915634155,
0.009713410399854183,
-0.03050953522324562,
0.020323121920228004,
-0.006329916417598724,
-0.006909491028636694,
0.023142362013459206,
0.03961184620857239,
0.01913437619805336,
-0.028967900201678276,
0.04216482490301132,
-0.04008272662758827,
-0.027508538216352463,
0.04765069857239723,
-0.012865002267062664,
0.006007758434861898,
0.013629723340272903,
0.0051875547505915165,
-0.046487778425216675,
-0.03765038773417473,
-0.02206696942448616,
-0.0615871362388134,
-0.008357060141861439,
0.03508444130420685,
0.008417068980634212,
-0.02073271945118904,
-0.022337187081575394,
0.01940242387354374,
0.002868210431188345,
-0.003692670026794076,
-0.011113672517240047,
0.004855840466916561,
-0.02817416377365589,
-0.003896057605743408,
0.010892943479120731,
-0.02621067874133587,
-0.026969825848937035,
-0.013826234266161919,
-0.03613053634762764,
0.030510051175951958,
0.007222064770758152,
-0.03480139747262001,
-0.054201461374759674,
-0.029309211298823357,
-0.0006191298016346991,
-0.07423754781484604,
0.015128088183701038,
0.018896378576755524,
-0.0493263378739357,
-0.02761395275592804,
-0.03523679077625275,
-0.02581029012799263,
-0.007338165771216154,
0.036831777542829514,
0.010462744161486626,
0.006610439158976078,
0.00286755058914423,
-0.023097416386008263,
0.0038557429797947407,
-0.08233770728111267,
0.0064578307792544365,
0.017210669815540314,
0.027160050347447395,
0.0196529533714056,
-0.00014514995564240962,
-0.007169476710259914,
-0.03097376972436905,
0.01391492411494255,
0.008358517661690712,
0.06810931861400604,
0.045058559626340866,
-0.016111478209495544,
0.02677079476416111,
-0.0058259060606360435,
-0.01635122112929821,
0.08131276071071625,
0.014042796567082405,
-0.0020282561890780926,
0.020379213616251945,
-0.03958408534526825,
-0.029912488535046577,
0.02849225327372551,
-0.0631454586982727,
-0.005395626649260521,
-0.047134313732385635,
-0.060386065393686295,
0.053059790283441544,
-0.04372436925768852,
-0.005282905418425798,
0.058936070650815964,
-0.03093143366277218,
0.018804708495736122,
0.010180465877056122,
-0.016834504902362823,
0.04369619861245155,
-0.006074749398976564,
0.03674188628792763,
-0.0018919726135209203,
-0.03349713608622551,
-0.025258976966142654,
-0.024283897131681442,
0.028302127495408058,
0.016450295224785805,
-0.01300209853798151,
0.07271013408899307,
0.0050018043257296085,
0.011468907818198204,
0.03827068954706192,
0.015012816525995731,
-0.012946274131536484,
-0.02354588359594345,
-0.013010458089411259,
0.00814120564609766,
0.029031412675976753,
0.029171394184231758,
0.024171367287635803,
0.08767963945865631,
-0.0059805503115057945,
0.0032296590507030487,
-0.01664569415152073,
0.020358631387352943,
-0.05087673291563988,
0.015079881064593792,
0.02257986180484295,
0.01826082542538643,
-0.010232792235910892,
-0.02767781913280487,
-0.035068050026893616,
-0.007335965055972338,
0.021041758358478546,
0.00044525842531584203,
0.0296257883310318,
0.0510299876332283,
0.013819619081914425,
0.0030381646938622,
0.009015384130179882,
-0.019507689401507378,
-0.009649185463786125,
0.06359200179576874,
0.008170747198164463,
0.013855400495231152,
0.008294287137687206,
0.008474946953356266,
0.006806388031691313,
0.031216269358992577,
-0.06817072629928589,
-0.053314004093408585,
-0.0016561110969632864,
0.052617523819208145,
0.03073127195239067,
-0.042787887156009674
] |
<p>So this appears in a problem which looks simple enough in its context; It's something like this:</p>
<blockquote>
<p><em>Two discs, <strong>A</strong> and <strong>B</strong>, are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ and $2I$ respectively about the common axis. Disc A is imparted an initial angular velocity $2\omega$ using the entire potential energy of a spring compressed by a distance $x_1$. Disc B is imparted an angular velocity $\omega$ by the same spring compressed by a distance $x_2$. Both the discs rotate in the clockwise direction.</em></p>
<p><em>When disc B was brought in contact with A, they acquire a common angular velocity in time $t$. The average frictional torque by the other during this period is: <strong>?</strong></em></p>
</blockquote>
<p>The answer ($2I\omega/3t$) was obtained by applying angular momentum conservation and is exactly what confused me. <strong>How can we apply angular momentum conservation when friction is present?</strong></p>
| 9,579 |
[
-0.04362304508686066,
-0.041605494916439056,
-0.041517224162817,
0.008217737078666687,
0.02509027160704136,
-0.021754855290055275,
-0.04628390446305275,
0.02870827168226242,
-0.00003879299038089812,
0.006743365898728371,
0.01633155159652233,
0.06441941112279892,
0.06590796262025833,
0.017506469041109085,
0.03127950802445412,
-0.0048860544338822365,
-0.020379982888698578,
-0.020054331049323082,
0.023814046755433083,
-0.019360700622200966,
-0.014560823328793049,
-0.026883350685238838,
0.02300293929874897,
-0.018455740064382553,
-0.0010300064459443092,
0.001569929183460772,
0.01576908864080906,
-0.03966537117958069,
-0.011866052635014057,
0.04680267348885536,
0.004129603039473295,
-0.011768545024096966,
-0.02885458804666996,
-0.015845337882637978,
0.0026068438310176134,
0.019638564437627792,
-0.05007961392402649,
0.002450747648254037,
-0.011547738686203957,
0.056591879576444626,
-0.04978104680776596,
0.0027234721928834915,
-0.030882863327860832,
0.06033499538898468,
-0.04389159381389618,
0.045660510659217834,
-0.018977219238877296,
0.014300817623734474,
0.02652690000832081,
-0.03025696612894535,
0.04806562885642052,
-0.012185095809400082,
0.04569993540644646,
0.020037267357110977,
-0.03414550796151161,
-0.02967580407857895,
0.09758540987968445,
0.0613093264400959,
-0.005095076747238636,
-0.02427307330071926,
-0.017348479479551315,
-0.015491053462028503,
-0.0018454890232533216,
0.01244510430842638,
-0.021045459434390068,
0.015806956216692924,
-0.007852653972804546,
-0.01576940156519413,
0.027326716110110283,
0.015272166579961777,
0.0380248948931694,
0.03549587354063988,
0.03493470326066017,
-0.02672213315963745,
-0.023943038657307625,
-0.03292171657085419,
0.03456626832485199,
0.024653494358062744,
0.02443712204694748,
0.02877231314778328,
-0.015540778636932373,
0.007648264989256859,
0.03381422162055969,
0.06975185126066208,
-0.0049176448956131935,
-0.020861104130744934,
0.0681452602148056,
0.006447209976613522,
-0.009577014483511448,
0.01339698489755392,
0.05426429212093353,
0.028094669803977013,
-0.009364057332277298,
-0.04073735326528549,
0.004778004717081785,
0.04279712587594986,
0.012959929183125496,
0.028658585622906685,
0.017026415094733238,
-0.00032510922756046057,
0.010946468450129032,
-0.017295094206929207,
0.032693348824977875,
0.03251073881983757,
-0.0058622341603040695,
-0.019042007625102997,
-0.017804745584726334,
0.021888921037316322,
-0.027642011642456055,
-0.008971858769655228,
-0.0570935420691967,
0.034303680062294006,
-0.00622617406770587,
0.005784906912595034,
-0.001613912172615528,
-0.020067302510142326,
-0.02611614391207695,
0.027810685336589813,
0.03650824353098869,
0.018503446131944656,
0.06798375397920609,
-0.04109176993370056,
-0.015178424306213856,
-0.055146247148513794,
-0.05229600518941879,
0.010833158157765865,
0.024000218138098717,
-0.0036390856839716434,
-0.031871553510427475,
0.00002627017966005951,
0.02710517682135105,
-0.024924153462052345,
0.0012604939984157681,
0.0004655715893022716,
-0.011994078755378723,
-0.03259233012795448,
-0.08741401880979538,
-0.042785827070474625,
0.04180053621530533,
-0.013780057430267334,
-0.05194079130887985,
-0.11256755888462067,
-0.012861019000411034,
0.03429421782493591,
0.06163816526532173,
0.006474287714809179,
0.000410199339967221,
0.0005518307443708181,
0.039793960750103,
-0.004339553415775299,
-0.02002117596566677,
-0.030468447133898735,
-0.017555199563503265,
-0.02774038165807724,
-0.01790960319340229,
-0.04950954392552376,
0.022190416231751442,
0.02413714863359928,
0.017647158354520798,
-0.01187470369040966,
0.04726199433207512,
-0.03803174942731857,
0.03796720132231712,
0.012220103293657303,
0.006200885865837336,
-0.029231231659650803,
0.05616921931505203,
0.00518936337903142,
0.0006658277125097811,
0.04813656955957413,
0.030287722125649452,
0.010247264988720417,
-0.005067164544016123,
0.02853177674114704,
0.06287489086389542,
-0.0722978264093399,
0.00576242757961154,
-0.010574688203632832,
-0.029071466997265816,
-0.029835984110832214,
-0.029730021953582764,
-0.05697911977767944,
-0.0010153010953217745,
-0.0010221605189144611,
-0.013266541063785553,
0.08035413920879364,
-0.00004624001667252742,
-0.03283721208572388,
-0.04342314973473549,
-0.021983392536640167,
-0.010824466124176979,
-0.06949375569820404,
0.02924163267016411,
-0.007606481667608023,
-0.05102667957544327,
0.03318232670426369,
-0.00030405292636714876,
0.061685964465141296,
-0.022500017657876015,
-0.03191673383116722,
0.010213203728199005,
0.036308351904153824,
0.023283500224351883,
-0.02061254158616066,
0.007621432654559612,
0.027623118832707405,
0.05736638233065605,
-0.0036644672509282827,
-0.010040338151156902,
-0.007967899553477764,
-0.021693482995033264,
0.01484201941639185,
-0.027928607538342476,
0.012889985926449299,
0.04933953657746315,
0.008706286549568176,
0.030596045777201653,
-0.007332494016736746,
-0.011692451313138008,
0.015875618904829025,
0.018284998834133148,
0.04430288076400757,
0.0741768628358841,
0.005901691969484091,
-0.0024879106786102057,
0.05297569930553436,
-0.034995876252651215,
-0.005622444674372673,
-0.0011846701381728053,
-0.05179866775870323,
-0.03702402859926224,
-0.006123231258243322,
0.023696452379226685,
0.04196902737021446,
-0.02553499862551689,
0.012557742185890675,
0.0194472074508667,
0.016475385054945946,
0.024595994502305984,
0.03548939526081085,
0.017418306320905685,
-0.02872171811759472,
0.021097850054502487,
0.014024291187524796,
0.010333447717130184,
0.018733205273747444,
0.011260668747127056,
0.029531117528676987,
0.006241976283490658,
-0.005826807580888271,
-0.02798326313495636,
0.03919914364814758,
0.005357856396585703,
0.017067015171051025,
0.00835413858294487,
-0.014657753519713879,
0.050996098667383194,
-0.01300350297242403,
0.016185026615858078,
0.033159513026475906,
0.024319464340806007,
0.015691958367824554,
-0.007214326411485672,
0.013027290813624859,
0.028914887458086014,
-0.017096538096666336,
-0.0006332862540148199,
-0.00727655878290534,
0.014238539151847363,
-0.005876854527741671,
-0.00240282341837883,
-0.003912637941539288,
-0.039869025349617004,
0.021854950115084648,
-0.012321151793003082,
0.028367450460791588,
0.027048815041780472,
0.059755150228738785,
-0.009781843982636929,
-0.03421143442392349,
-0.030445469543337822,
-0.013629213906824589,
-0.021179478615522385,
0.02233988046646118,
-0.04446005821228027,
0.01933935470879078,
-0.041668426245450974,
-0.028319522738456726,
0.04103681072592735,
-0.012621914967894554,
0.008044466376304626,
-0.009895115159451962,
-0.007651342544704676,
-0.07735159993171692,
-0.012119869701564312,
0.01750098541378975,
-0.004625696688890457,
-0.04939219728112221,
-0.01682179979979992,
0.07646489888429642,
-0.02840949036180973,
0.018017632886767387,
-0.0016412758268415928,
-0.021963585168123245,
-0.05325331911444664,
0.015533124096691608,
-0.00457026856020093,
0.046962834894657135,
-0.009423731826245785,
0.0035978909581899643,
-0.008858375251293182,
-0.044873714447021484,
-0.015890808776021004,
-0.04988248273730278,
-0.0165606290102005,
0.0056412098929286,
-0.014329904690384865,
0.04744935780763626,
-0.024895913898944855,
-0.03782510384917259,
0.10836511850357056,
0.015164322219789028,
-0.024777915328741074,
0.020391788333654404,
-0.03159142658114433,
0.01380336843430996,
-0.035497695207595825,
-0.045798856765031815,
-0.00963021069765091,
-0.03106316179037094,
0.03368893638253212,
0.011114636436104774,
-0.003157997503876686,
0.053171347826719284,
0.029693374410271645,
0.005464515183120966,
0.010357452556490898,
0.036687448620796204,
0.005245801527053118,
0.04451462998986244,
0.043550457805395126,
0.0140536455437541,
-0.0073254285380244255,
-0.029405180364847183,
0.028791427612304688,
0.0012870494974777102,
-0.07956980913877487,
0.055616311728954315,
0.0010995757766067982,
0.02862212434411049,
0.004515001084655523,
0.07387588173151016,
0.01665559411048889,
-0.019302161410450935,
-0.00027969785151071846,
0.029904397204518318,
0.030282776802778244,
-0.024060284718871117,
0.01419850904494524,
0.05569354444742203,
0.029390571638941765,
-0.00743414182215929,
-0.050018154084682465,
-0.010866247117519379,
0.021020933985710144,
0.022561147809028625,
-0.03931734710931778,
0.0008503210265189409,
0.008162539452314377,
0.004516503307968378,
0.033962544053792953,
-0.020869523286819458,
-0.061236996203660965,
0.014417674392461777,
-0.07208182662725449,
0.024684008210897446,
-0.033704813569784164,
0.03586957976222038,
0.008145860396325588,
0.03666821867227554,
0.014499001204967499,
0.019917072728276253,
0.0222101341933012,
-0.02339942753314972,
-0.07485496997833252,
0.03272330015897751,
-0.038187768310308456,
-0.029970292001962662,
0.0067170122638344765,
3.9170802779153746e-7,
0.02714337781071663,
-0.00013030676927883178,
-0.00030323053942993283,
-0.010521463118493557,
-0.005804337561130524,
-0.03753887861967087,
-0.007818466052412987,
-0.052698779851198196,
-0.03873848542571068,
-0.0013717969413846731,
0.0022023553028702736,
0.05041910707950592,
-0.03009321354329586,
0.04191930592060089,
0.07642391324043274,
-0.03862491622567177,
0.004299262538552284,
-0.02965170331299305,
-0.013253241777420044,
-0.02574787102639675,
0.003220973303541541,
0.025480441749095917,
0.009772160090506077,
0.049363873898983,
0.004181983880698681,
0.02128634601831436,
0.04738231003284454,
0.030667712911963463,
-0.003337664296850562,
-0.03750744089484215,
-0.05544367805123329,
-0.02226865291595459,
0.02056589536368847,
0.08775363862514496,
-0.026791449636220932,
0.020617440342903137,
0.013210782781243324,
0.044882651418447495,
-0.02211396023631096,
0.027943193912506104,
0.031452592462301254,
0.04563650116324425,
-0.006259170826524496,
-0.08014944195747375,
-0.017856251448392868,
-0.017310427501797676,
-0.04027332365512848,
0.007499081548303366,
-0.023639462888240814,
0.0031737845856696367,
-0.028607632964849472,
0.032652102410793304,
0.028061844408512115,
0.019491970539093018,
0.0899495854973793,
-0.05543121322989464,
0.009808347560465336,
-0.00977732427418232,
0.00910739041864872,
-0.0012891157530248165,
0.0311689805239439,
0.04833665117621422,
0.008856792002916336,
0.010534655302762985,
-0.02447926253080368,
-0.010533084161579609,
0.01694384030997753,
0.03975489363074303,
-0.014103001914918423,
0.00011933102359762415,
-0.04134324938058853,
-0.033875320106744766,
0.043133195489645004,
-0.03673592582345009,
0.08418040722608566,
-0.033927686512470245,
-0.003691332181915641,
-0.017948167398571968,
-0.03280782699584961,
-0.04356265813112259,
0.03944089636206627,
-0.027854910120368004,
0.028803516179323196,
-0.009310745634138584,
-0.04370797425508499,
-0.005353306420147419,
0.02440190501511097,
0.02966928668320179,
-0.014039820991456509,
-0.006110462825745344,
-0.01892164722084999,
-0.033938419073820114,
0.023197690024971962,
-0.016011616215109825,
-0.04703650623559952,
-0.013651366345584393,
-0.009808414615690708,
-0.025526463985443115,
-0.009455235674977303,
-0.0704624280333519,
-0.07113013416528702,
0.02700374275445938,
-0.02344282530248165,
-0.007514611817896366,
0.005698721390217543,
-0.018108854070305824,
0.03839723393321037,
0.0356639064848423,
-0.0027828747406601906,
0.015149252489209175,
0.026261799037456512,
-0.013178013265132904,
-0.018692240118980408,
-0.011531410738825798,
0.011291119270026684,
-0.0011071892222389579,
-0.000828204327262938,
-0.06279265880584717,
0.04702040180563927,
-0.019441043958067894,
0.05324383080005646,
0.009347328916192055,
0.01902742311358452,
-0.033159591257572174,
-0.04880162701010704,
-0.021949805319309235,
0.009236603043973446,
-0.015054267831146717,
-0.016452034935355186,
0.021714424714446068,
-0.010051551274955273,
-0.0004240325652062893,
0.0034709179308265448,
0.000887845060788095,
-0.025425322353839874,
0.019285844638943672,
0.056165486574172974,
-0.005670348182320595,
0.028719721361994743,
-0.04449768736958504,
-0.02460012398660183,
0.020733682438731194,
-0.03427502512931824,
0.025263898074626923,
-0.029448172077536583,
0.03368828818202019,
0.038305044174194336,
-0.04175394028425217,
-0.018162492662668228,
-0.006590116769075394,
-0.01269237045198679,
0.01924881339073181,
-0.08448681980371475,
-0.014246951788663864,
0.0285576730966568,
-0.009888050146400928,
0.0007560495287179947,
-0.05686262249946594,
0.0249018631875515,
-0.008122746832668781,
0.016920730471611023,
-0.029076946899294853,
-0.028843771666288376,
-0.0028878694865852594,
-0.039201248437166214,
-0.014611899852752686,
0.06882020086050034,
-0.03264308720827103,
-0.021001441404223442,
0.030667928978800774,
0.027089186012744904,
0.04815278574824333,
-0.016522763296961784,
-0.020994875580072403,
-0.0035109061282128096,
-0.0231556985527277,
-0.024128424003720284,
0.017828062176704407,
0.056951478123664856,
-0.0382089801132679,
-0.03846843168139458,
0.006165152415633202,
0.0192106906324625,
0.01629902981221676,
-0.006625753827393055,
0.05539437010884285,
0.030839240178465843,
-0.010366532020270824,
-0.008417278528213501,
0.01245021354407072,
0.03659762814640999,
0.01293746754527092,
0.03598092496395111,
-0.0062710074707865715,
-0.02587292157113552,
-0.02059301733970642,
-0.009622112847864628,
0.015914173796772957,
0.021015726029872894,
0.005076367873698473,
-0.012537906877696514,
0.03972091153264046,
-0.026268236339092255,
0.019794942811131477,
0.008557218126952648,
-0.018668124452233315,
0.03796776384115219,
0.012133212760090828,
0.0021211490966379642,
0.034095991402864456,
-0.032349880784749985,
-0.028295379132032394,
-0.021179506555199623,
-0.040964819490909576,
0.02819308452308178,
0.07456693798303604,
-0.06017465889453888,
0.06613617390394211,
0.05428823456168175,
0.008519143797457218,
-0.03958616405725479,
-0.01902211271226406,
-0.008884767070412636,
-0.018926657736301422,
0.018446018919348717,
0.010492755100131035,
-0.03570882976055145,
0.004259404726326466,
0.048346977680921555,
0.038859739899635315,
-0.026158783584833145,
-0.013725318014621735,
-0.005948386620730162,
0.01598583534359932,
0.01640220917761326,
0.006139681208878756,
-0.05545581877231598,
0.016869228333234787,
-0.014938372187316418,
0.05355880409479141,
-0.007197844795882702,
-0.04566608741879463,
0.05973034352064133,
0.020054951310157776,
0.0032350271940231323,
-0.0353667177259922,
-0.0016404998023062944,
-0.040436819195747375,
-0.004629175178706646,
0.014441789127886295,
0.00809010211378336,
-0.00035917648347094655,
0.012592082843184471,
0.045573655515909195,
0.019959863275289536,
0.0031176358461380005,
-0.04273541644215584,
-0.031998030841350555,
-0.013590236194431782,
-0.02329586073756218,
-0.033682044595479965,
0.0498274490237236,
0.020308304578065872,
-0.0113688874989748,
0.05259845405817032,
-0.025865105912089348,
0.027249833568930626,
0.0403909794986248,
0.025571588426828384,
-0.010803049430251122,
0.11600983142852783,
-0.004389712121337652,
0.02082109823822975,
-0.03248288109898567,
0.023463936522603035,
0.12738385796546936,
0.015684787184000015,
0.032092832028865814,
-0.023124223574995995,
0.019826563075184822,
-0.010829698294401169,
-0.0073726181872189045,
-0.02636934258043766,
-0.019640982151031494,
0.017598405480384827,
0.019418496638536453,
-0.0066943420097231865,
0.025311671197414398,
-0.007021723315119743,
-0.024065658450126648,
0.03266530856490135,
-0.016837915405631065,
-0.02240227907896042,
-0.009256027638912201,
-0.0008074568468146026,
-0.013678514398634434,
-0.05373251438140869,
-0.013493061065673828,
0.01618201844394207,
-0.02046598307788372,
-0.010163269937038422,
0.013134606182575226,
-0.044248562306165695,
-0.012584462761878967,
-0.004840550944209099,
-0.022645030170679092,
0.03945000097155571,
0.045642394572496414,
-0.030946562066674232,
-0.028087126091122627,
0.03387269005179405,
0.014426423236727715,
0.02690654993057251,
0.03133721277117729,
0.00425147358328104,
0.012412438169121742,
0.02680147811770439,
0.02230481058359146,
0.009790669195353985,
-0.02393893525004387,
0.005821932572871447,
-0.03081742860376835,
0.03486104682087898,
-0.014657162129878998,
0.023334713652729988,
-0.027669554576277733,
-0.037359945476055145,
0.02331005409359932,
-0.032569464296102524,
0.020243965089321136,
-0.016529960557818413,
0.0032844620291143656,
-0.0401766337454319,
-0.0036256485618650913,
-0.010353346355259418,
-0.010131914168596268,
0.02817593887448311,
0.025423500686883926,
-0.007110476493835449,
-0.023011626675724983,
0.011796187609434128,
0.010812456719577312,
0.029448293149471283,
-0.009928587824106216,
-0.009127682074904442,
-0.047418780624866486,
-0.0103136682882905,
-0.03524743765592575,
0.0029184503946453333,
0.00618003448471427,
0.017958417534828186,
0.01273148413747549,
-0.01955370046198368,
-0.03997837007045746,
-0.025473114103078842,
-0.0376034639775753,
0.021842962130904198,
-0.010308126918971539,
-0.014193768613040447,
-0.004006092436611652,
-0.0068962955847382545,
-0.026202719658613205,
0.04345588758587837,
-0.025767996907234192,
0.011746504344046116,
0.002263250993564725,
0.05513137951493263,
0.03806202858686447,
0.009079153649508953,
-0.027424056082963943,
0.0050043268129229546,
-0.031094977632164955,
-0.007864978164434433,
0.016165664419531822,
0.02691536396741867,
0.04015735164284706,
0.011547015979886055,
0.006638773716986179,
0.008659182116389275,
0.013027853332459927,
0.029949165880680084,
0.036610592156648636,
-0.036615755409002304,
-0.008672165684401989,
0.04350435733795166,
-0.00021505165204871446,
-0.03890165686607361,
0.00529971020296216,
-0.00810379721224308,
-0.00828300230205059,
-0.009886506013572216,
0.008958864025771618,
-0.04557022452354431,
-0.0032354360446333885,
-0.07916320860385895,
0.05999826639890671,
-0.03787144646048546,
0.005569365341216326,
-0.003125076415017247,
0.0022560968063771725,
0.023130837827920914,
0.009761765599250793,
-0.022388113662600517,
0.05860459804534912,
0.009768880903720856,
-0.01224676612764597,
-0.007070162799209356,
0.009326368570327759,
-0.01628989540040493,
0.02304406836628914,
0.01252004038542509,
0.0027759757358580828,
0.0434848889708519,
-0.031924158334732056,
-0.03270190581679344,
0.076645627617836,
-0.023142745718359947,
-0.05116043612360954,
0.03135649859905243,
-0.005515698809176683,
0.015354453586041927,
0.02626868151128292,
-0.05717712268233299,
-0.014685931615531445,
0.04146428406238556,
-0.03266376256942749,
-0.022210966795682907,
0.00641108863055706,
-0.012438626028597355,
-0.01435070764273405,
-0.04556986317038536,
0.008091791532933712,
-0.009017863310873508,
-0.00013533314631786197,
0.017481891438364983,
0.032263003289699554,
-0.021122820675373077,
-0.006255399901419878,
0.013944902457296848,
0.06231951341032982,
-0.013895546086132526,
0.02990260161459446,
0.04130161926150322,
0.018346915021538734,
0.05749809741973877,
-0.03503783047199249,
-0.024812784045934677,
0.0020339549519121647,
0.02175004780292511,
-0.09449930489063263,
-0.0071313828229904175,
0.018407205119729042,
0.009185774251818657,
0.01567007787525654,
-0.056573208421468735,
-0.028721995651721954,
0.010362595319747925,
-0.058833006769418716,
0.008306398056447506,
-0.04252041131258011,
-0.021559899672865868,
-0.03803553059697151,
-0.0006594774895347655,
0.003684289287775755,
0.020610956475138664,
0.0012232987210154533,
0.030841270461678505,
0.01567760482430458,
0.016874173656105995,
-0.03142651543021202,
-0.046440958976745605,
0.0007421879563480616,
0.04328404366970062,
-0.014869307167828083,
0.01265600323677063,
0.07071469724178314,
0.01370223518460989,
-0.03127995878458023,
0.034583959728479385,
-0.04786223918199539,
-0.01865348592400551,
-0.025447651743888855,
0.00013276068784762174,
-0.011311331763863564,
-0.0181582048535347,
0.008968724869191647,
-0.010935721918940544,
-0.002237222623080015,
0.009223426692187786,
0.02838072180747986,
0.012937992811203003,
-0.010638197883963585,
0.009330249391496181,
0.05132642760872841,
-0.03858479484915733,
-0.036565978080034256,
0.003929063677787781,
-0.0332600474357605,
0.030772706493735313,
0.01977071352303028,
0.035006240010261536,
0.022251170128583908,
-0.02375706471502781,
-0.029654141515493393,
-0.0175666231662035,
0.004803505726158619,
0.024311091750860214,
-0.02596154995262623,
0.007060415111482143,
0.03224687650799751,
0.02282242476940155,
-0.017368674278259277,
0.00064013188239187,
-0.007190922740846872,
-0.03203737363219261,
-0.06323686987161636,
-0.028582215309143066,
0.017506718635559082,
0.003558648284524679,
-0.014553328044712543,
-0.05364125967025757,
-0.06712552160024643,
0.02234709821641445,
0.004978041164577007,
-0.00814875215291977,
0.0024296354968100786,
-0.019932007417082787,
-0.03451259806752205,
-0.06247005611658096,
0.039595577865839005,
0.005176331382244825,
-0.034525495022535324,
-0.02986397035419941,
-0.019469942897558212,
-0.04339651018381119,
-0.011772367171943188,
0.03108290582895279,
0.021497942507267,
-0.017491187900304794,
0.04757549613714218,
-0.022325946018099785,
0.012911566533148289,
-0.018376175314188004,
0.0006732100155204535,
-0.03003101609647274,
0.022481994703412056,
0.04230490326881409,
-0.011887501925230026,
-0.019364869222044945,
-0.01654324308037758,
0.014255508780479431,
-0.018656400963664055,
0.039966683834791183,
0.03130437433719635,
-0.03833647817373276,
0.024225015193223953,
-0.05459147319197655,
0.018739746883511543,
0.0578581877052784,
0.027422094717621803,
0.03209184855222702,
0.031566817313432693,
-0.02605048380792141,
-0.06517484784126282,
0.05009692534804344,
-0.04585966467857361,
-0.007325842045247555,
-0.038425058126449585,
-0.012333585880696774,
0.03475164994597435,
-0.033172715455293655,
-0.011628743261098862,
0.034242622554302216,
-0.0060794297605752945,
0.004605710040777922,
-0.003248870139941573,
-0.0051714470610022545,
0.04392445087432861,
0.0042311339639127254,
0.03641765937209129,
0.014233685098588467,
-0.009873002767562866,
0.01896061562001705,
0.02620171383023262,
0.04162248969078064,
-0.006083606742322445,
-0.02566547505557537,
0.012409032322466373,
0.006556118372827768,
0.028732340782880783,
-0.012326758354902267,
0.041577547788619995,
-0.0006958059966564178,
-0.06715115159749985,
-0.018772577866911888,
-0.02430959977209568,
-0.004515490960329771,
0.01867647096514702,
0.010088023729622364,
0.06585412472486496,
-0.013048911467194557,
0.014849712140858173,
-0.02024230547249317,
0.03642144054174423,
-0.017627106979489326,
0.0034906596411019564,
0.019430194050073624,
0.015765873715281487,
-0.04758299142122269,
-0.002107575535774231,
-0.0060858591459691525,
-0.010185700841248035,
0.01922573521733284,
0.011925291270017624,
0.009324725717306137,
0.013585299253463745,
0.0019256426021456718,
0.014862796291708946,
-0.03449484333395958,
-0.017466766759753227,
-0.05536963790655136,
0.01871950738132,
0.030305832624435425,
0.02156492881476879,
-0.026188869029283524,
0.005428070202469826,
0.011172591708600521,
0.07244177162647247,
-0.05956282466650009,
0.008800024166703224,
0.01705339550971985,
0.05573691055178642,
0.02025514282286167,
-0.03851388394832611
] |
<p>The Hamiltonian for an electron of mass $m$ and charge $e$ in an exterior electromagnetic field is
$$H=\frac{1}{2m}(p-(e/c)A)^2+e\varphi.$$
The corresponding (via canonical quantization) quantum mechanical Hamiltonian is not invariant under Gauge transformations (for $A$ and $\varphi$). What's the physical meaning of this? And what is the physical meaning of the fact that the classical hamiltonian is not invariant under gauge transformations?</p>
| 9,580 |
[
-0.013409759849309921,
0.011854243464767933,
-0.0072420574724674225,
-0.039703041315078735,
0.04196671023964882,
0.014197315089404583,
-0.031653787940740585,
-0.019453683868050575,
-0.011360783129930496,
-0.031066158786416054,
0.04009517654776573,
0.0006189433624967933,
0.07757637649774551,
-0.022560572251677513,
0.03441370278596878,
0.02144601009786129,
0.010028586722910404,
-0.0008655967540107667,
-0.001005919766612351,
-0.02094300277531147,
-0.008700460195541382,
0.04870486259460449,
0.011577434837818146,
0.015041200444102287,
-0.0005027991137467325,
0.02502109855413437,
0.02389180101454258,
0.021656641736626625,
0.005024307873100042,
0.05536721646785736,
-0.008764265105128288,
-0.023740028962492943,
0.027108220383524895,
0.020167306065559387,
0.014423433691263199,
-0.010903439484536648,
-0.015244309790432453,
-0.07645942270755768,
0.007631735876202583,
-0.000044259017158765346,
-0.06368694454431534,
-0.060038477182388306,
-0.019338270649313927,
0.05620105564594269,
-0.012255010195076466,
0.0035689272917807102,
-0.006416683550924063,
0.0065874215215444565,
0.06130858138203621,
-0.04404284805059433,
0.08633244782686234,
0.016959436237812042,
0.01805330067873001,
0.004606964066624641,
-0.010480739176273346,
-0.01879039593040943,
0.06603089720010757,
0.03958325833082199,
-0.028129439800977707,
-0.050596583634614944,
-0.03626680374145508,
-0.051055680960416794,
0.012931895442306995,
-0.041084494441747665,
-0.021020492538809776,
0.04381505772471428,
0.010229675099253654,
-0.041819360107183456,
0.04523128643631935,
0.009991067461669445,
-0.0016074554296210408,
0.012821740470826626,
0.042839206755161285,
-0.05151135474443436,
0.03787078708410263,
-0.022212855517864227,
0.0066369944252073765,
0.01637112721800804,
0.008526367135345936,
0.01292918436229229,
-0.004249696619808674,
0.024365698918700218,
0.038946278393268585,
0.02594744972884655,
-0.009077665396034718,
-0.0276845321059227,
0.0545724481344223,
0.020635399967432022,
0.0007629158208146691,
0.04331309348344803,
-0.03353945538401604,
0.021262193098664284,
0.015671584755182266,
-0.02679293043911457,
-0.023402439430356026,
0.02768569439649582,
0.031937651336193085,
0.04897918179631233,
-0.006533701438456774,
-0.020420854911208153,
0.0207217950373888,
-0.001939377631060779,
0.01715516671538353,
0.05643116682767868,
-0.010719599202275276,
0.00899260863661766,
-0.023806829005479813,
0.0027784164994955063,
-0.0012264337856322527,
-0.009896105155348778,
-0.0024102237075567245,
-0.006017311010509729,
0.0007564836414530873,
-0.0052167801186442375,
0.013694453053176403,
-0.004976911935955286,
0.008323789574205875,
-0.023449143394827843,
0.034453269094228745,
0.04305830970406532,
0.012819627299904823,
-0.01140580978244543,
0.020611654967069626,
-0.027493229135870934,
-0.0505443774163723,
-0.013670912943780422,
0.05185356363654137,
0.026923561468720436,
-0.023282300680875778,
-0.013849489390850067,
-0.017243266105651855,
-0.027587763965129852,
-0.017250731587409973,
-0.03135338053107262,
0.002194348955526948,
-0.04338584095239639,
-0.14550501108169556,
-0.04840100184082985,
0.01850341074168682,
0.010637793689966202,
-0.043550461530685425,
-0.06714332848787308,
0.0007206534501165152,
0.013000596314668655,
0.08318527042865753,
0.0001449796836823225,
-0.0017024081898853183,
0.021361226215958595,
0.013290784321725368,
0.016760993748903275,
0.0036737611517310143,
0.0008264253265224397,
0.036987390369176865,
-0.03574012219905853,
0.007271698676049709,
-0.055561911314725876,
0.02535952627658844,
0.012249465100467205,
0.006149648688733578,
0.009791611693799496,
0.05859561637043953,
-0.024937670677900314,
0.01780940219759941,
0.011606190353631973,
-0.006032851524651051,
0.007239257451146841,
0.07710444927215576,
0.024354001507163048,
0.000021220132111920975,
0.027300985530018806,
0.023127268999814987,
0.04160112142562866,
0.01596827059984207,
0.04770214483141899,
0.037508442997932434,
-0.03395957127213478,
-0.01170775294303894,
-0.02982921153306961,
0.026966698467731476,
-0.008402792736887932,
-0.019060639664530754,
-0.05836554244160652,
0.016174493357539177,
0.025969546288251877,
0.0009409033227711916,
0.03256642818450928,
-0.0014625771436840296,
-0.0002660097961779684,
-0.026254737749695778,
-0.051028866320848465,
-0.0021785241551697254,
-0.06604895740747452,
0.054568324238061905,
0.03773273155093193,
-0.022870879620313644,
0.059925757348537445,
0.02979433164000511,
-0.005227967165410519,
-0.01942640356719494,
-0.07464707642793655,
0.029368383809924126,
0.033883508294820786,
-0.03306960314512253,
-0.005448942072689533,
0.020725969225168228,
0.021087270230054855,
0.03947972506284714,
0.024393640458583832,
0.018829897046089172,
-0.010710693895816803,
-0.05680062249302864,
-0.0006441258592531085,
-0.026799827814102173,
0.014794242568314075,
0.01890607550740242,
0.038087017834186554,
-0.0016508698463439941,
-0.02089444361627102,
-0.03280879557132721,
0.05067788437008858,
-0.02770298905670643,
0.0625462457537651,
0.01879693567752838,
-0.022592075169086456,
0.0020565218292176723,
0.045037560164928436,
-0.01176771055907011,
0.038319896906614304,
0.004909353796392679,
-0.014352870173752308,
-0.0009694997570477426,
0.014977898448705673,
0.029987502843141556,
0.02307753451168537,
-0.03185780718922615,
0.015757180750370026,
-0.0005689879762940109,
0.07191057503223419,
0.04427142068743706,
0.02467973344027996,
-0.04304362088441849,
-0.04499462619423866,
0.02403133176267147,
-0.008044534362852573,
-0.02891628071665764,
-0.0037497009616345167,
0.03639980033040047,
-0.015244678594172001,
0.015516657382249832,
-0.0026546758599579334,
-0.023404046893119812,
0.06667259335517883,
-0.02500009536743164,
-0.010824432596564293,
0.006248192861676216,
-0.04081054404377937,
0.030780037865042686,
-0.022478776052594185,
0.0681089460849762,
0.02320840023458004,
-0.03540564700961113,
0.011728639714419842,
-0.03540875017642975,
-0.02588002197444439,
0.01637984812259674,
-0.04278207942843437,
-0.018620770424604416,
-0.0076263598166406155,
0.01565134897828102,
-0.04115758836269379,
0.00345410592854023,
-0.020510109141469002,
-0.025090757757425308,
-0.008721718564629555,
-0.006294816732406616,
0.03414660692214966,
0.013495325110852718,
0.03005157969892025,
-0.02769123576581478,
-0.057189494371414185,
0.005836904048919678,
-0.06747549027204514,
0.017925115302205086,
0.022010555490851402,
0.0010373127879574895,
0.024578280746936798,
-0.07577134668827057,
0.011893757618963718,
0.09564197808504105,
-0.014605208300054073,
0.025886116549372673,
0.0044669173657894135,
-0.007466463837772608,
-0.047195203602313995,
0.0032154994551092386,
-0.02292831428349018,
-0.00859073456376791,
-0.022540025413036346,
-0.024116722866892815,
0.03457998111844063,
-0.011658402159810066,
0.006115696392953396,
-0.01262352429330349,
-0.03488096594810486,
-0.040237925946712494,
0.0038047977723181248,
-0.01070692390203476,
0.008698460645973682,
-0.04872191324830055,
0.0294207651168108,
0.037298157811164856,
-0.06248278543353081,
-0.004276737570762634,
-0.05277412012219429,
-0.03583948686718941,
-0.0015110644744709134,
-0.008293540216982365,
0.011920911259949207,
-0.007689794059842825,
-0.03685622289776802,
0.11079714447259903,
0.02859112061560154,
-0.05064322426915169,
0.002684677019715309,
0.005871669854968786,
-0.023387888446450233,
-0.04317634925246239,
-0.017535818740725517,
0.059590358287096024,
0.007986735552549362,
0.030199803411960602,
0.04350895434617996,
0.017961258068680763,
-0.011788216419517994,
0.009108608588576317,
-0.033472735434770584,
0.04607505351305008,
-0.010451806709170341,
0.038654450327157974,
0.058693334460258484,
0.015694718807935715,
-0.027170024812221527,
0.006327969022095203,
0.03278777748346329,
0.028241213411092758,
0.0004871831042692065,
-0.0456513836979866,
0.09182929247617722,
0.010687664151191711,
0.02170497179031372,
-0.020076461136341095,
0.05311395227909088,
-0.01411493867635727,
0.0154533376917243,
-0.01773909293115139,
0.03175712749361992,
-0.014434278942644596,
-0.04140225797891617,
0.015852097421884537,
0.026285387575626373,
0.027824940159916878,
-0.024383489042520523,
0.003867239458486438,
0.007646577898412943,
-0.005973187740892172,
0.049663059413433075,
-0.01229448989033699,
-0.04318242147564888,
0.0398118756711483,
0.02134254202246666,
0.04272525757551193,
-0.01626107096672058,
-0.055853426456451416,
-0.0033167332876473665,
-0.025294117629528046,
0.011632142588496208,
0.02233862690627575,
0.030773727223277092,
0.02341309003531933,
0.05652797967195511,
0.028970468789339066,
0.03686312958598137,
-0.0032582913991063833,
0.03936603292822838,
-0.04799850285053253,
0.018743177875876427,
-0.046535175293684006,
-0.021033991128206253,
-0.02319219894707203,
-0.010098865255713463,
-0.0013626524014398456,
-0.0101610217243433,
-0.029278796166181564,
-0.016199259087443352,
0.012384164147078991,
-0.02786179631948471,
0.005133944097906351,
-0.03126732259988785,
-0.037666141986846924,
-0.05315298214554787,
0.02414941042661667,
0.020159436389803886,
-0.031755246222019196,
0.01755453832447529,
0.05939467251300812,
-0.048126984387636185,
-0.02218727394938469,
-0.024919340386986732,
-0.000029237824492156506,
0.015317624434828758,
0.002972191898152232,
0.03761345520615578,
-0.004940103739500046,
0.0012580259935930371,
-0.0062149628065526485,
0.023094136267900467,
0.07473542541265488,
0.010757365263998508,
0.008394242264330387,
-0.0071895490400493145,
-0.025859704241156578,
-0.011286772787570953,
-0.004381836857646704,
0.06757525354623795,
0.006766334641724825,
0.015810247510671616,
0.026816727593541145,
0.007765527814626694,
0.0009590874542482197,
0.01933330111205578,
0.03806569427251816,
0.043849725276231766,
-0.03960370272397995,
-0.06154215335845947,
0.022873777896165848,
-0.036369405686855316,
-0.01355692371726036,
-0.029736774042248726,
-0.040206048637628555,
-0.009946591220796108,
-0.02380523458123207,
0.028718706220388412,
0.018495189025998116,
-0.021788517013192177,
-0.031702570617198944,
0.012233199551701546,
0.006035292986780405,
0.021238356828689575,
0.023870060220360756,
-0.017092464491724968,
0.0495404489338398,
0.04644962400197983,
-0.023636026307940483,
0.020317139104008675,
-0.059714753180742264,
-0.016364851966500282,
0.010795448906719685,
0.02349000610411167,
0.015284360386431217,
-0.020006349310278893,
-0.04603121802210808,
0.025652743875980377,
0.04805254191160202,
0.003042506752535701,
0.008518444374203682,
0.011689235456287861,
-0.017823364585638046,
-0.02167828381061554,
-0.022464454174041748,
-0.040135469287633896,
0.019446026533842087,
0.018359052017331123,
0.0155325373634696,
-0.04231833294034004,
-0.012660671025514603,
-0.037697069346904755,
0.014116471633315086,
-0.006524301134049892,
0.04277629405260086,
0.025393284857273102,
0.011871367692947388,
0.006989809684455395,
0.025810275226831436,
0.02154415100812912,
-0.1029517874121666,
-0.026405218988656998,
0.022424908354878426,
0.005132431164383888,
0.05407783389091492,
-0.06054479628801346,
-0.033658046275377274,
0.0021333578042685986,
-0.02237558551132679,
0.008847781457006931,
0.014034587889909744,
-0.024291295558214188,
0.04054936766624451,
0.012473959475755692,
-0.015978660434484482,
0.039324089884757996,
0.007677030749619007,
-0.030666958540678024,
-0.047001443803310394,
-0.03012162633240223,
0.042469218373298645,
-0.03581627830862999,
-0.0021047855261713266,
-0.018608037382364273,
0.0061303176917135715,
-0.04088222235441208,
0.06213807314634323,
-0.02525014989078045,
-0.00022452294069807976,
-0.025086671113967896,
-0.0328555554151535,
-0.009456655941903591,
0.0028571896255016327,
-0.01307740155607462,
-0.026433652266860008,
-0.018570655956864357,
0.014301678165793419,
-0.003681992646306753,
-0.03051549382507801,
0.02674572356045246,
0.018194077536463737,
-0.023463962599635124,
0.040696416050195694,
-0.01844654232263565,
0.024016426876187325,
-0.015415715053677559,
-0.02087329514324665,
0.023377034813165665,
-0.019419874995946884,
0.010752871632575989,
0.007050919812172651,
-0.024374430999159813,
0.016162632033228874,
-0.04800799489021301,
-0.05264071002602577,
-0.00396384485065937,
-0.01455223374068737,
0.04438285902142525,
-0.024532338604331017,
0.003398084081709385,
0.021585218608379364,
0.029979858547449112,
-0.05132452771067619,
-0.04755639657378197,
-0.003569657914340496,
0.021917453035712242,
-0.02889206074178219,
0.01580021344125271,
0.006975775584578514,
-0.05833031237125397,
-0.015582021325826645,
0.03648209944367409,
0.03169375658035278,
-0.04719388484954834,
0.01742519438266754,
0.004506648052483797,
0.023736508563160896,
0.042388733476400375,
-0.03471051901578903,
0.009074128232896328,
0.011532624252140522,
-0.030683262273669243,
0.010446911677718163,
-0.0051791551522910595,
0.07154034823179245,
-0.007836777716875076,
-0.027849115431308746,
-0.011356301605701447,
-0.032078538089990616,
-0.00034977024188265204,
-0.007842258550226688,
-0.01953274942934513,
0.03778666630387306,
0.011165326461195946,
0.003923122305423021,
0.015844691544771194,
0.019178712740540504,
-0.0020858964417129755,
0.05016766116023064,
0.008382749743759632,
-0.003348675789311528,
-0.03576378524303436,
-0.03862570971250534,
0.05550467222929001,
0.008893833495676517,
0.010731229558587074,
0.01215853076428175,
0.04227975010871887,
-0.0047741662710905075,
0.02329312451183796,
0.038199637085199356,
-0.02893632836639881,
-0.008201957680284977,
-0.02060527913272381,
0.002182623604312539,
0.004647578578442335,
-0.00542044872418046,
-0.03164106234908104,
-0.05172882601618767,
-0.027444127947092056,
0.0076177846640348434,
0.04477629438042641,
-0.002417659852653742,
0.06526196748018265,
0.01980787329375744,
0.02511460892856121,
-0.00936964526772499,
-0.016032010316848755,
-0.003395455190911889,
0.028264597058296204,
0.009847049601376057,
-0.0018662795191630721,
-0.005996200256049633,
0.002222648821771145,
0.026992667466402054,
0.04690893739461899,
-0.047189220786094666,
-0.02100934088230133,
0.024275243282318115,
0.04329775646328926,
-0.003908909857273102,
-0.0025806082412600517,
-0.03695160150527954,
0.04047684371471405,
-0.019719956442713737,
0.03263212367892265,
-0.002214485313743353,
-0.010234508663415909,
0.015530046075582504,
0.011108598671853542,
-0.013774465769529343,
-0.0010504081146791577,
-0.011080315336585045,
-0.026735741645097733,
0.040221117436885834,
0.013860318809747696,
0.007106509059667587,
-0.008411775343120098,
0.03014778159558773,
0.01289906445890665,
-0.018247388303279877,
-0.004729683510959148,
0.023919010534882545,
-0.046528253704309464,
-0.023293321952223778,
-0.03639504313468933,
-0.024484729394316673,
0.05339076742529869,
0.0019282982684671879,
-0.021831708028912544,
0.0007550572627224028,
0.0004931348958052695,
0.008092338219285011,
0.017427101731300354,
-0.001772976596839726,
-0.030966462567448616,
0.05678248777985573,
-0.01845073513686657,
0.004825338255614042,
-0.018241021782159805,
0.015025791712105274,
0.09538982808589935,
0.05325242131948471,
0.028562458232045174,
-0.07160269469022751,
0.008286618627607822,
-0.020639872178435326,
0.023387083783745766,
-0.027133790776133537,
0.01735299453139305,
-0.024372553452849388,
0.03324667364358902,
-0.008996948599815369,
0.045089203864336014,
0.030939603224396706,
0.00975007563829422,
0.05525845289230347,
-0.039516206830739975,
-0.04262354597449303,
-0.007310908287763596,
0.027750445529818535,
-0.0016188446898013353,
0.038652632385492325,
-0.04863718897104263,
0.025617515668272972,
-0.060712385922670364,
0.024875232949852943,
-0.038196861743927,
-0.05565257370471954,
0.018608924001455307,
0.004743458703160286,
-0.0216218251734972,
0.014890246093273163,
-0.008521933108568192,
-0.004855794366449118,
-0.07360712438821793,
0.013515309430658817,
0.026722483336925507,
0.01663176715373993,
0.04659461975097656,
0.021155446767807007,
0.001031540334224701,
0.00705130398273468,
0.0031660799868404865,
0.011557066813111305,
-0.04719345644116402,
0.0026558968238532543,
-0.035007037222385406,
0.07553237676620483,
-0.007853680290281773,
-0.013289602473378181,
0.002929246984422207,
-0.03048323281109333,
-0.01918676868081093,
-0.027585182338953018,
-0.006642600987106562,
-0.03856592997908592,
-0.005513331852853298,
-0.0108719477429986,
0.008324729278683662,
-0.04219377413392067,
0.027512764558196068,
-0.009707371704280376,
0.013474303297698498,
-0.01800159551203251,
-0.001322206575423479,
0.011922628618776798,
0.017084890976548195,
0.019347114488482475,
-0.0005505676963366568,
-0.04233580455183983,
-0.008421835489571095,
-0.0494152270257473,
-0.02316940575838089,
-0.04923178255558014,
0.021712256595492363,
0.02976590022444725,
0.075431227684021,
-0.012174808420240879,
-0.026183785870671272,
-0.011022575199604034,
-0.08742476254701614,
0.022311700507998466,
-0.017456624656915665,
-0.007723908871412277,
-0.02441919781267643,
-0.005372711922973394,
0.039232973009347916,
0.05467873811721802,
-0.03871563449501991,
0.003100806614384055,
0.0027667779941111803,
0.0005068788887001574,
0.025507919490337372,
-0.021247535943984985,
0.0224163681268692,
0.038994912058115005,
-0.03147529438138008,
0.004584275186061859,
-0.020719558000564575,
-0.004903079941868782,
0.017394226044416428,
-0.01647939532995224,
-0.030519891530275345,
0.05326346680521965,
0.026905471459031105,
-0.012270880863070488,
0.04702324420213699,
0.00022119759523775429,
0.03198928013443947,
0.025049295276403427,
0.010390456765890121,
-0.041184503585100174,
-0.027456512674689293,
-0.03961275890469551,
-0.014055613428354263,
-0.019248487427830696,
0.0070953769609332085,
-0.023251134902238846,
-0.0176650770008564,
-0.0028649100568145514,
0.041302312165498734,
-0.0262809656560421,
-0.0022367658093571663,
-0.06307278573513031,
0.042634133249521255,
-0.00007581377576570958,
-0.035784393548965454,
-0.020000984892249107,
0.03792673721909523,
0.0071207270957529545,
-0.030439293012022972,
0.029775621369481087,
0.05055226758122444,
-0.027066489681601524,
0.022598087787628174,
0.007254947442561388,
-0.0011095124064013362,
0.05077150836586952,
0.0030660992488265038,
-0.026472512632608414,
0.040478941053152084,
-0.04453757777810097,
-0.03353555127978325,
0.05101148411631584,
-0.023409252986311913,
0.025053570047020912,
0.02589491754770279,
-0.0193637702614069,
0.017717357724905014,
0.02385856956243515,
-0.016695160418748856,
0.010411295108497143,
-0.020715350285172462,
-0.07465030997991562,
-0.02939693070948124,
-0.03827247768640518,
0.03788705915212631,
-0.013937930576503277,
0.006971235387027264,
0.042767997831106186,
0.0413067452609539,
-0.028912967070937157,
-0.011895381845533848,
-0.0031114763114601374,
0.03557481989264488,
0.02783273160457611,
0.03893142566084862,
0.013036548160016537,
0.009142150171101093,
0.06755395233631134,
-0.04076647013425827,
0.00004801119939656928,
0.00039410567842423916,
-0.0012886089971289039,
-0.10172808915376663,
0.009002783335745335,
0.015899768099188805,
-0.004056916106492281,
0.03956123813986778,
-0.025239301845431328,
0.002803673269227147,
0.012552394531667233,
-0.07122968882322311,
-0.00784776546061039,
-0.011524239555001259,
-0.043613653630018234,
0.026432989165186882,
-0.014114178717136383,
-0.0016184489941224456,
0.09471762925386429,
0.023966489359736443,
0.02542048878967762,
0.017451779916882515,
-0.008292027749121189,
-0.0194178968667984,
-0.014247298240661621,
-0.030803702771663666,
0.03642604127526283,
-0.00012443495506886393,
-0.01720334216952324,
0.03638272359967232,
-0.017131811007857323,
-0.02094263769686222,
0.013574651442468166,
-0.026118168607354164,
-0.0007840535254217684,
-0.02770017832517624,
0.007023702375590801,
0.04138895124197006,
0.008442127145826817,
0.017414310947060585,
0.006506428588181734,
-0.05510362237691879,
-0.009015816263854504,
0.01879602111876011,
0.04237332567572594,
-0.037644483149051666,
0.028202412649989128,
-0.014053584076464176,
-0.03971487283706665,
-0.06422155350446701,
0.01801477186381817,
-0.02609003148972988,
-0.022033531218767166,
0.019635476171970367,
0.0049024662002921104,
-0.0030337197240442038,
-0.004753659013658762,
0.03323822095990181,
-0.02881493978202343,
-0.02644297108054161,
0.019737310707569122,
0.02363424375653267,
0.014198612421751022,
0.029547536745667458,
0.00002752728141786065,
-0.006730765104293823,
0.06363376975059509,
0.0332905650138855,
-0.013372656889259815,
-0.08515022695064545,
0.01125459372997284,
-0.005613978486508131,
-0.024024058133363724,
-0.007494885474443436,
-0.048992712050676346,
-0.03167548030614853,
0.01581437513232231,
0.0162708330899477,
0.01658257097005844,
-0.05370832234621048,
-0.03941197320818901,
0.01576182246208191,
-0.03375401720404625,
0.021094219759106636,
0.008814421482384205,
-0.0046281712129712105,
-0.008917092345654964,
-0.023814456537365913,
-0.009975438006222248,
0.004743852652609348,
0.05602019652724266,
0.0023252961691468954,
-0.00247602048330009,
0.034272145479917526,
-0.010088777169585228,
-0.01666068285703659,
-0.05718490108847618,
-0.025771023705601692,
-0.018800614401698112,
0.01648559235036373,
0.004343025386333466,
-0.00980219803750515,
-0.02006205916404724,
0.02489410527050495,
0.004798043053597212,
-0.004868568852543831,
0.024461297318339348,
0.012024986557662487,
-0.060935795307159424,
0.06967824697494507,
-0.0010714697418734431,
-0.01484652515500784,
0.07769674807786942,
0.004420014563947916,
0.03887208178639412,
0.04022641479969025,
-0.02321942150592804,
-0.01969710923731327,
0.018446417525410652,
-0.02758977934718132,
0.003809902584180236,
0.0038233124651014805,
0.027055205777287483,
0.028259843587875366,
-0.027993807569146156,
0.022146234288811684,
0.03897783160209656,
-0.04283211752772331,
-0.027737364172935486,
0.051464397460222244,
0.012690451927483082,
0.012516802176833153,
0.0407356359064579,
-0.01001556683331728,
0.009623507969081402,
0.009280399419367313,
0.032766543328762054,
0.03718306124210358,
0.047544702887535095,
-0.01932300254702568,
0.02104244753718376,
0.04301781952381134,
-0.005845824256539345,
-0.0032550340984016657,
0.030012056231498718,
0.031540580093860626,
-0.03493952751159668,
-0.010429289191961288,
0.023548193275928497,
-0.02278037928044796,
0.02631772868335247,
0.00590106938034296,
-0.040750276297330856,
0.0664595291018486,
-0.03678244352340698,
0.010611128062009811,
0.019960546866059303,
0.030651304870843887,
0.009725239127874374,
0.011079913005232811,
0.0059627206064760685,
0.06302966177463531,
-0.03210042789578438,
-0.01626976579427719,
-0.04539288207888603,
-0.003633336629718542,
-0.011284047737717628,
-0.037905529141426086,
0.008092966862022877,
0.008573518134653568,
-0.027684584259986877,
-0.022456062957644463,
-0.029759719967842102,
-0.019482746720314026,
-0.008400153368711472,
0.003677843138575554,
0.009606591425836086,
0.04726694896817207,
-0.012967068701982498,
-0.01587262749671936,
-0.045334696769714355,
0.03749619796872139,
-0.06673260778188705,
-0.02381499856710434,
-0.006086578592658043,
-0.009217354469001293,
-0.04971671104431152,
0.012860993854701519
] |
<p>In <a href="http://www.itp.uzh.ch/lectures/jetzer/GR2013/GR.pdf" rel="nofollow">these lecture notes</a> the static isotropic metric is treated as follows (p. 71):</p>
<p>Take a spherically symmetric, bounded, static distribution of matter, then we will have a spherically symmetric metric which is asymptotically the Minkowski metric. It has the form (in spherical coordinates):
$$ds^2=B(r)c^2dt^2-A(r)dr^2-C(r)r^2(d\theta^2+\sin^2\theta d\phi^2)$$
And then it goes on eliminating $C$ and expanding $A$ and $B$ in powers of $\frac{1}{r}$. No explanations are given on why we can assume that form for the metric. Could someone explain why, please?</p>
<p>Personally, I would rather assume the form (in cartesian coordinates):
$$ds^2=f(r)dt^2-g(r)(dx^2+dy^2+dz^2)$$
which would certainly give a spherically symmetric metric, and <em>then</em> change to spherical coordinates, obtaining something looking like:
$$ds^2=f(r)dt^2-g(r)(dr^2+r^2d\theta^2+r^2\sin^2\theta d\phi^2)$$
which looks substantially different from the above. Is this approach wrong? Why?</p>
<p>By the way, don't be afraid of getting technical. I have a pretty good mathematical basis on the subject (a course of one year on differential geometry).</p>
| 9,581 |
[
-0.04400530084967613,
-0.003636831883341074,
0.000654600968118757,
-0.023030458018183708,
0.03516968712210655,
0.01841210573911667,
-0.021901370957493782,
-0.033668018877506256,
-0.007170614320784807,
-0.03904356434941292,
0.028684575110673904,
0.005723371636122465,
0.08024221658706665,
0.0333499014377594,
0.05919525772333145,
-0.041267238557338715,
-0.01637437380850315,
-0.021695967763662338,
-0.01993677392601967,
-0.046785153448581696,
0.03178077191114426,
0.0021676355972886086,
0.023655470460653305,
-0.010008750483393669,
0.012726479209959507,
0.007002625148743391,
0.027960263192653656,
-0.008006091229617596,
-0.008116870187222958,
0.06767772138118744,
-0.02170420065522194,
0.008072980679571629,
-0.0062845186330378056,
0.017161907628178596,
0.014131112955510616,
-0.012056173756718636,
-0.06020508334040642,
-0.018699267879128456,
-0.016654953360557556,
0.011447728611528873,
-0.077720507979393,
-0.002846049377694726,
0.0019362970488145947,
0.06142360344529152,
-0.026230115443468094,
0.027160780504345894,
0.0013788461219519377,
-0.004948481917381287,
0.026806140318512917,
-0.057775650173425674,
0.0758625715970993,
0.026139963418245316,
0.030855078250169754,
0.018078982830047607,
-0.052603088319301605,
0.0023211915977299213,
0.08296015113592148,
0.06450986862182617,
-0.020084703341126442,
-0.041832853108644485,
-0.01785757765173912,
-0.01766257733106613,
-0.014063354581594467,
0.009781429544091225,
0.01985856518149376,
0.027794230729341507,
-0.015837691724300385,
-0.011454896070063114,
0.02660253830254078,
-0.029172096401453018,
-0.012004262767732143,
0.002075083088129759,
0.027742840349674225,
-0.008983217179775238,
0.02076374739408493,
0.0015572787960991263,
0.02708030864596367,
0.008941542357206345,
0.05845744162797928,
0.011644554324448109,
-0.014293748885393143,
0.009964456781744957,
0.02846483513712883,
0.04395819455385208,
0.004678415134549141,
0.018254529684782028,
0.05223727971315384,
0.018210336565971375,
-0.010515572503209114,
0.05881758779287338,
-0.0043947757221758366,
-0.016656436026096344,
0.055592894554138184,
-0.03533095493912697,
-0.026868820190429688,
0.03805521875619888,
-0.03097512386739254,
0.04627341777086258,
-0.023396173492074013,
-0.030267776921391487,
-0.016936026513576508,
-0.00028082128847017884,
0.0012652701698243618,
0.0645006000995636,
0.02130037732422352,
-0.01722453348338604,
-0.060448795557022095,
0.02929263934493065,
-0.02193254977464676,
-0.004397111013531685,
-0.028302671387791634,
0.0016727402107790112,
-0.008841504342854023,
-0.014939581044018269,
0.013807293958961964,
-0.009329406544566154,
-0.004258344881236553,
-0.01425385382026434,
0.011481773108243942,
0.047216977924108505,
0.059622570872306824,
0.02002212591469288,
0.0323089100420475,
-0.04971902444958687,
-0.02314740978181362,
0.011852381750941277,
0.03832569718360901,
-0.004851781763136387,
-0.015990400686860085,
-0.025874225422739983,
0.0105968052521348,
-0.003419761313125491,
-0.018994711339473724,
0.03167368844151497,
-0.006088444497436285,
-0.014669959433376789,
-0.08388598263263702,
-0.05408851057291031,
0.01910749264061451,
0.011658651754260063,
0.05680081248283386,
-0.07157740741968155,
-0.016882985830307007,
-0.0033438540995121002,
0.052454449236392975,
0.02519387938082218,
0.003904558951035142,
0.00465827202424407,
0.09626255929470062,
-0.017784668132662773,
-0.037677161395549774,
0.0021137429866939783,
-0.01736856810748577,
-0.0470125637948513,
0.001970738172531128,
-0.07121118903160095,
0.00228885724209249,
0.005674802698194981,
0.04841836541891098,
-0.0455031618475914,
0.07028240710496902,
-0.04212385043501854,
0.0011175473919138312,
-0.030899526551365852,
0.0033796026837080717,
0.025048337876796722,
0.06776995211839676,
0.0067901103757321835,
0.01577702909708023,
0.012196777388453484,
-0.04318299889564514,
0.023381346836686134,
-0.020629731938242912,
0.006598765030503273,
0.03714360296726227,
-0.042564913630485535,
0.01779758371412754,
-0.0476180836558342,
-0.01746651530265808,
0.007563007529824972,
0.008169404231011868,
-0.030246485024690628,
-0.007665698416531086,
-0.016608498990535736,
-0.014319723471999168,
0.059591323137283325,
0.029421338811516762,
0.013650316745042801,
0.0019710438791662455,
-0.036153241991996765,
-0.0077256979420781136,
-0.030307933688163757,
0.024816568940877914,
0.01711602881550789,
-0.045824382454156876,
0.03660107031464577,
0.012462914921343327,
0.026904376223683357,
0.01326274499297142,
-0.034451890736818314,
0.0039441236294806,
0.0419798381626606,
-0.006225012708455324,
0.003686872310936451,
0.03850279748439789,
0.06670097261667252,
0.043027326464653015,
0.012308206409215927,
-0.03216998651623726,
0.002703240839764476,
-0.031619273126125336,
-0.006141444202512503,
-0.0017342452192679048,
0.032010652124881744,
-0.010040619410574436,
0.0012508692452684045,
0.019823143258690834,
0.034962303936481476,
0.005540483631193638,
0.02272995375096798,
-0.08047188073396683,
0.061055656522512436,
0.07119636237621307,
0.004431089386343956,
0.020367499440908432,
0.06427247822284698,
0.004640344064682722,
0.026044204831123352,
0.01607741042971611,
-0.038172684609889984,
-0.032268114387989044,
0.002296044724062085,
0.05461521074175835,
0.015790587291121483,
-0.06806479394435883,
-0.011535423807799816,
0.01512658130377531,
0.05813133344054222,
0.006062749773263931,
0.012686406262218952,
-0.026804013177752495,
-0.058421459048986435,
0.024704359471797943,
0.0011758800828829408,
0.012810277752578259,
0.0047344909980893135,
0.018166188150644302,
-0.01906970702111721,
-0.013317017816007137,
-0.013110298663377762,
-0.005452014971524477,
0.030518913641572,
-0.016297489404678345,
0.004075527656823397,
-0.0039199283346533775,
0.03429491072893143,
0.039208102971315384,
-0.01885075867176056,
0.01213589683175087,
0.06476301699876785,
0.011350424028933048,
-0.002193400403484702,
-0.05664650723338127,
0.011577284894883633,
0.028410615399479866,
0.01778196543455124,
-0.002517466200515628,
-0.024739280343055725,
0.010187216103076935,
-0.0878731831908226,
-0.032108236104249954,
-0.03426642343401909,
-0.042367659509181976,
-0.012300624512135983,
0.015013998374342918,
0.014994620345532894,
0.02933471091091633,
-0.005155238788574934,
-0.004494828637689352,
-0.012886781245470047,
0.010191241279244423,
-0.018338769674301147,
-0.0007124236435629427,
0.03955685719847679,
-0.01685977540910244,
0.01503309141844511,
-0.046018946915864944,
0.010033470578491688,
0.020455654710531235,
0.016911610960960388,
0.02800118178129196,
-0.01885184273123741,
0.009686609730124474,
-0.025993429124355316,
-0.030548889189958572,
-0.003980455920100212,
0.008399249985814095,
-0.026212969794869423,
-0.004056134726852179,
0.03256154805421829,
-0.01063052099198103,
-0.02395150437951088,
0.0062477425672113895,
-0.024682611227035522,
-0.042813997715711594,
-0.012558357790112495,
0.0004883103538304567,
0.017301449552178383,
-0.024817567318677902,
0.012605429627001286,
0.05454636365175247,
-0.027258528396487236,
0.013289066962897778,
-0.06550733000040054,
-0.04635251313447952,
0.026264891028404236,
0.00421184441074729,
0.0367695577442646,
-0.009349379688501358,
-0.026731988415122032,
0.06890084594488144,
0.0142459562048316,
-0.020680896937847137,
-0.02200775407254696,
0.02692895196378231,
0.01078712660819292,
-0.019172677770256996,
0.004473658744245768,
0.027727950364351273,
-0.020063217729330063,
0.026983097195625305,
0.016782186925411224,
0.0013872422277927399,
0.01762557588517666,
0.008423627354204655,
-0.03483457863330841,
0.01655835658311844,
-0.0002251441910630092,
-0.006814212072640657,
0.04787605255842209,
0.021265748888254166,
-0.003998602274805307,
-0.01741645112633705,
-0.005092945881187916,
0.028688253834843636,
0.01736087165772915,
-0.05707741528749466,
0.0438765324652195,
-0.008589273318648338,
-0.0040528480894863605,
-0.011324708350002766,
0.021899502724409103,
0.0044421423226594925,
-0.03977745398879051,
0.013921353965997696,
0.010133437812328339,
0.05193208530545235,
-0.019714055582880974,
-0.019285954535007477,
0.007906830869615078,
0.04153849184513092,
-0.025031551718711853,
-0.00798302236944437,
-0.02012842893600464,
0.014844207093119621,
0.022936571389436722,
0.02784087508916855,
0.007050740532577038,
0.017444198951125145,
0.041167229413986206,
-0.0008212733082473278,
-0.03279424086213112,
-0.03156476840376854,
0.02982654981315136,
-0.08186356723308563,
-0.00823734700679779,
-0.016636846587061882,
0.008346917107701302,
-0.002924790373072028,
0.04222829267382622,
0.03720313683152199,
0.004283623304218054,
0.017386073246598244,
-0.003527930472046137,
-0.06757529824972153,
0.024993987753987312,
-0.01736391894519329,
-0.004447846207767725,
-0.010362833738327026,
0.013387790881097317,
0.0134284608066082,
0.002175629837438464,
-0.006208790931850672,
-0.0012582434574142098,
-0.0442231222987175,
-0.051257453858852386,
-0.0022368666250258684,
-0.027065476402640343,
-0.07626111060380936,
-0.03616097941994667,
0.038154441863298416,
0.04996794834733009,
-0.035551704466342926,
-0.00006863852468086407,
0.057990044355392456,
-0.038018811494112015,
0.002323342254385352,
-0.030639173462986946,
0.022085295990109444,
0.004518228583037853,
0.021376170217990875,
-0.004367670975625515,
0.014857780188322067,
0.038718510419130325,
-0.0025611775927245617,
0.006372776813805103,
0.04839669167995453,
-0.0027490442153066397,
-0.01936843991279602,
-0.040627166628837585,
-0.030538154765963554,
-0.03566214069724083,
-0.009078706614673138,
0.04179324209690094,
-0.007171304896473885,
0.02523188665509224,
0.028551943600177765,
0.003974673338234425,
0.032842930406332016,
0.04466740041971207,
0.05064808204770088,
-0.02231074869632721,
-0.03724818676710129,
-0.016264859586954117,
-0.03710365295410156,
-0.01281049009412527,
-0.022986939176917076,
0.06418594717979431,
0.001615885877981782,
-0.009893021546304226,
0.009197757579386234,
0.0291429590433836,
-0.01413918286561966,
-0.021733254194259644,
-0.02779572457075119,
-0.013873141258955002,
0.03724098578095436,
0.012377279810607433,
0.023166857659816742,
0.016582002863287926,
0.062004540115594864,
0.08440438657999039,
0.014762943610548973,
-0.011247589252889156,
-0.07925637066364288,
-0.013963490724563599,
0.01967071369290352,
-0.014363063499331474,
0.01140379998832941,
-0.004858682863414288,
-0.07528658211231232,
-0.004973511677235365,
0.03654186800122261,
-0.029678132385015488,
0.06122554838657379,
0.011469647288322449,
-0.024323713034391403,
-0.025259478017687798,
-0.031793732196092606,
-0.05277639254927635,
-0.001417816965840757,
-0.02029034122824669,
0.020740782842040062,
-0.03070526383817196,
0.011602072976529598,
-0.034076713025569916,
0.020664192736148834,
-0.02559683844447136,
0.05119474232196808,
0.0283756572753191,
-0.039150089025497437,
0.0012719887308776379,
0.01462814025580883,
-0.03220013901591301,
-0.05541389435529709,
-0.007335754111409187,
0.020379047840833664,
-0.01751069538295269,
0.028045544400811195,
-0.029630936682224274,
-0.07796335220336914,
0.02171258255839348,
-0.003675753017887473,
-0.001079560024663806,
0.03513091430068016,
-0.03419284522533417,
0.024906586855649948,
0.040289610624313354,
0.01651649735867977,
0.025561919435858727,
0.011790628544986248,
0.02043803595006466,
0.0006925952038727701,
-0.0337875597178936,
0.04024172201752663,
-0.02782580815255642,
-0.015158300288021564,
0.0017621481092646718,
-0.009375863708555698,
-0.04615141078829765,
0.032385483384132385,
0.012113138101994991,
-0.00757637107744813,
-0.021502399817109108,
-0.04467366635799408,
0.04507562145590782,
0.03323792666196823,
0.01833386719226837,
0.034397274255752563,
0.016945622861385345,
0.020101677626371384,
0.020103629678487778,
-0.011597678065299988,
0.01670178771018982,
-0.03185604512691498,
0.0018364361021667719,
0.013253110460937023,
-0.009212152101099491,
0.00347250048071146,
-0.02203376404941082,
-0.02932918630540371,
0.017217116430401802,
-0.06274885684251785,
0.058539003133773804,
-0.020958025008440018,
0.005401360336691141,
0.045173224061727524,
-0.05988343060016632,
-0.04205898195505142,
-0.015961728990077972,
0.00556372944265604,
-0.003107072552666068,
-0.04082587733864784,
-0.01759023219347,
0.03428295999765396,
-0.0037586221005767584,
-0.10197389125823975,
-0.02461869828402996,
0.04062630236148834,
0.0026150161866098642,
-0.01704290322959423,
-0.03927633538842201,
0.02223297208547592,
-0.024858979508280754,
-0.013597880490124226,
-0.03005778044462204,
0.03648902848362923,
-0.005942720454186201,
-0.035668134689331055,
-0.026363404467701912,
0.05846825987100601,
0.0414898544549942,
-0.036098554730415344,
-0.006329000927507877,
0.042623892426490784,
0.0033382028341293335,
0.02071828953921795,
-0.029256343841552734,
0.07199899852275848,
-0.03491707891225815,
-0.003796073142439127,
-0.023158488795161247,
-0.027643639594316483,
-0.036575593054294586,
-0.007265207823365927,
-0.01629352569580078,
0.02447318844497204,
-0.02048792690038681,
-0.0058061834424734116,
-0.018689816817641258,
-0.03351110592484474,
-0.020559590309858322,
0.013867777772247791,
-0.05337291583418846,
0.007546586450189352,
0.0072042751125991344,
-0.023433106020092964,
0.050658196210861206,
-0.006655285134911537,
0.011293403804302216,
-0.0119826290756464,
0.04452437534928322,
-0.006611910182982683,
-0.011627007275819778,
-0.009108999744057655,
0.010474134236574173,
0.02106911689043045,
0.014420997351408005,
-0.0009693180327303708,
0.012258128263056278,
0.009456158615648746,
-0.03088078275322914,
-0.03807620331645012,
-0.026726407930254936,
0.06816807389259338,
0.07001106441020966,
0.0028454919811338186,
0.03496744483709335,
0.004659935366362333,
-0.02357299067080021,
-0.012569272890686989,
-0.06463222205638885,
-0.011056746356189251,
-0.026515519246459007,
0.007438545115292072,
0.057602234184741974,
-0.030397407710552216,
-0.002416612347587943,
0.020587585866451263,
0.03442087396979332,
-0.017537061125040054,
0.014835440553724766,
0.02835169993340969,
0.0065279374830424786,
0.01471126638352871,
0.006864561233669519,
-0.03510485962033272,
0.02697538211941719,
-0.008980887942016125,
0.03940177708864212,
0.006171432789415121,
0.0072805569507181644,
0.04066405072808266,
0.0055159348994493484,
0.030513064935803413,
-0.007184023503214121,
-0.00673620356246829,
-0.04623226076364517,
0.0050309570506215096,
0.04419438913464546,
-0.010780910961329937,
-0.0020473317708820105,
-0.0304507277905941,
0.005642674397677183,
0.007278534583747387,
0.013559883460402489,
-0.029158679768443108,
-0.07166655361652374,
-0.004436154384166002,
-0.01697978749871254,
-0.07376120984554291,
0.06183724105358124,
0.004714661743491888,
-0.023445483297109604,
-0.0011180656729266047,
-0.011780262924730778,
-0.009794379584491253,
0.028303876519203186,
0.01007241103798151,
-0.018083469942212105,
0.09360401332378387,
-0.011169994249939919,
0.01836515963077545,
-0.0028645938728004694,
-0.020585523918271065,
0.1220029965043068,
0.03304043412208557,
0.017348702996969223,
-0.04739117994904518,
0.039028748869895935,
-0.022972187027335167,
0.013369346968829632,
-0.03411969169974327,
0.036979835480451584,
-0.015306880697607994,
0.009456097148358822,
0.011798388324677944,
0.051856040954589844,
0.0041600908152759075,
-0.021329374983906746,
0.03936343640089035,
-0.07437152415513992,
-0.021276243031024933,
0.001623822725377977,
0.04978868365287781,
-0.0004032407305203378,
-0.0025568355340510607,
-0.007226851768791676,
0.05950882285833359,
-0.04457898065447807,
0.01931677758693695,
-0.03198930248618126,
-0.016646139323711395,
-0.030315209180116653,
0.03140620142221451,
-0.04618064686655998,
0.0032819227781146765,
0.022207854315638542,
-0.032345425337553024,
-0.006021761801093817,
0.017313141375780106,
0.03230839595198631,
-0.011452222242951393,
0.04030553996562958,
0.008259585127234459,
-0.004220608621835709,
0.03498492389917374,
0.03281621262431145,
-0.004094602540135384,
-0.03253830969333649,
0.02340550348162651,
-0.0008230457897298038,
0.0843253806233406,
-0.034429095685482025,
0.023172561079263687,
0.009289146400988102,
-0.005030570551753044,
-0.0057000042870640755,
-0.05863015726208687,
0.01645307056605816,
-0.01846117340028286,
0.008163285441696644,
0.0019700322300195694,
-0.005783624015748501,
-0.02096528373658657,
0.03499818220734596,
0.0291811041533947,
0.022407421842217445,
-0.004128120373934507,
0.023294514045119286,
0.016109788790345192,
-0.02698199264705181,
0.07213892787694931,
0.009953418746590614,
-0.01779848523437977,
-0.03372890129685402,
-0.011547909118235111,
-0.028667151927947998,
-0.0027027660980820656,
-0.0052889687940478325,
-0.008665469475090504,
0.0555337592959404,
-0.0034926943480968475,
0.0060056098736822605,
0.013162553310394287,
-0.06889050453901291,
0.017192035913467407,
-0.012842722237110138,
-0.02770913578569889,
-0.026703502982854843,
0.0020078704692423344,
-0.009157691150903702,
0.026767941191792488,
-0.010129692032933235,
-0.0016509783454239368,
-0.02747749350965023,
0.031951893121004105,
-0.031013555824756622,
-0.010793089866638184,
-0.027286304160952568,
0.006745979189872742,
-0.012384156696498394,
-0.025143830105662346,
-0.0043076458387076855,
-0.018454812467098236,
0.043039705604314804,
0.048445604741573334,
-0.023309750482439995,
0.024996956810355186,
0.006906131282448769,
0.008984445594251156,
0.0003990299883298576,
-0.034336745738983154,
0.01547984592616558,
0.02581680752336979,
-0.0006700703524984419,
-0.038486555218696594,
-0.0005289666587486863,
-0.011898143216967583,
-0.011915728449821472,
-0.006611077580600977,
-0.0012537374859675765,
-0.012706519104540348,
-0.008155891671776772,
-0.03716282919049263,
-0.013468394055962563,
-0.06282798945903778,
0.006073259748518467,
-0.019808487966656685,
0.015341811813414097,
-0.025022488087415695,
-0.019809603691101074,
0.034838300198316574,
0.056151133030653,
-0.019769368693232536,
-0.01732267439365387,
0.031139323487877846,
0.01567276194691658,
-0.0111343739554286,
-0.00009863259765552357,
0.006633992772549391,
0.0011251403484493494,
0.02952462248504162,
0.005160698667168617,
-0.031120000407099724,
0.00006311207107501104,
-0.01972905732691288,
-0.07157330214977264,
0.007166098337620497,
-0.014658462256193161,
0.030298998579382896,
-0.0205855630338192,
-0.000509965349920094,
-0.0017228000797331333,
0.050942063331604004,
0.01210415456444025,
-0.012664185836911201,
0.013965924270451069,
-0.05073906481266022,
0.03636104613542557,
-0.045303307473659515,
0.03973914310336113,
-0.015875976532697678,
0.010384541004896164,
0.03085549920797348,
0.004035275895148516,
-0.019057979807257652,
0.0038928694557398558,
-0.01804971881210804,
-0.0324145182967186,
-0.0005372000741772354,
0.027596719563007355,
0.01275106705725193,
0.057893529534339905,
0.04766849800944328,
-0.019550908356904984,
0.015621306374669075,
0.007879321463406086,
0.01486981101334095,
-0.08275631070137024,
-0.024372940883040428,
0.016550159081816673,
-0.009090771898627281,
0.018412793055176735,
-0.056493792682886124,
0.010525002144277096,
0.012539895251393318,
-0.08588582277297974,
-0.02143685705959797,
-0.03772678226232529,
-0.021758118644356728,
-0.02481333166360855,
-0.038994163274765015,
-0.027657965198159218,
0.029106413945555687,
0.049831438809633255,
0.04137018322944641,
0.01908046007156372,
-0.007732166443020105,
-0.03964678570628166,
-0.019002411514520645,
-0.052159134298563004,
0.04846813902258873,
0.004265718162059784,
-0.005182261113077402,
0.08645915240049362,
0.030570462346076965,
-0.02647153101861477,
0.022014228627085686,
-0.051500629633665085,
-0.0016079879133030772,
0.01931462250649929,
-0.006136578973382711,
0.013538992032408714,
-0.0005483701243065298,
0.031176920980215073,
0.019524116069078445,
-0.03485384210944176,
-0.01197298988699913,
0.03852507844567299,
-0.004277382045984268,
-0.0433662123978138,
0.010121814906597137,
-0.005566808395087719,
-0.04174309968948364,
-0.019948357716202736,
0.03314511850476265,
-0.03738216310739517,
-0.0274793840944767,
-0.018278777599334717,
-0.029889041557908058,
0.04380983114242554,
-0.00412809569388628,
0.024239998310804367,
-0.058139409869909286,
0.007610782980918884,
0.02839810401201248,
0.009134650230407715,
-0.006864966358989477,
0.03598501905798912,
-0.0013858933234587312,
-0.043644215911626816,
-0.03578271344304085,
-0.04044993221759796,
0.019592631608247757,
-0.021575510501861572,
-0.010852235369384289,
-0.014560389332473278,
-0.02184274233877659,
0.03869123384356499,
-0.011410373263061047,
-0.021454693749547005,
0.04129240661859512,
0.05700713396072388,
-0.007019639015197754,
0.01033156830817461,
-0.03352992609143257,
-0.013520796783268452,
-0.08629260957241058,
0.011355945840477943,
0.006428182125091553,
-0.023223914206027985,
-0.006001540459692478,
-0.015863357111811638,
-0.015976186841726303,
0.01720000058412552,
0.06773803383111954,
0.007031548302620649,
0.006656280718743801,
0.015466052107512951,
0.006108607165515423,
0.025724712759256363,
-0.07579685002565384,
-0.0033551137894392014,
0.02138134464621544,
0.003511576447635889,
0.028807001188397408,
0.006652504671365023,
-0.006311274599283934,
0.01934121549129486,
0.021956702694296837,
-0.010736128315329552,
0.05192815139889717,
0.04980688914656639,
-0.01784317009150982,
0.03722049668431282,
-0.008784197270870209,
-0.018102964386343956,
0.07976170629262924,
0.01972385123372078,
0.0025405348278582096,
0.043251533061265945,
0.005783530883491039,
-0.02874218113720417,
0.03840943053364754,
-0.047358278185129166,
-0.03808257728815079,
-0.018618827685713768,
-0.01685340330004692,
0.017792610451579094,
-0.013039232231676579,
-0.012624727562069893,
0.05626269429922104,
-0.035057634115219116,
-0.01238167379051447,
0.046812936663627625,
0.012730072252452374,
0.035234302282333374,
0.03411457687616348,
-0.028977859765291214,
0.03470412269234657,
0.0033464774023741484,
-0.013966027647256851,
0.03713175281882286,
0.032057587057352066,
0.025028983131051064,
-0.016522884368896484,
0.02759760618209839,
-0.034121111035346985,
-0.0027081926818937063,
-0.01704108901321888,
0.07461776584386826,
-0.03489634394645691,
-0.005083257332444191,
0.010813377797603607,
-0.00006371391646098346,
0.021780729293823242,
-0.000014902612747391686,
-0.007875624112784863,
0.039959486573934555,
-0.014763840474188328,
0.010178144089877605,
-0.0398787222802639,
-0.028840219601988792,
-0.03504186496138573,
0.06404463946819305,
0.047619421035051346,
0.033720117062330246,
-0.009170562960207462,
0.021426379680633545,
-0.022071316838264465,
-0.00474988017231226,
0.021329592913389206,
0.004534667357802391,
0.01516900397837162,
0.002071158727630973,
-0.0076651806011796,
0.004067956004291773,
-0.032693538814783096,
-0.01612219586968422,
-0.03144802153110504,
0.05769065394997597,
0.03532203286886215,
0.03217580169439316,
-0.019984208047389984,
0.01648368500173092,
-0.039744507521390915,
0.07560639083385468,
-0.06782559305429459,
-0.01279183104634285,
-0.002886161208152771,
-0.01320625003427267,
-0.0012319411616772413,
-0.034115299582481384
] |
<p>For an harmonic oscillator we can write the Hamiltonian eigenvalues in the basis of the amplitude eigenvalues : for example the ground state is a gaussian : $⟨x|0⟩=a.e^{-b.x^{2}}$. </p>
<p>I was wondering if we can do that for the energy states of a field : can we calculate $⟨a|n⟩$ with |a⟩ an eigenvalue of the field operator $\phi$ (let's say a Klein-Gordon field) ?</p>
<p>I failed to carry out the ladder operator method, but I think we should be able to calculate (or at least have implicit equation of) any operator eigenvalue in any other operator eigenvalue basis, or is there something obvious that I missed ? </p>
<p>Because we always play to write state in all the basis we can : spin on position, energy on spin etc ..., but I have never seen in classes or in books energy states of a field written in the field operator basis.</p>
<p>EDIT : I'll look in the reference given by Peter : "Weinberg I" and try to explain how to do.</p>
<p>EDIT : I didn't find the answer in the given reference :(</p>
| 9,582 |
[
0.012282755225896835,
-0.006540230009704828,
0.010375740006566048,
0.0099342567846179,
0.048702504485845566,
-0.009786131791770458,
-0.055431071668863297,
-0.04750288650393486,
0.013752888888120651,
-0.030360886827111244,
0.010633143596351147,
-0.019961753860116005,
0.042340245097875595,
0.010058626532554626,
0.026708289980888367,
-0.009012374095618725,
-0.016646333038806915,
-0.03055759333074093,
-0.02300272509455681,
-0.03416733071208,
0.02710331231355667,
0.0376870296895504,
-0.021732069551944733,
0.008123960345983505,
-0.023099150508642197,
0.022857731208205223,
0.02370375767350197,
0.03019695356488228,
0.001035009860061109,
0.06429614871740341,
0.006430550944060087,
-0.055305320769548416,
0.0314527302980423,
0.051878731697797775,
0.044237393885850906,
-0.012904895469546318,
-0.055517397820949554,
-0.04838200658559799,
0.014381755143404007,
0.01763991080224514,
-0.05525442585349083,
-0.05480761453509331,
-0.004691427107900381,
0.0371086485683918,
0.008281695656478405,
-0.019279157742857933,
-0.0027079861611127853,
-0.03652188926935196,
0.04227793216705322,
-0.03505871817469597,
0.06755013018846512,
-0.003161112777888775,
-0.008700013160705566,
-0.017905566841363907,
-0.03338393196463585,
0.01268916018307209,
0.06040840595960617,
0.0339033417403698,
0.016053231433033943,
-0.07625991106033325,
-0.029930999502539635,
-0.03604107350111008,
-0.017293332144618034,
-0.027990369126200676,
-0.03380418196320534,
-0.0199555866420269,
0.010979719460010529,
-0.0063223401084542274,
0.016839485615491867,
-0.011571873910725117,
-0.02293718233704567,
-0.0009193256846629083,
0.031362563371658325,
-0.06258676946163177,
0.019584903493523598,
-0.011996383778750896,
0.015622606500983238,
-0.0002398391516180709,
0.01973060704767704,
-0.004487400874495506,
-0.04010218754410744,
0.03281617909669876,
0.021267710253596306,
0.007524736225605011,
-0.031412214040756226,
-0.0010121213272213936,
0.05611180141568184,
-0.011292917653918266,
-0.002392361406236887,
0.043314047157764435,
0.011404763907194138,
0.019762031733989716,
0.035434771329164505,
-0.04669639468193054,
-0.03694084659218788,
0.015026861801743507,
0.012941963970661163,
0.02525728940963745,
0.008026073686778545,
-0.014920435845851898,
0.01118007767945528,
-0.037363454699516296,
0.014069931581616402,
0.09109346568584442,
-0.02440992183983326,
0.002088072942569852,
-0.03211086243391037,
0.03164902329444885,
-0.01889936998486519,
-0.04228932783007622,
-0.025081923231482506,
-0.008833094500005245,
0.001427907613106072,
-0.0006643426022492349,
0.01285216398537159,
-0.047420866787433624,
0.018578965216875076,
-0.012083301320672035,
0.036014728248119354,
0.07505356520414352,
0.04653787240386009,
-0.030911237001419067,
0.04979461431503296,
-0.02469777502119541,
-0.06265135854482651,
-0.008899805136024952,
0.021005718037486076,
-0.015825292095541954,
-0.059088289737701416,
-0.03436152637004852,
0.013972611166536808,
-0.007319648750126362,
-0.003227597801014781,
0.011890692636370659,
0.049036748707294464,
-0.03442282974720001,
-0.11084864288568497,
-0.07172240316867828,
-0.005991674959659576,
-0.057354580610990524,
-0.020725799724459648,
-0.07152524590492249,
-0.015089155174791813,
0.040744878351688385,
0.06292879581451416,
0.0017043728148564696,
0.006336713209748268,
0.024348920211195946,
0.05104626342654228,
0.009080061689019203,
0.018177280202507973,
-0.050221703946590424,
-0.023057525977492332,
-0.04721001535654068,
-0.007422397378832102,
-0.03554064407944679,
0.03313727676868439,
0.0215475931763649,
-0.018429145216941833,
0.00978870876133442,
0.08858510851860046,
-0.05473467335104942,
0.007085795979946852,
0.02288164757192135,
0.012582008726894855,
-0.020894361659884453,
0.07611119747161865,
0.02397247776389122,
0.03155795484781265,
0.041518453508615494,
-0.007582915015518665,
0.02268301323056221,
0.01318787969648838,
0.0434359572827816,
0.06734340637922287,
-0.055033326148986816,
-0.05551278591156006,
-0.03986131399869919,
0.02389528602361679,
-0.014652026817202568,
-0.03286796435713768,
-0.0589553564786911,
0.007106343284249306,
0.010317201726138592,
-0.007216604892164469,
0.04291163384914398,
0.005384340416640043,
0.018848184496164322,
0.00006625598325626925,
-0.050146736204624176,
0.02880273200571537,
-0.05132810398936272,
0.0580315887928009,
0.019213629886507988,
-0.0010998595971614122,
0.05553080141544342,
0.037194110453128815,
0.0014858683571219444,
-0.039072390645742416,
-0.05539951100945473,
0.025311408564448357,
0.03163156658411026,
0.006149941124022007,
-0.058411236852407455,
0.025147873908281326,
0.014223016798496246,
0.02284078113734722,
0.0010992770548909903,
0.07736155390739441,
-0.03903341293334961,
-0.02828381396830082,
0.016965873539447784,
-0.013045551255345345,
0.036524124443531036,
0.003872221102938056,
0.003065616823732853,
-0.02698921225965023,
-0.036851100623607635,
-0.02093706838786602,
0.03476152941584587,
-0.04698292538523674,
0.0459105558693409,
0.04362287372350693,
-0.00481642410159111,
0.0088036535307765,
0.017564138397574425,
0.005397007334977388,
0.019035855308175087,
-0.006340665742754936,
-0.010428006760776043,
-0.030855078250169754,
-0.021720459684729576,
0.04506527632474899,
0.002614688128232956,
-0.057515695691108704,
0.00032848393311724067,
0.06437794119119644,
0.03805675357580185,
0.061068952083587646,
0.02303493767976761,
-0.032145675271749496,
-0.011706904508173466,
0.006441702134907246,
0.027846718207001686,
0.012782611884176731,
0.023795848712325096,
0.04189104959368706,
0.010188926942646503,
0.046619415283203125,
0.005631881766021252,
-0.012829938903450966,
0.04834260791540146,
-0.06935504078865051,
-0.007816546596586704,
0.020018935203552246,
-0.04393600672483444,
0.042863018810749054,
-0.05664530768990517,
0.0548909492790699,
0.017381658777594566,
-0.04765838757157326,
-0.015703564509749413,
0.01350318267941475,
-0.015481225214898586,
0.00932359043508768,
-0.04944051802158356,
-0.057882167398929596,
0.004830388352274895,
0.010627455078065395,
-0.015321416780352592,
0.013682439923286438,
-0.02063501998782158,
-0.012048709206283092,
-0.008909245021641254,
0.02340841107070446,
0.04071405157446861,
-0.01802249625325203,
0.008837138302624226,
-0.0133474450558424,
0.007290184497833252,
-0.0021578497253358364,
-0.03626251965761185,
0.02113170735538006,
0.008336896076798439,
-0.04775585979223251,
0.017046373337507248,
-0.06297317147254944,
-0.016497058793902397,
0.00953628122806549,
-0.04232741519808769,
-0.018270162865519524,
0.006772438529878855,
-0.009527926333248615,
-0.022621765732765198,
-0.004835410974919796,
-0.004472862463444471,
-0.0011214377591386437,
-0.020359793677926064,
0.013837882317602634,
0.019088812172412872,
-0.013010011054575443,
-0.021522849798202515,
0.003077142871916294,
0.017035899683833122,
-0.029518382623791695,
-0.00510785449296236,
-0.021091783419251442,
0.03457304462790489,
-0.019049502909183502,
0.06652748584747314,
0.013533011078834534,
-0.007794785778969526,
-0.004821932874619961,
-0.06592388451099396,
-0.04124800115823746,
0.015657179057598114,
0.011399839073419571,
0.01353432796895504,
-0.01528117060661316,
0.00015057723794598132,
0.09711402654647827,
0.0408458337187767,
-0.04007792845368385,
-0.030250567942857742,
-0.0006473978282883763,
0.016337251290678978,
-0.01873469166457653,
-0.007310287561267614,
0.007001053541898727,
-0.022486548870801926,
0.046808674931526184,
-0.00107810297049582,
-0.025044752284884453,
0.01765620708465576,
0.0035561900585889816,
-0.0036579619627445936,
-0.005728122778236866,
0.019160687923431396,
0.03090870939195156,
0.05752044543623924,
-0.035189006477594376,
-0.011462227441370487,
0.025588909164071083,
0.02992062270641327,
0.006304614245891571,
-0.01585209369659424,
-0.018628006801009178,
0.03474300727248192,
-0.01077544316649437,
0.020757412537932396,
-0.020958835259079933,
0.03783830627799034,
0.004257691092789173,
0.012856838293373585,
-0.013433423824608326,
0.050120528787374496,
0.012406118214130402,
-0.02285994589328766,
0.016246210783720016,
0.026650836691260338,
0.02899283543229103,
-0.026043418794870377,
-0.006306185387074947,
-0.0046929046511650085,
-0.006923965644091368,
0.04415694251656532,
-0.028994791209697723,
-0.0683211162686348,
0.03579255938529968,
0.052454520016908646,
0.003805645741522312,
-0.01934780552983284,
-0.02591339685022831,
0.00575318094342947,
-0.0691562369465828,
-0.025038141757249832,
0.01686870865523815,
0.04254855960607529,
0.008610821329057217,
0.06136338412761688,
0.013986827805638313,
0.013028954155743122,
0.015579256229102612,
0.00957512017339468,
-0.0572652593255043,
-0.016429787501692772,
-0.05409016087651253,
0.010746992193162441,
0.022158058360219002,
-0.024797961115837097,
0.01947331614792347,
0.039354048669338226,
-0.03502640500664711,
-0.010184633545577526,
0.0008274043793790042,
-0.041343703866004944,
0.01847766526043415,
-0.023223629221320152,
-0.03646572306752205,
-0.00975128822028637,
0.041166435927152634,
0.007488367147743702,
-0.014530555345118046,
-0.007253556977957487,
0.04987470805644989,
-0.032018475234508514,
0.022679926827549934,
0.001770342350937426,
0.00870937667787075,
0.006909593008458614,
0.05159810185432434,
0.06789703667163849,
0.04963406175374985,
-0.011782528832554817,
-0.03829343616962433,
-0.010415562428534031,
0.05331647768616676,
0.007265662308782339,
-0.017942147329449654,
0.04409772902727127,
-0.014943416230380535,
0.013103536330163479,
-0.012821916490793228,
0.08037020266056061,
-0.04022449627518654,
0.02919822931289673,
0.014639830216765404,
0.010839247144758701,
-0.019854269921779633,
0.04147075116634369,
0.0567324198782444,
0.00820885319262743,
0.003233938943594694,
-0.026045700535178185,
0.008401877246797085,
-0.027412619441747665,
-0.023963935673236847,
-0.04397029057145119,
-0.01620573177933693,
-0.0038514952175319195,
0.004084676504135132,
0.024779070168733597,
0.0008636306738480926,
0.005618573632091284,
-0.005653482396155596,
0.007490113377571106,
0.013456694781780243,
-0.008778640069067478,
-0.009010964073240757,
-0.019657978788018227,
0.009321348741650581,
0.04674368351697922,
0.03345932066440582,
0.01859649084508419,
-0.052715860307216644,
-0.013156570494174957,
0.036347709596157074,
0.02175699546933174,
0.042693719267845154,
-0.019065499305725098,
-0.005783468019217253,
-0.03936157748103142,
0.050888143479824066,
-0.0033025210723280907,
0.03992791101336479,
-0.005512894596904516,
-0.021743321791291237,
-0.015535477548837662,
-0.014983496628701687,
-0.015999585390090942,
0.024521740153431892,
-0.01701723225414753,
0.008954805321991444,
-0.03535353019833565,
-0.0028332751244306564,
-0.014609063044190407,
0.0157844927161932,
-0.017637252807617188,
0.0422203354537487,
0.03464681655168533,
0.0082431361079216,
0.017317069694399834,
0.036746636033058167,
-0.022225230932235718,
-0.08110543340444565,
-0.0005521273124031723,
0.04111848771572113,
0.014072851277887821,
0.014983524568378925,
-0.013406144455075264,
-0.04225509241223335,
0.016140852123498917,
0.03476674482226372,
-0.008732707239687443,
0.010028894059360027,
-0.03501005470752716,
0.061092592775821686,
0.017189670354127884,
0.016498157754540443,
0.06752175837755203,
0.04274292290210724,
-0.024064119905233383,
-0.03545393422245979,
-0.01890106126666069,
0.027870388701558113,
-0.030102865770459175,
0.02163657173514366,
-0.02115122228860855,
0.007930838502943516,
-0.026655640453100204,
0.03512090817093849,
-0.0429726168513298,
0.0036989981308579445,
0.0263680312782526,
-0.0246814526617527,
-0.02144966833293438,
0.023035384714603424,
-0.013898814097046852,
-0.021193863824009895,
-0.004153674468398094,
0.03197046369314194,
-0.005731120239943266,
-0.015919938683509827,
0.006800770293921232,
-0.00853466335684061,
-0.01531957183033228,
0.03182578459382057,
0.0055335271172225475,
0.05918382480740547,
-0.05811963602900505,
-0.0018299996154382825,
0.0258539617061615,
-0.08115261793136597,
0.019253818318247795,
-0.03268856927752495,
-0.00759093789383769,
-0.008067569695413113,
-0.039014674723148346,
-0.05358753353357315,
0.004465544130653143,
0.011242938227951527,
0.04436695575714111,
-0.014314833097159863,
-0.0072258333675563335,
0.024070901796221733,
0.021377524361014366,
-0.08222556859254837,
-0.04719748720526695,
-0.005930230487138033,
0.006787856109440327,
0.01510502677410841,
-0.006924487184733152,
0.015191245824098587,
-0.032631780952215195,
0.002791503444314003,
0.023107467219233513,
0.030923254787921906,
-0.054274436086416245,
-0.006536500528454781,
0.030568735674023628,
0.044066451489925385,
0.029764875769615173,
0.008740444667637348,
-0.02588408999145031,
0.012139789760112762,
-0.016465211287140846,
0.006123797036707401,
0.018692687153816223,
0.0604175440967083,
-0.01879660040140152,
-0.01949787512421608,
-0.03132767230272293,
0.01305127888917923,
0.03320934996008873,
0.018823159858584404,
-0.0071465326473116875,
0.041564296931028366,
0.03148539364337921,
0.021715911105275154,
0.03006540983915329,
-0.001398931723088026,
-0.0032916555646806955,
0.0304661113768816,
-0.027257539331912994,
-0.035448964685201645,
-0.025700213387608528,
-0.00806614849716425,
-0.005268819164484739,
-0.006370168644934893,
-0.026707839220762253,
-0.012517477385699749,
0.08466251194477081,
0.0064848121255636215,
0.001611718675121665,
0.03063761070370674,
-0.01872130110859871,
-0.002231702208518982,
-0.005293688271194696,
0.014866946265101433,
0.0037449037190526724,
0.0036116137634962797,
-0.02719261683523655,
-0.032545872032642365,
-0.028276434168219566,
0.010246483609080315,
0.04713189974427223,
0.012256288900971413,
0.04307394474744797,
0.03388975188136101,
0.03576107695698738,
-0.015649765729904175,
-0.007449623662978411,
-0.03158387541770935,
0.024946965277194977,
-0.024134056642651558,
0.06692356616258621,
-0.022153455764055252,
0.010860815644264221,
0.025447748601436615,
0.030002959072589874,
-0.021653763949871063,
0.020843246951699257,
0.01091392245143652,
0.02876252308487892,
0.018287459388375282,
0.016060736030340195,
-0.06814815104007721,
0.03477595001459122,
0.0032184456940740347,
0.016187584027647972,
0.0067841061390936375,
-0.05642811581492424,
0.021467868238687515,
0.026827163994312286,
0.02916114404797554,
-0.003670852165669203,
-0.037485040724277496,
-0.0567282997071743,
0.03159439191222191,
-0.001542885904200375,
-0.00018284308316651732,
-0.012680552899837494,
0.020597824826836586,
0.010766474530100822,
0.00895710289478302,
0.030122188851237297,
0.017961591482162476,
-0.029280463233590126,
-0.035165511071681976,
-0.060224249958992004,
-0.08098553121089935,
-0.01118349377065897,
0.0069223553873598576,
-0.018883205950260162,
0.02745092287659645,
-0.02050738036632538,
0.019161377102136612,
0.014584281481802464,
0.022047484293580055,
-0.011950379237532616,
0.0566522441804409,
0.007069408427923918,
0.00672219367697835,
0.010076111182570457,
0.018428610637784004,
0.12172331660985947,
0.07150857895612717,
0.009474393911659718,
-0.09999099373817444,
0.006857086438685656,
0.002336601261049509,
0.0015369962202385068,
-0.029705427587032318,
0.017381107434630394,
-0.011234503239393234,
-0.008951041847467422,
-0.03792070969939232,
0.08742426335811615,
-0.0008127095061354339,
-0.017182983458042145,
0.04446833208203316,
-0.028664452955126762,
-0.03596305847167969,
0.029253123328089714,
0.03212831914424896,
-0.002349037444218993,
0.0025535128079354763,
-0.016840411350131035,
0.008209018968045712,
0.010745726525783539,
0.01560275163501501,
-0.024724476039409637,
-0.0498577244579792,
0.014337781816720963,
0.0012676750775426626,
-0.04482745751738548,
-0.011041712947189808,
0.011321824975311756,
0.018044203519821167,
-0.022521937265992165,
0.019475528970360756,
0.004800452850759029,
0.025472046807408333,
0.035644251853227615,
0.042009707540273666,
-0.007941172458231449,
0.009685395285487175,
0.01633787900209427,
0.003541648620739579,
-0.017026841640472412,
-0.028620382770895958,
-0.02678290195763111,
0.06010248512029648,
-0.018297046422958374,
-0.02041163295507431,
-0.013511373661458492,
-0.030866334214806557,
0.03286721929907799,
-0.037152137607336044,
-0.011342955753207207,
-0.016130264848470688,
0.04330600053071976,
-0.049284711480140686,
0.010298270732164383,
-0.02365776151418686,
-0.00806557945907116,
0.0027277797926217318,
0.0008285798248834908,
-0.0032680903095752,
0.0019522779621183872,
0.03856215253472328,
-0.02906353585422039,
0.025416282936930656,
0.004221644718199968,
-0.04270989075303078,
0.03300224244594574,
-0.044713474810123444,
-0.05519416555762291,
-0.04486212506890297,
0.022746672853827477,
-0.007911215536296368,
0.022935491055250168,
0.01892736554145813,
0.007710225880146027,
-0.0182657390832901,
-0.06668571382761002,
0.008656546473503113,
-0.0189951341599226,
-0.014868163503706455,
0.007105668541043997,
0.0025240620598196983,
0.017863232642412186,
0.040405385196208954,
0.008676376193761826,
-0.005832211580127478,
0.007734013721346855,
-0.0100927809253335,
0.054564643651247025,
-0.023868318647146225,
-0.043916694819927216,
0.013459756039083004,
-0.02389942668378353,
-0.007924419827759266,
-0.040975313633680344,
-0.007862060330808163,
0.005225309170782566,
0.005498819053173065,
-0.008890405297279358,
0.043712593615055084,
-0.01680750586092472,
-0.04899619147181511,
-0.01010871585458517,
-0.03477419167757034,
0.013411217369139194,
0.020098285749554634,
0.023566432297229767,
-0.045011136680841446,
-0.05982362478971481,
-0.03643962740898132,
0.013061733916401863,
0.017495200037956238,
0.022910375148057938,
-0.04381653293967247,
-0.007905269972980022,
0.005911637097597122,
-0.006765786558389664,
-0.019184600561857224,
0.002618956146761775,
-0.05064920336008072,
0.013050256296992302,
0.0064546698704361916,
-0.009632769040763378,
-0.0007711078505963087,
0.020078154280781746,
0.00422577653080225,
-0.022458339110016823,
0.04022534191608429,
0.07314562797546387,
-0.021807879209518433,
0.014594100415706635,
0.02535288780927658,
0.011648069135844707,
0.028807638213038445,
0.019572850316762924,
-0.01821095123887062,
0.007454807870090008,
-0.04840724170207977,
-0.001992312725633383,
0.0466642789542675,
-0.012570198625326157,
0.022468937560915947,
0.041332051157951355,
-0.020146461203694344,
-0.010528254322707653,
0.017966538667678833,
-0.01686881110072136,
0.012027262710034847,
0.022974351420998573,
-0.04737212136387825,
-0.007098246831446886,
-0.005316420923918486,
0.014194762334227562,
0.0161282978951931,
0.007466410752385855,
-0.002896377583965659,
0.0190153568983078,
0.010625890456140041,
-0.0019005457870662212,
0.021610833704471588,
0.023327447474002838,
0.03616373613476753,
0.053274452686309814,
-0.013715589419007301,
0.003169785952195525,
0.039247214794158936,
-0.021801121532917023,
0.029898343607783318,
0.0317474901676178,
0.05557787045836449,
-0.07977765053510666,
-0.018914060667157173,
-0.009438258595764637,
0.027632949873805046,
0.033860884606838226,
-0.0603925958275795,
0.023617858067154884,
0.011965117417275906,
-0.06486313045024872,
0.045546334236860275,
-0.0007879417389631271,
0.027470696717500687,
-0.014714041724801064,
0.010818729177117348,
-0.03193650394678116,
0.047242093831300735,
0.026525072753429413,
0.043667275458574295,
0.012925978749990463,
-0.005871855653822422,
-0.005823427811264992,
-0.027308180928230286,
-0.011725219897925854,
0.044023457914590836,
0.006275918800383806,
-0.04281128942966461,
0.050897955894470215,
-0.03106032870709896,
-0.02887844666838646,
0.02021571435034275,
-0.026513947173953056,
-0.02041635476052761,
-0.03712635859847069,
0.014037585817277431,
-0.01531460601836443,
0.055182650685310364,
0.01328849047422409,
0.0005885966820642352,
-0.03500887006521225,
0.010364942252635956,
0.0415864922106266,
0.010203463956713676,
-0.012288156896829605,
0.007169931195676327,
0.000042519164708210155,
-0.02654007077217102,
-0.0578848235309124,
0.06143076717853546,
-0.0059911455027759075,
-0.017758050933480263,
-0.009509802795946598,
-0.01158156804740429,
0.02401326596736908,
-0.026966726407408714,
0.010164262726902962,
-0.039526358246803284,
-0.015570455230772495,
-0.025285422801971436,
-0.0002971323556266725,
0.008801332674920559,
0.013441404327750206,
0.002191676991060376,
-0.05259474739432335,
0.023402810096740723,
0.03418290615081787,
-0.051422182470560074,
-0.07478994876146317,
-0.004193325527012348,
0.006712743081152439,
-0.007888328284025192,
0.010169991292059422,
-0.027657827362418175,
-0.054256632924079895,
0.01354624330997467,
-0.022545281797647476,
0.022387748584151268,
-0.047632038593292236,
-0.03252425789833069,
-0.005503514315932989,
-0.044634055346250534,
0.019473759457468987,
0.04363376274704933,
-0.00020264404884073883,
-0.011755973100662231,
-0.008964491076767445,
0.016153376549482346,
-0.012110295705497265,
0.050357524305582047,
-0.03240778669714928,
-0.006429868284612894,
-0.023207684978842735,
-0.025007901713252068,
-0.017448991537094116,
-0.00557249179109931,
0.01217669527977705,
-0.0170635636895895,
-0.03134316951036453,
-0.003942223731428385,
-0.0022211552131921053,
-0.01854860968887806,
0.021981215104460716,
0.028882339596748352,
0.015361646190285683,
-0.009799475781619549,
-0.02537541091442108,
-0.01813141070306301,
0.05511290207505226,
-0.010359497740864754,
-0.01649145409464836,
0.06127425283193588,
-0.028466884046792984,
0.007166494149714708,
0.058488309383392334,
-0.05152963474392891,
-0.01637938804924488,
0.020798511803150177,
-0.04313613101840019,
-0.04638752341270447,
0.025554902851581573,
-0.011712098494172096,
0.006597964093089104,
-0.018104296177625656,
0.0034244509879499674,
0.039928138256073,
-0.02282492257654667,
-0.018050801008939743,
0.04937225580215454,
0.006373744923621416,
0.04011845961213112,
0.01915300264954567,
0.021025508642196655,
0.04461485520005226,
0.013027050532400608,
0.006346851587295532,
0.029639732092618942,
0.0094850342720747,
0.03597330302000046,
0.014558358117938042,
0.057246655225753784,
-0.026735130697488785,
0.014306697063148022,
0.020378950983285904,
0.016727475449442863,
-0.024884512647986412,
-0.0020474030170589685,
0.05445970222353935,
0.0018076450796797872,
-0.006597554311156273,
0.010343912057578564,
-0.051956649869680405,
0.07675065100193024,
-0.02517932467162609,
0.004786788020282984,
-0.07145519554615021,
0.005145422648638487,
-0.01767035387456417,
-0.0044907270930707455,
0.007366959936916828,
0.055202417075634,
-0.015519917011260986,
0.010039538145065308,
-0.015129173174500465,
-0.004559008404612541,
0.018793854862451553,
-0.06385521590709686,
-0.03200599178671837,
0.0004116066556889564,
-0.005727960728108883,
-0.010338849388062954,
-0.007611197419464588,
-0.015498899854719639,
-0.0013831699034199119,
-0.008853491395711899,
0.02209480293095112,
0.04224781692028046,
0.01068140659481287,
-0.009257897734642029,
-0.03494853153824806,
0.06658551841974258,
-0.03589601069688797,
-0.014410115778446198,
-0.014151988551020622,
-0.009008043445646763,
-0.006167986895889044,
0.04410198703408241
] |
<p>Two inertial frames K and k’ are considered. They are in relative uniform motion along the x-x’ direction with relative speed =v.
In the frame K’ we have a cuboidal piece of dielectric [at rest wrt K’]with a flat face perpendicular to the x-x’ direction, that is, this particular face is parallel to the y-z direction.The dielectric is homogeneous and isotropic within itself.
We now consider Maxwell’s equations [in a medium] wrt the dielectric in the rest frame of the dielectric,ie,K’.
If these equations are transformed, they should retain their form in K[according to the first postulate of SR]. But the individual values of the variables may change</p>
<p>With this information we proceed into the paradox.</p>
<p>Speed of light in the dielectric as observed from k’=nc [n is a positive fraction less than 1]</p>
<p>Relative speed between the frames, v=cn’[n’ is also a positive fraction less than 1]</p>
<p>For normal incidence:
Speed of light in the dielectric as observed from K[From Velocity-Addition Rule of SR]:
$v=\frac{nc+n’c}{1+nn’}$ ------------------- (1)</p>
<p>For oblique ray inside the medium at $\theta$ degrees degrees with respect to the x’ axis in the K’ frame:</p>
<p>$v’_x=ncCos (\theta)$</p>
<p>$v’_y=nc Sin(\theta)$</p>
<p>$v’_z=0$</p>
<p>[$v'_z$ has been taken to be zero for the convenience of calculations]</p>
<p>Observations from K:</p>
<p>$v_x=\frac{nc Cos(\theta)+n’c}{1+nn’Cos (\theta)}$</p>
<p>$v_y=\frac{nc Sin(\theta)}{1+nn’Cos(\theta)}\sqrt{1-n’^2}$</p>
<p>$v_z=0$
Therefore,</p>
<p>$v=\sqrt{[\frac{nc Cos(\theta)+n’c}{1+nn’Cos (\theta)}]^2+[\frac{nc Sin(\theta)}
{1+nn’Cos(\theta)}\sqrt{1-n’^2}]^2}$ ------------------- (2)</p>
<p>The results from (1) and (2) are not identical , though from the invariant Maxwell’s equations[in a medium] we understand that the speed of light should be the same in all directions inside the dielectric as observed from K.
What would be your answer to this paradox.
[My assessment:This paradoxical situation arises from the fact that we have applied SR in an incorrect context.It has been applied in an anisotropic and inhomogeneous configuration.
You could of course have a different assessment]
[The dielectric within itself is homogeneous and isotropic. But the overall space being considered is not homogeneous and isotropic] </p>
<p>If Maxwell's equations change their form wrt the Lorentz transformations,Gauss Law,Div B=0 etc may change if a piece of dielectric is loaded into a moving train!</p>
| 9,583 |
[
-0.02527107484638691,
-0.023356124758720398,
0.014992853626608849,
-0.04376189410686493,
0.0442521870136261,
0.023951280862092972,
-0.013761338777840137,
-0.005730841308832169,
-0.017995405942201614,
-0.006070513743907213,
0.052843015640974045,
0.022030653432011604,
0.06191386282444,
0.06717962771654129,
0.012337477877736092,
0.012955243699252605,
-0.008884605020284653,
0.037397824227809906,
-0.011622920632362366,
-0.06612226366996765,
0.017148012295365334,
0.029632780700922012,
0.031488195061683655,
0.016667166724801064,
-0.007255589589476585,
0.017753751948475838,
0.00189210067037493,
-0.056903768330812454,
-0.0010170164750888944,
0.03799469396471977,
0.01193178165704012,
0.024579858407378197,
-0.02427028678357601,
-0.01155187003314495,
0.011052665300667286,
-0.00959757249802351,
0.008476849645376205,
-0.026595070958137512,
0.031110983341932297,
0.031868938356637955,
-0.012011370621621609,
0.034367743879556656,
-0.021090146154165268,
0.05565698444843292,
-0.016009094193577766,
-0.019678322598338127,
0.03244224563241005,
0.02692246623337269,
0.05258850380778313,
-0.049263544380664825,
0.04871055483818054,
-0.0552855059504509,
-0.0025965592358261347,
0.028063708916306496,
-0.039047181606292725,
-0.017155032604932785,
0.08631466329097748,
0.054773926734924316,
-0.004622547421604395,
-0.06720191985368729,
0.019941071048378944,
-0.03544916585087776,
-0.021821659058332443,
0.0038280466105788946,
-0.008643227629363537,
0.002182629657909274,
-0.03678637742996216,
-0.012914261780679226,
0.013836915604770184,
-0.015805289149284363,
0.009936552494764328,
-0.007662327028810978,
-0.013903358951210976,
-0.005884834099560976,
0.017218057066202164,
-0.031032344326376915,
-0.005076562985777855,
0.04680991172790527,
-0.01148019265383482,
0.024101033806800842,
0.006340949330478907,
-0.0214801337569952,
0.0377124585211277,
0.013003532774746418,
0.0035775944124907255,
-0.01232228148728609,
0.05988462641835213,
-0.00447797542437911,
0.009985450655221939,
0.021138345822691917,
-0.006606347393244505,
0.0037043795455247164,
0.003677691100165248,
-0.009922918863594532,
-0.002042005304247141,
0.04198320582509041,
-0.021047502756118774,
0.050162173807621,
-0.024249956011772156,
-0.0585966520011425,
-0.017720350995659828,
-0.00815687607973814,
0.037813011556863785,
0.09687833487987518,
0.022059252485632896,
-0.023593606427311897,
-0.01868211105465889,
0.024034447968006134,
-0.035176899284124374,
-0.02621276304125786,
-0.009793865494430065,
0.026523074135184288,
0.002361277351155877,
0.034163761883974075,
-0.026019757613539696,
-0.03863363713026047,
0.023341963067650795,
-0.022879602387547493,
0.07266460359096527,
0.046546220779418945,
0.04349193349480629,
-0.017818262800574303,
-0.008545675314962864,
-0.030271407216787338,
-0.08496486395597458,
0.021728472784161568,
0.0015531154349446297,
0.008102399297058582,
-0.0021326292771846056,
-0.03379112109541893,
0.022381125018000603,
-0.010800058022141457,
0.01649482548236847,
-0.005871395114809275,
0.0048902579583227634,
0.010882200673222542,
-0.10392490774393082,
-0.05550963431596756,
0.05034879967570305,
0.005289898253977299,
0.0028515891171991825,
-0.08316226303577423,
0.003636142937466502,
0.03454839065670967,
0.08817186206579208,
0.008691870607435703,
0.011444322764873505,
-0.02808552235364914,
0.057100772857666016,
-0.012492891401052475,
-0.002848606090992689,
-0.025021782144904137,
0.0031539294868707657,
-0.03832906857132912,
-0.006554937921464443,
-0.06258948892354965,
0.02646922692656517,
0.02020256035029888,
-0.020482704043388367,
-0.0025133718736469746,
0.059578750282526016,
-0.036131128668785095,
0.0033313510939478874,
0.006167980842292309,
-0.02458563633263111,
-0.026885459199547768,
0.07776347547769547,
0.03332599997520447,
0.011587020009756088,
0.03259788453578949,
0.01203689631074667,
0.037605851888656616,
-0.03306280076503754,
-0.0012342430418357253,
0.031103193759918213,
-0.016950786113739014,
0.006262301001697779,
0.001979538705199957,
-0.033085897564888,
-0.003640704322606325,
-0.04919831454753876,
-0.032416656613349915,
0.010702025145292282,
-0.003461588639765978,
0.012912968173623085,
0.053990963846445084,
-0.012928050942718983,
-0.005765853449702263,
0.012718764133751392,
-0.04531073942780495,
-0.0042532384395599365,
-0.008703995496034622,
0.013443280942738056,
0.03745751455426216,
-0.033818475902080536,
0.03981023281812668,
-0.0005096243694424629,
0.016177834942936897,
-0.015582991763949394,
-0.02106705866754055,
-0.007790509611368179,
0.05202909931540489,
0.015275629237294197,
-0.00410047173500061,
0.03238428011536598,
0.02440514788031578,
0.044707290828228,
0.0024240894708782434,
-0.04713943973183632,
0.023448539897799492,
-0.028648167848587036,
0.041829392313957214,
-0.03416145220398903,
0.03486247360706329,
-0.01570437289774418,
0.024096155539155006,
0.02202620543539524,
0.03040865994989872,
0.014106819406151772,
0.01750740222632885,
-0.012318043038249016,
0.04219529777765274,
0.0400657095015049,
0.009031961672008038,
-0.009823707863688469,
0.06194865703582764,
-0.03445137292146683,
0.02866680733859539,
0.004517456982284784,
-0.05221927538514137,
-0.03000328503549099,
-0.01258587185293436,
0.0468280203640461,
0.010749513283371925,
-0.04909529536962509,
0.005109693855047226,
-0.0024254117161035538,
0.055726103484630585,
0.028575383126735687,
0.020580511540174484,
-0.0005429082666523755,
-0.10429122298955917,
0.024073874577879906,
-0.01686246320605278,
0.0182912889868021,
0.0050573027692735195,
-0.01312120072543621,
-0.02439305931329727,
-0.009656626731157303,
-0.024497536942362785,
0.0012338005471974611,
-0.003005418460816145,
0.01758638210594654,
0.013863008469343185,
0.005428799893707037,
-0.03191239759325981,
0.014455694705247879,
0.002241067588329315,
0.007211254443973303,
0.04121420904994011,
-0.0188408475369215,
0.030093545094132423,
-0.04700925946235657,
0.04226943105459213,
0.006109609734266996,
-0.001099329674616456,
-0.004618417471647263,
-0.04758257418870926,
0.022113636136054993,
-0.057291679084300995,
0.006054174154996872,
-0.009234326891601086,
-0.04432912543416023,
-0.016574490815401077,
-0.04491250962018967,
0.013635764829814434,
0.0394488126039505,
0.03604710102081299,
-0.018205299973487854,
-0.0028682055417448282,
0.02275494858622551,
-0.019426872953772545,
-0.008398602716624737,
0.013904341496527195,
-0.006765417754650116,
0.007720158435404301,
-0.03886322304606438,
-0.04787341132760048,
0.003523840568959713,
-0.019050393253564835,
-0.022449916228652,
0.03732837364077568,
-0.009763496927917004,
-0.07224322110414505,
-0.017786718904972076,
-0.025434741750359535,
-0.04254349321126938,
-0.05611922964453697,
-0.018408434465527534,
0.04986517131328583,
-0.018721383064985275,
-0.05333741381764412,
-0.016946464776992798,
-0.022381115704774857,
-0.05887306109070778,
-0.01614963449537754,
0.021868322044610977,
-0.005898302420973778,
-0.02158135548233986,
0.032623570412397385,
0.016374891623854637,
-0.02002071402966976,
-0.010128198191523552,
-0.03216054290533066,
-0.07141543179750443,
0.06127845123410225,
-0.006754276342689991,
0.05083572864532471,
-0.013259625993669033,
-0.011329366825520992,
0.04769438877701759,
0.05103444308042526,
0.004331916570663452,
-0.028126787394285202,
0.0003092016268055886,
-0.004811673890799284,
-0.04568811133503914,
-0.009907806292176247,
0.0296191293746233,
-0.002516152337193489,
0.020769206807017326,
0.03411291539669037,
0.03888483718037605,
0.016216402873396873,
0.018247881904244423,
0.011287633329629898,
0.004957791417837143,
0.006219684612005949,
-0.0002469978353474289,
0.030245710164308548,
0.07055997103452682,
-0.018695954233407974,
-0.01360140461474657,
-0.0031718723475933075,
0.048479847609996796,
0.02770114131271839,
-0.07093420624732971,
0.02573268488049507,
0.012564210221171379,
0.03901965916156769,
-0.004717536736279726,
0.02435820735991001,
0.0076189711689949036,
0.011403847485780716,
0.0019335742108523846,
0.03318558260798454,
0.030580367892980576,
-0.008185114711523056,
0.04907068982720375,
0.020557446405291557,
0.035572540014982224,
0.00045649963431060314,
-0.037402231246232986,
-0.014441147446632385,
-0.02507326379418373,
0.032684169709682465,
-0.040775541216135025,
-0.015944775193929672,
0.05055384710431099,
0.024962374940514565,
0.013125629164278507,
-0.011964065954089165,
-0.017683017998933792,
-0.007058810908347368,
-0.03684433177113533,
-0.006198536138981581,
-0.024733899161219597,
-0.004394243471324444,
0.01044966746121645,
0.04733986034989357,
0.033014483749866486,
0.001257397118024528,
-0.008060142397880554,
-0.0002944531152024865,
-0.09435053914785385,
-0.004017262253910303,
-0.009975109249353409,
-0.002074690768495202,
-0.02793470397591591,
-0.01530398242175579,
-0.0036297417245805264,
-0.013794169761240482,
0.0005985180614516139,
-0.005257636308670044,
-0.008806061930954456,
-0.0539863146841526,
0.030277211219072342,
0.005609097424894571,
-0.04242086037993431,
-0.026775801554322243,
0.046165578067302704,
0.07741397619247437,
-0.045429777354002,
-0.03826159983873367,
0.02230192720890045,
-0.040287040174007416,
-0.01920151524245739,
-0.022555144503712654,
0.002251019701361656,
0.026408635079860687,
0.0023202921729534864,
0.028776448220014572,
-0.04804448410868645,
0.03249429911375046,
0.055837783962488174,
0.012624349445104599,
0.042043086141347885,
0.03524027392268181,
-0.0036662397906184196,
-0.07038617134094238,
-0.022858280688524246,
-0.02767081931233406,
-0.04499850794672966,
0.08045046031475067,
0.002040117047727108,
-0.01324690505862236,
0.034297432750463486,
0.017114896327257156,
0.03443640470504761,
0.050577450543642044,
-0.011346534825861454,
0.019058438017964363,
-0.017681099474430084,
-0.05694417655467987,
-0.02370050549507141,
-0.002184545388445258,
0.010804407298564911,
0.05574667826294899,
-0.004299696069210768,
0.019232692196965218,
-0.01989036239683628,
-0.013468790799379349,
0.008815871551632881,
0.012923524715006351,
0.019683269783854485,
-0.05130377784371376,
-0.009809250943362713,
0.01722991280257702,
-0.0034036345314234495,
-0.02598300762474537,
0.014473632909357548,
0.03009084425866604,
0.00014935401850380003,
-0.006511389743536711,
-0.047860417515039444,
0.0056937322951853275,
0.028878014534711838,
0.021700678393244743,
-0.00676341587677598,
0.02326270379126072,
-0.05556364357471466,
0.020792867988348007,
-0.01163638848811388,
-0.02066747471690178,
0.05226067081093788,
-0.00693564023822546,
-0.0027006312739104033,
-0.027082374319434166,
-0.03838104009628296,
-0.04805796593427658,
-0.0030514546670019627,
-0.0085431057959795,
0.005095412489026785,
-0.024245411157608032,
-0.007504122797399759,
-0.012846067547798157,
0.008111782371997833,
0.02999720722436905,
0.02646232396364212,
-0.004721744917333126,
0.012565472163259983,
-0.017267165705561638,
-0.0037592826411128044,
-0.001289152423851192,
-0.05356881767511368,
0.013891036622226238,
0.033461201936006546,
0.03151974081993103,
0.024893995374441147,
-0.03423004969954491,
-0.04991922527551651,
0.053260017186403275,
0.022507479414343834,
-0.0003342691343277693,
0.03901955112814903,
-0.050985656678676605,
0.041201770305633545,
-0.01903189904987812,
-0.02477613463997841,
0.025621486827731133,
0.016968317329883575,
-0.022246476262807846,
-0.0077961101196706295,
-0.031756967306137085,
0.037611402571201324,
-0.005116492044180632,
-0.01011843141168356,
-0.007058040238916874,
0.026140470057725906,
-0.015201612375676632,
0.054900944232940674,
-0.008708208799362183,
0.01698611117899418,
-0.0223975982517004,
0.0014789402484893799,
0.0060547091998159885,
0.013533034361898899,
0.0013325506588444114,
0.02409873902797699,
-0.04817340150475502,
0.014837423339486122,
0.0032882760278880596,
-0.022305697202682495,
0.018592122942209244,
-0.0014676933642476797,
0.024083636701107025,
0.04782190918922424,
0.01772439479827881,
-0.005912183318287134,
-0.02051754854619503,
-0.01253840047866106,
0.004419414792209864,
-0.055518411099910736,
0.029406074434518814,
-0.012972921133041382,
0.025813067331910133,
0.01976250484585762,
-0.02327576093375683,
-0.04536375775933266,
0.02127286233007908,
0.0010953830787912011,
0.013394847512245178,
-0.05152736231684685,
-0.037987902760505676,
0.011652521789073944,
0.025671496987342834,
-0.06416305899620056,
-0.03596889227628708,
0.0242337454110384,
0.014568819664418697,
-0.018983308225870132,
-0.0021210063714534044,
-0.013723107054829597,
-0.03689593821763992,
-0.03395618498325348,
0.00165509560611099,
0.017471255734562874,
-0.015362897887825966,
-0.03953683376312256,
-0.024545075371861458,
0.021692823618650436,
0.02843453735113144,
-0.04138918220996857,
-0.012993869371712208,
0.0016900529153645039,
-0.028921550139784813,
-0.012931643053889275,
0.016128161922097206,
0.0226614810526371,
0.0005868840962648392,
-0.04093830659985542,
-0.027508210390806198,
-0.017952613532543182,
-0.0016553354216739535,
0.0015895781107246876,
-0.0028537733014672995,
0.013379966840147972,
-0.025860995054244995,
-0.0299278125166893,
-0.007668763864785433,
-0.004610056523233652,
0.014876428060233593,
0.014647740870714188,
0.03254121541976929,
-0.019746052101254463,
-0.05412712320685387,
-0.025682441890239716,
0.012868092395365238,
0.006363030523061752,
0.012259080074727535,
-0.017230859026312828,
0.08303073793649673,
-0.037953902035951614,
0.014743826352059841,
-0.006846792064607143,
0.00989884976297617,
0.026617493480443954,
0.0059510781429708,
0.0006823305739089847,
0.038944222033023834,
0.009078994393348694,
0.005643168464303017,
-0.03255276009440422,
-0.06973664462566376,
0.05082953721284866,
0.08194892853498459,
-0.014320078305900097,
0.031922440975904465,
0.011385684832930565,
-0.05526483431458473,
-0.03713969886302948,
-0.007235144264996052,
-0.0012018956476822495,
0.01314396969974041,
0.0019444380886852741,
0.018549812957644463,
-0.00936638843268156,
-0.03668833151459694,
0.02424623630940914,
0.0487980842590332,
-0.052142634987831116,
0.0000902585597941652,
0.014877422712743282,
0.02909870073199272,
0.0007471226854249835,
-0.017223970964550972,
-0.049445707350969315,
0.035701580345630646,
-0.016869626939296722,
0.03174363449215889,
0.02753978967666626,
-0.024035923182964325,
0.047305669635534286,
0.024430926889181137,
0.025395046919584274,
-0.05378378555178642,
-0.006157442927360535,
-0.018551645800471306,
0.004632869269698858,
-0.011134220287203789,
0.04018745198845863,
-0.013422826305031776,
-0.019412193447351456,
0.027880379930138588,
0.010151040740311146,
0.056480564177036285,
-0.015542310662567616,
-0.06264865398406982,
-0.02386479452252388,
-0.011369142681360245,
-0.0012927070492878556,
0.07102252542972565,
0.02072742208838463,
0.004636016674339771,
0.0037405535113066435,
-0.045754529535770416,
0.024493936449289322,
0.0648108422756195,
0.011144191958010197,
0.0160902738571167,
0.04243519902229309,
-0.019805289804935455,
0.01412978395819664,
-0.025212407112121582,
-0.023374037817120552,
0.1406075656414032,
0.06374244391918182,
0.0019889320246875286,
-0.04305185750126839,
0.016745787113904953,
-0.03647827357053757,
0.046732742339372635,
-0.022568950429558754,
0.025165682658553123,
-0.026030030101537704,
-0.02481917105615139,
0.013055605813860893,
0.021726764738559723,
-0.0011022994294762611,
-0.019034752622246742,
0.00460582273080945,
-0.05822328105568886,
0.00018971459940075874,
-0.008175716735422611,
0.017167164012789726,
-0.016695808619260788,
0.021471712738275528,
-0.00439859414473176,
0.021278521046042442,
-0.043251197785139084,
-0.019026637077331543,
-0.037799641489982605,
0.0021191088017076254,
-0.008594293147325516,
0.016172755509614944,
-0.04917244240641594,
0.01233240682631731,
0.01731419563293457,
-0.012607771903276443,
-0.033734437078237534,
-0.006574391387403011,
0.0263463594019413,
-0.01726219430565834,
0.03298687934875488,
0.00354021112434566,
-0.00020369159756228328,
0.02548249252140522,
0.051298413425683975,
0.020397739484906197,
-0.055369697511196136,
0.039912011474370956,
-0.00841135811060667,
0.05824773386120796,
0.011964778415858746,
-0.015503311529755592,
-0.011804861947894096,
-0.01901601068675518,
0.01329001598060131,
-0.04403821378946304,
0.017829032614827156,
0.006804094649851322,
0.014047391712665558,
0.0008196525159291923,
0.04593702778220177,
0.017430178821086884,
0.011173541657626629,
0.03705120459198952,
0.03880522772669792,
0.00040884880581870675,
0.0038742050528526306,
-0.04981577768921852,
0.010665738955140114,
0.059105467051267624,
-0.006802573334425688,
-0.011801975779235363,
-0.06866353750228882,
-0.03462328016757965,
-0.038807064294815063,
-0.0019214412895962596,
0.0008065632428042591,
0.029883012175559998,
0.02108415961265564,
-0.016163429245352745,
-0.014933456666767597,
-0.013947314582765102,
-0.0798390656709671,
-0.012947187758982182,
-0.022919366136193275,
-0.0012956226710230112,
-0.03459147736430168,
-0.0003061587631236762,
0.034141167998313904,
0.03573617711663246,
-0.050546880811452866,
-0.023174386471509933,
0.015446453355252743,
0.05262809991836548,
-0.0005700689507648349,
-0.00964142195880413,
-0.04497532919049263,
-0.032593127340078354,
0.005189708899706602,
-0.0015492875827476382,
0.011958753690123558,
-0.00046606207615695894,
0.023029329255223274,
0.020513059571385384,
0.002158308867365122,
0.029466988518834114,
-0.028389472514390945,
-0.029129672795534134,
0.01842179335653782,
-0.01989947259426117,
0.04201214015483856,
0.045907437801361084,
0.04937218874692917,
-0.009889163076877594,
-0.014778893440961838,
-0.004896251950412989,
0.0025517696049064398,
0.01571272499859333,
0.003027976956218481,
-0.006442496087402105,
-0.019078079611063004,
-0.030427983030676842,
0.0030106850899755955,
-0.024485407397150993,
-0.027228286489844322,
0.008176411502063274,
0.01944216899573803,
-0.009914279915392399,
0.02146892249584198,
-0.005060672294348478,
0.07562749832868576,
-0.039366465061903,
-0.02697904035449028,
-0.0017252271063625813,
0.02034689299762249,
-0.0021752219181507826,
-0.008856559172272682,
0.006669485475867987,
0.01478173304349184,
-0.002275545848533511,
-0.02966424822807312,
-0.06848100572824478,
-0.009002196602523327,
-0.003114045364782214,
-0.03956284373998642,
0.040465328842401505,
0.0046496083959937096,
0.02194773219525814,
0.029208894819021225,
0.00010004670184571296,
0.026180505752563477,
0.08277686685323715,
-0.025503426790237427,
-0.010080109350383282,
0.0018101680325344205,
-0.04951830208301544,
-0.00262841465882957,
-0.024605344980955124,
0.040094438940286636,
-0.002464153105393052,
0.003960358910262585,
0.04959188774228096,
-0.0027866766322404146,
-0.041050270199775696,
-0.001219393452629447,
-0.00156499445438385,
-0.04510371387004852,
-0.06201593577861786,
0.03096841089427471,
-0.0029073553159832954,
0.020746173337101936,
0.06713034212589264,
-0.028785502538084984,
0.05527555197477341,
0.00954557117074728,
0.01195652037858963,
-0.11489193141460419,
-0.015347864478826523,
0.03266722336411476,
0.08588165789842606,
0.05551503598690033,
-0.04450177028775215,
0.029639504849910736,
0.032333921641111374,
-0.08596023917198181,
0.0024049426428973675,
-0.0006367332534864545,
-0.014369726181030273,
-0.06906150281429291,
0.01222013495862484,
-0.03183770924806595,
0.0158995408564806,
0.04809601977467537,
0.0033318777568638325,
0.029996400699019432,
0.04047452285885811,
-0.02678186632692814,
-0.016064774245023727,
-0.025298254564404488,
0.024811644107103348,
-0.024216005578637123,
0.01312595047056675,
0.05609102174639702,
0.007298924960196018,
-0.00545269763097167,
0.014880349859595299,
0.005137492902576923,
-0.004848072305321693,
0.0034735354129225016,
0.020504578948020935,
-0.005401255562901497,
0.01352565735578537,
0.019755546003580093,
-0.012507427483797073,
-0.022977564483880997,
-0.02557140588760376,
0.017308367416262627,
0.0160589050501585,
0.022989453747868538,
-0.033140454441308975,
0.009745698422193527,
-0.07856541872024536,
-0.022815458476543427,
-0.009567437693476677,
-0.006444508209824562,
-0.029362371191382408,
0.03068731538951397,
0.026233742013573647,
0.03311014920473099,
-0.0019396491115912795,
0.011669598519802094,
-0.06689293682575226,
-0.02331049181520939,
0.010042413137853146,
0.00983026996254921,
-0.012842157855629921,
0.002943524392321706,
-0.00784965418279171,
-0.010713683441281319,
-0.0050224727019667625,
-0.025220850482583046,
0.023711970075964928,
-0.038348451256752014,
0.016578489914536476,
-0.040405504405498505,
-0.007831142283976078,
0.03142305091023445,
-0.010894670151174068,
-0.03332405909895897,
0.017265012487769127,
0.014718734659254551,
0.005916326306760311,
-0.012540459632873535,
-0.016542948782444,
-0.030877068638801575,
-0.05623713135719299,
-0.00047893173177726567,
-0.029430683702230453,
-0.028961297124624252,
-0.05011091008782387,
0.0037296945229172707,
-0.036195434629917145,
0.04408546909689903,
0.07091052085161209,
0.015445109456777573,
-0.03994087129831314,
-0.009506013244390488,
-0.005143085494637489,
-0.003002576529979706,
-0.06580588966608047,
-0.01262778788805008,
0.004259423818439245,
-0.04174138978123665,
0.02936869114637375,
-0.02008436992764473,
-0.007407618220895529,
0.006893004756420851,
0.004763734992593527,
-0.012142042629420757,
0.037998709827661514,
0.04227420315146446,
-0.0458812341094017,
0.016917482018470764,
-0.04224734380841255,
-0.008177211508154869,
0.051331885159015656,
0.006939053535461426,
0.028462450951337814,
0.042359523475170135,
-0.010957831516861916,
-0.07104755938053131,
0.004634625278413296,
-0.060971882194280624,
-0.007512709125876427,
-0.01520503219217062,
0.028395235538482666,
0.03710468113422394,
-0.022994598373770714,
0.0054125976748764515,
0.042613934725522995,
-0.05027804151177406,
0.00793861597776413,
0.04614108055830002,
-0.025598976761102676,
0.03293313458561897,
0.025778701528906822,
0.04117066040635109,
-0.01563451997935772,
0.008218815550208092,
0.020238272845745087,
0.06456723809242249,
0.010159636847674847,
-0.02987825684249401,
0.01328715868294239,
0.052682310342788696,
-0.010094113647937775,
0.019284995272755623,
-0.01131504401564598,
0.008940175175666809,
0.01235575508326292,
0.01618134044110775,
0.014349211938679218,
-0.03310166299343109,
-0.004213376902043819,
0.055399090051651,
0.025038233026862144,
0.027806900441646576,
-0.0016642988193780184,
0.01809169352054596,
-0.01852819323539734,
0.0051858448423445225,
-0.0029318942688405514,
0.0629105269908905,
0.04091045260429382,
0.017786208540201187,
-0.004921367391943932,
-0.005383758340030909,
0.004450436681509018,
-0.03946957364678383,
0.007370880804955959,
-0.02597055584192276,
-0.03165028616786003,
0.003094183513894677,
-0.00936705432832241,
0.056540269404649734,
-0.011485288850963116,
0.004536201246082783,
0.004665641579777002,
0.0021800443064421415,
0.009263746440410614,
0.028913510963320732,
-0.011329465545713902,
0.04170873761177063,
-0.0315244235098362,
0.06770546734333038,
-0.01890970580279827,
0.00988219678401947,
0.04244101420044899,
0.04033828526735306,
0.005244900938123465,
-0.01784292608499527
] |
<p>So the wave moves like. a wave, it moves up and down, up and down. But how do photons move? Do they follow the same path or do they just go straight forward without oscillating?</p>
| 9,584 |
[
0.001665700925514102,
-0.03019121289253235,
-0.00857461802661419,
-0.03943542391061783,
0.02893807366490364,
0.03294073045253754,
-0.004093888681381941,
-0.03262074664235115,
0.012168634682893753,
-0.01377254631370306,
0.02536519058048725,
0.04851977154612541,
0.03387176990509033,
-0.0064223650842905045,
0.03671668469905853,
0.0036517870612442493,
0.001766290282830596,
0.0031476595904678106,
-0.035051316022872925,
-0.03300726041197777,
-0.0298923272639513,
0.005505247041583061,
-0.01728040538728237,
0.028503742069005966,
-0.03142552450299263,
0.03226195648312569,
0.017948824912309647,
0.024093374609947205,
0.030656559392809868,
0.03326871991157532,
0.006370309740304947,
-0.03270632028579712,
0.010884974151849747,
0.06075228005647659,
0.03753114491701126,
-0.033115267753601074,
-0.033665016293525696,
-0.04906286671757698,
-0.01711629331111908,
-0.024788472801446915,
-0.004016118589788675,
-0.03527980297803879,
-0.0306746456772089,
0.024098223075270653,
-0.04277948662638664,
-0.006211058236658573,
0.026394624263048172,
0.006500701420009136,
0.06105101853609085,
-0.06736232340335846,
0.05555092543363571,
-0.021738272160291672,
0.03880709037184715,
0.026143020018935204,
0.01570821925997734,
0.0024467718321830034,
0.09425090253353119,
0.047384582459926605,
-0.015903808176517487,
-0.04081718996167183,
0.002573637291789055,
-0.011386544443666935,
0.0031038580927997828,
-0.02661924809217453,
-0.037751760333776474,
0.0243357103317976,
-0.022023657336831093,
-0.0164065919816494,
0.017560318112373352,
-0.010352804325520992,
0.0020320462062954903,
0.0277987290173769,
0.06610546261072159,
-0.017303140833973885,
0.006207150872796774,
-0.03803569823503494,
0.02526864968240261,
0.024894827976822853,
0.04003280773758888,
0.04459768161177635,
-0.004479922354221344,
-0.009488051757216454,
-0.006804012693464756,
0.017324458807706833,
-0.00846685841679573,
-0.031184954568743706,
0.07695243507623672,
-0.004968416877090931,
-0.015937188640236855,
0.01690872199833393,
-0.012889773584902287,
0.02629792131483555,
0.022540125995874405,
0.02280947007238865,
-0.012050658464431763,
0.018956130370497704,
0.015778541564941406,
0.03980841860175133,
0.02586730755865574,
-0.023463262245059013,
0.05405936762690544,
0.019906237721443176,
0.02876231074333191,
0.06962785124778748,
0.013146785087883472,
-0.00935913436114788,
-0.02718319557607174,
0.05203909054398537,
-0.04152865707874298,
-0.02530929259955883,
-0.04042176529765129,
0.021352723240852356,
0.009858482517302036,
0.007278007920831442,
0.03447292372584343,
-0.01892707496881485,
0.016544470563530922,
-0.01527511328458786,
0.06652460992336273,
0.08109722286462784,
0.010185332037508488,
-0.0523652657866478,
0.028244227170944214,
-0.01377270556986332,
-0.04432227090001106,
-0.008895684964954853,
0.04739482328295708,
-0.007702354341745377,
-0.07303200662136078,
0.023888101801276207,
-0.024278581142425537,
-0.0046843173913657665,
0.020526612177491188,
-0.023476412519812584,
0.029626140370965004,
0.0035705731716006994,
-0.1396922916173935,
-0.05348161235451698,
0.03361860662698746,
-0.008782467804849148,
-0.04241760075092316,
-0.061973754316568375,
-0.0074800425209105015,
0.03470252454280853,
0.09406355768442154,
-0.041644588112831116,
0.0059633697383105755,
0.005307917017489672,
0.023843498900532722,
-0.015658745542168617,
0.0040195658802986145,
-0.004814068786799908,
-0.004544085822999477,
-0.03257015720009804,
0.018844017758965492,
-0.046295199543237686,
0.002354095922783017,
0.06066662073135376,
-0.0036824794951826334,
-0.04389285668730736,
0.07066213339567184,
-0.023966824635863304,
0.024229124188423157,
0.007218873593956232,
-0.011101041920483112,
-0.03513306751847267,
0.05906185880303383,
0.028934428468346596,
-0.01540151983499527,
0.03349113091826439,
-0.024932974949479103,
0.007999717257916927,
-0.028299815952777863,
-0.007957376539707184,
0.010228605940937996,
-0.031077774241566658,
-0.03276201710104942,
0.008510950952768326,
0.01449110172688961,
0.004689955152571201,
-0.01449948363006115,
-0.0398312509059906,
0.009607036598026752,
0.022964632138609886,
0.001307603088207543,
0.03255263715982437,
-0.01371956430375576,
-0.0016785492189228535,
-0.03877425566315651,
-0.06466947495937347,
-0.005299018695950508,
-0.04769016429781914,
0.031290583312511444,
-0.000450202205684036,
0.0036010299809277058,
0.007928506471216679,
0.03695499151945114,
0.01618533581495285,
-0.021362237632274628,
-0.021973993629217148,
-0.006220887415111065,
0.052694808691740036,
-0.013186344876885414,
-0.005316459573805332,
0.039338208734989166,
0.09380684047937393,
0.03725086897611618,
0.013894212432205677,
0.021035952493548393,
-0.027368225157260895,
0.0032469627913087606,
0.03287266939878464,
-0.009773586876690388,
0.024400882422924042,
-0.005319158546626568,
0.004319194238632917,
-0.010804188437759876,
-0.004125307314097881,
-0.014292729087173939,
0.011587711051106453,
-0.020015591755509377,
0.058724407106637955,
0.04563327878713608,
-0.026731878519058228,
-0.01440716627985239,
0.0345994271337986,
-0.029524780809879303,
0.0165813397616148,
0.030700379982590675,
-0.033744558691978455,
-0.020419999957084656,
-0.0022405453491955996,
0.03242496773600578,
-0.018452277407050133,
-0.02069549448788166,
0.013116225600242615,
0.01702408492565155,
0.060312166810035706,
0.04013003408908844,
0.04523707926273346,
-0.03850727900862694,
-0.028057461604475975,
0.01685205101966858,
0.006256412249058485,
0.01035588700324297,
0.009325598366558552,
0.033604059368371964,
0.013426385819911957,
0.008077763952314854,
0.0024909921921789646,
-0.02333236113190651,
0.015878258273005486,
0.006550219841301441,
0.02528301812708378,
-0.01177749689668417,
-0.058848146349191666,
0.023702962324023247,
-0.02806030958890915,
-0.01571698859333992,
-0.018125034868717194,
-0.013754119165241718,
-0.001783585175871849,
-0.02849500998854637,
-0.00904246885329485,
-0.002936149714514613,
0.0206842590123415,
-0.009939293377101421,
-0.01973162591457367,
0.03462805598974228,
-0.003345439676195383,
0.03735126927495003,
-0.050545498728752136,
-0.0016078657936304808,
-0.014919915236532688,
-0.04228327050805092,
0.0630415827035904,
0.029667135328054428,
0.039691053330898285,
-0.043315447866916656,
-0.05644114688038826,
0.011413267813622952,
-0.02992323786020279,
-0.008742759004235268,
0.01165251899510622,
-0.056110724806785583,
0.03771847113966942,
-0.013274876400828362,
-0.039362017065286636,
0.038831356912851334,
0.010909725911915302,
0.034502919763326645,
0.027354758232831955,
-0.024763429537415504,
-0.0687304139137268,
-0.018914224579930305,
-0.03187458962202072,
-0.00574583699926734,
-0.00956281553953886,
0.03617949038743973,
0.06850156933069229,
-0.026571614667773247,
-0.009729105979204178,
-0.006988080218434334,
-0.017547378316521645,
-0.05848466232419014,
-0.012250661849975586,
-0.006746276747435331,
0.029307687655091286,
-0.04404192045331001,
0.025074755772948265,
0.006106329150497913,
-0.0784313827753067,
0.044344548135995865,
-0.040143657475709915,
-0.030566047877073288,
0.03392721712589264,
-0.00014146820467431098,
0.027820546180009842,
0.005437831394374371,
-0.005069485399872065,
0.05808223411440849,
0.02034628577530384,
-0.031868040561676025,
-0.028890134766697884,
-0.012645198032259941,
-0.029118908569216728,
-0.01946815475821495,
0.029556740075349808,
0.05145082622766495,
0.010277810506522655,
0.012004919350147247,
0.006796363275498152,
0.023393142968416214,
0.04214641451835632,
0.01282559335231781,
0.006546957418322563,
-0.005204293876886368,
0.03207771107554436,
-0.004592311102896929,
0.010106338188052177,
0.022034013643860817,
-0.0381278358399868,
0.04435291141271591,
0.005309500731527805,
0.006709394045174122,
0.01858770102262497,
0.001465093344449997,
0.07812348008155823,
0.016802558675408363,
-0.008681939914822578,
-0.046685267239809036,
0.03232509270310402,
0.006658261176198721,
0.009942611679434776,
-0.013159222900867462,
0.023957958444952965,
0.03756872937083244,
0.018278799951076508,
0.00981128215789795,
0.002348285634070635,
0.04259997978806496,
-0.03461507707834244,
-0.02365034818649292,
0.011864714324474335,
-0.025985633954405785,
0.010005570016801357,
-0.01280125416815281,
-0.028784843161702156,
0.08091646432876587,
-0.005231287330389023,
0.017034422606229782,
-0.0056666722521185875,
-0.04605996981263161,
-0.04809466376900673,
-0.025153379887342453,
0.0148877939209342,
0.02411019429564476,
-0.00017352616123389453,
-0.0028189802542328835,
0.06660173833370209,
0.006878778338432312,
0.04507733881473541,
0.031869180500507355,
-0.005075500346720219,
-0.08725608885288239,
0.003746516304090619,
-0.05804074928164482,
-0.013291013427078724,
-0.03335007280111313,
-0.0047336844727396965,
-0.051529888063669205,
-0.008903900161385536,
-0.021212853491306305,
-0.022059256210923195,
-0.06051583215594292,
-0.039992500096559525,
0.009910681284964085,
-0.036882802844047546,
-0.02287372760474682,
0.004831353202462196,
0.0034920910838991404,
0.014884148724377155,
-0.004889961332082748,
0.0026738939341157675,
0.040752846747636795,
-0.0203624926507473,
0.022325994446873665,
0.0015686566475778818,
0.00009204547677654773,
0.020744090899825096,
0.001267261803150177,
0.030325809493660927,
-0.010730860754847527,
-0.015334737487137318,
0.020772313699126244,
-0.007710983976721764,
0.03233611583709717,
0.027246130630373955,
-0.03192524611949921,
-0.01587044820189476,
-0.006451308261603117,
-0.001287858234718442,
-0.02357661910355091,
0.05101274698972702,
0.011942515149712563,
0.0002580583968665451,
0.04286068305373192,
0.002136272145435214,
-0.03583068028092384,
0.04985916242003441,
0.03338412195444107,
-0.002972652204334736,
0.0020630722865462303,
-0.0565955676138401,
-0.0033369322773069143,
-0.016065426170825958,
-0.02155238576233387,
0.003798994468525052,
-0.02793457731604576,
-0.02630138210952282,
0.029219435527920723,
0.014021501876413822,
0.004420510493218899,
0.028472144156694412,
-0.006631560157984495,
-0.0360635444521904,
-0.01049787923693657,
-0.002111272420734167,
-0.018175723031163216,
-0.00986693985760212,
0.04538755491375923,
0.020000524818897247,
-0.005587074439972639,
-0.026598576456308365,
-0.07134184241294861,
-0.007982071489095688,
0.02207169681787491,
0.024281248450279236,
-0.024709921330213547,
0.0019697118550539017,
-0.06129710003733635,
-0.028681812807917595,
0.03553367778658867,
-0.017256056889891624,
0.02767898514866829,
-0.018925970420241356,
-0.04115147516131401,
-0.002320022787898779,
0.0009544726344756782,
-0.011748552322387695,
0.022032296285033226,
-0.011629247106611729,
0.000465692748548463,
-0.005466587841510773,
0.01466328650712967,
-0.034692347049713135,
0.03326055780053139,
0.021183274686336517,
0.06966429203748703,
-0.01328388974070549,
0.03217494115233421,
-0.00544038275256753,
0.0076203728094697,
-0.03236011788249016,
-0.09875328838825226,
0.011173388920724392,
0.04071638360619545,
-0.016195077449083328,
0.039178408682346344,
0.003982791677117348,
-0.049658168107271194,
0.012167436070740223,
0.0016223016427829862,
0.018622713163495064,
-0.019152797758579254,
-0.037202928215265274,
0.016675610095262527,
0.013684372417628765,
-0.004699466284364462,
0.06683532893657684,
0.04650524631142616,
-0.05430631339550018,
-0.022512992843985558,
-0.008586675859987736,
0.07175009697675705,
-0.01342430617660284,
0.0016174758784472942,
-0.014619258232414722,
0.002516506938263774,
-0.018282679840922356,
0.0554719939827919,
0.003035465255379677,
-0.018792804330587387,
0.027374444529414177,
-0.018955811858177185,
-0.040166404098272324,
0.04668665677309036,
-0.01764531247317791,
-0.021808790042996407,
-0.02232324331998825,
0.029659729450941086,
-0.018127692863345146,
-0.03655759617686272,
0.011911393143236637,
-0.012057335115969181,
0.01379634253680706,
0.04391753301024437,
0.021211380138993263,
0.012945747002959251,
-0.054265256971120834,
-0.011728535406291485,
-0.0005988934426568449,
-0.05386551469564438,
0.03565197065472603,
-0.012223957106471062,
-0.024231070652604103,
0.03083709068596363,
-0.04809815436601639,
-0.04897260665893555,
-0.005743960849940777,
-0.01715696230530739,
0.02615344151854515,
-0.05166705325245857,
0.03754732757806778,
0.019581200554966927,
-0.000040917788282968104,
-0.0939987450838089,
-0.06871522217988968,
0.02240019664168358,
0.007448455318808556,
0.006190952844917774,
-0.009188676252961159,
0.05664411559700966,
-0.034836545586586,
-0.01826796494424343,
-0.017528994008898735,
0.010428644716739655,
-0.01775297150015831,
0.008485529571771622,
0.0023856405168771744,
-0.004342270083725452,
0.055593859404325485,
0.020049652084708214,
-0.03328967094421387,
0.002064122585579753,
-0.001407620613463223,
-0.01528169959783554,
-0.020017990842461586,
0.06827477365732193,
-0.006328537128865719,
-0.045583512634038925,
-0.01561789121478796,
-0.009361912496387959,
0.02262156642973423,
-0.04009244590997696,
0.0037063038907945156,
0.03459493815898895,
0.03631218522787094,
-0.005736845079809427,
-0.03426361456513405,
0.025221621617674828,
-0.024095172062516212,
0.02656138315796852,
0.02063821442425251,
-0.015861481428146362,
-0.033616285771131516,
-0.06199873238801956,
0.028564605861902237,
0.00689121475443244,
0.03030206821858883,
-0.004671784583479166,
0.05858660861849785,
-0.02544459141790867,
0.0017904234118759632,
0.018287550657987595,
-0.0063780369237065315,
-0.006207793951034546,
-0.022596633061766624,
0.01397225446999073,
-0.016206586733460426,
-0.02407100237905979,
-0.015559474937617779,
-0.004117547534406185,
-0.011955974623560905,
-0.04571818560361862,
0.06299010664224625,
-0.01200204249471426,
0.0411311499774456,
-0.008744161576032639,
-0.003939633257687092,
0.004140392877161503,
-0.009653626009821892,
-0.013369034975767136,
0.000595752673689276,
0.0057608275674283504,
0.02384086512029171,
-0.02270600013434887,
0.04383358359336853,
0.0028379084542393684,
0.06547100096940994,
0.007338358089327812,
-0.003935045097023249,
0.023366807028651237,
0.018220387399196625,
0.02013559825718403,
0.028715573251247406,
-0.036344826221466064,
0.023749206215143204,
-0.048099223524332047,
0.0326688215136528,
0.003596294205635786,
-0.03513209521770477,
0.051550380885601044,
-0.010153407230973244,
-0.02086094580590725,
0.010634491220116615,
0.010914705693721771,
-0.05163779854774475,
0.011721516028046608,
-0.0055318488739430904,
0.046921733766794205,
-0.00274455058388412,
0.01634019799530506,
0.03850863501429558,
0.01216115988790989,
0.011616842821240425,
-0.017276190221309662,
-0.05436236783862114,
-0.06960103660821915,
-0.021433763206005096,
-0.0346202477812767,
0.05380357429385185,
0.007136182393878698,
-0.018672803416848183,
0.005386736709624529,
-0.0325547531247139,
0.012872155755758286,
0.02287898026406765,
0.04343116655945778,
-0.025233633816242218,
0.03813935071229935,
-0.02527739852666855,
0.019032569602131844,
-0.01691097393631935,
-0.008003980852663517,
0.09518846869468689,
0.039962559938430786,
0.019459612667560577,
-0.06394902616739273,
-0.006770421285182238,
-0.035698581486940384,
0.03291056305170059,
-0.028288714587688446,
0.023153910413384438,
0.011280518025159836,
0.041463084518909454,
-0.018016016110777855,
0.049084268510341644,
0.006163507699966431,
0.024259168654680252,
0.022534675896167755,
-0.03507550433278084,
-0.04897218197584152,
0.015224401839077473,
0.005482943262904882,
0.009876241907477379,
0.05427100509405136,
-0.02369408868253231,
0.004737917799502611,
-0.05138295516371727,
-0.023668436333537102,
-0.02357042208313942,
-0.06643269211053848,
0.020497895777225494,
0.017588458955287933,
-0.061918437480926514,
-0.03661559894680977,
0.021206574514508247,
-0.02965705469250679,
-0.04263242334127426,
0.044219061732292175,
0.037760574370622635,
-0.02385183610022068,
0.026257401332259178,
-0.00837698020040989,
0.044627659022808075,
-0.001430653384886682,
0.014615942724049091,
0.004995403811335564,
-0.04522492364048958,
0.008931012824177742,
-0.0032368048559874296,
0.012326167896389961,
-0.008598458021879196,
0.03377789631485939,
0.0005010991008020937,
0.04046902060508728,
-0.01872766949236393,
-0.07162253558635712,
0.004847854841500521,
0.004807061981409788,
0.03156045451760292,
-0.009100165218114853,
-0.005821398925036192,
-0.008044302463531494,
-0.035546138882637024,
-0.009408719837665558,
0.0240434892475605,
-0.021960973739624023,
0.0200515016913414,
-0.002272701123729348,
-0.01272665522992611,
0.011583877727389336,
-0.04562899470329285,
-0.03035074472427368,
-0.00559846218675375,
-0.01405850239098072,
-0.059336721897125244,
-0.0073618353344500065,
0.04719579592347145,
0.04321381077170372,
-0.0015931648667901754,
0.00011595142132136971,
-0.011568729765713215,
-0.020334593951702118,
-0.06599850207567215,
0.01971905492246151,
-0.013010785914957523,
-0.03422968089580536,
0.005877173040062189,
-0.01518596988171339,
0.07761237025260925,
0.020291080698370934,
-0.020739926025271416,
0.03750183805823326,
-0.0039412956684827805,
0.005217410158365965,
0.025201426818966866,
-0.043279681354761124,
0.008969630114734173,
0.05124470591545105,
0.02343727834522724,
-0.015157234854996204,
-0.024251747876405716,
0.03790335729718208,
0.01554654911160469,
0.008179199881851673,
-0.016809014603495598,
0.021343689411878586,
-0.03651672601699829,
-0.0030272332951426506,
0.01808871701359749,
-0.012888830155134201,
0.009235712699592113,
0.02928144857287407,
0.017613328993320465,
-0.022833852097392082,
-0.06247544661164284,
-0.03250447288155556,
0.016561200842261314,
-0.006568433251231909,
0.012544666416943073,
-0.03601823374629021,
0.014046805910766125,
-0.0059340898878872395,
0.043252505362033844,
-0.019800996407866478,
-0.03149130940437317,
-0.04465976729989052,
0.026314983144402504,
-0.0030080843716859818,
-0.00334593141451478,
-0.011888517066836357,
0.023584987968206406,
-0.009947096928954124,
-0.014311435632407665,
0.016411416232585907,
0.05020039156079292,
0.024744553491473198,
0.02216109074652195,
0.052908070385456085,
-0.02092927135527134,
0.03797726333141327,
-0.017470229417085648,
-0.03326571360230446,
0.022032983601093292,
-0.012713467702269554,
-0.04671156033873558,
0.048999182879924774,
-0.013407898135483265,
0.01898213103413582,
0.028981555253267288,
-0.02180328778922558,
0.05791131779551506,
0.03748954087495804,
-0.031384702771902084,
-0.003914672881364822,
-0.024420905858278275,
-0.04870537668466568,
-0.0036291293799877167,
0.015516070649027824,
-0.002198195783421397,
-0.017693014815449715,
-0.05110904946923256,
0.062041155993938446,
0.025848975405097008,
0.011852271854877472,
0.02621379867196083,
-0.026635531336069107,
-0.03553849458694458,
0.004412715323269367,
-0.006339707877486944,
-0.0011277419980615377,
-0.00806309562176466,
0.05255996808409691,
-0.007893639616668224,
0.046940937638282776,
0.008982551284134388,
-0.010680090636014938,
-0.10935060679912567,
0.006803163327276707,
-0.009983480907976627,
0.004254711326211691,
0.032780151814222336,
-0.04632900282740593,
0.005419604945927858,
0.053381893783807755,
-0.06952667236328125,
0.04625134542584419,
-0.018766069784760475,
-0.00013996451161801815,
-0.011927520856261253,
0.013203771784901619,
-0.014630713500082493,
0.10292898118495941,
0.02702142670750618,
0.05777640640735626,
-0.005668007768690586,
-0.006140012759715319,
0.004699663259088993,
-0.004465154372155666,
-0.01872353069484234,
0.02287738397717476,
0.013849824666976929,
0.021810347214341164,
0.030089352279901505,
-0.0012987653026357293,
0.006531897932291031,
0.033609166741371155,
-0.004628896247595549,
0.041468869894742966,
-0.0026007164269685745,
0.020790819078683853,
0.022396409884095192,
-0.00471624406054616,
-0.002068859990686178,
-0.010405296459794044,
-0.031009772792458534,
0.030037086457014084,
0.03876043111085892,
0.03209573030471802,
-0.002854839665815234,
-0.01155022531747818,
0.026555949822068214,
-0.04655556380748749,
-0.030815033242106438,
0.023832743987441063,
0.0014439880615100265,
0.03795040026307106,
-0.023299437016248703,
0.01346964854747057,
0.010318271815776825,
-0.005316380877047777,
-0.013457906432449818,
-0.05388321354985237,
0.0015555039281025529,
-0.0040918816812336445,
0.005592240486294031,
-0.008525305427610874,
0.0051758079789578915,
0.014571161940693855,
-0.04090915620326996,
0.006905638612806797,
-0.00018491409718990326,
0.02016645483672619,
-0.023624086752533913,
-0.006186723709106445,
0.027938345447182655,
0.010353541933000088,
0.02750057354569435,
-0.01898101158440113,
-0.009404033422470093,
0.02276289090514183,
0.02189001999795437,
0.027467958629131317,
0.017777131870388985,
-0.026738950982689857,
-0.06700998544692993,
-0.05015924200415611,
0.05971050634980202,
0.015735430642962456,
-0.014222652651369572,
-0.046378474682569504,
-0.004770972300320864,
-0.009815002791583538,
0.03153498098254204,
0.043787747621536255,
-0.024487698450684547,
0.0037770981434732676,
0.0034858672879636288,
-0.010280262678861618,
0.03844475373625755,
-0.04685506224632263,
-0.036614879965782166,
-0.014411277137696743,
-0.04538949579000473,
-0.030323311686515808,
0.009962719865143299,
-0.06341563165187836,
0.0255095474421978,
0.008463718928396702,
-0.007932545617222786,
0.05235069990158081,
-0.025570008903741837,
-0.034680429846048355,
0.024378526955842972,
0.03631797432899475,
-0.03859299048781395,
0.05101864039897919,
-0.012999016791582108,
-0.002045285888016224,
0.05081067606806755,
-0.04361121356487274,
-0.03925471007823944,
0.015590786933898926,
-0.01823117770254612,
0.0011334358714520931,
0.003472881391644478,
-0.007349200546741486,
0.05087113752961159,
-0.055475328117609024,
-0.024522950872778893,
0.012358542531728745,
-0.05436614900827408,
0.01765560731291771,
0.045305415987968445,
-0.023799730464816093,
-0.003956409636884928,
0.01595650240778923,
0.027322441339492798,
0.040782831609249115,
0.0023542242124676704,
-0.0016469004331156611,
0.05914594233036041,
0.018199769780039787,
0.017043236643075943,
0.033188678324222565,
0.03573577478528023,
0.005326148122549057,
0.024704383686184883,
-0.0019283030414953828,
0.023733412846922874,
-0.01834278181195259,
-0.004953538998961449,
0.017231132835149765,
-0.006186896003782749,
-0.02980630286037922,
0.016813356429338455,
-0.03883447125554085,
0.0762651190161705,
-0.051444198936223984,
0.020046565681695938,
0.037094540894031525,
0.010852759703993797,
-0.011764436028897762,
0.002668610541149974,
0.0003951579565182328,
0.03220820799469948,
0.016094079241156578,
-0.02125411666929722,
-0.028824014589190483,
0.02844705618917942,
0.030083585530519485,
-0.06512658298015594,
0.013205528259277344,
-0.018630703911185265,
-0.015408456325531006,
0.008205324411392212,
-0.007061437238007784,
-0.03238838165998459,
-0.025366440415382385,
0.002980767283588648,
-0.007573988754302263,
-0.018393555656075478,
0.015347609296441078,
0.03112698905169964,
-0.030923519283533096,
0.05666084215044975,
-0.057056985795497894,
0.013499489985406399,
-0.03380079194903374,
0.033369675278663635,
-0.03362439200282097,
-0.0051575591787695885
] |
<p>Let's say I have a cylindrical piston filled with air and fitted with an electrical resistor. The resistor has a current going across it and a voltage for a certain amount of time. My system would be the air inside the piston.</p>
<p>In the first law of thermodynamics: Q - W = E,</p>
<p>Would the power from the resistor for a designated amount of time perform a heat transfer or a work transfer on the air?</p>
| 9,585 |
[
-0.012131749652326107,
-0.035262465476989746,
0.016573473811149597,
0.0052392748184502125,
0.009538531303405762,
-0.008594299666583538,
-0.013313493691384792,
0.0069946711882948875,
0.004040861967951059,
0.0252646803855896,
0.03787706419825554,
0.024120820686221123,
0.05858099088072777,
-0.03763844072818756,
-0.002345845801755786,
-0.02307513915002346,
-0.003120848210528493,
-0.022449426352977753,
-0.003937157336622477,
-0.009799312800168991,
-0.03621423989534378,
0.007317488081753254,
-0.0012203092919662595,
0.011940334923565388,
-0.06262294203042984,
0.06186363846063614,
0.019543008878827095,
-0.025871334597468376,
-0.011603894643485546,
0.0011308889370411634,
0.004106787499040365,
-0.017253872007131577,
0.014194716699421406,
0.027430078014731407,
0.04400637745857239,
-0.012759215198457241,
-0.06054043397307396,
-0.03128381818532944,
0.002140454947948456,
0.014106832444667816,
-0.053207412362098694,
-0.0006905554910190403,
0.04128380864858627,
0.0001630898186704144,
-0.01683959737420082,
0.022930389270186424,
0.01900099404156208,
0.012543239630758762,
0.02672342211008072,
-0.07173427194356918,
0.015064448118209839,
-0.0031469312962144613,
0.045386090874671936,
0.04748328775167465,
-0.03174958750605583,
0.02617507614195347,
0.06934260576963425,
0.06907737255096436,
0.004169792402535677,
-0.03630135580897331,
-0.007287051063030958,
0.04851556196808815,
-0.04485582187771797,
-0.02492247335612774,
-0.016480473801493645,
-0.006012910511344671,
-0.011097469367086887,
-0.0007134331972338259,
0.006745029706507921,
0.014967145398259163,
0.05548759922385216,
0.036237627267837524,
0.0346309058368206,
0.010064896196126938,
0.011105849407613277,
-0.007452018558979034,
0.015809200704097748,
0.018767893314361572,
0.04551471397280693,
0.04583224654197693,
-0.02115052565932274,
-0.02189355157315731,
0.027199797332286835,
0.06452807039022446,
-0.022160479798913002,
-0.04869035258889198,
0.057511378079652786,
-0.042887695133686066,
0.03433637693524361,
0.0267396979033947,
0.04827502742409706,
0.024841351434588432,
0.022679541260004044,
0.0329924114048481,
-0.007583383470773697,
0.01669953763484955,
-0.012370334006845951,
0.015493517741560936,
0.027400147169828415,
-0.032025787979364395,
0.002479635179042816,
-0.02651980146765709,
0.041728731244802475,
0.05428058281540871,
0.02773604542016983,
-0.03325416147708893,
-0.008802616968750954,
0.0004859469481743872,
0.013270252384245396,
0.011091897264122963,
-0.06537674367427826,
0.011411882005631924,
-0.03924590349197388,
-0.006227435078471899,
-0.028671512380242348,
-0.014941997826099396,
0.018056759610772133,
-0.0343119278550148,
0.04404402896761894,
0.02463456429541111,
0.017238806933164597,
-0.022329436615109444,
0.03504673019051552,
0.014906143769621849,
-0.03499079495668411,
0.03318187966942787,
0.016133233904838562,
-0.037693895399570465,
-0.008340176194906235,
0.03786063194274902,
-0.015279616229236126,
-0.029443994164466858,
-0.008563083596527576,
-0.009022495709359646,
0.040810614824295044,
-0.007122010458260775,
-0.08807367086410522,
-0.0590042918920517,
0.004864383488893509,
0.023677701130509377,
-0.019682634621858597,
-0.07645074278116226,
0.004471974913030863,
0.0580202117562294,
0.06918788701295853,
0.010637941770255566,
0.02571415714919567,
-0.028437534347176552,
0.027594631537795067,
0.000520764384418726,
0.01220238208770752,
-0.028540609404444695,
0.03657333925366402,
-0.05394749715924263,
0.03074054606258869,
-0.0398266427218914,
0.011754307895898819,
0.058858610689640045,
-0.004113723058253527,
0.008254880085587502,
0.027914758771657944,
-0.0374579094350338,
0.006911042146384716,
0.028607558459043503,
-0.012108405120670795,
-0.02267380617558956,
0.05252225324511528,
0.02339232712984085,
0.037775225937366486,
0.008547729812562466,
0.03494950011372566,
0.012744197621941566,
-0.001987983239814639,
0.015629900619387627,
0.04834625497460365,
-0.024728931486606598,
-0.01677171140909195,
-0.03686228767037392,
0.01130255963653326,
0.0008488050079904497,
-0.036794647574424744,
-0.03185654059052467,
-0.005571853835135698,
-0.012990058399736881,
-0.01748642325401306,
0.06311243772506714,
0.009800662286579609,
-0.010531757026910782,
0.00008669519593240693,
0.004171277862042189,
-0.05137119069695473,
-0.07049638032913208,
0.041104692965745926,
0.009840487502515316,
-0.02329203672707081,
0.029723452404141426,
0.0019493673462420702,
0.06632745265960693,
-0.04208321496844292,
-0.0005809059366583824,
-0.004511370323598385,
-0.0014075019862502813,
0.002304194960743189,
-0.02195036970078945,
0.006370656657963991,
0.027939114719629288,
0.04647951200604439,
-0.004776885267347097,
0.04392683133482933,
-0.034051407128572464,
-0.015260330401360989,
-0.011500071734189987,
-0.01964634470641613,
0.01765381544828415,
-0.002867902861908078,
0.02276586927473545,
0.02348024956882,
0.0060563646256923676,
0.01970319263637066,
0.0014836388872936368,
-0.0017845634138211608,
0.056422557681798935,
0.04752630740404129,
0.024378441274166107,
-0.015237557701766491,
0.04070161283016205,
-0.00001962439091585111,
-0.023647697642445564,
0.005835528951138258,
-0.034432440996170044,
-0.039813682436943054,
0.04823146387934685,
0.037192974239587784,
0.024587688967585564,
-0.013474751263856888,
0.02247622422873974,
0.052446283400058746,
0.038116052746772766,
0.024117516353726387,
0.027727579697966576,
-0.003005871083587408,
-0.01019490696489811,
0.04718942567706108,
-0.007572553586214781,
0.02395297959446907,
0.010558415204286575,
0.031462542712688446,
0.0200321264564991,
0.04079771786928177,
0.0026294239796698093,
-0.02708452008664608,
0.04381807520985603,
0.02411315031349659,
0.03878452628850937,
-0.017000455409288406,
-0.04204742982983589,
0.026565544307231903,
-0.048979490995407104,
0.0168167594820261,
-0.0024547921493649483,
0.00785779394209385,
0.033284470438957214,
-0.0005891639739274979,
-0.013174827210605145,
-0.03135879337787628,
-0.0020213464740663767,
0.016929080709815025,
-0.02846808172762394,
0.03256988897919655,
-0.024193430319428444,
0.03937887027859688,
-0.01715257577598095,
0.014416967518627644,
-0.03467516228556633,
0.003331001615151763,
-0.010393825359642506,
0.02876230515539646,
0.012332260608673096,
-0.05013669282197952,
-0.06353709101676941,
-0.007149755954742432,
-0.025895196944475174,
0.0042991917580366135,
0.013182586058974266,
-0.04394606128334999,
0.0013770536752417684,
-0.04552983492612839,
-0.032049015164375305,
0.040473006665706635,
-0.014568467624485493,
-0.033275920897722244,
0.00353394472040236,
-0.015528316609561443,
-0.03710325434803963,
0.020381158217787743,
-0.034863874316215515,
0.016183365136384964,
-0.011126115918159485,
0.000012517944924184121,
0.05858395993709564,
-0.026262128725647926,
-0.04595628380775452,
0.02362031117081642,
-0.06286145001649857,
-0.027741767466068268,
0.02542390115559101,
-0.003994033206254244,
0.042623791843652725,
-0.015535817481577396,
0.06189628317952156,
0.016780149191617966,
-0.039658401161432266,
-0.03191469982266426,
-0.03111734800040722,
-0.06502752751111984,
0.03001142293214798,
-0.03243706375360489,
0.009137118235230446,
-0.023808438330888748,
-0.051398493349552155,
0.0506926067173481,
-0.015417037531733513,
-0.018466949462890625,
0.0029727478977292776,
-0.05525777488946915,
-0.036958958953619,
-0.0357956625521183,
-0.005205806344747543,
0.039044395089149475,
-0.024908851832151413,
0.019107690081000328,
0.02988523803651333,
0.0375087633728981,
-0.003319122828543186,
0.027583006769418716,
-0.04678008332848549,
0.023729654029011726,
0.027193725109100342,
-0.003931492101401091,
0.04990137368440628,
0.008751289919018745,
0.029717257246375084,
0.06309336423873901,
-0.036625467240810394,
0.01658129133284092,
0.037262216210365295,
-0.052448421716690063,
0.0243249349296093,
-0.02075268141925335,
0.0049886987544596195,
-0.06016936153173447,
0.0546012744307518,
-0.029072485864162445,
0.011247964575886726,
-0.019793329760432243,
0.03194707632064819,
0.037507977336645126,
0.007533866912126541,
0.0073371827602386475,
0.009852109476923943,
0.0658390000462532,
-0.004167825914919376,
-0.021982984617352486,
-0.014289362356066704,
-0.010379294864833355,
0.041145093739032745,
0.01871619187295437,
-0.013243124820291996,
0.038661789149045944,
0.014589170925319195,
0.03015904128551483,
0.020288381725549698,
-0.03408830985426903,
0.014284666627645493,
-0.08142087608575821,
-0.013027334585785866,
-0.005739765707403421,
0.08326887339353561,
0.0040013957768678665,
0.07264329493045807,
0.006067940965294838,
0.00934906117618084,
0.039407774806022644,
-0.008360383100807667,
-0.06339209526777267,
0.043075717985630035,
-0.017804410308599472,
-0.023605361580848694,
-0.0008388971909880638,
-0.0006604800000786781,
0.003112750593572855,
-0.044244054704904556,
-0.005433349404484034,
0.007811132352799177,
-0.012973625212907791,
-0.043296776711940765,
0.021729260683059692,
-0.01827983558177948,
-0.04224177449941635,
-0.04052111133933067,
0.020871413871645927,
0.054465435445308685,
-0.049904126673936844,
0.04160884767770767,
0.04810938611626625,
-0.013829195871949196,
0.029941020533442497,
0.02571233920753002,
-0.04023244231939316,
0.007678415160626173,
0.0046301172114908695,
0.014820138923823833,
-0.018502751365303993,
-0.02152831107378006,
0.031499676406383514,
0.028345739468932152,
0.035203833132982254,
-0.009450332261621952,
-0.020888058468699455,
-0.027723534032702446,
-0.038744017481803894,
-0.02862706035375595,
0.02106989547610283,
0.04511342942714691,
0.01364120002835989,
0.03560575097799301,
-0.02979329787194729,
-0.03386252745985985,
-0.03181784227490425,
0.008474394679069519,
0.05199861526489258,
0.030543910339474678,
-0.03057706356048584,
-0.032493673264980316,
-0.01648722216486931,
-0.02563057839870453,
0.007463986519724131,
0.020792387425899506,
0.03551304340362549,
-0.03840339183807373,
0.009192954748868942,
-0.0067202746868133545,
0.01815749704837799,
-0.002404712839052081,
0.013444280251860619,
0.02605617605149746,
-0.00580414617434144,
0.00013553503958974034,
-0.013360381126403809,
0.06263436377048492,
0.007982083596289158,
-0.0193556509912014,
0.019987579435110092,
-0.004520625341683626,
-0.08448582142591476,
-0.021526318043470383,
0.04331681877374649,
0.02739144116640091,
-0.03214623034000397,
-0.02076273038983345,
-0.03882577642798424,
-0.02229068987071514,
0.05929742008447647,
-0.04740145057439804,
0.04747917130589485,
-0.0015970837557688355,
-0.0276657585054636,
-0.007142298389226198,
-0.06485629081726074,
-0.005954844877123833,
0.036615610122680664,
-0.024888675659894943,
0.04513592645525932,
0.0026993027422577143,
-0.03331854194402695,
0.025392286479473114,
-0.01829971931874752,
0.03595871478319168,
0.012039201334118843,
-0.034603655338287354,
0.029081271961331367,
-0.02774762362241745,
0.010001271963119507,
-0.01356348767876625,
-0.0703720673918724,
-0.008482229895889759,
-0.029592016711831093,
-0.04188680276274681,
0.018406638875603676,
-0.036699194461107254,
-0.028246045112609863,
0.044065676629543304,
0.0099501246586442,
0.01018276996910572,
-0.05940267816185951,
-0.054862722754478455,
0.04530768841505051,
0.024135924875736237,
0.013079282827675343,
0.06263917684555054,
0.07415828853845596,
-0.045065782964229584,
0.002358334604650736,
0.005045727826654911,
0.049264319241046906,
-0.014843488112092018,
0.0004522947419900447,
-0.006045147310942411,
0.00042171499808318913,
0.004181903321295977,
0.03399574011564255,
-0.0069273533299565315,
0.03045133501291275,
-0.026424728333950043,
-0.019447483122348785,
-0.007104834076017141,
-0.001893861684948206,
0.005799613427370787,
-0.02015496790409088,
-0.0071039991453289986,
0.04683484137058258,
-0.014732997864484787,
-0.01550853531807661,
0.007278847508132458,
0.015277049504220486,
0.016988253220915794,
0.017152059823274612,
0.013417360372841358,
0.019979316741228104,
-0.01345922239124775,
0.012813338078558445,
-0.0073363445699214935,
-0.027686048299074173,
0.03653167188167572,
-0.013309070840477943,
-0.01598011516034603,
0.035325221717357635,
-0.06646417826414108,
-0.007029639557003975,
0.009073173627257347,
0.005219230893999338,
0.006686123553663492,
-0.057041145861148834,
0.01974542811512947,
0.03824140876531601,
0.010197984986007214,
-0.055294428020715714,
-0.048591289669275284,
0.0184050090610981,
0.02528812550008297,
0.01715562306344509,
-0.03981095179915428,
-0.02311696670949459,
-0.03704806789755821,
-0.03635892644524574,
0.020559586584568024,
0.020026763901114464,
-0.029633548110723495,
0.03788851201534271,
0.02087385207414627,
0.022074604406952858,
0.018800530582666397,
0.03583405539393425,
-0.02216549590229988,
0.019005917012691498,
-0.007566662039607763,
-0.03983500972390175,
-0.009233858436346054,
0.0030880558770149946,
-0.04179491102695465,
0.0003314688801765442,
0.0017385659739375114,
0.01654798723757267,
0.008832919411361217,
0.024017974734306335,
-0.01915399730205536,
0.00989893451333046,
0.018386460840702057,
-0.03772252798080444,
-0.0032704449258744717,
0.03967871516942978,
0.01523217186331749,
-0.000837013591080904,
-0.009581116959452629,
-0.01698748953640461,
-0.054367441684007645,
-0.03045850247144699,
-0.016706721857190132,
0.0166352316737175,
-0.016440941020846367,
0.008084413595497608,
0.06286575645208359,
-0.03846282511949539,
0.01329491101205349,
0.029695574194192886,
-0.016358276829123497,
-0.0008552247891202569,
0.00937194749712944,
0.00678938627243042,
-0.0007304484024643898,
-0.014201550744473934,
-0.021367106586694717,
-0.026911640539765358,
-0.03823333978652954,
-0.04505148157477379,
0.07323954999446869,
-0.035250913351774216,
0.06385976076126099,
0.02386505715548992,
-0.02079368382692337,
0.02864048071205616,
0.0010030834237113595,
0.01601753756403923,
0.013206207193434238,
-0.008633015677332878,
0.008372492156922817,
0.02070736512541771,
-0.022295517846941948,
0.02516590617597103,
0.029728030785918236,
0.0033460368867963552,
-0.021884167566895485,
0.027152501046657562,
0.005192741751670837,
0.005131355952471495,
-0.028254792094230652,
-0.024216998368501663,
0.004641560837626457,
-0.04934103786945343,
0.0768471285700798,
-0.009103909134864807,
0.0334569476544857,
0.028083326295018196,
0.009762246161699295,
-0.014885748736560345,
-0.05599016323685646,
0.010387670248746872,
-0.05768987908959389,
0.017619147896766663,
-0.004862998146563768,
0.013870845548808575,
0.013317631557583809,
0.0050480421632528305,
0.06693439930677414,
-0.015402838587760925,
0.007930331863462925,
0.029606152325868607,
-0.027470871806144714,
0.02949122153222561,
-0.0029524618294090033,
-0.026427242904901505,
0.03780088573694229,
-0.029294434934854507,
-0.032527294009923935,
0.021371368318796158,
-0.021709561347961426,
0.0018943179165944457,
-0.013781015761196613,
0.024446241557598114,
-0.008000430651009083,
0.09665877372026443,
-0.015586280263960361,
-0.0237484872341156,
-0.011216185986995697,
0.02469128742814064,
0.11108948290348053,
0.03986682370305061,
0.029540890827775,
-0.022514307871460915,
0.008630375377833843,
-0.011011932045221329,
-0.0019349523354321718,
-0.021481169387698174,
0.003021474927663803,
-0.05634313076734543,
0.012925446964800358,
0.043598540127277374,
0.01889493688941002,
0.002692027948796749,
0.004827555269002914,
0.01912532187998295,
-0.0553327277302742,
0.008921920321881771,
0.0249054916203022,
0.023771243169903755,
0.008508286438882351,
0.04508751258254051,
-0.050656579434871674,
-0.01831601932644844,
-0.03512972220778465,
-0.0007035257876850665,
-0.003597433678805828,
-0.08946571499109268,
0.06635581701993942,
-0.008712450973689556,
-0.0364583283662796,
0.019496727734804153,
-0.008477105759084225,
-0.006477349437773228,
-0.009827123954892159,
0.010979730635881424,
0.008528873324394226,
0.0019095325842499733,
0.013975538313388824,
0.052797093987464905,
0.017045242711901665,
-0.017778534442186356,
-0.021117091178894043,
0.021322472020983696,
-0.06660447269678116,
-0.005336714908480644,
-0.046735331416130066,
0.004647410940378904,
-0.0053805941715836525,
0.04691195860505104,
0.0269230455160141,
0.0009822399588301778,
-0.009667957201600075,
-0.05699174851179123,
-0.03243568539619446,
0.0007660241099074483,
0.026852482929825783,
0.0026403735391795635,
-0.01615910977125168,
-0.030860481783747673,
0.027907779440283775,
-0.03701915219426155,
0.002189700026065111,
0.005050645675510168,
-0.02113039419054985,
0.0107266241684556,
0.010548984631896019,
0.02632739581167698,
-0.07094401121139526,
-0.041758663952350616,
-0.012756084091961384,
-0.02624776028096676,
-0.051750149577856064,
0.020985225215554237,
0.026655012741684914,
0.02959841676056385,
0.01694798842072487,
-0.013048109598457813,
-0.03201717138290405,
-0.05707312002778053,
-0.07159999758005142,
0.010733951814472675,
0.024398766458034515,
0.00698460079729557,
-0.027593368664383888,
-0.007050063461065292,
0.020418763160705566,
0.07701021432876587,
0.021360479295253754,
-0.014436953701078892,
0.03536298871040344,
0.021011315286159515,
0.0660339817404747,
-0.03268974646925926,
0.007077520713210106,
-0.00344374543055892,
-0.043816905468702316,
-0.014938205480575562,
-0.010261496528983116,
0.03830868750810623,
0.023013826459646225,
-0.024095162749290466,
-0.040737640112638474,
0.036033257842063904,
-0.01176844909787178,
0.011796322651207447,
0.023268071934580803,
-0.02260405570268631,
-0.03471546247601509,
0.008108004927635193,
0.010302052833139896,
-0.010092641226947308,
-0.04135192930698395,
-0.057833705097436905,
-0.012131022289395332,
-0.004597076680511236,
0.011184128001332283,
-0.005144334863871336,
0.027823083102703094,
-0.03681342676281929,
0.0527140311896801,
-0.05531980097293854,
0.0056493934243917465,
-0.06401485204696655,
-0.019854528829455376,
0.03695487231016159,
0.03982551023364067,
0.02953352965414524,
0.03990398347377777,
-0.04083388298749924,
0.007913907989859581,
0.0012419521808624268,
0.010291275568306446,
-0.031258195638656616,
-0.02339434251189232,
0.0008497649105265737,
-0.006122051738202572,
0.016184451058506966,
-0.013907238841056824,
-0.04924833029508591,
0.06466665863990784,
-0.029883135110139847,
-0.01726641319692135,
0.029992597177624702,
0.012361590750515461,
0.008460432291030884,
0.025967169553041458,
-0.033603690564632416,
-0.011861527338624,
0.05904868245124817,
-0.03743114694952965,
-0.0019723831210285425,
0.0007819542661309242,
-0.0652584657073021,
-0.010852965526282787,
-0.005200497340410948,
0.04794551432132721,
-0.009281432256102562,
-0.013918179087340832,
0.03538066893815994,
0.052020762115716934,
-0.007321756798774004,
-0.0022085439413785934,
0.010087843984365463,
-0.011438118293881416,
0.017498547211289406,
0.04158741980791092,
-0.0072402022778987885,
0.04215599596500397,
0.024614328518509865,
-0.032057274132966995,
0.02685219794511795,
-0.0036030851770192385,
-0.0562906451523304,
-0.11036600172519684,
0.006444893777370453,
0.011577128432691097,
-0.008833590894937515,
0.007607450243085623,
-0.0339260958135128,
0.015208238735795021,
0.01701490394771099,
-0.06910423189401627,
0.04103299602866173,
-0.026841122657060623,
-0.007897350937128067,
-0.01663311943411827,
0.025420058518648148,
-0.026220280677080154,
0.022847875952720642,
0.015471549704670906,
0.008853374049067497,
0.003909904509782791,
0.0355132631957531,
-0.003219479927793145,
-0.03510652855038643,
0.014916247688233852,
0.044124163687229156,
0.00856320746243,
0.016257472336292267,
0.011852016672492027,
-0.05790776014328003,
0.023925891146063805,
0.021836813539266586,
-0.02813679911196232,
0.0335737019777298,
-0.03615584969520569,
0.0011274486314505339,
-0.004165701102465391,
0.046561066061258316,
0.017023928463459015,
-0.029480183497071266,
-0.012568144127726555,
0.023263216018676758,
0.010395566932857037,
0.019787460565567017,
-0.02260155789554119,
-0.013643380254507065,
0.02928953990340233,
0.014178361743688583,
-0.043527547270059586,
0.03025699034333229,
0.021959213539958,
-0.016582535579800606,
0.05657330900430679,
-0.011830056086182594,
0.0225500650703907,
0.02466464415192604,
-0.021393021568655968,
-0.03165913745760918,
0.018791915848851204,
0.03140481561422348,
-0.006217372603714466,
-0.027987584471702576,
-0.01356466207653284,
-0.048888567835092545,
0.013792426325380802,
0.030620602890849113,
0.01311098225414753,
-0.010629291646182537,
-0.05740854889154434,
-0.01937035284936428,
-0.008298537693917751,
-0.030459100380539894,
-0.03529283031821251,
-0.042771220207214355,
0.017084989696741104,
0.008767238818109035,
0.03096267208456993,
0.017094632610678673,
0.007602084893733263,
-0.04472258687019348,
-0.007796177640557289,
-0.029055627062916756,
0.07113426923751831,
-0.0024667750112712383,
-0.011060580611228943,
-0.02571844682097435,
-0.053181182593107224,
0.009603023529052734,
0.01997784711420536,
0.06984034180641174,
-0.0006647782865911722,
-0.055735357105731964,
-0.01151794008910656,
-0.04377969354391098,
0.029354050755500793,
-0.0077013885602355,
0.022264845669269562,
-0.013659076765179634,
-0.011956818401813507,
-0.013141509145498276,
0.02706148661673069,
-0.0354490727186203,
0.029452577233314514,
0.059711914509534836,
-0.03754429891705513,
-0.03782021254301071,
-0.03885156288743019,
-0.03726057708263397,
0.02335348166525364,
0.022063396871089935,
-0.012908397242426872,
0.056418001651763916,
-0.027213091030716896,
0.02509077824652195,
0.006498158443719149,
-0.05420709773898125,
-0.03398866578936577,
0.006117729004472494,
-0.027441607788205147,
0.0252198688685894,
-0.00021550047677010298,
-0.03381810337305069,
0.026494337245821953,
-0.034371305257081985,
-0.025171346962451935,
0.005733775906264782,
-0.01681271567940712,
0.015043327584862709,
0.023026470094919205,
0.028154227882623672,
0.027420761063694954,
-0.039870038628578186,
0.0011295042932033539,
-0.03374921903014183,
0.029414532706141472,
-0.036553073674440384,
0.026048358529806137,
0.04514151066541672,
0.005207248963415623,
-0.014477122575044632,
0.029241416603326797,
-0.0316629633307457,
0.03361774608492851,
0.004018343053758144,
0.01261069718748331,
-0.033064406365156174,
-0.020696302875876427,
0.0022501121275126934,
-0.006166759412735701,
-0.02696596272289753,
0.02067846991121769,
-0.011300578713417053,
0.06324311345815659,
-0.02516215294599533,
-0.0006289798766374588,
-0.04561247676610947,
-0.04002543166279793,
-0.004877875093370676,
-0.01820444129407406,
0.03574468567967415,
0.02774703875184059,
0.02279842086136341,
-0.012310653924942017,
-0.020221877843141556,
-0.02743980847299099,
0.014307929202914238,
-0.033548299223184586,
0.0270571019500494,
0.011850395239889622,
0.01604275591671467,
-0.0415029302239418,
-0.002141756471246481,
-0.03436802327632904,
-0.014725510030984879,
0.038911886513233185,
0.06643163412809372,
0.025509318336844444,
0.0057443068362772465,
-0.017421355471014977,
-0.005509156733751297,
0.04170287400484085,
-0.01599081978201866,
0.0049046617932617664,
-0.009966081939637661,
0.05711260065436363,
0.06333379447460175,
0.010317028500139713
] |
<p>Not sure if this is perfectly a physics question:</p>
<p>A rope is wrapped around a cylinder of diameter D. The cylinder is slightly eccentric so that the distance between the axis of the cylinder and the axis of rotation is e. As the cylinder rotates, it pulls the rope. At t=0, the far end of the rope is at position 0.</p>
<p>What is the function of the rope position with respect to the angle of rotation of the cylinder? (This is not a homework question BTW)</p>
<p><img src="http://i.stack.imgur.com/no8wz.png" alt="enter image description here"></p>
| 9,586 |
[
-0.03023665025830269,
0.027045127004384995,
-0.018378952518105507,
-0.006547136232256889,
0.022130226716399193,
-0.008327622897922993,
-0.005320731084793806,
0.005532825831323862,
-0.0058169919066131115,
-0.03661420941352844,
0.034020405262708664,
0.06708108633756638,
0.028793012723326683,
0.04720122739672661,
0.020011350512504578,
0.0034168928395956755,
-0.01781759224832058,
-0.017512332648038864,
-0.004573707468807697,
-0.03150233253836632,
-0.032666295766830444,
0.01898587867617607,
-0.007629814092069864,
0.03784937784075737,
-0.028302352875471115,
0.019433600828051567,
0.05471311882138252,
0.0035915495827794075,
0.01643338054418564,
0.07096023857593536,
-0.009332694113254547,
-0.012594854459166527,
-0.017554422840476036,
0.02227773703634739,
0.032504599541425705,
0.04696222394704819,
-0.037709273397922516,
-0.01612868532538414,
-0.020447829738259315,
0.02646181918680668,
-0.011946871876716614,
0.0017628917703405023,
-0.02164130099117756,
0.05476094409823418,
-0.004268574994057417,
0.04394006356596947,
-0.026965580880641937,
0.005911726504564285,
0.09890146553516388,
-0.05055644363164902,
0.06601423025131226,
-0.015172678045928478,
0.01712053082883358,
-0.008061440661549568,
-0.009372682310640812,
-0.01523576583713293,
0.06489600241184235,
0.0278373584151268,
-0.03360378369688988,
-0.06606139242649078,
-0.039249714463949203,
-0.03187946975231171,
-0.03842723369598389,
-0.04096994176506996,
-0.011057782918214798,
0.0030132727697491646,
0.000543145346455276,
0.012963417917490005,
0.04912308230996132,
-0.009871921502053738,
-0.030367502942681313,
0.008691289462149143,
0.03377089276909828,
-0.04398128017783165,
0.024141399189829826,
-0.0579679012298584,
0.020784448832273483,
0.0103237833827734,
0.03256230428814888,
0.01680595800280571,
-0.020589232444763184,
-0.008163579739630222,
0.05842692777514458,
0.03748483955860138,
0.01999604143202305,
-0.024609658867120743,
0.048817116767168045,
0.01092651579529047,
0.031041854992508888,
0.05972429737448692,
0.0033696587197482586,
0.002375984098762274,
0.028798580169677734,
0.00366876064799726,
0.002753184176981449,
0.029605716466903687,
0.0016393180703744292,
0.04198601841926575,
0.014237898401916027,
-0.031127477064728737,
-0.013000466860830784,
-0.04457177221775055,
0.02821691334247589,
0.0521753691136837,
0.0067480215802788734,
0.02810954675078392,
0.03169536963105202,
-0.02209498919546604,
0.002551052253693342,
-0.0051345196552574635,
-0.003845162922516465,
0.001549989334307611,
-0.007496928796172142,
-0.03937448561191559,
-0.029196854680776596,
-0.021275222301483154,
0.0008254516287706792,
0.0007049795240163803,
0.05776266008615494,
0.0352330282330513,
0.0396583266556263,
-0.06399669498205185,
0.02593967691063881,
-0.029991839081048965,
-0.03293115645647049,
0.02121357060968876,
0.04943219572305679,
-0.032617874443531036,
-0.04121089354157448,
0.05193917080760002,
-0.0022083891090005636,
-0.01076191384345293,
0.0017126897582784295,
-0.00005823087485623546,
0.04502961039543152,
-0.019650882109999657,
-0.07280433923006058,
-0.06634771078824997,
0.028711184859275818,
0.048128411173820496,
-0.000015820161934243515,
-0.06033450365066528,
-0.027971435338258743,
0.017427563667297363,
0.0668955147266388,
0.009018894284963608,
0.017784396186470985,
-0.01414612028747797,
0.025076797232031822,
-0.0053045847453176975,
-0.005767481867223978,
0.013058611191809177,
-0.0023336850572377443,
-0.05128587782382965,
-0.02271757833659649,
-0.04074401408433914,
-0.005857508163899183,
0.028871258720755577,
-0.008279165253043175,
-0.03802885860204697,
0.0601203553378582,
-0.03278740122914314,
0.021640392020344734,
0.027934879064559937,
-0.04581695795059204,
-0.05029826611280441,
0.08353032916784286,
0.022725742310285568,
0.008832472376525402,
0.03225984051823616,
-0.0032127550803124905,
0.03401587903499603,
-0.01487454678863287,
0.012863819487392902,
0.02769918367266655,
-0.048794761300086975,
-0.013817120343446732,
-0.0044995322823524475,
0.02038850262761116,
0.0017841317458078265,
-0.02697008103132248,
-0.057604238390922546,
0.02206186205148697,
0.018231354653835297,
-0.00807974673807621,
0.06936777383089066,
-0.039010077714920044,
-0.004433253780007362,
-0.01844685897231102,
-0.0158771313726902,
0.001083635725080967,
-0.04221544787287712,
0.051841866225004196,
-0.0263151153922081,
-0.015622812323272228,
-0.02083849348127842,
0.0216230321675539,
0.027287835255265236,
-0.029688145965337753,
0.03901609033346176,
0.0026832749135792255,
0.022491198033094406,
0.005040119867771864,
0.0161444041877985,
0.0026498977094888687,
0.038031112402677536,
0.0423334538936615,
0.0038026527035981417,
0.006069884169846773,
-0.04131949692964554,
-0.008664482273161411,
-0.0013609821908175945,
-0.02184045873582363,
0.02270316705107689,
0.0018749355804175138,
0.01880890503525734,
0.0030967469792813063,
0.010796376504004002,
0.0010650195181369781,
0.028458451852202415,
-0.0015584788052365184,
0.09462029486894608,
0.014118138700723648,
0.007956670597195625,
0.03824923560023308,
0.025017406791448593,
0.0028581181541085243,
0.04153921455144882,
0.011325010098516941,
-0.035443466156721115,
-0.029053708538413048,
0.025103263556957245,
0.014222020283341408,
0.02829725109040737,
-0.03919025883078575,
0.000012996571058465634,
0.034062862396240234,
0.030851025134325027,
0.0033031688071787357,
0.029887082055211067,
-0.02830134704709053,
0.004550526849925518,
-0.010671177878975868,
0.007838726043701172,
-0.025283208116889,
0.001595009583979845,
0.019971145316958427,
0.03410356864333153,
0.05782337114214897,
0.018333040177822113,
-0.03998834267258644,
0.08631105720996857,
0.008280649781227112,
0.04584839195013046,
0.0016862597549334168,
-0.0363122783601284,
0.05344991385936737,
-0.031708959490060806,
-0.007770421914756298,
0.032896678894758224,
-0.0014672121033072472,
0.017836542800068855,
0.008068147115409374,
-0.015194070525467396,
0.013728553429245949,
-0.02239999920129776,
-0.023533515632152557,
-0.03291195258498192,
0.025620685890316963,
-0.019002309069037437,
0.0008015770581550896,
-0.015036473050713539,
0.004952073562890291,
-0.025637798011302948,
0.011853641830384731,
0.008510127663612366,
0.008917397819459438,
0.0387699231505394,
-0.02169199101626873,
-0.0368078388273716,
-0.011983530595898628,
-0.04925025999546051,
-0.005119480658322573,
0.009075138717889786,
-0.054599639028310776,
0.007546727079898119,
0.0003045037155970931,
-0.04515441879630089,
0.05764249712228775,
-0.009106085635721684,
-0.024057738482952118,
0.0076696304604411125,
-0.02817254327237606,
-0.021791638806462288,
-0.02597021870315075,
-0.02103160321712494,
0.03431122004985809,
-0.02307487465441227,
-0.0415993370115757,
0.04486360028386116,
-0.0050929817371070385,
0.010896137915551662,
0.06010347232222557,
-0.08359476923942566,
-0.035923223942518234,
-0.011011913418769836,
0.012574230320751667,
0.021262338384985924,
-0.027741247788071632,
-0.007169913966208696,
-0.023511525243520737,
-0.014565526507794857,
0.00793974008411169,
-0.06041932478547096,
-0.06588257849216461,
-0.027449339628219604,
0.008700389415025711,
0.01596500538289547,
-0.0068663000129163265,
-0.004394515883177519,
0.05455584079027176,
0.004734057001769543,
-0.036592260003089905,
-0.036796797066926956,
-0.021728860214352608,
-0.019426383078098297,
-0.004337048623710871,
0.012643243186175823,
0.01033561397343874,
-0.04079791530966759,
0.014456736855208874,
0.008310102857649326,
-0.014990908093750477,
0.04408919811248779,
0.04051090031862259,
-0.013041548430919647,
0.002666161395609379,
0.023168426007032394,
-0.01039073895663023,
0.080361507833004,
0.040620751678943634,
-0.007806628942489624,
0.029720798134803772,
-0.00882341805845499,
0.03485296666622162,
-0.005161892622709274,
-0.011174246668815613,
0.03709501400589943,
0.011522991582751274,
-0.0083460146561265,
0.026645099744200706,
0.0537659116089344,
0.006382342427968979,
-0.0077964989468455315,
-0.00912794191390276,
-0.0030010228510946035,
0.01857120916247368,
-0.023528192192316055,
-0.02737436629831791,
0.0479947030544281,
0.025713304057717323,
-0.025255592539906502,
-0.038039885461330414,
-0.034641750156879425,
0.0020624687895178795,
0.041209589689970016,
-0.043647829443216324,
-0.04095819219946861,
0.03160851076245308,
0.02832692489027977,
0.0494709275662899,
-0.005862933583557606,
-0.06714027374982834,
0.021164461970329285,
-0.05096350982785225,
-0.013837721198797226,
0.02700803615152836,
0.05037463828921318,
0.00043819789425469935,
0.07057715207338333,
0.01622002013027668,
0.02128509059548378,
0.029170874506235123,
0.06956589221954346,
-0.07478655874729156,
0.05102497339248657,
-0.032597701996564865,
-0.021076172590255737,
0.013052606955170631,
0.018590131774544716,
0.007009620778262615,
-0.045394424349069595,
0.004744693171232939,
0.016584299504756927,
-0.02752840146422386,
-0.04095679149031639,
-0.026792291551828384,
-0.022623885422945023,
-0.013145025819540024,
-0.018092213198542595,
0.011391069740056992,
0.009336556307971478,
-0.004935335833579302,
0.05698152258992195,
0.07083894312381744,
-0.04366343840956688,
0.009829598478972912,
0.0280243381857872,
-0.016912026330828667,
-0.031815774738788605,
0.055966008454561234,
0.016049856320023537,
0.005509449169039726,
-0.02700940892100334,
0.027995988726615906,
-0.00936654768884182,
0.05173198878765106,
0.04440625384449959,
-0.032200973480939865,
-0.015013505704700947,
-0.05783647298812866,
-0.04478022828698158,
-0.048127565532922745,
0.07770733535289764,
-0.015608185902237892,
-0.010051988065242767,
0.05175025761127472,
-0.020850207656621933,
-0.012869218364357948,
0.018404046073555946,
0.05776814743876457,
0.024658527225255966,
-0.04423518478870392,
-0.0506090484559536,
-0.026764478534460068,
-0.008308554999530315,
0.023145999759435654,
-0.019579743966460228,
-0.02520700916647911,
-0.015245436690747738,
-0.02476167306303978,
0.0016565945697948337,
0.004270540550351143,
-0.011938491836190224,
-0.003991891164332628,
-0.013270513154566288,
0.03238048776984215,
-0.023395227268338203,
0.02390426956117153,
0.03189394623041153,
0.01637672446668148,
0.057843439280986786,
-0.013222378678619862,
0.002336654579266906,
-0.07184585928916931,
-0.036478206515312195,
0.0428834930062294,
0.0411749891936779,
-0.03271782025694847,
-0.011286824010312557,
-0.0337304063141346,
-0.03859690949320793,
0.06207713857293129,
-0.051684800535440445,
0.03941451385617256,
-0.03939199447631836,
-0.01004017237573862,
-0.001114864950068295,
-0.016219163313508034,
-0.03922726958990097,
-0.008070239797234535,
-0.04137994349002838,
0.013878989964723587,
-0.02120845578610897,
-0.010522285476326942,
-0.013879654929041862,
0.005289457738399506,
0.04997912794351578,
0.02388457953929901,
-0.01782628707587719,
-0.029512543231248856,
0.0015514325350522995,
-0.00400132592767477,
-0.015818296000361443,
-0.05204862728714943,
0.02451232448220253,
-0.003388203913345933,
-0.010926666669547558,
0.011249144561588764,
-0.024368342012166977,
0.0020237809512764215,
0.01806536875665188,
-0.015352599322795868,
-0.0031953412108123302,
0.01485113613307476,
-0.037102069705724716,
-0.007107991725206375,
0.04397284612059593,
-0.0015372727066278458,
0.02963108941912651,
0.0708736702799797,
0.00082954834215343,
0.018951551988720894,
-0.023167576640844345,
0.031532131135463715,
0.007218512706458569,
-0.022179752588272095,
-0.028729790821671486,
0.009053281508386135,
-0.05145038291811943,
0.011650304310023785,
-0.002512682694941759,
0.01462673768401146,
-0.04649197310209274,
-0.008733141236007214,
-0.012263174168765545,
0.029055992141366005,
0.005769804120063782,
-0.009017188102006912,
0.029153235256671906,
-0.0033371716272085905,
0.005141390487551689,
-0.02287149988114834,
-0.019192811101675034,
-0.006447917781770229,
-0.0021109168883413076,
0.011189121752977371,
0.0008950653136707842,
-0.01487511582672596,
-0.0005171632510609925,
-0.006281145382672548,
-0.009608937427401543,
-0.07357349991798401,
0.0057878210209310055,
-0.03726081922650337,
-0.00020788070105481893,
0.018811143934726715,
-0.0618419386446476,
-0.020452821627259254,
-0.0021813372150063515,
-0.012988755479454994,
0.026484759524464607,
-0.017078079283237457,
0.017448486760258675,
-0.0023895881604403257,
-0.01562817394733429,
-0.010548334568738937,
-0.059899430721998215,
0.018008721992373466,
0.009963254444301128,
-0.01409192755818367,
0.010239414870738983,
-0.0056462702341377735,
-0.027850234881043434,
-0.016786964610219002,
-0.00912987906485796,
0.056778259575366974,
-0.016322722658514977,
-0.006022143643349409,
0.06562051922082901,
-0.038320548832416534,
0.07131817936897278,
0.023495204746723175,
0.0036038074176758528,
0.008436611853539944,
-0.014337952248752117,
-0.016732966527342796,
0.03266593813896179,
0.060616713017225266,
-0.02145758457481861,
-0.014331157319247723,
0.03536595404148102,
0.040087852627038956,
0.01094967033714056,
0.00024944954202510417,
0.017669642344117165,
0.003722738940268755,
0.02642989344894886,
0.009135568514466286,
-0.018349796533584595,
0.021607656031847,
0.022142358124256134,
0.002960500307381153,
0.016244813799858093,
0.013547929003834724,
-0.03233504667878151,
-0.05632087215781212,
0.002302555600181222,
-0.004066056106239557,
0.016325367614626884,
0.020248161628842354,
0.05481971427798271,
-0.008909638971090317,
-0.0015402197604998946,
-0.0057473997585475445,
0.037265148013830185,
0.04482555389404297,
0.024353792890906334,
-0.02857477031648159,
0.02419315278530121,
0.008263510651886463,
-0.025822347030043602,
-0.04618178308010101,
-0.012875773012638092,
-0.01721184514462948,
0.07596302777528763,
-0.016931183636188507,
0.07519980520009995,
-0.0020448609720915556,
0.03215556591749191,
0.004401858896017075,
0.0026693318504840136,
-0.006361765321344137,
-0.0027921078726649284,
0.05056168511509895,
-0.03408500924706459,
-0.02195923961699009,
0.0185847170650959,
0.03368367999792099,
0.026402156800031662,
-0.032035600394010544,
0.018813708797097206,
0.03129119426012039,
0.021024176850914955,
0.03265275061130524,
0.010841893963515759,
-0.019994959235191345,
0.013099783100187778,
0.001707954448647797,
0.06886518001556396,
0.009912258945405483,
-0.03897008299827576,
0.06374815106391907,
0.017913445830345154,
0.01748770847916603,
-0.01749248057603836,
-0.024910608306527138,
-0.020445644855499268,
-0.01065957359969616,
0.01296211313456297,
0.010550874285399914,
-0.01276371255517006,
0.017504842951893806,
0.045494213700294495,
-0.0172206349670887,
0.05112550035119057,
-0.03280840814113617,
-0.04692821204662323,
0.01590222306549549,
-0.01728241518139839,
-0.042365122586488724,
0.06577426940202713,
0.025465810671448708,
-0.039099182933568954,
0.012958432547748089,
0.008091190829873085,
-0.018752364441752434,
0.059117574244737625,
0.02113386057317257,
-0.024515027180314064,
0.07652498036623001,
-0.0024660027120262384,
-0.011733537539839745,
-0.047061339020729065,
0.008022447116672993,
0.10648129135370255,
0.003251598682254553,
-0.00011315508891129866,
-0.029439684003591537,
-0.01851559430360794,
-0.0030684920493513346,
0.018530357629060745,
-0.021673735231161118,
0.02296084351837635,
-0.026472147554159164,
0.00426538847386837,
-0.003744022687897086,
0.028583357110619545,
0.016023827716708183,
-0.009577234275639057,
0.030415788292884827,
-0.02632482536137104,
-0.03944390267133713,
-0.014726685360074043,
0.004100006073713303,
-0.006528891157358885,
-0.003923577256500721,
-0.03088025189936161,
0.011962193995714188,
-0.02925669029355049,
0.0006404520245268941,
-0.04702107980847359,
-0.06371773779392242,
0.022416051477193832,
-0.03466211259365082,
-0.05867273733019829,
0.022877342998981476,
-0.00577232101932168,
-0.02963995561003685,
-0.027703581377863884,
0.0774427056312561,
0.004282042384147644,
0.014457127079367638,
-0.011279774829745293,
0.026780232787132263,
0.018009012565016747,
-0.007205745205283165,
0.04558182880282402,
-0.0003423452435526997,
-0.03974862024188042,
0.009703880175948143,
-0.0263666994869709,
0.010565103963017464,
0.009145664982497692,
0.021140651777386665,
-0.004093611147254705,
0.006657698657363653,
-0.008065316826105118,
-0.05334705486893654,
0.004972944501787424,
-0.0008382099331356585,
0.025767823681235313,
0.011855864897370338,
-0.04143378511071205,
-0.02483595907688141,
0.050467535853385925,
-0.012902384623885155,
0.022376155480742455,
-0.01709008403122425,
-0.013301745057106018,
-0.009791228920221329,
-0.0017315595177933574,
0.06090501695871353,
-0.03348580002784729,
-0.026107674464583397,
0.0006618409533984959,
-0.03243071213364601,
-0.03478270396590233,
0.011269031092524529,
0.025672100484371185,
0.02717995084822178,
0.03817133978009224,
-0.0027911902870982885,
-0.026046128943562508,
-0.008694237098097801,
-0.047926440834999084,
0.013121446594595909,
0.01052949484437704,
-0.004571079276502132,
-0.06095553934574127,
-0.024520162492990494,
0.060922760516405106,
0.020445622503757477,
0.03288448229432106,
0.002655066316947341,
-0.0042412737384438515,
0.011745101772248745,
0.008516669273376465,
-0.014310787431895733,
-0.06974644958972931,
0.026431066915392876,
-0.018451860174536705,
0.006851705256849527,
-0.02640499174594879,
0.06298692524433136,
0.04277603328227997,
0.03206494450569153,
-0.03430439159274101,
0.013017660938203335,
-0.028268322348594666,
-0.002807174576446414,
-0.011266132816672325,
0.0033159982413053513,
-0.022359652444720268,
0.04218640178442001,
-0.021969538182020187,
-0.06939682364463806,
0.014302881434559822,
-0.018020782619714737,
-0.03692710027098656,
0.011459358036518097,
0.033803198486566544,
-0.018615232780575752,
0.005649857688695192,
-0.041326042264699936,
0.004294846206903458,
-0.03524332121014595,
0.003142651868984103,
-0.07011224329471588,
-0.0340217649936676,
0.037404149770736694,
0.0070290956646203995,
-0.026804789900779724,
0.006017875391989946,
-0.030337827280163765,
-0.008646175265312195,
-0.004957054741680622,
-0.024347223341464996,
-0.006406876724213362,
0.012758160009980202,
-0.00276643643155694,
-0.017212247475981712,
0.03887266293168068,
-0.015788033604621887,
-0.04732915759086609,
0.037309516221284866,
-0.03250591829419136,
-0.01945527456700802,
0.015739087015390396,
-0.007756121456623077,
0.05373625457286835,
0.0210451427847147,
-0.03602154925465584,
-0.016323735937476158,
0.03880677372217178,
0.012663495726883411,
0.000954851508140564,
-0.004502401687204838,
-0.06308631598949432,
0.01826917938888073,
-0.007463681977242231,
-0.031766027212142944,
-0.019528120756149292,
-0.011453905142843723,
0.014621103182435036,
0.04011358693242073,
-0.011139431037008762,
-0.020896557718515396,
0.037045687437057495,
0.03994889557361603,
-0.03362911939620972,
0.04074370115995407,
0.016542624682188034,
0.014160760678350925,
0.027127211913466454,
-0.02070452831685543,
0.04231814667582512,
0.0111936554312706,
0.0031727401074022055,
-0.09991195052862167,
0.02842533215880394,
0.01796247623860836,
-0.021535685285925865,
0.046074677258729935,
-0.05071419104933739,
-0.03214805945754051,
0.05134359747171402,
-0.07642868161201477,
0.007915046066045761,
-0.018659459426999092,
-0.026359541341662407,
0.001785346306860447,
0.000821880588773638,
0.004561737645417452,
0.04518865421414375,
0.013790188357234001,
0.035666435956954956,
0.010873356834053993,
-0.028670817613601685,
-0.016836652532219887,
-0.0353119894862175,
0.005293261259794235,
0.10515451431274414,
-0.00532567547634244,
0.016151919960975647,
0.024631764739751816,
0.0027300450019538403,
-0.005137335974723101,
0.04676270857453346,
-0.033790603280067444,
0.022470997646450996,
-0.0011600080179050565,
-0.029325004667043686,
0.023326395079493523,
0.041351318359375,
-0.00854339636862278,
-0.01899263821542263,
-0.036939412355422974,
-0.005184472072869539,
-0.030421201139688492,
0.037591602653265,
-0.02982695959508419,
0.015030396170914173,
-0.0037521792110055685,
-0.047774750739336014,
-0.030440984293818474,
0.06605236232280731,
-0.024054167792201042,
0.013242197223007679,
0.0036468144971877337,
-0.009561327286064625,
-0.01176163088530302,
-0.04309375584125519,
-0.007187601178884506,
-0.04565057158470154,
0.010694685392081738,
0.0382726788520813,
-0.011412189342081547,
-0.009141476824879646,
0.0007897730101831257,
0.03183601796627045,
-0.02353494241833687,
-0.004312138073146343,
-0.003943858668208122,
-0.051585759967565536,
-0.039579324424266815,
0.039207059890031815,
0.016286974772810936,
-0.023420508950948715,
0.0020280310418456793,
-0.02058940753340721,
-0.03696795552968979,
0.006547956261783838,
0.024967525154352188,
0.024928074330091476,
0.043159887194633484,
-0.06111222878098488,
-0.027427345514297485,
-0.08136716485023499,
0.0673350915312767,
0.010656081140041351,
-0.04330860823392868,
-0.04018005356192589,
-0.023638755083084106,
-0.011874906718730927,
0.04620395228266716,
0.024372918531298637,
-0.02681071124970913,
-0.021277563646435738,
-0.009380643256008625,
-0.008901946246623993,
-0.0031747857574373484,
-0.00643541757017374,
-0.001509923837147653,
0.005905681289732456,
-0.012649492360651493,
0.015369080938398838,
0.006370377726852894,
-0.024154584854841232,
0.008077504113316536,
0.012161643244326115,
0.004770161584019661,
0.04512833058834076,
-0.0247440654784441,
-0.0556638166308403,
0.014652146026492119,
0.034490566700696945,
-0.003505170112475753,
0.05728263780474663,
-0.0143691161647439,
0.003688087919726968,
-0.0019786020275205374,
-0.00021524608018808067,
-0.023265156894922256,
0.028794143348932266,
-0.053376972675323486,
-0.019848011434078217,
-0.012650744058191776,
-0.0114769097417593,
0.0660625547170639,
-0.03937937319278717,
0.012532143853604794,
0.03049844689667225,
-0.06163947656750679,
-0.034003254026174545,
0.05271861329674721,
0.03417832404375076,
0.029562054201960564,
-0.06055205687880516,
0.030531784519553185,
0.05074760317802429,
-0.04334636032581329,
0.026325015351176262,
0.0069984132423996925,
0.02300873212516308,
-0.02364834025502205,
-0.010100927203893661,
0.025163913145661354,
-0.02999597229063511,
0.038362741470336914,
-0.012931370176374912,
0.019763512536883354,
-0.002697065705433488,
-0.009623309597373009,
-0.0029120652470737696,
-0.03922433778643608,
0.0026990892365574837,
0.01673481985926628,
-0.02219010703265667,
0.03458991274237633,
-0.019426215440034866,
0.04216732829809189,
0.01668066903948784,
0.0016970516880974174,
-0.00219662394374609,
-0.010540015064179897,
0.018265286460518837,
-0.0037608062848448753,
-0.026214061304926872,
-0.00015990603424143046,
0.035052817314863205,
-0.017085209488868713,
0.0527414008975029,
-0.023568227887153625,
0.04443467780947685,
-0.014820016920566559,
-0.02329290471971035,
-0.04400404915213585,
-0.021340537816286087,
-0.03564963862299919,
-0.010460875928401947,
0.06079578399658203,
0.019591281190514565,
-0.00554768368601799,
-0.01843843050301075,
0.036480195820331573,
0.0013858966995030642,
0.06505117565393448,
-0.055144052952528,
-0.013982411473989487,
-0.0003783413558267057,
0.021498458459973335,
0.01210081484168768,
-0.027201874181628227
] |
<p>For example; is $$\partial_{\rho}\partial_{\sigma}h_{\mu\nu} - \partial_{\sigma}\partial_{\rho}h_{\mu\nu}=0$$ correct?</p>
| 9,587 |
[
-0.029446111992001534,
0.010856346227228642,
0.0001353495172224939,
-0.06095866486430168,
0.05124485120177269,
0.022690605372190475,
-0.02102310210466385,
0.009052245877683163,
0.006262918468564749,
-0.04925912991166115,
0.05772467330098152,
0.005915537942200899,
0.09161810576915741,
0.01447939220815897,
0.0380294993519783,
0.0057152328081429005,
-0.03569222241640091,
0.0032043529208749533,
-0.022157862782478333,
-0.014551104977726936,
0.003843883750960231,
0.048253562301397324,
0.010539907962083817,
-0.004499382805079222,
-0.044058676809072495,
0.04019887372851372,
0.030562784522771835,
0.008181478828191757,
0.0048192767426371574,
0.06440718472003937,
-0.02694491483271122,
-0.005543883424252272,
0.004190964158624411,
0.02682410553097725,
0.010784270241856575,
0.00887465663254261,
0.0031393629033118486,
-0.0022134361788630486,
-0.06742089986801147,
0.012755263596773148,
-0.04240183159708977,
0.020727405324578285,
0.0056397453881800175,
0.06308666616678238,
-0.019229264929890633,
-0.008075842633843422,
0.01860133744776249,
0.013945297338068485,
0.0561528354883194,
-0.059947408735752106,
0.07574453949928284,
-0.006710789632052183,
0.0479317381978035,
0.04927898198366165,
-0.02416113018989563,
-0.02570893056690693,
0.04273158311843872,
0.0701242983341217,
0.0039021812845021486,
-0.04184384271502495,
0.01042781863361597,
-0.0025023010093718767,
-0.0064916713163256645,
-0.029605738818645477,
-0.024698613211512566,
0.03965117037296295,
0.010121640749275684,
0.007064065895974636,
0.05931521952152252,
0.003475859062746167,
-0.018329177051782608,
-0.017542961984872818,
0.01919608563184738,
-0.002766180085018277,
0.04235922172665596,
-0.04813741520047188,
-0.002500595059245825,
-0.0009260099614039063,
0.02077983319759369,
0.008329194039106369,
0.0006658731726929545,
0.0011602159356698394,
0.0360858328640461,
0.01939493417739868,
-0.00045827816938981414,
-0.006822205148637295,
0.04956189915537834,
-0.011297855526208878,
0.021088186651468277,
0.03240715339779854,
0.016748160123825073,
0.02406013011932373,
0.020888304337859154,
0.003992864862084389,
-0.03824777528643608,
0.04096397012472153,
-0.0002435053320368752,
-0.002645118162035942,
0.013377205468714237,
-0.03637734428048134,
-0.04063764587044716,
-0.03114190697669983,
0.016016678884625435,
0.0345759391784668,
-0.006004836410284042,
-0.024265114217996597,
-0.0362803153693676,
-0.012506026774644852,
-0.02647208236157894,
-0.030462605878710747,
-0.045293502509593964,
0.009624413214623928,
-0.05235594883561134,
-0.01629868894815445,
-0.006938341073691845,
-0.026910310611128807,
0.015649890527129173,
-0.023781711235642433,
0.03813658654689789,
0.07425053417682648,
0.02118539623916149,
0.007007691077888012,
-0.0023267108481377363,
-0.01461795810610056,
-0.12392663955688477,
0.03238694742321968,
0.058429595082998276,
-0.015282649546861649,
-0.0593549981713295,
0.021797295659780502,
0.026202209293842316,
0.015531718730926514,
0.0007448755786754191,
-0.02406148426234722,
0.01739228330552578,
-0.03046007826924324,
-0.08898630738258362,
-0.06633738428354263,
-0.01278104167431593,
-0.03209199756383896,
-0.007277566473931074,
-0.054710593074560165,
-0.02585231140255928,
0.04251591116189957,
0.08000893145799637,
-0.014707805588841438,
-0.002915887627750635,
-0.013986690901219845,
0.024536456912755966,
-0.014720280654728413,
0.0016161489766091108,
-0.04824081435799599,
0.0018735462799668312,
-0.029272127896547318,
-0.027940860018134117,
-0.07704823464155197,
0.006396520417183638,
0.019480381160974503,
0.010844578966498375,
0.007458039093762636,
0.05886217579245567,
-0.01010133232921362,
0.024258742108941078,
0.01790568046271801,
-0.033790815621614456,
-0.04291854053735733,
0.07876534759998322,
0.024285798892378807,
0.031195461750030518,
-0.0019239244284108281,
0.0027264209929853678,
0.031948842108249664,
-0.02308475226163864,
0.024836484342813492,
0.059184715151786804,
-0.03393055498600006,
-0.004438352771103382,
-0.03639044612646103,
0.0358445979654789,
0.009744909591972828,
-0.024003006517887115,
-0.0018477151170372963,
-0.020007029175758362,
-0.0012415291275829077,
-0.03190193325281143,
0.012223649770021439,
0.006079303100705147,
-0.034892745316028595,
0.02487046644091606,
-0.04035700485110283,
0.006763855926692486,
-0.052561718970537186,
0.02098225988447666,
0.011613144539296627,
-0.03029766120016575,
0.03727833181619644,
0.03695176541805267,
0.011454259976744652,
-0.03371548280119896,
-0.042004626244306564,
0.0003216338809579611,
-0.0236061979085207,
0.004736296832561493,
-0.008140313439071178,
0.03916531801223755,
-0.004543839488178492,
0.025255277752876282,
-0.0009351422777399421,
0.06901544332504272,
-0.04284113645553589,
-0.009926953352987766,
-0.02004505693912506,
0.007761103566735983,
0.03546702116727829,
0.007828914560377598,
0.02701713889837265,
-0.02400321699678898,
0.0013404263881966472,
-0.016215259209275246,
0.021444665268063545,
-0.07747583836317062,
0.03949948772788048,
0.06669717282056808,
-0.003857908071950078,
0.03706695884466171,
0.0416252464056015,
0.02266373485326767,
0.02020357735455036,
0.007721886970102787,
-0.029271921142935753,
-0.019625114277005196,
0.02421870455145836,
0.03343880549073219,
0.013067052699625492,
-0.022821784019470215,
0.027303382754325867,
0.0203571580350399,
0.023574644699692726,
0.018444256857037544,
0.045470066368579865,
-0.010294777341187,
-0.06088283658027649,
0.025696568191051483,
0.006060498766601086,
-0.005275538191199303,
0.019826773554086685,
0.03369370475411415,
0.013313527218997478,
0.04613786190748215,
-0.015561668202280998,
0.00542920408770442,
0.0785561352968216,
-0.04011231288313866,
-0.04186360165476799,
0.01808551326394081,
-0.04295748099684715,
0.03363066166639328,
0.0020899882074445486,
0.05427136644721031,
0.011836254969239235,
-0.033291105180978775,
-0.0009177631000056863,
-0.05415422096848488,
-0.022161317989230156,
-0.02241404727101326,
0.011138762347400188,
0.010381374508142471,
-0.024928946048021317,
0.022151505574584007,
-0.055070001631975174,
-0.02792491391301155,
-0.04836052283644676,
0.012092327699065208,
-0.016832316294312477,
-0.012583954259753227,
0.05303791165351868,
0.003914316650480032,
0.04494838789105415,
-0.018544910475611687,
-0.061155930161476135,
0.0090013537555933,
0.001429272466339171,
0.017249932512640953,
0.026795970275998116,
-0.027748003602027893,
-0.011361923068761826,
-0.005003472790122032,
-0.020403612405061722,
0.0002176486887037754,
-0.004848499316722155,
-0.01190978568047285,
0.042452480643987656,
0.005506472662091255,
-0.026749974116683006,
-0.03533480316400528,
-0.014978136867284775,
0.0009066147613339126,
-0.0073235295712947845,
0.03460453078150749,
0.03648094832897186,
0.022577980533242226,
-0.01463722251355648,
0.020907782018184662,
-0.004669666290283203,
-0.06231950968503952,
-0.028855904936790466,
-0.009567595086991787,
0.016503391787409782,
-0.01870216429233551,
0.03847157210111618,
0.08319681882858276,
-0.03334536775946617,
-0.016924403607845306,
-0.0565921925008297,
-0.04796277731657028,
0.049047134816646576,
-0.020736241713166237,
0.014945754781365395,
0.009932258166372776,
-0.04239940643310547,
0.09641886502504349,
0.028729647397994995,
-0.03120620921254158,
0.013257366605103016,
-0.0018943136092275381,
-0.011394081637263298,
-0.047511450946331024,
-0.012037408538162708,
0.01261853612959385,
-0.004693788941949606,
0.03354054316878319,
0.037073295563459396,
0.037006061524152756,
0.0019910959526896477,
0.04544694721698761,
-0.013405499048531055,
0.01720655895769596,
0.012539556249976158,
-0.036662667989730835,
0.05964960530400276,
-0.007395447697490454,
0.026525048539042473,
0.03212730586528778,
0.0005573861417360604,
0.03477054089307785,
0.045384038239717484,
-0.05971084162592888,
0.05535368248820305,
-0.026912543922662735,
-0.0019400690216571093,
-0.045681048184633255,
0.047112252563238144,
0.01670146733522415,
-0.017412342131137848,
-0.02907988615334034,
0.02653850056231022,
0.048343196511268616,
-0.03649820014834404,
-0.02061844803392887,
0.05483907833695412,
-0.0029124626889824867,
-0.017521262168884277,
-0.023958394303917885,
0.0023268074728548527,
-0.008632652461528778,
0.012748915702104568,
-0.06339386850595474,
-0.0171060711145401,
0.047158047556877136,
0.049553416669368744,
0.008349034003913403,
-0.02052926830947399,
-0.05464613437652588,
-0.012614511884748936,
-0.09989102929830551,
0.04136405885219574,
0.007938963361084461,
0.03824746608734131,
0.00041713309474289417,
0.03726118803024292,
0.053252916783094406,
0.028129378333687782,
-0.007319070864468813,
0.017335280776023865,
-0.05686317756772041,
-0.00842675007879734,
0.00017730786930769682,
-0.03409470617771149,
0.012910475954413414,
-0.06196872517466545,
-0.003969845362007618,
-0.05239007622003555,
-0.03749753162264824,
0.0009001915459521115,
-0.008871872909367085,
-0.03625568374991417,
0.008245473727583885,
-0.04838686063885689,
-0.05359012633562088,
-0.029910113662481308,
0.027689481154084206,
0.030885810032486916,
-0.014805867336690426,
0.02773815393447876,
0.043152548372745514,
-0.002366170985624194,
0.007852870039641857,
-0.028853658586740494,
0.0299670472741127,
-0.012272507883608341,
0.051434166729450226,
0.03950882703065872,
0.03553253784775734,
-0.03283880278468132,
0.06930292397737503,
0.021568892523646355,
0.06743976473808289,
-0.010130499489605427,
-0.015354955568909645,
-0.03136323764920235,
-0.021029002964496613,
-0.03231273964047432,
-0.02746165171265602,
0.04118358716368675,
0.02230534516274929,
-0.01393919624388218,
0.014377436600625515,
-0.0047468398697674274,
-0.014282327145338058,
0.023101015016436577,
0.07214101403951645,
0.027841167524456978,
-0.00568651407957077,
-0.06840254366397858,
-0.016694743186235428,
-0.022874606773257256,
0.006257862783968449,
0.013518658466637135,
0.0015833433717489243,
-0.03804340958595276,
-0.016908708959817886,
-0.02203090861439705,
0.05206584930419922,
-0.006660606246441603,
0.030475635081529617,
0.026289595291018486,
0.014030735939741135,
-0.0013481107307597995,
0.02596123516559601,
0.035662032663822174,
0.054083481431007385,
0.05781865119934082,
0.009105078876018524,
-0.008981128223240376,
-0.06339668482542038,
0.008954975754022598,
0.032930150628089905,
0.02440393529832363,
-0.009593398310244083,
-0.0025519984774291515,
-0.05723798647522926,
0.014950328506529331,
0.027372634038329124,
-0.01834660768508911,
0.04185637831687927,
0.005817809607833624,
0.022952117025852203,
0.007042254786938429,
-0.030871354043483734,
-0.04492099583148956,
0.03460241109132767,
-0.012441323138773441,
-0.012848922051489353,
-0.0513308085501194,
-0.015610907226800919,
-0.013892313465476036,
0.016131682321429253,
0.030560562387108803,
0.02713140845298767,
0.0008701172773726285,
-0.012981919571757317,
-0.0034190297592431307,
0.02687784470617771,
-0.011929087340831757,
-0.10465342551469803,
0.023867199197411537,
0.003184630535542965,
-0.013185093179345131,
0.08180046081542969,
-0.021298078820109367,
-0.027061481028795242,
0.06953202188014984,
0.012485493905842304,
-0.04469694569706917,
0.00910582672804594,
-0.029868241399526596,
0.045994989573955536,
0.04953046888113022,
-0.019251756370067596,
0.03275897353887558,
0.0005138024571351707,
0.006846623029559851,
0.017272265627980232,
-0.06712846457958221,
0.021494688466191292,
-0.03335051238536835,
0.031407345086336136,
-0.04017612338066101,
0.009568054229021072,
-0.0015641909558326006,
0.01744048111140728,
-0.037770044058561325,
0.026182394474744797,
0.018749868497252464,
-0.008145362138748169,
-0.001388073549605906,
-0.0002385857660556212,
-0.0073320078663527966,
-0.014431411400437355,
0.04038647562265396,
0.04066276550292969,
0.013039646670222282,
0.0038240065332502127,
0.0018840004922822118,
0.009645754471421242,
0.0079730786383152,
0.04236989840865135,
-0.012413916178047657,
0.031624022871255875,
-0.016147375106811523,
-0.021215906366705894,
-0.0096940528601408,
-0.02931002713739872,
0.025647876784205437,
-0.05042365938425064,
0.001223412691615522,
0.0074677253141999245,
-0.009097561240196228,
0.007187754847109318,
0.02172401174902916,
-0.01990947499871254,
0.0056577036157250404,
-0.04718730226159096,
0.06768495589494705,
0.039237022399902344,
0.01691853441298008,
-0.08410653471946716,
-0.0035674599930644035,
0.004934248048812151,
0.023025231435894966,
0.010312320664525032,
-0.0336323007941246,
0.009861135855317116,
-0.013438810594379902,
-0.04483252391219139,
-0.00834256038069725,
0.02348172478377819,
-0.006288852076977491,
-0.025765985250473022,
0.013523336499929428,
0.0438680537045002,
0.06351005285978317,
-0.012300967238843441,
0.02557183802127838,
0.015044149942696095,
0.007796021644026041,
-0.007201038300991058,
0.014330701902508736,
0.04283290356397629,
0.014804530888795853,
-0.02348984405398369,
-0.005490191280841827,
-0.028645213693380356,
0.024527711793780327,
0.006460073869675398,
-0.02859133668243885,
0.004454673733562231,
0.019538456574082375,
0.004539559129625559,
-0.014931254088878632,
0.009219878353178501,
-0.049902040511369705,
0.026903310790657997,
0.025225667282938957,
0.0005854087066836655,
-0.013791871257126331,
-0.011486081406474113,
0.035149529576301575,
-0.011005805805325508,
0.0040168738923966885,
0.013279429636895657,
0.06531969457864761,
0.0031774493400007486,
-0.009507765993475914,
0.044037461280822754,
-0.01118223275989294,
0.021640202030539513,
-0.004166779108345509,
-0.007082911673933268,
-0.020068977028131485,
0.00010132698662346229,
-0.01993468590080738,
-0.056523196399211884,
-0.011265557259321213,
0.046373140066862106,
0.07440326362848282,
-0.012387027032673359,
0.023024726659059525,
-0.007495487574487925,
0.008012525737285614,
-0.025618424639105797,
-0.026372602209448814,
-0.020282255485653877,
-0.010611677542328835,
-0.007260510697960854,
0.06827837973833084,
-0.023547889664769173,
0.026795776560902596,
0.03611595183610916,
0.04436661675572395,
-0.0610969215631485,
0.0003677275381051004,
0.00022713959333486855,
0.027355574071407318,
0.03381925821304321,
-0.013073060661554337,
-0.028865082189440727,
0.03341791778802872,
-0.05492175742983818,
0.04134204238653183,
-0.016137421131134033,
-0.004879341926425695,
0.010376747697591782,
0.0038007344119250774,
0.015552682802081108,
-0.017847999930381775,
-0.02740836888551712,
0.008274323306977749,
0.02165805920958519,
0.00258122687228024,
-0.01262243464589119,
-0.020627634599804878,
-0.0029636092949658632,
0.07199632376432419,
-0.006825918797403574,
0.015006475150585175,
-0.011880210600793362,
-0.058402229100465775,
-0.019484523683786392,
-0.01822056993842125,
-0.03195223584771156,
0.05190557613968849,
-0.010651177726686,
-0.009732157923281193,
0.03311936929821968,
-0.021148059517145157,
0.012606478296220303,
0.014755249954760075,
0.022585401311516762,
0.01123393326997757,
0.04743677005171776,
0.015431025065481663,
0.02261720970273018,
-0.0011851841118186712,
0.0251462459564209,
0.11331057548522949,
0.07582789659500122,
0.04097888991236687,
-0.04269840195775032,
0.013467109762132168,
-0.029726654291152954,
0.006840724963694811,
-0.045506663620471954,
0.036448750644922256,
-0.016373423859477043,
0.0029569731559604406,
-0.003083290997892618,
0.05624649301171303,
0.008368553593754768,
0.000856500759255141,
0.0024560100864619017,
-0.030793165788054466,
-0.04160935431718826,
-0.012391137890517712,
0.008080731146037579,
-0.034579548984766006,
0.011145182885229588,
-0.03315480798482895,
0.01863805577158928,
0.00034972166758961976,
0.028807004913687706,
0.009473845362663269,
-0.02670830860733986,
0.01659267023205757,
0.0285214614123106,
-0.04832666739821434,
0.02800408937036991,
-0.004101901780813932,
0.03492415323853493,
0.0061816065572202206,
0.006712259724736214,
0.029266882687807083,
-0.02403474971652031,
0.0061787571758031845,
0.035062044858932495,
0.01212223619222641,
0.011043216101825237,
0.018061747774481773,
0.018240779638290405,
-0.05394120141863823,
0.010939355939626694,
-0.03765130043029785,
0.05284382030367851,
-0.03935461863875389,
0.005832449998706579,
0.01721453107893467,
-0.010417540557682514,
0.005440917797386646,
-0.05068107694387436,
-0.023898927494883537,
-0.0032514387276023626,
0.013192891143262386,
0.015917807817459106,
-0.012905951589345932,
0.010875586420297623,
0.028252242133021355,
0.004040309693664312,
0.031685493886470795,
0.026389066129922867,
-0.02807382494211197,
-0.002792463870719075,
-0.010902484878897667,
0.03747536987066269,
-0.04795108735561371,
-0.041813984513282776,
-0.01841050386428833,
-0.013754324056208134,
-0.03128813952207565,
-0.014299651607871056,
-0.011066462844610214,
0.03000023402273655,
0.04529702663421631,
-0.025951877236366272,
0.021620839834213257,
-0.0009171418496407568,
-0.08921891450881958,
0.010569673962891102,
-0.017701689153909683,
-0.016504429280757904,
-0.039130643010139465,
-0.013729742728173733,
0.018889490514993668,
0.0413937121629715,
-0.0007018553442321718,
-0.016297893598675728,
0.007957144640386105,
0.04945533722639084,
0.01986054517328739,
-0.038737427443265915,
-0.08343400061130524,
0.011720720678567886,
-0.03985271975398064,
0.007996827363967896,
0.01798202656209469,
0.00253684027120471,
0.00978055689483881,
0.05267617478966713,
0.013031643815338612,
0.05924668908119202,
0.008724772371351719,
-0.02200416289269924,
0.03267835080623627,
-0.0020958560053259134,
0.007376964204013348,
-0.01171610876917839,
0.00042057057726196945,
-0.013616356998682022,
-0.006283414084464312,
-0.015541400760412216,
0.0027579828165471554,
0.02163713425397873,
-0.0010758304269984365,
-0.03890157490968704,
0.009557951241731644,
-0.01783856749534607,
0.00022292287030722946,
-0.029107019305229187,
-0.0027102602180093527,
-0.04377485066652298,
-0.0018574573332443833,
0.015761110931634903,
-0.00944544654339552,
0.014925448223948479,
-0.00653040548786521,
-0.013138907961547375,
-0.03461495041847229,
0.04599308595061302,
-0.015710270032286644,
0.00618106359615922,
0.0033328954596072435,
0.01850004494190216,
0.031490836292505264,
0.03878190368413925,
0.008827969431877136,
-0.016941454261541367,
0.021803276613354683,
-0.0365201011300087,
-0.0321512371301651,
-0.003373152343556285,
0.026396607980132103,
0.027189895510673523,
0.009367777034640312,
-0.04311013221740723,
0.015294049866497517,
0.05909489095211029,
-0.008724343962967396,
0.011555705219507217,
0.009001476690173149,
-0.046955790370702744,
-0.032408662140369415,
-0.02156868390738964,
0.03258322551846504,
-0.00853721983730793,
0.009485694579780102,
0.029531434178352356,
0.015417607501149178,
-0.011538112536072731,
-0.01567440666258335,
-0.010419095866382122,
0.005109368357807398,
-0.006297877989709377,
0.0006470156367868185,
-0.019839324057102203,
0.009633852168917656,
0.0352737233042717,
-0.06354239583015442,
0.04468689113855362,
0.004320061765611172,
-0.008053094148635864,
-0.09095384180545807,
-0.049666229635477066,
0.037899747490882874,
0.011762985028326511,
0.007088075391948223,
-0.0403144471347332,
0.03214508295059204,
0.0016438835300505161,
-0.05138397216796875,
0.020482748746871948,
-0.019343461841344833,
-0.00014654021651949733,
-0.005269976332783699,
-0.0064556412398815155,
-0.011490968056023121,
0.027114853262901306,
0.016344742849469185,
0.032737672328948975,
-0.020715750753879547,
-0.0009247561683878303,
-0.0012989159440621734,
-0.007386140991002321,
-0.010955588892102242,
0.009412241168320179,
-0.005754836369305849,
-0.05977321043610573,
0.0488150529563427,
-0.020907439291477203,
-0.04105538874864578,
-0.0046127778477966785,
-0.02090945467352867,
-0.010522586293518543,
0.01149055827409029,
0.03809523954987526,
0.03673507645726204,
0.0023108776658773422,
0.018096445128321648,
-0.03056081384420395,
-0.015528443269431591,
0.01421275269240141,
-0.012343616224825382,
0.04793582111597061,
-0.038990870118141174,
-0.005307475104928017,
-0.0009824498556554317,
-0.03660232573747635,
-0.036580391228199005,
0.04116199165582657,
-0.04781714454293251,
-0.04305269941687584,
-0.03030133992433548,
-0.015312776900827885,
-0.005837937816977501,
-0.022964775562286377,
0.054110173135995865,
-0.052673645317554474,
0.009320272132754326,
0.02299432083964348,
0.04164949432015419,
-0.021720150485634804,
0.0007673684158362448,
-0.007292893249541521,
-0.026567859575152397,
0.029076313599944115,
-0.009808219969272614,
-0.015185557305812836,
-0.05169253423810005,
-0.014845320954918861,
-0.028350163251161575,
-0.01776265911757946,
-0.027428653091192245,
-0.045277003198862076,
-0.02833344042301178,
0.03892272710800171,
0.03890466317534447,
0.017347004264593124,
0.0053171576000750065,
-0.048647549003362656,
0.0014400220243260264,
-0.05615747347474098,
0.007383864372968674,
0.020113039761781693,
0.03250446170568466,
-0.009651010856032372,
0.008501112461090088,
-0.034521449357271194,
0.011674693785607815,
0.04540688544511795,
0.0028835665434598923,
-0.013024268671870232,
0.023781362920999527,
0.016140339896082878,
0.00706334738060832,
-0.035973671823740005,
0.024446073919534683,
0.00798093806952238,
-0.008115116506814957,
-0.002644610358402133,
-0.001664716168306768,
-0.0072136204689741135,
-0.0018398271640762687,
-0.025367258116602898,
-0.016639338806271553,
0.022161338478326797,
0.02416066825389862,
-0.026923470199108124,
0.04653408005833626,
0.031097039580345154,
-0.030048295855522156,
0.07697267085313797,
0.005678094923496246,
0.007703256793320179,
0.02183520793914795,
-0.026246897876262665,
-0.05641678720712662,
0.014300186187028885,
-0.016200140118598938,
-0.0331084169447422,
-0.031348440796136856,
0.006901791784912348,
0.01933683268725872,
-0.009815189056098461,
0.0007112874300219119,
0.033024467527866364,
-0.03918970376253128,
-0.02021416276693344,
0.006340870168060064,
0.006863314192742109,
0.009795831516385078,
0.020957132801413536,
-0.007148857694119215,
0.02626984380185604,
-0.0030703581869602203,
0.00797849241644144,
0.037576064467430115,
0.009198221378028393,
-0.004160630516707897,
0.0008798094349913299,
0.03787388280034065,
-0.0650240108370781,
-0.028367791324853897,
-0.01209363341331482,
0.022177204489707947,
-0.04323491454124451,
-0.006617806386202574,
0.014594891108572483,
-0.02836998738348484,
-0.006123985629528761,
-0.01526948157697916,
-0.003036392852663994,
0.07994323968887329,
-0.033012017607688904,
0.041857317090034485,
-0.03498856723308563,
0.002547917189076543,
-0.0015582859050482512,
0.029913345351815224,
0.03374248370528221,
0.06069603189826012,
-0.019453803077340126,
-0.03063524328172207,
-0.005755426362156868,
-0.047754984349012375,
0.015922052785754204,
-0.054360367357730865,
-0.005933385342359543,
-0.000816304178442806,
-0.0054090628400444984,
-0.01610291190445423,
-0.0006176021997816861,
-0.020160222426056862,
-0.008638957515358925,
0.006101665087044239,
0.026566535234451294,
-0.0097119165584445,
-0.009859357960522175,
-0.011106537654995918,
-0.025703806430101395,
0.025353098288178444,
-0.0842747762799263,
-0.007408336736261845,
-0.029163531959056854,
0.005246757064014673,
-0.027272792533040047,
-0.01147147174924612
] |
<p>First I must let you know that I don't have much understanding of neither GR nor quantum mechanics, and therefore this question.</p>
<p>I've mentally pictured Newtonian physics, GR and quantum mechanics all somewhat competing (in terms of use case) physics models. For one situation Newtonian physics model may be sufficient, but for another (e.g. interplanetary calculations) general relativity is needed. And then there's quantum mechanics.</p>
<p>Is it possible that the exact same exercise can be solved in Newtonian physics, GR and quantum mechanics? Under "solved" I mean that it can be calculated according to the model (Newtonian, GR or QM) but the answer would come different and hence illustrating the need of why and for what GR was required and the same for QM.</p>
<p>Basically what I mean is that is there any problem that could be solved with different physical models? For example if I would have a problem A, then by applying a solution based on Newtonian physics (NP), GR or QM, I would get different results, e.g:</p>
<pre><code>NP(A) = x
GR(A) = y
QM(A) = z
</code></pre>
<p>If it's possible, can someone please give an concrete example?</p>
| 9,588 |
[
-0.027463223785161972,
0.017718805000185966,
-0.017890851944684982,
-0.02502528764307499,
0.05528562515974045,
0.021597204729914665,
-0.03177137300372124,
-0.04392406344413757,
0.01625784859061241,
-0.007410275749862194,
0.02231612242758274,
0.05407212674617767,
0.05185215175151825,
-0.0010885529918596148,
0.0469704270362854,
-0.007286073174327612,
0.013909034430980682,
-0.02227911539375782,
0.00715215178206563,
-0.013212182559072971,
0.02221137285232544,
0.026949504390358925,
0.01848994940519333,
0.02009621448814869,
0.0012215154711157084,
0.038933489471673965,
0.025692466646432877,
-0.012165522202849388,
0.015239140950143337,
0.03736383095383644,
-0.0045271082781255245,
0.01387081854045391,
-0.0119509007781744,
0.07251271605491638,
0.023571789264678955,
0.03968066722154617,
-0.035697244107723236,
-0.01802663318812847,
-0.02271493710577488,
-0.014120706357061863,
-0.028892893344163895,
-0.0015375588554888964,
0.0032276620622724295,
0.027514107525348663,
-0.020014531910419464,
0.059309374541044235,
0.017028629779815674,
0.0015421996358782053,
0.04845398664474487,
-0.04961194097995758,
0.07251522690057755,
0.020757514983415604,
0.0354234017431736,
0.021046631038188934,
-0.04383431747555733,
0.0017636356642469764,
0.114705890417099,
0.08595189452171326,
-0.009368511848151684,
-0.045258164405822754,
-0.04786105081439018,
-0.007454604841768742,
0.015529964119195938,
-0.0211821049451828,
-0.013131883926689625,
0.04375326260924339,
-0.013056885451078415,
-0.03427887707948685,
0.013649659231305122,
-0.026103194802999496,
0.0008359645726159215,
0.004971606656908989,
0.037237923592329025,
-0.011413232423365116,
0.019679537042975426,
0.004047533962875605,
-0.01881846971809864,
0.013853062875568867,
0.02046317048370838,
-0.005597552750259638,
-0.02725984901189804,
0.024445082992315292,
0.05622990429401398,
0.029872950166463852,
-0.010298377834260464,
-0.006028099451214075,
0.04766866937279701,
-0.026289789006114006,
0.0006081697065383196,
0.015015427954494953,
-0.03707502782344818,
0.02469240315258503,
0.04631709307432175,
0.006068408954888582,
-0.02072071097791195,
0.025899091735482216,
0.002200586488470435,
0.031451571732759476,
0.019923709332942963,
-0.001240459969267249,
0.021418478339910507,
-0.022484274581074715,
-0.015151266008615494,
0.04551352933049202,
-0.03185074031352997,
-0.016112126410007477,
-0.03301957622170448,
-0.0010089118732139468,
0.0025360106956213713,
-0.008467908017337322,
-0.022571003064513206,
0.02595691755414009,
-0.011150837875902653,
0.007052794564515352,
0.021829470992088318,
-0.039007529616355896,
-0.005743904504925013,
-0.04198619723320007,
0.0561172254383564,
0.06315993517637253,
0.06235555559396744,
-0.037710025906562805,
0.020050082355737686,
-0.03758734464645386,
-0.042662303894758224,
-0.04086678847670555,
0.019412193447351456,
-0.0035594007931649685,
-0.011313561350107193,
0.0011032416950911283,
0.0049186632968485355,
0.009543228894472122,
-0.021101517602801323,
-0.0008875164785422385,
0.036545280367136,
-0.03417948633432388,
-0.08872760087251663,
-0.0698549672961235,
0.018470682203769684,
0.017452210187911987,
0.009982168674468994,
-0.031626489013433456,
0.023711249232292175,
0.029818901792168617,
0.08349922299385071,
0.034030091017484665,
0.014719115570187569,
0.013009311631321907,
0.028203750029206276,
-0.010516013950109482,
-0.0332755520939827,
0.03355834633111954,
0.011096779257059097,
-0.03318868950009346,
0.0080800736322999,
-0.12614159286022186,
-0.016892656683921814,
0.022390345111489296,
0.0035253691021353006,
-0.0076776170171797276,
0.038408149033784866,
-0.0188787542283535,
0.03138410300016403,
0.0052736378274858,
-0.009858155623078346,
-0.02119981311261654,
0.0705287978053093,
0.030384313315153122,
0.02734971046447754,
0.041252050548791885,
0.028833085671067238,
0.01368745882064104,
0.016280196607112885,
0.004950203467160463,
0.041242580860853195,
-0.041300758719444275,
-0.015452049672603607,
0.0037625853437930346,
0.02349146269261837,
0.009172300808131695,
-0.024898063391447067,
-0.04045810550451279,
0.01669522002339363,
-0.012383815832436085,
-0.016146009787917137,
0.022130213677883148,
0.021376334130764008,
0.014904238283634186,
0.011593371629714966,
-0.023977160453796387,
-0.0012586356606334448,
-0.05803501978516579,
0.03233666345477104,
0.00377777311950922,
-0.010511244647204876,
0.028181247413158417,
0.019833706319332123,
0.03433223441243172,
-0.012023686431348324,
-0.053361281752586365,
-0.007069007959216833,
0.021543676033616066,
-0.012951230630278587,
-0.007672579493373632,
0.013426274992525578,
0.05440559238195419,
0.024331646040081978,
-0.006151219364255667,
0.04680297151207924,
0.0012686135014519095,
-0.034547243267297745,
-0.004541117697954178,
-0.0029099611565470695,
0.01937173865735531,
0.006317285820841789,
-0.024804672226309776,
0.0017752759158611298,
0.013201087713241577,
-0.02310311794281006,
0.025131389498710632,
-0.06234981119632721,
0.08082639425992966,
0.04398571699857712,
0.005281235557049513,
-0.027523789554834366,
0.034441642463207245,
0.011564631015062332,
0.05318555608391762,
0.009949524886906147,
-0.018526552245020866,
-0.026616619899868965,
-0.033162593841552734,
0.034456055611371994,
0.042845696210861206,
-0.05272270739078522,
0.02284269779920578,
0.045850709080696106,
0.03057205118238926,
0.027010135352611542,
0.0248947124928236,
-0.03298259899020195,
-0.008335601538419724,
0.02465183287858963,
0.008799963630735874,
0.034778013825416565,
0.030458340421319008,
0.02524743415415287,
0.009563320316374302,
-0.01984100602567196,
-0.04478041082620621,
-0.03682597726583481,
0.05489307641983032,
-0.024168675765395164,
0.0038439715281128883,
0.023152854293584824,
-0.04057593271136284,
0.03144941106438637,
-0.019801080226898193,
0.017151162028312683,
0.061970263719558716,
-0.004660117905586958,
-0.046188000589609146,
-0.04555068910121918,
-0.038688693195581436,
0.0030511822551488876,
0.020800510421395302,
-0.033356230705976486,
0.0073508028872311115,
0.026245390996336937,
-0.0458691343665123,
-0.005708802025765181,
-0.012283658608794212,
-0.0047940765507519245,
-0.05216952785849571,
0.030800646170973778,
0.01190758217126131,
0.0014619523426517844,
0.04114678502082825,
-0.02358514815568924,
-0.02401180937886238,
0.006663316395133734,
-0.026517778635025024,
-0.02398739568889141,
0.0026277070865035057,
-0.05683239921927452,
0.048507899045944214,
-0.03238481655716896,
-0.02984568662941456,
0.04768472537398338,
-0.04664335772395134,
-0.0012687989510595798,
0.016752013936638832,
-0.030620774254202843,
-0.005801345221698284,
0.00874367542564869,
-0.05900067090988159,
0.03526910021901131,
-0.03320196270942688,
0.006550244055688381,
0.04791420325636864,
0.013344480656087399,
-0.03912918642163277,
-0.016300735995173454,
-0.02019723318517208,
-0.050019361078739166,
-0.0021432656794786453,
-0.00044731900561600924,
0.012336192652583122,
-0.02884916216135025,
-0.0012851328356191516,
0.02394656464457512,
-0.054913632571697235,
-0.009380760602653027,
-0.06371642649173737,
-0.038915328681468964,
0.04246922582387924,
0.009886425919830799,
0.009626864455640316,
-0.004243765026330948,
0.0016577565111219883,
0.07872818410396576,
0.05269155651330948,
-0.03801147639751434,
-0.038777247071266174,
0.021230069920420647,
-0.003071571933105588,
0.012840140610933304,
0.008801441639661789,
0.0018323262920603156,
-0.009278407320380211,
0.02416319027543068,
0.019716400653123856,
0.015543523244559765,
0.021758275106549263,
0.00493290601298213,
-0.012332912534475327,
0.009683927521109581,
0.03749574348330498,
0.002416018396615982,
0.034089941531419754,
0.013978265225887299,
-0.04603520408272743,
0.002001795219257474,
-0.01466994360089302,
0.029629135504364967,
-0.012064442038536072,
-0.023746376857161522,
0.04330474138259888,
0.01088124793022871,
0.021692875772714615,
-0.014038914814591408,
0.039260271936655045,
-0.0055090091191232204,
-0.019817091524600983,
0.0129290372133255,
0.03861910477280617,
0.01664602942764759,
-0.002943275962024927,
-0.0037008794024586678,
0.04388238489627838,
0.02987065352499485,
-0.026648955419659615,
0.007634386885911226,
-0.012778447940945625,
-0.02392508089542389,
0.040098752826452255,
-0.023720387369394302,
0.000011777957297454122,
0.06194788217544556,
0.014529327861964703,
0.04749458283185959,
0.018093015998601913,
-0.013954767026007175,
-0.013290767557919025,
-0.0706326961517334,
-0.026182986795902252,
-0.01894172839820385,
0.06191526725888252,
0.024497173726558685,
0.037647027522325516,
0.04564407840371132,
0.010463696904480457,
0.002794752363115549,
0.002878407947719097,
-0.080183245241642,
0.04870036616921425,
-0.022160610184073448,
-0.03560495749115944,
0.011664397083222866,
-0.012141073122620583,
-0.012013787403702736,
-0.05180663615465164,
-0.022000031545758247,
0.02104480378329754,
-0.006934255827218294,
-0.05871480330824852,
0.020330429077148438,
-0.03345787152647972,
-0.04661592096090317,
0.00247365259565413,
0.03728018328547478,
0.02157006599009037,
0.0019261110574007034,
0.0026637292467057705,
0.017040397971868515,
-0.026327354833483696,
-0.016234565526247025,
-0.0049432716332376,
0.027475377544760704,
0.031143922358751297,
0.046862196177244186,
0.02144642360508442,
0.0717703327536583,
-0.02255382016301155,
0.015053500421345234,
0.017251109704375267,
0.046135738492012024,
-0.003358737099915743,
-0.03958338126540184,
-0.026618128642439842,
-0.054582856595516205,
-0.024642692878842354,
0.012245592661201954,
0.036402393132448196,
-0.011215736158192158,
-0.013777688145637512,
-0.020250394940376282,
0.019027864560484886,
-0.018602196127176285,
0.00559591269120574,
0.09327691793441772,
-0.0024833239149302244,
-0.04079694673418999,
-0.012350587174296379,
-0.06608100235462189,
-0.03512221947312355,
0.0015930747613310814,
0.035158127546310425,
0.006194437853991985,
-0.01231704093515873,
0.04116412624716759,
0.006932656746357679,
-0.006573421880602837,
-0.04445052891969681,
-0.011594871059060097,
0.0403546541929245,
0.04627705737948418,
0.0035483557730913162,
-0.003382826456800103,
0.003321684431284666,
0.050758540630340576,
0.03468513861298561,
-0.021230466663837433,
0.02031428925693035,
-0.09322068840265274,
0.0022167738061398268,
0.05912196636199951,
-0.008511364459991455,
-0.010395735502243042,
-0.03917032107710838,
-0.04189015179872513,
-0.015520990826189518,
0.04133802652359009,
-0.02400471456348896,
0.03200875595211983,
0.030985798686742783,
0.011107809841632843,
0.016110341995954514,
-0.0004660812555812299,
0.005715264938771725,
0.021531101316213608,
-0.009609113447368145,
-0.015960747376084328,
-0.018835624679923058,
-0.002594457706436515,
-0.03049585036933422,
0.003157789120450616,
0.04574429988861084,
0.0553281232714653,
-0.02073751389980316,
-0.018034495413303375,
-0.017610842362046242,
0.0030904565937817097,
-0.0035474132746458054,
-0.09128578007221222,
-0.011364503763616085,
0.019564323127269745,
-0.030321983620524406,
0.0642554759979248,
-0.025177348405122757,
-0.027672529220581055,
0.04353930428624153,
-0.024834590032696724,
-0.005582976154983044,
0.013262039981782436,
-0.025477629154920578,
0.04417569935321808,
0.04717637225985527,
-0.005715424660593271,
0.010412502102553844,
-0.01004714798182249,
-0.017835203558206558,
-0.022049693390727043,
-0.022453298792243004,
0.01839718222618103,
-0.03316687420010567,
-0.0011835438199341297,
-0.04061153158545494,
0.04852773994207382,
-0.024716412648558617,
0.04013761878013611,
0.01643613912165165,
0.004101739730685949,
-0.0007120586233213544,
-0.028249621391296387,
-0.033870894461870193,
0.009968921542167664,
-0.009397787973284721,
-0.029975727200508118,
-0.008717089891433716,
0.009857917204499245,
-0.013392538763582706,
-0.017152829095721245,
-0.020790880545973778,
0.014386647380888462,
-0.023741284385323524,
0.03650902211666107,
-0.014002307318150997,
0.023933017626404762,
-0.018884820863604546,
0.008116659708321095,
0.04213450476527214,
-0.030828768387436867,
-0.008658826351165771,
0.00282103568315506,
-0.01467095036059618,
0.04782778397202492,
-0.08868713676929474,
-0.04185402765870094,
-0.0045848628506064415,
0.025355124846100807,
-0.007387262769043446,
-0.019148891791701317,
-0.02596505731344223,
0.017499543726444244,
-0.01702795922756195,
-0.06268924474716187,
-0.02626904286444187,
0.045467451214790344,
-0.0005471315234899521,
-0.004574129823595285,
-0.022492514923214912,
0.02423395775258541,
-0.05626346543431282,
-0.015797022730112076,
-0.009564731270074844,
0.06969176232814789,
-0.03715088590979576,
-0.003915286157280207,
0.013932021334767342,
0.023017168045043945,
0.05125775188207626,
-0.02005367912352085,
0.031471721827983856,
0.018775956705212593,
0.0014796159230172634,
0.019333919510245323,
0.014356095343828201,
0.04031473025679588,
-0.028054403141140938,
-0.03588101640343666,
-0.04121116176247597,
0.017907027155160904,
0.0497366227209568,
0.004526988603174686,
-0.03158966079354286,
0.05108268931508064,
-0.002367186127230525,
0.0007153645274229348,
-0.0270081777125597,
0.01489777211099863,
-0.007504593580961227,
0.010367527604103088,
-0.02170315571129322,
0.009521647356450558,
0.008766134269535542,
-0.05195007473230362,
0.03909406065940857,
-0.027923518791794777,
-0.03210447356104851,
0.006523658987134695,
0.06371618062257767,
0.01627781055867672,
-0.04191771149635315,
0.0013514128513634205,
-0.022177699953317642,
0.004690736066550016,
-0.024361878633499146,
0.013351616449654102,
0.0038355118595063686,
0.03108879178762436,
-0.0282291229814291,
-0.05743829905986786,
-0.01471671275794506,
-0.009272485040128231,
0.06295914947986603,
0.0025656570214778185,
0.05200665816664696,
0.050959084182977676,
0.01795346848666668,
-0.027485813945531845,
-0.010748150758445263,
-0.01910012774169445,
0.014435320161283016,
0.027023116126656532,
0.03689460828900337,
0.004877278581261635,
-0.012537202797830105,
0.04759825021028519,
0.03309935703873634,
0.03543351963162422,
0.006190012209117413,
0.007620074320584536,
0.036438848823308945,
-0.022189810872077942,
-0.01446146797388792,
-0.0416814386844635,
0.03418337181210518,
-0.049441855400800705,
0.045720431953668594,
-0.01130826398730278,
-0.03096788004040718,
0.03193141520023346,
0.026307372376322746,
-0.009789054282009602,
-0.03242650628089905,
-0.016563553363084793,
-0.06444007903337479,
0.031248433515429497,
0.01736704632639885,
0.026650093495845795,
-0.0047668032348155975,
0.047266885638237,
0.017119131982326508,
0.006228594109416008,
0.03155709058046341,
-0.009688151068985462,
-0.10042048990726471,
-0.04748497158288956,
-0.02944096364080906,
-0.03795085474848747,
0.04901908338069916,
0.005369091872125864,
-0.007373702712357044,
0.00042547800694592297,
-0.021589677780866623,
0.03133060410618782,
0.031485818326473236,
0.049904219806194305,
-0.038114771246910095,
0.05635340139269829,
-0.029779359698295593,
0.013429554179310799,
-0.024442613124847412,
0.015344019047915936,
0.08860818296670914,
0.06850283592939377,
0.023646537214517593,
-0.05488451570272446,
0.022562062367796898,
-0.01012022327631712,
0.007366333156824112,
-0.02173672430217266,
0.04746418818831444,
0.002189791761338711,
0.0007597445510327816,
-0.0028151441365480423,
0.016165753826498985,
0.02040608413517475,
-0.03824241831898689,
0.06315072625875473,
-0.058638956397771835,
-0.029196223244071007,
-0.00886853039264679,
0.022982554510235786,
-0.0016649094177410007,
0.0033223433420062065,
-0.025191575288772583,
0.02154943346977234,
-0.0483926497399807,
0.006020912900567055,
-0.03250055015087128,
-0.012961488217115402,
-0.0006383097497746348,
0.0051480685360729694,
-0.04736948385834694,
0.03611993044614792,
-0.0188272837549448,
-0.014886481687426567,
-0.018472835421562195,
0.036513615399599075,
0.021370792761445045,
-0.02764809876680374,
0.010223054327070713,
0.031887222081422806,
0.020463604480028152,
0.015866294503211975,
-0.04303478077054024,
-0.007055278867483139,
-0.04629902169108391,
0.021698661148548126,
-0.03405895456671715,
0.04744451865553856,
-0.018687009811401367,
-0.00595315545797348,
0.015097127296030521,
-0.023328248411417007,
-0.012712069787085056,
-0.04053935036063194,
-0.04760412499308586,
0.006587688811123371,
0.012838730588555336,
-0.011815155856311321,
0.009677414782345295,
0.019410349428653717,
0.049090079963207245,
-0.0029135458171367645,
0.009867706336081028,
0.010207854211330414,
-0.023577075451612473,
0.0178585983812809,
-0.018102651461958885,
0.017974141985177994,
-0.03362800180912018,
-0.01632903516292572,
-0.02323363721370697,
-0.0167333222925663,
-0.0329737551510334,
-0.04586091265082359,
0.029253019019961357,
0.0386539027094841,
0.029400141909718513,
-0.03152598813176155,
-0.010579724796116352,
-0.021334867924451828,
-0.045395951718091965,
0.01809767447412014,
-0.010872765444219112,
0.001790944254025817,
-0.026767496019601822,
-0.004156917799264193,
0.0570375956594944,
0.017298847436904907,
-0.006084725726395845,
-0.0023122206330299377,
-0.02769043855369091,
-0.008932600729167461,
0.010208475403487682,
-0.013153755106031895,
-0.028946736827492714,
0.006226502358913422,
-0.04381177946925163,
0.011943391524255276,
-0.03797883167862892,
0.02271030656993389,
0.03616299107670784,
0.0022034819703549147,
-0.02943570725619793,
0.05036533251404762,
-0.0024963165633380413,
0.017518186941742897,
0.014720712788403034,
-0.013674073852598667,
-0.011942822486162186,
0.026157990097999573,
0.02249750867486,
-0.06486799567937851,
-0.000846496201120317,
-0.04608369246125221,
-0.02815735898911953,
0.028804924339056015,
-0.003728805808350444,
-0.0025344083551317453,
0.015200406312942505,
0.0025387706700712442,
0.018211480230093002,
-0.03252599015831947,
0.03968817740678787,
-0.04480263963341713,
0.012368114665150642,
-0.027762800455093384,
-0.0716632604598999,
-0.017326578497886658,
0.0328996442258358,
0.010068807750940323,
-0.06936009228229523,
-0.0021194557193666697,
0.039822906255722046,
-0.014814228750765324,
0.00009708862489787862,
0.01885729469358921,
0.00951889157295227,
0.05634906142950058,
0.008515696041285992,
-0.022724824026226997,
0.007610568311065435,
-0.040145110338926315,
-0.039718735963106155,
0.023110967129468918,
-0.0473230704665184,
0.029172562062740326,
0.04947467893362045,
-0.033507365733385086,
-0.01062417309731245,
0.07118005305528641,
-0.004501399118453264,
0.003038847353309393,
0.020724615082144737,
-0.045513495802879333,
-0.03734099119901657,
-0.05087434872984886,
0.02206823043525219,
-0.006369023118168116,
-0.02171015925705433,
0.012826818972826004,
0.04795513302087784,
0.005121209193021059,
0.0026196392718702555,
0.021418210119009018,
-0.005894055590033531,
-0.001483163214288652,
0.04147465154528618,
-0.013831580057740211,
0.03528064489364624,
0.04172639176249504,
-0.05614043399691582,
0.027358856052160263,
0.02671351656317711,
0.026818497106432915,
-0.07170269638299942,
-0.0015824176371097565,
0.026005476713180542,
-0.014293075539171696,
0.0395377017557621,
-0.057536471635103226,
0.03995924070477486,
-0.02052154392004013,
-0.08074277639389038,
0.02241557091474533,
-0.0217107143253088,
-0.006402350962162018,
-0.010025891475379467,
0.012215819209814072,
-0.02848992682993412,
0.02535429410636425,
0.041243501007556915,
0.016037167981266975,
0.03146543726325035,
0.0062033929862082005,
-0.0035260405857115984,
-0.0019052807474508882,
-0.03181080147624016,
0.02041551284492016,
-0.018251480534672737,
-0.001816427567973733,
0.04252279922366142,
-0.043585143983364105,
-0.039647240191698074,
0.012357763946056366,
-0.027696138247847557,
-0.0046365163289010525,
-0.03225387632846832,
0.010218389332294464,
0.04747321084141731,
0.01833581179380417,
0.02547430992126465,
0.00016154733020812273,
-0.004861122462898493,
0.011296561919152737,
0.004021857399493456,
0.007855333387851715,
-0.003039601957425475,
0.045235905796289444,
-0.0059348782524466515,
-0.0469244085252285,
-0.029511187225580215,
-0.00867434125393629,
0.021601857617497444,
0.006468772888183594,
-0.015895646065473557,
0.027601003646850586,
0.015084759332239628,
-0.027000371366739273,
-0.023085936903953552,
-0.06818763166666031,
0.020008591935038567,
0.0025225456338375807,
0.04324367269873619,
-0.02495456114411354,
-0.014985686168074608,
-0.038812100887298584,
-0.03794752433896065,
0.002938218181952834,
-0.007839000783860683,
-0.006977733690291643,
-0.03954382240772247,
-0.0002797945053316653,
0.008755652233958244,
0.005716945044696331,
0.006812697276473045,
-0.06133732199668884,
-0.04688754677772522,
0.030397538095712662,
-0.02734055183827877,
0.027131633833050728,
-0.011879414319992065,
-0.006292578764259815,
0.0010161723475903273,
-0.0942419022321701,
0.032134752720594406,
-0.004850395955145359,
-0.0081871896982193,
-0.025600098073482513,
0.003247638698667288,
-0.05566684901714325,
0.021263236179947853,
0.057899925857782364,
-0.04656929522752762,
-0.011247923597693443,
0.008657998405396938,
-0.0007266971515491605,
0.01687448099255562,
-0.03928599879145622,
0.009549954906105995,
-0.017353437840938568,
-0.016527973115444183,
-0.013061871752142906,
-0.007398141082376242,
0.0030601981561630964,
0.020578037947416306,
0.04181433469057083,
-0.009625725448131561,
0.02600764110684395,
0.00703679583966732,
-0.028336280956864357,
0.03819860890507698,
-0.0032821199856698513,
0.014864602126181126,
0.040765102952718735,
0.007314559072256088,
0.010659164749085903,
0.05396520718932152,
0.0014801208162680268,
-0.024946290999650955,
0.03515751659870148,
-0.04769497364759445,
-0.038853731006383896,
-0.00977072212845087,
-0.025584978982806206,
0.023700591176748276,
-0.06890495866537094,
-0.009370866231620312,
0.029420528560876846,
-0.025664616376161575,
0.012524189427495003,
0.038612425327301025,
0.013111239299178123,
0.02385387010872364,
-0.012248748913407326,
-0.005427498370409012,
0.03186342492699623,
0.0009258135105483234,
-0.01960756629705429,
0.024285586550831795,
0.034303102642297745,
0.035484254360198975,
0.01966612972319126,
0.03939725458621979,
0.006521293427795172,
0.03544853627681732,
-0.0022475430741906166,
0.02107527293264866,
-0.03547121584415436,
0.007703485433012247,
0.058786455541849136,
0.006842473521828651,
0.022328156977891922,
-0.005724076181650162,
-0.042387112975120544,
0.06172939017415047,
-0.0635855495929718,
0.017491137608885765,
-0.024998893961310387,
0.010702387429773808,
-0.03985827416181564,
0.015477295033633709,
0.006611504126340151,
0.04324252903461456,
-0.000768201076425612,
-0.0025568907149136066,
-0.008291516453027725,
-0.006850967183709145,
-0.004750538617372513,
-0.04717450216412544,
0.002455356763675809,
-0.006007461808621883,
-0.011225303635001183,
0.003550126915797591,
-0.014487559907138348,
-0.03952818736433983,
-0.013287942856550217,
0.061833351850509644,
0.039259668439626694,
0.026744915172457695,
-0.04911023750901222,
-0.024037426337599754,
-0.037078820168972015,
0.05180438235402107,
-0.0573175847530365,
-0.03723589703440666,
-0.0025898029562085867,
0.016482515260577202,
0.005423020571470261,
-0.02252374216914177
] |
<p>A free particle moves along geodesics, one form being</p>
<p>\begin{split}
\ddot x^\mu &= -\Gamma^{\mu}_{\sigma \rho} \dot x^\sigma \dot x^\rho \\
&= -\frac{1}{2}g^{\mu \nu}(\partial_\sigma g_{\rho \nu} + \partial_\rho g_{\sigma \nu} - \partial_\nu g_{\rho \sigma}) \dot x^\sigma \dot x^\rho
\end{split}</p>
<p>Applying the lowering operator, we have</p>
<p>\begin{split}
\ddot x_\mu &= g_{\mu \alpha} \ddot x^\alpha \\
&= -\frac{1}{2}\delta^\mu_\nu(\partial_\sigma g_{\rho \nu} + \partial_\rho g_{\sigma \nu} - \partial_\nu g_{\rho \sigma}) \dot x^\sigma \dot x^\rho
\end{split}
Hence
$$\tag{1}
\ddot x_{\mu} = -\frac{1}{2}(\partial_\sigma g_{\rho \mu} + \partial_\rho g_{\sigma \mu} - \partial_\mu g_{\rho \sigma}) \dot x^\sigma \dot x^\rho
$$</p>
<p>Equivalently, using the intrinsic derivative, </p>
<p>$$
\frac{Dt_\mu}{D\tau} = 0 $$ for a free particle, so $$
\frac{dt_\mu}{d\tau} = \Gamma^\sigma_{\mu \rho} \dot x_\sigma \dot x^\rho
$$ </p>
<p>or </p>
<p>$$
\ddot x_\mu = \frac{1}{2}g^{\sigma \nu}(\partial_\mu g_{\rho \nu} + \partial_\rho g_{\mu \nu} - \partial_\nu g_{\rho \mu}) \dot x_\sigma \dot x^\rho
$$
Hence
$$\tag{2}
\ddot x_\mu= \frac{1}{2}\partial_\mu g_{\sigma \rho}\dot x^\sigma \dot x^\rho
$$
(The summation on $\sigma$ and $\rho$ in the last two terms cancels)</p>
<p>Clearly (1) $\neq$ (2). Does anyone know where my reasoning has gone astray?</p>
<p>Much Appreciated</p>
| 9,589 |
[
0.019887937232851982,
0.030893346294760704,
0.029636770486831665,
-0.02548271045088768,
0.0012996015138924122,
0.011300005950033665,
-0.04097773879766464,
-0.033705081790685654,
-0.008727729320526123,
-0.02834797464311123,
0.03570139408111572,
-0.0026762611232697964,
0.051681097596883774,
0.04289337992668152,
0.04250812157988548,
0.022305402904748917,
-0.018622661009430885,
-0.01768448017537594,
0.0005494495271705091,
-0.03443099185824394,
0.018992621451616287,
0.00017791804566513747,
0.000316696212394163,
0.003480244195088744,
-0.005545690655708313,
0.03200941160321236,
0.027469057589769363,
-0.014567703939974308,
-0.024357672780752182,
0.041203491389751434,
-0.01026203203946352,
-0.0024685778189450502,
-0.03843361884355545,
0.007839346304535866,
0.011195573955774307,
-0.0028547686524689198,
-0.00862818956375122,
-0.017709892243146896,
-0.025181850418448448,
0.016187550500035286,
-0.03081219457089901,
-0.022705456241965294,
-0.04977010563015938,
0.04404336214065552,
-0.010931652970612049,
-0.008798393420875072,
0.027782965451478958,
-0.0010982640087604523,
0.04987649619579315,
-0.03285357356071472,
0.05282469838857651,
-0.0092473728582263,
0.023310169577598572,
-0.046777043491601944,
-0.014725813642144203,
-0.04194175824522972,
0.05887402966618538,
0.05284057930111885,
-0.011085303500294685,
-0.062109023332595825,
-0.00024493280216120183,
-0.042448945343494415,
-0.02212507463991642,
-0.03524162620306015,
0.011144835501909256,
-0.0005511909257620573,
0.019024984911084175,
-0.017978308722376823,
0.03480794280767441,
-0.007262757979333401,
0.010922334156930447,
-0.04851236566901207,
0.009211947210133076,
-0.0006544121424667537,
0.023939210921525955,
0.01898707076907158,
-0.00978849083185196,
0.008427868597209454,
0.009671390056610107,
-0.0006833367515355349,
-0.009175892919301987,
-0.020588068291544914,
0.01359421107918024,
-0.007283741608262062,
-0.015288096852600574,
-0.01803102158010006,
0.09104519337415695,
0.00784203503280878,
0.012806234881281853,
0.052846577018499374,
0.007680862210690975,
0.014312776736915112,
0.05786781385540962,
-0.01091286726295948,
-0.03843424841761589,
0.045579880475997925,
0.0035032229498028755,
0.004176214337348938,
-0.017166966572403908,
-0.023912755772471428,
-0.03685641288757324,
-0.04775538668036461,
0.00896543450653553,
0.07141511887311935,
0.014118095859885216,
-0.001582809491083026,
-0.0412074513733387,
-0.01953020878136158,
-0.04992252215743065,
-0.05721157416701317,
-0.02911686711013317,
0.025825096294283867,
-0.0274821687489748,
-0.013440033420920372,
-0.02266024984419346,
-0.031276434659957886,
0.02787311188876629,
-0.000913359341211617,
0.021837826818227768,
0.05535956099629402,
0.04058106243610382,
-0.0446939580142498,
-0.0176702793687582,
-0.01254719216376543,
-0.10491368919610977,
0.012241218239068985,
0.046114109456539154,
-0.013693275861442089,
-0.046871572732925415,
-0.014209502376616001,
0.023083895444869995,
0.01531462837010622,
0.01658000238239765,
0.03571384772658348,
0.006987894885241985,
-0.011037350632250309,
-0.08013831079006195,
-0.020259976387023926,
0.01572555862367153,
0.011038712225854397,
0.00006918514554854482,
-0.07143145799636841,
-0.030088016763329506,
0.038034554570913315,
0.11213448643684387,
0.000018219621779280715,
0.02205018885433674,
0.008681762963533401,
-0.005307198502123356,
-0.03345709666609764,
0.021343640983104706,
-0.019774824380874634,
-0.014774136245250702,
-0.025630269199609756,
-0.039113517850637436,
-0.01902867667376995,
0.019729701802134514,
0.02648547664284706,
-0.031563255935907364,
0.02280394360423088,
0.06259085983037949,
-0.023390328511595726,
0.03439759090542793,
0.018535686656832695,
-0.02139091119170189,
-0.046738967299461365,
0.0570584237575531,
0.03987523540854454,
-0.009143701754510403,
0.02690126746892929,
0.018139196559786797,
0.022445961833000183,
-0.04546891897916794,
-0.011847174726426601,
0.03751395270228386,
-0.04142044857144356,
-0.01887962408363819,
0.009947370737791061,
-0.02357872948050499,
0.007054646499454975,
-0.027030067518353462,
-0.021532993763685226,
-0.04421741142868996,
0.008468466810882092,
0.005840898025780916,
-0.009810369461774826,
0.008597943931818008,
0.015714822337031364,
0.0009390432387590408,
-0.0584399588406086,
-0.00036968785570934415,
-0.04442399740219116,
0.020392684265971184,
0.012940643355250359,
-0.031975433230400085,
0.04668081924319267,
0.02473524585366249,
0.015759259462356567,
-0.010355023667216301,
-0.03857489302754402,
-0.0208452045917511,
0.018427783623337746,
0.021917423233389854,
-0.021607456728816032,
0.00495771411806345,
0.06456011533737183,
0.043040886521339417,
0.02595195360481739,
0.017628468573093414,
0.007739253807812929,
0.02073287032544613,
-0.011566057801246643,
0.0030257534235715866,
0.042861953377723694,
-0.00959064532071352,
0.04466228187084198,
-0.0036783358082175255,
-0.016149146482348442,
-0.025518357753753662,
-0.011272727511823177,
-0.09287657588720322,
0.021083423867821693,
0.07090727239847183,
0.0017585239838808775,
0.023801015689969063,
0.020599735900759697,
-0.012705668807029724,
0.04001326113939285,
0.016010262072086334,
-0.016517862677574158,
-0.0206262469291687,
-0.0255978312343359,
0.018845366314053535,
0.044947512447834015,
-0.03645171970129013,
0.013262788765132427,
0.033984050154685974,
0.013989359140396118,
0.020514898002147675,
0.034402307122945786,
0.02986920066177845,
-0.06227066367864609,
0.0444454587996006,
0.013317935168743134,
0.010652657598257065,
-0.015582813881337643,
0.037185393273830414,
-0.018578501418232918,
0.008938498795032501,
-0.004717743955552578,
-0.03751957044005394,
0.06600286811590195,
-0.00912113394588232,
-0.04090198501944542,
0.03295150771737099,
-0.02395721711218357,
0.04057135805487633,
0.02282065525650978,
0.034763265401124954,
0.061349283903837204,
-0.04610060527920723,
-0.007159561850130558,
-0.041843995451927185,
-0.009140712209045887,
-0.006216689944267273,
0.019768672063946724,
-0.004342753440141678,
-0.03612665459513664,
0.011277526617050171,
-0.06520513445138931,
-0.0134973656386137,
-0.014118270017206669,
-0.015688179060816765,
-0.005498488899320364,
-0.030855782330036163,
0.035102151334285736,
0.04831302538514137,
0.0043234615586698055,
-0.01549385953694582,
-0.010189894586801529,
0.04646215960383415,
0.004661298356950283,
0.030860386788845062,
0.045583732426166534,
-0.04066507890820503,
0.007894650101661682,
-0.04395183175802231,
-0.034601323306560516,
0.05135014280676842,
0.010426248423755169,
-0.00374741293489933,
0.04813385754823685,
-0.006203753873705864,
-0.041133709251880646,
-0.0416298471391201,
0.00929183978587389,
-0.045359693467617035,
-0.04476478323340416,
0.01703205332159996,
0.050849661231040955,
0.021913612261414528,
-0.01990717649459839,
-0.02574489824473858,
-0.03270809352397919,
-0.05657079815864563,
0.005497429054230452,
0.018531179055571556,
0.019179586321115494,
-0.008086205460131168,
0.04572208225727081,
0.05494367331266403,
0.015051040798425674,
0.001752505311742425,
-0.06608543545007706,
-0.02958262711763382,
0.051142238080501556,
0.018171189352869987,
-0.004014711827039719,
0.000914619246032089,
-0.019937554374337196,
0.08950089663267136,
0.03643497824668884,
-0.016418524086475372,
-0.022402657195925713,
0.0009634473826736212,
0.00020301708718761802,
-0.044027674943208694,
-0.008659289218485355,
0.015012441202998161,
-0.027385124936699867,
-0.018383540213108063,
0.0418364480137825,
0.04471919313073158,
0.031947724521160126,
-0.005580451805144548,
0.00321953184902668,
0.021557224914431572,
0.016001176089048386,
-0.030415598303079605,
0.05618363991379738,
-0.012723798863589764,
0.015333155170083046,
0.024540888145565987,
0.007686596363782883,
0.028245657682418823,
-0.014048117212951183,
-0.04279641434550285,
0.03450942039489746,
0.042383015155792236,
-0.0027133096009492874,
0.01903950423002243,
0.0005038906820118427,
0.006097127217799425,
-0.06950969994068146,
-0.035195037722587585,
-0.004449967294931412,
0.031356871128082275,
-0.02202405221760273,
0.009164644405245781,
0.038227539509534836,
0.004470465704798698,
-0.01219398993998766,
-0.029728835448622704,
0.0004096172924619168,
-0.026137422770261765,
0.010698196478188038,
-0.0006393150542862713,
-0.012799282558262348,
0.013610153459012508,
0.030981620773673058,
0.016575228422880173,
-0.025387266650795937,
-0.024599941447377205,
-0.05123048648238182,
-0.05757463350892067,
0.048491835594177246,
-0.0005299486219882965,
0.0371575690805912,
0.0013183197006583214,
0.06639978289604187,
0.011639022268354893,
0.043146684765815735,
-0.004679893609136343,
0.004490747582167387,
-0.09500815719366074,
0.021615231409668922,
-0.030675765126943588,
-0.014371090568602085,
0.019034193828701973,
-0.004927392117679119,
0.01617409475147724,
-0.040988583117723465,
-0.036224812269210815,
0.003950632642954588,
-0.018100256100296974,
-0.07727578282356262,
0.02892640233039856,
-0.062095627188682556,
-0.05603019893169403,
-0.012774578295648098,
0.0514054112136364,
0.02187906950712204,
0.0218882504850626,
-0.016673270612955093,
0.041071198880672455,
-0.0005962429568171501,
0.03086879476904869,
-0.016165748238563538,
0.0071651204489171505,
0.025392325595021248,
0.002272677142173052,
0.02034740149974823,
0.023996630683541298,
0.007242824882268906,
0.02063075080513954,
0.037981051951646805,
0.03400188311934471,
-0.01599179022014141,
-0.0276033878326416,
0.0023406052496284246,
-0.06620746850967407,
0.0028677438385784626,
-0.017617134377360344,
0.03512747958302498,
-0.004538515117019415,
-0.018710961565375328,
0.052283383905887604,
-0.005156965460628271,
0.037181057035923004,
0.050249308347702026,
0.029115766286849976,
0.021158410236239433,
-0.04846486076712608,
-0.046359919011592865,
-0.02100883238017559,
-0.024216098710894585,
0.004192914813756943,
0.026652611792087555,
-0.025238873437047005,
-0.023054128512740135,
0.008527321740984917,
-0.016950512304902077,
0.015975303947925568,
-0.032862648367881775,
-0.03071577101945877,
-0.012752555310726166,
0.008155662566423416,
-0.001472966163419187,
0.014268451370298862,
0.02218777872622013,
0.028185199946165085,
0.013826409354805946,
-0.0009371275082230568,
0.03975134342908859,
-0.08341235667467117,
-0.01682712882757187,
0.021212847903370857,
0.04248116537928581,
0.023342739790678024,
0.0037379369605332613,
-0.04848834499716759,
0.0005290286499075592,
0.029296081513166428,
0.012568015605211258,
0.04452412948012352,
0.036025628447532654,
-0.0015735870692878962,
-0.0016208674060180783,
-0.027686934918165207,
-0.05164787918329239,
0.03818732500076294,
0.009474954567849636,
-0.007631123531609774,
-0.03867078945040703,
0.010973569937050343,
0.016105979681015015,
0.021816566586494446,
0.004044781439006329,
0.0613102950155735,
0.006868244614452124,
0.0037120417691767216,
0.013929534703493118,
0.0229396503418684,
-0.022128676995635033,
-0.08349327743053436,
0.014438179321587086,
0.028645236045122147,
-0.00984332337975502,
0.050947483628988266,
-0.025028301402926445,
-0.04173901677131653,
0.05510754510760307,
0.027486873790621758,
0.012700955383479595,
0.028972910717129707,
-0.03897742182016373,
0.05907601863145828,
0.016850043088197708,
-0.056445714086294174,
0.05734014883637428,
0.009074478410184383,
-0.018787596374750137,
-0.003857088042423129,
-0.0520302951335907,
0.021765319630503654,
-0.04928956553339958,
-0.018337810412049294,
-0.05300070345401764,
-0.008571941405534744,
-0.0018429571064189076,
0.021251080557703972,
-0.0131505923345685,
0.0101286880671978,
0.031455449759960175,
-0.045032598078250885,
-0.004524364601820707,
0.03283155336976051,
-0.04819456860423088,
-0.007661697920411825,
0.02384803257882595,
0.03322109952569008,
0.016048939898610115,
-0.010047612711787224,
0.0031728732865303755,
-0.00511823408305645,
0.018316131085157394,
0.02880830690264702,
-0.03511399030685425,
0.0046982415951788425,
-0.041259028017520905,
-0.012499348260462284,
-0.004155003000050783,
-0.05083925649523735,
0.06774455308914185,
-0.009119044989347458,
0.015337876044213772,
0.03936496004462242,
0.007484440226107836,
-0.04167213663458824,
0.0007982777897268534,
0.00022959768830332905,
-0.010657189413905144,
-0.026188816875219345,
-0.0001530276786070317,
0.036059655249118805,
0.03142242878675461,
-0.08440089970827103,
-0.007168909534811974,
0.0216075386852026,
-0.027261126786470413,
0.0026800085324794054,
-0.004962547682225704,
0.06535742431879044,
-0.020737135782837868,
-0.022477397695183754,
0.003401094814762473,
0.005296144634485245,
-0.008060638792812824,
0.011902794241905212,
0.016672510653734207,
0.03095890022814274,
-0.0036615636199712753,
-0.016420945525169373,
-0.009615098126232624,
0.0062726386822760105,
0.02345718815922737,
-0.006853514350950718,
-0.007376071065664291,
0.07027436792850494,
-0.0034127598628401756,
-0.02453705295920372,
0.020625334233045578,
-0.03398522362112999,
0.0020813303999602795,
0.0013126006815582514,
-0.054384224116802216,
0.0078602135181427,
0.0388646200299263,
-0.00804917886853218,
-0.005456254351884127,
-0.01946689561009407,
-0.016753414645791054,
0.023569747805595398,
0.019049789756536484,
0.01575789414346218,
-0.0020488344598561525,
-0.02525944635272026,
0.038576748222112656,
-0.005327057559043169,
0.006900064647197723,
0.02327924221754074,
0.060706283897161484,
0.0006021533044986427,
-0.022540021687746048,
0.017006391659379005,
0.022132745012640953,
0.017694689333438873,
-0.0233378354460001,
0.004181923810392618,
0.016456257551908493,
0.019429659470915794,
-0.0134139284491539,
-0.004332982935011387,
-0.0388333834707737,
0.043295539915561676,
0.06389983743429184,
0.005441634450107813,
0.0034248169977217913,
0.011112743057310581,
-0.004172951448708773,
0.0013865709770470858,
-0.029134470969438553,
-0.01052767876535654,
0.00346021493896842,
-0.007859406992793083,
0.04889838770031929,
-0.04888986796140671,
-0.043618764728307724,
0.05059060454368591,
0.029808659106492996,
-0.10234475135803223,
-0.005848311353474855,
-0.012430147267878056,
0.019321000203490257,
-0.02854144014418125,
-0.04749060794711113,
-0.010668887756764889,
0.05886078625917435,
-0.025512121617794037,
0.07914318144321442,
-0.004848153796046972,
-0.021373257040977478,
0.008951627649366856,
0.045750267803668976,
0.010961124673485756,
-0.026760103181004524,
0.01118247490376234,
-0.037782520055770874,
0.03944062814116478,
0.027495456859469414,
-0.0350981242954731,
-0.01198576670140028,
0.006695120595395565,
0.06387889385223389,
-0.014396248385310173,
0.03699026256799698,
0.004326923750340939,
-0.030373668298125267,
0.016249792650341988,
-0.026917103677988052,
-0.043795034289360046,
0.07295778393745422,
-0.0018621351337060332,
0.008879246190190315,
0.021547392010688782,
-0.025370705872774124,
0.030110077932476997,
0.045438092201948166,
0.03508846461772919,
0.02896398864686489,
0.05918523296713829,
-0.00901732686907053,
0.016915641725063324,
-0.024851730093359947,
-0.009341081604361534,
0.16422758996486664,
0.0346028134226799,
-0.001304340548813343,
-0.022055981680750847,
-0.011972845532000065,
-0.01942775771021843,
0.035586174577474594,
-0.02821505069732666,
0.03690808638930321,
-0.0024898110423237085,
-0.032443106174468994,
-0.004762545693665743,
0.03876744210720062,
-0.016678424552083015,
-0.021816959604620934,
0.02046213671565056,
-0.03348275646567345,
-0.06678707152605057,
-0.02346290461719036,
0.004221949260681868,
-0.024993233382701874,
0.014756441116333008,
0.0030434983782470226,
0.04068853706121445,
-0.050223663449287415,
0.01923646219074726,
-0.02791954018175602,
-0.03450187295675278,
0.0007003957871347666,
-0.02678466960787773,
-0.06042793020606041,
0.00025081285275518894,
-0.006600467953830957,
-0.0033470250200480223,
0.004021232482045889,
0.024975376203656197,
0.024790288880467415,
-0.026253527030348778,
-0.00017174436652567238,
0.04020698368549347,
-0.01355014555156231,
0.027994167059659958,
0.02099195308983326,
0.02906826324760914,
-0.01042266096919775,
0.02809431590139866,
-0.013110941275954247,
0.061172910034656525,
-0.04241872951388359,
0.02511945553123951,
0.008586791343986988,
0.000017849652067525312,
-0.0017464918782934546,
-0.035355307161808014,
-0.0034690629690885544,
-0.004560645669698715,
0.017976198345422745,
0.00650671636685729,
0.020222997292876244,
0.03268284723162651,
0.010927790775895119,
0.028068315237760544,
0.0029569182079285383,
-0.045099690556526184,
0.005139483604580164,
-0.01114455796778202,
0.0034855559933930635,
0.05425949767231941,
-0.023792674764990807,
0.0013239573454484344,
-0.03222097456455231,
-0.012842515483498573,
-0.04473315551877022,
-0.017225123941898346,
-0.021636810153722763,
-0.014072488993406296,
0.010221293196082115,
0.007059404160827398,
0.020750384777784348,
-0.009768811985850334,
-0.06678406149148941,
0.02421010285615921,
0.00094949034973979,
0.00662959273904562,
-0.025665070861577988,
-0.02382477931678295,
0.0023437596391886473,
0.01834026165306568,
0.01073884591460228,
0.007159339264035225,
0.021246928721666336,
0.04364922642707825,
-0.00399075448513031,
-0.02102714776992798,
-0.07227097451686859,
0.030449725687503815,
-0.011838285252451897,
-0.011329001747071743,
0.008785052224993706,
0.005935430992394686,
0.013226458802819252,
0.04359963536262512,
-0.0037755772937089205,
0.0575769804418087,
-0.026893116533756256,
0.004550870507955551,
0.025043761357665062,
0.0029243002645671368,
-0.02439563162624836,
0.049451325088739395,
-0.009793602861464024,
-0.04469849541783333,
-0.00887301191687584,
0.014154693111777306,
0.008847312070429325,
-0.018499718979001045,
0.021492555737495422,
-0.01918133534491062,
-0.00516748521476984,
-0.025136101990938187,
0.004307342227548361,
-0.00030461946153081954,
0.00019336480181664228,
-0.008729255758225918,
0.04401114210486412,
-0.00782859418541193,
-0.04698074609041214,
-0.011294680647552013,
0.010800495743751526,
0.0023258698638528585,
-0.02570602297782898,
0.057480793446302414,
0.05320724472403526,
0.018513798713684082,
-0.01564466767013073,
0.059498485177755356,
0.0001978110522031784,
0.02981046587228775,
0.008562721312046051,
-0.036309316754341125,
-0.006746246479451656,
-0.022322768345475197,
-0.032393306493759155,
0.01362649630755186,
0.03656967729330063,
0.05494595691561699,
-0.016069838777184486,
-0.0451759472489357,
-0.0015178187750279903,
0.06868640333414078,
-0.037722181528806686,
-0.017579415813088417,
-0.037098757922649384,
-0.0853622704744339,
-0.01287271548062563,
-0.08927085995674133,
0.05688568949699402,
-0.008095044642686844,
-0.008671984076499939,
0.03557289019227028,
-0.022097749635577202,
-0.03516623005270958,
-0.005758082959800959,
0.010892467573285103,
-0.03695427253842354,
-0.027168331667780876,
0.00041102198883891106,
0.01610495336353779,
0.031291961669921875,
0.012781818397343159,
-0.0009572672424837947,
-0.017319614067673683,
-0.005340997129678726,
0.023756634443998337,
-0.07742031663656235,
-0.043448157608509064,
0.018213681876659393,
0.02928398922085762,
0.05262722447514534,
-0.06011947989463806,
0.022104939445853233,
0.020185023546218872,
-0.03545186296105385,
0.010856352746486664,
-0.028064532205462456,
0.03017929568886757,
-0.018594052642583847,
-0.0059825279749929905,
-0.008276871405541897,
0.06860478967428207,
0.03000943921506405,
0.027703842148184776,
-0.010343826375901699,
0.001963190035894513,
-0.019247815012931824,
-0.03273329883813858,
-0.025997532531619072,
0.01911049336194992,
-0.007733245845884085,
-0.033558137714862823,
0.04091695323586464,
-0.018779341131448746,
0.01807706616818905,
0.004589271731674671,
-0.014460002072155476,
-0.010416311211884022,
-0.001353832776658237,
0.055390216410160065,
0.02304636873304844,
-0.0032445862889289856,
0.009099094197154045,
0.008028683252632618,
0.022425072267651558,
-0.01830269955098629,
0.006064091809093952,
0.031717490404844284,
-0.009651681408286095,
-0.009986616671085358,
0.001808956265449524,
-0.03120971843600273,
-0.047506578266620636,
0.024649010971188545,
-0.05091681331396103,
-0.018259938806295395,
-0.013578435406088829,
0.01145946141332388,
-0.011201871559023857,
-0.011818412691354752,
0.027890721336007118,
-0.02426285110414028,
0.015264756977558136,
0.012519831769168377,
0.015513432212173939,
-0.05066448822617531,
0.000058036319387611,
-0.010809582658112049,
-0.023909641429781914,
0.0003242313105147332,
0.0063164145685732365,
0.018688606098294258,
-0.020619843155145645,
-0.01298485603183508,
-0.027048418298363686,
0.003250749548897147,
-0.0019116380717605352,
-0.01756058633327484,
-0.025142548605799675,
0.020043637603521347,
0.03206683322787285,
0.03737466782331467,
-0.03219877928495407,
-0.009395580738782883,
0.011359077878296375,
-0.0934852808713913,
-0.003504086984321475,
-0.0005249069654382765,
-0.025463614612817764,
-0.050318341702222824,
-0.012316737323999405,
-0.010695352219045162,
0.011102313175797462,
0.044688645750284195,
-0.012827957980334759,
0.0040716808289289474,
0.0376075878739357,
0.0490417554974556,
-0.007248752284795046,
-0.02573864907026291,
-0.010946507565677166,
-0.022979477420449257,
-0.026733241975307465,
-0.0008048561285249889,
0.036619435995817184,
-0.0002521237183827907,
0.03887306898832321,
0.005690295249223709,
0.006204660516232252,
0.02703554555773735,
0.0006461690063588321,
-0.03397874906659126,
0.030024247244000435,
0.007367146201431751,
-0.019794907420873642,
0.061869487166404724,
0.005882712081074715,
-0.00037193120806477964,
0.04144381731748581,
-0.035673219710588455,
-0.02768705226480961,
-0.0036639354657381773,
-0.008431047201156616,
-0.03207918629050255,
-0.023110052570700645,
-0.03345661982893944,
0.008202620781958103,
-0.01902245543897152,
0.007270979695022106,
0.029825158417224884,
-0.04084596782922745,
-0.022250166162848473,
0.018587719649076462,
0.005080043338239193,
0.018994217738509178,
0.052086103707551956,
0.041816215962171555,
0.013592205010354519,
0.014226991683244705,
0.024989105761051178,
0.03903151676058769,
0.021206382662057877,
-0.007561675272881985,
-0.004776726942509413,
0.024880781769752502,
-0.01730075106024742,
0.00016701919957995415,
0.006281103007495403,
0.021805696189403534,
0.01451906654983759,
-0.0013645351864397526,
0.05476768687367439,
-0.024223508313298225,
-0.0064483098685741425,
-0.016561223194003105,
-0.013476219959557056,
0.08203486353158951,
-0.029138119891285896,
-0.00736509682610631,
-0.004928485490381718,
0.014955186285078526,
0.008357931859791279,
0.03009580634534359,
0.015094045549631119,
0.05019758269190788,
-0.010318206623196602,
-0.0450051873922348,
-0.011072313413023949,
-0.05715905874967575,
0.0030208260286599398,
-0.02871801145374775,
0.03990234062075615,
0.060913700610399246,
-0.00028252831543795764,
0.006067519076168537,
-0.011265231296420097,
-0.0322621650993824,
-0.04711872339248657,
-0.004828863311558962,
0.015654027462005615,
-0.0012791873887181282,
0.0005404838011600077,
-0.006319092120975256,
-0.06178317964076996,
0.0691041573882103,
-0.040121980011463165,
-0.044747862964868546,
-0.03803427144885063,
0.009955900721251965,
-0.040164653211832047,
0.038379114121198654
] |
<p>Is there a software (open source preferred) where I would input something like "Ingoing: a fermion $(p1, s1)$ and a photon $(p2, s2)$. Output: A fermion $(k1, r1)$ and a photon $(k2, r2)$" and I would could then get each diagram (that is, each term in the Dyson series) up to whichever order I choose, also showing terms that evaluate to zero (just to see that they are there)?</p>
<p>I have tried to compute the above diagram to 2nd order and I'm just baffled with how many details there are to collect, this seems like the perfect job for a computer, but I can't find anything that would do such a symbolic calculation (hopefully showing the steps along the way) and not just the final result. </p>
| 9,590 |
[
-0.007077675778418779,
0.010618224740028381,
-0.013509277254343033,
0.02390964701771736,
0.02047930285334587,
-0.0064493343234062195,
0.0021944192703813314,
-0.00407623453065753,
0.005190475843846798,
-0.04820459708571434,
0.02962789312005043,
0.01685718260705471,
0.061498355120420456,
0.038569383323192596,
0.025049008429050446,
0.002620307495817542,
-0.024140771478414536,
-0.010613174177706242,
0.024062128737568855,
-0.036448460072278976,
-0.008431881666183472,
0.015780270099639893,
0.0035225411411374807,
-0.028855206444859505,
-0.007091507315635681,
0.021252889186143875,
0.023612691089510918,
-0.015273861587047577,
-0.0042239027097821236,
0.05333782359957695,
-0.030544091016054153,
-0.029115797951817513,
0.024820970371365547,
0.07838131487369537,
0.03485124930739403,
0.016841044649481773,
-0.018730036914348602,
-0.053140174597501755,
0.0012828941689804196,
-0.01891339384019375,
-0.03211414813995361,
-0.017403943464159966,
-0.042362868785858154,
0.06381453573703766,
0.004981467500329018,
-0.006656903773546219,
-0.03252418711781502,
0.013409867882728577,
0.03035552240908146,
-0.07058890163898468,
0.09722074121236801,
0.01368415355682373,
0.04491400718688965,
0.0012047372292727232,
-0.009180206805467606,
-0.0031309761106967926,
0.0499458909034729,
0.07748917490243912,
0.018316853791475296,
-0.07198882848024368,
-0.03582562133669853,
-0.007184721063822508,
-0.027214350178837776,
-0.01885451003909111,
-0.037999290972948074,
0.01220026146620512,
-0.018207663670182228,
-0.008101457729935646,
0.03295516222715378,
0.004169233608990908,
-0.026075556874275208,
0.001394942868500948,
0.07536264508962631,
-0.012686756439507008,
-0.014152633026242256,
-0.02312524802982807,
0.004588414914906025,
-0.006951985415071249,
0.0445682629942894,
0.020570917055010796,
-0.029900500550866127,
0.029269851744174957,
-0.017376352101564407,
0.03510820493102074,
-0.004017764236778021,
-0.004143443424254656,
0.05441524088382721,
-0.06842111796140671,
-0.02461010031402111,
0.024835795164108276,
-0.03042648173868656,
0.020298371091485023,
0.030526334419846535,
-0.00872066617012024,
-0.006393627729266882,
-0.020463837310671806,
-0.0023972117342054844,
0.030123742297291756,
0.0012471484951674938,
-0.050706442445516586,
0.024224504828453064,
0.006301892921328545,
-0.006258000619709492,
0.05861267074942589,
0.021564079448580742,
0.00805498007684946,
0.01475259754806757,
0.009035900235176086,
0.0035808738321065903,
-0.0007543226820416749,
-0.02891431748867035,
0.0027189520187675953,
0.0071304431185126305,
0.026857543736696243,
-0.030298834666609764,
-0.046997833997011185,
-0.03047858364880085,
0.009822589345276356,
0.07368291169404984,
0.0784631296992302,
0.02490011230111122,
-0.043069448322057724,
0.01660272106528282,
-0.05256932973861694,
-0.055680811405181885,
0.02169102616608143,
0.04190792143344879,
-0.0322653204202652,
-0.036984484642744064,
0.02431708574295044,
0.004349428229033947,
-0.01579238474369049,
0.0262425746768713,
-0.02188592590391636,
0.005696846637874842,
-0.019690824672579765,
-0.06377452611923218,
-0.07289303094148636,
0.0036302150692790747,
-0.0038200640119612217,
0.021457165479660034,
-0.07995623350143433,
0.03286033123731613,
0.055140212178230286,
0.07260815799236298,
0.014406257309019566,
-0.001066153752617538,
-0.023077286779880524,
0.047799039632081985,
0.014420555904507637,
-0.026580732315778732,
0.006310274824500084,
-0.02513890527188778,
-0.010122548788785934,
0.0001801077596610412,
-0.04856262728571892,
0.0530061312019825,
0.05858103930950165,
-0.016988905146718025,
0.018497543409466743,
0.06801123172044754,
0.027922552078962326,
0.022913960739970207,
0.013213683851063251,
0.0021833647042512894,
-0.026691462844610214,
0.0629895031452179,
0.017864858731627464,
0.03403632715344429,
0.005689479876309633,
-0.015605345368385315,
-0.01777062378823757,
-0.0001129492447944358,
0.018219739198684692,
0.06563351303339005,
-0.03363101929426193,
-0.024685265496373177,
0.003355323802679777,
0.02968539483845234,
-0.04446849599480629,
-0.030053576454520226,
-0.05689980089664459,
-0.005427807569503784,
0.012798262760043144,
-0.013720108196139336,
-0.001964351860806346,
-0.01035354845225811,
-0.022799674421548843,
-0.0009461271692998707,
-0.05022245645523071,
-0.03454123064875603,
-0.022331668063998222,
-0.0203727874904871,
0.0013274801895022392,
-0.011326830834150314,
0.022151298820972443,
0.02078055962920189,
0.02198782190680504,
0.008942837826907635,
-0.08112978935241699,
-0.0015975008718669415,
0.015471696853637695,
0.03618289902806282,
-0.012006298638880253,
0.03284706920385361,
0.04844965785741806,
0.10155913233757019,
-0.023531626909971237,
0.023338645696640015,
-0.0413142591714859,
-0.010120626538991928,
-0.015035726130008698,
-0.02825453132390976,
-0.0019043040229007602,
0.01722024567425251,
0.043167125433683395,
-0.013949969783425331,
0.0019158022478222847,
0.014845270663499832,
-0.005691962782293558,
-0.022044895216822624,
0.08346302807331085,
0.06169278174638748,
0.027939019724726677,
-0.0025109793059527874,
-0.0011949719628319144,
0.021422093734145164,
0.033301569521427155,
0.0013367877108976245,
-0.018759146332740784,
-0.01867101527750492,
0.021439258009195328,
0.041641343384981155,
0.025399906560778618,
-0.07361169159412384,
-0.00022150867152959108,
0.03289863467216492,
0.03194507583975792,
0.029223499819636345,
0.023349305614829063,
-0.06240271404385567,
0.012610867619514465,
0.006436588708311319,
0.04385131224989891,
-0.002672939794138074,
0.018482694402337074,
0.03435584902763367,
0.006552080158144236,
-0.0016081304056569934,
0.030082710087299347,
-0.049525417387485504,
0.024113697931170464,
-0.045914605259895325,
-0.026606179773807526,
0.003358808346092701,
-0.022941960021853447,
0.06873775273561478,
-0.04106205701828003,
0.032984357327222824,
0.0005211859242990613,
-0.029750604182481766,
0.013669922016561031,
-0.018431708216667175,
-0.009187538176774979,
0.029873035848140717,
-0.027610402554273605,
-0.02559763193130493,
0.014634380117058754,
0.034155093133449554,
-0.053359247744083405,
0.07369515299797058,
-0.04524211212992668,
-0.006719626020640135,
-0.05015726760029793,
0.0034411419183015823,
0.0042591700330376625,
0.02093825861811638,
-0.01569824106991291,
-0.026080895215272903,
0.009803833439946175,
0.022628910839557648,
-0.010841370560228825,
0.0337458960711956,
0.027085842564702034,
-0.07554583251476288,
0.02132795937359333,
-0.014206203632056713,
-0.042656365782022476,
0.05613504350185394,
-0.008668175898492336,
-0.014261660166084766,
0.03560149297118187,
-0.010074046440422535,
-0.0664752945303917,
-0.03839338198304176,
0.006648417562246323,
0.006163550075143576,
-0.04697926715016365,
0.01580146886408329,
-0.008845753036439419,
0.01167208980768919,
-0.02761242724955082,
0.006063398439437151,
-0.027079874649643898,
-0.010251607745885849,
-0.021856609731912613,
-0.008303230628371239,
0.0021896136458963156,
-0.045503225177526474,
0.012516540475189686,
0.020439451560378075,
-0.01296833623200655,
-0.02311292290687561,
-0.0479014627635479,
-0.04068274050951004,
-0.00046158715849742293,
0.02642921917140484,
0.016846243292093277,
0.016181129962205887,
-0.03759206458926201,
0.07182013988494873,
0.03370510786771774,
-0.03788701444864273,
-0.04504192993044853,
0.010692182928323746,
0.007711993530392647,
-0.01669194921851158,
0.007084409240633249,
-0.027758007869124413,
-0.0006749920430593193,
0.011229924857616425,
-0.004810295067727566,
0.02067742496728897,
0.031002290546894073,
-0.013007238507270813,
-0.012119271792471409,
0.07798822969198227,
-0.03301156312227249,
-0.00551438657566905,
0.024646814912557602,
0.007743880618363619,
-0.020260179415345192,
0.03148190304636955,
-0.004444240126758814,
0.02572987973690033,
0.019477438181638718,
-0.033764488995075226,
0.031740088015794754,
0.015814753249287605,
-0.012676715850830078,
-0.01898997277021408,
0.009840503334999084,
0.030474629253149033,
-0.040674224495887756,
-0.020909463986754417,
0.05945059657096863,
0.04802025109529495,
-0.027720242738723755,
0.016365714371204376,
0.04477439820766449,
0.02608352154493332,
-0.046297743916511536,
-0.00993443001061678,
0.03256449103355408,
-0.02400357834994793,
0.026219865307211876,
-0.02034185081720352,
-0.013991905376315117,
0.041404616087675095,
0.030944645404815674,
0.04282961040735245,
-0.006171273533254862,
-0.013470066711306572,
0.0021936341654509306,
-0.023845434188842773,
-0.0036197896115481853,
-0.036509208381175995,
0.08164626359939575,
-0.021239815279841423,
0.047679536044597626,
-0.004696777556091547,
0.008269173093140125,
-0.016064951196312904,
-0.029114099219441414,
-0.07749080657958984,
0.0298234224319458,
0.005006525199860334,
-0.013634126633405685,
0.01419284287840128,
0.028425022959709167,
-0.007681283168494701,
-0.04144039750099182,
-0.037468768656253815,
-0.00569451367482543,
-0.003264311933889985,
-0.007381313946098089,
0.005997469183057547,
-0.04282335937023163,
-0.043510522693395615,
0.02560693956911564,
0.028280381113290787,
0.01770881377160549,
-0.05205536633729935,
0.01843927800655365,
0.028699861839413643,
-0.02929236926138401,
0.0033478119876235723,
-0.035344138741493225,
0.006778261158615351,
0.006072792690247297,
0.011729571968317032,
0.060672786086797714,
0.04325779154896736,
-0.03071296587586403,
-0.0385652594268322,
-0.01171785220503807,
0.06641936302185059,
0.024816738441586494,
-0.022445794194936752,
0.014039224945008755,
-0.014850236475467682,
-0.015390560030937195,
-0.009250455535948277,
0.07100819796323776,
-0.03532266989350319,
0.06862903386354446,
0.044106267392635345,
0.007853175513446331,
-0.027365675196051598,
0.05012543126940727,
0.07997910678386688,
-0.06280550360679626,
-0.06364557892084122,
-0.008421090431511402,
-0.011737790890038013,
0.007969032973051071,
0.00602831831201911,
-0.02179950475692749,
0.031241169199347496,
-0.03509398177266121,
-0.02224118448793888,
-0.007308943197131157,
0.0053673963993787766,
-0.018069058656692505,
0.01978181302547455,
0.005053957924246788,
0.02750459499657154,
0.01119112130254507,
0.029850639402866364,
0.011324611492455006,
0.03560084477066994,
0.021929631009697914,
0.005965566728264093,
0.010788719169795513,
-0.05847286432981491,
0.008567007258534431,
0.036268699914216995,
0.07037409394979477,
0.005526485852897167,
0.006986998487263918,
-0.061668723821640015,
-0.020415769889950752,
0.05490247905254364,
-0.03364856541156769,
0.02637326903641224,
-0.007735196501016617,
-0.017731014639139175,
-0.018282443284988403,
0.024236181750893593,
-0.018779393285512924,
0.040152039378881454,
-0.02491491101682186,
0.028251979500055313,
-0.0373043529689312,
0.003909477032721043,
-0.04881730675697327,
0.028805706650018692,
0.0009102612966671586,
0.05156075581908226,
-0.017254384234547615,
-0.01819681189954281,
0.019913747906684875,
0.012995049357414246,
-0.04684192314743996,
-0.04890940710902214,
0.019798962399363518,
0.01447830256074667,
-0.02728184312582016,
0.06857254356145859,
-0.011034486815333366,
-0.05209789797663689,
0.018242739140987396,
0.025191286578774452,
0.03351600095629692,
-0.0396328866481781,
-0.0019947770051658154,
0.058665160089731216,
0.05668481066823006,
0.018588485196232796,
0.03469196707010269,
0.05192283168435097,
-0.02207951992750168,
0.023133613169193268,
-0.021257491782307625,
0.017272112891077995,
0.013088461942970753,
-0.003712693229317665,
-0.03009008802473545,
-0.012020657770335674,
-0.056155215948820114,
0.02178700640797615,
-0.021282149478793144,
0.02995656058192253,
-0.013175508007407188,
-0.015558428131043911,
-0.009700257331132889,
0.010819211602210999,
-0.011194546706974506,
-0.00012183481157990173,
-0.021139319986104965,
0.015691671520471573,
0.012447495013475418,
-0.033390112221241,
0.026538988575339317,
-0.0007483189110644162,
-0.007222295273095369,
0.005356479901820421,
-0.020312517881393433,
0.028247972950339317,
-0.025237515568733215,
-0.03385728970170021,
0.02373952977359295,
-0.007262751460075378,
0.04875270277261734,
-0.012546277604997158,
0.06819672137498856,
0.00040272349724546075,
-0.04914405941963196,
-0.05524885654449463,
0.01815735548734665,
0.007710755802690983,
-0.002328211208805442,
-0.026318717747926712,
0.0044021159410476685,
-0.016739197075366974,
-0.0028074909932911396,
-0.03881055489182472,
-0.05418086424469948,
0.03636808320879936,
-0.010671031661331654,
-0.048046745359897614,
-0.05998432636260986,
0.013721099123358727,
0.010476549156010151,
0.0010335149709135294,
0.02904188446700573,
0.028035124763846397,
-0.029143093153834343,
-0.013248921371996403,
0.0029901699163019657,
0.0043960376642644405,
0.02643035165965557,
0.018824798986315727,
0.014255952090024948,
0.007340721786022186,
-0.01066887192428112,
-0.020844973623752594,
0.03712635859847069,
0.02652372606098652,
-0.01632382906973362,
-0.049971189349889755,
-0.003707761876285076,
0.05378725379705429,
0.04073440283536911,
-0.05936933308839798,
0.009760222397744656,
0.047020409256219864,
0.030670395120978355,
0.009791545569896698,
-0.0335870198905468,
-0.006986744236201048,
-0.02180379629135132,
0.011488133110105991,
-0.013483506627380848,
-0.026829836890101433,
0.010661205276846886,
-0.025662215426564217,
-0.014518608339130878,
0.009492194280028343,
0.0012055817060172558,
0.030354777351021767,
0.03465887904167175,
0.036757130175828934,
-0.04095903038978577,
0.024606594815850258,
-0.04719236493110657,
-0.019740698859095573,
-0.01892787031829357,
0.029555603861808777,
0.005995842628180981,
0.016868723556399345,
-0.01667473465204239,
-0.029952844604849815,
-0.04398094117641449,
-0.0016124156536534429,
0.06719592213630676,
-0.00528043694794178,
0.04630934074521065,
0.03207291290163994,
0.03188047185540199,
-0.01688372902572155,
0.007025731261819601,
-0.02577536553144455,
0.010718476958572865,
0.023401271551847458,
0.049817223101854324,
-0.027259530499577522,
-0.015656016767024994,
0.009761154651641846,
0.0665125772356987,
-0.04223976656794548,
0.04311080649495125,
-0.008636084385216236,
0.005706089083105326,
0.04331652820110321,
-0.01629544422030449,
-0.029529746621847153,
-0.0050726840272545815,
-0.05504052713513374,
0.024101747199892998,
-0.004306950606405735,
-0.022900691255927086,
0.046739041805267334,
0.0012739157536998391,
0.004072503186762333,
-0.028159957379102707,
-0.0283222496509552,
-0.06498277932405472,
0.04983379691839218,
0.059536900371313095,
-0.024513879790902138,
0.01794537529349327,
0.0344899520277977,
0.017150485888123512,
0.01993650756776333,
0.015138507820665836,
-0.014883026480674744,
-0.03330887109041214,
-0.053618136793375015,
-0.04340648651123047,
-0.07582788914442062,
0.058491047471761703,
0.021689483895897865,
-0.0027682881336659193,
0.0012231905711814761,
0.0006950312526896596,
0.0393814854323864,
0.021398743614554405,
0.016468385234475136,
0.000301671854685992,
0.0593106709420681,
-0.04546006768941879,
0.012178516015410423,
-0.006747201085090637,
0.0027849283069372177,
0.12881162762641907,
0.040785063058137894,
0.01671762578189373,
-0.0718601867556572,
-0.01703089289367199,
0.0023883513640612364,
0.027870943769812584,
-0.004205519333481789,
0.0686727911233902,
-0.0025747381150722504,
-0.005358376074582338,
-0.003910835366696119,
0.05004730448126793,
-0.0165543332695961,
0.04673139005899429,
0.048147108405828476,
-0.01891351491212845,
-0.04306771606206894,
0.031127648428082466,
0.028283461928367615,
-0.007222928572446108,
0.0053153191693127155,
-0.06307923048734665,
-0.009945552796125412,
-0.015125776641070843,
0.01862936280667782,
-0.04015117138624191,
-0.03260800242424011,
0.06509236991405487,
0.01569829136133194,
-0.06617730855941772,
0.033844172954559326,
0.017688393592834473,
0.013214418664574623,
0.0156403798609972,
0.02369202859699726,
0.0452800989151001,
0.000985558028332889,
0.007396823260933161,
0.04059039428830147,
0.01403022464364767,
0.019670041278004646,
-0.02032475732266903,
-0.013617485761642456,
-0.02547774650156498,
-0.00898345373570919,
0.0012457971461117268,
0.03586818277835846,
0.008382671512663364,
-0.02172449789941311,
0.001036880654282868,
0.02029198221862316,
0.02002708427608013,
-0.02942928671836853,
-0.02836371585726738,
0.03199608996510506,
0.020066749304533005,
-0.02455965243279934,
0.007572665344923735,
0.01865611970424652,
0.02091134525835514,
0.00722302682697773,
0.012166830711066723,
-0.02060392126441002,
-0.04332967847585678,
0.0017771573038771749,
-0.0015499851433560252,
0.0358593612909317,
-0.018610524013638496,
-0.04577919840812683,
0.007671015337109566,
-0.03270330652594566,
0.009378883987665176,
-0.03537981957197189,
0.030968045815825462,
0.04823676869273186,
0.0024990246165543795,
-0.0032390279229730368,
-0.013641145080327988,
0.024268146604299545,
-0.020620670169591904,
-0.004786992445588112,
-0.040640272200107574,
-0.020244602113962173,
0.012942721135914326,
-0.04711935669183731,
0.05361950770020485,
0.03879254311323166,
-0.004667460918426514,
0.009451109915971756,
0.04247339069843292,
0.015120779164135456,
0.02283809892833233,
-0.027695132419466972,
-0.014054106548428535,
0.009139948524534702,
-0.03997819870710373,
0.005972915794700384,
-0.05316738784313202,
0.030607551336288452,
0.02381509728729725,
-0.0026947457809001207,
-0.0056434134021401405,
0.03740913048386574,
-0.0265481099486351,
0.006425654049962759,
-0.0019443983910605311,
-0.01832563430070877,
0.008653946220874786,
-0.02804625779390335,
-0.03438432142138481,
-0.026003926992416382,
0.006205902434885502,
-0.012497984804213047,
0.015026941895484924,
-0.017904462292790413,
-0.005086632911115885,
-0.06056645140051842,
0.028040824458003044,
-0.01175710465759039,
0.0028823688626289368,
0.002411271445453167,
0.04127982631325722,
-0.02009558491408825,
0.03293083235621452,
-0.030094876885414124,
0.003567093750461936,
0.008333499543368816,
0.03787046670913696,
0.0046463580802083015,
-0.0071479203179478645,
0.017473166808485985,
0.032883528620004654,
0.006436812691390514,
-0.035871077328920364,
0.018240507692098618,
-0.028896303847432137,
-0.00013811200915370136,
-0.02657029777765274,
-0.0162242092192173,
0.007228620816022158,
-0.05696002393960953,
-0.03785887733101845,
0.022743437439203262,
-0.0019538963679224253,
0.022954892367124557,
0.01090543158352375,
-0.029834674671292305,
-0.00810515321791172,
0.04002627730369568,
-0.02938038669526577,
-0.029567506164312363,
0.001428911811672151,
0.009694729931652546,
0.011195211671292782,
-0.013098162598907948,
0.00862237997353077,
-0.027852874249219894,
-0.03295997902750969,
0.0072938851080834866,
0.011381776072084904,
-0.02822190523147583,
-0.01989045739173889,
-0.026412369683384895,
-0.015560145489871502,
0.04276790842413902,
0.0451476126909256,
0.020876562222838402,
0.005747021175920963,
0.020254366099834442,
0.0012043191818520427,
0.037481363862752914,
0.029175305739045143,
0.02005445957183838,
-0.09482602775096893,
-0.022526610642671585,
-0.03187275677919388,
0.0046213227324187756,
0.016395561397075653,
-0.07787247747182846,
0.02424212172627449,
0.007506588473916054,
-0.04061762988567352,
0.02395283803343773,
-0.02442164719104767,
-0.009782375767827034,
-0.008462446741759777,
0.008015554398298264,
-0.0062387180514633656,
0.030271118506789207,
0.026695221662521362,
0.03634351119399071,
0.0031090721022337675,
-0.02535356394946575,
-0.011509537696838379,
0.01761164702475071,
-0.0030204830691218376,
0.011359352618455887,
-0.02004770003259182,
-0.02941538393497467,
0.03495344519615173,
-0.015416856855154037,
-0.004171700682491064,
-0.03189636394381523,
0.00196397234685719,
0.010200307704508305,
-0.017000015825033188,
0.049879737198352814,
0.002800069283694029,
0.05291544646024704,
0.01064293459057808,
-0.0012396746315062046,
-0.03158845007419586,
-0.020119525492191315,
0.024473370984196663,
0.019826307892799377,
-0.03479586914181709,
0.022049741819500923,
0.02341158501803875,
-0.005350150633603334,
-0.030666779726743698,
0.07256697863340378,
-0.021387340500950813,
-0.011786563321948051,
-0.02833399549126625,
-0.020624985918402672,
0.017902974039316177,
-0.04663964360952377,
-0.0058601931668818,
-0.09248565137386322,
-0.006504999008029699,
-0.011988616548478603,
0.01648668944835663,
0.026362692937254906,
0.00031718306127004325,
-0.03156052902340889,
-0.057109348475933075,
0.03114112839102745,
0.016369299963116646,
0.0018870291532948613,
-0.03119579888880253,
-0.016910279169678688,
0.01388857327401638,
-0.010469553992152214,
0.01959523931145668,
-0.022248903289437294,
-0.030695848166942596,
0.0262868944555521,
-0.009480251930654049,
0.020253494381904602,
0.02628590539097786,
-0.049246519804000854,
0.00016088147822301835,
-0.041143544018268585,
0.019048236310482025,
0.0008745710947550833,
-0.018916824832558632,
-0.026624415069818497,
0.032178476452827454,
0.0032526159193366766,
-0.011719990521669388,
0.015138564631342888,
-0.01840137131512165,
-0.0477483794093132,
-0.009292391128838062,
-0.00601081782951951,
0.03867334872484207,
-0.05029989778995514,
-0.00019650129252113402,
-0.039473291486501694,
0.0052029830403625965,
-0.03405081108212471,
-0.012929817661643028,
-0.003405072493478656,
0.035265859216451645,
0.024135375395417213,
-0.009961574338376522,
-0.023658746853470802,
-0.028454480692744255,
-0.03703118860721588,
0.019985558465123177,
-0.01648099720478058,
-0.005912414286285639,
0.06375252455472946,
0.0016641183756291866,
0.00838333647698164,
0.044602349400520325,
-0.006722068414092064,
-0.004975988995283842,
0.03452921658754349,
-0.01876801997423172,
-0.01578311063349247,
-0.02319035865366459,
-0.02881353162229061,
0.020318031311035156,
-0.03827659413218498,
0.018607361242175102,
-0.010528342798352242,
-0.0020544975996017456,
-0.02288167178630829,
0.04045486077666283,
-0.012120714411139488,
0.045222312211990356,
0.03413218632340431,
0.018056007102131844,
0.028524499386548996,
-0.017302438616752625,
0.037243615835905075,
0.04090661555528641,
0.020760247483849525,
0.05495545268058777,
0.01572355441749096,
-0.006558577995747328,
-0.01850743778049946,
0.006213773973286152,
-0.018531544134020805,
-0.0014233412221074104,
-0.024856137111783028,
-0.00376784591935575,
0.060099225491285324,
-0.018602555617690086,
0.030577316880226135,
-0.027704475447535515,
-0.027674183249473572,
0.0775269865989685,
-0.023815518245100975,
0.025313206017017365,
-0.03052373416721821,
-0.0033856560476124287,
-0.007093828171491623,
0.013578487560153008,
0.0049870735965669155,
0.033123210072517395,
-0.04691300541162491,
-0.008157668635249138,
-0.06939712166786194,
-0.00021767821453977376,
0.03123275376856327,
-0.06403540819883347,
-0.000897497811820358,
0.005704308860003948,
-0.011716839857399464,
0.004072658251971006,
-0.03339044377207756,
-0.015947962179780006,
-0.04286833107471466,
0.02627650462090969,
0.012183357030153275,
-0.019701402634382248,
-0.025542110204696655,
-0.015072602778673172,
-0.022606177255511284,
0.03506245091557503,
-0.014407881535589695,
-0.00003916506466339342,
-0.014430646784603596,
0.020550115033984184,
-0.0205229502171278,
-0.010544314980506897
] |
<p>I can not do the following problem:</p>
<p>Prove the identity:</p>
<p>$$\left( \frac{\partial x}{\partial y} \right)_{z}\left( \frac{\partial y}{\partial z} \right)_{x}\left( \frac{\partial z}{\partial x} \right)_{y}=-1$$</p>
<p>State the properties that must be $x=x(y,z)$, $y=y(x,z)$, $z=(x,y)$.</p>
<p>The truth is I do not know how to start, and they do not know how to interpret the functions $x$, $y$, $z$. Any help or explanation will be the most grateful.</p>
| 9,591 |
[
-0.005401355214416981,
0.0013373683905228972,
-0.004936902783811092,
0.015762466937303543,
0.03088323399424553,
0.011639067903161049,
-0.04769615828990936,
0.0019465479999780655,
0.007489711046218872,
0.0005216533900238574,
0.03525219485163689,
0.015196479856967926,
0.08231804519891739,
-0.00021130470850039274,
0.04601626843214035,
-0.004495897330343723,
-0.026560118421912193,
-0.014325138181447983,
-0.027959534898400307,
-0.021036386489868164,
0.013548260554671288,
0.0038864375092089176,
0.028123563155531883,
0.03622230142354965,
0.0032778694294393063,
0.012941135093569756,
-0.0060913837514817715,
-0.02493457682430744,
0.028218476101756096,
0.0667228102684021,
0.00021882771397940814,
-0.03627742454409599,
-0.005950042977929115,
0.03726193308830261,
0.0008031039615161717,
0.007655841298401356,
-0.04069981724023819,
-0.016482342034578323,
0.0038337737787514925,
0.006423197686672211,
0.002322534564882517,
-0.009988069534301758,
-0.012475837953388691,
0.060446321964263916,
-0.04241139814257622,
0.002871356438845396,
0.032895777374506,
-0.00936273206025362,
0.019115177914500237,
-0.04652978479862213,
0.06582622975111008,
0.007780473679304123,
0.05276230722665787,
0.04577388986945152,
-0.022188590839505196,
-0.016966719180345535,
0.0444662943482399,
0.0761396661400795,
0.027000756934285164,
-0.04326552525162697,
-0.01747843436896801,
-0.04258202761411667,
-0.006042876746505499,
-0.026848817244172096,
-0.04744183272123337,
0.028100665658712387,
-0.005109792109578848,
0.010288945399224758,
0.010084010660648346,
-0.003033070359379053,
0.023195000365376472,
0.02265617623925209,
0.04030925780534744,
-0.008324605412781239,
0.011924533173441887,
-0.02165360189974308,
0.026306768879294395,
-0.001951901358552277,
0.03173407167196274,
0.00008536589302821085,
-0.014129017479717731,
0.025675803422927856,
0.04476634040474892,
0.00009774292266229168,
-0.03309226781129837,
-0.011257875710725784,
0.10214128345251083,
0.029985686764121056,
0.03415009006857872,
-0.001857898780144751,
-0.0002294509467901662,
-0.007441919296979904,
0.029623422771692276,
0.0026000291109085083,
-0.028746603056788445,
0.043926090002059937,
-0.004536107648164034,
0.024465013295412064,
0.0029266495257616043,
-0.04184791073203087,
0.006996093783527613,
-0.03532880172133446,
0.0013798061991110444,
0.041810981929302216,
-0.026351120322942734,
-0.00023650217917747796,
-0.047424133867025375,
0.03620871528983116,
-0.015793828293681145,
-0.04435209557414055,
-0.011176402680575848,
0.044321607798337936,
-0.010068776085972786,
-0.01684654876589775,
0.008483989164233208,
-0.02630043961107731,
0.010870280675590038,
-0.023458436131477356,
0.024808751419186592,
0.024775300174951553,
0.06542139500379562,
-0.034256964921951294,
0.01964908093214035,
-0.022544194012880325,
-0.07948262244462967,
-0.023654315620660782,
0.027506396174430847,
0.006773864850401878,
0.004078082274645567,
0.05534863844513893,
0.0357147715985775,
-0.035433437675237656,
-0.006516534369438887,
0.01919715479016304,
0.04318695887923241,
0.004042913671582937,
-0.05990559607744217,
-0.060503315180540085,
0.012888265773653984,
-0.006267443299293518,
-0.005821764934808016,
-0.07702834904193878,
0.01567808911204338,
0.03314948454499245,
0.052354417741298676,
-0.026604941114783287,
0.0030598831363022327,
0.005376958288252354,
0.03073667362332344,
-0.0010451071429997683,
-0.00930375698953867,
-0.05969071388244629,
0.0009443946182727814,
-0.04306109994649887,
0.009549485519528389,
-0.028490524739027023,
0.028636112809181213,
0.013745574280619621,
-0.03777854144573212,
-0.044987838715314865,
0.05647848919034004,
0.005086115561425686,
0.013202793896198273,
0.018255652859807014,
0.012074513360857964,
-0.02367471717298031,
0.06346672773361206,
0.019827380776405334,
0.0035252058878540993,
0.06545928120613098,
-0.009415984153747559,
0.031034335494041443,
-0.00999354012310505,
0.033830322325229645,
0.025370514020323753,
-0.06111174076795578,
-0.042362917214632034,
-0.012979489751160145,
0.015050566755235195,
0.02131073735654354,
-0.024610938504338264,
-0.04366364702582359,
-0.025696806609630585,
0.04469498246908188,
-0.0028421287424862385,
0.021585840731859207,
0.012282111681997776,
-0.039147816598415375,
-0.0011389064602553844,
-0.009513303637504578,
-0.023773804306983948,
-0.06083454564213753,
-0.018425900489091873,
-0.012949355877935886,
-0.025858977809548378,
0.014141354709863663,
-0.007821114733815193,
0.016825467348098755,
-0.035558801144361496,
-0.02559441700577736,
0.02115003764629364,
-0.0033794487826526165,
0.03894039988517761,
-0.018046105280518532,
0.028215862810611725,
0.04015200212597847,
0.09014631062746048,
-0.00697837071493268,
0.03473914414644241,
-0.022928975522518158,
0.043164465576410294,
0.024055149406194687,
0.004655967932194471,
-0.010241148993372917,
-0.020398054271936417,
-0.01776382513344288,
-0.0026369690895080566,
0.008221236988902092,
0.008299008011817932,
0.026423346251249313,
-0.06884685903787613,
0.043986912816762924,
0.06831296533346176,
-0.006644101347774267,
-0.033010710030794144,
0.020864928141236305,
0.030224662274122238,
0.06885525584220886,
0.00457812799140811,
0.00493799289688468,
-0.04755997657775879,
-0.01770840212702751,
0.06445974111557007,
0.002418909454718232,
-0.040208905935287476,
0.010798458009958267,
0.043885789811611176,
0.046391624957323074,
0.020442428067326546,
0.011494442820549011,
0.0064968084916472435,
-0.03817930445075035,
0.0045786271803081036,
0.01840478740632534,
0.03437880799174309,
0.03924229368567467,
-0.009339825250208378,
-0.02377133071422577,
0.014529979787766933,
0.021510256454348564,
-0.012402238324284554,
0.06603115797042847,
-0.01577429473400116,
0.013262183405458927,
0.022194085642695427,
0.004152966197580099,
0.028370613232254982,
-0.01545608788728714,
-0.02375931292772293,
0.023762352764606476,
0.040340032428503036,
-0.02359396405518055,
0.004892381839454174,
0.020550237968564034,
-0.009307140484452248,
0.006967483088374138,
-0.0580168254673481,
-0.00952716451138258,
0.02514362335205078,
-0.025407107546925545,
-0.011147618293762207,
0.01404397003352642,
-0.04736236855387688,
-0.024237772449851036,
-0.04914800077676773,
0.019559940323233604,
0.030478529632091522,
0.022392839193344116,
-0.015603439882397652,
-0.028740273788571358,
0.021799471229314804,
-0.012542818672955036,
0.03140376880764961,
0.01975228078663349,
-0.05577400326728821,
0.0028984572272747755,
-0.04540519043803215,
0.0005702123162336648,
0.06166982278227806,
-0.0036887393798679113,
-0.004389197565615177,
-0.022485144436359406,
-0.011628171429038048,
-0.05214972421526909,
-0.02712980844080448,
-0.08589573204517365,
0.06076684594154358,
-0.04835520312190056,
0.0386163592338562,
0.04489235207438469,
0.00617958651855588,
-0.02731863036751747,
0.015863360837101936,
0.012495351023972034,
-0.030196303501725197,
-0.02879536896944046,
-0.010706133209168911,
0.021795978769659996,
-0.01390494778752327,
0.003129167715087533,
0.006027101073414087,
-0.01259528286755085,
-0.004709770902991295,
-0.0530175045132637,
-0.059257008135318756,
0.019672289490699768,
0.031267035752534866,
0.022183610126376152,
0.008952703326940536,
-0.0472397655248642,
0.04576035588979721,
0.0011665556812658906,
-0.04686741903424263,
-0.019713474437594414,
0.0097131272777915,
-0.006058117374777794,
-0.05204004794359207,
0.008067832328379154,
0.02514026314020157,
-0.022333918139338493,
0.06603046506643295,
0.0436151959002018,
-0.001758391153998673,
0.04051844775676727,
-0.01798124425113201,
0.0012168367393314838,
0.0018307475838810205,
0.004432118032127619,
0.0023001728113740683,
0.04145149141550064,
0.010547405108809471,
0.0068011535331606865,
-0.005210389848798513,
0.023138616234064102,
0.02821553871035576,
0.03140277415513992,
-0.025131937116384506,
0.039043329656124115,
-0.007853609509766102,
0.003352720756083727,
-0.033260609954595566,
0.04872007295489311,
-0.002104144310578704,
-0.01967468112707138,
0.01717897318303585,
-0.005068894941359758,
0.03595234081149101,
-0.0587184764444828,
0.03052544966340065,
0.033511895686388016,
-0.007206295151263475,
-0.061342447996139526,
-0.02487155981361866,
-0.023183392360806465,
-0.03145342320203781,
0.04220538213849068,
-0.0008872231119312346,
-0.003081176895648241,
0.03473455458879471,
0.02596907690167427,
-0.008720573969185352,
-0.0057651386596262455,
-0.061526644974946976,
0.028910838067531586,
-0.060374051332473755,
0.017943069338798523,
0.009843442589044571,
0.036933839321136475,
-0.0036980926524847746,
0.08554191887378693,
0.025753533467650414,
0.01061816792935133,
0.010161221027374268,
-0.0007315205875784159,
-0.08203550428152084,
0.019956940785050392,
-0.010824302211403847,
-0.0009472890524193645,
-0.013944894075393677,
-0.00156215054448694,
0.013479696586728096,
-0.031308043748140335,
-0.015485795214772224,
-0.0035740493331104517,
-0.04070170596241951,
-0.04965657740831375,
0.00783429853618145,
-0.04074255749583244,
-0.03938443213701248,
-0.0023327257949858904,
0.0412619449198246,
0.01679285615682602,
-0.04148724302649498,
-0.02675609476864338,
0.06269486248493195,
-0.010714491829276085,
-0.024610526859760284,
-0.0696965679526329,
-0.02296394295990467,
0.06473198533058167,
0.027156341820955276,
-0.003118797205388546,
0.041809264570474625,
0.0105534503236413,
0.01666932739317417,
-0.012991873547434807,
0.07279428094625473,
0.006152930203825235,
0.01761087216436863,
-0.03616424277424812,
-0.044576093554496765,
-0.03486499935388565,
0.0035729471128433943,
0.09725698083639145,
-0.009630510583519936,
0.024526551365852356,
0.027266066521406174,
0.020314276218414307,
-0.006118344608694315,
0.03895723819732666,
0.04705304652452469,
0.0029356249142438173,
-0.03338959068059921,
-0.0055960980243980885,
-0.008024096488952637,
-0.056867536157369614,
-0.056568123400211334,
0.0241065863519907,
0.008854194544255733,
-0.02908466011285782,
-0.025761468335986137,
0.009344146586954594,
0.013558194041252136,
0.03491782769560814,
0.010804569348692894,
-0.004876165650784969,
0.018484415486454964,
0.020285844802856445,
-0.04346756264567375,
0.023562051355838776,
0.057140808552503586,
0.037552446126937866,
-0.00011149192869197577,
-0.04712735116481781,
-0.024921784177422523,
0.02086736634373665,
0.031705085188150406,
0.03245396539568901,
-0.0236809179186821,
-0.0035083203110843897,
-0.04207077622413635,
-0.05822351947426796,
0.07366049289703369,
-0.027824878692626953,
0.009080550633370876,
-0.014536662958562374,
-0.00573065085336566,
-0.0037859908770769835,
-0.010627105832099915,
-0.07042575627565384,
0.006040753331035376,
-0.004816181492060423,
0.02659502811729908,
-0.025200510397553444,
-0.008620609529316425,
-0.0383683405816555,
0.017282016575336456,
0.01567157171666622,
0.05161072313785553,
-0.0013365807244554162,
-0.01252713706344366,
-0.020889511331915855,
0.03952571004629135,
-0.010143857449293137,
-0.07513957470655441,
0.003987508825957775,
0.0091471578925848,
-0.014862069860100746,
0.03055587410926819,
-0.02725541591644287,
-0.058771658688783646,
0.03264326974749565,
0.01101497933268547,
-0.006815424654632807,
0.03843601793050766,
-0.01846354268491268,
0.009369618259370327,
0.06323327124118805,
0.007501415908336639,
0.028676923364400864,
0.002271450124680996,
-0.03183319419622421,
-0.02129513770341873,
-0.016172749921679497,
-0.03452921658754349,
-0.020878270268440247,
-0.0075990790501236916,
-0.03657842427492142,
-0.002788425423204899,
-0.01155905332416296,
0.027445033192634583,
-0.03287921100854874,
-0.018162978813052177,
-0.05624398589134216,
-0.004999379627406597,
0.006611994002014399,
0.007397936191409826,
-0.021476969122886658,
0.01427213940769434,
-0.0031583020463585854,
0.0034248006995767355,
-0.009245112538337708,
-0.022626465186476707,
0.014685628935694695,
0.0064772251062095165,
-0.0182888675481081,
-0.0038044871762394905,
0.008449697867035866,
0.04417915642261505,
-0.031638000160455704,
-0.019397081807255745,
0.0219892431050539,
-0.04575258493423462,
0.00046089093666523695,
-0.0061074174009263515,
0.036652613431215286,
0.02252933196723461,
-0.03249428793787956,
-0.03974893316626549,
0.02785087190568447,
0.03929447755217552,
0.016409223899245262,
-0.03931961581110954,
0.008153929375112057,
0.009769442491233349,
-0.0061048180796206,
-0.0463871955871582,
-0.08408257365226746,
0.017079586163163185,
0.006026632152497768,
-0.01741528883576393,
-0.022639062255620956,
0.018303772434592247,
-0.022327594459056854,
-0.023088349029421806,
0.009406805038452148,
0.023856405168771744,
-0.04366098344326019,
-0.010019704699516296,
0.014456566423177719,
-0.0018524749903008342,
0.05979491397738457,
0.019194569438695908,
0.02160322293639183,
0.025100789964199066,
-0.038418207317590714,
-0.02811676450073719,
-0.012626850046217442,
0.007412562146782875,
-0.012008954770863056,
-0.029235683381557465,
-0.022804206237196922,
-0.012292368337512016,
0.01933516003191471,
-0.026541318744421005,
-0.02548310160636902,
0.025552019476890564,
0.03863000124692917,
-0.04408862441778183,
-0.05273466929793358,
0.014245853759348392,
-0.009077895432710648,
0.01861995831131935,
-0.01714239828288555,
0.012140581384301186,
-0.06302010267972946,
-0.01807573065161705,
0.019325200468301773,
0.000938624085392803,
0.005170905496925116,
0.0005520543782040477,
0.09337247163057327,
0.014040034264326096,
0.035999976098537445,
0.014627911150455475,
-0.00047684359014965594,
0.02499622292816639,
0.03329668566584587,
-0.020465966314077377,
-0.016352873295545578,
0.013940591365098953,
-0.03744460269808769,
0.005595637019723654,
-0.01525964681059122,
0.024172646924853325,
0.0664149671792984,
0.0032821055501699448,
0.05670008063316345,
0.0397183783352375,
0.006659895647317171,
0.015739554539322853,
-0.003808884648606181,
-0.01670129783451557,
-0.010946359485387802,
-0.027020499110221863,
0.06085031479597092,
-0.02027568407356739,
-0.002185086952522397,
0.0383945070207119,
0.03169579803943634,
-0.02020341530442238,
-0.0034432723186910152,
-0.008530955761671066,
-0.002092416165396571,
0.01066054217517376,
-0.01342058926820755,
-0.039338819682598114,
0.022792065516114235,
0.014988877810537815,
0.025731857866048813,
-0.00805523432791233,
0.004769096150994301,
0.05652967095375061,
0.022915685549378395,
-0.0029817400500178337,
0.0032466689590364695,
-0.024421505630016327,
-0.00024451097124256194,
0.02692483365535736,
0.048101428896188736,
0.018576839938759804,
0.0036610024981200695,
0.03861464932560921,
0.016732903197407722,
-0.021030766889452934,
0.05001309514045715,
-0.0037571799475699663,
-0.04361780360341072,
0.011132458224892616,
-0.04027099162340164,
-0.047978222370147705,
0.05412255972623825,
0.012213463895022869,
-0.01998726651072502,
0.007781887426972389,
-0.028664324432611465,
0.0012198026524856687,
0.018393002450466156,
0.019962914288043976,
-0.021597132086753845,
0.0639837384223938,
0.0053525990806519985,
0.04435962811112404,
0.012100894935429096,
0.017579182982444763,
0.10934751480817795,
0.035764265805482864,
0.003819057485088706,
-0.05311817675828934,
0.05528315529227257,
-0.046913761645555496,
-0.039230138063430786,
-0.04797239229083061,
0.06492910534143448,
-0.004368530120700598,
0.026495719328522682,
0.05259222909808159,
0.05390940606594086,
-0.008419735357165337,
0.03160906583070755,
0.05026622116565704,
-0.035744018852710724,
-0.050063151866197586,
-0.023979851976037025,
0.03228365257382393,
-0.01647159643471241,
-0.013169737532734871,
-0.028600051999092102,
0.008191503584384918,
-0.05642510950565338,
-0.02768293209373951,
-0.03302919119596481,
-0.06081928312778473,
0.03294164687395096,
0.012231712229549885,
-0.014693156816065311,
0.053423017263412476,
0.04610663652420044,
0.0011976240202784538,
-0.04389042407274246,
0.014004437252879143,
0.03255893290042877,
-0.018892686814069748,
0.02233516052365303,
0.02161821722984314,
0.0069673312827944756,
0.005708581302314997,
-0.026100333780050278,
0.01284433901309967,
-0.04713394492864609,
0.0007842850172892213,
-0.02003742754459381,
0.06458286941051483,
0.021128926426172256,
0.0017072338378056884,
-0.010736888274550438,
0.00023584156588185579,
0.022035451605916023,
-0.07663830369710922,
-0.007058207411319017,
0.012176568619906902,
0.0017446515848860145,
-0.05091555044054985,
0.027899155393242836,
-0.016695238649845123,
0.021862326189875603,
-0.01077660545706749,
0.0301713477820158,
-0.031096259132027626,
-0.035082653164863586,
0.027500921860337257,
-0.01880260743200779,
0.03069285675883293,
-0.018162116408348083,
-0.01660725846886635,
-0.019419388845562935,
-0.032318707555532455,
-0.003826250322163105,
-0.005228500347584486,
0.013424742966890335,
-0.001575935399159789,
0.030004899948835373,
-0.002958564553409815,
0.02549319714307785,
0.014427563175559044,
-0.06251730769872665,
0.0011273135896772146,
-0.007074633147567511,
-0.005188838113099337,
-0.02710469253361225,
-0.010807894170284271,
0.013368490152060986,
0.0512978658080101,
-0.002398584270849824,
-0.034636590629816055,
-0.014115349389612675,
0.018115637823939323,
-0.0008765661041252315,
-0.005442251916974783,
-0.018474308773875237,
-0.005363640375435352,
-0.01547220814973116,
-0.02068595588207245,
-0.00024535716511309147,
0.025565069168806076,
0.029813388362526894,
0.05766087770462036,
-0.025469204410910606,
0.034494541585445404,
-0.04798143729567528,
0.021162446588277817,
0.020011644810438156,
-0.022610964253544807,
0.02100321277976036,
0.029776833951473236,
0.03789202868938446,
-0.034589607268571854,
-0.011425373144447803,
0.004916721489280462,
0.011375360190868378,
0.0022847852669656277,
0.011387663893401623,
-0.041029609739780426,
-0.036203596740961075,
-0.010466057807207108,
0.0245448499917984,
-0.030526617541909218,
-0.008830024860799313,
-0.057611219584941864,
-0.006022061686962843,
0.010135795921087265,
-0.008066734299063683,
-0.02511843666434288,
0.016586754471063614,
0.015946179628372192,
-0.002672674832865596,
0.04520406574010849,
-0.006926992442458868,
-0.0037833007518202066,
-0.0038166786544024944,
0.02951856702566147,
0.018808847293257713,
0.04422871395945549,
-0.03439639136195183,
-0.029813367873430252,
0.023944662883877754,
-0.016114044934511185,
0.0012566790683194995,
-0.007877138443291187,
0.010404077358543873,
0.040345411747694016,
0.00014600747090298682,
-0.0424257256090641,
-0.039527423679828644,
0.06295610964298248,
0.00224484596401453,
0.030352354049682617,
-0.0363873690366745,
-0.03677332401275635,
-0.01976674422621727,
0.004616746678948402,
0.024255452677607536,
-0.009811297059059143,
-0.010764711536467075,
0.015794962644577026,
0.017995666712522507,
-0.014987495727837086,
-0.02653278037905693,
0.03846973925828934,
0.052475303411483765,
-0.0048794131726026535,
0.03506704792380333,
0.010208542458713055,
0.04191398620605469,
0.03751353174448013,
-0.015441928058862686,
0.01603550836443901,
-0.038076043128967285,
0.003707670606672764,
-0.08071991056203842,
-0.022410230711102486,
-0.0011637024581432343,
-0.018257537856698036,
0.036183301359415054,
-0.07516339421272278,
0.003105401759967208,
-0.011015216819941998,
-0.04896440729498863,
0.021570080891251564,
-0.01698865368962288,
-0.03280944377183914,
-0.015846246853470802,
-0.007514096796512604,
0.030467703938484192,
0.0639919862151146,
0.015349490568041801,
0.07108717411756516,
0.0251875352114439,
0.04648608714342117,
-0.013939758762717247,
0.021437400951981544,
-0.027072584256529808,
0.0177598986774683,
0.003487991401925683,
-0.029702086001634598,
0.0343286506831646,
0.0032971040345728397,
-0.01503951009362936,
0.0023617392871528864,
-0.01216333918273449,
-0.025197045877575874,
0.023904696106910706,
0.012552422471344471,
0.017573464661836624,
0.023320777341723442,
0.008273850195109844,
0.005372622516006231,
-0.039839036762714386,
-0.006781849078834057,
0.04947665333747864,
0.021082274615764618,
0.0042892699129879475,
-0.036021988838911057,
0.013413580134510994,
-0.024795889854431152,
-0.05948744714260101,
0.03939473628997803,
-0.0371834933757782,
-0.007191055919975042,
-0.010636653751134872,
-0.028740912675857544,
0.006316468585282564,
-0.042128775268793106,
0.031969498842954636,
-0.03656233474612236,
-0.025737425312399864,
0.054803550243377686,
-0.013450836762785912,
-0.012995625846087933,
-0.004334696102887392,
-0.009633765555918217,
-0.05290842056274414,
0.04079791158437729,
-0.01686437614262104,
0.030691443011164665,
-0.029546642675995827,
0.021580541506409645,
0.02502877078950405,
-0.008322701789438725,
0.027429983019828796,
-0.06889202445745468,
-0.008629736490547657,
0.03773847967386246,
0.019096417352557182,
-0.023788681253790855,
-0.03551542013883591,
-0.020772714167833328,
0.0069528925232589245,
-0.04964948073029518,
0.0001805299543775618,
0.03876015916466713,
-0.058426596224308014,
-0.021855859085917473,
0.0029774813447147608,
-0.009403131902217865,
-0.030848301947116852,
0.04767458140850067,
-0.025435658171772957,
-0.007114198058843613,
-0.00021513784304261208,
0.014385451562702656,
0.003906533122062683,
-0.04216713085770607,
0.010751187801361084,
-0.012467101216316223,
-0.0063778492622077465,
0.007933545857667923,
-0.030521458014845848,
-0.0035224356688559055,
0.008724688552320004,
0.04832136258482933,
-0.03475186973810196,
0.025957921519875526,
0.0037545457016676664,
-0.06705104559659958,
0.011274047195911407,
-0.014123981818556786,
-0.025126619264483452,
0.06409911066293716,
-0.008095446974039078,
-0.016691237688064575,
0.016299689188599586,
-0.019779028370976448,
-0.03744406998157501,
0.016632692888379097,
-0.08809728175401688,
-0.025270581245422363,
-0.004834327381104231,
0.0014309498947113752,
0.012635675258934498,
-0.03658740967512131,
0.004659207072108984,
0.029688961803913116,
-0.051515933126211166,
-0.01532751228660345,
0.043509528040885925,
0.010013467632234097,
0.0193607360124588,
-0.04360492527484894,
-0.0025035517755895853,
-0.028774335980415344,
-0.02039959654211998,
0.04184886813163757,
0.04937990754842758,
0.014133377932012081,
0.015133137814700603,
-0.010980958119034767,
0.027256669476628304,
-0.022272324189543724,
0.028469204902648926,
0.008543496951460838,
0.025242211297154427,
-0.011759036220610142,
0.02269468829035759,
0.011806429363787174,
-0.05061572790145874,
0.002282031113281846,
0.013257102109491825,
0.01932959072291851,
0.07350645214319229,
-0.028898000717163086,
0.018919672816991806,
-0.01198047399520874,
0.006860429886728525,
-0.07679817825555801,
0.03355718404054642,
0.059322845190763474,
0.018838638439774513,
-0.01704559661448002,
0.0048853387124836445,
-0.00864996574819088,
-0.03516550734639168,
0.006722136866301298,
0.02128102257847786,
-0.01149129681289196,
-0.015667643398046494,
-0.004594499245285988,
0.030474798753857613,
-0.034450724720954895,
-0.03344790264964104,
-0.013287752866744995,
0.06477181613445282,
0.04682280868291855,
0.011229540221393108,
-0.03332372382283211,
0.006469649262726307,
-0.05019016191363335,
0.06353975832462311,
-0.0776052176952362,
-0.006497558206319809,
0.015750546008348465,
0.012463905848562717,
0.005423964466899633,
-0.02405647747218609
] |
<p>Say I have a laser. If I spin the laser so that the beam sweeps in an arc along a very distant object, could that dot travel faster than the speed of light?</p>
<p>In Diagram form:
<img src="http://i.stack.imgur.com/tqv8C.jpg" alt="laser beam thought experiment"></p>
| 312 |
[
-0.03379913419485092,
-0.019910994917154312,
-0.005961019080132246,
-0.020769257098436356,
0.05988326296210289,
-0.012915241532027721,
-0.05238110572099686,
-0.0030250963754951954,
-0.000052845389291178435,
-0.008251960389316082,
0.03529686853289604,
0.05400810390710831,
0.050713688135147095,
-0.01692015677690506,
0.030693665146827698,
0.028673527762293816,
-0.02035609818994999,
-0.01485771406441927,
-0.005041180644184351,
-0.03302246704697609,
0.03490697219967842,
0.009844450280070305,
0.010740870609879494,
0.011014831252396107,
-0.015844643115997314,
0.014482400380074978,
0.029876913875341415,
0.0038579474203288555,
0.03240472823381424,
0.027010269463062286,
0.015044614672660828,
0.004366127774119377,
0.033581286668777466,
0.051826655864715576,
0.046793557703495026,
-0.01813550665974617,
-0.01941087283194065,
-0.02262609638273716,
0.015200747177004814,
0.032439880073070526,
0.003230341710150242,
-0.02800537832081318,
0.0007702021976001561,
0.0572957769036293,
-0.017182117328047752,
0.01743527315557003,
-0.007929825223982334,
-0.022622136399149895,
0.08859598636627197,
-0.024730615317821503,
0.07139125466346741,
-0.0328013151884079,
0.02443746104836464,
0.01849362999200821,
-0.031240202486515045,
0.0042694914154708385,
0.09885033220052719,
0.0734490305185318,
-0.03599858656525612,
-0.018249427899718285,
0.0023668166249990463,
-0.024435410276055336,
-0.018417958170175552,
-0.026324810460209846,
-0.05280302092432976,
0.019944556057453156,
-0.03072529099881649,
-0.0075882477685809135,
0.001673252321779728,
0.025547457858920097,
-0.00578036205843091,
0.0008375204633921385,
0.025047751143574715,
-0.004804830066859722,
0.003640497336164117,
-0.025919046252965927,
0.03307708725333214,
0.009595386683940887,
0.04571058228611946,
0.030463572591543198,
-0.011288469657301903,
-0.0026211694348603487,
0.029139049351215363,
0.025594130158424377,
0.02003873698413372,
0.005835746880620718,
0.03691333159804344,
-0.000003928010755771538,
0.025895897299051285,
0.031976088881492615,
-0.019300349056720734,
0.01920987106859684,
0.013486430048942566,
-0.0009262601961381733,
-0.006899706088006496,
0.021735209971666336,
-0.006787324324250221,
0.03717173635959625,
0.014849706552922726,
-0.028280051425099373,
-0.009756921790540218,
-0.014351199381053448,
0.027229303494095802,
0.06766016781330109,
0.011955667287111282,
-0.010008004494011402,
-0.002043735468760133,
0.03313648700714111,
-0.022137602791190147,
-0.015196229331195354,
-0.04536368325352669,
0.016326138749718666,
0.009548446163535118,
-0.026067256927490234,
0.017365969717502594,
-0.0439780168235302,
0.0011502361157909036,
-0.0384705513715744,
0.05540267750620842,
0.057770486921072006,
0.012959636747837067,
-0.057350073009729385,
0.02208484150469303,
-0.03168625384569168,
-0.02065720595419407,
0.03910435736179352,
0.04793378710746765,
-0.004946794826537371,
0.0016807911451905966,
0.0005191833479329944,
-0.003316463204100728,
-0.011050566099584103,
0.01592111401259899,
-0.023816263303160667,
0.05072053521871567,
-0.05729413777589798,
-0.09531471878290176,
-0.04918981343507767,
0.04611510410904884,
0.03990522027015686,
-0.03760862350463867,
-0.10437192022800446,
0.027804361656308174,
0.00883690919727087,
0.11342472583055496,
0.00882604718208313,
0.004981352481991053,
0.004925958346575499,
0.02353495918214321,
-0.00898883305490017,
-0.02742329239845276,
-0.009637463837862015,
0.03470800071954727,
-0.04259476438164711,
0.01974724605679512,
-0.10986539721488953,
-0.04012071713805199,
0.019354458898305893,
-0.022546859458088875,
-0.0053147850558161736,
-0.01400742307305336,
-0.04919245466589928,
0.0664958655834198,
0.01117385271936655,
-0.013807244598865509,
-0.023700490593910217,
0.12725259363651276,
0.02723957970738411,
-0.016186710447072983,
0.0628250241279602,
0.015309884212911129,
0.036678947508335114,
-0.0265048760920763,
-0.0063888742588460445,
0.06370393931865692,
-0.04852921888232231,
-0.0014974100049585104,
0.010607575997710228,
-0.008937805891036987,
-0.008594284765422344,
-0.0360059030354023,
-0.03998897969722748,
-0.03685978800058365,
0.015755364671349525,
0.023544413968920708,
0.061268698424100876,
-0.006540815345942974,
0.025335537269711494,
-0.023013656958937645,
-0.034203045070171356,
0.0027613574638962746,
-0.050451524555683136,
0.04034353792667389,
0.01628691516816616,
-0.0020686951465904713,
-0.00031577012850902975,
0.020079730078577995,
0.0634172186255455,
-0.025281475856900215,
-0.03590436652302742,
-0.022699376568198204,
0.054261934012174606,
-0.016205471009016037,
-0.012006591074168682,
0.0352354571223259,
0.08039583265781403,
0.02579227276146412,
-0.012258452363312244,
-0.0027070955839008093,
-0.010628270916640759,
-0.032489169389009476,
-0.0006287719588726759,
0.018581166863441467,
0.0065636117942631245,
0.033657047897577286,
0.014106727205216885,
0.023293117061257362,
0.020278654992580414,
-0.01149851456284523,
0.015054061077535152,
0.021121589466929436,
0.07569456845521927,
0.03389474377036095,
0.004858896601945162,
-0.007783197332173586,
0.03965925797820091,
0.02504720911383629,
-0.006188438273966312,
0.0067782108671963215,
-0.028316548094153404,
-0.010500938631594181,
0.00997094064950943,
0.01705983653664589,
0.03810673579573631,
-0.0507512129843235,
0.010973199270665646,
0.05517592281103134,
0.03365152329206467,
0.035784680396318436,
0.032232947647571564,
-0.05389008671045303,
-0.019957182928919792,
0.004675195086747408,
0.0436239130795002,
0.008382757194340229,
-0.015771063044667244,
0.060555245727300644,
0.018353933468461037,
0.009085115976631641,
0.015572447329759598,
-0.04483861103653908,
0.024009140208363533,
-0.03358057513833046,
-0.005140402819961309,
0.04223168268799782,
-0.02688269317150116,
0.055446527898311615,
-0.013147755526006222,
0.010648779571056366,
0.0267194714397192,
-0.014589053578674793,
0.028065118938684464,
-0.029952920973300934,
-0.011225538328289986,
-0.012178011238574982,
0.01068148948252201,
-0.013599362224340439,
-0.02546515315771103,
0.026157720014452934,
-0.027357250452041626,
0.014925766736268997,
-0.04154383763670921,
0.015921058133244514,
-0.0553448386490345,
0.0019104676321148872,
0.01473015733063221,
0.04085010662674904,
0.038963768631219864,
-0.012232834473252296,
-0.04576285183429718,
0.002342598047107458,
-0.034601159393787384,
-0.006085327826440334,
-0.0002694227732717991,
-0.056719180196523666,
0.01445816271007061,
-0.006577221676707268,
-0.02593720704317093,
0.039923932403326035,
-0.03468477725982666,
0.010354357771575451,
0.026031143963336945,
-0.027123691514134407,
-0.05109265446662903,
0.005638401489704847,
-0.03119575046002865,
0.022801028564572334,
-0.04300066828727722,
0.0008908250601962209,
0.04007549211382866,
0.002564731054008007,
-0.027879387140274048,
0.009234337136149406,
-0.0241603571921587,
-0.04557175561785698,
0.015519472770392895,
0.009126688353717327,
0.03412073105573654,
-0.05346331372857094,
0.02287023328244686,
-0.018172062933444977,
-0.03831220045685768,
0.020947333425283432,
-0.04827490448951721,
-0.02603897638618946,
0.048969853669404984,
0.007887747138738632,
0.014989618211984634,
-0.01888965629041195,
-0.020722581073641777,
0.07487247884273529,
0.028578603640198708,
-0.03279007226228714,
-0.044445641338825226,
-0.010675448924303055,
-0.002258793916553259,
-0.04314849525690079,
0.0016079364577308297,
-0.009781325235962868,
-0.05302144214510918,
-0.011990027502179146,
0.014027711935341358,
0.026291409507393837,
-0.003376391716301441,
0.03473052754998207,
-0.028756488114595413,
-0.011525842361152172,
-0.002885858528316021,
0.0085669606924057,
0.05508662760257721,
0.04510477930307388,
-0.03670988604426384,
0.01868186518549919,
-0.012538083828985691,
0.06325814127922058,
0.01935589499771595,
-0.05210346356034279,
0.054753825068473816,
0.006002273876219988,
0.01647612266242504,
0.004087147302925587,
0.041570331901311874,
-0.0009163086069747806,
0.007315463852137327,
0.0002423601836198941,
0.03727911040186882,
0.041118331253528595,
0.01038956455886364,
0.014398316852748394,
0.022523829713463783,
0.031248852610588074,
0.0017141327261924744,
0.0015300639206543565,
-0.031218770891427994,
-0.023814069107174873,
0.027474401518702507,
-0.024063337594270706,
-0.033879220485687256,
0.018429402261972427,
0.036512427031993866,
-0.019297529011964798,
-0.030152903869748116,
-0.018932906910777092,
0.01728234812617302,
-0.05192942917346954,
0.01637621596455574,
0.0074217659421265125,
0.029787182807922363,
0.00574078131467104,
0.04842203110456467,
0.040504369884729385,
0.003988051321357489,
0.016517585143446922,
-0.00908579770475626,
-0.08486417680978775,
0.03786935657262802,
-0.03949658200144768,
-0.03304805979132652,
-0.011759457178413868,
-0.020908130332827568,
-0.016412140801548958,
-0.026691537350416183,
0.00205304566770792,
-0.011257137171924114,
-0.030609574168920517,
-0.05454658716917038,
0.01333516277372837,
-0.018677445128560066,
-0.005686801392585039,
0.005735623650252819,
0.04112707078456879,
0.014527729712426662,
-0.017747005447745323,
0.03209245949983597,
0.0036039657425135374,
-0.05048871040344238,
0.01114982645958662,
-0.006911376491189003,
-0.008027837611734867,
-0.0043272655457258224,
0.026096666231751442,
0.05143442004919052,
0.018177473917603493,
-0.03502128645777702,
0.031504470854997635,
0.023851407691836357,
0.04975174739956856,
0.019726546481251717,
-0.014844388701021671,
-0.05153665319085121,
-0.04951660707592964,
-0.0003608692204579711,
-0.010933728888630867,
0.0903405249118805,
0.013215746730566025,
-0.004255519714206457,
0.020377300679683685,
-0.013145425356924534,
-0.00667360657826066,
0.0020769904367625713,
0.03025040775537491,
0.01853841356933117,
-0.03536192327737808,
-0.06505994498729706,
-0.04446059837937355,
-0.01477906759828329,
-0.01996292732656002,
0.0211307592689991,
-0.033392637968063354,
-0.04551912471652031,
0.00242803362198174,
-0.008574334904551506,
0.020781120285391808,
0.000015876730685704388,
0.025201426818966866,
-0.021901344880461693,
0.011168794706463814,
-0.015348575077950954,
0.0030034619849175215,
-0.01696952059864998,
0.009212896227836609,
0.016264941543340683,
0.008788312785327435,
0.01226641796529293,
-0.11687276512384415,
-0.02199922315776348,
0.05482763424515724,
0.05020149424672127,
-0.002343202941119671,
-0.0019326226320117712,
-0.03677298501133919,
-0.029017457738518715,
0.06004336476325989,
-0.024963045492768288,
0.05009150132536888,
-0.048836737871170044,
-0.03530043363571167,
-0.020201824605464935,
-0.012703491374850273,
-0.0010347095085307956,
0.031374476850032806,
-0.018902240321040154,
-0.022999519482254982,
-0.0260603129863739,
0.003915363922715187,
0.03754473850131035,
-0.011493826285004616,
0.02735385112464428,
0.06551383435726166,
0.0019193835323676467,
-0.015620943158864975,
-0.0014154749223962426,
0.014809460379183292,
-0.02878817729651928,
-0.0717356726527214,
0.004214751534163952,
0.021318616345524788,
-0.04290665313601494,
0.06906136870384216,
-0.04208488017320633,
-0.0020317351445555687,
0.05179829150438309,
0.017522888258099556,
-0.009183733724057674,
0.003840307705104351,
-0.04922765493392944,
-0.004279819782823324,
-0.0058134011924266815,
-0.011462611146271229,
0.02292792685329914,
0.04905007407069206,
-0.0051308623515069485,
-0.0012751000467687845,
0.008519681170582771,
0.06943470984697342,
-0.0021737704519182444,
0.010600538924336433,
-0.009012037888169289,
0.0044332100078463554,
-0.005626852158457041,
0.048624277114868164,
-0.03141168877482414,
0.0010801139287650585,
0.036695510149002075,
-0.048846177756786346,
-0.022749396041035652,
0.034508612006902695,
0.010999329388141632,
-0.024950532242655754,
-0.0373404324054718,
0.021817807108163834,
-0.016194067895412445,
-0.023896798491477966,
0.007232028059661388,
0.007531954441219568,
0.005683924537152052,
0.04108883813023567,
0.014388742856681347,
0.0365789569914341,
-0.0520206093788147,
-0.017066264525055885,
-0.009234687313437462,
-0.053130246698856354,
0.03003871999680996,
-0.011641769669950008,
-0.009874011389911175,
0.040843985974788666,
-0.06787283718585968,
-0.0006568855606019497,
0.014252876862883568,
-0.017921561375260353,
0.007143276743590832,
-0.04931715130805969,
0.010561115108430386,
-0.008953065611422062,
-0.0023353903088718653,
-0.03225387632846832,
-0.05893717706203461,
0.018022164702415466,
0.029552550986409187,
-0.008478867821395397,
0.0011634690454229712,
-0.006950626615434885,
-0.04267275705933571,
-0.023934030905365944,
-0.01574438437819481,
0.03875771909952164,
-0.029954370111227036,
-0.013989117927849293,
0.05827115848660469,
-0.034004852175712585,
0.0659441277384758,
0.010688756592571735,
-0.04919791221618652,
0.006237554829567671,
-0.015671798959374428,
-0.020492635667324066,
-0.009501227177679539,
0.06400036811828613,
-0.032312821596860886,
-0.08347064256668091,
-0.03336819261312485,
0.02507752738893032,
0.04968804121017456,
-0.014821668155491352,
-0.0027846095617860556,
0.014502410776913166,
-0.0038677745033055544,
0.02662663534283638,
-0.0001870015257736668,
0.020416414365172386,
0.021778112277388573,
-0.005280761513859034,
-0.005222813226282597,
0.019542308524250984,
-0.04524533450603485,
-0.03446577489376068,
0.016360566020011902,
0.021325940266251564,
0.03768512234091759,
-0.006791314110159874,
0.03073897771537304,
-0.018445244058966637,
-0.014702636748552322,
-0.008075064048171043,
-0.0167885459959507,
0.01763162948191166,
-0.0035644033923745155,
-0.0016660239780321717,
-0.005555045325309038,
0.005907692480832338,
-0.01335673313587904,
-0.0017473596381023526,
0.015961669385433197,
-0.046525392681360245,
0.08793944120407104,
-0.017379820346832275,
0.029178118333220482,
0.011717217043042183,
0.01932833343744278,
-0.011106590740382671,
-0.009501968510448933,
0.005931039806455374,
0.029112068936228752,
0.026324518024921417,
0.02259238064289093,
-0.0032710274681448936,
0.020235208794474602,
0.023543011397123337,
0.05050981044769287,
0.0029078673105686903,
-0.00163105723913759,
0.032961636781692505,
0.026283685117959976,
0.017537390813231468,
0.01403739769011736,
-0.010608408600091934,
0.029638255015015602,
-0.035033389925956726,
0.034901197999715805,
-0.02641242928802967,
-0.011815574951469898,
0.03742066025733948,
-0.025000551715493202,
0.028115781024098396,
-0.003338288050144911,
-0.026898706331849098,
-0.0314185656607151,
0.006227253936231136,
-0.0246723722666502,
0.03780286759138107,
0.007892861030995846,
-0.008443591184914112,
0.019595850259065628,
0.023921456187963486,
0.04977644234895706,
-0.028145909309387207,
-0.06713616102933884,
-0.06110955402255058,
-0.020245391875505447,
-0.03896195814013481,
0.04197675734758377,
0.041666049510240555,
-0.020276512950658798,
0.005274801980704069,
-0.03821210935711861,
0.0052646249532699585,
0.009971409104764462,
0.04342073202133179,
-0.001086370088160038,
0.07156345248222351,
0.009020315483212471,
0.03363832086324692,
0.0007586903520859778,
0.025309676304459572,
0.07145445793867111,
0.005036905407905579,
-0.018439842388033867,
-0.06691152602434158,
0.031916167587041855,
-0.03484625369310379,
0.023088039830327034,
-0.04802310839295387,
0.01725597307085991,
-0.04370366409420967,
-0.007874694652855396,
0.05664718523621559,
0.03698809817433357,
-0.01785247027873993,
0.009668790735304356,
0.030326543375849724,
-0.024129461497068405,
-0.017605332657694817,
0.019758518785238266,
0.02256958745419979,
0.018453264608979225,
0.02518061175942421,
-0.03278324007987976,
0.025386348366737366,
-0.047068338841199875,
-0.004128097090870142,
0.003015849506482482,
-0.043804462999105453,
0.02138965018093586,
-0.0201072096824646,
-0.03256047144532204,
-0.010697226971387863,
0.044285792857408524,
-0.032718390226364136,
-0.06452462822198868,
-0.0015695432666689157,
0.027689505368471146,
0.0025460815522819757,
-0.0003071266692131758,
0.03140615299344063,
-0.0019250893965363503,
0.034404609352350235,
0.020328283309936523,
0.014185387641191483,
-0.04344028979539871,
0.013198482804000378,
-0.013038060627877712,
0.01484689675271511,
-0.012542428448796272,
0.03096800483763218,
-0.010457949712872505,
0.01216347049921751,
0.03319220617413521,
-0.06468089669942856,
-0.020710047334432602,
-0.004476655274629593,
-0.007898989133536816,
0.015019679442048073,
-0.03083300217986107,
-0.02943735010921955,
0.015777194872498512,
0.028056826442480087,
0.014498990960419178,
-0.032802287489175797,
0.0009765898576006293,
0.016935283318161964,
0.007316719740629196,
0.0190372783690691,
-0.015670889988541603,
-0.030489888042211533,
-0.014640146866440773,
0.013011863455176353,
-0.026431383565068245,
0.027769092470407486,
0.05240890011191368,
0.026835212484002113,
-0.028798699378967285,
0.011000923812389374,
-0.005676113534718752,
-0.015364636667072773,
-0.04488452151417732,
0.00403550686314702,
-0.04625888913869858,
-0.029250765219330788,
-0.0068723889999091625,
-0.003734410973265767,
0.07573741674423218,
0.02125573344528675,
-0.010589753277599812,
0.02425181120634079,
-0.005756816361099482,
0.032109085470438004,
0.016535097733139992,
-0.016215404495596886,
-0.00590642262250185,
-0.0023151037748903036,
-0.00002464133831381332,
0.025855518877506256,
-0.02395784668624401,
0.015516958199441433,
0.042045943439006805,
-0.023791354149580002,
-0.008309540338814259,
0.012515519745647907,
-0.03595632314682007,
-0.020953582599759102,
0.0414980947971344,
-0.019460264593362808,
-0.0013046024832874537,
-0.00609102426096797,
-0.004431469365954399,
-0.044531844556331635,
0.0004582307883538306,
-0.03246701881289482,
-0.05231044441461563,
-0.025157062336802483,
0.01966005191206932,
0.00011966706370003521,
0.02701951190829277,
-0.003742912784218788,
0.0007287061889655888,
-0.04322395473718643,
0.014299921691417694,
-0.035223204642534256,
0.00608853530138731,
0.013423822820186615,
-0.00716023612767458,
-0.03022046759724617,
0.05063342675566673,
-0.03282904624938965,
-0.009257066063582897,
0.008984745480120182,
0.05699603632092476,
-0.03104832023382187,
-0.012977714650332928,
0.022856619209051132,
0.0109635004773736,
0.03662500157952309,
-0.05246086046099663,
-0.004671054892241955,
0.0463862307369709,
-0.03235720843076706,
-0.011921967379748821,
0.04280679300427437,
-0.05218280851840973,
0.04207133129239082,
0.002877652645111084,
-0.0045283492654562,
-0.00397196039557457,
0.05969790741801262,
-0.011040263809263706,
0.0030588239897042513,
0.013010624796152115,
-0.020390711724758148,
0.004890131298452616,
-0.0011483305133879185,
0.027611711993813515,
-0.018913934007287025,
-0.019841089844703674,
0.03734438866376877,
-0.008038578554987907,
-0.029640967026352882,
0.015879910439252853,
-0.020139245316386223,
-0.015214980579912663,
-0.007123882416635752,
0.015532496385276318,
-0.02269805781543255,
0.027707591652870178,
0.02565861865878105,
0.005763939116150141,
0.0505191907286644,
-0.0014563162112608552,
-0.01669497787952423,
-0.12745170295238495,
0.028443368151783943,
-0.007140487898141146,
0.004053918644785881,
0.04211796820163727,
-0.037624526768922806,
0.02466876618564129,
0.04202529042959213,
-0.07913838326931,
0.03936704248189926,
-0.03700686991214752,
-0.019808243960142136,
-0.05317376181483269,
0.01983039267361164,
0.017604710534214973,
0.05523554980754852,
0.021977541968226433,
0.032448213547468185,
0.013256232254207134,
0.010806395672261715,
-0.027199143543839455,
-0.03502151370048523,
-0.005746697075664997,
0.0365283377468586,
-0.011789857409894466,
0.018115440383553505,
0.03774459287524223,
-0.04653428867459297,
-0.008976289071142673,
0.0047169029712677,
0.009996488690376282,
0.0585508868098259,
-0.013416044414043427,
-0.01001711655408144,
0.0008896433282643557,
-0.006374409422278404,
0.009115470573306084,
-0.015012002550065517,
0.007021644152700901,
0.01416602823883295,
-0.015170001424849033,
0.025496259331703186,
-0.013770733028650284,
-0.007395010441541672,
0.013339297845959663,
-0.04721343517303467,
-0.06500814110040665,
0.026101088151335716,
-0.011668423190712929,
-0.009925898164510727,
0.01910230703651905,
0.012906552292406559,
0.023906100541353226,
-0.04460109770298004,
0.00424329424276948,
-0.06038418412208557,
0.03265008330345154,
0.01016873586922884,
-0.00498792203143239,
-0.03527669236063957,
-0.01521675568073988,
-0.0019448264501988888,
-0.0323665551841259,
0.017805233597755432,
-0.006768267601728439,
-0.0008780468488112092,
-0.07059859484434128,
-0.0018230538116768003,
-0.0006912912358529866,
-0.02608324959874153,
0.006156470160931349,
-0.023292049765586853,
-0.0017887434223666787,
0.017550062388181686,
0.011282222345471382,
-0.014064956456422806,
0.03655441477894783,
-0.012617618776857853,
-0.03476087376475334,
-0.06838006526231766,
-0.019210251048207283,
-0.02097579650580883,
0.004052428994327784,
-0.0517972894012928,
-0.033575449138879776,
0.007297272328287363,
0.01456755492836237,
0.0187583789229393,
-0.015328198671340942,
0.00990203209221363,
0.045371077954769135,
-0.037960752844810486,
-0.0009929107036441565,
-0.025827620178461075,
-0.027346882969141006,
-0.02348513901233673,
-0.03794674947857857,
-0.025200264528393745,
-0.03472933545708656,
-0.024662774056196213,
0.01772322691977024,
0.015381638891994953,
0.05679946392774582,
0.014047215692698956,
-0.0046753049828112125,
-0.052378248423337936,
0.02111547254025936,
-0.01450823899358511,
0.013261916115880013,
0.07421077787876129,
0.047325413674116135,
0.0075210509821772575,
0.026179751381278038,
-0.02299438789486885,
-0.021646270528435707,
0.02263801358640194,
-0.035621464252471924,
0.004899841267615557,
-0.051166925579309464,
-0.021873047575354576,
0.0044160508550703526,
-0.03509138152003288,
0.030477743595838547,
0.013101981021463871,
-0.023534124717116356,
-0.00211856490932405,
0.012384687550365925,
-0.00825341697782278,
0.02773444727063179,
-0.049005474895238876,
0.0240081325173378,
0.00436411565169692,
-0.006852107588201761,
-0.038724906742572784,
0.02869172766804695,
-0.003035027766600251,
0.012666068971157074,
0.0232753437012434,
0.04016811028122902,
0.014408914372324944,
-0.010522650554776192,
0.022057583555579185,
0.0669887512922287,
0.01672581024467945,
0.0005335950991138816,
0.012182619422674179,
-0.010489791631698608,
0.035610686987638474,
0.02442299574613571,
-0.03576625511050224,
0.04591649770736694,
-0.014412948861718178,
0.04544302448630333,
-0.003756556659936905,
-0.005095117725431919,
-0.004860853310674429,
0.012506191618740559,
-0.008355491794645786,
0.006270193494856358,
0.0010342998430132866,
-0.027301322668790817,
-0.02068575657904148,
-0.005123953800648451,
0.03689700737595558,
-0.044876374304294586,
0.036261603236198425,
-0.035002514719963074,
-0.012942872941493988,
-0.023539530113339424,
-0.025453541427850723,
-0.039139047265052795,
-0.009923825971782207,
-0.004520108923316002,
0.01526807900518179,
0.006970636546611786,
0.010655163787305355,
-0.0018946279305964708,
0.006461072247475386,
0.05334575101733208,
-0.0657387226819992,
-0.008997335098683834,
-0.03390179201960564,
0.04883865639567375,
-0.024031389504671097,
-0.008629485964775085
] |
<p>A candle is floating in a liquid placed in a container. The container is a cylinder of diameter $D$, and the candle is of width $d$. ($D>d$) The height of the liquid from the bottom of the container is $p$, and the height of the candle flame from the bottom is $h$. The density of the candle material is $p_c$ and that of the liquid is $p_l$.</p>
<p>If the length of the candle changes by $\Delta L$, find the change in the level of the liquid $\Delta p$, and the change in height of the flame $\Delta h$.</p>
<p>My attempt:</p>
<p>I'm trying to use Archimedes principle. Suppose $x$ is the height of the submerged candle when its length is $L$. Then, balancing gravitational and buoyant forces, $$p_c \pi \left(\frac{d}{2}\right)^2 L g = p_l \pi \left(\frac{d}{2}\right)^2 x g $$</p>
<p>So $$x = \frac{p_c}{p_l}L$$</p>
<p>Now suppose the length of the candle changes by $\Delta L$, causing the liquid height to change by $\Delta h$. I wrote: $$p_c \pi \left(\frac{d}{2}\right)^2 (L+\Delta L) g = p_l \pi \left(\frac{d}{2}\right)^2 (x+\Delta p) g$$</p>
<p>Which gives $$\Delta p = \frac{p_c}{p_l}\Delta L$$</p>
<p>Here I assumed that the change in liquid level would contribute to additional buoyant force. However, I'm not getting the right answer, which involves $D$ as well. So I'm not sure how to use Archimedes Principle for the required case. Any suggestions?</p>
| 9,592 |
[
-0.012909493409097195,
-0.018474072217941284,
0.025940749794244766,
0.004735621623694897,
0.008879894390702248,
-0.029992979019880295,
-0.022887324914336205,
-0.023728104308247566,
0.00963075552135706,
0.01629689708352089,
0.024737846106290817,
0.036147989332675934,
0.09221665561199188,
0.03782264515757561,
0.05618762969970703,
-0.009771537967026234,
0.0002076278906315565,
-0.0029288972727954388,
0.02011348493397236,
-0.05915530398488045,
-0.01715555414557457,
0.013666006736457348,
-0.00902215763926506,
-0.01983230747282505,
-0.025918636471033096,
0.03150744363665581,
0.01838342472910881,
0.012662631459534168,
-0.026148078963160515,
0.046116430312395096,
-0.01101778820157051,
0.007037363480776548,
0.01103146281093359,
0.028510097414255142,
0.03520626947283745,
0.04517170414328575,
-0.014164820313453674,
-0.0013267429312691092,
-0.02151651680469513,
0.013793278485536575,
-0.010514385998249054,
-0.006739071104675531,
0.024231044575572014,
0.04771400988101959,
-0.0007055581663735211,
0.01883419044315815,
-0.005569288972765207,
-0.0647328570485115,
0.07655926048755646,
-0.08663656562566757,
0.05513133481144905,
0.012522603385150433,
0.06701795756816864,
0.04095485061407089,
-0.01992873102426529,
0.004859211388975382,
0.05933753028512001,
0.06033768132328987,
-0.03269403427839279,
-0.019022606313228607,
-0.024519065394997597,
0.018729543313384056,
-0.011259791441261768,
-0.0048992205411195755,
-0.03627374395728111,
-0.01959671638906002,
-0.02125377021729946,
-0.03823058307170868,
-0.020832479000091553,
-0.02918318659067154,
-0.027253637090325356,
-0.027546776458621025,
0.05791902914643288,
0.024122057482600212,
0.016884474083781242,
-0.02703038789331913,
-0.006992867216467857,
0.05923773720860481,
0.02523965574800968,
0.03104250878095627,
0.011497787199914455,
-0.014680362306535244,
0.01299700140953064,
0.03598686307668686,
0.014293611980974674,
-0.015984784811735153,
0.05046771466732025,
0.013583840802311897,
0.02759961225092411,
0.034286368638277054,
-0.018232280388474464,
-0.008893735706806183,
0.0378572903573513,
-0.0015685687540099025,
0.013693461194634438,
-0.016402719542384148,
-0.017842812463641167,
0.021822435781359673,
-0.0029506105929613113,
-0.008642209693789482,
0.015051385387778282,
-0.007576306816190481,
0.04338322579860687,
0.09893587231636047,
-0.0058626760728657246,
-0.030180281028151512,
-0.02088022790849209,
0.0037730373442173004,
0.015356560237705708,
0.016917759552598,
-0.02356886677443981,
0.015585671178996563,
-0.01216459646821022,
-0.03439876437187195,
-0.024402104318141937,
-0.03434954583644867,
-0.015857169404625893,
-0.011569405905902386,
0.05637942999601364,
0.017799027264118195,
0.030134735628962517,
0.011144342832267284,
0.06714177131652832,
-0.0063396901823580265,
-0.07551831752061844,
0.05361604318022728,
-0.002935560420155525,
-0.029579462483525276,
-0.04188580438494682,
0.04876793175935745,
0.022443238645792007,
0.010725722648203373,
-0.009658814407885075,
0.0327584408223629,
0.03923347219824791,
0.012760337442159653,
-0.08473128080368042,
-0.022567393258213997,
0.05140441283583641,
0.003773725125938654,
0.0009210329735651612,
-0.07463311403989792,
0.0031458446756005287,
0.0653017908334732,
0.07996981590986252,
0.0006381049170158803,
0.0041912333108484745,
-0.03043603152036667,
0.01097921933978796,
-0.008620359934866428,
-0.023351499810814857,
-0.019702082499861717,
0.0482063814997673,
-0.025945352390408516,
0.007984977215528488,
-0.05213732272386551,
-0.016317710280418396,
0.03812924399971962,
-0.0039634197019040585,
-0.0022734408266842365,
0.08210922032594681,
0.011407991871237755,
-0.037300895899534225,
0.024080807343125343,
0.0022574635222554207,
-0.020391907542943954,
0.06433013826608658,
0.018175780773162842,
-0.024141287431120872,
0.0017650638474151492,
0.011382962577044964,
0.019870812073349953,
-0.02171356976032257,
-0.02002151869237423,
0.07452392578125,
-0.0019349452340975404,
-0.025475075468420982,
-0.03473058342933655,
0.03403964638710022,
0.09316287189722061,
-0.007153545506298542,
-0.03664306923747063,
-0.03366140276193619,
-0.04307389631867409,
0.038367003202438354,
0.043661411851644516,
0.01100463792681694,
-0.014032046310603619,
-0.013126716949045658,
-0.05708339437842369,
0.005860492121428251,
-0.07796862721443176,
0.030160116031765938,
0.009584617801010609,
0.006563988979905844,
0.004312224220484495,
-0.017061498016119003,
0.00929495319724083,
-0.055203381925821304,
-0.015235215425491333,
-0.008242408744990826,
-0.008913524448871613,
0.03979652374982834,
-0.015035544522106647,
0.03294890746474266,
0.009591998532414436,
0.03689764067530632,
0.01956845633685589,
0.017900487408041954,
-0.022384366020560265,
0.047849517315626144,
-0.016629815101623535,
-0.0012681802036240697,
-0.018976738676428795,
-0.030826272442936897,
0.016139745712280273,
0.02970387600362301,
0.001202547806315124,
0.008048749528825283,
0.06358208507299423,
-0.033461589366197586,
0.08807699382305145,
0.0739673376083374,
-0.015874724835157394,
0.013391113840043545,
0.010767254047095776,
0.03216829150915146,
0.04146033152937889,
0.0059606400318443775,
-0.061953477561473846,
-0.006516799330711365,
-0.00232311780564487,
-0.027499578893184662,
-0.001348284538835287,
-0.045005615800619125,
-0.0019938519690185785,
0.034961849451065063,
-0.007432415150105953,
0.03844686597585678,
0.04238208383321762,
-0.02507646195590496,
-0.02521730400621891,
0.016033487394452095,
0.013403310440480709,
-0.011678813956677914,
-0.003148769959807396,
0.03458918258547783,
0.042460713535547256,
0.014253676868975163,
-0.023200955241918564,
-0.010475965216755867,
-0.007542473264038563,
-0.0056173233315348625,
0.03975268453359604,
-0.04629567638039589,
0.017536574974656105,
0.05685267969965935,
-0.029265185818076134,
0.0073432838544249535,
0.0011170919751748443,
-0.009062533266842365,
-0.01583006978034973,
-0.040789518505334854,
0.006131955422461033,
0.036788079887628555,
0.013982945121824741,
-0.05556810274720192,
-0.03153868019580841,
0.010991886258125305,
-0.04116535559296608,
-0.004008670803159475,
-0.01301609817892313,
-0.0287883710116148,
-0.03612297773361206,
0.006150564178824425,
0.004343884065747261,
0.03331413120031357,
0.04520546272397041,
-0.04138929396867752,
-0.027747198939323425,
-0.03536306694149971,
-0.006423830520361662,
-0.0363263376057148,
-0.03421995788812637,
-0.055892422795295715,
-0.005280499812215567,
-0.014431202784180641,
-0.019405527040362358,
0.05387875437736511,
0.01237757969647646,
0.029545240104198456,
0.007519531529396772,
-0.013761441223323345,
-0.017631107941269875,
-0.011716286651790142,
-0.05035671964287758,
0.010614151135087013,
-0.023464007303118706,
0.029289091005921364,
0.01825864426791668,
0.04078760743141174,
-0.03613873943686485,
0.007191590964794159,
-0.05422911047935486,
-0.03195616602897644,
-0.010261787101626396,
0.01086084172129631,
0.013549488969147205,
-0.03551267087459564,
0.010345306247472763,
-0.01784888282418251,
-0.0064393687061965466,
0.04798911511898041,
-0.06628697365522385,
-0.08659565448760986,
0.00703901331871748,
0.019964808598160744,
0.03331807255744934,
0.003735799342393875,
-0.02382284216582775,
0.08610997349023819,
0.005218360107392073,
-0.04487375169992447,
-0.00843250285834074,
0.0074832625687122345,
0.03522634878754616,
-0.04587113484740257,
0.009376676753163338,
0.04250751808285713,
-0.037794079631567,
0.04033663868904114,
-0.009021082893013954,
0.01848256029188633,
0.03159695118665695,
0.024500207975506783,
0.00978144071996212,
0.04025086760520935,
0.03840269893407822,
0.023222293704748154,
0.04042212292551994,
0.0144365094602108,
0.00905560702085495,
0.019090494140982628,
-0.0072510624304413795,
0.024099988862872124,
-0.008620630949735641,
-0.010532326065003872,
0.05762278661131859,
0.018519986420869827,
-0.02211240492761135,
0.01976339891552925,
0.04883710667490959,
0.008704392239451408,
-0.03429586440324783,
0.040085237473249435,
0.02123226597905159,
0.03990551084280014,
-0.0033509191125631332,
-0.023262757807970047,
0.04661288857460022,
0.05336480215191841,
-0.023080801591277122,
-0.04766633361577988,
-0.0019180610543116927,
-0.004208768717944622,
0.06865616887807846,
-0.01665140502154827,
0.007213760167360306,
0.05921530723571777,
0.003737021004781127,
0.03196749463677406,
0.008293284103274345,
-0.028820253908634186,
0.006099035032093525,
-0.08825676143169403,
-0.014238383620977402,
0.004781762138009071,
0.07024510949850082,
-0.011594440788030624,
0.04320680722594261,
0.046773962676525116,
-0.008147060871124268,
0.055190276354551315,
0.04467032104730606,
-0.09560130536556244,
0.014509916305541992,
-0.014876462519168854,
0.02051498554646969,
-0.011605880223214626,
-0.006298028398305178,
0.005654801148921251,
-0.04839898645877838,
-0.030790137127041817,
-0.00648497836664319,
0.0070244683884084225,
-0.036578841507434845,
0.037304893136024475,
-0.015667712315917015,
-0.02833779901266098,
0.0266529843211174,
0.05040792375802994,
0.019218439236283302,
-0.02888559363782406,
0.007417505141347647,
0.05046219006180763,
-0.015515551902353764,
0.010620065033435822,
-0.0022028188686817884,
-0.02500029094517231,
0.0184039119631052,
0.017499808222055435,
0.008509485051035881,
0.02266315184533596,
-0.009630766697227955,
0.058164846152067184,
0.014974226243793964,
0.03289929777383804,
-0.013264034874737263,
0.006417189259082079,
-0.00377566902898252,
-0.03403329849243164,
-0.0068495008163154125,
-0.0051968577317893505,
0.05402996391057968,
-0.02370273694396019,
-0.004813387989997864,
0.017736678943037987,
-0.0035754782147705555,
-0.019262639805674553,
0.05368628725409508,
0.04952623322606087,
-0.006226790137588978,
-0.03103436902165413,
-0.026737645268440247,
0.011539426632225513,
-0.061118513345718384,
-0.004467869643121958,
0.005020255222916603,
0.009260228835046291,
-0.017735254019498825,
-0.016267484053969383,
0.04240293428301811,
0.034618012607097626,
-0.002951973583549261,
0.03951951488852501,
-0.008859421126544476,
0.009645413607358932,
-0.03204433619976044,
-0.005726302973926067,
0.010503796860575676,
0.01215161383152008,
-0.003309085499495268,
-0.03735506534576416,
-0.005803888197988272,
-0.06252148747444153,
-0.0177544467151165,
0.01452036201953888,
0.046919915825128555,
-0.027251850813627243,
0.03657915070652962,
-0.06648232042789459,
-0.022600838914513588,
0.03897867351770401,
-0.03209822252392769,
0.0050114113837480545,
-0.044938355684280396,
-0.014345338568091393,
0.045431919395923615,
-0.048642195761203766,
-0.007678929716348648,
-0.037954699248075485,
-0.029453791677951813,
-0.00019330772920511663,
-0.04140705615282059,
0.007250078488141298,
0.02432851493358612,
0.01869651861488819,
0.01570252701640129,
0.019840188324451447,
0.005760716274380684,
-0.03417707607150078,
0.012147655710577965,
0.005074182990938425,
-0.026318326592445374,
-0.062321458011865616,
-0.02376612275838852,
-0.027891406789422035,
0.0013382171746343374,
0.02252335287630558,
-0.045108113437891006,
-0.09371130168437958,
0.02204926498234272,
0.017916761338710785,
-0.023449202999472618,
0.02709878608584404,
0.010612699203193188,
0.019747460260987282,
0.07647856324911118,
0.001169579685665667,
0.03590241074562073,
0.05519973114132881,
-0.014893986284732819,
-0.04177569970488548,
-0.01220585498958826,
0.04049481824040413,
-0.01889973133802414,
-0.031396470963954926,
-0.05597114562988281,
0.03727499023079872,
-0.024102257564663887,
0.026820212602615356,
0.014273891225457191,
0.009681817144155502,
0.0040290504693984985,
-0.03278978914022446,
0.0518467053771019,
0.03231285512447357,
0.030326344072818756,
0.02187705598771572,
-0.01182263158261776,
0.0008706728694960475,
0.039901815354824066,
0.01102185994386673,
0.006566422991454601,
-0.0012346322182565928,
-0.007486895192414522,
-0.026190919801592827,
-0.014614114537835121,
0.02256910502910614,
-0.009015672840178013,
-0.03260985016822815,
-0.0022689849138259888,
-0.018485240638256073,
0.030169891193509102,
-0.006920681335031986,
0.014514571987092495,
0.000532822567038238,
-0.025764038786292076,
-0.004371875897049904,
-0.027520600706338882,
0.02895464189350605,
0.03266604617238045,
-0.08192669600248337,
0.009049354121088982,
-0.00012290517042856663,
-0.007325815502554178,
-0.06049096956849098,
-0.006233506835997105,
0.020543530583381653,
0.02506587654352188,
-0.013708575628697872,
-0.04935886338353157,
0.01593818888068199,
-0.0030434352811425924,
0.00850141141563654,
0.02140759862959385,
-0.004126815125346184,
-0.059015143662691116,
-0.01743142679333687,
0.016758956015110016,
0.03754037991166115,
0.01396088395267725,
-0.019572557881474495,
-0.003936903551220894,
-0.04021493345499039,
-0.0021273598540574312,
-0.012638014741241932,
-0.014191482216119766,
0.026877734810113907,
-0.03665933758020401,
-0.040822479873895645,
-0.02480158768594265,
-0.021927736699581146,
0.02204865776002407,
-0.01622738689184189,
-0.03174996376037598,
-0.004229721613228321,
0.03406153619289398,
-0.005938888061791658,
-0.010727263987064362,
0.003727432107552886,
-0.01927378959953785,
0.020896025002002716,
0.008251837454736233,
0.007739230990409851,
-0.0017579331761226058,
-0.017149077728390694,
-0.05306209251284599,
-0.0026898703072220087,
0.00947500392794609,
0.011673669330775738,
0.06806760281324387,
-0.024527575820684433,
-0.01673237420618534,
0.03777620568871498,
0.018736355006694794,
0.04736469313502312,
0.0010151122696697712,
0.00474841333925724,
0.0014863177202641964,
-0.001561650075018406,
-0.031346093863248825,
-0.06203214451670647,
-0.01562113594263792,
0.01313296239823103,
0.04225144907832146,
-0.0260216873139143,
0.045446284115314484,
0.010830671526491642,
-0.01670314557850361,
0.0404101125895977,
0.005506337154656649,
-0.0396772064268589,
0.00499757518991828,
-0.012851253151893616,
0.04491196572780609,
-0.05510110408067703,
-0.022131526842713356,
0.05224103108048439,
0.00680216820910573,
0.02053149975836277,
0.023490510880947113,
0.054280493408441544,
0.003346751444041729,
-0.02707817032933235,
-0.006699591409415007,
-0.022056199610233307,
0.06579556316137314,
-0.005477330647408962,
0.03091210499405861,
-0.05800608918070793,
-0.03137823939323425,
0.0443396158516407,
0.0074240355752408504,
0.002541554858908057,
-0.029286576434969902,
-0.022507568821310997,
-0.03419538214802742,
-0.007536011282354593,
0.03642451763153076,
0.009813280776143074,
-0.0006784457364119589,
0.02013462595641613,
0.00992667954415083,
0.005340665578842163,
0.004799686372280121,
-0.018547482788562775,
-0.061778225004673004,
-0.031971417367458344,
-0.00918866042047739,
-0.002776461886242032,
-0.0026496548671275377,
0.011580448597669601,
-0.03535333648324013,
0.024505753070116043,
-0.006581245455890894,
-0.01152769848704338,
0.017462437972426414,
0.01578381098806858,
-0.009389620274305344,
0.09277819097042084,
-0.026079539209604263,
-0.00380763434804976,
-0.03805520385503769,
0.0007341904565691948,
0.1291520595550537,
0.004853859078139067,
0.02469671331346035,
-0.043210577219724655,
0.015825921669602394,
0.004150335676968098,
0.01672324724495411,
-0.06779241561889648,
0.0024408334866166115,
-0.034176912158727646,
0.007425184361636639,
-0.004327211529016495,
0.071371890604496,
0.004227429162710905,
0.0027552300598472357,
0.01752512902021408,
-0.041140053421258926,
-0.03960072994232178,
0.03387263044714928,
0.0006056017591618001,
-0.040302399545907974,
0.05207274854183197,
0.004375460557639599,
0.03172546252608299,
-0.02787921205163002,
-0.003255262039601803,
-0.039306990802288055,
-0.009103624150156975,
-0.022551601752638817,
0.022724051028490067,
-0.05571684241294861,
-0.006835464853793383,
-0.008942222222685814,
-0.031519316136837006,
-0.033220075070858,
0.03599099814891815,
-0.010344267822802067,
-0.006593877449631691,
-0.007766369730234146,
0.038371797651052475,
0.017307361587882042,
0.010140998288989067,
0.027105623856186867,
0.040950335562229156,
-0.03974907472729683,
-0.044850967824459076,
-0.02396254800260067,
0.031278252601623535,
-0.007190981414169073,
-0.018521305173635483,
0.02447504736483097,
-0.008219360373914242,
-0.018103955313563347,
-0.041635360568761826,
-0.020043468102812767,
0.05362430214881897,
0.03474516049027443,
0.0019035598961636424,
-0.03864125907421112,
0.0024513814132660627,
0.03688102215528488,
-0.00650516152381897,
0.0025731867644935846,
-0.017951833084225655,
0.0033856115769594908,
-0.011946209706366062,
-0.017202597111463547,
0.042612720280885696,
-0.006801649462431669,
-0.02709558978676796,
-0.011699885129928589,
-0.0016059117624536157,
-0.039284396916627884,
-0.017340881749987602,
-0.006119888741523027,
0.027868453413248062,
0.008399820886552334,
0.0011399557115510106,
-0.028488753363490105,
-0.02649584785103798,
-0.047650400549173355,
0.05462377145886421,
0.0019613916520029306,
0.011466369032859802,
-0.02235715277493,
0.015437683090567589,
0.012571428902447224,
0.025489162653684616,
-0.018687637522816658,
-0.019186435267329216,
0.010675814934074879,
0.004947162698954344,
0.0030893238727003336,
-0.03345096856355667,
-0.026792289689183235,
-0.013987012207508087,
-0.008277266286313534,
-0.027829211205244064,
0.0183914415538311,
0.011258328333497047,
0.02708929404616356,
0.001990175573155284,
-0.0270860455930233,
0.04368602856993675,
-0.047991443425416946,
0.020537326112389565,
0.0026342598721385,
-0.011415218003094196,
-0.03031998500227928,
0.01089209970086813,
0.016655823215842247,
-0.006414369679987431,
-0.04379856958985329,
-0.02148098312318325,
-0.01562582701444626,
-0.023554222658276558,
0.007282341830432415,
-0.005202239379286766,
0.03266480937600136,
-0.033453766256570816,
-0.006411819253116846,
-0.02617586776614189,
0.004958088509738445,
-0.0725129172205925,
-0.034302957355976105,
0.01928563229739666,
-0.018516695126891136,
-0.032643985003232956,
0.03475502133369446,
-0.03288796916604042,
-0.02839156799018383,
-0.0044671110808849335,
0.006938910111784935,
0.01386668998748064,
-0.023372609168291092,
0.03352004662156105,
0.0022602148819714785,
0.03318694606423378,
-0.023960087448358536,
-0.05292961746454239,
-0.005967064760625362,
-0.0011736666783690453,
-0.008738788776099682,
0.0281605776399374,
-0.004837898537516594,
0.03317909315228462,
0.01428910717368126,
0.018377214670181274,
0.012895534746348858,
0.05901250243186951,
-0.018356487154960632,
-0.016915995627641678,
-0.04656173288822174,
-0.07337284833192825,
0.03270373493432999,
-0.0227203331887722,
0.012556580826640129,
-0.018590573221445084,
0.014469052664935589,
0.007792237214744091,
0.05650140717625618,
-0.0008779817726463079,
0.02467658370733261,
0.03590495139360428,
-0.023855751380324364,
-0.011680725030601025,
0.00935580674558878,
-0.009377853944897652,
0.03811284527182579,
0.016457343474030495,
-0.014737221412360668,
0.006766957696527243,
0.019950971007347107,
0.0029466403648257256,
-0.1169530600309372,
0.0006965840584598482,
0.0065966444090008736,
-0.018948573619127274,
0.04480323567986488,
-0.06344200670719147,
0.0010880727786570787,
0.018421370536088943,
-0.04339955002069473,
-0.009095771238207817,
-0.07447411864995956,
0.02109231986105442,
0.006282115820795298,
-0.028920071199536324,
0.0006730351014994085,
0.07276985794305801,
-0.002055080607533455,
0.02681870572268963,
-0.0001901906362036243,
-0.02849643863737583,
0.012632269412279129,
-0.052546437829732895,
0.011471878737211227,
0.046422556042671204,
-0.018699858337640762,
-0.04038066044449806,
0.03511644899845123,
-0.02290128916501999,
0.0255851112306118,
0.005197283811867237,
-0.02625221386551857,
0.013048957102000713,
-0.003336505498737097,
-0.0025111285503953695,
-0.02865818701684475,
0.022463174536824226,
-0.0452607087790966,
0.023002199828624725,
-0.014466511085629463,
0.02654855325818062,
0.019018007442355156,
0.011370732448995113,
-0.02795335277915001,
-0.010500307194888592,
0.03432983160018921,
-0.01596982404589653,
-0.032803725451231,
0.04060009866952896,
-0.022873738780617714,
0.03557361662387848,
0.015635013580322266,
0.009629464708268642,
0.014532865956425667,
-0.041230324655771255,
-0.044016554951667786,
-0.04349658638238907,
-0.005973164923489094,
0.06973104178905487,
0.011267425492405891,
-0.030897416174411774,
-0.014709518291056156,
0.004504119977355003,
-0.01348841842263937,
0.0003409773635212332,
0.003940960392355919,
-0.00981944426894188,
0.004942396655678749,
0.005081875715404749,
-0.011069211177527905,
-0.0017296989681199193,
0.04533378407359123,
-0.004150399938225746,
-0.04017719253897667,
0.0002530727651901543,
-0.004495076835155487,
0.02926670014858246,
-0.04454323649406433,
-0.0146871292963624,
-0.003075042273849249,
-0.05430709198117256,
0.039729803800582886,
-0.008212229236960411,
-0.016904274001717567,
0.0014328326797112823,
0.009469999931752682,
0.0029930337332189083,
0.00991059374064207,
0.01361804734915495,
-0.005880745127797127,
-0.009725159965455532,
0.00009872584632830694,
-0.004176926799118519,
0.0024040599819272757,
-0.0012158259050920606,
-0.017386483028531075,
0.022164778783917427,
-0.023328645154833794,
-0.038847751915454865,
0.044366009533405304,
0.018620507791638374,
-0.0209771990776062,
0.02762310765683651,
-0.0029153383802622557,
0.03303541615605354,
-0.009749019518494606,
-0.018039437010884285,
0.013094629161059856,
0.008423484861850739,
-0.0061558885499835014,
0.0579216405749321,
0.027840817347168922,
-0.023239661008119583,
0.031596116721630096,
-0.025388509035110474,
-0.05966349318623543,
0.03541252762079239,
-0.041175246238708496,
-0.03522677347064018,
-0.018476495519280434,
-0.04496197775006294,
0.004665874410420656,
0.0010371749522164464,
0.0009294158662669361,
0.03588610887527466,
-0.05888867750763893,
-0.04252338409423828,
0.035859040915966034,
0.017430702224373817,
0.04031776264309883,
-0.029112763702869415,
0.02740877866744995,
0.034246381372213364,
0.005574900656938553,
0.005555200390517712,
-0.020734908059239388,
0.03987833857536316,
0.027262696996331215,
-0.021324630826711655,
0.00847410224378109,
0.0049491035751998425,
0.010906482115387917,
0.027376137673854828,
-0.017397252842783928,
-0.003061169059947133,
-0.04151638224720955,
0.011673844419419765,
0.0015892351511865854,
-0.014886930584907532,
0.03966374322772026,
0.021900760009884834,
0.09563454985618591,
0.011736392974853516,
0.04273103177547455,
-0.01937013305723667,
-0.016682511195540428,
0.005711700301617384,
0.023672251030802727,
0.020418232306838036,
0.06505750119686127,
-0.028437934815883636,
0.012906585820019245,
0.02768375724554062,
-0.021800683811306953,
-0.020749883726239204,
0.0087242117151618,
0.015375894494354725,
-0.005883741658180952,
-0.02155272290110588,
-0.009469734504818916,
-0.04000918194651604,
-0.01172590535134077,
-0.0334952138364315,
0.058374546468257904,
0.04159364104270935,
0.022189542651176453,
-0.011768633499741554,
-0.005964458454400301,
0.013636589981615543,
0.0687563493847847,
-0.047935787588357925,
-0.04440898820757866,
-0.0034375397954136133,
-0.021150734275579453,
0.028916766867041588,
-0.022326596081256866
] |
<p>So I am wondering what kind of two dimensional Fermi surface is called quasi one dimensional, what is its character? Also, when there are orbital hybridization taking place in lattice site, what are characters of hybridized Fermi surface?</p>
| 9,593 |
[
0.010623635724186897,
-0.03534768894314766,
0.01488147210329771,
-0.0077897245064377785,
-0.0047206757590174675,
0.022772669792175293,
-0.011559896171092987,
-0.04154161363840103,
0.01128885243088007,
-0.047355931252241135,
0.05123962089419365,
0.010943296365439892,
0.052116282284259796,
0.042315524071455,
-0.0017921417020261288,
0.05100046098232269,
-0.0025616188067942858,
-0.0048201982863247395,
-0.05364898592233658,
-0.008577052503824234,
0.020846163854002953,
-0.006656081881374121,
0.01746678166091442,
0.034265484660863876,
-0.004615350626409054,
0.0019969160202890635,
-0.016470221802592278,
0.0036125306505709887,
0.05001934990286827,
0.01931147649884224,
-0.024731269106268883,
-0.07014933973550797,
0.03642299771308899,
-0.024369630962610245,
-0.005657580215483904,
-0.041225701570510864,
-0.03905579447746277,
-0.0364631712436676,
0.003013984765857458,
0.05037432163953781,
-0.00017408169514965266,
-0.07905242592096329,
-0.01148353610187769,
0.04543381184339523,
0.016016444191336632,
0.00007613296475028619,
-0.024003852158784866,
-0.0379488579928875,
0.08146730810403824,
-0.10325127094984055,
0.02285945415496826,
-0.004602739587426186,
0.043131668120622635,
0.005789817776530981,
0.032612111419439316,
0.020270969718694687,
0.048372190445661545,
0.03456888720393181,
-0.03247456252574921,
-0.047654274851083755,
-0.014703619293868542,
-0.025498727336525917,
0.049903180450201035,
-0.00445257592946291,
-0.03251943737268448,
0.026077447459101677,
-0.042439889162778854,
-0.05813402682542801,
-0.009291996248066425,
0.02936854213476181,
-0.01605282537639141,
0.02948545664548874,
-0.009576719254255295,
-0.013805774971842766,
0.02303488738834858,
-0.004325157031416893,
0.01263602264225483,
0.008477181196212769,
0.031962379813194275,
0.017652617767453194,
-0.02523576281964779,
0.009088952094316483,
-0.009174139238893986,
-0.005911917891353369,
-0.0016800868324935436,
-0.005460475105792284,
0.05919472128152847,
-0.019764533266425133,
-0.016240382567048073,
0.03612223640084267,
0.009511468932032585,
0.0072378781624138355,
0.06702139228582382,
-0.004520789720118046,
-0.0328044630587101,
0.022671526297926903,
0.030464651063084602,
0.020551089197397232,
-0.030485309660434723,
-0.04488305374979973,
0.0033303850796073675,
-0.034220609813928604,
0.02373463474214077,
0.054863400757312775,
-0.0027952194213867188,
-0.02563478983938694,
-0.023022186011075974,
0.012475056573748589,
-0.033353786915540695,
0.025734608992934227,
-0.018732847645878792,
0.051980242133140564,
-0.009198679588735104,
0.01492808572947979,
0.029700232669711113,
-0.003999424632638693,
0.019056234508752823,
0.011416664347052574,
0.005650382023304701,
0.08305583894252777,
0.007543133106082678,
-0.011946503072977066,
0.02898089401423931,
-0.02320820651948452,
-0.08977309614419937,
0.03780734911561012,
0.013446829281747341,
0.013112293556332588,
-0.018502209335565567,
0.019643688574433327,
-0.02595246583223343,
-0.01157352700829506,
0.035534728318452835,
0.0015801329864189029,
0.05387922376394272,
-0.019065389409661293,
-0.09127210080623627,
-0.046147629618644714,
0.02822229266166687,
-0.02676020935177803,
0.005346501246094704,
-0.07459286600351334,
0.04677698388695717,
0.017790082842111588,
0.0612185113132,
0.025705967098474503,
0.04640169441699982,
-0.003665641415864229,
0.02233930490911007,
0.0006941196043044329,
-0.010181440971791744,
-0.021611155942082405,
0.026187697425484657,
-0.05590298771858215,
0.012806336395442486,
-0.0020831734873354435,
0.03510867431759834,
0.012509948574006557,
0.003929527942091227,
-0.021848516538739204,
0.06142951920628548,
-0.030460620298981667,
-0.007840678095817566,
0.012824716977775097,
0.00036307511618360877,
-0.03863690793514252,
0.08020161837339401,
-0.016140762716531754,
0.019140588119626045,
0.08564431220293045,
-0.030865177512168884,
-0.009140065871179104,
0.01366187259554863,
0.0544096864759922,
0.004603460896760225,
-0.02586960978806019,
-0.06124231219291687,
-0.05269744619727135,
0.020164700224995613,
-0.028463425114750862,
-0.04521384835243225,
-0.04473204165697098,
0.010898139327764511,
0.01575232855975628,
-0.013743807561695576,
0.04105020686984062,
-0.0016191010363399982,
-0.029025902971625328,
0.004793652333319187,
-0.03406204283237457,
-0.028057647868990898,
-0.0077674840576946735,
-0.042876727879047394,
-0.01635882444679737,
0.00619077542796731,
0.03297959640622139,
0.0075502474792301655,
-0.006499383132904768,
-0.03154348209500313,
-0.01612153649330139,
-0.046157319098711014,
0.042162343859672546,
0.010013947263360023,
-0.0008573568775318563,
0.032675594091415405,
0.014993769116699696,
0.0241756159812212,
-0.03754693269729614,
0.04221435636281967,
-0.06847038865089417,
0.010871612466871738,
-0.0014126168098300695,
-0.03556106239557266,
0.029122984036803246,
0.025221718475222588,
0.027180030941963196,
-0.005861006211489439,
-0.002763391239568591,
-0.05232325568795204,
0.006635438185185194,
-0.00028390271472744644,
0.05186318978667259,
0.05209050700068474,
0.013870458118617535,
0.002620240906253457,
-0.013583078980445862,
0.011406715027987957,
0.009499439038336277,
-0.004945183638483286,
-0.01355309970676899,
-0.05090312659740448,
0.005320438649505377,
0.05517569184303284,
0.023799510672688484,
-0.021523507311940193,
0.019424444064497948,
0.019703341647982597,
0.03749225661158562,
0.06932138651609421,
-0.009853791445493698,
-0.06495831161737442,
0.0023085023276507854,
0.030065270140767097,
-0.012278323993086815,
-0.01664116233587265,
-0.0036517311818897724,
0.012064594775438309,
0.032909758388996124,
-0.00003268942964496091,
-0.050055574625730515,
-0.025815987959504128,
0.04229125753045082,
-0.0050269728526473045,
-0.01624016836285591,
-0.0056971232406795025,
-0.04581766575574875,
0.02707829512655735,
-0.024078916758298874,
0.024207191541790962,
0.02704101987183094,
-0.018538422882556915,
0.02568107843399048,
-0.021617231890559196,
0.006140401121228933,
0.006761658471077681,
0.008621275424957275,
-0.026420708745718002,
-0.04466613009572029,
0.04135611653327942,
0.00760052353143692,
0.011838773265480995,
-0.01854212023317814,
0.0033097579143941402,
0.003189532086253166,
0.013331891968846321,
0.04874396324157715,
0.02206118032336235,
0.03236823529005051,
-0.044170428067445755,
-0.053370147943496704,
0.013745570555329323,
-0.027239248156547546,
-0.010051512159407139,
0.009445005096495152,
-0.03830396384000778,
0.04648114740848541,
-0.06075483188033104,
-0.009204993024468422,
0.00723084295168519,
-0.006041851360350847,
0.004062441643327475,
0.004650878254324198,
-0.006602421402931213,
-0.04201440140604973,
-0.0007645930163562298,
-0.026189206168055534,
0.0273414496332407,
0.016892636194825172,
-0.027122819796204567,
0.016882063820958138,
-0.005434681195765734,
-0.017070185393095016,
-0.009163137525320053,
-0.001345684053376317,
-0.013888564892113209,
-0.006512025836855173,
-0.026743214577436447,
0.030306056141853333,
-0.03665996715426445,
0.023421144112944603,
0.05060064420104027,
-0.01973757892847061,
0.013165682554244995,
-0.029160019010305405,
-0.024662846699357033,
0.023606164380908012,
-0.013247434981167316,
0.008900312706828117,
-0.03400575369596481,
-0.060478389263153076,
0.04890359565615654,
0.0026741812471300364,
-0.043512262403964996,
-0.015599419362843037,
0.011362997815012932,
-0.01668461039662361,
-0.011318052187561989,
0.040154051035642624,
0.009482324123382568,
0.02081015706062317,
0.022621439769864082,
0.027882125228643417,
0.038475655019283295,
0.06350184977054596,
0.008158872835338116,
-0.027683185413479805,
0.01985415443778038,
0.0014048749580979347,
0.02453196607530117,
0.03400658443570137,
-0.019638093188405037,
-0.04036501795053482,
0.008650990203022957,
-0.0035244892351329327,
0.0035129180178046227,
0.06305713951587677,
-0.026385722681879997,
0.03281000629067421,
-0.008842040784657001,
0.032978035509586334,
-0.004332449287176132,
0.022703204303979874,
0.01260424591600895,
-0.005660949274897575,
-0.0006971810944378376,
0.036944642663002014,
0.02833179570734501,
-0.01520271971821785,
0.0047483607195317745,
0.017630811780691147,
0.04941239953041077,
-0.031126918271183968,
-0.018992474302649498,
0.06134336069226265,
-0.014283346012234688,
-0.001123953377828002,
-0.04487341269850731,
-0.02439071610569954,
0.040726833045482635,
0.04382025822997093,
0.05189171060919762,
0.019931433722376823,
0.004895802121609449,
-0.018594618886709213,
-0.03438366577029228,
-0.00934775359928608,
-0.0006671235896646976,
0.073944091796875,
-0.021828074008226395,
0.016928885132074356,
0.010014296509325504,
0.03109167329967022,
-0.021675189957022667,
-0.0009725046693347394,
-0.058204781264066696,
0.0011204738402739167,
-0.02200896665453911,
0.016436055302619934,
-0.024195002391934395,
-0.009776736609637737,
-0.0061785136349499226,
-0.0016501197824254632,
-0.02329176478087902,
-0.003120417706668377,
-0.019577832892537117,
-0.054511234164237976,
0.04079151153564453,
-0.01027651410549879,
-0.013322094455361366,
-0.03443972021341324,
0.06050220504403114,
0.023283295333385468,
-0.03288809955120087,
-0.009306482039391994,
0.017510108649730682,
-0.014418015256524086,
0.0024842002894729376,
0.01940280571579933,
0.004861533176153898,
0.0018071052618324757,
0.017172064632177353,
0.011821819469332695,
0.029515249654650688,
0.00018317288777325302,
-0.03609857335686684,
0.0016384711489081383,
0.0870528444647789,
0.03091301955282688,
0.014997807331383228,
0.00004343264299677685,
-0.038111284375190735,
-0.021996572613716125,
-0.035614073276519775,
0.031099852174520493,
-0.006800021510571241,
0.014362978748977184,
0.06098945811390877,
0.001814332907088101,
-0.04194915294647217,
0.04586924612522125,
0.06806487590074539,
0.04203709587454796,
-0.004334456752985716,
-0.03606528416275978,
-0.03741949796676636,
-0.04601731523871422,
-0.01513319555670023,
0.03603938966989517,
-0.017866648733615875,
-0.03656404837965965,
0.04170050844550133,
0.025996478274464607,
0.004095835145562887,
-0.04058445990085602,
-0.03967365622520447,
-0.0202654879540205,
0.014247963204979897,
-0.007400537841022015,
0.0014477950753644109,
-0.007446983363479376,
0.03157981112599373,
0.01597318984568119,
0.020597510039806366,
-0.003471702802926302,
-0.040580883622169495,
0.007201345171779394,
0.02994452975690365,
0.027384482324123383,
-0.006297483574599028,
-0.029155151918530464,
-0.04577332362532616,
0.01839713752269745,
0.021993957459926605,
0.009825171902775764,
0.0003074764390476048,
-0.026376988738775253,
-0.02533043920993805,
-0.05639836564660072,
0.021886317059397697,
-0.00009129948739428073,
0.0019516528118401766,
0.028103459626436234,
0.020248478278517723,
-0.04628119617700577,
0.013721724972128868,
-0.012950276955962181,
-0.000897794496268034,
-0.011169430799782276,
0.030512068420648575,
0.00986152421683073,
0.020307112485170364,
0.017894277349114418,
0.029622744768857956,
-0.015464670024812222,
-0.09083182364702225,
0.0036045927554368973,
0.04730316251516342,
0.038601044565439224,
0.02309524081647396,
-0.04433727636933327,
-0.031839121133089066,
-0.02153218910098076,
0.009030364453792572,
0.015527305193245411,
-0.018361113965511322,
-0.011083449237048626,
0.04733024910092354,
0.0109745217487216,
-0.02867397852241993,
0.017495086416602135,
0.03129452094435692,
-0.016767384484410286,
-0.015143424272537231,
-0.04191119968891144,
0.02909030392765999,
-0.03874737396836281,
0.010777861811220646,
0.01194413285702467,
-0.00341475079767406,
-0.045394472777843475,
0.0362105555832386,
-0.016831284388899803,
0.028399504721164703,
-0.024742048233747482,
-0.009636994451284409,
-0.045021798461675644,
0.03967759385704994,
0.01466591376811266,
-0.028167838230729103,
-0.010991081595420837,
-0.013743104413151741,
-0.006120996084064245,
-0.005652701482176781,
-0.014499739743769169,
-0.04213304817676544,
0.005885324906557798,
0.05377712845802307,
0.025462061166763306,
0.022471603006124496,
-0.03995642066001892,
-0.007639737334102392,
0.008797802962362766,
-0.07760882377624512,
0.0508577823638916,
-0.015005736611783504,
-0.012210750952363014,
0.0258414838463068,
-0.08491358160972595,
-0.001932629500515759,
0.029501257464289665,
0.05247218906879425,
-0.015285291709005833,
-0.009730344638228416,
0.040924664586782455,
0.030148014426231384,
0.010513090528547764,
-0.09538169950246811,
-0.05131350830197334,
-0.007863732986152172,
0.007905259728431702,
-0.04434029757976532,
-0.01142062433063984,
0.003251764690503478,
-0.01275233831256628,
0.005793491378426552,
0.041458070278167725,
0.011799300089478493,
-0.015745220705866814,
-0.05935388058423996,
0.028338095173239708,
-0.007079931441694498,
0.05592595040798187,
0.027840349823236465,
-0.022886281833052635,
-0.0014904538402333856,
-0.006450043525546789,
0.016752056777477264,
-0.0019054891308769584,
0.018305404111742973,
-0.032499320805072784,
0.01039815228432417,
-0.054211389273405075,
-0.018772371113300323,
0.022243162617087364,
-0.006465502083301544,
-0.0035944166593253613,
0.019545797258615494,
0.009043889120221138,
0.01768389157950878,
0.0016588455764576793,
0.009833321906626225,
-0.008877744898200035,
0.03350198641419411,
0.012473823502659798,
-0.012594558298587799,
-0.05090475454926491,
-0.02720252424478531,
-0.00012440542923286557,
-0.013958530500531197,
0.014282927848398685,
0.05525554344058037,
0.062645323574543,
-0.006036905571818352,
-0.00631721131503582,
0.04102528840303421,
-0.0642443522810936,
-0.04572087526321411,
-0.010835106484591961,
0.01658567413687706,
0.04953379184007645,
0.049158550798892975,
0.0032627275213599205,
-0.03454108536243439,
-0.027686890214681625,
0.014566950500011444,
0.0008751287823542953,
-0.015096490271389484,
0.009093482978641987,
0.03173364698886871,
-0.008428364060819149,
-0.025781797245144844,
-0.012775450944900513,
-0.024023931473493576,
0.02267458476126194,
-0.03966088220477104,
0.02895405888557434,
-0.03140570595860481,
0.00019862217595800757,
0.02455991506576538,
0.06230247765779495,
-0.008247984573245049,
0.034024160355329514,
0.04494445398449898,
0.024188142269849777,
0.026382282376289368,
0.008443295024335384,
-0.03598994016647339,
0.10538940876722336,
-0.01309953536838293,
0.039884041994810104,
0.02613699994981289,
-0.00659949379041791,
0.039095669984817505,
0.03141838312149048,
0.01656593382358551,
-0.036142416298389435,
-0.00035837196628563106,
-0.02007170021533966,
0.037723299115896225,
0.06142748147249222,
-0.004549255128949881,
-0.008985597640275955,
0.03239039331674576,
0.030067559331655502,
-0.005626121070235968,
0.010950365103781223,
0.01871493272483349,
-0.03723665326833725,
-0.015461951494216919,
-0.03603142127394676,
-0.05110788345336914,
0.007165615446865559,
-0.03005945309996605,
-0.010830957442522049,
0.01977270282804966,
-0.04379304125905037,
0.02735288441181183,
0.018407007679343224,
0.026084989309310913,
0.002575012855231762,
0.043917007744312286,
-0.01328654121607542,
0.05211792141199112,
0.010834543034434319,
-0.01139650959521532,
0.12621819972991943,
0.06271692365407944,
-0.000034398792195133865,
-0.09874428063631058,
-0.0009904083563014865,
0.0025950295384973288,
0.03796800598502159,
-0.017317282035946846,
-0.011563307605683804,
0.002470022067427635,
0.009000938385725021,
0.009747412987053394,
0.07977661490440369,
-0.04390750452876091,
0.022045550867915154,
-0.009273690171539783,
-0.011966930702328682,
-0.051018163561820984,
0.004214235581457615,
-0.014009666629135609,
-0.03924427181482315,
0.0051452405750751495,
-0.03518154099583626,
-0.0016025630757212639,
-0.007787656970322132,
0.025464456528425217,
-0.04901695251464844,
-0.03419066593050957,
0.0608353428542614,
0.02905578911304474,
-0.04291459172964096,
-0.010347256436944008,
0.023934144526720047,
-0.0036809113807976246,
-0.0028309240005910397,
0.029679473489522934,
0.018838107585906982,
0.022316336631774902,
-0.000006533804025821155,
0.07198824733495712,
0.009584847837686539,
-0.023088587448000908,
0.010836269706487656,
0.006527438759803772,
-0.02574562467634678,
0.009152689017355442,
0.003926524892449379,
0.005839714780449867,
-0.03323518857359886,
0.01182415708899498,
-0.005904000718146563,
0.00757569819688797,
0.015764907002449036,
0.011328916996717453,
-0.012146629393100739,
-0.033738311380147934,
0.04551628977060318,
-0.02480694279074669,
-0.004302715416997671,
-0.05026743561029434,
0.0051006958819925785,
-0.0349208302795887,
0.027955716475844383,
-0.025339225307106972,
-0.03427775949239731,
0.05084773525595665,
0.007964241318404675,
0.01649794541299343,
0.013885701075196266,
-0.0247041005641222,
-0.013656729832291603,
-0.008911374025046825,
-0.016288749873638153,
-0.0350513681769371,
-0.01972811296582222,
-0.006450215820223093,
0.0446208119392395,
0.01865372806787491,
-0.04121604561805725,
0.00619152607396245,
-0.027590744197368622,
0.011965571902692318,
-0.012428471818566322,
-0.003859349060803652,
-0.022631477564573288,
-0.011703887954354286,
0.012928600423038006,
0.03199337422847748,
0.00811434630304575,
0.016826918348670006,
0.0016002818010747433,
-0.011880859732627869,
0.006450112909078598,
-0.033383190631866455,
-0.020055454224348068,
-0.018297797068953514,
-0.021822812035679817,
0.008614580146968365,
-0.051947806030511856,
-0.007644908502697945,
0.031994808465242386,
-0.04725511744618416,
0.006114104762673378,
0.026396874338388443,
-0.04784829542040825,
0.00940747745335102,
0.00948542170226574,
-0.008396572433412075,
0.000009046758350450546,
0.011351973749697208,
-0.002679141005501151,
-0.04549618437886238,
-0.06294989585876465,
-0.018332980573177338,
-0.0016545592807233334,
-0.00015331734903156757,
0.018389087170362473,
-0.057882584631443024,
-0.0005098761175759137,
0.010356293059885502,
-0.02047429233789444,
-0.05438937246799469,
-0.010000412352383137,
-0.018101153895258904,
0.022760719060897827,
0.02622157707810402,
0.026926403865218163,
0.02840483747422695,
-0.008887997828423977,
-0.013882477767765522,
0.005143317859619856,
-0.004627319052815437,
0.055775318294763565,
-0.0194596778601408,
0.026671092957258224,
0.0024707545526325703,
0.015312796458601952,
0.052940186113119125,
-0.03339196741580963,
0.03723684698343277,
0.026085946708917618,
-0.05979226902127266,
-0.046465035527944565,
0.04117720574140549,
-0.003776217345148325,
0.03539702668786049,
-0.002859419910237193,
-0.03200913965702057,
-0.04743388667702675,
0.03331763669848442,
-0.04172011837363243,
-0.023009266704320908,
0.00589669169858098,
0.015222328715026379,
-0.025918500497937202,
-0.06396632641553879,
-0.05247538164258003,
-0.007984085008502007,
-0.009475531056523323,
0.02223983407020569,
0.016895152628421783,
-0.014189395122230053,
-0.015881802886724472,
-0.034228578209877014,
-0.007877454161643982,
0.040953997522592545,
0.04285208508372307,
0.004655575379729271,
0.02556154876947403,
0.03190087899565697,
-0.02232619933784008,
0.011929569765925407,
0.01972736418247223,
0.003990751225501299,
-0.05446220561861992,
-0.03844722360372543,
0.01753576658666134,
-0.025476204231381416,
0.0350184328854084,
-0.04898962005972862,
-0.030131911858916283,
0.020995594561100006,
-0.06896258890628815,
-0.008494270965456963,
-0.0029366291128098965,
-0.052822984755039215,
-0.03226565569639206,
-0.013002678751945496,
-0.009641092270612717,
0.058643463999032974,
0.006178128533065319,
0.031044993549585342,
0.037865836173295975,
0.01849674992263317,
-0.020115461200475693,
0.005183476023375988,
0.011994688771665096,
-0.00796504132449627,
-0.024628501385450363,
-0.021492850035429,
0.05803700536489487,
-0.02803669311106205,
-0.008030775003135204,
0.031418923288583755,
0.02166987583041191,
-0.03630722686648369,
0.013514025136828423,
0.023868931457400322,
-0.01586415432393551,
0.010509981773793697,
-0.0061514712870121,
-0.042108695954084396,
-0.031434379518032074,
0.0011661653406918049,
0.010569453239440918,
0.020681200549006462,
0.013844477944076061,
-0.01371768955141306,
0.011723525822162628,
-0.04844432324171066,
-0.002320053754374385,
0.052793487906455994,
-0.0186361875385046,
0.023365924134850502,
-0.030313190072774887,
-0.006118560675531626,
0.022558394819498062,
-0.04422260820865631,
0.019194046035408974,
-0.04341369494795799,
-0.011419517919421196,
-0.009984028525650501,
-0.0035353272687643766,
0.0562894344329834,
0.047601982951164246,
0.013240702450275421,
-0.06380701065063477,
0.03975182771682739,
0.015448283404111862,
-0.06454047560691833,
-0.03096066229045391,
-0.024102799594402313,
0.011366546154022217,
0.01240194495767355,
0.023351311683654785,
-0.031864091753959656,
0.002776307752355933,
0.03381634131073952,
-0.006780981086194515,
0.009718162007629871,
-0.03303183987736702,
-0.028436891734600067,
0.0029202415607869625,
-0.01862972415983677,
0.017529809847474098,
-0.02583956904709339,
-0.005641163792461157,
-0.006045013666152954,
-0.021517839282751083,
-0.0030286067631095648,
0.025246363133192062,
0.07274187356233597,
0.01869392581284046,
-0.009920718148350716,
-0.01919407583773136,
-0.006144432816654444,
0.016596367582678795,
-0.019574061036109924,
0.0014839493669569492,
-0.011005517095327377,
0.003753473050892353,
0.022429920732975006,
0.011032627895474434,
0.006733276415616274,
0.029744554311037064,
0.06487071514129639,
0.0019649912137538195,
-0.018586091697216034,
-0.015459991060197353,
-0.05931743606925011,
0.031717754900455475,
0.010053923353552818,
-0.0066728657111525536,
0.09114212542772293,
-0.028826145455241203,
0.011048116721212864,
0.04213197901844978,
-0.007105827331542969,
-0.010644198395311832,
0.034461475908756256,
-0.017928102985024452,
0.019703334197402,
0.015024389140307903,
-0.014325426891446114,
0.03868379071354866,
-0.04361852630972862,
-0.026310352608561516,
0.048591434955596924,
0.008787151426076889,
-0.016024520620703697,
0.04706374183297157,
0.012412081472575665,
0.028230411931872368,
-0.008787703700363636,
0.0020797993056476116,
-0.012715336866676807,
0.016852421686053276,
0.04201751574873924,
0.042958665639162064,
0.007545251864939928,
0.0374445766210556,
0.01808939315378666,
0.0011552984360605478,
-0.01991397701203823,
0.028580674901604652,
0.023765601217746735,
0.018136247992515564,
-0.05646059662103653,
0.007715362124145031,
0.08091817796230316,
-0.0005513721844181418,
-0.017854856327176094,
0.021044377237558365,
-0.04542521387338638,
0.08156491070985794,
-0.057507991790771484,
0.006454607471823692,
-0.013809213414788246,
-0.009890834800899029,
-0.0644867792725563,
-0.020447485148906708,
0.029169006273150444,
0.08057444542646408,
0.0011116977548226714,
-0.04328541085124016,
-0.03508647903800011,
0.031231243163347244,
0.04496344178915024,
-0.06812672317028046,
0.015217620879411697,
0.0035311165265738964,
-0.00017281633336097002,
0.002876471960917115,
0.027525102719664574,
-0.033197883516550064,
0.030953213572502136,
0.042045921087265015,
0.02579455077648163,
0.026908399537205696,
0.01714344136416912,
-0.016081862151622772,
-0.011687582358717918,
0.035360489040613174,
-0.0670536607503891,
-0.020102303475141525,
0.006029051262885332,
0.010669938288629055,
-0.032867785543203354,
0.0075243329629302025
] |
<p>I'm studying the introduction of flavour degrees of freedom in the AdS/CFT correspondence and now I'm supposed to calculate the mass spectrum of mesons in the <a href="http://www.google.com/search?as_q=coulomb+branch" rel="nofollow">Coulomb branch</a>. I have searched the concept but I always find very long and complex explanations. Could anyone explain it in a direct way, pointing out some physical intuition?</p>
| 9,594 |
[
0.03188273310661316,
-0.026668459177017212,
-0.02687292918562889,
-0.04609912633895874,
0.026676196604967117,
0.055048875510692596,
-0.002675964729860425,
-0.01283821277320385,
0.010596854612231255,
-0.04180442541837692,
0.018372664228081703,
0.011831933632493019,
0.05368921905755997,
0.028399687260389328,
-0.012238428927958012,
0.01897139847278595,
-0.01088267657905817,
-0.005110749509185553,
-0.002570981625467539,
-0.04489661380648613,
0.0105860261246562,
0.04284422844648361,
0.000977229094132781,
0.00025581486988812685,
0.018492408096790314,
0.045944973826408386,
0.042085595428943634,
-0.0005705524235963821,
0.027799904346466064,
0.02850169502198696,
-0.0318329744040966,
-0.03843842074275017,
0.024754337966442108,
0.012087002396583557,
0.02500302530825138,
-0.024283070117235184,
-0.015459095127880573,
-0.029265038669109344,
-0.003116755513474345,
0.036238234490156174,
-0.05988467484712601,
-0.0343628004193306,
-0.021823087707161903,
0.014091141521930695,
-0.021973172202706337,
-0.017757372930645943,
-0.008085029199719429,
-0.012394493445754051,
0.07023759186267853,
-0.03950497508049011,
0.09817306697368622,
0.026300443336367607,
0.019533181563019753,
-0.008233950473368168,
-0.00394672155380249,
-0.01694808341562748,
0.031099466606974602,
0.030307205393910408,
0.0051017748191952705,
-0.06146414205431938,
-0.038997355848550797,
-0.016319656744599342,
-0.02201015315949917,
-0.008792883716523647,
0.014759735204279423,
0.03229380026459694,
0.006565971300005913,
0.008619533851742744,
0.043966181576251984,
0.013970702886581421,
0.03988565504550934,
-0.0037150827702134848,
-0.015625393018126488,
-0.03666326403617859,
0.0326894111931324,
-0.02150137908756733,
0.016211310401558876,
0.015667280182242393,
0.04232865571975708,
0.015250328928232193,
-0.023345820605754852,
0.020937515422701836,
0.02072405442595482,
0.025733351707458496,
-0.0029393411241471767,
-0.010371554642915726,
0.07630996406078339,
-0.03231516107916832,
-0.007537580095231533,
0.08197019249200821,
-0.006659202743321657,
0.01494699064642191,
0.02117229625582695,
0.007544750347733498,
-0.03495008870959282,
0.03132842853665352,
-0.002695681294426322,
0.041405074298381805,
-0.010180468671023846,
0.0019245656440034509,
-0.02834470011293888,
-0.011957679875195026,
0.022668635472655296,
0.1104317381978035,
-0.011832638643682003,
0.03245830908417702,
-0.002006490947678685,
0.00538469897583127,
0.0021289903670549393,
-0.020871350541710854,
-0.016494449228048325,
-0.021939098834991455,
-0.006750157102942467,
-0.015486284159123898,
-0.001640478614717722,
-0.03384337201714516,
0.025343477725982666,
-0.03923961892724037,
0.058279093354940414,
0.051161181181669235,
0.059001315385103226,
-0.007518756669014692,
0.018458126112818718,
-0.05267539247870445,
-0.04325845465064049,
-0.030095532536506653,
0.04035450145602226,
-0.013625949621200562,
-0.017411595210433006,
0.02084675244987011,
-0.05076731741428375,
-0.012861073948442936,
0.010577444918453693,
-0.020900122821331024,
0.007065426092594862,
-0.04681394249200821,
-0.08600541204214096,
-0.03392653539776802,
0.016414370387792587,
-0.013193967752158642,
-0.010037614032626152,
-0.05901605263352394,
0.005765572655946016,
-0.0232562068849802,
0.07185836136341095,
-0.011281793005764484,
0.009339247830212116,
-0.03440745547413826,
0.04603084921836853,
0.033827055245637894,
-0.026966407895088196,
0.013669406995177269,
-0.043453529477119446,
-0.014543640427291393,
-0.028264345601201057,
-0.06834441423416138,
0.0419900044798851,
0.047638773918151855,
-0.005480766762048006,
-0.014704085886478424,
0.044180728495121,
-0.04096851125359535,
-0.01919565349817276,
0.00405582319945097,
0.0014436189085245132,
-0.04250456020236015,
0.07103170454502106,
0.015399865806102753,
-0.02216363325715065,
0.03826630115509033,
-0.013172181323170662,
0.024317078292369843,
0.047640182077884674,
0.023094162344932556,
0.027615798637270927,
-0.013537437655031681,
-0.022165870293974876,
-0.013168917037546635,
-0.00956578366458416,
-0.029457025229930878,
-0.018203211948275566,
-0.04084596037864685,
-0.04938847944140434,
0.012741250917315483,
-0.023275544866919518,
0.006519475486129522,
-0.019057493656873703,
-0.01614299602806568,
-0.0011776661267504096,
-0.05986486375331879,
0.01009492389857769,
-0.09705620259046555,
0.025646695867180824,
-0.03481956571340561,
0.004025487694889307,
0.04282313585281372,
-0.00985677819699049,
-0.010846384800970554,
-0.019017450511455536,
-0.051803238689899445,
0.009550786577165127,
0.026388417929410934,
0.013037637807428837,
-0.00517310481518507,
0.01996074616909027,
0.018980180844664574,
-0.01566927134990692,
-0.0062534138560295105,
0.01872887834906578,
0.0017237868160009384,
-0.032990939915180206,
-0.005741491913795471,
-0.013406410813331604,
0.009868807159364223,
0.010610786266624928,
0.016937322914600372,
-0.014648130163550377,
-0.008490650914609432,
0.012256160378456116,
0.05767480656504631,
-0.016338983550667763,
0.047157566994428635,
0.06502353399991989,
0.024835126474499702,
-0.00644401740282774,
0.04369538277387619,
0.018230170011520386,
-0.0033049085177481174,
-0.01121708657592535,
-0.028559189289808273,
-0.02010047249495983,
-0.021721195429563522,
0.03244415670633316,
0.045107536017894745,
-0.022332167252898216,
-0.029215136542916298,
0.03550810366868973,
0.04096098989248276,
0.022930799052119255,
-0.00869970303028822,
-0.02692594937980175,
-0.0236908420920372,
0.017805567011237144,
0.0032996549271047115,
-0.02270703762769699,
-0.027583926916122437,
0.025920530781149864,
0.02440113201737404,
0.008359802886843681,
0.0034976298920810223,
-0.029711276292800903,
0.029411548748612404,
-0.041645072400569916,
-0.019074417650699615,
0.010068533942103386,
-0.03033907152712345,
0.05115559324622154,
-0.01957838237285614,
0.04910692945122719,
0.03710685297846794,
-0.04202074557542801,
0.004197617992758751,
0.002325922017917037,
-0.011836303398013115,
-0.00016738164413254708,
0.0119185084477067,
0.016366567462682724,
-0.016258666291832924,
0.018017631024122238,
-0.07723885029554367,
0.03906778246164322,
-0.012086955830454826,
-0.04814543202519417,
-0.04100701957941055,
0.008547226898372173,
0.04372186213731766,
-0.002997196279466152,
0.04686949402093887,
-0.013208197429776192,
-0.029632680118083954,
0.023648226633667946,
-0.005080363713204861,
0.009017230942845345,
0.04568582400679588,
-0.047205567359924316,
0.027413276955485344,
-0.05859990045428276,
0.002938786055892706,
0.023500729352235794,
-0.033361006528139114,
0.03732491657137871,
-0.0015221044886857271,
-0.0320761613547802,
-0.00821565929800272,
-0.008814102970063686,
0.01342653576284647,
0.024389179423451424,
-0.05971739441156387,
0.025603430345654488,
0.03958390653133392,
0.0042768605053424835,
-0.001302291639149189,
0.020262710750102997,
-0.05852441117167473,
-0.051486071199178696,
-0.03429979085922241,
0.010477169416844845,
-0.01507281418889761,
-0.02744055539369583,
0.05210740864276886,
-0.015433140099048615,
-0.012956785969436169,
0.004147698637098074,
-0.04994460567831993,
-0.040877196937799454,
0.025553807616233826,
0.03181009367108345,
0.027127735316753387,
0.029000835493206978,
-0.039027296006679535,
0.10039995610713959,
0.029822155833244324,
-0.040641043335199356,
-0.0011703574564307928,
0.0006950274109840393,
-0.001012111664749682,
-0.002568303607404232,
0.042863134294748306,
0.028165679425001144,
-0.01572440192103386,
-0.0056051029823720455,
0.057155441492795944,
0.06310198456048965,
0.02784484252333641,
-0.009309438988566399,
-0.021036138758063316,
0.0110919289290905,
-0.019958006218075752,
0.012565516866743565,
0.03599505499005318,
-0.02029031701385975,
-0.03136958181858063,
0.004179045557975769,
0.007421671878546476,
0.01727444678544998,
0.030165940523147583,
-0.07047896832227707,
0.04363108053803444,
0.024183470755815506,
-0.002709216671064496,
0.021699372678995132,
0.03877917304635048,
-0.028774365782737732,
-0.04129504784941673,
0.02304128184914589,
0.030634360387921333,
0.026150956749916077,
-0.013470552861690521,
-0.027417095378041267,
0.037568528205156326,
0.026409095153212547,
-0.023449501022696495,
-0.017203183844685555,
-0.014154971577227116,
-0.013305140659213066,
-0.03377690538764,
-0.028367863968014717,
-0.05669920891523361,
0.020995279774069786,
0.04047536477446556,
0.00010868304525502026,
-0.007330103777348995,
-0.052924610674381256,
-0.007761274930089712,
-0.057573094964027405,
0.02646001987159252,
0.02613597735762596,
0.05750538781285286,
-0.02349053882062435,
0.06213889271020889,
0.01482210960239172,
-0.0023504123091697693,
-0.017273809760808945,
-0.004299751948565245,
-0.08253144472837448,
0.03478386625647545,
-0.010196060873568058,
0.007302225101739168,
-0.02923893928527832,
-0.02406981959939003,
-0.03020452708005905,
0.004728008061647415,
-0.044921960681676865,
-0.0018293459434062243,
-0.0020895551424473524,
-0.01938539370894432,
0.026702942326664925,
-0.028523599728941917,
-0.007631270214915276,
-0.028618114069104195,
0.023740017786622047,
0.0982169583439827,
-0.022290578112006187,
0.017569268122315407,
0.01833985187113285,
-0.039194319397211075,
-0.007737844251096249,
-0.0226411335170269,
0.04252314195036888,
0.03489062190055847,
0.04891527444124222,
0.036173559725284576,
-0.013137060217559338,
-0.029266133904457092,
0.017481081187725067,
0.0043971179984509945,
0.051793430000543594,
-0.024171818047761917,
-0.03235958144068718,
0.014783179387450218,
-0.05572237819433212,
-0.021552326157689095,
0.014869890175759792,
0.037932172417640686,
-0.004696666728705168,
0.03006892465054989,
0.03573710843920708,
0.023707961663603783,
-0.028896285220980644,
0.0454929918050766,
0.08545143902301788,
0.03367414325475693,
-0.029568282887339592,
-0.03625667095184326,
0.03184593841433525,
0.010069537907838821,
0.02835426852107048,
-0.0063762180507183075,
-0.018001291900873184,
-0.034167442470788956,
0.01769167371094227,
0.008293571881949902,
-0.0086611183360219,
-0.0391860194504261,
-0.006361589767038822,
0.008989660069346428,
0.03504813089966774,
-0.010218746028840542,
0.0008509179460816085,
0.03366123512387276,
0.0143373878672719,
0.01965366303920746,
0.02798529900610447,
0.022983472794294357,
-0.04016578942537308,
-0.000007967474630277138,
0.027067245915532112,
0.025611350312829018,
0.012003403156995773,
-0.010067716240882874,
-0.03213309869170189,
0.014253592118620872,
0.03827062249183655,
-0.011517636477947235,
0.03629579022526741,
-0.01119972113519907,
0.04008178785443306,
-0.031663667410612106,
0.0014395570615306497,
-0.02741122990846634,
0.04586251452565193,
0.0011634697439149022,
-0.02802884951233864,
-0.027627702802419662,
0.0010960918152704835,
-0.011020906269550323,
0.0325891338288784,
-0.000676593801472336,
0.03447120264172554,
0.017269061878323555,
0.010444155894219875,
0.018431270495057106,
0.0168133694678545,
-0.011359011754393578,
-0.0628257691860199,
-0.0056969402357935905,
-0.022599095478653908,
0.0030949432402849197,
0.01846703700721264,
-0.037819236516952515,
-0.03461334481835365,
-0.010563201270997524,
-0.0005491290357895195,
0.037966951727867126,
-0.021453702822327614,
-0.08072275668382645,
0.051184989511966705,
0.052653197199106216,
-0.020519079640507698,
0.027004331350326538,
-0.0054941908456385136,
-0.0444377101957798,
-0.009076885879039764,
0.012154953554272652,
0.060669317841529846,
0.01790786348283291,
-0.005922039970755577,
-0.029797008261084557,
-0.0032958986703306437,
-0.04472111910581589,
0.023157428950071335,
-0.01061377115547657,
0.031666100025177,
-0.0013747878838330507,
-0.014583795331418514,
-0.05071374773979187,
0.03759925439953804,
-0.02312534488737583,
-0.024597052484750748,
-0.01644597388803959,
0.021148348227143288,
0.011377457529306412,
-0.015372502617537975,
0.0547521710395813,
-0.02742057852447033,
-0.01157439686357975,
0.009415547363460064,
-0.011828556656837463,
0.003188125556334853,
-0.04515868425369263,
-0.004881138447672129,
0.019608231261372566,
-0.0666264146566391,
0.01696319319307804,
-0.018886318430304527,
-0.01913895271718502,
-0.015731187537312508,
-0.06966764479875565,
-0.05595123767852783,
0.027850976213812828,
-0.014511484652757645,
0.029889006167650223,
-0.008955198340117931,
0.012060354463756084,
-0.01658342219889164,
-0.006466111168265343,
-0.07681704312562943,
-0.04699299484491348,
0.02774510346353054,
0.034271176904439926,
-0.048007141798734665,
-0.007154826074838638,
-0.024263078346848488,
0.0022658028174191713,
-0.025597000494599342,
-0.009863345883786678,
0.04724634438753128,
-0.05588774383068085,
-0.004246836993843317,
0.05708140879869461,
0.03082237020134926,
0.0456220917403698,
0.007201420608907938,
-0.03922363370656967,
0.022696882486343384,
-0.013374782167375088,
0.001606997917406261,
0.01057193148881197,
0.024176862090826035,
0.010617758147418499,
-0.037092000246047974,
-0.00883947778493166,
0.017777014523744583,
-0.013275504112243652,
-0.023096401244401932,
-0.000936801137868315,
0.024799413979053497,
0.04102359339594841,
0.02794397994875908,
-0.01693587563931942,
-0.004594156052917242,
-0.006662549450993538,
0.047451335936784744,
0.012377710081636906,
-0.025755908340215683,
-0.012136745266616344,
-0.051094070076942444,
0.034940142184495926,
0.01668190397322178,
0.03459719941020012,
0.05560671538114548,
0.0015327170258387923,
-0.01750177890062332,
-0.022505976259708405,
0.029405860230326653,
-0.008372999727725983,
-0.013161659240722656,
-0.002438507042825222,
0.017914319410920143,
0.014540506526827812,
-0.012841938994824886,
-0.020902441814541817,
-0.02894614078104496,
-0.025438861921429634,
0.020862115547060966,
0.04789979010820389,
0.02013920247554779,
0.041973698884248734,
0.015057425014674664,
-0.03621113672852516,
-0.0032703010365366936,
0.0073750377632677555,
-0.05979166924953461,
0.01369362324476242,
-0.0010568182915449142,
0.018269818276166916,
-0.05956796929240227,
-0.019601520150899887,
0.021186282858252525,
0.05820969492197037,
-0.01232922077178955,
0.04182961583137512,
0.06371422111988068,
0.02832675911486149,
0.02605917863547802,
0.032372813671827316,
-0.05440973863005638,
0.04723796248435974,
-0.04353754222393036,
0.0077493502758443356,
-0.01876341924071312,
-0.007423431146889925,
0.008353779092431068,
0.025135980919003487,
0.01988075114786625,
-0.004664908163249493,
-0.03191133588552475,
-0.08277563005685806,
0.051573578268289566,
0.028658049181103706,
0.007212206721305847,
0.02583908475935459,
0.027028735727071762,
0.025314057245850563,
-0.0002527657197788358,
0.01605702005326748,
0.025723937898874283,
-0.04081542044878006,
-0.0281660258769989,
-0.01940581575036049,
-0.07933203130960464,
0.014514746144413948,
-0.04833235964179039,
-0.01914971135556698,
0.02941344864666462,
-0.03262224793434143,
0.0473347045481205,
0.011710003949701786,
0.011997122317552567,
-0.024880332872271538,
0.06326594948768616,
-0.020920375362038612,
0.0051818424835801125,
0.014961724169552326,
-0.005373547784984112,
0.12160728126764297,
0.06538426131010056,
0.007010997273027897,
-0.09147875010967255,
0.00794052705168724,
0.00025121212820522487,
0.013069968670606613,
-0.030710959807038307,
0.015241286717355251,
0.013452229090034962,
0.008600390516221523,
-0.020441947504878044,
0.0451214499771595,
0.00652323616668582,
0.0072364830411970615,
0.028210245072841644,
-0.04294341802597046,
-0.06278034299612045,
-0.0013779369182884693,
0.004185852594673634,
-0.011186369694769382,
-0.005385447293519974,
-0.0719175636768341,
0.04062309488654137,
0.00857484620064497,
0.001554186805151403,
-0.03054632991552353,
-0.008821205236017704,
-0.004979030229151249,
0.007952520623803139,
-0.03994610160589218,
0.024687325581908226,
0.021063046529889107,
-0.0045524160377681255,
-0.023348448798060417,
0.021929562091827393,
0.006764746271073818,
-0.013978821225464344,
0.02275879494845867,
0.02038806676864624,
-0.0006112881237640977,
-0.0027515902183949947,
0.001785001251846552,
0.00902640912681818,
-0.01476461160928011,
-0.016160404309630394,
0.0020830316934734583,
0.03646349161863327,
-0.03358826786279678,
-0.01151825301349163,
0.004384934436529875,
0.03413432836532593,
0.03590117394924164,
-0.020817957818508148,
0.020106323063373566,
-0.03289664536714554,
0.032201480120420456,
-0.03657744824886322,
-0.02310176007449627,
-0.039444711059331894,
0.02328154630959034,
-0.03415898233652115,
0.02408864162862301,
-0.009240937419235706,
0.01947152614593506,
0.0071374159306287766,
-0.022085947915911674,
0.05385018140077591,
0.01758970133960247,
0.007666436024010181,
0.01658206433057785,
0.007533772382885218,
-0.05138513818383217,
-0.03382178768515587,
0.02888314425945282,
-0.0004308442585170269,
0.03191111609339714,
0.014212407171726227,
-0.0372290275990963,
-0.0064409212209284306,
-0.003048232290893793,
0.04367826506495476,
-0.025621796026825905,
0.002265296643599868,
-0.0022833419498056173,
-0.002839441178366542,
0.027481188997626305,
0.06358775496482849,
0.018591871485114098,
0.015806350857019424,
-0.028624752536416054,
0.03244215250015259,
-0.004533007275313139,
-0.037554312497377396,
-0.0009061182499863207,
0.01598753035068512,
-0.033091556280851364,
-0.02085884101688862,
0.008974533528089523,
-0.0006290406454354525,
-0.025651680305600166,
0.01963450387120247,
-0.007857090793550014,
0.009412909857928753,
-0.02932846173644066,
0.0007503909291699529,
0.03795209527015686,
-0.04707341641187668,
0.05208788067102432,
0.012802844867110252,
-0.0385533906519413,
-0.03750525787472725,
-0.013111325912177563,
-0.01463672611862421,
0.034866392612457275,
0.012777713127434254,
0.03600990027189255,
-0.004224197473376989,
0.007933041080832481,
0.004770842846482992,
-0.02234322391450405,
0.007939223200082779,
0.02086724154651165,
-0.033826619386672974,
0.03136347979307175,
-0.015827996656298637,
-0.00882137380540371,
-0.021514665335416794,
0.03876345604658127,
-0.006095115561038256,
-0.042429376393556595,
-0.006540970876812935,
0.038282010704278946,
-0.013795265927910805,
-0.03903136029839516,
0.039283767342567444,
-0.015982922166585922,
0.02969483658671379,
0.009949084371328354,
0.013254429213702679,
0.013177941553294659,
-0.07872425764799118,
-0.018999574705958366,
0.028723791241645813,
-0.016308408230543137,
0.007261448074132204,
0.004662740509957075,
-0.014280285686254501,
-0.04588820040225983,
0.032953545451164246,
-0.05808881297707558,
-0.02188725769519806,
-0.028206227347254753,
-0.0029822965152561665,
0.030993934720754623,
0.02193590998649597,
-0.02290981262922287,
-0.00877472385764122,
0.00376110034994781,
0.03927724435925484,
0.054559070616960526,
-0.01707354374229908,
-0.005350602325052023,
-0.03958265855908394,
-0.004158113617449999,
0.026792678982019424,
0.028506668284535408,
0.06319791823625565,
0.01730399578809738,
0.05438540130853653,
-0.027371807023882866,
0.023598719388246536,
-0.011395681649446487,
0.025146838277578354,
-0.08536916971206665,
-0.02783234231173992,
-0.01297164335846901,
0.0032114507630467415,
0.052354101091623306,
-0.045184243470430374,
0.010532642714679241,
0.0017191452207043767,
-0.04022849723696709,
0.02682916447520256,
-0.025201814249157906,
-0.004352026153355837,
-0.016756998375058174,
-0.04426756128668785,
-0.03688356280326843,
0.07116200774908066,
0.02957092598080635,
0.02429818920791149,
0.056156549602746964,
-0.007127059157937765,
-0.01663239672780037,
-0.03153767064213753,
-0.002576138125732541,
0.045682258903980255,
-0.00098589772824198,
-0.015451706945896149,
0.06471265107393265,
-0.010950889438390732,
0.0018905147444456816,
0.04701686277985573,
-0.0005264814826659858,
-0.02062796987593174,
-0.0038460465148091316,
0.018565023317933083,
-0.0043566869571805,
0.028498686850070953,
0.01004046481102705,
0.009871489368379116,
-0.012399444356560707,
0.0015006517060101032,
0.03003387525677681,
0.01629493571817875,
0.003442182205617428,
0.02184555120766163,
0.015995169058442116,
-0.0557718351483345,
-0.05892283469438553,
0.014173133298754692,
0.00560850091278553,
-0.018456947058439255,
0.007615950424224138,
-0.023624327033758163,
-0.011919792741537094,
-0.05355742201209068,
0.03284696117043495,
-0.05371958017349243,
0.028296327218413353,
0.04621346667408943,
0.025538604706525803,
0.0023924049455672503,
0.013802873902022839,
-0.026738526299595833,
-0.015567464753985405,
0.010793072171509266,
0.036825209856033325,
-0.05589500814676285,
-0.01198794599622488,
-0.03974953666329384,
-0.013913583941757679,
0.024931006133556366,
0.0047144838608801365,
-0.0447990782558918,
-0.02755425125360489,
0.04676072299480438,
0.0029651890508830547,
0.039763253182172775,
-0.016062140464782715,
-0.029624326154589653,
0.0210650023072958,
-0.05792863294482231,
0.05434585362672806,
-0.011509747244417667,
-0.004080398008227348,
-0.04653838649392128,
-0.0383143424987793,
0.027673784643411636,
0.038698241114616394,
0.01910455897450447,
0.004100929480046034,
-0.005937688518315554,
0.027502400800585747,
-0.026926403865218163,
0.0037945806980133057,
-0.00638643279671669,
0.0025084533262997866,
0.007848535664379597,
-0.02448265440762043,
0.0001385937794111669,
-0.009108135476708412,
-0.011379914358258247,
0.019488230347633362,
0.011203493922948837,
0.0008579113055020571,
-0.000304236396914348,
-0.029631899669766426,
-0.06106318160891533,
0.03649013489484787,
0.012534473091363907,
0.007327517028898001,
0.07286152243614197,
0.018762459978461266,
-0.002097496297210455,
0.048429686576128006,
-0.008601652458310127,
-0.013674226589500904,
0.042009808123111725,
0.010717485100030899,
0.018221614882349968,
-0.014344402588903904,
-0.0328657366335392,
0.02022586017847061,
-0.02867756597697735,
-0.008787036873400211,
0.031180448830127716,
-0.048421263694763184,
0.0016691575292497873,
0.06945646554231644,
0.0016404027119278908,
0.05403224378824234,
-0.00567540293559432,
-0.013194349594414234,
0.008485477417707443,
-0.005102192983031273,
0.005449294578284025,
0.027230877429246902,
0.014306234195828438,
0.06359042227268219,
-0.0038097179494798183,
0.033274419605731964,
0.007892632856965065,
0.008656810969114304,
-0.016496440395712852,
0.015051239170134068,
-0.03878893703222275,
-0.021373022347688675,
0.015739046037197113,
-0.051361311227083206,
0.07026112079620361,
0.018988801166415215,
-0.057298120111227036,
0.10238029807806015,
-0.06159825623035431,
0.012246056459844112,
0.01218181662261486,
-0.02487719990313053,
-0.008454757742583752,
0.014051111415028572,
-0.008573073893785477,
0.033568307757377625,
-0.02588018774986267,
-0.02553301304578781,
-0.010680061765015125,
-0.01814495027065277,
0.010817569680511951,
-0.06627186387777328,
0.006510737352073193,
0.00733989616855979,
-0.015955692157149315,
-0.0069442796520888805,
-0.015238998457789421,
0.009008577093482018,
-0.0013806924689561129,
0.02044893056154251,
-0.002622264437377453,
0.0006408271146938205,
0.01519811525940895,
0.004516789223998785,
-0.034778282046318054,
0.032903656363487244,
-0.05262294411659241,
-0.034704286605119705,
-0.02424224093556404,
0.003328009508550167,
-0.022479025647044182,
0.01762702316045761
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/8659/invariant-spacetime-distance-circular-motion">Invariant spacetime - distance - Circular Motion</a> </p>
</blockquote>
<p>This is a question that I thought up a few years ago when I was taking mechanics. I asked the professor but didn't really get a straight answer. </p>
<p>Imagine a record spinning at relativistic speeds. In the lab frame, the circumference of the record should decrease according to the Lorentz contraction. However the radius of the record should remain fixed since it is orthogonal to the direction of motion. So does the shape of the record appear distorted since the circumference is smaller but the radius is the same? What would it look like?</p>
<p>I have a feeling the answer is obvious and/or well known since it would seem to be similar to the situation of relativistic particles traveling around a circular accelerator but I can't think of how it can be solved.</p>
| 306 |
[
-0.05881136655807495,
-0.03253617137670517,
0.013391386717557907,
-0.0039522843435406685,
0.023063115775585175,
-0.008798126131296158,
-0.023306954652071,
0.00002702364326978568,
-0.0049016401171684265,
0.031149713322520256,
0.019683705642819405,
0.0061281416565179825,
0.06123039871454239,
0.011389469727873802,
0.010002669878304005,
-0.02200687862932682,
0.017563272267580032,
0.005358547903597355,
-0.021069878712296486,
-0.03984323516488075,
0.03918759524822235,
0.029200490564107895,
-0.006766710430383682,
-0.007088208105415106,
-0.026814060285687447,
0.03084377571940422,
0.036248378455638885,
0.003230063710361719,
-0.01110653392970562,
0.05366463586688042,
-0.027768932282924652,
0.0077499267645180225,
0.02085701934993267,
0.0128689706325531,
0.024770226329565048,
0.007368785794824362,
-0.045589882880449295,
-0.013383598998188972,
0.027816839516162872,
0.020952483639121056,
-0.04371650144457817,
-0.017734019085764885,
-0.02819535695016384,
0.07507992535829544,
-0.010301494970917702,
0.03234200179576874,
-0.013108227401971817,
0.031724825501441956,
0.06867878139019012,
-0.012217709794640541,
0.0528385266661644,
-0.00268357340246439,
0.024537306278944016,
-0.009042822755873203,
0.018713703379034996,
-0.025058723986148834,
0.06877091526985168,
0.06750048696994781,
-0.02786642499268055,
-0.010370153933763504,
-0.003886985592544079,
-0.03281484171748161,
-0.022779027000069618,
-0.014425174333155155,
0.0009296319913119078,
0.011577327735722065,
-0.01538218092173338,
0.03263920173048973,
0.028619851917028427,
-0.016900306567549706,
0.012247136794030666,
0.01814923621714115,
0.001653587562032044,
-0.018396679311990738,
0.014180583879351616,
-0.019511627033352852,
0.0203195009380579,
0.020549222826957703,
0.03159061819314957,
0.02615097165107727,
-0.023872463032603264,
0.0211785975843668,
0.05862245336174965,
0.02261415496468544,
-0.001099156215786934,
-0.02977660670876503,
0.02951539307832718,
0.00003045081757591106,
0.00766000896692276,
0.06149985268712044,
0.0200897715985775,
-0.016154510900378227,
0.020077956840395927,
-0.003932070918381214,
-0.00992286205291748,
0.035270512104034424,
-0.01241331361234188,
0.07325412333011627,
0.005032848101109266,
-0.006599538028240204,
-0.011894261464476585,
-0.003272600006312132,
0.012783200480043888,
0.06378202140331268,
-0.016099026426672935,
-0.007414110004901886,
-0.03985817730426788,
0.0415462963283062,
-0.022764259949326515,
-0.030077600851655006,
-0.03768588602542877,
-0.0023619539570063353,
-0.00589993130415678,
0.0009607634274289012,
0.03262686729431152,
-0.025096990168094635,
-0.025945721194148064,
-0.014490630477666855,
0.05475896969437599,
0.05636809766292572,
0.039636045694351196,
-0.026165243238210678,
0.02032637968659401,
-0.0067214397713541985,
-0.03520132973790169,
-0.011393132619559765,
0.030613407492637634,
-0.015031697228550911,
-0.016542088240385056,
0.01765265129506588,
0.016730794683098793,
-0.03635917231440544,
0.011255349032580853,
-0.005158170126378536,
0.041526276618242264,
-0.0075655048713088036,
-0.12297187000513077,
-0.054045211523771286,
0.08247043192386627,
0.03580598905682564,
-0.03337224945425987,
-0.09971976280212402,
-0.019952701404690742,
0.008408773690462112,
0.10858115553855896,
-0.013602031394839287,
-0.00741717079654336,
0.028457066044211388,
0.0771946832537651,
0.02913747727870941,
0.009957467205822468,
0.00034982970100827515,
0.00013702317664865404,
-0.045010633766651154,
-0.0019257363164797425,
-0.06960679590702057,
-0.020025046542286873,
0.0437932014465332,
-0.01843123696744442,
-0.03449824079871178,
0.05144919455051422,
0.008921189233660698,
0.025117389857769012,
0.007832691073417664,
0.008814722299575806,
0.007844693027436733,
0.06278194487094879,
0.015802979469299316,
-0.047977298498153687,
0.037918247282505035,
-0.016902748495340347,
0.02489607222378254,
-0.032800398766994476,
-0.012103231623768806,
0.06772089004516602,
-0.03142944350838661,
-0.010565069504082203,
0.033565811812877655,
-0.016745828092098236,
0.010099667124450207,
-0.022984512150287628,
-0.013081002049148083,
-0.02390444278717041,
-0.014393961988389492,
0.03935990110039711,
0.0634935200214386,
-0.015488756820559502,
0.061500485986471176,
0.002904251217842102,
-0.022273246198892593,
0.004883384797722101,
-0.04099906235933304,
0.020756971091032028,
-0.013795397244393826,
-0.011423244141042233,
0.026196874678134918,
0.020763618871569633,
0.010786565020680428,
-0.0065678758546710014,
-0.0023656156845390797,
-0.0028803013265132904,
0.04687243700027466,
-0.01888658106327057,
0.014124032109975815,
0.015231617726385593,
0.029077138751745224,
0.047905467450618744,
-0.004659461323171854,
-0.03568961098790169,
-0.011669376865029335,
-0.018786760047078133,
0.001683353097178042,
-0.02601155824959278,
0.003938321489840746,
0.0004949371796101332,
0.01687769778072834,
0.002187090925872326,
0.01915751025080681,
0.018214572221040726,
0.011059077456593513,
-0.006879627704620361,
0.041849564760923386,
0.026251889765262604,
-0.02815111167728901,
0.027181189507246017,
0.02403753064572811,
0.015336744487285614,
0.009662586264312267,
-0.009283053688704967,
-0.04986540973186493,
-0.04222702980041504,
-0.011693107895553112,
0.04214269295334816,
0.015586995519697666,
-0.046310290694236755,
-0.0039938404224812984,
0.003952387720346451,
0.059929508715867996,
-0.023010918870568275,
-0.0029020183719694614,
-0.023134443908929825,
-0.07003508508205414,
0.02499716356396675,
-0.007910172455012798,
-0.01114125456660986,
-0.0011816141195595264,
0.02412601001560688,
0.0028922611381858587,
0.01661496050655842,
-0.007974463514983654,
-0.016952820122241974,
0.0021727874409407377,
-0.004196613095700741,
-0.007099699229001999,
0.0339646115899086,
-0.013331366702914238,
0.03886424005031586,
0.0123780257999897,
0.03457516431808472,
0.05022415146231651,
-0.023672444745898247,
0.00392388179898262,
-0.03621012717485428,
0.05323251336812973,
-0.005259505473077297,
0.0008347244584001601,
0.01904303766787052,
-0.04587795212864876,
0.010659861378371716,
-0.05919976159930229,
0.003099198918789625,
-0.01085942517966032,
0.0026014419272542,
0.02624453790485859,
-0.008395297452807426,
0.028861744329333305,
0.029746605083346367,
0.0019463507924228907,
-0.05255550891160965,
-0.0025093047879636288,
-0.006780329160392284,
-0.02107001096010208,
0.017160287126898766,
0.040171559900045395,
-0.05023942515254021,
0.04361409693956375,
-0.037306975573301315,
-0.016630133613944054,
0.00331583502702415,
-0.021416565403342247,
0.014685144647955894,
0.02119249850511551,
0.0026347311213612556,
-0.07630261033773422,
-0.006484030745923519,
-0.03750506043434143,
-0.007423661649227142,
-0.060468148440122604,
-0.006924687419086695,
0.07462525367736816,
0.04901440814137459,
-0.040400948375463486,
0.006461036391556263,
-0.044672880321741104,
-0.02770000323653221,
-0.023339027538895607,
0.022258948534727097,
0.03501933068037033,
-0.026725519448518753,
0.028515446931123734,
-0.0017006563721224666,
-0.0041604493744671345,
-0.01123956311494112,
-0.06434977054595947,
-0.029229504987597466,
-0.00343351811170578,
-0.010949620977044106,
0.03727686405181885,
0.01906932331621647,
-0.0070559014566242695,
0.0701216459274292,
0.03819485753774643,
-0.03666798397898674,
-0.05157232657074928,
-0.01715477928519249,
-0.005348055623471737,
-0.06062508001923561,
-0.02725570648908615,
0.023673897609114647,
-0.01075367908924818,
-0.006874456070363522,
0.04612097516655922,
0.02407115511596203,
0.003098957473412156,
0.052778009325265884,
-0.014960039407014847,
-0.0018120082095265388,
0.005447547882795334,
0.0044841887429356575,
0.045906614512205124,
0.018845530226826668,
-0.03868752717971802,
-0.00797378458082676,
0.0039326283149421215,
0.02823961339890957,
0.03076626919209957,
-0.11618324369192123,
0.061007656157016754,
0.0018644561059772968,
-0.017846757546067238,
0.026267843320965767,
0.0008728866232559085,
-0.012464426457881927,
0.0132021214812994,
-0.00714331679046154,
0.01669355109333992,
0.03341982141137123,
0.020508620887994766,
0.019243119284510612,
0.03440933674573898,
0.053868331015110016,
-0.004936502780765295,
-0.009356420487165451,
-0.026223640888929367,
-0.013945471495389938,
0.017557913437485695,
-0.023046765476465225,
-0.0227144006639719,
0.04453035444021225,
0.03223074600100517,
-0.011595349758863449,
-0.0023792607244104147,
-0.0500972718000412,
-0.0038616007659584284,
-0.05944494530558586,
-0.015056672506034374,
-0.015934623777866364,
0.02539743110537529,
0.03881458565592766,
0.03811141848564148,
0.03786591440439224,
-0.015316635370254517,
0.010794035159051418,
0.009155306965112686,
-0.06473003327846527,
0.02511036954820156,
-0.06673136353492737,
-0.011656372807919979,
0.00863948930054903,
0.024624334648251534,
-0.006741453893482685,
-0.001160654705017805,
0.019953062757849693,
-0.0053078895434737206,
-0.008204877376556396,
-0.05195339024066925,
0.015731211751699448,
-0.0038612396456301212,
-0.05534061789512634,
-0.04464422166347504,
0.06947372108697891,
0.04795790836215019,
-0.02997157908976078,
0.03436042740941048,
0.00846864189952612,
-0.03736020624637604,
-0.015013138763606548,
-0.030128978192806244,
-0.0018381396075710654,
0.015101637691259384,
0.029401399195194244,
0.023647816851735115,
-0.014638037420809269,
-0.029606979340314865,
0.0033107572235167027,
0.038284603506326675,
0.007837352342903614,
0.007234200369566679,
0.006394154857844114,
-0.05831903964281082,
-0.053023118525743484,
-0.004665273241698742,
-0.031269270926713943,
0.08180326223373413,
-0.004189389292150736,
0.02135113812983036,
0.03855809196829796,
0.0110487574711442,
-0.0043441904708743095,
-0.023449072614312172,
0.03069210611283779,
-0.001266744453459978,
0.011978776194155216,
-0.04452122375369072,
-0.016675235703587532,
-0.011204717680811882,
-0.0026164327282458544,
-0.018797460943460464,
-0.011385653167963028,
-0.01927727833390236,
0.015947513282299042,
0.02447662129998207,
0.015922825783491135,
-0.02797895483672619,
0.030622126534581184,
-0.045136380940675735,
0.021893706172704697,
0.0024504975881427526,
0.0004831345286220312,
0.008427060209214687,
0.04533759132027626,
0.05689797177910805,
0.021177854388952255,
0.020275956019759178,
-0.06399335712194443,
-0.023392923176288605,
-0.00882396288216114,
0.03244350478053093,
0.008781070820987225,
-0.02908601239323616,
-0.03993185609579086,
-0.04735751077532768,
0.06527462601661682,
-0.05234679579734802,
0.031088488176465034,
-0.034112848341464996,
-0.026831384748220444,
-0.021852876991033554,
-0.035338543355464935,
-0.03245671093463898,
-0.004550819750875235,
-0.02786446548998356,
-0.027226373553276062,
-0.03587309643626213,
0.024289054796099663,
0.014940096996724606,
-0.01273330207914114,
0.04472285881638527,
0.03188448026776314,
0.0013242334825918078,
0.028571603819727898,
0.013236609287559986,
0.058341607451438904,
-0.042589690536260605,
-0.059685103595256805,
0.007016062270849943,
0.03714023903012276,
-0.003526108106598258,
0.018624482676386833,
-0.024429375305771828,
-0.01058295276015997,
0.0001277124392800033,
-0.02111007645726204,
-0.0056118411011993885,
0.008082345128059387,
-0.061031341552734375,
0.008562800474464893,
0.021681994199752808,
-0.02701728418469429,
0.03585679829120636,
0.07291138172149658,
-0.0021584636997431517,
-0.015659993514418602,
-0.01556338556110859,
0.01989581622183323,
-0.026269156485795975,
-0.00940824393182993,
-0.020170439034700394,
0.050476446747779846,
-0.0481363981962204,
0.05754349008202553,
-0.005593220703303814,
0.015904191881418228,
-0.00388998887501657,
-0.024271005764603615,
-0.010197318159043789,
0.03352274373173714,
-0.009878831915557384,
0.01082061231136322,
-0.001783244893886149,
0.014911821112036705,
0.015702618286013603,
-0.06269653141498566,
0.03161369264125824,
0.019896816462278366,
-0.008456147275865078,
0.044585127383470535,
0.006614277604967356,
0.019506823271512985,
-0.02472587488591671,
-0.026875538751482964,
0.0013447238598018885,
-0.06436850130558014,
0.060706838965415955,
-0.019438309594988823,
-0.010869719088077545,
0.057392776012420654,
-0.018075473606586456,
-0.019322726875543594,
0.006595672108232975,
-0.052715543657541275,
0.026260267943143845,
-0.04942616820335388,
-0.024732602760195732,
0.02217823825776577,
0.018329527229070663,
-0.08428524434566498,
-0.05327560752630234,
0.039803195744752884,
-0.03218326345086098,
-0.00481604877859354,
-0.023163195699453354,
-0.005287857726216316,
-0.0400237999856472,
-0.02461439184844494,
-0.020991170778870583,
0.032249145209789276,
-0.043699029833078384,
-0.022301161661744118,
0.011318434961140156,
-0.02127094753086567,
0.043633218854665756,
-0.016475599259138107,
-0.012291966937482357,
-0.01511144358664751,
-0.009832018986344337,
-0.023194365203380585,
0.013552562333643436,
0.06624092906713486,
-0.025831347331404686,
-0.07986040413379669,
-0.03275620937347412,
0.010305921547114849,
-0.010488821193575859,
-0.04553944990038872,
-0.013876994140446186,
0.009275119751691818,
-0.024805381894111633,
-0.015123199671506882,
-0.01237917598336935,
0.01869138702750206,
0.00446111848577857,
-0.00031281900010071695,
-0.008077378384768963,
-0.005664703901857138,
-0.00884662102907896,
-0.040470097213983536,
0.013160170055925846,
0.046478573232889175,
-0.0024836028460413218,
0.0067076063714921474,
0.04866213724017143,
-0.048072654753923416,
-0.03355695679783821,
0.004314050078392029,
-0.032332804054021835,
0.01652560383081436,
-0.037054769694805145,
-0.003169100033119321,
-0.0048400587402284145,
-0.015157467685639858,
-0.054331716150045395,
-0.03727571666240692,
-0.0358181931078434,
-0.004688588436692953,
0.05973087623715401,
0.011088337749242783,
0.04306064546108246,
0.03792927786707878,
0.021209245547652245,
-0.0206973385065794,
-0.022001270204782486,
0.03811730444431305,
-0.012645029462873936,
-0.0060167196206748486,
0.05436941981315613,
-0.013503782451152802,
-0.01757091097533703,
0.010461091995239258,
0.04192699119448662,
-0.019785122945904732,
-0.02824990265071392,
0.007720648311078548,
0.013815859332680702,
0.002854424761608243,
0.025439327582716942,
-0.016129299998283386,
0.0052126431837677956,
-0.02154405415058136,
0.028535962104797363,
0.02330022118985653,
0.012500117532908916,
0.05526995286345482,
-0.002710864180698991,
0.024186478927731514,
-0.02752740867435932,
-0.005927170626819134,
-0.06240628659725189,
-0.002043886575847864,
0.01721997559070587,
0.027316614985466003,
0.003935914486646652,
0.007406098302453756,
0.060346003621816635,
-0.010017864406108856,
0.016189437359571457,
-0.06139645725488663,
-0.04707380756735802,
0.007983259856700897,
-0.03295786678791046,
-0.0461309552192688,
0.027481459081172943,
0.018494319170713425,
-0.003899425035342574,
0.014177798293530941,
-0.03997433930635452,
-0.00006197142647579312,
0.026891101151704788,
0.023585589602589607,
-0.013580654747784138,
0.05391212925314903,
0.007994604296982288,
-0.004708480555564165,
-0.03201090171933174,
0.011935488320887089,
0.0956740751862526,
0.020367762073874474,
0.009569606743752956,
-0.06710018962621689,
0.007236072793602943,
0.018276570364832878,
-0.008460436947643757,
-0.029897011816501617,
0.02752765268087387,
-0.023109178990125656,
0.015798872336745262,
0.029128069058060646,
0.057910047471523285,
0.015201743692159653,
0.01590610295534134,
0.04967182129621506,
-0.043216582387685776,
0.014544175937771797,
0.005902853328734636,
-0.0051387399435043335,
0.0075220330618321896,
0.04618603736162186,
-0.018442340195178986,
0.04844153672456741,
-0.03865441679954529,
-0.007864970713853836,
-0.052505943924188614,
-0.03266769275069237,
-0.004539203830063343,
-0.01619855873286724,
-0.01574738137423992,
0.04194266349077225,
-0.02278825081884861,
-0.022583942860364914,
-0.07350106537342072,
0.001813962939195335,
0.006640202831476927,
0.013185948133468628,
0.026650497689843178,
0.012540576048195362,
0.0035625507589429617,
0.017016621306538582,
0.04091555252671242,
0.02383732795715332,
-0.03039115108549595,
-0.001367784570902586,
-0.039538703858852386,
0.03548748791217804,
0.003241539467126131,
0.005521985702216625,
0.010464325547218323,
0.02107354812324047,
0.004568465519696474,
-0.07447533309459686,
0.014085186645388603,
0.016356587409973145,
-0.008668103255331516,
0.05076354742050171,
-0.008079186081886292,
-0.010526055470108986,
0.03802921995520592,
0.030118411406874657,
-0.010679122991859913,
-0.020880160853266716,
0.008341754786670208,
-0.00444131251424551,
-0.00409077201038599,
0.05690178647637367,
0.011567777954041958,
-0.012245147489011288,
-0.049106255173683167,
0.032687000930309296,
-0.008318840526044369,
0.03456679731607437,
0.0012417965335771441,
0.015353774651885033,
0.026518268510699272,
0.013083020225167274,
0.001502027502283454,
0.025223618373274803,
-0.04438421502709389,
0.012606161646544933,
-0.01743682660162449,
-0.03554297983646393,
-0.04660575091838837,
-0.00012908439384773374,
0.01061411201953888,
0.02071242779493332,
-0.038067009299993515,
0.02537035383284092,
0.0012276333291083574,
0.03676716610789299,
0.000026990635888068937,
0.0059906370006501675,
-0.009359201416373253,
0.00934364553540945,
-0.033202484250068665,
0.004376635421067476,
-0.0365271270275116,
0.05197328329086304,
0.05223209783434868,
0.005675652530044317,
0.017767969518899918,
0.01969553902745247,
-0.01824123226106167,
-0.005547313019633293,
0.03474416583776474,
-0.030665526166558266,
0.01761597767472267,
0.007593825925141573,
0.03033503144979477,
-0.08010128885507584,
0.00244726100936532,
0.0014225644990801811,
-0.04827771335840225,
-0.0036086649633944035,
0.01056703645735979,
-0.011900459416210651,
0.03628084436058998,
-0.05715111643075943,
0.0051451176404953,
-0.03587739169597626,
0.011759941466152668,
-0.041588131338357925,
0.008937596343457699,
-0.028093047440052032,
-0.018701842054724693,
0.013735556975007057,
0.07005476951599121,
-0.0013625631108880043,
-0.014561951160430908,
-0.029969073832035065,
0.02173543907701969,
-0.026512708514928818,
0.01765330880880356,
0.027276869863271713,
0.02021050825715065,
0.008794252760708332,
-0.014332432299852371,
-0.033471766859292984,
0.024474771693348885,
-0.025585807859897614,
-0.03313736245036125,
0.02699759043753147,
-0.02821090631186962,
0.03274400904774666,
-0.010242092423141003,
-0.015546712093055248,
0.02196476049721241,
0.04504531994462013,
-0.00008965705637820065,
-0.02548913285136223,
-0.016209444031119347,
-0.038241662085056305,
0.05852073058485985,
-0.000752723659388721,
0.05598044395446777,
-0.0006141441408544779,
-0.042529456317424774,
0.032085221260786057,
0.017623649910092354,
-0.049927257001399994,
0.04422365128993988,
-0.007891914807260036,
-0.01362921204417944,
-0.026064064353704453,
-0.014187624678015709,
0.04594743624329567,
0.04042500630021095,
0.04276382923126221,
-0.03308170288801193,
0.02349740080535412,
0.039326105266809464,
-0.01043017115443945,
-0.1057855412364006,
0.0031499925535172224,
0.006781380623579025,
0.014551984146237373,
0.027453739196062088,
-0.043664563447237015,
0.021704403683543205,
0.03535240516066551,
-0.07856099307537079,
0.025892971083521843,
-0.03789001330733299,
-0.02982715517282486,
-0.03935854882001877,
-0.01710604503750801,
-0.027305353432893753,
0.02461337111890316,
0.05522872507572174,
0.06079034134745598,
0.02461124397814274,
0.022771576419472694,
-0.05305744335055351,
-0.03588804230093956,
-0.01540693361312151,
0.011130125261843204,
0.019600333645939827,
-0.003562425496056676,
0.058399099856615067,
0.015351295471191406,
-0.003243234008550644,
0.031558096408843994,
-0.01090348418802023,
0.03227774426341057,
-0.03383997082710266,
-0.01715109683573246,
0.019164199009537697,
0.00947527214884758,
0.007686067838221788,
-0.0044942982494831085,
-0.006503235083073378,
0.0003895449626725167,
0.021546607837080956,
-0.015941757708787918,
0.0022735558450222015,
-0.01066652312874794,
0.018582262098789215,
-0.03882717341184616,
-0.016346313059329987,
0.03280554711818695,
-0.000816217390820384,
0.008260179311037064,
-0.023271599784493446,
0.007475001737475395,
0.0008153385133482516,
-0.019118549302220345,
0.010856740176677704,
-0.037991367280483246,
0.018664641305804253,
-0.0018441779538989067,
-0.004557231906801462,
-0.022480176761746407,
0.03214774280786514,
-0.014751746319234371,
-0.013242661021649837,
-0.02693665772676468,
-0.00910942442715168,
-0.017921891063451767,
-0.04664907231926918,
-0.012674604542553425,
-0.013029295019805431,
0.003544378560036421,
0.006583480630069971,
-0.011799763888120651,
-0.035607390105724335,
0.04628375172615051,
0.04379988834261894,
0.020980261266231537,
0.0018477151170372963,
-0.012168878689408302,
-0.03579025715589523,
-0.0827486664056778,
-0.0015811267076060176,
0.019642407074570656,
-0.014236780814826488,
-0.03021758235991001,
-0.03140527755022049,
0.0025586646515876055,
0.014682880602777004,
0.07305000722408295,
0.029748570173978806,
-0.019911855459213257,
0.04141136258840561,
-0.036441948264837265,
-0.02694309875369072,
-0.04164491221308708,
-0.03372795134782791,
0.013039217330515385,
0.010028930380940437,
0.028498943895101547,
-0.017453808337450027,
-0.0504581592977047,
0.015326538123190403,
0.028804954141378403,
-0.0026995092630386353,
0.022257864475250244,
0.023670358583331108,
-0.04661215469241142,
0.014247128739953041,
-0.008855323307216167,
0.021558012813329697,
0.07539421319961548,
0.03929304704070091,
-0.016964329406619072,
0.053466178476810455,
-0.019413139671087265,
-0.030421530827879906,
0.03893014416098595,
-0.05476139485836029,
-0.016956361010670662,
-0.013834632933139801,
0.001699007349088788,
0.038022760301828384,
-0.04101875051856041,
0.008872518315911293,
0.07285016775131226,
-0.044722799211740494,
-0.014897752553224564,
0.039792273193597794,
0.010692913085222244,
0.013879537582397461,
-0.017327846959233284,
-0.002516156295314431,
0.00679983664304018,
-0.03512604162096977,
-0.01569993980228901,
0.032339245080947876,
0.04809791222214699,
0.015282881446182728,
-0.011414909735321999,
0.04474605247378349,
0.0029827395919710398,
0.032060787081718445,
0.004183989949524403,
0.04347919300198555,
-0.021045949310064316,
0.0015983048360794783,
0.02309906855225563,
-0.05468861013650894,
-0.00907465722411871,
0.04173995926976204,
-0.007683178409934044,
0.07205002009868622,
0.005660847295075655,
0.024494538083672523,
-0.011135819368064404,
0.00352253089658916,
-0.026827793568372726,
0.02201036922633648,
0.024644901975989342,
0.015323208644986153,
0.00013508796109817922,
-0.02252044901251793,
-0.0004561605746857822,
-0.017013056203722954,
0.004481748677790165,
-0.023235367611050606,
-0.02878045290708542,
0.00769813684746623,
-0.005074154119938612,
-0.009732087142765522,
-0.019633613526821136,
-0.013344642706215382,
0.024388737976551056,
0.02490847371518612,
0.025959253311157227,
0.04542741924524307,
0.00832965224981308,
0.007724078372120857,
-0.02057895064353943,
0.050057362765073776,
-0.09680215269327164,
-0.020007451996207237,
0.01766940951347351,
0.025814898312091827,
-0.03616011142730713,
0.016193972900509834
] |
<p>I have difficulty understanding the following vector calculus example. Text can be found <a href="http://www.nhn.ou.edu/~shaferry/41832005_files/l9.pdf" rel="nofollow">here</a>. It is the 5th Q&A -- starting with equation (31.1035).It concerns finding the vector potential of a current loop.</p>
<p>I get the argument up to $$\vec A=\frac{\mu I}{4\pi r^3}\oint \vec r'\cdot \vec r \,\,\,d\vec l'$$.
But I don't understand why $$\oint \vec r'\cdot \vec r \,\,\,d\vec l'=\left(\int d\vec a\right)\times \vec r$$</p>
<p><em><strong>[ADDED]</em></strong>: Definitions of the terms:</p>
<p>This describes a current loop, with a current $I$ flowing in it.</p>
<p>$\vec r$ is the position vector of an arbitrary point in space. $\vec r'$ is a position vector of a point on the loop. $d\vec l'$ is an infinitesimal line element along the loop.</p>
<p>$\vec A(\vec r)$ is the vector potential, given by $$\frac{\mu I}{4\pi}\oint \frac{d\vec l'}{|\vec r'-\vec r|}$$
The above expression is obtained by Taylor expanding this definition.</p>
<hr>
<p>The first thing I tried is the vector triple product identity
$$(\vec r'\cdot \vec r )\,\,\,d\vec l'=\vec r\times(d\vec l'\times \vec r')+(\vec r\cdot d\vec l')\vec r'$$
The first term looks like it's doing the right sort of thing, but I don't see why the second term vanishes (or fits in) ...Maybe I have missed out something quite obvious?</p>
| 9,595 |
[
-0.0005303894286043942,
0.02535371668636799,
0.02479124255478382,
-0.04829984903335571,
0.047073956578969955,
-0.013249102979898453,
-0.031169766560196877,
-0.03941916301846504,
-0.002106840256601572,
-0.005127655807882547,
0.006687880959361792,
0.02555769495666027,
0.07841099798679352,
0.008442945778369904,
0.03177386894822121,
0.06541705131530762,
0.030121007934212685,
-0.015600434504449368,
0.01564771868288517,
-0.037346526980400085,
0.025627490133047104,
0.02625509537756443,
0.0020347945392131805,
0.00825414340943098,
-0.0005655147251673043,
0.044626254588365555,
0.035916395485401154,
-0.002992271911352873,
-0.0027161994948983192,
0.05030903220176697,
-0.009314975701272488,
-0.04850110039114952,
-0.015947306528687477,
0.01995771750807762,
0.012038048356771469,
0.05062532797455788,
-0.02215365506708622,
0.007795311044901609,
0.004677092656493187,
0.04674086719751358,
-0.04443978890776634,
0.008719838224351406,
-0.004169559106230736,
0.08169493824243546,
-0.049785103648900986,
0.022835060954093933,
-0.007172836922109127,
0.002353899646550417,
0.04324350133538246,
-0.0046131908893585205,
0.09358156472444534,
0.02519833669066429,
0.01914922334253788,
0.010387281887233257,
-0.015897106379270554,
0.011785848997533321,
0.0720159187912941,
0.043063268065452576,
-0.01579534448683262,
-0.04078342020511627,
-0.028231514617800713,
-0.029759211465716362,
-0.009216489270329475,
-0.027359621599316597,
0.015534138306975365,
0.0044767605140805244,
0.02865859866142273,
0.017223583534359932,
0.007749015465378761,
-0.017978224903345108,
-0.003004553262144327,
0.001864108839072287,
-0.023973599076271057,
-0.038225963711738586,
0.0014610565267503262,
-0.008426361717283726,
-0.0016634964849799871,
-0.010132478550076485,
0.053573716431856155,
0.0038806400261819363,
-0.05465088039636612,
0.029933415353298187,
0.011384187266230583,
0.0578460693359375,
0.030569452792406082,
-0.020868947729468346,
0.03488478437066078,
-0.0035906322300434113,
0.011304110288619995,
-0.011682524345815182,
-0.005129440687596798,
0.02459772117435932,
0.005015437491238117,
-0.013621271587908268,
-0.013710656203329563,
0.0352763757109642,
-0.0064237951301038265,
0.0300847627222538,
0.010763578116893768,
-0.004189508967101574,
-0.010225258767604828,
-0.020315926522016525,
-0.009079018607735634,
0.04027164727449417,
0.030043091624975204,
-0.02556954137980938,
0.004838034976273775,
0.023822179064154625,
-0.02455395832657814,
-0.06249097362160683,
-0.06488529592752457,
0.05112167447805405,
-0.011975443921983242,
0.03950696066021919,
-0.017679130658507347,
-0.031077992171049118,
-0.01720086857676506,
0.04207431152462959,
0.05406622588634491,
0.04831240698695183,
0.003250066889449954,
-0.06213483214378357,
0.006181125994771719,
-0.058206796646118164,
-0.04348759353160858,
0.005684849340468645,
-0.0020465513225644827,
-0.016596786677837372,
-0.037301886826753616,
0.032663166522979736,
0.021727127954363823,
0.025471534579992294,
-0.027289433404803276,
0.0411858931183815,
0.004063932690769434,
-0.021425755694508553,
-0.09923262149095535,
-0.031836383044719696,
0.06877172738313675,
0.006362840998917818,
0.004490619990974665,
-0.04614768549799919,
0.014199428260326385,
0.030005216598510742,
0.09987321496009827,
-0.009961960837244987,
-0.015655964612960815,
0.011738085187971592,
0.01937648095190525,
0.0007539374637417495,
-0.011749759316444397,
-0.01093719806522131,
-0.02533981017768383,
-0.02717544138431549,
0.003427681513130665,
-0.028948144987225533,
0.0468476302921772,
0.014046551659703255,
0.0065419492311775684,
0.01939006894826889,
0.06972521543502808,
0.010023084469139576,
0.023419003933668137,
0.038200631737709045,
-0.04329218342900276,
0.008960849605500698,
0.07170908898115158,
-0.01208151038736105,
-0.01366699393838644,
0.049156635999679565,
-0.012507650069892406,
0.026427367702126503,
-0.024639543145895004,
0.03678636625409126,
0.08770903944969177,
-0.06880342960357666,
0.012062043882906437,
-0.04223411902785301,
0.0002919814141932875,
-0.006166230421513319,
-0.04955817759037018,
-0.02779979072511196,
-0.01043905783444643,
-0.027444183826446533,
0.017565879970788956,
0.04511936381459236,
-0.00871832575649023,
0.025503646582365036,
-0.017286477610468864,
-0.02027714252471924,
0.047582294791936874,
-0.04268426075577736,
0.012365293689072132,
0.006219683215022087,
-0.06415056437253952,
0.018614808097481728,
0.0042057703249156475,
-0.00010814562119776383,
-0.01897682435810566,
-0.036820776760578156,
-0.016257235780358315,
0.041768625378608704,
-0.020870845764875412,
-0.020218603312969208,
0.017758356407284737,
0.06359817832708359,
0.039259765297174454,
0.020948607474565506,
-0.02368859574198723,
-0.021266261115670204,
0.013828501105308533,
0.032028928399086,
0.014882365241646767,
0.04079651087522507,
0.03435838222503662,
-0.004174094647169113,
-0.017630526795983315,
0.02527081035077572,
-0.004163799807429314,
0.031110890209674835,
-0.01601616106927395,
0.04737953096628189,
0.06630483269691467,
0.024669697508215904,
0.005353410262614489,
0.05138464644551277,
-0.027778450399637222,
0.016914211213588715,
-0.001121516223065555,
-0.037478044629096985,
-0.04598506912589073,
0.016746222972869873,
0.03899477422237396,
0.04116375744342804,
-0.019931470975279808,
-0.01723526418209076,
0.04108073189854622,
0.05454055964946747,
0.008485340513288975,
0.056810323148965836,
-0.005151121877133846,
-0.03546762838959694,
0.01795468106865883,
0.020119348540902138,
-0.03418666496872902,
-0.008843994699418545,
0.056750357151031494,
-0.004137882497161627,
0.050310369580984116,
-0.0034577148035168648,
-0.033642932772636414,
0.02976561151444912,
-0.038078710436820984,
0.015512373298406601,
0.04613544046878815,
0.0013571529416367412,
0.023411955684423447,
-0.015111526474356651,
0.006390529219061136,
0.025829732418060303,
-0.008184599690139294,
0.014452905394136906,
-0.05819305405020714,
-0.011758673936128616,
-0.005345719400793314,
-0.02601414918899536,
-0.012751193717122078,
-0.036859188228845596,
0.01686585508286953,
-0.012740879319608212,
-0.02029513567686081,
0.010391180403530598,
-0.02878367342054844,
-0.029366936534643173,
-0.005451051518321037,
0.008402077481150627,
-0.006468145176768303,
-0.02554796077311039,
-0.01834969036281109,
-0.008257759734988213,
-0.00906563550233841,
0.00783977098762989,
0.015492414124310017,
0.03898315876722336,
-0.04211888834834099,
0.010171124711632729,
-0.03850309178233147,
-0.06284178793430328,
0.019073013216257095,
0.04039609059691429,
-0.021507546305656433,
0.030542487278580666,
0.009615430608391762,
-0.06367533653974533,
-0.023815464228391647,
-0.01625698432326317,
0.03994577005505562,
-0.029836736619472504,
-0.001340985530987382,
0.06440585106611252,
-0.012610138393938541,
-0.06790818274021149,
0.017428001388907433,
-0.05014210194349289,
-0.008205436170101166,
0.021943701431155205,
-0.02694583684206009,
-0.0142135601490736,
-0.0039411927573382854,
0.057691410183906555,
0.027957379817962646,
-0.009664680808782578,
-0.008053744211792946,
-0.0713760256767273,
-0.02564101479947567,
-0.029681401327252388,
0.031459782272577286,
0.049890559166669846,
-0.012389501556754112,
-0.05352035164833069,
0.0772789791226387,
0.02745574712753296,
-0.054984696209430695,
-0.010921366512775421,
0.001574171707034111,
-0.009841199964284897,
-0.028654780238866806,
0.010928674601018429,
0.03266172856092453,
-0.04733918234705925,
-0.0009692959720268846,
-0.005045813042670488,
0.06696519255638123,
0.015784261748194695,
0.020724497735500336,
0.013963248580694199,
0.0352778434753418,
-0.008362957276403904,
0.002336884383112192,
0.045433808118104935,
0.0026451461017131805,
-0.02189454808831215,
-0.02244560793042183,
0.01788290962576866,
0.04716635122895241,
0.02707996405661106,
-0.009951933287084103,
0.03668425604701042,
0.01650891825556755,
0.00652514910325408,
-0.0367334820330143,
0.03782576695084572,
-0.009120465256273746,
-0.063355952501297,
-0.015057595446705818,
0.006395062897354364,
0.07094161212444305,
-0.04158416762948036,
-0.005994248669594526,
0.014685779809951782,
0.03974386677145958,
-0.037899699062108994,
-0.01422224473208189,
-0.030057620257139206,
-0.007562779355794191,
0.005860204342752695,
-0.0406946986913681,
0.01854916475713253,
0.03915327414870262,
0.06318347901105881,
-0.04975312203168869,
-0.039479754865169525,
-0.0226504597812891,
-0.008714939467608929,
-0.03585271164774895,
-0.008872455917298794,
0.0033933776430785656,
0.04065238684415817,
0.006427501328289509,
0.05528782308101654,
0.009870722889900208,
-0.02520512230694294,
0.022404251620173454,
-0.003029537620022893,
-0.025434015318751335,
-0.004737292882055044,
0.03558720275759697,
-0.04497404396533966,
-0.02595074288547039,
-0.023439155891537666,
0.0007512886659242213,
-0.028975507244467735,
-0.0251765176653862,
-0.02664356306195259,
-0.0428827665746212,
-0.0527181476354599,
0.026136767119169235,
-0.009800130501389503,
-0.020853763446211815,
-0.030530700460076332,
0.03726288676261902,
0.10071782022714615,
-0.05567888170480728,
0.04083159193396568,
0.024475278332829475,
-0.04799089580774307,
-0.013061183504760265,
-0.009350859560072422,
-0.006575650069862604,
0.03785762935876846,
-0.01815657503902912,
0.00426710257306695,
0.010954429395496845,
0.0034977635368704796,
0.006743317004293203,
-0.01571795716881752,
0.05060219019651413,
0.03964248299598694,
-0.042130328714847565,
0.007954311557114124,
-0.04510154202580452,
0.014258946292102337,
-0.013385102152824402,
0.06784617900848389,
0.02128712646663189,
0.03978962078690529,
0.02166617102921009,
0.02467583306133747,
-0.008582552894949913,
0.03319624811410904,
0.024608155712485313,
-0.007421265821903944,
-0.005486641079187393,
-0.05521401762962341,
0.015741242095828056,
-0.00840829499065876,
-0.019850924611091614,
0.029556697234511375,
-0.021163083612918854,
-0.013057317584753036,
-0.04823872447013855,
0.010278106667101383,
0.011049038730561733,
-0.027672138065099716,
0.016941942274570465,
-0.0011211512610316277,
-0.011337724514305592,
-0.01688261516392231,
-0.005841576959937811,
-0.008422411046922207,
0.028068235144019127,
0.05526508390903473,
0.00595298083499074,
0.009771950542926788,
-0.07818330079317093,
-0.03417498245835304,
0.03302830085158348,
0.032607145607471466,
0.012594100087881088,
-0.02411789633333683,
-0.052805475890636444,
-0.0036670579575002193,
0.044151999056339264,
-0.03926020860671997,
0.02843639627099037,
-0.0172223299741745,
-0.011712083593010902,
-0.05865718796849251,
-0.0633484348654747,
-0.02768300287425518,
0.003632750827819109,
-0.046901267021894455,
0.026623645797371864,
-0.03397589549422264,
-0.002107391832396388,
0.014331362210214138,
0.006566280033439398,
0.0088976314291358,
0.01673545129597187,
0.03586040437221527,
-0.013417483307421207,
-0.008220415562391281,
0.0368441566824913,
-0.002777474233880639,
-0.04309242591261864,
0.050213612616062164,
-0.009711872786283493,
0.020233947783708572,
0.016963504254817963,
-0.03345987945795059,
-0.05712149292230606,
0.026433737948536873,
-0.008966180495917797,
0.014176507480442524,
0.0060052513144910336,
-0.04521467536687851,
0.0303618386387825,
0.021229906007647514,
0.014213591814041138,
0.03921665623784065,
-0.003961572423577309,
0.006325796712189913,
-0.028654366731643677,
-0.012480993755161762,
0.0011537738610059023,
0.0007359439041465521,
-0.018188323825597763,
-0.021656109020113945,
0.028422608971595764,
0.009922987781465054,
0.06350970268249512,
-0.04236789792776108,
0.0009386462043039501,
-0.026954269036650658,
-0.012085449881851673,
-0.020715083926916122,
0.010452352464199066,
-0.03787767142057419,
-0.009686462581157684,
0.018892580643296242,
0.0035409422125667334,
0.013082842342555523,
-0.010399927385151386,
0.003284093691036105,
-0.032649509608745575,
0.00014000180817674845,
0.0381479375064373,
0.023041749373078346,
0.0021007114555686712,
0.014531097374856472,
0.0030032715294510126,
0.04525215923786163,
-0.05051015689969063,
0.051751501858234406,
0.0025514739099889994,
-0.02554093673825264,
-0.00874392595142126,
-0.061949532479047775,
-0.0641278550028801,
-0.009439780376851559,
-0.02227923646569252,
-0.004910281393676996,
-0.02170233614742756,
0.0010325855109840631,
0.060939863324165344,
0.03098156489431858,
-0.045408107340335846,
-0.028807228431105614,
0.03526091203093529,
-0.04694239795207977,
-0.03768221661448479,
-0.011433173902332783,
-0.021799413487315178,
0.008248819038271904,
-0.012460737489163876,
0.009150047786533833,
0.02168605849146843,
-0.05915956199169159,
-0.02680465765297413,
0.004331447649747133,
0.049969371408224106,
0.0259049441665411,
-0.028361286967992783,
-0.008965319953858852,
0.01794201135635376,
-0.029894994571805,
0.03304806351661682,
0.02701929397881031,
0.024364130571484566,
-0.0028114551678299904,
-0.012901180423796177,
-0.013236207887530327,
-0.02507285214960575,
0.01056243758648634,
-0.009636444970965385,
-0.009846034459769726,
0.0020970457699149847,
0.013395997695624828,
-0.0113235367462039,
-0.027929410338401794,
-0.025024818256497383,
0.02670668624341488,
0.01947926916182041,
-0.00010955135803669691,
-0.010230067186057568,
-0.03941181302070618,
0.010288635268807411,
0.02883005514740944,
-0.00802615750581026,
0.016454052180051804,
-0.02644944377243519,
0.049849726259708405,
-0.020519042387604713,
0.016269396990537643,
0.0043298909440636635,
0.024884767830371857,
0.010775011964142323,
-0.04961909353733063,
-0.03006398119032383,
0.017058342695236206,
-0.0016690193442627788,
-0.03148849308490753,
0.005846707616001368,
-0.05573320761322975,
0.040944065898656845,
0.05206967517733574,
-0.013337142765522003,
0.04270276427268982,
0.030377097427845,
-0.028738945722579956,
0.016775580123066902,
-0.0005666130455210805,
-0.049652863293886185,
0.007062376942485571,
-0.004797268193215132,
0.021483927965164185,
-0.05001411214470863,
-0.02648984268307686,
0.026342183351516724,
0.023239701986312866,
-0.057062018662691116,
-0.05614905804395676,
0.013833398930728436,
0.008638925850391388,
-0.0036636844743043184,
0.007873356342315674,
-0.032201677560806274,
0.027062276378273964,
0.0018477470148354769,
0.0019257259555161,
0.02255980297923088,
-0.026390958577394485,
0.02544381655752659,
0.0010664998553693295,
-0.0005861930549144745,
-0.00763127813115716,
-0.016635356470942497,
-0.06281326711177826,
0.010033276863396168,
0.04021609202027321,
-0.03333305940032005,
-0.012367920950055122,
0.0067550805397331715,
0.02738085575401783,
0.00818659644573927,
0.0009390888153575361,
-0.011287996545433998,
-0.04309443384408951,
-0.009456413798034191,
-0.027886850759387016,
-0.011579870246350765,
0.05583354830741882,
-0.011630495078861713,
-0.019043931737542152,
0.010424596257507801,
-0.027248596772551537,
0.05851958319544792,
0.02727344073355198,
0.012128230184316635,
-0.028680963441729546,
0.08697512000799179,
-0.010880452580749989,
0.033357884734869,
-0.03196191042661667,
-0.02738572284579277,
0.11165518313646317,
0.05181513726711273,
-0.012312685139477253,
-0.05223924666643143,
0.02118338830769062,
-0.009163114242255688,
0.005328257102519274,
-0.05656970292329788,
0.016782740131020546,
-0.01921716518700123,
-0.03803776577115059,
-0.01010202243924141,
-0.000857126316986978,
-0.0299387089908123,
0.008700589649379253,
0.024099359288811684,
-0.03444064408540726,
-0.05123774707317352,
-0.010627632029354572,
0.024081433191895485,
-0.0017303491476923227,
0.03089897893369198,
-0.04384790360927582,
0.020569417625665665,
-0.05205678194761276,
-0.0037355292588472366,
-0.02769658900797367,
0.0003182622604072094,
0.022159453481435776,
0.00517579959705472,
-0.012894482351839542,
0.0006451581721194088,
0.0027229045517742634,
-0.029787549749016762,
-0.02107839100062847,
0.051405616104602814,
0.050954800099134445,
-0.009570199064910412,
0.03228895738720894,
0.03673088178038597,
0.012580246664583683,
-0.019886154681444168,
0.019040070474147797,
0.06262946873903275,
-0.049735113978385925,
-0.024436648935079575,
-0.012438037432730198,
0.03678864985704422,
-0.05067591369152069,
-0.004965337458997965,
-0.025231335312128067,
0.04726045951247215,
-0.008817576803267002,
-0.06221826374530792,
-0.01904400996863842,
-0.034356649965047836,
0.04133281484246254,
-0.02482304349541664,
0.0017714143032208085,
-0.020185431465506554,
-0.009500428102910519,
0.018442390486598015,
0.01643352583050728,
-0.013250825926661491,
-0.01098773255944252,
0.004257448948919773,
-0.0070317634381353855,
0.05132496356964111,
-0.0002430387248750776,
-0.004218535032123327,
-0.017247073352336884,
-0.03153618052601814,
-0.007361199241131544,
0.011124949902296066,
-0.006924215704202652,
0.012371585704386234,
0.01723521016538143,
0.003430416574701667,
-0.010103914886713028,
0.02638702280819416,
-0.06865010410547256,
-0.008411421440541744,
-0.002601181622594595,
-0.019773416221141815,
-0.030208168551325798,
0.0002723530924413353,
-0.009721670299768448,
0.04631560295820236,
0.020471440628170967,
0.00931299477815628,
0.007543813902884722,
0.05081256479024887,
0.029684865847229958,
-0.012625242583453655,
-0.03225039318203926,
0.03171183541417122,
0.0176691934466362,
0.0016849980456754565,
-0.003032489912584424,
-0.006364266853779554,
0.030252665281295776,
-0.013041950762271881,
-0.02775128372013569,
0.04210573434829712,
-0.020794717594981194,
-0.0360100157558918,
0.029842056334018707,
0.008025999180972576,
0.024794716387987137,
0.033689986914396286,
0.016738343983888626,
-0.06036321073770523,
0.030987095087766647,
0.011197524145245552,
-0.0007869686232879758,
-0.003956028260290623,
-0.0030755880288779736,
-0.03773042559623718,
-0.03414266183972359,
-0.036016084253787994,
-0.00783024076372385,
-0.00803577620536089,
-0.019330529496073723,
-0.053718652576208115,
0.03183504566550255,
-0.04956638067960739,
0.011490503326058388,
-0.0596773661673069,
0.04394860565662384,
0.0009454661631025374,
-0.004790432285517454,
0.031132984906435013,
0.01545717567205429,
-0.005974292289465666,
-0.03353360295295715,
0.0063016884960234165,
-0.007241200655698776,
0.022706354036927223,
-0.0037807237822562456,
-0.0508403480052948,
0.021606434136629105,
-0.03877027705311775,
0.006145345512777567,
0.01209625881165266,
0.03406110778450966,
0.019803378731012344,
0.019312018528580666,
-0.005533501971513033,
-0.010922970250248909,
0.026910360902547836,
0.017611676827073097,
0.009757454507052898,
0.00909391324967146,
-0.07460588216781616,
0.025267308577895164,
-0.005331280641257763,
0.012215928174555302,
-0.003920361399650574,
0.01079979632049799,
-0.025051599368453026,
0.01917644776403904,
-0.027537180110812187,
-0.0034739268012344837,
0.04940887540578842,
-0.0010616474319249392,
-0.013875368982553482,
0.028154071420431137,
-0.031648147851228714,
0.024183232337236404,
0.02837972156703472,
-0.012648927979171276,
0.016217082738876343,
0.015565704554319382,
0.03320317342877388,
-0.06926374137401581,
0.00888358149677515,
0.002546316245570779,
0.013879402540624142,
0.014486978761851788,
-0.05075210705399513,
-0.01577010564506054,
0.04516448825597763,
-0.055851444602012634,
0.009087570011615753,
-0.02763361856341362,
0.03936941549181938,
-0.023247040808200836,
-0.029594728723168373,
-0.00336231361143291,
0.044856444001197815,
0.03971805423498154,
0.0334308035671711,
0.02105735056102276,
0.009514246135950089,
-0.01788119599223137,
-0.03553523123264313,
-0.025510048493742943,
0.06169538199901581,
0.012840251438319683,
-0.016950126737356186,
0.05205761641263962,
0.01452464610338211,
0.004094251897186041,
0.03468228131532669,
0.02791779674589634,
-0.013388860039412975,
0.003978048916906118,
0.027295434847474098,
0.030895518139004707,
0.04757068306207657,
0.03227004036307335,
0.006474363151937723,
-0.01803165301680565,
-0.03856518492102623,
0.027194643393158913,
-0.0217447392642498,
0.0013241204433143139,
-0.03034920059144497,
0.036254990845918655,
-0.023722929880023003,
-0.02818901091814041,
0.059192053973674774,
-0.015384606085717678,
0.029189113527536392,
0.020449383184313774,
0.0018904156750068069,
0.011334538459777832,
-0.03425125032663345,
-0.002243044786155224,
-0.014812592417001724,
0.0042426250874996185,
0.03138815611600876,
-0.027840545400977135,
-0.033791933208703995,
0.02025151252746582,
-0.027021188288927078,
-0.03585921600461006,
0.025506967678666115,
-0.00845276564359665,
-0.02353755198419094,
-0.09975092858076096,
-0.0015595660079270601,
0.017613327130675316,
-0.011665649712085724,
-0.007517773658037186,
-0.006406731437891722,
-0.04182642325758934,
0.023582540452480316,
0.043458372354507446,
-0.016286032274365425,
0.004497684072703123,
-0.014654112048447132,
-0.02012772671878338,
-0.050155993551015854,
0.032289449125528336,
0.041160788387060165,
-0.058296795934438705,
-0.04042867198586464,
-0.05981548875570297,
0.0017875619232654572,
0.02200145833194256,
0.0550081692636013,
0.0010645976290106773,
-0.047663815319538116,
0.037194766104221344,
0.007371760904788971,
0.044847264885902405,
-0.05361313745379448,
-0.007769167888909578,
0.023226145654916763,
0.018417982384562492,
0.02731369435787201,
0.01592784933745861,
-0.014123942703008652,
0.010838368907570839,
0.002233214909210801,
0.021591033786535263,
0.015441272407770157,
-0.01604338362812996,
-0.02649097330868244,
0.01052294485270977,
0.0070921326987445354,
-0.023570699617266655,
0.05848180502653122,
0.017724450677633286,
0.010241757147014141,
0.008756829425692558,
-0.021245360374450684,
-0.0349184051156044,
0.0025343133602291346,
-0.032793473452329636,
0.002522976603358984,
-0.011445263400673866,
-0.036492545157670975,
0.05982350930571556,
-0.0319918654859066,
-0.03306255862116814,
0.045574210584163666,
-0.03129070997238159,
-0.052121926099061966,
0.07542932033538818,
-0.014759010635316372,
0.057917188853025436,
0.028074417263269424,
0.03956237807869911,
0.004874897189438343,
-0.033316999673843384,
0.017573226243257523,
0.02409018948674202,
0.05615657940506935,
-0.02021964080631733,
-0.028912100940942764,
0.04604498669505119,
0.0032435415778309107,
0.02261093258857727,
0.007128463592380285,
0.031203407794237137,
-0.039697397500276566,
0.015772394835948944,
0.01972695253789425,
-0.05807333067059517,
-0.01376443263143301,
0.041434191167354584,
-0.017086494714021683,
0.07307077199220657,
-0.017297156155109406,
0.01527701411396265,
-0.015234085731208324,
0.0430133081972599,
-0.020440850406885147,
0.05541122704744339,
-0.0255439355969429,
0.037696678191423416,
-0.012838959693908691,
-0.0039661419577896595,
-0.034303516149520874,
-0.038995057344436646,
0.014106044545769691,
-0.027362417429685593,
0.0034074117429554462,
0.08474456518888474,
-0.00906626507639885,
-0.014977896586060524,
0.012883971445262432,
-0.011292736046016216,
-0.03155050799250603,
0.012496309354901314,
0.030265377834439278,
-0.00901693943887949,
0.019416948780417442,
0.002750510349869728,
-0.01289114635437727,
0.039872460067272186,
-0.05877162143588066,
-0.030481066554784775,
-0.0012293547624722123,
0.022494954988360405,
0.012986700050532818,
0.02384655736386776
] |
<p>In a nutshell, Noether's theorem states that for every continuous symmetry a corresponding conserved quantity exists.</p>
<p>Now, the Hamiltonian equations of motion (let's talk about a classical system here) are invarinat under addition of any constant to the Hamiltonian function</p>
<p>$$H\rightarrow H+ \text{const.}$$</p>
<p>Is there a corresponding conserved quantity?</p>
| 9,596 |
[
-0.036775484681129456,
-0.02045276015996933,
-0.008892028592526913,
0.009685744531452656,
0.02640802599489689,
-0.007475356571376324,
-0.06280829012393951,
-0.013704117387533188,
0.011849310249090195,
-0.05955949425697327,
-0.004671690985560417,
-0.010861311107873917,
0.02503429539501667,
0.005063837859779596,
0.012454451061785221,
0.010767660103738308,
0.0019830327946692705,
0.00032516554347239435,
0.00901729054749012,
0.01085261907428503,
-0.02947281114757061,
0.028416473418474197,
0.02799735963344574,
-0.00885751098394394,
0.00012483104364946485,
0.019577965140342712,
0.00011383675155229867,
-0.010458233766257763,
0.05399658530950546,
0.057195600122213364,
0.01327790692448616,
-0.015161536633968353,
0.01329154521226883,
0.08899180591106415,
0.01096940878778696,
0.010585339739918709,
-0.013642610050737858,
-0.02307617850601673,
0.0036681918427348137,
-0.015220914967358112,
-0.03380206227302551,
-0.024347351863980293,
-0.00048713202704675496,
0.06334042549133301,
-0.011461743153631687,
0.015382762998342514,
-0.01739666610956192,
-0.021971315145492554,
0.033043164759874344,
-0.05805922672152519,
0.08241597563028336,
0.017068805173039436,
0.04652644321322441,
0.0005469635361805558,
-0.03571576997637749,
0.007214836310595274,
0.05024535953998566,
0.056055210530757904,
-0.0012732130708172917,
-0.04786122962832451,
-0.023129496723413467,
-0.02973657287657261,
-0.005233141593635082,
-0.01007865834981203,
-0.034040600061416626,
0.02601723186671734,
-0.0014721619663760066,
-0.03379577025771141,
0.03130602836608887,
0.0035918548237532377,
-0.018247434869408607,
0.017499662935733795,
0.04878230020403862,
-0.06336528807878494,
0.025243466719985008,
-0.01845584809780121,
0.014085500501096249,
-0.026577124372124672,
0.023723039776086807,
0.02308870293200016,
0.03024914488196373,
-0.0008353808079846203,
0.020427528768777847,
0.047379009425640106,
0.020846780389547348,
-0.0025081608910113573,
0.0425381064414978,
-0.01379416324198246,
0.02577204257249832,
0.05169224739074707,
-0.0036604558117687702,
-0.01577852852642536,
-0.0017601706786081195,
-0.011095206253230572,
-0.019062625244259834,
0.010856875218451023,
0.008979212492704391,
0.04858887568116188,
0.006003741640597582,
-0.008251329883933067,
0.022984150797128677,
-0.03145191818475723,
0.026873745024204254,
0.05406025052070618,
-0.006819928530603647,
0.00008406122651649639,
-0.01583450473845005,
-0.019739683717489243,
-0.015566045418381691,
0.014342461712658405,
-0.0779738500714302,
0.011297683231532574,
0.007860728539526463,
-0.002764798002317548,
0.014759769663214684,
-0.022324101999402046,
0.009945105761289597,
-0.028252365067601204,
0.05245190113782883,
0.05453548580408096,
0.05062601715326309,
-0.006681550294160843,
0.019894232973456383,
0.01159505732357502,
-0.06362883746623993,
0.0016952541191130877,
0.012516940012574196,
0.015725841745734215,
-0.034265488386154175,
0.0009729047305881977,
-0.003724584821611643,
-0.025329332798719406,
-0.019156649708747864,
0.019295709207654,
0.034680724143981934,
-0.022321129217743874,
-0.10335657745599747,
-0.06367963552474976,
0.01628027856349945,
-0.016477957367897034,
-0.06744126975536346,
-0.0642658993601799,
0.009218396618962288,
0.009682209230959415,
0.07320559769868851,
-0.007127384189516306,
-0.016865180805325508,
0.030876262113451958,
0.020122328773140907,
0.040872279554605484,
0.009824954904615879,
-0.041028354316949844,
0.04895599186420441,
-0.033341094851493835,
-0.024004725739359856,
-0.09074459224939346,
0.0012884971220046282,
0.015899671241641045,
0.035907477140426636,
-0.01609150692820549,
0.05375555530190468,
-0.009751878678798676,
0.004930066876113415,
-0.015667425468564034,
0.0075769005343317986,
-0.019690677523612976,
0.05944988876581192,
-0.012941813096404076,
0.021560324355959892,
0.003152169520035386,
0.04710717126727104,
0.022134309634566307,
-0.0022575710900127888,
0.03423919156193733,
0.05334468185901642,
-0.03599749878048897,
-0.030496831983327866,
-0.010555516928434372,
0.007631659507751465,
0.038920819759368896,
-0.00047120629460550845,
-0.037061650305986404,
0.026112422347068787,
0.017877496778964996,
-0.0012704110704362392,
0.027725838124752045,
-0.0003369895275682211,
0.011243829503655434,
-0.01283864863216877,
-0.025461113080382347,
0.007439006119966507,
-0.08280067145824432,
0.038762789219617844,
0.011849579401314259,
-0.03822464495897293,
0.053364649415016174,
0.0647135004401207,
0.01778036542236805,
-0.04226359352469444,
-0.03894845396280289,
0.001140758628025651,
0.03296705707907677,
0.001515959040261805,
-0.03761863335967064,
0.030245458707213402,
0.02536896802484989,
0.045029252767562866,
0.031342312693595886,
0.04653563350439072,
-0.0003301881661172956,
-0.04736859351396561,
-0.00585043802857399,
-0.034795843064785004,
0.0010204677237197757,
-0.01463955920189619,
0.026718009263277054,
0.008409491740167141,
-0.05933041125535965,
0.002457204507663846,
0.06712273508310318,
-0.03439633548259735,
0.07561345398426056,
0.036793582141399384,
0.005458058323711157,
0.021509245038032532,
0.023875929415225983,
-0.007130268961191177,
0.0055255223996937275,
-0.01579141803085804,
-0.012466223910450935,
-0.03178461268544197,
-0.007105093449354172,
0.026280740275979042,
0.055779438465833664,
-0.03676250949501991,
-0.02029748633503914,
0.021662401035428047,
0.045899275690317154,
0.044549793004989624,
0.009471938014030457,
-0.032074712216854095,
-0.03006499819457531,
0.025654079392552376,
0.029279444366693497,
0.02942199446260929,
0.02499103546142578,
0.023444751277565956,
0.0026109975297003984,
0.022007863968610764,
0.009539259597659111,
0.001682668924331665,
0.033455174416303635,
0.025608310475945473,
0.028115974739193916,
0.01373292040079832,
-0.011314262636005878,
0.019595131278038025,
0.001749601447954774,
0.05961643531918526,
0.02875198796391487,
-0.014101603999733925,
-0.013346943072974682,
-0.01155166607350111,
-0.024510446935892105,
0.00030276525649242103,
-0.03717196732759476,
-0.03465338423848152,
-0.0154492212459445,
0.022702088579535484,
-0.017569759860634804,
-0.013591322116553783,
-0.04077162593603134,
-0.007297614589333534,
-0.012929542921483517,
-0.029527513310313225,
0.008459266275167465,
0.0020038955844938755,
0.036937300115823746,
-0.038850437849760056,
-0.004894521087408066,
-0.0019279110711067915,
-0.06635210663080215,
-0.025631815195083618,
0.006923687178641558,
-0.043169282376766205,
0.03179143741726875,
-0.02939514070749283,
-0.008549670688807964,
0.03831547498703003,
-0.018033988773822784,
0.02911425568163395,
0.010427509434521198,
-0.02461082488298416,
-0.06458573043346405,
-0.0029757109005004168,
-0.044919151812791824,
0.012475046329200268,
-0.04821180924773216,
0.01489036250859499,
0.005564459599554539,
-0.021292442455887794,
-0.017574070021510124,
0.011718540452420712,
0.010535512119531631,
-0.035562604665756226,
-0.028626669198274612,
0.002128354739397764,
0.013169444166123867,
-0.02766367234289646,
0.007714154664427042,
0.012405707500874996,
-0.05541572719812393,
-0.010339586064219475,
-0.04688197001814842,
-0.04807886853814125,
0.012252037413418293,
-0.023112298920750618,
0.027865884825587273,
0.007649665232747793,
-0.051782187074422836,
0.09818220883607864,
0.03618888184428215,
-0.02887672372162342,
-0.006580800283700228,
-0.040156085044145584,
0.014700614847242832,
-0.026435578241944313,
-0.010410127229988575,
0.03925784304738045,
-0.000933851464651525,
0.021028833463788033,
0.033845867961645126,
0.019905341789126396,
0.007658895570784807,
0.007395013235509396,
-0.0288567915558815,
0.036342792212963104,
0.039568111300468445,
0.03926324471831322,
0.062321558594703674,
0.02357526868581772,
-0.03647679090499878,
0.007119171321392059,
-0.008588000200688839,
0.026563173159956932,
-0.007478389889001846,
-0.05986357107758522,
0.0690235123038292,
0.011394953355193138,
0.028866931796073914,
-0.04189913719892502,
0.04436797276139259,
-0.00752353435382247,
0.022841373458504677,
-0.009744163602590561,
0.04578811302781105,
0.027176035568118095,
-0.011574702337384224,
0.022851087152957916,
0.010407277382910252,
0.010383069515228271,
-0.02790673077106476,
-0.010689967311918736,
0.004467374179512262,
-0.016417382284998894,
0.03434339910745621,
-0.012258910574018955,
-0.0222314465790987,
0.014515440911054611,
0.0023505748249590397,
0.03230425715446472,
0.023878879845142365,
-0.04980301856994629,
0.0022723174188286066,
-0.06405661255121231,
-0.013925852254033089,
-0.00035757641308009624,
0.04003582149744034,
-0.0012589643010869622,
0.0724589079618454,
0.0001524827821413055,
0.03354838117957115,
0.021473735570907593,
-0.014943062327802181,
-0.08250617980957031,
0.06671826541423798,
-0.03409135341644287,
-0.005319507792592049,
-0.001999437576159835,
-0.03377007693052292,
0.00532562704756856,
-0.028263404965400696,
-0.010301413014531136,
-0.008797883056104183,
0.002852245233952999,
-0.05608184635639191,
-0.014311353676021099,
-0.05175332352519035,
-0.0422222837805748,
-0.013995434157550335,
0.017726898193359375,
0.026348460465669632,
-0.04491358995437622,
0.02389238029718399,
0.02716086432337761,
-0.03155878186225891,
-0.03022204339504242,
-0.006924104876816273,
0.00011782705405494198,
0.0018201540224254131,
0.012239729054272175,
0.04204755276441574,
0.034949544817209244,
0.0064908829517662525,
0.00039405759889632463,
0.009871861897408962,
0.06910315155982971,
0.019616438075900078,
0.04061329364776611,
0.012665231712162495,
-0.05032918602228165,
-0.019885098561644554,
0.01032701600342989,
0.04507582634687424,
0.01940699853003025,
0.012881588190793991,
0.021938491612672806,
0.019171055406332016,
-0.034447506070137024,
0.014795560389757156,
0.029050692915916443,
0.06338783353567123,
-0.03730820119380951,
-0.06890712678432465,
0.02455388382077217,
-0.06844233721494675,
-0.0016363458707928658,
-0.025349926203489304,
-0.012173858471214771,
-0.029377371072769165,
0.0034480539616197348,
-0.0008818110218271613,
0.028696410357952118,
-0.014070427976548672,
-0.03187411278486252,
0.017827868461608887,
0.03850119933485985,
0.011396916583180428,
0.010125190019607544,
0.024389225989580154,
0.03289494663476944,
0.020187534391880035,
-0.012399446219205856,
0.0021876937244087458,
-0.09072571992874146,
0.011454340070486069,
0.010467157699167728,
0.01968339830636978,
-0.004579138942062855,
0.011433446779847145,
-0.047517161816358566,
-0.03670961409807205,
0.06152328476309776,
-0.011013630777597427,
0.03628721833229065,
0.009019793011248112,
-0.016964135691523552,
-0.005955291446298361,
-0.02498776838183403,
-0.03896291181445122,
0.03338512033224106,
-0.03209145739674568,
0.013379587791860104,
-0.039547450840473175,
0.02241816371679306,
-0.01867537386715412,
0.04868478327989578,
0.01706446334719658,
0.059762805700302124,
0.025076674297451973,
0.0004539976653177291,
-0.012839226052165031,
0.018413107842206955,
-0.022332463413476944,
-0.08055604994297028,
-0.0034433561377227306,
0.03714451566338539,
0.00728435255587101,
0.02936098538339138,
-0.03239414095878601,
-0.0329742431640625,
-0.002630965318530798,
0.0006069198134355247,
-0.016061685979366302,
0.05488790571689606,
-0.011046433821320534,
0.04627075791358948,
0.05704521760344505,
0.01799570396542549,
0.02247811295092106,
0.042573340237140656,
0.014457497745752335,
-0.01882239617407322,
-0.025049563497304916,
0.04251775145530701,
-0.019948212429881096,
-0.01744683086872101,
-0.04346610605716705,
-0.009568889625370502,
-0.034158818423748016,
0.024497995153069496,
0.008496800437569618,
0.002934762742370367,
-0.007486135233193636,
0.004873813595622778,
-0.012529305182397366,
0.02338770404458046,
0.006923221983015537,
-0.0220414437353611,
0.0022265389561653137,
0.03303315490484238,
0.03254863992333412,
-0.020960506051778793,
0.019015276804566383,
-0.01117685716599226,
-0.05452705919742584,
0.03333910554647446,
-0.01557249017059803,
0.04093993827700615,
-0.006289542652666569,
-0.03246520087122917,
0.02516844868659973,
-0.0010712207295000553,
0.020494313910603523,
-0.019771577790379524,
-0.008777167648077011,
0.037778567522764206,
-0.05916669964790344,
-0.012398906983435154,
0.018314799293875694,
-0.007422994822263718,
0.0027442453429102898,
-0.04833841696381569,
0.03604965656995773,
0.034543558955192566,
0.007753326557576656,
-0.07479898631572723,
-0.03962438181042671,
0.008712398819625378,
0.005032709799706936,
-0.023662222549319267,
-0.011828579008579254,
-0.022148076444864273,
-0.018551921471953392,
-0.039707913994789124,
0.006480007898062468,
0.024031544104218483,
-0.03257764130830765,
0.010772719979286194,
0.008046095259487629,
0.00020943816343788058,
0.039017051458358765,
-0.006815474014729261,
-0.0025452945847064257,
-0.027682367712259293,
-0.02231322042644024,
-0.0026453863829374313,
0.012039054185152054,
0.06499914824962616,
-0.028550799936056137,
-0.003790405346080661,
0.0059380680322647095,
-0.022401131689548492,
0.04697948694229126,
0.013043828308582306,
-0.011817623861134052,
0.0364532507956028,
-0.013968848623335361,
-0.006233422085642815,
-0.03517826646566391,
-0.011026445776224136,
-0.04371020942926407,
0.05101671814918518,
0.01125648245215416,
-0.002605771878734231,
-0.031346578150987625,
-0.026617789641022682,
0.019093679264187813,
0.03459840640425682,
-0.004853999242186546,
-0.019374467432498932,
0.05533720552921295,
-0.016863876953721046,
-0.030611258000135422,
0.026488708332180977,
0.0033947236370295286,
0.003080353606492281,
-0.01989133097231388,
-0.01818644441664219,
-0.037625618278980255,
-0.0002759589988272637,
-0.05322074517607689,
-0.03340982273221016,
-0.026088815182447433,
0.044297099113464355,
0.06470504403114319,
-0.027421431615948677,
0.0504162535071373,
0.02505156584084034,
-0.014244237914681435,
-0.012263935059309006,
0.004375176504254341,
-0.016696961596608162,
0.012905929237604141,
0.03725181147456169,
0.01285164337605238,
0.0019139084033668041,
0.019069524481892586,
0.04181290045380592,
0.0624050535261631,
-0.04409581050276756,
0.009941053576767445,
0.012813569977879524,
0.009957066737115383,
-0.009743161499500275,
-0.014515288174152374,
-0.02031286060810089,
0.025022389367222786,
-0.03524288162589073,
0.07812923192977905,
-0.02758605405688286,
-0.04601466655731201,
0.037830695509910583,
0.005710418336093426,
0.00277453544549644,
-0.007761743385344744,
-0.037088245153427124,
0.00364543404430151,
0.05115588754415512,
-0.02339359000325203,
0.0198329109698534,
-0.03180165961384773,
0.01638505980372429,
0.04660550877451897,
0.007276078220456839,
-0.007761629298329353,
-0.011982271447777748,
-0.061818886548280716,
-0.0025886783841997385,
-0.04006410762667656,
-0.021438399329781532,
0.041254132986068726,
0.038618046790361404,
-0.0353035070002079,
0.023459283635020256,
-0.0035346313379704952,
0.0005663100746460259,
0.00872349925339222,
0.03602970391511917,
0.0004027494869660586,
0.07659437507390976,
-0.0010098577477037907,
0.024720197543501854,
-0.01492555532604456,
0.04093280807137489,
0.09898246824741364,
0.05552759766578674,
-0.01503397524356842,
-0.051615435630083084,
0.027202049270272255,
-0.019449172541499138,
-0.007142859976738691,
-0.015888769179582596,
0.03065554052591324,
0.007349201012402773,
-0.002793700434267521,
-0.002140832133591175,
0.025507567450404167,
-0.043305423110723495,
0.001576934359036386,
0.08543280512094498,
-0.0259197186678648,
-0.010078325867652893,
-0.005868854001164436,
0.01765020750463009,
0.02027386613190174,
0.010701078921556473,
-0.02468060329556465,
-0.018671749159693718,
-0.02799271047115326,
0.010665458627045155,
-0.04833373799920082,
-0.06310561299324036,
0.01940670982003212,
0.01076305191963911,
-0.024714885279536247,
0.020102374255657196,
0.024782316759228706,
-0.016959205269813538,
-0.07577183842658997,
-0.020905751734972,
0.036380570381879807,
0.02184186689555645,
0.030180102214217186,
0.057198554277420044,
0.022536395117640495,
0.01739613525569439,
-0.017100738361477852,
0.006188167259097099,
-0.02996165119111538,
0.01216187421232462,
-0.04046103358268738,
0.021765882149338722,
0.0009371775668114424,
0.05849669501185417,
-0.001176441553980112,
-0.030147623270750046,
-0.018779544159770012,
-0.05072862282395363,
-0.03238522633910179,
-0.010645687580108643,
0.002232328522950411,
-0.00687792245298624,
-0.026917653158307076,
-0.04053004831075668,
-0.02451120689511299,
-0.020156841725111008,
-0.0038342848420143127,
-0.019882602617144585,
-0.025722891092300415,
0.024813411757349968,
0.008737758733332157,
0.01575227826833725,
-0.023915844038128853,
-0.04187649115920067,
-0.02739083766937256,
-0.029073361307382584,
-0.03510384261608124,
-0.027522137388586998,
-0.015225066803395748,
0.021089838817715645,
0.03902728483080864,
0.00813597347587347,
-0.01556481420993805,
-0.008499088697135448,
-0.050612710416316986,
0.022405341267585754,
-0.003487373935058713,
-0.016392407938838005,
-0.003328850492835045,
-0.00934917014092207,
0.02433379366993904,
0.045102864503860474,
-0.06339509040117264,
0.014676433056592941,
-0.0026490692980587482,
0.004427780397236347,
0.039530616253614426,
0.002609581919386983,
-0.0020734115969389677,
0.022226087749004364,
-0.03798867017030716,
-0.00038459565257653594,
-0.02066730335354805,
0.02089417539536953,
0.02482447400689125,
0.015446001663804054,
0.01431801076978445,
0.04618227481842041,
-0.015207713469862938,
0.018338609486818314,
0.038233641535043716,
-0.011713690124452114,
0.027074865996837616,
0.009216710925102234,
0.0215164702385664,
-0.04930821433663368,
-0.03173131123185158,
-0.02447447180747986,
0.028902990743517876,
0.0076342495158314705,
0.01797742024064064,
-0.04478306323289871,
0.005926238372921944,
-0.026664018630981445,
0.05178169906139374,
-0.04642924666404724,
-0.002947963774204254,
-0.06627930700778961,
0.03237055987119675,
0.05077046528458595,
0.0030377765651792288,
-0.01633678376674652,
0.04228968918323517,
0.001934785395860672,
-0.02588004805147648,
0.02967148646712303,
0.038837697356939316,
0.004947276320308447,
-0.0012984529603272676,
0.011627398431301117,
0.008893999271094799,
0.04495365545153618,
-0.01828143186867237,
-0.05085454508662224,
0.06563221663236618,
-0.04095863923430443,
-0.021309098228812218,
0.023654138669371605,
-0.03248703479766846,
-0.005149985197931528,
0.021861400455236435,
-0.0052929045632481575,
0.004454222973436117,
0.0017218783032149076,
-0.007083865348249674,
0.01084644254297018,
0.012761781923472881,
-0.04335767403244972,
-0.018581563606858253,
-0.038801487535238266,
0.010460784658789635,
-0.01647711917757988,
0.00004898195402347483,
0.02633821591734886,
0.049320150166749954,
-0.026022499427199364,
0.021171391010284424,
-0.031286537647247314,
0.006276242434978485,
0.004265594761818647,
0.036307115107774734,
0.004741450306028128,
0.006708034314215183,
0.0664243996143341,
-0.06389198452234268,
0.02984732948243618,
0.034785196185112,
0.0033587731886655092,
-0.10134370625019073,
-0.01494374219328165,
-0.013832449913024902,
-0.010538807138800621,
0.030928613618016243,
-0.05633861944079399,
0.022706517949700356,
0.026609713211655617,
-0.062410321086645126,
0.027345329523086548,
-0.06454296410083771,
-0.016980117186903954,
-0.027578050270676613,
-0.025149570778012276,
-0.019507326185703278,
0.0755310133099556,
0.029285475611686707,
0.027029789984226227,
0.0472114123404026,
-0.0035649144556373358,
0.011496460996568203,
-0.0291742030531168,
-0.017298515886068344,
0.0058348821476101875,
0.003964885603636503,
-0.01868700608611107,
0.03267725184559822,
0.0037667842116206884,
-0.05601751431822777,
-0.017382824793457985,
-0.031715262681245804,
-0.002273053862154484,
-0.010870043188333511,
-0.004669355694204569,
0.006295633036643267,
0.036694057285785675,
-0.005131943617016077,
-0.02012450434267521,
-0.041869621723890305,
-0.003889702260494232,
0.02374664880335331,
0.03375571593642235,
-0.0160670168697834,
0.017118319869041443,
0.025153806433081627,
-0.06995891779661179,
-0.05166184902191162,
0.050552863627672195,
-0.02406742051243782,
0.008052472025156021,
0.02329595386981964,
-0.010266994126141071,
0.0037055995780974627,
-0.01976804994046688,
-0.008817809633910656,
-0.04186289757490158,
-0.0036322942469269037,
0.033822204917669296,
-0.0036137900315225124,
0.011103861965239048,
-0.010478716343641281,
0.010138587094843388,
-0.019198540598154068,
0.02978060394525528,
0.03027670457959175,
-0.00994101818650961,
-0.07555053383111954,
-0.0034588670823723078,
0.00676006032153964,
-0.010957764461636543,
-0.016989002004265785,
-0.05619879066944122,
-0.015985555946826935,
0.04641811177134514,
0.0207462627440691,
-0.024074580520391464,
-0.03540531173348427,
-0.0380825512111187,
-0.013256486505270004,
-0.060161441564559937,
0.029243851080536842,
0.037480372935533524,
-0.005764316767454147,
-0.01699851267039776,
0.012985553592443466,
-0.029979893937706947,
-0.01962781697511673,
0.029601197689771652,
-0.025558171793818474,
-0.03452540561556816,
0.04130220785737038,
0.005361184012144804,
0.011000780388712883,
-0.04845426231622696,
0.0017415109323337674,
-0.009047584608197212,
0.02141650579869747,
0.0046896361745893955,
-0.019624246284365654,
-0.01287935022264719,
-0.0033657560124993324,
0.03806614130735397,
-0.016971617937088013,
0.043002475053071976,
-0.004163037985563278,
-0.05017252266407013,
0.048041462898254395,
0.019756248220801353,
-0.014622142538428307,
0.06965695321559906,
-0.018077626824378967,
0.025658370926976204,
0.03126716986298561,
-0.03502654656767845,
-0.05240897461771965,
0.00019344608881510794,
-0.05799628421664238,
-0.027833595871925354,
-0.008841662667691708,
0.0046022511087358,
0.021192092448472977,
-0.02140713669359684,
0.022597335278987885,
0.08493206650018692,
-0.01287054643034935,
-0.03057972714304924,
0.04574405401945114,
0.027143795043230057,
0.03833933174610138,
0.0023410075809806585,
0.006650847848504782,
0.02510770596563816,
0.007392858620733023,
-0.002599467756226659,
0.06312902271747589,
0.030382120981812477,
-0.015049274079501629,
0.011890345253050327,
0.02195465750992298,
-0.02171439677476883,
0.0010575703345239162,
0.02752777934074402,
0.03110702708363533,
-0.03602166101336479,
-0.03332863748073578,
0.027284955605864525,
-0.010112613439559937,
0.03827062249183655,
0.017520705237984657,
-0.018291771411895752,
0.0814550369977951,
-0.00875759869813919,
0.005949551239609718,
-0.01753167249262333,
0.03895135968923569,
-0.020967263728380203,
-0.047094155102968216,
0.019703436642885208,
0.03723013401031494,
-0.0063518136739730835,
-0.0005833025788888335,
-0.02192070707678795,
0.019874656572937965,
-0.002709865104407072,
-0.03980473801493645,
0.036030590534210205,
0.005108964629471302,
0.0102089149877429,
-0.002799035981297493,
-0.024576712399721146,
-0.034305114299058914,
-0.01324949599802494,
0.03346727415919304,
0.03889293223619461,
0.06183875352144241,
-0.00952701736241579,
-0.01578575186431408,
-0.030387181788682938,
0.05908520519733429,
-0.04332291707396507,
-0.03590615838766098,
-0.008117320016026497,
0.02277253195643425,
-0.019942522048950195,
-0.02097516693174839
] |
<p>The action</p>
<p>$$S=\int L \;\mathrm{d}t$$</p>
<p>is an important physical quantity. But can it be understood more intuitively? The Hamiltonian corresponds to the energy, whereas the action has dimension of energy × time, the same as angular momentum.</p>
<p>I've heard the action being described as a measure of <em>change</em>, although I don't know how this description can be justified.</p>
| 9,597 |
[
-0.012051993981003761,
0.009024836122989655,
-0.005882971454411745,
-0.034144189208745956,
0.040490105748176575,
0.012874003499746323,
-0.0328972190618515,
-0.005906068254262209,
-0.01310661155730486,
-0.021332236006855965,
0.0377434678375721,
0.007752369623631239,
0.015654366463422775,
0.021340373903512955,
-0.003775019897148013,
0.004276870749890804,
0.018389729782938957,
-0.027603251859545708,
-0.018079174682497978,
-0.0072058383375406265,
0.015663934871554375,
0.016099514439702034,
-0.040582507848739624,
0.004681730642914772,
0.005479751620441675,
0.03772314637899399,
-0.0004462387878447771,
-0.0056397151201963425,
0.021647252142429352,
0.06373520195484161,
-0.01145215518772602,
-0.01164502277970314,
0.026560252532362938,
0.03542303666472435,
0.022974001243710518,
-0.00580257223919034,
-0.01268303208053112,
-0.04234962910413742,
0.0006458536954596639,
0.031998828053474426,
-0.01801205240190029,
-0.007626668084412813,
-0.018701566383242607,
0.0489322803914547,
-0.058669038116931915,
0.055572621524333954,
-0.02988431043922901,
-0.0052495235577225685,
0.03342091292142868,
-0.045280616730451584,
0.06277786195278168,
0.016017355024814606,
0.017412155866622925,
-0.017532076686620712,
-0.010904165916144848,
-0.005930855870246887,
0.03734690323472023,
0.06342658400535583,
-0.023127244785428047,
-0.04759065806865692,
-0.04713067784905434,
0.0008530514896847308,
0.019851550459861755,
-0.03727260231971741,
0.024100003764033318,
0.002488975180312991,
0.027188844978809357,
-0.037139616906642914,
0.026175759732723236,
0.006390771362930536,
-0.036819927394390106,
0.043172985315322876,
0.029674427583813667,
0.014911824837327003,
0.0124084847047925,
-0.04782041907310486,
0.041462741792201996,
0.02953498438000679,
0.03214922919869423,
0.032504867762327194,
-0.005912088323384523,
0.0017812623409554362,
0.0374152809381485,
0.03833462670445442,
0.030300429090857506,
-0.01898346096277237,
0.04867824167013168,
0.021828103810548782,
0.011866684071719646,
0.023318372666835785,
-0.01655951887369156,
0.024186192080378532,
-0.001221235143020749,
-0.027359476312994957,
-0.023174045607447624,
0.02764780819416046,
0.024343710392713547,
0.04487500712275505,
0.019631395116448402,
0.017079055309295654,
0.012820495292544365,
-0.03108755126595497,
0.014392335899174213,
0.03937060013413429,
-0.013231675140559673,
-0.03877148777246475,
-0.05441613122820854,
-0.000370317924534902,
-0.010788971558213234,
-0.0034380319993942976,
-0.041278690099716187,
0.0008377775666303933,
0.036222971975803375,
0.010704552754759789,
-0.0151978163048625,
-0.015258747152984142,
-0.02560512162744999,
0.003971898928284645,
0.060210227966308594,
0.05558925122022629,
0.03845889866352081,
-0.050102878361940384,
0.0061112516559660435,
-0.00709378719329834,
-0.053979191929101944,
0.03448229283094406,
0.05684174597263336,
-0.006353460252285004,
-0.04056733474135399,
0.027916712686419487,
-0.016302643343806267,
-0.01093976479023695,
-0.024728264659643173,
0.003115373430773616,
0.026606209576129913,
0.019212868064641953,
-0.09578511863946915,
-0.02960486337542534,
0.04505571350455284,
-0.0022749658674001694,
-0.059640128165483475,
-0.07342597097158432,
-0.036014705896377563,
0.00995818991214037,
0.06163458526134491,
0.023603754118084908,
0.0018159595783799887,
0.015364613384008408,
0.003873181762173772,
0.02308921329677105,
-0.047377366572618484,
0.003823609557002783,
0.03175611048936844,
-0.04119935631752014,
-0.010471945628523827,
-0.042617280036211014,
-0.016506914049386978,
0.06309528648853302,
0.007249298505485058,
0.018503960222005844,
0.05543940141797066,
-0.005990935489535332,
0.008401918224990368,
0.018648158758878708,
0.001500757527537644,
-0.013318349607288837,
0.06602147966623306,
-0.02411406859755516,
0.011873332783579826,
0.039598457515239716,
0.04341622069478035,
0.026152431964874268,
0.002651926828548312,
0.04356091842055321,
0.03626425191760063,
-0.008991953916847706,
-0.015688303858041763,
-0.0025121846701949835,
-0.026582544669508934,
-0.028276531025767326,
-0.034755561500787735,
-0.06873071193695068,
-0.04524989426136017,
0.020021840929985046,
-0.02393372915685177,
0.04232674837112427,
-0.007057978305965662,
0.018363991752266884,
-0.015300060622394085,
-0.02809717133641243,
-0.0406203530728817,
-0.0835672914981842,
0.051877886056900024,
0.008230443112552166,
-0.023459644988179207,
0.04149162024259567,
0.02860681526362896,
0.040626175701618195,
-0.021814942359924316,
-0.044115327298641205,
-0.004045627545565367,
0.015486717224121094,
-0.02574687823653221,
-0.021698402240872383,
0.013722434639930725,
0.04642220214009285,
0.029846275225281715,
-0.000048771991714602336,
0.006328969728201628,
-0.017838625237345695,
-0.06435226649045944,
0.020451970398426056,
-0.013481760397553444,
0.04213663190603256,
0.04298210144042969,
-0.006825795862823725,
-0.019584892317652702,
-0.02262837626039982,
0.005584074184298515,
0.038469843566417694,
-0.0350821353495121,
0.06584787368774414,
0.04462256655097008,
-0.005507270339876413,
0.032586611807346344,
0.08658606559038162,
-0.02802736684679985,
0.01953992247581482,
0.006678791716694832,
-0.018594374880194664,
-0.03393920511007309,
0.0017907841829583049,
0.021768324077129364,
0.06025421991944313,
0.004943166859447956,
-0.015017191879451275,
0.04484330862760544,
0.023109378293156624,
0.01162303239107132,
0.007987082935869694,
-0.03287685662508011,
-0.038657501339912415,
0.019688252359628677,
-0.01055296789854765,
-0.004134293179959059,
-0.02105705626308918,
0.02884426899254322,
0.00567925488576293,
0.01855279877781868,
0.033880382776260376,
-0.016199110075831413,
0.03903064876794815,
-0.019642019644379616,
-0.006209544837474823,
0.00956711731851101,
-0.0334925651550293,
0.027240287512540817,
-0.007091575302183628,
0.025418801233172417,
0.02583931013941765,
-0.010276317596435547,
0.005288443528115749,
-0.013838636688888073,
-0.030348604544997215,
-0.0018318893853574991,
-0.003484199056401849,
0.017551302909851074,
-0.03573166951537132,
0.043152835220098495,
-0.03679179400205612,
0.014827785082161427,
0.01422935351729393,
-0.008361092768609524,
-0.037217769771814346,
-0.011566080152988434,
-0.01558301318436861,
-0.007764964364469051,
0.016056878492236137,
-0.021594977006316185,
-0.055053677409887314,
0.014199824072420597,
-0.014003630727529526,
0.030329350382089615,
0.035023897886276245,
-0.036783527582883835,
0.0008607228519394994,
-0.042299091815948486,
-0.009455608204007149,
0.032651569694280624,
-0.016796888783574104,
0.001956993481144309,
-0.0014129530172795057,
0.01535580400377512,
-0.05142463371157646,
-0.015012514777481556,
-0.016108497977256775,
0.036859359592199326,
-0.00977817177772522,
-0.007430489175021648,
0.05052062124013901,
-0.04254112020134926,
-0.027003968134522438,
-0.019997479394078255,
-0.018262432888150215,
-0.029970895498991013,
-0.013613231480121613,
0.0012590332189574838,
0.023786211386322975,
-0.004778249654918909,
-0.00869445875287056,
0.03606150671839714,
-0.06205832213163376,
-0.018322082236409187,
-0.09415844082832336,
-0.02250618301331997,
0.024127481505274773,
-0.007374884095042944,
0.02332305535674095,
-0.03069373033940792,
-0.01915118657052517,
0.09758837521076202,
0.03973596543073654,
-0.01493219006806612,
0.01756705902516842,
-0.0016635885694995522,
-0.029908545315265656,
-0.014114465564489365,
0.007197853643447161,
0.03832004591822624,
-0.0022861245088279247,
0.05707492306828499,
0.010819132439792156,
0.05674131214618683,
-0.01497492752969265,
0.03301876783370972,
-0.04092250391840935,
0.030460961163043976,
-0.010773392394185066,
0.01765803061425686,
0.031915538012981415,
0.03359019383788109,
-0.011409085243940353,
0.003170344978570938,
0.014763398095965385,
0.01830917038023472,
0.007699816953390837,
-0.048027295619249344,
0.08104535937309265,
0.02179901860654354,
0.008909525349736214,
-0.0006908244686201215,
0.031068427488207817,
-0.022920235991477966,
0.0028668998274952173,
-0.002118764678016305,
0.05049819126725197,
0.039512984454631805,
0.005655171815305948,
0.013740095309913158,
0.021885612979531288,
0.0309450700879097,
-0.00016447025700472295,
-0.036656226962804794,
0.007367988117039204,
-0.02792101353406906,
0.002908726455643773,
-0.017280571162700653,
-0.018460065126419067,
-0.012487944215536118,
0.027408301830291748,
0.016994750127196312,
-0.010535149835050106,
-0.05406853184103966,
-0.020637720823287964,
-0.05629966780543327,
-0.008191858418285847,
0.015014108270406723,
0.03766888380050659,
0.03957320749759674,
0.04872675985097885,
0.00565223628655076,
0.021947160363197327,
0.03967840597033501,
-0.02661299519240856,
-0.0956723764538765,
0.03688191995024681,
-0.038084596395492554,
0.0013650876935571432,
-0.003957981243729591,
0.006106465123593807,
0.02182437665760517,
-0.027301203459501266,
-0.013509380631148815,
-0.040989503264427185,
-0.007058841176331043,
-0.04094314947724342,
-0.01692849211394787,
-0.007568690925836563,
-0.003192066913470626,
-0.020383257418870926,
0.02269534021615982,
0.052476897835731506,
-0.041374824941158295,
-0.01397061999887228,
0.052736714482307434,
-0.015549932606518269,
-0.020406637340784073,
-0.019139805808663368,
-0.018479295074939728,
0.017937570810317993,
-0.0013820157619193196,
0.04276029020547867,
-0.001266634208150208,
-0.009178617969155312,
0.04174094274640083,
0.01715475134551525,
0.013654214330017567,
0.0006073115509934723,
-0.010292590595781803,
-0.005349663086235523,
-0.06237061321735382,
0.011445938609540462,
-0.0029734624549746513,
0.058747198432683945,
0.030101966112852097,
0.02705315686762333,
0.03552419692277908,
0.0111906873062253,
-0.005076846573501825,
0.03847242146730423,
0.0019932545255869627,
0.0022465786896646023,
-0.037429288029670715,
-0.035578131675720215,
0.007610999513417482,
-0.032539140433073044,
-0.00969197042286396,
0.007786753587424755,
-0.008455188944935799,
-0.015787549316883087,
-0.010046488605439663,
-0.007314568385481834,
0.0027656012680381536,
-0.04098159819841385,
-0.03730225935578346,
-0.01746285706758499,
-0.017539096996188164,
0.03626640513539314,
0.001746355090290308,
0.021123530343174934,
0.03952615708112717,
0.018482143059372902,
-0.004552365746349096,
0.021056704223155975,
-0.07681022584438324,
-0.003673914587125182,
0.03902412950992584,
0.031498122960329056,
-0.01528722234070301,
-0.023945951834321022,
-0.0105339540168643,
-0.016702255234122276,
0.04771542549133301,
-0.03586707264184952,
0.030166510492563248,
-0.0069252606481313705,
-0.012077637016773224,
-0.0699000209569931,
-0.03862882778048515,
-0.015054577961564064,
0.042109668254852295,
-0.011265195906162262,
0.016088230535387993,
-0.018022319301962852,
-0.02564353495836258,
-0.005729897879064083,
0.020321745425462723,
-0.0034527170937508345,
0.008378196507692337,
0.021142903715372086,
-0.008463100530207157,
-0.005394561216235161,
0.04650494083762169,
-0.03852762654423714,
-0.09179893136024475,
-0.025693872943520546,
0.045857131481170654,
-0.02017504908144474,
0.027937639504671097,
-0.054214995354413986,
-0.047786831855773926,
0.02110792137682438,
-0.0005348911508917809,
-0.01456014160066843,
-0.002054173033684492,
-0.04024900123476982,
0.025302110239863396,
0.07404342293739319,
0.010245569050312042,
0.0346076637506485,
-0.004236160311847925,
-0.02248184196650982,
-0.004783256910741329,
0.021778972819447517,
0.03347911313176155,
-0.015871422365307808,
-0.004735048394650221,
-0.05724656954407692,
0.015009164810180664,
-0.031055256724357605,
0.06862399727106094,
-0.01229803916066885,
0.004869099240750074,
-0.024924060329794884,
-0.006209507118910551,
-0.0702609047293663,
0.00547986151650548,
0.027695976197719574,
-0.03827239200472832,
0.026418093591928482,
0.00941524188965559,
0.010968663729727268,
-0.0202734787017107,
-0.007028088439255953,
-0.00381071656011045,
0.006776300724595785,
0.02201787754893303,
0.02801411785185337,
0.04083701968193054,
0.005692531354725361,
-0.036961715668439865,
0.02566510997712612,
-0.034682709723711014,
0.028103001415729523,
0.00217401678673923,
-0.014441258274018764,
0.007515651173889637,
-0.013254567049443722,
-0.03382297605276108,
-0.033400844782590866,
-0.022464068606495857,
-0.019286872819066048,
-0.01969408243894577,
0.010291250422596931,
0.016923701390624046,
0.01681406795978546,
-0.08026380836963654,
-0.06622029095888138,
-0.0032460500951856375,
-0.0051039112731814384,
-0.026912866160273552,
0.01569279283285141,
-0.00743076391518116,
-0.02416028454899788,
-0.03301675617694855,
0.02229352295398712,
0.06510535627603531,
-0.043941933661699295,
0.006711847614496946,
0.006771699525415897,
0.04297444969415665,
0.07006525993347168,
-0.017676852643489838,
-0.0144642423838377,
-0.005697941407561302,
-0.022754793986678123,
0.004592872224748135,
-0.026701293885707855,
0.06544844806194305,
-0.043646201491355896,
-0.02108384482562542,
-0.004844462964683771,
0.023298507556319237,
0.03926120698451996,
-0.004127381835132837,
0.01185010839253664,
0.016333652660250664,
-0.006657480262219906,
-0.021023619920015335,
-0.022101448848843575,
-0.0337354876101017,
0.016526799649000168,
0.0390092097222805,
0.0206619780510664,
0.004320012405514717,
-0.012916650623083115,
-0.014723985455930233,
0.0015926607884466648,
0.031474366784095764,
0.00327339768409729,
-0.012687839567661285,
0.038680873811244965,
0.005505388602614403,
0.024014130234718323,
0.042457591742277145,
0.010305210947990417,
0.030112259089946747,
-0.031516000628471375,
0.00688435323536396,
0.014545375481247902,
-0.02328365296125412,
-0.04566211998462677,
-0.047403205186128616,
-0.0034143251832574606,
0.04494630917906761,
0.03452351689338684,
-0.0076599144376814365,
0.07347531616687775,
0.005325394682586193,
-0.03634079918265343,
0.04334069415926933,
-0.012284597381949425,
-0.0038083249237388372,
-0.005757445469498634,
0.005884008016437292,
0.003971092402935028,
-0.011067237704992294,
-0.020548416301608086,
0.07204186171293259,
0.04109042137861252,
-0.057589877396821976,
0.02838882803916931,
0.06661323457956314,
0.006099245045334101,
0.037321966141462326,
-0.0075310152024030685,
-0.04031480476260185,
0.015748703852295876,
-0.04741111025214195,
0.03597601130604744,
-0.00924864411354065,
0.033642467111349106,
0.03264894708991051,
0.014836911112070084,
-0.01742994412779808,
0.00032164069125428796,
0.0003505790082272142,
-0.054843347519636154,
-0.0005691993283107877,
0.022571563720703125,
0.01766807772219181,
0.00600862130522728,
-0.0002937921090051532,
0.0287395678460598,
-0.02646481618285179,
-0.025577876716852188,
0.04180607944726944,
-0.0402425192296505,
-0.007850858382880688,
-0.03503325209021568,
-0.06246588006615639,
0.053177423775196075,
-0.034482378512620926,
-0.0075346557423472404,
-0.009129069745540619,
-0.016838863492012024,
0.000530831515789032,
0.012783972546458244,
0.023275600746273994,
-0.013824105262756348,
0.09435670077800751,
-0.004090015310794115,
0.017276175320148468,
-0.02248449996113777,
-0.0017706730868667364,
0.12275204807519913,
0.04859936609864235,
-0.02282642014324665,
-0.06174244359135628,
-0.00046838726848363876,
0.00892395619302988,
-0.0030608591623604298,
0.0023071567993611097,
-0.02302463911473751,
0.014822086319327354,
0.00626889755949378,
-0.011124399490654469,
0.04910753667354584,
-0.005748213268816471,
-0.04037592560052872,
0.027903426438570023,
-0.0504724495112896,
-0.024513667449355125,
0.01848357915878296,
0.0009113515843637288,
-0.03727535903453827,
0.017644161358475685,
-0.06412582099437714,
0.0035179858095943928,
-0.008901678957045078,
0.0282355435192585,
-0.017702175304293633,
-0.05008118227124214,
-0.002527741715312004,
0.01784331165254116,
-0.029950039461255074,
0.007467054761946201,
0.008778942748904228,
0.0049884142354130745,
-0.03697442635893822,
0.024068525061011314,
-0.011061827652156353,
0.025375526398420334,
0.02880675345659256,
0.06714873760938644,
0.014977628365159035,
-0.010844769887626171,
-0.027393247932195663,
0.012707152403891087,
-0.04523395001888275,
-0.03451040759682655,
-0.007824043743312359,
0.041358787566423416,
-0.00790640152990818,
-0.005935146473348141,
-0.02309703826904297,
-0.01106179878115654,
-0.024939795956015587,
-0.06734021753072739,
-0.02216276153922081,
-0.009050206281244755,
0.03449435159564018,
0.003032580018043518,
-0.005985774099826813,
-0.017843594774603844,
-0.025542624294757843,
-0.01766982115805149,
0.00827367976307869,
-0.011025916785001755,
0.008578917011618614,
0.0063434140756726265,
0.031967293471097946,
0.00763818621635437,
-0.02008708007633686,
-0.017208855599164963,
-0.035720597952604294,
0.01728060282766819,
-0.048388686031103134,
0.01123412512242794,
-0.025376802310347557,
0.03266338258981705,
0.01327934954315424,
0.005617352668195963,
-0.028064798563718796,
-0.04414995387196541,
-0.08603286743164062,
0.019240470603108406,
0.002357898745685816,
-0.012528758496046066,
0.003381586167961359,
-0.0015012206276878715,
0.030466966331005096,
0.02181815356016159,
-0.023975642397999763,
0.023756137117743492,
-0.0015591405099257827,
0.040566716343164444,
0.03937528282403946,
-0.004754325840622187,
-0.003329336177557707,
0.02998402528464794,
-0.014474705792963505,
0.012154342606663704,
0.013147177174687386,
0.009689681231975555,
0.01224106177687645,
-0.016577713191509247,
-0.01199077907949686,
0.04520208388566971,
-0.00834654550999403,
-0.01001560129225254,
0.032536111772060394,
-0.021078087389469147,
-0.03163721412420273,
0.01710815541446209,
-0.008805529214441776,
-0.036129098385572433,
-0.021646710112690926,
-0.050694841891527176,
0.01696191541850567,
-0.026953835040330887,
0.024359863251447678,
-0.029216669499874115,
0.03289226070046425,
-0.03361167386174202,
0.02879553847014904,
-0.05235942080616951,
-0.009967130608856678,
-0.0844474509358406,
0.031140930950641632,
0.0015540000749751925,
0.023606497794389725,
0.013825342990458012,
0.052810803055763245,
0.01625644788146019,
-0.02614773064851761,
-0.005015361588448286,
0.0377262644469738,
-0.028738772496581078,
0.013480204157531261,
-0.012996136210858822,
-0.04705846682190895,
0.0444394126534462,
-0.0025005489587783813,
-0.04339854419231415,
0.03314431011676788,
-0.03419521823525429,
-0.02987368404865265,
0.047575030475854874,
-0.01611444167792797,
0.015578314661979675,
0.019539015367627144,
0.0008619822910986841,
-0.002649805275723338,
-0.0081164026632905,
-0.019018130376935005,
-0.012234256602823734,
0.014097428880631924,
-0.06075238063931465,
-0.053859174251556396,
-0.031176503747701645,
0.07117362320423126,
0.023599674925208092,
0.0016621362883597612,
0.0035866224206984043,
0.02599610760807991,
-0.006844744086265564,
0.0364951491355896,
0.0020880030933767557,
-0.06277941912412643,
0.03487749397754669,
0.01021586824208498,
-0.03848044201731682,
0.027781523764133453,
0.0586584210395813,
-0.045414768159389496,
0.017603028565645218,
-0.009975683875381947,
0.015466771088540554,
-0.09333141148090363,
0.01703505590558052,
-0.011540975421667099,
-0.025324974209070206,
0.017688216641545296,
-0.052529484033584595,
0.019911659881472588,
0.015452048741281033,
-0.05901603400707245,
0.029630161821842194,
-0.05918530747294426,
0.016211118549108505,
0.02020968310534954,
-0.01024581864476204,
-0.047239240258932114,
0.08504733443260193,
0.04239493981003761,
0.022612206637859344,
0.03635273873806,
0.02682415209710598,
0.032288163900375366,
-0.02092161774635315,
0.008059408515691757,
0.0644288882613182,
-0.0026935460045933723,
-0.013720660470426083,
0.06987033039331436,
-0.00874196458607912,
-0.03608081862330437,
0.01259508915245533,
-0.02942100167274475,
0.03404051810503006,
-0.044730328023433685,
-0.014529988169670105,
0.019001994282007217,
0.05234010890126228,
0.035431135445833206,
-0.031089823693037033,
-0.01860121823847294,
0.0004223764408379793,
0.016122497618198395,
0.012707413174211979,
-0.005665141623467207,
-0.029361272230744362,
0.02394258975982666,
-0.05097680538892746,
-0.012099284678697586,
0.02390015497803688,
0.016675464808940887,
-0.018904492259025574,
-0.004682502709329128,
-0.026803825050592422,
0.050326038151979446,
-0.030512195080518723,
0.011186421848833561,
-0.023013442754745483,
-0.028963260352611542,
0.03399854153394699,
-0.02139252983033657,
-0.0011578615522012115,
-0.0019947593100368977,
0.02701432630419731,
-0.03328271582722664,
0.022328270599246025,
0.03077225759625435,
-0.02991170436143875,
-0.07661014795303345,
-0.014586463570594788,
0.0025670162867754698,
-0.017103955149650574,
0.003207787871360779,
0.005089467857033014,
-0.06917712837457657,
0.021333880722522736,
0.012561872601509094,
0.010223796591162682,
-0.010742653161287308,
-0.05865100398659706,
0.02131364308297634,
-0.06111884117126465,
0.039939045906066895,
0.03519473224878311,
-0.01907983422279358,
-0.023335985839366913,
-0.018581373617053032,
-0.0025223754346370697,
0.002695178147405386,
0.06427478790283203,
0.018242130056023598,
-0.052670467644929886,
0.017627298831939697,
0.008823619224131107,
0.020390482619404793,
-0.02386963553726673,
-0.027113964781165123,
-0.04887042194604874,
0.002661183476448059,
-0.023996194824576378,
-0.022442031651735306,
-0.014886855147778988,
0.020360885187983513,
0.0203071478754282,
-0.03796875849366188,
0.01697496511042118,
-0.02435864880681038,
-0.022189373150467873,
0.07033972442150116,
0.011053314432501793,
-0.008007651194930077,
0.023714378476142883,
0.017252957448363304,
0.038495808839797974,
0.029489008709788322,
-0.029719972983002663,
-0.014353401027619839,
0.0353599414229393,
-0.043075043708086014,
-0.012090838514268398,
0.009605319239199162,
-0.0026777847670018673,
0.011489746160805225,
-0.004537316504865885,
-0.020874619483947754,
0.06898943334817886,
-0.010293294675648212,
-0.02550332434475422,
0.008475322276353836,
0.003390057012438774,
0.050542499870061874,
0.008183651603758335,
0.016835041344165802,
0.016739455983042717,
0.049442488700151443,
0.03165195882320404,
0.059480488300323486,
0.06701526045799255,
-0.007969779893755913,
-0.008442978374660015,
0.032276932150125504,
-0.02417057380080223,
-0.0010798880830407143,
0.044127028435468674,
0.04936454817652702,
-0.01627391390502453,
0.006725316401571035,
0.0024590904358774424,
-0.006876063533127308,
0.03468852862715721,
0.05778920277953148,
-0.01402733102440834,
0.06115640699863434,
-0.017447656020522118,
-0.020868172869086266,
-0.03612815961241722,
0.009867001324892044,
-0.034271903336048126,
-0.006431820336729288,
0.061181921511888504,
0.044238265603780746,
0.013624602928757668,
0.009967026300728321,
-0.02741112746298313,
0.02816065214574337,
-0.00221333559602499,
-0.02489667758345604,
0.026736760511994362,
0.0223369300365448,
-0.020116060972213745,
-0.005939237307757139,
-0.023816604167222977,
-0.014678853563964367,
-0.029302161186933517,
0.021372247487306595,
0.030909614637494087,
0.056084565818309784,
0.03313235193490982,
-0.007866534404456615,
-0.04120698198676109,
0.05068711191415787,
-0.04784153774380684,
-0.03709816932678223,
-0.0358424112200737,
0.014936769381165504,
-0.0006907907081767917,
-0.022858520969748497
] |
<p>I've had this conceptual problem with Faraday's law and inductance for a while now.</p>
<p>Take the example of a simple current loop with increasing area in a constant field (as in <a href="http://physics.stackexchange.com/a/1790/12255">this answer</a>). So Faraday's law states that the increasing flux (due to the increasing area) causes an EMF and hence a current. Due to the minus sign in Faraday's law, or by Lenz's law the direction of the current is such that the magnetic field it creates opposes the external field.</p>
<p>Now why do we never consider the magnetic field created by the induced current, when calculating the change in flux? All workings I have seen always calculate the flux from $\underline{\mathbf B} \cdot \underline{\mathbf A}(t)$. Why is $\underline{\mathbf B}$ not adjusted by the induced magnetic field? Is it just <em>that</em> small that we can neglect it unconditionally?</p>
<p>I have the same problem with self-inductance in AC circuits (although, maybe if I understood the above problem, this would become apparent to me as well). Say we start from current $I=0 \text{A}$. Then the EMF in the circuit increases (but is still very low), which increases $I$, which in turn creates an increasing $\underline{\mathbf B}$ inside the coil. Wouldn't the induced counter-EMF be much greater than the external EMF applied to the circuit? And if so, how come there is current moving in the first place, if the slightest increase in EMF causes a counter-EMF which acts to stop the current?</p>
<p>Is it just that I am looking at idealised situations or that the magnitudes of the external and induced effects differ greatly? Or do I have a conceptual misunderstanding about how (self-)inductance works?</p>
| 9,598 |
[
-0.029385635629296303,
0.011255115270614624,
-0.020193321630358696,
-0.019270453602075577,
0.05762375518679619,
0.014577880501747131,
-0.055241554975509644,
-0.005571824498474598,
-0.003396437270566821,
-0.01931868866086006,
0.030831826850771904,
0.04316107556223869,
0.061955638229846954,
0.003942329436540604,
0.02328883484005928,
-0.02897009626030922,
0.0013271465431898832,
-0.016785355284810066,
0.01736740581691265,
0.0020049752201884985,
-0.01504908874630928,
0.044721487909555435,
0.022234510630369186,
0.020916251465678215,
-0.01827418990433216,
0.02714984118938446,
0.021039951592683792,
0.006957682315260172,
0.006124561652541161,
0.05151231214404106,
0.021068977192044258,
-0.025880834087729454,
-0.025877520442008972,
0.008182313293218613,
0.0327623151242733,
0.02789265662431717,
-0.03663498908281326,
-0.04863036796450615,
0.0005714537692256272,
0.037231311202049255,
-0.01975385658442974,
-0.00017377082258462906,
-0.00590111780911684,
0.04010258615016937,
-0.02504870295524597,
0.01692786067724228,
-0.0005977526307106018,
0.021347923204302788,
0.033060722053050995,
-0.0685221403837204,
0.03709009289741516,
-0.01996137574315071,
0.05805765464901924,
0.030257316306233406,
-0.013804186135530472,
-0.03299926221370697,
0.0973828136920929,
0.0302533358335495,
-0.005022247787564993,
-0.03759193420410156,
-0.017740139737725258,
-0.010491007938981056,
-0.004696599207818508,
-0.017203480005264282,
-0.009684743359684944,
0.03657787665724754,
-0.023154553025960922,
0.014195403084158897,
0.010635264217853546,
-0.010852132923901081,
0.01983092539012432,
0.028139470145106316,
-0.02642614021897316,
-0.02149663120508194,
0.0030898714903742075,
-0.0031289849430322647,
0.0272916741669178,
0.01171828992664814,
0.03405497968196869,
0.03949612379074097,
-0.033639777451753616,
-0.013703417032957077,
0.017774581909179688,
0.05114726722240448,
0.027578657492995262,
0.0010908416006714106,
0.019841428846120834,
-0.022063247859477997,
0.03492525592446327,
-0.00725473091006279,
-0.003288367995992303,
0.028681037947535515,
0.023636313155293465,
-0.05820006877183914,
0.012312356382608414,
0.04018993303179741,
-0.007255086209625006,
0.046011440455913544,
0.005040823481976986,
-0.034396693110466,
0.024779336526989937,
-0.014931431040167809,
0.015237629413604736,
0.05334354192018509,
0.006334520410746336,
-0.03911249339580536,
-0.04051025211811066,
0.016508452594280243,
-0.0067923953756690025,
-0.025701608508825302,
-0.02832799218595028,
0.036564167588949203,
0.038556843996047974,
0.013212627731263638,
0.026765303686261177,
-0.03957461565732956,
0.01981036737561226,
-0.012990055605769157,
0.03628283366560936,
0.04416589066386223,
0.04732505977153778,
-0.04089632257819176,
0.04317917674779892,
-0.02118496224284172,
-0.05198320001363754,
-0.010391823016107082,
-0.0044844187796115875,
0.0061679682694375515,
-0.021985061466693878,
0.012101516127586365,
0.017056293785572052,
-0.04796496778726578,
-0.004348618444055319,
0.032948147505521774,
0.04232262074947357,
0.005242403130978346,
-0.059214141219854355,
-0.06457404792308807,
0.03847856447100639,
-0.047029703855514526,
0.009002597071230412,
-0.0758906677365303,
-0.018811896443367004,
0.037661340087652206,
0.09660892188549042,
-0.011322567239403725,
-0.03235333412885666,
0.007270819041877985,
0.03348546102643013,
0.007873942144215107,
-0.024189015850424767,
-0.014162438921630383,
-0.02122986689209938,
-0.0020367344841361046,
-0.0024018087424337864,
-0.04524380713701248,
0.07839489728212357,
0.030641945078969002,
0.025871748104691505,
-0.018119294196367264,
0.08562028408050537,
-0.026158731430768967,
0.006136454176157713,
0.0031367414630949497,
-0.01887308433651924,
0.0011253181146457791,
0.10617250949144363,
0.008107136003673077,
0.03674594312906265,
0.048529110848903656,
0.014315479435026646,
0.007863616570830345,
0.004962297156453133,
0.010401122272014618,
0.06822246313095093,
-0.06196916475892067,
-0.03051247075200081,
-0.01421350333839655,
0.017519228160381317,
-0.006359175778925419,
-0.022645417600870132,
-0.057289376854896545,
-0.012994569726288319,
0.013212699443101883,
0.0049575320445001125,
0.037938762456178665,
-0.034866441041231155,
-0.026305288076400757,
0.005083732772618532,
-0.0513935387134552,
-0.0204627625644207,
-0.05141107365489006,
0.05086374282836914,
-0.020319482311606407,
-0.04709555581212044,
0.0447646863758564,
0.007394721731543541,
0.024693045765161514,
-0.029847335070371628,
-0.041121892631053925,
0.004561891779303551,
0.026075422763824463,
0.00738757336512208,
-0.03284835070371628,
0.0039260415360331535,
0.022132867947220802,
0.007786568254232407,
0.019264934584498405,
0.05723860114812851,
-0.030657727271318436,
-0.060733940452337265,
0.013982252217829227,
-0.03703901544213295,
0.000986646511591971,
0.023242773488163948,
-0.03435174748301506,
-0.02275197021663189,
-0.03475821390748024,
-0.012852693907916546,
0.02702770195901394,
-0.004473806358873844,
0.09241915494203568,
0.056256599724292755,
0.02810959704220295,
0.004725331906229258,
0.05132853984832764,
-0.004133690148591995,
-0.012317054904997349,
-0.03728710114955902,
-0.04826652631163597,
-0.05763540789484978,
-0.001495799166150391,
0.036322783678770065,
0.019037414342164993,
-0.03273135796189308,
0.01970558613538742,
0.0030274116434156895,
0.03841172531247139,
0.0309204813092947,
0.029286356642842293,
-0.0069146528840065,
-0.04356330260634422,
-0.009240459650754929,
0.053766246885061264,
-0.004248662851750851,
0.00979681871831417,
0.0023439135402441025,
-0.006894153077155352,
0.021459152922034264,
0.008522707037627697,
-0.019147656857967377,
0.039025940001010895,
-0.018729887902736664,
0.014378435909748077,
0.026003899052739143,
-0.021622706204652786,
-0.005134246312081814,
-0.019754238426685333,
0.019169049337506294,
-0.0100615369156003,
-0.031198076903820038,
0.04053892567753792,
-0.017825309187173843,
-0.007541002240031958,
0.004453875590115786,
-0.06685777008533478,
-0.040112774819135666,
-0.026528282091021538,
0.00703034270554781,
-0.035064131021499634,
0.021076112985610962,
-0.013021726161241531,
0.010524231940507889,
-0.08258498460054398,
-0.014356985688209534,
-0.005842174869030714,
0.0010685664601624012,
0.037136249244213104,
-0.046457525342702866,
-0.00315871718339622,
-0.030457330867648125,
-0.030648836866021156,
0.02672319859266281,
0.0022109609562903643,
-0.039464112371206284,
0.02144363522529602,
-0.035375431180000305,
-0.019247734919190407,
0.06110450252890587,
0.01794201321899891,
-0.019864730536937714,
0.003740875981748104,
0.012124300934374332,
-0.0759037509560585,
-0.005455263890326023,
-0.0338885560631752,
-0.002747475868090987,
0.01578124426305294,
-0.0030261364299803972,
0.07070115953683853,
-0.01959768868982792,
-0.019777366891503334,
0.013239439576864243,
-0.015908069908618927,
-0.025892261415719986,
0.018342677503824234,
-0.020743869245052338,
0.012153786607086658,
-0.02619212493300438,
-0.002876403508707881,
0.012259338051080704,
-0.06642915308475494,
-0.028855709359049797,
-0.04748595505952835,
-0.00553511455655098,
-0.010829461738467216,
-0.006243251264095306,
0.05604899674654007,
-0.002961887512356043,
-0.03885363042354584,
0.058654699474573135,
0.05311652272939682,
-0.03916577994823456,
-0.007394907996058464,
-0.0423869863152504,
0.007577530574053526,
-0.046450577676296234,
-0.04017885774374008,
0.06051773950457573,
-0.03554295375943184,
0.017555037513375282,
0.018075572326779366,
0.04473280534148216,
-0.002559980610385537,
0.029758669435977936,
0.014282016083598137,
0.017881901934742928,
0.006931941490620375,
0.009074641391634941,
0.06731133162975311,
0.01668030209839344,
0.019338911399245262,
0.003601503325626254,
0.030358893796801567,
0.037417009472846985,
0.025120489299297333,
0.006858070380985737,
0.057361900806427,
-0.0348622165620327,
0.03656206279993057,
-0.0474584586918354,
0.03012329898774624,
-0.009495475329458714,
0.012958378531038761,
-0.008746922016143799,
0.01991846226155758,
0.019897887483239174,
-0.05587589368224144,
-0.0017485381104052067,
0.010675161145627499,
0.010860966518521309,
-0.016917355358600616,
-0.039505548775196075,
-0.007502294145524502,
-0.01741589419543743,
0.013597617857158184,
-0.0031793401576578617,
-0.010606395080685616,
0.05349734053015709,
0.062037743628025055,
0.01985817588865757,
0.00040878119762055576,
-0.022621557116508484,
-0.010405589826405048,
-0.05408473312854767,
-0.04236351326107979,
-0.024802640080451965,
0.04167621210217476,
0.022662505507469177,
-0.009655733592808247,
-0.009403681382536888,
0.0017070465255528688,
-0.00015200642519630492,
-0.011322728358209133,
-0.1150500699877739,
0.032399922609329224,
-0.04586547613143921,
-0.005390093196183443,
-0.031940311193466187,
0.023791728541254997,
0.018861299380660057,
-0.0018425513990223408,
0.010294140316545963,
-0.05236905440688133,
0.00389227457344532,
-0.0355156846344471,
-0.01763402484357357,
-0.029817624017596245,
-0.027586083859205246,
-0.04163099825382233,
0.019497273489832878,
0.023630661889910698,
-0.06216339021921158,
0.009208411909639835,
-0.0038602210115641356,
-0.03160269185900688,
-0.006297013256698847,
-0.03035803698003292,
-0.00726016890257597,
0.03749854862689972,
0.008602473884820938,
0.06825536489486694,
-0.009671317413449287,
-0.036665432155132294,
0.017259879037737846,
0.058049626648426056,
0.04190066456794739,
0.027509469538927078,
-0.02141660265624523,
-0.01459715235978365,
-0.05876731500029564,
-0.06169518455862999,
-0.0038578694220632315,
0.05531248450279236,
0.030512792989611626,
0.033259451389312744,
0.020525911822915077,
0.014172529801726341,
-0.013113243505358696,
0.018234603106975555,
0.021838238462805748,
0.007401696871966124,
0.0023742204066365957,
-0.028358781710267067,
-0.031277913600206375,
-0.02920123003423214,
0.0013603395782411098,
0.03386717662215233,
-0.012933281250298023,
-0.02050039730966091,
-0.031838223338127136,
0.02770376391708851,
0.014466796070337296,
0.013136545196175575,
0.006672956049442291,
0.010963180102407932,
0.017414133995771408,
0.05249829962849617,
0.03219487890601158,
0.02816731482744217,
0.022110754624009132,
0.08351018279790878,
-0.00868487823754549,
-0.009076513350009918,
-0.09576603770256042,
-0.03762166574597359,
0.019784102216362953,
0.043641071766614914,
-0.031205086037516594,
-0.00649524200707674,
-0.05534845218062401,
-0.03383805975317955,
0.026650629937648773,
-0.049659691751003265,
0.04095975682139397,
-0.024200620129704475,
-0.014600325375795364,
-0.0330500453710556,
-0.04322527348995209,
-0.023677470162510872,
0.029593097046017647,
0.0030532923992723227,
0.045233406126499176,
-0.02115638181567192,
0.00031338646658696234,
0.005237791687250137,
-0.014064987190067768,
0.025414401665329933,
0.02279891073703766,
-0.02869727462530136,
0.008120570331811905,
0.011554128490388393,
0.06551717966794968,
-0.0018698778003454208,
-0.0619145967066288,
0.0008152851951308548,
-0.011413238011300564,
-0.02109328657388687,
0.02126288041472435,
-0.003703456372022629,
-0.04851072281599045,
0.0045173922553658485,
0.015498188324272633,
0.0017626468325033784,
-0.020828546956181526,
-0.022434666752815247,
0.06081441789865494,
0.006975748110562563,
-0.013899516314268112,
0.05774948000907898,
-0.0008014170452952385,
-0.009819615632295609,
-0.0101725272834301,
0.01201864704489708,
0.03492274880409241,
-0.012517936527729034,
0.01393909938633442,
-0.03957570716738701,
0.007512914948165417,
-0.023812657222151756,
0.0944940522313118,
-0.0015011470532044768,
-0.04301445558667183,
-0.030848141759634018,
-0.0007195129292085767,
0.022500913590192795,
0.012035578489303589,
-0.010907238349318504,
-0.01629936695098877,
0.006833615712821484,
0.04264221712946892,
0.001092619844712317,
-0.03698661923408508,
0.02519361488521099,
-0.014220122247934341,
0.03715148940682411,
0.038460250943899155,
-0.03155319020152092,
-0.0010697963880375028,
-0.02886866219341755,
-0.026921000331640244,
-0.014940861612558365,
-0.027035972103476524,
0.0307272057980299,
-0.010087929666042328,
-0.01863972470164299,
-0.01828235760331154,
-0.012620862573385239,
-0.017250292003154755,
-0.012301098555326462,
-0.005957170855253935,
0.018309298902750015,
-0.06116173416376114,
0.014591194689273834,
0.03608907386660576,
-0.024124350398778915,
-0.0768924131989479,
-0.07741156220436096,
0.026384593918919563,
-0.0022950435522943735,
0.020256802439689636,
-0.012280131690204144,
-0.029142457991838455,
0.0006054877303540707,
-0.05198211595416069,
-0.0074337017722427845,
0.04571378603577614,
-0.05498664453625679,
-0.00827060267329216,
0.03868231177330017,
0.03392040729522705,
0.03800394386053085,
-0.017433632165193558,
0.009303629398345947,
-0.0010781046003103256,
-0.06854921579360962,
-0.010887451469898224,
-0.0039184922352433205,
0.026768723502755165,
-0.02736697718501091,
-0.005897779017686844,
0.02765400893986225,
-0.024292107671499252,
0.06359928846359253,
-0.023919081315398216,
-0.013415159657597542,
0.04008513689041138,
-0.00857148040086031,
-0.021861225366592407,
-0.019630488008260727,
-0.022981764748692513,
0.02112392894923687,
0.0608091801404953,
0.010434737429022789,
-0.03132888302206993,
-0.05593759939074516,
-0.018985766917467117,
0.007079001981765032,
0.02446947805583477,
-0.0029126324225217104,
-0.030436517670750618,
0.05175815150141716,
-0.022914526984095573,
0.014088352210819721,
0.0008201699238270521,
0.00015895710384938866,
0.034333884716033936,
-0.004693211056292057,
0.011846352368593216,
0.02697005867958069,
-0.017825447022914886,
-0.04904300346970558,
-0.01972305402159691,
-0.03505494445562363,
0.005565939471125603,
0.042694494128227234,
-0.0195132028311491,
0.05906571075320244,
0.0033872504718601704,
-0.012502357363700867,
0.008185873739421368,
-0.025655511766672134,
-0.02375587821006775,
-0.00004483234806684777,
-0.019498489797115326,
0.009896455332636833,
-0.010383701883256435,
-0.00006408045737771317,
0.033800020813941956,
0.03119301050901413,
-0.029378943145275116,
-0.01652652397751808,
0.04990638792514801,
0.02752445638179779,
0.017719458788633347,
0.007488017901778221,
-0.04489688202738762,
0.03189418464899063,
-0.03325190395116806,
0.02220161445438862,
-0.0056189000606536865,
-0.0031218542717397213,
0.06984996050596237,
0.0086662657558918,
0.02136261574923992,
-0.030845794826745987,
-0.018752381205558777,
-0.03235006704926491,
-0.013524472713470459,
0.0034549222327768803,
0.03673139959573746,
0.019755464047193527,
0.005271792411804199,
0.009975338354706764,
-0.013619177043437958,
0.02351374365389347,
-0.0038211506325751543,
-0.04615113139152527,
-0.022363660857081413,
-0.029015690088272095,
-0.020750602707266808,
0.07508878409862518,
0.010392062366008759,
-0.015372724272310734,
0.016832608729600906,
-0.027562707662582397,
0.051591452211141586,
0.022797930985689163,
0.014916781336069107,
-0.005438835360109806,
0.046936243772506714,
-0.029517285525798798,
0.04965854808688164,
-0.032326605170965195,
-0.002346539404243231,
0.12172587960958481,
0.028962375596165657,
0.00861524697393179,
-0.06359053403139114,
0.024112068116664886,
-0.0498361773788929,
0.014598087407648563,
-0.03898151218891144,
0.03545825555920601,
-0.012425142340362072,
0.0008322283974848688,
0.01648937538266182,
0.04415721818804741,
0.00405023293569684,
0.0029518220108002424,
0.058307748287916183,
-0.0370439812541008,
-0.01329999789595604,
0.010454274713993073,
0.0379301942884922,
0.019622521474957466,
0.002291078446432948,
-0.0558423213660717,
0.013386333361268044,
-0.02671409770846367,
0.0042951228097081184,
-0.02124001272022724,
-0.027623144909739494,
0.0156389232724905,
-0.024855617433786392,
-0.06414838880300522,
0.034816160798072815,
0.01001134142279625,
-0.03606375679373741,
-0.06730980426073074,
0.027717161923646927,
0.021696310490369797,
0.01209943275898695,
0.002946837106719613,
0.03174540400505066,
0.03763609379529953,
0.0044200122356414795,
0.038751158863306046,
0.03699000924825668,
-0.024222826585173607,
0.0014558512484654784,
-0.027206486091017723,
0.034079134464263916,
0.0007651529158465564,
0.03863506019115448,
0.01002142671495676,
0.05398320406675339,
0.031309209764003754,
-0.031587086617946625,
-0.048705507069826126,
-0.0030848297756165266,
0.020136002451181412,
-0.004159554373472929,
-0.004389744717627764,
-0.001889083650894463,
0.040326427668333054,
-0.0060625234618783,
0.004035203717648983,
0.01780853420495987,
-0.02707963064312935,
0.016228433698415756,
0.027521468698978424,
0.04555628448724747,
0.015438339672982693,
0.004258302506059408,
-0.021529093384742737,
0.002884974703192711,
-0.01989600993692875,
0.0029136210214346647,
0.013299275189638138,
0.011563383042812347,
0.018895430490374565,
-0.013191001489758492,
-0.03564659133553505,
0.004559745546430349,
-0.07548347860574722,
0.02278633415699005,
0.019495544955134392,
0.029218431562185287,
-0.03341485187411308,
-0.00434698723256588,
0.0003471693198662251,
0.014081445522606373,
-0.01069787796586752,
0.0008252948173321784,
0.0198723953217268,
0.041176456958055496,
-0.00816949363797903,
0.02079683355987072,
-0.045788608491420746,
0.012817803770303726,
-0.02294173650443554,
0.011560175567865372,
0.042487937957048416,
0.03601131960749626,
0.022817563265562057,
-0.005953126586973667,
-0.015080220997333527,
0.029799602925777435,
-0.008406449109315872,
0.002485469449311495,
0.0023509159218519926,
-0.038951627910137177,
0.0053514293394982815,
0.005492629017680883,
0.018095174804329872,
-0.027881156653165817,
-0.029304593801498413,
0.012155212461948395,
0.025528620928525925,
0.03633460775017738,
0.02920594997704029,
-0.008243356831371784,
-0.012592737562954426,
-0.006656528916209936,
0.0014444629196077585,
-0.05323532968759537,
-0.03571227565407753,
-0.05995667353272438,
-0.010314960964024067,
0.023501455783843994,
0.011151541024446487,
0.00976147036999464,
0.05794268846511841,
-0.008165428414940834,
-0.01695532537996769,
0.010355130769312382,
0.02767789736390114,
-0.015312758274376392,
0.002122439444065094,
0.00295637478120625,
0.0013099571224302053,
0.02199440822005272,
-0.016883673146367073,
-0.04699508100748062,
0.056174807250499725,
-0.0035707270726561546,
-0.046693917363882065,
0.03982623293995857,
-0.0009920988231897354,
-0.011346399784088135,
0.0046579791232943535,
-0.008960912004113197,
-0.009329077787697315,
0.011030075140297413,
0.014074587263166904,
0.016589855775237083,
-0.003365998389199376,
-0.02124638296663761,
-0.020125675946474075,
-0.04326595738530159,
0.02129419334232807,
0.004011253826320171,
0.0011260457104071975,
-0.02203040011227131,
0.04760279878973961,
0.03191813826560974,
-0.018859218806028366,
0.006123612634837627,
0.0162584837526083,
-0.006547688506543636,
0.03330397978425026,
0.014538068324327469,
0.0006527250516228378,
0.026821494102478027,
-0.01577056385576725,
0.0009535414865240455,
-0.02058391459286213,
0.012010891921818256,
-0.07723037153482437,
0.014541903510689735,
0.0043489052914083,
-0.0052489941008389,
-0.001776703167706728,
-0.04620731994509697,
-0.0073619019240140915,
0.020112842321395874,
-0.08755683153867722,
-0.015234018675982952,
-0.04537172242999077,
-0.00708327442407608,
-0.001883547636680305,
-0.027428699657320976,
-0.021317701786756516,
0.014009736478328705,
0.01591378264129162,
0.031161226332187653,
0.00393132446333766,
-0.015778400003910065,
-0.016750192269682884,
-0.036468151956796646,
-0.028946200385689735,
0.025946427136659622,
-0.008549243211746216,
-0.01618656888604164,
0.039413485676050186,
0.0026741791516542435,
0.00014829717110842466,
0.0201349426060915,
-0.04610593989491463,
-0.0012307591969147325,
-0.0018590525723993778,
0.021799152716994286,
0.0021221223287284374,
0.049726393073797226,
-0.004296398721635342,
-0.0038393116556108,
-0.010777011513710022,
0.031141603365540504,
0.020766882225871086,
0.014958326704800129,
-0.021507281810045242,
-0.005743046291172504,
0.04659087583422661,
-0.02794482931494713,
0.013784506358206272,
0.00755776884034276,
-0.0479087270796299,
-0.012139992788434029,
-0.009580514393746853,
0.030747605487704277,
0.019600030034780502,
-0.03752335533499718,
0.022306187078356743,
-0.02339118719100952,
-0.04450160264968872,
0.024182982742786407,
0.00781648326665163,
0.018349600955843925,
-0.012202968820929527,
0.034312304109334946,
-0.02591351978480816,
0.03288383409380913,
0.019828030839562416,
0.011414413340389729,
-0.05629556253552437,
0.01776168867945671,
0.0017154223751276731,
-0.017529133707284927,
0.013983636163175106,
-0.05393126606941223,
-0.05572221800684929,
0.04080886393785477,
0.0054296343587338924,
0.002154006389901042,
-0.01692986488342285,
-0.08494094759225845,
-0.01427546702325344,
-0.032321810722351074,
0.05480940267443657,
-0.02780929207801819,
-0.038038089871406555,
-0.03621886298060417,
-0.02837584912776947,
0.007594605442136526,
0.013680404983460903,
0.054933108389377594,
-0.0019637399818748236,
-0.008005522191524506,
0.04441571235656738,
0.013625976629555225,
0.04760108143091202,
-0.03582514822483063,
0.027435077354311943,
0.005318860523402691,
0.024970613420009613,
0.013044285587966442,
-0.035496458411216736,
-0.03446563705801964,
0.028799057006835938,
0.009710200130939484,
0.03812114894390106,
0.028181392699480057,
-0.024119095876812935,
-0.015463335439562798,
0.024386553093791008,
0.010296527296304703,
-0.0009962944313883781,
0.06626855581998825,
0.0220602136105299,
0.04059157520532608,
0.013960279524326324,
-0.0111087029799819,
-0.05354444310069084,
0.004982793238013983,
-0.017151519656181335,
0.016132816672325134,
-0.043416544795036316,
0.0010880791814997792,
0.06611806899309158,
-0.03236440569162369,
-0.03449524566531181,
0.028905199840664864,
-0.014655571430921555,
-0.0037714443169534206,
0.03278141841292381,
-0.009440252557396889,
0.0047707101330161095,
-0.026128632947802544,
0.04326315596699715,
0.01087921392172575,
0.029799291864037514,
-0.007834683172404766,
0.0328444167971611,
0.016343098133802414,
-0.026346946135163307,
0.00412414176389575,
0.08682198077440262,
-0.014890692196786404,
0.012381261214613914,
0.0037781817372888327,
0.003667928045615554,
-0.029279330745339394,
-0.03364523500204086,
0.03307556360960007,
-0.021955519914627075,
0.0007091076695360243,
0.026626184582710266,
-0.018745485693216324,
0.08014120906591415,
-0.03665871545672417,
0.028761273249983788,
-0.011510845273733139,
0.022896964102983475,
-0.0001321292802458629,
0.009993286803364754,
0.008056508377194405,
0.0534399040043354,
-0.011335466988384724,
-0.023444119840860367,
-0.010478764772415161,
-0.01566815935075283,
0.048802927136421204,
-0.005039263051003218,
0.02750161662697792,
0.0018920503789559007,
-0.036258433014154434,
-0.04996505379676819,
-0.018314775079488754,
-0.022277910262346268,
-0.05140473321080208,
0.04763421416282654,
0.050086598843336105,
0.045233093202114105,
0.002561003202572465,
-0.01956470124423504,
-0.023271551355719566,
0.06848202645778656,
-0.05833866074681282,
-0.004693131428211927,
-0.009334922768175602,
0.011362475343048573,
0.026615753769874573,
-0.005914862733334303
] |
<p>I've had a wild idea which I can not discuss at length in this forum, but it comes down to the following problem:</p>
<p>A sphere of radius R=~10μm and mass m=~10-16Kgr is travelling towards the earth at v = ~10^8m/sec. The sphere carries a charge Q and intersects the earth's magnetic field perpendicularly, at a distance r, such that it enters an elliptic orbit. Given an electron wave function of ~5eV, is there any possible configuration of Q and r that would
allow the sphere to end up in a stable geo-stationary orbit?</p>
<p>Would releasing charges at particular points of each rotation make any difference?</p>
<p>Even though I did get a physics BS 13 years ago, I took a different direction and the calculations required are way beyond my current capabilities. If anyone finds the problem interesting, I'll be glad to hear from you.</p>
| 9,599 |
[
-0.03468342125415802,
0.0033048284240067005,
0.01009277906268835,
-0.016093431040644646,
0.02704548090696335,
-0.01680200919508934,
-0.008524768985807896,
-0.01315909344702959,
0.026119552552700043,
-0.04240609332919121,
0.0053953430615365505,
0.04854771867394447,
0.04969913139939308,
0.02353017032146454,
0.0019613904878497124,
-0.008921939879655838,
0.0037390338256955147,
-0.029226355254650116,
0.006633311044424772,
-0.049222301691770554,
0.016403449699282646,
0.0026344654615968466,
0.0062663559801876545,
0.002764770295470953,
0.0009003314771689475,
0.001776673598214984,
0.04814700409770012,
-0.0070221927016973495,
0.014907239004969597,
0.04813618212938309,
0.00739578902721405,
-0.004577835090458393,
0.0363180972635746,
0.024327673017978668,
0.013824609108269215,
-0.007160206325352192,
-0.017584240064024925,
-0.030842190608382225,
-0.015675660222768784,
0.02828887850046158,
-0.04626629129052162,
-0.013937289826571941,
-0.03452880308032036,
0.06748473644256592,
-0.0010518147610127926,
0.007289506029337645,
0.006514445412904024,
-0.02408123016357422,
0.09496555477380753,
-0.05496250465512276,
0.041909437626600266,
0.003926237113773823,
0.00956819113343954,
0.02442486584186554,
0.013140827417373657,
-0.024404972791671753,
0.09178995341062546,
0.06625186651945114,
-0.0076799714006483555,
-0.013208603486418724,
-0.01431874930858612,
-0.037700045853853226,
0.014270316809415817,
-0.01718774624168873,
-0.0255555622279644,
0.025901077315211296,
0.020892174914479256,
0.00949656218290329,
0.03215131163597107,
0.021630562841892242,
0.01734314300119877,
0.020847709849476814,
-0.017919884994626045,
-0.022130513563752174,
0.01875339075922966,
-0.009455244056880474,
0.022747891023755074,
-0.031107837334275246,
0.016146373003721237,
0.00023642077576369047,
-0.029716731980443,
0.017000310122966766,
0.03779729828238487,
0.07336749881505966,
-0.02491997368633747,
0.038122229278087616,
0.010382052510976791,
-0.03378472849726677,
0.01680929586291313,
0.05781329795718193,
0.0025739737320691347,
0.025597266852855682,
0.04975540563464165,
-0.00790537241846323,
-0.04413887485861778,
0.04754967242479324,
0.00419862475246191,
0.059549007564783096,
0.005310308653861284,
-0.01234786119312048,
0.022748775780200958,
-0.01564786396920681,
0.012506967410445213,
0.07109668105840683,
0.0287395678460598,
-0.033106785267591476,
-0.026742497459053993,
-0.0319223552942276,
-0.008088667877018452,
-0.05592622980475426,
-0.04180885851383209,
-0.003061610506847501,
-0.007736286148428917,
-0.022528981789946556,
0.01711103320121765,
-0.01190745085477829,
-0.024333955720067024,
-0.03495491296052933,
0.0061333514750003815,
0.033319566398859024,
0.03496496006846428,
-0.007552448194473982,
0.034733254462480545,
-0.03662458807229996,
-0.030562270432710648,
-0.006351858377456665,
0.042107608169317245,
0.006860401015728712,
0.0036192089319229126,
-0.014872374013066292,
0.017062900587916374,
-0.01690555363893509,
0.011852757073938847,
-0.044608719646930695,
0.049167126417160034,
-0.020113686099648476,
-0.08131273090839386,
-0.031147172674536705,
0.03407843038439751,
0.0059815263375639915,
0.006037015933543444,
-0.07775966078042984,
-0.0026428825221955776,
-0.017702452838420868,
0.0833025574684143,
-0.005518257152289152,
-0.016924545168876648,
-0.014167367480695248,
0.06799933314323425,
0.0328427292406559,
-0.018496911972761154,
0.024673428386449814,
0.003151723649352789,
-0.07731156051158905,
-0.007874188013374805,
-0.06619913130998611,
0.02465178444981575,
-0.012150988914072514,
0.019742943346500397,
-0.018706144765019417,
0.03441629931330681,
-0.017383629456162453,
0.029792629182338715,
-0.029608935117721558,
-0.005959480535238981,
-0.010603181086480618,
0.10062579065561295,
0.015373348258435726,
-0.013116148300468922,
0.008856290951371193,
0.01120056863874197,
0.038418062031269073,
0.007693387567996979,
0.02235569804906845,
0.02754243277013302,
-0.061397138983011246,
0.034141965210437775,
-0.08388873934745789,
0.038719698786735535,
-0.022708099335432053,
-0.019179876893758774,
-0.04230744019150734,
0.017443735152482986,
-0.013764542527496815,
-0.00884420145303011,
0.08537275344133377,
-0.03414623439311981,
0.0028041379991918802,
-0.03073548898100853,
-0.04113130271434784,
0.016706950962543488,
-0.021576181054115295,
0.04284314066171646,
-0.0028417068533599377,
-0.02415302023291588,
0.01974974386394024,
-0.02152731455862522,
0.03428864851593971,
-0.024257704615592957,
-0.027627969160676003,
0.0025233011692762375,
0.037540365010499954,
-0.02715286612510681,
-0.013037558645009995,
0.0058822352439165115,
0.05044761672616005,
-0.012330659665167332,
0.010851152241230011,
0.021900948137044907,
-0.015224634669721127,
-0.025914987549185753,
-0.035486336797475815,
0.0018514363327994943,
0.05999033525586128,
0.057132430374622345,
0.0015297248028218746,
0.004838539287447929,
0.02484557218849659,
0.011812814511358738,
0.01325131207704544,
-0.02061591111123562,
0.09782394021749496,
0.03098559007048607,
0.003198184771463275,
0.006355247925966978,
0.06349991261959076,
0.03878164291381836,
-0.00817053858190775,
-0.00419951044023037,
-0.030778205022215843,
-0.00923447497189045,
0.02805018611252308,
0.04333260655403137,
0.015433946624398232,
-0.03708695247769356,
0.03276684135198593,
0.03382354602217674,
0.06710097193717957,
0.035448841750621796,
0.002469491446390748,
-0.010191553272306919,
-0.0119198989123106,
0.023212185129523277,
0.00006895034312037751,
-0.009225361980497837,
0.013238715939223766,
0.051099807024002075,
0.002972936723381281,
-0.033427894115448,
-0.008451101370155811,
-0.04194781184196472,
0.03104957565665245,
-0.00912414863705635,
-0.009522868320345879,
0.005065669305622578,
-0.02765880711376667,
0.04711516201496124,
-0.029218368232250214,
0.037882059812545776,
0.014393096789717674,
-0.00938744843006134,
0.006543885916471481,
-0.04528283700346947,
0.023261085152626038,
-0.0007598132942803204,
-0.009183011017739773,
-0.011044264771044254,
0.005430208053439856,
0.027576830238103867,
-0.06929759681224823,
-0.021728606894612312,
-0.006888999603688717,
0.01627998985350132,
0.013937816023826599,
0.009999788366258144,
0.031593043357133865,
0.014099202118813992,
0.006823005620390177,
-0.0013011107221245766,
-0.04629380255937576,
-0.005970119498670101,
-0.016376733779907227,
-0.004283476155251265,
0.0458090640604496,
-0.03984091430902481,
0.006981388200074434,
-0.023010771721601486,
-0.023172227665781975,
0.06233206391334534,
0.007460795808583498,
0.009665651246905327,
0.03548125550150871,
-0.00018328746955376118,
-0.04530493542551994,
0.00430289888754487,
-0.03284357488155365,
0.0029328279197216034,
-0.03725862503051758,
-0.0007674816297367215,
0.05906476825475693,
-0.002539062174037099,
-0.014783167280256748,
-0.013247160241007805,
-0.06718388944864273,
-0.049646563827991486,
0.004961359314620495,
0.01629648171365261,
0.01800144650042057,
-0.02895503304898739,
0.042541857808828354,
-0.017971549183130264,
-0.030198533087968826,
-0.014717615209519863,
-0.04614618048071861,
-0.020944809541106224,
0.0018312656320631504,
-0.013858254998922348,
0.049458760768175125,
-0.012205390259623528,
-0.05786953121423721,
0.09273658692836761,
0.01740962266921997,
-0.016941478475928307,
-0.026265472173690796,
-0.01434090081602335,
-0.030331695452332497,
-0.013289432972669601,
-0.013070426881313324,
0.04670943319797516,
-0.01611754111945629,
-0.0006741664838045835,
0.02422560751438141,
0.015163252130150795,
-0.017690591514110565,
0.024777185171842575,
-0.012781876139342785,
0.03630606830120087,
0.008847622200846672,
0.033770851790905,
0.0536324642598629,
-0.007722887210547924,
-0.044998619705438614,
0.0065950267016887665,
-0.01924804225564003,
0.044519927352666855,
0.020136043429374695,
-0.07579805701971054,
0.04975859448313713,
-0.021992869675159454,
0.04826498404145241,
0.02033136412501335,
0.017386775463819504,
0.005633327178657055,
-0.022479237988591194,
0.00966775044798851,
0.02644139528274536,
0.049870558083057404,
-0.0036257938481867313,
-0.03788910433650017,
0.0250309556722641,
0.05518471449613571,
0.0005037165828980505,
-0.02548556588590145,
-0.031810227781534195,
0.01644091121852398,
0.04001133143901825,
-0.012434841133654118,
-0.04700702056288719,
0.025306906551122665,
0.012743361294269562,
0.045350778847932816,
0.027833139523863792,
-0.02936580218374729,
0.004778045229613781,
-0.09252173453569412,
-0.014780164696276188,
-0.006424226798117161,
0.06503228098154068,
0.04613558202981949,
0.036771535873413086,
0.02532411739230156,
0.0057516335509717464,
-0.02727319858968258,
0.03493470326066017,
-0.09001881629228592,
0.02569228783249855,
-0.04005733132362366,
-0.05021653324365616,
0.002762823598459363,
0.007171996403485537,
-0.027452966198325157,
-0.0024510144721716642,
-0.015256773680448532,
-0.0018323410768061876,
0.015255711041390896,
-0.044386133551597595,
0.0009727524593472481,
-0.01142239198088646,
0.0006125401705503464,
-0.05269801989197731,
0.031523291021585464,
0.03177345171570778,
-0.026582704856991768,
0.022027045488357544,
0.015058698132634163,
-0.0629643052816391,
0.03448786586523056,
-0.011835654266178608,
0.036119114607572556,
0.009015724062919617,
0.007760613691061735,
-0.0130425114184618,
0.021752633154392242,
-0.018059618771076202,
0.004433989059180021,
-0.003186375368386507,
0.02493838220834732,
0.007870514877140522,
0.022556323558092117,
-0.04926872253417969,
-0.03880307823419571,
-0.001551626599393785,
0.006545249372720718,
0.03491336852312088,
-0.00980485137552023,
0.009541582316160202,
0.03781968727707863,
-0.033563658595085144,
0.01571277715265751,
-0.011144407093524933,
0.06149382144212723,
0.005964057520031929,
-0.014657244086265564,
-0.03293516859412193,
-0.04091532528400421,
-0.010843358002603054,
0.007821815088391304,
0.0040748873725533485,
-0.019899895414710045,
-0.026502108201384544,
-0.013220753520727158,
0.029121629893779755,
0.015379024669528008,
0.0008663696353323758,
0.015103794634342194,
0.003666273783892393,
0.05813317745923996,
-0.009018965996801853,
0.0066865673288702965,
0.008980735205113888,
-0.019518312066793442,
0.05704005807638168,
0.02090185321867466,
0.007228362374007702,
-0.06872162967920303,
-0.008870708756148815,
0.02513343282043934,
0.028107885271310806,
0.03501608967781067,
-0.008359936065971851,
-0.08197706937789917,
-0.023580176755785942,
0.06552247703075409,
-0.0343954861164093,
0.03219757229089737,
0.00855964981019497,
-0.0048563298769295216,
-0.009508048184216022,
-0.04333801940083504,
-0.027207840234041214,
0.007756575010716915,
-0.003388529410585761,
0.02906356006860733,
-0.03248116746544838,
0.0038846509996801615,
0.018266625702381134,
0.029659651219844818,
0.05345367267727852,
0.04228019714355469,
0.05708606541156769,
-0.00465363310649991,
0.005666749086230993,
-0.013567388989031315,
-0.004391880705952644,
-0.11105676740407944,
-0.025146912783384323,
0.008313617669045925,
-0.0010611966717988253,
0.045218195766210556,
-0.05705523490905762,
-0.044357072561979294,
0.02944358065724373,
-0.000713356479536742,
0.02753238007426262,
0.013456865213811398,
-0.04937666282057762,
0.03608844801783562,
0.02518390864133835,
0.012238091789186,
0.01745699718594551,
0.005879710428416729,
-0.02382357232272625,
0.010782613418996334,
-0.025904834270477295,
0.025042902678251266,
-0.03492940589785576,
-0.0001356966677121818,
0.01927017979323864,
0.029711008071899414,
-0.003747844835743308,
0.021701309829950333,
-0.011247067712247372,
-0.004260284826159477,
-0.01447173673659563,
-0.0335034504532814,
-0.0023341176565736532,
0.018169527873396873,
-0.032766398042440414,
0.0029513163026422262,
-0.0007372134132310748,
0.020243026316165924,
-0.014500108547508717,
-0.026658741757273674,
-0.007927203550934792,
0.00964937824755907,
0.009489922784268856,
0.038161832839250565,
-0.029632598161697388,
-0.033400751650333405,
-0.0407915897667408,
0.0022702699061483145,
-0.01702285185456276,
-0.07093118131160736,
0.08031672239303589,
-0.020031170919537544,
-0.03960472345352173,
0.047422945499420166,
-0.08593690395355225,
-0.028451653197407722,
0.03422092646360397,
-0.0027292040176689625,
0.010619242675602436,
-0.028940560296177864,
-0.023165762424468994,
0.006779661867767572,
0.02511155605316162,
-0.058690402656793594,
-0.03307503089308739,
0.04072485491633415,
0.03000248223543167,
-0.026911448687314987,
-0.005710786674171686,
-0.001785450498573482,
-0.03577743470668793,
-0.031963128596544266,
-0.00008979073027148843,
0.02663096971809864,
-0.0570724681019783,
0.006677108816802502,
0.033294521272182465,
0.0015771766193211079,
0.07571668922901154,
-0.03648308292031288,
-0.006181569304317236,
0.021042130887508392,
-0.0477818064391613,
0.006855008192360401,
-0.03991281986236572,
0.034896135330200195,
-0.04068898782134056,
-0.05648544058203697,
-0.03298989310860634,
-0.0009734081104397774,
-0.002678890246897936,
0.0025816448032855988,
-0.049700818955898285,
0.06537331640720367,
-0.01791135035455227,
0.016121644526720047,
0.004596437327563763,
0.039389681071043015,
-0.03551815450191498,
0.009647290222346783,
-0.0005961632705293596,
0.028565337881445885,
-0.03881378099322319,
-0.044955745339393616,
0.026402920484542847,
-0.003786553628742695,
0.019018834456801414,
0.018009677529335022,
0.024197431281208992,
-0.004016073886305094,
-0.045502856373786926,
0.023746522143483162,
0.026459110900759697,
-0.012316307052969933,
-0.026567211374640465,
-0.007391041610389948,
-0.005512387491762638,
0.013044798746705055,
-0.020271096378564835,
-0.044258903712034225,
-0.0077088940888643265,
0.005162123125046492,
0.06121826171875,
-0.018705250695347786,
0.01911621168255806,
0.01854116842150688,
0.0020814950112253428,
-0.07036289572715759,
-0.024328457191586494,
-0.0028463825583457947,
-0.008837735280394554,
0.009798991493880749,
0.022538870573043823,
-0.013802212662994862,
0.012363376095890999,
-0.005064699333161116,
0.05571819469332695,
-0.021048374474048615,
0.04031353443861008,
0.02389637567102909,
0.01807437278330326,
0.04274845868349075,
0.0011835627956315875,
-0.045400362461805344,
0.012896195985376835,
-0.07269230484962463,
0.05491693317890167,
0.005816643591970205,
-0.008768707513809204,
0.037258751690387726,
0.023262398317456245,
0.02280561439692974,
-0.0045869005843997,
-0.03362296149134636,
-0.045473746955394745,
0.033770810812711716,
0.03367333114147186,
-0.02712453342974186,
-0.010998910292983055,
0.026125900447368622,
0.028659647330641747,
0.029652059078216553,
-0.0015286655398085713,
-0.030562663450837135,
-0.07518348842859268,
-0.022022899240255356,
-0.028083104640245438,
-0.058220576494932175,
0.06849486380815506,
0.02373376488685608,
-0.01933298259973526,
-0.004359020385891199,
-0.018376147374510765,
0.03226952627301216,
0.06056464836001396,
0.040981341153383255,
-0.04391127824783325,
0.07554178684949875,
-0.02761230804026127,
-0.01847158931195736,
-0.019610630348324776,
0.02398756332695484,
0.12291637808084488,
0.05757633224129677,
0.013089059852063656,
-0.03258723020553589,
0.012396691367030144,
-0.038926657289266586,
0.04046482965350151,
-0.020093820989131927,
-0.00232063140720129,
-0.022525446489453316,
-0.01642460562288761,
0.0005833988543599844,
0.05455183610320091,
-0.03682858496904373,
-0.020545747131109238,
0.0587913952767849,
-0.013469766825437546,
-0.034187473356723785,
-0.01174335740506649,
0.03401614725589752,
0.017292160540819168,
0.022521724924445152,
-0.030498245730996132,
0.03956659883260727,
-0.07593320310115814,
-0.04078521206974983,
-0.05492585524916649,
-0.019459843635559082,
0.040647488087415695,
0.009539823047816753,
-0.04549402743577957,
0.01066178921610117,
0.002623822772875428,
-0.01872251182794571,
0.0019394450355321169,
0.0382268987596035,
0.023261783644557,
-0.019012704491615295,
0.021120481193065643,
0.029413491487503052,
-0.014364179223775864,
0.009698341600596905,
0.024669546633958817,
0.011281044222414494,
-0.043690405786037445,
0.009093749336898327,
-0.04689178988337517,
0.05352897569537163,
-0.030773457139730453,
0.004022970795631409,
0.004006580915302038,
0.02081923745572567,
0.01701457053422928,
-0.06305571645498276,
-0.010533248074352741,
-0.04675605148077011,
0.010737456381320953,
0.027754267677664757,
-0.015790807083249092,
-0.022673096507787704,
0.018981246277689934,
0.03404158726334572,
0.010766602121293545,
0.002331256167963147,
-0.008250502869486809,
0.000016388406947953627,
-0.0121593177318573,
0.05172634869813919,
-0.0074110920540988445,
-0.0520760752260685,
-0.015704317018389702,
-0.01612711139023304,
-0.04156683757901192,
-0.0003325819270685315,
0.018042849376797676,
0.0379335880279541,
0.040219496935606,
-0.015871061012148857,
-0.007355187088251114,
0.006885843817144632,
-0.06005079671740532,
0.01323043555021286,
0.00448363833129406,
-0.00885404646396637,
-0.017229169607162476,
0.012729356996715069,
0.014031853526830673,
0.027597209438681602,
-0.029414838179945946,
-0.0013830065727233887,
-0.007928549312055111,
0.017780950292944908,
-0.016872059553861618,
-0.019177226349711418,
-0.014528912492096424,
0.009222988970577717,
-0.024736743420362473,
0.022574525326490402,
-0.040124520659446716,
0.05713166296482086,
0.003817526390776038,
-0.0009325447608716786,
0.004628861788660288,
0.03365032747387886,
-0.008337931707501411,
0.011961228214204311,
0.010407746769487858,
0.003109193639829755,
-0.05239465460181236,
0.016403697431087494,
-0.026346592232584953,
-0.0041328854858875275,
0.007478783372789621,
-0.007561340928077698,
-0.014770780690014362,
-0.01823185570538044,
0.01149795576930046,
-0.026974927634000778,
0.03176295757293701,
-0.01647779531776905,
0.0001246849715244025,
-0.04004230350255966,
0.036900173872709274,
-0.027143122628331184,
-0.004062146879732609,
-0.018559226766228676,
0.0032459138892591,
-0.004534524865448475,
0.013812180608510971,
-0.021056877449154854,
-0.031227190047502518,
0.022245248779654503,
0.006381967104971409,
0.0009894901886582375,
0.0013129169819876552,
0.010869297198951244,
0.02078690007328987,
0.08313742280006409,
-0.030767148360610008,
0.0016069815028458834,
-0.01246448140591383,
-0.025084082037210464,
-0.051245320588350296,
0.03230860456824303,
-0.018869983032345772,
0.031975507736206055,
0.03289434686303139,
-0.024253077805042267,
-0.014832810498774052,
0.0941990539431572,
0.0018529087537899613,
-0.001058948808349669,
0.0444776751101017,
-0.03518315777182579,
-0.008220764808356762,
-0.020731395110487938,
0.03629474341869354,
-0.039301611483097076,
0.018537379801273346,
0.02434186078608036,
-0.0008488172898069024,
-0.019661327823996544,
0.0010816337307915092,
-0.023577895015478134,
0.008134003728628159,
-0.03865163028240204,
0.013480830937623978,
-0.009064708836376667,
0.02024213597178459,
0.030801784247159958,
-0.045346494764089584,
0.008666625246405602,
0.017375372350215912,
-0.015592210926115513,
-0.04724719747900963,
-0.018202893435955048,
0.015215313993394375,
-0.00569742638617754,
0.04970115050673485,
-0.03590474650263786,
0.020575562492012978,
0.025837881490588188,
-0.09215397387742996,
-0.016090042889118195,
-0.04354950785636902,
0.007930412888526917,
-0.04873335361480713,
-0.015695633366703987,
-0.044660426676273346,
0.011492147110402584,
0.022871555760502815,
0.027115095406770706,
0.022402502596378326,
0.020466838032007217,
-0.01793055795133114,
-0.044111624360084534,
0.004683856852352619,
0.04901343956589699,
-0.001921202871017158,
0.026855751872062683,
0.056092165410518646,
-0.040223997086286545,
-0.025828776881098747,
0.01759394071996212,
-0.02009308710694313,
0.03157594054937363,
-0.03290906921029091,
0.029052507132291794,
0.012531326152384281,
0.02614494226872921,
0.018771324306726456,
-0.003605529898777604,
-0.0035706092603504658,
-0.00788208469748497,
0.03376762941479683,
0.009646615944802761,
-0.03225448727607727,
0.014354435727000237,
-0.005523679777979851,
-0.005505354143679142,
-0.007274935953319073,
0.013565490022301674,
-0.02698572352528572,
0.009328784421086311,
0.0033284062519669533,
0.03295081481337547,
0.018421467393636703,
-0.017365407198667526,
-0.0038407978136092424,
-0.06599005311727524,
-0.002990296110510826,
-0.009001055732369423,
-0.015115683898329735,
0.04823781177401543,
0.001319832168519497,
-0.010046866722404957,
-0.029872508719563484,
0.018108662217855453,
-0.02297224849462509,
0.02076154574751854,
-0.055317964404821396,
0.004491449799388647,
0.0215035118162632,
-0.0022806718479841948,
0.0021189020480960608,
-0.044251490384340286,
0.009070579893887043,
0.016650540754199028,
0.01775605045258999,
0.04150411859154701,
0.01491786353290081,
-0.035164136439561844,
0.020976033061742783,
-0.060978055000305176,
0.016189463436603546,
-0.01071626041084528,
0.0072457571513950825,
0.011296178214251995,
-0.0751141682267189,
-0.0003340515831951052,
0.008132019080221653,
0.042808566242456436,
-0.009162172675132751,
0.028886068612337112,
0.04763741418719292,
-0.03903326392173767,
0.0077422200702130795,
-0.053189974278211594,
-0.006466528866440058,
0.005503821652382612,
-0.011308827437460423,
0.034769535064697266,
-0.0008933013887144625,
-0.02422892116010189,
-0.026654016226530075,
0.04156376048922539,
-0.0025828725192695856,
-0.007191231474280357,
0.010721676982939243,
-0.029225647449493408,
0.026075944304466248,
0.015229935757815838,
0.007434662897139788,
0.05100662633776665,
0.007884794846177101,
0.0008053015335462987,
-0.021161599084734917,
-0.026384763419628143,
-0.03333202004432678,
0.05041057616472244,
-0.04027741402387619,
-0.002669168869033456,
-0.04230153560638428,
-0.026053277775645256,
0.014768592081964016,
-0.03015509434044361,
-0.007936093024909496,
0.029592473059892654,
-0.04140665754675865,
0.013389145024120808,
0.01964867115020752,
0.007317254785448313,
0.05062362924218178,
-0.009320754557847977,
0.0029218951240181923,
0.015696099027991295,
-0.0009722024551592767,
0.004828006494790316,
0.014555064029991627,
0.014948596246540546,
0.007699353154748678,
0.012800329364836216,
0.027164239436388016,
0.027100611478090286,
0.017354940995573997,
0.010052505880594254,
0.041894085705280304,
-0.022017601877450943,
-0.010643047280609608,
0.022357726469635963,
-0.023937715217471123,
0.00881168246269226,
0.004884457681328058,
-0.03304706886410713,
0.056753359735012054,
-0.016369180753827095,
-0.035051800310611725,
0.0009072673274204135,
0.003954398445785046,
-0.014307602308690548,
0.05060138553380966,
-0.017571214586496353,
0.044283974915742874,
-0.016988612711429596,
-0.01786426082253456,
-0.03139053285121918,
0.01720988005399704,
0.03814868628978729,
-0.0020269874949008226,
0.03802407905459404,
-0.012154130265116692,
0.00614267447963357,
0.006841936148703098,
-0.005938596557825804,
-0.025913169607520103,
-0.03250095248222351,
0.02408500202000141,
0.011288441717624664,
0.05006404593586922,
-0.015925683081150055,
-0.0224760714918375,
-0.012775550596415997,
0.03270707279443741,
-0.019657308235764503,
-0.04525597020983696,
-0.017592469230294228,
0.031088219955563545,
-0.02324901893734932,
0.03092379681766033
] |
<p>Wigner crystal and FQH effect are both due to strong electron-electron interaction under magnetic field. As we know, Landau's symmetry-breaking cannot be used to describe FQH state. But can it be used to describe Wigner crystal state and which symmetries are broken in Wigner crystal?</p>
| 9,600 |
[
-0.022891122847795486,
-0.014775807969272137,
0.006784554570913315,
-0.020408017560839653,
0.05574070289731026,
-0.0052403295412659645,
-0.0502483956515789,
-0.03200235590338707,
0.016571350395679474,
-0.024093691259622574,
0.036751266568899155,
-0.025721611455082893,
0.03186289221048355,
0.025667084380984306,
-0.004245631396770477,
0.04493323341012001,
-0.001917399698868394,
-0.014379419386386871,
-0.015505786053836346,
0.011564482934772968,
-0.044659897685050964,
0.05984925851225853,
-0.023112697526812553,
0.004132538102567196,
-0.03378888964653015,
0.023911241441965103,
0.04761701822280884,
0.046484172344207764,
0.04524026811122894,
0.025771068409085274,
-0.0007989454315975308,
-0.026074355468153954,
0.02709319442510605,
-0.012505895458161831,
0.007260184269398451,
-0.03465248644351959,
-0.008568527176976204,
-0.05862197279930115,
0.02924616076052189,
0.017849059775471687,
-0.016946982592344284,
-0.024793285876512527,
0.009162585251033306,
0.04806606099009514,
-0.03463108837604523,
0.011528893373906612,
-0.006731483619660139,
-0.03269076719880104,
0.04945545643568039,
-0.05886553227901459,
0.043288007378578186,
0.006830232217907906,
0.022712817415595055,
-0.02334805577993393,
-0.01681607961654663,
0.022301990538835526,
0.029765643179416656,
0.060545433312654495,
0.02658092975616455,
-0.04423050954937935,
-0.011854398064315319,
-0.02575327642261982,
0.040593020617961884,
-0.04188916087150574,
-0.0377693772315979,
0.035134878009557724,
-0.014348423108458519,
-0.03719125688076019,
-0.007331010885536671,
0.026509782299399376,
-0.0348874069750309,
0.018560757860541344,
0.045218974351882935,
0.0006690979935228825,
0.05344584956765175,
0.004069800488650799,
0.014108140021562576,
0.008654233999550343,
0.03353350982069969,
0.021243544295430183,
0.00975760817527771,
0.0424240306019783,
0.012643939815461636,
0.036359384655952454,
-0.0043970621190965176,
-0.022352857515215874,
0.04634598642587662,
-0.014578613452613354,
-0.0016935075400397182,
0.04803537577390671,
0.005549624562263489,
0.01170735340565443,
0.020579708740115166,
0.006988054141402245,
-0.06150374934077263,
-0.025922738015651703,
0.010334715247154236,
0.021961068734526634,
0.000471439678221941,
-0.005179357714951038,
0.04988750070333481,
-0.021195130422711372,
0.017267698422074318,
0.05647357553243637,
-0.002013432327657938,
-0.021891484037041664,
0.007429955992847681,
-0.00352413859218359,
-0.02416859194636345,
-0.01111247856169939,
-0.011876048520207405,
0.0015895598335191607,
-0.004524444229900837,
0.006742537021636963,
0.012893353588879108,
0.0024173278361558914,
-0.035087887197732925,
-0.04018103703856468,
0.051818475127220154,
0.06298132985830307,
0.024951525032520294,
-0.008103825151920319,
0.012126535177230835,
-0.019533004611730576,
-0.08212779462337494,
0.008709242567420006,
0.02623061090707779,
-0.03676534444093704,
-0.02858935110270977,
0.017048804089426994,
0.012020605616271496,
-0.016836682334542274,
0.01583118550479412,
-0.010021413676440716,
0.0543525256216526,
-0.006549724377691746,
-0.09433787316083908,
-0.03471347317099571,
0.05388721078634262,
-0.04159213602542877,
0.011561091989278793,
-0.08409744501113892,
0.011194328777492046,
0.014124112203717232,
0.07249052822589874,
-0.009229072369635105,
0.034288376569747925,
0.02008040063083172,
0.04907137155532837,
0.030390338972210884,
-0.02557750977575779,
0.00419591786339879,
0.01960127055644989,
-0.0375511460006237,
-0.004431514069437981,
-0.0677659809589386,
0.012432355433702469,
0.03057459555566311,
-0.01635797508060932,
-0.00036361656384542584,
0.06342920660972595,
-0.009924730286002159,
0.0050240312702953815,
0.013469122350215912,
-0.02155553735792637,
-0.016163814812898636,
0.09336669743061066,
-0.01592901349067688,
0.024739285930991173,
0.059873901307582855,
-0.023857183754444122,
-0.006100361235439777,
0.025362230837345123,
0.0037374673411250114,
0.013686809688806534,
-0.04536142200231552,
0.003225067164748907,
-0.00381014053709805,
0.03277787193655968,
-0.055103763937950134,
-0.044931281358003616,
-0.01889115199446678,
-0.007183947134763002,
0.03260929137468338,
-0.014079483225941658,
0.026858031749725342,
-0.02234463021159172,
0.006875886116176844,
-0.001880962518043816,
-0.0535515658557415,
-0.02466619573533535,
-0.05674039572477341,
0.021151620894670486,
-0.014547275379300117,
-0.026678627356886864,
0.05008600652217865,
0.004562207031995058,
0.015022615902125835,
-0.022277280688285828,
-0.006676788441836834,
-0.005504351109266281,
0.01048236433416605,
-0.036771904677152634,
0.003480624407529831,
0.029889637604355812,
0.03144799917936325,
0.010749020613729954,
-0.015915730968117714,
0.029572779312729836,
-0.004443524405360222,
-0.04826568439602852,
0.021785078570246696,
0.01109289936721325,
0.04402213171124458,
0.03584590181708336,
-0.030343415215611458,
-0.0009279584628529847,
0.0015631007263436913,
-0.02527354285120964,
0.029109163209795952,
-0.004328135401010513,
0.04537520557641983,
0.01080538984388113,
-0.006126626394689083,
0.013151813298463821,
0.01225573755800724,
0.04130900278687477,
-0.008509967476129532,
-0.00012471644731704146,
0.0004590089083649218,
-0.05179736390709877,
0.014700237661600113,
0.018514137715101242,
0.02539723366498947,
-0.046535592526197433,
0.045158274471759796,
0.009169678203761578,
0.009429444558918476,
0.04562392458319664,
0.01696399599313736,
-0.05393518880009651,
-0.026569083333015442,
0.02364399842917919,
0.018982665613293648,
0.03317061439156532,
0.013907949440181255,
0.014475255273282528,
0.00509082293137908,
0.012757569551467896,
-0.03530682995915413,
-0.03329921141266823,
0.058591119945049286,
0.003677594708278775,
-0.02837526798248291,
0.016504503786563873,
-0.06183227151632309,
-0.02975294180214405,
-0.020693231374025345,
0.013506281189620495,
0.021613219752907753,
-0.03339851275086403,
0.006783530581742525,
-0.03374963998794556,
-0.018898824229836464,
0.011132869869470596,
-0.05052035674452782,
-0.020958222448825836,
-0.013413844630122185,
0.039301905781030655,
-0.021882444620132446,
-0.019864153116941452,
-0.030657852068543434,
0.0209638811647892,
0.005267599131911993,
0.013908866792917252,
0.05053291097283363,
-0.021880000829696655,
0.003927287645637989,
-0.04311656951904297,
-0.035138245671987534,
-0.00981611292809248,
-0.05037708207964897,
0.022683078423142433,
0.021869158372282982,
-0.035502783954143524,
0.021864954382181168,
-0.07104196399450302,
-0.014244883321225643,
-0.011246876791119576,
0.027463115751743317,
0.033910155296325684,
-0.01833329349756241,
-0.00938097108155489,
-0.021717501804232597,
0.008918026462197304,
-0.01193349901586771,
0.042351655662059784,
-0.025995586067438126,
0.004644077271223068,
0.0032726447097957134,
-0.03477688506245613,
-0.0016987150302156806,
-0.006747541483491659,
0.020877152681350708,
-0.017149997875094414,
0.011492477729916573,
0.002803831361234188,
0.011186427436769009,
-0.022130809724330902,
0.010849575512111187,
0.05269754305481911,
-0.060067735612392426,
0.009613404981791973,
-0.06249219551682472,
-0.01998472586274147,
0.01574709638953209,
-0.026483649387955666,
0.017394710332155228,
-0.008633114397525787,
-0.04217999055981636,
0.02709725871682167,
0.006983576808124781,
-0.029178136959671974,
-0.017295878380537033,
-0.0054937670938670635,
-0.0430709645152092,
-0.031015804037451744,
-0.0009764145943336189,
0.05870210751891136,
0.020492054522037506,
0.027696752920746803,
0.018996279686689377,
0.009272963739931583,
0.0388144813477993,
0.025165673345327377,
-0.07502756267786026,
-0.017370592802762985,
0.001990923658013344,
0.015745189040899277,
0.013621091842651367,
-0.017630944028496742,
-0.004426207393407822,
-0.010182172060012817,
0.041874054819345474,
0.0327305868268013,
0.02623671479523182,
-0.045250583440065384,
0.06217244267463684,
-0.01683882251381874,
0.03374626114964485,
-0.03389449417591095,
0.046348076313734055,
0.026849079877138138,
0.017238005995750427,
-0.003149589989334345,
0.04050964489579201,
0.014237023890018463,
-0.02136293426156044,
0.02406409941613674,
0.023429512977600098,
-0.012741787359118462,
0.006057499907910824,
-0.06058565899729729,
0.017576230689883232,
-0.03556070476770401,
0.03133834898471832,
-0.03624368831515312,
0.002576021011918783,
0.03988168016076088,
0.01756271719932556,
0.04976668208837509,
0.024393228814005852,
-0.0014074533246457577,
-0.008685391396284103,
0.0010287821060046554,
0.042960457503795624,
0.04320483282208443,
0.03864923119544983,
0.023257290944457054,
0.041676733642816544,
0.060250647366046906,
0.020008303225040436,
-0.013954000547528267,
-0.036220256239175797,
-0.08795706182718277,
-0.007318571209907532,
-0.01601756364107132,
-0.004408658482134342,
0.000695259019266814,
-0.015098857693374157,
0.005462947767227888,
-0.006982678547501564,
0.002129537519067526,
-0.06347603350877762,
-0.019187986850738525,
-0.054217029362916946,
0.01279333233833313,
-0.018176153302192688,
-0.018855763599276543,
-0.029429785907268524,
0.043161969631910324,
0.06321385502815247,
-0.03538558632135391,
0.03567861393094063,
0.02187236212193966,
-0.041102197021245956,
0.0016955093014985323,
-0.009476623497903347,
0.038547057658433914,
0.03394296392798424,
0.03572199121117592,
0.01754661463201046,
0.03748510405421257,
-0.03165287896990776,
-0.008640103042125702,
-0.0009007016196846962,
0.09459393471479416,
0.02663612551987171,
0.023288730531930923,
-0.015719130635261536,
-0.03083537146449089,
-0.02127445861697197,
-0.036154281347990036,
0.057955171912908554,
-0.0020314943976700306,
0.01337998267263174,
0.027281157672405243,
0.011167632415890694,
-0.07101070135831833,
0.021600797772407532,
0.04850456863641739,
0.014251216314733028,
-0.018672792240977287,
-0.020036237314343452,
-0.031308364123106,
-0.03188468515872955,
-0.021772122010588646,
0.0003089153906330466,
-0.02137088030576706,
-0.04598737508058548,
0.08243181556463242,
0.050855159759521484,
0.04087435081601143,
-0.028728246688842773,
-0.037328146398067474,
0.021582532674074173,
0.026580555364489555,
0.012477739714086056,
0.0330696664750576,
-0.030648911371827126,
0.018154123798012733,
0.01945367455482483,
-0.0023913467302918434,
-0.023914862424135208,
-0.07425893843173981,
0.020356440916657448,
0.03402530029416084,
0.03561761975288391,
0.0271042101085186,
-0.0224853977560997,
-0.06530959159135818,
-0.022570403292775154,
0.010943153873085976,
-0.006521040108054876,
0.049242544919252396,
-0.027054976671934128,
-0.017938319593667984,
-0.058457158505916595,
-0.002131967106834054,
-0.013630094937980175,
0.039351265877485275,
0.009673064574599266,
-0.002262503607198596,
-0.04279458150267601,
0.01753060519695282,
0.026459526270627975,
0.0015425910241901875,
0.009582947939634323,
0.012822736985981464,
0.029185649007558823,
0.03649395331740379,
0.010844722390174866,
0.06406667083501816,
-0.050873640924692154,
-0.12707257270812988,
-0.0008825305267237127,
0.007730687037110329,
0.010134359821677208,
0.04224183037877083,
-0.03126825764775276,
-0.05358291417360306,
0.005527745001018047,
0.0005500986590050161,
0.024841392412781715,
-0.01970614492893219,
-0.0026674687396734953,
0.044118549674749374,
0.028496570885181427,
-0.012317457236349583,
0.07543053478002548,
0.002599515952169895,
-0.00800994224846363,
-0.01190450880676508,
-0.0114161791279912,
0.03755994513630867,
-0.03081180900335312,
0.0330820307135582,
-0.025562847033143044,
0.04202260822057724,
-0.04797232896089554,
0.08127404749393463,
-0.03650657460093498,
0.00827912986278534,
-0.004945308435708284,
0.015997406095266342,
-0.008968155831098557,
-0.008673131465911865,
-0.007575416937470436,
-0.025649134069681168,
-0.037545133382081985,
0.040753841400146484,
-0.011218770407140255,
0.004175622947514057,
0.014740747399628162,
-0.030297281220555305,
0.003452450968325138,
0.019529428333044052,
0.00008049330062931404,
0.023572036996483803,
-0.03368835151195526,
-0.015005944296717644,
-0.014841297641396523,
-0.02639494091272354,
0.02880174107849598,
-0.02076602727174759,
-0.004283097106963396,
0.01807362399995327,
-0.05686444416642189,
0.010685697197914124,
0.03386551886796951,
-0.015065784566104412,
-0.000725013785995543,
-0.0011741564376279712,
0.06953291594982147,
0.04517371207475662,
-0.018620295450091362,
-0.09229610115289688,
-0.04161999747157097,
0.016101473942399025,
0.016110775992274284,
-0.034504737704992294,
0.000850895419716835,
-0.030285589396953583,
-0.049417439848184586,
-0.04004879295825958,
0.01577235758304596,
0.04152533784508705,
-0.0210993941873312,
-0.010569659061729908,
0.031623221933841705,
-0.007149232551455498,
0.036604441702365875,
0.008036009967327118,
-0.04202653467655182,
0.004398005083203316,
-0.032562728971242905,
0.016809727996587753,
0.02122749388217926,
0.04299166053533554,
-0.0013250920455902815,
-0.031974125653505325,
-0.022980637848377228,
-0.01815975271165371,
0.038115840405225754,
0.00008928597526391968,
0.0011669456725940108,
0.032718684524297714,
0.0007538837962783873,
0.012166951783001423,
-0.04005344212055206,
-0.005480491556227207,
-0.008622067980468273,
0.056737013161182404,
-0.021500399336218834,
-0.012955518439412117,
-0.06432297825813293,
-0.00992295891046524,
0.020666958764195442,
0.006291796453297138,
-0.041694168001413345,
0.007636840455234051,
0.0664374902844429,
-0.01576034352183342,
-0.014194440096616745,
0.0011825560359284282,
-0.03282244876027107,
-0.009815018624067307,
-0.023057375103235245,
0.004188143648207188,
0.012600632384419441,
0.038097187876701355,
-0.03200294449925423,
-0.04190492257475853,
-0.040359433740377426,
0.0037358799017965794,
0.05624900385737419,
-0.013815904967486858,
0.009822383522987366,
0.019536174833774567,
-0.004949754569679499,
-0.04005894437432289,
-0.026392174884676933,
0.013728605583310127,
0.04083407297730446,
-0.038943272083997726,
0.0405924953520298,
0.022757546976208687,
0.025102268904447556,
0.03272433951497078,
0.04852282628417015,
-0.028564361855387688,
0.022435925900936127,
0.04534580186009407,
0.010809379629790783,
-0.014224090613424778,
0.008409240283071995,
-0.017284216359257698,
0.08772706985473633,
-0.057611607015132904,
0.039791692048311234,
0.009494668804109097,
-0.006470586638897657,
0.034725505858659744,
0.008150193840265274,
0.002616406884044409,
-0.008087348192930222,
-0.016731278970837593,
-0.028884362429380417,
0.046915385872125626,
0.007169938646256924,
0.014216757379472256,
0.009831882081925869,
-0.012778554111719131,
0.042208123952150345,
0.032209381461143494,
-0.0008981756400316954,
0.0062741003930568695,
-0.03337964043021202,
-0.011911947280168533,
0.006313443183898926,
0.015736203640699387,
0.037475552409887314,
-0.014100137166678905,
-0.01754722185432911,
0.03849819302558899,
-0.028237823396921158,
0.02907661162316799,
-0.009420102462172508,
0.03365867957472801,
0.010670204646885395,
0.011204805225133896,
-0.03574668616056442,
0.02237914688885212,
0.008044593967497349,
6.6521289454613e-7,
0.11693301051855087,
0.008497591130435467,
-0.005026380531489849,
-0.09467232972383499,
0.020733065903186798,
-0.0005037327646277845,
0.030838897451758385,
-0.033266644924879074,
-0.015913205221295357,
0.011452988721430302,
0.055218495428562164,
-0.016201777383685112,
0.04926412180066109,
0.007165559567511082,
0.022999731823801994,
0.02397545799612999,
-0.0746387243270874,
-0.04601054638624191,
0.012514909729361534,
0.00018543917394708842,
0.03581208363175392,
0.0011961405398324132,
-0.025211721658706665,
-0.01847120188176632,
-0.023307934403419495,
0.010553454048931599,
-0.018630903214216232,
-0.036770280450582504,
-0.00011435595661168918,
-0.026506545022130013,
-0.04687405750155449,
0.014211422763764858,
0.014020776376128197,
-0.008023344911634922,
-0.06323986500501633,
-0.004886716604232788,
-0.042359016835689545,
0.0005062490236014128,
0.03468301147222519,
0.010258178226649761,
0.013137313537299633,
-0.04463512450456619,
0.0020588708575814962,
0.0005423669354058802,
-0.016350068151950836,
0.007366767153143883,
-0.012024931609630585,
-0.007518486585468054,
-0.001437680097296834,
0.014430703595280647,
0.022651158273220062,
-0.015527679584920406,
-0.005706420633941889,
-0.04406650736927986,
-0.015068917535245419,
-0.022329216822981834,
0.024952547624707222,
-0.020260291174054146,
-0.02419959381222725,
-0.052284277975559235,
-0.008207466453313828,
-0.02252146601676941,
-0.0008468996384181082,
-0.032152578234672546,
0.01358142588287592,
0.07442184537649155,
0.007534495554864407,
0.02849861979484558,
0.017014378681778908,
-0.012630715034902096,
-0.06307603418827057,
-0.0018291628221049905,
-0.02926083281636238,
-0.017031455412507057,
0.009889130480587482,
-0.02022082731127739,
0.04913049936294556,
0.002983702113851905,
-0.02562291920185089,
-0.0009958024602383375,
-0.079002745449543,
0.03927747905254364,
0.027733562514185905,
0.001577025162987411,
0.005469141528010368,
-0.006396821234375238,
0.053722083568573,
0.02938840724527836,
-0.053843747824430466,
0.020589672029018402,
-0.004983029793947935,
0.012370201759040356,
0.012990972958505154,
-0.029451187700033188,
-0.02645929343998432,
0.015529809519648552,
0.003134407103061676,
-0.005328697618097067,
-0.045453883707523346,
0.023693593218922615,
0.03540204092860222,
-0.01294348668307066,
-0.012564868666231632,
0.05632956326007843,
-0.01962338574230671,
-0.03008301928639412,
0.027277972549200058,
0.0023607201874256134,
0.003579118987545371,
0.03072984516620636,
-0.01104746013879776,
-0.03003476932644844,
-0.05247563496232033,
-0.038694191724061966,
-0.039281636476516724,
-0.0029437215998768806,
0.01037655957043171,
-0.044417209923267365,
0.006761545315384865,
0.001191500574350357,
0.007506235968321562,
-0.030754785984754562,
-0.0216648131608963,
0.002938587451353669,
0.04342704266309738,
-0.0022409341763705015,
0.011372254230082035,
-0.0203094482421875,
0.04086652398109436,
-0.005925492383539677,
0.015080133453011513,
0.008898003026843071,
0.07843879610300064,
0.0030560442246496677,
-0.0297114085406065,
0.01837809570133686,
0.014910847879946232,
0.03712139651179314,
-0.017346292734146118,
-0.013060307130217552,
0.03682202473282814,
-0.05390903726220131,
-0.03920873999595642,
0.0491487942636013,
0.0001967946154763922,
-0.0006286643329076469,
0.003528326516970992,
-0.0033138254657387733,
-0.01605862006545067,
0.021777162328362465,
-0.008449171669781208,
0.0017454845365136862,
0.029426831752061844,
-0.032512251287698746,
-0.0351715087890625,
-0.03382204473018646,
0.006187109276652336,
-0.010889129713177681,
-0.03672778233885765,
0.03474561125040054,
0.09623805433511734,
0.01280378457158804,
-0.000137487004394643,
0.006253957748413086,
-0.002406156389042735,
0.0524577870965004,
0.04113974794745445,
-0.015498969703912735,
0.04667346924543381,
0.02200680784881115,
0.023085055872797966,
0.00787360966205597,
-0.04138033837080002,
-0.0001250541681656614,
-0.09558576345443726,
-0.035680558532476425,
0.02966342680156231,
-0.011936761438846588,
0.05118463933467865,
-0.05184907093644142,
0.04018387198448181,
0.01449968945235014,
-0.06388489156961441,
-0.012519891373813152,
-0.018654659390449524,
-0.01816314458847046,
-0.014332199469208717,
0.006657718680799007,
-0.04410406947135925,
0.07620183378458023,
0.03985481336712837,
0.013811715878546238,
0.040275633335113525,
0.03206971287727356,
-0.009867084212601185,
-0.015334385447204113,
-0.019957285374403,
0.012044635601341724,
0.02021530084311962,
-0.03821166232228279,
0.0518951453268528,
-0.004941249266266823,
-0.02826882153749466,
-0.023066483438014984,
-0.00887471716850996,
-0.022341661155223846,
0.011363588273525238,
0.022106889635324478,
-0.00460424367338419,
0.047644082456827164,
-0.00029533778433687985,
-0.013875427655875683,
-0.01799027808010578,
0.018864817917346954,
0.012971250340342522,
0.040917977690696716,
0.009029767476022243,
-0.04465920105576515,
-0.013474907726049423,
-0.016694501042366028,
0.016806045547127724,
0.033685412257909775,
-0.006220037583261728,
0.00655251694843173,
0.003716491162776947,
0.018387645483016968,
0.016755910590291023,
-0.02306298166513443,
0.029389478266239166,
-0.03684978932142258,
-0.020724032074213028,
-0.004550853278487921,
0.0023970408365130424,
0.03301241248846054,
0.017525162547826767,
-0.027262555435299873,
-0.02395446226000786,
0.02439064346253872,
0.03444109112024307,
-0.009850678965449333,
-0.021891992539167404,
-0.004111756104975939,
0.013637872412800789,
0.029276594519615173,
0.025404958054423332,
-0.029278812929987907,
-0.04620163515210152,
0.012756489217281342,
-0.0010620318353176117,
0.03542341664433479,
-0.03781639039516449,
-0.016989510506391525,
0.0009965191129595041,
-0.032692503184080124,
0.015033337287604809,
-0.005952888168394566,
0.0057850987650454044,
0.005337167996913195,
-0.01906449906527996,
0.015543872490525246,
0.026541724801063538,
0.047558221966028214,
0.0337383933365345,
-0.0361323282122612,
0.04406328871846199,
-0.016067011281847954,
0.016162050887942314,
-0.02119101770222187,
-0.008239470422267914,
-0.030801596119999886,
0.016531020402908325,
-0.008990328758955002,
-0.0043551423586905,
-0.04820674657821655,
0.009612929075956345,
0.00852480810135603,
0.011247845366597176,
0.005175760947167873,
0.016809875145554543,
-0.05012648552656174,
0.06510530412197113,
0.01921609789133072,
-0.051026102155447006,
0.059666119515895844,
-0.040193408727645874,
0.014087245799601078,
0.02745003253221512,
-0.016847873106598854,
-0.023669006302952766,
-0.004786310717463493,
-0.047733284533023834,
-0.023647800087928772,
0.0015375299844890833,
0.00712823448702693,
0.015569937415421009,
-0.033314112573862076,
-0.02065674029290676,
0.04066191986203194,
-0.08625948429107666,
0.013676156289875507,
0.044610049575567245,
0.027140649035573006,
0.05264158174395561,
-0.02386835776269436,
0.0036812887992709875,
-0.008774694055318832,
0.0011895728530362248,
0.005451071076095104,
0.03216632083058357,
0.021543845534324646,
0.02451753243803978,
0.0326973982155323,
0.01876099221408367,
-0.014879904687404633,
-0.006491472013294697,
0.061896659433841705,
0.017054127529263496,
-0.016973666846752167,
-0.00732537591829896,
0.02269062213599682,
0.02179805189371109,
0.005427604075521231,
0.020263930782675743,
-0.028442608192563057,
0.07814153283834457,
-0.02262716367840767,
0.03476199507713318,
-0.01898735761642456,
-0.0008232516702264547,
-0.024772008880972862,
0.012634697370231152,
0.017977789044380188,
0.06059055030345917,
-0.0030326261185109615,
-0.020197266712784767,
-0.024825319647789,
0.022188700735569,
-0.009754285216331482,
-0.06641913950443268,
-0.0012222270015627146,
-0.025505932047963142,
-0.023952463641762733,
-0.01494903676211834,
-0.010493190959095955,
-0.05234130099415779,
-0.006739689502865076,
0.007864506915211678,
0.025473427027463913,
0.021912707015872,
-0.03408755362033844,
-0.011472129262983799,
-0.0364668108522892,
0.01932765729725361,
-0.0412566252052784,
-0.0051606022752821445,
-0.008123320527374744,
0.01151771005243063,
-0.059726130217313766,
-0.004804140422493219
] |
<p><em>Note:</em> This is a rewrite of the original question, which was titled <a href="http://physics.stackexchange.com/revisions/20511/2">What would time be for 2D beings?</a></p>
<hr>
<p>In my current, non-physicist's understanding, every instant of our three‑dimensional world is just another 'slice' of a four‑dimensional body. I don't mean that as an analogy, but quite literally... Obviously, it would not be a straight 'slice', it would still be bent and curved by gravity, speed and other relativistic factors. Is this wrong?</p>
<p>Also, both 'spacial' and 'temporal' dimensions are — in my mind — fundamentally the same thing, given different names because we experience them differently because of our nature. I've had people explicitly say in the comments that this is wrong and that time and space are not the same 'type' of dimension. I'd like to understand what are the fundamental differences.</p>
<hr>
<p><em>In my original question</em> I used these two assumptions of mine (that space is a slice of time and that all dimensions are fundamentally the same) to make an analogy.</p>
<p>I noted that taking two-dimensional slices of a three-dimensional body — just as a slice of four‑dimensional time is three‑dimensional space — and displaying them is rapid succession looks like a bunch of matter that is changing over time (like in this brain scan below). </p>
<p><img src="http://i.stack.imgur.com/rezJs.gif" alt="Brain scan"></p>
<p>Assuming all dimensions, temporal or spatial, are fundamentally the same, would that mean that for a hypothetical two‑dimensional being time would be the thrid dimension, not that fourth?</p>
<p>The same question in a more general form: for any $n$‑dimensional being, would time for it be the $n+1$ dimension?</p>
<p>In particular, what would time be for a being living in a hypothetical fifth dimension?</p>
| 9,601 |
[
-0.004943307023495436,
-0.01089028362184763,
0.012802843004465103,
-0.03280828893184662,
0.06250463426113129,
0.006224468350410461,
-0.021884461864829063,
-0.03528573364019394,
0.010641402564942837,
-0.04266837239265442,
0.04337398707866669,
0.02025546133518219,
0.034957315772771835,
0.03975063934922218,
0.0001658115943428129,
0.013254901394248009,
-0.01522565633058548,
-0.011997434310615063,
-0.025395486503839493,
-0.04555400833487511,
0.06661436706781387,
-0.014773296192288399,
0.007772715762257576,
0.027985768392682076,
-0.035250235348939896,
0.018018502742052078,
0.032115425914525986,
-0.012612036429345608,
0.030096521601080894,
0.052059318870306015,
-0.02750643528997898,
-0.02334982343018055,
0.010258670896291733,
-0.002039519604295492,
-0.004416591953486204,
-0.03261448070406914,
-0.035648759454488754,
-0.012330899015069008,
0.01393141970038414,
0.04595605656504631,
-0.016282901167869568,
0.018926292657852173,
-0.04905767738819122,
0.060686517506837845,
-0.05003499612212181,
0.04198954626917839,
-0.02781645767390728,
0.013186076655983925,
0.036026839166879654,
-0.02784471958875656,
0.07332251220941544,
-0.02974558062851429,
0.046787917613983154,
-0.008304349146783352,
-0.0281964298337698,
0.00759608531370759,
0.07077633589506149,
0.07850635796785355,
-0.02316557988524437,
-0.034810516983270645,
-0.05123452842235565,
0.0013313477393239737,
0.021289566531777382,
-0.0010590323945507407,
-0.02408878318965435,
0.02482205256819725,
-0.014740955084562302,
-0.00736717414110899,
-0.012325393967330456,
-0.041617684066295624,
-0.010925056412816048,
-0.004686463624238968,
0.029786832630634308,
0.003494192846119404,
-0.014716153033077717,
-0.020558269694447517,
0.013752603903412819,
0.015674790367484093,
0.05210127681493759,
0.0362834706902504,
-0.04247871786355972,
-0.008244084194302559,
0.018042970448732376,
0.0038636550307273865,
0.029842976480722427,
-0.02280106581747532,
0.07692597806453705,
-0.033656831830739975,
-0.02845003455877304,
0.022367306053638458,
0.00013804824266117066,
0.04074286296963692,
0.03623539209365845,
-0.019191671162843704,
0.013319303281605244,
0.024130528792738914,
0.018747719004750252,
-0.0004045125388074666,
-0.007490903604775667,
-0.01699839159846306,
-0.01750105805695057,
-0.007705668918788433,
0.021936792880296707,
0.05708163231611252,
-0.006106471177190542,
0.004100428428500891,
-0.01324491761624813,
0.015585997141897678,
-0.0055748033337295055,
-0.02768266201019287,
-0.03918474167585373,
0.015001690946519375,
-0.00463342247530818,
0.030275918543338776,
0.007308202795684338,
-0.04043116793036461,
0.028621653094887733,
-0.018101103603839874,
0.04828361049294472,
0.08164539188146591,
0.01650533266365528,
-0.05787855014204979,
0.0011865253327414393,
-0.02312362752854824,
-0.07341574877500534,
-0.0001391867990605533,
0.0443958081305027,
-0.013925598934292793,
-0.01434206310659647,
0.005030690226703882,
-0.011616528034210205,
0.0008622423629276454,
0.044625818729400635,
0.0021490175276994705,
0.047380656003952026,
0.03163671866059303,
-0.10952690988779068,
-0.05057142674922943,
0.056495338678359985,
0.03702153265476227,
-0.04693090543150902,
-0.07994996011257172,
0.028590049594640732,
-0.018489336594939232,
0.07789979130029678,
0.008877968415617943,
0.03691950812935829,
0.018632633611559868,
0.018072858452796936,
0.03392793983221054,
-0.0369623601436615,
0.028609544038772583,
-0.0004691204521805048,
-0.03404701128602028,
0.005415342282503843,
-0.026385312899947166,
0.01073969155550003,
0.044565580785274506,
0.02207689918577671,
-0.0033025648444890976,
0.05855549871921539,
0.032298095524311066,
-0.009859529323875904,
0.030183708295226097,
0.0071834418922662735,
-0.015899943187832832,
0.08164041489362717,
-0.006035665515810251,
0.0076044886372983456,
0.02213297039270401,
-0.0050688860937952995,
0.012190903536975384,
-0.009059643372893333,
0.024990493431687355,
0.044424545019865036,
-0.004231676459312439,
-0.039472367614507675,
0.03738638386130333,
-0.05547836050391197,
-0.026573162525892258,
-0.058378398418426514,
-0.0234504584223032,
-0.012995872646570206,
-0.035114701837301254,
0.00799552071839571,
0.04100548475980759,
-0.014653272926807404,
-0.01582295633852482,
-0.012598702684044838,
-0.023297294974327087,
-0.019463572651147842,
-0.07421476393938065,
-0.02049821801483631,
0.012264484539628029,
-0.01554369367659092,
0.027124006301164627,
-0.0027862321585416794,
0.04223664849996567,
-0.031136970967054367,
-0.028857585042715073,
-0.03223838284611702,
0.060486964881420135,
0.023411458358168602,
-0.006767970509827137,
0.029575670138001442,
0.07111604511737823,
0.013621306046843529,
-0.011454204097390175,
-0.004315393511205912,
0.012061478570103645,
-0.027312466874718666,
0.025217261165380478,
-0.0125352768227458,
0.06994957476854324,
-0.0025161108933389187,
0.008016696199774742,
0.018177490681409836,
0.03717454895377159,
-0.05289914831519127,
0.03236217424273491,
-0.012753253802657127,
0.04928356036543846,
0.02065216191112995,
-0.03534745052456856,
-0.023189740255475044,
0.04312381148338318,
0.019464462995529175,
0.005948738660663366,
0.028008993715047836,
-0.04790108650922775,
-0.033068303018808365,
-0.012907811440527439,
0.03778828680515289,
0.04744347929954529,
-0.02058522030711174,
0.024073302745819092,
0.008654789067804813,
0.04532623291015625,
-0.004705097526311874,
-0.010811356827616692,
-0.0023818030022084713,
-0.06940458714962006,
-0.015997344627976418,
-0.026927553117275238,
0.019065285101532936,
0.015243588015437126,
0.0010252934880554676,
-0.010625001043081284,
0.023189447820186615,
0.0024997065775096416,
0.018585413694381714,
0.03425958752632141,
-0.04097979888319969,
0.02187361754477024,
0.021101199090480804,
-0.03815658390522003,
0.03177884593605995,
0.002242261078208685,
-0.0006781214033253491,
0.037661243230104446,
0.0016224435530602932,
-0.034011680632829666,
-0.05267340689897537,
-0.013959451578557491,
-0.01407619472593069,
0.05473477393388748,
-0.012309678830206394,
-0.021916594356298447,
0.037963297218084335,
-0.003410014556720853,
0.01308054756373167,
-0.014163984917104244,
-0.031150909140706062,
-0.008483399637043476,
-0.002575545571744442,
0.02749803103506565,
0.01234948355704546,
-0.0016122868983075023,
-0.02539527229964733,
0.005147176329046488,
0.0348699577152729,
0.012312349863350391,
-0.0029688680078834295,
-0.011419728398323059,
-0.05364343896508217,
0.02361692674458027,
-0.025939036160707474,
-0.024271365255117416,
0.0029470266308635473,
0.004061570856720209,
0.023966440930962563,
0.03321375697851181,
-0.008420768193900585,
-0.07010872662067413,
0.011993606574833393,
-0.03096095100045204,
0.05270593613386154,
-0.027338828891515732,
-0.020414208993315697,
0.06189149618148804,
-0.004312640056014061,
-0.05745052173733711,
0.014558330178260803,
-0.0355805866420269,
-0.033013977110385895,
-0.027271470054984093,
-0.004954229108989239,
0.006282735615968704,
-0.029044225811958313,
0.007751366123557091,
0.03485487401485443,
-0.024594426155090332,
-0.010167240165174007,
-0.043091099709272385,
-0.06724153459072113,
0.024907516315579414,
-0.016434060409665108,
0.0796915665268898,
-0.01089868787676096,
-0.011650211177766323,
0.04754088446497917,
-0.007990711368620396,
-0.006374453194439411,
-0.0307569932192564,
0.005662247072905302,
0.0029955904465168715,
-0.04103829711675644,
0.03027833066880703,
0.005627820733934641,
-0.006646235007792711,
-0.019851427525281906,
0.03023744933307171,
0.06645137816667557,
0.04429725930094719,
0.006359597202390432,
-0.012873563915491104,
0.020197957754135132,
0.026700656861066818,
-0.013857683166861534,
0.009321632795035839,
0.01271793618798256,
-0.02830868400633335,
-0.001660013571381569,
-0.016314947977662086,
0.032705433666706085,
0.03194297477602959,
-0.05438586696982384,
0.08502111583948135,
0.00047874971642158926,
0.025065215304493904,
-0.002875217469409108,
0.01868331991136074,
-0.04306502640247345,
-0.02625594660639763,
0.005469486117362976,
0.011883891187608242,
0.034860216081142426,
0.01788032427430153,
0.03472031280398369,
0.034177228808403015,
0.034835103899240494,
-0.02322152629494667,
-0.0023985474836081266,
-0.0036971396766602993,
-0.0002275285660289228,
0.04381122812628746,
-0.006910715717822313,
-0.009402656927704811,
0.032486312091350555,
0.07055602222681046,
0.033907923847436905,
0.005684169940650463,
-0.004106380511075258,
-0.0259670652449131,
-0.06497721374034882,
-0.007216479163616896,
-0.0012325022835284472,
0.04485905542969704,
0.011897056363523006,
0.033602192997932434,
0.005814412608742714,
0.0007309216889552772,
-0.014453750103712082,
0.006241816561669111,
-0.06798543781042099,
-0.015223503112792969,
-0.03337038308382034,
0.007939837872982025,
-0.014539950527250767,
-0.006100338883697987,
0.00832840520888567,
-0.0238135177642107,
-0.00961171556264162,
0.007805279456079006,
-0.02112760581076145,
-0.0695006251335144,
0.021238286048173904,
-0.024807387962937355,
0.009038188494741917,
-0.016965016722679138,
0.0427284799516201,
0.06327073276042938,
0.007590447552502155,
0.014690449461340904,
0.0105524817481637,
-0.005707159172743559,
0.03104778751730919,
0.03165411204099655,
0.003914866130799055,
0.0287084449082613,
0.01869414746761322,
-0.0006479959120042622,
-0.020946761593222618,
-0.03968731686472893,
0.02954460121691227,
0.005003221798688173,
0.028617579489946365,
-0.03442833200097084,
-0.04323144629597664,
-0.016789598390460014,
-0.038765210658311844,
-0.00456750625744462,
-0.022887038066983223,
0.08042526245117188,
0.012919427827000618,
0.009919334203004837,
0.011585290543735027,
0.0172737929970026,
-0.0007017773459665477,
0.05144331231713295,
0.06053312495350838,
-0.041243214160203934,
-0.04240813106298447,
-0.04448728263378143,
-0.015360037796199322,
-0.028341785073280334,
-0.021116124466061592,
0.022761384025216103,
0.003465363522991538,
-0.02190452255308628,
0.008230124600231647,
0.005575684364885092,
-0.03653005510568619,
-0.026485035195946693,
0.014837697148323059,
-0.028017301112413406,
-0.016975995153188705,
-0.0029275224078446627,
0.016795897856354713,
-0.025084668770432472,
0.03816181421279907,
0.03555671125650406,
-0.008975736796855927,
-0.026160230860114098,
-0.07936353236436844,
-0.01054870244115591,
0.020578229799866676,
0.045734208077192307,
-0.022296573966741562,
-0.01722332462668419,
-0.03943410888314247,
-0.024502990767359734,
0.029117949306964874,
-0.013013469986617565,
0.020131316035985947,
0.00720218475908041,
-0.02310735173523426,
-0.03723149746656418,
-0.01946648582816124,
0.025479426607489586,
-0.0011001076782122254,
0.006690541282296181,
0.04843248054385185,
-0.00618093041703105,
0.017828505486249924,
-0.005198296159505844,
0.009541557170450687,
0.02661741152405739,
0.028290636837482452,
0.005032516084611416,
0.009636086411774158,
-0.00009162131027551368,
-0.02556472271680832,
-0.05607810616493225,
-0.05848143249750137,
0.032645877450704575,
0.05358399450778961,
-0.02609596587717533,
0.03341232240200043,
-0.019628487527370453,
-0.04841584712266922,
0.03267167881131172,
-0.014985015615820885,
0.02099669724702835,
0.03125317022204399,
-0.03724663332104683,
0.056516725569963455,
0.03065037913620472,
0.00421889265999198,
0.021268319338560104,
0.027886012569069862,
0.01749982126057148,
0.020468851551413536,
-0.022307483479380608,
0.06434851139783859,
-0.0531061589717865,
-0.0014166448963806033,
-0.016008727252483368,
-0.03036143071949482,
-0.03624176234006882,
0.044429730623960495,
-0.02611580863595009,
-0.0063364384695887566,
0.010855920612812042,
-0.021522916853427887,
-0.02970544435083866,
0.006402516737580299,
0.03390820696949959,
0.015989428386092186,
-0.011216027662158012,
-0.018748020753264427,
-0.004081299062818289,
-0.0020605481695383787,
-0.012177640572190285,
-0.00019143079407513142,
-0.009957107715308666,
0.05247349292039871,
0.011606915853917599,
-0.007888264954090118,
-0.03673644736409187,
-0.004183729644864798,
0.011335949413478374,
-0.053578294813632965,
0.027453746646642685,
-0.02014666236937046,
-0.011367621831595898,
0.026857102289795876,
-0.07217811048030853,
-0.034756552428007126,
-0.004118689335882664,
-0.013873481191694736,
-0.012510647997260094,
-0.011429062113165855,
0.023972876369953156,
0.02008005976676941,
0.008694450370967388,
-0.09873535484075546,
-0.034266792237758636,
0.0382164791226387,
0.012280969880521297,
-0.014542737975716591,
-0.015082416124641895,
0.01201517041772604,
-0.021013136953115463,
-0.02108864299952984,
-0.025470837950706482,
0.051273975521326065,
-0.00014616041153203696,
-0.04713914170861244,
0.005565518978983164,
0.02973046898841858,
0.050622571259737015,
-0.014855500310659409,
0.009269636124372482,
-0.01772838830947876,
-0.021483538672327995,
0.019559666514396667,
-0.019628487527370453,
0.05034961551427841,
-0.02439548820257187,
-0.027770549058914185,
-0.03584831953048706,
-0.011682165786623955,
0.016597449779510498,
-0.04427159205079079,
0.012123077176511288,
0.0390891470015049,
-0.04378165304660797,
-0.02146623469889164,
-0.05246971920132637,
0.02252885326743126,
-0.0005464825080707669,
0.009219622239470482,
-0.04705752432346344,
0.013019166886806488,
0.00530784297734499,
-0.06183275580406189,
0.026971880346536636,
-0.012957464903593063,
-0.01232991460710764,
0.01587349735200405,
-0.002856107661500573,
-0.01838053949177265,
0.0012180291814729571,
0.013951538130640984,
-0.02828007936477661,
0.031339216977357864,
0.0073925163596868515,
-0.01577441394329071,
0.030334733426570892,
-0.005907940678298473,
-0.017233099788427353,
-0.016587547957897186,
-0.0403975211083889,
0.020501932129263878,
0.06479237228631973,
-0.017368938773870468,
0.051041994243860245,
0.029293229803442955,
-0.036338552832603455,
0.01476235780864954,
-0.029899654909968376,
0.038166895508766174,
0.010160593315958977,
0.021569767966866493,
0.04116953909397125,
-0.02930591069161892,
-0.014040764421224594,
0.04284914582967758,
0.04028961434960365,
-0.029298318549990654,
0.03385048359632492,
0.028368903324007988,
0.0016970515716820955,
0.05041758716106415,
-0.019147120416164398,
-0.028589358553290367,
0.03396746143698692,
-0.034094326198101044,
-0.005601665936410427,
0.021522218361496925,
-0.010723820887506008,
0.041891101747751236,
0.010717994533479214,
0.012433091178536415,
-0.040960293263196945,
0.008982470259070396,
-0.05944261699914932,
-0.05432361364364624,
0.02136615850031376,
0.03597589582204819,
0.0014084186404943466,
-0.02410120889544487,
0.05188652127981186,
-0.011854056268930435,
-0.01346786692738533,
0.02657056227326393,
-0.05828743427991867,
-0.00520585011690855,
-0.023844994604587555,
-0.044665541499853134,
0.075898177921772,
0.002695451956242323,
-0.027930406853556633,
-0.028592374175786972,
-0.046640973538160324,
0.025073856115341187,
0.030569642782211304,
0.06374189257621765,
-0.049462176859378815,
0.037543825805187225,
-0.020591314882040024,
0.01506521925330162,
-0.04879860579967499,
-0.013494069688022137,
0.11168450117111206,
0.0325404554605484,
0.001029627164825797,
-0.03709643706679344,
0.044589243829250336,
-0.01315298955887556,
0.005991440732032061,
0.00410697516053915,
-0.006288968957960606,
0.008657152764499187,
0.0028051298577338457,
0.02230112999677658,
0.07396762818098068,
0.01916646584868431,
-0.04862643778324127,
0.025032680481672287,
-0.03434810787439346,
0.010118977166712284,
-0.018936432898044586,
0.028198016807436943,
0.01666126400232315,
0.02922881580889225,
-0.03577400743961334,
0.05350693687796593,
-0.01121505256742239,
0.0501013807952404,
-0.03708813339471817,
0.0062207323499023914,
0.020918328315019608,
0.020303137600421906,
-0.04261042922735214,
-0.008783942088484764,
-0.0011569899506866932,
-0.04860948771238327,
-0.0235443115234375,
0.02189301699399948,
0.019437851384282112,
-0.029788212850689888,
0.03227422758936882,
0.046062905341386795,
0.01114333514124155,
0.015214541926980019,
0.015288029797375202,
0.00450447853654623,
-0.05670594424009323,
-0.04024548828601837,
-0.043469320982694626,
0.01800420507788658,
0.0056013562716543674,
-0.029073845595121384,
-0.009456800296902657,
-0.009457857348024845,
0.012536869384348392,
-0.09679289907217026,
0.000248663971433416,
0.00340290111489594,
0.04353952407836914,
0.007586326450109482,
0.004740926902741194,
-0.002151602879166603,
0.017164334654808044,
-0.014073478057980537,
0.022016391158103943,
-0.014347147196531296,
0.02516809292137623,
0.023224839940667152,
-0.014112901873886585,
-0.007224762346595526,
0.008482743985950947,
0.021621979773044586,
-0.03919392079114914,
0.022722560912370682,
-0.031181124970316887,
0.01650696061551571,
0.020118864253163338,
0.060058217495679855,
0.015800537541508675,
0.010366705246269703,
-0.016068996861577034,
-0.006138570141047239,
-0.01630685105919838,
0.019844602793455124,
0.0003685740230139345,
-0.009278262965381145,
0.0015456666005775332,
0.015253040939569473,
0.04112504795193672,
0.0152185820043087,
-0.0026102541014552116,
0.04126648232340813,
-0.026041677221655846,
0.028091775253415108,
0.03118976205587387,
-0.02445315755903721,
0.03165232390165329,
0.032973967492580414,
-0.017053235322237015,
0.0031163953244686127,
-0.031621433794498444,
0.00047912681475281715,
0.025493228808045387,
-0.006136171519756317,
-0.015066105872392654,
0.05760487541556358,
-0.0027412883937358856,
0.0041933185420930386,
0.023470833897590637,
-0.0347188264131546,
0.009166417643427849,
0.014539753086864948,
0.014708049595355988,
-0.06326772272586823,
-0.025199921801686287,
-0.03449466824531555,
0.0025555745232850313,
-0.00830909889191389,
-0.012067222036421299,
-0.0062609403394162655,
0.019966144114732742,
-0.02648606151342392,
-0.00600609602406621,
-0.03471629321575165,
0.00032731815008446574,
-0.0630171075463295,
0.010878201574087143,
-0.018609724938869476,
-0.004857451654970646,
0.021695777773857117,
0.0424257330596447,
-0.03967008739709854,
-0.036890361458063126,
0.031828951090574265,
0.006464841775596142,
-0.0389396995306015,
0.001861650263890624,
0.01958371140062809,
0.014478112570941448,
0.03324306011199951,
0.010426844470202923,
-0.04515201970934868,
0.017532218247652054,
-0.01608622632920742,
-0.04054684191942215,
0.03354542329907417,
-0.019207490608096123,
0.0009631442953832448,
0.06242845207452774,
-0.0065225218422710896,
-0.007642992306500673,
0.08242921531200409,
-0.039705075323581696,
-0.0004953202442266047,
0.025375625118613243,
-0.022987928241491318,
-0.021399641409516335,
-0.025274714455008507,
0.006544944364577532,
0.02357504703104496,
-0.035466425120830536,
0.02266543358564377,
-0.008746436797082424,
0.0013201249530538917,
-0.019807282835245132,
-0.007557705510407686,
-0.04778756573796272,
0.00020660248992498964,
-0.0029349098913371563,
-0.012470056302845478,
0.005603089928627014,
0.06626315414905548,
-0.06471940875053406,
0.02968790754675865,
0.02141469717025757,
-0.02533559687435627,
-0.09091714769601822,
0.011875182390213013,
0.039777033030986786,
0.03448335453867912,
0.012901858426630497,
-0.05094153806567192,
-0.01195563469082117,
0.03002493642270565,
-0.09416241943836212,
0.03256094455718994,
0.004301002249121666,
-0.012631973251700401,
-0.013221628032624722,
-0.004564173519611359,
-0.013956718146800995,
0.017346790060400963,
0.017909634858369827,
0.029471896588802338,
-0.006901087239384651,
0.024867447093129158,
-0.0554928332567215,
-0.05431245267391205,
-0.01916080340743065,
0.05748709663748741,
-0.009326047264039516,
0.03727009892463684,
0.06397176533937454,
-0.009741764515638351,
-0.018089953809976578,
0.04780263453722,
0.01605888456106186,
0.037011101841926575,
-0.009800681844353676,
-0.0215788371860981,
0.013506375253200531,
-0.015411268919706345,
0.014654927887022495,
-0.02580706961452961,
0.0007389815873466432,
0.008726165629923344,
0.0014431135496124625,
0.002885627094656229,
0.011798802763223648,
-0.014409370720386505,
0.02147972583770752,
-0.03756158798933029,
-0.0037701379042118788,
0.01780376024544239,
-0.012186300940811634,
-0.0023257103748619556,
0.007733871228992939,
-0.007506644818931818,
0.041201479732990265,
-0.0026669956278055906,
-0.014727573841810226,
-0.052206940948963165,
0.0039374646730721,
0.026490120217204094,
-0.022136658430099487,
-0.017867740243673325,
0.03829754516482353,
-0.015255652368068695,
-0.013377145864069462,
-0.008686218410730362,
0.005742822308093309,
-0.02944769896566868,
-0.039566051214933395,
-0.03241807967424393,
-0.01611350104212761,
0.011382833123207092,
-0.00007849212124710903,
-0.027371179312467575,
-0.026901070028543472,
0.014727039262652397,
0.01752568781375885,
0.018148019909858704,
-0.003043530276045203,
-0.04107329621911049,
-0.05780762806534767,
-0.10259950906038284,
0.009944259189069271,
0.019366594031453133,
-0.034254029393196106,
-0.06791143119335175,
-0.009478168562054634,
-0.03998645395040512,
0.07793404161930084,
0.0700228288769722,
0.010108739137649536,
0.013930882327258587,
0.01190961990505457,
0.03511130437254906,
0.037509385496377945,
-0.054842881858348846,
-0.04354199767112732,
0.0058118849992752075,
-0.024666422978043556,
0.030444832518696785,
-0.00930623710155487,
-0.0354209765791893,
0.007815615274012089,
0.04642074927687645,
-0.006636385805904865,
0.022123605012893677,
0.009884530678391457,
-0.023919979110360146,
0.03247680142521858,
-0.0033372733741998672,
-0.009002575650811195,
0.037142422050237656,
-0.009472612291574478,
0.00001628583595447708,
0.021783199161291122,
-0.007344410289078951,
0.01533329114317894,
-0.022863084450364113,
-0.03864337503910065,
0.007849001325666904,
-0.018265901133418083,
-0.03382328897714615,
0.05345267802476883,
-0.029897049069404602,
-0.00045352111919783056,
0.0328853465616703,
-0.002574595157057047,
0.017344962805509567,
0.06000291928648949,
0.02336708828806877,
-0.005667973309755325,
0.002112835180014372,
0.007822444662451744,
0.03550635650753975,
0.002124464837834239,
0.023374345153570175,
0.03126406669616699,
0.055081870406866074,
0.004694355186074972,
-0.010013720951974392,
0.034230589866638184,
-0.004076983779668808,
0.023805757984519005,
0.005039628129452467,
0.05183594301342964,
-0.044838737696409225,
-0.017547648400068283,
0.009777328930795193,
-0.005320740398019552,
-0.014277709648013115,
0.0078018102794885635,
-0.02299451269209385,
0.09134514629840851,
0.014755615033209324,
0.011721299961209297,
0.006670953240245581,
-0.012198302894830704,
-0.029984833672642708,
0.04187954217195511,
0.026259848847985268,
0.014835702255368233,
-0.025121811777353287,
-0.0055445898324251175,
-0.013670017011463642,
-0.0007349603110924363,
0.023130960762500763,
-0.0125831114128232,
-0.006890015676617622,
0.015340758487582207,
0.0110853873193264,
-0.016908837482333183,
-0.018237726762890816,
-0.005149809643626213,
-0.02947946824133396,
0.0350399985909462,
-0.004667561501264572,
0.03500451520085335,
-0.013998987153172493,
0.021199336275458336,
-0.04499034211039543,
0.03222406655550003,
-0.09290892630815506,
-0.03746931254863739,
-0.01201059203594923,
0.03703964129090309,
0.003524173516780138,
-0.024889109656214714
] |
<p>How do we estimate the energy released from knocking on a wooden table or a door?</p>
| 9,602 |
[
-0.054369885474443436,
-0.03363289311528206,
-0.01575952209532261,
-0.0521891824901104,
0.013748491182923317,
0.02401329018175602,
-0.035543810576200485,
-0.016251172870397568,
0.022824525833129883,
0.010901828296482563,
0.04664849117398262,
0.060892701148986816,
0.012956712394952774,
0.016098635271191597,
-0.010039134882390499,
0.014497931115329266,
0.0166359543800354,
-0.009416216984391212,
-0.027868026867508888,
-0.038005564361810684,
0.015227957628667355,
-0.029598424211144447,
-0.0176224447786808,
-0.004338698927313089,
-0.05473059043288231,
0.0013424159260466695,
0.0520947091281414,
-0.025490736588835716,
0.02440742217004299,
0.06232598051428795,
-0.0139309735968709,
-0.020487314090132713,
0.006637063808739185,
-0.004858875181525946,
0.007063251454383135,
-0.0247566569596529,
-0.04976515471935272,
-0.030705977231264114,
-0.007284584455192089,
0.02440240979194641,
-0.026335569098591805,
-0.0006335971993394196,
0.007656922563910484,
0.04674435406923294,
-0.039739321917295456,
0.011945506557822227,
-0.03108394145965576,
-0.022361263632774353,
0.03152477741241455,
-0.07550427317619324,
0.04902307689189911,
-0.027612341567873955,
0.04474392160773277,
-0.0011208296054974198,
-0.013331425376236439,
0.0011236630380153656,
0.08676287531852722,
0.0470038503408432,
-0.018203051760792732,
-0.046178001910448074,
-0.019857486709952354,
-0.007640705909579992,
-0.007164097391068935,
-0.046609871089458466,
-0.011698674410581589,
0.0011862023966386914,
-0.0006774663343094289,
-0.038191791623830795,
0.05871874839067459,
0.0011968183098360896,
0.04639198258519173,
0.02194848656654358,
0.05407081916928291,
-0.0015914349351078272,
0.001372873899526894,
-0.021397868171334267,
0.019786760210990906,
0.047581467777490616,
0.03396698087453842,
0.05475190281867981,
-0.01021217554807663,
-0.02875245176255703,
0.05430208519101143,
0.06814220547676086,
0.031240899115800858,
-0.03698677942156792,
0.07171982526779175,
-0.006345217116177082,
-0.013778462074697018,
0.002655810909345746,
0.018298882991075516,
0.005402866750955582,
0.019004568457603455,
0.005822795908898115,
0.010301763191819191,
0.016209043562412262,
-0.011439062654972076,
0.065020851790905,
0.033762864768505096,
-0.017131224274635315,
0.02298782393336296,
-0.0030175168067216873,
0.018711235374212265,
0.058255381882190704,
-0.02900156006217003,
-0.012396861799061298,
-0.021590637043118477,
0.028587084263563156,
0.005088945385068655,
0.00036163508775644004,
-0.03189745172858238,
0.0010268347105011344,
-0.017584018409252167,
0.02059076353907585,
0.0035594890359789133,
-0.011941234581172466,
-0.015557641163468361,
-0.007142690010368824,
0.034897301346063614,
0.05172644555568695,
-0.0008547038887627423,
-0.010500452481210232,
-0.01057826541364193,
-0.058377914130687714,
-0.05809482932090759,
0.0217308197170496,
0.030152862891554832,
-0.0502009280025959,
-0.0481940396130085,
0.02216644026339054,
0.009461183100938797,
-0.025991378352046013,
0.016652148216962814,
-0.0316602922976017,
0.027042802423238754,
-0.001178853795863688,
-0.10754188150167465,
-0.06827486306428909,
0.05088036507368088,
0.003877070965245366,
-0.01858261413872242,
-0.0741502195596695,
-0.01581631787121296,
0.023158637806773186,
0.03014475852251053,
-0.013878504745662212,
-0.0008661100873723626,
0.002727890620008111,
0.023276636376976967,
-0.02575192041695118,
-0.015854988247156143,
0.0002518359979148954,
-0.03046051226556301,
0.004699264653027058,
0.01998642086982727,
-0.03220827877521515,
0.02733023464679718,
0.025700360536575317,
-0.0019998562056571245,
-0.02484295703470707,
0.03919123858213425,
-0.028294624760746956,
-0.05109887197613716,
-0.00825453083962202,
0.03337760642170906,
-0.057963043451309204,
0.06793655455112457,
0.01197198685258627,
0.0006750359898433089,
0.02269236370921135,
-0.0006160076591186225,
0.01909281499683857,
0.008285433053970337,
-0.00007550416194135323,
0.020372280851006508,
-0.0606270395219326,
-0.009656510315835476,
0.009212619625031948,
0.04368261992931366,
0.008529793471097946,
-0.04517395421862602,
-0.0062858788296580315,
0.03397972881793976,
-0.027847066521644592,
0.022756759077310562,
0.006742397788912058,
-0.02352510578930378,
-0.03663194924592972,
-0.029129868373274803,
-0.026509426534175873,
-0.05878184363245964,
-0.09149347990751266,
0.041978489607572556,
-0.007092514541000128,
0.03679225593805313,
0.011917104944586754,
-0.003481269348412752,
0.020179670304059982,
-0.04462162405252457,
-0.031256675720214844,
-0.0071584125980734825,
0.0016637237276881933,
0.018082356080412865,
-0.02427235245704651,
-0.014464871026575565,
0.03549501299858093,
0.07377087324857712,
0.015073259361088276,
0.020884906873106956,
-0.022911522537469864,
-0.014381841756403446,
-0.005964240524917841,
-0.052868906408548355,
-0.0061464086174964905,
0.019694659858942032,
-0.030179595574736595,
0.02189004421234131,
-0.017975807189941406,
-0.016227584332227707,
0.030195511877536774,
0.019444741308689117,
0.058186620473861694,
0.04790312424302101,
0.016829732805490494,
-0.0012600887566804886,
-0.00005402466922532767,
-0.013217584230005741,
0.010974601842463017,
0.0022554192692041397,
-0.03639386221766472,
-0.044589634984731674,
-0.03634099289774895,
0.024110395461320877,
-0.021386491134762764,
-0.016626765951514244,
-0.01474929228425026,
0.04643155261874199,
-0.0021039380226284266,
0.011089828796684742,
0.028407815843820572,
-0.015382899902760983,
-0.001962596084922552,
0.025713110342621803,
0.038952071219682693,
0.00526325311511755,
0.02525794506072998,
0.027713574469089508,
0.03380146995186806,
-0.0024415524676442146,
0.012959213927388191,
-0.011342433281242847,
0.023720785975456238,
-0.008821336552500725,
0.02613845281302929,
-0.022205540910363197,
-0.022223517298698425,
0.016242079436779022,
-0.013277363032102585,
0.0038773107808083296,
0.0023331837728619576,
-0.009228797629475594,
0.014398445375263691,
0.00219558784738183,
-0.027908524498343468,
0.00254364893771708,
-0.028604919090867043,
-0.002024626825004816,
0.013933989219367504,
0.0557713508605957,
-0.030574839562177658,
0.044174108654260635,
-0.005406501702964306,
-0.0337812602519989,
0.022830793634057045,
-0.020599057897925377,
0.0210260096937418,
0.0004841228073928505,
0.023734785616397858,
-0.042444776743650436,
-0.02272091992199421,
-0.0030717728659510612,
-0.006498957052826881,
-0.021360967308282852,
0.01950102113187313,
-0.020524870604276657,
0.03941425308585167,
-0.037097059190273285,
-0.028188850730657578,
0.009672318585216999,
0.004769209306687117,
-0.007671653293073177,
0.05453048273921013,
0.0388382188975811,
-0.05277688056230545,
0.013199194334447384,
0.00045975326793268323,
0.012810047715902328,
-0.01713184453547001,
0.027944879606366158,
0.02445310354232788,
0.015559586696326733,
-0.020540345460176468,
0.0009219445055350661,
0.00468253530561924,
-0.024834297597408295,
-0.009606834501028061,
-0.04727504402399063,
0.022325238212943077,
-0.012801378965377808,
0.021132050082087517,
0.019897067919373512,
-0.038890693336725235,
0.0076477001421153545,
-0.04437774419784546,
-0.034647975116968155,
0.004993515554815531,
-0.009140033274888992,
0.06532835960388184,
-0.006481113377958536,
-0.06423001736402512,
0.06540394574403763,
-0.012933943420648575,
-0.04824090749025345,
0.008911415934562683,
-0.08434571325778961,
0.013438379392027855,
-0.014511842280626297,
-0.027803687378764153,
0.053760942071676254,
0.0008515301160514355,
0.049620985984802246,
-0.03621378168463707,
-0.01265992596745491,
0.006175096146762371,
0.045146018266677856,
-0.016363123431801796,
-0.0203093234449625,
-0.02557416819036007,
-0.010405815206468105,
0.033742669969797134,
-0.03485625982284546,
-0.03260981664061546,
0.016830382868647575,
-0.017948614433407784,
-0.0007583093829452991,
0.003925078082829714,
-0.029360895976424217,
0.05353528633713722,
-0.000567337847314775,
-0.015638399869203568,
-0.06546712666749954,
0.051072195172309875,
-0.003035150468349457,
-0.026416106149554253,
0.003403047099709511,
0.05138803645968437,
0.04435162618756294,
0.011115039698779583,
0.0070433542132377625,
0.05253130570054054,
0.0437939278781414,
-0.008403710089623928,
-0.03656988590955734,
-0.009561357088387012,
0.0016319315182045102,
-0.0008828343125060201,
0.017011621966958046,
0.009663059376180172,
0.010579337365925312,
0.022023014724254608,
0.03561815246939659,
0.022154556587338448,
-0.003936522640287876,
0.004283017944544554,
-0.03057328797876835,
-0.012989668175578117,
-0.01980804093182087,
0.04196351021528244,
-0.005148638505488634,
0.05780906602740288,
0.013782483525574207,
-0.027610857039690018,
0.051182013005018234,
-0.02361675351858139,
-0.052986714988946915,
0.0018712166929617524,
-0.030470481142401695,
-0.014871143735945225,
-0.016146186739206314,
-0.027335528284311295,
-0.007192094344645739,
0.0018646158277988434,
-0.012948838993906975,
-0.027316268533468246,
0.005250467453151941,
-0.05389251187443733,
0.015112975612282753,
-0.014647341333329678,
-0.04459002614021301,
0.020335132256150246,
0.021687744185328484,
0.03261205554008484,
-0.005911512300372124,
-0.026809385046362877,
0.04537980630993843,
0.017807764932513237,
-0.02257939800620079,
0.016064424067735672,
0.002163647674024105,
-0.03630382940173149,
0.0604810006916523,
-0.0019984962418675423,
0.01665886864066124,
-0.0523560605943203,
0.011641683988273144,
-0.014673272147774696,
0.021270597353577614,
0.011298054829239845,
-0.03470958024263382,
-0.045601505786180496,
-0.009126562625169754,
0.008457527495920658,
0.026047589257359505,
0.033507075160741806,
-0.04816346615552902,
0.05761248618364334,
-0.005067524500191212,
0.01905777119100094,
-0.013507767580449581,
0.03738356754183769,
0.04595924913883209,
0.02283794805407524,
-0.028933947905898094,
-0.04316242039203644,
0.0159943625330925,
-0.010628573596477509,
-0.0385129339993,
-0.010211756452918053,
0.01352924108505249,
-0.002130956621840596,
0.03727714344859123,
-0.0019901127088814974,
-0.01903625950217247,
-0.028192706406116486,
0.029132170602679253,
0.008538355119526386,
0.0028265148866921663,
0.007319663651287556,
-0.02554432488977909,
0.024995004758238792,
0.020266762003302574,
0.02984568476676941,
-0.010291578248143196,
-0.04764040932059288,
-0.08290261030197144,
-0.019750267267227173,
0.02812979370355606,
0.03371269628405571,
-0.02483055554330349,
0.018417710438370705,
-0.028998056426644325,
-0.023166269063949585,
0.024673068895936012,
-0.04476340115070343,
0.004343651235103607,
-0.0259286817163229,
0.02234819531440735,
-0.04135092347860336,
-0.008835922926664352,
-0.03930532559752464,
0.017921090126037598,
-0.0018418561667203903,
0.014346112497150898,
-0.0022622798569500446,
-0.03503129631280899,
-0.022424327209591866,
0.043798718601465225,
0.037139732390642166,
0.03225173056125641,
-0.013460329733788967,
0.03789416700601578,
-0.030858220532536507,
0.03230206295847893,
-0.023577962070703506,
-0.05042744055390358,
0.022554198279976845,
0.000045258500904310495,
0.002734929556027055,
0.04960814490914345,
-0.020271586254239082,
-0.04625974968075752,
0.019097043201327324,
-0.027790429070591927,
0.007982492446899414,
-0.027955763041973114,
-0.05293390899896622,
0.02525532804429531,
0.035067472606897354,
0.010652996599674225,
0.06945104897022247,
0.05399021506309509,
-0.05214633047580719,
0.04194357618689537,
-0.012631922028958797,
0.00620103906840086,
-0.03573903068900108,
0.012061798013746738,
-0.02148827351629734,
0.02989625744521618,
-0.03834814950823784,
0.05286729708313942,
-0.02275044098496437,
0.041197147220373154,
-0.0032895090989768505,
-0.054918717592954636,
-0.03621489927172661,
0.03242448344826698,
0.021120602265000343,
0.032739780843257904,
-0.0051299333572387695,
0.006470611784607172,
0.012151583097875118,
-0.008641312830150127,
0.0025392896495759487,
-0.005193572491407394,
0.047221262007951736,
-0.013415630906820297,
-0.019111178815364838,
0.021865826100111008,
-0.05396539345383644,
-0.012529744766652584,
0.0639820471405983,
-0.042137157171964645,
0.04150623083114624,
-0.04263043776154518,
0.02399824745953083,
0.004955046810209751,
-0.03503140062093735,
-0.03512077406048775,
0.01534578949213028,
0.013461580500006676,
0.07713763415813446,
-0.02008705772459507,
0.04508597403764725,
0.015109344385564327,
0.003205769695341587,
-0.03334009647369385,
0.008992046117782593,
0.018176313489675522,
0.010008195415139198,
0.008107637986540794,
-0.048919953405857086,
-0.01720573753118515,
-0.035292088985443115,
-0.00790689792484045,
-0.0005775223835371435,
0.015923911705613136,
-0.013927910476922989,
0.04611624404788017,
0.005843796767294407,
-0.04125473275780678,
0.028030861169099808,
0.040594980120658875,
-0.006289436481893063,
0.03129398822784424,
-0.011551842093467712,
-0.05073980614542961,
-0.023545052856206894,
0.023040493950247765,
-0.031885918229818344,
0.007546455133706331,
0.011406305246055126,
0.016996007412672043,
0.026641784235835075,
-0.03674028813838959,
0.03905993700027466,
0.03543319180607796,
0.030799120664596558,
-0.034308791160583496,
-0.021674778312444687,
0.06020156294107437,
0.04140269011259079,
0.04454965516924858,
0.0057596913538873196,
-0.007128779776394367,
-0.021730633452534676,
0.0012716454220935702,
-0.006848583929240704,
-0.008132810704410076,
-0.009832754731178284,
-0.023014485836029053,
0.07159436494112015,
0.011347784660756588,
-0.011152888648211956,
0.041312310844659805,
-0.02172374725341797,
0.03902096673846245,
-0.01941819302737713,
0.030687246471643448,
0.02173399180173874,
-0.014226417988538742,
-0.027933726087212563,
-0.06364592164754868,
-0.029577260836958885,
-0.030353859066963196,
0.03349696472287178,
-0.013527573086321354,
0.06473147124052048,
-0.0032981939148157835,
-0.005286676809191704,
0.007943435572087765,
-0.0016804714687168598,
0.039107080549001694,
-0.0047383238561451435,
0.0021976050920784473,
0.032627809792757034,
0.008676601573824883,
0.005410885438323021,
0.01792786456644535,
-0.006913402117788792,
-0.03302453085780144,
0.02810312993824482,
0.03042423538863659,
0.058191921561956406,
0.03087189421057701,
-0.07478547096252441,
-0.027198543772101402,
0.024536294862627983,
-0.05308269336819649,
-0.01233613956719637,
-0.010277455672621727,
-0.004619133658707142,
0.04823719337582588,
0.029360326007008553,
-0.0149088678881526,
-0.014587229117751122,
0.02898188680410385,
-0.08412228524684906,
-0.0038204025477170944,
-0.003816277952864766,
0.00877068005502224,
-0.011061047203838825,
0.013947638683021069,
-0.015874691307544708,
0.009752392768859863,
0.004122831393033266,
-0.0034147377591580153,
-0.07301444560289383,
0.004366226028650999,
-0.044367093592882156,
-0.04140394926071167,
0.03421716019511223,
-0.029283378273248672,
-0.0189894400537014,
0.05904228612780571,
-0.027468977496027946,
0.02155626192688942,
-0.011537724174559116,
0.03213295713067055,
-0.023989973589777946,
0.07952403277158737,
-0.015017235651612282,
0.008717273361980915,
-0.04747645929455757,
0.040093496441841125,
0.13694973289966583,
0.046189721673727036,
0.022915750741958618,
-0.06634800136089325,
0.016407383605837822,
-0.00513672549277544,
-0.024421436712145805,
0.017269914969801903,
0.002253843704238534,
0.018698446452617645,
0.010804381221532822,
0.0003790121409110725,
0.053104303777217865,
-0.02170516923069954,
-0.008444811217486858,
0.03195101022720337,
-0.01988205686211586,
-0.039897795766592026,
0.0395757295191288,
0.03634249046444893,
-0.0021405003499239683,
0.010185499675571918,
0.0011261875042691827,
0.009727244265377522,
-0.004340607672929764,
-0.044129855930805206,
0.006172573659569025,
-0.0434892475605011,
0.04177692532539368,
-0.006714767310768366,
-0.018333453685045242,
0.01157794613391161,
0.031296949833631516,
0.01445949450135231,
-0.013613592833280563,
0.02807229943573475,
0.06570470333099365,
0.018963458016514778,
0.017322836443781853,
0.03162321820855141,
0.018686871975660324,
-0.0160715039819479,
-0.01191164180636406,
0.012768741697072983,
-0.0691908448934555,
-0.023051247000694275,
-0.023173274472355843,
0.026345139369368553,
0.006005213595926762,
0.021731464192271233,
-0.0008715534931980073,
0.0061662509106099606,
-0.015708928927779198,
-0.03718823939561844,
-0.024762673303484917,
0.0016747468616813421,
0.022148583084344864,
-0.029584871605038643,
-0.06004788726568222,
-0.052243463695049286,
0.005101614631712437,
-0.013389070518314838,
0.0272273737937212,
0.0052046701312065125,
0.011058722622692585,
-0.002980234567075968,
0.000694628048222512,
0.020098812878131866,
-0.004095192067325115,
-0.032292407006025314,
-0.04198100045323372,
-0.06785796582698822,
-0.04138399288058281,
-0.00909162126481533,
-0.03827877342700958,
0.03423691168427467,
0.03985258936882019,
0.010378401726484299,
0.014465264044702053,
-0.048547904938459396,
-0.08582647144794464,
0.05877676233649254,
-0.05276913940906525,
-0.021110624074935913,
-0.023688670247793198,
-0.015357582829892635,
0.01803928054869175,
0.03911054506897926,
-0.022676972672343254,
0.013691584579646587,
0.0057141138240695,
0.01604221574962139,
0.04024886712431908,
-0.008567824959754944,
-0.03315533697605133,
-0.00791957974433899,
0.003950045444071293,
-0.004985058214515448,
-0.02370697446167469,
0.02299526147544384,
-0.0004871117998845875,
-0.0406707264482975,
0.012051869183778763,
0.0013492832658812404,
-0.017989253625273705,
-0.015126119367778301,
0.00008268671081168577,
-0.049769286066293716,
-0.030428003519773483,
-0.011108074337244034,
0.007590843830257654,
-0.03132924810051918,
-0.009278563782572746,
-0.019916268065571785,
-0.002461804775521159,
-0.014397667720913887,
0.029865775257349014,
-0.028641825541853905,
0.010350868105888367,
-0.028056560084223747,
0.037160150706768036,
-0.04429761320352554,
-0.01595701463520527,
0.0034240437671542168,
-0.02339676208794117,
0.03724954277276993,
-0.05301739647984505,
-0.0024151981342583895,
0.007169707678258419,
-0.0039099776186048985,
0.011845432221889496,
0.03996635973453522,
0.006836110260337591,
0.012315742671489716,
0.02182832732796669,
0.041262224316596985,
-0.041584618389606476,
0.02605355717241764,
0.0227042343467474,
-0.020815405994653702,
0.04030080512166023,
-0.08059155941009521,
-0.06626340746879578,
0.04181773588061333,
-0.021656496450304985,
0.034253448247909546,
0.07109714299440384,
-0.03910939022898674,
0.028195394203066826,
0.048218291252851486,
-0.055590420961380005,
-0.02048889733850956,
-0.0025917505845427513,
0.019965238869190216,
0.0030302992090582848,
0.007040855009108782,
0.02240183763206005,
0.0024096635170280933,
-0.02591829001903534,
0.058464180678129196,
0.00023147559841163456,
0.006655891425907612,
-0.001146550988778472,
-0.0012266006087884307,
-0.05096158757805824,
0.028440918773412704,
0.00015632603026460856,
0.005919619929045439,
-0.01596026122570038,
0.03134419396519661,
-0.018795151263475418,
0.020631317049264908,
-0.007034678477793932,
-0.03804590180516243,
-0.09039972722530365,
-0.002591815311461687,
-0.036585841327905655,
-0.02148483693599701,
0.055887531489133835,
-0.04373043030500412,
0.054105181246995926,
0.024279827252030373,
-0.034156352281570435,
0.042977914214134216,
0.002835427178069949,
-0.017114875838160515,
-0.019373329356312752,
0.027843598276376724,
0.024216029793024063,
0.014724439941346645,
-0.00005386925477068871,
0.06153528764843941,
0.025864586234092712,
0.044952474534511566,
0.005941253155469894,
-0.0011186165502294898,
0.03568092733621597,
0.04210025444626808,
-0.013293695636093616,
0.005498779937624931,
0.055906809866428375,
-0.04584510251879692,
-0.019324900582432747,
0.022319065406918526,
0.009234246797859669,
0.01824973337352276,
-0.011293133720755577,
0.01750064268708229,
-0.004625586327165365,
0.022706056013703346,
0.009783171117305756,
-0.0491153858602047,
-0.00791234988719225,
0.05031006783246994,
-0.009611575864255428,
0.007772178389132023,
-0.024005277082324028,
0.0022703749127686024,
0.020757151767611504,
0.0006640425999648869,
-0.015200380235910416,
0.011759315617382526,
-0.009114157408475876,
-0.013567277230322361,
0.042651113122701645,
-0.0126429982483387,
0.011224831454455853,
-0.007972145453095436,
-0.041597362607717514,
-0.0407850556075573,
0.0031077684834599495,
0.01696539856493473,
0.01945747248828411,
-0.013782420195639133,
0.026548782363533974,
0.004048007540404797,
-0.022750481963157654,
0.02154090255498886,
0.02476610243320465,
-0.032949574291706085,
-0.08454865217208862,
0.012575826607644558,
0.00668581947684288,
0.018480144441127777,
-0.009764249436557293,
-0.034884579479694366,
-0.046859268099069595,
0.006566723342984915,
0.0013480652123689651,
0.024782266467809677,
0.012947211042046547,
-0.015022525563836098,
-0.03511961176991463,
-0.0495382584631443,
0.048019275069236755,
0.00892693642526865,
-0.0016906755045056343,
-0.0451730415225029,
-0.018320055678486824,
0.025156253948807716,
-0.022617176175117493,
0.06818714737892151,
0.010150891728699207,
-0.06820713728666306,
-0.00041301350574940443,
-0.005966985132545233,
0.015250077471137047,
-0.004105919972062111,
0.041341669857501984,
-0.03666544333100319,
0.027373943477869034,
-0.029101619496941566,
-0.04470246657729149,
-0.005995334126055241,
0.016457824036478996,
0.02264316938817501,
-0.007411183789372444,
-0.020951269194483757,
-0.018769141286611557,
-0.029054677113890648,
0.06854663789272308,
0.025888865813612938,
0.021409040316939354,
0.04616645723581314,
-0.03191739320755005,
0.020413869991898537,
-0.014333920553326607,
-0.036336034536361694,
-0.02098247781395912,
0.039411935955286026,
-0.012598108500242233,
-0.0015170270344242454,
0.02996712177991867,
0.017359910532832146,
0.018039677292108536,
-0.04423549026250839,
-0.02198737859725952,
0.05109645426273346,
-0.02206987887620926,
-0.0005082326824776828,
0.01097888220101595,
0.043553464114665985,
0.04077916219830513,
-0.002249469282105565,
0.043887581676244736,
0.040810275822877884,
0.048350740224123,
-0.019872236996889114,
0.049168143421411514,
0.01411652285605669,
-0.016460174694657326,
0.010937812738120556,
0.030438700690865517,
-0.01087411679327488,
0.0283606369048357,
0.07370272278785706,
0.003624099539592862,
-0.007287777028977871,
-0.04086926952004433,
-0.012546934187412262,
0.00679699145257473,
-0.010195454582571983,
0.01654236391186714,
-0.010720168240368366,
0.08452977240085602,
0.023534730076789856,
-0.0049577392637729645,
-0.04278835654258728,
-0.006306579802185297,
0.004831566940993071,
0.008277912624180317,
0.013288372196257114,
0.0188561100512743,
-0.00006929571100044996,
0.06265174597501755,
-0.02494601346552372,
0.02196718193590641,
0.03117254748940468,
-0.028975412249565125,
0.016128435730934143,
-0.005398315843194723,
-0.0010405995417386293,
-0.04218331724405289,
0.0074898600578308105,
-0.0052146692760288715,
-0.023912427946925163,
0.05378997325897217,
0.0720827654004097,
0.03484131395816803,
0.016792036592960358,
0.010168633423745632,
0.01714307628571987,
0.04530714824795723,
-0.04928364232182503,
0.01303891185671091,
-0.02776453271508217,
0.018371980637311935,
-0.012510903179645538,
0.013810773380100727
] |
<p>I am learning about circular motion and not quite sure how to approach this particular problem. Any help would be greatly appreciated!</p>
<blockquote>
<p>A particle moves along a circular path over a horizontal $x$-$y$ coordinate system, at constant speed. At time $t_1 = 5$ s, it is at point ($4.00$ m, $8.00$ m) with velocity ($1.60$ m/s)$\hat{\mathbf{j}}$ and acceleration in the positive $x$ direction. At time $t_2 = 8$ s, it has velocity ($-1.6$ m/s)$\hat{\mathbf{i}}$ and acceleration in the positive $y$ direction. What are the coordinates of the center of the circular path?</p>
</blockquote>
| 9,603 |
[
0.004671928472816944,
-0.03713588789105415,
-0.006696037948131561,
-0.006408488843590021,
0.05659572035074234,
-0.021317774429917336,
-0.022946253418922424,
-0.0050057400949299335,
0.017022879794239998,
0.011364065110683441,
0.002098121214658022,
0.06454101949930191,
0.027719469740986824,
0.03983154520392418,
0.0120041873306036,
0.004377563484013081,
-0.033580414950847626,
-0.004194838926196098,
-0.019243622198700905,
-0.02578832395374775,
0.012037784792482853,
-0.028718098998069763,
0.0015759525122120976,
-0.006710211746394634,
-0.012610367499291897,
0.044140104204416275,
0.02621978148818016,
-0.010994164273142815,
-0.005766468588262796,
0.06693383306264877,
-0.030461911112070084,
0.012984302826225758,
0.007385220378637314,
0.01786988042294979,
0.02020953968167305,
0.004728166852146387,
-0.06167472153902054,
-0.02019735798239708,
-0.01456548273563385,
0.042207662016153336,
-0.05360736325383186,
-0.025405362248420715,
-0.015298711135983467,
0.04541614279150963,
-0.0016375783598050475,
0.013395615853369236,
-0.00095905433408916,
0.02563554048538208,
0.05282822996377945,
-0.03614930808544159,
0.10974987596273422,
-0.03854435309767723,
0.01774202659726143,
0.01239121612161398,
-0.001996339065954089,
-0.01303196232765913,
0.05923110246658325,
0.051263052970170975,
0.0173258688300848,
-0.01012148056179285,
-0.010631194338202477,
-0.018547693267464638,
-0.0006825222517363727,
-0.019700966775417328,
-0.02130166068673134,
-0.004618500359356403,
-0.01817144826054573,
-0.006983728148043156,
-0.019846517592668533,
-0.011490286327898502,
0.01855180412530899,
0.032345000654459,
0.06391323357820511,
-0.052081841975450516,
0.01593034714460373,
-0.04609910771250725,
0.04726605862379074,
0.039167631417512894,
0.011142005212605,
0.012972347438335419,
0.0007658360409550369,
0.044726334512233734,
0.037393782287836075,
0.0350852832198143,
-0.0003689924778882414,
-0.015537100844085217,
0.033432282507419586,
0.016795221716165543,
0.04558546096086502,
0.02956721931695938,
-0.0035188256297260523,
0.00703134760260582,
0.04560007527470589,
-0.0019102620426565409,
-0.009972007013857365,
0.01836824230849743,
0.007512853015214205,
0.04549628496170044,
0.01962381973862648,
0.011695741675794125,
0.008681917563080788,
-0.06559101492166519,
0.009181730449199677,
0.06288257986307144,
-0.004197778645902872,
0.006440662778913975,
-0.013348893262445927,
-0.007027599029242992,
-0.012709599919617176,
-0.059052132070064545,
-0.07922559976577759,
-0.010306487791240215,
0.012896045111119747,
0.004892404656857252,
0.013857569545507431,
-0.0407438687980175,
-0.03192664682865143,
0.0020880140364170074,
0.07059657573699951,
-0.000984368147328496,
0.0780726745724678,
-0.04148220270872116,
-0.011893129907548428,
-0.004635839257389307,
-0.047909244894981384,
-0.03168797120451927,
0.021796757355332375,
-0.0036289270501583815,
-0.012731527909636497,
0.019196003675460815,
0.036424025893211365,
-0.0027735924813896418,
0.03417747840285301,
-0.0034414781257510185,
0.0064354524947702885,
-0.0020032168831676245,
-0.10443414747714996,
-0.09991717338562012,
0.028125734999775887,
0.0056991493329405785,
-0.039075110107660294,
-0.08898095041513443,
0.02067725732922554,
0.04184158518910408,
0.05505857616662979,
-0.03647557646036148,
-0.0029931985773146152,
0.03238213062286377,
0.04298299923539162,
0.02019372209906578,
-0.03252551332116127,
-0.022843243554234505,
-0.040041420608758926,
-0.031132616102695465,
0.023940712213516235,
-0.042975716292858124,
-0.013034037314355373,
0.033078860491514206,
-0.0015284511027857661,
-0.03495568037033081,
0.05702289193868637,
0.007219610270112753,
0.012554352171719074,
0.024647323414683342,
0.00570668512955308,
-0.03036869689822197,
0.06393657624721527,
0.02053266577422619,
-0.015494001097977161,
0.04654407873749733,
0.01985211856663227,
0.00530431279912591,
-0.007579924538731575,
0.019770188257098198,
0.07350216060876846,
-0.04182108864188194,
-0.004183657933026552,
-0.0000021911371277383296,
0.002316633705049753,
0.0151798902079463,
-0.02355904132127762,
-0.05320935323834419,
-0.024439096450805664,
-0.002715542446821928,
0.01176697202026844,
0.07636962085962296,
0.007693541701883078,
0.007651099003851414,
-0.01952197402715683,
-0.04272282123565674,
0.03532537817955017,
-0.06788097321987152,
-0.01792965643107891,
-0.01626032032072544,
0.005546807311475277,
0.026393238455057144,
0.0212592463940382,
0.03246855363249779,
-0.02090461738407612,
0.013426482677459717,
0.006228850223124027,
0.043366238474845886,
0.01689482480287552,
-0.027940360829234123,
0.009295995347201824,
0.04680578410625458,
0.03923827037215233,
0.022650260478258133,
0.011702277697622776,
-0.024494079872965813,
0.02508057840168476,
0.002093026414513588,
0.014325818978250027,
0.026453765109181404,
0.054880231618881226,
-0.01744592934846878,
-0.019552087411284447,
-0.0024407757446169853,
0.015040694735944271,
0.04009269177913666,
-0.016286274418234825,
0.07563884556293488,
0.011041934601962566,
-0.03109014593064785,
0.0037418706342577934,
0.01804897002875805,
-0.0006595535087399185,
0.04611848294734955,
0.00738584203645587,
-0.023068707436323166,
-0.006598257925361395,
-0.01589038223028183,
0.037174124270677567,
0.03529014065861702,
-0.061599332839250565,
-0.00884037371724844,
0.05726367607712746,
0.03952797129750252,
0.008156247437000275,
0.010369445197284222,
-0.006850250996649265,
-0.04404187947511673,
0.011063002981245518,
0.03628954663872719,
-0.03261131793260574,
0.015153417363762856,
0.02389688789844513,
0.01885184273123741,
0.03852471709251404,
0.015622545033693314,
-0.03268568962812424,
0.017606185749173164,
-0.0047857630997896194,
0.010819130577147007,
0.020607147365808487,
-0.010669231414794922,
0.06774415075778961,
0.01779118739068508,
0.006625267677009106,
0.03469688817858696,
-0.022755470126867294,
0.013889004476368427,
-0.007373511791229248,
0.010975562036037445,
0.006932015996426344,
-0.0020778037142008543,
-0.0246723759919405,
0.007873719558119774,
0.011987646110355854,
-0.02407856471836567,
0.01931498385965824,
-0.03356646001338959,
-0.00297677144408226,
0.008590332232415676,
-0.002154914429411292,
0.03571305423974991,
0.033138759434223175,
0.021373331546783447,
-0.03489623963832855,
-0.05074873939156532,
-0.02185015007853508,
0.00021078278950881213,
0.015954069793224335,
0.02255832776427269,
-0.06115990877151489,
0.01959913596510887,
-0.062320273369550705,
-0.014940430410206318,
0.03724948689341545,
0.021168628707528114,
0.0014727977104485035,
-0.0070658656768500805,
-0.04107712581753731,
-0.06924805045127869,
-0.025946052744984627,
-0.0205229502171278,
0.032920241355895996,
-0.06141413748264313,
0.03392038866877556,
0.05904190242290497,
-0.01371859572827816,
-0.012963683344423771,
0.04538816958665848,
-0.05290931835770607,
-0.04233540967106819,
-0.020907368510961533,
0.01113981008529663,
0.026334663853049278,
-0.009425358846783638,
0.041257087141275406,
-0.019582616165280342,
0.019903920590877533,
0.03383852541446686,
-0.057718731462955475,
-0.0317588746547699,
0.0210613664239645,
-0.0012575716245919466,
0.015039151534438133,
0.023530801758170128,
0.0011809365823864937,
0.09965750575065613,
0.015470466576516628,
-0.01659487746655941,
-0.01430988684296608,
-0.008617517538368702,
-0.022131461650133133,
-0.003498629666864872,
-0.007846957072615623,
0.047601368278265,
-0.0071499645709991455,
-0.026828519999980927,
0.01472975593060255,
0.011901536956429482,
0.06932125985622406,
0.0061753252521157265,
0.007769713178277016,
-0.03530365601181984,
0.029438059777021408,
-0.012172273360192776,
0.050435442477464676,
0.008281348273158073,
-0.012919911183416843,
0.03486951068043709,
0.011148899793624878,
0.012775027193129063,
0.007817612029612064,
-0.027000416070222855,
0.012013224884867668,
-0.030460944399237633,
-0.0018684733659029007,
0.0042936475947499275,
0.0015019410056993365,
0.0013288281625136733,
0.00013576690980698913,
0.0004994587507098913,
0.02719961851835251,
0.035580817610025406,
-0.007272525690495968,
-0.0160662978887558,
0.034303732216358185,
-0.024920953437685966,
-0.02108086831867695,
-0.019575288519263268,
-0.006976224947720766,
0.0114644980058074,
0.045053400099277496,
-0.041076645255088806,
-0.029804334044456482,
0.015693210065364838,
0.024764003232121468,
-0.0021821572445333004,
0.003093221690505743,
-0.06494728475809097,
0.01202770508825779,
-0.06406386941671371,
0.017663614824414253,
0.011594675481319427,
0.026053031906485558,
-0.008505936712026596,
0.02365517057478428,
0.009026017971336842,
-0.010795500129461288,
0.03898407518863678,
-0.0032231390941888094,
-0.060392916202545166,
0.029933655634522438,
-0.0228568147867918,
0.003674877807497978,
-0.011935536749660969,
0.04060869663953781,
0.04229805991053581,
-0.026374951004981995,
0.02424498088657856,
0.013631189242005348,
-0.0032535765785723925,
-0.017197594046592712,
0.017287010326981544,
-0.023934170603752136,
-0.025649886578321457,
-0.02008334919810295,
0.03530760481953621,
0.05298830196261406,
-0.052157867699861526,
0.05525275319814682,
0.02646980807185173,
-0.05508201941847801,
0.019070900976657867,
-0.030396083369851112,
-0.023661475628614426,
0.04446987062692642,
0.018084490671753883,
0.03188541904091835,
0.04442662000656128,
-0.003554936032742262,
0.009844701737165451,
-0.015397929586470127,
0.047712281346321106,
0.011369291692972183,
-0.023144973441958427,
-0.036672987043857574,
-0.04955386742949486,
0.0027913625817745924,
-0.0005808232817798853,
0.060645703226327896,
-0.023242754861712456,
0.02823224849998951,
0.05267397686839104,
0.00013231998309493065,
0.00023926699941512197,
0.015513415448367596,
0.05945632606744766,
0.013520460575819016,
0.020289743319153786,
-0.037982068955898285,
-0.00836131814867258,
-0.04537050798535347,
-0.002860870910808444,
0.027106469497084618,
0.0001843435748014599,
-0.04686884582042694,
-0.013300430029630661,
0.046693187206983566,
0.036221589893102646,
0.01750899851322174,
0.04530120640993118,
-0.029009005054831505,
0.05291837826371193,
0.011896739713847637,
0.0010445606894791126,
0.015751386061310768,
0.01419775653630495,
0.026270264759659767,
-0.014551236294209957,
-0.003029844257980585,
-0.02569500170648098,
-0.01531201135367155,
0.036957934498786926,
0.04966399073600769,
-0.03252251073718071,
0.01631997898221016,
-0.06957604736089706,
-0.015140058472752571,
0.053126025944948196,
-0.05900963395833969,
0.03847421333193779,
-0.01057299692183733,
0.011031714268028736,
-0.006501025054603815,
0.0005217065918259323,
-0.05000835284590721,
-0.010523878037929535,
-0.045958563685417175,
0.015436059795320034,
-0.011191386729478836,
-0.005316604394465685,
-0.019609276205301285,
0.007232709787786007,
0.02453157864511013,
0.06383863091468811,
0.031773969531059265,
-0.009903280064463615,
-0.00040040098247118294,
0.007905836217105389,
-0.006667045876383781,
-0.05367700755596161,
-0.01217508316040039,
-0.011536583304405212,
-0.012400761246681213,
0.05766415223479271,
-0.038530267775058746,
-0.03416840359568596,
0.04096832498908043,
0.019333548843860626,
0.00037123390939086676,
-0.008105638436973095,
-0.04138161614537239,
0.02920081652700901,
0.0523747093975544,
0.006842050235718489,
0.015096941962838173,
0.009820415638387203,
0.001570286345668137,
-0.03640132024884224,
-0.025472944602370262,
0.018413715064525604,
0.00940535869449377,
0.011287054978311062,
-0.004849172662943602,
0.0182887464761734,
-0.010730063542723656,
0.05331648141145706,
0.014843053184449673,
0.011569852009415627,
-0.03670349344611168,
-0.04081418737769127,
0.009930441156029701,
0.04466455429792404,
-0.0011779284104704857,
-0.0004221143026370555,
-0.0032547623850405216,
0.022445175796747208,
-0.00254898052662611,
-0.05429646372795105,
0.00796190369874239,
-0.0424649715423584,
0.0041909366846084595,
0.020292043685913086,
-0.013932136818766594,
-0.008087712340056896,
-0.031567759811878204,
-0.013584155589342117,
-0.038421500474214554,
-0.06399509310722351,
0.03791654855012894,
-0.026451321318745613,
0.0033676428720355034,
0.03501639887690544,
-0.04641566425561905,
-0.05209614336490631,
0.02050303854048252,
-0.0024674073792994022,
0.023679140955209732,
-0.08705765008926392,
0.0231029000133276,
0.01518563274294138,
0.044920023530721664,
-0.03569852188229561,
-0.06063474714756012,
0.011982585303485394,
0.027101663872599602,
-0.04514765739440918,
-0.03793220967054367,
-0.02680227719247341,
-0.016490263864398003,
-0.034649938344955444,
-0.026625866070389748,
0.037871796637773514,
-0.02265257202088833,
-0.03262675181031227,
0.03012528084218502,
0.02460446022450924,
0.053762152791023254,
-0.0025978542398661375,
0.032885272055864334,
0.0019430378451943398,
0.018733453005552292,
-0.010888141579926014,
-0.002259226981550455,
0.07590164989233017,
-0.01924877241253853,
-0.061943091452121735,
0.0036137516144663095,
0.049199268221855164,
0.03416421636939049,
-0.006371698342263699,
-0.01304942462593317,
-0.004553256090730429,
0.013323466293513775,
-0.05195637419819832,
-0.014899752102792263,
-0.010340035893023014,
-0.0027403770945966244,
-0.018841484561562538,
0.006118012126535177,
0.006521190516650677,
0.0004413521382957697,
-0.003194687655195594,
0.03966884687542915,
-0.002484224969521165,
-0.0036919463891535997,
0.01159020233899355,
0.062151506543159485,
-0.009584319777786732,
0.019989460706710815,
0.01278825756162405,
0.0015504219336435199,
0.015458447858691216,
-0.0007266800967045128,
-0.04483633115887642,
0.015179723501205444,
-0.011177381500601768,
-0.031356777995824814,
-0.018817897886037827,
-0.020794682204723358,
0.025671808049082756,
0.054012104868888855,
-0.0079850098118186,
0.05145939812064171,
0.04099459573626518,
0.033748824149370193,
-0.016890205442905426,
0.014600217342376709,
0.0007050646818242967,
-0.015513081103563309,
0.003463129512965679,
0.0525558665394783,
-0.00873496849089861,
0.00371573562733829,
0.01618194207549095,
0.06645460426807404,
0.0015439520357176661,
-0.01941918022930622,
0.010657140053808689,
-0.02679184079170227,
0.021790210157632828,
-0.0074004740454256535,
-0.03185107558965683,
-0.019494323059916496,
-0.0062840222381055355,
0.06954406201839447,
-0.010589027777314186,
-0.05866718664765358,
0.060346461832523346,
0.013872414827346802,
-0.006923681125044823,
-0.030662547796964645,
-0.011152309365570545,
-0.03260715678334236,
-0.006917058955878019,
0.027174850925803185,
-0.013614734634757042,
-0.023021310567855835,
0.05140796676278114,
0.025796007364988327,
-0.01757158152759075,
0.03154276683926582,
-0.05882313475012779,
-0.07105311006307602,
0.0031201692763715982,
-0.05339236930012703,
-0.018122611567378044,
0.006332662887871265,
0.011509478092193604,
-0.03918362408876419,
0.03292619064450264,
-0.011383086442947388,
0.002198269823566079,
-0.00042262679198756814,
0.015432044863700867,
-0.001083148061297834,
0.08495503664016724,
-0.013054832816123962,
-0.03598800301551819,
-0.01077788695693016,
0.01669601909816265,
0.09074185788631439,
0.04844546318054199,
-0.02915833704173565,
-0.04830189049243927,
0.009013742208480835,
-0.019837820902466774,
0.004429219756275415,
-0.05959560349583626,
0.03739376366138458,
0.01239056047052145,
-0.011484667658805847,
0.03927907347679138,
0.02517080493271351,
0.011557115241885185,
-0.0011336872121319175,
0.04192193225026131,
-0.034254174679517746,
-0.026872754096984863,
-0.03819911926984787,
-0.015306372195482254,
0.006691609043627977,
0.02871117554605007,
-0.03019791468977928,
0.03008718229830265,
-0.05572647973895073,
-0.017968377098441124,
-0.025528734549880028,
-0.05854760855436325,
0.025740131735801697,
0.006855362560600042,
-0.03376016020774841,
0.04250999540090561,
-0.0006762290722690523,
-0.009597137570381165,
-0.038745004683732986,
0.024002129212021828,
-0.017222339287400246,
-0.02004745602607727,
0.06794390827417374,
0.02313995361328125,
-0.00007830062531866133,
0.018634559586644173,
0.0361461378633976,
0.012499399483203888,
-0.03194405138492584,
-0.010585459880530834,
-0.047352876514196396,
0.0551658496260643,
-0.028450505807995796,
-0.006307694595307112,
-0.00455832201987505,
0.024220727384090424,
0.006743050646036863,
-0.0717371255159378,
-0.00502914609387517,
0.007650311104953289,
0.004547277931123972,
-0.04460662603378296,
-0.005037554539740086,
-0.061336636543273926,
-0.004583410453051329,
0.02584903873503208,
-0.01524096168577671,
0.021823294460773468,
-0.014871165156364441,
0.00513931829482317,
-0.017814289778470993,
0.05391785874962807,
-0.03265068307518959,
-0.020549679175019264,
0.012414813973009586,
-0.007470367942005396,
-0.023176908493041992,
0.0033613929990679026,
0.028055420145392418,
0.004253654275089502,
0.001977979438379407,
0.01800321601331234,
-0.0240771621465683,
-0.02710256539285183,
-0.0503099299967289,
0.0007199134561233222,
0.004303396213799715,
-0.008052550256252289,
-0.014294423162937164,
-0.025972217321395874,
0.05111009255051613,
0.022530343383550644,
-0.06079714372754097,
0.009884446859359741,
0.015534937381744385,
0.027873339131474495,
0.0021474275272339582,
-0.015974009409546852,
0.0003456663980614394,
0.026050640270113945,
0.014373010955750942,
0.023657120764255524,
-0.04179251939058304,
0.07317059487104416,
0.011732951737940311,
0.0211821086704731,
0.011096473783254623,
0.018633989617228508,
0.023511769250035286,
-0.02322578802704811,
0.043774183839559555,
-0.0520799420773983,
-0.012725993990898132,
0.04311952367424965,
0.028637532144784927,
-0.059106193482875824,
0.002244026865810156,
-0.025830505415797234,
-0.0002708773245103657,
0.026261458173394203,
-0.006110235117375851,
-0.021986734122037888,
0.022691311314702034,
-0.0501617006957531,
0.013194955885410309,
-0.03881911560893059,
0.023505525663495064,
-0.04606517776846886,
0.01477025542408228,
0.010700621642172337,
-0.01207036804407835,
-0.030616402626037598,
-0.0008342951186932623,
-0.010691224597394466,
-0.01907327212393284,
0.012125121429562569,
0.002512414241209626,
0.007381956558674574,
-0.008618690073490143,
-0.005736995488405228,
0.03270067274570465,
0.040705423802137375,
-0.05322779715061188,
0.0033485109452158213,
0.0432058610022068,
-0.008076292462646961,
-0.019379746168851852,
0.018175296485424042,
-0.016941795125603676,
0.026094721630215645,
0.005029112100601196,
-0.0405338853597641,
0.01977696269750595,
0.05039815977215767,
-0.013638048432767391,
0.020649636164307594,
-0.012837163172662258,
-0.010319280438125134,
-0.01820574328303337,
-0.012990267015993595,
-0.009322562254965305,
-0.022024791687726974,
-0.015527254901826382,
0.05140407010912895,
0.042698752135038376,
-0.01695435494184494,
0.01933715119957924,
0.009095333516597748,
0.04829160496592522,
0.027959583327174187,
0.05059843510389328,
-0.002966643776744604,
0.04367376118898392,
0.030872849747538567,
-0.043234676122665405,
-0.0005782219814136624,
0.00021417494281195104,
0.011905120685696602,
-0.08436430245637894,
0.01849585957825184,
0.012831462547183037,
0.0024271737784147263,
0.03266702592372894,
-0.04983365908265114,
-0.013676612637937069,
0.04199617728590965,
-0.020886976271867752,
0.0010950117139145732,
-0.06801416724920273,
-0.038868267089128494,
-0.012811870314180851,
-0.03431981801986694,
0.007507889065891504,
0.04851452261209488,
0.02714035101234913,
0.024733765050768852,
0.017389435321092606,
0.008514603599905968,
-0.0357939712703228,
-0.0662963017821312,
0.017113078385591507,
0.01695442572236061,
-0.0012663695961236954,
-0.052375905215740204,
0.05759302154183388,
-0.06014364957809448,
-0.02884252369403839,
0.008864086121320724,
-0.003534178715199232,
0.005594109650701284,
-0.022066079080104828,
-0.011353708803653717,
-0.019442683085799217,
0.03579474240541458,
-0.007430653553456068,
-0.027246776968240738,
-0.022446846589446068,
-0.003085897769778967,
0.003648729296401143,
0.026177844032645226,
0.0037942607887089252,
-0.004794517066329718,
0.012265012599527836,
0.0014318493194878101,
-0.053902290761470795,
0.027030285447835922,
0.002178428927436471,
-0.005948722828179598,
0.008415188640356064,
0.012557017616927624,
0.01705065742135048,
-0.06017151102423668,
0.00987447239458561,
-0.017430473119020462,
0.03133650869131088,
-0.0031241937540471554,
-0.03345455229282379,
-0.028271742165088654,
-0.03695079684257507,
0.003201049752533436,
-0.00921004731208086,
0.015594747848808765,
0.01588275656104088,
-0.0034120548516511917,
-0.051724713295698166,
0.014766240492463112,
0.020129818469285965,
-0.0078069004230201244,
-0.013556760735809803,
-0.0486026406288147,
-0.021964607760310173,
0.02391202002763748,
-0.0029593741055577993,
0.011056321673095226,
-0.006363230757415295,
-0.005226215347647667,
-0.05681803449988365,
-0.06215466931462288,
0.02911629155278206,
0.02995160035789013,
-0.06311755627393723,
-0.009413912892341614,
-0.004292574245482683,
-0.032649289816617966,
-0.00698715029284358,
0.05868721753358841,
-0.007491911295801401,
-0.027178345248103142,
0.016377286985516548,
-0.021204452961683273,
-0.001365692587569356,
-0.07002167403697968,
-0.008679337799549103,
0.01463081780821085,
-0.03764879330992699,
0.012864734046161175,
-0.01505601778626442,
-0.0198077242821455,
0.02031845413148403,
0.018279949203133583,
0.01751435361802578,
0.06364985555410385,
-0.009623054414987564,
-0.01413772813975811,
-0.014255453832447529,
0.016502834856510162,
0.013784351758658886,
0.07892144471406937,
0.03399469330906868,
0.01827293448150158,
0.04351896047592163,
-0.0363217256963253,
-0.0311648678034544,
0.009825264103710651,
-0.037207119166851044,
-0.05417744070291519,
-0.0332769937813282,
-0.015643563121557236,
0.019418073818087578,
-0.09747985005378723,
-0.004737138282507658,
0.014754144474864006,
-0.037799593061208725,
-0.02213933877646923,
0.005738637410104275,
0.04340071603655815,
0.05054875835776329,
-0.0398455485701561,
0.016864178702235222,
0.010922008194029331,
-0.04015495628118515,
0.023966863751411438,
0.016323039308190346,
0.015201576985418797,
0.031259581446647644,
0.013290232978761196,
-0.007625493686646223,
-0.013228722847998142,
0.05212006717920303,
-0.04839131608605385,
0.0372777096927166,
0.013761336915194988,
-0.0366012379527092,
-0.025086572393774986,
-0.038663238286972046,
0.001002950593829155,
0.02873232029378414,
-0.029687996953725815,
0.04384449124336243,
-0.008057503961026669,
-0.026959113776683807,
0.024618467316031456,
-0.023700878024101257,
-0.04918918013572693,
0.025652242824435234,
-0.007678483612835407,
0.007092982064932585,
0.003708927659317851,
-0.01136451680213213,
-0.0008094121003523469,
-0.024650894105434418,
0.025558630004525185,
-0.03953235223889351,
0.011501409113407135,
0.012131608091294765,
0.01885462924838066,
-0.01158969011157751,
-0.02771993726491928,
0.0032623775769025087,
-0.021767131984233856,
0.005926551762968302,
0.06827858090400696,
0.028611797839403152,
-0.05196177586913109,
0.007272632792592049,
0.016642728820443153,
0.03803978115320206,
-0.08528972417116165,
-0.006770968437194824,
-0.009511775337159634,
0.006070264615118504,
-0.00048752143629826605,
-0.005278802942484617
] |
<p>When you boil a liquid the KE stays the same (as temp is the same), so where does the extra energy go? I know the extra energy put in breaks bonds between the molecules/ atoms, but once it has broken the bonds where does the energy go?</p>
<p>And where does the potential energy in a liquid go- as (ideal) gases don't have PE? I've heard it's turned to latent heat, but what is this, how is it stored?</p>
| 9,604 |
[
-0.023402506485581398,
-0.002828877652063966,
-0.016945376992225647,
-0.026194026693701744,
0.010638058185577393,
-0.006251888815313578,
-0.03647112846374512,
-0.03196350857615471,
-0.0018180070910602808,
-0.04261307418346405,
0.02634303830564022,
0.03698372468352318,
0.01862615905702114,
-0.011054763570427895,
0.01984086073935032,
0.019300132989883423,
0.0011811144649982452,
-0.04277460649609566,
-0.007816088385879993,
-0.00910238828510046,
-0.029359139502048492,
0.00846887193620205,
-0.0235137939453125,
0.010293507017195225,
-0.04397711902856827,
0.05033987760543823,
0.00492185028269887,
-0.006620573811233044,
0.0657721757888794,
0.04138260334730148,
0.02577308565378189,
-0.0710269883275032,
0.017181234434247017,
-0.003144302871078253,
0.009491235949099064,
0.0022923042997717857,
-0.022157596424221992,
-0.03927626088261604,
-0.04796415939927101,
0.004307596478611231,
-0.059346187859773636,
-0.017257971689105034,
0.00103632768150419,
0.01656496152281761,
-0.014007537625730038,
-0.011968178674578667,
-0.00223433505743742,
-0.02590314671397209,
0.016564413905143738,
-0.06095070764422417,
0.014057282358407974,
-0.0030197063460946083,
0.02824481762945652,
0.04005975276231766,
-0.00316513329744339,
0.04781591147184372,
0.08545438200235367,
0.04141201823949814,
-0.016436589881777763,
-0.07670202106237411,
0.0126376086845994,
0.006199072580784559,
0.015348488464951515,
-0.006428735330700874,
-0.03871891275048256,
-0.004966916050761938,
0.0011960084084421396,
-0.03996724262833595,
0.023507151752710342,
0.00211805640719831,
0.012300893664360046,
0.014245033264160156,
0.035759951919317245,
-0.01144294161349535,
0.013860947452485561,
-0.033281587064266205,
0.007553720846772194,
0.021268697455525398,
0.04840673506259918,
0.0663081631064415,
0.014833252876996994,
0.015298910439014435,
0.04849331080913544,
0.05806989222764969,
-0.013269774615764618,
0.006590662058442831,
0.0750584825873375,
-0.0036838569212704897,
0.04470205307006836,
0.05130897834897041,
0.00555069325491786,
0.01770053431391716,
-0.018651561811566353,
0.0024857213720679283,
0.012353613041341305,
-0.01919357292354107,
-0.005305049940943718,
0.062494855374097824,
0.014078475534915924,
0.00037440084270201623,
0.035343531519174576,
0.002818076405674219,
0.012542711570858955,
0.07460502535104752,
0.005513712298125029,
-0.07303551584482193,
-0.03980690613389015,
0.002320704283192754,
0.03125101700425148,
-0.016112156212329865,
-0.0037850539665669203,
0.008938542567193508,
-0.003037690883502364,
-0.0335179939866066,
-0.011342430487275124,
-0.038227785378694534,
0.022165635600686073,
-0.03267502412199974,
0.014620702713727951,
0.03106437809765339,
0.026991501450538635,
-0.050461605191230774,
0.01189100369811058,
0.020076856017112732,
-0.0526290163397789,
0.030032921582460403,
0.01839381828904152,
-0.040922872722148895,
-0.05698573961853981,
0.017710138112306595,
-0.04372473061084747,
-0.008147447369992733,
-0.0029259035363793373,
-0.01184994075447321,
0.0345752127468586,
-0.005336730740964413,
-0.08720780164003372,
-0.017990201711654663,
0.04729525372385979,
-0.030205845832824707,
-0.04138276353478432,
-0.0839143693447113,
0.005631122272461653,
0.0015448222402483225,
0.04546374827623367,
-0.020983479917049408,
-0.04012296721339226,
-0.03818782791495323,
-0.015285247936844826,
0.009751484729349613,
-0.021867476403713226,
-0.03477213531732559,
-0.0038152115885168314,
-0.04337453097105026,
0.022578923031687737,
-0.0306183360517025,
-0.003645147429779172,
0.06562946736812592,
-0.004963276442140341,
0.00748525932431221,
0.05224235728383064,
-0.018743690103292465,
-0.012845701538026333,
0.00593054573982954,
-0.0007635987130925059,
-0.0504726767539978,
0.07752250880002975,
0.012531667947769165,
0.02224188670516014,
-0.005589496809989214,
0.0062545957043766975,
-0.008330551907420158,
-0.020782627165317535,
0.0333712063729763,
0.05675416812300682,
0.01745414175093174,
-0.009408733807504177,
-0.022901127114892006,
0.07930407673120499,
0.018861055374145508,
-0.07018975913524628,
0.0005255696596577764,
0.04216654971241951,
-0.03776882216334343,
0.005503491032868624,
0.042658377438783646,
-0.009147700853645802,
0.004276425112038851,
-0.0365607813000679,
-0.04480338096618652,
-0.012946043163537979,
-0.07865700870752335,
0.044829968363046646,
-0.006377376150339842,
0.008163667283952236,
0.025304770097136497,
0.04201324284076691,
0.05068885535001755,
-0.06291807442903519,
-0.045840468257665634,
-0.002675543073564768,
0.026561155915260315,
0.004287869669497013,
-0.021139156073331833,
0.033451687544584274,
0.04487365484237671,
0.024557234719395638,
0.0025118894409388304,
-0.019526800140738487,
-0.004498240537941456,
0.002597808837890625,
-0.013065000995993614,
-0.03663913533091545,
0.011917469091713428,
-0.014210927300155163,
-0.03766248747706413,
-0.004281328059732914,
0.008083292283117771,
0.0068405563943088055,
0.01910393126308918,
-0.02545144222676754,
0.03868351876735687,
0.016852937638759613,
0.0061534978449344635,
-0.018944747745990753,
0.033318281173706055,
-0.016462257131934166,
0.013952089473605156,
-0.0182467233389616,
-0.034763649106025696,
-0.02717743255198002,
-0.0030129614751785994,
0.040503617376089096,
0.03230612352490425,
-0.035506781190633774,
0.010048729367554188,
0.0060810670256614685,
0.012806401588022709,
0.030206095427274704,
-0.0038404965307563543,
-0.017569178715348244,
-0.01775312051177025,
0.02787899225950241,
-0.004765302874147892,
0.00016970091382972896,
0.022994425147771835,
0.04214520752429962,
0.04699292778968811,
0.03445252403616905,
-0.007524996995925903,
0.006341785192489624,
0.04026961699128151,
0.015175933949649334,
0.028626175597310066,
-0.023181432858109474,
-0.030389171093702316,
0.027843762189149857,
-0.0219136793166399,
0.021834205836057663,
-0.03391506150364876,
0.017725132405757904,
0.0051412321627140045,
-0.05651788040995598,
-0.04732048884034157,
-0.02497021295130253,
0.014928008429706097,
-0.004102060105651617,
-0.020353466272354126,
0.006452107336372137,
-0.009366260841488838,
0.037907205522060394,
-0.014601453207433224,
0.032725125551223755,
-0.015242621302604675,
0.021250681951642036,
0.005244687665253878,
-0.023837706074118614,
0.024608327075839043,
-0.04301576688885689,
-0.048946768045425415,
-0.025705775246024132,
-0.05079532042145729,
-0.030793089419603348,
-0.014678562059998512,
-0.04273543879389763,
0.013369673863053322,
0.010748020373284817,
-0.010433411225676537,
0.035828959196805954,
0.0034729696344584227,
0.011650987900793552,
0.013472729362547398,
-0.02655130997300148,
-0.024573760107159615,
0.014559829607605934,
-0.016955992206931114,
-0.021211007609963417,
-0.022135581821203232,
0.00013774455874226987,
0.06396973133087158,
-0.02102668583393097,
-0.04092935845255852,
0.02330491878092289,
-0.06342891603708267,
-0.05322300270199776,
-0.006378902588039637,
-0.016824111342430115,
0.01926225796341896,
-0.025076985359191895,
0.03714427724480629,
0.04050176963210106,
-0.09090158343315125,
-0.011269227601587772,
-0.036693770438432693,
-0.03444812446832657,
0.017098119482398033,
-0.0163608156144619,
0.02286870777606964,
-0.004703828599303961,
-0.02488255873322487,
0.052754856646060944,
-0.01892188750207424,
-0.05240752547979355,
-0.006961787585169077,
-0.007252244278788567,
0.012193022295832634,
-0.06555892527103424,
0.026122482493519783,
0.019927121698856354,
-0.015008937567472458,
0.012349878437817097,
0.008089552633464336,
0.07427114248275757,
0.022468291223049164,
0.0006864031311124563,
0.004208170808851719,
-0.012067136354744434,
0.012433474883437157,
0.007041786797344685,
0.025799887254834175,
-0.009726463817059994,
-0.028355028480291367,
0.028241198509931564,
0.01820169761776924,
0.04027876630425453,
0.04421449080109596,
-0.03974658623337746,
0.08723389357328415,
-0.01776602864265442,
-0.012362422421574593,
-0.07835329324007034,
0.03808421269059181,
-0.023927364498376846,
0.000818423752207309,
0.04290767014026642,
0.043620526790618896,
0.041964370757341385,
-0.0007467434625141323,
0.02237413078546524,
0.013693578541278839,
0.03374871239066124,
0.0008153003291226923,
-0.03812310844659805,
0.012880854308605194,
-0.011024071834981441,
0.01475298497825861,
0.01676364056766033,
-0.012721516191959381,
0.05172004923224449,
0.00021179611212573946,
0.0035834824666380882,
0.008739518001675606,
-0.04133614897727966,
-0.022338077425956726,
-0.06293335556983948,
-0.029492508620023727,
0.015069957822561264,
0.04336824640631676,
-0.02233022078871727,
0.06633774936199188,
0.012083128094673157,
0.0351465605199337,
0.014690248295664787,
0.027574703097343445,
-0.0992906391620636,
0.01868540234863758,
-0.021544888615608215,
-0.021322030574083328,
-0.019465172663331032,
0.013733511790633202,
0.012711790390312672,
-0.044981151819229126,
-0.01688571646809578,
0.030429372563958168,
-0.015616821125149727,
-0.04164019972085953,
0.031081926077604294,
-0.02278033085167408,
-0.006929685827344656,
-0.03660803660750389,
0.0045769596472382545,
0.05244169011712074,
-0.03108842484652996,
0.013390530832111835,
0.04189853370189667,
-0.0035222130827605724,
0.008663210086524487,
0.009954116307199001,
-0.017075737938284874,
0.024735229089856148,
0.027399428188800812,
0.03961101919412613,
-0.013317127712070942,
0.018107764422893524,
0.01596185564994812,
0.023251071572303772,
0.01851852796971798,
0.012674099765717983,
-0.004947612527757883,
-0.013659399002790451,
-0.03165365755558014,
-0.013185995630919933,
-0.01013933215290308,
0.030516106635332108,
0.0034609425347298384,
0.048206329345703125,
-0.0455937422811985,
0.0015324038686230779,
-0.030625637620687485,
0.05180942267179489,
0.07615460455417633,
0.012587684206664562,
-0.040092624723911285,
-0.033336542546749115,
-0.010862473398447037,
-0.043487682938575745,
0.0049745929427444935,
0.002528207842260599,
-0.014556275680661201,
-0.01174409594386816,
-0.00611939886584878,
0.012481714598834515,
-0.029165586456656456,
0.019722698256373405,
-0.0346703939139843,
0.0363614559173584,
0.018332624807953835,
-0.02943526767194271,
-0.01972893998026848,
0.02266533486545086,
0.03182612359523773,
0.00465010479092598,
-0.0074455467984080315,
0.02113434486091137,
-0.07664091140031815,
-0.004014391452074051,
0.035781241953372955,
0.03280619904398918,
-0.02419448457658291,
-0.006961855571717024,
-0.03947960585355759,
-0.030737923458218575,
0.004683224018663168,
-0.034389570355415344,
0.017399229109287262,
-0.02927079051733017,
0.027554480358958244,
-0.010479350574314594,
-0.03410887345671654,
0.031058741733431816,
0.011626489460468292,
0.003690802026540041,
0.04714997112751007,
-0.021379243582487106,
0.0030694901943206787,
-0.021845540031790733,
0.02876303531229496,
-0.0035837865434587,
0.03820520639419556,
0.005037152208387852,
-0.012070232070982456,
0.010439404286444187,
0.020389428362250328,
-0.007559749763458967,
-0.07726826518774033,
-0.01701359823346138,
-0.004791452083736658,
0.0012586632510647178,
0.015312815085053444,
-0.04756409674882889,
-0.08022986352443695,
0.018509887158870697,
0.020831936970353127,
-0.027149653062224388,
-0.016298523172736168,
-0.024477072060108185,
0.04516381397843361,
0.03012423776090145,
-0.007205504924058914,
0.06201262027025223,
0.04007957875728607,
-0.046761851757764816,
0.014423181302845478,
-0.05010610073804855,
0.025110261514782906,
-0.06753148883581161,
-0.0014215445844456553,
-0.020436005666851997,
0.028803281486034393,
-0.033029332756996155,
0.022402413189411163,
-0.040577687323093414,
0.0307597853243351,
-0.02970411814749241,
-0.043913841247558594,
-0.007859040051698685,
0.02593929134309292,
0.04646627977490425,
0.0024970793165266514,
0.03002971224486828,
0.0155204301699996,
-0.009811121970415115,
-0.027010129764676094,
0.0164034441113472,
0.025649849325418472,
0.002623547799885273,
0.010771513916552067,
-0.02683464251458645,
0.034526363015174866,
0.01763184927403927,
0.0038338089361786842,
0.04369528964161873,
0.009183450601994991,
0.0093675646930933,
-0.00008229537343140692,
0.007092600222676992,
0.012788783758878708,
-0.062411896884441376,
-0.006187095772475004,
-0.009743236005306244,
0.004547548945993185,
-0.006945351604372263,
-0.010687720961868763,
0.06219225376844406,
0.02620646357536316,
0.021037688478827477,
-0.08246876299381256,
-0.02740401029586792,
0.046200573444366455,
0.00036386671126820147,
-0.04380638897418976,
-0.025372883304953575,
-0.02191230095922947,
-0.039465755224227905,
-0.02012590505182743,
0.02028018981218338,
0.016402820125222206,
-0.03168401122093201,
0.008037036284804344,
0.017873413860797882,
0.03111228533089161,
0.050480566918849945,
0.007047866005450487,
-0.00353293027728796,
0.007545863278210163,
-0.01835823245346546,
-0.04474866762757301,
-0.02349286712706089,
0.030587002635002136,
-0.006637066602706909,
0.02751568704843521,
0.006190085783600807,
-0.008609662763774395,
0.06316401809453964,
-0.014921697787940502,
0.018863076344132423,
0.006306781433522701,
0.004159676376730204,
-0.01279109250754118,
-0.030071211978793144,
0.02182452194392681,
0.023494763299822807,
0.0705549567937851,
0.030655311420559883,
-0.011066515929996967,
-0.019116176292300224,
-0.019815707579255104,
-0.012950069271028042,
0.007755067199468613,
0.011649718508124352,
-0.000795762287452817,
0.045160118490457535,
0.03543416038155556,
0.0017154972301796079,
-0.004704223480075598,
-0.028722820803523064,
0.061964262276887894,
0.021921047940850258,
-0.00992597360163927,
0.011200115084648132,
0.023062104359269142,
-0.036131344735622406,
-0.04934443533420563,
-0.049231432378292084,
-0.013018661178648472,
0.05045125260949135,
-0.005025687627494335,
0.03299613669514656,
0.010851186700165272,
-0.008049367927014828,
0.010428880341351032,
-0.021593818441033363,
0.013936430215835571,
0.034606970846652985,
-0.05057074874639511,
0.012521745637059212,
-0.0026415660977363586,
0.01698024943470955,
0.010848764330148697,
0.06491860747337341,
-0.007869258522987366,
0.029409540817141533,
0.03713497892022133,
0.02102748490869999,
-0.0006600528140552342,
-0.018489807844161987,
-0.04927428439259529,
0.02730642817914486,
-0.022904975339770317,
0.045311179012060165,
-0.023491397500038147,
-0.008518402464687824,
0.04861338436603546,
0.01737760193645954,
0.004644647240638733,
-0.06375469267368317,
0.000682540237903595,
-0.04661146178841591,
0.007523260544985533,
-0.017968695610761642,
-0.020132040604948997,
-0.009119920432567596,
0.009898201562464237,
-0.0022532485891133547,
0.009673750959336758,
-0.018942009657621384,
0.017373129725456238,
-0.046713367104530334,
-0.00894841831177473,
0.0025223258417099714,
-0.014088171534240246,
-0.016442183405160904,
-0.005592010449618101,
-0.04294203966856003,
0.018992776051163673,
-0.021479589864611626,
0.024520227685570717,
-0.012911376543343067,
0.024476338177919388,
-0.00890433881431818,
0.06639250367879868,
0.0012233086163178086,
0.007705509662628174,
-0.019377242773771286,
0.03886466845870018,
0.11072281748056412,
0.043063484132289886,
0.0018865366000682116,
-0.05897115543484688,
0.008022038266062737,
-0.0033747912384569645,
0.005951445084065199,
-0.025906790047883987,
-0.014115625061094761,
-0.02439720928668976,
0.053392961621284485,
0.0344354547560215,
0.0879501923918724,
-0.018244678154587746,
0.03812707960605621,
0.01825515739619732,
-0.032219354063272476,
-0.022839698940515518,
0.022521615028381348,
0.009835489094257355,
-0.018991118296980858,
0.03184137120842934,
-0.012698996812105179,
0.001899696420878172,
-0.006008031778037548,
0.011978927068412304,
-0.0426812507212162,
-0.0288937259465456,
0.027895694598555565,
0.005310534965246916,
-0.03612995892763138,
0.0017298279562965035,
-0.05363744869828224,
0.010979076847434044,
-0.012700701132416725,
0.04270054027438164,
0.03825920447707176,
0.0005452975747175515,
0.001984599744901061,
0.006198165938258171,
0.01190148200839758,
0.00341085740365088,
0.0078005981631577015,
0.018203211948275566,
-0.02164725959300995,
-0.0534093976020813,
-0.021440941840410233,
0.054878853261470795,
-0.011597312055528164,
-0.013863489031791687,
-0.005815570242702961,
-0.013913890346884727,
0.025213608518242836,
0.014546147547662258,
-0.048404544591903687,
0.01275449339300394,
0.036130111664533615,
-0.009430807083845139,
-0.03224746882915497,
-0.07345562428236008,
-0.0018565419595688581,
-0.02199544385075569,
0.02881423942744732,
-0.011160142719745636,
0.03165610507130623,
-0.0032924457918852568,
-0.013662219047546387,
0.0008977379184216261,
0.0043870932422578335,
-0.003599652787670493,
-0.014157804660499096,
-0.03857807815074921,
-0.0292467400431633,
-0.029310110956430435,
0.03224027901887894,
0.022773968055844307,
0.030319811776280403,
-0.015512497164309025,
0.009127025492489338,
-0.03467652574181557,
-0.04787749424576759,
0.06421954929828644,
-0.012251896783709526,
-0.019532447680830956,
-0.013063927181065083,
0.03454190865159035,
0.01687883585691452,
0.04787462577223778,
-0.006584295071661472,
-0.008337060920894146,
-0.0056212712079286575,
-0.01844058185815811,
0.05168309435248375,
-0.030037011951208115,
-0.011598795652389526,
0.011757107451558113,
-0.058013610541820526,
0.001138332299888134,
0.009610060602426529,
0.030497197061777115,
0.024139270186424255,
-0.008025058545172215,
0.0319274477660656,
0.0031743005383759737,
-0.015123994089663029,
-0.00043855627882294357,
0.014975286088883877,
-0.02329131029546261,
-0.012807703576982021,
0.0039014474023133516,
0.0006254234467633069,
0.026809055358171463,
-0.03268468379974365,
-0.014532018452882767,
0.016625283285975456,
-0.003394087078049779,
0.039594847708940506,
-0.025747481733560562,
0.033820152282714844,
-0.02140464074909687,
0.06321752071380615,
-0.04514298960566521,
0.008040006272494793,
-0.09005801379680634,
-0.001215409254655242,
0.051056914031505585,
-0.009693298488855362,
-0.005036438349634409,
-0.0011031939648091793,
0.004200863651931286,
0.020749786868691444,
0.026514261960983276,
0.026811668649315834,
0.021770067512989044,
-0.04297564923763275,
0.021969640627503395,
-0.06656178086996078,
0.054749809205532074,
-0.023952573537826538,
-0.04812628775835037,
0.04197501018643379,
-0.023642947897315025,
-0.025998402386903763,
0.009816267527639866,
-0.007008218206465244,
0.009073449298739433,
0.06559702754020691,
0.01486979890614748,
-0.02188216708600521,
0.0656343549489975,
0.012583008967339993,
0.0009410405182279646,
-0.00020301259064581245,
-0.026343761011958122,
0.004970405716449022,
0.03873148933053017,
0.018162978813052177,
-0.041448697447776794,
0.02047930285334587,
0.059780579060316086,
0.037581369280815125,
0.003978417254984379,
-0.002732125110924244,
0.007492091506719589,
0.014582732692360878,
-0.004285430535674095,
0.04096938297152519,
0.011379431001842022,
0.005845756735652685,
0.04590577259659767,
-0.05105668678879738,
0.04468926042318344,
0.04784834384918213,
-0.0061506484635174274,
-0.09133801609277725,
0.016013253480196,
-0.04370712861418724,
-0.024816883727908134,
0.013791889883577824,
-0.01482448074966669,
0.00393717223778367,
0.04568614810705185,
-0.09863857179880142,
0.001565121696330607,
-0.03807695582509041,
0.024226650595664978,
-0.010673806071281433,
0.010086697526276112,
-0.042048946022987366,
0.07093434780836105,
0.018459847196936607,
0.036756228655576706,
0.0106001365929842,
-0.021074414253234863,
0.04620218649506569,
0.0008449232554994524,
-0.02794007398188114,
0.02648172341287136,
0.003039791015908122,
-0.008455295115709305,
0.06260526925325394,
-0.03895385563373566,
-0.013959475792944431,
0.011312054470181465,
-0.04228091612458229,
0.009467990137636662,
0.004757131915539503,
-0.019262436777353287,
-0.026272788643836975,
0.02737985923886299,
-0.026936717331409454,
-0.02403641678392887,
0.00725700194016099,
0.02820405177772045,
0.03844431787729263,
0.01656177267432213,
0.007477795239537954,
0.01144812349230051,
0.014881585724651814,
-0.038418248295784,
-0.039694976061582565,
0.034817926585674286,
-0.028119448572397232,
-0.007243442814797163,
0.018034011125564575,
0.01889907754957676,
0.032719552516937256,
-0.010203234851360321,
-0.03001306764781475,
-0.04157494008541107,
-0.0016511662397533655,
0.04230986163020134,
0.027236443012952805,
0.031043870374560356,
0.0346154049038887,
0.019336048513650894,
0.002694798167794943,
0.0024441033601760864,
-0.002106824889779091,
-0.035832054913043976,
-0.03942717984318733,
-0.023896856233477592,
0.010412377305328846,
-0.037136029452085495,
-0.03763124719262123,
-0.022114552557468414,
-0.020985934883356094,
0.04303276166319847,
0.02664574421942234,
0.03757213428616524,
-0.008196109905838966,
-0.056918416172266006,
-0.02745886519551277,
-0.0382566936314106,
0.016823461279273033,
-0.030130358412861824,
0.0032953692134469748,
-0.05083199590444565,
-0.021418379619717598,
0.04939928278326988,
0.015298977494239807,
0.03835124149918556,
0.009436451829969883,
-0.0025427963119000196,
-0.04308425262570381,
-0.012066405266523361,
0.037088826298713684,
-0.049006614834070206,
0.0032735930290073156,
-0.004290743265300989,
-0.02059117518365383,
0.014597469940781593,
-0.015204694122076035,
-0.029141929000616074,
0.040764473378658295,
0.06470531225204468,
-0.05239931866526604,
-0.002633010735735297,
-0.032707035541534424,
0.01956610009074211,
0.04353509470820427,
0.04758273437619209,
-0.03625347092747688,
0.08174804598093033,
-0.023825837299227715,
-0.004336790647357702,
0.01958164945244789,
-0.0008365465910173953,
-0.02438969723880291,
0.05639757961034775,
-0.04269442707300186,
0.037464797496795654,
0.00231541832908988,
-0.029324501752853394,
0.018846025690436363,
-0.03685040399432182,
0.01883039064705372,
0.03231289982795715,
-0.040002159774303436,
-0.0031040962785482407,
0.053576357662677765,
0.013447982259094715,
0.014202248305082321,
0.008653486147522926,
0.00047972772154025733,
-0.01391360443085432,
0.033457957208156586,
0.01892840676009655,
0.06790538132190704,
0.04847656190395355,
0.0007306250045076013,
-0.010887849144637585,
-0.03388197347521782,
-0.017725111916661263,
0.026716753840446472,
0.004641360603272915,
0.014041466638445854,
-0.04710709676146507,
-0.04480750486254692,
0.017319010570645332,
-0.008125756867229939,
0.03314585238695145,
-0.012778202071785927,
-0.008099844679236412,
0.06960080564022064,
-0.0196994598954916,
-0.01032610610127449,
0.0017882423708215356,
0.005002043209969997,
-0.010741285979747772,
-0.002517903922125697,
-0.005617754999548197,
0.06529564410448074,
0.013056755065917969,
0.004103921353816986,
-0.028356824070215225,
0.035164181143045425,
0.020227737724781036,
-0.024971935898065567,
0.017757758498191833,
-0.004193386062979698,
-0.018351929262280464,
-0.048417236655950546,
-0.013888171873986721,
-0.03598965331912041,
-0.04003630951046944,
0.017640497535467148,
0.027731234207749367,
0.02108565717935562,
0.047155968844890594,
-0.03741554543375969,
-0.0045413663610816,
0.055512819439172745,
-0.05020696669816971,
0.005831744056195021,
0.010399328544735909,
0.024901317432522774,
0.001675299135968089,
0.010625467635691166
] |
<p>Let's say we have two systems A and B. Each system is described by a density matrix $\rho_A$ and $\rho_B$. I'm wondering about the formal notation to write down the expectation value of an operator that takes us from system A to system B or vice versa.</p>
<p>Normally the expectation value of an operator M acting on a system X is just:</p>
<p>$ <M> = Tr(\rho_X M)$.</p>
<p>But how would I write this for two systems? Would it be a tensor product of the two density matrices: $\rho_A \otimes \rho_B \rightarrow$ $ <M> = Tr(\rho_A \otimes \rho_B M)$ ?</p>
<p>If I would use state vectors I would just write: $<M_{ij}> = <i|M|j>$ and get my expectation value for a specific M or for all M if I do that for all possible states (in this case pure states for simplification).
Any idea how to express this in the density matrix trace formalism? How would it look for pure and mixed states?</p>
| 9,605 |
[
0.00665642973035574,
0.003097018925473094,
-0.0008829843136481941,
-0.02941119484603405,
0.019331274554133415,
0.035654112696647644,
-0.03297388553619385,
0.009594124741852283,
0.04069273918867111,
-0.008729412220418453,
0.036464374512434006,
0.028141986578702927,
0.07730764895677567,
-0.031875498592853546,
0.02427177131175995,
0.01734449528157711,
-0.01703283004462719,
-0.033559441566467285,
-0.041604623198509216,
-0.020275836810469627,
0.034068480134010315,
0.018574731424450874,
0.03677168861031532,
-0.011864127591252327,
0.03178645670413971,
0.04056364297866821,
0.00781896524131298,
-0.015569777227938175,
0.03791700676083565,
0.04576248303055763,
-0.005980638321489096,
-0.05830610543489456,
0.019732043147087097,
0.008668429218232632,
0.006349183619022369,
-0.013928107917308807,
-0.03246493265032768,
-0.009276682510972023,
0.017199162393808365,
-0.0014006965793669224,
-0.07995551079511642,
0.01170669961720705,
-0.027036257088184357,
0.023087309673428535,
-0.013243387453258038,
0.026817796751856804,
0.001874788897112012,
0.006650582887232304,
0.0038474290631711483,
-0.06665141880512238,
0.07250726968050003,
0.011401579715311527,
0.04606166481971741,
0.014384441077709198,
-0.01632164791226387,
0.02933790534734726,
0.0727650374174118,
0.06011301279067993,
0.04901616647839546,
-0.061504095792770386,
-0.008564881980419159,
-0.03244614228606224,
0.01684061624109745,
-0.04187445342540741,
-0.020580925047397614,
-0.005179739091545343,
0.024005016312003136,
0.0015693684108555317,
0.02523322030901909,
-0.015997745096683502,
0.005198899190872908,
0.019522640854120255,
0.040793899446725845,
-0.042429860681295395,
0.02956000342965126,
-0.04103025421500206,
0.05213258042931557,
0.013022213242948055,
0.049626585096120834,
0.009284043684601784,
-0.006442666053771973,
0.02009286731481552,
-0.0004572142497636378,
0.02067672461271286,
-0.016350630670785904,
-0.012140647508203983,
0.08139197528362274,
-0.002398484153673053,
0.022546138614416122,
0.020144984126091003,
0.0014802856603637338,
0.01511488575488329,
0.03539859130978584,
0.022713953629136086,
-0.07361701875925064,
0.019916262477636337,
-0.003586011938750744,
0.038666967302560806,
0.0035713016986846924,
-0.03815972059965134,
-0.021192682906985283,
-0.02213129587471485,
0.011829037219285965,
0.053827278316020966,
0.004699817392975092,
0.03625989705324173,
-0.047627806663513184,
-0.015415921807289124,
-0.02076607011258602,
-0.00026017194613814354,
-0.02042541280388832,
0.048486024141311646,
-0.0016912610735744238,
0.03668014332652092,
-0.028232969343662262,
-0.048776596784591675,
0.00832154881209135,
-0.0158754363656044,
0.062307193875312805,
0.06910006701946259,
0.03513960912823677,
-0.03329520300030708,
0.027493128553032875,
-0.01985001564025879,
-0.06814590841531754,
0.02263343520462513,
0.022253094241023064,
0.000918966718018055,
-0.06471772491931915,
-0.0023037546779960394,
-0.011912242509424686,
-0.018518555909395218,
0.00791324581950903,
0.007619781419634819,
0.015531022101640701,
-0.07674587517976761,
-0.10210656374692917,
-0.06660408526659012,
-0.01766234263777733,
-0.012589866295456886,
-0.0038360205944627523,
-0.06894859671592712,
-0.001068189973011613,
0.05692126229405403,
0.058152224868535995,
0.009411364793777466,
0.020469853654503822,
0.015775393694639206,
0.0360097698867321,
-0.0006734101916663349,
-0.029958223924040794,
-0.04117630049586296,
-0.014116328209638596,
-0.017367897555232048,
0.009105682373046875,
-0.04675286263227463,
0.020100457593798637,
0.04648637771606445,
-0.01719878986477852,
0.03200206533074379,
0.07146427780389786,
0.0017197695560753345,
-0.011612964794039726,
0.024513689801096916,
0.023659035563468933,
-0.02383296936750412,
0.07440962642431259,
-0.003606293583288789,
0.06363969296216965,
0.04518476128578186,
0.002856292761862278,
-0.0005496660596691072,
0.010506548918783665,
0.04863932728767395,
0.03801700472831726,
-0.028987271711230278,
-0.013402934186160564,
-0.01294589601457119,
0.01669851318001747,
-0.009775773622095585,
-0.057247988879680634,
-0.02018227055668831,
-0.011759385466575623,
0.009151773527264595,
-0.0009403856238350272,
-0.004144749138504267,
-0.005208437796682119,
-0.01775241829454899,
-0.02223360911011696,
-0.044060442596673965,
0.001460492261685431,
-0.06673845648765564,
0.010790039785206318,
-0.010443096980452538,
-0.026983076706528664,
0.06505317240953445,
0.0035821578931063414,
0.03065894916653633,
-0.010824586264789104,
-0.0540178082883358,
-0.028429703786969185,
0.017488423734903336,
-0.014864805154502392,
-0.04063411429524422,
0.02983936294913292,
0.0490470714867115,
0.058439161628484726,
0.021765045821666718,
0.03972143307328224,
-0.017414670437574387,
-0.03210272639989853,
-0.012933269143104553,
0.014880454167723656,
0.016616661101579666,
0.050188422203063965,
0.0049989474937319756,
-0.046008456498384476,
-0.01991431415081024,
-0.021148206666111946,
-0.01736932434141636,
-0.06413256376981735,
0.038914382457733154,
0.061216652393341064,
0.023680811747908592,
-0.016282696276903152,
0.019220417365431786,
0.019578171893954277,
-0.002651943126693368,
-0.018626458942890167,
-0.05721857398748398,
-0.01241583377122879,
0.020781435072422028,
0.017963435500860214,
0.023212619125843048,
-0.04111247882246971,
0.025676438584923744,
0.0346316397190094,
0.002381988102570176,
0.027146730571985245,
0.030575726181268692,
-0.03858082741498947,
-0.00019386084750294685,
0.023245422169566154,
0.042788244783878326,
-0.010732193477451801,
0.04344489425420761,
0.022155961021780968,
-0.023635827004909515,
0.041564829647541046,
0.004277107771486044,
-0.011609370820224285,
0.04717152938246727,
-0.023742111399769783,
0.007996109314262867,
-0.0020691687241196632,
-0.03129790723323822,
0.03808223828673363,
-0.014137514866888523,
0.03819756209850311,
0.02131498232483864,
-0.025397352874279022,
0.0010553855681791902,
0.006419201847165823,
-0.032314740121364594,
-0.0073043713346123695,
-0.004421979654580355,
-0.02660331502556801,
-0.00303159118629992,
0.007717679720371962,
-0.022981351241469383,
0.03950287029147148,
-0.030916322022676468,
0.004770719911903143,
-0.0016198207158595324,
-0.006836529355496168,
0.03603270649909973,
-0.003051159670576453,
0.004922846332192421,
-0.045887239277362823,
-0.029127731919288635,
-0.019362032413482666,
-0.02451428957283497,
0.03585028275847435,
0.009722215123474598,
-0.06897975504398346,
0.01963989995419979,
-0.06950852274894714,
-0.0601813904941082,
0.02543030120432377,
-0.019429169595241547,
-0.02693452499806881,
0.014794513583183289,
-0.029729684814810753,
-0.060796819627285004,
-0.06595310568809509,
0.03218762204051018,
0.004923166241496801,
-0.0032910718582570553,
0.02227836474776268,
0.043218061327934265,
-0.04368533939123154,
-0.031895093619823456,
-0.005533894989639521,
-0.017290839925408363,
-0.05918819457292557,
0.018412861973047256,
-0.036243993788957596,
0.016245290637016296,
-0.01932471990585327,
0.05266670137643814,
0.04381541907787323,
-0.043429967015981674,
-0.02304733358323574,
-0.05559656769037247,
-0.03802868723869324,
0.04678288474678993,
0.017652424052357674,
0.024700136855244637,
0.040410906076431274,
-0.051317013800144196,
0.08555743843317032,
0.0075344606302678585,
-0.007995696738362312,
-0.017380226403474808,
0.008382908068597317,
-0.011739256791770458,
-0.01554346177726984,
0.015034924261271954,
0.02096407674252987,
-0.01757846586406231,
0.038830965757369995,
0.023244159296154976,
0.011843496933579445,
0.03284651041030884,
0.008579100482165813,
-0.0003988457901868969,
0.020777205005288124,
0.032945990562438965,
-0.02563690021634102,
0.04835205525159836,
-0.006048203445971012,
0.010215317830443382,
0.0009973124833777547,
-0.008851036429405212,
0.030984878540039062,
-0.029359789565205574,
-0.044506367295980453,
0.025704016909003258,
-0.011005471460521221,
-0.002573604229837656,
-0.034971874207258224,
0.034279778599739075,
-0.005745586473494768,
-0.006770696025341749,
0.005924998316913843,
0.039660435169935226,
-0.020850811153650284,
-0.03225472941994667,
0.008679392747581005,
0.04875168949365616,
0.015302510000765324,
-0.02628423646092415,
-0.00025120077771134675,
0.01373601146042347,
0.0053453897126019,
0.018811486661434174,
-0.013605206273496151,
-0.0185875054448843,
0.034289129078388214,
0.005357359070330858,
0.0033133833203464746,
-0.0022829214576631784,
-0.02959107980132103,
-0.0077728526666760445,
-0.08382613956928253,
-0.007756798528134823,
0.003393280552700162,
0.0401487872004509,
0.014074232429265976,
0.0614551343023777,
0.006396997254341841,
-0.016163622960448265,
0.02045259065926075,
-0.02531338855624199,
-0.037816837430000305,
0.01771252229809761,
-0.004630859941244125,
-0.004649998154491186,
-0.010038879700005054,
-0.019654851406812668,
0.028005432337522507,
-0.029814764857292175,
-0.05007444694638252,
-0.019122524186968803,
-0.007631542626768351,
-0.05572564899921417,
0.006880892440676689,
-0.018177276477217674,
-0.06970968097448349,
-0.008788912557065487,
0.02977883070707321,
0.014318712055683136,
0.008479597046971321,
0.018544070422649384,
0.025547238066792488,
-0.04322608932852745,
-0.005674242973327637,
-0.007248511537909508,
-0.006310977041721344,
-0.005277459509670734,
-0.006134463474154472,
0.05441804602742195,
0.03786887601017952,
-0.02192043513059616,
0.008543528616428375,
-0.021044136956334114,
0.09995805472135544,
-0.010289885103702545,
-0.022517427802085876,
0.030540961772203445,
-0.026294922456145287,
0.0014828976709395647,
-0.003935663495212793,
0.044030554592609406,
-0.012516648508608341,
0.02765384316444397,
0.011585711501538754,
0.022837597876787186,
-0.04709282144904137,
0.025218123570084572,
0.06603223830461502,
0.012181716039776802,
-0.00028978270711377263,
-0.03422780707478523,
0.02419332228600979,
-0.024965697899460793,
0.010324401780962944,
0.012937107123434544,
-0.03351809084415436,
-0.009343436919152737,
-0.006065236404538155,
0.01724042370915413,
0.004186974838376045,
-0.027613220736384392,
0.004464763216674328,
0.022913234308362007,
0.00880550965666771,
0.0019972228910773993,
-0.030664611607789993,
0.019223228096961975,
0.029560422524809837,
0.01753111183643341,
0.004589226562529802,
0.04588089883327484,
-0.05665993690490723,
-0.005814310163259506,
0.038426317274570465,
0.01030480396002531,
0.005422432906925678,
-0.013105454854667187,
-0.022448813542723656,
-0.03403860703110695,
0.023389019072055817,
0.029618442058563232,
0.01831905171275139,
0.0034467566292732954,
-0.047896433621644974,
-0.009943128563463688,
-0.008854491636157036,
-0.019453134387731552,
0.036601368337869644,
0.02471933513879776,
0.0025749225169420242,
-0.0153555478900671,
0.010422770865261555,
-0.012323448434472084,
0.01906442828476429,
0.015407642349600792,
0.04302449896931648,
-0.0006382883293554187,
-0.04003177955746651,
0.016376031562685966,
0.04006202518939972,
-0.005291928071528673,
-0.06419283151626587,
0.02689249999821186,
0.007224242202937603,
-0.012553514912724495,
0.058441776782274246,
0.006500324700027704,
-0.04369846358895302,
0.02145419828593731,
-0.017511673271656036,
0.01861712709069252,
0.02454141154885292,
0.002264498732984066,
0.09017784148454666,
0.013036061078310013,
-0.015618839301168919,
0.06340041756629944,
0.005633501335978508,
-0.006396292708814144,
0.022923963144421577,
-0.031882062554359436,
0.057215575128793716,
-0.031247930601239204,
0.012906117364764214,
-0.06405074894428253,
-0.007139747496694326,
-0.011595504358410835,
0.046583082526922226,
-0.0054731788113713264,
-0.000053169424063526094,
0.0066499956883490086,
-0.017363887280225754,
-0.002318847458809614,
0.03537123277783394,
-0.03819401562213898,
-0.039898939430713654,
0.018795929849147797,
0.03322199359536171,
0.004904329776763916,
-0.02079744264483452,
-0.021172817796468735,
-0.009612479247152805,
0.0008323956863023341,
0.00948385801166296,
-0.028302714228630066,
0.08262738585472107,
-0.049658238887786865,
-0.010304280556738377,
0.020256809890270233,
-0.04048263281583786,
0.041154637932777405,
-0.008417101576924324,
0.022914832457900047,
0.0041717360727488995,
-0.030511068180203438,
-0.029485460370779037,
0.009050978347659111,
-0.00814745295792818,
0.011712539941072464,
-0.039885830134153366,
0.019259102642536163,
0.018021296709775925,
-0.01205664686858654,
-0.08463722467422485,
-0.03593452274799347,
0.015856510028243065,
-0.019547615200281143,
-0.0015445495955646038,
-0.03159628063440323,
0.04470212385058403,
-0.033645741641521454,
-0.0004005243827123195,
-0.005677605047821999,
0.04648824781179428,
-0.050191085785627365,
-0.0026821927167475224,
0.0229257270693779,
0.02004779689013958,
0.04994668811559677,
0.010716664604842663,
-0.019121238961815834,
0.008468401618301868,
0.011197499930858612,
0.010996962897479534,
0.009631499648094177,
0.030575159937143326,
0.001035804278217256,
-0.027900198474526405,
-0.047463010996580124,
0.0142549779266119,
0.019874699413776398,
-0.03282814100384712,
0.02259899489581585,
-0.012321301735937595,
0.04924355074763298,
0.023283708840608597,
-0.017194246873259544,
-0.016408944502472878,
-0.0064866929315030575,
0.028307147324085236,
0.028578558936715126,
0.01923610456287861,
-0.013266044668853283,
-0.0038702639285475016,
0.02036375179886818,
-0.006931001786142588,
-0.01373532135039568,
-0.018540004268288612,
0.06494095921516418,
0.03223314508795738,
0.0014943401329219341,
0.04619574546813965,
0.016970664262771606,
-0.0007639708928763866,
-0.037025269120931625,
0.0028872182592749596,
0.05928952991962433,
-0.005948174279183149,
-0.04973337799310684,
-0.04063178971409798,
-0.0710415244102478,
0.009467650204896927,
0.019839785993099213,
-0.025279566645622253,
0.028125392273068428,
0.02707160823047161,
0.009099407121539116,
-0.0027237599715590477,
-0.002228736411780119,
-0.030300118029117584,
0.03220769017934799,
-0.0002381988597335294,
0.03552448749542236,
-0.03552866354584694,
0.007712283171713352,
0.0150741683319211,
0.06987618654966354,
-0.037610363215208054,
0.029916301369667053,
0.016506031155586243,
0.0031922038178890944,
0.03335249423980713,
0.0065479641780257225,
-0.011369802989065647,
0.03602425009012222,
-0.05238204449415207,
0.012883340939879417,
-0.03180203214287758,
-0.02753612771630287,
0.03397767245769501,
0.03820878267288208,
0.00604300806298852,
-0.03713690862059593,
-0.03732753172516823,
-0.07631922513246536,
0.05451944097876549,
0.005087523255497217,
-0.01702343486249447,
0.029329296201467514,
0.008255723863840103,
0.0262108463793993,
-0.0017230157973244786,
0.025728100910782814,
-0.019740870222449303,
-0.04986182972788811,
-0.03709011524915695,
-0.04690046235918999,
-0.022104263305664062,
-0.0030080119613558054,
-0.00777391018345952,
-0.0006491162930615246,
0.017517907544970512,
-0.009970895014703274,
0.04976488649845123,
-0.018284287303686142,
0.006051328498870134,
-0.02220897749066353,
0.06609249114990234,
0.020969364792108536,
0.030563047155737877,
0.013781242072582245,
0.0008999507990665734,
0.10495855659246445,
0.0611438974738121,
0.035128235816955566,
-0.08905841410160065,
0.016121238470077515,
-0.013370619155466557,
0.0015556898433715105,
-0.014901193790137768,
0.028357960283756256,
0.029011469334363937,
0.02064371667802334,
-0.008701606653630733,
0.007723826915025711,
0.028094423934817314,
-0.004563343245536089,
0.0303562693297863,
-0.03220907971262932,
-0.04774511605501175,
-0.018887493759393692,
0.025978371500968933,
-0.04301253333687782,
-0.017094627022743225,
-0.0521734356880188,
-0.030942663550376892,
-0.012277012690901756,
0.027581017464399338,
-0.008381999097764492,
-0.02765670232474804,
0.002049767877906561,
0.03037089854478836,
0.008436363190412521,
0.01991572044789791,
0.022715043276548386,
0.02097887359559536,
0.014151107519865036,
0.013853918761014938,
0.02718563936650753,
0.0036223260685801506,
0.017349664121866226,
0.034274253994226456,
0.0012557749869301915,
-0.016165072098374367,
0.03524882718920708,
-0.014836999587714672,
-0.027433520182967186,
-0.020874397829174995,
0.0029013033490628004,
0.06562246382236481,
-0.04116224870085716,
-0.015221266075968742,
-0.00784019473940134,
-0.034162487834692,
-0.023584844544529915,
-0.035770345479249954,
-0.02606379985809326,
-0.01635550893843174,
0.06642710417509079,
-0.018815837800502777,
0.015426397323608398,
-0.02359083481132984,
0.015126042068004608,
0.0019515921594575047,
0.01772104948759079,
-0.00027042467263527215,
-0.004149510525166988,
0.006562413647770882,
0.011816916055977345,
0.045588694512844086,
-0.016253819689154625,
-0.009760870598256588,
-0.03605376556515694,
-0.011207987554371357,
-0.013460840098559856,
-0.06920187920331955,
0.054628901183605194,
-0.013588893227279186,
0.04353703558444977,
0.006153870839625597,
0.0212778951972723,
0.020368950441479683,
-0.05897039547562599,
-0.0004847091331612319,
-0.004899767693132162,
-0.037406399846076965,
-0.014348901808261871,
0.02363164909183979,
0.02871646359562874,
0.05288621410727501,
-0.021895188838243484,
0.009671678766608238,
0.028563320636749268,
0.02104639820754528,
0.06119653210043907,
-0.02828812785446644,
0.0038167783059179783,
0.027306510135531425,
-0.015758153051137924,
-0.018096329644322395,
-0.02834446169435978,
0.0034845462068915367,
0.021488310769200325,
0.005352851934731007,
-0.031907819211483,
0.04105852544307709,
0.010617045685648918,
-0.0021560268942266703,
0.0015716764610260725,
-0.028808271512389183,
-0.014679593034088612,
-0.010040421038866043,
-0.019127344712615013,
-0.030638476833701134,
-0.01049927156418562,
-0.037291064858436584,
-0.0014540009433403611,
-0.00513701606541872,
-0.0031799576245248318,
-0.04628102108836174,
-0.011819224804639816,
-0.02480337768793106,
0.0028587658889591694,
0.005234620999544859,
0.00011836818157462403,
-0.03919022157788277,
-0.009803778491914272,
0.02664066106081009,
0.00628287298604846,
0.0016739745624363422,
-0.002544935792684555,
0.001593098510056734,
-0.0362732894718647,
0.047654926776885986,
0.03776337578892708,
0.008936123922467232,
-0.009037777781486511,
0.01342208031564951,
-0.009875020012259483,
0.04793240875005722,
-0.03336814418435097,
-0.009770882315933704,
0.03328443318605423,
-0.036981601268053055,
0.04009231925010681,
-0.013968493789434433,
0.0383838415145874,
0.07191792875528336,
0.050221141427755356,
-0.014378509484231472,
-0.04082517698407173,
0.035014793276786804,
-0.03367643803358078,
0.011083227582275867,
-0.004600320477038622,
-0.018738729879260063,
-0.0070598372258245945,
-0.040282879024744034,
0.004466603044420481,
0.024181878194212914,
0.003151439130306244,
0.004894575569778681,
0.004315681289881468,
-0.006760420277714729,
-0.0185133945196867,
0.018596511334180832,
0.03315754979848862,
0.04372791945934296,
0.02958451770246029,
0.011766785755753517,
0.008661700412631035,
0.03455270826816559,
-0.016646798700094223,
0.010098044760525227,
0.03362424671649933,
0.006435619201511145,
-0.0755680575966835,
-0.021409017965197563,
0.004456214141100645,
-0.04134851694107056,
0.02087186463177204,
-0.031108135357499123,
0.005553383380174637,
0.03917188569903374,
-0.0660567581653595,
0.017655085772275925,
-0.026232317090034485,
-0.01702587865293026,
-0.0005354050663299859,
0.010455960407853127,
-0.03613290935754776,
0.053386345505714417,
0.002553495578467846,
0.012135456316173077,
0.03100862354040146,
0.0034131943248212337,
-0.010960113257169724,
-0.05010403320193291,
-0.03131542354822159,
0.02948082610964775,
0.0029016986954957247,
-0.04970771446824074,
0.06765671074390411,
-0.042268577963113785,
-0.06014750152826309,
0.04077724739909172,
-0.0006821846473030746,
0.0016606315039098263,
-0.016613982617855072,
0.04483272507786751,
0.016513904556632042,
0.02834920585155487,
0.013052449561655521,
-0.032496415078639984,
-0.012957347556948662,
0.006196037400513887,
0.03511837124824524,
-0.010945343412458897,
-0.05519886687397957,
-0.016711795702576637,
0.005168883129954338,
-0.008302127942442894,
-0.07264100015163422,
0.04961683228611946,
-0.009830254130065441,
-0.033965423703193665,
-0.04422592371702194,
-0.012587519362568855,
0.01047512050718069,
-0.02726719342172146,
0.024912714958190918,
-0.013486694544553757,
0.008119236677885056,
0.029760273173451424,
0.026075562462210655,
-0.029537977650761604,
-0.004269358702003956,
-0.03382265567779541,
-0.03684292733669281,
0.03451095148921013,
0.002777941757813096,
-0.05577215179800987,
-0.0659269392490387,
-0.019984683021903038,
0.014213158749043941,
0.0012755622155964375,
-0.03288416564464569,
-0.053521834313869476,
-0.06491455435752869,
0.019616447389125824,
0.002947732340544462,
0.03670019656419754,
-0.012935119681060314,
-0.04276508837938309,
-0.01381003763526678,
-0.048357971012592316,
0.04558807238936424,
0.026394231244921684,
0.00006633943121414632,
-0.044739872217178345,
-0.0019486203091219068,
0.00006871391087770462,
-0.025083372369408607,
0.05386381223797798,
0.03548361733555794,
-0.02588401548564434,
-0.018970435485243797,
0.03337336704134941,
0.04345596954226494,
-0.03943660110235214,
0.01841130293905735,
-0.04797070100903511,
-0.012224388308823109,
-0.01708601973950863,
0.009430027566850185,
-0.001614337437786162,
0.03107447735965252,
0.010373083874583244,
-0.021549707278609276,
-0.03939502313733101,
-0.00447268970310688,
-0.03254890441894531,
0.047295551747083664,
0.007648203056305647,
-0.015402868390083313,
0.05096114054322243,
-0.010830968618392944,
0.009487702511250973,
0.021677596494555473,
0.0017382822697982192,
-0.01594727672636509,
-0.0007981625967659056,
-0.026324491947889328,
-0.03099852241575718,
-0.0009514385019429028,
-0.0007844570209272206,
0.02344689331948757,
-0.054408445954322815,
-0.0007772704120725393,
0.012898688204586506,
-0.0454191155731678,
-0.003036228008568287,
0.05691336467862129,
0.01890113763511181,
0.0589238777756691,
0.02601717785000801,
0.03269772231578827,
0.02598435990512371,
-0.007853216491639614,
0.016597136855125427,
0.024605371057987213,
0.04152615740895271,
0.030387703329324722,
0.022138573229312897,
0.004410918336361647,
-0.05518093705177307,
0.04025975987315178,
0.008754116483032703,
0.04887581244111061,
-0.03334534540772438,
-0.0017664482584223151,
0.06402351707220078,
-0.015128166414797306,
0.004998898599296808,
-0.012042185291647911,
-0.04622625559568405,
0.0878206193447113,
-0.034748375415802,
-0.002977343276143074,
-0.06652126461267471,
0.023936500772833824,
0.0015406389720737934,
-0.015659429132938385,
0.005825637839734554,
0.04679255932569504,
-0.004370073787868023,
0.008336670696735382,
-0.03196242079138756,
-0.020265646278858185,
0.02966502495110035,
-0.04684995487332344,
0.02518080733716488,
-0.0013750017387792468,
-0.030206069350242615,
-0.004747409839183092,
-0.006542903836816549,
-0.01387307234108448,
-0.03069528006017208,
0.006752935238182545,
0.026020903140306473,
0.046732097864151,
-0.01728532835841179,
-0.034790437668561935,
-0.0023508048616349697,
0.002148834988474846,
-0.06567525863647461,
-0.008660382591187954,
-0.03627566620707512,
-0.0023714748676866293,
0.00506289629265666,
0.01798134669661522
] |
<p>I have to find the Lagrangian for a system.
In the point of interest I have come up with the following position coordinates:</p>
<p>$$x = Rcos(\omega t)+\ell sin(\phi)$$
and
$$y = Rsin(\omega t)-\ell cos(\phi)$$
Now, since I want to find the Lagrangian I need to take the derivative with respect to $t$ of both of them (To get the $\dot{x}$ and $\dot{y}$), and plug it into the formula for kinetic energy. Although it seems easy, the result I should get I'm a little confused about.</p>
<p>In my opinion only the first term in each equation is the only ones that is dependent of $t$, but I know that the answer should be:</p>
<p>$$\dot{x} = -R \omega sin(\omega t)+\ell cos(\phi)\dot{\phi}$$
and
$$\dot{y} = R \omega cos(\omega t)+\ell sin(\phi)\dot{\phi}$$</p>
<p>So my question is, mathematically, how do I justify, that I just take the derivative of the second term in each equation, as it was dependent of $t$ (Which is obviously is), and the just put a $\dot{\phi}$ outside?</p>
| 9,606 |
[
-0.009777838364243507,
-0.00005832898386870511,
-0.010287327691912651,
0.039472371339797974,
-0.03179332986474037,
-0.010738096199929714,
-0.0358252227306366,
-0.007370010484009981,
-0.004786590579897165,
-0.005221027880907059,
0.008000710979104042,
0.035691097378730774,
0.07037046551704407,
-0.0045997570268809795,
0.030573325231671333,
-0.006545170210301876,
-0.025272127240896225,
0.0018980596214532852,
0.003722295630723238,
-0.0287233404815197,
0.008120519109070301,
-0.027119187638163567,
-0.018093448132276535,
0.01051707100123167,
-0.035911425948143005,
0.013568548485636711,
0.025464162230491638,
-0.01860012859106064,
0.015248466283082962,
0.03820622339844704,
-0.011624771170318127,
-0.028150510042905807,
0.02065146528184414,
0.0019156609196215868,
0.030293311923742294,
0.032619960606098175,
-0.0684044286608696,
-0.01634528674185276,
0.008342788554728031,
-0.0024421964772045612,
-0.05001222342252731,
-0.009495899081230164,
-0.0152191873639822,
0.07690272480249405,
-0.054298337548971176,
0.03717388957738876,
0.032456040382385254,
0.006240058224648237,
0.07897145301103592,
-0.03653362765908241,
0.10337898135185242,
0.0007088487036526203,
0.04824327304959297,
0.05495985969901085,
-0.03287284076213837,
0.014717333018779755,
0.05160097777843475,
0.06444088369607925,
-0.014514854177832603,
-0.03739162161946297,
-0.009362850338220596,
-0.045410577207803726,
0.012626133859157562,
-0.03278116136789322,
0.015457026660442352,
-0.0036154179833829403,
0.01785430498421192,
0.005082494113594294,
0.033635158091783524,
-0.015326396562159061,
0.012589067220687866,
-0.022299960255622864,
0.02884756214916706,
-0.025578003376722336,
-0.017107874155044556,
-0.005105698946863413,
0.029486021026968956,
0.0067839412949979305,
-0.008909533731639385,
0.013492705300450325,
0.004235992673784494,
0.02309088222682476,
0.04345767945051193,
0.06392404437065125,
-0.03301049396395683,
-0.04684557393193245,
0.04497263580560684,
0.03520800173282623,
0.031589437276124954,
0.005018964875489473,
-0.0033614570274949074,
0.0045251245610415936,
0.04870687425136566,
-0.0026269222144037485,
-0.0015541600296273828,
0.04322485253214836,
0.014586237259209156,
0.024861643090844154,
0.03610466048121452,
-0.015048275701701641,
-0.009094099514186382,
-0.05274802818894386,
0.008474837988615036,
0.05404281243681908,
0.0005490484763868153,
-0.009600898250937462,
-0.03519188612699509,
0.009605713188648224,
-0.00270336982794106,
-0.037539537996053696,
-0.04071073234081268,
0.017129400745034218,
-0.038297563791275024,
0.01686955615878105,
0.013825400732457638,
-0.01430536713451147,
-0.021104367449879646,
-0.011538480408489704,
0.052833445370197296,
0.062439847737550735,
0.05484365299344063,
-0.04188966378569603,
0.019671527668833733,
0.0022027234081178904,
-0.04281945899128914,
0.016822505742311478,
0.02003921940922737,
-0.018553853034973145,
0.01166923251003027,
-0.01506694033741951,
-0.006697098258882761,
-0.002221758244559169,
-0.0147877661511302,
0.01053012628108263,
0.018304940313100815,
-0.014310675673186779,
-0.0965547189116478,
-0.06021194905042648,
-0.008193559013307095,
0.005625019781291485,
-0.015285412780940533,
-0.041580770164728165,
-0.0003614795277826488,
0.03166356310248375,
0.06814473122358322,
-0.044949959963560104,
-0.0023724648635834455,
0.021472087129950523,
0.03490333631634712,
-0.044489696621894836,
-0.007094346918165684,
-0.03087311051785946,
-0.01817295514047146,
-0.05205176770687103,
0.0009231615113094449,
-0.06389062106609344,
0.01267248671501875,
0.02624099887907505,
-0.011615769006311893,
0.009621137753129005,
0.05558101832866669,
-0.017156291753053665,
0.014224649406969547,
0.030119771137833595,
-0.003320444608107209,
-0.034423936158418655,
0.06383786350488663,
-0.007973920553922653,
0.017765110358595848,
0.048328861594200134,
0.025389038026332855,
0.029241235926747322,
-0.021799370646476746,
0.03955638408660889,
0.04308027774095535,
-0.026885854080319405,
-0.030133964493870735,
-0.015232454985380173,
-0.019763752818107605,
-0.015883764252066612,
-0.06132643297314644,
-0.06277763098478317,
0.020518729463219643,
-0.03160400688648224,
-0.0031152276787906885,
0.05511016398668289,
0.01388856302946806,
0.0005215535638853908,
-0.03799061477184296,
-0.03695512190461159,
-0.0009525857167318463,
-0.056450992822647095,
-0.001142662949860096,
-0.031148536130785942,
-0.017538834363222122,
0.024097848683595657,
0.02055552415549755,
0.016919804736971855,
-0.015927722677588463,
-0.020770782604813576,
-0.007663258817046881,
0.04477963224053383,
-0.0070066736079752445,
-0.01990143582224846,
0.04067884758114815,
0.0397445373237133,
0.017576437443494797,
0.0373174324631691,
0.018335556611418724,
-0.017974546179175377,
-0.010725071653723717,
-0.00015586960944347084,
-0.04226093739271164,
0.006723536644130945,
0.019772877916693687,
-0.02358940988779068,
0.002807765267789364,
0.00931223388761282,
-0.03618461266160011,
0.008917533792555332,
-0.040042445063591,
0.06623560190200806,
0.060029689222574234,
0.006291409954428673,
-0.005875502247363329,
0.0633731409907341,
0.005466481205075979,
0.0491686575114727,
0.017269276082515717,
-0.03134044259786606,
-0.01589047908782959,
0.005628027021884918,
0.0325775109231472,
0.030417734757065773,
-0.049649789929389954,
-0.01068288367241621,
0.05702774226665497,
0.0142367510125041,
0.04237927496433258,
0.03507931903004646,
-0.0033628088422119617,
-0.03563260659575462,
0.06028396263718605,
0.01951410062611103,
-0.056701358407735825,
0.016126541420817375,
0.05103688687086105,
0.015093795023858547,
0.01621381565928459,
0.03162050619721413,
-0.02947990782558918,
0.06560738384723663,
-0.0023809392005205154,
0.013032674789428711,
0.024487430229783058,
-0.007001351099461317,
0.07072440534830093,
-0.00961313210427761,
0.08141163736581802,
0.03518956899642944,
0.011582626961171627,
-0.02745976485311985,
0.010922035202383995,
0.01683010905981064,
-0.00999443233013153,
-0.004599917214363813,
-0.06387622654438019,
0.01665445603430271,
0.020984986796975136,
-0.04891030862927437,
-0.011418531648814678,
0.014007816091179848,
-0.018758205696940422,
-0.021890606731176376,
-0.015001267194747925,
0.003290849504992366,
0.014271557331085205,
0.013316627591848373,
-0.0026670589577406645,
-0.024398507550358772,
0.0002821168745867908,
-0.01939432881772518,
-0.003597985953092575,
0.020874885842204094,
-0.058829452842473984,
0.009426468051970005,
-0.060613468289375305,
-0.04202231019735336,
0.04361400753259659,
-0.008340544998645782,
-0.013069627806544304,
-0.0008124076412059367,
0.0018036620458588004,
-0.07974492013454437,
-0.016667695716023445,
-0.023582587018609047,
0.021795397624373436,
-0.025525609031319618,
-0.0013015923323109746,
0.043677832931280136,
0.01403818093240261,
-0.01504701841622591,
0.006373581010848284,
-0.06268461793661118,
-0.018601899966597557,
0.018936030566692352,
0.007835925556719303,
0.008418852463364601,
-0.0012140246108174324,
-0.0005058851675130427,
0.014442580752074718,
0.003469577059149742,
-0.010597754269838333,
-0.04404841363430023,
-0.03531418368220329,
0.025380777195096016,
0.00047949832514859736,
0.036504920572042465,
-0.014383863657712936,
-0.054877568036317825,
0.10585430264472961,
0.05292951315641403,
-0.0018793765921145678,
0.0189046710729599,
0.01760418340563774,
-0.03510883450508118,
-0.017566725611686707,
-0.014149877242743969,
0.0031670427415519953,
-0.0021598786115646362,
0.027095185592770576,
0.01977594755589962,
0.00351340277120471,
0.010807570070028305,
-0.00804569385945797,
0.02014336548745632,
-0.010165789164602757,
0.031159238889813423,
0.007396466564387083,
0.05088777840137482,
0.012819950468838215,
0.003254994284361601,
0.008021012879908085,
0.005979741923511028,
0.029731987044215202,
-0.0003997063322458416,
-0.08008085936307907,
0.014252865687012672,
0.021694188937544823,
-0.03810068964958191,
0.008401629514992237,
0.048543162643909454,
0.021580707281827927,
-0.024368450045585632,
0.01235784962773323,
0.019328009337186813,
0.0301606934517622,
-0.017745114862918854,
0.009762636385858059,
0.019821148365736008,
0.04716747999191284,
-0.013162439689040184,
-0.04570408910512924,
-0.008346052840352058,
-0.006536613684147596,
0.048804473131895065,
-0.00039864701102487743,
-0.0313478447496891,
0.032070569694042206,
-0.010712914168834686,
0.015918735414743423,
-0.052223414182662964,
-0.046599142253398895,
0.02024776302278042,
-0.09649716317653656,
0.000493767554871738,
0.008811693638563156,
0.07586898654699326,
-0.00586258340626955,
0.07697063684463501,
0.0019606342539191246,
0.007566456682980061,
0.03856914862990379,
0.005492071155458689,
-0.01900821179151535,
0.04899214208126068,
-0.016296688467264175,
-0.027591248974204063,
-0.008093370124697685,
0.02796795405447483,
0.026896977797150612,
-0.0467633381485939,
0.005621503572911024,
-0.0009411803912371397,
-0.025044409558176994,
-0.051977936178445816,
0.016272399574518204,
-0.0656394436955452,
-0.02831656113266945,
-0.00013302097795531154,
0.03468651697039604,
0.0016641482943668962,
-0.016696995124220848,
0.010429277084767818,
0.07604620605707169,
-0.023486850783228874,
-0.020058168098330498,
-0.07221868634223938,
-0.013622584752738476,
0.03273157402873039,
0.009150710888206959,
0.0008422576356679201,
0.024884123355150223,
0.05318856239318848,
0.019098585471510887,
-0.020787173882126808,
0.05963730067014694,
0.022926269099116325,
0.005348894279450178,
-0.011668059974908829,
-0.04548470675945282,
-0.013630073517560959,
0.010070559568703175,
0.07290010154247284,
0.011252635158598423,
-0.022860633209347725,
0.032327234745025635,
0.0070353620685637,
0.02164769545197487,
-0.0013650243636220694,
0.005846688058227301,
0.014998543076217175,
-0.04800202324986458,
-0.06241463124752045,
0.011124379001557827,
-0.0014165391912683845,
-0.008130109868943691,
-0.010185174643993378,
0.01170028280466795,
-0.0065988413989543915,
0.009335794486105442,
0.014041081070899963,
0.020456083118915558,
0.019168619066476822,
0.038390856236219406,
-0.006957075092941523,
0.03299485892057419,
-0.005460457410663366,
-0.021745087578892708,
0.0323251448571682,
0.014592548832297325,
0.032290391623973846,
-0.010671970434486866,
0.0014013113686814904,
-0.0456404946744442,
-0.0018030398059636354,
0.02384236827492714,
0.00913987960666418,
-0.03241025283932686,
-0.016970282420516014,
-0.029901299625635147,
-0.030795928090810776,
0.039083801209926605,
-0.02758159302175045,
0.03679733723402023,
0.01373231504112482,
-0.00855651218444109,
0.011010355316102505,
-0.04388924688100815,
-0.05175251141190529,
-0.001725660520605743,
-0.00508937006816268,
0.01163236889988184,
-0.04334816336631775,
0.0008906159200705588,
-0.000740588060580194,
0.01479875948280096,
0.009294073097407818,
0.08487489819526672,
0.0024589241947978735,
-0.050349779427051544,
-0.04904982075095177,
0.02090001106262207,
-0.0051343063823878765,
-0.05572089925408363,
-0.00663701631128788,
0.020534759387373924,
0.012401607818901539,
0.039477236568927765,
-0.02500062622129917,
-0.05024651437997818,
0.06277545541524887,
0.023763382807374,
-0.027766622602939606,
0.006596860010176897,
-0.04266226664185524,
0.023201175034046173,
0.06407912075519562,
0.013432139530777931,
0.023909054696559906,
0.043804705142974854,
0.0005749733536504209,
-0.017169974744319916,
0.005325282923877239,
0.03474762663245201,
-0.014351141639053822,
-0.004587750416249037,
-0.02893364429473877,
0.012101450935006142,
-0.005727899726480246,
-0.004180050455033779,
-0.011121335439383984,
0.01564466953277588,
-0.039200641214847565,
-0.005631816107779741,
0.012709601782262325,
0.020075783133506775,
0.010492431931197643,
-0.020042141899466515,
0.0037616610061377287,
0.031247785314917564,
-0.006983004044741392,
-0.019226454198360443,
-0.024685027077794075,
-0.01791919581592083,
-0.009306601248681545,
0.048214830458164215,
-0.015349668450653553,
0.0441109836101532,
-0.021617304533720016,
0.005518317222595215,
0.0029098009690642357,
-0.0755913257598877,
0.028756169602274895,
0.008329052478075027,
-0.0008046017028391361,
0.016896678134799004,
-0.040019676089286804,
-0.09866631031036377,
-0.00002923137799371034,
0.022401414811611176,
0.008862260729074478,
-0.04966485872864723,
0.005748986266553402,
0.018310191109776497,
-0.0014491463080048561,
-0.07243941724300385,
-0.05722480267286301,
-0.015917183831334114,
-0.00285908579826355,
-0.031130971387028694,
-0.0399971604347229,
0.03180256113409996,
-0.042221006006002426,
-0.003313409397378564,
0.021938800811767578,
0.007058622315526009,
-0.02659822255373001,
0.007073019631206989,
0.006060532759875059,
0.014016401953995228,
0.01654878258705139,
-0.011272086761891842,
0.007168121635913849,
0.03888668492436409,
-0.011364288628101349,
-0.024734260514378548,
0.011065165512263775,
0.0245223231613636,
-0.010816901922225952,
-0.014838079921901226,
-0.026184964925050735,
-0.0008527501486241817,
0.02121257223188877,
-0.003778125625103712,
-0.031355924904346466,
0.025660408660769463,
0.02812650054693222,
-0.0072365556843578815,
-0.028021838515996933,
-0.0037898060400038958,
-0.01378339622169733,
0.0037784012965857983,
0.005098066292703152,
0.006263212766498327,
-0.011578531935811043,
-0.02101554162800312,
0.019699271768331528,
-0.005366784520447254,
0.005919797345995903,
0.004873675759881735,
0.08002447336912155,
-0.0028977240435779095,
0.0075965216383337975,
0.02924737147986889,
0.04961613193154335,
0.034278951585292816,
0.013099231757223606,
-0.013059252873063087,
0.03852603957056999,
-0.013755016960203648,
-0.046038009226322174,
-0.015832824632525444,
-0.03743373602628708,
0.027135202661156654,
0.0948520228266716,
-0.0510743111371994,
0.07034645229578018,
-0.0022997185587882996,
-0.00027240553754381835,
0.02538284659385681,
0.03235746547579765,
-0.019484378397464752,
-0.030710116028785706,
-0.0015493208775296807,
0.05611127242445946,
-0.03660018742084503,
-0.0235615074634552,
0.008416612632572651,
0.012290380895137787,
-0.022263215854763985,
0.016857368871569633,
0.003318306989967823,
0.02266095206141472,
-0.008178613148629665,
0.007800286170095205,
-0.05193797126412392,
0.005526293069124222,
-0.019646091386675835,
0.0513383224606514,
-0.015323235653340816,
-0.06691693514585495,
0.06397467851638794,
0.02613215520977974,
0.014180838130414486,
-0.05469786003232002,
-0.004722126759588718,
-0.015165130607783794,
0.0449710488319397,
0.03661021590232849,
0.03125131130218506,
0.00873805396258831,
0.02680947631597519,
0.07791905850172043,
0.012556889094412327,
0.03608567640185356,
-0.012684477493166924,
-0.044590968638658524,
0.006537947803735733,
-0.058767013251781464,
-0.07200273126363754,
0.02058919332921505,
-0.015185374766588211,
-0.0061691938899457455,
0.01650809310376644,
-0.022103507071733475,
0.01920752041041851,
0.005247792229056358,
0.041589513421058655,
-0.014949480071663857,
0.09803629666566849,
-0.01224852167069912,
0.00953009445220232,
-0.010188937187194824,
-0.0044406019151210785,
0.10974085330963135,
0.05803831294178963,
-0.0022461602929979563,
-0.03881024196743965,
0.002995269140228629,
-0.02492736652493477,
-0.0033213200513273478,
-0.06336095929145813,
0.03382331505417824,
0.010407749563455582,
-0.004039457067847252,
-0.009994454681873322,
0.023339184001088142,
-0.01364052016288042,
-0.00885352399200201,
0.03508370369672775,
-0.04686949774622917,
-0.050085607916116714,
0.01611926220357418,
0.012267446145415306,
0.006152784917503595,
-0.020307626575231552,
-0.002185179851949215,
0.05027322098612785,
-0.03849497064948082,
0.014337928034365177,
-0.03409125283360481,
-0.045590415596961975,
-0.007352957967668772,
0.009845614433288574,
-0.034446027129888535,
-0.0012502010213211179,
0.01623157598078251,
-0.017515577375888824,
-0.03332619369029999,
-0.004435060545802116,
0.02413680963218212,
-0.008285836316645145,
0.03148839250206947,
0.022366857156157494,
-0.003286919556558132,
0.038597021251916885,
0.01626507192850113,
0.02236301638185978,
-0.031043659895658493,
-0.012699880637228489,
-0.03245864808559418,
0.07093912363052368,
-0.014112571254372597,
0.04184180498123169,
-0.020065870136022568,
0.022015836089849472,
-0.0151455607265234,
-0.04181458055973053,
-0.02649122104048729,
-0.0029678097926080227,
0.030544940382242203,
-0.009964223019778728,
0.016611607745289803,
-0.06295117735862732,
0.0005990333156660199,
0.004048535134643316,
0.02892395481467247,
-0.013270989991724491,
0.016769178211688995,
-0.020528556779026985,
0.01786765083670616,
0.0520368292927742,
-0.0356748029589653,
-0.01816299930214882,
-0.016500456258654594,
-0.029756268486380577,
-0.018087444826960564,
0.006380909588187933,
0.021332833915948868,
0.004278457257896662,
0.019235754385590553,
-0.01985146850347519,
-0.0012161416234448552,
-0.03821085765957832,
-0.04976969584822655,
0.01796281337738037,
-0.005880899727344513,
-0.03376030921936035,
-0.008973474614322186,
-0.0008594539249315858,
-0.0074335867539048195,
0.07554039359092712,
-0.011902740225195885,
-0.008097994141280651,
0.023337021470069885,
0.02336454950273037,
0.03553003817796707,
-0.02713603526353836,
-0.05578552186489105,
0.00400822376832366,
-0.008648257702589035,
-0.011030700989067554,
-0.019553422927856445,
-0.004218675661832094,
0.018727270886301994,
0.033620983362197876,
0.02070276252925396,
0.027264267206192017,
-0.0333770327270031,
-0.003646623343229294,
0.025780780240893364,
-0.011037650518119335,
-0.002373902825638652,
0.01741562969982624,
0.008653719909489155,
-0.036732304841279984,
-0.000673473987262696,
-0.01048299577087164,
-0.00410845410078764,
0.016701295971870422,
-0.013748737052083015,
-0.022253287956118584,
0.012125793844461441,
-0.03725442290306091,
0.031590282917022705,
-0.02962869219481945,
0.039284780621528625,
-0.05600418522953987,
0.03517657518386841,
-0.016686173155903816,
-0.010047754272818565,
-0.043798498809337616,
0.04052325710654259,
-0.0303731057792902,
-0.02142086997628212,
0.0021873214282095432,
0.016502078622579575,
-0.005599203519523144,
-0.012551963329315186,
0.025774922221899033,
-0.009668894112110138,
0.06278426200151443,
-0.03790678456425667,
0.0012205922976136208,
-0.0018641747301444411,
-0.028885258361697197,
-0.01952347159385681,
-0.0018696780316531658,
0.027326541021466255,
0.03895072638988495,
0.02884713001549244,
-0.03207875043153763,
-0.032213181257247925,
0.0457778237760067,
-0.019512617960572243,
-0.005418137181550264,
0.02883847989141941,
-0.028818968683481216,
-0.028467390686273575,
-0.03713986277580261,
0.006272200029343367,
-0.02068497985601425,
0.030960872769355774,
0.00867608841508627,
0.01611330732703209,
-0.00970358494669199,
0.0050160763785243034,
0.02443561889231205,
0.010073901154100895,
0.011273469775915146,
0.002887451322749257,
0.025222260504961014,
0.018865296617150307,
0.037632055580616,
0.003490667324513197,
-0.012905387207865715,
0.04896481707692146,
0.03278649225831032,
-0.06769658625125885,
0.006462892517447472,
-0.007214348763227463,
0.01413034088909626,
0.06382187455892563,
-0.05217040330171585,
0.025955336168408394,
0.024139417335391045,
-0.052863188087940216,
-0.01781887747347355,
-0.023677710443735123,
0.03017899952828884,
0.005200274288654327,
-0.01314579788595438,
0.005532111041247845,
0.04645555466413498,
0.037969738245010376,
0.037084534764289856,
0.021199839189648628,
0.03341522067785263,
-0.007970483973622322,
-0.0418526865541935,
0.009180882014334202,
0.02334880456328392,
-0.0079262126237154,
-0.0431511215865612,
0.07596393674612045,
-0.016304301097989082,
-0.03791937232017517,
-0.007528733462095261,
-0.010266526602208614,
-0.021793443709611893,
-0.00006600299093406647,
0.050407979637384415,
0.004079410806298256,
0.01690356619656086,
-0.001309450133703649,
-0.029090240597724915,
-0.03243298456072807,
0.014639440923929214,
0.03877102583646774,
-0.004611198790371418,
-0.050719961524009705,
-0.04334736615419388,
0.04949512705206871,
-0.03811280056834221,
-0.03859981894493103,
0.04048828035593033,
-0.014326504431664944,
0.010189377702772617,
0.0248893890529871,
-0.014793193899095058,
-0.006486068479716778,
-0.020071519538760185,
-0.030508290976285934,
-0.02617771551012993,
0.005074437707662582,
0.018557103350758553,
-0.01730423793196678,
-0.018069904297590256,
0.0019296640530228615,
-0.01317022554576397,
-0.049104560166597366,
0.017015086486935616,
-0.007891155779361725,
0.001650932477787137,
-0.09759347140789032,
0.03240961953997612,
-0.0003426765906624496,
-0.01852923072874546,
-0.05153815075755119,
-0.02986006624996662,
-0.05322520062327385,
0.04076218605041504,
0.018467335030436516,
0.0012554518179968,
0.01980094611644745,
-0.006964818574488163,
-0.005083953496068716,
-0.07247365266084671,
0.0009022546000778675,
0.026310930028557777,
-0.04613591358065605,
-0.012572746723890305,
-0.06000293418765068,
-0.024739492684602737,
0.02420387603342533,
0.05340788513422012,
-0.005889256484806538,
-0.0046622962690889835,
0.04565047472715378,
-0.012151566334068775,
0.0009027449414134026,
-0.02962549775838852,
-0.015915976837277412,
-0.0069839381612837315,
0.007204722613096237,
0.03184979781508446,
-0.014146116562187672,
-0.007816317491233349,
0.05522463098168373,
0.04336396977305412,
0.006326164584606886,
0.01958741806447506,
0.012017454020678997,
-0.03160739317536354,
0.007653259206563234,
-0.04669775441288948,
0.015512070618569851,
0.051230333745479584,
0.010938331484794617,
-0.007430052850395441,
0.0341435931622982,
-0.03910202905535698,
-0.03486292064189911,
0.02108156681060791,
-0.059686239808797836,
-0.027341503649950027,
0.0012294583721086383,
-0.029008105397224426,
0.02367815002799034,
-0.05095990374684334,
0.0018943499308079481,
0.01915183663368225,
-0.03912236541509628,
-0.027868466451764107,
0.0456601083278656,
0.0012942338362336159,
0.020227128639817238,
0.009271195158362389,
0.013579885475337505,
0.035963091999292374,
-0.031253308057785034,
0.006690489128232002,
0.03413214161992073,
0.034999873489141464,
0.01588044874370098,
0.00994892418384552,
0.01745227724313736,
-0.014816338196396828,
0.03765961900353432,
-0.03185867890715599,
0.03574215993285179,
-0.043822627514600754,
-0.0035208335611969233,
-0.009067729115486145,
-0.0210048109292984,
-0.016822736710309982,
-0.0005002964753657579,
-0.023680832237005234,
0.04579704999923706,
-0.02518044225871563,
-0.0088129173964262,
0.0031279597897082567,
0.03370271995663643,
-0.0004291819059289992,
0.023330558091402054,
-0.010311390273272991,
0.029284847900271416,
0.009968232363462448,
0.03920992836356163,
-0.05503972992300987,
-0.020107677206397057,
0.006054833997040987,
-0.05028889700770378,
-0.005351371597498655,
0.019550342112779617,
0.009917838498950005,
0.04827454686164856,
-0.028787221759557724,
-0.024628791958093643,
-0.01927170529961586,
0.027728894725441933,
0.039241109043359756,
0.028866291046142578,
-0.024388328194618225,
-0.018449317663908005,
-0.04853067547082901,
0.05980532616376877,
-0.060636356472969055,
-0.0383547842502594,
0.009326516650617123,
0.003390398807823658,
-0.004141258541494608,
-0.009925447404384613
] |
<p>I posted this in the mathematical forums. Maybe you will help me. I found an hard article <a href="http://prola.aps.org/abstract/PR/v105/i3/p776_1" rel="nofollow">http://prola.aps.org/abstract/PR/v105/i3/p776_1</a> of yang huang and luttinger. The authors begins with the sum: $$\frac{{E_2 }}{{E_0 }} = \frac{{16\pi ^2 a^2 \lambda ^2 }}{{V^2 }}\sum\limits_{} {'\frac{{\langle n_\alpha \rangle \langle n_\gamma \rangle \langle n_\lambda \rangle }}{{\frac{1}{2}\left( {k_\alpha ^2 + k_\beta ^2 - k_\gamma ^2 - k_\lambda ^2 } \right)}}\delta \left( {\vec k{}_\alpha + \vec k{}_\beta - \vec k{}_\gamma - \vec k{}_\lambda } \right)} $$ which represents the second order perturbation term of the energy of a bose gas. ${\langle n_\alpha \rangle }$ is: $$\langle n_\alpha \rangle = \sum\limits_{n = 0}^\infty {n\left( {ze^{ - \beta \varepsilon _\alpha } } \right)} ^n /\sum\limits_{n = 0}^\infty {\left( {ze^{ - \beta \varepsilon _\alpha } } \right)} ^n = \frac{{ze^{ - \beta \varepsilon _\alpha } }}{{1 - ze^{ - \beta \varepsilon _\alpha } }} $$ In the sum the terms with a vanishing denominator are omitted. There is also the restriction ${\vec k{}_\alpha \ne \vec k{}_\beta }\ \ $ and ${\vec k{}_\gamma \ne \vec k{}_\lambda }\ \ $. Now the passage that is unclear to me is the passage to the integral: $$\frac{{E_2 }}{{E_0 }} = \frac{{16\pi a^2 \lambda ^2 }}{{V^2 }}\left( {\frac{{4V^3 }}{{\pi ^3 \lambda ^5 }}} \right)\sum\limits_{i,j,k}^\infty {\frac{{z^{j + k + l} }}{{\left( {j + k + l} \right)^{1/2} \left( {j - k} \right)l}}} \frac{{\partial J}}{{\partial u}} $$ where: $$J = \int\limits_0^\infty {\int\limits_0^\infty {dqdq\frac{{\cosh \left( {upq} \right)}}{{q^2 - p^2 }}} } e^{ - vq^2 - wp^2 } $$ and: $$u = \frac{{\hbar ^2 \beta }}{{2m}}\left( {\frac{{2\left( {j - k} \right)l}}{{j + k + l}}} \right) $$ $$v = \frac{{\hbar ^2 \beta }}{{2m}}\left( {\frac{{\left( {j + k} \right)l}}{{j + k + l}}} \right) $$ $$w = \frac{{\hbar ^2 \beta }}{{2m}}\left( {\frac{{\left( {j + k} \right)l + 4jk}}{{j + k + l}}} \right) $$ $\frac{{\partial J}}{{\partial u}}$ is calculated here: <a href="http://math.stackexchange.com/questions/63534/difficult-integral">http://math.stackexchange.com/questions/63534/difficult-integral</a>
Maybe we don't have to do thermal average of n and we need : $$n = \frac{1}{{z^{ - 1} e^{\varepsilon /kT} - 1}} = \sum\limits_{n = 1}^\infty {\left( {ze^{ - \varepsilon /kT} } \right)^l } $$ so: $$\sum\limits_{} {'... = \sum\limits_{i,j,k = 1}^\infty {\sum\limits_{} ' } } z^{ijk} \frac{{e^{ - \frac{{\hbar ^2 k_a^2j }}{{2m}}} e^{ - \frac{{\hbar ^2 k_\gamma ^2k }}{{2m}}} e^{ - \frac{{\hbar ^2 k_\lambda ^2l }}{{2m}}} }}{{\frac{1}{2}\left( {k_a^2 + k_b^2 - k_\gamma ^2 - k_\lambda ^2 } \right)}} $$ This explain the factor $z^{ijk}$ and the sum. How can we continue?Now we have to transform the sum' in a integral. The density of state depends of $kdk$ so i think we have to evaluate: $$\int\limits_0^\infty {\frac{{e^{ - \frac{{\hbar ^2 k_a^2j }}{{2m}}} e^{ - \frac{{\hbar ^2 k_\gamma ^2k }}{{2m}}} e^{ - \frac{{\hbar ^2 k_\lambda ^2l }}{{2m}}} }}{{\frac{1}{2}\left( {k_a^2 + k_b^2 - k_\gamma ^2 - k_\lambda ^2 } \right)}}k_a k_b k_\gamma k_\lambda } dk_a dk_b dk_\gamma dk_\lambda $$ We have to evaluate two integrals, i think. Do you have any suggestion?</p>
| 9,607 |
[
-0.026048187166452408,
-0.02418849617242813,
0.024269243702292442,
0.0037485668435692787,
0.0460224486887455,
-0.010346979834139347,
-0.0245986245572567,
-0.03214675188064575,
0.0018638101173564792,
-0.07883394509553909,
0.05943754315376282,
0.010727886110544205,
0.07361625134944916,
0.03136112913489342,
0.006855817046016455,
0.013446194119751453,
-0.015801168978214264,
-0.0036656514275819063,
-0.033590175211429596,
-0.02020721510052681,
0.02423069253563881,
0.002349474932998419,
-0.022771455347537994,
0.0010958686470985413,
-0.01582999899983406,
0.04784948378801346,
-0.0013523678062483668,
0.012928311713039875,
-0.007704742718487978,
0.06989189237356186,
0.0005608706269413233,
-0.023495100438594818,
0.031010355800390244,
-0.000008742693353269715,
0.029111331328749657,
0.042709458619356155,
-0.024137582629919052,
-0.029764721170067787,
-0.024028904736042023,
0.026407692581415176,
-0.04625476151704788,
-0.0070679765194654465,
-0.00043277337681502104,
0.012071887031197548,
-0.005377825815230608,
0.026079222559928894,
0.03312684968113899,
-0.040822871029376984,
0.041641369462013245,
-0.011957405135035515,
0.05853479355573654,
0.0024130165111273527,
0.03475480526685715,
0.02235446870326996,
-0.008954807184636593,
-0.03495287150144577,
0.029528986662626266,
0.09066096693277359,
0.033333417028188705,
-0.06632919609546661,
0.026368696242570877,
-0.0034736550878733397,
-0.01147348340600729,
0.017310122027993202,
0.0024025922175496817,
0.02500518597662449,
-0.0012356656370684505,
-0.016603080555796623,
0.012205474078655243,
-0.002463407116010785,
0.0322159007191658,
-0.031141482293605804,
0.04337119683623314,
-0.016388731077313423,
-0.007729770615696907,
0.02831636741757393,
-0.028947418555617332,
0.011453814804553986,
0.00504609290510416,
0.0329626128077507,
-0.005628128070384264,
0.03080369532108307,
0.04599739611148834,
0.019151655957102776,
-0.014612549915909767,
0.019672397524118423,
0.0717482790350914,
-0.03442753851413727,
0.017449911683797836,
0.06189601495862007,
-0.005664615426212549,
0.057488661259412766,
0.031126441434025764,
-0.014188180677592754,
-0.019904781132936478,
0.02174326218664646,
0.033029742538928986,
0.049335986375808716,
-0.0071453214623034,
-0.02003416232764721,
-0.018864192068576813,
-0.006823445204645395,
0.0035879313945770264,
0.09325609356164932,
0.03200375661253929,
-0.05345190316438675,
-0.02326853759586811,
0.008112710900604725,
-0.03284125402569771,
-0.03892391175031662,
-0.04653836414217949,
0.00029405386885628104,
-0.02275802567601204,
-0.015997741371393204,
-0.03957909718155861,
-0.04599236696958542,
-0.017806701362133026,
0.028729967772960663,
0.04633580893278122,
0.06969296932220459,
-0.0004894789308309555,
0.003236448159441352,
-0.00032150617334991693,
-0.04066651687026024,
-0.07174818962812424,
-0.002099927281960845,
0.08328277617692947,
0.010655341669917107,
-0.052593380212783813,
0.006870369892567396,
0.03593500703573227,
0.004830555059015751,
0.007349295541644096,
-0.026876240968704224,
0.04249436408281326,
-0.04345516487956047,
-0.0703357458114624,
-0.051025450229644775,
0.03344064950942993,
-0.026415377855300903,
0.003080581082031131,
-0.052912238985300064,
-0.020727595314383507,
0.05369574949145317,
0.08584058284759521,
-0.0004058646154589951,
0.014316964894533157,
-0.030001170933246613,
0.022772569209337234,
0.02329651266336441,
-0.025425985455513,
-0.05431290343403816,
-0.019206741824746132,
-0.02072256989777088,
-0.012834255583584309,
-0.03917793184518814,
0.03717861324548721,
0.021529773250222206,
0.04530886560678482,
0.01391589641571045,
0.058930639177560806,
-0.02954285964369774,
-0.004512113053351641,
0.00882443692535162,
-0.001605805940926075,
-0.058224547654390335,
0.04233846440911293,
0.04835320636630058,
0.013354768045246601,
0.013528731651604176,
-0.016112184152007103,
-0.0033071672078222036,
-0.03066292405128479,
-0.000043717202061088756,
0.0489167645573616,
-0.026355236768722534,
-0.02113252505660057,
-0.06449075043201447,
0.016315262764692307,
0.014240756630897522,
-0.05879293009638786,
0.007679539266973734,
-0.027817558497190475,
0.04465719312429428,
-0.01216502208262682,
0.0030282181687653065,
0.0020816223695874214,
-0.011128630489110947,
-0.02298959530889988,
-0.055382270365953445,
-0.019980937242507935,
-0.03173264488577843,
0.0056250616908073425,
0.0017282526241615415,
-0.012739565223455429,
0.048757895827293396,
0.011920662596821785,
-0.005063584540039301,
0.0008914070785976946,
-0.03536633774638176,
0.006651473231613636,
-0.008630608208477497,
0.04325193166732788,
-0.010124774649739265,
0.047458335757255554,
0.02969866432249546,
0.03447103872895241,
-0.004549215082079172,
0.06495463848114014,
-0.023078955709934235,
-0.038431741297245026,
0.0033780408557504416,
-0.0035270173102617264,
0.05858929082751274,
-0.006509640719741583,
0.03532996401190758,
0.0030293508898466825,
-0.024989131838083267,
0.022888587787747383,
-0.0032935969065874815,
-0.039689596742391586,
0.020880183205008507,
0.05855647474527359,
0.037731871008872986,
-0.011921195313334465,
0.0345265232026577,
0.00018207229732070118,
0.027880359441041946,
-0.03177991881966591,
-0.014906280674040318,
-0.062072429805994034,
0.005050302483141422,
0.049726713448762894,
0.046709250658750534,
-0.04163074865937233,
-0.013110507279634476,
0.036263640969991684,
0.010815727524459362,
0.06371795386075974,
-0.0030552693642675877,
-0.022951237857341766,
-0.01667163521051407,
0.027413226664066315,
-0.014647021889686584,
0.01734800450503826,
0.0049440874718129635,
0.024535898119211197,
-0.016284994781017303,
0.03801124915480614,
0.0015544210327789187,
-0.05749717727303505,
0.0048844837583601475,
-0.023440144956111908,
-0.005825656931847334,
-0.015075149945914745,
-0.036411963403224945,
0.048701297491788864,
-0.02377200499176979,
0.052733391523361206,
0.045154016464948654,
-0.013172752223908901,
0.034321583807468414,
-0.01937824673950672,
-0.005180005449801683,
0.01456520427018404,
-0.031975988298654556,
-0.048952993005514145,
0.003717112122103572,
0.016477784141898155,
-0.027475256472826004,
0.013265201821923256,
0.01791241765022278,
0.005992759019136429,
-0.007391320541501045,
0.027088982984423637,
-0.002868593903258443,
0.011942204087972641,
-0.01773500256240368,
-0.0062074968591332436,
-0.032859668135643005,
0.029085593298077583,
0.012779821641743183,
0.023201648145914078,
0.054772134870290756,
-0.0395076684653759,
0.0018722076201811433,
-0.013555353507399559,
-0.04507779702544212,
0.061164598912000656,
-0.025408649817109108,
-0.002113777445629239,
0.03964849188923836,
-0.0005491972551681101,
-0.01492256484925747,
-0.006620266940444708,
-0.02520264871418476,
-0.01018986664712429,
-0.05376053974032402,
0.0019135940819978714,
0.027111131697893143,
0.02387411519885063,
-0.08353941887617111,
0.03149247169494629,
0.012844636105000973,
-0.03930487483739853,
-0.023960351943969727,
-0.014296849258244038,
0.012180504389107227,
-0.0174744613468647,
0.04871325194835663,
0.0041482108645141125,
-0.01744564063847065,
0.004722211509943008,
-0.03453313931822777,
-0.02971882000565529,
0.022917138412594795,
-0.005486757960170507,
0.048829615116119385,
-0.006795801222324371,
-0.03588922694325447,
0.11720962822437286,
0.018582183867692947,
0.008867542259395123,
-0.03861374035477638,
0.018075676634907722,
-0.012314931489527225,
-0.029230276122689247,
0.017023641616106033,
0.020027589052915573,
-0.008637352846562862,
0.045448604971170425,
-0.013391750864684582,
0.042466651648283005,
0.04695775359869003,
-0.003020990639925003,
-0.010754935443401337,
0.05084490403532982,
0.01203569583594799,
0.0028129073325544596,
0.04484906047582626,
-0.00772520387545228,
-0.006473114248365164,
0.008650979958474636,
0.012001990340650082,
0.008619078435003757,
0.015791554003953934,
-0.06534865498542786,
0.0404505617916584,
0.01639183983206749,
-0.038547731935977936,
-0.03547284007072449,
0.0459345281124115,
0.035575393587350845,
-0.030891327187418938,
0.013639116659760475,
0.008301354944705963,
0.02762315608561039,
-0.0279303640127182,
0.03867298364639282,
0.03365397825837135,
0.04988905042409897,
0.00655611464753747,
-0.05139151215553284,
-0.001100566703826189,
0.023273708298802376,
-0.008422404527664185,
-0.03564893826842308,
-0.02564174123108387,
0.00525081530213356,
0.031997065991163254,
-0.01080226805061102,
-0.03205107897520065,
-0.027405261993408203,
0.001046542776748538,
-0.049655430018901825,
-0.010687364265322685,
-0.049510665237903595,
0.016612721607089043,
0.008168753236532211,
0.04201222211122513,
-0.001097075524739921,
0.003693445585668087,
0.024362875148653984,
-0.009960117749869823,
-0.07785378396511078,
0.005737822502851486,
0.0053984192200005054,
-0.00801850575953722,
0.038253188133239746,
-0.013576211407780647,
-0.028269924223423004,
-0.030807236209511757,
-0.018466444686055183,
0.0036961499135941267,
-0.015746140852570534,
-0.020335445180535316,
0.035257983952760696,
-0.037378545850515366,
-0.04013780876994133,
0.0017444522818550467,
0.016987215727567673,
0.04879828169941902,
-0.017964841797947884,
-0.008116822689771652,
0.03617320582270622,
-0.012427638284862041,
-0.01655608043074608,
-0.032793283462524414,
0.007840810343623161,
0.024904031306505203,
0.014818870462477207,
0.02187412418425083,
-0.00703742541372776,
-0.018066324293613434,
-0.024940701201558113,
0.01947680301964283,
0.026549488306045532,
0.015884041786193848,
0.004781350027769804,
0.03207562118768692,
-0.031034458428621292,
0.003954245708882809,
-0.012871766462922096,
0.0849643424153328,
0.020059801638126373,
0.019180353730916977,
0.006487801671028137,
-0.024315260350704193,
-0.020306184887886047,
0.02906973659992218,
0.044727809727191925,
-0.009460890665650368,
-0.011715613305568695,
-0.04335791990160942,
0.012763208709657192,
0.0073538050055503845,
-0.0011905295541509986,
-0.010819226503372192,
-0.029632732272148132,
-0.03637659549713135,
0.007813110016286373,
0.020829029381275177,
0.001714987331070006,
-0.02506786584854126,
-0.005391912534832954,
0.00718267448246479,
0.0005280137993395329,
-0.0009669411228969693,
-0.01690361462533474,
0.013501613400876522,
0.009870911948382854,
0.043380171060562134,
0.013331915251910686,
0.01215704157948494,
-0.02663901261985302,
-0.07553572952747345,
0.0438867062330246,
0.052727073431015015,
0.02367251366376877,
0.010199361480772495,
-0.07051769644021988,
-0.037909384816884995,
0.006247645244002342,
-0.009443233720958233,
0.043044086545705795,
0.003283436642959714,
0.0017655955161899328,
0.01275912020355463,
-0.04886762797832489,
-0.03131262958049774,
0.006173048634082079,
0.011452097445726395,
-0.007923485711216927,
-0.03822844848036766,
-0.008702893741428852,
-0.01998930238187313,
-0.002928804373368621,
0.013057953678071499,
0.06046286225318909,
0.01553769689053297,
-0.04359038174152374,
0.010616051033139229,
-0.01427339855581522,
-0.046634938567876816,
-0.09804319590330124,
0.02480992302298546,
0.021937644109129906,
-0.0009973072446882725,
0.016044925898313522,
-0.03396158292889595,
-0.06083881855010986,
0.029552951455116272,
0.03917659819126129,
-0.032593727111816406,
-0.014624888077378273,
-0.03325311839580536,
0.09466814994812012,
0.04638316482305527,
-0.013059787452220917,
0.07622501254081726,
0.047633763402700424,
-0.02991619147360325,
0.03773144260048866,
-0.0386371985077858,
0.00536621967330575,
-0.0070648822002112865,
0.04118402674794197,
-0.06418445706367493,
0.0037030738312751055,
-0.007728901691734791,
0.03329833969473839,
-0.03588775917887688,
0.00899170245975256,
-0.005723884329199791,
-0.019510671496391296,
-0.021449418738484383,
0.029346439987421036,
-0.010964510962367058,
-0.023217353969812393,
-0.008905213326215744,
0.027964551001787186,
0.034491319209337234,
0.007125901523977518,
0.06098366156220436,
0.008938205428421497,
0.010451093316078186,
0.050541579723358154,
-0.028363224118947983,
0.01830117404460907,
-0.01462399959564209,
-0.01904139667749405,
0.025941045954823494,
-0.039539869874715805,
0.007370158098638058,
0.008672196418046951,
0.008154542185366154,
0.002371841110289097,
-0.03335357457399368,
-0.0616363100707531,
0.02231498993933201,
-0.0190987940877676,
-0.009977247565984726,
-0.010944981127977371,
0.00822858139872551,
0.02048276551067829,
0.005362889263778925,
-0.08347786962985992,
-0.0032442836090922356,
0.00783044844865799,
-0.046040505170822144,
-0.04460877552628517,
0.000999068608507514,
-0.05102340504527092,
0.007540115155279636,
-0.01806216686964035,
0.03463499993085861,
0.03302011638879776,
-0.023769957944750786,
-0.0020393666345626116,
0.03156360238790512,
0.04338536784052849,
0.013237412087619305,
0.008730648085474968,
-0.02689218707382679,
-0.0014916377840563655,
-0.009594007395207882,
-0.013247315771877766,
0.02916247397661209,
0.03905460610985756,
-0.03056229092180729,
-0.02106321044266224,
-0.028019536286592484,
-0.012208758853375912,
-0.006746606435626745,
-0.0017831431468948722,
-0.041786372661590576,
0.0345151387155056,
0.040804579854011536,
0.0076891216449439526,
-0.015097517520189285,
-0.04260006919503212,
0.01690853014588356,
0.05667058005928993,
-0.01889236643910408,
-0.048251308500766754,
-0.04876159504055977,
-0.019501391798257828,
0.03921464458107948,
0.00855810847133398,
-0.009437025524675846,
-0.02551046572625637,
0.05753254517912865,
-0.0031793005764484406,
0.002480291062965989,
0.02043915167450905,
-0.026357457041740417,
0.005743987858295441,
0.017738427966833115,
0.02774926833808422,
0.02999008819460869,
0.023719601333141327,
-0.03201669082045555,
-0.03850015997886658,
-0.0736875832080841,
0.012813772074878216,
0.060779672116041183,
0.012593585066497326,
0.013720016926527023,
-0.014883200637996197,
-0.008669709786772728,
-0.02468232624232769,
-0.038193054497241974,
-0.01613098569214344,
-0.0016146611887961626,
-0.00709638511762023,
0.010458206757903099,
-0.05871596187353134,
-0.03283415734767914,
0.01095411367714405,
0.02181032858788967,
-0.05502784997224808,
0.034769508987665176,
0.006387271452695131,
0.03525419905781746,
0.0008831091690808535,
-0.015577285550534725,
-0.035787347704172134,
0.06777580827474594,
-0.015273362398147583,
0.06940770149230957,
-0.002305152826011181,
-0.030423974618315697,
0.021089255809783936,
0.015438604168593884,
0.013301605358719826,
-0.045581068843603134,
-0.026245204731822014,
-0.02897660993039608,
0.020434992387890816,
0.0030123875476419926,
-0.04191408306360245,
0.030469322577118874,
0.007986028678715229,
0.019851291552186012,
0.009829172864556313,
0.001523817190900445,
-0.025806346908211708,
-0.00821034237742424,
0.015199342742562294,
-0.03260335326194763,
-0.05317769572138786,
0.02690894901752472,
-0.0033039546106010675,
-0.05029958859086037,
0.022453850135207176,
0.009466656483709812,
0.03369560465216637,
0.009074632078409195,
0.004989705979824066,
0.019549474120140076,
0.06429656594991684,
-0.038208380341529846,
0.02049846202135086,
0.0038334480486810207,
0.014304676093161106,
0.15160410106182098,
0.05905358865857124,
0.024551725015044212,
-0.05950821936130524,
0.03224199637770653,
0.019124243408441544,
0.03204208239912987,
-0.05020422488451004,
-0.007916989736258984,
-0.02752583660185337,
-0.036939483135938644,
-0.007644984405487776,
0.0704042911529541,
-0.02936372719705105,
-0.019676625728607178,
0.03235035389661789,
-0.044934820383787155,
-0.04028157889842987,
0.024237900972366333,
0.0008470443426631391,
0.006106045562773943,
0.010425102896988392,
-0.005305514670908451,
0.008501550182700157,
0.0027007628232240677,
0.043197207152843475,
-0.03780457377433777,
-0.00536644970998168,
0.05502733960747719,
-0.014820082113146782,
-0.038321301341056824,
0.001281057600863278,
-0.01378331333398819,
-0.0009306390420533717,
0.021032191812992096,
-0.008317509666085243,
0.027605116367340088,
-0.01826087385416031,
0.04957643151283264,
-0.0003811101196333766,
-0.009401961229741573,
0.023066379129886627,
0.03501960635185242,
0.03261348605155945,
-0.008613567799329758,
-0.017898768186569214,
-0.011805779300630093,
0.06162922829389572,
-0.02068854495882988,
-0.02229006588459015,
0.009246103465557098,
-0.0020825073588639498,
0.02178875543177128,
-0.01794511266052723,
0.008615861646831036,
-0.011679775081574917,
0.027631321921944618,
-0.048828013241291046,
0.006790704093873501,
-0.005145828239619732,
0.0008691285038366914,
0.02511592209339142,
0.003343670628964901,
-0.02521728351712227,
-0.006917142774909735,
-0.016455980017781258,
-0.028039943426847458,
0.03680573031306267,
-0.03336052969098091,
0.004319917876273394,
0.016455259174108505,
0.0027269739657640457,
-0.05765926092863083,
-0.04261850193142891,
-0.011475561186671257,
0.002084038918837905,
0.04367658495903015,
-0.01116886455565691,
0.004237288609147072,
-0.020954949781298637,
-0.06291787326335907,
-0.008960113860666752,
-0.0035750872921198606,
-0.042326975613832474,
-0.008768065832555294,
-0.011617769487202168,
0.004572726786136627,
0.04980067163705826,
-0.01932399906218052,
0.0035741166211664677,
0.030012482777237892,
0.04159514978528023,
0.023452885448932648,
-0.03678891435265541,
-0.0516512505710125,
0.005169954616576433,
-0.02729974314570427,
0.013188346289098263,
-0.025158699601888657,
-0.017404356971383095,
0.00048609034274704754,
0.012704938650131226,
0.008588663302361965,
0.016351299360394478,
-0.05660271644592285,
-0.025952689349651337,
-0.008435975760221481,
-0.024235570803284645,
0.01686132699251175,
0.028918322175741196,
0.05474507436156273,
-0.03209660202264786,
-0.007963195443153381,
-0.013880969025194645,
-0.009869340807199478,
-0.004763260018080473,
0.026641296222805977,
-0.051256030797958374,
-0.011465766467154026,
0.0036689939443022013,
-0.006125845480710268,
-0.03917033225297928,
-0.014867412857711315,
-0.006150146946310997,
0.04454781115055084,
-0.018525324761867523,
0.048921965062618256,
-0.02055145427584648,
0.02108151465654373,
-0.004266329109668732,
-0.005490988492965698,
0.045455507934093475,
0.04123128950595856,
-0.027553165331482887,
-0.027629917487502098,
0.003382237395271659,
-0.011907417327165604,
0.01816396228969097,
0.010785561054944992,
-0.03642973676323891,
0.024586772546172142,
-0.04062352702021599,
-0.055439695715904236,
0.01209221314638853,
0.0009083774057216942,
0.011101835407316685,
0.028632035478949547,
0.027538325637578964,
-0.05501485615968704,
0.057997193187475204,
-0.04140578955411911,
-0.010163445957005024,
-0.009609355591237545,
-0.048725537955760956,
-0.031067853793501854,
-0.025134552270174026,
0.002280334010720253,
0.022243358194828033,
0.006908964831382036,
0.020338362082839012,
0.030881348997354507,
-0.05734408646821976,
-0.017540600150823593,
-0.030621225014328957,
-0.02925289422273636,
0.009033356793224812,
0.008715491741895676,
0.015931084752082825,
-0.010534604080021381,
0.0704842358827591,
-0.044150836765766144,
0.055153172463178635,
-0.004345807712525129,
0.0006969189271330833,
-0.0762999877333641,
-0.02575811557471752,
-0.016467347741127014,
0.021111857146024704,
0.05600328743457794,
-0.06599588692188263,
0.07816165685653687,
-0.011261804960668087,
-0.03595643863081932,
0.049070458859205246,
-0.0021027910988777876,
0.017866021022200584,
-0.049870993942022324,
0.009323202073574066,
-0.05698588490486145,
0.04056965559720993,
0.026417318731546402,
0.04541561380028725,
0.014957462437450886,
0.0195266492664814,
0.02412482537329197,
-0.011945567093789577,
-0.008163228631019592,
0.03315090760588646,
0.0019909474067389965,
-0.012799720279872417,
0.04418770968914032,
-0.046543147414922714,
-0.029498757794499397,
0.026687180623412132,
0.01769239827990532,
-0.012377087958157063,
-0.026049721986055374,
0.0260297954082489,
0.0002361154038226232,
0.050289738923311234,
0.030771145597100258,
-0.005135121755301952,
0.02623922936618328,
-0.025252237915992737,
0.015300125814974308,
-0.0057508135214447975,
-0.004952182061970234,
-0.004094128031283617,
0.04385414719581604,
-0.01814478635787964,
-0.058452244848012924,
0.0482776053249836,
-0.01283988356590271,
-0.019442904740571976,
-0.00458757346495986,
-0.011241529136896133,
0.014268939383327961,
-0.021940717473626137,
0.01815195567905903,
-0.0474628284573555,
0.015091361477971077,
0.02627679891884327,
0.023277826607227325,
-0.009288719855248928,
0.030951516702771187,
-0.014752727933228016,
-0.03966585546731949,
0.03880350664258003,
-0.0015632275026291609,
-0.008863590657711029,
-0.04931337386369705,
-0.029856912791728973,
-0.020310278981924057,
-0.004000747110694647,
0.0067357164807617664,
-0.005883300676941872,
-0.021746879443526268,
0.00024983903858810663,
-0.010688940063118935,
0.04194590821862221,
-0.05439513921737671,
-0.03805577754974365,
0.023887237533926964,
-0.0735415667295456,
0.01573827676475048,
0.010731649585068226,
0.014826380647718906,
-0.010436173528432846,
-0.030363548547029495,
0.03609296679496765,
-0.005442095920443535,
0.03713615611195564,
0.006859774235635996,
-0.03696025162935257,
-0.011400661431252956,
-0.010326976887881756,
0.015639862045645714,
0.0022560791112482548,
0.029683483764529228,
-0.032295484095811844,
-0.021542863920331,
-0.0037749053444713354,
0.009653260931372643,
-0.031539201736450195,
0.02593146450817585,
0.0431128665804863,
0.008505330421030521,
-0.006109805777668953,
0.0003148967516608536,
-0.036939311772584915,
0.03132690489292145,
0.022050317376852036,
0.0016971968580037355,
0.056057076901197433,
-0.020345505326986313,
0.025989508256316185,
0.03109603561460972,
-0.04224022105336189,
-0.03918838873505592,
-0.008023135364055634,
-0.003796083852648735,
-0.012245960533618927,
-0.006594257894903421,
-0.010040651075541973,
0.04194038733839989,
-0.006155541632324457,
0.015528733842074871,
0.021910835057497025,
-0.009061618708074093,
-0.05711038038134575,
0.05527131259441376,
-0.01056738756597042,
0.02800223045051098,
0.03882777318358421,
0.014581287279725075,
0.01340247131884098,
-0.003797210520133376,
0.01892378181219101,
0.0002927452733274549,
0.024714335799217224,
0.01443338394165039,
0.025205004960298538,
-0.005124584771692753,
-0.01784631796181202,
0.015351057052612305,
-0.008894682861864567,
-0.019242029637098312,
-0.014094776473939419,
-0.006839044392108917,
0.05990411341190338,
0.00043047519284300506,
-0.011928824707865715,
-0.008638362400233746,
-0.007891199551522732,
0.07645008713006973,
-0.03823406621813774,
0.04173264652490616,
-0.007732412777841091,
0.006091330200433731,
-0.019637305289506912,
0.010250172577798367,
-0.009249631315469742,
0.06262516230344772,
0.005913248285651207,
-0.0027599986642599106,
-0.025222172960639,
0.006858196575194597,
-0.007385668810456991,
-0.07002191990613937,
-0.012753324583172798,
0.04541092738509178,
0.005074216518551111,
0.006489177700132132,
-0.0034266323782503605,
-0.009907162748277187,
-0.02446996048092842,
0.00012223891098983586,
0.016093291342258453,
-0.015855059027671814,
-0.004751282278448343,
-0.027223002165555954,
0.007314310874789953,
0.05660374090075493,
-0.013234635815024376,
0.004507449455559254,
-0.012387990020215511,
0.017357878386974335,
0.013654367066919804,
-0.01905110478401184
] |
<p>I have action as shown below
$$S=\int \mathrm{d}t \int \mathrm{d}x^3 \bar\psi\left(i\partial_t\psi +\frac1{2m}\bar\nabla^2\psi-V(x)\psi\right)$$ </p>
<p>How do I manipulate it to obtain the Lagrangian density in Standard form
$$\mathcal{L}\left(\{\varphi_r\},\{\partial_\mu\varphi_r\} \right)$$ </p>
| 9,608 |
[
0.01981527730822563,
0.025890639051795006,
-0.005347104277461767,
-0.017266931012272835,
0.030961789190769196,
0.0006342399283312261,
-0.023053143173456192,
-0.015413263812661171,
0.009177504107356071,
-0.02333773300051689,
0.05488767847418785,
0.02309512346982956,
0.09171920269727707,
0.014318378642201424,
0.026513738557696342,
-0.0064593032002449036,
0.019945647567510605,
0.005392573773860931,
0.013266956433653831,
-0.04388047754764557,
-0.022503390908241272,
0.024454854428768158,
-0.014883935451507568,
-0.010985479690134525,
-0.025376254692673683,
0.03540848195552826,
-0.02543715573847294,
0.003842945210635662,
-0.016436083242297173,
0.05643490329384804,
-0.06385963410139084,
-0.029742944985628128,
0.039633505046367645,
0.028921181336045265,
0.011683881282806396,
0.024256275966763496,
-0.05037110671401024,
-0.04978238791227341,
-0.02095949463546276,
0.013912235386669636,
-0.05457222834229469,
0.014610798098146915,
-0.016582414507865906,
0.05621714890003204,
-0.02183411456644535,
0.013043214567005634,
0.018410565331578255,
-0.036901362240314484,
0.052172232419252396,
-0.0543229766190052,
0.0821528211236,
0.03902942314743996,
0.01579647697508335,
0.047863904386758804,
-0.000318454927764833,
-0.02257140725851059,
0.04478537663817406,
0.042908795177936554,
0.024780793115496635,
-0.04290925711393356,
-0.04175296053290367,
-0.050181303173303604,
0.0024718574713915586,
-0.047526050359010696,
0.007259787525981665,
-0.01628616265952587,
0.004153591115027666,
-0.006487617269158363,
0.030782049521803856,
-0.03704236447811127,
0.016875742003321648,
0.02750638872385025,
-0.009223497472703457,
-0.023090213537216187,
0.026798373088240623,
0.007028728257864714,
0.027234097942709923,
-0.0056740655563771725,
0.0034743708092719316,
0.023470019921660423,
0.018390122801065445,
0.028874101117253304,
0.015554007142782211,
0.035708021372556686,
-0.015137376263737679,
-0.035347651690244675,
0.07427971810102463,
0.03257856145501137,
-0.025783633813261986,
0.03498499467968941,
-0.03774207830429077,
0.002004204085096717,
0.03977101296186447,
0.0009368911269120872,
-0.03093656338751316,
0.012745707295835018,
0.018039552494883537,
0.07382497936487198,
0.010489481501281261,
-0.006039384752511978,
-0.01681695505976677,
-0.04421721398830414,
-0.007381427101790905,
0.06109718605875969,
-0.003133718855679035,
-0.01333985012024641,
-0.025367621332406998,
0.01348277647048235,
-0.008630702272057533,
-0.03476402536034584,
-0.05027007311582565,
0.026098594069480896,
-0.01636478863656521,
-0.016361434012651443,
-0.0044476003386080265,
-0.02457287721335888,
-0.0325278639793396,
-0.0456380657851696,
0.028744075447320938,
0.03605915606021881,
0.04000542312860489,
0.003640387672930956,
0.05592375993728638,
-0.0074667902663350105,
-0.06567727774381638,
0.039054326713085175,
0.04536309465765953,
-0.016359012573957443,
-0.016057521104812622,
0.03145141154527664,
-0.00969334039837122,
-0.026120500639081,
0.007867550477385521,
-0.005220700055360794,
0.011299483478069305,
-0.03085007518529892,
-0.08714104443788528,
-0.02598581463098526,
0.009153085760772228,
0.006676316726952791,
-0.006032484583556652,
-0.05979534238576889,
-0.024674301967024803,
0.059643812477588654,
0.06266102194786072,
0.02175314351916313,
0.016914628446102142,
0.02161630056798458,
0.018756520003080368,
-0.0070550767704844475,
-0.01832433231174946,
-0.025092681869864464,
-0.027103256434202194,
-0.048254478722810745,
-0.010353950783610344,
-0.03061531111598015,
0.03341303765773773,
0.014385095797479153,
-0.011622494086623192,
-0.017830384895205498,
0.09508978575468063,
-0.019777866080403328,
0.002111688954755664,
-0.006134354043751955,
-0.03519714996218681,
-0.0026147521566599607,
0.05663431063294411,
-0.0067206271924078465,
0.0032645410392433405,
-0.006918754428625107,
-0.007371859159320593,
0.008672553114593029,
-0.019241392612457275,
0.035242579877376556,
0.05401589721441269,
-0.033120330423116684,
-0.0014413329772651196,
-0.014247726649045944,
-0.01749473437666893,
0.015414265915751457,
0.005100109148770571,
-0.0453927256166935,
-0.02520766668021679,
-0.014621243812143803,
0.006984972395002842,
0.03550565615296364,
0.0040654209442436695,
-0.00297671090811491,
-0.023170555010437965,
-0.06365377455949783,
-0.043015796691179276,
-0.0617712177336216,
0.03156858682632446,
0.0034214393235743046,
-0.05444614961743355,
0.01890931837260723,
0.005159134045243263,
0.037962593138217926,
0.024123046547174454,
-0.04650910198688507,
0.00037377222906798124,
-0.006304055918008089,
-0.010902225971221924,
0.00025958268088288605,
0.010990554466843605,
0.015786653384566307,
0.022116830572485924,
-0.021444544196128845,
0.01315771322697401,
-0.009502558037638664,
-0.028751637786626816,
-0.0008061296539381146,
-0.009209130890667439,
0.0221474040299654,
-0.0072561404667794704,
-0.029143983498215675,
-0.0036236620508134365,
0.026299966499209404,
0.004131014924496412,
0.04121871665120125,
-0.03917812928557396,
0.08559003472328186,
0.07422219216823578,
0.012573834508657455,
-0.0027961076702922583,
0.02122540958225727,
-0.03864716365933418,
0.029042085632681847,
0.005304383113980293,
0.002572183031588793,
-0.02052583359181881,
0.0024725033435970545,
0.0117369769141078,
0.03292568027973175,
-0.06272400915622711,
0.006862977519631386,
0.04065372794866562,
0.0006549302488565445,
0.06770847737789154,
0.012596046552062035,
-0.02912755124270916,
-0.03793763741850853,
0.048764120787382126,
0.03778362646698952,
-0.02059786207973957,
-0.0007592416950501502,
0.04113946110010147,
0.02442251890897751,
0.004430230241268873,
0.007618937641382217,
-0.038556501269340515,
0.054764315485954285,
-0.04308125004172325,
-0.030354619026184082,
-0.0020579553674906492,
-0.037406206130981445,
0.066815584897995,
-0.009265867993235588,
0.058884147554636,
0.08354250341653824,
-0.006197586189955473,
0.008887333795428276,
-0.013022522442042828,
0.028067979961633682,
0.030965441837906837,
0.015277703292667866,
-0.004319341853260994,
-0.0000023724846869299654,
0.03481132909655571,
-0.031721197068691254,
-0.0044590774923563,
-0.007252842653542757,
0.027026105672121048,
-0.05147707462310791,
0.008423428982496262,
0.004836155101656914,
-0.007429978344589472,
-0.006583500653505325,
0.010167811997234821,
-0.05031011253595352,
0.018007956445217133,
0.024252422153949738,
0.04004847630858421,
0.03927627205848694,
-0.05624983459711075,
0.009582050144672394,
-0.02910504676401615,
-0.024252407252788544,
0.03845726326107979,
0.0053682588040828705,
-0.01021122932434082,
-0.005650719627737999,
-0.022683054208755493,
-0.08435046672821045,
-0.010582992807030678,
0.004107952583581209,
0.009871386922895908,
-0.009094922803342342,
0.014515054412186146,
0.020747970789670944,
0.005622194614261389,
-0.0456308014690876,
-0.015425690449774265,
-0.0376063697040081,
-0.0207855012267828,
-0.0160867590457201,
0.014098797924816608,
-0.019797734916210175,
-0.06153137609362602,
0.02803378738462925,
0.04441166669130325,
-0.007309706415981054,
0.021143559366464615,
-0.0660829171538353,
0.009474057704210281,
-0.005271041765809059,
0.024062903597950935,
-0.010409301146864891,
-0.0003133879799861461,
-0.04141603410243988,
0.09662668406963348,
0.044049665331840515,
-0.025541601702570915,
0.014239823445677757,
-0.005621663294732571,
-0.005991501267999411,
-0.02442043460905552,
0.030064573511481285,
0.02256082370877266,
-0.006392637267708778,
0.03426477685570717,
0.008390351198613644,
0.022522712126374245,
0.018877927213907242,
0.00996360182762146,
-0.022829603403806686,
0.05060978978872299,
-0.03164681792259216,
-0.009513181634247303,
0.08421338349580765,
-0.01777070388197899,
-0.01519637368619442,
-0.007606251630932093,
0.00076795689528808,
0.017135679721832275,
0.002611245261505246,
-0.04017621651291847,
0.058722641319036484,
0.02924944832921028,
-0.01408360991626978,
-0.010447013191878796,
0.03497730568051338,
0.011305374093353748,
-0.04164290055632591,
-0.012862218543887138,
0.04257366061210632,
0.015013997443020344,
-0.0009094196720980108,
-0.00750258332118392,
-0.0008249912061728537,
0.04854010045528412,
-0.025310534983873367,
-0.08459832519292831,
-0.024177195504307747,
-0.02229679934680462,
0.04575834795832634,
-0.01002686470746994,
-0.047368016093969345,
0.027507297694683075,
0.009862642735242844,
0.003230221103876829,
-0.026617739349603653,
-0.021397648379206657,
0.013195409439504147,
-0.056485507637262344,
0.009812369011342525,
0.01254399586468935,
0.044315680861473083,
0.045336440205574036,
0.03425326570868492,
0.019159676507115364,
-0.02135690674185753,
0.02221710979938507,
0.004177973140031099,
-0.05497864633798599,
0.06420353055000305,
0.008373863995075226,
-0.033661723136901855,
0.012035353109240532,
-0.008761418052017689,
0.01852921023964882,
-0.0365523025393486,
-0.0032921675592660904,
-0.010094664059579372,
-0.020574545487761497,
-0.06656365096569061,
-0.019198058173060417,
-0.03158670291304588,
0.011036534793674946,
-0.05507364869117737,
0.03132680803537369,
0.008955279365181923,
-0.017150260508060455,
0.0009266558336094022,
0.04173584282398224,
-0.012837435118854046,
-0.023265531286597252,
-0.027546148747205734,
0.0036024674773216248,
-0.004236022476106882,
0.02451077662408352,
0.0071493834257125854,
-0.00838586874306202,
-0.0029284332413226366,
0.04276997596025467,
0.0018068929202854633,
0.039130620658397675,
0.035755544900894165,
0.003885766724124551,
-0.012043117545545101,
-0.02798071689903736,
-0.015851685777306557,
0.03732271492481232,
0.05289936065673828,
-0.003576332936063409,
0.010172776877880096,
0.029307479038834572,
0.0351267047226429,
-0.01350508164614439,
0.0388437956571579,
0.045014310628175735,
-0.012630395591259003,
-0.006586574483662844,
-0.08353208005428314,
0.005907581653445959,
-0.002896440913900733,
-0.003731924807652831,
0.014313974417746067,
0.012346167117357254,
-0.010263236239552498,
-0.008329324424266815,
0.0037909166421741247,
0.02683676965534687,
-0.0012548202648758888,
-0.02837331034243107,
0.041519057005643845,
0.006501621101051569,
0.026399897411465645,
-0.010305971838533878,
0.023819101974368095,
0.07257018238306046,
0.030113795772194862,
-0.007015015464276075,
0.016839487478137016,
-0.0698307603597641,
-0.015110205858945847,
0.026093358173966408,
0.01698174700140953,
0.01032460667192936,
0.0034344939049333334,
-0.03291128948330879,
-0.03352776914834976,
0.07320356369018555,
-0.02733706682920456,
0.02302670292556286,
-0.007120701018720865,
0.009950307197868824,
0.02063598297536373,
-0.04123669117689133,
-0.03416573628783226,
0.011990553699433804,
-0.019546009600162506,
0.02808411978185177,
-0.02120506763458252,
0.004076535813510418,
-0.00841523613780737,
0.022124480456113815,
0.007917407900094986,
0.06214336305856705,
0.05135645344853401,
0.0060568517073988914,
-0.021247414872050285,
0.046200938522815704,
-0.03977586701512337,
-0.08735297620296478,
-0.01356913149356842,
-0.010620958171784878,
0.01189032755792141,
0.019929418340325356,
-0.003870852757245302,
-0.014092417433857918,
0.04561303183436394,
0.0233230609446764,
-0.0006277637439779937,
0.01324797049164772,
-0.0433979406952858,
0.01672443374991417,
0.04148109257221222,
0.02281227894127369,
0.06503374874591827,
0.022506847977638245,
0.012343441136181355,
-0.0007474605808965862,
-0.00553381722420454,
0.0006667074630968273,
-0.0050296420231461525,
-0.02534303069114685,
-0.02917228266596794,
0.006848185323178768,
-0.01977151818573475,
0.053114283829927444,
-0.019796527922153473,
0.017544390633702278,
-0.027235988527536392,
0.0019588943105190992,
-0.02721402980387211,
0.005175620783120394,
0.0249283779412508,
-0.018928593024611473,
0.02767784334719181,
0.016104254871606827,
0.03536662459373474,
-0.027285723015666008,
-0.004640469327569008,
-0.015587194822728634,
-0.015341326594352722,
0.0025324441958218813,
0.002577886451035738,
0.036947447806596756,
-0.0006641917279921472,
-0.03321395814418793,
-0.005918429233133793,
-0.06886611878871918,
0.046737927943468094,
0.02591569535434246,
0.007790008094161749,
0.00853770412504673,
-0.015442955307662487,
-0.04621915519237518,
-0.019662652164697647,
-0.004932447802275419,
0.016903867945075035,
-0.08432383835315704,
0.030246052891016006,
0.009697049856185913,
0.03757738694548607,
-0.10425207018852234,
-0.049112170934677124,
-0.014231485314667225,
-0.0020095135550945997,
-0.038418032228946686,
-0.03107447177171707,
0.007702493108808994,
-0.058831874281167984,
-0.024728922173380852,
-0.015037299133837223,
0.03692404553294182,
-0.0065401471219956875,
0.016867483034729958,
-0.022374959662556648,
0.013042433187365532,
0.018978925421833992,
-0.04488671198487282,
-0.006514022126793861,
-0.0035267507191747427,
-0.02747979201376438,
-0.014278843067586422,
-0.04019278287887573,
0.04229135066270828,
-0.02066821977496147,
0.00392918661236763,
-0.004501701798290014,
-0.031773410737514496,
0.032400768250226974,
-0.02027401700615883,
-0.011243553832173347,
-0.00018429520423524082,
0.03342384845018387,
0.008951012045145035,
-0.01795503869652748,
-0.026017874479293823,
0.000398130709072575,
0.01554641779512167,
0.00540615851059556,
0.010738787241280079,
-0.03201815485954285,
-0.005715740378946066,
0.04190864786505699,
-0.0006668417481705546,
-0.007956990040838718,
-0.007003627717494965,
0.09053325653076172,
-0.010189631953835487,
0.015095677226781845,
0.03812609240412712,
0.04040524736046791,
-0.03317725285887718,
-0.01926213689148426,
0.01977086439728737,
0.04167983680963516,
-0.014811595901846886,
-0.016169875860214233,
-0.011133052408695221,
-0.023656656965613365,
0.05133529379963875,
0.04760676249861717,
-0.020997755229473114,
0.05247894302010536,
0.003847019746899605,
-0.027508025988936424,
0.026189366355538368,
0.0038582421839237213,
-0.04928162321448326,
0.00820032600313425,
-0.003588352119550109,
0.047255538403987885,
-0.019643055275082588,
0.007142335642129183,
0.019360197708010674,
0.03138038143515587,
-0.0577547550201416,
0.04667244106531143,
0.0201459601521492,
0.005880151409655809,
-0.0014065838186070323,
0.009201336652040482,
-0.02584472857415676,
0.047133106738328934,
-0.03448472544550896,
0.034388549625873566,
-0.004136267118155956,
-0.003236564574763179,
0.01474374532699585,
0.0011091980850324035,
-0.006013310980051756,
-0.009498407132923603,
-0.03190348297357559,
-0.0259197149425745,
0.014145147055387497,
0.055738989263772964,
0.0020200598519295454,
0.03422074392437935,
0.035617150366306305,
0.039465706795454025,
-0.006332626100629568,
0.006894015707075596,
0.0077586667612195015,
-0.04984443634748459,
-0.010932273231446743,
-0.03180301561951637,
-0.04229402914643288,
0.06356266140937805,
-0.03556591272354126,
-0.008944567292928696,
0.016064124181866646,
-0.004640894941985607,
0.0395372100174427,
-0.00006236501940293238,
-0.00015264084504451603,
0.015446767210960388,
0.13330350816249847,
0.027634138241410255,
0.02306376025080681,
0.0017829292919486761,
-0.0005893858615309,
0.11099206656217575,
0.08209077268838882,
0.02946188859641552,
-0.09220543503761292,
-0.006353569682687521,
-0.012297973968088627,
-0.007976371794939041,
-0.034065112471580505,
0.028824087232351303,
0.019596638157963753,
-0.02093375287950039,
-0.045048460364341736,
0.07548628002405167,
-0.02597993239760399,
-0.000876485020853579,
0.01827545277774334,
-0.013879423029720783,
-0.05291564390063286,
-0.0026555999647825956,
0.01789241097867489,
-0.03238137066364288,
-0.00395677424967289,
-0.0664425939321518,
0.02356676757335663,
-0.011212526820600033,
0.0067157261073589325,
-0.02861049771308899,
-0.04821588844060898,
0.042601969093084335,
-0.0015511553501710296,
-0.01599826104938984,
-0.024944409728050232,
-0.009464031085371971,
0.016576573252677917,
-0.030291644856333733,
-0.04931400343775749,
0.0035707259085029364,
-0.014937451109290123,
0.0711505115032196,
0.06074444577097893,
0.0022574521135538816,
0.03948729485273361,
-0.015702493488788605,
-0.0009493325487710536,
-0.03602800518274307,
-0.032372165471315384,
-0.02506369911134243,
0.07518438249826431,
-0.02313128113746643,
-0.028270231559872627,
0.0020481296814978123,
0.031270772218704224,
-0.002254799474030733,
-0.03022358939051628,
-0.02320363186299801,
-0.012714425101876259,
0.02475905977189541,
-0.01668773777782917,
0.0009938058210536838,
-0.02803518995642662,
-0.0047943126410245895,
0.01131982821971178,
0.023085983470082283,
-0.024201948195695877,
0.036488860845565796,
-0.03458121791481972,
-0.01304619014263153,
0.005214022472500801,
-0.020767327398061752,
-0.01661384105682373,
-0.054397422820329666,
-0.031028475612401962,
-0.0331960991024971,
-0.019809439778327942,
0.00996257085353136,
0.02400793507695198,
0.01594817452132702,
-0.010152140632271767,
-0.019030997529625893,
-0.032832998782396317,
-0.06989923864603043,
0.014838460832834244,
-0.03070220537483692,
-0.011954897083342075,
0.0006471186061389744,
-0.0017701562028378248,
-0.001902268035337329,
0.04295608773827553,
-0.00472621712833643,
-0.004810001701116562,
0.02375718578696251,
0.058254681527614594,
0.005400525871664286,
-0.0502748042345047,
-0.03632420301437378,
-0.013751225546002388,
-0.02177562564611435,
0.030004743486642838,
-0.00788918137550354,
-0.01885119453072548,
-0.011537083424627781,
0.0304317194968462,
-0.015867037698626518,
0.041376374661922455,
0.025802619755268097,
0.0006768297753296793,
0.0001941923110280186,
-0.015149618498980999,
-0.0004018234903924167,
0.03321182355284691,
0.017205165699124336,
-0.00526654114946723,
-0.023156223818659782,
-0.009895321913063526,
-0.012275412678718567,
-0.011972780339419842,
-0.005039524752646685,
-0.04352188855409622,
0.0009900646982714534,
-0.01836887188255787,
0.005623676348477602,
0.010421780869364738,
0.01656464673578739,
-0.03952116146683693,
0.02641485072672367,
-0.029925761744379997,
0.004248299170285463,
-0.04173552617430687,
0.0037079299800097942,
-0.01884308084845543,
0.004077805206179619,
-0.02105870097875595,
0.0025182210374623537,
0.0028312173672020435,
-0.023339558392763138,
-0.006400547921657562,
0.03246796876192093,
0.030667422339320183,
0.030665498226881027,
-0.014651846140623093,
0.02221287600696087,
-0.053696878254413605,
-0.016674363985657692,
0.06326065957546234,
0.034793201833963394,
0.040521953254938126,
0.0482339933514595,
-0.01944812200963497,
-0.0009931474924087524,
0.041904184967279434,
0.0134877385571599,
-0.01044334564357996,
0.0034752897918224335,
-0.05811676010489464,
-0.011724723502993584,
-0.01713857613503933,
0.028640033677220345,
0.019358158111572266,
0.003288566367700696,
-0.004982044920325279,
0.01318322867155075,
-0.022686658427119255,
0.013742953538894653,
0.030476374551653862,
-0.012952486053109169,
0.019542928785085678,
-0.008059617131948471,
-0.010652988217771053,
0.025505002588033676,
0.0424395352602005,
-0.009716860018670559,
-0.010434248484671116,
0.002430886495858431,
0.00540853152051568,
-0.08046583831310272,
-0.01004405040293932,
-0.019011782482266426,
-0.024589262902736664,
0.062054891139268875,
-0.06682457029819489,
0.028492502868175507,
0.03432360664010048,
-0.0220482237637043,
-0.0217795018106699,
-0.03893061727285385,
-0.040711015462875366,
-0.007023389916867018,
-0.016826365143060684,
-0.005124988500028849,
0.06169833615422249,
0.030817123129963875,
0.015727050602436066,
0.050437308847904205,
0.01830240711569786,
0.003140052780508995,
-0.017237048596143723,
0.008110396564006805,
0.0061044576577842236,
0.003942549228668213,
-0.02597571723163128,
0.06598442792892456,
-0.0022385441698133945,
-0.06664871424436569,
0.022264963015913963,
0.02386040799319744,
-0.013667069375514984,
-0.0022643497213721275,
0.015404408797621727,
-0.011133239604532719,
0.03656556084752083,
0.03493015468120575,
0.007402205374091864,
0.039127279072999954,
-0.003485057270154357,
0.05012895539402962,
0.0026413018349558115,
-0.0643840804696083,
0.0008875229395925999,
0.01745269075036049,
-0.006167719140648842,
-0.02638980932533741,
0.06554308533668518,
-0.02254040539264679,
-0.03685692697763443,
-0.02461700141429901,
-0.01675276644527912,
0.04646001756191254,
-0.0491286925971508,
0.017672747373580933,
-0.036079153418540955,
0.001818940625526011,
0.03232525289058685,
-0.01805095002055168,
-0.022094406187534332,
0.010125691071152687,
-0.00678179832175374,
-0.054753828793764114,
0.0072598508559167385,
0.014960628002882004,
-0.0027942750602960587,
-0.061845846474170685,
-0.022078564390540123,
-0.009467138908803463,
-0.02000221610069275,
-0.010266214609146118,
-0.01308163907378912,
-0.06283050030469894,
0.04242701828479767,
-0.014571422711014748,
0.00043014943366870284,
0.016635527834296227,
-0.0025489218533039093,
0.008078478276729584,
-0.047140564769506454,
-0.007902693934738636,
0.03547842055559158,
-0.05929768085479736,
-0.011992428451776505,
-0.00019471418636385351,
-0.0019586998969316483,
-0.00002267443051096052,
0.0281255841255188,
-0.00974011979997158,
-0.011253484524786472,
0.014419225975871086,
0.022432725876569748,
0.02088424563407898,
-0.037420306354761124,
-0.043746404349803925,
0.01934419386088848,
-0.02634092979133129,
-0.032877858728170395,
0.027325458824634552,
0.010706760920584202,
0.010133453644812107,
-0.0044209910556674,
0.03690631315112114,
-0.004009851720184088,
0.015756573528051376,
-0.042246438562870026,
0.014524615369737148,
-0.008711174130439758,
0.007487866561859846,
0.03372280299663544,
0.03581817075610161,
0.022228993475437164,
0.05548160523176193,
-0.03764159977436066,
-0.020684165880084038,
0.012236415408551693,
-0.03928571194410324,
-0.03248588740825653,
0.017042752355337143,
0.011219605803489685,
-0.0022506951354444027,
-0.0593000166118145,
-0.010567689314484596,
0.047610729932785034,
-0.04034755006432533,
-0.020725760608911514,
0.04495982825756073,
0.0018309481674805284,
0.05710265040397644,
0.020359590649604797,
0.01968587003648281,
0.026159226894378662,
-0.001138935680501163,
0.022540975362062454,
0.023698240518569946,
0.037429001182317734,
-0.016541682183742523,
-0.008518420159816742,
0.03695804998278618,
-0.04517517238855362,
0.02773115783929825,
0.004269236233085394,
0.032460786402225494,
-0.018229341134428978,
0.017375275492668152,
0.016629014164209366,
-0.007468711584806442,
0.03970622271299362,
0.0007019593031145632,
-0.01688440889120102,
0.06134916469454765,
-0.045820850878953934,
-0.00819654855877161,
-0.014611559920012951,
-0.014288944192230701,
-0.03763706982135773,
0.02407444640994072,
0.033401280641555786,
0.06795156747102737,
-0.004406894091516733,
-0.01380591094493866,
-0.033075544983148575,
-0.009763997048139572,
0.034896403551101685,
-0.020528854802250862,
-0.0041674361564219,
0.013362477533519268,
-0.011368227191269398,
-0.010390039533376694,
-0.01820315606892109,
-0.009635870344936848,
-0.02175150066614151,
0.008210905827581882,
0.01856395974755287,
0.04111262410879135,
-0.009563164785504341,
-0.016945848241448402,
-0.030977198854088783,
0.06320668011903763,
-0.054193802177906036,
-0.03937387093901634,
-0.03099755570292473,
0.008948408998548985,
-0.014900964684784412,
0.007332868408411741
] |
<p>how electronic ink display retains the particles on top of micro capsule when
charge on electrode is released or when device is powered off?</p>
<p>Doesnt that make particles loose on the dielectric fluid on capsule after volatge on electrode is removed?</p>
<p>How e ink maintains image even when device is powered off?</p>
<p>I have understood basics of E ink , couldnt understand this part</p>
| 9,609 |
[
-0.028382040560245514,
-0.03856366127729416,
0.05213479697704315,
0.012131291441619396,
-0.01396900974214077,
-0.006122687831521034,
-0.031190183013677597,
0.0037593499291688204,
0.0010295609245076776,
-0.015608563087880611,
0.014841658994555473,
0.05109632387757301,
0.04182709380984306,
0.01094569731503725,
-0.01641792245209217,
-0.008431628346443176,
0.02079990692436695,
-0.04625338688492775,
0.014988989569246769,
-0.01342359371483326,
-0.04955500736832619,
-0.004715671297162771,
0.014597207307815552,
0.019002357497811317,
-0.03591204807162285,
0.024640550836920738,
0.031235836446285248,
-0.009877227246761322,
0.03320668637752533,
0.062317002564668655,
-0.02791127748787403,
-0.03130589425563812,
-0.017100417986512184,
-0.02052467130124569,
-0.007995382882654667,
-0.037751320749521255,
-0.02754373848438263,
-0.05366804078221321,
0.0055934954434633255,
-0.008494218811392784,
-0.007372383959591389,
-0.002321970649063587,
0.021340856328606606,
0.05476832389831543,
-0.018951747566461563,
-0.00640110345557332,
-0.012009861879050732,
0.007250810042023659,
0.048568565398454666,
-0.08743756264448166,
0.02087520807981491,
-0.007530823349952698,
0.06173465773463249,
0.02836129441857338,
0.023341044783592224,
0.01803503930568695,
0.06687653809785843,
0.08593523502349854,
-0.008303586393594742,
-0.032372694462537766,
0.002684080507606268,
-0.00867453869432211,
-0.01570221036672592,
-0.02389606647193432,
-0.039036743342876434,
0.00939162913709879,
0.011540411040186882,
-0.019372662529349327,
0.036443617194890976,
-0.0013529547723010182,
0.005584768019616604,
-0.006524926051497459,
-0.021331101655960083,
-0.025198372080922127,
0.043108172714710236,
-0.044650543481111526,
0.005736652296036482,
0.034792087972164154,
0.029436202719807625,
0.06634471565485,
0.013615366071462631,
0.01854206807911396,
0.018659193068742752,
0.04420500993728638,
-0.0032827791292220354,
-0.016559133306145668,
0.06192369386553764,
-0.0023110045585781336,
0.05882112309336662,
0.05615578219294548,
-0.002816111082211137,
0.03233275189995766,
0.04983961954712868,
0.03409406915307045,
-0.052744437009096146,
0.027840593829751015,
0.0082148602232337,
0.04499402642250061,
-0.01824396289885044,
-0.03628770262002945,
0.034875303506851196,
0.024884235113859177,
0.036220043897628784,
0.05980667471885681,
0.005297854542732239,
-0.018983710557222366,
-0.016294581815600395,
-0.0018359336536377668,
-0.013845697045326233,
0.027743585407733917,
-0.033786069601774216,
-0.03421095758676529,
-0.0035569886676967144,
-0.016074536368250847,
0.02858828939497471,
0.008114549331367016,
0.02248043194413185,
-0.01923440955579281,
0.035877764225006104,
0.06020338460803032,
0.0036823777481913567,
-0.01074974238872528,
-0.001370903686620295,
-0.026078978553414345,
-0.0805141031742096,
0.04052140191197395,
0.0180645864456892,
0.02330791763961315,
-0.03711172938346863,
0.03221994265913963,
-0.029947884380817413,
-0.007951187901198864,
0.03637206181883812,
-0.009996801614761353,
0.021934347227215767,
0.024408727884292603,
-0.0902816578745842,
-0.00046914847916923463,
0.03649606928229332,
-0.02926989085972309,
0.006008577067404985,
-0.08076804131269455,
-0.013438542373478413,
0.03516368567943573,
0.026908790692687035,
-0.0073820422403514385,
-0.005399222485721111,
-0.02746177837252617,
0.036124370992183685,
0.0020961659029126167,
-0.0022602081298828125,
-0.012307984754443169,
0.030536964535713196,
-0.013566452078521252,
0.008714832365512848,
-0.047076113522052765,
0.023558756336569786,
0.04376360401511192,
-0.0009066201164387167,
-0.04683339595794678,
0.04526285454630852,
-0.014205703511834145,
0.01704990305006504,
-0.01713130623102188,
0.018544431775808334,
-0.049958236515522,
0.046822816133499146,
0.03884660452604294,
0.029873153194785118,
0.023352883756160736,
0.007295458577573299,
0.0749865472316742,
-0.010119597427546978,
0.00975106842815876,
0.02732960134744644,
-0.010339975357055664,
-0.020858239382505417,
-0.05264941602945328,
0.03211216628551483,
0.024869441986083984,
-0.06425133347511292,
-0.041416168212890625,
0.015174615196883678,
0.04438187927007675,
0.0032514389604330063,
-0.018028749153017998,
0.0030541911255568266,
-0.01856100931763649,
-0.031087657436728477,
-0.027911674231290817,
-0.06251285970211029,
-0.05860510095953941,
0.08207782357931137,
-0.006438797805458307,
-0.040640201419591904,
0.014024011790752411,
-0.0422288179397583,
0.008047248236835003,
-0.008150558918714523,
0.004390536807477474,
-0.045058608055114746,
0.015601497143507004,
-0.024766085669398308,
-0.018783824518322945,
-0.016252953559160233,
0.019716573879122734,
0.0015686382539570332,
-0.00635168980807066,
-0.012382176704704762,
-0.014996319077908993,
-0.0014834695030003786,
-0.03748597949743271,
0.025164049118757248,
0.020443784072995186,
-0.012851833365857601,
-0.056177590042352676,
0.032528165727853775,
0.02958705835044384,
0.021244952455163002,
0.021039653569459915,
-0.022850198671221733,
0.048506613820791245,
0.06812393665313721,
-0.010636959224939346,
0.01333946269005537,
0.030410075560212135,
0.007264250889420509,
0.01566263847053051,
0.031430602073669434,
-0.005051581189036369,
-0.03628314286470413,
0.005919191054999828,
-0.0050761522725224495,
0.043588388711214066,
-0.008176448754966259,
0.02790994569659233,
0.026309797540307045,
0.012512370944023132,
0.010752231813967228,
-0.00032546365400776267,
-0.004846388474106789,
-0.03196784108877182,
0.035577528178691864,
0.038409970700740814,
-0.03109694831073284,
0.0020329048857092857,
-0.0074754152446985245,
-0.015508294105529785,
-0.000984936603344977,
-0.0014946049777790904,
-0.017904167994856834,
0.042906127870082855,
0.013808528892695904,
0.015065545216202736,
-0.025275832042098045,
-0.028099026530981064,
0.02738203853368759,
-0.05961371213197708,
0.022684121504426003,
0.0023158076219260693,
0.00989298615604639,
0.0025487453676760197,
-0.04279640316963196,
-0.020473740994930267,
-0.02367549203336239,
0.027586115524172783,
-0.013821056112647057,
-0.05253824219107628,
0.0024733743630349636,
-0.011084557510912418,
0.029865384101867676,
0.008589569479227066,
-0.018908122554421425,
-0.021524619311094284,
0.04959197714924812,
0.06692107021808624,
0.005242816638201475,
0.017131518572568893,
-0.035494521260261536,
-0.04200612008571625,
-0.003484695218503475,
-0.021876132115721703,
-0.017010508105158806,
-0.0196657944470644,
-0.07868169248104095,
0.0046689570881426334,
-0.031802114099264145,
-0.015520308166742325,
0.06911971420049667,
0.0014505647122859955,
0.021672101691365242,
-0.003465883433818817,
-0.0058187213726341724,
-0.04201124981045723,
-0.0054872590117156506,
-0.0054570212960243225,
-0.013370752334594727,
0.0172153040766716,
-0.03284464776515961,
0.021436171606183052,
0.00016662805865053087,
-0.022026319056749344,
0.021032629534602165,
-0.053039759397506714,
-0.02591843344271183,
-0.007168328855186701,
0.0040405816398561,
0.023050004616379738,
-0.0541733093559742,
0.03681549057364464,
0.03824061155319214,
-0.027563050389289856,
-0.016996154561638832,
-0.056634917855262756,
-0.03690054640173912,
0.03613574057817459,
-0.03637963533401489,
0.036101292818784714,
-0.04088227078318596,
-0.006446013227105141,
0.0542125403881073,
-0.0029193898662924767,
-0.05213618278503418,
0.0015132289845496416,
-0.026336366310715675,
-0.039713505655527115,
-0.033533837646245956,
-0.02594771794974804,
0.042859986424446106,
-0.007467427756637335,
-0.017409689724445343,
0.025516701862215996,
0.001321552786976099,
0.01268253568559885,
-0.0030167135410010815,
-0.01955990307033062,
-0.026048045605421066,
0.018321584910154343,
-0.003327131737023592,
0.012522362172603607,
0.024967821314930916,
-0.021221444010734558,
0.02335331216454506,
0.00616174703463912,
0.07554131746292114,
0.006893650628626347,
-0.04987672343850136,
0.006993175484240055,
-0.02979043498635292,
0.005856256932020187,
-0.004379736725240946,
0.03545631468296051,
-0.00018137606093659997,
-0.0010742309968918562,
-0.011464725248515606,
0.010957549326121807,
0.07199214398860931,
-0.014069333672523499,
-0.012388237752020359,
0.04254968464374542,
0.038479141891002655,
-0.008590901270508766,
-0.04530773684382439,
0.011199715547263622,
0.0032546150032430887,
0.020021088421344757,
-0.07254110276699066,
-0.024306317791342735,
0.027682660147547722,
-0.00015306008572224528,
0.03706852346658707,
0.022210340946912766,
-0.046539098024368286,
-0.018887072801589966,
-0.08302810788154602,
-0.004677766002714634,
0.04810899496078491,
0.04497142136096954,
-0.011006827466189861,
0.07006221264600754,
0.007007126230746508,
0.029391417279839516,
-0.012619486078619957,
0.01844283938407898,
-0.08456932753324509,
0.028606006875634193,
0.029198458418250084,
-0.015297920443117619,
-0.017849741503596306,
0.03300340101122856,
0.013052276335656643,
-0.037691760808229446,
-0.025795524939894676,
-0.007518528029322624,
0.025408247485756874,
-0.036813993006944656,
0.014240551739931107,
-0.005415099672973156,
-0.011957727372646332,
-0.03843868151307106,
0.03384597226977348,
-0.015081200748682022,
-0.015083793550729752,
0.04135706275701523,
0.039793554693460464,
-0.0662679448723793,
-0.01676288992166519,
0.03814341500401497,
-0.025335608050227165,
0.03172176703810692,
0.020468760281801224,
0.04043416306376457,
0.0064667207188904285,
0.013943235389888287,
-0.01737094484269619,
0.018512289971113205,
0.06010716035962105,
0.020025266334414482,
-0.008561229333281517,
-0.025805598124861717,
-0.04572632163763046,
-0.05447685346007347,
0.004707711283117533,
0.026296256110072136,
0.006220887415111065,
-0.0036992167588323355,
0.024980666115880013,
-0.028311362490057945,
-0.009391093626618385,
0.027695149183273315,
0.04151918739080429,
0.03592636436223984,
-0.00770085584372282,
-0.057296764105558395,
0.03306867182254791,
-0.012522634118795395,
0.02051623724400997,
0.03631255030632019,
0.03164907544851303,
-0.027015486732125282,
-0.005388443358242512,
0.016719738021492958,
-0.02257855422794819,
0.000967787520494312,
-0.03652265667915344,
-0.012099865823984146,
-0.01360492967069149,
-0.033244531601667404,
0.028172671794891357,
0.047114767134189606,
0.048576921224594116,
0.012153182178735733,
0.04998960718512535,
-0.01900688372552395,
-0.07981736212968826,
-0.011867513880133629,
0.027654245495796204,
0.0503075048327446,
-0.017338665202260017,
-0.005183506291359663,
-0.08139105141162872,
-0.02098134718835354,
0.023952364921569824,
-0.041803088039159775,
0.004859751556068659,
-0.029173729941248894,
-0.002732509048655629,
-0.023761408403515816,
-0.009268789552152157,
0.017540644854307175,
-0.0015731415478512645,
-0.032997481524944305,
0.03076104447245598,
-0.033810149878263474,
-0.006748252082616091,
-0.021997053176164627,
0.017490962520241737,
-0.00007570136949652806,
0.0660526230931282,
-0.013189922086894512,
0.019633473828434944,
-0.010008198209106922,
-0.003015731694176793,
-0.05952826142311096,
-0.062902070581913,
-0.00409273337572813,
-0.04329709708690643,
0.010731949470937252,
0.04246360808610916,
-0.005038372706621885,
-0.013208662159740925,
0.0048782904632389545,
0.04665530472993851,
-0.0021538001019507647,
-0.06364241987466812,
-0.047212500125169754,
0.010157795622944832,
-0.016561131924390793,
-0.05711880698800087,
0.0031508200336247683,
-0.0012122915359213948,
0.0020276205614209175,
0.020657142624258995,
-0.023414330556988716,
0.025695526972413063,
-0.046984679996967316,
-0.0019632040057331324,
-0.01388955395668745,
0.03627621755003929,
-0.036459796130657196,
0.058608803898096085,
0.021766643971204758,
0.019457101821899414,
-0.027265707030892372,
-0.03997248411178589,
0.011542066000401974,
0.02798759937286377,
0.01246096845716238,
0.010125410743057728,
-0.018594883382320404,
-0.001214527990669012,
0.0013750771759077907,
-0.016915734857320786,
0.01789809949696064,
-0.008636855520308018,
-0.007277217227965593,
0.008279533125460148,
-0.01869628019630909,
0.004395436495542526,
-0.009427297860383987,
0.006802167743444443,
-0.0006235527107492089,
-0.02563498727977276,
0.025905244052410126,
-0.009708317928016186,
0.0174153670668602,
0.0238620825111866,
-0.07642156630754471,
-0.035102471709251404,
0.029728131368756294,
-0.019161678850650787,
0.036330122500658035,
-0.03802306205034256,
0.05459359660744667,
0.02684544399380684,
0.01242789439857006,
-0.030458146706223488,
-0.05161106958985329,
0.02892228029668331,
0.03147818520665169,
-0.023738518357276917,
-0.008167588151991367,
0.03511390835046768,
-0.023837337270379066,
-0.038619264960289,
0.030983146280050278,
-0.004926673136651516,
-0.020588399842381477,
-0.0013708581682294607,
0.033293966203927994,
-0.013944840058684349,
0.0469987653195858,
0.007979214191436768,
-0.015728600323200226,
-0.017628325149416924,
0.0007127727731131017,
0.001359768444672227,
-0.04466281831264496,
0.03249571472406387,
0.012654082849621773,
-0.020575789734721184,
-0.004610032308846712,
-0.0017383532831445336,
0.024938877671957016,
-0.034950513392686844,
0.0021219097543507814,
-0.014869743958115578,
0.01866498775780201,
-0.0014596304390579462,
-0.019357234239578247,
0.021300608292222023,
-0.010170289315283298,
0.052347324788570404,
0.001154187135398388,
-0.00654113432392478,
-0.027789480984210968,
-0.022978344932198524,
0.011141437105834484,
-0.0007326769409701228,
0.030058899894356728,
0.006366399582475424,
0.06661630421876907,
-0.030212828889489174,
0.031254734843969345,
0.01965414546430111,
-0.03532017394900322,
0.01262402068823576,
-0.05224573612213135,
-0.007631298154592514,
-0.0010177221847698092,
0.014930728822946548,
0.012273631058633327,
0.012450059875845909,
-0.054840877652168274,
-0.00798159372061491,
0.0167445819824934,
0.0027528684586286545,
0.027029113844037056,
0.02335711382329464,
0.004437834955751896,
-0.02547571249306202,
-0.01777622476220131,
-0.0066759418696165085,
0.0024765089619904757,
-0.05214664712548256,
0.044049907475709915,
0.0039578028954565525,
-0.014424804598093033,
-0.006224324926733971,
0.07544434815645218,
-0.03872371092438698,
-0.0015390128828585148,
0.04223975911736488,
0.02194926328957081,
0.007909543812274933,
-0.023873306810855865,
-0.046231843531131744,
0.02920457534492016,
-0.023535506799817085,
0.06304191052913666,
-0.002804623683914542,
-0.043558742851018906,
0.044273845851421356,
0.009549848735332489,
-0.001873405184596777,
-0.023885339498519897,
-0.010460253804922104,
-0.040799323469400406,
0.03706299513578415,
0.015253798104822636,
-0.026274120435118675,
-0.03825042396783829,
0.007044758182018995,
0.025080326944589615,
-0.011978741735219955,
0.02094276249408722,
-0.01780351623892784,
-0.056541383266448975,
-0.02226880192756653,
0.003794742515310645,
-0.0024809411261230707,
0.01954694837331772,
-0.014472580514848232,
0.02931232750415802,
-0.013524933718144894,
0.0011855829507112503,
0.04023738577961922,
0.026532955467700958,
0.027080360800027847,
-0.0013382293982431293,
0.0453944094479084,
0.0003494965785648674,
0.034841086715459824,
-0.013813257217407227,
0.015472430735826492,
0.12850509583950043,
0.050907690078020096,
0.008481595665216446,
-0.0586983785033226,
-0.03700181841850281,
-0.009276995435357094,
0.026187581941485405,
-0.023026496171951294,
0.042714931070804596,
-0.023734821006655693,
0.045361436903476715,
0.03211662545800209,
0.04222704470157623,
0.020187780261039734,
0.021075347438454628,
-0.005320432595908642,
-0.036615919321775436,
-0.07803777605295181,
-0.023607896640896797,
-0.007110079284757376,
-0.05278650298714638,
0.05266421660780907,
-0.09458591789007187,
0.025386767461895943,
0.0192799624055624,
-0.03173067793250084,
-0.05300327017903328,
-0.05020669102668762,
0.03605112433433533,
-0.011150741949677467,
-0.00963793694972992,
-0.04028022661805153,
-0.032960619777441025,
-0.008161555044353008,
-0.04936014115810394,
0.0073708426207304,
-0.0222291499376297,
0.007819067686796188,
-0.003028247272595763,
0.024042436853051186,
0.01961761899292469,
-0.015734028071165085,
0.03942733630537987,
0.020264796912670135,
-0.013673660345375538,
0.026910658925771713,
-0.03614503890275955,
0.08483850955963135,
-0.04396570101380348,
0.008455333299934864,
-0.0028836107812821865,
0.00683897128328681,
-0.023731183260679245,
-0.04417203366756439,
-0.059072114527225494,
0.033124104142189026,
-0.0017306439112871885,
-0.005732933059334755,
-0.0064741140231490135,
-0.036240722984075546,
0.00012578153109643608,
0.00004283899033907801,
0.009658989496529102,
0.01351845357567072,
0.037650417536497116,
-0.0001550788147142157,
0.0010027772514149547,
0.02867303602397442,
-0.02714192308485508,
0.0002609951770864427,
0.011081766337156296,
-0.014416202902793884,
-0.038944851607084274,
-0.017112020403146744,
0.01871778443455696,
0.05083499103784561,
0.013137968257069588,
-0.002090993570163846,
-0.018444588407874107,
0.007256971672177315,
-0.06401599198579788,
0.08342305570840836,
0.02186286449432373,
-0.0109390364959836,
-0.032884374260902405,
0.02219243533909321,
0.04772660508751869,
0.04007307067513466,
-0.017479319125413895,
0.00730019761249423,
-0.0052319779060781,
0.026336513459682465,
-0.014237540774047375,
-0.028744075447320938,
-0.0069052185863256454,
0.023637128993868828,
-0.03992896154522896,
0.02025020495057106,
-0.045081231743097305,
0.03673015534877777,
-0.00258184433914721,
0.016243165358901024,
0.0019396062707528472,
0.013602842576801777,
-0.020625732839107513,
-0.009246984496712685,
-0.00798385962843895,
0.0059946454130113125,
0.01329660415649414,
-0.0039620730094611645,
-0.0030169538222253323,
-0.015138701535761356,
-0.000575889484025538,
-0.008365029469132423,
-0.01571350358426571,
0.003403657814487815,
0.029701929539442062,
0.012991384603083134,
0.009797901846468449,
-0.044310152530670166,
0.061789169907569885,
-0.02127828449010849,
-0.004441840574145317,
-0.07653771340847015,
0.0018617918249219656,
0.04067809879779816,
0.018272506073117256,
-0.0013896776363253593,
0.019507842138409615,
-0.02851935662329197,
0.015948140993714333,
0.004715657792985439,
-0.0069982982240617275,
0.01038876548409462,
-0.003541771322488785,
0.007490859366953373,
-0.018379483371973038,
0.03922241926193237,
-0.015928512439131737,
-0.02157720923423767,
0.04951034113764763,
-0.022678574547171593,
-0.03992346301674843,
-0.03672701120376587,
-0.015726914629340172,
-0.0035182195715606213,
0.061003848910331726,
0.000555941485799849,
0.013207818381488323,
0.054143574088811874,
0.03675375506281853,
-0.024891171604394913,
0.009235035628080368,
-0.0351468101143837,
0.007044724654406309,
-0.0038138930685818195,
-0.015183578245341778,
-0.02129545621573925,
-0.006245066877454519,
0.057628292590379715,
0.03176630660891533,
0.040316469967365265,
-0.025803621858358383,
0.027946069836616516,
0.021726714447140694,
0.036756597459316254,
0.04836089909076691,
0.02789541520178318,
0.016925564035773277,
0.03161589801311493,
-0.019382581114768982,
-0.01179068349301815,
0.009792030788958073,
-0.025158317759633064,
-0.09655297547578812,
-0.025722740218043327,
-0.016401059925556183,
-0.006287859287112951,
0.012085833586752415,
-0.05150298774242401,
-0.007296751253306866,
0.03567224740982056,
-0.08239549398422241,
-0.023191729560494423,
-0.05820881575345993,
-0.028799040243029594,
-0.02616717666387558,
0.030062628909945488,
0.0034972173161804676,
0.04454812780022621,
0.03775928542017937,
0.018284205347299576,
0.024011963978409767,
0.01959685981273651,
-0.006443656515330076,
-0.00922409724444151,
-0.04254545643925667,
0.0665891021490097,
-0.0025619377847760916,
-0.009580777026712894,
0.08509271591901779,
-0.04433056339621544,
0.017774656414985657,
0.02024070732295513,
0.0085340216755867,
0.006572754587978125,
-0.007702155504375696,
0.01735684648156166,
0.007989255711436272,
0.006943947169929743,
-0.00901265162974596,
-0.0025406305212527514,
-0.02432139962911606,
-0.006390929222106934,
0.037576641887426376,
-0.007255468517541885,
0.015756025910377502,
0.015009693801403046,
0.0385851189494133,
0.028818661347031593,
0.025746861472725868,
0.05175290256738663,
-0.015995658934116364,
-0.024416055530309677,
0.019916679710149765,
0.02140244096517563,
0.03511979430913925,
-0.02889605052769184,
0.0011464509880170226,
-0.05000874400138855,
0.002555455546826124,
-0.01748255081474781,
0.052619028836488724,
0.023246625438332558,
0.021147513762116432,
-0.007749789394438267,
-0.042588990181684494,
0.029551949352025986,
-0.0025653953198343515,
-0.002889693249017,
-0.05269206315279007,
0.026388093829154968,
0.022143734619021416,
0.01359814964234829,
0.009486480616033077,
-0.04303782433271408,
-0.023470865562558174,
0.035698987543582916,
0.029698438942432404,
-0.0032594744116067886,
0.012434745207428932,
-0.049425918608903885,
0.009501318447291851,
-0.03888535499572754,
0.012447444722056389,
-0.02561827190220356,
-0.030135324224829674,
-0.03142467886209488,
-0.0593416728079319,
0.012287452816963196,
0.07184614986181259,
0.069656603038311,
-0.002450808882713318,
-0.010852555744349957,
-0.0029919904191046953,
0.0026593527290970087,
0.006414879113435745,
-0.04592576250433922,
0.02223096787929535,
-0.011214087717235088,
-0.004897196311503649,
-0.001087785349227488,
0.04799028858542442,
-0.02795339561998844,
0.017330598086118698,
0.057929787784814835,
-0.03514128178358078,
-0.006818187423050404,
-0.021366896107792854,
-0.020791564136743546,
-0.008677894249558449,
0.047136999666690826,
0.00031536092865280807,
0.11492995917797089,
-0.033414676785469055,
0.010664500296115875,
0.004874557722359896,
0.00525273522362113,
-0.028874050825834274,
0.0042168921791017056,
-0.031055258587002754,
0.016953274607658386,
-0.019273608922958374,
0.010575474239885807,
0.05313214287161827,
-0.05462024360895157,
0.005992414895445108,
-0.026794884353876114,
-0.015992606058716774,
-0.01735302060842514,
0.07718786597251892,
0.019897332414984703,
0.015722770243883133,
0.010333665646612644,
0.013798770494759083,
0.003191035706549883,
0.01761801354587078,
0.005127240903675556,
0.06329396367073059,
0.007689930498600006,
-0.012544834986329079,
0.04174915328621864,
-0.004232568666338921,
0.014185703359544277,
0.05097782611846924,
-0.03891071304678917,
0.006242524366825819,
-0.010706140659749508,
-0.03171217069029808,
-0.001341997180134058,
-0.011251483112573624,
-0.04196647182106972,
0.036188654601573944,
-0.024515416473150253,
0.05827304720878601,
-0.06721457839012146,
0.000051981241995235905,
0.00048153509851545095,
-0.0017466999124735594,
-0.023612190037965775,
0.033661022782325745,
0.030487297102808952,
0.01547275111079216,
0.024958785623311996,
-0.023758387193083763,
-0.012635042890906334,
0.02464788407087326,
0.00860008504241705,
0.005610722117125988,
0.025532912462949753,
-0.008478582836687565,
-0.01855756901204586,
0.009055027738213539,
0.0005813917960040271,
-0.023402204737067223,
-0.00335254636593163,
0.0006312672048807144,
0.013814367353916168,
0.021782414987683296,
0.007867048494517803,
-0.03681716322898865,
-0.03005915880203247,
0.05499478057026863,
-0.03447495400905609,
-0.029104329645633698,
0.014219596050679684,
0.013126064091920853,
-0.0008890090975910425,
-0.003430592129006982
] |
<p>I have a question on the reformulation of the Klein Gordon equation in terms of Killing fields.
Suppose we have a static spacetime with timelike Killingfield $\xi^{\mu}$
(e.g. Schwarzschild).
Then the wave eq. ($\nabla_{\mu}\nabla^{\mu}-m^{2})\phi=0$
can be rewritten in the following form
$$
\partial_{t}^{2}\phi=VD^{i}(VD_{i})\phi-V^{2}m^{2}\phi
$$</p>
<p>with $V^{2}=-\xi_{\mu}\xi^{\mu}$
and $D_{a}$
being the spatial covariant derivative.</p>
<p>Can anybody tell me how this comes about?</p>
| 9,610 |
[
0.027128683403134346,
-0.007191288284957409,
0.03732821345329285,
-0.020793244242668152,
0.05087820440530777,
0.020943596959114075,
-0.038711678236722946,
-0.04339266195893288,
-0.00993140134960413,
-0.02466573938727379,
0.030103862285614014,
0.03457627445459366,
0.047700509428977966,
0.013974372297525406,
0.04088256508111954,
-0.02769060619175434,
-0.04236769303679466,
-0.030337702482938766,
-0.010478649288415909,
-0.025904228910803795,
0.025715090334415436,
0.014008971862494946,
0.006720125209540129,
0.007228043396025896,
-0.01472562924027443,
0.013140524737536907,
0.00192861573304981,
0.0013741633156314492,
-0.007847975939512253,
0.03873605653643608,
-0.006773137487471104,
-0.031382136046886444,
-0.020142382010817528,
0.014328229241073132,
0.003523231251165271,
-0.006830491125583649,
-0.05359082669019699,
-0.052454814314842224,
0.011693382635712624,
0.0196352768689394,
-0.031124060973525047,
-0.02030879445374012,
-0.030634643509984016,
0.07344410568475723,
-0.04513401538133621,
0.017290275543928146,
0.0003700055240187794,
-0.015456958673894405,
0.044045425951480865,
-0.034804899245500565,
0.0921676754951477,
0.0044136447831988335,
0.026961296796798706,
0.025302497670054436,
-0.034910332411527634,
-0.005593703128397465,
0.06603683531284332,
0.06737978011369705,
-0.019973546266555786,
-0.033518701791763306,
-0.021089157089591026,
-0.015057087875902653,
-0.02342393808066845,
-0.016678469255566597,
0.001847826992161572,
0.03884159401059151,
-0.008187803439795971,
-0.01280090119689703,
0.022718727588653564,
-0.024864299222826958,
0.0037742217537015676,
-0.03378155454993248,
0.019437164068222046,
-0.05994069576263428,
-0.0011217084247618914,
-0.014210237190127373,
0.0247699823230505,
0.023899631574749947,
-0.0042645554058253765,
-0.016611022874712944,
-0.010395963676273823,
0.018700920045375824,
0.04484283924102783,
0.06276793777942657,
-0.014289529994130135,
-0.009137674234807491,
0.06331507861614227,
0.004035862162709236,
0.0017732330597937107,
0.03672434762120247,
-0.014975655823946,
0.010099655948579311,
0.03212016448378563,
-0.0219022948294878,
-0.022445006296038628,
0.02733839862048626,
0.002133140806108713,
0.06946978718042374,
0.013429488986730576,
0.0057691605761647224,
-0.012306800112128258,
0.0019003889756277204,
0.011255152523517609,
0.06308578699827194,
0.0112076997756958,
-0.04827378690242767,
-0.06912490725517273,
0.017951790243387222,
-0.03656621649861336,
-0.029270216822624207,
-0.03758607432246208,
0.027008045464754105,
-0.01940198801457882,
-0.02090546488761902,
0.008891207166016102,
-0.025630075484514236,
0.0016128156566992402,
-0.026377851143479347,
0.010017307475209236,
0.043475326150655746,
0.04805240035057068,
-0.0006160112679935992,
0.053328342735767365,
-0.035664934664964676,
-0.06205137446522713,
-0.002656309399753809,
0.04775943607091904,
-0.011239857412874699,
-0.024461613968014717,
-0.01978970132768154,
0.0038940117228776217,
0.0036989410873502493,
-0.004648137371987104,
0.04241900146007538,
0.02863858826458454,
-0.05629067122936249,
-0.11033280193805695,
-0.06690681725740433,
0.002232885919511318,
-0.0389690101146698,
-0.0031970690470188856,
-0.06817668676376343,
-0.01869615912437439,
0.007764194160699844,
0.09869939833879471,
-0.0212546456605196,
0.003941166680306196,
0.01898219622671604,
0.0545419417321682,
-0.00027665437664836645,
-0.0022024086210876703,
-0.02013249509036541,
-0.02263806201517582,
-0.041992586106061935,
0.0017795520834624767,
-0.06548918038606644,
-0.004398675169795752,
0.014493045397102833,
-0.008975272998213768,
-0.01741720177233219,
0.08158387243747711,
0.004693417809903622,
0.012737139128148556,
0.002769079990684986,
-0.03760722279548645,
-0.017633365467190742,
0.08408478647470474,
0.0012239281786605716,
-0.012705818749964237,
0.03649965301156044,
0.0030300761573016644,
0.018126972019672394,
-0.014870736747980118,
0.04935209080576897,
0.03752337396144867,
-0.04031819477677345,
-0.005034665111452341,
-0.001389547367580235,
-0.0004957171040587127,
0.0016162984538823366,
0.018145738169550896,
-0.05462806299328804,
0.00809225719422102,
0.022826390340924263,
0.007572295144200325,
0.040015943348407745,
0.0029563256539404392,
0.0321941077709198,
-0.03358970582485199,
-0.060098182410001755,
-0.0008400680962949991,
-0.033447496592998505,
0.05787200108170509,
0.015542053617537022,
0.00149369309656322,
0.019702386111021042,
0.02190086804330349,
-0.0033552581444382668,
0.0021011484786868095,
-0.041771020740270615,
-0.00274654827080667,
0.03974177688360214,
-0.007718352135270834,
-0.020488908514380455,
0.02050638385117054,
0.012794207781553268,
0.034632835537195206,
0.03419271484017372,
0.04608003795146942,
0.020005986094474792,
-0.012379862368106842,
-0.018083827570080757,
0.014436082914471626,
0.039982136338949203,
-0.021873442456126213,
0.01528443768620491,
0.007977111265063286,
-0.0015021075960248709,
-0.02182077057659626,
0.03561798855662346,
-0.041176121681928635,
0.042664963752031326,
0.07241401076316833,
-0.01354751642793417,
0.0026748981326818466,
0.0562075674533844,
-0.016132760792970657,
0.05121336877346039,
0.03555325046181679,
-0.05786154791712761,
0.000602011161390692,
0.02479511871933937,
0.03328913450241089,
-0.02614377997815609,
-0.061123691499233246,
0.016054607927799225,
0.024245699867606163,
0.03534252941608429,
0.05074504762887955,
0.05544233322143555,
-0.005849609151482582,
-0.044587258249521255,
0.005978989414870739,
0.005935048218816519,
-0.01546911709010601,
-0.0066039059311151505,
0.05778283625841141,
-0.0061530801467597485,
-0.011802691966295242,
-0.00542802456766367,
-0.03492576628923416,
0.02601577341556549,
-0.05471592769026756,
-0.017590492963790894,
0.004580730106681585,
0.0020510952454060316,
0.05164135619997978,
0.011503026820719242,
0.02942994236946106,
0.08420338481664658,
-0.0012431459035724401,
-0.015183557756245136,
-0.03165694326162338,
-0.0016821320168673992,
0.038108017295598984,
-0.005283720325678587,
0.0029069576412439346,
-0.0011328107211738825,
0.0031658150255680084,
-0.04598646238446236,
-0.020210178568959236,
0.0016507748514413834,
0.001769827213138342,
-0.0164154302328825,
0.0021462521981447935,
0.02934344671666622,
0.03584045544266701,
0.0314914770424366,
0.009779557585716248,
-0.03769133612513542,
0.016554445028305054,
0.0035936820786446333,
0.027711085975170135,
0.037964411079883575,
-0.032952312380075455,
0.01210022997111082,
-0.0439179465174675,
-0.03187962621450424,
0.05374424159526825,
-0.0008186711929738522,
0.029081003740429878,
0.012069541960954666,
-0.04541129246354103,
-0.019808761775493622,
-0.024971360340714455,
-0.030474036931991577,
0.024015864357352257,
-0.023510722443461418,
0.03543165698647499,
0.014582219533622265,
0.05689970403909683,
-0.016113227233290672,
0.003476747777312994,
-0.0017680565360933542,
-0.045757416635751724,
-0.02402394264936447,
-0.013472625985741615,
0.04134908691048622,
-0.045336123555898666,
0.06372204422950745,
0.035039011389017105,
-0.03316070884466171,
0.03906531259417534,
-0.04372563585639,
-0.03626425936818123,
0.034339841455221176,
0.026473119854927063,
0.016809538006782532,
-0.004712653812021017,
-0.02883017808198929,
0.08318115025758743,
0.022120893001556396,
-0.020339034497737885,
0.013203030452132225,
0.006219007540494204,
0.00954985897988081,
-0.029815014451742172,
-0.009486254304647446,
-0.00648832181468606,
-0.017504774034023285,
0.02932119555771351,
-0.00309077394194901,
0.02267233468592167,
0.04224362224340439,
-0.002680607372894883,
-0.023501930758357048,
0.01767725870013237,
0.0010937177576124668,
0.0309310220181942,
0.05345825478434563,
-0.012313093058764935,
-0.027509301900863647,
0.015315592288970947,
-0.004687326028943062,
0.0065163616091012955,
-0.00017154346278402954,
-0.024087755009531975,
0.018354391679167747,
0.0057340278290212154,
-0.019625946879386902,
-0.030381258577108383,
0.00910618994385004,
-0.007570598740130663,
-0.018472328782081604,
-0.009206653572618961,
0.0014557972317561507,
0.02762008085846901,
-0.03232307359576225,
-0.008112150244414806,
-0.009687969461083412,
-0.01438869908452034,
-0.02789526991546154,
-0.008569411002099514,
-0.023084621876478195,
0.022344229742884636,
0.06996261328458786,
-0.009395420551300049,
-0.01628194935619831,
0.036710117012262344,
0.023278066888451576,
0.005353765096515417,
-0.012893549166619778,
-0.025740081444382668,
0.013485151343047619,
-0.0900242030620575,
-0.012218915857374668,
0.014748698100447655,
0.044804055243730545,
0.003513183444738388,
0.047366492450237274,
0.05069982632994652,
0.027297457680106163,
0.03545103967189789,
0.03614017367362976,
-0.04652716964483261,
0.01355700846761465,
-0.06934747844934464,
-0.02249528467655182,
-0.027720995247364044,
-0.03223487734794617,
-0.004653211683034897,
-0.020635876804590225,
-0.04096922278404236,
-0.004821083974093199,
-0.03955872356891632,
-0.06600417196750641,
0.019274821504950523,
-0.038981448858976364,
-0.020850835368037224,
-0.03590451553463936,
0.06138439103960991,
0.016068901866674423,
-0.02748168259859085,
-0.03613560274243355,
0.040662962943315506,
-0.036201830953359604,
0.01561546791344881,
-0.017661213874816895,
-0.019398918375372887,
0.0391860157251358,
0.026336416602134705,
0.007711971644312143,
0.033225610852241516,
0.008023649454116821,
0.007662594318389893,
0.016115635633468628,
0.048887304961681366,
0.016605276614427567,
0.009854481555521488,
-0.043076902627944946,
-0.04956060275435448,
0.010881598107516766,
0.01268693245947361,
0.1125541478395462,
0.004102908540517092,
-0.0015330234309658408,
0.004598645027726889,
0.031989458948373795,
-0.0262755099684,
0.011248009279370308,
0.04242488741874695,
-0.023941243067383766,
-0.009047748520970345,
-0.014096086844801903,
0.049302831292152405,
-0.003667275421321392,
-0.02687467448413372,
-0.003618626156821847,
-0.023177549242973328,
-0.011920380406081676,
-0.019274160265922546,
0.002930558519437909,
-0.013517222367227077,
-0.00987832061946392,
0.002700262004509568,
0.036120954900979996,
-0.01811443455517292,
0.022940514609217644,
0.010515175759792328,
0.001198743935674429,
0.06405168771743774,
0.06254591792821884,
0.0014290246181190014,
0.02057689242064953,
-0.061763010919094086,
-0.043613873422145844,
0.030581645667552948,
-0.012719246558845043,
0.025905029848217964,
-0.027386125177145004,
-0.07485723495483398,
-0.022728517651557922,
0.037852030247449875,
-0.0254644975066185,
0.04014156013727188,
0.04439135268330574,
0.012272265739738941,
-0.010946396738290787,
-0.01213755365461111,
-0.023503750562667847,
0.02189994789659977,
-0.007816178724169731,
0.010692637413740158,
-0.02483374997973442,
0.003909548744559288,
-0.03988944739103317,
-0.006955159828066826,
-0.025515366345643997,
0.05151274427771568,
0.01078860368579626,
-0.02676333673298359,
-0.013205832801759243,
0.016699105501174927,
-0.04860163480043411,
-0.06949260830879211,
-0.010395273566246033,
0.04612627625465393,
-0.017683126032352448,
0.06691714376211166,
-0.01526294369250536,
0.0006854694220237434,
0.04244751110672951,
0.020519021898508072,
0.004508409183472395,
0.02608371526002884,
-0.0590292252600193,
0.03697354719042778,
0.0163971446454525,
-0.0040675317868590355,
0.030085489153862,
0.025730235502123833,
-0.013986324891448021,
-0.04076845571398735,
-0.03131834790110588,
0.04434891417622566,
-0.03884667530655861,
0.002606102032586932,
-0.01916518248617649,
0.008532772772014141,
-0.04032111540436745,
0.05707636475563049,
-0.016743188723921776,
-0.000020899942683172412,
-0.0020393470767885447,
-0.011746326461434364,
-0.013020239770412445,
0.04239526018500328,
-0.03397371247410774,
-0.01824578270316124,
0.00010437736636959016,
0.006930557545274496,
0.002984220627695322,
-0.01720813289284706,
0.0309535451233387,
-0.015503196977078915,
-0.0319080576300621,
0.03777032345533371,
-0.015837427228689194,
0.02282770723104477,
-0.01230395957827568,
-0.039884403347969055,
-0.0005555980023927987,
-0.06308232992887497,
0.011806934140622616,
-0.01477812696248293,
-0.027589216828346252,
0.03356747701764107,
-0.04326914995908737,
-0.01849672943353653,
-0.0048828572034835815,
-0.00837806798517704,
0.035629432648420334,
-0.022391648963093758,
0.022745570167899132,
0.07650932669639587,
0.03779323399066925,
-0.09602470695972443,
-0.01935560256242752,
0.031257327646017075,
-0.03849634900689125,
-0.019774332642555237,
-0.027586868032813072,
0.03424486890435219,
-0.019192766398191452,
-0.03140215948224068,
0.014641070738434792,
0.04475979506969452,
-0.03278818354010582,
0.009480315260589123,
-0.016138210892677307,
0.053515784442424774,
0.01889711059629917,
-0.0350668840110302,
-0.024301651865243912,
0.013221542350947857,
-0.03575347363948822,
0.0013782524038106203,
0.030034421011805534,
0.07274122536182404,
-0.014123030938208103,
-0.022931691259145737,
-0.014267297461628914,
-0.00925590842962265,
0.010221712291240692,
0.0010655694641172886,
-0.010952573269605637,
0.03329630568623543,
0.01733246073126793,
0.012821891345083714,
-0.03947680816054344,
-0.02484883740544319,
-0.04901200905442238,
0.025740623474121094,
-0.025538748130202293,
-0.031804099678993225,
-0.005199614446610212,
-0.018043331801891327,
0.01642097905278206,
-0.00408583227545023,
0.02513827383518219,
0.00270273070782423,
0.04858323931694031,
-0.035963501781225204,
-0.006806785706430674,
0.012401927262544632,
-0.011352457106113434,
0.0045053292997181416,
-0.012551670894026756,
0.021723672747612,
0.016375552862882614,
0.0009538677404634655,
-0.024523857980966568,
-0.011487503536045551,
-0.042910341173410416,
0.04043789580464363,
0.10082069784402847,
-0.05191665515303612,
0.023677781224250793,
0.016502084210515022,
0.010746062733232975,
-0.015315685421228409,
-0.028419869020581245,
-0.014848010614514351,
-0.004161314107477665,
-0.002939013997092843,
0.04275455325841904,
-0.04609168693423271,
-0.01880514807999134,
0.022335203364491463,
0.038691889494657516,
-0.028604716062545776,
0.02000281773507595,
-0.01751626841723919,
0.03880386799573898,
0.00252864439971745,
0.021798325702548027,
-0.06489047408103943,
0.013702336698770523,
-0.0070478119887411594,
0.04036952182650566,
0.01830439269542694,
0.01687736064195633,
0.02168600633740425,
0.02432021126151085,
0.028108486905694008,
0.015614664182066917,
-0.0036742377560585737,
-0.05971435457468033,
0.005309492815285921,
0.017070844769477844,
0.008317357860505581,
0.014718504622578621,
0.024346373975276947,
0.04278070107102394,
0.014062362723052502,
0.0022949569392949343,
-0.0006171770510263741,
-0.02215593308210373,
0.007695021107792854,
-0.0435609370470047,
-0.05636415258049965,
0.019120724871754646,
-0.001972713740542531,
-0.013385153375566006,
-0.011095214635133743,
-0.002246666932478547,
0.016228584572672844,
0.003879911731928587,
0.017814170569181442,
-0.014551178552210331,
0.09620839357376099,
-0.03225257247686386,
0.006607977673411369,
-0.005558321718126535,
-0.01126452162861824,
0.1014849990606308,
0.050775639712810516,
0.04554428532719612,
-0.05059117451310158,
0.02588319405913353,
-0.04019273817539215,
-0.0016994992038235068,
-0.057407934218645096,
0.044743407517671585,
0.01501368172466755,
-0.03690190613269806,
0.00828062929213047,
0.038054611533880234,
-0.023017559200525284,
0.011866088956594467,
0.07041309773921967,
-0.01898755133152008,
-0.05728432908654213,
0.006266969256103039,
0.00319166318513453,
-0.002235835650935769,
0.02059035748243332,
-0.010615536011755466,
0.05140002816915512,
-0.007725940085947514,
0.017453297972679138,
-0.038930293172597885,
-0.05952505022287369,
-0.0007560882950201631,
-0.004935511387884617,
-0.07412467151880264,
0.01283322088420391,
0.01200055330991745,
-0.000018907094272435643,
-0.018398215994238853,
0.005108036566525698,
0.017277348786592484,
0.004533307161182165,
0.05528540164232254,
0.009397827088832855,
0.01796417310833931,
0.03216899186372757,
0.024880709126591682,
0.020564911887049675,
-0.02238921821117401,
0.007385903969407082,
-0.02133730612695217,
0.05015259236097336,
-0.004161126911640167,
-0.03968563675880432,
-0.011849128641188145,
-0.018630169332027435,
-0.012758677825331688,
-0.02572796493768692,
-0.03261040896177292,
-0.00047469892888329923,
0.02577149122953415,
0.010366247035562992,
0.018806245177984238,
-0.026461444795131683,
0.021694356575608253,
0.022167064249515533,
-0.005434277001768351,
-0.01695936545729637,
0.015592184849083424,
-0.009791463613510132,
-0.03204890713095665,
0.020415257662534714,
-0.015198645181953907,
-0.06530385464429855,
0.008839466609060764,
-0.03358852118253708,
-0.03857531026005745,
-0.05313928425312042,
0.00020898952789139003,
-0.011720700189471245,
0.041508354246616364,
-0.027941549196839333,
-0.00018304963305126876,
-0.025424590334296227,
-0.09611477702856064,
0.03565015271306038,
-0.025562210008502007,
-0.0251170564442873,
0.010029925964772701,
0.010896154679358006,
0.007018338423222303,
0.058435264974832535,
-0.03144076094031334,
0.024341197684407234,
-0.021604306995868683,
0.017790663987398148,
-0.002120518358424306,
-0.03385550156235695,
-0.029243608936667442,
-0.006395665463060141,
0.002878789324313402,
-0.0001029346531140618,
-0.020686328411102295,
-0.01700408384203911,
0.046286147087812424,
0.014995936304330826,
-0.006352836731821299,
0.02893565595149994,
-0.002465790370479226,
0.0005137149710208178,
0.008505964651703835,
-0.028460830450057983,
0.019311821088194847,
0.030378812924027443,
0.024427680298686028,
-0.04446405544877052,
0.0030246092937886715,
-0.012997995130717754,
-0.004180030431598425,
-0.014315100386738777,
0.0011477411026135087,
-0.0147626968100667,
-0.010531247593462467,
-0.013578157871961594,
-0.0030503759626299143,
-0.04027623310685158,
-0.008838124573230743,
-0.029710955917835236,
0.04620703309774399,
-0.03838162124156952,
-0.010672471486032009,
0.0029866453260183334,
0.044895730912685394,
-0.02278982661664486,
-0.0360511839389801,
0.003898113965988159,
0.03556395322084427,
-0.03997369855642319,
0.043503277003765106,
0.05263272672891617,
0.024598490446805954,
0.028150876984000206,
0.017215337604284286,
-0.018302857875823975,
-0.008798724040389061,
-0.04992908611893654,
-0.035813432186841965,
0.05550677329301834,
0.004803019110113382,
0.01881464757025242,
0.04152180254459381,
-0.0037405886687338352,
0.0023953733034431934,
0.0806182473897934,
0.0030495815444737673,
0.0004988922737538815,
0.006625605281442404,
-0.06855316460132599,
0.007621182594448328,
-0.024562878534197807,
0.0062692309729754925,
-0.014459815807640553,
-0.002009275136515498,
0.04876077547669411,
-0.014827477745711803,
-0.012935987673699856,
0.004878065083175898,
0.004683933220803738,
-0.028597263619303703,
0.022265607491135597,
0.04575750231742859,
-0.00011519021063577384,
0.023289302363991737,
0.09620199352502823,
-0.009307701140642166,
-0.015048392117023468,
0.03963449224829674,
0.025699332356452942,
-0.0855255126953125,
0.008428509347140789,
0.009867710992693901,
0.022816793993115425,
0.047248855233192444,
-0.028086459264159203,
0.047960348427295685,
-0.0003631981380749494,
-0.05735311657190323,
-0.004881867673248053,
-0.015191549435257912,
-0.0047291964292526245,
0.006679128389805555,
-0.03192674741148949,
-0.04013518989086151,
0.06539183855056763,
0.06961219012737274,
0.03719022125005722,
0.015018968842923641,
0.006925269030034542,
-0.026020433753728867,
-0.02351420372724533,
-0.009710267186164856,
0.057007089257240295,
0.001169601222500205,
-0.024899326264858246,
0.06314246356487274,
-0.0030330733861774206,
-0.050962358713150024,
0.02208889089524746,
-0.02608381025493145,
-0.02923327125608921,
0.016740815714001656,
0.04172946512699127,
0.04779214411973953,
-0.01891198195517063,
0.014563553966581821,
0.007002596277743578,
0.009216622449457645,
-0.010834002867341042,
0.05267059803009033,
-0.012845276854932308,
0.005607049446552992,
0.009142547845840454,
0.022612258791923523,
-0.032538630068302155,
-0.006410219240933657,
0.0424867682158947,
-0.039392560720443726,
-0.022120343521237373,
-0.01147235557436943,
-0.021282590925693512,
0.04571732506155968,
-0.011199265718460083,
0.006172850262373686,
-0.05332363024353981,
0.004265687428414822,
0.03545656427741051,
-0.01542966440320015,
-0.009239545091986656,
0.016045747324824333,
-0.008867022581398487,
-0.06539468467235565,
0.016566772013902664,
0.005582229234278202,
-0.0015548018272966146,
-0.059430819004774094,
-0.01370974164456129,
-0.0022699711844325066,
0.001523655722849071,
-0.0015985029749572277,
-0.023868542164564133,
-0.01868213340640068,
0.026279501616954803,
0.010390697047114372,
-0.0053518908098340034,
-0.06417965143918991,
-0.024336613714694977,
-0.009655036963522434,
-0.026651646941900253,
-0.007723881863057613,
0.00023056153440847993,
-0.02602764405310154,
-0.019429421052336693,
-0.021302787587046623,
-0.0036898974794894457,
0.030648311600089073,
0.05525381118059158,
-0.03391507267951965,
0.00249598384834826,
0.029900550842285156,
0.0019646859727799892,
0.0020393135491758585,
-0.03112027235329151,
-0.01925763301551342,
0.006207081023603678,
-0.02453678473830223,
0.01444559171795845,
0.009897910989820957,
-0.027412479743361473,
0.04891913756728172,
0.008935520425438881,
-0.0078003862872719765,
0.029483117163181305,
0.015835262835025787,
-0.03130693361163139,
-0.010672949254512787,
-0.030270064249634743,
-0.012846133671700954,
0.07077734917402267,
-0.0147319994866848,
0.02985593117773533,
0.030314451083540916,
-0.004351078998297453,
-0.02970518358051777,
-0.009247959591448307,
-0.023062817752361298,
0.0033204646315425634,
0.0012022843584418297,
-0.021101398393511772,
0.019422881305217743,
-0.04172869771718979,
-0.035132285207509995,
0.0213809534907341,
-0.043373096734285355,
-0.020314650610089302,
0.0650782436132431,
0.029706723988056183,
0.0068266624584794044,
0.046093523502349854,
-0.039383307099342346,
0.014775851741433144,
0.008825271390378475,
0.011449196375906467,
0.03135461360216141,
0.012862717732787132,
0.010522148571908474,
-0.015843814238905907,
-0.006819351110607386,
-0.008785497397184372,
0.013372670859098434,
-0.02286791056394577,
0.037112098187208176,
-0.02649933472275734,
-0.024819592013955116,
-0.003914294298738241,
-0.015691494569182396,
0.002269703894853592,
0.012707714922726154,
-0.019713617861270905,
0.057030316442251205,
-0.007959951646625996,
0.026054777204990387,
-0.032117895781993866,
-0.015517833642661572,
0.0063088154420256615,
0.03798156976699829,
0.0304305087774992,
0.058033160865306854,
0.0016238660318776965,
-0.0075398641638457775,
-0.016879543662071228,
-0.003086600685492158,
0.027311591431498528,
-0.04419851675629616,
-0.017319293692708015,
0.033275287598371506,
-0.026667295023798943,
0.013203049078583717,
-0.03672768920660019,
0.008698752149939537,
-0.020886335521936417,
0.020957427099347115,
0.009033015929162502,
0.008032647892832756,
0.007279409095644951,
0.011328710243105888,
-0.04085243493318558,
0.0334332212805748,
-0.02563919499516487,
-0.01144055463373661,
0.0009975745342671871,
-0.02865142747759819,
-0.048568688333034515,
0.02738078124821186
] |
<p>Inspired by <a href="http://arxiv.org/abs/1401.5761" rel="nofollow">Stephen Hawking</a> I recently tripped upon an idea of what is really inside a black hole.</p>
<p>I thought if NASA (or any other space agency) could send a super protected camera into a black hole, then we could see what's inside black hole.</p>
<p>Is this even possible?</p>
| 9,611 |
[
-0.022154171019792557,
-0.04306340962648392,
0.01950516179203987,
-0.04883389547467232,
0.0113286841660738,
-0.007509286981076002,
-0.03290018066763878,
-0.03879837691783905,
-0.03600028157234192,
-0.04407496005296707,
-0.006073756609112024,
0.04476647824048996,
0.03011687658727169,
0.02128054015338421,
-0.019581666216254234,
-0.02134575881063938,
-0.03215021640062332,
-0.011246556416153908,
-0.020996812731027603,
-0.01677362620830536,
0.01428554579615593,
0.03959251940250397,
0.01420592050999403,
-0.000808339100331068,
-0.04582317918539047,
0.014326087199151516,
-0.0034846365451812744,
-0.034404508769512177,
0.025251448154449463,
0.05564936250448227,
-0.001440511317923665,
-0.021354729309678078,
0.013073601759970188,
0.023067256435751915,
-0.0010481261415407062,
-0.04310811683535576,
-0.025455905124545097,
0.014057601802051067,
-0.003237255150452256,
0.016718681901693344,
0.0021761565003544092,
-0.04053555428981781,
0.0241696760058403,
0.08573827892541885,
-0.05910126119852066,
-0.00555001012980938,
-0.020657574757933617,
-0.0262453593313694,
0.022687016054987907,
-0.06410109996795654,
0.05645065754652023,
0.02999657578766346,
0.05631627142429352,
0.03515821322798729,
-0.010508328676223755,
0.013247999362647533,
0.08496205508708954,
0.1033952534198761,
-0.027505718171596527,
-0.018112540245056152,
-0.013362963683903217,
-0.008825122378766537,
-0.023827452212572098,
-0.007772406097501516,
-0.027440158650279045,
0.00594557449221611,
-0.035022880882024765,
0.013434501364827156,
0.0266241617500782,
-0.0016857446171343327,
-0.00759154511615634,
0.008340490981936455,
0.0009923101169988513,
0.015808839350938797,
-0.037036530673503876,
-0.04559823498129845,
0.013010619208216667,
-0.014359565451741219,
0.03963811695575714,
0.027064649388194084,
0.0035202964209020138,
0.004607760347425938,
0.03444523736834526,
0.030510270968079567,
0.018598124384880066,
0.013476208783686161,
0.09447971731424332,
-0.011136976070702076,
0.014599468559026718,
0.001247482025064528,
-0.016981124877929688,
0.015131369233131409,
0.002070243936032057,
-0.026716049760580063,
-0.036764662712812424,
-0.000035174707591068,
-0.020816272124648094,
0.07980511337518692,
-0.03393217548727989,
-0.06435931473970413,
0.017137931659817696,
0.045728087425231934,
0.0013400971656665206,
0.05187646299600601,
0.029367057606577873,
-0.03189953789114952,
-0.02932722494006157,
0.027342332527041435,
-0.004457860253751278,
-0.011842640116810799,
-0.09829007834196091,
0.03364039584994316,
0.011464742012321949,
-0.04195920750498772,
0.05076553300023079,
-0.05481114238500595,
-0.01884285733103752,
-0.048134975135326385,
0.045114949345588684,
0.073926642537117,
0.029812755063176155,
-0.0023308717645704746,
0.006787597667425871,
-0.04331269860267639,
-0.040790166705846786,
0.03325216472148895,
0.03294326364994049,
-0.008713196031749249,
0.0004659613477997482,
0.008491117507219315,
0.006193837616592646,
-0.0004426505765877664,
-0.0033607950899749994,
0.006514721550047398,
0.042147859930992126,
-0.021543871611356735,
-0.10217945277690887,
-0.05402708798646927,
0.05039997771382332,
0.022632494568824768,
-0.019356684759259224,
-0.057973310351371765,
-0.0025687310844659805,
0.06246263533830643,
0.08373411744832993,
-0.0165566299110651,
-0.006985279731452465,
0.030889730900526047,
0.03284600004553795,
-0.002848139964044094,
-0.003656318411231041,
0.018324723467230797,
0.0059343259781599045,
-0.0108426408842206,
0.02587844990193844,
-0.07842876017093658,
-0.005309646017849445,
0.0018348805606365204,
-0.001749148708768189,
-0.04935458302497864,
0.07200094312429428,
-0.008852868340909481,
-0.0031888792291283607,
0.0005207080394029617,
-0.04304758459329605,
-0.02883348986506462,
0.054289039224386215,
0.021963300183415413,
0.0091340821236372,
0.0407041534781456,
0.02177930623292923,
0.024837153032422066,
0.03217422217130661,
-0.020171334967017174,
0.005600735079497099,
-0.06202865391969681,
0.016519485041499138,
-0.005614598747342825,
0.03830868378281593,
-0.024529241025447845,
-0.04335077106952667,
-0.022861290723085403,
0.01354843471199274,
0.01313608419150114,
0.029250960797071457,
0.041134484112262726,
-0.01315310224890709,
-0.043995440006256104,
-0.009080789051949978,
-0.035316891968250275,
-0.010784238576889038,
-0.025443173944950104,
0.013007226400077343,
0.003590821288526058,
0.01867102086544037,
0.008713715709745884,
0.009109738282859325,
0.0538209043443203,
-0.011436588130891323,
-0.033292777836322784,
0.0035174645017832518,
0.04030590504407883,
0.0006085257628001273,
0.008081674575805664,
-0.011524117551743984,
0.02015099674463272,
0.03255268186330795,
-0.0031551376450806856,
0.010631369426846504,
0.027089757844805717,
-0.01996355690062046,
-0.006048507522791624,
-0.02727937325835228,
0.009315075352787971,
-0.0032096640206873417,
-0.018339471891522408,
0.051282286643981934,
0.016913248226046562,
0.02372567728161812,
0.013787085190415382,
0.012836824171245098,
0.08286875486373901,
-0.01646382361650467,
0.03244248405098915,
0.00015235865430440754,
-0.04363255202770233,
0.045539382845163345,
-0.008843054063618183,
-0.009433673694729805,
0.00413578050211072,
-0.05920535698533058,
-0.00636783242225647,
0.02063952572643757,
0.014893263578414917,
-0.037828873842954636,
0.014823013916611671,
0.04411769285798073,
0.0034077775198966265,
0.020903969183564186,
0.007781526073813438,
-0.0004886784590780735,
-0.006790662184357643,
-0.007808780763298273,
0.007338165771216154,
-0.009997623041272163,
0.02605830878019333,
0.03458834066987038,
0.019131164997816086,
0.028875600546598434,
-0.012414473108947277,
-0.0006776670343242586,
0.026700062677264214,
-0.0517437569797039,
0.03279881924390793,
0.0013693226501345634,
-0.007901829667389393,
0.00959430355578661,
-0.012685075402259827,
-0.004868839401751757,
-0.003539761994034052,
0.01743973046541214,
-0.00498575484380126,
-0.04620176926255226,
0.018060624599456787,
0.006269289180636406,
0.025955326855182648,
-0.008335815742611885,
0.017215076833963394,
0.02965252846479416,
-0.07391439378261566,
0.05098237469792366,
-0.026484163478016853,
0.024430233985185623,
-0.03682643175125122,
0.04297104850411415,
0.025590334087610245,
0.017294779419898987,
-0.00015378528041765094,
-0.020867783576250076,
-0.06262191385030746,
0.01840314455330372,
-0.037435803562402725,
0.009182159788906574,
0.04340856894850731,
-0.057550959289073944,
0.007408229634165764,
-0.039653509855270386,
-0.03066609613597393,
0.021693235263228416,
-0.007544883992522955,
0.011972459964454174,
-0.032588809728622437,
-0.028642667457461357,
-0.013774068094789982,
0.04305750131607056,
-0.014057062566280365,
0.01041798759251833,
-0.02587893232703209,
0.00844148825854063,
0.03288602828979492,
0.0016975072212517262,
-0.0061987219378352165,
0.01894913800060749,
0.017586033791303635,
-0.03974422812461853,
-0.00017098845273721963,
0.006634475663304329,
0.004161329939961433,
-0.030063962563872337,
0.029762359336018562,
0.03242810443043709,
-0.0472416877746582,
0.012249569408595562,
-0.019733689725399017,
-0.03306519612669945,
0.04544207826256752,
0.03433624282479286,
-0.00872852187603712,
-0.006840817164629698,
-0.012160009704530239,
0.06071363016963005,
0.017439579591155052,
-0.029331162571907043,
-0.01976848766207695,
-0.043137338012456894,
-0.049417294561862946,
-0.02434329129755497,
-0.006160488352179527,
0.010501631535589695,
-0.008520635776221752,
0.010013789869844913,
0.0005001698154956102,
0.006629760377109051,
0.016630539670586586,
0.02939203567802906,
-0.05238163843750954,
-0.0496910884976387,
-0.0018948091892525554,
0.04212595522403717,
0.058623913675546646,
0.00011587394692469388,
-0.03074648603796959,
0.020950503647327423,
0.008387548848986626,
0.023249231278896332,
0.04501979798078537,
-0.009573657996952534,
0.009187515825033188,
0.017027970403432846,
0.02778877317905426,
-0.0006081102765165269,
0.00390802463516593,
-0.018862606957554817,
0.027362162247300148,
0.018315555527806282,
0.015500153414905071,
0.05883944407105446,
0.016092784702777863,
-0.021914910525083542,
0.017536699771881104,
0.05042298510670662,
0.0003033698885701597,
-0.02778288908302784,
-0.021276650950312614,
-0.02495516836643219,
0.025875551626086235,
0.018499121069908142,
-0.009020174853503704,
0.030080175027251244,
0.015853866934776306,
0.03312624618411064,
0.018848082050681114,
0.013818880543112755,
0.0077481577172875404,
-0.0515734888613224,
-0.029763096943497658,
0.0032744333148002625,
0.007601412944495678,
0.01878107711672783,
0.032551027834415436,
0.04019056633114815,
0.031613871455192566,
0.004018865060061216,
-0.012194279581308365,
-0.08407291769981384,
-0.0056297616101801395,
-0.01740109547972679,
-0.0030463910661637783,
-0.017052583396434784,
-0.03755825385451317,
-0.0012082726461812854,
-0.005812793038785458,
-0.0423487089574337,
0.005114386323839426,
0.009178919717669487,
-0.051207706332206726,
0.013456773944199085,
-0.00821103435009718,
-0.0045365747064352036,
-0.030285662040114403,
0.06389783322811127,
0.05593367666006088,
0.021802637726068497,
-0.018860643729567528,
0.00693328445777297,
-0.024025822058320045,
-0.005750701297074556,
0.023078639060258865,
0.00534013332799077,
-0.010722137987613678,
0.07501818239688873,
0.03726844862103462,
0.008946167305111885,
-0.04097747057676315,
-0.02301839180290699,
-0.000011607633496169001,
0.015794379636645317,
-0.05064980685710907,
-0.008632293902337551,
-0.04699099808931351,
-0.05359993502497673,
-0.028938518837094307,
0.0017442433163523674,
0.050991617143154144,
-0.03672543913125992,
-0.003570808097720146,
0.02323736436665058,
-0.02970142848789692,
-0.029765648767352104,
0.01773126609623432,
0.057032350450754166,
0.007959922775626183,
-0.025910086929798126,
-0.04025226831436157,
-0.06943605095148087,
-0.04075118526816368,
-0.011378787457942963,
-0.0021042940206825733,
0.003821815364062786,
-0.053933288902044296,
0.018924381583929062,
0.014597256667912006,
-0.0121036721393466,
-0.04365480691194534,
0.002635692013427615,
-0.022297509014606476,
0.01730499416589737,
-0.02873387560248375,
0.061429984867572784,
0.028638746589422226,
0.049487292766571045,
0.047331057488918304,
0.01605348102748394,
-0.023275751620531082,
-0.06796753406524658,
-0.038291919976472855,
0.0208152886480093,
0.024559399113059044,
0.04751762002706528,
-0.02960345335304737,
-0.08048500120639801,
-0.027918031439185143,
0.048765990883111954,
-0.023864448070526123,
0.043207742273807526,
0.010248011909425259,
-0.00007855518924770877,
0.007643161807209253,
0.0037868109066039324,
0.015308943577110767,
0.02152474969625473,
-0.040348418056964874,
-0.016231654211878777,
-0.013069932349026203,
0.008215612731873989,
-0.006746512837707996,
0.041044771671295166,
0.028874335810542107,
0.06939252465963364,
0.06179168447852135,
0.012068324722349644,
-0.0010773086687549949,
0.022317659109830856,
-0.05466766282916069,
-0.06337544322013855,
0.011911858804523945,
0.016927912831306458,
-0.07456941902637482,
0.042936597019433975,
-0.03756404668092728,
-0.015024194493889809,
0.04348519816994667,
0.015802182257175446,
-0.009233776479959488,
0.009776354767382145,
-0.06294360756874084,
-0.028442014008760452,
0.02470632642507553,
0.007905835285782814,
0.018348634243011475,
0.02493433840572834,
0.03130309656262398,
0.0047584581188857555,
-0.017548924311995506,
0.050637926906347275,
-0.035159844905138016,
-0.02859887294471264,
-0.005278381984680891,
0.018463676795363426,
-0.06082679703831673,
0.047738224267959595,
0.015429009683430195,
0.01665845885872841,
0.01498787384480238,
-0.033471282571554184,
0.004986792802810669,
0.016489475965499878,
-0.0030102748423814774,
0.035056326538324356,
0.0068783811293542385,
0.016777459532022476,
0.014724820852279663,
-0.008531301282346249,
-0.01257134135812521,
-0.016507519409060478,
-0.010999881662428379,
0.04515465348958969,
-0.0049911499954760075,
0.013913199305534363,
-0.017384309321641922,
-0.00818595290184021,
0.02145146019756794,
-0.04920516908168793,
0.03981363773345947,
-0.01697128638625145,
0.0018233944429084659,
0.0030868661124259233,
-0.047026410698890686,
0.009267446584999561,
0.0011944775469601154,
-0.001983389025554061,
0.02132825180888176,
-0.036984290927648544,
0.021800316870212555,
0.049743276089429855,
0.02288930118083954,
-0.06933039426803589,
-0.02149735577404499,
0.03819190710783005,
0.018425893038511276,
0.012007034383714199,
-0.04624040424823761,
0.042346373200416565,
-0.033943161368370056,
-0.03324884548783302,
-0.025678936392068863,
0.01186638418585062,
-0.03848757967352867,
0.006401995196938515,
0.023059837520122528,
0.0029401991050690413,
0.016948269680142403,
-0.006422764156013727,
-0.008440886624157429,
0.021003300324082375,
0.03801174461841583,
-0.013137603178620338,
0.014025022275745869,
0.0249637421220541,
-0.03526538610458374,
-0.03566371276974678,
-0.047460831701755524,
-0.004999892320483923,
0.019423145800828934,
-0.02953212521970272,
0.036903996020555496,
0.03793506696820259,
0.017371848225593567,
0.01987675204873085,
-0.026003267616033554,
0.013642888516187668,
-0.030740797519683838,
-0.0032362500205636024,
-0.023256314918398857,
0.009232856333255768,
-0.005883835721760988,
-0.05044185370206833,
0.054502371698617935,
0.02730889618396759,
-0.0025133208837360144,
-0.023690374568104744,
0.02731315977871418,
0.010916098952293396,
-0.029102642089128494,
-0.027881428599357605,
-0.0376003198325634,
0.013095381669700146,
0.0046551707200706005,
0.04027753695845604,
0.032802581787109375,
0.04259626939892769,
-0.014861805364489555,
-0.04081933945417404,
-0.026166845113039017,
-0.015060888603329659,
0.06742405146360397,
-0.002574966289103031,
0.027524849399924278,
-0.007323525380343199,
-0.013893702067434788,
-0.021555447950959206,
-0.05343545228242874,
0.009368308819830418,
0.03577285259962082,
-0.0030349185690283775,
0.0033912688959389925,
0.0076642814092338085,
0.0019377974094823003,
0.025614293292164803,
0.03995529189705849,
0.02198748104274273,
0.04491490125656128,
0.007940221577882767,
0.03216055780649185,
0.024854162707924843,
-0.001846656552515924,
-0.023975303396582603,
0.03060540370643139,
-0.040522363036870956,
0.03208722919225693,
-0.001557999406941235,
0.015783345326781273,
0.01564924605190754,
-0.032681383192539215,
0.030374668538570404,
-0.012914636172354221,
-0.04681260138750076,
-0.057621944695711136,
0.03488718718290329,
-0.009207665920257568,
0.017184756696224213,
0.00516419718042016,
0.0062436750158667564,
0.008855841122567654,
-0.002003847388550639,
0.02878819778561592,
0.0069027547724545,
-0.08752615004777908,
-0.06034474074840546,
-0.026755856350064278,
-0.027313997969031334,
0.0559425912797451,
0.02113357000052929,
-0.0007992322789505124,
0.026882514357566833,
-0.047035641968250275,
0.0031342245638370514,
0.03587082773447037,
0.08024230599403381,
-0.021038459613919258,
0.041998934000730515,
-0.02351859211921692,
0.027955610305070877,
-0.0029066423885524273,
0.02185908891260624,
0.11701241135597229,
0.04879561439156532,
-0.010380559600889683,
-0.09081161022186279,
0.0024541516322642565,
-0.03096880204975605,
0.0065473453141748905,
-0.023035861551761627,
0.031982969492673874,
-0.005909193307161331,
0.006192460656166077,
-0.01444699801504612,
0.03463015705347061,
0.0019054108997806907,
-0.021375412121415138,
0.05362715944647789,
-0.01903477869927883,
0.008242283947765827,
-0.007475034799426794,
0.030654318630695343,
-0.027609577402472496,
0.020754648372530937,
-0.0424225814640522,
0.027553196996450424,
-0.021252857521176338,
-0.03894023224711418,
-0.024160897359251976,
-0.0408584289252758,
-0.005796436220407486,
-0.04146048426628113,
-0.038618054240942,
-0.02366640977561474,
-0.014062167145311832,
-0.04539511725306511,
0.014326552860438824,
0.010727833956480026,
0.008717230521142483,
0.00007741325680399314,
0.014931552112102509,
0.0004988221335224807,
0.007810235023498535,
0.015602072700858116,
-0.01758747175335884,
0.008621926419436932,
-0.03628244623541832,
0.0013869921676814556,
-0.0039658937603235245,
0.05481894686818123,
-0.008457205258309841,
0.0045717270113527775,
-0.016759663820266724,
-0.016581391915678978,
0.01637035422027111,
-0.05519779026508331,
-0.010067976079881191,
0.0018552510300651193,
0.018843911588191986,
0.023957714438438416,
-0.05682361498475075,
0.0031963849905878305,
0.04173124209046364,
0.031707800924777985,
0.03835666552186012,
-0.014551312662661076,
0.03908994048833847,
0.02376375161111355,
-0.0009344573481939733,
0.03966449573636055,
-0.009588729590177536,
-0.022253597155213356,
-0.03915618360042572,
0.010342412628233433,
-0.022130796685814857,
-0.006315045524388552,
0.019134338945150375,
0.027121713384985924,
-0.0218669306486845,
0.0475732758641243,
0.02650417387485504,
-0.0010933100711554289,
-0.009854269213974476,
0.033125363290309906,
-0.04152993485331535,
-0.008842420764267445,
-0.004796032328158617,
-0.023979870602488518,
0.03097984939813614,
0.05346512049436569,
-0.0274018794298172,
-0.032537493854761124,
0.04118138551712036,
0.008977553807199001,
0.0221563633531332,
-0.012827271595597267,
-0.01752166822552681,
-0.0029850872233510017,
-0.04720039293169975,
0.017046013846993446,
-0.025197289884090424,
0.03593038022518158,
0.02314937859773636,
0.020450590178370476,
0.008839776739478111,
0.029821280390024185,
-0.08516614139080048,
0.00019714419613592327,
0.012293477542698383,
-0.011678109876811504,
-0.01911950297653675,
-0.025209298357367516,
0.02739109843969345,
-0.01325333584100008,
-0.007477404549717903,
-0.01239048969000578,
0.003153183264657855,
-0.03580714389681816,
0.03287938982248306,
-0.00016389909433200955,
0.03617530316114426,
0.023423749953508377,
0.006500816438347101,
-0.03574461489915848,
0.020478302612900734,
-0.02102789282798767,
0.012901341542601585,
0.005692348815500736,
-0.029921958222985268,
-0.02088577300310135,
0.006558495573699474,
-0.03008251078426838,
-0.025409700348973274,
-0.011108695529401302,
0.01355769857764244,
-0.04819976165890694,
-0.019223488867282867,
0.050186336040496826,
0.0022414573468267918,
0.04786720499396324,
0.01878400705754757,
0.002902986016124487,
0.04123952239751816,
-0.04754294827580452,
-0.04275626316666603,
0.04078636318445206,
0.004508898127824068,
0.016090787947177887,
0.01619327813386917,
-0.046155478805303574,
-0.005191223695874214,
0.035079605877399445,
-0.008035186678171158,
-0.025785205885767937,
0.02643989771604538,
-0.009932121261954308,
-0.02745964750647545,
0.005516643635928631,
0.051859308034181595,
-0.05827838182449341,
0.004696541465818882,
0.02808072604238987,
-0.019147712737321854,
0.014035148546099663,
0.0037676363717764616,
-0.002413853071630001,
-0.011047993786633015,
0.023793336004018784,
-0.002869498450309038,
0.004731408320367336,
0.0209853183478117,
0.04085170850157738,
-0.04331512749195099,
0.06954757124185562,
0.04833144694566727,
0.011757006868720055,
-0.12874570488929749,
0.012964061461389065,
0.02359667420387268,
0.010115633718669415,
0.035554833710193634,
-0.06119582802057266,
0.03728318214416504,
0.023402288556098938,
-0.0736040398478508,
0.022670427337288857,
-0.0485912524163723,
-0.027293404564261436,
-0.023342378437519073,
0.0502440519630909,
-0.023814409971237183,
0.0033752142917364836,
0.03865358605980873,
0.002672721864655614,
0.01084284856915474,
-0.0017980382544919848,
-0.018052123486995697,
-0.017539886757731438,
-0.0016475687734782696,
0.012743420898914337,
-0.00891052559018135,
-0.002272830344736576,
0.0870341882109642,
-0.012511656619608402,
-0.01904289983212948,
0.0014775882009416819,
0.010063494555652142,
0.003852393478155136,
0.001516264514066279,
0.019100109115242958,
0.032394688576459885,
0.0079198582097888,
0.043591324239969254,
-0.0015442890580743551,
0.024427376687526703,
0.001383549184538424,
0.03961026668548584,
0.03521069511771202,
0.009574620984494686,
0.00331056653521955,
-0.020340388640761375,
-0.026054495945572853,
-0.010249782353639603,
0.006053522229194641,
-0.015378931537270546,
-0.013037914410233498,
0.008525165729224682,
0.0014624145114794374,
-0.008706817403435707,
-0.04673366993665695,
-0.015617265366017818,
-0.056432005017995834,
0.022367633879184723,
0.02004774659872055,
-0.006743925623595715,
0.007939133793115616,
0.01461429987102747,
0.00020528180175460875,
-0.041101593524217606,
0.009795795194804668,
-0.02584630809724331,
0.004698690492659807,
-0.03141266480088234,
-0.021262789145112038,
0.01950860768556595,
0.0012836047681048512,
0.053510382771492004,
-0.025570828467607498,
0.007234311196953058,
0.04180338233709335,
0.017136579379439354,
0.03276978060603142,
0.0008257387089543045,
-0.06000235676765442,
-0.03546556457877159,
-0.0838022232055664,
0.01817440055310726,
-0.00264185993000865,
0.01871078833937645,
-0.040123675018548965,
-0.02947344444692135,
0.003996803890913725,
-0.010149069130420685,
0.037725284695625305,
-0.006669605616480112,
0.013401421718299389,
0.02801169641315937,
0.008647263050079346,
0.0034520181361585855,
-0.04270022362470627,
0.005983450915664434,
-0.019042693078517914,
-0.06813685595989227,
-0.03899697959423065,
-0.0006898013525642455,
-0.016533661633729935,
0.01547428872436285,
0.04371548444032669,
0.003651886712759733,
0.03785093501210213,
-0.003798986319452524,
0.019234362989664078,
0.03756256774067879,
-0.022338714450597763,
0.0025248872116208076,
0.03411376476287842,
0.014078743755817413,
0.004297201056033373,
0.02800508588552475,
-0.00959006603807211,
0.018414782360196114,
0.0005945745506323874,
-0.016220243647694588,
-0.018682170659303665,
-0.010475462302565575,
-0.02205989509820938,
0.003341285279020667,
-0.06505060195922852,
-0.016122914850711823,
0.03573503717780113,
-0.06536085903644562,
-0.017795667052268982,
0.056770313531160355,
-0.0076320841908454895,
0.04100365191698074,
-0.013747110962867737,
0.04295908287167549,
0.018706578761339188,
0.008023543283343315,
-0.04385559260845184,
0.04314948990941048,
0.025456780567765236,
-0.031520601361989975,
0.0006814189255237579,
0.03434605523943901,
0.017602594569325447,
0.024242015555500984,
-0.01179242879152298,
0.06486395746469498,
-0.033723026514053345,
-0.022912774235010147,
-0.006186229642480612,
-0.024046914651989937,
0.010057068429887295,
-0.0025302590802311897,
-0.02556423842906952,
0.08098188042640686,
-0.011431680992245674,
-0.008088548667728901,
-0.04760337248444557,
-0.008737458847463131,
-0.025634221732616425,
0.06317199021577835,
-0.0003214108292013407,
0.051896385848522186,
-0.011838044971227646,
-0.00975195411592722,
0.0013728549238294363,
0.026671776548027992,
0.0026812490541487932,
-0.039160046726465225,
0.016300324350595474,
-0.05273347720503807,
0.012919656932353973,
-0.011118926107883453,
-0.04382903873920441,
0.0009297342621721327,
-0.013519272208213806,
0.011538608931005001,
-0.006639310624450445,
0.008256514556705952,
0.03995532914996147,
-0.029443221166729927,
-0.03246224299073219,
0.060555268079042435,
-0.045540615916252136,
-0.00833648256957531,
-0.016212699934840202,
0.047159593552351,
-0.011766890063881874,
0.007742502260953188
] |
<p>A recent paper by the CDMS collaboration (<a href="http://prl.aps.org/abstract/PRL/v111/i25/e251301">PRL here</a> and <a href="http://cdms.berkeley.edu/CDMSII_Si_DM_Results.pdf">free text here</a>) makes this statement in the abstract:</p>
<blockquote>
<p>This blind analysis of 140.2 kg day of data taken between July 2007 and September 2008 revealed three WIMP-candidate events...The probability that the known backgrounds would produce three or more events in the signal region is 5.4%.</p>
</blockquote>
<p>I am not part of the particle physics communities or the dark matter communities so my questions are:</p>
<ol>
<li>Is this convincing evidence for the existence of WIMPs?</li>
<li>What does this say, if anything, about the overall composition of dark matter? I.E. is this convincing evidence that a large fraction of dark matter is from WIMPs?</li>
</ol>
| 9,612 |
[
0.0020451645832508802,
-0.01610657200217247,
0.006190672982484102,
-0.07085800915956497,
0.06475977599620819,
0.03565141186118126,
-0.012667711824178696,
-0.05142208933830261,
0.009739076718688011,
-0.09291858971118927,
0.019093915820121765,
0.04205945506691933,
0.03518810495734215,
0.01137847825884819,
0.009982019662857056,
0.014638674445450306,
0.012862290255725384,
0.0037104112561792135,
0.024786707013845444,
-0.038757212460041046,
0.032633040100336075,
0.030519984662532806,
-0.006039293948560953,
-0.026183312758803368,
-0.030251819640398026,
-0.00034356367541477084,
-0.013772377744317055,
0.009369485080242157,
0.02539399079978466,
0.054064951837062836,
-0.04269592836499214,
-0.020934654399752617,
0.032394587993621826,
0.018880894407629967,
0.003692337777465582,
0.005655078217387199,
-0.003904470009729266,
-0.0372040681540966,
-0.0010633975034579635,
0.03791097551584244,
-0.028823401778936386,
-0.03098774328827858,
-0.008624113164842129,
0.032796602696180344,
-0.06245174631476402,
0.008498158305883408,
0.03221645578742027,
-0.0227066483348608,
0.06222141906619072,
-0.05694267153739929,
0.07499273121356964,
0.0005647799698635936,
0.052755892276763916,
0.01123164314776659,
-0.0064398678950965405,
-0.007898100651800632,
0.04953443631529808,
0.07949976623058319,
0.012158998288214207,
-0.01851877197623253,
-0.019139045849442482,
-0.027056893333792686,
0.013316280208528042,
0.006179716903716326,
-0.00934150442481041,
0.06386449187994003,
-0.03134880214929581,
-0.011381504125893116,
0.008572590537369251,
0.02506631426513195,
0.04417423531413078,
-0.009363490156829357,
0.026657722890377045,
-0.01364167407155037,
-0.013757438398897648,
-0.018351871520280838,
0.0018527301726862788,
-0.009704919531941414,
0.01142351608723402,
0.035599492490291595,
-0.009097857400774956,
0.024597376585006714,
0.01724283955991268,
0.0249496940523386,
0.04221436753869057,
-0.02084348164498806,
0.07526478171348572,
-0.03970344737172127,
-0.007468507159501314,
0.034996259957551956,
-0.01633976772427559,
0.004091970156878233,
0.008379301056265831,
0.019422238692641258,
-0.02210347168147564,
0.005632488057017326,
-0.005058811511844397,
0.049929648637771606,
-0.025952070951461792,
-0.00454559363424778,
-0.019865453243255615,
0.004502467345446348,
0.0005218783626332879,
0.06259741634130478,
-0.02480192482471466,
-0.01723518781363964,
-0.06013829633593559,
0.0060464488342404366,
-0.07211380451917648,
0.012668692506849766,
-0.030134817585349083,
0.030978208407759666,
0.03474287688732147,
-0.04080142080783844,
-0.012230954132974148,
0.0028266781009733677,
0.018892711028456688,
-0.03176821023225784,
0.06470547616481781,
0.04497388005256653,
0.04191077873110771,
-0.013215080834925175,
-0.008218124508857727,
-0.06289146840572357,
-0.03506927937269211,
-0.007543365471065044,
0.02000322751700878,
0.006425659637898207,
-0.03904392197728157,
0.032209448516368866,
0.02751767262816429,
0.014920929446816444,
0.029242925345897675,
-0.008104384876787663,
0.013607093133032322,
-0.013052032329142094,
-0.049992892891168594,
-0.07429120689630508,
0.055093470960855484,
-0.006433120928704739,
0.0000577875689486973,
-0.05444084107875824,
-0.03850751370191574,
0.044703319668769836,
0.05801654979586601,
-0.02447025291621685,
0.025236912071704865,
-0.03277566656470299,
0.042153581976890564,
0.00698606064543128,
-0.01840924099087715,
-0.001264395541511476,
-0.004708125721663237,
-0.023346204310655594,
-0.031212229281663895,
-0.11823464930057526,
0.020791172981262207,
0.02343328297138214,
0.006650072988122702,
-0.01384219154715538,
0.02608504332602024,
0.0032827474642544985,
0.022428495809435844,
-0.015273138880729675,
-0.002985746366903186,
-0.006330493371933699,
0.0466553159058094,
-0.009548972360789776,
0.01659974828362465,
0.030212629586458206,
-0.008871321566402912,
0.05644925683736801,
0.033744242042303085,
0.028594501316547394,
0.031835269182920456,
-0.06127621605992317,
-0.0041414047591388226,
-0.011726833879947662,
0.011892973445355892,
-0.031144991517066956,
-0.026764847338199615,
-0.021924855187535286,
-0.0011863517574965954,
0.024297451600432396,
0.0159909650683403,
0.029850352555513382,
0.00505569064989686,
-0.031316131353378296,
0.033398959785699844,
-0.058986056596040726,
-0.021009329706430435,
-0.05685408413410187,
-0.04921550303697586,
-0.024873077869415283,
-0.020494069904088974,
0.02092675119638443,
0.0010259513510391116,
0.01728038862347603,
-0.0006083588814362884,
-0.016057005152106285,
-0.009256565012037754,
-0.012806173413991928,
0.05189434066414833,
-0.008349981158971786,
0.0004360270104371011,
0.022050531581044197,
0.016391953453421593,
-0.0014199245488271117,
-0.006355063058435917,
-0.0032522391993552446,
-0.0592852346599102,
-0.004263514652848244,
-0.015180209651589394,
-0.02284412458539009,
-0.008618580177426338,
0.0097587825730443,
0.050189338624477386,
0.024829717352986336,
-0.0024891600478440523,
0.0344938300549984,
-0.032488320022821426,
0.0694141685962677,
0.014251669868826866,
0.022988513112068176,
-0.036389462649822235,
-0.003226528177037835,
0.0041591692715883255,
-0.009138084948062897,
-0.027319081127643585,
-0.012539447285234928,
-0.08887475728988647,
-0.009243577718734741,
0.06428211182355881,
-0.010964028537273407,
-0.02843603491783142,
0.0696740597486496,
0.02435334213078022,
0.014604267664253712,
0.000634897209238261,
0.008547932840883732,
-0.028602534905076027,
-0.045034121721982956,
0.021923836320638657,
0.02519797906279564,
0.014619470573961735,
0.03034983202815056,
0.04022226110100746,
0.003356428351253271,
0.009919247590005398,
-0.01855349726974964,
-0.035175275057554245,
0.06524387747049332,
-0.030505232512950897,
0.0013386406935751438,
-0.005526396911591291,
-0.018585091456770897,
0.030687708407640457,
-0.014545345678925514,
0.016667846590280533,
0.03289132937788963,
0.009493599645793438,
0.008754496462643147,
-0.012575386092066765,
-0.04472304508090019,
0.007344726473093033,
0.01268222089856863,
-0.054702915251255035,
-0.01284195575863123,
0.014534994028508663,
-0.0765204206109047,
-0.003227422246709466,
-0.027835166081786156,
-0.03388432785868645,
-0.04286164417862892,
0.004691318143159151,
0.007182941772043705,
-0.005316132679581642,
0.03371921181678772,
-0.048894334584474564,
-0.05501817539334297,
0.013649399392306805,
0.02635357528924942,
-0.02689993940293789,
0.03732719644904137,
-0.05804065242409706,
0.011804785579442978,
-0.040408022701740265,
-0.02526261657476425,
0.036427706480026245,
-0.04806806147098541,
-0.006097620353102684,
0.012639697641134262,
-0.0019096091855317354,
-0.024282831698656082,
-0.03110058605670929,
-0.012976222671568394,
-0.01158921793103218,
-0.03657746687531471,
-0.013033207505941391,
0.04428615793585777,
0.020868521183729172,
-0.01569483056664467,
0.005405755247920752,
-0.019348088651895523,
-0.031049629673361778,
-0.024519946426153183,
0.013323218561708927,
0.014509116299450397,
-0.037322625517845154,
0.0718616470694542,
0.003852002788335085,
-0.04428587481379509,
0.05951164662837982,
-0.06842675060033798,
-0.08146150410175323,
0.020699525251984596,
-0.021072732284665108,
0.018939802423119545,
-0.011595210991799831,
-0.04275112971663475,
0.08431181311607361,
0.035355016589164734,
-0.01494631264358759,
0.00800203625112772,
0.004558749031275511,
-0.018574582412838936,
-0.024972235783934593,
-0.012574479915201664,
0.005189516581594944,
0.025934383273124695,
0.01528249029070139,
0.019930053502321243,
0.01355354581028223,
0.016767412424087524,
-0.046473994851112366,
-0.020210808143019676,
0.020123254507780075,
-0.008818401955068111,
-0.0379045195877552,
0.00999101996421814,
0.02468010038137436,
-0.02788390778005123,
0.013935459777712822,
-0.01417485624551773,
0.030258039012551308,
-0.002714520087465644,
-0.06542174518108368,
0.03932163864374161,
-0.0063835191540420055,
0.03001346066594124,
-0.0007258718251250684,
0.010641459375619888,
0.037966832518577576,
-0.006593596190214157,
0.04284996911883354,
-0.030845778062939644,
0.030308764427900314,
0.007005034945905209,
0.011685456149280071,
0.04184025526046753,
0.02899201586842537,
0.006832517683506012,
-0.033103544265031815,
-0.03120645321905613,
-0.008493553847074509,
-0.02496339939534664,
0.016938958317041397,
-0.02534496784210205,
0.04657237231731415,
0.04325409606099129,
0.024078574031591415,
-0.02500343881547451,
-0.01409777719527483,
-0.0020372290164232254,
-0.061592407524585724,
0.007501943036913872,
-0.021531634032726288,
0.009221616201102734,
-0.027994999662041664,
0.024974774569272995,
0.020089933648705482,
-0.0028813909739255905,
0.025721359997987747,
0.011178080923855305,
-0.046854738146066666,
0.02811301127076149,
-0.017055679112672806,
0.024211455136537552,
0.006325935944914818,
-0.02301114611327648,
0.007709806319326162,
0.0010443442733958364,
-0.04962565004825592,
-0.03025125339627266,
0.01700441911816597,
-0.05289662256836891,
0.022825390100479126,
-0.0353146530687809,
-0.03634952753782272,
0.02757318876683712,
0.009512128308415413,
0.03597616031765938,
-0.005621445365250111,
0.008124656043946743,
-0.004931726958602667,
-0.03324577212333679,
-0.01869688741862774,
-0.008530265651643276,
0.03812567517161369,
-0.01630076766014099,
0.040262769907712936,
0.013708683662116528,
0.03920811042189598,
-0.06694869697093964,
0.022676074877381325,
0.03442774713039398,
0.037824470549821854,
0.023820234462618828,
0.003943095915019512,
-0.021776415407657623,
-0.07586080580949783,
-0.008166112005710602,
0.054377418011426926,
0.018841883167624474,
-0.003879646072164178,
0.010081607848405838,
0.053074274212121964,
0.020619669929146767,
-0.025780631229281425,
0.02328743040561676,
0.03998977318406105,
-0.023009086027741432,
-0.007375380955636501,
-0.0889723002910614,
-0.011582596227526665,
0.002703107427805662,
-0.0032759711612015963,
0.04039007052779198,
0.01800423674285412,
0.004037690814584494,
0.011486216448247433,
0.0007506827241741121,
0.022189034149050713,
-0.04204447939991951,
0.0042928727343678474,
-0.02360185794532299,
0.03972974419593811,
-0.03725035861134529,
0.0015744537813588977,
0.04054121673107147,
0.09170787036418915,
0.03307344391942024,
0.006326305214315653,
-0.040462568402290344,
-0.08296705782413483,
0.022549936547875404,
0.0672651082277298,
0.09036891907453537,
-0.028014345094561577,
0.003158939303830266,
-0.06598179042339325,
0.03836428001523018,
0.01862240582704544,
-0.015566297806799412,
0.024663535878062248,
0.010242228396236897,
0.02939234860241413,
-0.0057166521437466145,
0.0015677439514547586,
0.011727496050298214,
0.025843972340226173,
-0.009512419812381268,
0.027789250016212463,
-0.03154948726296425,
-0.0361509807407856,
-0.03544961288571358,
0.014265219680964947,
0.05677398294210434,
0.04123985394835472,
0.023581720888614655,
-0.003332593711093068,
0.005108674522489309,
-0.0023065812420099974,
-0.014361074194312096,
-0.0747009813785553,
0.022743703797459602,
-0.04633072763681412,
-0.032547563314437866,
0.04202184081077576,
-0.05333894491195679,
-0.03982802480459213,
0.000502931245137006,
0.023513134568929672,
-0.005842788610607386,
0.003081532660871744,
-0.06487204879522324,
0.04908928647637367,
0.04849351942539215,
-0.005161252338439226,
0.010651952587068081,
0.0422082357108593,
-0.00501747103407979,
0.005090734455734491,
-0.02064388431608677,
0.019263269379734993,
-0.055005524307489395,
0.0333392396569252,
-0.03933284059166908,
-0.005717640742659569,
-0.045788902789354324,
0.007335145026445389,
0.020804882049560547,
0.025478539988398552,
0.03944949805736542,
-0.046780429780483246,
-0.008871788159012794,
0.030807742848992348,
-0.00554971769452095,
0.002971591427922249,
-0.06591606140136719,
0.0359807088971138,
-0.01137668825685978,
-0.029735879972577095,
0.038854051381349564,
-0.01564117893576622,
-0.00829196535050869,
-0.005149343051016331,
-0.016873011365532875,
0.010410095565021038,
-0.015876278281211853,
0.0030407619196921587,
0.021863965317606926,
-0.02893703244626522,
0.011094081215560436,
-0.011205865070223808,
0.030510829761624336,
0.04789474606513977,
-0.07338958233594894,
-0.035923052579164505,
-0.0013510790886357427,
-0.021125752478837967,
0.026418106630444527,
-0.04309486597776413,
0.03097902610898018,
0.02419460378587246,
0.039173852652311325,
-0.06456127762794495,
-0.035904135555028915,
0.012975010089576244,
0.04462889954447746,
-0.02154218964278698,
-0.002867792034521699,
-0.013707729987800121,
-0.028681933879852295,
-0.0243512075394392,
-0.030119409784674644,
0.0700039342045784,
-0.023443730548024178,
-0.021229399368166924,
0.007391622290015221,
0.02458646148443222,
0.05150355398654938,
-0.01971345581114292,
-0.006587496493011713,
0.013330968096852303,
0.010242336429655552,
-0.022145356982946396,
0.016107765957713127,
0.002096896292641759,
-0.01302950456738472,
-0.039064958691596985,
-0.004931331612169743,
-0.008590446785092354,
0.0445653535425663,
-0.04978771135210991,
-0.026000507175922394,
0.039247073233127594,
0.005536850541830063,
0.036183517426252365,
-0.011646474711596966,
0.04299916326999664,
-0.013063490390777588,
0.007602136582136154,
-0.013296041637659073,
0.0055457064881920815,
0.0069770910777151585,
-0.031478725373744965,
0.05322323366999626,
-0.049363475292921066,
-0.018948940560221672,
0.01656404510140419,
0.02878229133784771,
0.0038365593645721674,
-0.016508737578988075,
-0.015108237974345684,
-0.025200216099619865,
0.009509365074336529,
-0.01414775475859642,
0.03711596503853798,
0.024965617805719376,
-0.01041442807763815,
-0.038167648017406464,
-0.040421679615974426,
-0.028929611667990685,
-0.02716929279267788,
0.0382365956902504,
-0.000025240724426112138,
0.034024614840745926,
0.0009857786353677511,
-0.02427367866039276,
0.00663928035646677,
-0.04121119901537895,
0.002687046304345131,
0.010065027512609959,
0.02651052735745907,
0.02537762001156807,
-0.07699788361787796,
-0.017540793865919113,
0.030085032805800438,
0.009433824568986893,
-0.023351965472102165,
0.016769051551818848,
0.01267955731600523,
-0.025043468922376633,
0.01882588118314743,
-0.018208488821983337,
-0.030849488452076912,
0.023318158462643623,
-0.01320213358849287,
0.027037421241402626,
0.004433253780007362,
-0.03296782821416855,
0.036719538271427155,
0.007186444941908121,
0.011390751227736473,
-0.023384472355246544,
-0.023378070443868637,
-0.031609296798706055,
0.037048861384391785,
0.04270213842391968,
0.017668386921286583,
0.0035966807045042515,
0.024994853883981705,
0.028093988075852394,
0.05590008199214935,
-0.009149476885795593,
0.007533045019954443,
-0.07336068153381348,
-0.053267769515514374,
-0.030223943293094635,
-0.041924044489860535,
0.010924573987722397,
-0.04063466936349869,
-0.04741494730114937,
-0.005961028393357992,
-0.005976678337901831,
0.021514330059289932,
-0.0023551424965262413,
0.012192192487418652,
-0.015243888832628727,
0.038879748433828354,
-0.024899980053305626,
0.024378053843975067,
-0.02652657777070999,
0.014625762589275837,
0.12551434338092804,
0.044484324753284454,
0.023283179849386215,
-0.03575606644153595,
0.026008252054452896,
0.009542400948703289,
0.008391103707253933,
0.004953588824719191,
0.028325755149126053,
-0.012021957896649837,
-0.0018743948312476277,
-0.00708033237606287,
0.03057447448372841,
0.00038494591717608273,
0.0029718726873397827,
0.050895657390356064,
-0.0018505272455513477,
-0.029017729684710503,
0.015473700128495693,
0.03289766237139702,
-0.007618729956448078,
-0.029132027179002762,
-0.058462001383304596,
0.036303866654634476,
0.03606492653489113,
-0.018631072714924812,
0.013031940907239914,
-0.03328736871480942,
-0.0248262919485569,
0.011334558948874474,
-0.04896051809191704,
-0.04729234799742699,
0.04181172698736191,
0.007850667461752892,
-0.0473017618060112,
0.02518913894891739,
-0.015275923535227776,
-0.03170341998338699,
0.023612437769770622,
0.041203275322914124,
0.05085685849189758,
-0.01880861632525921,
0.0012114237761124969,
0.020601991564035416,
-0.029538176953792572,
-0.037946850061416626,
0.001285361940972507,
0.048067156225442886,
-0.007022067438811064,
-0.027783099561929703,
-0.0027197101153433323,
0.023347551003098488,
0.015917154029011726,
-0.02557605318725109,
0.015146642923355103,
-0.004724752623587847,
-0.012717618606984615,
-0.041238512843847275,
-0.03685862571001053,
0.0004999518860131502,
0.03289349004626274,
-0.02514316700398922,
0.03803675249218941,
-0.00010764880425995216,
-0.014192303642630577,
-0.01732669025659561,
-0.004503120202571154,
0.05424680933356285,
-0.017692049965262413,
0.00491168862208724,
-0.03288239240646362,
0.018701333552598953,
-0.04362662509083748,
-0.015754634514451027,
-0.00197261618450284,
-0.02927977778017521,
0.05034583434462547,
0.037583209574222565,
-0.005662953481078148,
-0.0053969076834619045,
-0.03583906590938568,
0.0361776128411293,
-0.009825910441577435,
-0.02506667748093605,
0.0024475902318954468,
0.026330895721912384,
0.02372216247022152,
0.025313597172498703,
-0.010381198488175869,
0.01389032881706953,
-0.0020229911897331476,
0.037712812423706055,
0.002730404492467642,
-0.045917246490716934,
0.0020829669665545225,
0.0065744370222091675,
-0.02033238485455513,
0.01297825574874878,
0.014222481288015842,
0.048896096646785736,
-0.0184561125934124,
0.009688361547887325,
0.0486530065536499,
0.011189085431396961,
0.001629789243452251,
0.004250933416187763,
0.01122917328029871,
-0.04299677535891533,
-0.011026284657418728,
0.0018704524263739586,
-0.00228405580855906,
-0.04185962677001953,
-0.027083393186330795,
-0.06781746447086334,
0.026816321536898613,
0.02616802230477333,
0.005028990563005209,
-0.08275072276592255,
0.020233385264873505,
-0.003945338539779186,
-0.007469871547073126,
0.005876449402421713,
-0.021295977756381035,
-0.023069214075803757,
-0.036672309041023254,
-0.028960008174180984,
0.006346453446894884,
0.06719980388879776,
0.04265571013092995,
0.017750917002558708,
-0.010859145782887936,
0.04320240393280983,
0.0032952940091490746,
-0.04853357374668121,
0.007511031813919544,
0.027007611468434334,
-0.01084313727915287,
0.03713000938296318,
0.004178134724497795,
-0.03070623241364956,
0.05549829453229904,
-0.016312703490257263,
-0.036458808928728104,
0.04299971088767052,
-0.014779753983020782,
0.01314685121178627,
-0.0009880299912765622,
-0.007258906029164791,
-0.02364610694348812,
0.055758047848939896,
-0.039857037365436554,
-0.0013737236149609089,
0.016658218577504158,
0.015683624893426895,
0.017622366547584534,
-0.004220949020236731,
-0.011125796474516392,
0.027401771396398544,
-0.0016116161132231355,
0.05200126767158508,
0.025446193292737007,
0.018574325367808342,
0.012281791307032108,
0.011318360455334187,
-0.021198788657784462,
0.0043135290034115314,
-0.01578468829393387,
0.041033800691366196,
0.032057855278253555,
0.05157214030623436,
-0.05900537595152855,
0.06284806877374649,
0.021476633846759796,
0.0041312179528176785,
-0.09289585798978806,
-0.0057368045672774315,
-0.012319575995206833,
0.018945377320051193,
0.019458753988146782,
-0.041215356439352036,
0.03400101512670517,
0.0014935542130842805,
-0.04662910848855972,
-0.0181066133081913,
-0.04160573333501816,
-0.03206740319728851,
-0.05124064162373543,
0.01301723811775446,
-0.010371336713433266,
0.027231020852923393,
0.014742032624781132,
-0.0013659019023180008,
0.010308731347322464,
0.04387468472123146,
0.029852675274014473,
-0.0026345772203058004,
-0.04472487047314644,
0.017597001045942307,
0.024201827123761177,
-0.024985089898109436,
0.07476698607206345,
0.011128204874694347,
-0.0004258557746652514,
0.0355955995619297,
0.0302716176956892,
0.0070772008039057255,
0.006738163530826569,
0.001888768863864243,
0.002987951971590519,
0.0013582033570855856,
0.04161689057946205,
-0.006638011895120144,
0.0011489337775856256,
-0.01942555606365204,
0.02616775408387184,
0.029028937220573425,
-0.004368305206298828,
0.003740763058885932,
-0.0156475231051445,
-0.026314672082662582,
-0.009350521489977837,
0.011455325409770012,
-0.017921481281518936,
0.027516348287463188,
-0.0013666285667568445,
0.006200331728905439,
0.010959342122077942,
-0.025608262047171593,
0.04172305017709732,
-0.05229412764310837,
0.005669805686920881,
0.02370772883296013,
0.025828128680586815,
-0.02508804388344288,
0.014162186533212662,
-0.0025731311179697514,
-0.03212686628103256,
0.0034014014527201653,
-0.0026696205604821444,
-0.014990530908107758,
-0.020436374470591545,
0.02825074829161167,
0.006735317874699831,
0.04802326858043671,
0.004048565402626991,
-0.013222654350101948,
-0.052757956087589264,
0.05873464420437813,
-0.02919568307697773,
0.009278618730604649,
0.003797021694481373,
-0.026759102940559387,
-0.002764948643743992,
-0.059830572456121445,
0.07266855984926224,
-0.0061027915216982365,
0.017238344997167587,
-0.0394083708524704,
-0.03214466571807861,
-0.008131985552608967,
-0.01856812834739685,
0.0550123006105423,
-0.006222592666745186,
-0.006375001277774572,
0.01902032643556595,
0.04631004482507706,
-0.025209786370396614,
-0.04567285627126694,
-0.0011396355694159865,
0.02217850834131241,
0.010723339393734932,
0.005336242727935314,
-0.04464596137404442,
0.017145751044154167,
0.008056805469095707,
0.05766499787569046,
-0.007847943343222141,
0.036569010466337204,
0.0037745684385299683,
-0.0003130346885882318,
0.042666979134082794,
-0.005844712723046541,
-0.027718545868992805,
0.07770533114671707,
-0.04512006789445877,
0.010003561154007912,
0.041242122650146484,
-0.016579989343881607,
-0.05813228711485863,
0.03537062183022499,
-0.01699274405837059,
-0.02376296930015087,
0.03660225868225098,
-0.001986951567232609,
0.060145001858472824,
-0.052737604826688766,
-0.012294136919081211,
0.013739202171564102,
-0.012320831418037415,
-0.006787406746298075,
0.03951516002416611,
-0.0020706772338598967,
0.03497568517923355,
0.008074536919593811,
0.028941264376044273,
0.02418564446270466,
-0.007002940867096186,
0.014759198762476444,
0.02458660863339901,
0.04142317920923233,
0.026136869564652443,
0.008489511907100677,
-0.008432028815150261,
0.009081462398171425,
0.01945241168141365,
-0.008884645998477936,
0.044248029589653015,
-0.03708886355161667,
-0.0016410229727625847,
0.007991817779839039,
0.02544042468070984,
-0.004568660631775856,
0.008402335457503796,
0.025630753487348557,
0.08638134598731995,
-0.007775536272674799,
-0.00006455831316998228,
-0.021689195185899734,
-0.038427628576755524,
-0.031039917841553688,
0.018925664946436882,
0.0023454162292182446,
0.022153565660119057,
0.013603219762444496,
0.001582958037033677,
0.01115389820188284,
0.02293342910706997,
0.03653891384601593,
-0.041199203580617905,
-0.01600106805562973,
-0.007067157421261072,
0.007488331291824579,
-0.00928328838199377,
-0.013761484064161777,
0.028986800462007523,
0.0035851632710546255,
0.005529914982616901,
0.015651199966669083,
-0.008193327113986015,
-0.027212701737880707,
-0.006025085691362619,
-0.05025536194443703,
0.021581323817372322,
-0.014675443060696125,
0.004964431282132864,
-0.057188503444194794,
0.05359506234526634,
0.005240039899945259,
-0.03398716449737549
] |
<p><img src="http://i.stack.imgur.com/MEo7X.jpg" alt="enter image description here">
<img src="http://i.stack.imgur.com/U1dyL.png" alt="enter image description here"></p>
<p>My interpretation: When we have no angular momentum, the potential well looks like this, my question is: How do you find the point where the wavefunction penetrates its classical forbidden region, i.e. quantum tunnelling effect? The answer is $r>2a_0$ where $a_0$ is the Bohr's radius. </p>
<p>My answer: It seems you have to equate the Coulomb potential with the energy of the ground state of the hydrogen atom.</p>
<p>And what would the wavefunction intersect? Does it pass through $(0,0)$? Can we view the infinite deep well, as a infinite barrier, by imagining we shift the zero reference level down to infinity?</p>
<p>I'm quite confused by the idea of having negative energy. Does it mean I need infinite energy to get out of the well? Just like an infinite square well?</p>
| 9,613 |
[
-0.0519714280962944,
-0.0027426902670413256,
-0.0018627425888553262,
-0.0033121537417173386,
0.035028595477342606,
-0.012161674909293652,
-0.03985627740621567,
-0.05635729059576988,
-0.0016722508007660508,
-0.011248202994465828,
0.05898858979344368,
0.019491009414196014,
0.025250233709812164,
0.004588478710502386,
0.021518612280488014,
0.009591007605195045,
-0.023100964725017548,
-0.0383622944355011,
-0.014303997159004211,
-0.01566346362233162,
0.025101231411099434,
0.044282007962465286,
-0.006180771626532078,
0.020610440522432327,
-0.02581269107758999,
0.03254273533821106,
0.02965422347187996,
-0.00641071330755949,
-0.022621216252446175,
0.07173974812030792,
0.00865666288882494,
-0.027990931645035744,
0.02599099650979042,
0.01392926275730133,
0.015735063701868057,
-0.01819375343620777,
-0.009268292225897312,
-0.033061496913433075,
-0.038127437233924866,
0.021231187507510185,
-0.029555484652519226,
-0.022509438917040825,
-0.035086072981357574,
0.060542214661836624,
-0.01895422488451004,
-0.004921564366668463,
-0.005374437663704157,
-0.01657005585730076,
0.024225980043411255,
-0.041261766105890274,
0.008652753196656704,
0.007943542674183846,
0.045066479593515396,
-0.004206555429846048,
0.03701617941260338,
-0.0388052836060524,
0.06548145413398743,
0.10217471420764923,
0.004134864546358585,
-0.05099612474441528,
-0.024525225162506104,
0.0024924972094595432,
-0.022667180746793747,
-0.011121397837996483,
-0.008454215712845325,
-0.009083493612706661,
0.014807021245360374,
-0.005289142951369286,
-0.011433210223913193,
-0.018144741654396057,
0.031220775097608566,
0.016531290486454964,
0.018874943256378174,
-0.007656890898942947,
0.03748933598399162,
-0.034114014357328415,
0.018209224566817284,
0.01837669499218464,
-0.0037698503583669662,
0.0452897883951664,
-0.012397514656186104,
0.02113169990479946,
0.03630567714571953,
0.025202076882123947,
0.00839883740991354,
-0.0073648071847856045,
0.040376026183366776,
0.0020277227740734816,
0.0048579559661448,
0.05171120539307594,
0.006827130448073149,
0.005264866165816784,
0.020777549594640732,
-0.033894628286361694,
-0.041542187333106995,
0.03249425068497658,
-0.0028572778683155775,
0.05357814580202103,
0.009751486591994762,
-0.016986705362796783,
0.0035891872830688953,
-0.027787836268544197,
0.03526019677519798,
0.07244525104761124,
-0.000452191976364702,
-0.027336975559592247,
-0.01416501123458147,
0.03652280196547508,
-0.0044885254465043545,
-0.05412755534052849,
-0.03795762360095978,
0.04354233294725418,
0.027760954573750496,
-0.022251930087804794,
-0.012516660615801811,
-0.04034699499607086,
-0.02945665828883648,
-0.025753160938620567,
0.048378195613622665,
0.039379604160785675,
0.05502007529139519,
-0.03232604265213013,
0.03450336679816246,
-0.04241613671183586,
-0.06142798066139221,
-0.017735296860337257,
0.06322181969881058,
0.00851853284984827,
-0.030837157741189003,
0.01169784925878048,
0.030662087723612785,
0.013506099581718445,
0.01667364500463009,
0.016795337200164795,
0.06734725087881088,
-0.022509003058075905,
-0.1019648015499115,
-0.07805753499269485,
0.03205327317118645,
-0.004818412475287914,
-0.0354316271841526,
-0.06586234271526337,
-0.01336165051907301,
0.027429495006799698,
0.08655700087547302,
-0.010706235654652119,
-0.007123428862541914,
-0.010172024369239807,
0.023524969816207886,
0.013704966753721237,
-0.007788299582898617,
-0.0018038249108940363,
-0.008918682113289833,
-0.0093755591660738,
-0.01595968008041382,
-0.06655152142047882,
0.05895570293068886,
0.028051014989614487,
0.01564411260187626,
-0.03263465315103531,
0.08211740106344223,
-0.03460794314742088,
-0.005681681912392378,
0.01931629702448845,
-0.035520996898412704,
-0.027515271678566933,
0.08833974599838257,
0.02564428560435772,
-0.029216310009360313,
0.054569706320762634,
0.026716046035289764,
0.040239740163087845,
-0.0008243641932494938,
0.01634272187948227,
-0.011878442019224167,
-0.04061593487858772,
0.02734338492155075,
-0.06854885816574097,
0.031450238078832626,
-0.02611437812447548,
-0.04728448763489723,
-0.017056969925761223,
-0.007741936016827822,
0.014289232902228832,
0.025148140266537666,
0.04242022708058357,
-0.0003958056040573865,
0.0028004988562315702,
-0.028705615550279617,
-0.020456833764910698,
0.006993225775659084,
-0.07545816898345947,
0.04328635334968567,
0.018149154260754585,
0.004254200495779514,
0.0279052946716547,
0.004343703389167786,
0.033419132232666016,
-0.03629976511001587,
-0.008584048599004745,
-0.02451252192258835,
0.04915114492177963,
0.0030861455015838146,
-0.0052625685930252075,
0.035607222467660904,
0.06108408421278,
0.026796111837029457,
0.004793927539139986,
0.021848265081644058,
-0.02293555624783039,
-0.010071523487567902,
0.021134644746780396,
-0.014150372706353664,
0.05571938678622246,
0.04523415490984917,
0.00465756980702281,
-0.007768808398395777,
0.0032508759759366512,
0.008524258621037006,
0.004003668669611216,
-0.027622021734714508,
0.03221095725893974,
-0.006739949807524681,
0.048514433205127716,
-0.014218311756849289,
0.03416106477379799,
-0.006107781082391739,
0.012567542493343353,
-0.02028913050889969,
-0.00799966137856245,
-0.028573669493198395,
0.018399007618427277,
0.030013013631105423,
0.03634984791278839,
-0.04371589422225952,
-0.014701626263558865,
-0.0009183179936371744,
0.012410410679876804,
0.010645556263625622,
0.021145394071936607,
-0.043395839631557465,
-0.01138715073466301,
-0.0039243814535439014,
0.02473508007824421,
-0.019767319783568382,
0.028633493930101395,
0.03708320111036301,
0.03567260876297951,
0.031793612986803055,
-0.015394192188978195,
-0.011722934432327747,
0.03308967873454094,
-0.028100209310650826,
0.01652596704661846,
-0.009200669825077057,
-0.0067427922040224075,
-0.001690781326033175,
-0.02091240882873535,
-0.0011155401589348912,
0.021582305431365967,
-0.05322191119194031,
0.01106943003833294,
-0.034040533006191254,
-0.006773998029530048,
0.02062227576971054,
0.0014952031197026372,
-0.004705944564193487,
0.001067851553671062,
0.02079589292407036,
-0.015825338661670685,
0.058288443833589554,
-0.012755971401929855,
0.001200472004711628,
-0.008825969882309437,
-0.015739595517516136,
0.014435065910220146,
0.025382941588759422,
0.010479995980858803,
-0.04710022732615471,
-0.06513695418834686,
0.006401004735380411,
-0.008609832264482975,
0.003015011316165328,
0.03383198380470276,
-0.016552872955799103,
-0.010866448283195496,
-0.05897677317261696,
0.0068529932759702206,
0.04609325900673866,
-0.0019783596508204937,
0.03351433202624321,
-0.019989343360066414,
-0.021123139187693596,
-0.04064756631851196,
-0.008558961562812328,
-0.01577002927660942,
0.021962953731417656,
-0.03763056546449661,
-0.022344667464494705,
0.06146083027124405,
-0.006444329395890236,
-0.030827339738607407,
0.02691444382071495,
-0.025899525731801987,
-0.05892600491642952,
-0.029875116422772408,
-0.007443401962518692,
0.05031672492623329,
-0.02410317398607731,
0.04190943390130997,
-0.02474328503012657,
-0.04314620792865753,
0.005089037586003542,
-0.049132999032735825,
-0.04043532535433769,
0.01797509752213955,
0.01881190948188305,
-0.004074710421264172,
-0.016930704936385155,
-0.0073837838135659695,
0.07736209034919739,
0.016924284398555756,
-0.0237025935202837,
-0.017976226285099983,
-0.03255443647503853,
-0.017255287617444992,
-0.019226977601647377,
-0.03341609612107277,
0.04050268605351448,
-0.012342538684606552,
0.017087066546082497,
-0.013792752288281918,
0.07187061756849289,
0.017459401860833168,
0.015656359493732452,
-0.011335157789289951,
0.0048869638703763485,
0.008685079403221607,
0.029097147285938263,
0.07820220291614532,
-0.03064504824578762,
0.00188140117097646,
0.0030494474340230227,
-0.013528222218155861,
0.007015945855528116,
0.04075852781534195,
-0.0311321709305048,
0.040083445608615875,
0.00998017005622387,
0.03233250975608826,
-0.013483857735991478,
0.05645868182182312,
0.007476760074496269,
-0.026343677192926407,
0.01777695119380951,
-0.002301743719726801,
0.04615367576479912,
-0.026749571785330772,
-0.018625210970640182,
0.03492541238665581,
-0.006698353681713343,
-0.02021183632314205,
-0.018327441066503525,
0.022082768380641937,
0.0019932615105062723,
0.02218727581202984,
0.0072089736349880695,
-0.06666722893714905,
-0.005812779534608126,
0.06453974545001984,
0.008115577511489391,
-0.02267272025346756,
-0.03634893521666527,
-0.023803172633051872,
-0.036470264196395874,
-0.014448996633291245,
-0.01196745503693819,
0.055345356464385986,
0.008298403583467007,
0.04306625574827194,
0.0317082442343235,
0.022520404309034348,
0.024014875292778015,
-0.01921801082789898,
-0.06917822360992432,
-0.006898768246173859,
-0.038567088544368744,
-0.00519535131752491,
-0.010231142863631248,
-0.002669584471732378,
-0.0073290360160171986,
-0.022006910294294357,
-0.026359962299466133,
0.0014145742170512676,
-0.032458800822496414,
-0.03583385422825813,
0.007259892299771309,
-0.013705814257264137,
-0.010245157405734062,
-0.04714144766330719,
0.03572786971926689,
0.04467195272445679,
-0.0049077291041612625,
0.03786100074648857,
0.02258642204105854,
-0.02974436618387699,
-0.003489888971671462,
-0.009591716341674328,
-0.007384102325886488,
0.019717711955308914,
0.0356120765209198,
0.05720261111855507,
0.034940555691719055,
0.0016352959210053086,
-0.02435731142759323,
0.0004533702740445733,
0.034221209585666656,
-0.004086101893335581,
0.01184175070375204,
0.0012156006414443254,
-0.015099403448402882,
0.006443307269364595,
-0.012537908740341663,
0.05754724144935608,
-0.0019717442337423563,
0.047007005661726,
0.050003040581941605,
-0.013061167672276497,
-0.026475759223103523,
0.03341413661837578,
0.04013071581721306,
0.039604585617780685,
-0.0047605931758880615,
-0.03320436552166939,
-0.03431108966469765,
-0.05099467933177948,
0.010784212499856949,
-0.029505601152777672,
-0.01679195463657379,
-0.032011814415454865,
0.006508376449346542,
0.0375993512570858,
0.035880301147699356,
-0.007780868094414473,
0.005387207493185997,
-0.01632535271346569,
0.017713220790028572,
-0.017915012314915657,
0.0005474783829413354,
0.03878911957144737,
-0.008589117787778378,
0.03729293867945671,
-0.014592082239687443,
0.02217279188334942,
-0.057398129254579544,
-0.06387811154127121,
0.03633613511919975,
0.061498142778873444,
0.03178577125072479,
-0.016654018312692642,
-0.055249761790037155,
-0.055216606706380844,
0.02624695561826229,
-0.046167802065610886,
0.0526614710688591,
-0.040740396827459335,
0.004086630884557962,
-0.023443039506673813,
-0.05721590667963028,
-0.038982536643743515,
0.01227624248713255,
-0.014748725108802319,
-0.0197449941188097,
-0.03649483248591423,
-0.008714008145034313,
-0.026736628264188766,
0.007333625573664904,
-0.030084365978837013,
0.04563109576702118,
0.006439668592065573,
0.01325346902012825,
0.01655798964202404,
0.02390625886619091,
0.00042325598769821227,
-0.08472645282745361,
0.004494771361351013,
0.009692602790892124,
-0.004158434923738241,
0.05068157613277435,
-0.04371394217014313,
-0.025909779593348503,
0.025658540427684784,
-0.0038043942768126726,
0.004145730286836624,
0.053449489176273346,
-0.02970639243721962,
0.06425818055868149,
0.026924526318907738,
0.0008960796403698623,
0.05912307649850845,
0.022123785689473152,
-0.004317755810916424,
-0.0033229945693165064,
-0.034506235271692276,
0.01968666911125183,
-0.020447684451937675,
-0.02567991241812706,
-0.08393347263336182,
0.007324834819883108,
-0.019382920116186142,
0.011918127536773682,
-0.036628447473049164,
-0.006424219813197851,
0.006373788230121136,
-0.043905649334192276,
0.011332898400723934,
0.0009191498393192887,
-0.020217977464199066,
-0.02268674224615097,
-0.0370648093521595,
-0.008562550880014896,
0.009130189195275307,
-0.035854753106832504,
-0.007373306900262833,
0.022033559158444405,
0.016553016379475594,
0.04848145693540573,
-0.011119848117232323,
0.03473483398556709,
-0.021483393386006355,
-0.031117476522922516,
0.0044142333790659904,
-0.07310391217470169,
0.007852899841964245,
-0.0245989877730608,
-0.024236029013991356,
-0.021781207993626595,
-0.023914413526654243,
-0.028749333694577217,
0.002638787031173706,
-0.026102079078555107,
-0.01002679392695427,
-0.007849306799471378,
0.02040269412100315,
0.017483633011579514,
-0.0033657292369753122,
-0.0568348728120327,
-0.02526204101741314,
0.012786542065441608,
0.00008583672024542466,
-0.034401535987854004,
-0.006163858342915773,
-0.016475409269332886,
-0.004110479727387428,
-0.023603303357958794,
-0.00038721656892448664,
0.0065321908332407475,
-0.0540531724691391,
0.02164374478161335,
0.04701649770140648,
0.033480312675237656,
0.06025472283363342,
0.007050220388919115,
-0.020507246255874634,
0.0311723705381155,
-0.006608400959521532,
-0.027614790946245193,
-0.0026011159643530846,
0.04216587543487549,
-0.028609033674001694,
-0.037703294306993484,
-0.009394867345690727,
-0.013232347555458546,
0.037272196263074875,
-0.028182024136185646,
-0.034008774906396866,
-0.013861079700291157,
0.0028215795755386353,
-0.024900680407881737,
0.016828326508402824,
-0.009287822991609573,
0.005064156372100115,
0.05531998723745346,
0.013733656145632267,
-0.03785243630409241,
-0.03669508919119835,
-0.05767766013741493,
0.02045300416648388,
-0.0013882187195122242,
-0.0022454154677689075,
-0.0062927319668233395,
0.05806366726756096,
-0.0028032551053911448,
0.009436655789613724,
0.002503991359844804,
-0.03552725538611412,
-0.00795143935829401,
-0.030214587226510048,
-0.012923767790198326,
0.029736081138253212,
0.02913680300116539,
-0.021681392565369606,
-0.06912937015295029,
-0.03635813668370247,
0.00006468416540883482,
0.03806654363870621,
-0.006690070498734713,
0.03878178820014,
-0.02726759947836399,
0.0039004110731184483,
-0.02393427863717079,
-0.026030363515019417,
-0.026846881955862045,
0.004508227109909058,
0.021642813459038734,
0.004780223127454519,
-0.032927725464105606,
0.02343037538230419,
0.05427094176411629,
0.030174417421221733,
-0.010361852124333382,
0.027756724506616592,
0.06612842530012131,
0.016406722366809845,
0.009732555598020554,
-0.0067697083577513695,
-0.03779638186097145,
0.02120901271700859,
-0.02314571663737297,
0.04380316659808159,
0.01833961345255375,
-0.03562845289707184,
0.02857997640967369,
0.016674207523465157,
0.04040718078613281,
-0.028362920507788658,
0.006194738671183586,
-0.04796150326728821,
0.02327745594084263,
-0.007041196804493666,
0.023859912529587746,
-0.02990296669304371,
0.015105082653462887,
0.009714266285300255,
0.009997705928981304,
0.012829241342842579,
-0.005511770956218243,
-0.032956045120954514,
-0.008607316762208939,
-0.03295110538601875,
-0.05680672451853752,
0.005153023637831211,
0.010398024693131447,
-0.027222953736782074,
0.023760728538036346,
-0.04054219275712967,
-0.0053464812226593494,
0.0011459996458142996,
0.011752639897167683,
-0.015573366545140743,
0.037321120500564575,
0.012157825753092766,
0.03260397911071777,
0.001577993156388402,
0.02703646756708622,
0.12059537321329117,
0.0455365888774395,
0.008798218332231045,
-0.0660218745470047,
-0.0222175233066082,
-0.014049412682652473,
0.023423170670866966,
-0.025143641978502274,
0.005786145571619272,
-0.030047321692109108,
-0.026445496827363968,
-0.012071787379682064,
0.028936244547367096,
-0.023904364556074142,
0.039149168878793716,
0.06286288797855377,
-0.0337197482585907,
-0.051214780658483505,
0.012374810874462128,
0.01576540246605873,
-0.002231061225757003,
0.03342866897583008,
-0.02344268374145031,
0.0409293994307518,
-0.044772710651159286,
0.020366838201880455,
-0.02663520909845829,
-0.029229721054434776,
0.03284299746155739,
-0.0036723646335303783,
-0.06607045233249664,
-0.017254112288355827,
-0.014438753947615623,
-0.007068780716508627,
-0.01950852945446968,
0.0041454872116446495,
0.011631985194981098,
-0.014183003455400467,
0.02239539474248886,
0.045996181666851044,
-0.005071685649454594,
0.013009044341742992,
0.022048993036150932,
0.020299598574638367,
-0.023763446137309074,
-0.007011506240814924,
0.01987360045313835,
0.02908061072230339,
-0.05764482542872429,
-0.01132946740835905,
-0.028694961220026016,
-0.028294816613197327,
0.026408394798636436,
-0.038140278309583664,
-0.017589502036571503,
-0.021389348432421684,
0.041517022997140884,
-0.00015022199659142643,
-0.03908831626176834,
-0.005656677298247814,
-0.011167564429342747,
0.036463554948568344,
0.005730980075895786,
-0.05554153025150299,
0.0024252228904515505,
0.05373475328087807,
0.020844541490077972,
0.05004353076219559,
-0.011257980950176716,
-0.005621157120913267,
-0.022933779284358025,
-0.00439829146489501,
-0.05602547153830528,
0.008502542041242123,
0.055618882179260254,
0.03516426682472229,
0.061397310346364975,
0.016418054699897766,
-0.0034850132651627064,
-0.016329796984791756,
-0.08104719966650009,
0.0265880785882473,
-0.030488016083836555,
-0.01891227625310421,
0.0003289697924628854,
0.002137318719178438,
0.003986038267612457,
0.047908585518598557,
-0.03362339362502098,
0.014308419078588486,
0.016272978857159615,
0.03314633667469025,
0.03880854323506355,
-0.02441597916185856,
-0.027583129703998566,
0.004551857244223356,
-0.0400150902569294,
0.01969592645764351,
-0.007546724285930395,
-0.025849536061286926,
-0.013864200562238693,
0.03479721024632454,
-0.0016496634343639016,
0.050244588404893875,
-0.04259142279624939,
0.01568511687219143,
-0.011906221508979797,
-0.00558867584913969,
0.004526887554675341,
0.010779059492051601,
0.06802580505609512,
-0.030536964535713196,
0.000664004881400615,
-0.02283981256186962,
-0.010504280216991901,
0.0301204863935709,
0.03556213527917862,
-0.02440560981631279,
-0.0005927268066443503,
-0.01583547331392765,
0.008817475289106369,
-0.03492650017142296,
-0.016122708097100258,
-0.0640396922826767,
0.029533442109823227,
0.02659742534160614,
0.00032384751830250025,
-0.015518730506300926,
0.018993381410837173,
0.002164575271308422,
-0.028658486902713776,
0.028135571628808975,
0.027280103415250778,
-0.06252051144838333,
0.038909852504730225,
0.03670353442430496,
-0.01043302658945322,
0.05575835332274437,
0.0035709128715097904,
0.00743271317332983,
0.033216431736946106,
-0.018930843099951744,
-0.05532164126634598,
0.025723302736878395,
0.017787296324968338,
0.03328242152929306,
0.029658958315849304,
-0.055695973336696625,
-0.02768428809940815,
0.03990764915943146,
-0.0033073031809180975,
-0.0016141742235049605,
-0.013534296303987503,
-0.01952313631772995,
-0.0017719923052936792,
0.0049962145276367664,
0.028799330815672874,
-0.01909126155078411,
0.0033619843889027834,
0.05074173957109451,
0.017008334398269653,
-0.000862652959767729,
-0.0024023759178817272,
0.013024503365159035,
0.012194336391985416,
0.019849976524710655,
0.006793181411921978,
-0.015913449227809906,
0.006358693819493055,
0.05749528110027313,
-0.026589753106236458,
0.04922559857368469,
0.04361372068524361,
0.004106482956558466,
-0.07806571573019028,
-0.018849875777959824,
0.012485194019973278,
0.02431599237024784,
0.03232290595769882,
-0.043013911694288254,
-0.014157337136566639,
0.029505431652069092,
-0.08153560012578964,
0.017938293516635895,
-0.010666176676750183,
0.022531181573867798,
-0.0013009884860366583,
-0.017634466290473938,
-0.05551406741142273,
0.0313800685107708,
0.0029812303837388754,
0.0766196995973587,
0.03695712238550186,
0.031142976135015488,
-0.05051999166607857,
-0.053252629935741425,
0.0053259460255503654,
0.05513663589954376,
-0.019593510776758194,
-0.007460801862180233,
0.07658996433019638,
-0.013570566661655903,
-0.016396932303905487,
0.03264651447534561,
-0.03857879713177681,
0.022665636613965034,
-0.005367721430957317,
0.0010816747089847922,
0.011029933579266071,
0.03856643661856651,
0.028087487444281578,
0.020019790157675743,
-0.01884489506483078,
0.032683733850717545,
0.026920579373836517,
0.010395782999694347,
0.011103539727628231,
0.0001844533981056884,
0.00805266946554184,
-0.0392734669148922,
-0.03571305796504021,
0.053619999438524246,
0.009286677464842796,
0.01934272050857544,
0.01752004213631153,
0.01184921059757471,
0.028772763907909393,
-0.02540070377290249,
-0.014251863583922386,
-0.0019074073061347008,
-0.01595725305378437,
0.022918272763490677,
-0.010679695755243301,
-0.019888898357748985,
0.026536161080002785,
-0.0012355551589280367,
-0.05964692309498787,
0.05490413308143616,
0.0021626362577080727,
-0.04801751300692558,
-0.05650171637535095,
0.0035136546939611435,
-0.018849825486540794,
-0.018409036099910736,
0.022361932322382927,
-0.028642216697335243,
-0.05319078266620636,
0.033745624125003815,
-0.02440115064382553,
0.020153475925326347,
0.0026375919114798307,
-0.06766466796398163,
-0.052123118191957474,
-0.059870097786188126,
0.03191966563463211,
-0.009734131395816803,
0.0029229121282696724,
-0.011109400540590286,
-0.04675289988517761,
0.0008020374225452542,
0.018498562276363373,
0.09470783919095993,
-0.02825850434601307,
-0.011536010541021824,
0.020532425493001938,
-0.002098621567711234,
0.045143622905015945,
0.012217890471220016,
0.01290277298539877,
0.006205343641340733,
-0.028746532276272774,
-0.0036292588338255882,
0.016193946823477745,
-0.016115330159664154,
0.025929179042577744,
0.012237044982612133,
-0.009899899363517761,
0.001927989418618381,
-0.0033957893028855324,
-0.02779231406748295,
0.05467570573091507,
0.03786122053861618,
0.0021317803766578436,
0.06181469187140465,
0.013279179111123085,
0.026684243232011795,
0.029097294434905052,
-0.021384691819548607,
-0.007729116827249527,
0.012310998514294624,
-0.026715798303484917,
-0.041481319814920425,
-0.006885448470711708,
-0.03132938966155052,
0.019770586863160133,
-0.03558846935629845,
-0.032391659915447235,
0.049110155552625656,
-0.03346829116344452,
-0.01885002665221691,
0.07074152678251266,
-0.011755159124732018,
0.07776645570993423,
-0.016630150377750397,
0.03152349591255188,
-0.02879863977432251,
0.04248210787773132,
0.020347600802779198,
0.027117274701595306,
0.03996898606419563,
-0.010976909659802914,
-0.005680430680513382,
0.05177590996026993,
0.017832184210419655,
0.004718161653727293,
0.009148938581347466,
0.02991972118616104,
-0.050595879554748535,
0.005461500957608223,
0.018201004713773727,
-0.015932239592075348,
-0.023171916604042053,
0.015597660094499588,
-0.025281786918640137,
0.09277492016553879,
-0.009378368966281414,
0.016553498804569244,
-0.007322365418076515,
0.00634931493550539,
-0.00565656553953886,
0.016511516645550728,
-0.035204578191041946,
0.026134371757507324,
-0.024848032742738724,
-0.05530489236116409,
-0.019502583891153336,
0.033156413584947586,
0.015021036379039288,
-0.05523449182510376,
-0.0007158255903050303,
0.01324092410504818,
-0.02569545805454254,
-0.03213321045041084,
-0.017991928383708,
0.000646200031042099,
0.0006336799706332386,
0.014485610648989677,
0.03038649447262287,
0.0364079549908638,
0.012227189727127552,
0.02763667143881321,
-0.00761856883764267,
0.044388338923454285,
-0.048278383910655975,
0.012825587764382362,
0.006075647659599781,
0.006540654692798853,
-0.007670070510357618,
-0.01885846257209778
] |
<p>Suppose you accelerate a body to very near the speed of light $c$ where $v = c - \epsilon$. Although this would take an enormous energy, is it possible the last arbitrarily small velocity needed -- $\epsilon$ -- could be overcome with a minor bump in velocity due to the <a href="http://en.wikipedia.org/wiki/Uncertainty_principle" rel="nofollow">uncertainty principle</a>?</p>
| 9,614 |
[
0.008611207827925682,
-0.05548210069537163,
-0.0005931796622462571,
-0.028259962797164917,
0.03832453116774559,
0.012169255875051022,
-0.03815003111958504,
-0.036334600299596786,
-0.01617138274013996,
-0.03226151317358017,
-0.014775608666241169,
0.06110169738531113,
0.06117909029126167,
-0.01487158052623272,
0.009204707108438015,
0.023105287924408913,
-0.015131935477256775,
-0.016075991094112396,
-0.029561422765254974,
-0.03392181545495987,
0.02577245980501175,
0.02225947193801403,
0.027255911380052567,
-0.007416636683046818,
-0.012624397873878479,
0.01483310479670763,
0.04425923898816109,
-0.0016612798208370805,
-0.0037559322081506252,
0.059935446828603745,
-0.006429804489016533,
0.01681412011384964,
0.01808781549334526,
0.022550858557224274,
-0.014182483777403831,
0.0014894363703206182,
-0.013792615383863449,
-0.03846259042620659,
0.004406332969665527,
0.010577527806162834,
-0.05082084983587265,
0.03728107362985611,
-0.007131359074264765,
0.07877033203840256,
-0.021088534966111183,
0.019461212679743767,
0.011993413791060448,
-0.030937273055315018,
0.06233002245426178,
-0.041442953050136566,
0.05831551551818848,
-0.011887951754033566,
0.02514801174402237,
0.00498954625800252,
0.0012094697449356318,
-0.006501514930278063,
0.10469348728656769,
0.1063699871301651,
-0.021279186010360718,
0.0006253354367800057,
-0.02200753055512905,
-0.02686971053481102,
0.019158175215125084,
0.0008286537486128509,
-0.006825525313615799,
0.03376371040940285,
-0.04005329683423042,
-0.005473393946886063,
0.01155207771807909,
0.006512247957289219,
0.017331261187791824,
0.0051346695981919765,
0.044769249856472015,
-0.00407422473654151,
0.04319870471954346,
-0.03897339105606079,
0.02521609514951706,
0.019352497532963753,
0.01609206572175026,
0.08946367353200912,
-0.01799422688782215,
0.0019599231891334057,
0.05510773882269859,
0.027083709836006165,
0.02424171380698681,
-0.011618221178650856,
0.018720727413892746,
-0.02225322090089321,
0.023831326514482498,
0.0393526665866375,
-0.029790276661515236,
0.004390980117022991,
0.011999288573861122,
-0.02015841007232666,
-0.02378077432513237,
0.04193578660488129,
0.012429943308234215,
0.03805730864405632,
0.007205172907561064,
-0.040164537727832794,
0.007961738854646683,
-0.007084670476615429,
0.013750799931585789,
0.0780394971370697,
0.012434868142008781,
-0.03515968099236488,
-0.03796659782528877,
0.008487260900437832,
-0.019166355952620506,
0.009238635189831257,
-0.02590819261968136,
0.004885413218289614,
0.011330884881317616,
0.00244714692234993,
0.012462988495826721,
-0.011531008407473564,
-0.03007185459136963,
-0.043505098670721054,
0.08227434754371643,
0.03303925320506096,
0.04623899608850479,
-0.01818813383579254,
0.012462676502764225,
0.009898923337459564,
-0.028294850140810013,
0.020805440843105316,
0.009714102372527122,
-0.02847941778600216,
-0.02178099937736988,
0.007322667166590691,
-0.00947545189410448,
-0.018685638904571533,
0.015492165461182594,
0.0010976981138810515,
0.04783206433057785,
-0.020034166052937508,
-0.10356486588716507,
-0.07154523581266403,
0.03295404091477394,
-0.016069967299699783,
-0.023415962234139442,
-0.08236712217330933,
0.018577774986624718,
0.02873264066874981,
0.10606735199689865,
0.0019287422765046358,
-0.02252708375453949,
-0.0015306600835174322,
0.01423699501901865,
0.021177085116505623,
0.012302005663514137,
-0.01365729421377182,
0.0230578500777483,
-0.03746618703007698,
0.013826251961290836,
-0.09125711768865585,
0.030736776068806648,
0.03279668092727661,
0.01891881600022316,
-0.010450214147567749,
0.033003829419612885,
-0.05128271132707596,
0.03177646920084953,
-0.036546748131513596,
0.02707461453974247,
-0.005484094377607107,
0.10332220047712326,
0.04976867511868477,
-0.008969781920313835,
0.04053110629320145,
0.04657036066055298,
0.02725811116397381,
0.014626308344304562,
0.021513570100069046,
0.07764947414398193,
-0.048243723809719086,
-0.025657976046204567,
-0.004043084103614092,
0.00838562287390232,
-0.005342232063412666,
-0.039071764796972275,
-0.05609699711203575,
0.004528042860329151,
0.00843044463545084,
0.015341958031058311,
0.03853357210755348,
-0.0033095127437263727,
0.02592562884092331,
-0.009886365383863449,
-0.03758775815367699,
0.005871920846402645,
-0.06869744509458542,
0.006630797870457172,
0.04461603984236717,
-0.0024274266324937344,
0.036233317106962204,
-0.0009647918632254004,
0.013051855377852917,
-0.032011330127716064,
-0.023809682577848434,
0.0031636273488402367,
0.05509627237915993,
-0.006957371719181538,
-0.03469971567392349,
0.024704497307538986,
0.04267424717545509,
0.049183934926986694,
0.009236849844455719,
0.019192300736904144,
0.03580532222986221,
-0.04937305301427841,
0.026439569890499115,
-0.03342405706644058,
0.03755458444356918,
0.013542328029870987,
0.039773937314748764,
-0.0032367627136409283,
0.007196794264018536,
0.0011861227685585618,
0.038726676255464554,
-0.02336394600570202,
0.10782171785831451,
0.014477667398750782,
0.02458963543176651,
-0.020145822316408157,
0.046879202127456665,
0.02242423966526985,
-0.001186349312774837,
0.0003060251474380493,
-0.050008002668619156,
-0.0034801955334842205,
-0.021007021889090538,
0.0031150926370173693,
0.04111197590827942,
-0.038011498749256134,
0.01521459873765707,
0.0468858927488327,
0.021693341434001923,
0.057486869394779205,
0.04812803119421005,
-0.012032843194901943,
-0.028644690290093422,
0.008620387874543667,
-0.018085043877363205,
-0.0016679984983056784,
0.003764634020626545,
0.00956401601433754,
0.02876497618854046,
-0.0025606187991797924,
-0.029211783781647682,
0.0143289715051651,
-0.0039025614969432354,
0.014452733099460602,
-0.00036138444556854665,
-0.010097512044012547,
-0.032605137676000595,
0.05024879425764084,
-0.02281975746154785,
0.02752688340842724,
0.024214185774326324,
0.008589533157646656,
0.02052660845220089,
-0.0400148406624794,
-0.018817059695720673,
0.01671803742647171,
0.019651081413030624,
-0.03745665028691292,
-0.0004046665853820741,
0.017078788951039314,
-0.04573959857225418,
0.008841685019433498,
-0.03611668571829796,
0.027089964598417282,
-0.019045954570174217,
-0.007795864250510931,
0.021423978731036186,
-0.00472493888810277,
0.06576007604598999,
-0.046053238213062286,
-0.02671126462519169,
-0.017315395176410675,
-0.045767754316329956,
-0.006590716075152159,
0.015118726529181004,
-0.018262309953570366,
0.02681061439216137,
-0.03458692133426666,
-0.06127706915140152,
0.060613375157117844,
-0.021783415228128433,
0.038057539612054825,
0.029302192851901054,
-0.02506786584854126,
-0.06691591441631317,
0.00024913999368436635,
-0.036732081323862076,
-0.009842447936534882,
-0.030575545504689217,
-0.001341789262369275,
0.0680186077952385,
-0.009411861188709736,
-0.03274688497185707,
-0.003080597147345543,
-0.01017982978373766,
-0.037116799503564835,
-0.018537793308496475,
0.01715896464884281,
0.008169620297849178,
-0.039950963109731674,
0.0222354494035244,
-0.003528906963765621,
-0.03421211242675781,
0.005884366575628519,
-0.042113713920116425,
-0.07109500467777252,
0.027762725949287415,
0.015084799379110336,
0.06030209735035896,
-0.012514247559010983,
-0.004571804776787758,
0.08351609855890274,
0.0319027304649353,
-0.012413793243467808,
-0.01428074762225151,
-0.03085407055914402,
0.03477320820093155,
0.014047284610569477,
-0.022910309955477715,
0.028571616858243942,
-0.028469013050198555,
0.016950061544775963,
0.01620267517864704,
0.006006347481161356,
0.014604262076318264,
0.0203112605959177,
-0.01355135627090931,
-0.007273302413523197,
-0.009965521283447742,
0.020790960639715195,
0.010171928443014622,
0.0015337534714490175,
-0.02260339818894863,
0.02497989684343338,
-0.021190503612160683,
0.06536105275154114,
0.007140944711863995,
-0.030590509995818138,
0.06014009937644005,
0.013322790153324604,
0.005018352530896664,
-0.020837070420384407,
0.0613376647233963,
0.005357977002859116,
0.013360525481402874,
0.015464391559362411,
0.02565869688987732,
0.05604309216141701,
-0.014140002429485321,
0.042637184262275696,
-0.006202124524861574,
0.02983437478542328,
-0.019823387265205383,
-0.007646799087524414,
-0.0028878855518996716,
-0.01160262618213892,
0.01857326552271843,
-0.04285677149891853,
-0.024754222482442856,
0.03386492654681206,
0.03556050732731819,
0.0230606347322464,
0.013654258102178574,
0.0011002366663888097,
0.038532666862010956,
-0.05365186184644699,
-0.0471748486161232,
-0.0033967436756938696,
0.026026494801044464,
0.023306915536522865,
0.04310046136379242,
0.026598265394568443,
0.013817409984767437,
0.03223118558526039,
0.008629214949905872,
-0.11100378632545471,
0.02074529230594635,
-0.046086933463811874,
-0.030020074918866158,
-0.02173728682100773,
-0.0061856526881456375,
-0.03592821955680847,
-0.013079149648547173,
-0.03400426730513573,
-0.03480046987533569,
0.024542653933167458,
-0.047204017639160156,
0.021664084866642952,
-0.025768660008907318,
-0.04086931049823761,
-0.002927787136286497,
0.02649371512234211,
0.034528303891420364,
-0.03483245149254799,
-0.025418998673558235,
0.021322835236787796,
-0.05636024847626686,
-0.018976544961333275,
0.010782024823129177,
-0.0034698687959462404,
-0.009129258804023266,
0.037756387144327164,
0.029431870207190514,
0.031198233366012573,
-0.010956937447190285,
0.007643566001206636,
0.025705963373184204,
0.05531078577041626,
0.014857042580842972,
0.006758294999599457,
-0.05336887389421463,
-0.037461455911397934,
-0.004963934421539307,
0.021630875766277313,
0.03227418661117554,
-0.021164342761039734,
0.02112491987645626,
0.00953924935311079,
-0.003297517541795969,
-0.02635621279478073,
0.009660938754677773,
0.05353504791855812,
0.011347144842147827,
-0.003464834066107869,
-0.06336647272109985,
0.007549583911895752,
-0.0367765948176384,
-0.017657581716775894,
0.016920574009418488,
-0.0211863461881876,
-0.03455096483230591,
-0.012460420839488506,
0.009022301994264126,
0.03157207742333412,
-0.04592057690024376,
0.0059242527931928635,
-0.020252777263522148,
0.01692761853337288,
0.01488438155502081,
0.005172602366656065,
0.0074151307344436646,
-0.0261542871594429,
0.03232848644256592,
-0.011764171533286572,
0.013730611652135849,
-0.07581053674221039,
-0.019046302884817123,
0.026104234158992767,
0.04527893662452698,
-0.023749928921461105,
0.005891178268939257,
-0.08632472902536392,
-0.02228950522840023,
0.07888495177030563,
-0.018556542694568634,
0.019708022475242615,
-0.016616174951195717,
-0.021062051877379417,
-0.013585620559751987,
-0.023723619058728218,
-0.022428998723626137,
0.003838698845356703,
0.008224202319979668,
-0.04263583943247795,
-0.031108543276786804,
0.021581660956144333,
-0.0020260110031813383,
0.012019253335893154,
0.05909711867570877,
0.07071690261363983,
0.029226845130324364,
-0.0366438552737236,
-0.035729508846998215,
0.02413927949965,
-0.026809418573975563,
-0.08077752590179443,
-0.031642746180295944,
0.01324696745723486,
-0.006867744028568268,
0.026293037459254265,
-0.06551175564527512,
-0.038216762244701385,
0.05687400698661804,
0.03227636218070984,
-0.041178736835718155,
-0.012191524729132652,
-0.0452907420694828,
0.022520406171679497,
0.03321748971939087,
-0.01761445589363575,
0.024737238883972168,
0.05230824276804924,
-0.017969921231269836,
0.010988133028149605,
0.004130961839109659,
0.010389585979282856,
-0.040931783616542816,
0.00021032853692304343,
-0.02175832912325859,
0.001025946345180273,
-0.03035777062177658,
0.04463043436408043,
-0.03804898262023926,
0.002800566842779517,
0.024909986183047295,
-0.043044738471508026,
-0.0264084804803133,
0.0213218592107296,
0.026018282398581505,
0.006158743519335985,
-0.018283266574144363,
0.0006431135116145015,
-0.01820184662938118,
-0.0029376756865531206,
-0.008655070327222347,
0.01862756721675396,
0.031427230685949326,
0.04060807824134827,
0.0004886452225036919,
0.012565507553517818,
-0.02335044927895069,
0.0006039972649887204,
0.01898147538304329,
-0.044611331075429916,
0.02739744447171688,
-0.021761786192655563,
-0.01963181421160698,
-0.004772655665874481,
-0.037267543375492096,
-0.042297352105379105,
-0.00783778727054596,
-0.009283095598220825,
0.0245345626026392,
-0.06305799633264542,
0.02953823283314705,
0.021962638944387436,
0.014873386360704899,
-0.06470143049955368,
-0.02978907711803913,
0.018798287957906723,
0.01787763461470604,
0.008279292844235897,
-0.02393944188952446,
-0.01888744905591011,
-0.05209005996584892,
-0.006520776078104973,
0.009845172055065632,
0.04188800975680351,
0.0002077527024084702,
0.005358275957405567,
-0.008920600637793541,
-0.014716398902237415,
0.044383615255355835,
-0.009544665925204754,
0.009628599509596825,
0.04123218357563019,
-0.009903481230139732,
-0.012409677729010582,
-0.00033316356712020934,
0.09109599143266678,
-0.05045875534415245,
-0.040678609162569046,
-0.009354786016047001,
0.0012654121965169907,
0.017047790810465813,
-0.02926991507411003,
-0.02146151289343834,
0.07412740588188171,
0.007821746170520782,
0.02691602148115635,
0.00597304105758667,
0.017626775428652763,
0.004856259562075138,
-0.0021978486329317093,
0.044192031025886536,
0.012194642797112465,
-0.02471100352704525,
-0.04072511941194534,
0.0298074372112751,
-0.000529885699506849,
0.027366381138563156,
-0.04519689455628395,
0.02685721404850483,
-0.028644757345318794,
-0.02508336864411831,
0.007125000935047865,
-0.0034680208191275597,
-0.0015894179232418537,
-0.02665294148027897,
-0.027324633672833443,
0.029390178620815277,
0.011532045900821686,
-0.0395987406373024,
-0.017153510823845863,
-0.028942115604877472,
-0.029465822502970695,
0.05194329842925072,
-0.02050895057618618,
0.027952255681157112,
0.0044169859029352665,
0.0031142921652644873,
-0.03176635503768921,
0.00006089288945076987,
-0.03894569352269173,
-0.002047410700470209,
0.01080323662608862,
-0.0007430780678987503,
0.006718969438225031,
-0.0013137480709701777,
0.009076355956494808,
0.03408244624733925,
-0.007941946387290955,
0.02338155172765255,
0.007186034694314003,
0.03586380183696747,
0.028149884194135666,
0.006848166696727276,
-0.01697700470685959,
0.033094797283411026,
-0.020045127719640732,
0.03281467780470848,
0.0019253646023571491,
-0.022891219705343246,
0.02212723344564438,
0.00969413947314024,
0.021022366359829903,
-0.03727182373404503,
-0.020492196083068848,
-0.018570587038993835,
0.02496107667684555,
0.0028386011254042387,
0.03110610507428646,
0.015870070084929466,
0.0009096835274249315,
0.0061498889699578285,
0.026936395093798637,
0.018294064328074455,
-0.03416111320257187,
-0.0598946250975132,
-0.04023849591612816,
-0.042288392782211304,
-0.033538028597831726,
0.01720474660396576,
0.026602668687701225,
-0.01848546788096428,
0.024637868627905846,
-0.03649178892374039,
0.018414709717035294,
0.016314564272761345,
0.04367871582508087,
-0.020532116293907166,
0.07408430427312851,
0.009665420278906822,
-0.0035062371753156185,
-0.02775079570710659,
0.03285630792379379,
0.10478083044290543,
0.046747494488954544,
-0.017561325803399086,
-0.03854009509086609,
0.05729515478014946,
-0.020510854199528694,
0.004171300213783979,
-0.042510341852903366,
0.011821952648460865,
-0.01302017830312252,
-0.00956584233790636,
-0.008358500897884369,
0.040336158126592636,
-0.04432616010308266,
-0.02958713285624981,
0.03147175535559654,
-0.021576566621661186,
-0.023927699774503708,
-0.004659025464206934,
0.010657803155481815,
0.0071255601942539215,
-0.0009367193561047316,
0.02217765338718891,
0.010799326002597809,
-0.042632944881916046,
-0.01347116194665432,
-0.013955099508166313,
-0.046518370509147644,
-0.004054795950651169,
-0.0102405846118927,
-0.06321639567613602,
0.004002873320132494,
0.02050023339688778,
-0.011264896020293236,
-0.025579744949936867,
0.05548952892422676,
0.013917878270149231,
0.003952862694859505,
0.01634347066283226,
0.03139277547597885,
0.007495473138988018,
0.02222214825451374,
-0.0156797356903553,
-0.006072381976991892,
-0.05352173000574112,
-0.0021941603627055883,
-0.03025009296834469,
0.044733211398124695,
-0.0011953954817727208,
0.005173637066036463,
0.01265414897352457,
-0.015153754502534866,
0.028895758092403412,
-0.05011240020394325,
-0.019161496311426163,
0.010212772525846958,
0.008635714650154114,
0.007663934025913477,
-0.009869042783975601,
-0.04359773173928261,
0.029479902237653732,
0.008063898421823978,
0.008385855704545975,
-0.011911017820239067,
-0.03703270107507706,
-0.0012763593113049865,
0.014168861322104931,
0.0102557223290205,
0.0010492998408153653,
-0.033278774470090866,
-0.012028852477669716,
0.006212719716131687,
-0.02725134789943695,
0.000015608606190653518,
0.0009600759949535131,
0.03789519518613815,
-0.004022195003926754,
0.004940152633935213,
-0.012555344961583614,
-0.033612314611673355,
-0.06619366258382797,
0.04453296214342117,
-0.03113914467394352,
-0.011117654852569103,
-0.01760132424533367,
-0.015595969744026661,
0.03103836253285408,
0.04468477517366409,
-0.03814522922039032,
0.03440951555967331,
-0.04277390241622925,
0.05017208307981491,
0.040823616087436676,
0.0014518683310598135,
-0.014842729084193707,
-0.021043382585048676,
-0.001118412590585649,
0.05352269858121872,
-0.004022808279842138,
0.050500355660915375,
0.011922809295356274,
-0.011028606444597244,
-0.0093419523909688,
-0.005975976120680571,
-0.030525632202625275,
-0.014050082303583622,
0.03659719601273537,
-0.016352318227291107,
-0.018661078065633774,
0.003874355461448431,
0.052822571247816086,
-0.022793442010879517,
-0.0052289580926299095,
-0.01531150657683611,
-0.016514312475919724,
-0.051420584321022034,
0.0164676271378994,
0.009176738560199738,
0.005057881586253643,
-0.006311944220215082,
0.009007273241877556,
-0.04303339868783951,
-0.0017565407324582338,
-0.029727857559919357,
0.01598784141242504,
-0.013446195982396603,
-0.009564612060785294,
-0.024832941591739655,
0.03414400294423103,
-0.03608066961169243,
-0.03510330244898796,
-0.0011473187478259206,
0.0042654285207390785,
-0.01565103977918625,
0.011743634007871151,
0.0244006235152483,
0.004570214077830315,
0.0349356010556221,
-0.029293693602085114,
-0.026307443156838417,
0.05140404403209686,
-0.04525446519255638,
-0.06915123015642166,
0.05544066056609154,
-0.051094722002744675,
0.023693762719631195,
0.025329817086458206,
-0.015517236664891243,
-0.030280644074082375,
0.0686284527182579,
-0.007334161549806595,
0.002559359185397625,
0.03941268473863602,
-0.006673001684248447,
-0.04633241519331932,
0.0020867502316832542,
0.01288511324673891,
-0.00432910630479455,
-0.006185710895806551,
0.04516715556383133,
0.021758513525128365,
-0.03066989779472351,
0.03575459122657776,
0.004533588886260986,
-0.04552919790148735,
0.027040190994739532,
-0.012597080320119858,
0.01844315230846405,
0.028798531740903854,
0.019435591995716095,
-0.021424297243356705,
0.040669035166502,
0.021825002506375313,
0.010065038688480854,
-0.12333009392023087,
-0.006235221400856972,
-0.015569333918392658,
0.03121991828083992,
0.041495904326438904,
-0.04679456725716591,
0.04446820914745331,
0.03595425933599472,
-0.05404319241642952,
0.0056471144780516624,
-0.06334293633699417,
-0.019922081381082535,
-0.02546471543610096,
0.008014190010726452,
-0.00673317164182663,
0.024928826838731766,
0.027987489476799965,
0.024745183065533638,
0.03772864490747452,
0.0004900162457488477,
-0.02366524003446102,
-0.026932507753372192,
-0.0013742423616349697,
0.03526405990123749,
-0.005506996531039476,
-0.008029632270336151,
0.08139167726039886,
-0.02669461816549301,
-0.02662152610719204,
0.017687996849417686,
0.004761755466461182,
0.0214850977063179,
-0.0071361190639436245,
0.0019422268960624933,
0.02347436733543873,
0.023622777312994003,
0.01205131970345974,
0.006640833802521229,
0.01544672530144453,
0.015150396153330803,
0.003163656685501337,
0.01654871553182602,
0.014597054570913315,
0.008705571293830872,
0.030165700241923332,
-0.04034695029258728,
-0.02841196209192276,
0.0292093176394701,
-0.0019119861535727978,
-0.002541984198614955,
0.00566305173560977,
0.012393206357955933,
-0.002569623989984393,
-0.043865080922842026,
-0.012818786315619946,
-0.06313871592283249,
-0.02729986421763897,
0.03160756453871727,
-0.01521037146449089,
-0.04426229000091553,
-0.0011639709118753672,
-0.008077098056674004,
-0.040941063314676285,
0.001268243184313178,
0.021245896816253662,
-0.010874131694436073,
-0.06700783967971802,
0.0003425751638133079,
0.0013839761959388852,
-0.005212169606238604,
0.006867716088891029,
-0.036227088421583176,
-0.026058174669742584,
0.03648165240883827,
0.006031903903931379,
0.03618187457323074,
-0.018326086923480034,
-0.00243215449154377,
-0.05408995971083641,
-0.06897852569818497,
0.013851571828126907,
0.00028175374609418213,
0.008067009970545769,
-0.032420992851257324,
-0.028560293838381767,
0.012993372045457363,
-0.008551644161343575,
0.03670793026685715,
-0.028265293687582016,
-0.02448677085340023,
0.02952313795685768,
-0.00835433043539524,
0.007179127540439367,
-0.03849053382873535,
-0.002906538313254714,
-0.010899413377046585,
-0.000021495750843314454,
-0.028336817398667336,
-0.022126657888293266,
-0.009809207171201706,
0.00034643980325199664,
-0.0008935360237956047,
0.015410195104777813,
0.03279665857553482,
-0.016306668519973755,
-0.0206300038844347,
0.06296756863594055,
0.008215876296162605,
-0.015084188431501389,
0.04599512740969658,
0.002694114577025175,
0.05610116198658943,
0.01627541147172451,
-0.004634560085833073,
-0.027786478400230408,
0.0070036668330430984,
-0.019562507048249245,
-0.04037417471408844,
-0.029261821880936623,
0.013234155252575874,
-0.014435256831347942,
-0.06103522703051567,
0.010250546969473362,
0.04743826016783714,
-0.021710099652409554,
0.001625707489438355,
0.07828723639249802,
-0.023623047396540642,
0.029301390051841736,
0.01188645325601101,
0.0071549382992088795,
0.028748033568263054,
0.006540004163980484,
-0.031565066426992416,
0.015750987455248833,
0.0018618881003931165,
-0.034768298268318176,
0.025577854365110397,
0.04456620290875435,
0.004686267580837011,
-0.014803962782025337,
0.011232268065214157,
0.005140090826898813,
-0.03444988280534744,
-0.023018958047032356,
-0.01601475290954113,
-0.03328049182891846,
0.05871905758976936,
0.023355377838015556,
-0.024232806637883186,
0.06976214796304703,
-0.009328694082796574,
0.029154285788536072,
-0.01672947220504284,
0.015368446707725525,
-0.023075604811310768,
0.028535110875964165,
-0.018903736025094986,
0.04454842582345009,
-0.0018255061004310846,
0.0019065174274146557,
-0.01182070653885603,
0.02892877347767353,
0.02139275148510933,
-0.05794142186641693,
0.013827170245349407,
0.00011030178575310856,
-0.0028775676619261503,
-0.025849463418126106,
-0.012032839469611645,
-0.011565756984055042,
-0.03154973313212395,
-0.001963163260370493,
0.0419943630695343,
0.008586090058088303,
0.011484946124255657,
-0.012818940915167332,
0.007719206623733044,
0.05923723429441452,
-0.040108684450387955,
0.0377470888197422,
-0.004529380239546299,
0.033056098967790604,
-0.036681726574897766,
-0.03977149352431297
] |
<p>It appears that velocity is a quantity of motion meaning that all objects can have assigned to them a particular velocity. Through the application of forces (ex: gravity, E&m) we measure changes in velocity, which is called acceleration but here is the crux:</p>
<p>Once the force ceases to be applied the body will stop accelerating.... Meaning that while forces can be applied there is no actual quantity of force</p>
<p>There exists a quantity called momentum (mv) such that a body of mass m with momentum Q will move indefinitely velocity Q/m unless acted on by a force (m*a)</p>
<p>There theoretically could be this thing called 2nd momentum (ma) such that a body of mass m with 2nd momentum Q would accelerate indefinitely unless acted upon by a 2nd order force (mass*jerk) </p>
<p>The reason the above ^ does not occur is because for it to occur would require a constantly increasing amount of energy... ie infinite energy.</p>
<p>But we don't actually mean energy, we mean the quantity 1/2 * mv^2 would grow arbitrarily large for this to occur... </p>
<p>In an abstract mathematical world where it is not 1/2 mv^2 that is conserved but rather the quantity 1/2 m*a^2 that is conserved objects could be in a state of uniform acceleration indefinitely and still satisfy conservation of 2nd order momentum... </p>
<p>But obviously our universe IS NOT that abstract mathematical world of the 2nd kind... It is of the first... Why? What dictated that momentum (mv) became the quantity of motion and not (ma) or for that matter (mass *jerk) or why not fractional derivatives of velocity?</p>
| 9,615 |
[
-0.009606490842998028,
-0.000312920194119215,
-0.014138164930045605,
-0.01849774830043316,
0.044526778161525726,
0.013405228033661842,
-0.036481890827417374,
-0.021164778620004654,
-0.026978058740496635,
-0.03863600641489029,
-0.005975347477942705,
0.018778933212161064,
0.0403875894844532,
0.008014514110982418,
0.03778073191642761,
0.0010216638911515474,
0.002881184220314026,
-0.020051198080182076,
-0.016059499233961105,
-0.022287623956799507,
-0.0038644408341497183,
-0.014639962464571,
0.016336889937520027,
0.011062376201152802,
-0.014868654310703278,
0.013929102569818497,
0.00814262218773365,
-0.010866299271583557,
0.028707418590784073,
0.06034937500953674,
-0.0011291108094155788,
-0.0035612238571047783,
-0.015282664448022842,
0.018982836976647377,
0.017299577593803406,
0.02977057732641697,
-0.043415285646915436,
-0.05212102830410004,
0.004744861740618944,
0.04132967069745064,
-0.02320811152458191,
-0.026021603494882584,
-0.015701914206147194,
0.06391430646181107,
-0.037265095859766006,
0.00684315524995327,
0.020735373720526695,
0.005062628537416458,
0.05665598064661026,
-0.03584469109773636,
0.0824480652809143,
0.007771398406475782,
0.06680161505937576,
0.02410045638680458,
0.003547950182110071,
-0.010127547197043896,
0.07787758857011795,
0.042390357702970505,
-0.010102472268044949,
-0.035482257604599,
-0.03650921583175659,
-0.0032636953983455896,
-0.0030529701616615057,
-0.012521331198513508,
0.02005552314221859,
0.013067561201751232,
-0.03546296805143356,
-0.014842567034065723,
0.023975111544132233,
0.013307345099747181,
0.03874778002500534,
-0.006092854775488377,
0.034353576600551605,
0.010976663790643215,
0.017321037128567696,
-0.010642247274518013,
0.03902342915534973,
-0.02969735488295555,
0.06103375926613808,
0.05192233994603157,
-0.0018845034064725041,
-0.017307572066783905,
0.03877472132444382,
0.00377846066839993,
0.020184265449643135,
0.010831131599843502,
0.0415775403380394,
0.01400680560618639,
0.00733821140602231,
0.041351817548274994,
-0.0035138868261128664,
-0.002641872502863407,
0.02813674509525299,
-0.01753160171210766,
-0.01904883049428463,
0.03462182357907295,
-0.0016751473303884268,
0.028318826109170914,
-0.0026065523270517588,
-0.021431423723697662,
0.02073766477406025,
0.014214561320841312,
0.01127166673541069,
0.04884861409664154,
0.0025752452202141285,
-0.027090711519122124,
-0.03170069307088852,
0.001950902515091002,
-0.06104563921689987,
-0.01949438638985157,
-0.005939089693129063,
0.010073699057102203,
0.014343161135911942,
0.0075513385236263275,
0.017669064924120903,
-0.03812304139137268,
-0.019286375492811203,
-0.01777002029120922,
0.05722750350832939,
0.054093893617391586,
0.047667525708675385,
-0.01526353694498539,
0.005640833638608456,
-0.028352998197078705,
-0.07396713644266129,
0.010637889616191387,
0.027028415352106094,
0.025728050619363785,
-0.02891438826918602,
0.011197769083082676,
0.011598145589232445,
-0.032385874539613724,
0.025282494723796844,
-0.011112070642411709,
0.06695977598428726,
-0.030956536531448364,
-0.10725103318691254,
-0.06458398699760437,
0.020097404718399048,
-0.0026944437995553017,
-0.027629349380731583,
-0.10743378102779388,
0.018383167684078217,
0.028014255687594414,
0.07727817445993423,
-0.0005217588040977716,
-0.02307235077023506,
0.026362407952547073,
0.031714484095573425,
0.017526013776659966,
-0.026563171297311783,
-0.0412081703543663,
0.016554277390241623,
-0.05321917310357094,
0.011615250259637833,
-0.057561784982681274,
0.0190676748752594,
0.017431681975722313,
0.003307638457044959,
-0.03481706604361534,
0.03732618689537048,
-0.05439937487244606,
0.004237656947225332,
0.008822204545140266,
-0.007205145433545113,
-0.0014305553631857038,
0.07691656053066254,
0.03784708306193352,
0.03872179239988327,
0.02821352146565914,
0.05151396617293358,
0.041288066655397415,
-0.01133108139038086,
0.03597631677985191,
0.03109346330165863,
-0.03751429542899132,
-0.047526951879262924,
-0.02499403804540634,
-0.016505293548107147,
-0.008022505789995193,
-0.04510856419801712,
-0.06332788616418839,
-0.004000900313258171,
-0.005380798596888781,
-0.0022232476621866226,
0.020094187930226326,
0.027887878939509392,
0.031064050272107124,
0.0045371572487056255,
-0.018208211287856102,
-0.020716264843940735,
-0.10318823158740997,
0.030166717246174812,
0.011224227026104927,
0.012711725197732449,
-0.014531991444528103,
-0.010059704072773457,
-0.0025367774069309235,
-0.04597427323460579,
0.02269413135945797,
0.004957287572324276,
0.051621682941913605,
0.004506971687078476,
-0.027474045753479004,
-0.011490200646221638,
0.028426213189959526,
0.004906791727989912,
0.005854617804288864,
-0.018951138481497765,
0.027573321014642715,
-0.03195040673017502,
0.015179558657109737,
-0.029998956248164177,
0.013765495270490646,
-0.0016176474746316671,
-0.0016915349988266826,
0.023708216845989227,
-0.021253710612654686,
-0.008576460182666779,
0.047224484384059906,
-0.027164818719029427,
0.08833552151918411,
0.032963719218969345,
-0.0006528071244247258,
-0.03785447031259537,
0.061707381159067154,
-0.01757519319653511,
-0.010308071039617062,
-0.01982211135327816,
-0.02574208378791809,
-0.027463097125291824,
0.009876898489892483,
0.026149742305278778,
0.0402291975915432,
-0.02140944078564644,
0.029358625411987305,
0.02498231641948223,
0.05172161012887955,
0.0304623581469059,
0.031072301790118217,
-0.018367158249020576,
-0.0615069642663002,
0.021192224696278572,
-0.006892850622534752,
0.027367955073714256,
0.047492772340774536,
0.02206835336983204,
0.007988744415342808,
0.008652535267174244,
-0.021052999421954155,
0.011765897274017334,
0.01800895854830742,
0.02238253876566887,
-0.0003173105069436133,
-0.0027511203661561012,
-0.04599209874868393,
0.013229697942733765,
0.024989580735564232,
0.030488505959510803,
0.014503945596516132,
0.008235192857682705,
-0.04124388471245766,
-0.07626782357692719,
-0.029466766864061356,
0.018252715468406677,
-0.02550024539232254,
-0.0349624939262867,
-0.08524433523416519,
0.013838007114827633,
0.015489359386265278,
-0.004940316546708345,
0.006103601306676865,
-0.01872139796614647,
-0.028803357854485512,
-0.0295440461486578,
0.014344885013997555,
0.02076408453285694,
0.03241089731454849,
-0.023890461772680283,
-0.02151613123714924,
0.013406941667199135,
-0.05208694934844971,
-0.0058921100571751595,
-0.018552154302597046,
-0.04127020016312599,
0.033544231206178665,
-0.019152749329805374,
-0.03342144191265106,
0.06639952212572098,
0.014140847139060497,
0.05857105180621147,
0.024823449552059174,
-0.014256112277507782,
-0.08895386010408401,
-0.0036254827864468098,
-0.046795908361673355,
-0.01675236038863659,
0.005822914186865091,
-0.0032132058404386044,
0.05079062283039093,
0.0020988069009035826,
-0.060492563992738724,
0.005020042881369591,
-0.056214720010757446,
-0.03298083692789078,
-0.033824943006038666,
0.006895983126014471,
0.028495702892541885,
-0.020721979439258575,
0.033673375844955444,
0.02180558629333973,
-0.03781864419579506,
0.0024197723250836134,
-0.05825364962220192,
-0.04742495343089104,
-0.005550607107579708,
-0.004993548151105642,
0.057727452367544174,
-0.004725981038063765,
-0.050212472677230835,
0.07497011870145798,
0.05077221617102623,
-0.012331805191934109,
-0.010519183240830898,
-0.0062045687809586525,
0.02701433189213276,
-0.04275520518422127,
-0.0017655608244240284,
-0.002011593198403716,
-0.011627770029008389,
0.001299471827223897,
0.028678549453616142,
0.03805523365736008,
-0.008557029068470001,
-0.01813056878745556,
-0.013527754694223404,
0.0012305165873840451,
0.01424899697303772,
0.01337821688503027,
0.012467378750443459,
0.03652898967266083,
-0.03193444758653641,
0.04534737765789032,
0.005317001137882471,
0.0362645760178566,
-0.027928795665502548,
-0.034673526883125305,
0.04911014810204506,
0.0020212512463331223,
0.0272039994597435,
-0.025408120825886726,
0.02225913666188717,
0.01252049021422863,
-0.0065791672095656395,
0.02693130634725094,
0.003209345741197467,
0.018045645207166672,
0.007449091412127018,
0.05201205611228943,
0.0011915912618860602,
0.02902100421488285,
0.013100901618599892,
-0.035334181040525436,
-0.012087998911738396,
0.03270994871854782,
0.013606185093522072,
-0.027916597202420235,
0.02012692205607891,
0.04160151258111,
-0.011718343943357468,
0.022036561742424965,
0.010548415593802929,
-0.028514035046100616,
0.007610487286001444,
-0.03460203856229782,
0.016855331137776375,
-0.0097326235845685,
0.034327391535043716,
-0.021084416657686234,
0.07454673945903778,
0.019458340480923653,
0.04161714389920235,
-0.021719662472605705,
0.006465614773333073,
-0.12145793437957764,
0.0181563887745142,
-0.06455649435520172,
-0.010272350162267685,
-0.018033575266599655,
0.017936915159225464,
-0.05225707218050957,
-0.008186589926481247,
0.025775691494345665,
0.014994615688920021,
-0.040577203035354614,
-0.0832519680261612,
-0.010465902276337147,
-0.07772969454526901,
-0.05844816565513611,
-0.049065109342336655,
0.007157914340496063,
0.06425516307353973,
-0.0006663601379841566,
0.02370789460837841,
0.01942875050008297,
-0.027791716158390045,
-0.036432936787605286,
-0.011340776458382607,
-0.024515880271792412,
0.03935011476278305,
0.017025483772158623,
0.03331133350729942,
0.01510707102715969,
-0.0029342989437282085,
0.038583166897296906,
0.010178680531680584,
0.06853393465280533,
0.010267418809235096,
0.016110563650727272,
-0.035068951547145844,
-0.05505962669849396,
-0.02558838203549385,
0.01858893409371376,
0.02931174263358116,
0.020725080743432045,
-0.013734567910432816,
0.0004219072579871863,
0.011803903616964817,
-0.02237054333090782,
0.0484461784362793,
0.05930890515446663,
-0.018398933112621307,
-0.03238733485341072,
-0.05251580849289894,
0.009234643541276455,
-0.01099972054362297,
-0.037521086633205414,
0.0023937819059938192,
-0.015262632630765438,
-0.020242977887392044,
-0.011534892953932285,
0.020565850660204887,
-0.0004839975154027343,
-0.028253043070435524,
-0.0037959767505526543,
-0.009945215657353401,
0.022526077926158905,
0.02081780508160591,
-0.0008275729487650096,
0.00429499801248312,
0.02527318149805069,
0.015372552908957005,
-0.0012555812718346715,
-0.007678169757127762,
-0.05224478244781494,
-0.0026740566827356815,
0.009675167500972748,
0.04156027361750603,
0.001448205322958529,
0.008672616444528103,
-0.03370072692632675,
-0.07400517910718918,
0.026675187051296234,
-0.039158377796411514,
0.033237524330616,
-0.011518064886331558,
0.0076836999505758286,
-0.007347376085817814,
-0.024845102801918983,
0.013881159014999866,
0.018323123455047607,
-0.018377376720309258,
-0.02247020974755287,
-0.006803189404308796,
0.013735856860876083,
-0.04185330122709274,
0.011545214802026749,
0.004763930570334196,
0.0366225428879261,
0.018145792186260223,
0.02466515079140663,
-0.009026691317558289,
-0.00495343841612339,
-0.02402348443865776,
-0.06934067606925964,
0.004347306676208973,
-0.0029197901021689177,
-0.016140785068273544,
0.006689760833978653,
-0.02955605275928974,
-0.0602799691259861,
0.044847242534160614,
-0.014377566054463387,
0.0058213528245687485,
0.004107852000743151,
-0.03244353458285332,
0.02407768741250038,
0.015007284469902515,
-0.0030301506631076336,
0.03645593672990799,
0.026192501187324524,
-0.007725956384092569,
-0.029931431636214256,
0.00252756685949862,
0.04805116355419159,
-0.020051181316375732,
0.001997418701648712,
-0.06864020228385925,
0.010819223709404469,
-0.05073138326406479,
0.05584438145160675,
0.029885515570640564,
-0.012242961674928665,
-0.01095951534807682,
-0.02417057938873768,
-0.01693522185087204,
0.04054498299956322,
0.0386708565056324,
-0.023974930867552757,
-0.023500287905335426,
0.03252105414867401,
-0.01561647281050682,
-0.01200488768517971,
0.016638372093439102,
0.010084902867674828,
-0.028221571817994118,
0.04790768399834633,
-0.005003566388040781,
0.010942692868411541,
0.013600334525108337,
-0.0246464591473341,
0.027486681938171387,
-0.012275686487555504,
0.019914645701646805,
-0.019707543775439262,
0.01853536255657673,
0.024935979396104813,
-0.06169443577528,
-0.0632699728012085,
0.023889370262622833,
-0.008443347178399563,
0.01155125629156828,
-0.05131179466843605,
0.03567482531070709,
0.03123934380710125,
0.03525267913937569,
-0.06488706171512604,
-0.028395354747772217,
0.021879635751247406,
0.012526401318609715,
-0.00911092571914196,
0.00918294582515955,
0.007399614900350571,
-0.0445452518761158,
-0.0015293725300580263,
0.02020619995892048,
0.061314795166254044,
-0.00015460299619007856,
-0.00023338192841038108,
0.021050233393907547,
0.041120849549770355,
-0.005039872135967016,
-0.0045571159571409225,
-0.04617179557681084,
-0.006661700550466776,
0.019014565274119377,
-0.010235477238893509,
0.01875944435596466,
0.06783882528543472,
-0.0327758863568306,
0.02123277634382248,
-0.0059672570787370205,
-0.04329100251197815,
0.003117759246379137,
0.011392772197723389,
0.024032535031437874,
0.03609597310423851,
-0.0034092124551534653,
0.01310703530907631,
-0.017231211066246033,
0.02994055114686489,
0.021424157544970512,
0.036877140402793884,
0.02450556494295597,
-0.03458395227789879,
-0.03015069104731083,
-0.036418184638023376,
0.012837356887757778,
0.030853651463985443,
0.013745326548814774,
0.0024046748876571655,
0.03014932945370674,
-0.03355373442173004,
-0.008790269494056702,
0.014005158096551895,
-0.0020406083203852177,
0.0146997245028615,
0.0009784987196326256,
-0.008293727412819862,
0.007169912103563547,
-0.02707717753946781,
-0.02313106134533882,
0.004583023954182863,
-0.010292123071849346,
-0.00278584030456841,
0.06355699896812439,
-0.0482349619269371,
0.0195076372474432,
-0.01119281630963087,
0.0055887121707201,
-0.01301307138055563,
-0.02194085158407688,
-0.021677806973457336,
-0.00003870228101732209,
-0.015087633393704891,
-0.000007095125965861371,
-0.025495946407318115,
-0.01967310905456543,
0.03721345588564873,
0.010697836056351662,
-0.026097452268004417,
-0.0055214096792042255,
0.008183908648788929,
0.024377021938562393,
0.018643952906131744,
-0.006169003434479237,
-0.00018405226001050323,
0.02511308155953884,
-0.011258134618401527,
0.026614459231495857,
0.02965184673666954,
-0.03983556479215622,
0.04727713763713837,
0.016719214618206024,
-0.024863585829734802,
-0.0459807813167572,
-0.0015481330920010805,
-0.05481455475091934,
0.009837443940341473,
0.008314264938235283,
0.004635763820260763,
0.007511775940656662,
0.0005693114944733679,
0.0017040526727214456,
0.02712312713265419,
0.014766967855393887,
0.016269570216536522,
-0.048392802476882935,
-0.021853197365999222,
-0.02208068035542965,
-0.027600623667240143,
0.04267066344618797,
0.03383299335837364,
-0.04416058957576752,
-0.022046267986297607,
-0.016222979873418808,
0.007517028134316206,
-0.00026417174376547337,
0.009901612997055054,
-0.028979996219277382,
0.07821812480688095,
0.013438248075544834,
0.0343732014298439,
-0.043192848563194275,
0.014839667826890945,
0.10393548756837845,
0.050812169909477234,
0.0033230010885745287,
-0.004867370240390301,
0.034093499183654785,
-0.034451842308044434,
0.03217644244432449,
-0.030002010986208916,
0.059952471405267715,
0.04111238569021225,
0.03514089807868004,
0.010756401345133781,
0.05194316431879997,
0.0121817197650671,
-0.0002190166705986485,
0.08454456925392151,
-0.02274284139275551,
-0.057259704917669296,
-0.03525442257523537,
0.013038798235356808,
-0.024695677682757378,
0.03155016526579857,
-0.007056246977299452,
0.02972245030105114,
0.02660110965371132,
0.014459635131061077,
-0.010399799793958664,
-0.02727700024843216,
0.00020639601279981434,
0.001475134864449501,
-0.033757440745830536,
0.007786169648170471,
0.024781642481684685,
-0.024058738723397255,
-0.0715147852897644,
-0.0011079213581979275,
0.0151720205321908,
0.021426893770694733,
0.009374253451824188,
0.03188134357333183,
0.06648349016904831,
0.020602203905582428,
-0.005543570499867201,
-0.0015678810887038708,
-0.04701247811317444,
-0.013343479484319687,
-0.028441481292247772,
0.061573371291160583,
-0.040366534143686295,
0.017805133014917374,
0.0053319139406085014,
-0.02178860828280449,
-0.020450612530112267,
-0.05241412669420242,
-0.004561742302030325,
-0.007180396467447281,
0.03896032273769379,
0.030240477994084358,
0.008680294267833233,
-0.03642871975898743,
-0.01104526687413454,
0.011121171526610851,
0.03363807126879692,
-0.020095452666282654,
-0.018009040504693985,
-0.03033420257270336,
-0.008801832795143127,
0.02617334946990013,
-0.05181460455060005,
-0.013431939296424389,
-0.004638160113245249,
-0.020759625360369682,
-0.06676466763019562,
-0.0009566392400301993,
0.00957315694540739,
0.01948738470673561,
0.010927966795861721,
-0.0017683727201074362,
0.016749432310461998,
-0.04241422191262245,
-0.012072408571839333,
0.0453420914709568,
0.0009074058616533875,
-0.024741817265748978,
-0.03119402565062046,
0.004580630920827389,
-0.018536675721406937,
0.02628680318593979,
-0.06964342296123505,
-0.02536732889711857,
-0.04956240579485893,
-0.005600114353001118,
0.02912949025630951,
-0.014174955897033215,
-0.01274174265563488,
0.005242808256298304,
-0.017535420134663582,
0.009940971620380878,
-0.015637636184692383,
0.025740358978509903,
0.01732989400625229,
0.003555823815986514,
-0.018761223182082176,
0.01809423789381981,
-0.014088302850723267,
0.0550864040851593,
0.05077206715941429,
-0.011011422611773014,
0.015138231217861176,
0.012693319469690323,
0.02402620203793049,
0.00041020786738954484,
-0.01527354121208191,
-0.02389107272028923,
-0.0017668124055489898,
-0.03628626838326454,
0.06127814203500748,
-0.006548916455358267,
-0.004683441482484341,
-0.04404829069972038,
0.059549398720264435,
-0.06840003281831741,
0.006092926021665335,
-0.037653788924217224,
-0.0012108557857573032,
0.0010234996443614364,
-0.030525829643011093,
-0.021973906084895134,
0.05065590888261795,
-0.032535795122385025,
-0.014906666241586208,
0.006384172011166811,
0.003487042849883437,
-0.044526129961013794,
-0.0062893955036997795,
0.03071867860853672,
-0.012944663874804974,
0.017680509015917778,
-0.019834425300359726,
-0.05155152827501297,
0.0348186157643795,
-0.01687668450176716,
-0.07630923390388489,
0.050584565848112106,
-0.024712208658456802,
0.036672402173280716,
0.020223964005708694,
-0.015182163566350937,
-0.041073136031627655,
0.08838098496198654,
-0.030500872060656548,
0.009997202083468437,
0.008439606986939907,
-0.04546378552913666,
-0.02876650169491768,
-0.011150083504617214,
0.027083270251750946,
-0.03160201385617256,
-0.007635692600160837,
0.03785400837659836,
0.01289976667612791,
-0.003021259792149067,
-0.021572599187493324,
0.016997160390019417,
-0.005646617617458105,
0.029121099039912224,
0.05706261843442917,
0.03091374598443508,
0.03163248673081398,
0.05280923843383789,
-0.036641668528318405,
0.011163730174303055,
0.0016902090283110738,
-0.005520613864064217,
-0.06935425847768784,
-0.0005709708202630281,
-0.01186097040772438,
0.05296412482857704,
0.03222518041729927,
-0.028301019221544266,
-0.01514191459864378,
0.003582744626328349,
-0.07592424005270004,
-0.018684063106775284,
-0.06698352098464966,
-0.015851672738790512,
0.00833403691649437,
-0.009371419437229633,
-0.01897449605166912,
0.06574531644582748,
0.05523839592933655,
0.04287604242563248,
0.02717246301472187,
-0.02365954779088497,
0.0005166112678125501,
-0.0020455950871109962,
-0.0031296939123421907,
0.024444177746772766,
-0.046699151396751404,
0.033630214631557465,
0.06608910113573074,
0.005099753383547068,
-0.006544593255966902,
0.028957931324839592,
-0.009433049708604813,
0.02487366273999214,
-0.010072593577206135,
0.021833131089806557,
0.01693355292081833,
0.0377623476088047,
-0.00774578470736742,
0.0066689737141132355,
-0.03728744015097618,
-0.0035372681450098753,
0.01937543973326683,
0.04330265149474144,
0.0003102482296526432,
-0.020120568573474884,
0.037345390766859055,
-0.04825310409069061,
-0.007696561049669981,
0.007674050983041525,
-0.03643936291337013,
-0.01675526238977909,
-0.003725239308550954,
0.008185513317584991,
-0.012351694516837597,
-0.01238244492560625,
0.014104368165135384,
-0.0192626491189003,
-0.04972754418849945,
0.041906800121068954,
-0.008880958892405033,
0.01481569278985262,
0.03918026387691498,
0.030901094898581505,
-0.0020862610545009375,
0.02708064578473568,
0.01212378777563572,
-0.009073296561837196,
-0.06300549954175949,
-0.014272480271756649,
0.018835557624697685,
-0.026578467339277267,
0.010142603889107704,
-0.05563794821500778,
-0.03969936817884445,
0.04083933308720589,
0.04859180748462677,
0.025479882955551147,
-0.010045597329735756,
-0.03071214258670807,
-0.008430755697190762,
-0.07951290160417557,
0.042993731796741486,
-0.0008668411755934358,
-0.02015174925327301,
-0.03844359517097473,
-0.0028198810759931803,
0.027445685118436813,
0.012468649074435234,
0.03118714690208435,
0.0017630226211622357,
-0.0026416247710585594,
0.05322873592376709,
0.0031174749601632357,
0.01444322895258665,
-0.01661263220012188,
-0.03939593955874443,
-0.017946043983101845,
0.008985844440758228,
-0.010345974937081337,
0.008615698665380478,
-0.01789109967648983,
-0.008632573299109936,
0.03922687843441963,
-0.01178232952952385,
0.04230119660496712,
0.013220071792602539,
-0.04162685200572014,
0.019066087901592255,
-0.009402109310030937,
-0.029953669756650925,
0.04587791487574577,
-0.0035615141969174147,
0.014127963222563267,
0.034283582121133804,
-0.00038106797728687525,
-0.038298919796943665,
0.018894225358963013,
0.0034128453116863966,
0.0018910294165834785,
-0.019389089196920395,
-0.01783948391675949,
0.03499576821923256,
-0.04189036041498184,
0.011426077224314213,
0.05484919250011444,
-0.00829868670552969,
-0.005027256906032562,
0.03541838005185127,
0.022284265607595444,
0.012031312100589275,
0.04249664768576622,
0.008953788317739964,
0.016260210424661636,
0.007708454970270395,
-0.012647406198084354,
0.019730480387806892,
0.028867436572909355,
-0.02445855364203453,
0.0039553954266011715,
0.026841474696993828,
-0.009112288244068623,
0.010953808203339577,
0.016716454178094864,
0.04150911793112755,
-0.04970556125044823,
-0.015898970887064934,
-0.008792703971266747,
-0.03178517147898674,
0.023266660049557686,
0.016188057139515877,
-0.019185801967978477,
0.09430646151304245,
-0.004970069043338299,
0.008372475393116474,
0.017748814076185226,
-0.0030588291119784117,
-0.04667304828763008,
-0.012528476305305958,
0.03462466970086098,
0.00750621547922492,
0.005039340816438198,
0.00555282412096858,
-0.006648627109825611,
-0.009486510418355465,
0.029171718284487724,
0.002768248785287142,
0.030673444271087646,
0.0087127685546875,
-0.020855501294136047,
-0.02874874696135521,
-0.023279307410120964,
-0.04692842811346054,
-0.037736184895038605,
0.038053788244724274,
0.01813521608710289,
0.05350712686777115,
-0.017236657440662384,
0.0019372589886188507,
-0.028048602864146233,
0.08496938645839691,
-0.05484450235962868,
0.0038568980526179075,
-0.0032144589349627495,
0.023304646834731102,
-0.0029093739576637745,
-0.022811083123087883
] |
<p>What's the physical difference between the quantities $\left\langle v_{i}v_{j}\right\rangle $ and $\left\langle v_{i}\right\rangle \left\langle v_{j}\right\rangle $? </p>
<p>Where $\left\langle v_{i}\right\rangle$ is the mean value of the $v_{i}$ velocity component with $i=1,2,3$. </p>
<p>(Same story with $v_{j}$.)</p>
<p>This is in the context of stars' velocities in galaxies.</p>
| 9,616 |
[
-0.03534030541777611,
-0.02927684411406517,
-0.04083743318915367,
-0.03097624145448208,
0.05796783044934273,
0.021844862028956413,
-0.023144539445638657,
-0.0025716987438499928,
0.010881522670388222,
-0.03373408690094948,
0.06143628805875778,
0.05868274345993996,
0.07747452706098557,
0.008770664222538471,
0.0477244034409523,
0.03613833338022232,
-0.00004824501957045868,
-0.013071335852146149,
-0.018263839185237885,
-0.0036089615896344185,
-0.0040983944199979305,
0.007614217698574066,
0.045130711048841476,
-0.006787958554923534,
-0.004968691151589155,
0.03423731029033661,
0.02493579126894474,
-0.010321579873561859,
0.01379239372909069,
0.022747447714209557,
-0.0046445708721876144,
-0.0086903665214777,
-0.005134156905114651,
0.007565473206341267,
-0.006743483245372772,
0.006175593473017216,
-0.01928054541349411,
-0.035144031047821045,
-0.017996102571487427,
0.017532015219330788,
-0.07800329476594925,
0.006483062636107206,
-0.012381179258227348,
0.009353685192763805,
-0.003131745383143425,
0.006239347625523806,
0.016597960144281387,
-0.00523475743830204,
0.037621695548295975,
-0.021442381665110588,
0.08791429549455643,
0.013351055793464184,
0.015718435868620872,
0.01900743879377842,
-0.04169154167175293,
0.0296133141964674,
0.08494288474321365,
0.08314816653728485,
-0.010279223322868347,
-0.08754689991474152,
-0.02501046657562256,
-0.006639441940933466,
-0.0033695457968860865,
0.0009418023400940001,
0.002236825879663229,
0.05255003273487091,
-0.038389917463064194,
-0.039490628987550735,
0.02429496869444847,
0.01973012648522854,
0.041172124445438385,
-0.0034242093097418547,
0.018181469291448593,
-0.033389825373888016,
0.0101268095895648,
-0.0003488765505608171,
0.01571335271000862,
0.021990373730659485,
0.039221275597810745,
0.02244320884346962,
0.012439548037946224,
0.0009586860542185605,
0.03949594125151634,
0.01877702586352825,
-0.013467580080032349,
-0.006706477142870426,
0.08436668664216995,
0.007354078348726034,
0.003147271228954196,
0.058447446674108505,
-0.010421699844300747,
0.029371749609708786,
0.02708660438656807,
-0.01505870558321476,
-0.032861292362213135,
0.02338293381035328,
-0.012922419235110283,
0.03430116921663284,
0.01432935893535614,
-0.03731440752744675,
-0.0029071462340652943,
-0.028399191796779633,
0.03287295252084732,
0.07688572257757187,
-0.019620025530457497,
-0.026056556031107903,
-0.05261952802538872,
0.005778860300779343,
-0.07901901751756668,
-0.006124947685748339,
0.005986993666738272,
0.02513628639280796,
0.001686106901615858,
0.03210322558879852,
0.019705770537257195,
-0.02298114448785782,
0.021175500005483627,
0.0008812645100988448,
0.07371371984481812,
0.059163227677345276,
0.04756028205156326,
-0.025151168927550316,
-0.012002368457615376,
-0.01855836994946003,
-0.049198780208826065,
0.016654159873723984,
0.05498681217432022,
0.009772353805601597,
-0.027568647637963295,
-0.005785130430012941,
-0.011825405061244965,
0.010185793042182922,
0.03287215158343315,
-0.01668776385486126,
0.00825736578553915,
-0.04024866595864296,
-0.1308732032775879,
-0.06380841135978699,
0.06364486366510391,
-0.024518344551324844,
-0.028511399403214455,
-0.07934193313121796,
0.010957291349768639,
0.03930332884192467,
0.06997229158878326,
-0.0036832033656537533,
0.0034649784211069345,
0.01301161665469408,
0.04240444302558899,
0.009643797762691975,
-0.005658944137394428,
-0.027117792516946793,
-0.026425763964653015,
-0.029576698318123817,
-0.003934573847800493,
-0.06871795654296875,
0.024118999019265175,
0.036085281521081924,
-0.020145278424024582,
-0.0008091029594652355,
0.07458639144897461,
-0.05110449343919754,
0.00994046125560999,
0.03519952669739723,
0.03403854742646217,
-0.003973077517002821,
0.04604749009013176,
0.009624690748751163,
0.004359019920229912,
0.06013793870806694,
0.008436758071184158,
0.010118653997778893,
-0.002038257662206888,
0.04604360833764076,
0.06992541998624802,
-0.01975119113922119,
-0.011111903004348278,
-0.0030357157811522484,
0.018576277419924736,
-0.03812789171934128,
-0.011395675130188465,
-0.05844876542687416,
-0.01724988967180252,
0.0011278812307864428,
-0.011378288269042969,
0.030660979449748993,
0.031937237828969955,
0.03397642448544502,
-0.0070823123678565025,
-0.022696562111377716,
0.00917878095060587,
-0.07037954777479172,
-0.004013338591903448,
0.007380190305411816,
-0.04434852674603462,
0.05387519299983978,
0.03814193233847618,
0.00435757078230381,
-0.00788519810885191,
-0.0019951462745666504,
0.02542801760137081,
0.049111783504486084,
0.02270469069480896,
-0.031179601326584816,
0.01844952069222927,
0.03688465431332588,
0.03794972226023674,
0.02074236236512661,
0.01713549718260765,
0.018011687323451042,
-0.052296124398708344,
0.013924440369009972,
-0.011631540954113007,
0.01159581821411848,
0.02901662141084671,
0.003423414658755064,
0.011912203393876553,
0.02822561003267765,
0.01105932705104351,
0.033193327486515045,
-0.031219450756907463,
0.07749002426862717,
0.04860193654894829,
-0.0068967449478805065,
-0.0061088004149496555,
0.049397457391023636,
-0.02904234267771244,
0.023934386670589447,
-0.009081739000976086,
-0.02490714192390442,
-0.0530196912586689,
0.015162143856287003,
0.05489978939294815,
0.03045268915593624,
-0.024325426667928696,
0.01116771250963211,
0.060018423944711685,
0.04721871763467789,
0.032745569944381714,
0.017543889582157135,
-0.029562178999185562,
-0.03268564119935036,
0.00797909963876009,
-0.002417902462184429,
-0.008361120708286762,
0.0015025335596874356,
0.03409164771437645,
0.012534791603684425,
0.040687091648578644,
-0.01546355802565813,
-0.0012309766607359052,
0.04396836459636688,
-0.009931587614119053,
-0.008789041079580784,
0.024837380275130272,
-0.04737978056073189,
0.029789123684167862,
-0.02663961797952652,
-0.00030247794347815216,
0.018486926332116127,
-0.005235050339251757,
-0.006814276333898306,
-0.02796955406665802,
-0.015862246975302696,
0.012996706180274487,
0.009161291643977165,
-0.019879072904586792,
-0.006369077134877443,
0.006361490581184626,
-0.020803257822990417,
0.008937881328165531,
-0.05088901147246361,
-0.003143617883324623,
-0.044311799108982086,
-0.02242346480488777,
0.032537829130887985,
-0.009052393026649952,
0.022773809731006622,
-0.025595158338546753,
-0.032700248062610626,
0.00773880910128355,
-0.03395654261112213,
-0.01083445269614458,
-0.001035774708725512,
-0.027436992153525352,
0.021563997492194176,
-0.06074713543057442,
-0.031066203489899635,
0.02690880559384823,
-0.01737406477332115,
-0.0187974963337183,
0.008652390912175179,
-0.023883381858468056,
-0.06605584919452667,
0.00025155997718684375,
-0.008961997926235199,
0.03398294001817703,
-0.01851622760295868,
-0.01655094139277935,
0.05355077236890793,
-0.0660068690776825,
-0.030474526807665825,
-0.007258737925440073,
-0.03490486741065979,
-0.06546620279550552,
-0.02427874319255352,
-0.0225992314517498,
0.022170718759298325,
-0.03729015961289406,
0.006891954690217972,
0.06366073340177536,
-0.020886506885290146,
0.00392749160528183,
-0.06279625743627548,
-0.042753808200359344,
0.003840399207547307,
-0.001140496344305575,
0.05210620537400246,
-0.004712020047008991,
-0.02348855324089527,
0.0707792416214943,
0.04032924771308899,
0.004622017964720726,
-0.00008932227501645684,
0.03625379130244255,
-0.030533481389284134,
0.0043367790058255196,
0.028349703177809715,
0.03315005823969841,
0.003421770641580224,
0.045751024037599564,
0.027064964175224304,
0.029204271733760834,
0.030857009813189507,
0.010651065967977047,
-0.03896980732679367,
0.0023092010524123907,
-0.0218197014182806,
0.013467961922287941,
0.09085914492607117,
0.010564063675701618,
-0.03939212113618851,
0.021699724718928337,
-0.017353756353259087,
0.04987993836402893,
-0.008574534207582474,
-0.05988578870892525,
0.05344387888908386,
0.02370058372616768,
-0.013620428740978241,
-0.01721530221402645,
0.05458053946495056,
0.023232564330101013,
0.007035731337964535,
0.011208231560885906,
0.03729606419801712,
0.047107625752687454,
-0.030964503064751625,
0.018808631226420403,
0.0236587543040514,
0.016681194305419922,
-0.03797381743788719,
-0.006015062797814608,
-0.005821633152663708,
-0.032546136528253555,
0.024090372025966644,
-0.04359639436006546,
-0.044434208422899246,
0.05913430452346802,
0.000926508626434952,
0.00015669965068809688,
-0.02266046218574047,
-0.05350872874259949,
0.02392290160059929,
-0.05555940791964531,
0.026935787871479988,
0.009669335559010506,
0.027730200439691544,
0.02608412317931652,
0.0719078853726387,
0.00323493592441082,
0.02712957002222538,
0.009070971049368382,
-0.04911113902926445,
-0.0671171322464943,
0.016982030123472214,
-0.031187299638986588,
-0.03765612095594406,
-0.038142647594213486,
-0.033722423017024994,
-0.017725398764014244,
-0.03829284757375717,
0.01850230246782303,
-0.006300028879195452,
-0.0016104696551337838,
-0.035171106457710266,
0.014336070977151394,
-0.04920654371380806,
-0.04310872033238411,
-0.02421851083636284,
-0.003315515583381057,
0.050398651510477066,
-0.02635946311056614,
0.04165755584836006,
0.003244902240112424,
0.008115612901747227,
-0.028129421174526215,
-0.014655030332505703,
-0.023651299998164177,
0.02134087309241295,
-0.012980831786990166,
0.03349106386303902,
0.011238791979849339,
-0.0011395069304853678,
0.01807335577905178,
0.02074793353676796,
0.03891553357243538,
0.023567941039800644,
-0.015118454582989216,
0.022941842675209045,
-0.04335854575037956,
0.008131111040711403,
0.0022756012622267008,
0.08041400462388992,
-0.008389714173972607,
0.0007346426718868315,
0.03610708564519882,
0.02617126703262329,
-0.026334580034017563,
0.032535992562770844,
0.029682748019695282,
-0.014855904504656792,
0.005107807461172342,
-0.061768535524606705,
-0.0042794314213097095,
-0.02176494337618351,
-0.030626095831394196,
0.0399337075650692,
-0.0020880841184407473,
0.0024414800573140383,
-0.006334885489195585,
-0.012830845080316067,
0.006258578971028328,
-0.038509707897901535,
-0.008798749186098576,
-0.006342216860502958,
-0.009472477249801159,
-0.01951754279434681,
-0.004609111696481705,
-0.003969079349189997,
0.03712964802980423,
0.028575202450156212,
-0.02055247128009796,
0.013873421587049961,
-0.07251282781362534,
-0.024107545614242554,
0.030332112684845924,
0.030330197885632515,
-0.032609399408102036,
-0.037768952548503876,
-0.04813198745250702,
-0.028300300240516663,
0.04345196112990379,
-0.03784910589456558,
0.026440374553203583,
-0.00694746570661664,
-0.0374152772128582,
0.01470255572348833,
-0.022019105032086372,
-0.029348690062761307,
0.03124329075217247,
-0.004090821370482445,
0.013753758743405342,
-0.021935034543275833,
0.014895927160978317,
-0.021079903468489647,
0.009205874986946583,
0.02667427994310856,
0.042187757790088654,
-0.011280032806098461,
0.011404244229197502,
-0.0009699693764559925,
0.013465245254337788,
-0.009818212129175663,
-0.08336273580789566,
0.00154864729847759,
0.02738260291516781,
0.013163329102098942,
0.04457699880003929,
-0.052108284085989,
-0.07699696719646454,
0.044550687074661255,
0.007669189479202032,
-0.016661379486322403,
0.0081933056935668,
-0.012181386351585388,
0.025938479229807854,
0.02614092081785202,
-0.008503577671945095,
0.05071018636226654,
0.0018880687421187758,
-0.021837638691067696,
-0.0011540325358510017,
-0.03387024998664856,
0.049645885825157166,
-0.03221707046031952,
-0.010831340216100216,
-0.045034535229206085,
0.004362821578979492,
0.003343975869938731,
0.05431929603219032,
-0.00025760187418200076,
0.012080964632332325,
-0.008371236734092236,
-0.038366589695215225,
-0.0037978102918714285,
0.020613905042409897,
0.019894393160939217,
-0.02592405118048191,
-0.0047181895934045315,
0.015643702819943428,
0.008299765177071095,
-0.022361740469932556,
0.03611551597714424,
-0.008209181018173695,
-0.005865007638931274,
0.04387694597244263,
-0.003860190976411104,
0.011960235424339771,
-0.042585499584674835,
-0.004256960935890675,
0.05894660949707031,
-0.03325507789850235,
0.028782496228814125,
-0.015958791598677635,
0.006133328191936016,
0.0020456372294574976,
-0.026951033622026443,
-0.0423041470348835,
-0.03533961996436119,
-0.06070740148425102,
0.02565843053162098,
-0.0059772999957203865,
0.03276141360402107,
-0.010409107431769371,
0.03786391392350197,
-0.07919320464134216,
-0.002190364757552743,
0.0029916695784777403,
0.015057206153869629,
-0.029494842514395714,
-0.006109520327299833,
0.002991092624142766,
-0.029692109674215317,
-0.018200336024165154,
0.010116687044501305,
0.05816817656159401,
-0.014925888739526272,
-0.06090238690376282,
-0.01270123291760683,
0.04666456580162048,
0.04254315420985222,
-0.02904043346643448,
-0.025828756392002106,
-0.004053935874253511,
0.01073866244405508,
-0.0004369520756881684,
0.013436755165457726,
0.06712076812982559,
-0.04173235222697258,
-0.03883194923400879,
-0.025478053838014603,
-0.007550646550953388,
0.020179584622383118,
-0.033532943576574326,
0.0330677293241024,
0.03047356940805912,
-0.015467764809727669,
0.029190951958298683,
-0.015251166187226772,
0.009487607516348362,
0.0024670457933098078,
0.02571212686598301,
-0.019734753295779228,
-0.008314437232911587,
-0.008221647702157497,
-0.029736191034317017,
0.031176691874861717,
0.044143326580524445,
0.001159314881078899,
0.0036171204410493374,
0.036332324147224426,
-0.005490398500114679,
0.049343813210725784,
0.016597798094153404,
0.006317030172795057,
0.023776648566126823,
-0.018466247245669365,
-0.008636388927698135,
0.029792606830596924,
0.016022130846977234,
-0.009630831889808178,
-0.010326718911528587,
-0.05035626143217087,
0.015006649307906628,
0.07931778579950333,
-0.01762946881353855,
0.07206213474273682,
-0.01891402155160904,
-0.00031212129397317767,
-0.0017438146751374006,
-0.03658231720328331,
-0.03589358925819397,
0.015153561718761921,
-0.02867298759520054,
0.010790474712848663,
-0.018997646868228912,
-0.028449947014451027,
0.032759811729192734,
0.03599436581134796,
-0.023418474942445755,
-0.0038410937413573265,
0.03273267671465874,
0.023785458877682686,
-0.0049168020486831665,
-0.022622639313340187,
-0.025165019556879997,
0.0346829853951931,
-0.033172640949487686,
0.008051901124417782,
-0.0021266520489007235,
0.0037727379240095615,
0.03983381763100624,
0.008291319012641907,
-0.0038940859958529472,
-0.07022220641374588,
0.00784576777368784,
-0.05815260857343674,
-0.008683632127940655,
0.03814786672592163,
0.0062370942905545235,
0.00698426179587841,
0.004896668717265129,
0.0338779091835022,
-0.014423600398004055,
0.01770617999136448,
-0.011161384172737598,
-0.058188531547784805,
-0.01768653094768524,
0.010135270655155182,
-0.03966978192329407,
0.051115408539772034,
0.004269469995051622,
-0.04158075898885727,
0.003176889382302761,
-0.03664126992225647,
0.019402286037802696,
0.0136356046423316,
0.010748472064733505,
-0.0367114320397377,
0.053956370800733566,
0.020239660516381264,
-0.00023238688299898058,
0.004998437128961086,
0.018840206786990166,
0.10460264980792999,
0.041592713445425034,
0.01980782113969326,
-0.028886273503303528,
0.028768880292773247,
-0.00244624144397676,
0.019515687599778175,
-0.03481178730726242,
0.010143246501684189,
0.020968133583664894,
0.04141070693731308,
-0.010063228197395802,
0.02657255344092846,
-0.03209180384874344,
-0.02541065402328968,
0.020295221358537674,
-0.04388566315174103,
-0.008313152007758617,
-0.0012995107099413872,
0.00836625974625349,
0.005094747059047222,
0.02295679599046707,
-0.039128683507442474,
0.02805907279253006,
-0.012602909468114376,
-0.0029708093497902155,
-0.012534452602267265,
-0.0523948073387146,
0.00993924681097269,
0.02677331119775772,
-0.02841595932841301,
0.002855788916349411,
0.019475029781460762,
-0.013948366977274418,
0.011268575675785542,
0.019122350960969925,
0.018924957141280174,
-0.05602658912539482,
0.03244071081280708,
0.004492147825658321,
-0.010948995128273964,
0.00866642128676176,
-0.011281369253993034,
-0.009010820649564266,
-0.06164568290114403,
-0.004591406788676977,
-0.041853856295347214,
0.04447995126247406,
0.006276331376284361,
0.014190290123224258,
-0.02708752639591694,
0.002677961951121688,
-0.0348583459854126,
-0.06644989550113678,
-0.002977031981572509,
-0.0017691851826384664,
0.0055405208840966225,
-0.009755389764904976,
0.005123103503137827,
-0.03307202458381653,
0.010701070539653301,
-0.009288799948990345,
0.0331079326570034,
-0.0029099995736032724,
0.0006312434561550617,
0.0056577143259346485,
0.02167443558573723,
0.03231651708483696,
-0.0010750008514150977,
0.000372278067516163,
0.001640190603211522,
0.0006457485724240541,
-0.054766327142715454,
-0.019718067720532417,
0.02174486219882965,
0.007525363005697727,
0.04141561686992645,
0.0038396224845200777,
-0.02554178424179554,
0.0023927418515086174,
-0.08806485682725906,
0.03087644837796688,
0.01139475591480732,
-0.03784485533833504,
0.0005047845188528299,
-0.011263418942689896,
0.0014030698221176863,
0.012521129101514816,
0.006464553531259298,
0.003042528172954917,
0.00587689783424139,
0.04572539031505585,
0.044736962765455246,
-0.020570045337080956,
-0.04232322424650192,
0.03598032146692276,
-0.0234603863209486,
0.011756571009755135,
-0.022864721715450287,
0.02441805601119995,
0.023338282480835915,
-0.011957451701164246,
-0.023752914741635323,
0.011910075321793556,
-0.022376636043190956,
0.006832255981862545,
0.029977427795529366,
0.005413539241999388,
-0.0026749824173748493,
0.026082592085003853,
0.005488244350999594,
-0.022719180211424828,
-0.02831381745636463,
-0.039758145809173584,
-0.0233085285872221,
0.01859101839363575,
-0.02124103531241417,
-0.0056931315921247005,
0.009305155836045742,
-0.03570208325982094,
0.023702463135123253,
-0.025277812033891678,
-0.009101726114749908,
-0.061590876430273056,
0.038495685905218124,
-0.021947408095002174,
-0.007467278279364109,
-0.024099603295326233,
0.01092418935149908,
-0.027483195066452026,
-0.014161837287247181,
0.015198620036244392,
0.022180700674653053,
0.02730805240571499,
-0.012501404620707035,
0.0037938670720905066,
-0.016679346561431885,
0.03702662140130997,
-0.009615689516067505,
-0.029666604474186897,
0.030637286603450775,
0.00425833510234952,
-0.047678399831056595,
0.04265351966023445,
-0.005963747855275869,
0.034031275659799576,
0.021451817825436592,
-0.011630910448729992,
-0.03565235435962677,
0.08292605727910995,
-0.02931864932179451,
-0.011416223831474781,
-0.006426052190363407,
-0.0510014109313488,
-0.021793242543935776,
-0.013537793420255184,
0.013330507092177868,
0.0108528733253479,
-0.022293969988822937,
0.02134939469397068,
0.033245474100112915,
-0.02891760692000389,
0.011055979877710342,
-0.014656094834208488,
0.01369854249060154,
0.05497972294688225,
0.02298847585916519,
-0.004572219680994749,
0.0404336079955101,
0.02945670485496521,
-0.023869046941399574,
0.044794030487537384,
0.02277144230902195,
0.009286551736295223,
-0.10507744550704956,
-0.038152147084474564,
-0.01848975196480751,
0.02489999122917652,
0.005260381381958723,
-0.06811250746250153,
0.028127167373895645,
-0.008696780540049076,
-0.05138857662677765,
0.01088921632617712,
-0.04463675990700722,
-0.029093734920024872,
-0.05598940700292587,
0.004220806062221527,
-0.011440743692219257,
0.028018513694405556,
0.03443526849150658,
-0.007279261946678162,
-0.02559155412018299,
0.024264777079224586,
-0.016575846821069717,
-0.01564820110797882,
-0.016117874532938004,
0.037760406732559204,
-0.013239864259958267,
-0.01210629753768444,
0.05752623453736305,
-0.025310296565294266,
-0.022560467943549156,
0.04658033326268196,
0.02387729473412037,
0.01656164601445198,
-0.015264809131622314,
-0.021582402288913727,
-0.0035672583617269993,
0.025000354275107384,
0.023310508579015732,
-0.00034133862936869264,
-0.03513103723526001,
0.006387379020452499,
-0.008571585640311241,
0.027869053184986115,
0.01868712343275547,
-0.03936747834086418,
0.057452838867902756,
-0.057628486305475235,
-0.01647999696433544,
0.007961224764585495,
0.0038456700276583433,
-0.009625975042581558,
-0.0075066545978188515,
0.005475896410644054,
0.040160056203603745,
-0.04135417565703392,
0.04990387707948685,
-0.05718906968832016,
-0.02501087449491024,
0.043442219495773315,
-0.009434562176465988,
-0.017183685675263405,
0.0075070359744131565,
-0.006057918071746826,
0.001886584679596126,
-0.024760860949754715,
0.025455523282289505,
-0.007741705048829317,
-0.05730167776346207,
-0.023482803255319595,
0.027908828109502792,
-0.028145816177129745,
-0.008480801247060299,
-0.035436853766441345,
-0.024286624044179916,
0.041600510478019714,
0.028160706162452698,
0.01138483639806509,
-0.024021688848733902,
-0.00588106969371438,
-0.04424809291958809,
-0.0672513023018837,
0.022449124604463577,
0.04592001810669899,
-0.017095716670155525,
-0.044436968863010406,
-0.04623033478856087,
-0.026613757014274597,
0.008776652626693249,
0.06714244931936264,
0.04718361049890518,
-0.034703053534030914,
0.02257382683455944,
-0.002414742484688759,
0.027839232236146927,
-0.045292679220438004,
0.002320367842912674,
-0.022188419476151466,
-0.005097269546240568,
0.012342056259512901,
-0.020287003368139267,
-0.03456226736307144,
0.0033930055797100067,
0.04370493441820145,
-0.008438573218882084,
0.032457899302244186,
0.020666861906647682,
-0.006897730752825737,
0.06020396202802658,
0.0005721648340113461,
0.007472151890397072,
0.06623075157403946,
0.018290959298610687,
0.009403637610375881,
0.03808467462658882,
0.01037668064236641,
-0.03507006913423538,
0.036020081490278244,
-0.00511852465569973,
-0.01998118869960308,
-0.00021025251771789044,
-0.028872910887002945,
0.0018411497585475445,
-0.04544570669531822,
0.008980744518339634,
0.029796065762639046,
-0.00862198043614626,
-0.014027192257344723,
0.03835888206958771,
0.04336417093873024,
0.038915906101465225,
-0.004323088563978672,
0.020498160272836685,
0.02155337855219841,
-0.025231407955288887,
-0.005759413819760084,
0.03410680964589119,
0.035507578402757645,
0.04574736952781677,
0.012969480827450752,
0.023887064307928085,
-0.012142456136643887,
0.03540768101811409,
0.011685049161314964,
0.005491478368639946,
-0.02114843763411045,
-0.01416304986923933,
0.0031829173676669598,
-0.005991609301418066,
0.0048216464929282665,
-0.009786725975573063,
0.006824125070124865,
0.0973656103014946,
-0.05049304664134979,
-0.009830913506448269,
-0.038250647485256195,
-0.02446647174656391,
-0.03049388714134693,
-0.014772459864616394,
-0.013202445581555367,
0.01685936003923416,
-0.008814411237835884,
-0.020519711077213287,
-0.024563275277614594,
-0.0238457340747118,
0.0193600133061409,
-0.06635171920061111,
0.009747565723955631,
0.02192075550556183,
0.00661038514226675,
-0.0027588806115090847,
0.013537473045289516,
-0.032927028834819794,
-0.0025358800776302814,
0.005536206997931004,
0.055288929492235184,
0.013951610773801804,
-0.0027558146975934505,
0.010848790407180786,
0.014228450134396553,
0.031063418835401535,
-0.05734355002641678,
-0.04845363274216652,
-0.02128831297159195,
0.0315813347697258,
0.03323794901371002,
-0.02046906016767025
] |
<p>A pion is made out of a pair of up and/or down quarks. A neutron or proton is three up or down quarks. So naively I'd expect a pion to be about 2/3 the mass of a nucleon.</p>
<p>In fact it's less than 1/6 the mass. Why is it so much lighter? Is there some reason why a lot less energy is contained in the gluon field of a pion than in the gluon field of a nucleon?</p>
| 9,617 |
[
-0.011124967597424984,
0.0014645077753812075,
-0.0243219081312418,
-0.05364370346069336,
0.021991951391100883,
0.050334859639406204,
-0.018458373844623566,
-0.051199592649936676,
-0.006666432600468397,
-0.03293122723698616,
0.03404402360320091,
0.028816865757107735,
0.06174207851290703,
-0.005552403628826141,
0.0041097174398601055,
0.030278639867901802,
0.01943851262331009,
-0.0149924848228693,
-0.01214651856571436,
-0.03191504254937172,
0.011749578639864922,
0.036353159695863724,
0.005265077576041222,
0.03040580078959465,
-0.02752128429710865,
0.04736368730664253,
0.053906697779893875,
0.0020430872682482004,
0.035249918699264526,
0.07413305342197418,
0.015672553330659866,
-0.010340354405343533,
0.018813908100128174,
0.018650421872735023,
0.03948729485273361,
-0.010651994496583939,
-0.009493404068052769,
-0.023641977459192276,
0.004252005834132433,
0.023499881848692894,
-0.03924981504678726,
-0.04071047529578209,
-0.032004810869693756,
0.014856467954814434,
-0.014775910414755344,
-0.0006247765850275755,
0.01359776221215725,
-0.04009277746081352,
0.07127156853675842,
-0.07080627977848053,
0.02040480077266693,
0.04877582937479019,
0.014904511161148548,
0.02475418709218502,
-0.007853294722735882,
-0.019243407994508743,
0.05155683308839798,
0.06099655106663704,
-0.03936377540230751,
-0.062425706535577774,
-0.03412269055843353,
-0.02845611982047558,
-0.02103978581726551,
0.0010458604665473104,
-0.007992152124643326,
-0.0010003659408539534,
-0.03318284451961517,
-0.018572820350527763,
-0.008599206805229187,
-0.0017654165858402848,
0.026908215135335922,
0.004795385990291834,
0.008305869065225124,
-0.012094859033823013,
0.03151087462902069,
-0.019610442221164703,
0.00863092765212059,
0.007493643090128899,
0.03295913338661194,
0.059206608682870865,
-0.04584569111466408,
0.026793286204338074,
0.019171401858329773,
0.007344985846430063,
0.013850100338459015,
-0.006050741299986839,
0.05795050784945488,
-0.023353230208158493,
-0.02788303978741169,
0.06206602603197098,
-0.00622529536485672,
0.0012568958336487412,
0.0063053336925804615,
0.01958511397242546,
-0.006244410760700703,
0.020177004858851433,
0.003504063468426466,
0.018391959369182587,
0.029566600918769836,
0.016301635652780533,
0.022456202656030655,
0.0052795205265283585,
0.020793940871953964,
0.10047582536935806,
-0.0022567573469132185,
0.0018154130084440112,
-0.05668860673904419,
0.017409905791282654,
-0.01251134555786848,
0.005365698132663965,
-0.0409393236041069,
-0.02266664057970047,
-0.03148331493139267,
-0.018024200573563576,
0.004230169113725424,
-0.055542923510074615,
0.03226887807250023,
0.004154345951974392,
0.058798134326934814,
0.053562622517347336,
0.042982831597328186,
-0.005107985343784094,
-0.007024866063147783,
-0.05368795618414879,
-0.045253314077854156,
-0.0016618696972727776,
0.03652675077319145,
0.00064411002676934,
-0.028585657477378845,
0.02915511466562748,
-0.017774559557437897,
0.006487921345978975,
0.004752323497086763,
-0.007600441109389067,
0.034697066992521286,
0.0034789107739925385,
-0.09537357091903687,
-0.0328097827732563,
0.044968489557504654,
-0.014962991699576378,
-0.05533912405371666,
-0.10619935393333435,
-0.010077683255076408,
0.02331043966114521,
0.06651851534843445,
0.006481325253844261,
-0.022110911086201668,
-0.016746997833251953,
0.015135353431105614,
-0.00328945298679173,
0.004853245802223682,
-0.034027572721242905,
-0.0072950744070112705,
-0.021563861519098282,
0.014596251770853996,
-0.04785452410578728,
0.005123408045619726,
0.009732582606375217,
-0.002321589970961213,
-0.003323023207485676,
0.0660305842757225,
-0.03487992286682129,
-0.0020606545731425285,
0.0032688057981431484,
-0.002861067419871688,
-0.03379913419485092,
0.06321419775485992,
0.00907094869762659,
-0.0029079278465360403,
0.08092684298753738,
-0.013327362947165966,
0.0165102481842041,
0.030634529888629913,
0.010681181214749813,
0.08165403455495834,
-0.023026004433631897,
-0.07072120159864426,
-0.023205358535051346,
0.002761747222393751,
0.02795601263642311,
-0.05299008637666702,
-0.037161875516176224,
-0.022173721343278885,
-0.000008177658855856862,
0.0031605020631104708,
0.022949982434511185,
0.002424886217340827,
-0.03428742289543152,
0.022663777694106102,
-0.04506078362464905,
-0.01377868838608265,
-0.05139268562197685,
0.005567359738051891,
0.011008771136403084,
0.008998588658869267,
0.013667436316609383,
0.044009819626808167,
-0.004123545251786709,
-0.033716652542352676,
-0.049279361963272095,
-0.02091355435550213,
0.028018364682793617,
0.007865138351917267,
0.015843549743294716,
-0.000014297239431471098,
0.023241903632879257,
-0.00654398649930954,
-0.007586784195154905,
0.009025233797729015,
-0.012869476340711117,
-0.011976825073361397,
0.004113147035241127,
-0.015782807022333145,
-0.015947554260492325,
-0.03479883074760437,
-0.006043015513569117,
0.031744953244924545,
-0.020181918516755104,
-0.010755270719528198,
0.06043274700641632,
0.0007693436346016824,
0.09748579561710358,
0.015598283149302006,
-0.007132872939109802,
0.013258424587547779,
0.027634799480438232,
-0.005285419058054686,
0.02462174743413925,
-0.009466894902288914,
0.002684033242985606,
-0.034364957362413406,
-0.05558614805340767,
0.0499020554125309,
0.024433771148324013,
-0.032932937145233154,
0.014513813890516758,
0.044632598757743835,
0.019676297903060913,
0.010242780670523643,
0.014610533602535725,
-0.04121368005871773,
-0.06332382559776306,
0.02886202186346054,
0.041851744055747986,
-0.026641467586159706,
0.012775415554642677,
0.047822415828704834,
-0.0009883149759843946,
0.0014278492890298367,
-0.03052978217601776,
-0.05755389854311943,
0.054258428514003754,
-0.025703784078359604,
-0.002681170357391238,
0.012541410513222218,
-0.04741509631276131,
0.04057765379548073,
-0.03589724004268646,
0.0197772029787302,
0.00823450367897749,
-0.053638290613889694,
0.0057189068756997585,
-0.016618940979242325,
-0.009553040377795696,
0.011948056519031525,
0.004427544306963682,
-0.032977163791656494,
-0.004659790080040693,
0.011465292423963547,
-0.06108545884490013,
0.013043629005551338,
-0.009039388038218021,
-0.010020621120929718,
-0.02716047503054142,
0.005551572423428297,
0.01756449230015278,
-0.007203986402601004,
0.030505767092108727,
-0.03294093534350395,
-0.013651690445840359,
0.024646257981657982,
-0.04787717014551163,
-0.013283127918839455,
0.037698160856962204,
-0.02486732415854931,
0.039402373135089874,
-0.05792166665196419,
-0.018259037286043167,
0.00922299176454544,
-0.02296307124197483,
0.025831416249275208,
-0.00660314504057169,
-0.00860623363405466,
-0.039838362485170364,
0.026730326935648918,
-0.006595643237233162,
-0.007709351368248463,
-0.016442565247416496,
-0.00035015097819268703,
0.0416843555867672,
-0.020587746053934097,
-0.022811811417341232,
0.014811142347753048,
-0.023612990975379944,
-0.03043792024254799,
-0.020571615546941757,
0.06990008056163788,
0.017214391380548477,
-0.008138160221278667,
0.03493428975343704,
0.04162679240107536,
-0.038104262202978134,
0.01777934841811657,
-0.03940778225660324,
-0.0020705354399979115,
0.006895582191646099,
-0.011867038905620575,
0.043014802038669586,
0.017967792227864265,
-0.029791533946990967,
0.10748903453350067,
0.04150758311152458,
-0.029096893966197968,
0.002290972974151373,
-0.022704655304551125,
-0.02955092117190361,
-0.004015673417598009,
0.012421557679772377,
0.03836353123188019,
-0.017882777377963066,
0.013661982491612434,
0.023548709228634834,
0.04191964119672775,
0.008218520320951939,
0.011084257625043392,
-0.01751367188990116,
0.01949014514684677,
0.020356755703687668,
-0.021587930619716644,
0.044004954397678375,
-0.008736531250178814,
-0.04670068249106407,
-0.01645103096961975,
0.03310766816139221,
0.01967519335448742,
-0.023700475692749023,
-0.029359452426433563,
0.07969050854444504,
-0.004118344280868769,
0.012911546044051647,
-0.02423594333231449,
0.043337225914001465,
-0.020560532808303833,
-0.01798861473798752,
0.038023289293050766,
-0.005953779444098473,
0.050913941115140915,
-0.0206944327801466,
0.008429315872490406,
0.002283947542309761,
0.05786791816353798,
-0.0485667921602726,
-0.01822846196591854,
-0.011306583881378174,
0.004865830298513174,
0.005109994672238827,
-0.024673718959093094,
0.004193129483610392,
0.029230404645204544,
0.03542555496096611,
0.023280709981918335,
-0.02480497770011425,
-0.023436695337295532,
-0.009568720124661922,
-0.07375843077898026,
-0.013164174742996693,
0.010749319568276405,
0.04926247522234917,
0.028490513563156128,
0.043007612228393555,
0.02504783682525158,
0.017694614827632904,
0.0027006801683455706,
-0.025755053386092186,
-0.0901925191283226,
0.007877218537032604,
-0.05215395614504814,
0.002221607370302081,
-0.03266599774360657,
-0.009694314561784267,
-0.042740851640701294,
-0.012958337552845478,
-0.04843854904174805,
-0.04436009004712105,
-0.014845702797174454,
-0.013512818142771721,
0.06350016593933105,
-0.05786285549402237,
-0.016710594296455383,
-0.012533859349787235,
0.03118167258799076,
0.06466127187013626,
-0.011446353048086166,
0.006533399224281311,
0.0024436679668724537,
-0.03430140018463135,
-0.01872323825955391,
-0.008458198048174381,
0.024425683543086052,
-0.01679973490536213,
0.0038441165816038847,
0.008711228147149086,
0.038580164313316345,
-0.013182089664041996,
-0.03417555242776871,
0.005076191388070583,
0.014296375215053558,
0.020986776798963547,
-0.01619814522564411,
0.013212248682975769,
-0.051432691514492035,
-0.039268188178539276,
-0.004444008693099022,
0.0329926535487175,
-0.008964912965893745,
0.02571059763431549,
-0.017302053049206734,
0.01624879240989685,
-0.007692280225455761,
0.04090582951903343,
0.030810076743364334,
0.008726407773792744,
-0.037069085985422134,
-0.06381376087665558,
0.010798550210893154,
-0.032376352697610855,
-0.01825195923447609,
-0.004411936271935701,
-0.026004977524280548,
-0.01892770826816559,
-0.00010090097202919424,
0.027803165838122368,
-0.03132538124918938,
-0.01439587026834488,
-0.005344526842236519,
-0.007081609684973955,
-0.008450567722320557,
-0.021647322922945023,
-0.019218403846025467,
0.009220829233527184,
0.051051393151283264,
0.07306309789419174,
0.032633326947689056,
0.007995416410267353,
-0.04131476581096649,
-0.02331404760479927,
0.044116340577602386,
0.07426432520151138,
-0.006206334102898836,
-0.009517675265669823,
-0.04331476241350174,
0.01564864069223404,
0.03870786726474762,
-0.04124845936894417,
0.00139784871134907,
-0.03523008152842522,
-0.012341377325356007,
-0.040084853768348694,
-0.018023887649178505,
-0.029261521995067596,
0.036451295018196106,
-0.03433576971292496,
-0.0241596307605505,
-0.06809701025485992,
-0.032018084079027176,
-0.03799401968717575,
0.0372157022356987,
0.02448117733001709,
0.026468917727470398,
0.054678093641996384,
0.05399348959326744,
0.03697694092988968,
0.008860601112246513,
-0.0019831701647490263,
-0.0844518169760704,
-0.0025294830556958914,
-0.013339019380509853,
0.022825459018349648,
0.05792870372533798,
-0.05458000302314758,
-0.0833723172545433,
-0.03290271759033203,
0.002618292812258005,
-0.019549576565623283,
-0.04212439805269241,
-0.0894569531083107,
0.024161480367183685,
0.037429213523864746,
-0.027179939672350883,
0.040436338633298874,
0.037611834704875946,
-0.0448988638818264,
-0.02986130490899086,
-0.061744313687086105,
0.003547554835677147,
-0.040509436279535294,
0.01063602790236473,
-0.00840690452605486,
-0.0024505150504410267,
-0.006954459473490715,
0.05474449321627617,
-0.019224148243665695,
0.052259307354688644,
0.029934179037809372,
-0.06453805416822433,
-0.044487737119197845,
-0.016445554792881012,
0.001720355125144124,
-0.012186556123197079,
0.010102453641593456,
-0.012446274049580097,
0.012361876666545868,
-0.021943630650639534,
0.020612427964806557,
0.03501712903380394,
0.009649364277720451,
-0.02143905498087406,
-0.021967293694615364,
0.04458732530474663,
-0.016065113246440887,
-0.0245079156011343,
0.01815974898636341,
-0.04168340191245079,
0.06528591364622116,
-0.011292793788015842,
-0.026445157825946808,
0.021439267322421074,
-0.05446269363164902,
-0.03098994679749012,
-0.009419988840818405,
-0.03379884362220764,
-0.004187118727713823,
-0.0324447937309742,
0.02697264403104782,
-0.010729791596531868,
0.026147086173295975,
-0.08446283638477325,
-0.026946650817990303,
0.023319648578763008,
0.00032333031413145363,
0.0095458859577775,
-0.023534534499049187,
0.0011366346152499318,
-0.01401832327246666,
-0.014440523460507393,
0.012176633812487125,
0.016408530995249748,
-0.0348147414624691,
-0.0070824702270329,
-0.0038672068621963263,
0.02367336116731167,
0.055294543504714966,
-0.026667345315217972,
-0.0548744797706604,
0.01278957910835743,
-0.020107604563236237,
-0.0017509370809420943,
-0.004245455376803875,
0.061661507934331894,
-0.010626253671944141,
-0.042332910001277924,
0.024083919823169708,
0.005503037944436073,
0.024606751278042793,
-0.038290996104478836,
0.016311200335621834,
0.04234306514263153,
0.020565414801239967,
0.018438978120684624,
-0.01204554084688425,
0.012600328773260117,
0.012376594357192516,
0.060138192027807236,
-0.014632129110395908,
-0.003624985460191965,
-0.03768005967140198,
-0.03412867709994316,
0.031434010714292526,
0.005787224974483252,
0.035366278141736984,
-0.01468262542039156,
0.007567970547825098,
-0.005555317737162113,
-0.018023695796728134,
0.017757553607225418,
-0.02469072863459587,
0.012727021239697933,
0.02341747097671032,
0.021469978615641594,
0.010149222798645496,
-0.0036497842520475388,
-0.010052721947431564,
0.011583708226680756,
-0.02490362711250782,
-0.025943540036678314,
0.0321054607629776,
-0.0031447482760995626,
0.028276052325963974,
0.01502527017146349,
-0.02965528890490532,
-0.01018229778856039,
-0.009858757257461548,
-0.01097860001027584,
-0.0015697007765993476,
-0.028632519766688347,
0.021563788875937462,
-0.03258621320128441,
-0.016617778688669205,
0.03478230535984039,
0.05232534930109978,
-0.021593846380710602,
0.03692266345024109,
0.05023792386054993,
0.03701416403055191,
0.0005853939801454544,
-0.01581077091395855,
-0.05747290700674057,
0.03836832195520401,
-0.007239361759275198,
0.04147884622216225,
0.00609192531555891,
-0.021377507597208023,
0.05474940314888954,
-0.028624992817640305,
0.0314503088593483,
0.004213789943605661,
-0.0012876796536147594,
-0.02170409820973873,
0.005571156274527311,
0.038306910544633865,
0.007399799767881632,
-0.030943356454372406,
0.014562685042619705,
0.020874526351690292,
0.04132504016160965,
0.02262946590781212,
0.03894280269742012,
-0.023202409967780113,
-0.041746754199266434,
-0.041341014206409454,
-0.05336054041981697,
0.022673165425658226,
-0.050184447318315506,
-0.03865146264433861,
0.03793521970510483,
0.008123490028083324,
0.016592448577284813,
-0.02622210793197155,
0.011604124680161476,
-0.021429788321256638,
0.02932131662964821,
-0.028871580958366394,
0.012374474667012691,
-0.00916039478033781,
0.010718769393861294,
0.11982274800539017,
0.04979189485311508,
0.008547230623662472,
-0.06353990733623505,
0.008858857676386833,
-0.04677798971533775,
0.04970631003379822,
-0.03555218130350113,
0.009404832497239113,
-0.001533977803774178,
0.009075128473341465,
-0.004710279405117035,
0.06143278628587723,
-0.0026872893795371056,
-0.01587407849729061,
0.0579257607460022,
-0.021027296781539917,
-0.04655899107456207,
-0.004745887592434883,
0.05111274495720863,
-0.00486243050545454,
0.01101155299693346,
-0.035475946962833405,
0.05776682496070862,
0.001591188251040876,
0.01905221864581108,
-0.0226104948669672,
-0.05840090662240982,
0.018186552450060844,
-0.01711210235953331,
-0.045956842601299286,
0.003337272210046649,
-0.006157673429697752,
-0.004545086994767189,
-0.01599455438554287,
0.014154029078781605,
-0.0026769505348056555,
-0.03370629996061325,
-0.03477057069540024,
0.029487980529665947,
0.020326828584074974,
-0.0029331897385418415,
0.011514274403452873,
0.019491957500576973,
-0.04427330195903778,
-0.005844626575708389,
-0.005117698572576046,
0.040697719901800156,
-0.02060621604323387,
0.002937832847237587,
0.02208932489156723,
0.03280534967780113,
0.008006050251424313,
-0.028081456199288368,
-0.019516535103321075,
0.014478740282356739,
0.008150757290422916,
-0.02010284550487995,
-0.024661539122462273,
-0.004428823944181204,
0.02789168804883957,
-0.01062053069472313,
0.04347914457321167,
0.01739511825144291,
0.0029439127538353205,
-0.0005386354168877006,
-0.008157924748957157,
0.027174312621355057,
-0.012490923516452312,
0.012202009558677673,
-0.00781311560422182,
0.017421698197722435,
-0.0394040010869503,
-0.04375859722495079,
0.01841595210134983,
0.016921445727348328,
0.04726084694266319,
0.002507812110707164,
-0.013981613330543041,
-0.003316868096590042,
-0.04366312921047211,
0.0654725432395935,
-0.0011806944385170937,
0.005930093117058277,
-0.029829805716872215,
0.005702919326722622,
0.0007890590932220221,
0.03236754611134529,
0.008658116683363914,
0.0602862611413002,
-0.04578367620706558,
0.0032877845223993063,
-0.009062517434358597,
-0.023154253140091896,
-0.015372863970696926,
0.020467013120651245,
-0.02984037436544895,
-0.00010978574573528022,
0.008568589575588703,
0.0035322760231792927,
0.02632163278758526,
-0.00698096351698041,
0.029700972139835358,
0.017706546932458878,
-0.030306078493595123,
-0.014938236214220524,
0.03754597529768944,
-0.023808086290955544,
0.003039705101400614,
0.011125851422548294,
0.004198033362627029,
-0.03144190087914467,
-0.04582997411489487,
-0.02066485770046711,
-0.015188845805823803,
0.027386339381337166,
0.06584510952234268,
-0.010284088551998138,
-0.021947218105196953,
-0.044632986187934875,
0.018042970448732376,
-0.016781166195869446,
0.0012074728729203343,
-0.054183170199394226,
0.012268050573766232,
-0.0034594142343848944,
-0.002279767533764243,
-0.0348283015191555,
0.022243613377213478,
-0.04811257869005203,
0.005722313188016415,
0.029763126745820045,
-0.018702536821365356,
-0.02055058255791664,
-0.0030235182493925095,
0.028727171942591667,
-0.01050824485719204,
0.045770011842250824,
-0.014568145386874676,
-0.02837381698191166,
0.04475737735629082,
-0.025546159595251083,
-0.05179857835173607,
0.004557926207780838,
-0.002531210193410516,
0.016422990709543228,
0.039827343076467514,
-0.029902182519435883,
-0.011989296413958073,
0.07120859622955322,
-0.024409327656030655,
-0.026989342644810677,
-0.012333232909440994,
-0.005704297684133053,
0.02376599796116352,
-0.019807947799563408,
-0.009968722239136696,
-0.0007271096110343933,
-0.037850674241781235,
0.06283573061227798,
0.01221044734120369,
-0.0007667199824936688,
-0.0068596904166042805,
-0.023899631574749947,
-0.008931667543947697,
0.008416013792157173,
0.016092879697680473,
0.039798397570848465,
0.009215042926371098,
0.019171031191945076,
-0.025876658037304878,
0.03849656507372856,
-0.011966477148234844,
0.02369890734553337,
-0.07932502031326294,
-0.014078180305659771,
-0.013474786654114723,
-0.02888943813741207,
0.03101928159594536,
-0.041256558150053024,
0.0410216823220253,
0.010973945260047913,
-0.08195634186267853,
0.013287325389683247,
-0.02886815555393696,
-0.033692680299282074,
-0.05549727752804756,
-0.03917015716433525,
-0.0015122747281566262,
0.07056629657745361,
0.0024665382225066423,
0.05696885287761688,
0.03321555256843567,
0.022935274988412857,
0.012770350091159344,
0.012900527566671371,
-0.014802832156419754,
0.03828953579068184,
-0.014430553652346134,
-0.014490466564893723,
0.05655630677938461,
-0.014187313616275787,
0.003421475412324071,
0.03526367247104645,
0.02738923206925392,
-0.003670145757496357,
0.0008097648387774825,
-0.0031502002384513617,
0.010468315333127975,
0.038898222148418427,
0.011981953866779804,
-0.017705924808979034,
-0.000194709311472252,
0.025975072756409645,
0.02019830420613289,
0.03684470057487488,
0.021080894395709038,
0.02953292615711689,
0.005835676100105047,
-0.022792357951402664,
0.00296360463835299,
0.03793001174926758,
-0.014345010742545128,
-0.005960299167782068,
-0.02690594084560871,
0.02009044960141182,
0.019375665113329887,
-0.02105216681957245,
0.01867229864001274,
-0.03586416691541672,
0.0012818246614187956,
-0.0029894004110246897,
0.007469408679753542,
-0.0004056574252899736,
0.061737000942230225,
0.025098606944084167,
0.01863955333828926,
-0.04187684506177902,
0.029625700786709785,
0.013363173231482506,
-0.004469604231417179,
0.02039387822151184,
0.03976774960756302,
0.029252182692289352,
0.026645006611943245,
-0.04170028865337372,
-0.06511888653039932,
0.02081829309463501,
0.014436053112149239,
0.04326426237821579,
-0.016734739765524864,
-0.003070657607167959,
0.0038581464905291796,
-0.06618737429380417,
0.031594887375831604,
0.009439341723918915,
-0.00004841537884203717,
-0.04466668516397476,
-0.00534134590998292,
0.002355920383706689,
0.01807469129562378,
0.060575760900974274,
0.03839380294084549,
-0.04926770552992821,
0.00651982706040144,
-0.006751654669642448,
0.0037740704137831926,
-0.03497147932648659,
-0.01885276474058628,
0.0008743088692426682,
-0.033681366592645645,
0.0030478755943477154,
-0.01126858964562416,
-0.017400940880179405,
0.05432409420609474,
0.04077140986919403,
0.00862208753824234,
-0.002992973430082202,
0.004100179299712181,
-0.030532604083418846,
0.0602697916328907,
-0.03045131452381611,
0.013703643344342709,
0.07094403356313705,
0.010653501376509666,
0.019686082378029823,
0.035149235278367996,
-0.02091357111930847,
-0.042473409324884415,
0.03147820755839348,
-0.023559046909213066,
-0.00787737499922514,
0.004941203631460667,
-0.02215578779578209,
0.02965620718896389,
-0.034869562834501266,
0.02475145272910595,
0.03640255704522133,
-0.038513313978910446,
-0.02642250433564186,
0.03473556041717529,
0.0551045760512352,
0.056290145963430405,
0.00506202969700098,
0.02815786562860012,
0.029198551550507545,
0.015370523557066917,
0.0007257607649080455,
0.05620121955871582,
0.03174819424748421,
0.0159791000187397,
0.014126977883279324,
0.021817872300744057,
0.006016366183757782,
-0.015141013078391552,
0.036014895886182785,
0.003141244873404503,
-0.011467856355011463,
-0.02706129662692547,
0.030437804758548737,
0.003908522892743349,
0.03386035934090614,
0.021495383232831955,
-0.0271537397056818,
0.09854967892169952,
-0.011339148506522179,
-0.00807110220193863,
-0.0029817374888807535,
-0.0018086038762703538,
0.015422835014760494,
-0.0017392601585015655,
-0.004777283873409033,
0.05147041007876396,
0.017864324152469635,
0.002381541533395648,
-0.021841995418071747,
-0.03113783523440361,
0.008890337310731411,
-0.020478982478380203,
0.010589583776891232,
0.02028243988752365,
0.00633986946195364,
-0.04367747902870178,
0.005798459518700838,
-0.015480659902095795,
-0.021744543686509132,
0.04551589488983154,
0.03324313834309578,
0.03747066855430603,
0.02049328200519085,
-0.024235080927610397,
-0.016318146139383316,
0.045479610562324524,
-0.02030627429485321,
0.01311840582638979,
-0.048990726470947266,
0.012277595698833466,
-0.03106350265443325,
-0.0102744922041893
] |
<p>We tried to measure background radiation using a geiger counter for a experiment at school. The meter showed $0.12$-$0.21$ microSv/h during the day averaging at about $0.14$ mcSv/h.</p>
<p>As we tried to see ways how to shield incoming radiotion nothing seemed to work. Taking a cue from nuclear power plant we put the meter into a watertigt glasscontainer and sank it in the gym pool so that the container had a good three feet of water all around. The measurement did not budge at all. We tried all settings fast/slow/auto. The geiger meter should be okay as it had recently been calibrated.</p>
<p>Can someone explain. </p>
| 9,618 |
[
0.005650058388710022,
-0.023182593286037445,
0.004414844326674938,
0.014185882173478603,
0.02718977816402912,
0.0010005820076912642,
-0.042609989643096924,
-0.01922762021422386,
0.007457084953784943,
-0.041664887219667435,
0.07781857997179031,
0.052206214517354965,
0.055120065808296204,
0.035993415862321854,
0.04295201599597931,
-0.0052645266987383366,
0.0027716457843780518,
0.0019315986428409815,
0.010210620239377022,
-0.06339994817972183,
-0.01547791063785553,
0.032936517149209976,
-0.033454060554504395,
-0.04275268316268921,
-0.03271111845970154,
0.015517533756792545,
-0.016582796350121498,
-0.0031557930633425713,
-0.009835021570324898,
0.011270099319517612,
-0.04617751017212868,
-0.040420133620500565,
-0.015777049586176872,
-0.04161081463098526,
0.008274970576167107,
0.022346265614032745,
-0.0157619696110487,
-0.06728281825780869,
-0.020269077271223068,
0.062107495963573456,
-0.03654468432068825,
-0.0019548002164810896,
0.0175456739962101,
0.045472923666238785,
-0.03851224109530449,
0.016882481053471565,
0.0036690947599709034,
-0.001802423968911171,
0.06570807844400406,
-0.04295368120074272,
0.046129871159791946,
0.007423975970596075,
0.03679753467440605,
0.05224725604057312,
-0.0117673734202981,
0.016902269795536995,
0.06299781799316406,
0.08431191742420197,
-0.009762109257280827,
-0.03321949392557144,
-0.013938168063759804,
-0.023948734626173973,
-0.05689665675163269,
-0.010532917454838753,
0.020863140001893044,
0.007152565289288759,
-0.02461877651512623,
-0.01060792151838541,
0.01113097369670868,
-0.021686125546693802,
0.06709574908018112,
0.0018977196887135506,
0.035022325813770294,
0.009866773150861263,
0.038301803171634674,
-0.023623978719115257,
0.0244852676987648,
0.029361294582486153,
0.032429855316877365,
0.01396077498793602,
0.00548979640007019,
-0.009585116058588028,
0.014989711344242096,
0.016439318656921387,
0.03334980830550194,
-0.021986084058880806,
0.05942881107330322,
-0.014004099182784557,
0.003313215682283044,
0.033731408417224884,
-0.01605117693543434,
0.027024561539292336,
0.0300284493714571,
0.03208345174789429,
-0.015981340780854225,
0.06738163530826569,
-0.0014987901085987687,
0.08052606135606766,
-0.014907256700098515,
-0.02188735269010067,
0.038422465324401855,
0.027494318783283234,
0.023631922900676727,
0.07181349396705627,
0.00221669627353549,
-0.01748376153409481,
-0.030639084056019783,
-0.03207697346806526,
0.013009277172386646,
-0.004188986029475927,
-0.06979013979434967,
0.0003875550755765289,
0.02286999113857746,
-0.035611800849437714,
0.017650779336690903,
-0.018193254247307777,
0.007552738767117262,
-0.006743584293872118,
0.04365263506770134,
0.011463435366749763,
0.05376195162534714,
0.010851666331291199,
0.001879319199360907,
-0.06046535447239876,
-0.03390370309352875,
0.01962144672870636,
-0.007549829315394163,
0.01309378445148468,
-0.09691247344017029,
0.04648846015334129,
0.000616404868196696,
0.008211595006287098,
0.05799069628119469,
-0.04982590675354004,
0.05515515059232712,
-0.03995449095964432,
-0.11113929003477097,
-0.0588575042784214,
0.060950491577386856,
0.010632023215293884,
-0.03038911707699299,
-0.08126787841320038,
-0.007940527983009815,
0.019358785822987556,
0.0651736855506897,
-0.007868819870054722,
0.020286457613110542,
-0.0008075269288383424,
0.01660846173763275,
-0.01132669486105442,
0.004926305264234543,
-0.020131981000304222,
0.029174702242016792,
-0.014719936065375805,
-0.00030773511389270425,
-0.03992655500769615,
0.007238652091473341,
0.03717822581529617,
-0.010164780542254448,
-0.0029534639324992895,
0.026013890281319618,
-0.008544559590518475,
-0.0050137219950556755,
-0.03277964144945145,
-0.020054921507835388,
-0.05661892518401146,
0.024191444739699364,
0.0007375239511020482,
-0.00990206003189087,
-0.004384075291454792,
0.026996897533535957,
0.07772097736597061,
0.009625410661101341,
-0.008203892968595028,
0.039852745831012726,
-0.018941786140203476,
-0.00042158440919592977,
-0.01165042631328106,
0.01944289170205593,
0.013948342762887478,
-0.012658176943659782,
0.012582405470311642,
-0.028064511716365814,
0.030752278864383698,
0.015069129876792431,
0.004432110581547022,
0.027555527165532112,
-0.009768666699528694,
0.01995280012488365,
0.0012053190730512142,
-0.021729353815317154,
-0.03623775765299797,
0.002854995196685195,
-0.02213188260793686,
-0.0060803540982306,
-0.01329535711556673,
-0.0036418249364942312,
0.02647804468870163,
-0.002050571609288454,
-0.0586279034614563,
0.028627360239624977,
0.015210408717393875,
0.043025147169828415,
0.0027213634457439184,
0.010963144712150097,
0.04231954738497734,
0.0480567142367363,
-0.0024641205091029406,
-0.0007556912023574114,
-0.01583675853908062,
0.0007456406601704657,
-0.027297381311655045,
-0.04282287508249283,
0.0024693317245692015,
0.008260119706392288,
-0.0189681313931942,
0.02198753133416176,
-0.014022651128470898,
0.018590597435832024,
0.025477496907114983,
-0.014775742776691914,
0.06694434583187103,
0.016734668985009193,
0.012025696225464344,
0.006424105726182461,
0.038180429488420486,
0.010449549183249474,
0.007406013086438179,
-0.0021924548782408237,
-0.05758412927389145,
-0.047240640968084335,
-0.007116451859474182,
0.00952247902750969,
-0.013988019898533821,
-0.012775739654898643,
0.041424110531806946,
0.017523232847452164,
0.028965895995497704,
0.008756470866501331,
-0.006176403257995844,
0.004149191081523895,
-0.025616392493247986,
0.019288308918476105,
0.05327871814370155,
-0.0036201027687639,
0.003936829976737499,
0.021084435284137726,
-0.00684361020103097,
0.0009992867708206177,
-0.03436488285660744,
0.01713446155190468,
-0.010127554647624493,
0.01774408482015133,
0.04149830713868141,
-0.028207626193761826,
-0.04830815643072128,
0.030660266056656837,
-0.008580723777413368,
0.021936722099781036,
-0.01387430727481842,
-0.01734277792274952,
-0.007628188002854586,
-0.034040648490190506,
-0.037354353815317154,
-0.02352377213537693,
0.00974954292178154,
-0.020036712288856506,
-0.02523324079811573,
0.02861911617219448,
-0.02948485128581524,
0.006177349481731653,
-0.026573900133371353,
-0.008719397708773613,
-0.03215891867876053,
-0.020946454256772995,
0.06782004237174988,
0.019907856360077858,
0.04992513731122017,
-0.0736522451043129,
-0.034604351967573166,
0.007362700067460537,
-0.0077291084453463554,
-0.010308589786291122,
0.0026574290823191404,
-0.018558917567133904,
0.00889818649739027,
0.02445916086435318,
0.0016289609484374523,
0.037186138331890106,
-0.0035813902504742146,
0.018469857051968575,
0.04507729783654213,
-0.006233641877770424,
0.015154099091887474,
-0.03102991357445717,
-0.016802558675408363,
-0.03116089478135109,
0.010146204382181168,
-0.022226186469197273,
0.058860428631305695,
0.004775826819241047,
-0.035170163959264755,
0.012866263277828693,
-0.06563064455986023,
-0.026658054441213608,
-0.04933805391192436,
-0.002044776687398553,
-0.015854405239224434,
-0.03518575429916382,
0.0233239084482193,
0.014897673390805721,
-0.04171479865908623,
-0.0015504083130508661,
-0.04516807571053505,
-0.05021896958351135,
0.03944438323378563,
0.007596502546221018,
0.052885908633470535,
0.0019401430618017912,
0.01511312648653984,
0.06503921002149582,
0.01572047732770443,
0.006741445045918226,
-0.022648615762591362,
-0.02270086482167244,
-0.013938152231276035,
-0.07464803010225296,
-0.013658489100635052,
0.06286454945802689,
0.0012966766953468323,
0.0049639600329101086,
-0.03524797782301903,
0.023720217868685722,
0.041136737912893295,
0.01280429121106863,
-0.009076590649783611,
0.007266640197485685,
0.02836359478533268,
0.02326836995780468,
0.06645967066287994,
0.018007472157478333,
-0.014500156044960022,
-0.02179589495062828,
0.007330436259508133,
0.02133418433368206,
0.004897977225482464,
-0.03178665041923523,
0.07326747477054596,
0.037855446338653564,
0.03494933992624283,
-0.06429423391819,
0.014840728603303432,
0.002317789476364851,
-0.011965449899435043,
-0.00045432971091941,
0.004476799629628658,
0.03980085253715515,
-0.005505482200533152,
0.030368370935320854,
0.048828743398189545,
0.05674568936228752,
0.010252373293042183,
-0.04216831922531128,
-0.022872095927596092,
0.00696679437533021,
0.0036367210559546947,
-0.004423857666552067,
-0.015421898104250431,
0.03192133456468582,
0.013286101631820202,
0.031221361830830574,
-0.03116675093770027,
-0.022512204945087433,
-0.06531992554664612,
-0.04798925295472145,
-0.004895519465208054,
-0.015213645994663239,
0.04299161583185196,
0.0008713628631085157,
-0.004342943895608187,
0.04365142434835434,
-0.00038101678364910185,
0.014443976804614067,
-0.00118319655302912,
-0.031296923756599426,
0.028626814484596252,
-0.019502906128764153,
-0.011440122500061989,
0.019844666123390198,
-0.014783181250095367,
-0.026761237531900406,
0.003573034657165408,
-0.029783641919493675,
-0.019282277673482895,
0.007909230887889862,
-0.005082099698483944,
0.027140283957123756,
0.021685799583792686,
-0.02887636050581932,
-0.032253578305244446,
0.021173354238271713,
0.021381588652729988,
-0.019110631197690964,
-0.014672442339360714,
0.017138779163360596,
-0.02643999084830284,
-0.032080866396427155,
-0.01361691765487194,
0.005241525825113058,
0.0025746612809598446,
0.023287663236260414,
0.03756411746144295,
0.015386109240353107,
-0.022129924967885017,
-0.016630634665489197,
0.04300723224878311,
0.011019257828593254,
0.025751492008566856,
-0.015793150290846825,
-0.023404939100146294,
-0.054179634898900986,
-0.028207290917634964,
0.01732722669839859,
-0.0054141078144311905,
-0.024995971471071243,
0.027872830629348755,
0.012265353463590145,
-0.014006238430738449,
-0.023255838081240654,
0.009325669147074223,
0.08934660255908966,
-0.008417640812695026,
-0.03522789850831032,
-0.026688138023018837,
-0.007306347135454416,
-0.0025380724109709263,
-0.018974049016833305,
-0.012406847439706326,
0.030418861657381058,
-0.014667165465652943,
-0.03955017402768135,
0.03548501059412956,
0.00783921405673027,
0.01500757597386837,
0.022009465843439102,
0.006170523352921009,
0.010966278612613678,
0.008123901672661304,
-0.008078230544924736,
0.016807006672024727,
0.0658910870552063,
0.05167388916015625,
-0.015093640424311161,
0.012421143241226673,
-0.07804232835769653,
-0.032204944640398026,
0.005838543642312288,
0.08930111676454544,
0.0009730023448355496,
0.0007033035508356988,
-0.06463144719600677,
-0.025858871638774872,
0.034701116383075714,
-0.031118184328079224,
0.06075669080018997,
-0.02773471176624298,
-0.010384347289800644,
-0.017071491107344627,
-0.033761169761419296,
-0.011138839647173882,
-0.009902117773890495,
-0.0313098318874836,
0.01852123998105526,
-0.02871987596154213,
-0.030899155884981155,
-0.03704245761036873,
-0.02015008218586445,
0.02744395285844803,
0.02367112599313259,
-0.0065610650926828384,
0.005950674880295992,
0.025610612705349922,
-0.001916532521136105,
-0.018948502838611603,
-0.04869787022471428,
0.00887061282992363,
-0.027039889246225357,
-0.028020402416586876,
0.04355204105377197,
-0.009570225141942501,
-0.01561899483203888,
0.019599920138716698,
0.024918152019381523,
-0.021746790036559105,
-0.041170064359903336,
-0.06881040334701538,
0.035457588732242584,
0.05967825651168823,
0.010670563206076622,
0.04786200821399689,
0.06952055543661118,
-0.020946823060512543,
0.03045506589114666,
-0.04139232635498047,
0.029371511191129684,
-0.04410365968942642,
-0.0011101571144536138,
0.017231015488505363,
-0.011457509361207485,
-0.021651972085237503,
0.04528011009097099,
0.011350705288350582,
0.03292084112763405,
0.014022380113601685,
-0.019147949293255806,
0.03213122487068176,
0.003943560644984245,
-0.02805093489587307,
-0.0023411535657942295,
-0.005333513021469116,
0.00617999630048871,
-0.0004730883811134845,
-0.02972300723195076,
0.015674330294132233,
-0.04334124177694321,
-0.02024727500975132,
0.01978963240981102,
-0.04084093123674393,
-0.0013749806676059961,
-0.02342120185494423,
-0.016594933345913887,
0.014910155907273293,
-0.03395533189177513,
0.015143475495278835,
-0.04732334613800049,
0.011423967778682709,
0.01300381775945425,
-0.0299762524664402,
-0.03202195465564728,
-0.0058947401121258736,
-0.0406566858291626,
0.03733175992965698,
-0.023838017135858536,
0.05751541256904602,
0.010574407875537872,
0.051763955503702164,
-0.07417966425418854,
-0.016647538170218468,
0.02189667522907257,
-0.0054947081953287125,
-0.02227385900914669,
-0.043697938323020935,
-0.021583518013358116,
-0.022110676392912865,
-0.03795338049530983,
-0.022031622007489204,
-0.0028126982506364584,
-0.023222191259264946,
-0.01163196936249733,
-0.013776445761322975,
0.024957679212093353,
0.05415145307779312,
-0.04551228508353233,
-0.016739200800657272,
0.008922876790165901,
-0.007718207780271769,
-0.052200838923454285,
0.006226690020412207,
0.021075956523418427,
-0.05613052845001221,
-0.009825784713029861,
0.05160143971443176,
0.004502844996750355,
0.03920407220721245,
-0.026324085891246796,
-0.009555230848491192,
0.0017747683450579643,
-0.005455886013805866,
-0.009762045927345753,
-0.000520529632922262,
0.05925728753209114,
0.01703556813299656,
0.015024020336568356,
-0.018639490008354187,
0.002534741535782814,
-0.08739375323057175,
-0.0502014085650444,
0.0436277836561203,
0.010184412822127342,
0.0018560454482212663,
-0.04657142609357834,
0.0849589928984642,
0.010114115662872791,
-0.022143661975860596,
-0.015803663060069084,
0.0158778578042984,
-0.003526445245370269,
-0.022127844393253326,
0.028084855526685715,
0.026151996105909348,
0.006370351184159517,
-0.021534712985157967,
-0.02345605008304119,
-0.04691352695226669,
-0.04037398472428322,
0.0568278543651104,
-0.02301626279950142,
0.0473322831094265,
0.005488063208758831,
-0.019553860649466515,
0.039577167481184006,
-0.021882757544517517,
-0.034850381314754486,
0.017307819798588753,
0.00255374307744205,
0.034897517412900925,
-0.02025454118847847,
0.02178069017827511,
-0.0024697028566151857,
0.021192345768213272,
0.0004811035469174385,
0.0344640389084816,
0.05795598030090332,
0.022548269480466843,
0.009584728628396988,
-0.01569613441824913,
-0.03927641361951828,
0.02509658969938755,
-0.02505640685558319,
0.012983227148652077,
-0.010137312114238739,
-0.0249782707542181,
0.03972809016704559,
-0.01625995524227619,
-0.03703305125236511,
-0.07061626762151718,
-0.004219248425215483,
-0.05213870480656624,
-0.005025709513574839,
0.01845722086727619,
0.011634127236902714,
-0.029683690518140793,
0.0389956571161747,
0.05162511393427849,
0.006418909411877394,
0.01062125526368618,
-0.010646505281329155,
-0.04183918237686157,
0.011558768339455128,
-0.030791448429226875,
-0.05724604055285454,
0.07446589320898056,
-0.004642370622605085,
-0.03454752638936043,
0.00555580435320735,
-0.0198381207883358,
0.01823899708688259,
0.011982262134552002,
-0.012192988768219948,
-0.0072344145737588406,
0.03658970817923546,
-0.013188214041292667,
0.014028702862560749,
0.023445578292012215,
0.00892527587711811,
0.12476107478141785,
0.05360499769449234,
-0.011682048439979553,
-0.0346040353178978,
-0.021566973999142647,
-0.009313464164733887,
0.024906424805521965,
0.001681977417320013,
-0.025788990780711174,
-0.010791823267936707,
0.006125498563051224,
0.015368560329079628,
0.02273014560341835,
0.026494430378079414,
0.007462510373443365,
0.01251150481402874,
-0.022922461852431297,
-0.019330568611621857,
0.03380352631211281,
-0.004925539251416922,
-0.026582354679703712,
0.03515974432229996,
-0.019529690966010094,
0.06230001524090767,
0.0018926558550447226,
-0.022051190957427025,
-0.027668913826346397,
-0.024764008820056915,
0.024587221443653107,
0.013187766075134277,
-0.04936889931559563,
0.024060169234871864,
-0.024175968021154404,
-0.007156073115766048,
-0.04945670813322067,
-0.012792019173502922,
0.03402261063456535,
0.017742501571774483,
-0.019708074629306793,
0.013578883372247219,
0.009898140095174313,
-0.014930522069334984,
0.0031142989173531532,
0.031791068613529205,
-0.052110202610492706,
-0.0030642712954431772,
-0.0035727976355701685,
0.08346385508775711,
0.008784870617091656,
-0.03901859000325203,
-0.005337952636182308,
0.0015918927965685725,
0.012219872325658798,
-0.03768418729305267,
-0.00532583286985755,
-0.005419460125267506,
0.026388464495539665,
-0.059270452708005905,
-0.01828181929886341,
0.006788710597902536,
0.02175549417734146,
-0.008114499039947987,
0.019221371039748192,
0.03333831578493118,
0.02560023032128811,
-0.01591159962117672,
-0.038824379444122314,
0.045104287564754486,
-0.008786152116954327,
0.009108070284128189,
-0.007346965838223696,
0.019148308783769608,
-0.028242746368050575,
-0.01187419518828392,
0.025539953261613846,
0.006882097106426954,
0.01859441213309765,
0.03531443700194359,
-0.022699272260069847,
0.0036221935879439116,
-0.024845702573657036,
0.051268238574266434,
-0.04375837370753288,
0.002258752705529332,
-0.04464734345674515,
-0.0649046078324318,
-0.02664998546242714,
0.019318286329507828,
0.012218935415148735,
-0.024223310872912407,
0.009993277490139008,
0.04706567898392677,
0.01564909517765045,
-0.002281425055116415,
-0.0024588776286691427,
0.027751462534070015,
-0.02844918891787529,
0.028481686487793922,
-0.012827666476368904,
0.017961040139198303,
0.0011847589630633593,
-0.00933744665235281,
0.02368433214724064,
-0.019542744383215904,
-0.05197955295443535,
0.012549019418656826,
0.01626075804233551,
-0.027060067281126976,
-0.021543696522712708,
-0.03690453618764877,
0.009104302152991295,
-0.009346801787614822,
-0.008334603160619736,
-0.03807991370558739,
0.006079755257815123,
-0.007872015237808228,
0.045989230275154114,
-0.011626801453530788,
0.02865244448184967,
-0.05138256028294563,
-0.010655405931174755,
-0.0017345102969557047,
0.02187504991889,
-0.055093176662921906,
-0.022145956754684448,
-0.00255785696208477,
0.0010144722182303667,
-0.047433700412511826,
0.03377272188663483,
-0.01952812820672989,
-0.001503935782238841,
0.0374218113720417,
0.016283221542835236,
-0.014278472401201725,
0.036282774060964584,
0.051405105739831924,
0.025424815714359283,
0.04240953177213669,
-0.028542347252368927,
-0.005303340032696724,
0.04137576371431351,
-0.021829063072800636,
-0.031971435993909836,
0.021440263837575912,
0.01615554839372635,
0.008230922743678093,
-0.0023123910650610924,
-0.010018660686910152,
0.02147013694047928,
0.040764760226011276,
-0.00014346079842653126,
0.008052581921219826,
-0.011996861547231674,
0.011717013083398342,
0.015471109189093113,
-0.0049271732568740845,
-0.0057160137221217155,
0.011797767132520676,
-0.015229249373078346,
0.021723812445998192,
0.0035871872678399086,
0.015630220994353294,
0.026267778128385544,
-0.06716354936361313,
-0.05480398237705231,
-0.03766300156712532,
0.014864454045891762,
-0.010852678678929806,
0.0010592053877189755,
0.04735387861728668,
-0.05669773742556572,
0.032436810433864594,
-0.0047103893011808395,
-0.012774587608873844,
-0.08815492689609528,
-0.0053294068202376366,
-0.003476423677057028,
0.024104727432131767,
0.045215919613838196,
-0.059519633650779724,
-0.006839422043412924,
0.0294229444116354,
-0.10096894204616547,
-0.05895841866731644,
-0.025693031027913094,
-0.05084777623414993,
-0.05415455996990204,
0.027178291231393814,
-0.013399960473179817,
0.03725817799568176,
0.003589739790186286,
0.027342738583683968,
0.005977069493383169,
0.02911742404103279,
-0.008717196062207222,
-0.022603563964366913,
-0.02494705654680729,
0.004269156139343977,
0.041875921189785004,
0.020528174936771393,
0.025990920141339302,
-0.013084971345961094,
0.01792774721980095,
0.012120957486331463,
-0.02047499269247055,
0.03425862267613411,
-0.031407129019498825,
0.055687565356492996,
0.023092254996299744,
0.044487468898296356,
0.008203450590372086,
0.032372359186410904,
0.008326099254190922,
-0.004807814955711365,
0.016737177968025208,
0.012691012583673,
0.05150160938501358,
-0.011080991476774216,
0.07976984232664108,
-0.035058632493019104,
-0.01361444778740406,
0.01615411788225174,
-0.002975504146888852,
0.003282176563516259,
0.06193765997886658,
-0.01451578363776207,
0.04302816465497017,
-0.05162552744150162,
0.020571578294038773,
-0.050187334418296814,
-0.0061645726673305035,
0.05240289866924286,
0.01292916014790535,
-0.00927429087460041,
0.020049473270773888,
-0.02112470753490925,
-0.020137248560786247,
0.00015000013809185475,
0.03171907737851143,
-0.02097579650580883,
-0.015914199873805046,
0.0051957969553768635,
-0.016582898795604706,
0.00760088674724102,
0.004996951669454575,
-0.010614785365760326,
-0.06181017681956291,
0.024676155298948288,
0.02899736911058426,
-0.007121788803488016,
0.04230115935206413,
0.002271058037877083,
-0.008822115138173103,
-0.06854138523340225,
0.028551330789923668,
-0.014688019640743732,
0.029096262529492378,
-0.017963316291570663,
-0.01575998216867447,
-0.012278863228857517,
0.018320541828870773,
0.046271760016679764,
-0.012271900661289692,
-0.004651861730962992,
0.00934070535004139,
-0.005565214902162552,
0.009977252222597599,
-0.05571708455681801,
0.051454078406095505,
0.0034026172943413258,
-0.035790350288152695,
0.019494308158755302,
-0.020248353481292725,
-0.015584663487970829,
-0.008551727049052715,
0.018117913976311684,
0.006414396688342094,
-0.02526184171438217,
-0.016853883862495422,
-0.0034313322976231575,
0.03132243454456329,
-0.013291269540786743,
-0.02025204338133335,
0.026731643825769424,
-0.018995366990566254,
0.025687705725431442,
0.07686567306518555,
-0.0015120140742510557,
-0.06233065575361252,
0.01842639222741127,
0.01214972510933876,
0.012184777297079563,
0.008898050524294376,
0.026974357664585114,
0.02198583260178566,
-0.013366248458623886,
0.010707272216677666,
0.03594450280070305,
-0.025255318731069565,
-0.002709816675633192,
0.07684348523616791,
0.00015237827028613538,
0.0005290770204737782,
0.018582969903945923,
0.03050338104367256,
0.003545910120010376,
0.017419997602701187,
-0.00732796173542738,
0.07970061898231506,
0.029004445299506187,
-0.009009142406284809,
0.03911791741847992,
0.06787887215614319,
-0.011554881930351257,
0.02054012008011341,
0.0529780238866806,
-0.00953703559935093,
-0.006162075791507959,
-0.019185978919267654,
0.027884436771273613,
0.0031669754534959793,
-0.03877641260623932,
0.04990594834089279,
0.007331700064241886,
0.05921606719493866,
-0.03905192017555237,
-0.011287159286439419,
-0.025219375267624855,
-0.041947416961193085,
0.034132033586502075,
0.03163246810436249,
0.04265904799103737,
0.043254200369119644,
-0.015655554831027985,
0.01547928899526596,
-0.028782106935977936,
0.007168879732489586,
0.0036382069811224937,
-0.04970765486359596,
0.005506573244929314,
-0.01581531949341297,
-0.0005791736766695976,
0.001990579767152667,
-0.029900144785642624,
-0.008958377875387669,
-0.03595370054244995,
0.032329194247722626,
0.027787109836935997,
-0.02943998947739601,
0.004920089151710272,
-0.03781428933143616,
-0.01793728396296501,
0.09525665640830994,
-0.0850042924284935,
-0.009817307814955711,
0.008234146051108837,
0.003437445964664221,
-0.023929636925458908,
-0.03898485377430916
] |
<p>So I am told that pressure = Force per Area --> F/A..</p>
<p>When considering the units of Force I find that force = kg * m/s^2</p>
<p>When considering the units of Area I find that area = m^2</p>
<p>Thus the units of Pressure = kg/s^2 *1/m = d^2(mass)/dt^2 * 1/m </p>
<p>If I interpret this correctly that means that if one had a long glass tube </p>
<p>(picture below):</p>
<p>=========================================================================</p>
<p>=========================================================================</p>
<p>And we considered a segment of the tube </p>
<pre><code> this is the segment:
</code></pre>
<p>===============|===================================|=====================</p>
<p>===============|===================================|=====================</p>
<p>and we assumed that there was matter flowing through the entire tube:</p>
<p>===============|===================================|=====================</p>
<p><strong>* * *</strong> * * <strong><em>*</em>**</strong> * * <strong><em>*</em>*</strong> * * * * * * <strong><em>*</em>*</strong> * * * * * * ** * * <strong><em>*</em>**</strong> *</p>
<p>===============|===================================|=====================</p>
<p>Then at any given moment: the pressure in this particular segment could be given by:</p>
<p>The change in the rate of mass flow/length of segment:</p>
<p>= d^2(mass in segment)/dt^2 *1/length</p>
<p>Is this correct?</p>
| 9,619 |
[
-0.0030901608988642693,
-0.009446651674807072,
-0.033994052559137344,
-0.032992228865623474,
0.058564964681863785,
-0.012820923700928688,
0.0019961358048021793,
-0.030469119548797607,
-0.022513456642627716,
0.016556669026613235,
0.060251712799072266,
0.021102258935570717,
0.050527043640613556,
0.012878768146038055,
0.015328650362789631,
0.02307191491127014,
0.003174565499648452,
-0.01330963522195816,
0.02750919573009014,
-0.05137057602405548,
0.0056574419140815735,
0.0011433339677751064,
-0.023665273562073708,
-0.009219622239470482,
0.0072926487773656845,
0.05021906644105911,
0.039577122777700424,
-0.04014125466346741,
0.005760551895946264,
0.01804514043033123,
-0.04300934076309204,
-0.02357562445104122,
0.008944536559283733,
0.017552947625517845,
0.034052774310112,
0.02270236611366272,
-0.043537065386772156,
-0.02523510344326496,
-0.0214553140103817,
0.039941009134054184,
-0.002755463123321533,
0.026733756065368652,
0.015016401186585426,
0.017848430201411247,
-0.031083978712558746,
0.05680275335907936,
0.0012748909648507833,
0.01907636970281601,
0.021743621677160263,
-0.07382582128047943,
0.03735008090734482,
0.01222294382750988,
0.08225386589765549,
0.027951272204518318,
-0.0035102851688861847,
-0.023285457864403725,
0.050225093960762024,
0.048085156828165054,
-0.03137966990470886,
-0.07472790777683258,
-0.014493647031486034,
0.014170857146382332,
-0.046882208436727524,
-0.022919634357094765,
-0.010885185562074184,
-0.017852744087576866,
-0.03329140320420265,
-0.033128585666418076,
0.02080572210252285,
-0.007103261537849903,
0.02917329967021942,
0.019038833677768707,
0.04724210500717163,
-0.004505048505961895,
0.011333851143717766,
-0.0022167207207530737,
0.03509432077407837,
0.000008215081834350713,
0.04042012616991997,
0.053480349481105804,
-0.012644197791814804,
-0.0061890920624136925,
0.04946700111031532,
0.02215530537068844,
0.025881540030241013,
-0.03006676584482193,
0.06564231961965561,
-0.010239500552415848,
-0.00714390492066741,
0.010285170748829842,
0.021861568093299866,
0.007233962416648865,
0.009718399494886398,
0.01474974025040865,
0.03692590445280075,
0.04241478070616722,
0.007422576658427715,
0.05351778119802475,
0.012961032800376415,
-0.0020356569439172745,
0.006858604494482279,
-0.01300937682390213,
0.022280607372522354,
0.07323787361383438,
0.015974832698702812,
-0.015363982878625393,
-0.043200235813856125,
-0.007030160166323185,
-0.00022516056196764112,
0.016703160479664803,
-0.00905764289200306,
-0.02588845230638981,
-0.014963701367378235,
-0.028703562915325165,
-0.017104636877775192,
-0.030198676511645317,
0.005602733232080936,
0.008903531357645988,
0.03037170320749283,
0.011333666741847992,
0.05810095742344856,
0.000047561879910063,
0.015215728431940079,
-0.02524818666279316,
-0.07093176990747452,
-0.005627478938549757,
-0.026573093608021736,
-0.00372077408246696,
-0.006560483481734991,
0.04151998832821846,
0.012781222350895405,
-0.008817934431135654,
0.02591305784881115,
0.0007578989025205374,
0.03462646156549454,
0.002052562776952982,
-0.05369598791003227,
-0.07845760881900787,
0.04259099066257477,
0.010637665167450905,
-0.026700662449002266,
-0.07644961774349213,
0.02057638205587864,
0.027103831991553307,
0.06386672705411911,
-0.017221318557858467,
-0.019768154248595238,
-0.009814752265810966,
0.013736833818256855,
-0.0012598776957020164,
-0.007911347784101963,
0.039334602653980255,
-0.004568945616483688,
-0.026042502373456955,
0.020739635452628136,
-0.02454729750752449,
-0.00927971675992012,
0.028695791959762573,
0.008033977821469307,
-0.017329903319478035,
0.02241828292608261,
-0.041632432490587234,
0.0008387406705878675,
0.004136561416089535,
-0.047869570553302765,
-0.02155686356127262,
0.04503640905022621,
0.007197948172688484,
0.006548909470438957,
0.03558766469359398,
0.023911720141768456,
0.015968728810548782,
-0.009387265890836716,
-0.0273741427809,
0.06377774477005005,
-0.009675990790128708,
-0.006650565657764673,
-0.01941940002143383,
0.020672600716352463,
0.010589202865958214,
-0.0204647034406662,
-0.07190249860286713,
-0.03857763111591339,
0.01956244930624962,
0.06515918672084808,
0.0389387384057045,
0.022821271792054176,
-0.009198250249028206,
-0.0017540251137688756,
-0.05492621660232544,
-0.04863081872463226,
-0.048824917525053024,
0.02151370234787464,
-0.043950051069259644,
-0.017237385734915733,
-0.020090371370315552,
-0.00943051092326641,
0.011694078333675861,
-0.009176292456686497,
-0.016201915219426155,
-0.019751183688640594,
0.029306042939424515,
0.027776485309004784,
0.004594452679157257,
-0.01432881411164999,
0.07513625919818878,
0.04116225987672806,
-0.00755080534145236,
0.004759550094604492,
0.011559689417481422,
0.026713231578469276,
0.014519804157316685,
-0.019851628690958023,
0.009470168501138687,
-0.020191937685012817,
-0.02873503603041172,
0.03346160426735878,
0.014306306838989258,
0.021221591159701347,
0.02536999247968197,
-0.040948085486888885,
0.0908302515745163,
0.07678910344839096,
-0.01566001959145069,
0.027414118871092796,
-0.03257373347878456,
0.004010441247373819,
0.04030698537826538,
0.022442344576120377,
-0.007891200482845306,
-0.048854999244213104,
-0.016541142016649246,
0.001624871976673603,
0.011468353681266308,
-0.02335178107023239,
-0.018254265189170837,
0.04300544410943985,
-0.025035515427589417,
0.03309895470738411,
0.007829157635569572,
-0.0040389359928667545,
-0.023275839164853096,
0.006311331409960985,
0.04665291681885719,
0.006585706025362015,
-0.001563185709528625,
0.011368664912879467,
0.04937528446316719,
0.036505866795778275,
-0.014912385493516922,
0.0315927118062973,
0.023513348773121834,
-0.004122668877243996,
-0.00024399362155236304,
-0.009098656475543976,
-0.006995704490691423,
0.04024721682071686,
-0.007861734367907047,
-0.02091817557811737,
0.05499163642525673,
0.021651946008205414,
-0.0026536518707871437,
-0.07423476129770279,
-0.004321614280343056,
-0.01708398014307022,
0.021460453048348427,
-0.0066195297986269,
-0.028691746294498444,
0.02928217686712742,
-0.024243725463747978,
0.007079865783452988,
-0.03666245564818382,
-0.0050238389521837234,
-0.05304306000471115,
0.005464685615152121,
0.017357854172587395,
0.030786098912358284,
0.03886207938194275,
-0.048513565212488174,
-0.016703180968761444,
-0.004628251772373915,
-0.02110036090016365,
-0.016701430082321167,
-0.01581599935889244,
-0.018111908808350563,
-0.003648575861006975,
-0.011326847597956657,
-0.022540351375937462,
0.0419054813683033,
-0.01469862088561058,
-0.027603521943092346,
0.04227851703763008,
0.003081041155382991,
-0.019294586032629013,
-0.007811321411281824,
-0.03608838468790054,
0.028863543644547462,
-0.013728754594922066,
0.021746596321463585,
0.07052183896303177,
0.00851986464112997,
-0.036641668528318405,
0.011077349074184895,
-0.0674784779548645,
-0.03456678241491318,
-0.03193613141775131,
0.00666637672111392,
0.014367157593369484,
-0.01883820630609989,
-0.00380366831086576,
0.020075485110282898,
-0.033637531101703644,
-0.02804541401565075,
-0.020119372755289078,
-0.018730971962213516,
0.021602962166070938,
0.03723322972655296,
0.06151428073644638,
0.004167092498391867,
-0.057072605937719345,
0.08057542145252228,
-0.022478414699435234,
-0.06282725930213928,
-0.02641959674656391,
-0.020570149645209312,
0.005865114275366068,
-0.06204517185688019,
0.007030641660094261,
0.0630280002951622,
-0.05234261229634285,
0.0013675929512828588,
0.013792294077575207,
0.04927946999669075,
0.0402788445353508,
0.024633340537548065,
0.023911846801638603,
-0.0014178158016875386,
0.026367556303739548,
-0.03412092849612236,
0.06966576725244522,
0.018744559958577156,
0.0038880137726664543,
0.001959682209417224,
-0.023846352472901344,
0.02375798672437668,
0.024704478681087494,
-0.04375854507088661,
0.025003405287861824,
0.0071371677331626415,
-0.011426059529185295,
-0.060238998383283615,
-0.00899417418986559,
-0.035252589732408524,
-0.019870594143867493,
-0.00033897333196364343,
0.034606557339429855,
0.041111551225185394,
-0.010100753046572208,
-0.03908564895391464,
0.04987110570073128,
0.02760210819542408,
-0.004619169980287552,
-0.03211488947272301,
0.011129628866910934,
-0.013426851481199265,
0.051125504076480865,
-0.007981772534549236,
-0.022879263386130333,
0.07429840415716171,
0.03708009049296379,
0.0357380174100399,
0.012007436715066433,
-0.010186991654336452,
0.01949409767985344,
-0.06979361176490784,
-0.013345438055694103,
-0.02130577154457569,
0.05394091084599495,
-0.017424384132027626,
0.0887313112616539,
0.01466328278183937,
0.01878231018781662,
0.03009500913321972,
0.01181761734187603,
-0.08905848860740662,
0.006257555913180113,
0.004323124885559082,
-0.019038330763578415,
0.014729814603924751,
-0.01711060293018818,
-0.019726911559700966,
-0.046673160046339035,
0.017761407420039177,
0.026913613080978394,
0.014482076279819012,
-0.02571585401892662,
0.03997443988919258,
0.007168801035732031,
0.004603118635714054,
-0.03767038881778717,
0.039340484887361526,
0.0574009008705616,
0.010018205270171165,
0.047440845519304276,
0.03758115693926811,
-0.02182011865079403,
-0.0013095940230414271,
0.02526160143315792,
0.01477108709514141,
0.0463545098900795,
0.04061565920710564,
0.02756957896053791,
-0.0009538661688566208,
-0.024745462462306023,
-0.017777258530259132,
0.0200063344091177,
0.023415042087435722,
-0.0030241734348237514,
-0.020587828010320663,
-0.023416096344590187,
-0.015282650478184223,
-0.014108018018305302,
0.027610400691628456,
0.03193218633532524,
-0.02078339084982872,
-0.0014108509058132768,
-0.019153105095028877,
-0.009791402146220207,
-0.01857493817806244,
0.05311746522784233,
0.08873405307531357,
0.0034313504584133625,
-0.057068612426519394,
-0.07657627761363983,
-0.0015914872055873275,
-0.05764373391866684,
-0.004743581172078848,
-0.007208788767457008,
0.07093696296215057,
-0.01807141676545143,
0.019808469340205193,
0.0066657778806984425,
-0.006707360967993736,
-0.029390955343842506,
0.03025970794260502,
-0.01766977459192276,
-0.014239351265132427,
-0.005850456655025482,
0.010424848645925522,
0.04165897145867348,
0.03530227392911911,
-0.011265335604548454,
0.02544676698744297,
-0.024450406432151794,
-0.08888865262269974,
-0.04747806861996651,
0.04673726484179497,
0.05956388637423515,
-0.01886090077459812,
0.010202486999332905,
-0.04092037305235863,
-0.01713901199400425,
0.061237137764692307,
-0.03635425865650177,
0.016572462394833565,
-0.012034757062792778,
0.04602780193090439,
0.005156685132533312,
-0.07853251695632935,
-0.03536497801542282,
0.01020119246095419,
-0.04216701164841652,
-0.016092155128717422,
-0.008866436779499054,
-0.013629046268761158,
0.0067487359046936035,
-0.00593020161613822,
0.02908538281917572,
0.012678975239396095,
-0.03817324712872505,
-0.017179038375616074,
-0.004035636782646179,
0.02403155528008938,
-0.0271433275192976,
-0.05066683888435364,
0.014564461074769497,
-0.0190198365598917,
0.007986397482454777,
0.012756522744894028,
-0.03443619981408119,
-0.03567027673125267,
0.0571557879447937,
0.009033105336129665,
0.016547514125704765,
0.012547515332698822,
-0.024273889139294624,
0.07236281037330627,
0.04123137146234512,
0.014633787795901299,
0.03179521858692169,
0.03083452582359314,
-0.02377370558679104,
-0.019726188853383064,
-0.06085125356912613,
0.0017715345602482557,
-0.0009503965848125517,
-0.014813261106610298,
-0.0697176605463028,
0.033120401203632355,
-0.020769093185663223,
0.014411605894565582,
0.02051599882543087,
0.019838327541947365,
0.004575529135763645,
-0.02695317007601261,
0.02179870195686817,
0.031539518386125565,
0.00965980626642704,
0.016819501295685768,
-0.0013609896413981915,
-0.00421726331114769,
0.0022672186605632305,
-0.03588653355836868,
0.026733823120594025,
0.0019167226273566484,
0.034958112984895706,
0.01827625185251236,
-0.03504732996225357,
-0.011967247352004051,
-0.009103354997932911,
-0.03509901091456413,
0.028012491762638092,
-0.06478685885667801,
0.060785312205553055,
-0.01233817357569933,
0.028345612809062004,
0.03940416872501373,
-0.030169375240802765,
-0.00958248507231474,
0.03598998486995697,
0.000868866394739598,
0.0035838971380144358,
-0.033042848110198975,
0.030627815052866936,
-0.0013345105107873678,
0.01949380338191986,
-0.04054005816578865,
-0.039508648216724396,
0.06119503825902939,
-0.004333395976573229,
-0.03767596185207367,
0.007181898690760136,
-0.0417863130569458,
-0.00668626232072711,
-0.029469167813658714,
-0.001490596099756658,
0.04001392424106598,
-0.055712711066007614,
-0.007909800857305527,
0.023433474823832512,
-0.016062229871749878,
0.072388656437397,
0.05395062640309334,
-0.019055254757404327,
-0.012702048756182194,
-0.019698478281497955,
-0.021311786025762558,
-0.03939288854598999,
0.029509281739592552,
-0.03693617880344391,
-0.019597290083765984,
-0.012042517773807049,
0.0003093546547461301,
0.06408878415822983,
-0.011637233197689056,
0.039069026708602905,
-0.010830335319042206,
0.003053651424124837,
-0.02415546588599682,
-0.005034076515585184,
0.01809818111360073,
-0.006729729939252138,
0.031753432005643845,
-0.04407770186662674,
0.006187361665070057,
-0.04922361671924591,
-0.024074552580714226,
-0.015530327335000038,
-0.012279498390853405,
-0.013506218791007996,
-0.011114677414298058,
0.051184531301259995,
-0.022396709769964218,
-0.010883797891438007,
-0.01059566717594862,
-0.046631891280412674,
0.021760961040854454,
0.0334598533809185,
-0.02745293267071247,
0.013930361717939377,
-0.0031985933892428875,
-0.03223796933889389,
-0.013601645827293396,
-0.025188954547047615,
-0.005188796669244766,
0.03613625839352608,
-0.005032424349337816,
0.06520749628543854,
-0.0052573541179299355,
-0.03244072198867798,
0.026898939162492752,
-0.003318111877888441,
-0.030653012916445732,
0.028764791786670685,
0.026750486344099045,
0.0474039763212204,
-0.0010912672150880098,
-0.04625460505485535,
0.04292439669370651,
0.0046392991207540035,
-0.01402298454195261,
-0.0204902533441782,
0.03833264112472534,
-0.03523094579577446,
0.0024288916029036045,
-0.03858957067131996,
-0.02044576033949852,
0.03554597869515419,
-0.041507501155138016,
0.03699216619133949,
-0.023284927010536194,
-0.0003789370821323246,
0.06131737679243088,
0.021604925394058228,
-0.03910471871495247,
-0.06286513805389404,
0.03089124523103237,
-0.03949008882045746,
-0.007040470372885466,
0.03382967785000801,
-0.025237517431378365,
0.0014288476668298244,
0.0006521987961605191,
0.020774507895112038,
-0.008371069096028805,
0.03653543442487717,
0.0019762744195759296,
-0.016399823129177094,
0.006208307575434446,
-0.012574959546327591,
-0.031905267387628555,
0.07456132769584656,
0.0047157928347587585,
0.0044146035797894,
-0.007291366811841726,
-0.06051607057452202,
0.03874550759792328,
0.01991727575659752,
-0.014274638146162033,
-0.003361311974003911,
0.07203073799610138,
-0.013289744965732098,
0.02782304212450981,
-0.012302731163799763,
0.005723115056753159,
0.1668921709060669,
0.04518003389239311,
0.035866353660821915,
-0.012878155335783958,
0.02473299205303192,
-0.01226006355136633,
0.0255501177161932,
-0.017704369500279427,
0.0320613831281662,
-0.010483774356544018,
-0.01851603575050831,
0.004959646612405777,
0.04323429614305496,
-0.009133894927799702,
0.029824206605553627,
0.0541035458445549,
-0.05404207482933998,
-0.006459577940404415,
-0.00009995868458645418,
-0.009331416338682175,
-0.05945529788732529,
0.03872057795524597,
-0.024293461814522743,
0.0354142002761364,
-0.010116932913661003,
0.013628048822283745,
-0.05769495293498039,
-0.022825120016932487,
0.012069771997630596,
-0.016383035108447075,
-0.04936274141073227,
0.019816473126411438,
-0.0005645679775625467,
-0.017215969040989876,
-0.037311479449272156,
0.019175035879015923,
0.01620451547205448,
-0.027829820290207863,
-0.01428626012057066,
0.020049644634127617,
0.012968089431524277,
0.0037702855188399553,
-0.004983001854270697,
0.01149012241512537,
-0.03376676142215729,
0.011698557995259762,
-0.012827602215111256,
0.03965756297111511,
0.010568507947027683,
-0.023641956970095634,
-0.003475492587313056,
0.0074499305337667465,
-0.0029768766835331917,
-0.0587698295712471,
-0.022808656096458435,
-0.006171370390802622,
0.023994995281100273,
0.027761349454522133,
-0.014191883616149426,
0.0032649466302245855,
-0.0076308404095470905,
-0.03646210581064224,
0.003200074192136526,
-0.028206681832671165,
0.03220471367239952,
-0.01376317348331213,
0.011179755441844463,
0.04736792668700218,
-0.03647705912590027,
0.02625531144440174,
0.004277557134628296,
0.006544057279825211,
-0.06452684849500656,
0.018621092662215233,
0.001328617800027132,
0.06383448094129562,
0.028917238116264343,
0.007450023666024208,
-0.023091040551662445,
-0.023250799626111984,
-0.03652443736791611,
0.04937952384352684,
-0.009259069338440895,
-0.014260263182222843,
-0.032035548239946365,
0.00848301500082016,
-0.007893139496445656,
0.05597890168428421,
-0.008822084404528141,
-0.019260097295045853,
-0.01148431096225977,
0.06110987439751625,
0.018689816817641258,
-0.040643900632858276,
-0.05438793823122978,
0.020921066403388977,
0.0026001459918916225,
0.008717207238078117,
0.014504660852253437,
0.0483403280377388,
0.02770031988620758,
-0.0015946633648127317,
0.005949939135462046,
0.012608891353011131,
-0.01997988484799862,
-0.004353714175522327,
0.016403665766119957,
-0.012545059435069561,
0.011377660557627678,
0.025562958791851997,
-0.018630376085639,
-0.04688055068254471,
0.013782705180346966,
-0.02115497924387455,
-0.015566649846732616,
-0.015333587303757668,
0.030125360935926437,
-0.012921072542667389,
-0.00015116606664378196,
-0.04373878985643387,
-0.02414129301905632,
-0.01775999367237091,
0.02400643192231655,
-0.04360874369740486,
-0.028719905763864517,
0.01101730577647686,
0.008143248036503792,
-0.05481177940964699,
0.055517423897981644,
-0.031192904338240623,
0.008203588426113129,
-0.0017137376125901937,
0.01752864383161068,
-0.01877361536026001,
-0.008348073810338974,
0.02963733859360218,
0.007386006414890289,
0.003473542630672455,
0.0027361412066966295,
-0.03761632740497589,
0.012005769647657871,
-0.006741719786077738,
-0.05494183301925659,
0.017006000503897667,
0.015318631194531918,
0.03362732753157616,
0.02830299735069275,
-0.00018992240075021982,
-0.012607122771441936,
0.08561751246452332,
-0.021047651767730713,
-0.008181137032806873,
-0.025264156982302666,
-0.06123953312635422,
0.021172193810343742,
-0.037293028086423874,
-0.0055875699035823345,
-0.015013265423476696,
0.015625230967998505,
-0.001459654769860208,
0.03371257334947586,
0.007330331951379776,
-0.017870845273137093,
0.0037067411467432976,
0.0015402225544676185,
0.03223472833633423,
0.030281919986009598,
-0.004360001068562269,
0.00880315899848938,
0.01107602845877409,
-0.030304010957479477,
-0.005860835313796997,
-0.033353447914123535,
-0.006365443114191294,
-0.104643315076828,
-0.008044048212468624,
-0.02116292156279087,
-0.011017394252121449,
0.033578041940927505,
-0.03637644648551941,
-0.03957568109035492,
0.01325302291661501,
-0.06084048002958298,
-0.015238587744534016,
-0.020787399262189865,
-0.010643265210092068,
-0.024399472400546074,
0.002360560931265354,
-0.03354582190513611,
0.061622217297554016,
0.003194293938577175,
0.03681063652038574,
0.03869473934173584,
0.003800581209361553,
0.002299314131960273,
-0.015677032992243767,
-0.00007679237751290202,
0.036231283098459244,
-0.01825413852930069,
0.002550455741584301,
0.033773794770240784,
-0.018978171050548553,
0.003264589235186577,
0.018074868246912956,
-0.02492820844054222,
0.02794940210878849,
-0.011674894951283932,
-0.012612341903150082,
0.0009811148047447205,
0.04438633844256401,
0.002832167549058795,
0.046694815158843994,
-0.01281022746115923,
-0.0000017430218122171937,
-0.0031844410113990307,
0.0033086149487644434,
-0.033002860844135284,
0.0021684104576706886,
0.011509211733937263,
-0.025407863780856133,
-0.014405678026378155,
0.02091045491397381,
-0.05212263762950897,
0.001892191474325955,
-0.01432675402611494,
-0.008309499360620975,
0.004687949549406767,
-0.040499646216630936,
-0.024233121424913406,
-0.06761667877435684,
0.03732020780444145,
0.03763852268457413,
-0.012837463058531284,
-0.02727220207452774,
0.009635401889681816,
0.05308976396918297,
-0.005202870350331068,
0.00545331509783864,
-0.0035589865874499083,
-0.03935040533542633,
-0.017734190449118614,
-0.008004055358469486,
-0.01897580735385418,
0.012271013110876083,
0.028771551325917244,
-0.03639685735106468,
-0.0055487207137048244,
0.008485503494739532,
0.05147801339626312,
0.004304725211113691,
0.017902648076415062,
-0.018580695614218712,
0.0122045474126935,
-0.10425438731908798,
0.01950462907552719,
-0.007990576326847076,
-0.056479670107364655,
-0.05000080540776253,
-0.012502631172537804,
0.005927673075348139,
0.05446423590183258,
0.04216921329498291,
-0.001711590331979096,
-0.010788405314087868,
-0.03308873623609543,
0.016476638615131378,
0.025764407590031624,
-0.06392528116703033,
0.006934324279427528,
-0.014491713605821133,
-0.03081701509654522,
0.020400336012244225,
0.014416023157536983,
-0.018825236707925797,
0.0007480060448870063,
0.04337674751877785,
-0.019335338845849037,
0.015596768818795681,
-0.031285300850868225,
-0.013904787600040436,
-0.019254302605986595,
0.003364038420841098,
0.004815735854208469,
0.07586659491062164,
-0.003447439055889845,
0.0016021010233089328,
0.024536408483982086,
0.002070164540782571,
-0.026394758373498917,
0.01047893799841404,
-0.04144720733165741,
0.027117503806948662,
-0.030714139342308044,
-0.01809745654463768,
0.04830648750066757,
-0.05501013249158859,
-0.0028350031934678555,
0.035203561186790466,
-0.0437292642891407,
-0.044553302228450775,
0.05846184492111206,
0.0406256727874279,
0.006521178409457207,
-0.047580648213624954,
0.0301755852997303,
0.004032800439745188,
-0.0032464934047311544,
-0.0022984331008046865,
0.035118818283081055,
0.04196135327219963,
0.0008463528356514871,
0.0010912284487858415,
0.03986034542322159,
-0.011364210397005081,
-0.012047545053064823,
-0.002596781123429537,
0.029456326737999916,
-0.03328428044915199,
-0.0273112952709198,
-0.007721531204879284,
-0.014564426615834236,
0.015154656954109669,
0.06063122674822807,
-0.012503426522016525,
0.050973113626241684,
-0.0063795424066483974,
0.030214356258511543,
-0.023890670388936996,
-0.003569528693333268,
-0.003225791733711958,
0.009724491275846958,
0.02793196402490139,
0.014552858658134937,
-0.037396300584077835,
-0.01358851045370102,
-0.0022745600435882807,
-0.018090318888425827,
-0.009521391242742538,
-0.024121854454278946,
0.02550715021789074,
-0.004179953131824732,
0.005957294255495071,
-0.046424176543951035,
-0.011247456073760986,
-0.014179183170199394,
-0.013680873438715935,
0.07881809771060944,
-0.007578564807772636,
-0.021497702226042747,
-0.008501912467181683,
0.01962391473352909,
-0.022208958864212036,
0.040645111352205276,
-0.02399078942835331,
-0.00950439553707838,
-0.01444861851632595,
0.027311643585562706,
0.028131229802966118,
-0.021705791354179382
] |
<p>Consider the following problem taken from a problem booklet. My questions are:</p>
<ol>
<li>What is displacement vector?</li>
<li>And how to determine the direction of displacement vector at a certain point?</li>
<li>Where is the position with zero displacement vector?</li>
</ol>
<p><img src="http://i.stack.imgur.com/XuGiu.png" alt="enter image description here"></p>
| 9,620 |
[
0.012242671102285385,
0.0019693614449352026,
0.02477548085153103,
-0.000457660760730505,
0.05144617334008217,
-0.005892991553992033,
-0.044883426278829575,
-0.01373536791652441,
-0.01714031957089901,
-0.02114102430641651,
0.03205113112926483,
0.028253715485334396,
0.05253111198544502,
0.007133310195058584,
0.03999903425574303,
0.009016705676913261,
-0.020977621898055077,
-0.02047487534582615,
-0.008877767249941826,
0.00043776159873232245,
0.0066847349517047405,
-0.019129548221826553,
0.008426276035606861,
0.003625421319156885,
-0.00009947246871888638,
0.019623367115855217,
0.06718388944864273,
0.007085904013365507,
0.0024144898634403944,
0.057744983583688736,
-0.023475483059883118,
-0.03010443039238453,
-0.0006689949077554047,
-0.008183334022760391,
0.012800578027963638,
-0.011424781754612923,
-0.012234353460371494,
-0.028538305312395096,
-0.0167617779225111,
0.031831081956624985,
0.006628607865422964,
-0.02047031559050083,
-0.009003981947898865,
0.06802112609148026,
-0.02271990291774273,
0.04904169589281082,
0.0350491888821125,
-0.024641064926981926,
0.049010928720235825,
-0.04712970182299614,
0.04250912740826607,
-0.004419086501002312,
0.03782322630286217,
-0.0013405672507360578,
0.01839505136013031,
-0.012136301957070827,
0.07307194173336029,
0.044056493788957596,
-0.021918652579188347,
-0.04468903690576553,
0.00771266408264637,
-0.01767417974770069,
-0.017255371436476707,
-0.04410138726234436,
-0.04789457097649574,
-0.006596866529434919,
-0.01716991700232029,
0.004319530446082354,
0.02034299448132515,
-0.012004612945020199,
-0.021253231912851334,
0.016632890328764915,
0.0014829648425802588,
-0.033774200826883316,
0.011477419175207615,
-0.09000382572412491,
0.014409872703254223,
0.02989400178194046,
0.011938510462641716,
0.038300082087516785,
0.01539913285523653,
0.01481552328914404,
0.031692005693912506,
0.0287723857909441,
0.006125918123871088,
-0.05193455517292023,
0.04364022612571716,
0.007160923443734646,
0.013264738023281097,
0.01818653754889965,
0.0011877930955961347,
0.007680973503738642,
0.00366711663082242,
-0.015472039580345154,
0.0012038048589602113,
0.016175877302885056,
-0.026932373642921448,
0.04902645945549011,
0.023617178201675415,
-0.037859171628952026,
0.014696098864078522,
-0.026302773505449295,
0.03711468353867531,
0.05970248952507973,
-0.0231307465583086,
0.017795898020267487,
-0.034309811890125275,
0.05190639942884445,
-0.019772576168179512,
-0.04269789904356003,
-0.018023628741502762,
0.031581200659275055,
-0.0035194118972867727,
0.024039607495069504,
0.025171853601932526,
0.0006829523481428623,
-0.011982486583292484,
-0.019513441249728203,
0.0387909971177578,
0.06075611710548401,
0.04801361635327339,
-0.05584695190191269,
0.0026629632338881493,
0.009612304158508778,
-0.05628945305943489,
-0.02101336605846882,
0.05040767416357994,
-0.002637149766087532,
-0.022754279896616936,
0.030558308586478233,
-0.0010910732671618462,
0.016800547018647194,
0.004361517261713743,
0.02832573466002941,
0.005307077895849943,
0.009895595721900463,
-0.0707898661494255,
-0.06543967127799988,
0.07952920347452164,
0.003815665142610669,
-0.016830909997224808,
-0.04379238560795784,
-0.027025451883673668,
0.027654847130179405,
0.05598029866814613,
-0.008912053890526295,
0.016259288415312767,
0.03152482956647873,
0.029647940769791603,
-0.01362892147153616,
0.027053816244006157,
0.003770798910409212,
-0.025783812627196312,
-0.05637948215007782,
0.000015932260794215836,
-0.01826227270066738,
0.014142969623208046,
0.027928665280342102,
0.014915934763848782,
-0.062181200832128525,
0.044432513415813446,
0.0021520827431231737,
-0.03822635859251022,
0.05833595246076584,
-0.027748053893446922,
-0.02232358232140541,
0.058726828545331955,
0.019713036715984344,
-0.012931090779602528,
0.03683102875947952,
-0.011900137178599834,
0.05565812066197395,
-0.007031576707959175,
0.012053140439093113,
0.062370672821998596,
-0.03740924596786499,
-0.029108598828315735,
-0.021198172122240067,
0.009782640263438225,
-0.02085229940712452,
-0.04627959057688713,
-0.03212396427989006,
0.0071540046483278275,
0.01195935346186161,
0.019299590960144997,
0.054711733013391495,
-0.0112531129270792,
0.026210499927401543,
-0.02036198228597641,
-0.0160539373755455,
-0.0006899618310853839,
-0.0514102503657341,
0.05823858082294464,
-0.007572361268103123,
-0.016530614346265793,
0.004252330865710974,
0.023006290197372437,
0.0007458206382580101,
-0.044447291642427444,
-0.010656430386006832,
-0.012227864004671574,
0.009474541991949081,
-0.011365089565515518,
-0.025429729372262955,
0.01798844151198864,
0.07708906382322311,
0.07004512846469879,
-0.01860174722969532,
-0.0009854506934061646,
-0.03635287284851074,
0.0007087335688993335,
0.009787467308342457,
0.012057945132255554,
0.02332293428480625,
-0.006427909713238478,
0.005338923539966345,
-0.024631112813949585,
0.020543014630675316,
-0.011752213351428509,
0.009375683031976223,
-0.027774153277277946,
0.07752438634634018,
0.07670173794031143,
-0.010137670673429966,
0.024826515465974808,
0.01721610687673092,
0.03250552713871002,
0.006607051007449627,
0.03270336985588074,
0.004895472899079323,
-0.07206954061985016,
-0.012603160925209522,
0.026081152260303497,
0.0029037650674581528,
-0.04186081141233444,
-0.005806810688227415,
0.025591401383280754,
0.0030811398755759,
0.007676392327994108,
0.00794116873294115,
-0.003899692790582776,
-0.03058898076415062,
0.011010979302227497,
0.042604897171258926,
-0.00061650515999645,
0.038919102400541306,
0.02779899723827839,
0.03619719669222832,
0.059107474982738495,
-0.000038975551433395594,
-0.017638076096773148,
0.07522833347320557,
0.01537467259913683,
0.010479343123733997,
0.02974850684404373,
0.011675380170345306,
0.022423632442951202,
-0.012408646754920483,
-0.014268509112298489,
0.03274112939834595,
-0.01740260422229767,
0.014293582178652287,
0.00041632322245277464,
0.019982798025012016,
0.01508414652198553,
0.014695161953568459,
-0.0314115434885025,
0.008822950534522533,
0.030329447239637375,
-0.042940568178892136,
0.015378993935883045,
-0.04646442085504532,
-0.023347953334450722,
0.018943503499031067,
-0.013294056989252567,
0.04518971964716911,
0.03109549731016159,
-0.022655535489320755,
-0.0533006377518177,
0.016812646761536598,
-0.006402567494660616,
-0.06915012747049332,
0.017146959900856018,
0.012875829823315144,
-0.06704283505678177,
0.021610165014863014,
-0.04236067086458206,
-0.05305814743041992,
0.03894268348813057,
0.02979077585041523,
0.022696873173117638,
0.028415173292160034,
-0.02136324718594551,
-0.053983911871910095,
-0.06718277186155319,
-0.044984329491853714,
0.0032815318554639816,
-0.0688571110367775,
-0.012743595987558365,
0.057104747742414474,
-0.05757000297307968,
-0.0036083641462028027,
0.011814800091087818,
-0.03529324010014534,
-0.02975117787718773,
-0.039983440190553665,
0.009468221105635166,
0.07326085865497589,
0.0012687264243140817,
0.006405665539205074,
-0.010391303338110447,
-0.0017457061912864447,
0.01341897714883089,
-0.059360772371292114,
-0.03616100177168846,
-0.024520955979824066,
0.004093818366527557,
0.06567515432834625,
-0.009204581379890442,
0.009075559675693512,
0.08287045359611511,
0.02363157458603382,
-0.06261712312698364,
-0.014051203615963459,
0.00658006314188242,
-0.024982985109090805,
-0.021948939189314842,
-0.006217708811163902,
0.03610888496041298,
-0.007487810682505369,
0.021846795454621315,
-0.015252546407282352,
0.02847260795533657,
0.02797478809952736,
0.0467740036547184,
-0.010356305167078972,
-0.016206437721848488,
0.025045515969395638,
-0.028268959373235703,
0.029491983354091644,
0.004066553432494402,
-0.025874465703964233,
-0.004410604480654001,
0.006092752330005169,
0.05315352976322174,
0.011703417636454105,
-0.02435825578868389,
-0.002082319464534521,
0.0025564872194081545,
-0.0038210598286241293,
-0.03945969045162201,
0.06038312613964081,
0.038569238036870956,
0.02935655042529106,
-0.0022444191854447126,
-0.024137597531080246,
0.026788245886564255,
-0.02288597635924816,
-0.032638490200042725,
0.03800630196928978,
-0.0293443500995636,
-0.03460652753710747,
-0.02884816750884056,
-0.01686694473028183,
-0.006413409020751715,
0.0110237505286932,
-0.006919891107827425,
-0.028177836909890175,
0.029297424480319023,
0.036125849932432175,
0.028726905584335327,
0.024972135201096535,
-0.03973855823278427,
-0.0064028226770460606,
-0.035152867436409,
-0.021665772423148155,
0.04106365889310837,
0.04118791222572327,
0.006326218601316214,
0.05285736545920372,
0.02428627572953701,
0.04312760755419731,
0.015355934388935566,
0.03334185481071472,
-0.08942022174596786,
0.0101490942761302,
-0.03347306698560715,
-0.006285428535193205,
-0.0023712506517767906,
-0.004588904790580273,
0.017101092264056206,
-0.06885059177875519,
-0.027656840160489082,
0.019953662529587746,
0.009008443914353848,
-0.05073312297463417,
0.03381486237049103,
-0.014423844404518604,
-0.0023905993439257145,
-0.002232481725513935,
0.015141765587031841,
0.011002748273313046,
-0.019843555986881256,
0.028660813346505165,
0.08874974399805069,
-0.006123240105807781,
0.004874060396105051,
-0.003674916224554181,
-0.012670012190937996,
-0.004586333408951759,
0.03952387720346451,
0.005525084678083658,
0.055928997695446014,
-0.007638444192707539,
0.029960043728351593,
-0.01785009168088436,
0.044224612414836884,
0.024886438623070717,
-0.009196363389492035,
-0.03761588782072067,
-0.021610252559185028,
0.011396021582186222,
-0.0383923165500164,
0.03728966414928436,
-0.02715742401778698,
0.013484487310051918,
0.06706275790929794,
0.00597947696223855,
-0.016225049272179604,
0.051269907504320145,
0.05817234888672829,
0.030136169865727425,
-0.009989773854613304,
-0.055369243025779724,
-0.014873308129608631,
-0.043250568211078644,
0.0005737812607549131,
0.018810279667377472,
-0.013941803015768528,
0.00063836679328233,
-0.002474813023582101,
0.018990080803632736,
0.023882323876023293,
-0.009326579980552197,
0.025360463187098503,
-0.040308982133865356,
0.030809640884399414,
-0.00451741274446249,
-0.0025938504841178656,
0.007856608368456364,
0.000954858202021569,
0.03581666573882103,
-0.013916164636611938,
-0.025203192606568336,
-0.09404350072145462,
-0.023247210308909416,
0.021998511627316475,
0.04866556450724602,
-0.006785854697227478,
0.03249979391694069,
-0.04535667225718498,
-0.04025760293006897,
0.06341216713190079,
-0.05972159281373024,
0.025356385856866837,
-0.0359099842607975,
-0.00854971632361412,
-0.02442883513867855,
-0.02317887544631958,
-0.06396620720624924,
0.009571097791194916,
-0.022636394947767258,
0.01880479045212269,
-0.0240759439766407,
0.013809876516461372,
-0.038725174963474274,
0.0010137506760656834,
0.041993360966444016,
0.051223669201135635,
0.03733925148844719,
-0.006344127468764782,
0.012503618374466896,
0.037348952144384384,
-0.02623332478106022,
-0.04970960691571236,
0.016107669100165367,
0.021070878952741623,
-0.004091630224138498,
0.02417711913585663,
-0.028454812243580818,
-0.07147135585546494,
0.034923966974020004,
-0.004942982457578182,
-0.018219804391264915,
0.012883130460977554,
-0.04632160812616348,
0.007936825975775719,
0.021326037123799324,
0.007384477183222771,
0.03801243379712105,
0.022668804973363876,
-0.019380081444978714,
-0.002665660809725523,
-0.03069649264216423,
-0.021848956122994423,
-0.023669734597206116,
-0.017921455204486847,
-0.01750159077346325,
0.053077034652233124,
-0.03103916347026825,
0.0644487589597702,
0.014231789857149124,
0.007889240980148315,
0.0021361717954277992,
-0.022175151854753494,
-0.023148516193032265,
0.009289711713790894,
-0.0010077765909954906,
0.02328937128186226,
0.002334268530830741,
0.006145309656858444,
-0.011612589471042156,
-0.041168589144945145,
0.003695577848702669,
-0.04259757325053215,
0.014411726966500282,
0.02856173738837242,
-0.00419696606695652,
0.02983689494431019,
-0.022539738565683365,
-0.01902247965335846,
0.0011309193214401603,
-0.04464513435959816,
0.055603187531232834,
-0.008167077787220478,
-0.00499348621815443,
0.01123364269733429,
-0.05973851680755615,
-0.06158868223428726,
0.03472571820020676,
0.01603531651198864,
0.03488237410783768,
-0.02572672814130783,
0.02826344221830368,
0.03096657246351242,
0.018773995339870453,
-0.03432030230760574,
-0.06724298745393753,
0.0006241005612537265,
0.031121663749217987,
-0.018869655206799507,
-0.02597685717046261,
0.028374429792165756,
0.002711324719712138,
-0.024080926552414894,
0.01115945540368557,
0.05263154208660126,
-0.020537707954645157,
-0.033998120576143265,
0.040737785398960114,
-0.01145436242222786,
0.07200974971055984,
-0.026150349527597427,
-0.004882941022515297,
0.024567795917391777,
-0.0006681546801701188,
-0.004239451140165329,
-0.010974529199302197,
0.0609470009803772,
-0.034715838730335236,
-0.03696846961975098,
-0.029868442565202713,
0.011759631335735321,
0.05519950017333031,
0.007508870214223862,
-0.007353265304118395,
0.014258387498557568,
0.018587034195661545,
-0.07092858850955963,
-0.04209515079855919,
0.0265335775911808,
0.0070732273161411285,
-0.008925342932343483,
0.008325646631419659,
0.014998513273894787,
-0.05151616036891937,
-0.038670144975185394,
-0.010900570079684258,
-0.007043897639960051,
0.021026335656642914,
-0.02065618708729744,
0.04906526952981949,
-0.04931790381669998,
0.01700950786471367,
0.027703439816832542,
0.008434353396296501,
0.022570110857486725,
-0.006705081555992365,
-0.019070161506533623,
0.023662405088543892,
0.018012311309576035,
-0.04539741575717926,
-0.010669505223631859,
-0.03674362599849701,
0.02121572382748127,
0.09597326070070267,
0.026172403246164322,
0.01488463580608368,
0.03232325613498688,
0.018890636041760445,
0.01419961266219616,
0.03294316679239273,
-0.0027769459411501884,
-0.00851678941398859,
0.014520161785185337,
0.018507951870560646,
-0.05929262563586235,
-0.0015478458954021335,
0.013589544221758842,
-0.006062213331460953,
-0.029649648815393448,
-0.03192291408777237,
0.018196793273091316,
-0.0009574622963555157,
0.030697111040353775,
-0.022519195452332497,
-0.035962920635938644,
0.025999663397669792,
-0.020144328474998474,
0.05104944482445717,
-0.00985187292098999,
-0.05300580710172653,
0.06284750252962112,
0.00574022950604558,
0.006295772269368172,
-0.041608065366744995,
0.030161410570144653,
-0.04007524624466896,
0.01388747151941061,
-0.025814060121774673,
0.025447143241763115,
-0.010965744033455849,
0.016709277406334877,
0.04264802858233452,
-0.024893753230571747,
0.019000718370079994,
-0.014079221524298191,
-0.08229413628578186,
0.0000886832713149488,
-0.03332025930285454,
-0.04890197142958641,
0.025700891390442848,
-0.001556537114083767,
-0.01871410757303238,
0.01295235101133585,
-0.03475923091173172,
0.02946765162050724,
0.029505154117941856,
0.04438943415880203,
-0.030959080904722214,
0.061596550047397614,
-0.02246648445725441,
0.01622101105749607,
-0.012067830190062523,
0.0009323525009676814,
0.10797867923974991,
0.06578190624713898,
0.004148287698626518,
-0.055025555193424225,
0.0173536017537117,
-0.015868207439780235,
-0.011852400377392769,
-0.02348674088716507,
0.04869377240538597,
-0.01587529480457306,
0.026928341016173363,
0.002844636095687747,
0.022004803642630577,
-0.005949566140770912,
-0.005862519610673189,
0.03429460525512695,
-0.042673878371715546,
-0.08179090917110443,
-0.026626499369740486,
0.009041075594723225,
-0.021535499021410942,
0.02468842640519142,
-0.025598963722586632,
0.02226203680038452,
-0.021526886150240898,
-0.04805558919906616,
-0.07145871222019196,
-0.04917982220649719,
0.028129827231168747,
-0.02908429503440857,
-0.0319860465824604,
-0.0028090421110391617,
0.02005373314023018,
-0.023852907121181488,
-0.07842772454023361,
0.046645935624837875,
-0.023822810500860214,
-0.0279114730656147,
0.03290285915136337,
0.022917302325367928,
-0.016603227704763412,
0.00237362296320498,
0.013941163197159767,
-0.004098936449736357,
-0.010673830285668373,
0.007249447517096996,
-0.0394902341067791,
0.08256468921899796,
-0.015890954062342644,
-0.0014628436183556914,
-0.02429349161684513,
0.02831694670021534,
-0.004127790220081806,
-0.05888403579592705,
-0.01688120886683464,
0.01849687471985817,
0.04857099428772926,
-0.014121018350124359,
-0.03757941722869873,
-0.04547626152634621,
0.008911843411624432,
-0.006685404572635889,
0.01528445165604353,
0.012264972552657127,
-0.007679386995732784,
0.0134935537353158,
0.01895996369421482,
0.08765760809183121,
-0.011978143826127052,
0.0010343259200453758,
-0.007272826973348856,
0.002443042118102312,
-0.007000533863902092,
0.016152773052453995,
-0.010126881301403046,
0.023703541606664658,
-0.01486728060990572,
0.009936211630702019,
-0.0036037282552570105,
-0.002503862837329507,
-0.07430368661880493,
0.016311878338456154,
-0.014159845188260078,
-0.026416219770908356,
-0.007060214877128601,
0.008705390617251396,
0.02604932337999344,
0.04923094063997269,
0.008797606453299522,
0.031933944672346115,
0.017332397401332855,
0.02120121568441391,
0.004760376643389463,
-0.00877611804753542,
-0.01999698206782341,
0.011133658699691296,
-0.019545359537005424,
0.044201526790857315,
0.0032952253241091967,
0.06528764218091965,
0.03435605391860008,
0.03693580627441406,
-0.015465485863387585,
0.008349099196493626,
-0.04440445080399513,
-0.014097635634243488,
0.006708220113068819,
-0.03626659885048866,
-0.020460214465856552,
0.02675388567149639,
0.00848331581801176,
-0.05864640325307846,
-0.004445511382073164,
-0.01692400500178337,
-0.00973980501294136,
0.02538483403623104,
0.03592516481876373,
-0.026534603908658028,
0.0038220970891416073,
-0.048255421221256256,
0.022474341094493866,
-0.01044501643627882,
-0.0232926644384861,
-0.0296834297478199,
-0.011433889158070087,
0.02005409263074398,
-0.006701377220451832,
-0.024294132366776466,
0.007052671629935503,
-0.004533701576292515,
0.030119208618998528,
0.0294618122279644,
0.02453990839421749,
0.026093902066349983,
0.01708400808274746,
0.009870041161775589,
-0.0038815108127892017,
0.05518386885523796,
-0.0012836100067943335,
-0.00721316272392869,
0.023883156478405,
-0.01948048733174801,
-0.014917438849806786,
-0.0013224442955106497,
0.013463564217090607,
0.03155803680419922,
0.004127723164856434,
-0.004892522003501654,
0.006216129288077354,
0.03459329158067703,
0.02518474869430065,
0.012716634199023247,
-0.002831727731972933,
-0.04112439602613449,
-0.025088252499699593,
-0.023365559056401253,
-0.033714573830366135,
-0.026154523715376854,
-0.04657009243965149,
0.009019313380122185,
0.01330547034740448,
0.014706793241202831,
0.008697636425495148,
0.025005163624882698,
0.008444050326943398,
-0.019667968153953552,
0.030116764828562737,
-0.021916702389717102,
-0.027360966429114342,
0.03458882495760918,
-0.01130931917577982,
0.017338421195745468,
0.01089391577988863,
0.01629718951880932,
-0.11424365639686584,
-0.003352170577272773,
0.03545302897691727,
-0.0003943615301977843,
0.05144480988383293,
-0.05017191916704178,
-0.020421337336301804,
0.06654193252325058,
-0.038310542702674866,
0.04124443233013153,
-0.02818104811012745,
0.01199560146778822,
0.0017491655889898539,
-0.013481429778039455,
-0.005534237716346979,
0.06123540550470352,
0.019233547151088715,
0.04136510565876961,
0.0352514311671257,
0.03342701494693756,
-0.01111389696598053,
-0.03508494049310684,
0.011792129836976528,
0.031093450263142586,
-0.01931135728955269,
-0.02469954825937748,
0.02771667204797268,
0.006889192387461662,
-0.009534989483654499,
0.0019058072939515114,
-0.028625011444091797,
0.019845854490995407,
0.025829659774899483,
0.0027670247945934534,
-0.026923226192593575,
0.06123516708612442,
0.015128553844988346,
-0.0035051314625889063,
-0.029913125559687614,
0.005278661847114563,
-0.010640650056302547,
0.015773247927427292,
0.002992849098518491,
-0.004515720531344414,
0.004509629216045141,
-0.026021940633654594,
0.009005112573504448,
0.04902542755007744,
-0.043905578553676605,
0.006461847573518753,
0.019230350852012634,
-0.0038259609136730433,
-0.0182337686419487,
-0.029047230258584023,
0.01949305087327957,
-0.04362903907895088,
-0.018594441935420036,
0.012943503446877003,
-0.020694615319371223,
-0.04329574108123779,
0.009060004726052284,
0.005709408316761255,
-0.04771622642874718,
-0.00036623378400690854,
-0.03576226159930229,
-0.017073802649974823,
-0.08485796302556992,
0.02547542378306389,
0.0009552546544000506,
-0.02746686153113842,
-0.024979891255497932,
-0.012810609303414822,
-0.03011503256857395,
0.019115321338176727,
0.008787687867879868,
0.005695727653801441,
0.003380248788744211,
-0.01927497237920761,
-0.04640088602900505,
-0.09042933583259583,
0.055633533746004105,
0.04216920584440231,
-0.043956220149993896,
-0.03199593350291252,
-0.03862544521689415,
-0.007166518364101648,
0.023471059277653694,
0.042637359350919724,
-0.006530064158141613,
0.0014724403154104948,
0.0022770967334508896,
-0.027015812695026398,
0.04901923984289169,
-0.013936381787061691,
-0.015714436769485474,
0.00916636548936367,
-0.01702319085597992,
0.023741211742162704,
0.007444098126143217,
-0.024913102388381958,
-0.02816813997924328,
0.001604672521352768,
-0.015095096081495285,
0.021638289093971252,
-0.025111323222517967,
-0.01723165437579155,
-0.006486872676759958,
0.059248294681310654,
0.003912472166121006,
0.05346636846661568,
-0.011702069081366062,
-0.0015924174804240465,
0.03806726634502411,
-0.02739996649324894,
-0.04741554707288742,
0.0011852976167574525,
-0.06514241546392441,
-0.03961722180247307,
0.015971826389431953,
-0.005507062189280987,
0.0673135444521904,
-0.05909110605716705,
-0.009335901588201523,
0.028718765825033188,
-0.05868680030107498,
-0.0015603256179019809,
0.014038370922207832,
0.00455773901194334,
0.018448641523718834,
0.003829872701317072,
0.0483926385641098,
0.03329281136393547,
-0.020834796130657196,
0.028054308146238327,
0.006229965016245842,
-0.0032124354038387537,
-0.022659756243228912,
-0.008051146753132343,
0.028705187141895294,
-0.006080186925828457,
0.028582777827978134,
-0.014908417128026485,
0.005684496834874153,
-0.026197899132966995,
0.019528351724147797,
0.0030973416287451982,
-0.010681319050490856,
-0.02517472580075264,
0.027025634422898293,
0.0008848370634950697,
0.0462961420416832,
0.004360762424767017,
-0.0036681818310171366,
-0.03391280397772789,
0.025997135788202286,
-0.040031544864177704,
0.024543777108192444,
0.0007091459701769054,
0.018931545317173004,
-0.01829441264271736,
-0.007465313654392958,
0.0202313382178545,
0.023047683760523796,
0.032093197107315063,
-0.021966544911265373,
0.018924828618764877,
-0.010333220474421978,
-0.013323081657290459,
-0.02131437510251999,
-0.0024719436187297106,
-0.040215399116277695,
0.010005099698901176,
0.05112847685813904,
0.02071491628885269,
-0.002802174538373947,
0.007597251329571009,
0.004706684034317732,
-0.034880559891462326,
0.038511089980602264,
-0.05166124179959297,
-0.012222840450704098,
-0.010797915980219841,
0.008702722378075123,
-0.006250794976949692,
-0.02137436531484127
] |
<p>I'm trying to write down the bath Hamiltonian for a system of dimers and trimers. Imagine each of the monomers in the excited state can interact with several phonons with given frequencies. The bath Hamiltonian has the following form
$\sum\limits_{n = 1}^N {\sum\limits_{j = 1}^M {{\omega _{nj}}} } a_{nj}^\dagger {a_{nj}}$. Here N is the number of monomers and M is the number of vibrational modes. I don't understand how the matrix of vibrational modes look like for a trimer with lets say four modes. It looks like I will have a 3-by-4 matrix, where all the rows are the same since I have the same modes for all the monomers. This doesn't make sense to me, since I'm supposed to diagonalize this matrix. Another ambiguity arises when I'm trying to figure out what values the number operator takes for each element of this matrix, since it looks to me it has to be 1 for each element. Imagine, you have two or three monomers which are all coupled to the same modes.</p>
<p>I will appreciate your comments! </p>
| 9,621 |
[
0.009151346981525421,
-0.0065584322437644005,
-0.008491268381476402,
-0.009425981901586056,
0.05681823566555977,
-0.004361799452453852,
-0.04424956813454628,
-0.031218521296977997,
0.03593210503458977,
-0.025560371577739716,
0.04316489025950432,
0.009856577962636948,
0.037673961371183395,
0.029070349410176277,
0.032055240124464035,
0.01113782450556755,
-0.009482813067734241,
-0.033506739884614944,
-0.010534701868891716,
-0.015571175143122673,
0.009140235371887684,
0.020209698006510735,
0.03605072200298309,
-0.027872439473867416,
-0.015697361901402473,
0.05966150760650635,
0.008318193256855011,
-0.023291468620300293,
0.049068715423345566,
-0.004472833592444658,
-0.02398352324962616,
-0.04045701026916504,
0.03712022677063942,
0.020447611808776855,
0.01097666472196579,
-0.011858130805194378,
-0.05227505788207054,
0.0011614569230005145,
-0.00435083219781518,
0.024084413424134254,
-0.04703152924776077,
-0.027421006932854652,
-0.01883080042898655,
-0.005487843416631222,
-0.013365758582949638,
-0.0077959634363651276,
0.0276845321059227,
-0.021693535149097443,
0.0163420457392931,
-0.05533227324485779,
0.11479843407869339,
0.02437279187142849,
0.04262165352702141,
0.021299367770552635,
-0.015102536417543888,
0.01579137332737446,
0.06335492432117462,
0.06143620237708092,
0.029092786833643913,
-0.07841580361127853,
-0.009975908324122429,
-0.02944037690758705,
-0.01553873810917139,
-0.008325179107487202,
-0.03018871881067753,
0.016022512689232826,
0.016074253246188164,
-0.04527629166841507,
0.029995137825608253,
0.014766456559300423,
0.008350213058292866,
-0.0038226256147027016,
0.08817869424819946,
-0.05287059023976326,
-0.0063734943978488445,
-0.003954711835831404,
0.03296331688761711,
0.03657257929444313,
0.04929346218705177,
0.003955656196922064,
0.013019910082221031,
0.022458087652921677,
-0.010461729019880295,
0.020421048626303673,
-0.020462604239583015,
-0.04385079815983772,
0.046574320644140244,
-0.0013064637314528227,
0.01799454167485237,
0.012637476436793804,
-0.012943138368427753,
0.026876239106059074,
0.04839249327778816,
0.009021235629916191,
-0.031456273049116135,
-0.010952247306704521,
-0.005732672289013863,
0.04640183225274086,
-0.0015548100927844644,
-0.018420595675706863,
-0.012853222899138927,
-0.02741994522511959,
0.02055943012237549,
0.05061963200569153,
-0.017218004912137985,
0.029422497376799583,
-0.06555276364088058,
0.043029382824897766,
-0.002757469890639186,
-0.0037503927014768124,
-0.05360453948378563,
0.011838901787996292,
-0.013997728936374187,
-0.008600684814155102,
-0.027516892179846764,
-0.029205014929175377,
-0.007497827522456646,
0.001123351394198835,
0.010153554379940033,
0.10440699011087418,
0.01265997439622879,
-0.03897964209318161,
0.028508896008133888,
-0.038762181997299194,
-0.0791960060596466,
0.01358621846884489,
0.01629425771534443,
-0.006735010072588921,
-0.04248756915330887,
0.034272849559783936,
0.007650703191757202,
-0.031262483447790146,
0.015161837451159954,
-0.013966570608317852,
-0.0006516224821098149,
-0.038396935909986496,
-0.11807569861412048,
-0.05027610436081886,
0.0014333347789943218,
-0.02610446885228157,
-0.011524850502610207,
-0.06257902085781097,
0.01640116050839424,
0.04109078645706177,
0.07759608328342438,
-0.0002586067421361804,
0.024229353293776512,
0.009542846120893955,
0.025703895837068558,
0.014024234376847744,
-0.0011871011229231954,
-0.035135965794324875,
-0.019440244883298874,
-0.017163975164294243,
-0.016582293435931206,
-0.026684047654271126,
0.0466541051864624,
0.03968495875597,
0.0355929471552372,
-0.0002473662025295198,
0.04357139766216278,
0.031398285180330276,
-0.0058023142628371716,
0.03928685933351517,
0.03147139772772789,
-0.04349375143647194,
0.04553760960698128,
-0.003414042526856065,
0.0227354746311903,
0.02074441686272621,
-0.015316774137318134,
-0.013438757508993149,
-0.04808555915951729,
0.042283616960048676,
0.015797503292560577,
-0.010113507509231567,
-0.0038379020988941193,
-0.03672255203127861,
0.02791190892457962,
0.02680327743291855,
-0.019090045243501663,
-0.05201655253767967,
0.020628858357667923,
0.0002237372100353241,
-0.005109657067805529,
0.005779220722615719,
0.019184544682502747,
0.011997029185295105,
-0.008506587706506252,
-0.025266705080866814,
-0.007282955106347799,
-0.05139574781060219,
0.00900320801883936,
-0.013210455887019634,
-0.03143854811787605,
0.05281040444970131,
0.022316299378871918,
0.005058090668171644,
0.025783633813261986,
-0.023414067924022675,
-0.0011276063742116094,
-0.001953675178810954,
0.03172388672828674,
-0.03876104950904846,
0.04826539382338524,
0.04453348368406296,
0.034589946269989014,
0.009870847687125206,
0.05835304036736488,
-0.02399122342467308,
-0.027273721992969513,
-0.00608314573764801,
-0.005118806846439838,
0.019144589081406593,
0.01035329420119524,
-0.0008707791566848755,
-0.022632893174886703,
-0.060573384165763855,
-0.026878349483013153,
0.02049393393099308,
-0.06170184165239334,
0.0611417256295681,
0.03839234635233879,
-0.011008822359144688,
-0.014658113941550255,
0.03718293458223343,
-0.00003743575143744238,
0.03265463933348656,
-0.01355139072984457,
0.000981233431957662,
-0.02393505908548832,
0.017136620357632637,
0.03944588825106621,
0.02929736115038395,
-0.040597621351480484,
0.009212822653353214,
0.059644803404808044,
0.022684315219521523,
0.02435639500617981,
-0.024002833291888237,
-0.016676245257258415,
0.018656333908438683,
0.03428336977958679,
0.026258813217282295,
-0.01664493791759014,
0.024503108114004135,
0.018792949616909027,
-0.007816843688488007,
0.03136565163731575,
-0.025595612823963165,
-0.021626245230436325,
0.04302835464477539,
-0.03391500189900398,
-0.004556003026664257,
-0.040867745876312256,
-0.01198255643248558,
0.039292678236961365,
-0.021800711750984192,
0.05345870926976204,
0.04668393358588219,
0.0139345433562994,
-0.015712875872850418,
-0.006765506695955992,
-0.021324940025806427,
-0.005280693992972374,
-0.020806001499295235,
-0.03877279534935951,
-0.028425399214029312,
0.01558608002960682,
-0.034148573875427246,
0.024603858590126038,
-0.04410421475768089,
0.009521020576357841,
-0.0056978571228682995,
0.014080367051064968,
0.045251380652189255,
-0.004098066128790379,
0.04945883899927139,
-0.04531310498714447,
-0.019384097307920456,
0.008740982972085476,
-0.010923853144049644,
0.006253365892916918,
0.017072167247533798,
-0.049616750329732895,
-0.015518059022724628,
-0.044808279722929,
-0.0271838940680027,
0.03797128051519394,
-0.0029381478670984507,
-0.014354386366903782,
-0.012181024067103863,
-0.0011896663345396519,
-0.02167399786412716,
-0.05823657289147377,
0.024438779801130295,
0.007127603515982628,
-0.04203352704644203,
-0.000950185873080045,
0.022790638729929924,
-0.020803671330213547,
0.001871847896836698,
0.0004317173734307289,
-0.02115190587937832,
-0.03624170273542404,
-0.012763742357492447,
-0.04190860688686371,
0.02614060416817665,
-0.00019869855896104127,
0.004388873465359211,
0.05255645141005516,
-0.024258285760879517,
0.0038450220599770546,
-0.06951582431793213,
-0.03134012222290039,
-0.004613177385181189,
0.002477639354765415,
0.06440412998199463,
0.027983728796243668,
-0.006286120042204857,
0.0877673402428627,
0.0034101365599781275,
-0.032836899161338806,
0.0010221994016319513,
0.014289243146777153,
0.016569018363952637,
-0.0583520345389843,
0.047005683183670044,
0.028788305819034576,
-0.01459449715912342,
0.0494195781648159,
0.021474221721291542,
0.04103139415383339,
0.08465532213449478,
-0.026771746575832367,
-0.017768606543540955,
0.045549966394901276,
0.030955752357840538,
0.01565082184970379,
0.05846540257334709,
0.002017796039581299,
0.0024322078097611666,
0.03884571045637131,
-0.0092814015224576,
-0.003715564962476492,
-0.01747317798435688,
-0.0917525440454483,
0.042684394866228104,
0.015405002050101757,
0.021168077364563942,
-0.010889631696045399,
0.030948463827371597,
-0.013693107292056084,
-0.026646118611097336,
0.023542502894997597,
0.062686987221241,
0.042770788073539734,
-0.04240204021334648,
0.025673091411590576,
0.053537871688604355,
0.004177894443273544,
-0.009367447346448898,
0.005205964203923941,
0.03306897357106209,
-0.02512294054031372,
0.002625166205689311,
-0.030071131885051727,
-0.042419467121362686,
0.016384966671466827,
-0.00547788618132472,
0.046142034232616425,
0.0018548892112448812,
-0.058622363954782486,
0.001411894685588777,
-0.07030321657657623,
-0.025826072320342064,
-0.031054280698299408,
0.04370133578777313,
-0.006944912485778332,
0.0892445370554924,
0.017612967640161514,
0.002432226436212659,
0.024129249155521393,
-0.01101022306829691,
-0.03710435330867767,
0.024443943053483963,
0.008330116048455238,
-0.005936884321272373,
-0.002251082332804799,
-0.005417869426310062,
-0.0011105614248663187,
-0.00274177105166018,
-0.045504894107580185,
0.012182523496448994,
0.01693662256002426,
-0.07281065732240677,
0.02490345574915409,
-0.03130395710468292,
-0.01952340453863144,
-0.0353584960103035,
0.026778385043144226,
0.046085745096206665,
-0.01920139417052269,
0.005507693625986576,
0.05966523289680481,
-0.01875542663037777,
0.022676946595311165,
-0.04185342416167259,
-0.008074857294559479,
0.017157619819045067,
0.018981236964464188,
0.03643326088786125,
0.05217659845948219,
0.014327822253108025,
-0.04112793877720833,
0.014193427748978138,
0.060512617230415344,
0.008433492854237556,
-0.01416834443807602,
0.0376221239566803,
-0.009294366464018822,
0.033736374229192734,
0.00476472545415163,
0.05348483473062515,
0.011876882053911686,
0.03271432965993881,
0.008466162718832493,
0.012054173275828362,
-0.013253661803901196,
0.02086453139781952,
0.04939515143632889,
0.030592141672968864,
-0.01640956476330757,
-0.08090045303106308,
0.034803859889507294,
-0.02496320568025112,
0.011901848018169403,
-0.027373293414711952,
0.004115752410143614,
-0.012001972645521164,
0.01015456486493349,
0.014405927620828152,
-0.013249918818473816,
0.003949454519897699,
-0.0020373233128339052,
0.004268426448106766,
0.02271764911711216,
-0.02564108930528164,
-0.014874176122248173,
0.0004273965023458004,
0.041936736553907394,
0.024414215236902237,
-0.008693765848875046,
0.0035509075969457626,
-0.07126614451408386,
-0.0048917196691036224,
0.0142013318836689,
0.04283531755208969,
0.013152975589036942,
0.014899235218763351,
-0.005688061472028494,
-0.020556414499878883,
0.03255975991487503,
-0.010823726654052734,
0.05068192631006241,
0.008147882297635078,
-0.0420512892305851,
-0.0005027115694247186,
0.0064100478775799274,
-0.030822457745671272,
0.016246646642684937,
0.024229934439063072,
0.058448676019907,
-0.017773877829313278,
0.0007579834200441837,
-0.017175966873764992,
0.003848880995064974,
-0.004375130403786898,
0.03211027756333351,
-0.03344191983342171,
-0.025678493082523346,
0.02659451961517334,
0.02319202944636345,
-0.0038023556116968393,
-0.053589481860399246,
0.022453147917985916,
-0.004578643944114447,
0.015918752178549767,
0.03878093138337135,
-0.05310531333088875,
-0.05246500298380852,
0.01156193483620882,
0.027206730097532272,
-0.015991557389497757,
-0.010618195869028568,
-0.02435377612709999,
0.060856834053993225,
0.015222118236124516,
-0.03206239640712738,
0.058089159429073334,
0.048456158488988876,
-0.017829420045018196,
0.029555149376392365,
-0.022308815270662308,
0.036122847348451614,
-0.011131640523672104,
0.007676688954234123,
-0.034334857016801834,
0.0009640746284276247,
-0.021267740055918694,
0.017170211300253868,
-0.04488376900553703,
0.028433745726943016,
0.012780551798641682,
-0.019664527848362923,
0.007227012421935797,
0.04851929843425751,
-0.03231920301914215,
-0.007238384336233139,
0.030063742771744728,
0.011241712607443333,
0.005201633088290691,
-0.004252862650901079,
0.036277659237384796,
-0.04649738967418671,
-0.009893781505525112,
0.01715088076889515,
-0.01200820505619049,
0.02271270751953125,
-0.026697002351284027,
-0.026386382058262825,
0.01706189662218094,
-0.06206833943724632,
0.0504738949239254,
-0.015597845427691936,
0.04095355048775673,
-0.028814297169446945,
-0.03463428467512131,
-0.0318823978304863,
-0.017007185146212578,
-0.02774069644510746,
0.0005306706298142672,
-0.010905840434134007,
0.028108011931180954,
-0.011754248291254044,
0.003566307481378317,
-0.05876142531633377,
-0.023416727781295776,
0.0058508701622486115,
0.010891526006162167,
-0.03362491354346275,
-0.0021848867181688547,
0.018797507509589195,
-0.0008738260366953909,
-0.022123614326119423,
0.018736552447080612,
0.0035225506871938705,
-0.025778131559491158,
0.009569593705236912,
0.06707614660263062,
0.049457255750894547,
0.04890948161482811,
-0.014189783483743668,
-0.0075629036873579025,
0.010092882439494133,
-0.0332813523709774,
-0.014317295514047146,
-0.013407083228230476,
0.004619454499334097,
-0.05281923711299896,
-0.022804677486419678,
-0.024270780384540558,
0.028159409761428833,
0.05260813236236572,
-0.031813669949769974,
-0.01847134716808796,
-0.041375432163476944,
0.03843974694609642,
0.024177365005016327,
-0.04158099740743637,
-0.008322494104504585,
-0.009879445657134056,
-0.006301247514784336,
0.006599505431950092,
0.013048522174358368,
-0.027950488030910492,
-0.03190043941140175,
-0.008698646910488605,
-0.004126051906496286,
0.0027923849411308765,
0.01209017913788557,
0.09076811373233795,
0.004938628524541855,
0.024889487773180008,
0.039362214505672455,
-0.0064145601354539394,
0.023391906172037125,
0.0162381399422884,
0.01718205027282238,
0.006589007098227739,
-0.00007428021490341052,
-0.005902392789721489,
-0.06533322483301163,
-0.07642397284507751,
0.05206291750073433,
0.06743326038122177,
0.0006738426745869219,
0.008222238160669804,
0.029722094535827637,
-0.00833052583038807,
0.026086337864398956,
-0.0014157668920233846,
-0.0294340830296278,
0.04139016568660736,
-0.002801336348056793,
0.04700356349349022,
-0.04503364488482475,
-0.0145085658878088,
0.013308893889188766,
0.0401788055896759,
-0.036657094955444336,
0.010989957489073277,
0.025435451418161392,
0.030081843957304955,
0.01700940914452076,
0.009524684399366379,
-0.025277603417634964,
0.031921371817588806,
-0.004705492407083511,
0.0413583405315876,
-0.003919211216270924,
-0.017257198691368103,
0.04047233983874321,
0.03528827801346779,
0.007446333300322294,
-0.04197518900036812,
0.004377716686576605,
0.009147857315838337,
0.04643202945590019,
0.03579537197947502,
-0.01147434487938881,
0.02522871270775795,
0.023744450882077217,
0.02908395789563656,
0.0007743493188172579,
0.034561485052108765,
0.013516712933778763,
-0.0070099313743412495,
-0.010495979338884354,
-0.0075819422490894794,
-0.05581041797995567,
0.02554853819310665,
-0.007716227788478136,
-0.026808682829141617,
0.04179377108812332,
0.008888854645192623,
0.040473178029060364,
-0.0034447889775037766,
0.026934219524264336,
-0.026228517293930054,
0.0644214004278183,
0.022166799753904343,
0.03568606823682785,
0.04733337089419365,
0.01309655886143446,
0.10195142030715942,
0.07401813566684723,
0.047425925731658936,
-0.054205521941185,
-0.006973594427108765,
0.024510014802217484,
-0.028568744659423828,
-0.0038922750391066074,
-0.01449608150869608,
0.014358198270201683,
0.0008635587873868644,
-0.004888780415058136,
0.029847998172044754,
-0.03340005502104759,
0.01082866545766592,
0.026918698102235794,
-0.009641285985708237,
-0.06752204149961472,
0.01779744401574135,
0.012366856448352337,
-0.005630619823932648,
-0.019844358786940575,
-0.04714636877179146,
0.03304225578904152,
0.0007334360852837563,
-0.009265045635402203,
-0.05714075267314911,
-0.01899750903248787,
0.03917486220598221,
0.02973361127078533,
0.008090111427009106,
-0.004728980362415314,
0.012028983794152737,
-0.007679577451199293,
0.03224817290902138,
0.03449225053191185,
0.03186260163784027,
-0.01707175001502037,
0.020768379792571068,
0.03134715184569359,
-0.003922284580767155,
-0.010222340002655983,
0.013369554653763771,
-0.010469471104443073,
-0.04038538783788681,
-0.04319285601377487,
-0.016009554266929626,
0.044038113206624985,
-0.02306903339922428,
-0.02858649753034115,
-0.03851454704999924,
0.011272084899246693,
0.020841125398874283,
-0.07143270969390869,
0.014509865082800388,
0.012379106134176254,
0.05827753618359566,
-0.08167650550603867,
-0.013460599817335606,
-0.037129562348127365,
-0.016651775687932968,
0.00032154517248272896,
0.0002236445143353194,
-0.013388359919190407,
0.0018874478992074728,
-0.005615621339529753,
-0.025869375094771385,
0.020649945363402367,
0.03307700157165527,
-0.025440409779548645,
-0.041230473667383194,
-0.03894723579287529,
-0.048096612095832825,
-0.034806814044713974,
-0.005088543985038996,
0.032448288053274155,
0.05661945790052414,
-0.005245864391326904,
-0.015954498201608658,
-0.003141581080853939,
-0.06759694218635559,
-0.03978678211569786,
-0.01676672138273716,
-0.05739683285355568,
0.02375338040292263,
-0.02149343490600586,
0.017855284735560417,
0.020655499771237373,
-0.048931632190942764,
0.03924865648150444,
0.01875302381813526,
0.0006135966395959258,
0.05490816384553909,
-0.016447028145194054,
-0.015780141577124596,
-0.03101780079305172,
-0.03245805576443672,
-0.005803421139717102,
-0.0035728442016988993,
-0.014540786854922771,
0.016638193279504776,
-0.0384594090282917,
-0.0028478794265538454,
0.047631677240133286,
-0.027559148147702217,
-0.04094773530960083,
-0.008980605751276016,
-0.038857296109199524,
0.007696140091866255,
0.0158369280397892,
-0.021017011255025864,
-0.059196438640356064,
-0.046652812510728836,
-0.019918331876397133,
-0.009090018458664417,
0.0021446007303893566,
-0.010523008182644844,
-0.01602097414433956,
-0.03137964755296707,
-0.029115362092852592,
-0.009071942418813705,
-0.0077659450471401215,
-0.016555922105908394,
-0.06619786471128464,
-0.001389655051752925,
-0.003025597892701626,
0.03695231303572655,
-0.03384983167052269,
0.01388607919216156,
-0.003115920117124915,
-0.04360733926296234,
0.006109928712248802,
0.06815076619386673,
0.03310348466038704,
-0.04798796772956848,
-0.0047393497079610825,
-0.009211902506649494,
0.07131297886371613,
-0.0004325945337768644,
-0.008960429579019547,
0.02588006667792797,
-0.015382629819214344,
0.025965100154280663,
0.0055020712316036224,
-0.002419685944914818,
0.028213076293468475,
0.04408786818385124,
0.0009641355136409402,
-0.04363209381699562,
0.042334288358688354,
-0.07270213216543198,
0.009219864383339882,
0.022191358730196953,
-0.007322676479816437,
-0.012236530892550945,
-0.015064832754433155,
-0.038061343133449554,
0.016789095476269722,
0.011394524946808815,
0.000402277335524559,
0.029402032494544983,
0.022228237241506577,
0.0035518209915608168,
0.0008497438975609839,
0.02037547528743744,
0.028805363923311234,
0.026514124125242233,
0.010608294047415257,
-0.02770114690065384,
0.05943519249558449,
-0.013625855557620525,
0.047633253037929535,
0.031050950288772583,
0.034278202801942825,
-0.06295337527990341,
-0.024497879669070244,
-0.03166503459215164,
-0.03517388552427292,
0.017050307244062424,
-0.06262514740228653,
0.023504028096795082,
0.040517717599868774,
-0.07703352719545364,
0.035268764942884445,
-0.018894750624895096,
-0.03126122057437897,
-0.02392193302512169,
0.009815128520131111,
-0.011457867920398712,
0.05651763454079628,
0.017616087570786476,
-0.002472413470968604,
0.0002985620521940291,
0.00010268297046422958,
-0.02739408239722252,
-0.02559771202504635,
-0.020313378423452377,
0.028234323486685753,
0.006540908012539148,
-0.03679138794541359,
0.017826901748776436,
-0.04066752642393112,
-0.07027076184749603,
0.026650747284293175,
-0.06636734306812286,
-0.008064743131399155,
-0.000027460677301860414,
0.019292842596769333,
-0.010984769091010094,
0.019140366464853287,
0.031090153381228447,
-0.027975227683782578,
0.011703342199325562,
-0.01273051556199789,
0.03949977457523346,
0.005493601784110069,
0.0007110086735337973,
0.013878178782761097,
0.03134879469871521,
-0.017885293811559677,
-0.06977012008428574,
0.018734777346253395,
-0.01019955798983574,
0.020124701783061028,
-0.03938474506139755,
-0.005733526777476072,
0.01126075815409422,
-0.06766605377197266,
0.020790791139006615,
-0.046213652938604355,
-0.020662108436226845,
0.025607341900467873,
0.05396287515759468,
-0.0015628718538209796,
0.013603173196315765,
-0.018034176900982857,
-0.029072793200612068,
0.001781980274245143,
0.0006145606748759747,
-0.0527040995657444,
-0.0651950091123581,
-0.00897759199142456,
-0.00012879408313892782,
0.02590375766158104,
-0.003497867379337549,
-0.030365794897079468,
-0.030450399965047836,
0.02431241236627102,
-0.007412128150463104,
-0.00753796985372901,
-0.018646640703082085,
-0.04688092693686485,
-0.0017695402493700385,
-0.05444834381341934,
0.008446864783763885,
0.030180390924215317,
-0.009907754138112068,
-0.009281540289521217,
0.000367539789294824,
0.0226918812841177,
0.02090580388903618,
0.039516303688287735,
0.016839342191815376,
0.008386676199734211,
-0.023011334240436554,
0.0066069914028048515,
0.024943146854639053,
-0.008024322800338268,
0.011828708462417126,
-0.015373663045465946,
-0.00012880221765954047,
-0.015467777848243713,
-0.0019396910211071372,
-0.010835668072104454,
-0.0028975720051676035,
0.007696980144828558,
-0.02825777977705002,
0.0039986250922083855,
0.0016892486019060016,
-0.04363565891981125,
0.027961397543549538,
-0.038098253309726715,
-0.014918223023414612,
0.06267906725406647,
-0.006143148057162762,
0.011997330002486706,
0.045164804905653,
-0.03513690456748009,
-0.056736964732408524,
-0.013957550749182701,
-0.03508186712861061,
0.007034532725811005,
0.00004705462924903259,
0.008919024839997292,
0.025121048092842102,
-0.008095300756394863,
0.019407013431191444,
0.029041888192296028,
-0.014445188455283642,
-0.0238359272480011,
0.021057602018117905,
0.008698074147105217,
0.016823383048176765,
0.019255410879850388,
0.038672685623168945,
0.0012077956926077604,
-0.018433596938848495,
0.0066328938119113445,
0.0526573546230793,
0.004279783461242914,
0.009833605028688908,
0.02584001049399376,
-0.004523744806647301,
-0.05295611172914505,
0.01468818448483944,
0.002144643571227789,
-0.001420647487975657,
0.013733894564211369,
-0.015355980955064297,
0.045127734541893005,
-0.03164137899875641,
-0.013606465421617031,
0.01335061900317669,
-0.0020648539066314697,
0.0735940933227539,
-0.030110320076346397,
-0.001330271945334971,
-0.03452436625957489,
-0.030517330393195152,
-0.02393370494246483,
-0.024154730141162872,
-0.014879420399665833,
0.04230980575084686,
-0.021149853244423866,
0.009395436383783817,
-0.059761546552181244,
-0.0011400508228689432,
0.03050166741013527,
-0.07054634392261505,
0.0019520112546160817,
-0.002257017884403467,
-0.00044150123721919954,
0.010452710092067719,
-0.011404786258935928,
-0.011208608746528625,
-0.0034168094862252474,
0.06394242495298386,
0.030704479664564133,
-0.015878736972808838,
0.006046258378773928,
0.014253631234169006,
-0.0032321561593562365,
0.02777797169983387,
-0.020047727972269058,
-0.04780254513025284,
-0.02454858273267746,
0.0000514967723574955,
0.014403603039681911,
0.017329569905996323
] |
<p>Why <a href="http://en.wikipedia.org/wiki/Perpetual_motion" rel="nofollow">perpetual motion</a> wouldn't be possible if we are so technological advanced?</p>
<p>It is just a thing that I was wondering for too long. I mean, we are able to create so powerful permanent magnets, like neodymium magnets which can store an massive quantity of energy for a long period of time, but we are not able to use that energy at all. Why?</p>
| 9,622 |
[
-0.03478582948446274,
-0.02030005119740963,
0.017634317278862,
-0.03257229924201965,
0.058452364057302475,
-0.0024522829335182905,
-0.05756990611553192,
-0.01031406782567501,
-0.03209343180060387,
-0.02228584699332714,
0.014431661926209927,
0.051912058144807816,
0.01732977293431759,
0.037351515144109726,
0.0068997968919575214,
0.0013127290876582265,
0.014077575877308846,
-0.029760727658867836,
-0.026682456955313683,
-0.019354645162820816,
-0.01862224191427231,
0.010724606923758984,
-0.030620917677879333,
0.026723463088274002,
-0.02093283087015152,
0.000808811979368329,
0.03996912017464638,
0.006875198800116777,
0.0013047909596934915,
0.06679125875234604,
0.01854739524424076,
-0.043466031551361084,
0.0222903024405241,
0.01853811927139759,
0.01842440478503704,
-0.00013083124940749258,
-0.045091185718774796,
-0.023503856733441353,
-0.0016084143426269293,
0.01446104608476162,
-0.023928791284561157,
-0.03507021814584732,
-0.003942060749977827,
0.058448534458875656,
-0.041027218103408813,
0.028530096635222435,
0.00993884913623333,
-0.015814654529094696,
0.03340844810009003,
-0.05464479327201843,
0.02768736518919468,
0.03106103464961052,
0.045490894466638565,
0.021221818402409554,
0.02662089839577675,
-0.022099720314145088,
0.0809640884399414,
0.05046474188566208,
-0.01683138497173786,
-0.06349384784698486,
-0.01957971416413784,
0.012365390546619892,
-0.006622036453336477,
-0.02940228581428528,
-0.006744904909282923,
0.025153471156954765,
0.0024900713469833136,
0.010748101398348808,
0.047918666154146194,
-0.009037286043167114,
0.03664476424455643,
0.026465533301234245,
0.010079181753098965,
0.011271157301962376,
0.01160716637969017,
-0.04090137779712677,
0.0028848734218627214,
0.01476068701595068,
0.04122704640030861,
0.07590512186288834,
-0.03455570712685585,
-0.004284216556698084,
0.05003085732460022,
0.05023447051644325,
0.01485857181251049,
-0.02322329767048359,
0.047378286719322205,
0.017188694328069687,
0.05152108520269394,
0.04086051881313324,
0.028902297839522362,
0.002411555266007781,
0.05018258094787598,
-0.011911081150174141,
-0.018151286989450455,
0.04046007618308067,
0.01159359049052,
0.02820258028805256,
0.02744700014591217,
-0.003820005338639021,
0.026878278702497482,
0.003825087333098054,
0.0196673646569252,
0.05267082899808884,
0.02539563924074173,
-0.05656909942626953,
-0.026615217328071594,
0.018056945875287056,
0.014942319132387638,
-0.00305868755094707,
-0.004661913029849529,
0.024823138490319252,
0.02554488740861416,
0.001679069478996098,
-0.025820989161729813,
-0.02393285185098648,
0.015627866610884666,
-0.013289636000990868,
0.05706005543470383,
0.06845688819885254,
-0.01334256399422884,
-0.028515713289380074,
0.020704952999949455,
-0.03972003981471062,
-0.047318458557128906,
-0.0012082726461812854,
0.035136718302965164,
-0.01215407531708479,
-0.02625925838947296,
0.018100522458553314,
-0.0074933418072760105,
-0.012218345887959003,
0.000017457319700042717,
-0.008488643914461136,
0.07070102542638779,
0.01110586617141962,
-0.10718678683042526,
-0.019653134047985077,
0.07225147634744644,
0.0011259691091254354,
-0.02710527926683426,
-0.08301159739494324,
0.03245790675282478,
0.02568911388516426,
0.068629190325737,
-0.006188814993947744,
-0.0329238660633564,
0.00683444831520319,
0.015286748297512531,
0.00171134143602103,
-0.0179708544164896,
-0.01298558060079813,
0.04872255027294159,
-0.04124753549695015,
-0.004585506394505501,
-0.07594163715839386,
0.030469587072730064,
0.04280207306146622,
0.02445099875330925,
-0.015273514203727245,
0.04751210659742355,
0.003097971435636282,
-0.011800473555922508,
-0.002706285333260894,
-0.031047722324728966,
-0.03574822470545769,
0.06951306760311127,
0.004081730265170336,
0.04758494719862938,
0.03334235027432442,
0.011286369524896145,
0.04141123592853546,
0.0029754070565104485,
0.02377050742506981,
0.024732785299420357,
-0.03871585801243782,
-0.017244236543774605,
-0.012977310456335545,
-0.0020846943370997906,
0.0437559075653553,
-0.06849856674671173,
-0.02191915176808834,
0.022891219705343246,
0.003816391108557582,
0.026915671303868294,
0.05170952528715134,
-0.012150918133556843,
0.019551310688257217,
-0.015084546059370041,
-0.022410284727811813,
-0.025963960215449333,
-0.08155877888202667,
0.011686011217534542,
-0.010041521862149239,
-0.02548716403543949,
-0.014867343939840794,
-0.006644614040851593,
0.016047539189457893,
-0.021295296028256416,
-0.024505561217665672,
0.012139593251049519,
0.06071978807449341,
0.018174191936850548,
0.009304512292146683,
-0.004346002358943224,
0.05313350260257721,
0.04845330864191055,
0.028897354379296303,
0.017719529569149017,
-0.002447502687573433,
-0.04955111816525459,
0.0038112979382276535,
-0.0436122789978981,
0.017868753522634506,
0.04330093041062355,
-0.03138062730431557,
0.0460343174636364,
0.01400615181773901,
-0.03142089769244194,
0.027994617819786072,
0.0056475563906133175,
0.07947073131799698,
0.003714505583047867,
0.014833817258477211,
0.0038261653389781713,
0.02529933676123619,
-0.019362673163414,
0.02300924062728882,
-0.007908354513347149,
-0.01914907991886139,
-0.058796029537916183,
-0.0032877882476896048,
0.0027683647349476814,
0.06276960670948029,
-0.03837667405605316,
0.04247412458062172,
0.000006337587365123909,
0.04936324059963226,
0.017066441476345062,
0.01729784905910492,
-0.01813211664557457,
-0.020303241908550262,
0.004688804037868977,
0.015892812982201576,
0.01725759357213974,
0.07305129617452621,
0.06104326620697975,
0.038847096264362335,
-0.019989145919680595,
0.0042246924713253975,
0.0052168844267725945,
0.06361435353755951,
0.013551900163292885,
-0.017926692962646484,
0.03466644883155823,
-0.029782520607113838,
0.027127986773848534,
-0.024530557915568352,
0.0026769537944346666,
-0.038028534501791,
0.031933750957250595,
0.004971281159669161,
-0.03818967565894127,
-0.021151527762413025,
-0.01225542463362217,
-0.0011436702916398644,
-0.019334135577082634,
-0.04383126273751259,
0.014445715583860874,
0.014689024537801743,
0.002953797345981002,
-0.028668463230133057,
0.0172487311065197,
-0.015035080723464489,
-0.004836867097765207,
0.008214103057980537,
0.0035276897251605988,
0.02399243228137493,
-0.006507067941129208,
-0.023657584562897682,
-0.0006987429223954678,
-0.05438537895679474,
-0.0015590182738378644,
0.0009954283013939857,
-0.046823661774396896,
0.00014138422557152808,
0.027045220136642456,
-0.02361149527132511,
0.06050565466284752,
0.009006325155496597,
0.04150518402457237,
0.00436312286183238,
0.005602673627436161,
-0.07193434238433838,
-0.016599269583821297,
-0.003890967695042491,
-0.001462411368265748,
-0.008444591425359249,
-0.008722578175365925,
0.06432109326124191,
-0.023677436634898186,
-0.06123213842511177,
0.011122933588922024,
-0.057069264352321625,
-0.04943821579217911,
0.02273719199001789,
0.0051378593780100346,
0.006693084258586168,
-0.035922642797231674,
0.0245259590446949,
-0.01568099856376648,
-0.09148378670215607,
-0.014854763634502888,
-0.06596875190734863,
-0.02624339796602726,
0.013867327943444252,
-0.03158608824014664,
0.026139015331864357,
-0.03860732540488243,
-0.03023906983435154,
0.07414059340953827,
0.04320516064763069,
-0.023428410291671753,
-0.01939222402870655,
-0.04848097264766693,
0.002851354656741023,
-0.038853928446769714,
0.008742141537368298,
0.040449295192956924,
-0.05852746218442917,
-0.0214756578207016,
-0.010575981810688972,
0.010176215320825577,
0.027439143508672714,
0.011053679510951042,
-0.019161729142069817,
-0.024382837116718292,
-0.005329581443220377,
0.03227996826171875,
0.048745542764663696,
-0.010479146614670753,
-0.03235578536987305,
0.001767874346114695,
-0.005743680987507105,
0.040247030556201935,
0.009306451305747032,
-0.035801321268081665,
0.05125179886817932,
0.0016025390941649675,
0.01505135279148817,
-0.053126636892557144,
0.044528692960739136,
-0.03598533198237419,
-0.025386864319443703,
0.000540883163921535,
0.013781413435935974,
0.03300712630152702,
0.011575354263186455,
0.013439704664051533,
0.007735632359981537,
0.04859878495335579,
-0.042802538722753525,
-0.028976615518331528,
-0.010736031457781792,
0.019705628976225853,
-0.01724838651716709,
-0.0035271726083010435,
0.03444971889257431,
0.036298882216215134,
0.04237188771367073,
0.028867453336715698,
0.012268715538084507,
0.01007575448602438,
-0.029280882328748703,
-0.08796544373035431,
0.0037282786797732115,
-0.018926149234175682,
0.04365169629454613,
0.03237435966730118,
0.015482098795473576,
-0.00039147635106928647,
0.04335493594408035,
0.011225392110645771,
-0.03761766850948334,
-0.09344761073589325,
0.03696851804852486,
-0.03922589495778084,
-0.031081533059477806,
0.01009358186274767,
0.009836290962994099,
-0.014875644817948341,
-0.010781112127006054,
-0.05104893073439598,
-0.04876339063048363,
0.006259779445827007,
-0.04713928699493408,
-0.023552944883704185,
-0.030865378677845,
-0.015870429575443268,
-0.02280578203499317,
0.029675031080842018,
0.03833729028701782,
-0.04459989070892334,
0.02746140956878662,
-0.003288730513304472,
-0.054048649966716766,
0.01926417462527752,
-0.006067860871553421,
-0.026482855901122093,
0.016795342788100243,
-0.01291003730148077,
0.02130730450153351,
0.028306126594543457,
-0.002355949953198433,
-0.0020713701378554106,
0.01516399160027504,
0.013964779675006866,
0.025756577029824257,
0.030836131423711777,
-0.05965513736009598,
-0.032453976571559906,
0.0070350696332752705,
0.03650791943073273,
0.045125074684619904,
0.020525464788079262,
0.00570916710421443,
-0.022436533123254776,
-0.0176036786288023,
-0.02110498957335949,
0.00259963097050786,
0.008522882126271725,
-0.0055859629064798355,
-0.005749042611569166,
-0.059735581278800964,
-0.027895119041204453,
-0.026734543964266777,
0.012595990672707558,
-0.004320309031754732,
0.007815544493496418,
-0.02420189045369625,
-0.021160464733839035,
0.006593833211809397,
-0.008394687436521053,
-0.012206345796585083,
0.040423501282930374,
0.008418019860982895,
0.0012567758094519377,
0.01280052401125431,
0.0005031528417021036,
0.025497786700725555,
0.010052761994302273,
0.04547092691063881,
-0.0227753147482872,
-0.01433023251593113,
-0.10799942165613174,
-0.005860577337443829,
0.018954308703541756,
0.02435333840548992,
-0.0021772340405732393,
-0.0320599339902401,
-0.04235798865556717,
-0.03344983235001564,
0.027014663442969322,
-0.044970620423555374,
0.05864330008625984,
-0.03090330958366394,
-0.020627835765480995,
-0.05765919014811516,
-0.044835157692432404,
0.017264937981963158,
-0.01500431727617979,
-0.013282474130392075,
0.04040500521659851,
0.005091631319373846,
0.023426316678524017,
0.007804341148585081,
0.021041203290224075,
0.012984950095415115,
0.03563797473907471,
-0.00664942292496562,
0.043174512684345245,
0.009661766700446606,
0.0041406964883208275,
-0.02863260544836521,
-0.06280861049890518,
0.03005785122513771,
-0.013385003432631493,
-0.0125122657045722,
0.017129523679614067,
-0.04827537760138512,
-0.06939667463302612,
0.024391846731305122,
-0.012767497450113297,
-0.01451953873038292,
-0.0323733426630497,
-0.057121917605400085,
0.011826717294752598,
0.04413580521941185,
0.01124502532184124,
0.047822006046772,
0.08053278923034668,
-0.0455106683075428,
0.009848207235336304,
-0.02077760547399521,
-0.014420067891478539,
-0.030353300273418427,
0.01439330168068409,
-0.023814456537365913,
0.0017100785626098514,
-0.0367000438272953,
0.0379590205848217,
-0.019392473623156548,
0.009574192576110363,
-0.004560484550893307,
0.002578158862888813,
-0.02599819004535675,
0.0050103082321584225,
0.0451725609600544,
-0.028839465230703354,
-0.029813669621944427,
0.009224829263985157,
-0.020527303218841553,
-0.006489884108304977,
0.03572246432304382,
0.007309144362807274,
-0.014503336511552334,
0.05362534523010254,
0.020312216132879257,
0.006934828124940395,
0.009951213374733925,
-0.0007771866512484848,
0.008762041106820107,
-0.00301289651542902,
0.06156657263636589,
-0.019427182152867317,
0.03022567555308342,
0.03381893411278725,
-0.042101141065359116,
-0.04392355680465698,
-0.009220792911946774,
-0.022737016901373863,
0.013765422627329826,
-0.011089466512203217,
0.015264075249433517,
0.010128871537744999,
0.017987657338380814,
-0.012314842082560062,
-0.05462086573243141,
0.03869923576712608,
-0.013937021605670452,
-0.009145999327301979,
-0.004212528467178345,
0.021192265674471855,
-0.014704158529639244,
-0.01867515966296196,
0.0030249813571572304,
0.020117077976465225,
-0.05406581982970238,
0.02499847486615181,
0.03286920487880707,
-0.0033268118277192116,
0.07182807475328445,
0.009240033105015755,
-0.047181468456983566,
0.027472957968711853,
-0.006650306284427643,
-0.01055521797388792,
-0.04172585532069206,
0.02324766479432583,
-0.022823289036750793,
-0.03536297380924225,
0.03152251988649368,
0.001256164745427668,
0.014896475709974766,
-0.008794309571385384,
-0.0271254014223814,
0.05254554748535156,
0.008011742495000362,
-0.01231630053371191,
-0.02439936064183712,
0.039678286761045456,
0.022118641063570976,
0.02122422866523266,
-0.022060604766011238,
-0.028711579740047455,
-0.003949552308768034,
-0.06366023421287537,
0.022890053689479828,
0.009136497043073177,
-0.01790263131260872,
-0.007368307560682297,
0.06498455256223679,
-0.03225310519337654,
-0.03157659247517586,
0.02249387465417385,
-0.02723034843802452,
0.025558046996593475,
0.017213182523846626,
0.010139437392354012,
-0.03819186985492706,
-0.015195201151072979,
-0.03928406164050102,
-0.030317800119519234,
0.011029315181076527,
0.010708396323025227,
0.023024512454867363,
-0.019737284630537033,
0.07602514326572418,
0.0017727859085425735,
-0.0022605883423238993,
-0.005933847278356552,
-0.031109072268009186,
-0.02859186753630638,
0.0383358858525753,
-0.0030806218273937702,
-0.006670303642749786,
0.005780280567705631,
0.02316088229417801,
0.06867888569831848,
0.024234483018517494,
-0.009427647106349468,
0.00807605218142271,
0.029613075777888298,
0.022307170554995537,
0.006512224208563566,
0.02052597887814045,
-0.043934162706136703,
0.025897379964590073,
-0.024613555520772934,
0.027864187955856323,
0.01569545455276966,
-0.016550617292523384,
0.027309134602546692,
-0.025734083727002144,
-0.018073733896017075,
-0.04956010729074478,
-0.00239666854031384,
-0.03548387810587883,
0.007007826119661331,
0.025255482643842697,
0.007401543669402599,
0.01544392853975296,
-0.015196737833321095,
0.005687565542757511,
0.0019252977799624205,
0.0021539919544011354,
0.01494810450822115,
-0.06380505114793777,
-0.012065762653946877,
-0.007133312989026308,
-0.03201435133814812,
0.04537510499358177,
0.019188320264220238,
-0.025930149480700493,
0.009540780447423458,
-0.028341274708509445,
-0.003266151063144207,
0.015132080763578415,
0.0168264489620924,
-0.04016610234975815,
0.029258785769343376,
-0.009042620658874512,
0.06111723557114601,
-0.03347913920879364,
0.030933791771531105,
0.12229041755199432,
-0.0062114219181239605,
0.018725808709859848,
-0.022198891267180443,
0.026152625679969788,
-0.014254928566515446,
-0.0017324220389127731,
-0.049001503735780716,
0.011110609397292137,
-0.02199719287455082,
0.02163546532392502,
0.01494603231549263,
0.017761249095201492,
-0.006043852306902409,
0.033884476870298386,
0.038346100598573685,
-0.061846472322940826,
-0.009336593560874462,
0.02769611030817032,
0.00005793050513602793,
-0.03645657002925873,
-0.012285910546779633,
-0.012991217896342278,
0.038833875209093094,
-0.046252474188804626,
-0.021225277334451675,
0.004045647569000721,
-0.02037663571536541,
0.01768413931131363,
0.007382303476333618,
-0.039556536823511124,
0.023057768121361732,
-0.00231359014287591,
-0.029203644022345543,
-0.04408480226993561,
0.015057987533509731,
0.013991635292768478,
0.014216949231922626,
-0.0293723214417696,
0.04292939230799675,
0.030795419588685036,
-0.0027873495128005743,
0.012848292477428913,
0.02812548168003559,
-0.04214513674378395,
0.014241416938602924,
-0.03773779422044754,
0.012531406246125698,
-0.026796875521540642,
0.042629849165678024,
0.006152310874313116,
0.00604964280501008,
0.0007986297132447362,
0.006321512628346682,
-0.01816478744149208,
0.0066157011315226555,
0.001378775225020945,
0.01391924824565649,
-0.024580251425504684,
-0.017872994765639305,
-0.003555055009201169,
-0.0079238535836339,
0.03167736530303955,
-0.04687032848596573,
0.003727837698534131,
0.03696873039007187,
0.00733725493773818,
-0.018142957240343094,
-0.028147682547569275,
0.009643727913498878,
-0.03579002991318703,
-0.015989135950803757,
-0.03873257339000702,
0.013858824968338013,
0.010601505637168884,
-0.003806974273175001,
-0.009110933169722557,
-0.01387579645961523,
-0.007813096046447754,
-0.02156718261539936,
0.010528724640607834,
0.06573350727558136,
-0.0031131042633205652,
-0.013596595264971256,
-0.012265417724847794,
-0.0020700176246464252,
0.04116827994585037,
0.044988177716732025,
-0.026429304853081703,
0.02421342208981514,
0.01309033390134573,
-0.006490296684205532,
0.03519820049405098,
0.005231108516454697,
-0.023865224793553352,
-0.01575372740626335,
-0.05187505856156349,
0.013385379686951637,
-0.0004165298887528479,
0.04316164553165436,
0.05831575021147728,
-0.014997647143900394,
0.011826826259493828,
0.00534190284088254,
-0.0219714492559433,
0.00302137341350317,
0.05028087645769119,
-0.01160803809762001,
-0.04373687133193016,
0.0009152445709332824,
-0.01851215586066246,
-0.016422787681221962,
-0.01843355968594551,
-0.007870528846979141,
-0.01650114916265011,
0.010562911629676819,
0.051596224308013916,
0.008816028945147991,
0.008113573305308819,
-0.01683865115046501,
0.06161743775010109,
-0.04526660218834877,
0.005468284711241722,
-0.05856098607182503,
-0.002247860888019204,
-0.005453331861644983,
0.005168235395103693,
-0.04045690596103668,
0.010584899224340916,
-0.0001803639461286366,
0.003127066418528557,
0.024744542315602303,
0.011342581361532211,
-0.03295018896460533,
-0.01477685198187828,
0.01339251920580864,
0.00970715843141079,
0.032689739018678665,
-0.017934909090399742,
-0.02700798772275448,
0.040119949728250504,
-0.011189218610525131,
-0.051891300827264786,
-0.045750219374895096,
-0.009643335826694965,
0.0065014781430363655,
0.03735201805830002,
-0.036938197910785675,
-0.019341163337230682,
0.05020938068628311,
-0.0313383974134922,
0.009587876498699188,
0.005446664523333311,
0.018221992999315262,
0.009051036089658737,
0.028218848630785942,
-0.01577114127576351,
-0.037682149559259415,
-0.00385117856785655,
0.021072398871183395,
0.04397440701723099,
0.009514248929917812,
-0.03275574743747711,
-0.006953934207558632,
-0.00010502682562218979,
-0.0177236869931221,
0.0351850800216198,
0.0010852606501430273,
0.014794419519603252,
0.017949452623724937,
-0.01908865012228489,
0.016378941014409065,
0.0030352501198649406,
-0.0164133682847023,
-0.0826852098107338,
0.01141654048115015,
-0.021070754155516624,
-0.05345745012164116,
0.026279786601662636,
-0.02974187582731247,
0.004546698182821274,
0.04095204174518585,
-0.09439083933830261,
0.03797139227390289,
-0.017282187938690186,
-0.028491731733083725,
-0.02599014900624752,
0.018949437886476517,
-0.0038112157490104437,
0.07474994659423828,
0.040290653705596924,
0.04369353875517845,
0.01558961533010006,
0.007996129803359509,
-0.0059357741847634315,
-0.03035857528448105,
-0.02226187475025654,
0.009620051831007004,
-0.037036098539829254,
0.006444347091019154,
0.05737784504890442,
-0.013951403088867664,
0.010229835286736488,
0.020545415580272675,
-0.022615086287260056,
0.020066143944859505,
0.003621552139520645,
0.06012791767716408,
-0.000927716784644872,
0.03727049008011818,
0.001274505048058927,
-0.010490721091628075,
-0.02333430014550686,
0.029751600697636604,
0.022507328540086746,
0.03901878744363785,
0.029007481411099434,
0.014388618990778923,
0.02135201171040535,
-0.02726678177714348,
0.007027163170278072,
0.016839634627103806,
-0.027308208867907524,
0.00569656677544117,
0.020620185881853104,
0.04903212934732437,
0.0017746123485267162,
-0.022699998691678047,
-0.025336749851703644,
0.0048652528785169125,
-0.0291262436658144,
0.02197493053972721,
-0.02281670831143856,
-0.0049811783246695995,
0.044000476598739624,
-0.004705365747213364,
-0.004744526464492083,
0.04098023101687431,
0.01774582639336586,
-0.011606561951339245,
-0.033872347325086594,
0.011770723387598991,
0.023534037172794342,
0.0032313356641680002,
0.009249367751181126,
-0.02281836047768593,
-0.053528159856796265,
0.036011915653944016,
0.05999636650085449,
0.0013803988695144653,
-0.010941551066935062,
-0.033606451004743576,
-0.022885970771312714,
-0.05997772514820099,
0.045938890427351,
-0.07161029428243637,
-0.00962859857827425,
-0.05339464917778969,
-0.040648892521858215,
0.005652820225805044,
-0.018054218962788582,
0.06795688718557358,
-0.05494211986660957,
-0.006986082065850496,
0.03787117078900337,
-0.017605135217308998,
0.03353255242109299,
-0.02910681627690792,
0.03359910100698471,
0.02531626634299755,
-0.02269405871629715,
0.02632523700594902,
-0.010950547643005848,
-0.03643406927585602,
0.025233689695596695,
0.04904767498373985,
-0.02084396965801716,
-0.0009348744642920792,
0.009836224839091301,
-0.009057528339326382,
0.021393006667494774,
0.0005258303135633469,
-0.03562677279114723,
0.03308660164475441,
-0.015119723044335842,
0.04863101989030838,
-0.03832690790295601,
-0.014617704786360264,
-0.02863437309861183,
0.006487525068223476,
-0.034304309636354446,
0.03181581199169159,
-0.04435133934020996,
-0.0659259632229805,
0.05763879045844078,
-0.03517448157072067,
-0.0034169843420386314,
0.04410579055547714,
-0.04565132036805153,
-0.0033262688666582108,
0.05472647771239281,
0.0038227434270083904,
0.027610087767243385,
-0.01557177770882845,
0.05620592087507248,
-0.047168005257844925,
0.0015242511872202158,
0.0054384153336286545,
0.05783173069357872,
0.03400147333741188,
-0.012610520236194134,
0.019660547375679016,
0.03740154951810837,
0.024832112714648247,
0.0010205012513324618,
0.03954056277871132,
0.05764630809426308,
-0.029805129393935204,
-0.041969992220401764,
0.012304154224693775,
-0.03730091452598572,
0.0076583558693528175,
0.043027956038713455,
-0.015829283744096756,
0.11308442056179047,
-0.0189212616533041,
0.008360217325389385,
-0.0022383646573871374,
0.002287918468937278,
0.016168661415576935,
-0.038059405982494354,
-0.012589964084327221,
0.02681577205657959,
-0.017505386844277382,
-0.021787410601973534,
-0.010768555104732513,
0.03421354666352272,
0.010482201352715492,
0.0022688645403832197,
0.03821008652448654,
0.00964607484638691,
0.005234710872173309,
-0.031586285680532455,
0.010164198465645313,
-0.05885579437017441,
-0.05347568914294243,
0.027306057512760162,
0.017037726938724518,
0.02780330367386341,
-0.009293749928474426,
-0.04209024831652641,
-0.015531109645962715,
0.0333426259458065,
-0.06592616438865662,
0.021552735939621925,
-0.038114894181489944,
0.0015834002988412976,
-0.015408290550112724,
-0.0006979487952776253
] |
<p>I was going through <a href="http://arxiv.org/abs/quant-ph/0001106" rel="nofollow">arXiv:quant-ph/0001106v1</a>, the first paper by Farhi on adiabatic quantum computation.
Equation 2.24 says, $$\tilde{H}(s) = (1-s)H_B + sH_P$$ which means the adiabatic evolution starts from the ground state of $H_B$ and slowly evolves until it arrives at the ground state of $H_P$. In section 3.1, the one qubit example has the adiabatic Hamiltonian as $$\tilde{H}(s) = \begin{pmatrix}
s & \epsilon (1-s) \\
\epsilon (1-s) & 1-s
\end{pmatrix}$$
I don't see how the plot of Figure 1 is drawn. In figure 1, Farhi plotted eigenvalues of the Hamiltonian for s while the range for s was 0 to 1. The Hamiltonian is supposed to evolve according to the Schrodinger equation (eq 2.1), $$i \frac{d}{dt} |\Psi (t) \rangle = H(t) |\Psi (t) \rangle$$
Was this evolution solved to draw the plot? Or did Farhi derive the formula for eigenvalues in terms of s using just matrix math and plotted accordingly?</p>
| 9,623 |
[
-0.0008509408799000084,
0.020447205752134323,
-0.005664402153342962,
-0.0070237647742033005,
0.0506262369453907,
-0.01654721051454544,
-0.052978064864873886,
-0.007223354186862707,
-0.004962276667356491,
-0.04453570768237114,
0.023460231721401215,
0.004875349812209606,
0.028038376942276955,
0.0154035072773695,
0.03916934132575989,
0.009452343918383121,
0.0043678986839950085,
-0.02218705415725708,
-0.020544713363051414,
-0.006386838853359222,
0.017511732876300812,
0.010527788661420345,
0.0015571914846077561,
-0.04168795421719551,
0.0005582278245128691,
0.01563386432826519,
0.006630122661590576,
0.032294128090143204,
0.00044989315210841596,
0.06476407498121262,
-0.02742736041545868,
-0.04468294233083725,
0.041094377636909485,
0.035756852477788925,
0.021110624074935913,
-0.006288059521466494,
-0.03980608657002449,
-0.08186691254377365,
-0.03046267293393612,
0.004233859479427338,
-0.021520139649510384,
-0.005207016598433256,
-0.009112410247325897,
0.06525853276252747,
-0.014915763400495052,
-0.0002102685539284721,
0.00400489941239357,
-0.005892837420105934,
0.06399786472320557,
-0.0808945968747139,
0.06946196407079697,
0.03515255078673363,
0.024782415479421616,
0.010695612989366055,
-0.02506367117166519,
0.00910790916532278,
0.061327118426561356,
0.05731628090143204,
-0.002015321049839258,
-0.038551319390535355,
-0.022911131381988525,
-0.02947096712887287,
-0.028645595535635948,
-0.02992394007742405,
-0.026399539783596992,
-0.00047463621012866497,
0.027472516521811485,
-0.009439586661756039,
0.036639612168073654,
0.002864748239517212,
0.012393650598824024,
0.02739383839070797,
0.04561786726117134,
-0.03219590708613396,
0.0368373803794384,
-0.016955142840743065,
0.003853809554129839,
0.020950712263584137,
0.03181152045726776,
0.027878114953637123,
0.003523469902575016,
0.02477933093905449,
-0.009420501068234444,
0.011336823925375938,
-0.03571883589029312,
-0.011957974173128605,
0.06735958904027939,
-0.017170576378703117,
0.0043248278088867664,
0.03755561634898186,
-0.006230505649000406,
0.03441698104143143,
0.0518752746284008,
-0.0028993363957852125,
0.0005113087245263159,
0.033850640058517456,
0.0012967074289917946,
0.02687026374042034,
-0.027688145637512207,
-0.06264370679855347,
-0.01837773062288761,
-0.05526173859834671,
0.038640353828668594,
0.05328270047903061,
0.01399566512554884,
0.02653217874467373,
-0.023736396804451942,
0.02832651324570179,
-0.008727550506591797,
-0.009971430525183678,
-0.05011257901787758,
0.06058906018733978,
0.01484895683825016,
0.023737600073218346,
-0.05582844838500023,
-0.031088029965758324,
-0.0006682532839477062,
-0.0029613864608108997,
0.05530137941241264,
0.020202085375785828,
0.0015606280649080873,
0.002528625540435314,
0.02898324653506279,
-0.041420623660087585,
-0.05148166045546532,
0.01575070433318615,
0.0367005318403244,
0.0009467513882555068,
-0.05519785359501839,
0.007101672701537609,
0.011262468993663788,
0.01060299202799797,
0.029306596145033836,
-0.017136139795184135,
0.0259820818901062,
-0.04536938667297363,
-0.10157027095556259,
-0.06391242146492004,
0.014827840961515903,
-0.026333149522542953,
0.007498242426663637,
-0.06918144226074219,
0.024830035865306854,
0.06057481840252876,
0.0745609924197197,
-0.02031807415187359,
-0.008973484858870506,
-0.0017827466363087296,
0.021736057475209236,
0.02155211754143238,
-0.027516024187207222,
-0.010213474743068218,
-0.018613062798976898,
-0.030234171077609062,
-0.017934326082468033,
-0.034288372844457626,
-0.005053090862929821,
0.03992284834384918,
0.012567778117954731,
-0.025095859542489052,
0.07239754498004913,
0.022191690281033516,
0.010724150575697422,
0.00707757705822587,
-0.003058971604332328,
-0.03461429849267006,
0.06325902044773102,
-0.006855507381260395,
0.0005162713350728154,
0.022678155452013016,
-0.013907679356634617,
-0.004539401736110449,
-0.0014809663407504559,
0.02449733205139637,
-0.0076403007842600346,
-0.03889032080769539,
-0.002898865146562457,
-0.04427056387066841,
-0.016839811578392982,
0.017265433445572853,
-0.010666687972843647,
-0.03887011110782623,
-0.015347030013799667,
-0.005395704414695501,
-0.02990075945854187,
0.0024793024640530348,
-0.036542341113090515,
-0.0019206765573471785,
-0.02237345650792122,
-0.06878182291984558,
-0.031190451234579086,
-0.05167851224541664,
0.008847997523844242,
0.031147608533501625,
-0.0247571412473917,
0.0664835125207901,
0.0191599503159523,
0.02519441768527031,
0.027622275054454803,
-0.017696956172585487,
-0.008445657789707184,
0.03381309285759926,
-0.004458377603441477,
-0.04126425459980965,
0.03359820693731308,
0.081648088991642,
0.009628715924918652,
0.05326240137219429,
0.033469390124082565,
-0.03304264694452286,
-0.04677240550518036,
0.007343622390180826,
-0.0034084676299244165,
0.020372258499264717,
0.003940110094845295,
0.0033133116085082293,
-0.03330622985959053,
-0.030888376757502556,
0.004810217302292585,
0.026110438629984856,
-0.031771909445524216,
0.07039228826761246,
0.06360644102096558,
0.020384015515446663,
-0.009489291347563267,
0.051501039415597916,
-0.005403181537985802,
-0.0006905306363478303,
-0.016868846490979195,
-0.012063154950737953,
-0.015100275166332722,
0.016634324565529823,
0.022040579468011856,
0.02923715114593506,
-0.0020560359116643667,
0.0022067346144467592,
0.03438274562358856,
0.01140928827226162,
0.014348983764648438,
0.03953838348388672,
-0.04983356222510338,
-0.015628227964043617,
0.04266750440001488,
0.009933375753462315,
-0.02868005633354187,
-0.015202982351183891,
0.01848423294723034,
0.007427001837641001,
-0.018092481419444084,
0.031085874885320663,
-0.03695450723171234,
0.053105324506759644,
-0.053779929876327515,
-0.019916236400604248,
-0.016734464094042778,
-0.010904187336564064,
0.016799196600914,
-0.01696891523897648,
0.005157005973160267,
0.018227629363536835,
-0.007434407714754343,
-0.008662348613142967,
-0.010803434066474438,
-0.04857533052563667,
0.008013895712792873,
-0.007058458868414164,
-0.01722465641796589,
-0.020807622000575066,
0.019015807658433914,
-0.0030784530099481344,
0.0576728880405426,
-0.06182410567998886,
0.009799674153327942,
-0.009882085025310516,
0.009463743306696415,
0.056876592338085175,
0.011645777150988579,
-0.0021680875215679407,
-0.08446531742811203,
-0.016396187245845795,
-0.009349605068564415,
0.01255824789404869,
0.03530697152018547,
0.022052418440580368,
-0.06095757707953453,
0.005921546369791031,
-0.05630217120051384,
-0.0438271090388298,
0.03850771486759186,
-0.008403971791267395,
-0.017615454271435738,
-0.00534661952406168,
0.01663077250123024,
-0.03638142719864845,
-0.04083075746893883,
-0.031467173248529434,
0.005628733895719051,
-0.038024745881557465,
0.022534562274813652,
0.028852352872490883,
0.0005263328203000128,
0.009498152881860733,
0.025991249829530716,
0.005743307061493397,
-0.025458266958594322,
0.006485751364380121,
-0.0050409212708473206,
0.02486632764339447,
0.0076365843415260315,
0.04378020018339157,
0.036049697548151016,
-0.0038246531039476395,
-0.04540330544114113,
-0.0627334788441658,
-0.0651932880282402,
0.03827143833041191,
0.021394982933998108,
0.008360516279935837,
0.01057606004178524,
-0.027286799624562263,
0.0905592292547226,
0.011143147014081478,
0.0009592417045496404,
-0.02173553965985775,
0.029591364786028862,
0.0019459332106634974,
-0.008948393166065216,
-0.005129883531481028,
0.04800008609890938,
-0.008544833399355412,
0.04727940261363983,
-0.03960411623120308,
0.04089896008372307,
0.06124194711446762,
-0.028105715289711952,
-0.02519127167761326,
0.03281410411000252,
-0.014290702529251575,
0.03407436981797218,
0.031961433589458466,
-0.03574337065219879,
-0.009491155855357647,
0.036852285265922546,
-0.0025701967533677816,
0.043927550315856934,
-0.016769476234912872,
-0.05003141984343529,
0.06786782294511795,
0.003942130133509636,
0.003897744696587324,
-0.016190817579627037,
0.030452875420451164,
-0.019107872620224953,
-0.003471681382507086,
-0.028666576370596886,
0.04967951029539108,
0.0383315272629261,
-0.03675428032875061,
0.017269456759095192,
0.05390067771077156,
-0.022615378722548485,
-0.0312727615237236,
-0.012760823592543602,
0.01654517650604248,
-0.02292739972472191,
0.007971576415002346,
-0.03230543062090874,
-0.05466524884104729,
-0.003031799802556634,
-0.0006794528453610837,
0.005639249924570322,
-0.009989853948354721,
-0.019066547974944115,
-0.018558168783783913,
-0.030480746179819107,
-0.01848732680082321,
0.013003145344555378,
0.041795261204242706,
0.0241822712123394,
0.04371946305036545,
-0.016678180545568466,
0.045242276042699814,
0.008353098295629025,
-0.007593522779643536,
-0.03869954124093056,
0.022208133712410927,
-0.014954552985727787,
-0.03990938514471054,
0.0001684530288912356,
0.0028584618121385574,
0.04229347035288811,
-0.040039513260126114,
-0.008607879281044006,
0.02099969983100891,
-0.01203242503106594,
-0.03603387251496315,
0.01653750240802765,
-0.02998686209321022,
-0.0022655422799289227,
-0.05734967067837715,
-0.017281237989664078,
0.020901476964354515,
-0.027656754478812218,
0.03002917394042015,
0.051643453538417816,
-0.03506797179579735,
0.025487439706921577,
-0.005356219597160816,
0.03764844313263893,
0.027049340307712555,
0.011494801379740238,
0.054110102355480194,
0.024792497977614403,
0.006302542053163052,
-0.0043467190116643906,
-0.0017836063634604216,
0.09898526966571808,
0.022801902145147324,
-0.03956354781985283,
0.030421657487750053,
-0.04688945785164833,
0.0016436713049188256,
0.02920108288526535,
0.05727945268154144,
-0.019518796354532242,
0.058527830988168716,
0.02118736132979393,
0.0011869698064401746,
-0.039970505982637405,
0.025270896032452583,
0.052494116127491,
-0.011816725134849548,
-0.005050347186625004,
-0.049904100596904755,
0.00759935611858964,
-0.024939725175499916,
-0.004286764655262232,
0.021009977906942368,
-0.00896227452903986,
-0.029311422258615494,
0.028517166152596474,
0.020924853160977364,
0.021295078098773956,
0.01986987516283989,
-0.00075194874079898,
-0.005008794367313385,
0.018752245232462883,
0.025776086375117302,
0.02106204628944397,
0.019106891006231308,
0.013606411404907703,
0.01870223693549633,
-0.03217184916138649,
0.025023117661476135,
-0.053537238389253616,
-0.028366362676024437,
0.0024365177378058434,
0.024326151236891747,
0.0228858795017004,
0.02641056291759014,
-0.07944180071353912,
-0.03308635577559471,
0.023256931453943253,
-0.01303158514201641,
0.0728665292263031,
0.024498434737324715,
-0.010294551961123943,
-0.02764739654958248,
-0.01878439076244831,
-0.002133893547579646,
0.018154354766011238,
0.02769700437784195,
-0.0017979418626055121,
0.009691836312413216,
-0.027963321655988693,
-0.03142370656132698,
0.017698362469673157,
0.0059530469588935375,
0.05238394811749458,
-0.01894698478281498,
-0.010531305335462093,
-0.0027480991557240486,
0.0240679532289505,
-0.03271392360329628,
-0.06097045913338661,
0.017826074734330177,
-0.02839798852801323,
-0.0012798384996131063,
0.031743910163640976,
-0.05342613905668259,
-0.06493860483169556,
0.04399363696575165,
0.0421985425055027,
-0.01528917159885168,
0.004635136108845472,
-0.02298026904463768,
0.07719838619232178,
0.0343933142721653,
-0.009285343810915947,
0.05037678778171539,
0.02103237994015217,
-0.02689744159579277,
0.0037824076134711504,
-0.01367477048188448,
0.02896684966981411,
-0.016340188682079315,
0.032698024064302444,
-0.05300791561603546,
0.021801605820655823,
-0.0227160956710577,
0.007587832864373922,
0.0009781672852113843,
0.009682800620794296,
-0.04028675705194473,
-0.02836248278617859,
-0.00847628153860569,
0.004917751997709274,
0.005372622050344944,
0.026176095008850098,
-0.012812490575015545,
0.030771341174840927,
-0.003322371281683445,
-0.02439575456082821,
-0.00932373758405447,
-0.028589414432644844,
-0.013780949637293816,
0.05382730811834335,
-0.012012048624455929,
0.06608503311872482,
-0.035229481756687164,
-0.0040023187175393105,
0.029066821560263634,
-0.05337615683674812,
0.04095516353845596,
-0.0232577845454216,
-0.028690367937088013,
-0.004915561992675066,
-0.028580574318766594,
-0.03324604779481888,
-0.009218591265380383,
-0.018903004005551338,
-0.047077905386686325,
-0.037887051701545715,
0.010738342069089413,
0.004799528978765011,
0.008568634279072285,
-0.08290617913007736,
-0.015511970035731792,
0.027102230116724968,
0.00047118414659053087,
-0.05692363902926445,
0.006461053621023893,
0.01036347821354866,
-0.0027982196770608425,
-0.01083155907690525,
0.023153839632868767,
0.0063888318836688995,
-0.04338899254798889,
-0.009520665742456913,
-0.0025763283483684063,
0.04588997736573219,
0.023205816745758057,
-0.0096321115270257,
0.03434017300605774,
-0.019511649385094643,
-0.009897734969854355,
-0.020330049097537994,
0.012814080342650414,
0.05044032260775566,
-0.01976977288722992,
0.008553116582334042,
-0.032015345990657806,
0.013131161220371723,
0.04942558705806732,
-0.010994031094014645,
-0.0033212837297469378,
-0.01335405558347702,
-0.015337539836764336,
0.0540166050195694,
-0.0012318129884079099,
-0.046595193445682526,
0.021951692178845406,
0.03349614515900612,
0.03125573322176933,
-0.04027550294995308,
0.005209052469581366,
-0.029582589864730835,
0.018176516517996788,
0.002606128342449665,
0.00947913620620966,
0.0026390471030026674,
0.08578566461801529,
-0.014988348819315434,
0.006960319820791483,
0.04388841241598129,
-0.02433706633746624,
0.010316765867173672,
-0.018455207347869873,
-0.003468605224043131,
0.014571077190339565,
-0.007662342861294746,
-0.03144986927509308,
-0.028899027034640312,
-0.06405219435691833,
0.03434471786022186,
0.038103219121694565,
0.031335316598415375,
0.014596709981560707,
0.014368342235684395,
-0.009288914501667023,
0.00433365348726511,
-0.014399397186934948,
-0.04709810018539429,
0.018283750861883163,
-0.00008700472244527191,
0.0361616387963295,
-0.017632387578487396,
-0.0054378570057451725,
0.017061760649085045,
0.02747926488518715,
-0.06569892913103104,
0.04010099917650223,
0.058947719633579254,
-0.003064882941544056,
0.027088552713394165,
0.00660407030954957,
-0.023561730980873108,
0.03219848498702049,
-0.00678868405520916,
0.05384976044297218,
-0.0002553063677623868,
-0.038631875067949295,
0.03496813774108887,
0.053328946232795715,
-0.0007897294708527625,
-0.022438732907176018,
-0.03666815161705017,
-0.03307963162660599,
0.020952118560671806,
0.0014299355680122972,
0.0028629859443753958,
0.01632186584174633,
0.04204288125038147,
0.0370107926428318,
0.05248308554291725,
0.02657199464738369,
-0.00555154075846076,
-0.0008720268961042166,
0.023655187338590622,
-0.017776822671294212,
-0.03348991647362709,
0.03496430069208145,
0.0076041193678975105,
-0.014425670728087425,
0.04899900034070015,
-0.01350343320518732,
0.019999176263809204,
-0.01442024763673544,
0.017700588330626488,
-0.03558342158794403,
0.07598692178726196,
-0.015921147540211678,
0.007500992156565189,
0.018709516152739525,
0.00033575581619516015,
0.10562057048082352,
0.10546737164258957,
0.023108087480068207,
-0.05951287969946861,
0.002164419973269105,
-0.00017014254990499467,
0.017389949411153793,
-0.014892452396452427,
0.024476001039147377,
0.014977114275097847,
0.02639365941286087,
-0.050888948142528534,
0.035405490547418594,
-0.03517203405499458,
0.013186264783143997,
0.00608667591586709,
-0.07418903708457947,
-0.03668712452054024,
0.018053455278277397,
0.03211740404367447,
-0.009637954644858837,
-0.012221534736454487,
-0.02263972908258438,
-0.022823937237262726,
-0.02371288649737835,
0.011992888525128365,
-0.023578934371471405,
-0.04466712102293968,
0.017274901270866394,
0.004161460790783167,
-0.02233203686773777,
0.009265855886042118,
0.01207813061773777,
0.004312728065997362,
-0.0013278138358145952,
0.017747998237609863,
-0.021860193461179733,
-0.0020962620619684458,
0.000945736188441515,
0.07384887337684631,
0.039368897676467896,
-0.019672421738505363,
0.0319436751306057,
-0.004894474521279335,
-0.011704818345606327,
-0.016428394243121147,
-0.025256352499127388,
0.05744929239153862,
-0.03420000523328781,
-0.039860960096120834,
-0.009263756684958935,
-0.010032976046204567,
-0.00630227942019701,
-0.04018356278538704,
0.016335854306817055,
-0.014111991040408611,
0.016557389870285988,
0.010874016210436821,
-0.007838819175958633,
-0.008813696913421154,
-0.02248857170343399,
0.012917361222207546,
-0.02064032480120659,
0.015200180932879448,
0.010042168200016022,
0.01674579456448555,
0.005537498742341995,
0.01633329689502716,
-0.017505884170532227,
0.017237737774848938,
-0.0395563468337059,
-0.021288972347974777,
-0.06293493509292603,
-0.06540904194116592,
0.024544456973671913,
-0.00008624347537988797,
0.04927217215299606,
0.017198221758008003,
-0.02154647186398506,
-0.04812442883849144,
-0.09426815062761307,
0.02870052494108677,
0.009350674226880074,
-0.04673688858747482,
-0.02219526842236519,
-0.025812070816755295,
0.02939654141664505,
0.0317331999540329,
-0.05485003441572189,
0.03920268267393112,
0.021744098514318466,
0.015086573548614979,
0.032917093485593796,
-0.03654517978429794,
0.023087099194526672,
0.01143796369433403,
-0.03096413053572178,
0.00916430726647377,
-0.02918728068470955,
0.011757024563848972,
-0.020655198022723198,
0.02872661128640175,
-0.014288957230746746,
0.01718284748494625,
-0.005027753300964832,
-0.0015574470162391663,
0.0057657561264932156,
-0.03160746023058891,
0.015801114961504936,
0.011755998246371746,
0.03609714284539223,
-0.05875774100422859,
-0.02992290072143078,
-0.032410234212875366,
-0.016917089000344276,
0.003365582088008523,
0.00501834973692894,
-0.0363861508667469,
-0.002757083857432008,
-0.017618466168642044,
0.018661292269825935,
-0.020021215081214905,
0.009256932884454727,
-0.017614727839827538,
0.031006107106804848,
0.005838986486196518,
0.02557103894650936,
0.009172888472676277,
0.03483168035745621,
0.013332159258425236,
-0.027016473934054375,
0.015585584565997124,
0.03271066024899483,
-0.020255044102668762,
0.0036321626976132393,
0.01968167908489704,
0.015052525326609612,
0.01339515671133995,
-0.03115551732480526,
-0.018694376572966576,
0.010868912562727928,
-0.039713479578495026,
-0.024862563237547874,
0.03330794721841812,
0.006574277766048908,
-0.0072807446122169495,
0.03700162470340729,
-0.030656518414616585,
0.0007514892495237291,
0.016784729436039925,
-0.04354378953576088,
-0.0042296648025512695,
0.05461285263299942,
-0.03161051869392395,
-0.003154515288770199,
0.00690678134560585,
-0.028512530028820038,
-0.005291392561048269,
-0.0030323565006256104,
0.023504992946982384,
0.024520667269825935,
-0.027709389105439186,
0.024751583114266396,
-0.021804533898830414,
-0.030263734981417656,
0.062284789979457855,
0.05169692263007164,
-0.018127499148249626,
0.028991203755140305,
0.03465176001191139,
-0.008375147357583046,
-0.011455535888671875,
-0.0019284546142444015,
0.008118576370179653,
-0.07858217507600784,
-0.0065422821789979935,
-0.016034387052059174,
0.011439369060099125,
0.021605229005217552,
-0.06495671719312668,
0.01720842719078064,
0.034493010491132736,
-0.07561098784208298,
0.03178343549370766,
-0.03859688341617584,
0.015213793143630028,
-0.01285440381616354,
0.013401029631495476,
-0.04126253351569176,
0.06386101990938187,
0.04235699400305748,
0.019174832850694656,
0.0299356859177351,
-0.005869811866432428,
-0.026894723996520042,
-0.029268594458699226,
-0.01796676218509674,
0.044799480587244034,
-0.006252751685678959,
-0.05076858773827553,
0.020419850945472717,
-0.011914224363863468,
0.002767580794170499,
-0.0013752818340435624,
-0.002275713486596942,
-0.007492800708860159,
-0.00962728913873434,
0.008435619063675404,
0.040366288274526596,
0.004695253446698189,
0.017222745344042778,
-0.025240829214453697,
-0.013890527188777924,
-0.012684209272265434,
-0.001347315963357687,
0.03942226618528366,
0.01348445750772953,
0.000012573656022141222,
0.04941732808947563,
-0.045543402433395386,
-0.06222245842218399,
0.03519980609416962,
-0.011408653110265732,
-0.0003772999916691333,
0.01073662843555212,
-0.036347053945064545,
0.00545818405225873,
-0.03947913646697998,
0.01521003246307373,
-0.037483200430870056,
-0.044297266751527786,
0.05721145123243332,
0.02753342315554619,
-0.0015222923830151558,
-0.00611089589074254,
-0.028813181445002556,
-0.0660703033208847,
0.05344798415899277,
0.026146134361624718,
-0.02521904557943344,
-0.06749918311834335,
-0.017719082534313202,
-0.019648702815175056,
0.0032027587294578552,
0.002248208737000823,
-0.00933501310646534,
-0.03173741325736046,
0.01992826536297798,
-0.003205596935003996,
0.034370824694633484,
-0.018312616273760796,
-0.03823782131075859,
-0.046650905162096024,
-0.050910063087940216,
0.04422668740153313,
-0.01400737650692463,
-0.036057598888874054,
-0.022785991430282593,
0.014957809820771217,
0.005699490662664175,
0.028025217354297638,
0.023077916353940964,
-0.011462348513305187,
-0.012650711461901665,
0.0301657821983099,
-0.03808661177754402,
0.05134693905711174,
0.0067891026847064495,
0.00805872306227684,
-0.01095912791788578,
0.022703662514686584,
-0.013018835335969925,
-0.00011394059401936829,
-0.026004519313573837,
0.042496006935834885,
0.003489299211651087,
0.0134661216288805,
0.014871058985590935,
0.00022837586584500968,
-0.049730658531188965,
0.04138977825641632,
-0.00046417172416113317,
-0.014428772032260895,
0.0892711728811264,
0.02266620472073555,
0.005806236062198877,
0.0408996120095253,
-0.038735076785087585,
-0.03274785727262497,
0.024442197754979134,
-0.013753330335021019,
-0.018983634188771248,
-0.004995469469577074,
-0.02335960417985916,
0.029307210817933083,
-0.04976550489664078,
-0.03029130958020687,
0.002041141502559185,
-0.011426164768636227,
-0.01708054542541504,
0.025904078036546707,
-0.01963246427476406,
0.024969715625047684,
-0.0005595043185167015,
0.036793481558561325,
-0.005449387244880199,
0.02327531762421131,
0.02927439473569393,
0.07036270946264267,
-0.008861788548529148,
0.015635844320058823,
0.03231700509786606,
0.01376353483647108,
-0.04431691765785217,
0.021093856543302536,
0.025636281818151474,
0.016938256099820137,
-0.005202277097851038,
-0.0054737841710448265,
0.048074182122945786,
-0.010339554399251938,
-0.04143843427300453,
0.013304422609508038,
-0.034577563405036926,
0.07557646930217743,
-0.01664290949702263,
0.02402460016310215,
-0.009848025627434254,
-0.011143049225211143,
-0.033905576914548874,
0.00776907242834568,
0.012850209139287472,
0.08376491814851761,
-0.021131794899702072,
-0.0055298637598752975,
-0.03578970208764076,
0.023711850866675377,
0.011148720048367977,
-0.04982878640294075,
-0.028579052537679672,
0.026714248582720757,
-0.02233763411641121,
-0.03501293435692787,
-0.022509481757879257,
0.02413296326994896,
-0.01814126782119274,
0.033069103956222534,
0.030748525634407997,
-0.010715778917074203,
-0.046295177191495895,
0.007286673877388239,
0.004433566238731146,
0.06524799764156342,
-0.04832834750413895,
-0.01794145442545414,
-0.00619185995310545,
0.012393626384437084,
-0.01050114817917347,
0.012341770343482494
] |
<p>I am given the following equations.
$$\frac{\partial ^2\tilde \psi(x,\omega)}{\partial x^2}+k^2(x,\omega)\tilde\psi(x,\omega)=0 $$
Where
$$k^2 =\frac{2m\omega}{\hbar}$$
And then
$$\frac{\partial ^2\tilde E(x,\omega)}{\partial x^2}+\frac{n^2(x)\omega^2}{c^2}\tilde E(x,\omega)=0$$
We have the boundary conditions:
$$\tilde\psi(\pm a/2)=\tilde E(\pm a/2)=0$$
I am asked for the allowed values of $\omega$ and $k$ and then the normalized mode functions. </p>
<p>I did this in the same way we treat the Infinite Well in QM. I took that the solution was $Ae^{ikx}+Be^{-ikx}$ and then found each solution was of the same form, which was $\sqrt{2/a}\sin(kx)$ for both. But then the allowed values of k and $\omega$ were different depending on the k values above. Am I doing this correctly?</p>
| 9,624 |
[
0.02598607912659645,
-0.006262814160436392,
0.008712640963494778,
-0.009364498779177666,
0.02034442313015461,
-0.03340347856283188,
-0.03710220009088516,
-0.07567490637302399,
-0.0008637242717668414,
0.004568356554955244,
0.03812437132000923,
0.007769605610519648,
0.059107761830091476,
0.02238827757537365,
0.008029559627175331,
0.008081463165581226,
-0.030759157612919807,
-0.021696966141462326,
-0.005917985457926989,
-0.042275119572877884,
0.0009607030660845339,
0.04364496469497681,
-0.016117092221975327,
-0.033391911536455154,
-0.032617196440696716,
0.02762380987405777,
0.03250235319137573,
-0.0008886470459401608,
0.026806233450770378,
0.03174041211605072,
0.03046533465385437,
-0.028953291475772858,
0.03245329484343529,
0.05530388653278351,
-0.0057546477764844894,
0.0025219013914465904,
-0.04975396767258644,
-0.008292299695312977,
-0.024694208055734634,
0.05847683176398277,
-0.036631569266319275,
-0.01863785646855831,
0.014306253753602505,
0.04565878212451935,
0.02383684180676937,
-0.006168809719383717,
0.04855481535196304,
-0.031560249626636505,
0.05078994110226631,
-0.060264889150857925,
0.07367948442697525,
0.009497495368123055,
0.056643158197402954,
0.029842302203178406,
-0.010314398445189,
-0.046859659254550934,
0.06468041241168976,
0.06995651125907898,
0.03698281571269035,
-0.045315250754356384,
0.00426076166331768,
-0.0011688683880493045,
-0.001298781717196107,
0.01360723003745079,
-0.042354702949523926,
-0.022724466398358345,
0.01892203278839588,
-0.025452017784118652,
0.003207697533071041,
-0.030029816552996635,
0.019579198211431503,
0.010199952870607376,
0.017899613827466965,
-0.03133510425686836,
0.014373349957168102,
0.005667765159159899,
-0.02005709707736969,
0.06095730885863304,
0.013448376208543777,
0.015305365435779095,
0.005535170901566744,
0.01966153457760811,
0.022469010204076767,
0.01468215137720108,
-0.03323200345039368,
-0.002304068300873041,
0.06470125913619995,
0.0014991782372817397,
-0.011961149051785469,
0.0321396104991436,
0.008142699487507343,
0.030135488137602806,
0.04782387614250183,
-0.04756111651659012,
-0.01119712833315134,
0.00438645901158452,
0.027941547334194183,
0.03134173899888992,
-0.016325760632753372,
-0.02162754535675049,
-0.00446988083422184,
-0.0732560008764267,
0.008554678410291672,
0.05529545992612839,
0.015474965795874596,
0.03999704495072365,
-0.04251902922987938,
0.03143796697258949,
-0.02928296849131584,
-0.005131589714437723,
-0.02007627859711647,
0.009008373133838177,
-0.023763641715049744,
0.011531011201441288,
-0.019056782126426697,
-0.027495838701725006,
-0.022831890732049942,
-0.061060089617967606,
0.038056861609220505,
0.044522568583488464,
0.04021533951163292,
-0.006792647298425436,
0.009657221846282482,
-0.024564648047089577,
-0.07476456463336945,
-0.00845253188163042,
0.004051979631185532,
0.003918802365660667,
-0.043621793389320374,
0.006299455184489489,
0.012204822152853012,
0.006455102004110813,
-0.013128851540386677,
0.005074070300906897,
0.02646268531680107,
-0.026337333023548126,
-0.09547704458236694,
-0.05983066186308861,
0.010539435781538486,
-0.03043828159570694,
0.009532430209219456,
-0.07893585413694382,
-0.029808564111590385,
0.07669251412153244,
0.0855480507016182,
-0.012006872333586216,
0.01387953944504261,
-0.01094700489193201,
0.05164105072617531,
0.020416732877492905,
-0.028261074796319008,
-0.010683140717446804,
-0.037588465958833694,
-0.03391952067613602,
-0.02334136702120304,
-0.014759557321667671,
-0.001578348921611905,
0.037124153226614,
-0.002717273775488138,
0.01610049046576023,
0.07902801781892776,
-0.009967583231627941,
-0.006200676783919334,
0.03020571917295456,
0.01748950220644474,
-0.048101555556058884,
0.07289937138557434,
0.043740708380937576,
0.0017110606422647834,
0.03435993939638138,
-0.018776409327983856,
0.017161620780825615,
-0.01364149060100317,
-0.006180861033499241,
0.008001605980098248,
-0.032708100974559784,
0.01767331175506115,
-0.07252030819654465,
0.02809072844684124,
0.04578321799635887,
-0.04623233899474144,
-0.007198904640972614,
0.02892901748418808,
0.03465665131807327,
0.0038307346403598785,
0.04969080537557602,
-0.031246474012732506,
-0.014040272682905197,
-0.014298352412879467,
-0.05469192937016487,
-0.009579639881849289,
-0.018563006073236465,
0.0327594019472599,
-0.005221018102020025,
-0.017018085345625877,
0.015398548915982246,
-0.017558665946125984,
0.013059723190963268,
-0.001693969825282693,
-0.03551478311419487,
-0.01354735717177391,
0.002761291339993477,
0.011729803867638111,
-0.01634978875517845,
0.04279530793428421,
0.05759890004992485,
-0.00023457738279830664,
0.0029361548367887735,
0.06849204748868942,
-0.022878412157297134,
-0.017013881355524063,
-0.0056586479768157005,
-0.026242190971970558,
0.05059396103024483,
0.001129988464526832,
-0.03409989923238754,
-0.01921354979276657,
0.005654216278344393,
0.017180457711219788,
0.021560458466410637,
-0.03590960428118706,
0.0594741590321064,
0.056863002479076385,
-0.008266523480415344,
-0.02971046045422554,
0.04867283254861832,
0.0018293086905032396,
0.053775567561388016,
-0.03085622936487198,
-0.030162429437041283,
-0.036185745149850845,
-0.011230383068323135,
0.03281379118561745,
0.004659864120185375,
-0.04831693693995476,
0.011551070027053356,
0.06055520102381706,
0.009141319431364536,
0.04086893051862717,
-0.0017505065770819783,
0.007352285552769899,
-0.02328876592218876,
0.027848292142152786,
0.04243314638733864,
0.021550843492150307,
0.01668553054332733,
0.04768091067671776,
-0.01928170956671238,
0.006677632685750723,
-0.018400417640805244,
-0.01014209259301424,
0.05172140523791313,
-0.0541825070977211,
-0.01749323680996895,
-0.019031917676329613,
0.009256867691874504,
0.01181403174996376,
-0.01011977344751358,
0.00954813975840807,
0.050839152187108994,
-0.025111939758062363,
-0.029992448166012764,
-0.004346128087490797,
0.04027218744158745,
0.05574629828333855,
-0.02448590286076069,
-0.002880766289308667,
-0.005950028542429209,
0.02016289159655571,
-0.008932583034038544,
-0.011424154974520206,
-0.04046138748526573,
-0.012539682909846306,
-0.023927981033921242,
-0.032773327082395554,
0.03123760223388672,
0.01098934467881918,
0.026752160862088203,
-0.03525596112012863,
-0.03923396021127701,
-0.009240370243787766,
-0.004127789754420519,
-0.011833511292934418,
0.022175179794430733,
-0.025548692792654037,
0.029920117929577827,
-0.04147700220346451,
0.016351627185940742,
0.02778320200741291,
-0.013062422163784504,
-0.00020195500110276043,
-0.0073526157066226006,
-0.022154970094561577,
0.0005469976458698511,
-0.008121817372739315,
-0.02676980197429657,
0.014533146284520626,
-0.007145358715206385,
-0.0002249301760457456,
0.0650409609079361,
0.017615173012018204,
0.00024240526545327157,
0.03532923385500908,
-0.0025098007172346115,
-0.02676301635801792,
-0.009261651895940304,
-0.021833745762705803,
0.040808480232954025,
-0.03439270704984665,
0.014328905381262302,
0.0016565762925893068,
-0.03402553126215935,
0.004222140181809664,
-0.03775615617632866,
-0.04367124289274216,
0.037413496524095535,
-0.01637924648821354,
0.031396396458148956,
0.023106543347239494,
-0.016391562297940254,
0.08566226810216904,
0.0391501821577549,
-0.016688097268342972,
0.0028408030048012733,
0.030651940032839775,
-0.020900849252939224,
-0.05108150839805603,
-0.04761064052581787,
0.05912521854043007,
-0.026097869500517845,
0.052222058176994324,
-0.020548555999994278,
0.017389902845025063,
0.044786013662815094,
-0.03463156893849373,
-0.043923813849687576,
0.036004260182380676,
0.011770081706345081,
0.014596753753721714,
0.09455493092536926,
0.010829237289726734,
0.027420956641435623,
-0.04219451919198036,
0.010818896815180779,
-0.007897361181676388,
0.013919609598815441,
-0.044815242290496826,
0.023727135732769966,
-0.01712256297469139,
-0.0047413669526577,
-0.01947781629860401,
0.025879427790641785,
-0.012906113639473915,
-0.02175280638039112,
-0.012713463976979256,
0.0062322900630533695,
0.03344988822937012,
-0.01380686555057764,
0.02765747718513012,
0.03975953161716461,
-0.006358656100928783,
0.012389538809657097,
-0.02255965955555439,
-0.013010715134441853,
-0.000744747812859714,
0.037010665982961655,
-0.040081337094306946,
-0.05678938701748848,
0.02743961662054062,
0.032895926386117935,
0.03222425654530525,
-0.015856128185987473,
-0.03167727589607239,
0.002023086417466402,
-0.06142893061041832,
-0.031922388821840286,
-0.03584660217165947,
0.054458726197481155,
0.022375501692295074,
0.03852566331624985,
0.04256239905953407,
0.00012595039152074605,
0.0025099373888224363,
0.009417390450835228,
-0.03454689681529999,
-0.007003088481724262,
-0.03591311722993851,
-0.016897065564990044,
-0.01754401996731758,
-0.023213334381580353,
0.020006293430924416,
-0.022349143400788307,
-0.01799623668193817,
0.01784193329513073,
-0.023562150076031685,
-0.04480968043208122,
0.0057205017656087875,
-0.04056546092033386,
-0.029002444818615913,
-0.021885721012949944,
0.05440213903784752,
0.02044156938791275,
-0.012760001234710217,
-0.0007423029746860266,
0.05861604958772659,
-0.05122571438550949,
-0.0025935256853699684,
-0.0035690939985215664,
-0.0045038857497274876,
0.008030342869460583,
0.047088541090488434,
0.026306679472327232,
0.0075667803175747395,
-0.012097240425646305,
0.004559833090752363,
0.04103776440024376,
0.062290165573358536,
0.02178042009472847,
-0.019368557259440422,
-0.0028120907954871655,
-0.012287198565900326,
0.008346804417669773,
-0.00863826647400856,
0.07895658165216446,
0.005125721450895071,
-0.004373517353087664,
0.009734980762004852,
-0.016295645385980606,
-0.01322435587644577,
0.03761403262615204,
0.029673229902982712,
0.0070969159714877605,
-0.0034532565623521805,
-0.058253269642591476,
-0.007843279279768467,
-0.02159913443028927,
0.0012010149657726288,
-0.032113246619701385,
-0.015105140395462513,
0.02305692434310913,
0.023865053430199623,
0.059792667627334595,
0.00020103449060115963,
0.006225446704775095,
0.01239235419780016,
-0.0006755295326001942,
-0.006282154470682144,
-0.01765662431716919,
-0.020919201895594597,
0.026367096230387688,
0.013739579357206821,
0.05199412256479263,
-0.019366499036550522,
-0.002558627165853977,
-0.05585351958870888,
-0.018228691071271896,
0.042291976511478424,
0.011349482461810112,
0.05770424008369446,
-0.02902764081954956,
-0.07266063988208771,
-0.03543722257018089,
0.01123448833823204,
-0.0015040187863633037,
0.06018214672803879,
0.005881175864487886,
0.020447857677936554,
-0.006894494406878948,
-0.045027654618024826,
-0.03842342272400856,
0.004643680993467569,
0.029190799221396446,
-0.013163401745259762,
-0.0316711962223053,
-0.02528897300362587,
-0.012516098096966743,
0.00790622178465128,
0.020178956910967827,
0.06898889690637589,
-0.018471963703632355,
-0.062168754637241364,
0.010530984960496426,
0.009108160622417927,
-0.02782324142754078,
-0.06254907697439194,
0.015281583182513714,
0.012080935761332512,
0.0267332810908556,
0.03917182236909866,
0.005860422737896442,
-0.03039550967514515,
0.0348309688270092,
0.032484084367752075,
-0.012418471276760101,
0.01854352094233036,
-0.013371200300753117,
0.07676739990711212,
0.0007197569357231259,
0.03925221785902977,
0.07004569470882416,
0.026649683713912964,
-0.007039713207632303,
-0.014648492448031902,
-0.03010689653456211,
0.009970146231353283,
-0.030296919867396355,
0.005289878696203232,
-0.0504508875310421,
0.02070058137178421,
-0.0205294918268919,
0.03339933976531029,
-0.007209235802292824,
0.044230297207832336,
-0.031950708478689194,
-0.0384548045694828,
0.02135505899786949,
0.027840951457619667,
0.025560643523931503,
0.005562020931392908,
-0.01892077550292015,
0.00362463784404099,
0.01909792236983776,
0.01809817925095558,
0.0031374061945825815,
-0.04328802600502968,
0.013985753059387207,
0.0437861829996109,
-0.007455986458808184,
0.03846832364797592,
-0.025734666734933853,
-0.01231139525771141,
-0.023258095607161522,
-0.08020634204149246,
0.029132328927516937,
-0.019174110144376755,
-0.001362108625471592,
0.017703888937830925,
-0.02721339464187622,
-0.006880861707031727,
-0.015350967645645142,
-0.0050660353153944016,
0.019975483417510986,
-0.029365379363298416,
0.021205931901931763,
0.040029361844062805,
0.020114418119192123,
-0.08674241602420807,
-0.025210682302713394,
0.010385127738118172,
-0.013925629667937756,
0.011742564849555492,
0.01765923947095871,
0.014710744842886925,
-0.03204391151666641,
-0.027573302388191223,
0.012466070242226124,
0.002183112781494856,
-0.04371671378612518,
-0.02456221543252468,
0.025220630690455437,
0.07766290754079819,
0.01613151654601097,
0.023616017773747444,
-0.005486670881509781,
0.04223677143454552,
-0.025603706017136574,
-0.03691384941339493,
-0.004074188880622387,
0.04525262117385864,
-0.02534255012869835,
-0.013876525685191154,
-0.04434800520539284,
-0.014979691244661808,
0.0725032389163971,
0.0046239071525633335,
-0.04275010526180267,
-0.009363336488604546,
-0.0024622036144137383,
0.019081009551882744,
-0.004570392891764641,
-0.04837777838110924,
0.0030476374085992575,
0.02507650852203369,
-0.021708017215132713,
-0.000445690646301955,
-0.04180515557527542,
-0.053481459617614746,
0.02953295037150383,
-0.01863246038556099,
-0.026814205572009087,
-0.012512453831732273,
0.11461355537176132,
-0.03302515670657158,
-0.008213215507566929,
-0.021084250882267952,
-0.007105741184204817,
0.002453552559018135,
0.010333884507417679,
-0.029798896983265877,
0.025064054876565933,
0.0076917908154428005,
-0.009829812683165073,
-0.08013450354337692,
-0.052092842757701874,
0.03137018904089928,
0.0295669287443161,
0.006565398536622524,
0.023470185697078705,
0.005057762376964092,
0.01548625249415636,
-0.03474464267492294,
-0.020728951320052147,
-0.019403334707021713,
0.011826837435364723,
-0.002523900242522359,
0.05163446068763733,
-0.05366044491529465,
-0.0073731583543121815,
0.011869060806930065,
0.036182951182127,
-0.012838027440011501,
-0.01758081279695034,
0.02231108956038952,
0.04434366524219513,
-0.022812293842434883,
0.02250979281961918,
-0.020257780328392982,
0.0411100871860981,
-0.02717573195695877,
0.06964601576328278,
-0.007194804027676582,
-0.029075272381305695,
0.04043743759393692,
0.05308280512690544,
-0.01207219809293747,
-0.04060064256191254,
0.025641867890954018,
-0.001246649189852178,
0.0020533278584480286,
0.013813029043376446,
-0.015417910180985928,
0.039714179933071136,
0.037716642022132874,
0.02611309476196766,
0.02594151720404625,
0.011301778256893158,
0.009230874478816986,
-0.04342619329690933,
-0.00024230532289948314,
-0.03350265324115753,
-0.06324844807386398,
0.0016800565645098686,
-0.04141790047287941,
-0.011049211956560612,
0.06350196897983551,
-0.021910082548856735,
0.01931694895029068,
0.006422560196369886,
0.0008720196783542633,
-0.02578592114150524,
0.037629567086696625,
0.01852761022746563,
0.0045069181360304356,
-0.012406636960804462,
-0.0071843513287603855,
0.13242751359939575,
0.06996235996484756,
0.04496416449546814,
-0.0675240308046341,
0.03753405809402466,
0.0015231921570375562,
0.036913223564624786,
-0.031183792278170586,
-0.009522274136543274,
-0.016590679064393044,
-0.004475830588489771,
-0.01092491950839758,
0.03867902234196663,
-0.01374785602092743,
0.01657739467918873,
0.018496887758374214,
-0.01303019467741251,
-0.06590108573436737,
0.016982711851596832,
0.0026508155278861523,
-0.022038787603378296,
-0.0075337644666433334,
-0.012342138215899467,
0.055578745901584625,
-0.049311693757772446,
0.019277894869446754,
-0.014617052860558033,
-0.02285534329712391,
0.04509779065847397,
-0.01722109690308571,
-0.02954653650522232,
-0.0024705789983272552,
0.01912958361208439,
-0.028253355994820595,
0.009791683405637741,
0.035244591534137726,
0.026683853939175606,
-0.022711249068379402,
0.041547130793333054,
0.03412248566746712,
-0.010969297960400581,
-0.03054468147456646,
0.009026145562529564,
0.008576576597988605,
-0.014540014788508415,
-0.026061158627271652,
-0.001335061271674931,
0.059561461210250854,
0.012068637646734715,
-0.04002325236797333,
-0.009222781285643578,
-0.014884626492857933,
-0.012265434488654137,
-0.018399322405457497,
-0.0008128713816404343,
-0.012794681824743748,
0.017217842862010002,
-0.03199942782521248,
0.003119993256404996,
0.011304168030619621,
-0.00794613640755415,
0.0382210910320282,
0.0011432304745540023,
-0.009131568484008312,
-0.0011307387612760067,
0.011737070046365261,
-0.010581252165138721,
0.024639595299959183,
0.004080845508724451,
-0.01481860876083374,
-0.005305679515004158,
-0.004205609206110239,
-0.056520015001297,
-0.02101638913154602,
0.012022169306874275,
0.009906648658216,
0.10097935795783997,
-0.01130194403231144,
-0.014187043532729149,
-0.07916106283664703,
-0.07743123173713684,
-0.006201324984431267,
-0.005969229619950056,
-0.029680054634809494,
-0.007989207282662392,
-0.006367365829646587,
0.00003604733865358867,
0.03705814853310585,
-0.03524845466017723,
0.015519902110099792,
0.039576880633831024,
0.01307198777794838,
0.02327098697423935,
-0.03547869250178337,
-0.0633733794093132,
0.016892220824956894,
-0.05365370213985443,
0.03236487880349159,
-0.0037493384443223476,
0.011343810707330704,
-0.008195068687200546,
0.034343622624874115,
0.019024014472961426,
0.07625982165336609,
-0.0477505587041378,
-0.01587299257516861,
-0.008770106360316277,
-0.04524209350347519,
0.038062844425439835,
0.03823147714138031,
0.03905213251709938,
-0.038698967546224594,
-0.048948440700769424,
-0.01001922320574522,
0.0047769807279109955,
0.0346217043697834,
-0.016756555065512657,
-0.014410876668989658,
-0.003998579923063517,
-0.03167002275586128,
-0.03841787204146385,
-0.02841728739440441,
0.02401089109480381,
-0.0074570272117853165,
0.01888754963874817,
0.014369562268257141,
0.00902075506746769,
-0.028794601559638977,
0.012984742410480976,
-0.0100281136110425,
-0.03137143701314926,
0.008978360332548618,
0.05605281516909599,
-0.01961396634578705,
-0.018854830414056778,
-0.0020835017785429955,
0.022909441962838173,
0.04543846473097801,
-0.0004026758542750031,
-0.025264596566557884,
0.007233810145407915,
-0.04381650313735008,
-0.01923076994717121,
0.00012369759497232735,
0.030797239392995834,
0.013387617655098438,
0.04580911248922348,
-0.004670148249715567,
-0.011617103591561317,
0.04209233075380325,
-0.014675532467663288,
-0.007545046973973513,
-0.003482828149572015,
-0.021900471299886703,
0.0027840598486363888,
-0.022682109847664833,
-0.014644944109022617,
-0.006956019438803196,
-0.0036105788312852383,
0.0389166884124279,
0.010158604010939598,
-0.03069770522415638,
-0.01926557719707489,
0.017150580883026123,
0.009547211229801178,
0.006187920458614826,
0.02463362365961075,
0.03119475767016411,
0.03899335116147995,
0.03666413202881813,
-0.024874966591596603,
0.039322927594184875,
0.0026940738316625357,
0.025898955762386322,
-0.06544430553913116,
-0.014700238592922688,
-0.01015897374600172,
0.014735933393239975,
0.03976551443338394,
-0.01411622203886509,
0.02004394307732582,
0.013477401807904243,
-0.05204177275300026,
0.0013917147880420089,
-0.004726058337837458,
0.010341853834688663,
-0.047829803079366684,
0.010234338231384754,
-0.029536662623286247,
0.007559905294328928,
0.058283109217882156,
0.01923503540456295,
0.0041898214258253574,
-0.004475681111216545,
-0.0001714023674139753,
-0.0145315146073699,
0.005778721999377012,
0.03769659250974655,
-0.00021353967895265669,
-0.017863804474473,
0.03400062769651413,
-0.043020956218242645,
-0.02946179360151291,
-0.006636177189648151,
-0.013563642278313637,
-0.02188454382121563,
-0.009143834933638573,
0.008486328646540642,
0.016774857416749,
0.02839760109782219,
0.018582792952656746,
-0.001738804392516613,
0.013612559996545315,
-0.007247564848512411,
0.02330118790268898,
-0.011523328721523285,
-0.026677722111344337,
-0.014393950812518597,
0.0036880061961710453,
-0.0585818774998188,
-0.046890370547771454,
0.04176197573542595,
-0.019993659108877182,
-0.002273119054734707,
-0.024845173582434654,
-0.01895218715071678,
0.0174452755600214,
-0.035761553794145584,
0.0028425976634025574,
-0.013885226100683212,
-0.0020701668690890074,
0.00227152812294662,
-0.0021296958439052105,
-0.004692018963396549,
0.003726707771420479,
-0.01765771210193634,
-0.06392338126897812,
0.02990606240928173,
0.016024839133024216,
-0.013733647763729095,
-0.043281689286231995,
-0.006868334021419287,
-0.05009867995977402,
0.01860148087143898,
0.016538430005311966,
-0.0008929094183258712,
-0.044289905577898026,
0.026195300742983818,
-0.0279065128415823,
0.01848834753036499,
-0.04812771454453468,
-0.05599801614880562,
-0.04352203756570816,
-0.06840698421001434,
0.02599419094622135,
0.0297161266207695,
-0.007486442569643259,
-0.005734914448112249,
-0.0021217812318354845,
-0.0022764226887375116,
0.03593968227505684,
0.05001349374651909,
-0.004652117379009724,
-0.011914531700313091,
0.003983022179454565,
-0.010626253671944141,
0.03523440659046173,
-0.0478220209479332,
0.012051030062139034,
0.000342957820976153,
0.00572601705789566,
-0.013533770106732845,
0.0025829016231000423,
0.004573019687086344,
0.03765973448753357,
0.0034172721207141876,
-0.01233740709722042,
0.010797974653542042,
0.024143880233168602,
-0.041679829359054565,
0.014015881344676018,
-0.01902761496603489,
0.009017040021717548,
0.07251780480146408,
0.018506627529859543,
0.019069867208600044,
0.025729291141033173,
-0.028550516813993454,
-0.012087983079254627,
0.04448280110955238,
-0.05396704375743866,
-0.007535822223871946,
-0.012480656616389751,
-0.02768554538488388,
0.03986617922782898,
-0.03317005932331085,
-0.04258770868182182,
0.047339312732219696,
-0.04068807512521744,
-0.03325619548559189,
0.04205537214875221,
0.007008956279605627,
0.028281264007091522,
-0.004712454508990049,
0.029691560193896294,
0.005974507890641689,
0.011616264469921589,
0.032795801758766174,
-0.006359460297971964,
0.02994987927377224,
0.03346515819430351,
0.014118324965238571,
0.02581622637808323,
-0.04796241596341133,
0.021081967279314995,
-0.03390287235379219,
-0.005265599582344294,
-0.038976386189460754,
-0.048091866075992584,
0.05913246423006058,
-0.003143220441415906,
-0.020304182544350624,
0.026394164189696312,
-0.04575182870030403,
0.05295564979314804,
-0.028206996619701385,
0.039356838911771774,
-0.020124327391386032,
0.00024478964041918516,
0.02764439396560192,
0.0310044065117836,
0.0010621650144457817,
0.015971913933753967,
-0.0017444976838305593,
-0.01912652887403965,
-0.012730923481285572,
-0.02043306641280651,
0.01106994692236185,
-0.08742622286081314,
-0.014231901615858078,
-0.0240589901804924,
-0.02757103182375431,
0.0211932472884655,
-0.028923019766807556,
0.02516927197575569,
-0.012397979386150837,
0.026512159034609795,
0.043599747121334076,
0.022769786417484283,
-0.012212540954351425,
0.006395046599209309,
-0.0015561167383566499,
0.06945493817329407,
-0.036834124475717545,
0.02074798010289669,
0.021044187247753143,
-0.012938774190843105,
0.02718334272503853,
-0.0029289815574884415
] |
<p>My questions are:</p>
<ol>
<li>How does a black body absorb photons? </li>
<li>Why does a black body absorb the most photons of all objects (e.g. those with another color)? </li>
<li>Are there any relationship between the electron and a black body?</li>
</ol>
| 9,625 |
[
-0.03720446676015854,
-0.04504234716296196,
0.03496384248137474,
-0.038593024015426636,
-0.009638373740017414,
0.01020791381597519,
-0.027213288471102715,
-0.02936260960996151,
-0.018256211653351784,
-0.03626291826367378,
0.07537423819303513,
0.028144672513008118,
0.060136325657367706,
0.03267592191696167,
-0.0014393884921446443,
-0.008425431326031685,
-0.02290843054652214,
-0.03002907522022724,
0.0003463974571786821,
-0.019114138558506966,
0.023992100730538368,
0.03678214177489281,
0.01534227468073368,
0.027166040614247322,
-0.04735592380166054,
0.01737334579229355,
-0.0015038832789286971,
0.014830386266112328,
0.024238718673586845,
0.05194477736949921,
-0.021238131448626518,
-0.01454030442982912,
0.03284049779176712,
0.013781674206256866,
0.014177109114825726,
-0.016129514202475548,
-0.023811612278223038,
-0.02532493881881237,
-0.01883522979915142,
0.0015317971119657159,
-0.0009026514017023146,
-0.03076982870697975,
-0.020230131223797798,
0.04006874933838844,
0.006691779475659132,
-0.009766979143023491,
0.009775876998901367,
-0.024981452152132988,
0.021258186548948288,
-0.07854674756526947,
0.0719345286488533,
0.007078562397509813,
0.06437814980745316,
0.03819308057427406,
-0.011344668455421925,
-0.03713534399867058,
0.07863093912601471,
0.10883131623268127,
-0.02299298532307148,
-0.034151364117860794,
0.01420565228909254,
0.0027793876361101866,
-0.03020644374191761,
0.030164482071995735,
-0.03131549432873726,
0.04381830245256424,
-0.024437962099909782,
-0.03908621519804001,
0.030318325385451317,
0.0014241257449612021,
0.031006518751382828,
0.001764967804774642,
0.007921144366264343,
-0.0005986354663036764,
-0.02020297385752201,
-0.06147052347660065,
-0.0020945316646248102,
0.04962323233485222,
0.035057056695222855,
0.021475443616509438,
-0.03664780408143997,
0.00010103681415785104,
0.00249641016125679,
0.01890215463936329,
-0.029156574979424477,
0.002886191476136446,
0.09913818538188934,
0.007309140637516975,
0.0005187987699173391,
-0.002732365159317851,
-0.011712816543877125,
0.00858125276863575,
0.02762080542743206,
0.009058703668415546,
-0.017638159915804863,
0.026727285236120224,
-0.00624441122636199,
0.057843614369630814,
0.002606015419587493,
-0.005270582158118486,
0.020087065175175667,
0.005788515321910381,
0.0450606569647789,
0.0667787566781044,
0.005388669669628143,
-0.00455140508711338,
-0.05078527703881264,
0.05645278841257095,
0.00837390311062336,
0.0013657924719154835,
-0.028467057272791862,
0.039717286825180054,
-0.00025828569778241217,
-0.020788131281733513,
-0.0036724975798279047,
-0.03273622691631317,
0.041362300515174866,
-0.03881974518299103,
0.0480160266160965,
0.0781458392739296,
0.00022688460012432188,
-0.028747448697686195,
-0.013301471248269081,
-0.01889146864414215,
-0.04047626256942749,
0.021144866943359375,
0.04087534174323082,
-0.0002295271842740476,
-0.02831733413040638,
0.013073933310806751,
-0.00783682893961668,
-0.035150133073329926,
-0.0014660381712019444,
0.0021346977446228266,
0.034073419868946075,
-0.03202025592327118,
-0.130905881524086,
-0.05981776863336563,
0.013666492886841297,
0.0021776834037154913,
-0.03072802908718586,
-0.038338690996170044,
0.017175519838929176,
0.017363939434289932,
0.07490268349647522,
0.010614526458084583,
-0.022229548543691635,
0.028578100726008415,
0.020702295005321503,
0.013016780838370323,
0.0178657416254282,
0.00002567770025052596,
0.002297013532370329,
-0.022595489397644997,
0.025584014132618904,
-0.06893254071474075,
0.01040665339678526,
0.009277159348130226,
0.01081936340779066,
-0.007784221787005663,
0.07473328709602356,
-0.017128797248005867,
0.009794789366424084,
0.027590112760663033,
-0.011614586226642132,
-0.04662792757153511,
0.058313801884651184,
0.0237576924264431,
0.02222421020269394,
0.033189740031957626,
-0.0016086379764601588,
0.027298659086227417,
0.0032268529757857323,
0.02519044280052185,
-0.017853062599897385,
-0.028273610398173332,
-0.04894700646400452,
-0.0442548543214798,
0.001383432187139988,
-0.0034489338286221027,
-0.06861337274312973,
-0.042440254241228104,
-0.0014466398861259222,
-0.0008918691892176867,
0.04309849068522453,
0.04261773079633713,
0.01288681197911501,
-0.04040020704269409,
-0.009639939293265343,
-0.04415522888302803,
-0.019410761073231697,
-0.06075748801231384,
0.02259623073041439,
-0.005082910880446434,
-0.015549886971712112,
0.00476017314940691,
-0.006082857493311167,
-0.01820375584065914,
-0.02205250971019268,
-0.01254380401223898,
-0.016351237893104553,
0.0355018675327301,
-0.0024063200689852238,
0.013602218590676785,
-0.00887185987085104,
0.05385776236653328,
0.038447387516498566,
-0.031866416335105896,
0.008498207665979862,
-0.03364601731300354,
-0.04920794442296028,
0.004217991605401039,
-0.016832895576953888,
0.03052707388997078,
-0.008327682502567768,
-0.008221740834414959,
0.03666861727833748,
0.0044311475940048695,
-0.018605124205350876,
0.0334320031106472,
-0.014466676861047745,
0.08262650668621063,
-0.0037006072234362364,
-0.023157799616456032,
0.006000647321343422,
0.054873064160346985,
0.00858884584158659,
0.021441347897052765,
0.015548928640782833,
-0.010615999810397625,
-0.06528554856777191,
0.03094162419438362,
0.000328301073750481,
0.01965261436998844,
-0.07519633322954178,
0.04032495990395546,
-0.021306196227669716,
0.034402646124362946,
0.01924886181950569,
-0.016451219096779823,
-0.02156207710504532,
-0.04076850414276123,
0.0018553324043750763,
-0.03996486961841583,
-0.008477659896016121,
0.02285817265510559,
0.009149921126663685,
-0.011580312624573708,
0.03371819481253624,
-0.03869033604860306,
-0.010059401392936707,
0.06624145805835724,
0.006290143821388483,
-0.00680262316018343,
-0.005167078692466021,
-0.03455161675810814,
0.04271918162703514,
-0.043025121092796326,
0.003867612686008215,
0.026887977495789528,
-0.03148404508829117,
0.010593331418931484,
-0.038113754242658615,
-0.038995273411273956,
0.008960308507084846,
0.026861580088734627,
-0.0164941418915987,
0.009690665639936924,
0.02354195900261402,
-0.03266478702425957,
0.00540964026004076,
-0.010921308770775795,
-0.007475631777197123,
-0.052514635026454926,
0.010966080240905285,
0.00012089226947864518,
0.029755989089608192,
0.03888120874762535,
-0.03526889160275459,
-0.01898222789168358,
-0.0071909138932824135,
-0.025850318372249603,
-0.002580939792096615,
0.010677797719836235,
-0.05086441710591316,
-0.00595750892534852,
-0.039145585149526596,
-0.03296295180916786,
0.02017883211374283,
-0.014074387960135937,
0.01706567034125328,
0.01507876068353653,
-0.023266274482011795,
-0.03487478196620941,
0.006809169892221689,
0.007276293821632862,
0.010641406290233135,
-0.04466823488473892,
-0.005640885792672634,
0.05503664165735245,
-0.012538227252662182,
-0.006751036271452904,
0.010090356692671776,
-0.029283689334988594,
-0.04344506561756134,
0.004442404489964247,
-0.00784567091614008,
-0.0013186694122850895,
-0.020618166774511337,
-0.011154360137879848,
0.04082121700048447,
-0.031878214329481125,
0.019558917731046677,
-0.0460970401763916,
-0.01566147804260254,
0.01345968246459961,
-0.00023385741224046797,
0.031123928725719452,
-0.005196858197450638,
-0.013303960673511028,
0.027573781087994576,
0.03768608719110489,
-0.030877863988280296,
-0.04142438992857933,
-0.026578787714242935,
-0.0524914376437664,
-0.04169376939535141,
0.04639779031276703,
0.03363122418522835,
-0.011316178366541862,
-0.017984407022595406,
0.022972721606492996,
0.04854213073849678,
0.028499316424131393,
-0.008028874173760414,
-0.027690930292010307,
-0.028615308925509453,
-0.003884862642735243,
-0.03419733792543411,
0.051658641546964645,
0.0013571447925642133,
-0.012393911369144917,
0.03733386844396591,
-0.020394640043377876,
0.02211737260222435,
0.012745882384479046,
-0.06056947633624077,
0.03459565341472626,
0.007063204888254404,
-0.004595886450260878,
-0.04307292401790619,
0.04663154110312462,
0.012304840609431267,
-0.022293394431471825,
0.007764875888824463,
-0.004625136032700539,
0.04427516832947731,
-0.011231569573283195,
0.0014478778466582298,
0.05309418961405754,
0.06815392524003983,
-0.048557691276073456,
-0.021008316427469254,
-0.013577217236161232,
-0.010443070903420448,
0.010448608547449112,
-0.02095448412001133,
0.011469170451164246,
0.037259530276060104,
0.03723130375146866,
0.05679091811180115,
0.018601931631565094,
-0.027423877269029617,
-0.03955858573317528,
-0.0711083635687828,
-0.011577331461012363,
0.01687457412481308,
0.08264896273612976,
0.00034568406408652663,
0.05911678448319435,
0.04491959512233734,
0.026985837146639824,
0.048255521804094315,
0.022730519995093346,
-0.10348525643348694,
0.0041086720302701,
-0.03858353942632675,
0.006990252062678337,
-0.02305455692112446,
0.004245119635015726,
-0.00831141509115696,
-0.02709059603512287,
-0.02157827466726303,
-0.011468551121652126,
-0.014485307037830353,
-0.04609641060233116,
0.035442061722278595,
-0.053744200617074966,
-0.03594788908958435,
0.014380132779479027,
0.05995485931634903,
-0.011762510053813457,
-0.021942906081676483,
0.0044166045263409615,
0.029771391302347183,
-0.033006615936756134,
0.011311826296150684,
0.0065176477655768394,
0.022842153906822205,
0.01621752418577671,
0.03822222352027893,
0.008956135250627995,
0.004756261594593525,
-0.027818713337183,
-0.0015767373843118548,
0.021935390308499336,
0.04655414819717407,
0.013934305869042873,
-0.026262814179062843,
-0.018045054748654366,
-0.06367381662130356,
-0.00998263992369175,
-0.02392638847231865,
0.05795227736234665,
-0.005779782310128212,
-0.023902658373117447,
0.0482897125184536,
-0.011043362319469452,
-0.017046933993697166,
0.0170578733086586,
0.03901524096727371,
0.00541825732216239,
-0.03370814025402069,
-0.024054883047938347,
-0.01579303666949272,
-0.013938028365373611,
0.0237739235162735,
0.005308309104293585,
-0.008317396976053715,
-0.010107859969139099,
-0.007982168346643448,
0.029163401573896408,
0.008350432850420475,
-0.03614131361246109,
-0.028395438566803932,
-0.0022191465832293034,
0.025784075260162354,
-0.01943005621433258,
0.0038148434832692146,
-0.019724883139133453,
0.051147717982530594,
0.07477738708257675,
-0.01787976548075676,
-0.00014987503527663648,
-0.05196338891983032,
-0.0283823162317276,
0.05076846852898598,
0.04848533123731613,
-0.00767144188284874,
0.004289173521101475,
-0.04377684369683266,
0.013619923032820225,
0.05099932849407196,
-0.033148009330034256,
0.04908505082130432,
-0.02479897066950798,
0.0019279285334050655,
-0.04924263805150986,
-0.02831776812672615,
0.01012295950204134,
0.02181960828602314,
-0.004633545409888029,
0.0247610155493021,
-0.037887778133153915,
-0.00856013037264347,
-0.017883483320474625,
0.05324043706059456,
0.03764170780777931,
0.05531846731901169,
-0.02124440297484398,
0.007471449673175812,
0.015800870954990387,
0.0004870402335654944,
-0.030758919194340706,
-0.10505016893148422,
0.006788480561226606,
-0.019784679636359215,
-0.03854361176490784,
0.04179660975933075,
-0.02461952716112137,
-0.035067133605480194,
0.022809362038969994,
0.0011347997933626175,
-0.04873133450746536,
-0.011292407289147377,
-0.08848730474710464,
0.012167801149189472,
0.01864807680249214,
-0.03147894889116287,
0.03633638098835945,
0.030197415500879288,
-0.02695801667869091,
0.0026773307472467422,
-0.03846433386206627,
0.038142040371894836,
-0.006887602619826794,
-0.009239640086889267,
0.006578541360795498,
-0.023567810654640198,
-0.04359830915927887,
0.05452965199947357,
0.008653918281197548,
0.027110598981380463,
0.007886235602200031,
-0.052669063210487366,
-0.011333724483847618,
-0.004736016504466534,
-0.0036152522079646587,
0.034002240747213364,
-0.020228680223226547,
0.006066666916012764,
0.0012801126576960087,
-0.023041730746626854,
0.02521691843867302,
0.02151581272482872,
-0.012595757842063904,
0.01892591267824173,
-0.009195984341204166,
0.04087227210402489,
-0.030419420450925827,
0.010779800824820995,
0.00239936332218349,
-0.038795195519924164,
0.05689919739961624,
-0.017475685104727745,
-0.006598449777811766,
0.04538523405790329,
-0.07097667455673218,
-0.03053390234708786,
0.018615085631608963,
-0.012355959042906761,
0.025001734495162964,
-0.042623113840818405,
0.06667666882276535,
0.03239525109529495,
0.013724876567721367,
-0.0538320355117321,
-0.03920745849609375,
0.007927684113383293,
0.030825918540358543,
-0.013902869075536728,
-0.014900519512593746,
0.04632507264614105,
-0.03409808501601219,
-0.026347696781158447,
0.02312769554555416,
0.007252959068864584,
-0.04511965438723564,
-0.011176185682415962,
0.007466648239642382,
-0.007774315308779478,
0.029210472479462624,
-0.015595514327287674,
-0.02110736444592476,
0.007372154388576746,
0.007426201365888119,
-0.0003590072738006711,
-0.028682352975010872,
0.04080866649746895,
-0.01254516001790762,
-0.06242206692695618,
-0.013666435144841671,
0.01824992522597313,
0.05526624992489815,
-0.00006272016617003828,
-0.018863070756196976,
0.040703561156988144,
0.03473268821835518,
-0.03447918966412544,
-0.021661777049303055,
0.029042581096291542,
0.0027871730271726847,
0.033671893179416656,
0.0075114015489816666,
0.019912101328372955,
-0.04106330871582031,
-0.06379444152116776,
0.03818027302622795,
-0.011663160286843777,
0.024911921471357346,
0.020711584016680717,
0.07226041704416275,
-0.007012318354099989,
0.002883490640670061,
0.03216737508773804,
-0.03556070476770401,
0.020555272698402405,
0.011767217889428139,
0.013306831941008568,
0.046396590769290924,
0.015822255983948708,
0.002422077115625143,
-0.003426701994612813,
-0.01572898030281067,
-0.02633405104279518,
0.06392404437065125,
0.0010754236718639731,
0.0484822615981102,
0.029440468177199364,
0.006275160238146782,
0.007073307875543833,
-0.03444940224289894,
0.0038049437571316957,
-0.0025146636180579662,
0.031930748373270035,
0.03310128673911095,
-0.000713587854988873,
0.024277471005916595,
0.007595027796924114,
0.052077896893024445,
-0.02983584813773632,
0.022074313834309578,
0.023513205349445343,
0.016692642122507095,
0.024891681969165802,
-0.01210350263863802,
-0.014614528976380825,
0.04037241265177727,
-0.03899760544300079,
0.04043225571513176,
-0.0009636713075451553,
-0.02211153693497181,
0.02891879342496395,
0.0025859836023300886,
0.03584246337413788,
-0.012941693887114525,
-0.031682562083005905,
-0.04464282467961311,
0.028764571994543076,
0.022194920107722282,
-0.005339851602911949,
-0.015342757105827332,
0.015880580991506577,
0.032239049673080444,
-0.0015003759181126952,
0.012807256542146206,
-0.016713153570890427,
-0.0675409659743309,
-0.0027749943546950817,
-0.03583650663495064,
-0.06440726667642593,
0.035171881318092346,
-0.019068483263254166,
0.003009902313351631,
0.039291396737098694,
-0.03391677886247635,
0.034480445086956024,
0.009071544744074345,
0.04488448426127434,
0.013767204247415066,
0.026764508336782455,
-0.007488300558179617,
-0.007967840880155563,
0.008932618424296379,
0.003035783302038908,
0.08308316022157669,
0.050005022436380386,
0.019793951883912086,
-0.031783513724803925,
-0.005023467820137739,
-0.01392638124525547,
0.03777768090367317,
-0.009502703323960304,
0.02665797248482704,
-0.03951207175850868,
0.007263027131557465,
0.013422837480902672,
0.026521673426032066,
0.014922035858035088,
-0.03165561705827713,
0.034399110823869705,
-0.044370997697114944,
-0.02964353747665882,
0.01312173530459404,
0.02657920867204666,
-0.019522929564118385,
0.037883300334215164,
-0.045920152217149734,
0.02894437313079834,
-0.015817347913980484,
-0.01753769814968109,
-0.051684580743312836,
-0.03343826159834862,
0.009837216697633266,
-0.030992232263088226,
-0.0161700751632452,
0.019078699871897697,
-0.005415848456323147,
-0.030993234366178513,
-0.03550906106829643,
0.02032981999218464,
0.03942730277776718,
-0.004764379933476448,
0.02410566806793213,
0.0024542633909732103,
0.0242304727435112,
0.029752304777503014,
0.014725706540048122,
0.03305335342884064,
-0.0526903010904789,
0.011345051229000092,
-0.0050949156284332275,
0.04507003724575043,
-0.019764436408877373,
-0.007724146358668804,
-0.00976238027215004,
0.007525577675551176,
-0.0023820120841264725,
-0.04815645143389702,
-0.007966171950101852,
-0.013347005471587181,
0.01521213073283434,
-0.05612789839506149,
-0.06947248429059982,
-0.04021648317575455,
0.0329584963619709,
-0.006457124836742878,
0.04290952533483505,
-0.011880144476890564,
0.019695622846484184,
-0.00490725738927722,
-0.03101280890405178,
0.010032393038272858,
-0.01474782358855009,
0.015521159395575523,
-0.01644965447485447,
-0.01718621701002121,
-0.023899072781205177,
-0.03843563050031662,
0.03455223888158798,
0.035970915108919144,
0.021924056112766266,
0.017491556704044342,
0.029088091105222702,
-0.039994608610868454,
-0.07797934114933014,
0.016160987317562103,
-0.001301174983382225,
-0.012868656776845455,
-0.02861567959189415,
0.004901244770735502,
0.030759679153561592,
0.020403409376740456,
-0.010022231377661228,
0.0023946205619722605,
0.024684946984052658,
0.010304668918251991,
0.014930197969079018,
-0.03604649007320404,
-0.005918983370065689,
0.009666573256254196,
-0.013788181357085705,
0.02478213980793953,
-0.0186323169618845,
0.018492519855499268,
-0.01531127654016018,
0.01309672836214304,
0.013743999414145947,
0.03165840357542038,
-0.0407540537416935,
-0.03619496524333954,
0.02210414782166481,
-0.026877280324697495,
-0.0005267835222184658,
0.012789900414645672,
0.007318340707570314,
-0.01580357924103737,
-0.02237554080784321,
-0.025692353025078773,
-0.009460138157010078,
-0.012367527931928635,
0.014018693938851357,
-0.009961365722119808,
0.01430296991020441,
-0.027537282556295395,
0.02586112916469574,
-0.033003050833940506,
0.0017566977767273784,
-0.07535317540168762,
0.005956517998129129,
0.008733712136745453,
-0.017299966886639595,
-0.007921348325908184,
0.01152912899851799,
-0.008872455917298794,
-0.03359846770763397,
0.04135226830840111,
0.03802920877933502,
-0.021539604291319847,
-0.01755138672888279,
0.006925471127033234,
-0.011134065687656403,
0.05717189982533455,
0.03560272976756096,
-0.020473530516028404,
0.07649806886911392,
-0.029270857572555542,
0.00400889478623867,
0.04458294436335564,
-0.02885313145816326,
0.031124968081712723,
-0.0000903337640920654,
0.006693112198263407,
0.01513378880918026,
0.052791744470596313,
-0.008349879644811153,
-0.016228385269641876,
-0.008268840610980988,
-0.053205832839012146,
-0.014171697199344635,
0.005363279953598976,
0.029880264773964882,
-0.014837145805358887,
0.002323415596038103,
0.043655507266521454,
0.006791707128286362,
-0.0008744551450945437,
0.0003017389972228557,
-0.014387071132659912,
0.016103031113743782,
0.005379929672926664,
0.019220538437366486,
0.026462629437446594,
0.015319162979722023,
0.03530881181359291,
-0.03139832615852356,
0.11622186005115509,
0.018466778099536896,
-0.010962866246700287,
-0.07983943074941635,
0.02941601723432541,
0.007163697388023138,
0.0071166204288601875,
0.032298002392053604,
-0.02208755351603031,
0.004823921248316765,
0.024973154067993164,
-0.04994304105639458,
0.021563135087490082,
0.004107029177248478,
-0.019965745508670807,
-0.030098704621195793,
0.042199768126010895,
-0.02114526554942131,
-0.005783914588391781,
0.02560773678123951,
0.050847455859184265,
0.007722421549260616,
0.058963458985090256,
0.024688566103577614,
-0.05206545069813728,
-0.024350114166736603,
0.026750221848487854,
-0.005194016266614199,
-0.016754712909460068,
0.04975171387195587,
-0.00493633234873414,
0.009238635189831257,
0.0030129801016300917,
0.010071412660181522,
0.014319071546196938,
0.014025378040969372,
-0.02461637184023857,
-0.015312381088733673,
0.02098175883293152,
0.008701038546860218,
0.0042640650644898415,
-0.02253248542547226,
0.003940165974199772,
0.04982146620750427,
0.03114277310669422,
-0.00010101979569299147,
0.017024770379066467,
0.027086926624178886,
-0.044817667454481125,
-0.01981700398027897,
0.036141764372587204,
-0.0001507365086581558,
-0.006947627291083336,
-0.004474633373320103,
0.037136852741241455,
0.010016980580985546,
-0.01930209994316101,
-0.005353093147277832,
-0.05819125473499298,
-0.01379680261015892,
-0.013154850341379642,
0.02259702794253826,
0.012819456867873669,
0.03818303719162941,
-0.0010176736395806074,
-0.010579019784927368,
0.01523217186331749,
0.00414737593382597,
0.027904171496629715,
-0.016296392306685448,
0.01679169572889805,
0.029270129278302193,
0.024717556312680244,
-0.017587268725037575,
-0.059276383370161057,
-0.04629282280802727,
-0.008855953812599182,
-0.0234034713357687,
0.008834018371999264,
-0.016416316851973534,
-0.02973608486354351,
-0.026270508766174316,
-0.07365841418504715,
0.01813669688999653,
-0.03215823695063591,
-0.005269835703074932,
-0.03310740366578102,
-0.020980264991521835,
-0.010703670792281628,
0.062250714749097824,
0.029859675094485283,
-0.012887386605143547,
-0.03346315026283264,
-0.00261044898070395,
-0.018041511997580528,
0.03265748545527458,
-0.0427096001803875,
0.024434052407741547,
-0.0019965809769928455,
-0.036478202790021896,
-0.01767537370324135,
-0.011176479049026966,
0.006872933823615313,
0.04247748479247093,
0.03717178478837013,
-0.018227528780698776,
0.024400928989052773,
-0.029383277520537376,
-0.03659088537096977,
0.036282386630773544,
0.024270186200737953,
-0.016371021047234535,
0.06269825249910355,
-0.016258347779512405,
0.049604710191488266,
0.061549071222543716,
-0.02409643493592739,
-0.020348140969872475,
0.02274264208972454,
-0.023404410108923912,
-0.024136124178767204,
0.009571706876158714,
-0.02677648328244686,
0.03812979534268379,
-0.06884478032588959,
-0.0010609917808324099,
0.03335905820131302,
-0.020374003797769547,
-0.021710019558668137,
0.043768007308244705,
0.007873311638832092,
0.014170728623867035,
0.01364548783749342,
0.01976540870964527,
-0.002762931166216731,
-0.03056054748594761,
-0.04714115336537361,
0.04965376853942871,
0.03521687164902687,
-0.015467708930373192,
0.01973976567387581,
0.04991110414266586,
0.027235813438892365,
0.007519643288105726,
-0.0023537117522209883,
0.0023978715762495995,
-0.03514700010418892,
-0.006208752281963825,
0.01083425898104906,
0.04020743817090988,
0.016047101467847824,
0.0198623426258564,
-0.02491028420627117,
0.07889214903116226,
-0.04054392874240875,
0.010291406884789467,
-0.0010942675871774554,
0.0020733242854475975,
-0.03912593051791191,
0.04075045883655548,
0.04750468581914902,
0.06335624307394028,
0.001345755299553275,
-0.027443451806902885,
-0.038779884576797485,
0.02159281261265278,
0.026293901726603508,
-0.060116469860076904,
0.03552135452628136,
0.0006934131379239261,
-0.03206808492541313,
-0.004332796670496464,
0.00605431292206049,
0.007694069761782885,
-0.02391902543604374,
0.04840870574116707,
0.028441620990633965,
-0.0037164967507123947,
0.01044466346502304,
0.010947689414024353,
-0.027820104733109474,
0.03911513462662697,
-0.048703812062740326,
-0.02276298962533474,
-0.009015822783112526,
0.00395618099719286,
-0.06067270040512085,
-0.051123037934303284
] |
<p>Does the inverse square law have anything to do with conservative behavior of the central forces? </p>
| 9,626 |
[
-0.037360742688179016,
-0.020855799317359924,
0.022659199312329292,
-0.009329613298177719,
0.05779818445444107,
0.004558897577226162,
-0.02675384096801281,
0.02258366532623768,
0.00937007274478674,
-0.05603006109595299,
0.03734224662184715,
-0.02420102432370186,
0.0379737988114357,
0.003744804998859763,
0.004840434528887272,
0.002488212427124381,
-0.014313613064587116,
0.024138158187270164,
-0.0025597179774194956,
-0.04559709504246712,
-0.003250479931011796,
0.02904469519853592,
0.012714265845716,
0.023056354373693466,
-0.05245193466544151,
0.03493669256567955,
-0.0007192611810751259,
-0.01876245066523552,
0.01387532614171505,
0.07414188235998154,
-0.028969569131731987,
0.006759395357221365,
0.002905523404479027,
0.03634136915206909,
0.03312048316001892,
-0.0007518645143136382,
-0.000010644969734130427,
-0.0315033458173275,
0.0013529444113373756,
0.026980388909578323,
-0.04431290179491043,
-0.021454334259033203,
-0.013795249164104462,
0.05072394758462906,
-0.02748296968638897,
0.01893061399459839,
-0.031484976410865784,
-0.0025796634145081043,
0.05302688106894493,
-0.036049846559762955,
0.0690898448228836,
0.0009906516643241048,
0.043344300240278244,
0.034103114157915115,
-0.011541598476469517,
-0.028823932632803917,
0.08852501958608627,
0.016098253428936005,
0.022831793874502182,
-0.059524647891521454,
0.014578086324036121,
0.0043140375055372715,
-0.02725420892238617,
-0.04615682363510132,
-0.01416885294020176,
0.05612924322485924,
0.013652652502059937,
-0.0011935371439903975,
0.043024756014347076,
0.008270843885838985,
-0.02205176092684269,
-0.00028289048350416124,
0.028032483533024788,
-0.045538678765296936,
0.030240284278988838,
-0.032520342618227005,
0.02502361312508583,
0.018736988306045532,
0.0031950748525559902,
0.010773621499538422,
-0.006522546522319317,
0.005713541526347399,
0.03151751309633255,
0.030731599777936935,
-0.0022984913084656,
0.019164949655532837,
0.0493176095187664,
-0.028478553518652916,
0.015087093226611614,
0.026084311306476593,
-0.019492512568831444,
0.006038481369614601,
0.04610389098525047,
-0.019266437739133835,
-0.01928228698670864,
0.0078018661588430405,
0.0027606647927314043,
0.04070628061890602,
-0.00858877319842577,
0.003935236483812332,
-0.010678274556994438,
-0.000055059557780623436,
-0.02108743041753769,
0.054969970136880875,
0.01352642197161913,
-0.029834900051355362,
-0.05643843486905098,
0.006045408546924591,
-0.036286428570747375,
-0.03031758777797222,
-0.08710511028766632,
-0.02061663568019867,
-0.01564229093492031,
-0.034452278167009354,
0.022853918373584747,
-0.010092342272400856,
-0.0033449202310293913,
-0.009447896853089333,
0.060488492250442505,
0.04721973091363907,
0.019909417256712914,
-0.015400969423353672,
0.022496892139315605,
-0.03293916955590248,
-0.0221223346889019,
-0.000648883287794888,
0.025329647585749626,
-0.018995322287082672,
-0.04749399051070213,
0.019739443436264992,
0.021937664598226547,
-0.029368776828050613,
-0.021936941891908646,
-0.011347053572535515,
0.05377735197544098,
0.00521157868206501,
-0.0870760977268219,
-0.07907018065452576,
0.06777502596378326,
-0.03459739685058594,
-0.025291714817285538,
-0.08259176462888718,
-0.012215263210237026,
0.038961075246334076,
0.06506503373384476,
-0.00236327713355422,
-0.013604364357888699,
0.0013531092554330826,
0.05000302195549011,
0.014802846126258373,
0.008508596569299698,
-0.030257482081651688,
-0.000263511756202206,
-0.03134912624955177,
0.004857844207435846,
-0.08261609077453613,
0.030181696638464928,
0.00939090270549059,
0.003813449526205659,
-0.009616510011255741,
0.02743295207619667,
-0.030749037861824036,
0.05217326059937477,
-0.013549495488405228,
-0.016174258664250374,
-0.02347375825047493,
0.06668549031019211,
-0.022619882598519325,
-0.015558102168142796,
0.023425545543432236,
0.01667381264269352,
0.012256207875907421,
0.012867962941527367,
0.00826486386358738,
0.05963771045207977,
-0.02433754689991474,
0.014334787614643574,
-0.041999008506536484,
-0.007751777768135071,
0.0025339857675135136,
-0.05268728733062744,
-0.024566253647208214,
-0.024296117946505547,
-0.0022279820404946804,
-0.01216926146298647,
0.06931661069393158,
-0.010000077076256275,
0.0004844224895350635,
0.042146947234869,
-0.04614197090268135,
-0.0019163194810971618,
-0.06669547408819199,
0.05013546347618103,
0.028518924489617348,
-0.028549274429678917,
0.02585502341389656,
0.0369383804500103,
0.05064353719353676,
-0.010942806489765644,
-0.012357337400317192,
0.0068002063781023026,
0.006824756506830454,
0.018190769478678703,
-0.007071486674249172,
0.05986471846699715,
0.04484572261571884,
0.01928270421922207,
0.015511774457991123,
0.051210541278123856,
0.009043097496032715,
-0.04944213107228279,
0.01375480368733406,
-0.03855165094137192,
0.0318295881152153,
0.0019080638885498047,
-0.015743674710392952,
0.035190481692552567,
0.0032823316287249327,
0.02471964620053768,
0.06683766096830368,
-0.019691146910190582,
0.05364960804581642,
0.009720731526613235,
0.01103976834565401,
0.02602236531674862,
0.056245140731334686,
0.0042031388729810715,
-0.0003992182028014213,
-0.0003090064274147153,
-0.00765962852165103,
-0.03588353469967842,
-0.01702282205224037,
0.024274641647934914,
0.058951377868652344,
-0.0510975643992424,
0.019428595900535583,
0.061691030859947205,
0.023434996604919434,
0.010167133063077927,
-0.005749971140176058,
-0.028507821261882782,
-0.06269055604934692,
0.01807834766805172,
0.006501144263893366,
0.02246711775660515,
-0.0021954600233584642,
-0.013046440668404102,
0.02624993398785591,
0.02973710186779499,
-0.002360249636694789,
-0.02324928715825081,
-0.013182261027395725,
0.017933791503310204,
0.009083263576030731,
0.012636075727641582,
-0.024701250717043877,
0.01213856041431427,
0.02513340301811695,
0.02876276895403862,
0.004705891478806734,
-0.005319762509316206,
0.01909445971250534,
-0.04216063767671585,
-0.01627466082572937,
0.006484151817858219,
-0.011879283003509045,
-0.02696271240711212,
-0.005777597427368164,
0.042101357132196426,
-0.036002032458782196,
-0.01556677557528019,
-0.010711669921875,
-0.0040422664023935795,
-0.02887655608355999,
-0.03386465460062027,
0.006767261307686567,
0.04035656154155731,
0.024244681000709534,
-0.040751636028289795,
-0.000655005278531462,
0.028968313708901405,
-0.005096275359392166,
-0.0034521701745688915,
0.03264717757701874,
-0.005096990615129471,
0.04196006804704666,
-0.04355793073773384,
-0.021665336564183235,
-0.007579976227134466,
0.010622784495353699,
0.02013714425265789,
0.027821553871035576,
-0.030166001990437508,
-0.06509031355381012,
-0.004898415878415108,
-0.05841365084052086,
-0.005352586507797241,
-0.005945952143520117,
-0.008933175355196,
0.051313936710357666,
-0.031626470386981964,
-0.021667059510946274,
-0.007020839489996433,
-0.04938745126128197,
-0.07342645525932312,
-0.041474975645542145,
-0.0014603122835978866,
-0.00032339245080947876,
-0.008540975861251354,
0.028444454073905945,
0.058147188276052475,
-0.0480756051838398,
-0.012062986381351948,
-0.05924198776483536,
-0.02913137711584568,
0.002559628337621689,
-0.013231541961431503,
0.04803892597556114,
-0.022905778139829636,
-0.030545353889465332,
0.07645513862371445,
0.029327042400836945,
-0.033780019730329514,
-0.0014576722169294953,
-0.0406532920897007,
-0.022711774334311485,
-0.02984659932553768,
0.04629397392272949,
0.023152537643909454,
-0.039000146090984344,
-0.01295385044068098,
0.030882904306054115,
0.031121550127863884,
0.001058119349181652,
-0.010422135703265667,
-0.005790588911622763,
0.048220857977867126,
0.01842508465051651,
0.00408135773614049,
0.04691952094435692,
0.006943375803530216,
0.003795722033828497,
0.024908190593123436,
-0.005717657972127199,
0.02696731686592102,
0.006515626795589924,
-0.07128656655550003,
0.07416249811649323,
-0.0341944582760334,
0.053634002804756165,
-0.03015366941690445,
0.04477730765938759,
0.019072744995355606,
0.0015683528035879135,
0.001236903015524149,
0.02452649548649788,
0.03807569667696953,
-0.002109476365149021,
-0.01509444136172533,
0.03350001573562622,
0.04654814302921295,
-0.007495523896068335,
0.0009786194423213601,
0.012328379787504673,
-0.006418957374989986,
0.012079179286956787,
-0.0007109528523869812,
-0.004341988358646631,
0.03315509110689163,
0.035033661872148514,
-0.02291267178952694,
0.03749599680304527,
-0.03268318623304367,
-0.02594553679227829,
-0.05533312261104584,
-0.010445657186210155,
-0.029521292075514793,
0.0027291500009596348,
0.011175347492098808,
0.060157664120197296,
0.0018657298060134053,
0.01641402393579483,
-0.00019511273421812803,
0.003643731353804469,
-0.08210569620132446,
0.035157281905412674,
-0.06558051705360413,
-0.02624387852847576,
-0.0016586316050961614,
0.00458123255521059,
0.008806469850242138,
0.004960843827575445,
-0.025166084989905357,
-0.02093767374753952,
-0.000395626004319638,
-0.02742956019937992,
0.0058955359272658825,
-0.022864291444420815,
-0.04255026578903198,
0.003539998782798648,
0.010699240490794182,
0.050155673176050186,
-0.0734737291932106,
0.039509959518909454,
0.03427218645811081,
-0.026464952155947685,
-0.006991444155573845,
-0.014232831075787544,
0.014572658576071262,
0.03253564238548279,
-0.009844549931585789,
0.025870753452181816,
0.01250598393380642,
-0.037127986550331116,
-0.004525379277765751,
0.05219191685318947,
0.023622635751962662,
-0.02038070745766163,
-0.03255728632211685,
-0.02467985451221466,
-0.07432430982589722,
-0.039461590349674225,
0.020697548985481262,
0.04138294234871864,
-0.002537286141887307,
0.01625634729862213,
0.0408036932349205,
0.028993044048547745,
0.012904045172035694,
0.02020815759897232,
0.029488878324627876,
0.029118435457348824,
-0.02862330712378025,
-0.05358292534947395,
-0.009628978557884693,
-0.022731687873601913,
-0.009400859475135803,
0.009736256673932076,
-0.02554730325937271,
-0.02487974241375923,
0.009546778164803982,
0.02257399633526802,
0.03172888606786728,
0.005570109933614731,
-0.007718118838965893,
-0.02864087000489235,
0.031232362613081932,
-0.025974152609705925,
0.0021873093210160732,
0.019968576729297638,
0.018484538421034813,
0.04262981191277504,
0.024321429431438446,
0.009076236747205257,
-0.07445211708545685,
-0.005147049203515053,
0.01861259900033474,
0.040753401815891266,
-0.025014422833919525,
0.009172583930194378,
-0.05098698288202286,
-0.04943811148405075,
0.027714377269148827,
0.0054781134240329266,
0.047975536435842514,
0.00970213022083044,
-0.007775766309350729,
-0.00031190740992315114,
-0.023711305111646652,
-0.028860457241535187,
0.018605371937155724,
-0.0013369674561545253,
-0.004331424832344055,
-0.0316956527531147,
0.02053214982151985,
-0.04306513071060181,
0.0023942517582327127,
0.00915867742151022,
0.027248498052358627,
-0.01096576452255249,
0.028400540351867676,
-0.014275137335062027,
0.008555962704122066,
-0.043979063630104065,
-0.07616178691387177,
0.004484438803046942,
-0.003037702525034547,
0.0126412408426404,
0.03832060098648071,
-0.019083483144640923,
-0.03041069768369198,
0.000817707390524447,
0.016860399395227432,
0.029715340584516525,
-0.006112196948379278,
-0.013428440317511559,
0.022160205990076065,
0.019626427441835403,
-0.035336609929800034,
0.025647960603237152,
0.04756312444806099,
-0.026143254712224007,
-0.06129177659749985,
-0.023889951407909393,
0.022259270772337914,
-0.019837455824017525,
0.005653744097799063,
-0.04439195245504379,
0.02512102574110031,
-0.025155143812298775,
0.024438150227069855,
-0.006000457797199488,
0.03417225554585457,
-0.03454824164509773,
-0.012177227064967155,
0.01131419651210308,
0.031229738146066666,
0.005995320156216621,
0.021332021802663803,
-0.014022803865373135,
0.04399888589978218,
-0.0005497375386767089,
-0.04833724722266197,
-0.004712173715233803,
0.0375690832734108,
0.007466552779078484,
-0.006783843971788883,
-0.005676444619894028,
0.010023938491940498,
-0.012446925044059753,
-0.03196278214454651,
-0.03172958642244339,
-0.032451312988996506,
0.031126204878091812,
-0.02945668250322342,
-0.02962547354400158,
0.006985396146774292,
-0.021380919963121414,
-0.007885966449975967,
0.03542390465736389,
-0.02545427717268467,
-0.008032959885895252,
-0.027640683576464653,
0.010008998215198517,
0.006932381074875593,
0.004012873861938715,
-0.08504492044448853,
-0.024581244215369225,
-0.010706841014325619,
-0.003370008897036314,
-0.003586363745853305,
-0.024545464664697647,
-0.010338159278035164,
-0.009565675631165504,
-0.03658917546272278,
-0.011607921682298183,
0.03802868351340294,
-0.0000922233666642569,
0.025512421503663063,
0.0019990061409771442,
-0.023354757577180862,
0.020138666033744812,
-0.0037234320770949125,
-0.017381832003593445,
0.0019936002790927887,
-0.011845597997307777,
-0.01664878986775875,
0.001282850163988769,
0.06370024383068085,
-0.03715013712644577,
0.025040213018655777,
0.007652300409972668,
0.011358979158103466,
0.0017831956502050161,
0.0030247762333601713,
0.01046888716518879,
0.054966144263744354,
-0.00943695567548275,
-0.018603112548589706,
-0.011401773430407047,
0.004802416544407606,
0.006965441629290581,
0.03844248503446579,
0.01259492989629507,
-0.010085002519190311,
0.011331077665090561,
-0.032571785151958466,
0.024687720462679863,
-0.0030306780245155096,
0.003162747947499156,
-0.0023077966179698706,
0.07826703786849976,
0.040247075259685516,
-0.048327621072530746,
-0.02351144514977932,
-0.01009037159383297,
0.012345433235168457,
-0.018618810921907425,
-0.010777235962450504,
-0.0250789113342762,
0.019243493676185608,
-0.03622322902083397,
-0.013436703011393547,
-0.005705098621547222,
0.039614900946617126,
0.061891403049230576,
-0.03303339704871178,
0.04342212900519371,
0.0005603525787591934,
-0.005635908339172602,
-0.013444526121020317,
-0.053105130791664124,
0.029105262830853462,
0.004490911029279232,
0.024443069472908974,
0.023157969117164612,
-0.03240152820944786,
0.002654497278854251,
0.04926824942231178,
0.03891696035861969,
-0.023691654205322266,
-0.00955135002732277,
0.03551480174064636,
0.010248531587421894,
-0.005258564371615648,
-0.00928759016096592,
-0.05390710383653641,
0.03399940952658653,
-0.03867773339152336,
0.05617699399590492,
-0.016480866819620132,
-0.02053667977452278,
0.032650917768478394,
0.0025733388029038906,
0.03056904301047325,
-0.03400137275457382,
-0.02684282511472702,
-0.018668264150619507,
0.0207559484988451,
-0.006064504850655794,
0.00909724086523056,
-0.057279206812381744,
0.015271393582224846,
0.01883472129702568,
0.026242557913064957,
-0.009764496237039566,
-0.0007533085299655795,
-0.07045803964138031,
-0.022693246603012085,
-0.013692003674805164,
-0.03998810052871704,
0.025516565889120102,
-0.006339814513921738,
-0.05896487087011337,
0.042649608105421066,
0.0005007055005989969,
0.03744751214981079,
-0.010000981390476227,
-0.0034251874312758446,
0.0022317899856716394,
0.058666642755270004,
0.01900741085410118,
0.018379392102360725,
-0.019542459398508072,
0.018142294138669968,
0.14645524322986603,
0.03701123967766762,
-0.004842071328312159,
-0.05637052655220032,
0.015030186623334885,
-0.018610412254929543,
0.016602830961346626,
-0.005889733321964741,
-0.0012466681655496359,
-0.0036230182740837336,
-0.0034530709963291883,
0.040306899696588516,
0.07034613937139511,
0.0021870669443160295,
-0.040648944675922394,
0.030170317739248276,
-0.028538351878523827,
-0.04655076935887337,
-0.0042715477757155895,
0.024095185101032257,
-0.03282991051673889,
0.021606765687465668,
-0.020841659978032112,
0.03640821576118469,
-0.058496590703725815,
-0.014731911942362785,
-0.00928419828414917,
-0.012932900339365005,
-0.0035098411608487368,
0.0009586098021827638,
-0.05635944381356239,
0.019265659153461456,
0.027582719922065735,
-0.00030267005786299706,
-0.061750538647174835,
0.034646354615688324,
0.01474569458514452,
-0.004220242146402597,
0.02432565949857235,
0.024057256057858467,
-0.0021336476784199476,
0.03046468086540699,
0.02287224866449833,
-0.018994195386767387,
-0.05127738416194916,
0.030579790472984314,
-0.01742781326174736,
0.029663408175110817,
-0.013344432227313519,
0.041143711656332016,
0.0377526693046093,
0.000832141435239464,
0.015020412392914295,
-0.04560994729399681,
0.0074745845049619675,
0.010318613611161709,
0.01882779411971569,
-0.031378742307424545,
-0.006282944232225418,
-0.020086808130145073,
0.008217447437345982,
-0.0018729089060798287,
-0.005349339451640844,
-0.0009186429088003933,
-0.015432333573698997,
-0.008274228312075138,
0.006075437180697918,
0.05654539912939072,
-0.042655881494283676,
-0.03967396169900894,
-0.03110497258603573,
-0.018158555030822754,
-0.043880559504032135,
-0.0034121109638363123,
0.0003864095197059214,
0.04537899047136307,
0.03355489298701286,
-0.006195484660565853,
-0.005067920777946711,
-0.04925667494535446,
-0.08792988955974579,
0.03657037392258644,
-0.032740529626607895,
0.025251705199480057,
-0.018425647169351578,
-0.00198624306358397,
0.04843256622552872,
0.04483228176832199,
-0.03462772071361542,
0.026019403710961342,
-0.015876131132245064,
0.030366431921720505,
0.028269795700907707,
-0.020669717341661453,
-0.024835899472236633,
-0.003982621245086193,
-0.041496071964502335,
-0.023657668381929398,
-0.010055952705442905,
0.01199103519320488,
0.020944569259881973,
-0.002013007178902626,
0.017903326079249382,
0.016975771635770798,
0.01614762656390667,
0.004801291972398758,
0.05751754716038704,
-0.04420877993106842,
0.01031671091914177,
0.025745544582605362,
0.0057804943062365055,
-0.026401253417134285,
-0.05345449596643448,
-0.00979777704924345,
-0.009224246256053448,
-0.0061131310649216175,
0.07608695328235626,
-0.04461340233683586,
0.00887763686478138,
-0.025565799325704575,
0.027936328202486038,
-0.036754246801137924,
-0.019733915105462074,
-0.056537412106990814,
-0.022954681888222694,
0.00796989444643259,
-0.016290588304400444,
0.017269372940063477,
0.027157500386238098,
0.007122979499399662,
0.038043271750211716,
0.02029457315802574,
0.010629789903759956,
-0.0033621718175709248,
-0.028098328039050102,
0.021578025072813034,
0.006332618650048971,
0.05175948515534401,
-0.0071748970076441765,
-0.04251508787274361,
0.058001477271318436,
-0.03812147676944733,
-0.08568709343671799,
0.024103796109557152,
-0.013854525983333588,
0.013812476769089699,
0.003859997959807515,
0.0011451169848442078,
0.006190945859998465,
0.02380303665995598,
-0.05167146399617195,
-0.0024041878059506416,
0.00977635383605957,
-0.03998951613903046,
0.03550077974796295,
-0.01959710195660591,
0.016885824501514435,
-0.004160699434578419,
0.018193630501627922,
0.015690980479121208,
0.05538206547498703,
-0.014182288199663162,
-0.01744699478149414,
-0.0015460364520549774,
-0.03358881175518036,
0.029460927471518517,
0.0036468696780502796,
0.026448529213666916,
0.013970046304166317,
0.05826651677489281,
-0.04736243188381195,
0.00633896654471755,
0.042485855519771576,
0.026283159852027893,
-0.10870333760976791,
-0.01666463352739811,
-0.01970723457634449,
0.0006649576826021075,
0.019204653799533844,
-0.06064369156956673,
-0.004467724822461605,
0.007082381751388311,
-0.0669364482164383,
0.05674043670296669,
-0.03439228609204292,
-0.019778987392783165,
-0.024868212640285492,
0.009086109697818756,
0.012551591731607914,
0.045038238167762756,
0.005638753529638052,
0.052431728690862656,
-0.0027705819811671972,
0.0017618027050048113,
0.015843892470002174,
0.025309361517429352,
0.017116202041506767,
-0.0066827996633946896,
0.020521171391010284,
-0.0003882212331518531,
0.005810896400362253,
0.013544928282499313,
-0.039499156177043915,
0.03193749114871025,
-0.022291487082839012,
0.03933526575565338,
-0.044523272663354874,
0.02034056931734085,
0.007205970119684935,
0.038342904299497604,
0.007410742808133364,
-0.049867600202560425,
0.007754627149552107,
0.014655817300081253,
0.026436753571033478,
0.0356704518198967,
0.004534042440354824,
0.027753790840506554,
0.039010632783174515,
-0.04573408514261246,
-0.006762670818716288,
0.00869019329547882,
-0.0033196613658219576,
0.00835304707288742,
0.008806337602436543,
0.010564814321696758,
0.00003683192699099891,
0.01830410026013851,
0.053788863122463226,
-0.0449393056333065,
-0.004281969275325537,
0.011473647318780422,
0.025348927825689316,
-0.012535023503005505,
-0.0017860959051176906,
0.0443953275680542,
0.004454415291547775,
0.012403524480760098,
-0.010455655865371227,
0.016436545178294182,
-0.06059833616018295,
-0.01903573051095009,
-0.009170453064143658,
-0.02400686778128147,
-0.04302578419446945,
-0.061591435223817825,
-0.04962794855237007,
0.00007098042260622606,
0.04463186115026474,
0.014412732794880867,
-0.025670183822512627,
-0.06436865031719208,
-0.02755318395793438,
-0.05820140987634659,
0.02215052954852581,
-0.015261825174093246,
0.01765141822397709,
-0.01218707486987114,
-0.013031783513724804,
-0.02590279094874859,
-0.032808586955070496,
0.05558706447482109,
0.03182979300618172,
-0.0029940728563815355,
0.013924140483140945,
0.009369533509016037,
0.03841360658407211,
-0.03732163459062576,
0.026534607633948326,
-0.035349391400814056,
0.02108149044215679,
0.005399308633059263,
-0.027647607028484344,
0.01098501868546009,
0.005758332554250956,
0.0020500761456787586,
-0.01883729174733162,
-0.001603095792233944,
0.014686214737594128,
-0.049970295280218124,
0.04175524041056633,
0.029319128021597862,
-0.0185835063457489,
0.10775066167116165,
-0.009818780235946178,
0.014935482293367386,
0.02872631698846817,
-0.022197356447577477,
-0.05738961324095726,
0.013994431123137474,
-0.01631626859307289,
-0.03406281769275665,
0.0011879714438691735,
0.03022976778447628,
0.029077166691422462,
-0.033107172697782516,
-0.043231673538684845,
0.05538327246904373,
-0.04371478036046028,
-0.002036190824583173,
-0.0195468757301569,
0.020455513149499893,
0.05567650496959686,
-0.014422964304685593,
0.003793788142502308,
0.0335925817489624,
0.044074755162000656,
0.002642516978085041,
0.06490205228328705,
0.0406046137213707,
0.006100064143538475,
-0.022493546828627586,
0.04803283512592316,
-0.0295794066041708,
0.003434582380577922,
0.007071082480251789,
0.023324906826019287,
-0.020124312490224838,
-0.014229902066290379,
0.017413383349776268,
-0.038977108895778656,
0.07028238475322723,
0.008415563963353634,
0.005290834233164787,
0.054308969527482986,
-0.03149964660406113,
0.027696950361132622,
-0.020876478403806686,
-0.016730457544326782,
-0.03959612548351288,
-0.006059690378606319,
0.049472659826278687,
0.0384826734662056,
-0.006691078655421734,
-0.03136429935693741,
-0.022798504680395126,
-0.0058431304059922695,
0.028569374233484268,
-0.016362186521291733,
0.0019753635860979557,
0.03254054859280586,
0.02530175819993019,
-0.009229343384504318,
0.018909620121121407,
-0.042615797370672226,
-0.03683089092373848,
0.03614127263426781,
0.046392038464546204,
0.059870678931474686,
0.025711387395858765,
0.0035593623761087656,
-0.026911666616797447,
0.034346431493759155,
-0.04703903570771217,
-0.029701082035899162,
-0.029692159965634346,
0.04396923631429672,
-0.005692308768630028,
-0.0034848537761718035
] |
<p>The book I am reading takes the unjustified step $$e^{-\frac{i}{\hbar}\vec{p}\cdot\vec{r}}f(\vec{p}) = f(\frac{\hbar}{i}\vec{\nabla})e^{-\frac{i}{\hbar}\vec{p}\cdot\vec{r}}$$</p>
<p>and similarly, he uses elsewhere $$e^{-\frac{i}{\hbar}\vec{p}\cdot\vec{r}}g(\vec{r}) = g(i\hbar\vec{\nabla}_p)e^{-\frac{i}{\hbar}\vec{p}\cdot\vec{r}}$$</p>
<p>I have a gut feeling this follows somehow from the commutation relation $[r^i,p_j] = i\hbar\delta^i_j$ but I cannot justify this. </p>
<p>Anyhow, the book has not introduced the standard commutation relations, and is working only with the fact that $\phi(\vec{p},t)$ and $\psi(\vec{r},t)$ are Fourier transforms of each other, and $f(\vec{p})$ and $g(\vec{r})$ are analytic. </p>
<p>Could someone give me a hint?</p>
| 9,627 |
[
0.007244567386806011,
-0.02684028260409832,
0.000002264795966766542,
-0.022781888023018837,
0.0372980535030365,
-0.01931176520884037,
-0.016726095229387283,
-0.023246819153428078,
-0.013594070449471474,
-0.01143217645585537,
-0.006262798327952623,
0.024264665320515633,
0.06046181544661522,
0.017742186784744263,
0.01872924342751503,
0.019049834460020065,
-0.024063657969236374,
-0.0071006109938025475,
0.00812216941267252,
-0.0054057082161307335,
-0.006718362215906382,
0.04268117994070053,
-0.00398575235158205,
-0.008314099162817001,
-0.010331754572689533,
0.01615677960216999,
-0.017458854243159294,
0.021610092371702194,
-0.030166778713464737,
0.0424637608230114,
-0.019354868680238724,
0.006559336092323065,
-0.01705166883766651,
0.021829642355442047,
-0.009632980450987816,
0.030521368607878685,
-0.03635416179895401,
-0.039473921060562134,
-0.024632003158330917,
0.005442015826702118,
-0.05809292197227478,
0.008464695885777473,
0.0068010869435966015,
0.04642508178949356,
0.0008068269235081971,
0.0521392859518528,
0.019225606694817543,
0.02496897615492344,
0.03797758370637894,
-0.06052745133638382,
0.0711585134267807,
0.02344750426709652,
0.002377693774178624,
0.013642662204802036,
-0.026899848133325577,
0.034905582666397095,
0.0716041773557663,
0.04791795834898949,
-0.004197431728243828,
-0.08455732464790344,
-0.019463930279016495,
-0.03010467253625393,
-0.04422691464424133,
-0.017623571678996086,
-0.005302354693412781,
-0.032127875834703445,
0.02917409874498844,
-0.034593526273965836,
0.03549696505069733,
-0.01381240040063858,
0.020091921091079712,
0.018258145079016685,
0.02723289467394352,
-0.04638231545686722,
0.030017703771591187,
-0.012111654505133629,
-0.002435299102216959,
0.03809269890189171,
0.009923486039042473,
-0.001929299789480865,
0.018608050420880318,
0.010681909509003162,
0.024484550580382347,
0.03940105810761452,
0.007103608921170235,
-0.0003405243915040046,
0.08780226856470108,
0.012791493907570839,
0.011165984906256199,
0.049183014780282974,
0.0014411318115890026,
0.008485273458063602,
-0.0018977121217176318,
0.001884429482743144,
-0.005578054580837488,
0.047898612916469574,
0.0011597431730479002,
0.015299927443265915,
0.00713334558531642,
-0.02738078124821186,
-0.026966718956828117,
-0.0104210888966918,
0.028679056093096733,
0.030083924531936646,
0.001376370433717966,
-0.0008365648100152612,
-0.04377473145723343,
0.02468799613416195,
0.0046988786198198795,
-0.038768086582422256,
-0.054873425513505936,
0.02927102893590927,
-0.016854260116815567,
0.02068512700498104,
-0.017371531575918198,
-0.0039016148075461388,
0.025999248027801514,
0.010877775028347969,
0.03776295855641365,
0.07129248231649399,
0.042674291878938675,
-0.031081650406122208,
0.007261374965310097,
-0.029217524453997612,
-0.07011774182319641,
0.010616377927362919,
0.050941284745931625,
-0.010502346791327,
-0.04363621026277542,
0.012890934944152832,
0.0009463540627621114,
0.032736632972955704,
-0.01220556441694498,
0.02652444876730442,
-0.033412668853998184,
-0.0011506004957482219,
-0.09457989037036896,
-0.056477971374988556,
0.02755938284099102,
-0.04892944544553757,
0.01306016743183136,
-0.06523958593606949,
0.0012246080441400409,
0.02774154208600521,
0.10283501446247101,
-0.023253681138157845,
0.007373250555247068,
-0.011702482588589191,
0.0401855930685997,
-0.006435519549995661,
0.014930003322660923,
-0.05734318122267723,
-0.01789921335875988,
-0.02228321135044098,
-0.016654346138238907,
-0.04989096149802208,
0.057391997426748276,
0.037034325301647186,
0.014839130453765392,
0.006719865370541811,
0.06356938183307648,
-0.0061711883172392845,
-0.005858715157955885,
-0.03264184668660164,
-0.0068711088970303535,
-0.022726714611053467,
0.06001969426870346,
0.01074646133929491,
0.013977198861539364,
0.0076435827650129795,
0.013633585534989834,
0.031632669270038605,
-0.006655056495219469,
0.020497288554906845,
0.0206613726913929,
-0.06070621311664581,
-0.02134871855378151,
-0.04107976332306862,
-0.011908210813999176,
-0.006158816162496805,
0.008879845961928368,
-0.02643544226884842,
-0.023476513102650642,
0.008973914198577404,
-0.01253666914999485,
0.013524442911148071,
-0.002262087306007743,
0.010056357830762863,
-0.004901905078440905,
-0.03972013667225838,
0.02652408927679062,
-0.0561397522687912,
0.009800062514841557,
0.01414554100483656,
-0.0568537712097168,
0.07401421666145325,
-0.001621450181119144,
0.03850260004401207,
0.030458366498351097,
-0.09902961552143097,
0.02887122891843319,
-0.0006032805540598929,
-0.0029255920089781284,
-0.023986347019672394,
0.008491329848766327,
0.048370108008384705,
0.030186720192432404,
0.045572832226753235,
0.050092846155166626,
-0.004872594494372606,
-0.05166509374976158,
0.025863319635391235,
-0.018325773999094963,
0.016587523743510246,
0.041169244796037674,
-0.009876850992441177,
0.015232945792376995,
0.00010591294994810596,
-0.0010450002737343311,
0.01952340453863144,
-0.05489586293697357,
0.01804007962346077,
0.047209519892930984,
0.04886825010180473,
-0.0015668037813156843,
0.03982342407107353,
0.00982167012989521,
0.04113612323999405,
0.005272572860121727,
-0.03239237144589424,
-0.02552412822842598,
0.005301571451127529,
0.011063973419368267,
0.044503699988126755,
-0.03242101892828941,
-0.007198295556008816,
0.0016591373132541776,
0.07070056349039078,
0.03689570724964142,
0.02326309122145176,
-0.0017182005103677511,
-0.05803774297237396,
0.03059415891766548,
0.012606431730091572,
0.005925784818828106,
-0.008795175701379776,
0.04426654428243637,
-0.04020505025982857,
0.017517242580652237,
-0.0044053103774785995,
-0.030427705496549606,
0.021473145112395287,
-0.010411008261144161,
0.019324641674757004,
0.02940439060330391,
-0.0007121976232156157,
0.03796927258372307,
-0.01230026688426733,
0.017718303948640823,
0.0448312871158123,
-0.02282821200788021,
-0.028678908944129944,
-0.038189806044101715,
-0.01776961423456669,
0.028213145211338997,
-0.0011137445690110326,
-0.03844141960144043,
-0.005614599213004112,
0.008673084899783134,
-0.09675654023885727,
-0.006537518929690123,
-0.02537309192121029,
0.0028623677790164948,
-0.039180900901556015,
-0.0013901820639148355,
0.0069397930055856705,
0.04069076478481293,
0.057123515754938126,
-0.023212317377328873,
-0.011777626350522041,
0.03152506425976753,
-0.005683815572410822,
0.027971472591161728,
0.01281016692519188,
-0.044620271772146225,
0.030700473114848137,
-0.04581461101770401,
-0.019496876746416092,
0.0589938722550869,
-0.021404484286904335,
0.019688911736011505,
-0.011980985291302204,
0.0005506282905116677,
-0.03762643039226532,
-0.014511135406792164,
0.0010578823275864124,
0.05177273228764534,
-0.062182433903217316,
-0.009492950513958931,
0.009914927184581757,
-0.019677456468343735,
-0.010090510360896587,
0.022174710407853127,
-0.024918893352150917,
-0.017330879345536232,
0.000538127264007926,
-0.01960117556154728,
-0.023554686456918716,
-0.02156810648739338,
0.02661970444023609,
0.022111214697360992,
-0.01919572986662388,
-0.016659434884786606,
-0.044826801866292953,
-0.0390058197081089,
0.012126059271395206,
0.02450733631849289,
0.01722060889005661,
0.017544081434607506,
-0.006598505657166243,
0.07918933779001236,
-0.009464072063565254,
-0.03814868628978729,
0.0019096819451078773,
0.02780584990978241,
-0.008534513413906097,
-0.016493037343025208,
0.003538184566423297,
0.06923113018274307,
0.006905571557581425,
0.041018761694431305,
0.010887588374316692,
0.005133374594151974,
0.028425313532352448,
-0.0019443562487140298,
-0.008921502158045769,
0.06341094523668289,
-0.028106678277254105,
0.01311550009995699,
0.05557926371693611,
-0.019660180434584618,
0.004240768495947123,
-0.03223462402820587,
-0.0015181933995336294,
-0.007546405773609877,
0.03441747650504112,
-0.04424433782696724,
0.02630160003900528,
0.03130285069346428,
0.0033285096287727356,
-0.03111116960644722,
0.04501323774456978,
-0.0077629899606108665,
-0.028063496574759483,
-0.030655037611722946,
0.018921855837106705,
0.04283233359456062,
-0.023539122194051743,
0.031007403507828712,
0.021116094663739204,
0.012983848340809345,
-0.04197082296013832,
-0.036653757095336914,
-0.011312742717564106,
0.001598720089532435,
0.06286483258008957,
-0.031870320439338684,
-0.04443853348493576,
0.06139253079891205,
0.0032061096280813217,
0.030565356835722923,
-0.04059172794222832,
-0.0299923587590456,
0.009599649347364902,
-0.040458839386701584,
0.04685336723923683,
-0.019948681816458702,
0.06638579070568085,
-0.0006567980744875968,
0.061332955956459045,
0.04418429732322693,
0.020061839371919632,
0.03154560178518295,
0.029769238084554672,
-0.07914448529481888,
0.009407010860741138,
-0.021658051759004593,
-0.024128641933202744,
-0.039196163415908813,
-0.016052063554525375,
0.004009665455669165,
-0.021474124863743782,
0.0038498875219374895,
-0.013406905345618725,
-0.05394931510090828,
-0.04622562602162361,
0.039372436702251434,
-0.07385765016078949,
-0.06413594633340836,
-0.0037650533486157656,
0.00908841285854578,
0.04313845932483673,
0.011799556203186512,
0.0031292419880628586,
0.024081900715827942,
-0.017194543033838272,
-0.01605559140443802,
-0.027425691485404968,
0.0016900936607271433,
0.009790677577257156,
0.03365897387266159,
0.001784037216566503,
0.023551205173134804,
0.020854739472270012,
0.023521726951003075,
-0.0057389987632632256,
0.04289381206035614,
0.002640834543853998,
-0.043037980794906616,
-0.0069001843221485615,
-0.026309989392757416,
-0.011362281627953053,
0.019338838756084442,
0.08783940970897675,
0.02182604745030403,
-0.00543606374412775,
0.02176387794315815,
0.014744549058377743,
-0.011551082134246826,
0.023843344300985336,
0.03828476741909981,
0.009864901192486286,
-0.018513571470975876,
-0.02852282114326954,
0.02397371083498001,
0.0182053130120039,
-0.007403420750051737,
0.020489823073148727,
0.011875925585627556,
-0.01245147455483675,
-0.008786235004663467,
0.013539104722440243,
0.04736229032278061,
-0.0025046246591955423,
0.002472434425726533,
-0.00699424697086215,
-0.009965191595256329,
-0.005451029632240534,
-0.018884599208831787,
0.041788432747125626,
0.060358040034770966,
0.06582598388195038,
0.005966306664049625,
-0.0068953391164541245,
-0.06408201903104782,
0.012520327232778072,
0.027021829038858414,
0.01956327259540558,
-0.029517238959670067,
0.010077736340463161,
-0.04984698444604874,
-0.019712984561920166,
0.04022802785038948,
0.005898113828152418,
0.030832381919026375,
-0.022867627441883087,
-0.007460854481905699,
-0.021084312349557877,
-0.06217532977461815,
-0.062175992876291275,
0.01668931357562542,
-0.014426310546696186,
0.018823901191353798,
-0.06669559329748154,
-0.03475575894117355,
-0.05517038330435753,
-0.010405544191598892,
0.017822030931711197,
0.0659000352025032,
0.01629689708352089,
-0.02082817815244198,
-0.029704539105296135,
0.06356575340032578,
-0.029141992330551147,
-0.06079750880599022,
-0.002299829386174679,
0.0026610861532390118,
-0.0024525311309844255,
0.02795773558318615,
-0.019530966877937317,
-0.07003763318061829,
0.028340190649032593,
0.031073808670043945,
-0.017230598255991936,
0.03216997906565666,
-0.03655195236206055,
0.05639951303601265,
0.015181108377873898,
0.004339720122516155,
0.0840921700000763,
0.004688204266130924,
-0.036347389221191406,
-0.014411873184144497,
-0.022518478333950043,
0.04420505836606026,
-0.02485383301973343,
0.024303104728460312,
-0.01983959786593914,
-0.010679217986762524,
-0.03095870651304722,
0.024398209527134895,
0.003534877672791481,
0.025714708492159843,
-0.00799752026796341,
-0.03922806680202484,
-0.004150571767240763,
0.008619495667517185,
-0.06788939237594604,
-0.009602907113730907,
0.027475032955408096,
0.03425849229097366,
0.02329467236995697,
-0.02682816982269287,
0.010956404730677605,
-0.005123544484376907,
0.029443912208080292,
0.035025227814912796,
0.0035478961654007435,
0.04089382290840149,
-0.023570310324430466,
0.01596849225461483,
0.02337563782930374,
-0.06501780450344086,
0.014611011371016502,
-0.03496856987476349,
0.00922725722193718,
0.023946963250637054,
-0.0049289134331047535,
-0.028391888365149498,
-0.013665053993463516,
-0.01490624900907278,
0.03125607222318649,
-0.05800727754831314,
0.007701450027525425,
0.018705086782574654,
-0.01703767478466034,
-0.06061287596821785,
-0.059065837413072586,
0.031271059066057205,
0.005091342143714428,
-0.04085792601108551,
-0.03819839283823967,
0.02223433554172516,
-0.04245718941092491,
-0.021294377744197845,
-0.010070530697703362,
0.018237266689538956,
-0.021246498450636864,
-0.0043303584679961205,
-0.017038540914654732,
0.014741695486009121,
0.019749462604522705,
-0.016749199479818344,
0.0069752163253724575,
0.047910138964653015,
-0.039750564843416214,
-0.012178439646959305,
-0.0009625208913348615,
0.07393497228622437,
0.0045655639842152596,
-0.008469320833683014,
0.012524380348622799,
0.003482684027403593,
0.035281792283058167,
-0.014054324477910995,
-0.03160747513175011,
0.039644356817007065,
0.003634961321949959,
0.015538918785750866,
0.008640474639832973,
-0.019031578674912453,
-0.0039051370695233345,
0.020434992387890816,
-0.01482558436691761,
-0.014197850599884987,
-0.003165127709507942,
-0.04378032684326172,
0.02607254683971405,
-0.01594367064535618,
0.014551145024597645,
0.018711650744080544,
0.05803597345948219,
-0.02847495675086975,
0.004219674039632082,
0.04706166684627533,
0.029228847473859787,
0.00161480822134763,
-0.013112030923366547,
0.03958204761147499,
0.018815746530890465,
-0.024709172546863556,
-0.03419650346040726,
-0.023237574845552444,
-0.050541408360004425,
0.028323810547590256,
0.059896208345890045,
0.037375252693891525,
0.059021610766649246,
0.013350797817111015,
0.009404885582625866,
-0.021647058427333832,
0.01794539950788021,
-0.017754890024662018,
0.015058663673698902,
-0.012868819758296013,
0.022859737277030945,
-0.030153505504131317,
0.024625258520245552,
0.02637776918709278,
0.02538306452333927,
-0.029244162142276764,
-0.01063115056604147,
0.006030984688550234,
0.03562377020716667,
-0.027149882167577744,
-0.020098621025681496,
-0.04440043866634369,
0.04003779590129852,
-0.0439009889960289,
0.06134020537137985,
-0.013047661632299423,
-0.0012660336215049028,
0.018810372799634933,
0.04316005855798721,
0.0035876042675226927,
-0.01603049971163273,
-0.016950001940131187,
-0.02941175177693367,
0.013251534663140774,
0.02702922560274601,
-0.006586235016584396,
-0.009909161366522312,
-0.00232742284424603,
0.04787509888410568,
0.02118990756571293,
0.0224049873650074,
-0.011432647705078125,
-0.03793945163488388,
0.010306142270565033,
-0.04589452967047691,
-0.05568962171673775,
0.021623797714710236,
-0.04037179425358772,
-0.027452724054455757,
0.01360344234853983,
-0.017065024003386497,
0.04191860184073448,
0.014210044406354427,
0.024826616048812866,
-0.004894919227808714,
0.08084560930728912,
0.026788612827658653,
-0.01088204886764288,
0.00994121003895998,
-0.022471170872449875,
0.1258016675710678,
0.04484850540757179,
0.015982596203684807,
-0.023611973971128464,
0.028149019926786423,
-0.03031589649617672,
0.0007892469293437898,
-0.021011797711253166,
0.035058293491601944,
-0.013102355413138866,
0.0021502813324332237,
0.01105616893619299,
0.06609493494033813,
-0.01200809609144926,
-0.032776396721601486,
0.010678818449378014,
-0.07068974524736404,
-0.01959902234375477,
0.008455764502286911,
0.0006887869676575065,
-0.022390039637684822,
-0.00646246038377285,
-0.020595580339431763,
0.012444326654076576,
-0.03339536860585213,
0.021677166223526,
-0.04272059351205826,
-0.026233671233057976,
0.03013523295521736,
0.014415810815989971,
-0.03444765508174896,
-0.002649441361427307,
0.0005379830836318433,
-0.008308058604598045,
-0.006885542534291744,
0.04732208326458931,
0.02276928536593914,
-0.018767070025205612,
0.05886479839682579,
0.028326254338026047,
0.010655933059751987,
0.02082737721502781,
0.01552172377705574,
0.010565304197371006,
-0.025867754593491554,
-0.021790996193885803,
-0.04800772666931152,
0.09920206665992737,
-0.011302381753921509,
0.007147843483835459,
0.0025249221362173557,
-0.018857570365071297,
0.012479298748075962,
-0.053816717118024826,
-0.004144479986280203,
-0.02429032139480114,
-0.003689885837957263,
0.0005531974020414054,
0.0014117159880697727,
-0.049020688980817795,
0.019867675378918648,
0.02653747983276844,
0.01692015677690506,
-0.013040732592344284,
-0.04081420600414276,
0.007715330924838781,
0.0006267763674259186,
0.047101348638534546,
-0.003929872065782547,
-0.00011748578253900632,
-0.008114275522530079,
-0.052865494042634964,
-0.047861866652965546,
-0.042386531829833984,
0.004387646913528442,
0.01713513769209385,
0.0392003171145916,
-0.0004892690922133625,
-0.023397279903292656,
-0.04680299758911133,
-0.08592823147773743,
0.01938932202756405,
0.0039217788726091385,
-0.03671269118785858,
0.002406689105555415,
-0.02519126422703266,
0.010784017853438854,
0.029331017285585403,
-0.005884777754545212,
-0.004774064756929874,
0.0043424093164503574,
0.02735302411019802,
0.054376766085624695,
0.011245089583098888,
-0.057192329317331314,
-0.015626167878508568,
-0.01497990544885397,
0.02218436263501644,
0.0247415229678154,
-0.016987724229693413,
0.02194378338754177,
-0.006484854966402054,
-0.004171230364590883,
0.01708703674376011,
-0.01360990945249796,
-0.009085086174309254,
0.004125839099287987,
-0.03049393557012081,
0.015573541633784771,
0.02916792221367359,
-0.005036205984652042,
-0.049477510154247284,
0.005594591144472361,
-0.02829747088253498,
0.012128118425607681,
-0.03834898769855499,
0.002841903595253825,
-0.030932847410440445,
-0.0005351178115233779,
-0.0213811993598938,
0.029107190668582916,
-0.011208451353013515,
0.00343867065384984,
-0.062147852033376694,
0.044619373977184296,
-0.008380436338484287,
0.008832881227135658,
-0.0331110917031765,
0.03829753398895264,
-0.06259839236736298,
-0.054195720702409744,
0.03819887340068817,
0.0008594286628067493,
-0.01366519182920456,
0.00352731766179204,
0.0004988418659195304,
-0.04620562866330147,
-0.0026670382358133793,
0.009677688591182232,
-0.03379969671368599,
0.040307264775037766,
-0.05047592520713806,
-0.02558707818388939,
0.014031183905899525,
0.037135206162929535,
0.025128884240984917,
-0.006026655901223421,
-0.02048923261463642,
-0.011005307547748089,
0.04052296280860901,
0.013995994813740253,
-0.008177430368959904,
-0.01343568880110979,
-0.05656621605157852,
-0.016685212031006813,
-0.024942155927419662,
0.030220143496990204,
-0.025720719248056412,
0.017442625015974045,
0.025807710364460945,
0.006823696196079254,
-0.0215874332934618,
-0.00018091159290634096,
-0.015854936093091965,
0.01527953241020441,
0.02801235020160675,
0.04987301304936409,
-0.02770158275961876,
0.04633399099111557,
0.031066520139575005,
-0.02218066155910492,
-0.0006402275757864118,
0.008760294876992702,
0.006937454920262098,
-0.0687677189707756,
-0.02821880765259266,
-0.010873367078602314,
-0.006054029334336519,
0.010867016389966011,
-0.0531533919274807,
-0.0025860301684588194,
0.0015175002627074718,
-0.06167667731642723,
0.030706850811839104,
-0.01993529684841633,
-0.0006500673480331898,
-0.028145400807261467,
0.0049700625240802765,
0.000764629163313657,
0.01650119014084339,
0.022020893171429634,
0.027410009875893593,
-0.011825199238955975,
-0.005120305810123682,
-0.001580362324602902,
-0.0144520727917552,
-0.03862735629081726,
0.021765131503343582,
0.003915362525731325,
-0.040124766528606415,
0.023389557376503944,
-0.012902047485113144,
-0.01900746114552021,
0.002690655877813697,
-0.02424348145723343,
-0.012127947993576527,
-0.014271816238760948,
0.049743056297302246,
0.03534708172082901,
0.02676115185022354,
0.006637644022703171,
-0.006787573453038931,
-0.03364596515893936,
-0.014928922057151794,
0.027639115229249,
-0.011270076036453247,
-0.013455906882882118,
-0.015323983505368233,
0.015887221321463585,
-0.022019214928150177,
-0.016777068376541138,
0.03514622524380684,
-0.025250138714909554,
-0.00360201601870358,
0.005072328262031078,
-0.005855203606188297,
0.004503806121647358,
-0.008483123034238815,
0.051208317279815674,
-0.044243939220905304,
0.0006772327469661832,
-0.000019000019165105186,
0.0018260084325447679,
-0.02345183491706848,
0.012592489831149578,
-0.05983741208910942,
-0.04792692884802818,
0.007112239021807909,
0.03448859602212906,
-0.007113132160156965,
-0.0305781327188015,
-0.02944846823811531,
0.01788487657904625,
0.0033881766721606255,
-0.003659446956589818,
-0.04456450045108795,
-0.06237964704632759,
0.00006171352288220078,
0.034113768488168716,
0.014957891777157784,
-0.027838805690407753,
0.011083945631980896,
-0.006850003264844418,
-0.04531921073794365,
0.01684725098311901,
0.036243800073862076,
-0.03894907608628273,
-0.023794138804078102,
-0.05574391037225723,
0.002363271312788129,
0.04854340851306915,
0.06091077998280525,
-0.03160807117819786,
-0.049697745591402054,
0.01944032870233059,
-0.0030669416300952435,
0.03374296426773071,
-0.0709947720170021,
0.013005079701542854,
0.024844668805599213,
-0.005068791564553976,
0.012584591284394264,
0.006199819501489401,
-0.013562140055000782,
0.033662497997283936,
-0.024318719282746315,
-0.007346099242568016,
0.0038242076989263296,
0.01032518595457077,
-0.0786677896976471,
0.028709447011351585,
-0.016651393845677376,
0.018255015835165977,
0.058461789041757584,
0.020692873746156693,
0.0068881576880812645,
0.02694454789161682,
-0.023143220692873,
-0.03087788261473179,
0.023428097367286682,
-0.03850413113832474,
-0.008701341226696968,
0.0200031865388155,
0.027796955779194832,
0.024959782138466835,
-0.025118660181760788,
0.025957070291042328,
0.04099208489060402,
-0.055101677775382996,
-0.01853504404425621,
0.056910887360572815,
0.03041088953614235,
-0.004385131411254406,
0.030513806268572807,
-0.01046469621360302,
0.01936173439025879,
-0.004517359659075737,
0.03493671864271164,
0.055908601731061935,
0.021412694826722145,
0.022421684116125107,
0.014604679308831692,
0.023837927728891373,
-0.02077171392738819,
0.026394495740532875,
0.009605787694454193,
0.039915554225444794,
-0.054249107837677,
0.020116183906793594,
0.0033774934709072113,
-0.01778354123234749,
0.0006080526509322226,
0.06332601606845856,
-0.017775580286979675,
0.08338125795125961,
-0.02313045598566532,
0.02098453976213932,
0.0217419546097517,
0.015612299554049969,
-0.01221906766295433,
0.01700284518301487,
0.045419368892908096,
0.036908458918333054,
-0.00848449021577835,
-0.009976857341825962,
-0.07360050827264786,
0.0002164593170164153,
-0.02119898423552513,
-0.06946411728858948,
-0.011471247300505638,
0.042970649898052216,
-0.027894314378499985,
-0.002460629213601351,
-0.03645538166165352,
-0.00721447728574276,
-0.023643339052796364,
0.011888531967997551,
0.04937219247221947,
0.01815778762102127,
0.0070443227887153625,
0.031835462898015976,
0.002630256349220872,
0.04070844128727913,
-0.05094728246331215,
0.0006108004599809647,
0.008758644573390484,
0.03079714998602867,
-0.007423819042742252,
0.03951524570584297
] |
<p>I know that by Heisenberg's Uncertainty Principle that it is not possible to know the exact values of position and momentum of a particle simultaneously, but can we know the exact values of momentum and velocity of a particle simultaneously? I would think the answer would be no because even if we were 100% certain of the particle's position, we would be completely unsure of the particle's momentum, thus making us also completely unsure of the particle's velocity. Does anyone have any insight into this?</p>
| 9,628 |
[
0.020704222843050957,
-0.039109762758016586,
0.016435867175459862,
-0.025009313598275185,
0.04822799935936928,
-0.014600813388824463,
-0.05014707148075104,
-0.006286825053393841,
-0.01626455783843994,
-0.037307269871234894,
0.022046316415071487,
0.056500330567359924,
0.014703991822898388,
0.011721573770046234,
0.02015576884150505,
0.02800152078270912,
-0.007024131249636412,
-0.013192505575716496,
-0.02395145781338215,
-0.021534118801355362,
-0.004328830633312464,
0.010972420684993267,
0.01869071274995804,
-0.003666398348286748,
0.007499391678720713,
0.0131085105240345,
0.04132482782006264,
0.028302118182182312,
0.019284218549728394,
0.06838443130254745,
0.005053551867604256,
-0.010997959412634373,
0.025051049888134003,
0.05515781790018082,
0.024528710171580315,
-0.02133852243423462,
-0.02721196785569191,
-0.017303908243775368,
-0.04325253143906593,
0.018116632476449013,
-0.055187154561281204,
0.005239713005721569,
-0.0032557854428887367,
0.04964495450258255,
-0.023543812334537506,
0.027198519557714462,
0.009944938123226166,
-0.018424566835165024,
0.05108270421624184,
-0.04018465802073479,
0.0839909017086029,
0.008002041839063168,
0.03293106332421303,
0.005689671263098717,
0.00973720196634531,
0.012744205072522163,
0.08673285692930222,
0.08125853538513184,
-0.010000105015933514,
-0.05187007784843445,
-0.015429450199007988,
-0.003641946939751506,
0.022376544773578644,
-0.040407996624708176,
-0.03235907852649689,
0.02586485631763935,
-0.015034891664981842,
-0.02735629864037037,
0.002170649589970708,
-0.004684623796492815,
-0.007555022370070219,
-0.0003832062939181924,
0.06598297506570816,
-0.01622059941291809,
0.02023952081799507,
-0.05103857070207596,
0.02472774311900139,
0.024921704083681107,
0.027578266337513924,
0.034439388662576675,
0.0014713341370224953,
0.013777483254671097,
0.05013018473982811,
0.03503873199224472,
-0.0011187891941517591,
-0.02091040275990963,
0.030380286276340485,
-0.0078074270859360695,
0.032104432582855225,
0.054601382464170456,
-0.027577389031648636,
0.015837348997592926,
0.02624824456870556,
0.004410888534039259,
-0.028576934710144997,
0.023910345509648323,
0.014794230461120605,
0.04584832862019539,
-0.006072259973734617,
-0.044620759785175323,
0.05151236802339554,
0.00226613599807024,
0.02492336556315422,
0.06402113288640976,
-0.010303760878741741,
-0.01715272292494774,
-0.007048584055155516,
0.02593890018761158,
-0.013534590601921082,
0.0006543066701851785,
0.006406364031136036,
0.030126821249723434,
-0.007185554597526789,
0.00737975537776947,
0.03692231327295303,
-0.021789807826280594,
-0.023123836144804955,
-0.014919023029506207,
0.07088305801153183,
0.05660412088036537,
0.012796743772923946,
-0.05466330051422119,
-0.005954646039754152,
-0.027811694890260696,
-0.06722071766853333,
-0.01205536350607872,
0.017554251477122307,
0.0020590792410075665,
-0.04461301863193512,
0.04146120697259903,
0.016876522451639175,
0.0002339394559385255,
0.026719046756625175,
0.010597556829452515,
0.03707987815141678,
-0.025289561599493027,
-0.10410328954458237,
-0.05172539874911308,
0.025636155158281326,
-0.020625576376914978,
-0.02231977880001068,
-0.09633437544107437,
0.009289337322115898,
0.035607095807790756,
0.056243691593408585,
-0.017038632184267044,
0.02203468792140484,
0.008145219646394253,
0.023076744750142097,
0.016630252823233604,
-0.009998941794037819,
-0.013701053336262703,
0.014401965774595737,
-0.038722675293684006,
0.010801377706229687,
-0.07014688849449158,
0.018129441887140274,
0.03906640782952309,
-0.024813516065478325,
-0.027385162189602852,
0.027604451403021812,
-0.016004670411348343,
-0.0006277046632021666,
0.0011938256211578846,
0.012355773709714413,
-0.028551900759339333,
0.08296076953411102,
0.016747288405895233,
0.00633148243650794,
0.03798574581742287,
0.014466256834566593,
0.022524341940879822,
-0.0014851430896669626,
0.016452400013804436,
0.06518298387527466,
-0.04290077090263367,
-0.05635780468583107,
-0.022612443193793297,
0.027701999992132187,
-0.029681574553251266,
-0.04258163273334503,
-0.04444902762770653,
-0.0003173608856741339,
0.057747431099414825,
-0.009319896809756756,
0.039193201810121536,
0.027782287448644638,
-0.001934545231051743,
-0.037184860557317734,
-0.04249110817909241,
0.020475978031754494,
-0.05246759206056595,
0.00694363284856081,
-0.0017670572269707918,
-0.01697944849729538,
0.04532948508858681,
0.01341535709798336,
0.019940173253417015,
-0.04407721385359764,
-0.038679346442222595,
0.009909503161907196,
0.055036094039678574,
0.0009216499165631831,
-0.02272977866232395,
0.02393978089094162,
0.049624133855104446,
0.03302853927016258,
0.015816161409020424,
0.021338293328881264,
0.008247082121670246,
-0.03906143456697464,
0.007171230390667915,
-0.0006468748324550688,
0.025598816573619843,
0.038564857095479965,
0.001448203343898058,
0.012654404155910015,
0.00012432872608769685,
0.005993611644953489,
0.01540930476039648,
-0.018500059843063354,
0.08615859597921371,
0.02478843368589878,
0.0027382296975702047,
-0.014159702695906162,
0.03545419126749039,
0.033734776079654694,
-0.014020832255482674,
0.010912430472671986,
-0.037792760878801346,
-0.02868296205997467,
-0.003748327260836959,
0.005089242476969957,
0.03294700011610985,
-0.023224737495183945,
0.017163118347525597,
0.01610129326581955,
0.05546842887997627,
0.04178706929087639,
0.054185640066862106,
-0.00936602521687746,
-0.03691574186086655,
-0.01717638596892357,
0.021164437755942345,
-0.00927711557596922,
0.01703977957367897,
0.05103733390569687,
0.03421966731548309,
0.03147947043180466,
-0.024213772267103195,
-0.03290869668126106,
0.03548375144600868,
-0.035061247646808624,
-0.021035555750131607,
0.011771142482757568,
-0.06168645992875099,
0.01167074590921402,
-0.02552904188632965,
0.02955288626253605,
-0.011204555630683899,
-0.009344504214823246,
-0.031137097626924515,
-0.017969967797398567,
-0.02867795154452324,
0.014740349724888802,
0.005343858152627945,
-0.04731852933764458,
0.024007070809602737,
0.009097603149712086,
-0.03412190452218056,
-0.011751568876206875,
-0.01784554123878479,
0.008104083128273487,
0.015707993879914284,
-0.0020522214472293854,
0.05362913757562637,
0.0003055811976082623,
0.03785715624690056,
-0.03002154640853405,
-0.05497433990240097,
-0.0056921252980828285,
-0.06368642300367355,
0.007041906006634235,
0.0010843139607459307,
-0.05405360460281372,
0.043047945946455,
-0.026336776092648506,
-0.051685214042663574,
0.01830372028052807,
-0.033892180770635605,
0.05753948539495468,
0.021174125373363495,
-0.0564003549516201,
-0.06912509351968765,
-0.002023162553086877,
-0.016612781211733818,
0.009867451153695583,
-0.02850448340177536,
0.031747665256261826,
0.024803292006254196,
-0.015773175284266472,
-0.04806826636195183,
0.025354459881782532,
0.003915941342711449,
-0.06254806369543076,
-0.0031982138752937317,
0.007878903299570084,
0.005323636811226606,
-0.02318594977259636,
0.022147944197058678,
0.0428774431347847,
-0.03943677991628647,
-0.016711730509996414,
-0.020611001178622246,
-0.057791151106357574,
0.029203111305832863,
0.02969309128820896,
0.008703896775841713,
-0.02820836380124092,
0.005147786810994148,
0.0935521200299263,
-0.015536988154053688,
-0.0353100448846817,
-0.008587827906012535,
-0.001888483646325767,
-0.012312338687479496,
0.0009076132555492222,
-0.0066350167617201805,
-0.008831114508211613,
-0.009587080217897892,
0.041301123797893524,
0.03018386848270893,
0.01430077850818634,
0.03181445226073265,
0.04363550990819931,
0.01585044153034687,
-0.03562304005026817,
0.008384715765714645,
-0.019826453179121017,
0.025472106412053108,
0.0018919984577223659,
-0.04274137690663338,
0.002994515234604478,
0.014235551469027996,
0.053665388375520706,
-0.0017806529067456722,
0.0048742471262812614,
0.06353582441806793,
0.01260469015687704,
0.017922183498740196,
-0.04685221612453461,
0.03358468785881996,
-0.006414890289306641,
0.022815024480223656,
-0.018299777060747147,
0.00259844190441072,
0.043092966079711914,
-0.0049050054512917995,
0.02315611205995083,
0.06053268164396286,
-0.00047260033898055553,
-0.04891696572303772,
-0.02554135210812092,
0.0007973970496095717,
0.0019147171406075358,
0.0443774089217186,
-0.04462478682398796,
-0.044681891798973083,
0.015196953900158405,
0.03562762588262558,
0.01924809440970421,
0.008505675941705704,
-0.016151398420333862,
0.019585171714425087,
-0.06581272929906845,
-0.010737916454672813,
0.018350565806031227,
0.02744564786553383,
0.012137765064835548,
0.08898577839136124,
0.040305882692337036,
0.002845514565706253,
-0.014772013761103153,
0.012089371681213379,
-0.07881420105695724,
-0.005817013792693615,
-0.04397446662187576,
-0.011760012246668339,
-0.014859077520668507,
-0.034442249685525894,
0.018326139077544212,
-0.046200044453144073,
-0.023102063685655594,
-0.005640590097755194,
-0.019947398453950882,
-0.059640828520059586,
0.023547787219285965,
-0.030286170542240143,
-0.028140971437096596,
-0.04340627044439316,
0.05744807794690132,
0.011209351941943169,
-0.01653791032731533,
0.02997995726764202,
0.03519028425216675,
-0.031010039150714874,
0.008778880350291729,
-0.009248190559446812,
0.005972463171929121,
0.0014530080370604992,
0.04708756506443024,
0.028490832075476646,
0.028728531673550606,
-0.010939344763755798,
0.007171986158937216,
-0.01845182478427887,
0.08983119577169418,
0.005737872328609228,
-0.0368741899728775,
-0.020432373508810997,
-0.02605571039021015,
0.004723832476884127,
-0.009699948132038116,
0.03301249071955681,
-0.0283323023468256,
0.02742086723446846,
0.03470952808856964,
0.004151838831603527,
-0.02757653035223484,
0.03103630430996418,
0.05193614959716797,
-0.0023907737340778112,
-0.013126576319336891,
-0.04678860679268837,
0.03031536564230919,
-0.02863084338605404,
-0.023006437346339226,
0.0028003754559904337,
0.000025222887416020967,
-0.028298394754529,
-0.01631050370633602,
0.005770145915448666,
0.022575363516807556,
-0.029318328946828842,
0.008758769370615482,
-0.000549309013877064,
0.029145782813429832,
0.006267253775149584,
0.008428352884948254,
-0.008065077476203442,
0.01076121162623167,
0.0008479750249534845,
0.0075394934974610806,
0.006758319213986397,
-0.04453412815928459,
0.010796930640935898,
0.018868301063776016,
0.05356040224432945,
-0.026473527774214745,
0.0458504892885685,
-0.01227215863764286,
-0.025897016748785973,
0.0638251081109047,
-0.017390327528119087,
0.012531508691608906,
-0.029459159821271896,
-0.02512173354625702,
-0.006541740614920855,
-0.01710539124906063,
-0.008490539155900478,
0.02070339396595955,
-0.036089200526475906,
-0.03369118273258209,
-0.03576898202300072,
0.013121929951012135,
-0.013086564838886261,
0.010201449505984783,
0.03894732519984245,
0.05632251873612404,
0.052687883377075195,
0.0007596311043016613,
-0.012900064699351788,
0.02857668697834015,
-0.04708538576960564,
-0.09422636032104492,
0.014937156811356544,
-0.003296205308288336,
0.00047308861394412816,
0.045733582228422165,
-0.046457041054964066,
-0.06036045774817467,
0.054515641182661057,
-0.02649621106684208,
0.000987633946351707,
-0.0022223948035389185,
-0.015128768049180508,
0.01350065041333437,
0.01860780455172062,
-0.01787663996219635,
0.03313770145177841,
0.010336814448237419,
-0.0014532553032040596,
-0.005759531166404486,
0.008821584284305573,
0.029143914580345154,
-0.04175296053290367,
0.010719171725213528,
-0.008253763429820538,
0.009290221147239208,
-0.0222212765365839,
0.062418438494205475,
0.008536622859537601,
0.009581507183611393,
0.03670560196042061,
-0.025200920179486275,
-0.04922463744878769,
0.02301030233502388,
0.034112125635147095,
-0.015083367936313152,
-0.03377000615000725,
0.0060411253944039345,
-0.02838423289358616,
-0.03578304499387741,
-0.015271908603608608,
0.016937661916017532,
0.009478126652538776,
0.03011397086083889,
-0.018718967214226723,
0.032189566642045975,
-0.03796631842851639,
-0.0009433274390175939,
0.029427221044898033,
-0.05368856340646744,
0.01643521338701248,
-0.03971582278609276,
-0.008149747736752033,
0.004407650791108608,
-0.08347921818494797,
-0.056828517466783524,
0.012340213172137737,
-0.014694628305733204,
0.024582862854003906,
-0.058026671409606934,
0.02852870710194111,
0.006132442504167557,
0.012721744365990162,
-0.05506953224539757,
-0.011488767340779305,
0.013486044481396675,
0.030138321220874786,
-0.014884387142956257,
-0.0057130190543830395,
0.02079416625201702,
-0.03153768926858902,
-0.010879293084144592,
-0.017526928335428238,
0.045288629829883575,
0.024606073275208473,
-0.020136971026659012,
-0.006478980183601379,
-0.010636257007718086,
0.039352674037218094,
-0.006032138597220182,
-0.013412556611001492,
-0.000576408754568547,
0.006724962964653969,
0.018731530755758286,
0.03165855258703232,
0.03987709432840347,
-0.016182195395231247,
-0.021933365613222122,
0.006200524978339672,
-0.015445753000676632,
0.024910708889365196,
-0.013263259083032608,
0.02864455059170723,
0.03676784411072731,
0.02604529820382595,
0.023112962022423744,
-0.008571728132665157,
0.006242960691452026,
0.012852917425334454,
0.006113108247518539,
0.02331136167049408,
0.0006225395482033491,
-0.013466794975101948,
-0.031743425875902176,
0.024321120232343674,
-0.03237369284033775,
-0.013001584447920322,
-0.01825917512178421,
0.03125802427530289,
0.009624093770980835,
-0.010005978867411613,
0.011742109432816505,
0.01811854913830757,
-0.015902237966656685,
-0.035497527569532394,
0.020113371312618256,
0.008267758414149284,
0.026528721675276756,
-0.030574342235922813,
-0.006232758052647114,
-0.034326110035181046,
-0.004526789300143719,
0.04968062415719032,
-0.029484059661626816,
0.06630118191242218,
0.015440195798873901,
0.021165229380130768,
-0.02735593169927597,
-0.007968506775796413,
-0.02817559987306595,
0.007719055283814669,
0.014772148802876472,
0.025817662477493286,
-0.014911998063325882,
-0.018130401149392128,
0.0398147776722908,
0.049595996737480164,
-0.010908270254731178,
-0.00403593061491847,
0.004200753755867481,
0.024629799649119377,
0.031622231006622314,
0.022125300019979477,
-0.046339161694049835,
0.008454366587102413,
-0.012034008279442787,
0.00883528683334589,
-0.005768434144556522,
-0.024449044838547707,
0.02380097284913063,
-0.015573810786008835,
0.002346034860238433,
0.01563103124499321,
-0.016526540741324425,
-0.03361580893397331,
0.04200485721230507,
-0.010169308632612228,
0.04080132395029068,
-0.016964269801974297,
0.0017305000219494104,
0.0059984102845191956,
0.03792177885770798,
-0.004771239589899778,
0.0053369938395917416,
-0.08114014565944672,
-0.052364468574523926,
-0.016042156144976616,
-0.020642293617129326,
0.013079051859676838,
-0.013204366900026798,
-0.036370038986206055,
0.01291912142187357,
-0.00674237497150898,
0.045276012271642685,
-0.009889770299196243,
0.031246161088347435,
-0.020304283127188683,
0.06026162579655647,
0.011776365339756012,
0.030413631349802017,
-0.01836583763360977,
0.043480705469846725,
0.09758082032203674,
0.04135178029537201,
0.012759711593389511,
-0.041830841451883316,
-0.006214733701199293,
-0.022691158577799797,
0.023668011650443077,
-0.03138549625873566,
0.04292801395058632,
0.039157308638095856,
0.006561770103871822,
-0.009354444220662117,
0.04037516936659813,
-0.009183323942124844,
0.003952347673475742,
0.03530589118599892,
-0.011292794719338417,
-0.0545361265540123,
-0.03841672092676163,
0.0345798060297966,
0.0028184717521071434,
0.0017857380444183946,
-0.010447750799357891,
0.01827700063586235,
-0.04954806715250015,
0.0017480376409366727,
0.014019409194588661,
-0.05829903855919838,
0.010421622544527054,
-0.011206554248929024,
-0.03527793660759926,
-0.0072448644787073135,
0.024707095697522163,
-0.004988227970898151,
-0.0533384270966053,
0.03163868561387062,
0.029629429802298546,
0.004443070385605097,
-0.011259603314101696,
0.017258519306778908,
0.00568474642932415,
0.008927080780267715,
-0.011909636668860912,
-0.0013992415042594075,
-0.03725327551364899,
-0.031028904020786285,
-0.015424535609781742,
0.03556692227721214,
-0.021441444754600525,
0.014456999488174915,
-0.0003183624939993024,
-0.035101067274808884,
0.003225061809644103,
-0.0509040430188179,
-0.022288085892796516,
0.007967958226799965,
0.027104884386062622,
-0.010362895205616951,
0.005337504204362631,
-0.049248140305280685,
0.01870308816432953,
-0.005602465942502022,
0.021054808050394058,
-0.019684135913848877,
-0.014475292526185513,
-0.0031710073817521334,
0.020355526357889175,
0.031021183356642723,
-0.025197243317961693,
-0.03435474634170532,
0.012259206734597683,
-0.02462760917842388,
-0.0563940666615963,
-0.01596471481025219,
0.05861496552824974,
0.011893206275999546,
0.005153061356395483,
-0.0031972143333405256,
-0.015589430928230286,
0.008275831118226051,
-0.05744696781039238,
0.026635412126779556,
-0.051039475947618484,
-0.03955669701099396,
0.0005437954678200185,
0.03757266700267792,
0.05918204039335251,
0.06321103125810623,
-0.060556262731552124,
0.007724494207650423,
-0.02305421605706215,
-0.010326559655368328,
0.026767952367663383,
-0.02154901996254921,
-0.008388243615627289,
0.019791848957538605,
-0.05042701214551926,
0.03226031735539436,
-0.03026934713125229,
0.008278955705463886,
0.053257253021001816,
0.044556934386491776,
-0.012994611635804176,
0.023466933518648148,
0.003984101116657257,
0.0011596267577260733,
0.01891927793622017,
-0.001291657448746264,
-0.028609242290258408,
0.018980473279953003,
0.03843037411570549,
-0.03272455558180809,
-0.010168839246034622,
-0.05895422771573067,
0.016821911558508873,
-0.011902238242328167,
-0.0042284331284463406,
-0.016794241964817047,
-0.006476860959082842,
0.007756364531815052,
0.015177402645349503,
-0.037294648587703705,
0.02161453105509281,
-0.036017972975969315,
0.00763967540115118,
-0.022916801273822784,
-0.036697812378406525,
-0.04228351637721062,
-0.00789907667785883,
-0.010045726783573627,
-0.02953234501183033,
0.055049072951078415,
0.026852887123823166,
-0.017234254628419876,
-0.033828169107437134,
0.05194638669490814,
0.011804817244410515,
0.0527462512254715,
-0.02019183151423931,
-0.003857732517644763,
0.028842220082879066,
-0.04284774512052536,
-0.06008101627230644,
0.04279736801981926,
-0.007194210309535265,
0.033041711896657944,
0.07422786951065063,
-0.03166916221380234,
-0.03890826180577278,
0.050575871020555496,
-0.013126615434885025,
0.02716171368956566,
0.0449344776570797,
-0.017534656450152397,
-0.03201105073094368,
0.0072067431174218655,
0.01594293676316738,
-0.030372818931937218,
-0.03148231655359268,
0.04258853197097778,
-0.004965322557836771,
0.024087974801659584,
0.011211604811251163,
0.03206470236182213,
0.015709202736616135,
0.06404205411672592,
0.058620963245630264,
-0.02266264520585537,
0.038147054612636566,
0.05998070165514946,
-0.014664072543382645,
0.051238059997558594,
0.03559907525777817,
0.04391259700059891,
-0.09542113542556763,
0.0010746308835223317,
0.010467044077813625,
0.006452819798141718,
0.023807723075151443,
-0.00845324993133545,
0.024865102022886276,
0.052229076623916626,
-0.06150741130113602,
-0.013363635167479515,
-0.06213502585887909,
-0.013198995031416416,
-0.01223717536777258,
0.007748949807137251,
-0.04286699369549751,
0.057650886476039886,
0.03322174772620201,
0.04987548291683197,
0.007018481381237507,
-0.005275183357298374,
-0.009988626465201378,
-0.015524276532232761,
-0.05067268759012222,
0.03347179293632507,
-0.015094354748725891,
-0.016336793079972267,
0.06364907324314117,
-0.04781845957040787,
-0.03637472912669182,
0.023361921310424805,
-0.021381819620728493,
-0.005135475657880306,
-0.03826088458299637,
0.03844892233610153,
0.029822662472724915,
0.016467023640871048,
-0.00012042634625686333,
-0.0029321610927581787,
-0.019589340314269066,
0.018158866092562675,
-0.007220146711915731,
0.024000709876418114,
0.010690846480429173,
-0.01810508593916893,
-0.005824218038469553,
-0.03553147614002228,
-0.04803932085633278,
0.016737766563892365,
-0.027198482304811478,
-0.01734916679561138,
0.001395904109813273,
0.0013501130742952228,
-0.02393827773630619,
-0.05190801993012428,
0.024335423484444618,
-0.08234710991382599,
-0.035699259489774704,
0.007778785657137632,
0.013981074094772339,
-0.012598318047821522,
0.009364542551338673,
-0.012858996167778969,
-0.02800576016306877,
0.03673165291547775,
0.00285454117693007,
-0.029376188293099403,
-0.05406833440065384,
0.0010926915565505624,
0.049956951290369034,
-0.008025210350751877,
0.007498437073081732,
-0.06696196645498276,
-0.01875447668135166,
0.03471417352557182,
0.007481085602194071,
0.036124635487794876,
-0.010707907378673553,
-0.0007094765896908939,
-0.028115836903452873,
-0.048862274736166,
0.04917373135685921,
0.014897926710546017,
0.00478585297241807,
-0.027115030214190483,
-0.008431370370090008,
0.012623910792171955,
-0.01892036944627762,
0.029609452933073044,
-0.040138911455869675,
-0.006847466342151165,
0.03897562623023987,
-0.013963030651211739,
0.02499314770102501,
-0.008516238071024418,
-0.027920667082071304,
-0.044456955045461655,
-0.044646527618169785,
-0.014685450121760368,
-0.03177735209465027,
-0.031061850488185883,
0.030979273840785027,
0.01944008842110634,
-0.0160473994910717,
0.018926195800304413,
-0.022358715534210205,
-0.02370009571313858,
0.06347905099391937,
0.0028347810730338097,
-0.019596941769123077,
0.03322754427790642,
0.007770974189043045,
0.02062261663377285,
0.04442024603486061,
-0.005035004578530788,
-0.0447244755923748,
0.002013877034187317,
-0.024654759094119072,
-0.02295197732746601,
0.005726441740989685,
0.0058558606542646885,
0.01915828324854374,
-0.03992721438407898,
-0.005498775281012058,
0.017236540094017982,
-0.03185288980603218,
0.010122953914105892,
0.06984169036149979,
0.0025970102287828922,
0.031045963987708092,
0.003711996367201209,
-0.003796942299231887,
0.04752996936440468,
-0.021101847290992737,
0.019784357398748398,
0.03097725845873356,
0.013942544348537922,
-0.0018964865012094378,
0.027432527393102646,
0.03494289517402649,
0.0031649621669203043,
0.010839231312274933,
0.010076697915792465,
0.0372575968503952,
-0.01973448321223259,
-0.024731285870075226,
-0.020419808104634285,
-0.03986211493611336,
0.000926938490010798,
-0.0037563126534223557,
-0.0585501529276371,
0.0905223861336708,
-0.03479215130209923,
-0.0023339942563325167,
-0.023311691358685493,
0.015643034130334854,
0.00399831822142005,
-0.03280266746878624,
0.0055654002353549,
0.02220146916806698,
-0.00243721273727715,
-0.04082820564508438,
-0.02397562377154827,
0.013494506478309631,
0.026197046041488647,
-0.06094871833920479,
0.009402541443705559,
-0.021772343665361404,
0.005674405489116907,
-0.04132989048957825,
-0.025633567944169044,
-0.043100420385599136,
-0.028318269178271294,
0.033432550728321075,
0.013482430018484592,
0.03455273434519768,
-0.02231415919959545,
-0.020560042932629585,
-0.030047843232750893,
0.07989722490310669,
-0.051618289202451706,
-0.00001624917786102742,
-0.03411860764026642,
0.019877124577760696,
0.003627611557021737,
-0.01146806962788105
] |
<p>I'm a little confused.. When I write the equation of the circuit, do I have to keep the signs of the induced emf and self-inductance opposite?</p>
<p>I'll try to explain better my doubt:
Consider a coil that has resistance R and inductance L. Running a current will give rise to both an induced emf and self-inductance, and the situation is:</p>
<p>induced emf= -k </p>
<p>self-inductance= $-L \frac{dI}{dt}$</p>
<p>Now, my question is: the equation of the circuit is given by:</p>
<p>$-k -L \frac{dI}{dt}=RI$</p>
<p>or by </p>
<p>$k -L \frac{dI}{dt}=RI$ ?</p>
| 9,629 |
[
-0.012531454674899578,
0.020144952461123466,
-0.014181879349052906,
0.00037738188984803855,
0.024911122396588326,
0.010194900445640087,
-0.02587016113102436,
0.009956584312021732,
0.03294215351343155,
0.006411949172616005,
0.01014522835612297,
0.03721116855740547,
0.07308358699083328,
-0.00485251983627677,
0.02207886055111885,
0.0027250994462519884,
-0.028615791350603104,
0.004417737014591694,
0.013217599131166935,
-0.020381763577461243,
-0.010699853301048279,
0.036132726818323135,
0.0233193039894104,
0.01980568841099739,
-0.04290125519037247,
0.057953089475631714,
0.05859090015292168,
0.019384142011404037,
0.02445618249475956,
0.04071991890668869,
-0.007752959616482258,
-0.025588829070329666,
-0.01318369247019291,
0.02146582119166851,
0.03666899353265762,
0.03721299022436142,
-0.002572745317593217,
-0.017973776906728745,
-0.006190369371324778,
0.013521034270524979,
0.009296956472098827,
0.027261395007371902,
0.03805093467235565,
0.05476047098636627,
-0.006972515024244785,
0.018372269347310066,
0.02878851257264614,
0.024844709783792496,
0.028135444968938828,
-0.07604891061782837,
0.06107177957892418,
-0.03753950074315071,
0.06135464832186699,
0.03413531184196472,
-0.0253332257270813,
0.01054877694696188,
0.0733182355761528,
0.046043697744607925,
-0.0034710087347775698,
-0.05041477456688881,
0.01980535499751568,
-0.030550511553883553,
0.0029276085551828146,
-0.007308111526072025,
-0.02998100221157074,
0.02739582397043705,
0.015979308634996414,
0.007746904157102108,
0.023959342390298843,
-0.014327069744467735,
0.026882080361247063,
-0.004023042973130941,
-0.0050660534761846066,
-0.034393295645713806,
0.030516305938363075,
-0.029785241931676865,
-0.008618613705039024,
0.024444274604320526,
0.012057586573064327,
0.023943692445755005,
-0.058782193809747696,
0.015469996258616447,
0.01044947188347578,
0.03978634253144264,
0.00982566550374031,
-0.024448594078421593,
0.02172752656042576,
0.02254745550453663,
0.05145503953099251,
0.0015551981050521135,
0.019092530012130737,
0.05375383049249649,
0.024536773562431335,
-0.05408642813563347,
0.019919132813811302,
0.005244535859674215,
0.0024712211452424526,
0.05090124160051346,
-0.00333440862596035,
-0.02434804104268551,
0.00031733757350593805,
-0.022368544712662697,
-0.0033818683587014675,
0.0619538351893425,
-0.009166383184492588,
-0.03346889838576317,
-0.028521761298179626,
0.023227808997035027,
0.00301710469648242,
-0.016210392117500305,
-0.02198706939816475,
0.023582374677062035,
-0.0006687722052447498,
0.004498717375099659,
0.02089839242398739,
-0.01806149259209633,
0.00309898448176682,
-0.0022552432492375374,
0.016217438504099846,
0.03395261988043785,
0.03428591787815094,
-0.05624473839998245,
0.04893535375595093,
0.03122798539698124,
-0.055000994354486465,
0.002487990539520979,
0.028668183833360672,
0.03165776655077934,
-0.00606450904160738,
0.010488989762961864,
0.010155148804187775,
-0.045228708535432816,
0.00472806952893734,
0.02439345046877861,
0.04287625849246979,
-0.007755718659609556,
-0.05236652120947838,
-0.06976617872714996,
-0.010438268072903156,
-0.03606853261590004,
0.029402075335383415,
-0.08255185931921005,
-0.012225279584527016,
0.04278471693396568,
0.07026473432779312,
0.003308825194835663,
-0.019250838086009026,
0.013925709761679173,
0.006390368565917015,
0.008430855348706245,
-0.0027465829625725746,
-0.041509959846735,
-0.005132599268108606,
-0.029680456966161728,
-0.02838754840195179,
-0.027249174192547798,
0.042875099927186966,
0.03879592940211296,
0.0183885358273983,
-0.008912275545299053,
0.08532550185918808,
-0.03090491332113743,
0.01441187597811222,
0.0471939891576767,
-0.04040401801466942,
-0.036006372421979904,
0.11235790699720383,
0.0002751146676018834,
0.017937183380126953,
0.014215088449418545,
0.03830265998840332,
0.007833924144506454,
-0.01883707568049431,
0.01900823414325714,
0.0820109099149704,
-0.04471919685602188,
-0.04117210581898689,
-0.032216668128967285,
0.032094359397888184,
-0.014170142821967602,
-0.025939522311091423,
-0.0500478520989418,
0.014781889505684376,
0.0121461758390069,
-0.007778585888445377,
0.03996039927005768,
-0.019747605547308922,
-0.017960721626877785,
0.050517041236162186,
-0.023814165964722633,
-0.031248722225427628,
-0.019956713542342186,
0.031008083373308182,
0.0012914452236145735,
-0.03826342895627022,
0.00793472584336996,
0.02459469810128212,
0.030163416638970375,
-0.02333977445960045,
-0.006711255759000778,
0.024523915722966194,
0.005225109867751598,
-0.011603140272200108,
-0.03259781748056412,
0.038992516696453094,
0.03539527580142021,
0.03535466268658638,
-0.01613665372133255,
0.06353247910737991,
-0.05440431088209152,
-0.005670367740094662,
0.02194085717201233,
-0.022273574024438858,
-0.011240714229643345,
0.02963414043188095,
-0.013335703872144222,
0.002989123109728098,
-0.015507779084146023,
0.012409167364239693,
0.0377068854868412,
-0.02305571176111698,
0.07444358617067337,
0.07231612503528595,
0.028436388820409775,
0.02308502234518528,
0.035315826535224915,
-0.006105251610279083,
0.03940087929368019,
-0.03877051919698715,
-0.025235626846551895,
-0.032133471220731735,
-0.02050754241645336,
0.02543633244931698,
-0.0004480432835407555,
-0.04051882401108742,
0.03650391101837158,
0.029042143374681473,
0.02315688692033291,
0.026016561314463615,
0.03276461735367775,
-0.021859493106603622,
-0.03798772022128105,
-0.012772513553500175,
0.04186765104532242,
-0.03476686403155327,
0.010271181352436543,
0.0051176175475120544,
0.0054116444662213326,
0.01582224667072296,
0.004977513570338488,
-0.0234218742698431,
0.05430188775062561,
-0.0319901742041111,
0.01281515508890152,
0.03581618890166283,
-0.03347480669617653,
0.040738437324762344,
-0.043182455003261566,
0.019400523975491524,
-0.008217185735702515,
-0.018029319122433662,
0.03377775847911835,
0.007866649888455868,
0.009242847561836243,
-0.015539901331067085,
-0.03660909831523895,
-0.03497226908802986,
-0.043780624866485596,
0.015471968799829483,
-0.049836624413728714,
0.020054634660482407,
-0.011315956711769104,
-0.011196947656571865,
-0.053019795566797256,
-0.02170049585402012,
0.0009388349135406315,
-0.019081057980656624,
0.011884041130542755,
-0.0050277444534003735,
-0.010617009364068508,
-0.02933286689221859,
-0.020215610042214394,
0.02872280776500702,
0.0338604710996151,
-0.060461755841970444,
0.021663084626197815,
-0.02708454802632332,
-0.03711149841547012,
0.062317539006471634,
0.002040340332314372,
-0.008315912447869778,
-0.004838128108531237,
0.0030626440420746803,
-0.0751127153635025,
-0.038652051240205765,
-0.04703438654541969,
0.023919126018881798,
0.00253383070230484,
-0.012394237332046032,
0.08320390433073044,
-0.008391915820538998,
-0.024456964805722237,
-0.010290397331118584,
-0.05038372799754143,
-0.024155709892511368,
0.00030743444222025573,
-0.023326847702264786,
0.039663154631853104,
0.0022901545744389296,
0.00036592831020243466,
0.025695068761706352,
-0.07101014256477356,
-0.01437402330338955,
-0.07040547579526901,
-0.048131994903087616,
0.004012010060250759,
-0.013197461143136024,
0.05564713850617409,
0.01847670041024685,
-0.05776107683777809,
0.07727733254432678,
0.05580315738916397,
-0.03799755126237869,
-0.009620056487619877,
-0.03348391875624657,
-0.02379784919321537,
-0.09069062024354935,
-0.04023023694753647,
0.03838123381137848,
-0.008917486295104027,
0.04425415024161339,
0.03001638874411583,
0.02403184026479721,
-0.01706838421523571,
0.03686248138546944,
0.001703348127193749,
-0.004753642715513706,
-0.0005000325618311763,
-0.015810338780283928,
0.09028887003660202,
0.0360882431268692,
-0.010902315378189087,
0.021219588816165924,
-0.0008420288795605302,
0.05563576892018318,
0.02042742818593979,
-0.011729654856026173,
0.025879696011543274,
-0.054921187460422516,
0.01876790262758732,
-0.024210279807448387,
0.01987450383603573,
0.00800248421728611,
0.04105706140398979,
-0.005795933771878481,
-0.003689952427521348,
0.039328817278146744,
-0.06923746317625046,
0.02024984359741211,
0.021761031821370125,
-0.008021894842386246,
-0.01285693421959877,
-0.031169988214969635,
0.019314583390951157,
-0.04884648695588112,
0.012284256517887115,
-0.004024336114525795,
-0.01550354529172182,
0.046234507113695145,
0.015214666724205017,
0.02411997877061367,
0.012264245189726353,
-0.017860978841781616,
0.006200595758855343,
-0.09167661517858505,
-0.044399116188287735,
0.015365471132099628,
0.040395986288785934,
0.009421891532838345,
0.007353037130087614,
0.01018289290368557,
-0.01319484505802393,
0.0005588791682384908,
-0.005385004449635744,
-0.07470839470624924,
0.07403596490621567,
-0.04791834577918053,
-0.03555184602737427,
-0.0028994919266551733,
-0.006576948333531618,
0.0036229523830115795,
-0.05329657718539238,
-0.0185372494161129,
0.003479833947494626,
-0.02740977704524994,
-0.05303493142127991,
0.0032792307902127504,
-0.01739543490111828,
-0.0213753841817379,
-0.03729947283864021,
0.028243010863661766,
0.055018264800310135,
-0.055812615901231766,
0.014843674376606941,
0.03496066480875015,
-0.050625935196876526,
-0.000860206491779536,
-0.04697363078594208,
-0.010218152776360512,
0.0301508828997612,
0.02550269104540348,
0.06672482192516327,
-0.02966587245464325,
-0.03736032545566559,
0.02046671137213707,
0.03572067618370056,
0.03941376134753227,
0.017758581787347794,
-0.0331152081489563,
-0.03768358752131462,
-0.05676557868719101,
-0.029347291216254234,
-0.011024112813174725,
0.04692500829696655,
0.01343223825097084,
0.02039801888167858,
0.01914140395820141,
0.012407511472702026,
-0.01452623400837183,
0.030681924894452095,
0.043303512036800385,
-0.0037658915389329195,
-0.0233266931027174,
-0.022910811007022858,
-0.03228862211108208,
-0.025220585986971855,
-0.008825474418699741,
0.013703609816730022,
0.009405134245753288,
-0.031140629202127457,
0.012325081042945385,
0.049421947449445724,
0.015353275462985039,
0.038172684609889984,
0.03932216390967369,
0.012313805520534515,
0.05205376446247101,
0.01290107797831297,
0.014070305041968822,
0.04317811504006386,
0.03826943784952164,
0.026350338011980057,
0.010001773945987225,
-0.01187113393098116,
-0.05719375237822533,
-0.027261776849627495,
0.02290118858218193,
0.05128355696797371,
-0.023152586072683334,
-0.011988637037575245,
-0.0848534107208252,
-0.03646557778120041,
0.0463203527033329,
-0.05427219346165657,
0.04843653738498688,
-0.009865856729447842,
-0.031259454786777496,
0.010413913056254387,
-0.038121968507766724,
-0.01622580736875534,
0.028766293078660965,
0.024825870990753174,
0.0338033027946949,
-0.02294228784739971,
-0.008062454871833324,
0.01361427828669548,
-0.020312823355197906,
0.02186705358326435,
0.05828332155942917,
-0.020161299034953117,
-0.023595593869686127,
-0.009614878334105015,
0.04441710561513901,
-0.012363214045763016,
-0.05289629101753235,
0.04015675559639931,
-0.030241934582591057,
0.04289238899946213,
0.04277466610074043,
0.00012846887693740427,
-0.03744672238826752,
-0.005475687328726053,
0.03173455595970154,
0.0373787097632885,
-0.013852102681994438,
-0.033887945115566254,
0.03319890424609184,
0.029840055853128433,
0.006087374873459339,
0.04805196449160576,
0.012038028798997402,
0.004654224496334791,
0.01604345068335533,
-0.009951048530638218,
0.006426210515201092,
-0.03071620874106884,
0.02852410264313221,
-0.02030358277261257,
0.032152287662029266,
-0.02352181077003479,
0.058130864053964615,
-0.0382523275911808,
0.015769220888614655,
-0.030481290072202682,
0.010260703042149544,
0.0006091701216064394,
0.008273307234048843,
-0.007198439911007881,
-0.023107774555683136,
0.023193765431642532,
0.023560652509331703,
0.014844623394310474,
-0.049437474459409714,
0.007567964494228363,
-0.023811394348740578,
-0.0005393560859374702,
0.03848784789443016,
-0.017533468082547188,
0.018541567027568817,
-0.03907866030931473,
-0.04820016771554947,
0.00962765421718359,
-0.04370254650712013,
0.0007677152752876282,
-0.02629394456744194,
-0.02139495685696602,
-0.016776883974671364,
-0.0036154044792056084,
-0.019764434546232224,
0.0044734845869243145,
0.018218277022242546,
0.0031845918856561184,
-0.05347732454538345,
0.04793005809187889,
0.03508096933364868,
-0.0426979586482048,
-0.0722351148724556,
-0.07921093702316284,
0.0122894998639822,
-0.0189051516354084,
-0.007312099914997816,
0.014905266463756561,
-0.022044772282242775,
-0.0008237691363319755,
-0.03520014137029648,
0.014039158821105957,
0.04589182138442993,
-0.029294298961758614,
-0.0012165484949946404,
0.036946509033441544,
0.00813963171094656,
0.06278824806213379,
0.020152967423200607,
0.010677412152290344,
0.00367578212171793,
-0.08116163313388824,
-0.004846951458603144,
-0.0047113546170294285,
0.04693174362182617,
-0.023115376010537148,
-0.026706840842962265,
-0.01302876602858305,
-0.010476077906787395,
0.06243409216403961,
0.008148937486112118,
-0.02203056775033474,
0.0179845429956913,
-0.008925355970859528,
-0.027258535847067833,
-0.021544992923736572,
-0.006889084819704294,
0.004606809001415968,
0.013677077367901802,
0.04043729230761528,
-0.02686777152121067,
-0.05645258352160454,
-0.02118695341050625,
-0.02755630947649479,
0.007822663523256779,
0.02165508083999157,
-0.030662717297673225,
0.06830563396215439,
-0.016120990738272667,
-0.014030133374035358,
0.008403060026466846,
-0.014005112461745739,
0.03617452085018158,
-0.05004075542092323,
0.008837827481329441,
0.0006907319184392691,
-0.02554994635283947,
-0.046799998730421066,
-0.04585716128349304,
-0.028368497267365456,
0.013134695589542389,
0.06595412641763687,
-0.004488577134907246,
0.0461413636803627,
0.018707409501075745,
0.009557395242154598,
0.02813504822552204,
-0.021250873804092407,
-0.019974859431385994,
-0.028069952502846718,
-0.03401567414402962,
0.039926860481500626,
0.0027573832776397467,
0.027882520109415054,
0.016080331057310104,
0.03941378742456436,
-0.011481582187116146,
-0.008732067421078682,
0.023289190605282784,
0.007025287486612797,
-0.021156279370188713,
0.04123041406273842,
-0.04578012228012085,
0.03984195366501808,
-0.025104518979787827,
0.0448283925652504,
-0.01635463908314705,
-0.007067359518259764,
0.05237536132335663,
-0.009650260210037231,
0.009884551167488098,
-0.010497089475393295,
-0.012009265832602978,
-0.004205411300063133,
-0.00958849024027586,
0.009966268204152584,
0.024750446900725365,
0.016441427171230316,
0.01494930125772953,
0.04942777007818222,
-0.005572820082306862,
0.026345321908593178,
-0.021389110013842583,
-0.045944903045892715,
-0.004019418265670538,
-0.02430923469364643,
-0.0261805709451437,
0.032834190875291824,
-0.008519423194229603,
0.005391979124397039,
0.01531336922198534,
-0.01715150848031044,
0.04744656756520271,
0.06038643792271614,
0.014895565807819366,
-0.020495399832725525,
0.06218857690691948,
-0.00460446160286665,
0.03601903095841408,
-0.030114077031612396,
0.0026119148824363947,
0.11942261457443237,
0.03907802328467369,
0.009899085387587547,
-0.06891743093729019,
0.020104985684156418,
-0.01989504136145115,
0.022923463955521584,
-0.013890676200389862,
0.052895087748765945,
-0.023893922567367554,
-0.014114528894424438,
0.03249112889170647,
0.008279029279947281,
-0.01895502768456936,
0.011790980584919453,
0.010986852459609509,
-0.032416969537734985,
-0.047189462929964066,
-0.016362613067030907,
0.02615957334637642,
0.020572513341903687,
0.0041299983859062195,
-0.036023180931806564,
0.039602503180503845,
-0.02724694274365902,
0.010380137711763382,
-0.02130712941288948,
-0.03354709967970848,
0.07034849375486374,
0.02799859829246998,
-0.04819483682513237,
0.021076632663607597,
0.020542971789836884,
-0.012868732213973999,
-0.03256747126579285,
0.019230160862207413,
0.020397640764713287,
-0.02256208285689354,
0.012449044734239578,
0.024761222302913666,
0.04013098403811455,
-0.018065236508846283,
0.029649682343006134,
0.008145580068230629,
-0.05098189413547516,
0.03109079785645008,
-0.022953657433390617,
0.013868572190403938,
0.02863149717450142,
0.02863878756761551,
0.011485910974442959,
0.04182236269116402,
0.04208691418170929,
-0.07342342287302017,
-0.03304065391421318,
0.012497815303504467,
0.02080460451543331,
-0.03160155937075615,
-0.019612953066825867,
-0.0283184926956892,
0.02179647982120514,
-0.0256834477186203,
-0.014590923674404621,
0.01746392250061035,
-0.024889416992664337,
0.010017524473369122,
-0.009389837272465229,
0.028684576973319054,
0.01059899851679802,
-0.028693152591586113,
-0.012943116016685963,
0.003358859336003661,
-0.014403135515749454,
-0.006872290745377541,
0.017002105712890625,
0.0352788120508194,
0.05430762842297554,
-0.01733344793319702,
-0.029991254210472107,
0.013564563356339931,
-0.0643383264541626,
0.022405777126550674,
0.0235198475420475,
-0.010310341604053974,
-0.017907235771417618,
-0.005717105697840452,
0.015758560970425606,
0.019496707245707512,
-0.009170738980174065,
0.030715130269527435,
0.01328948698937893,
0.028444679453969002,
-0.013198730535805225,
-0.010928241536021233,
-0.02954963594675064,
0.016945363953709602,
-0.05886782705783844,
0.02686273865401745,
0.02627452276647091,
0.04084687680006027,
0.026126055046916008,
0.0285317525267601,
-0.029339732602238655,
0.045642465353012085,
0.0024164209607988596,
-0.005850635003298521,
-0.010809685103595257,
-0.023703785613179207,
0.04226914420723915,
-0.005772456526756287,
0.033630866557359695,
-0.004593146499246359,
-0.0346166230738163,
0.004104417748749256,
0.02830415777862072,
0.03701157122850418,
0.0101894810795784,
-0.03890391066670418,
-0.0036686856765300035,
-0.02091817557811737,
-0.009474770165979862,
-0.05959545075893402,
-0.022943224757909775,
-0.06417284160852432,
-0.023235267028212547,
0.009968055412173271,
-0.005965712945908308,
-0.006592830177396536,
0.027727579697966576,
-0.000078121833212208,
0.017676426097750664,
0.005247114226222038,
0.012573054060339928,
-0.0023857338819652796,
-0.03326531872153282,
0.0057117086835205555,
-0.003185753710567951,
0.030272332951426506,
-0.03748425096273422,
-0.0033209940884262323,
0.030771298334002495,
-0.004314573481678963,
0.012610153295099735,
-0.01265380997210741,
0.01660011149942875,
0.0008636958664283156,
0.033309150487184525,
-0.011799534782767296,
-0.005225273780524731,
0.04112374037504196,
0.008097057230770588,
0.024780098348855972,
0.014579882845282555,
-0.048572953790426254,
0.005879284348338842,
-0.028311079367995262,
-0.02714977040886879,
0.012566998600959778,
-0.006038276012986898,
-0.02722192369401455,
0.04477136209607124,
0.006145973689854145,
-0.013213731348514557,
0.0093549694865942,
0.031730182468891144,
-0.0028259088285267353,
0.026008881628513336,
0.014489464461803436,
0.005505549721419811,
-0.006735286209732294,
-0.01674351841211319,
-0.004928946495056152,
-0.007837540470063686,
0.008390531875193119,
-0.060058485716581345,
0.0017099573742598295,
0.019324932247400284,
0.016409512609243393,
0.0016904599033296108,
-0.049031879752874374,
-0.01048528216779232,
0.02638860046863556,
-0.030985135585069656,
-0.024202819913625717,
-0.03289296105504036,
-0.005393040832132101,
-0.035640452057123184,
-0.031206609681248665,
-0.011727540753781796,
0.011047711595892906,
0.04450137913227081,
0.0317930169403553,
-0.00009194469021167606,
-0.02892553247511387,
-0.01211600098758936,
0.002232795814052224,
-0.042312655597925186,
0.004286913201212883,
-0.008576899766921997,
-0.02686493843793869,
0.023913435637950897,
-0.03587016835808754,
0.003625784767791629,
0.025653446093201637,
-0.02516288124024868,
0.006076112389564514,
0.009806901216506958,
0.028994537889957428,
0.013472062535583973,
0.04180743545293808,
0.010254845023155212,
-0.026455290615558624,
-0.03198792040348053,
0.014845171943306923,
0.012046460062265396,
0.013462640345096588,
0.0020957670640200377,
-0.008628107607364655,
-0.0012946741189807653,
-0.03814605996012688,
-0.026971789076924324,
0.033716313540935516,
-0.05327682942152023,
-0.017217788845300674,
-0.04641122370958328,
0.008872214704751968,
0.01592637412250042,
-0.04633975774049759,
0.01052593532949686,
-0.021662840619683266,
-0.003626129822805524,
0.030162695795297623,
-0.02545296773314476,
0.00918649509549141,
-0.002851077588275075,
0.013802545145154,
-0.057845573872327805,
0.04031277820467949,
0.007363039068877697,
-0.011552952229976654,
-0.07168777287006378,
0.015104745514690876,
0.015255104750394821,
-0.007613511756062508,
0.012805469334125519,
-0.043347835540771484,
-0.029706019908189774,
0.036803554743528366,
0.014897661283612251,
0.016036443412303925,
0.00999667588621378,
-0.0767112597823143,
-0.022673988714814186,
-0.01792062073945999,
0.05172760784626007,
-0.002491849008947611,
-0.03140835091471672,
-0.037946101278066635,
-0.03995460271835327,
-0.000845552422106266,
0.017474450170993805,
0.05118348449468613,
0.019893204793334007,
-0.035543665289878845,
0.03660237044095993,
0.0028918541502207518,
0.024422036483883858,
-0.05283893644809723,
0.001909791026264429,
0.004226252902299166,
0.018650490790605545,
0.025680162012577057,
-0.01215014886111021,
-0.03223014622926712,
0.05193610489368439,
0.012731227092444897,
0.02494668774306774,
0.041241418570280075,
-0.031067175790667534,
-0.03358832746744156,
-0.02964027039706707,
0.024593859910964966,
-0.017904939129948616,
0.08811089396476746,
-0.017310434952378273,
0.015020834282040596,
0.0232084970921278,
-0.03458867222070694,
-0.043236467987298965,
0.01681753806769848,
-0.02773345075547695,
-0.0034473922569304705,
-0.014144867658615112,
-0.024592533707618713,
0.043247707188129425,
-0.020450996235013008,
-0.027960777282714844,
0.027306463569402695,
-0.014642616733908653,
-0.012813395820558071,
0.0346677266061306,
-0.005297718569636345,
0.007918826304376125,
-0.03517061844468117,
0.024348996579647064,
0.02419857494533062,
0.0050238254480063915,
-0.0031893965788185596,
0.024268707260489464,
0.0039340294897556305,
0.0050790621899068356,
-0.03175026923418045,
0.07185393571853638,
-0.017987806349992752,
-0.0010003114584833384,
0.0021452761720865965,
-0.00029485850245691836,
-0.029568223282694817,
-0.008723250590264797,
0.016664233058691025,
-0.03727157413959503,
-0.000781459326390177,
0.02776232734322548,
-0.028362737968564034,
0.04431428760290146,
-0.04544007405638695,
0.030069250613451004,
-0.03305117040872574,
0.018285028636455536,
-0.0263492651283741,
0.01675216294825077,
-0.003162338165566325,
0.025921931490302086,
-0.037504296749830246,
-0.011055666022002697,
-0.004880846478044987,
-0.016146261245012283,
0.05744723230600357,
-0.049642689526081085,
0.0018269021529704332,
-0.013668362982571125,
-0.041667986661195755,
-0.06380421668291092,
-0.017146343365311623,
-0.02264111489057541,
-0.05144193395972252,
0.03574436157941818,
0.0282149538397789,
-0.0053788237273693085,
-0.028071444481611252,
-0.021272147074341774,
-0.006180341821163893,
0.02640288509428501,
-0.05580398812890053,
0.0007673681247979403,
-0.004399444442242384,
0.008116534911096096,
0.04980627819895744,
-0.002252219943329692
] |
<p>Dynamic structure factor is the spatial and temporal Fourier transform of Van Hoves time dependent pair correlation function. It is written as</p>
<p>$$ S(k,\omega)= \frac{1}{2\pi}\int F(k,t)\exp(i\omega t)dt $$</p>
<p>$F(k,t)$ is intermediate scattering function.
My question is how did we use spatial and temporal Fourier Transform of Van Hoves to get dynamic structure factor? and what does spatial and temporal Fourier transform mean?</p>
| 9,630 |
[
0.03195184841752052,
-0.02921886369585991,
0.021863380447030067,
-0.02498790994286537,
0.05949946492910385,
0.029429152607917786,
0.02063005603849888,
-0.05253979563713074,
0.038190338760614395,
-0.04666100814938545,
0.04054174944758415,
0.05695347115397453,
0.03157234191894531,
-0.02557722106575966,
0.006382370367646217,
0.02218569628894329,
0.020128775388002396,
0.03688871115446091,
-0.009974516928195953,
-0.02292417362332344,
0.0073793367482721806,
-0.009450635872781277,
0.007555940188467503,
-0.02800036408007145,
-0.020795561373233795,
0.04417112097144127,
0.023149540647864342,
0.01003205869346857,
0.0193153228610754,
0.037132952362298965,
-0.008715838193893433,
-0.030915262177586555,
-0.008422606624662876,
0.005618276074528694,
-0.013802853412926197,
-0.025787917897105217,
-0.05121580883860588,
-0.06575462222099304,
0.015000156126916409,
0.048175811767578125,
-0.0451996810734272,
-0.02460528165102005,
-0.021846232935786247,
0.0560016855597496,
-0.009064788930118084,
0.014892379753291607,
0.01403855811804533,
0.004070621449500322,
0.034666284918785095,
-0.04167518392205238,
0.05214216187596321,
-0.04582734778523445,
0.01652674190700054,
-0.020175300538539886,
-0.002271996345371008,
0.02135080099105835,
0.05912507325410843,
0.053450752049684525,
-0.012182984501123428,
-0.04556930437684059,
-0.026835288852453232,
-0.04673561826348305,
-0.0006047695060260594,
-0.0031779278069734573,
0.007967856712639332,
0.005763610824942589,
-0.023805133998394012,
-0.008531245402991772,
0.005210361443459988,
-0.022387322038412094,
-0.004420537501573563,
-0.029287556186318398,
0.016362832859158516,
-0.03930202126502991,
0.004376780241727829,
-0.017251024022698402,
0.01776803284883499,
0.00027833334752358496,
0.007337166462093592,
0.03514894098043442,
0.01602240838110447,
0.018077518790960312,
-0.023646406829357147,
-0.008661001920700073,
0.009286832064390182,
0.0049761813133955,
0.04793019965291023,
-0.026761431246995926,
-0.021853510290384293,
0.03789073973894119,
-0.02536662481725216,
0.06382088363170624,
0.04519623517990112,
-0.014705133624374866,
-0.021451784297823906,
-0.015264185145497322,
0.025430312380194664,
0.061983104795217514,
-0.02968788333237171,
-0.03543178364634514,
0.012134016491472721,
-0.04321980103850365,
0.0213107168674469,
0.07999404519796371,
-0.036363109946250916,
0.01121440902352333,
-0.02400638721883297,
0.0012575732544064522,
-0.002901176456362009,
-0.012254230678081512,
-0.04435588791966438,
0.019093871116638184,
-0.02749532461166382,
0.035065341740846634,
0.027881711721420288,
-0.03419001027941704,
-0.0018562775803729892,
0.01396158430725336,
0.03886554762721062,
0.09024080634117126,
0.02849060483276844,
-0.015444666147232056,
-0.012163763865828514,
0.016823528334498405,
-0.09146102517843246,
0.02949376218020916,
0.02586241625249386,
0.014380372129380703,
-0.010993373580276966,
0.0391436405479908,
-0.018685558810830116,
-0.008941569365561008,
0.02724059857428074,
0.005614225286990404,
-0.004863726906478405,
0.006794187240302563,
-0.098113514482975,
-0.0027913260273635387,
0.07255467027425766,
-0.03565593808889389,
-0.007692812941968441,
-0.07959239929914474,
0.018324529752135277,
0.015184322372078896,
0.06000431627035141,
0.002337654819712043,
-0.011042687110602856,
-0.022039012983441353,
0.04670749604701996,
0.02212560549378395,
-0.04406808316707611,
-0.04063306748867035,
-0.019328633323311806,
-0.033380646258592606,
-0.018977826461195946,
-0.03508833050727844,
0.04184095934033394,
0.025891276076436043,
-0.002439969452098012,
-0.017841758206486702,
0.06615059077739716,
0.007274301256984472,
-0.04077824950218201,
0.01178655307739973,
-0.0351097546517849,
-0.021553894504904747,
0.03449391946196556,
0.00015364898717962205,
0.0007343842298723757,
0.010019795037806034,
-0.013961292803287506,
-0.03145274147391319,
0.00833696499466896,
0.025298019871115685,
0.0012957259314134717,
-0.003610899206250906,
-0.008042617700994015,
0.023013338446617126,
-0.03577950969338417,
-0.023101577535271645,
-0.03206406533718109,
-0.05221962928771973,
-0.01632067561149597,
0.008706271648406982,
0.02178477682173252,
0.07122242450714111,
-0.017203439027071,
0.014418207108974457,
0.009671074338257313,
-0.0639481395483017,
-0.03670411556959152,
-0.02791152149438858,
-0.024671655148267746,
-0.02794380486011505,
-0.024947622790932655,
0.039240479469299316,
0.008073550648987293,
0.04722936823964119,
0.005275767762213945,
-0.018900763243436813,
-0.03218128904700279,
-0.00017426795966457576,
0.016939960420131683,
-0.012022735550999641,
0.049486350268125534,
-0.0014981260756030679,
0.019665168598294258,
-0.004227392841130495,
-0.017123013734817505,
-0.030962172895669937,
-0.017424501478672028,
0.0018574204295873642,
-0.03202094882726669,
0.051628146320581436,
-0.02170952595770359,
-0.046226851642131805,
0.020137641578912735,
0.024663390591740608,
-0.005410563200712204,
-0.01875949837267399,
0.0002455568755976856,
0.050181131809949875,
0.09804327040910721,
0.01090161595493555,
0.02704414166510105,
0.07260073721408844,
0.005987846292555332,
0.02164173312485218,
0.011382590979337692,
-0.032608408480882645,
-0.05884172394871712,
-0.044917937368154526,
0.06727380305528641,
0.05598321557044983,
-0.02803145907819271,
0.027625542134046555,
0.02254316583275795,
0.016804952174425125,
0.06442749500274658,
0.02430395595729351,
-0.040466535836458206,
-0.009489222429692745,
0.017349857836961746,
0.01472211629152298,
0.006024210713803768,
-0.02628716081380844,
0.005996998865157366,
0.017246441915631294,
0.001714525162242353,
-0.01494850218296051,
-0.04257575049996376,
0.04618183895945549,
-0.0026752883568406105,
-0.03475257381796837,
-0.01980128139257431,
-0.03794100880622864,
0.02813761867582798,
-0.024008287116885185,
0.026419447734951973,
0.04855964705348015,
-0.035227157175540924,
0.018875909969210625,
-0.012447063811123371,
-0.021862367168068886,
0.009862931445240974,
-0.0019276821985840797,
-0.012884027324616909,
-0.02410176955163479,
0.005734189413487911,
-0.04849110543727875,
-0.021933123469352722,
-0.00613362854346633,
-0.007933656685054302,
-0.0195312462747097,
-0.006563242524862289,
0.06256455183029175,
-0.01594713144004345,
0.03548470139503479,
0.006934181787073612,
-0.007861856371164322,
0.007242698222398758,
-0.004689904861152172,
0.003677132772281766,
0.008027974516153336,
-0.04794596508145332,
0.0387570858001709,
0.0031170991715043783,
-0.015041184611618519,
0.02083360217511654,
-0.05129152908921242,
-0.002382684499025345,
0.001872777589596808,
-0.010454821400344372,
-0.08967892825603485,
-0.012683616951107979,
0.00500099454075098,
0.02081446908414364,
-0.039928894490003586,
-0.005715159699320793,
0.026734881103038788,
0.015971681103110313,
-0.0037913143169134855,
0.016197998076677322,
-0.022339334711432457,
0.0016509398119524121,
-0.023966040462255478,
-0.012763958424329758,
-0.001474653952755034,
-0.05323171615600586,
0.03219074010848999,
-0.007086466997861862,
-0.03946882486343384,
0.005363150965422392,
-0.02695823274552822,
-0.00460655614733696,
0.013567499816417694,
0.032198987901210785,
0.06897514313459396,
0.0019746271427720785,
-0.05712505429983139,
0.05544763803482056,
0.008046857081353664,
0.0023074981290847063,
-0.01490224152803421,
-0.006022725719958544,
-0.044546227902173996,
-0.02213161811232567,
0.026006504893302917,
0.022953636944293976,
0.05269087105989456,
0.05060487240552902,
0.004479578230530024,
0.0022609473671764135,
0.043505724519491196,
0.000362339080311358,
-0.01806168258190155,
0.03232423588633537,
-0.020992735400795937,
-0.005003239493817091,
0.05501808971166611,
0.009915871545672417,
-0.04780005291104317,
-0.003535578725859523,
0.003380970563739538,
-0.01420376356691122,
0.01671985723078251,
-0.06320507079362869,
0.058827247470617294,
0.008726249448955059,
-0.03295893222093582,
-0.033451974391937256,
0.010850616730749607,
-0.005500102415680885,
-0.011934873647987843,
-0.013443644158542156,
0.02928079292178154,
0.047723438590765,
0.02133827470242977,
0.0049557993188500404,
0.03347225487232208,
0.029640043154358864,
0.015353281982243061,
-0.03221368417143822,
-0.04686642810702324,
0.002856637816876173,
0.06175129860639572,
-0.025740688666701317,
-0.0631202757358551,
0.037771619856357574,
0.023780763149261475,
0.040810804814100266,
-0.00527177844196558,
-0.009803342632949352,
-0.0019433279521763325,
-0.03568277880549431,
-0.0078268526121974,
-0.03055420145392418,
0.05094681680202484,
0.03736889362335205,
0.04728483036160469,
0.04350299388170242,
-0.005920929368585348,
-0.003370707156136632,
-0.0193643756210804,
-0.04522141441702843,
-0.00023534132924396545,
0.01843051239848137,
-0.0024864915758371353,
-0.015553471632301807,
0.015924379229545593,
0.038248877972364426,
-0.021389193832874298,
-0.01061976421624422,
0.0225521232932806,
0.03034878335893154,
-0.05129165202379227,
0.009477256797254086,
-0.033820949494838715,
0.030543198809027672,
-0.04042653366923332,
0.049246687442064285,
0.060467641800642014,
-0.035765573382377625,
0.031317781656980515,
0.07272125780582428,
0.005576577037572861,
0.050341445952653885,
-0.03541838005185127,
-0.008670463226735592,
0.030530467629432678,
0.0066909887827932835,
0.029126642271876335,
0.004731025081127882,
-0.02625715360045433,
0.001463764114305377,
0.009059781208634377,
0.05791368708014488,
0.03558235615491867,
-0.002424858743324876,
-0.01757345162332058,
-0.028541436418890953,
0.016894878819584846,
-0.001824596431106329,
0.044583700597286224,
0.01568193919956684,
0.003657759865745902,
0.017010027542710304,
0.01218718383461237,
-0.027120517566800117,
0.03455892950296402,
0.025931894779205322,
-0.004996909759938717,
0.009344661608338356,
-0.05930287763476372,
-0.006152659188956022,
0.0003552444977685809,
-0.025795692577958107,
0.0412953682243824,
0.011262154206633568,
0.00431253993883729,
0.06703503429889679,
0.01811894401907921,
-0.0045305900275707245,
-0.00990536343306303,
-0.02330924943089485,
-0.016650399193167686,
0.013867432251572609,
-0.012927231378853321,
-0.0050162444822490215,
-0.016733452677726746,
0.0642772987484932,
0.05078386515378952,
0.02056349441409111,
-0.011952557601034641,
-0.050548117607831955,
-0.020584985613822937,
0.03986258804798126,
0.03279179707169533,
-0.0043660057708621025,
0.006013751961290836,
-0.05188865214586258,
-0.003183797001838684,
0.014862526208162308,
-0.057511210441589355,
0.029641088098287582,
-0.006938573904335499,
0.002422511810436845,
-0.04062304273247719,
-0.031886328011751175,
-0.006531508173793554,
0.004887184128165245,
0.0005306214443407953,
-0.005449303891509771,
-0.06303709745407104,
-0.021286074072122574,
0.009081226773560047,
0.05430757999420166,
0.027261463925242424,
0.023773428052663803,
0.013786300085484982,
0.010683799162507057,
-0.030330471694469452,
0.012357095256447792,
-0.04352244734764099,
-0.05143823102116585,
0.013597050681710243,
0.031096115708351135,
0.05315785855054855,
0.04205488786101341,
-0.02929341048002243,
-0.01884021796286106,
-0.011375263333320618,
0.018502624705433846,
-0.017102789133787155,
-0.01899190992116928,
-0.00404669065028429,
0.04652094095945358,
0.029317284002900124,
-0.0447426475584507,
0.05971928685903549,
0.03508564084768295,
-0.01880660466849804,
-0.004251526203006506,
-0.03268935903906822,
0.07064169645309448,
-0.0017554947407916188,
0.033610448241233826,
-0.03238252177834511,
0.03445453196763992,
-0.038251522928476334,
0.04543976113200188,
-0.03798215836286545,
0.017084073275327682,
-0.011839871294796467,
0.006062001455575228,
-0.016713064163923264,
0.05074040964245796,
-0.014510358683764935,
-0.013039113022387028,
-0.002002398017793894,
0.014261092059314251,
0.005751245189458132,
-0.022252175956964493,
-0.022853903472423553,
-0.0302946325391531,
-0.02381182834506035,
-0.003621181705966592,
0.04011981189250946,
0.006668230518698692,
-0.04668363556265831,
-0.004771446343511343,
0.01600087806582451,
-0.05024932324886322,
0.020984407514333725,
-0.0337463840842247,
-0.039870452135801315,
0.030932936817407608,
-0.07529158145189285,
-0.015923602506518364,
0.02544207125902176,
-0.0033654742874205112,
0.04021245613694191,
-0.023246536031365395,
0.011830399744212627,
-0.03243868425488472,
0.011995965614914894,
-0.07052816450595856,
-0.03197449445724487,
0.010592183098196983,
0.01347082294523716,
-0.04597894102334976,
-0.03620884194970131,
-0.004726050421595573,
-0.031058773398399353,
-0.006851110607385635,
0.019309774041175842,
0.030571969226002693,
-0.003541767131537199,
-0.04098872095346451,
-0.008800712414085865,
-0.0009503390174359083,
-0.006561038084328175,
0.006692695431411266,
0.024879612028598785,
0.025296997278928757,
0.014643927104771137,
-0.021148117259144783,
0.007801844738423824,
0.018150268122553825,
-0.024316901341080666,
-0.017954839393496513,
-0.02993273176252842,
-0.010381391271948814,
0.03626704961061478,
-0.01793794147670269,
-0.04950987920165062,
-0.0034833301324397326,
-0.009705737233161926,
0.04248933494091034,
-0.025060273706912994,
0.012858424335718155,
0.005929247010499239,
0.04151308536529541,
0.042979951947927475,
0.009188525378704071,
-0.043811846524477005,
-0.023624220862984657,
0.01990777999162674,
-0.029682815074920654,
-0.006759872194379568,
0.017550259828567505,
0.010908938013017178,
-0.030697500333189964,
0.02403426542878151,
0.022649677470326424,
0.00011698343587340787,
0.018454641103744507,
0.005467652343213558,
0.03766683489084244,
0.04455014318227768,
0.044652897864580154,
-0.009632441215217113,
-0.020620761439204216,
-0.06665138900279999,
-0.014655809849500656,
0.05352415144443512,
-0.044305745512247086,
0.04024979844689369,
0.017826884984970093,
-0.03158528357744217,
-0.008282426744699478,
-0.058911725878715515,
-0.005477185361087322,
-0.000047569727030349895,
-0.023910431191325188,
0.04049019515514374,
-0.027644354850053787,
-0.006894775666296482,
0.03139705955982208,
0.047214657068252563,
-0.004095481708645821,
0.043942779302597046,
0.028678152710199356,
0.022695887833833694,
0.009161700494587421,
-0.021602753549814224,
-0.04511629790067673,
0.0456245020031929,
0.008774767629802227,
0.02870507352054119,
-0.0023584661539644003,
-0.007507464848458767,
0.05567751079797745,
0.05674144625663757,
0.00394042395055294,
-0.06755030900239944,
0.009325126186013222,
-0.024770518764853477,
0.031039247289299965,
0.014225845225155354,
-0.02393874153494835,
0.05232773348689079,
0.03542359545826912,
0.03386491909623146,
0.004585046786814928,
0.012012585066258907,
0.026614835485816002,
-0.05852149426937103,
-0.011467649601399899,
0.0055323513224720955,
-0.013168534263968468,
0.0453290157020092,
-0.0507909432053566,
-0.0375022254884243,
0.01248391717672348,
-0.016287490725517273,
0.023892998695373535,
0.0040861316956579685,
0.012142308056354523,
-0.05226564407348633,
0.08272303640842438,
-0.02146751433610916,
0.007533082272857428,
0.0018511493690311909,
-0.006748601328581572,
0.1364724040031433,
0.022413570433855057,
0.005774381570518017,
-0.047254160046577454,
-0.04355618357658386,
0.0052731456235051155,
0.049426279962062836,
-0.04851111024618149,
-0.02090286836028099,
0.04528971016407013,
0.0038657053373754025,
0.0008400093647651374,
0.03802236169576645,
0.048332370817661285,
-0.03253883123397827,
0.025511255487799644,
-0.037955671548843384,
-0.029241245239973068,
0.02840317226946354,
-0.0006574164726771414,
-0.024406705051660538,
0.010787326842546463,
-0.039096347987651825,
-0.0059448182582855225,
-0.014133651740849018,
-0.010760876350104809,
-0.05583038926124573,
-0.0366075225174427,
0.04291459545493126,
0.005618185270577669,
-0.029437391087412834,
0.016292409971356392,
0.010667125694453716,
0.028348954394459724,
-0.007845587097108364,
0.01655692048370838,
-0.024105407297611237,
-0.021060150116682053,
0.01868419349193573,
0.02016068436205387,
0.018526513129472733,
-0.008508682250976562,
0.024978306144475937,
-0.014834045432507992,
-0.018772853538393974,
-0.027244314551353455,
-0.014679388143122196,
0.05615387484431267,
0.01814817078411579,
-0.01945236697793007,
-0.029935922473669052,
-0.0005055583314970136,
0.040306489914655685,
-0.01939203031361103,
-0.0048006377182900906,
0.02319980226457119,
0.05162825435400009,
-0.04901241883635521,
0.011317681521177292,
-0.07291393727064133,
0.0071967970579862595,
-0.03906921297311783,
0.0371011421084404,
0.0008393169846385717,
-0.0005737531464546919,
0.007995324209332466,
-0.023686284199357033,
0.04153284803032875,
-0.013537921942770481,
-0.023751530796289444,
-0.017431361600756645,
0.03078727424144745,
-0.028893407434225082,
-0.015218026004731655,
0.017055818811058998,
0.013126331381499767,
0.041890017688274384,
0.0009228964918293059,
-0.0401768796145916,
-0.040625911206007004,
-0.08205555379390717,
0.013059712015092373,
-0.02401115372776985,
-0.06368795782327652,
0.00869724527001381,
0.023571182042360306,
0.02351250685751438,
0.03295447677373886,
-0.036298416554927826,
0.012563010677695274,
-0.053021982312202454,
-0.006235911976546049,
0.006123863626271486,
-0.04961925745010376,
-0.042233776301145554,
0.039826180785894394,
0.041659802198410034,
-0.017308497801423073,
-0.049533262848854065,
0.027205253019928932,
0.04885038733482361,
-0.018816161900758743,
-0.0227394700050354,
0.02125592716038227,
-0.03436668962240219,
-0.02267833985388279,
0.042318712919950485,
-0.0032929680310189724,
0.028510043397545815,
0.008727053180336952,
0.00913192331790924,
-0.012687032110989094,
0.0013244793517515063,
0.01415815856307745,
-0.015510739758610725,
0.0050588506273925304,
0.006341245491057634,
-0.03635271638631821,
-0.016965273767709732,
-0.03389497846364975,
-0.0009787722956389189,
-0.012569377198815346,
0.011072494089603424,
-0.032047223299741745,
0.03766418620944023,
-0.044254615902900696,
0.029743775725364685,
-0.008638309314846992,
0.03280230611562729,
-0.030445188283920288,
-0.006370145827531815,
0.006016224157065153,
0.028876690194010735,
0.03379964828491211,
-0.035454172641038895,
0.009343195706605911,
-0.010674091055989265,
0.055795636028051376,
0.018757326528429985,
-0.027353350073099136,
0.024716971442103386,
-0.04298653453588486,
-0.056163493543863297,
0.01356534380465746,
0.03736047074198723,
0.018747607246041298,
0.0396176315844059,
0.05714721605181694,
0.010554839856922626,
0.04319685697555542,
-0.015417675487697124,
-0.015116781927645206,
-0.01037713885307312,
-0.05749642103910446,
0.015037965029478073,
-0.027870124205946922,
0.008210588246583939,
0.024034284055233,
-0.010876854881644249,
0.026729417964816093,
0.008782073855400085,
-0.017815688624978065,
0.00204069702886045,
0.004297665785998106,
-0.013613023795187473,
0.005204875487834215,
0.023886894807219505,
-0.012076841667294502,
0.043447937816381454,
0.05963282287120819,
0.02721501886844635,
0.005170899443328381,
-0.003744130488485098,
-0.006790377199649811,
-0.09139028936624527,
0.009932544082403183,
0.0012014791136607528,
0.02348131313920021,
0.04322493448853493,
-0.021133163943886757,
0.02633994072675705,
0.020148079842329025,
-0.02598048374056816,
0.07090664654970169,
0.00009785615839064121,
0.00909380428493023,
-0.04873931035399437,
0.022734280675649643,
-0.029845498502254486,
0.054355788975954056,
0.05607690289616585,
-0.023626117035746574,
0.017570415511727333,
-0.0032973389606922865,
0.029463695362210274,
-0.005970622878521681,
-0.015768399462103844,
0.012821570038795471,
0.0009440883295610547,
-0.03365599364042282,
0.07757735252380371,
-0.011519575491547585,
-0.029748503118753433,
0.019151628017425537,
-0.006477561313658953,
-0.008193599060177803,
-0.01211676374077797,
0.018405940383672714,
0.025159185752272606,
0.032699961215257645,
0.018643870949745178,
-0.0386640764772892,
0.003839752869680524,
0.006593962199985981,
-0.025775469839572906,
0.005219867918640375,
0.021239427849650383,
-0.006683600600808859,
-0.05178612098097801,
-0.037032827734947205,
0.00002072992174362298,
0.04407568275928497,
-0.019027771428227425,
-0.04626176506280899,
0.023663807660341263,
-0.029052456840872765,
0.019944606348872185,
-0.0037264060229063034,
0.009246014058589935,
-0.03222702816128731,
-0.02050476148724556,
0.018572743982076645,
-0.006733772344887257,
-0.010347787290811539,
-0.000992159708403051,
-0.05120011419057846,
-0.033707939088344574,
0.026910563930869102,
0.01226459164172411,
-0.0191092099994421,
-0.04848753660917282,
-0.025371339172124863,
0.00906634982675314,
-0.014444357715547085,
-0.007945040240883827,
0.03514363244175911,
-0.04676101356744766,
0.04019631817936897,
-0.004191229585558176,
0.03766906261444092,
0.003682993585243821,
-0.035725586116313934,
-0.017673863098025322,
-0.0603351816534996,
0.028887124732136726,
0.01765228994190693,
-0.06222982704639435,
-0.03620165213942528,
-0.018536826595664024,
0.01030888594686985,
0.006699359510093927,
-0.002685019513592124,
0.024090608581900597,
-0.02050032652914524,
-0.03251584246754646,
-0.025906402617692947,
0.0030753291212022305,
-0.023083757609128952,
-0.0007674027001485229,
-0.024995354935526848,
-0.006761530414223671,
0.04080239310860634,
-0.020285721868276596,
-0.017749417573213577,
0.03807302936911583,
-0.01787618361413479,
-0.048525549471378326,
0.03008268214762211,
-0.0056230975314974785,
-0.044254858046770096,
0.016748223453760147,
0.011076079681515694,
0.008359973318874836,
0.03292177617549896,
-0.0007091478328220546,
0.02035931684076786,
-0.005152393598109484,
0.002066424349322915,
-0.008797580376267433,
0.00043066832586191595,
-0.07984144985675812,
-0.024301141500473022,
0.013510194607079029,
-0.0008085001609288156,
0.03177472949028015,
-0.056656792759895325,
-0.010949778370559216,
0.05371560901403427,
-0.041333626955747604,
0.003887040540575981,
0.061987295746803284,
-0.002320906613022089,
0.010755063965916634,
0.007594541180878878,
0.023324936628341675,
-0.009292894043028355,
-0.024895045906305313,
-0.0011781234061345458,
0.04948476701974869,
0.013626528903841972,
-0.002019963227212429,
0.04059100151062012,
-0.001258153817616403,
0.0005564121529459953,
0.003615351626649499,
0.014612025581300259,
0.029947014525532722,
-0.01898583024740219,
0.02017405815422535,
0.009607258252799511,
-0.03649109601974487,
0.01261188369244337,
0.014218786731362343,
0.006919936276972294,
0.0798485055565834,
-0.02553715929389,
-0.009887093678116798,
-0.0023581376299262047,
-0.01857401803135872,
-0.05668341740965843,
0.018227769061923027,
0.05976026505231857,
0.013727416284382343,
-0.03988137096166611,
0.016933076083660126,
0.010915186256170273,
-0.005717950407415628,
0.03470361605286598,
-0.050136126577854156,
0.005027350038290024,
0.00045498728286474943,
-0.008019682951271534,
0.042132262140512466,
0.005547736305743456,
-0.0445331372320652,
-0.024607518687844276,
0.038746897131204605,
0.050494641065597534,
0.015066259540617466,
0.01482968870550394,
-0.0074912142008543015,
0.025860639289021492,
0.041189949959516525,
-0.0782381072640419,
0.037683214992284775,
-0.02604282647371292,
0.016697673127055168,
-0.018830977380275726,
0.0020564247388392687
] |
<p>Connect the positive terminal of a battery to a piece of p-doped semiconductor, say, silicon doped with boron. Will the terminal pull electrons out of the doped silicon, or equivalently, inject holes into it?</p>
<p>The atomic structure of p-doped semiconductors certainly <em>accepts</em> electrons freely, but I feel like it should be stingier than an insulator when it comes to <em>donating</em> electrons. As an example of an insulator, undoped silicon is unwilling to give away electrons, or accept holes, because that would rip gaps in the stable crystalline bonding. P-type silicon should behave similarly here; thus, I would guess that the p-type block remains neutral, unlike a copper block which would take on the same charge as the terminal. However, if it were connected to a negative terminal, it would accept enough electrons to basically saturate it and give it a negative charge. Is this understanding correct? Or could the p-type somehow donate electrons/accept holes because of some kind of instability associated with doping?</p>
<p>EDIT: Admittedly, this is a rather petty question, and I doubt that anyone has ever bothered to check the answer in a published experiment. Still, knowing that the p-type stays neutral would confirm most people's (or at least my) model of why doped semiconductors conduct. Their conductivity possesses a kind of asymmetry, unlike that of copper, which gives and takes electrons equally freely.</p>
| 9,631 |
[
-0.04082304984331131,
-0.0043022348545491695,
0.02935744635760784,
0.000355330208549276,
-0.0019644121639430523,
0.015112476423382759,
0.003736610757187009,
0.005200224928557873,
-0.008788245730102062,
-0.02393587864935398,
0.0456012599170208,
0.020284922793507576,
0.002155032241716981,
0.036440011113882065,
0.003985826391726732,
0.016087902709841728,
0.005066572688519955,
-0.07493270188570023,
-0.021078016608953476,
0.007581868674606085,
0.0008700113394297659,
0.03497372567653656,
0.002277432242408395,
0.041553571820259094,
-0.0070360153913497925,
0.004545269068330526,
-0.004520702641457319,
-0.027788063511252403,
0.015837710350751877,
0.039672981947660446,
0.015963096171617508,
-0.04264235496520996,
0.009723499417304993,
0.005880679003894329,
0.03236483782529831,
-0.01696447841823101,
-0.013713273219764233,
-0.07007120549678802,
-0.030533164739608765,
0.036424845457077026,
0.0117934700101614,
0.028683872893452644,
0.029262810945510864,
0.015512012876570225,
-0.014397522434592247,
0.0009753524209372699,
0.0030893352814018726,
-0.022647272795438766,
0.017900966107845306,
-0.08089469373226166,
0.02427849918603897,
-0.012886677868664265,
0.04870094358921051,
0.04490797594189644,
-0.026187052950263023,
-0.013572716154158115,
0.09995250403881073,
0.07527856528759003,
-0.004025753121823072,
-0.05275431647896767,
-0.0012340282555669546,
-0.03592299669981003,
-0.029768412932753563,
-0.026816029101610184,
-0.03780714422464371,
0.022677067667245865,
0.02131977677345276,
-0.07213227450847626,
0.03972402215003967,
-0.019749144092202187,
0.01255691610276699,
0.011171342805027962,
0.025291742756962776,
-0.01771249622106552,
0.027285991236567497,
-0.01520494557917118,
0.036338064819574356,
0.040178801864385605,
0.031846992671489716,
0.030100852251052856,
-0.03779127821326256,
0.0015584788052365184,
0.0095866359770298,
0.06026643514633179,
-0.010486803948879242,
-0.06457135081291199,
0.06854324787855148,
-0.022169774398207664,
0.021439697593450546,
0.01766621321439743,
0.0017651986563578248,
-0.00024109908554237336,
0.019756317138671875,
-0.024733172729611397,
-0.040799856185913086,
0.02840583771467209,
-0.01772408001124859,
0.07980788499116898,
-0.0009996762964874506,
0.015945253893733025,
-0.01385459117591381,
0.02263522334396839,
0.03921337425708771,
0.05265742540359497,
0.002006653929129243,
-0.04957512766122818,
-0.0008506985031999648,
0.042951662093400955,
0.0051175192929804325,
0.011309570632874966,
-0.03227374330163002,
0.0005248740199021995,
-0.009528711438179016,
-0.020441817119717598,
0.04372264817357063,
-0.03445538505911827,
-0.019022734835743904,
-0.04708446189761162,
0.015048686414957047,
0.042131319642066956,
0.04341766983270645,
-0.008123361505568027,
0.06130705028772354,
-0.016593199223279953,
-0.06291139870882034,
-0.01580117829144001,
-0.010136772878468037,
-0.010330911725759506,
0.00445763161405921,
-0.00932477880269289,
0.0016531117726117373,
-0.008998752571642399,
0.011162744835019112,
-0.014081337489187717,
0.07815799117088318,
0.031232427805662155,
-0.0654149204492569,
-0.05711502954363823,
-0.0005958816036581993,
0.011654708534479141,
-0.009046618826687336,
-0.07759163528680801,
-0.0017834919271990657,
0.011958527378737926,
0.08620331436395645,
-0.025656774640083313,
-0.004399942234158516,
0.010872875340282917,
0.01916944421827793,
0.01309389341622591,
0.0027951914817094803,
-0.05105279013514519,
0.008931356482207775,
-0.02608305774629116,
-0.00013670514454133809,
-0.0689004436135292,
0.04696677252650261,
-0.009288639761507511,
0.012411488220095634,
-0.010678411461412907,
0.039643675088882446,
0.012037410400807858,
-0.027058850973844528,
-0.01789652742445469,
-0.033133700489997864,
-0.01926461048424244,
0.07970107346773148,
0.0011276639997959137,
0.01335237268358469,
0.04415737837553024,
0.022086605429649353,
0.04025104641914368,
0.010506238788366318,
0.02664179541170597,
0.015161514282226562,
-0.05174597352743149,
-0.046441204845905304,
-0.04251895099878311,
0.04584502428770065,
-0.027048563584685326,
-0.06518777459859848,
-0.02494417130947113,
0.0004085118998773396,
0.024292772635817528,
-0.0015071302186697721,
0.033153411000967026,
0.02319083921611309,
-0.033442702144384384,
0.016799025237560272,
-0.05000901222229004,
-0.044144898653030396,
-0.04708448052406311,
0.032034631818532944,
0.003672999097034335,
-0.022433394566178322,
0.048984821885824203,
-0.036171212792396545,
0.0033591517712920904,
-0.030660036951303482,
-0.015374421142041683,
-0.009118800982832909,
0.009972378611564636,
0.015902332961559296,
-0.00853889063000679,
0.020041856914758682,
0.06176739186048508,
0.002105096122249961,
0.045428551733493805,
0.030709417536854744,
0.004839269910007715,
-0.04144470766186714,
0.015588942915201187,
-0.051883257925510406,
-0.009862232021987438,
0.022786425426602364,
0.003636967157945037,
0.017714278772473335,
-0.026960475370287895,
-0.00016348219651263207,
0.029047280550003052,
0.006026270799338818,
0.0660279244184494,
0.043388865888118744,
0.03549952805042267,
-0.010570922866463661,
0.01954055391252041,
-0.015890920534729958,
0.022335682064294815,
-0.019816851243376732,
-0.019851872697472572,
-0.04599038138985634,
0.00831796694546938,
0.030342211946845055,
0.011986251920461655,
-0.028057381510734558,
0.02213474176824093,
-0.015535120852291584,
-0.0013482627691701055,
0.003989913500845432,
0.032537851482629776,
-0.021497558802366257,
0.00786934420466423,
0.05097395181655884,
-0.028338517993688583,
-0.004100778140127659,
0.008514044806361198,
0.001189474482089281,
-0.04605134204030037,
-0.02125594951212406,
-0.0003678117645904422,
-0.017618853598833084,
-0.009927954524755478,
0.04156286269426346,
0.027123481035232544,
-0.0011704122880473733,
-0.046715203672647476,
0.004139062017202377,
-0.020705802366137505,
0.007318221498280764,
0.009731918573379517,
-0.021654780954122543,
0.00029577058739960194,
-0.010064169764518738,
-0.01812346652150154,
0.0120951933786273,
0.0282710250467062,
0.001063539762981236,
-0.033875029534101486,
0.02830122783780098,
-0.04875560104846954,
0.027508411556482315,
-0.016062473878264427,
0.033700473606586456,
-0.01832733117043972,
0.04169560596346855,
0.0014743430074304342,
0.02720494382083416,
0.03477936610579491,
-0.03988192602992058,
-0.031040173023939133,
-0.03411348909139633,
-0.008166346698999405,
0.0372701920568943,
0.02399882674217224,
0.00944276712834835,
-0.016414498910307884,
-0.010292786173522472,
-0.04128347337245941,
0.053822021931409836,
0.02222905121743679,
-0.0018006879836320877,
-0.00858044158667326,
-0.006929690949618816,
-0.009869959205389023,
-0.005842622835189104,
0.002276289975270629,
-0.011537288315594196,
-0.015709176659584045,
-0.00531969778239727,
0.017798224464058876,
0.008108708076179028,
-0.019161531701683998,
0.05463781580328941,
-0.06098781153559685,
-0.02620418556034565,
0.031255174428224564,
-0.026617400348186493,
0.02135421894490719,
-0.0037180986255407333,
0.051920559257268906,
0.025079546496272087,
-0.02967832237482071,
0.005308294203132391,
-0.05143023654818535,
-0.04181736335158348,
0.020708851516246796,
-0.016985561698675156,
-0.006032315548509359,
0.0047157746739685535,
-0.00707792304456234,
0.08498524129390717,
-0.00969264842569828,
-0.02783859707415104,
0.02555566467344761,
-0.05699087679386139,
-0.056095726788043976,
-0.016920920461416245,
0.04826715216040611,
0.07646828889846802,
0.027604416012763977,
0.0004643747233785689,
0.02905772626399994,
0.08185552060604095,
0.006638477556407452,
0.03416328877210617,
-0.01049961056560278,
0.018566947430372238,
-0.0025660719256848097,
0.002215336076915264,
0.03858174756169319,
0.017159612849354744,
-0.007628737948834896,
0.01630077138543129,
-0.03104202263057232,
0.020706547424197197,
0.032406970858573914,
-0.029234785586595535,
0.020084304735064507,
-0.023235302418470383,
0.035778071731328964,
-0.03088575229048729,
0.025503545999526978,
0.026948511600494385,
-0.0037702040281146765,
-0.01540470402687788,
0.023345759138464928,
0.04630771651864052,
-0.02866857498884201,
0.012491708621382713,
0.011117725633084774,
0.034668680280447006,
-0.03653498739004135,
-0.05160188674926758,
0.037184327840805054,
-0.012254790402948856,
0.0029691269155591726,
0.008069678209722042,
-0.00034033023985102773,
0.04266936331987381,
-0.00009352889173896983,
0.03070952743291855,
0.009412191808223724,
-0.029890602454543114,
0.002739845309406519,
-0.04324299097061157,
-0.009357836097478867,
0.006646709516644478,
0.05459539592266083,
-0.004062561318278313,
0.04521646723151207,
0.041340894997119904,
0.047641828656196594,
-0.04678628221154213,
0.0002872130135074258,
-0.08023111522197723,
0.00294167036190629,
-0.0036215754225850105,
-0.006419208832085133,
-0.05048854649066925,
0.0013010367983952165,
0.020364370197057724,
-0.03659182786941528,
-0.0242666844278574,
-0.016261275857686996,
-0.027421927079558372,
-0.04686088487505913,
0.03940725326538086,
-0.034863829612731934,
-0.052857231348752975,
-0.021715600043535233,
0.0002684851933736354,
0.031012628227472305,
-0.00920498464256525,
-0.021941645070910454,
-0.012093717232346535,
-0.0069159772247076035,
0.010041383095085621,
-0.0066255833953619,
-0.034223392605781555,
0.007846969179809093,
0.03147904574871063,
0.022911518812179565,
0.029109133407473564,
0.00359603064134717,
-0.017022961750626564,
-0.024130763486027718,
0.04220243915915489,
0.03812805563211441,
-0.012016593478620052,
0.005364826414734125,
-0.06745561957359314,
-0.049042459577322006,
-0.013814382255077362,
0.06143767759203911,
-0.01997746154665947,
0.026065373793244362,
0.03359801694750786,
-0.002585628069937229,
-0.011323261074721813,
0.04930352047085762,
0.010516326874494553,
0.035787153989076614,
-0.04715253785252571,
-0.04708215221762657,
-0.034465573728084564,
-0.022055022418498993,
-0.011870568618178368,
0.04156399890780449,
0.016593949869275093,
-0.025633683428168297,
0.003881732700392604,
0.028796261176466942,
0.022352933883666992,
-0.008997827768325806,
0.024113547056913376,
0.01953575760126114,
0.02471080608665943,
-0.03415561467409134,
0.02726195938885212,
0.027998417615890503,
0.019422076642513275,
0.015738626942038536,
0.018758513033390045,
-0.0028355857357382774,
-0.11200667917728424,
0.01458539068698883,
0.03207075223326683,
0.05276840552687645,
-0.019357234239578247,
-0.017789343371987343,
-0.04773712158203125,
0.004102509468793869,
0.024977674707770348,
0.0015260378131642938,
0.0331382118165493,
0.011176398023962975,
-0.00021975679555907845,
-0.05952654778957367,
-0.01811005175113678,
-0.029105838388204575,
-0.016166245564818382,
0.006333136931061745,
0.015748735517263412,
-0.024588914588093758,
-0.06593397259712219,
-0.02623789943754673,
0.030987868085503578,
0.024400245398283005,
0.08168599754571915,
-0.017219942063093185,
0.033368900418281555,
0.00565840769559145,
0.013508119620382786,
-0.023070696741342545,
-0.12401038408279419,
-0.0036194503773003817,
-0.002587299095466733,
0.005621166899800301,
0.04319153353571892,
-0.06035327911376953,
-0.07541234791278839,
0.009026438929140568,
-0.002140820724889636,
0.005052139516919851,
0.002215499756857753,
-0.0087371114641428,
0.03517681732773781,
-0.0017070292960852385,
0.037661366164684296,
0.03343022242188454,
0.042087946087121964,
-0.042496465146541595,
-0.01973683014512062,
-0.03314146772027016,
0.0476674810051918,
-0.018363021314144135,
0.007770100608468056,
-0.009300671517848969,
0.011891086585819721,
0.0033737202174961567,
0.03953142836689949,
0.041007086634635925,
0.0489739254117012,
0.00042639882303774357,
-0.07330484688282013,
0.01700880005955696,
-0.01716172695159912,
-0.039993766695261,
0.005852012895047665,
0.0000636577169643715,
0.018932310864329338,
0.007816379889845848,
-0.0317833349108696,
-0.027372444048523903,
-0.007142499554902315,
0.029070379212498665,
0.01722775027155876,
-0.018146630376577377,
0.018228381872177124,
-0.0378340519964695,
0.003484070533886552,
-0.0076436251401901245,
-0.028150249272584915,
0.046121157705783844,
0.002135536167770624,
-0.0038811087142676115,
0.014111394993960857,
-0.04715733230113983,
-0.008417612873017788,
0.058874040842056274,
-0.008183316327631474,
0.0033747979905456305,
-0.045615628361701965,
0.05324992164969444,
-0.01071152277290821,
-0.0014878069050610065,
-0.1032906323671341,
-0.05128944292664528,
0.03784448653459549,
0.013577270321547985,
-0.0680873692035675,
-0.01695466972887516,
-0.014082535170018673,
0.03407253324985504,
-0.06594348698854446,
0.045903295278549194,
0.04211313650012016,
-0.04892057925462723,
-0.00036749933497048914,
0.000038455662433989346,
-0.01993788778781891,
0.07199416309595108,
-0.001387593219988048,
-0.016170509159564972,
0.004670531954616308,
-0.05225931107997894,
0.02631724625825882,
-0.009814443998038769,
0.024413153529167175,
-0.018463971093297005,
-0.009497902356088161,
-0.006135881878435612,
-0.002308269962668419,
0.031748633831739426,
-0.006132657639682293,
-0.029254870489239693,
0.03886522725224495,
-0.0017193184467032552,
-0.01974227838218212,
-0.004909695126116276,
0.003656655317172408,
0.015216296538710594,
0.014561210758984089,
0.030676044523715973,
0.009947002865374088,
-0.02583185024559498,
-0.03453642129898071,
0.0017874472541734576,
0.018460942432284355,
0.016914615407586098,
-0.0002893823548220098,
0.030539758503437042,
0.011433758772909641,
0.009515922516584396,
0.0520215779542923,
0.020772481337189674,
0.05646626651287079,
-0.00411277124658227,
0.00021172748529352248,
-0.05269932001829147,
0.014470076188445091,
-0.014875384047627449,
-0.04451676830649376,
-0.007299202494323254,
-0.0054772463627159595,
0.04811960458755493,
0.0016584331169724464,
0.016740601509809494,
0.021454254165291786,
-0.015721622854471207,
-0.006916596554219723,
-0.024413323029875755,
0.015036646276712418,
-0.016505811363458633,
-0.013991578482091427,
0.011665450409054756,
0.0036031135823577642,
-0.00008026570139918476,
0.04100141301751137,
0.03684014081954956,
-0.03684699907898903,
0.045471593737602234,
0.04258513078093529,
0.010342469438910484,
0.07722434401512146,
-0.012661879882216454,
-0.04448390752077103,
0.03591746464371681,
-0.038241542875766754,
0.013340850360691547,
0.021257929503917694,
-0.034040819853544235,
0.04280511289834976,
-0.01891707256436348,
0.02376389503479004,
-0.018884053453803062,
-0.04116649553179741,
-0.04972754046320915,
0.008472633548080921,
0.0012740071397274733,
0.009027260355651379,
-0.045647554099559784,
0.0005465139402076602,
0.02323390543460846,
0.02641385979950428,
-0.013617697171866894,
0.0048804632388055325,
-0.08289163559675217,
-0.024131134152412415,
-0.006026401650160551,
0.00997581984847784,
0.03406195342540741,
0.003067024052143097,
-0.004082101862877607,
0.011821752414107323,
-0.03251160308718681,
0.029039649292826653,
-0.015764042735099792,
0.05143123120069504,
-0.01398930512368679,
0.04847903922200203,
-0.0525842048227787,
0.03310928866267204,
-0.035562943667173386,
-0.009342646226286888,
0.11635740101337433,
0.05547914281487465,
0.02205258421599865,
-0.04816610738635063,
0.015476512722671032,
-0.03871559724211693,
0.03599431738257408,
-0.013645216822624207,
0.025199774652719498,
0.016473466530442238,
0.00841422751545906,
-0.003716301405802369,
0.008406971581280231,
-0.005458496976643801,
0.02984398975968361,
0.04540286958217621,
-0.04381131753325462,
-0.02288670465350151,
0.018001103773713112,
0.02289043739438057,
-0.02193765714764595,
0.010910219512879848,
-0.02138599194586277,
0.004605674650520086,
-0.031167220324277878,
0.0038169396575540304,
-0.056560467928647995,
-0.03222595900297165,
0.04894338548183441,
0.05164560675621033,
-0.004447474144399166,
-0.018411828204989433,
0.033022571355104446,
0.020410681143403053,
0.003075761953368783,
0.009284631349146366,
-0.0013993805041536689,
0.022498514503240585,
-0.003401018911972642,
0.03301477059721947,
0.029369451105594635,
-0.00836428627371788,
0.014867180027067661,
0.0019009013194590807,
-0.052982229739427567,
0.008879580534994602,
0.0035759706515818834,
0.011485620401799679,
-0.008969658054411411,
-0.019363103434443474,
0.00009378273534821346,
0.03599746152758598,
0.009112285450100899,
-0.03212876245379448,
-0.06089913845062256,
-0.013788350857794285,
0.03272844851016998,
0.024967487901449203,
-0.007752607110887766,
0.01437221746891737,
0.038936156779527664,
0.019387751817703247,
-0.008769864216446877,
0.00040140777127817273,
-0.018650848418474197,
-0.0031391456723213196,
0.0050683231092989445,
0.03754455968737602,
-0.016881654039025307,
-0.014962725341320038,
-0.023242024704813957,
-0.004320280160754919,
-0.054332390427589417,
-0.0202409066259861,
0.014142033644020557,
0.04518679901957512,
0.026451142504811287,
-0.017540931701660156,
0.023184046149253845,
0.006219088565558195,
-0.06074909493327141,
0.055818378925323486,
0.020465010777115822,
0.013017019256949425,
-0.042847372591495514,
0.0026943956036120653,
0.02975497394800186,
0.01659298874437809,
-0.04243263229727745,
0.007600556593388319,
0.0018044656608253717,
0.02153109572827816,
0.001342984032817185,
-0.05861477181315422,
-0.02578572928905487,
0.004157375078648329,
-0.060888078063726425,
0.02363371104001999,
0.00281535810790956,
0.0005125232855789363,
-0.0028497506864368916,
0.006222724914550781,
-0.0031660336535423994,
-0.0031604240648448467,
-0.024060221388936043,
-0.0027693253941833973,
0.0116041274741292,
0.004720696248114109,
-0.007913917303085327,
0.0004975790507160127,
0.01347662415355444,
0.004457763396203518,
-0.03200847655534744,
0.006760637741535902,
0.0016320786671712995,
-0.0009018254349939525,
0.03126584365963936,
-0.022889461368322372,
0.0009291692986153066,
-0.044070545583963394,
0.00008957240061135963,
-0.024051852524280548,
-0.007261376362293959,
-0.09303867071866989,
-0.04197372496128082,
0.014994725584983826,
0.02507598139345646,
0.03696234151721001,
0.009991401806473732,
-0.043600719422101974,
0.008125347085297108,
0.037453021854162216,
0.024895798414945602,
-0.03308824449777603,
-0.0027411633636802435,
0.0031907467637211084,
-0.018766239285469055,
0.007630221080034971,
-0.033321477472782135,
-0.038726307451725006,
0.05307586491107941,
-0.036017075181007385,
-0.013745777308940887,
-0.011192478239536285,
0.0012677160557359457,
0.018519602715969086,
-0.023929649963974953,
-0.02013220824301243,
-0.015797968953847885,
0.03707354888319969,
-0.0290804635733366,
-0.021576518192887306,
0.01235052291303873,
-0.04585334658622742,
-0.00028132915031164885,
0.0277055986225605,
-0.017870543524622917,
-0.0190324317663908,
0.02528787963092327,
0.04532049223780632,
0.016180774196982384,
-0.014163105748593807,
-0.004163983277976513,
-0.020384881645441055,
0.012238296680152416,
0.00852121040225029,
0.01565452106297016,
0.02624187059700489,
-0.00965723767876625,
0.018445122987031937,
0.02005552127957344,
0.05033759027719498,
0.015313473530113697,
0.011760969646275043,
-0.03188015893101692,
-0.04980190470814705,
0.0506712906062603,
-0.011980865150690079,
-0.007314577233046293,
-0.029738208279013634,
-0.030544161796569824,
-0.02445918694138527,
-0.11061321943998337,
0.005770142190158367,
-0.00831680092960596,
-0.04920801520347595,
-0.0489453449845314,
-0.025918524712324142,
-0.023867813870310783,
-0.025676239281892776,
0.017066078260540962,
0.058857642114162445,
-0.015267656184732914,
0.005077657289803028,
0.01640586368739605,
0.019295446574687958,
-0.036239489912986755,
0.050781864672899246,
0.020818745717406273,
0.017287487164139748,
0.02521524764597416,
-0.026319416239857674,
0.017098834738135338,
0.017071126028895378,
0.01464102789759636,
-0.04849647358059883,
0.0029766354709863663,
0.017182322219014168,
0.003378310240805149,
0.05862170457839966,
-0.020051555708050728,
-0.029720960184931755,
-0.023116229102015495,
-0.015821920707821846,
0.053270380944013596,
0.03379840403795242,
-0.016259148716926575,
0.037875041365623474,
-0.01724006049335003,
-0.03429928049445152,
0.011338643729686737,
0.01775701716542244,
-0.0177121814340353,
0.02360541746020317,
-0.01066017895936966,
-0.015372968278825283,
0.03646364063024521,
0.00025428569642826915,
-0.031315479427576065,
-0.0447675921022892,
-0.01777050830423832,
0.021160200238227844,
-0.01009502075612545,
0.038211338222026825,
-0.0014242592733353376,
-0.031037794426083565,
0.006702711805701256,
0.028911378234624863,
0.030222177505493164,
0.00886126235127449,
-0.026755504310131073,
-0.015908649191260338,
0.024919793009757996,
-0.00011742278002202511,
0.00801173411309719,
-0.03977102041244507,
-0.001252718036994338,
0.07773961871862411,
0.01936388947069645,
0.06102662906050682,
-0.006121351849287748,
-0.07684671878814697,
0.02589675784111023,
-0.06303093582391739,
0.0350005067884922,
-0.014302157796919346,
0.02090962789952755,
-0.04197182133793831,
-0.03975716233253479,
0.023719239979982376,
0.04391869902610779,
0.06933646649122238,
-0.007148883771151304,
-0.03915751725435257,
-0.02389639802277088,
-0.037163496017456055,
-0.0011675170389935374,
-0.02118162252008915,
-0.00654333271086216,
0.028366928920149803,
-0.03290500119328499,
-0.00901704654097557,
-0.026617031544446945,
-0.02339017204940319,
0.02046690508723259,
0.03588961437344551,
0.0015379802789539099,
-0.02410891465842724,
-0.012403064407408237,
-0.010949796997010708,
0.052690520882606506,
0.005988676100969315,
0.018617520108819008,
0.11325356364250183,
0.004193934611976147,
0.01832825131714344,
-0.0007380796014331281,
-0.023846443742513657,
-0.03527286648750305,
0.03544413670897484,
-0.035572223365306854,
-0.021524500101804733,
-0.00280379387550056,
0.017818884924054146,
0.02797899767756462,
0.008793865330517292,
0.002057034522294998,
0.0162405613809824,
-0.03608376532793045,
-0.017040200531482697,
0.025041848421096802,
0.016040239483118057,
0.040593378245830536,
-0.011868111789226532,
-0.014717008918523788,
0.0022837985306978226,
0.030785873532295227,
-0.01807856559753418,
0.05023092031478882,
0.03145672753453255,
-0.01342766173183918,
-0.026899250224232674,
0.028485650196671486,
0.01056106761097908,
0.00593526428565383,
-0.012920642271637917,
0.01515206415206194,
-0.02656564675271511,
-0.0032562187407165766,
0.03873381391167641,
0.007570256944745779,
0.03151613473892212,
-0.006968388333916664,
-0.018702181056141853,
0.05444405600428581,
-0.0008997193654067814,
0.02993522398173809,
-0.0292659904807806,
0.020032938569784164,
0.029075613245368004,
0.010582798160612583,
0.02703620307147503,
0.03482944890856743,
-0.003991744946688414,
-0.0605594627559185,
-0.031117461621761322,
0.011597850359976292,
0.03142017498612404,
-0.04549649357795715,
-0.002933831885457039,
-0.02857985533773899,
-0.005598946008831263,
-0.004168483428657055,
0.00883570034056902,
-0.03116728737950325,
-0.014299223199486732,
0.039876703172922134,
0.040562018752098083,
0.004559926688671112,
0.005240282975137234,
0.02947925217449665,
0.019677717238664627,
0.04586192965507507,
-0.04219982028007507,
-0.00461462652310729,
-0.03788907080888748,
0.006887886207550764,
-0.02069670520722866,
0.004901946987956762
] |
<p>In inflationary theory, many papers start off by making the slow-roll approximation, on which many things depend. This approximation is usually presented by requiring that two 'slow-roll parameters' are small:
$$\epsilon_V\equiv\frac{1}{16\pi G}\left(\frac{V'}{V}\right)^2 \ll 1$$
$$|\eta_V|\equiv \frac{1}{8\pi G}\left(\frac{V''}{V}\right)\ll 1$$
We then have
$$H^2=\frac{8\pi G}{3}V$$
$$3H\dot{\phi}=-V'$$
Now, the first of these two conditions is reasonably easily derived:
\begin{align*}
\frac{\ddot{a}}{a}&\gg 0\\
\dot{H}+H^2 &\gg 0\\
-\frac{\dot{H}}{H^2}&\ll 1\\
\frac{1}{16\pi G}\left(\frac{V'}{V}\right)^2=\epsilon_V&\ll 1 \hspace{1cm}\text{used slow roll approx.}
\end{align*}</p>
<p>However, I'm not sure how to find the second one (note that I am <em>not</em> asking for an intuitive explanation, I understand what the second parameter represents, I just wanna know how to derive it). Could someone tell me how to derive it (or what the original premise, analogous to $\ddot{a}/a\gg 0$ for $\epsilon_V$, is)?</p>
| 9,632 |
[
0.029369501397013664,
-0.026706665754318237,
0.04084412008523941,
0.0017420360818505287,
0.011043068952858448,
-0.014544619247317314,
-0.020025093108415604,
-0.01720043644309044,
-0.014215534552931786,
-0.024991651996970177,
-0.02678730897605419,
-0.000307545909890905,
0.05088624730706215,
-0.004826838616281748,
0.028324441984295845,
0.0008452415931969881,
-0.02767554670572281,
-0.00445126835256815,
-0.016306674107909203,
-0.06610376387834549,
0.042820949107408524,
0.01017911545932293,
-0.0037843359168618917,
0.009447832591831684,
-0.004267847631126642,
0.02796931192278862,
0.047359418123960495,
0.008074515499174595,
-0.013863307423889637,
0.04777621477842331,
-0.05575352534651756,
-0.009156772866845131,
-0.018586590886116028,
-0.011580420657992363,
0.026823192834854126,
-0.019437476992607117,
0.011637173593044281,
-0.022050831466913223,
-0.02036607638001442,
0.030587438493967056,
-0.0920831635594368,
0.034424446523189545,
-0.004983995109796524,
0.018937082961201668,
0.002250513294711709,
0.012701719999313354,
-0.013827822171151638,
-0.02529655396938324,
0.08899635821580887,
-0.06608760356903076,
0.035846222192049026,
0.016883771866559982,
0.0005291486158967018,
0.03580770269036293,
-0.0003335144720040262,
-0.024640507996082306,
0.07060015946626663,
0.048801977187395096,
-0.024010036140680313,
-0.026278527453541756,
-0.030700018629431725,
-0.03481205180287361,
0.005835668183863163,
-0.011770851910114288,
0.02265876904129982,
0.035875238478183746,
-0.028745410963892937,
-0.011510117910802364,
0.015315145254135132,
-0.03167913854122162,
0.03007880412042141,
-0.02418031170964241,
0.049607496708631516,
0.007576753851026297,
0.04085531830787659,
0.01414559967815876,
0.006007864139974117,
0.030477136373519897,
0.03943365812301636,
0.06090725213289261,
-0.02156807854771614,
-0.007134588435292244,
0.0263838991522789,
0.0427064448595047,
-0.007193855941295624,
0.019117912277579308,
0.07310283929109573,
-0.03297754377126694,
0.006533436942845583,
0.016043007373809814,
-0.051132846623659134,
0.01886942982673645,
0.023804210126399994,
-0.02043122984468937,
-0.03825648874044418,
0.06149287521839142,
0.005492924712598324,
0.015460639260709286,
-0.0026448890566825867,
-0.023674525320529938,
-0.044570475816726685,
-0.01791055127978325,
0.00923448521643877,
0.10754470527172089,
0.01776304468512535,
-0.03008502721786499,
-0.02050282247364521,
0.0015109509695321321,
-0.06899293512105942,
-0.05465735122561455,
-0.0069749075919389725,
0.004108585882931948,
-0.016978183761239052,
0.013867398723959923,
-0.005837298464030027,
0.008230448700487614,
0.015158495865762234,
-0.04789207875728607,
0.026255983859300613,
0.04916505888104439,
0.06240979582071304,
0.0038477254565805197,
0.017552707344293594,
-0.020025474950671196,
-0.04985274001955986,
0.02721533738076687,
0.06450662761926651,
-0.028979860246181488,
-0.03522228077054024,
0.011771469376981258,
0.04426538944244385,
-0.028241893276572227,
0.013706239871680737,
0.0135646415874362,
0.0445089228451252,
0.012981551699340343,
-0.09043397754430771,
-0.0286246407777071,
0.0247341338545084,
-0.004591670352965593,
-0.015128868632018566,
-0.08100883662700653,
0.010116728022694588,
0.05636299028992653,
0.07193617522716522,
0.026578517630696297,
0.0023982878774404526,
-0.03553679212927818,
0.0060677663423120975,
0.025842051953077316,
-0.052751485258340836,
-0.0353466235101223,
-0.029356641694903374,
-0.043707966804504395,
-0.016380779445171356,
-0.058718759566545486,
0.019314315170049667,
0.01878216862678528,
-0.012179208919405937,
-0.024102970957756042,
0.09450513124465942,
-0.035831268876791,
0.01743561215698719,
-0.017738064751029015,
-0.01964818313717842,
-0.029361585155129433,
0.057634636759757996,
0.011968935839831829,
-0.005769356619566679,
0.03803469240665436,
0.0018912821542471647,
0.02882937714457512,
-0.026727592572569847,
0.042584922164678574,
0.055917393416166306,
-0.03500532731413841,
0.00752946175634861,
-0.038228631019592285,
-0.016529370099306107,
0.017286567017436028,
-0.002454969799146056,
-0.015462690964341164,
-0.022276541218161583,
0.015468602068722248,
0.0022833615075796843,
-0.015280753374099731,
0.012612417340278625,
0.004128171596676111,
-0.01525937207043171,
-0.06813620030879974,
0.008039788343012333,
-0.06209748238325119,
-0.03107229433953762,
0.030895255506038666,
-0.017502756789326668,
0.08221057802438736,
0.004399296827614307,
-0.026402734220027924,
0.009095738641917706,
-0.034234289079904556,
-0.004453748930245638,
0.029613707214593887,
0.02285505272448063,
-0.03126290440559387,
0.03503629192709923,
0.048761263489723206,
0.01072042528539896,
-0.015796897932887077,
0.01550497766584158,
-0.01844787411391735,
-0.03272491320967674,
0.039649318903684616,
-0.004056999925523996,
0.023996179923415184,
-0.034513164311647415,
0.00001804512066883035,
-0.013509830459952354,
-0.0021588115487247705,
0.00750588346272707,
0.04497507959604263,
-0.06699024140834808,
0.05647498369216919,
0.059309884905815125,
0.006554477382451296,
-0.04074674844741821,
0.05590930953621864,
-0.015716558322310448,
0.028455838561058044,
-0.03341784328222275,
-0.028678398579359055,
-0.04603537544608116,
-0.028281057253479958,
0.008342062123119831,
-0.0040667434222996235,
0.001343407784588635,
-0.002699772361665964,
0.05481927841901779,
0.016644394025206566,
0.04935487359762192,
-0.00288364733569324,
0.005262487102299929,
-0.011395498178899288,
0.041639700531959534,
0.0003900201991200447,
-0.003768152091652155,
0.008851740509271622,
0.029996933415532112,
0.006617297418415546,
0.02518431656062603,
-0.002214464358985424,
-0.030138282105326653,
0.022658292204141617,
-0.013891708105802536,
-0.010656136088073254,
0.0027252426370978355,
-0.01204525027424097,
0.06468724459409714,
-0.030129099264740944,
0.029209692031145096,
0.02715340629220009,
0.010842502117156982,
0.00207336014136672,
-0.05244208127260208,
-0.012936878949403763,
0.04354485869407654,
0.006020669359713793,
-0.0310848169028759,
-0.03247639536857605,
0.018811089918017387,
-0.02905542589724064,
0.007852628827095032,
-0.03860720992088318,
-0.00522278668358922,
-0.013550573028624058,
-0.028817322105169296,
0.02542581409215927,
0.022092098370194435,
-0.021347612142562866,
-0.03071329928934574,
-0.017647260800004005,
0.02972826175391674,
0.005049600265920162,
0.009169461205601692,
-0.00198382418602705,
-0.025833535939455032,
0.011811298318207264,
-0.008200408890843391,
-0.024104084819555283,
0.026017427444458008,
0.01694047451019287,
-0.017003212124109268,
-0.006813290063291788,
0.014102778397500515,
-0.06135090813040733,
-0.020971091464161873,
-0.025453926995396614,
-0.007198314182460308,
-0.04507855698466301,
-0.011068017221987247,
0.07531286776065826,
-0.02261604182422161,
-0.01791945844888687,
0.02152230776846409,
-0.037713807076215744,
-0.057113584131002426,
0.003311151871457696,
0.016678495332598686,
-0.023255249485373497,
-0.040664564818143845,
0.03587789461016655,
0.012233547866344452,
0.010438874363899231,
-0.02910696528851986,
-0.06370317190885544,
-0.032877855002880096,
0.039434872567653656,
0.02260950207710266,
0.02564314380288124,
0.0033738245256245136,
-0.04161403328180313,
0.08318539708852768,
0.04078191518783569,
-0.008187288418412209,
-0.008584297262132168,
-0.0036068405024707317,
-0.0029199698474258184,
-0.037043407559394836,
-0.0005010276800021529,
0.01864231377840042,
0.003851398127153516,
0.014182551763951778,
0.02244858257472515,
0.03772912919521332,
0.014710783958435059,
0.01393972896039486,
-0.030438385903835297,
0.0017663452308624983,
0.013158505782485008,
0.004332190845161676,
-0.0020671640522778034,
-0.004668353125452995,
0.015069750137627125,
-0.0006441128789447248,
-0.0037277054507285357,
0.05127314478158951,
-0.029760967940092087,
-0.028899189084768295,
0.06130404397845268,
0.0010918335756286979,
-0.014263465069234371,
0.019522156566381454,
0.012473094277083874,
0.026524165645241737,
-0.0019767070189118385,
0.009512707591056824,
0.019339781254529953,
0.03954126685857773,
-0.034231893718242645,
0.02275298722088337,
0.025940461084246635,
0.014241947792470455,
-0.00907904002815485,
-0.024966157972812653,
-0.018030891194939613,
-0.016778700053691864,
0.015104400925338268,
-0.04861525446176529,
0.017482483759522438,
0.04604783281683922,
0.034358881413936615,
-0.004293486010283232,
-0.028865182772278786,
0.0034703712444752455,
0.022761574015021324,
-0.08509358763694763,
0.0016862422926351428,
-0.0036749723367393017,
-0.0039000012911856174,
0.0009737692889757454,
0.0420934334397316,
0.027125054970383644,
-0.007569977547973394,
0.004463916644454002,
0.007098517846316099,
-0.06262355297803879,
0.009287955239415169,
-0.007298209238797426,
-0.026003221049904823,
0.010031274519860744,
0.01882275380194187,
0.012604059651494026,
-0.030518030747771263,
-0.012642311863601208,
-0.04374590516090393,
-0.015687011182308197,
-0.017318615689873695,
0.021976392716169357,
-0.041049785912036896,
-0.0028613749891519547,
-0.013749395497143269,
0.003983234521001577,
0.07961703836917877,
0.02073550783097744,
-0.03103134222328663,
0.07670367509126663,
-0.03967032954096794,
-0.0008365688845515251,
-0.014606314711272717,
0.020197540521621704,
-0.02211643010377884,
0.003076300723478198,
0.023325130343437195,
0.012224175967276096,
-0.011363646946847439,
0.008386881090700626,
0.024132559075951576,
0.020628981292247772,
0.040463779121637344,
-0.023283934220671654,
0.021461013704538345,
-0.0470065139234066,
-0.025568583980202675,
-0.006757036782801151,
0.06985422223806381,
0.0015411415370181203,
0.013445907272398472,
0.040042079985141754,
0.00894648302346468,
0.02123245969414711,
0.02207670360803604,
0.06453697383403778,
-0.02235078625380993,
-0.028911737725138664,
-0.0700392872095108,
-0.022286882624030113,
-0.0001316956040682271,
0.004837397951632738,
0.05456484481692314,
-0.012395545840263367,
-0.026127086952328682,
-0.018739450722932816,
0.0008603243040852249,
-0.013695206493139267,
0.0168813094496727,
0.00774279423058033,
-0.01302346307784319,
0.004467666149139404,
-0.006690840236842632,
0.0013981192605569959,
0.0028961305506527424,
0.0788535550236702,
0.05015673115849495,
-0.004207497462630272,
0.021443231031298637,
-0.07828253507614136,
-0.02126498706638813,
0.018718166276812553,
-0.0074458373710513115,
0.005372451152652502,
-0.01119739655405283,
-0.078682541847229,
-0.042958684265613556,
0.019754746928811073,
-0.025378437712788582,
0.020910033956170082,
0.01780068688094616,
-0.019893862307071686,
-0.012411702424287796,
0.0012582448543980718,
-0.02462901547551155,
0.04714130237698555,
0.008981555700302124,
-0.006561858579516411,
-0.01711266115307808,
0.03004455752670765,
-0.04176231473684311,
0.0013817755971103907,
0.00026674853870645165,
0.05889977514743805,
0.006744679529219866,
-0.01013887021690607,
-0.0025477653834968805,
0.011989801190793514,
-0.0007879187469370663,
-0.08066821843385696,
0.012485306710004807,
-0.018492387607693672,
-0.037009891122579575,
0.02071472443640232,
-0.03695737197995186,
0.006663093343377113,
0.06448293477296829,
0.029550056904554367,
-0.00229584239423275,
0.01635170541703701,
-0.05846575275063515,
0.021747581660747528,
-0.000838964304421097,
0.0089513398706913,
0.06290946900844574,
0.010038833133876324,
-0.02167619578540325,
-0.002630663802847266,
-0.03329543024301529,
0.0008976099779829383,
-0.03613048419356346,
0.03276392072439194,
-0.017476189881563187,
0.004124916158616543,
-0.04710397496819496,
0.050832051783800125,
-0.018683064728975296,
0.02824202924966812,
0.0028545656241476536,
-0.014409909956157207,
-0.01648806594312191,
0.025435660034418106,
0.0063941217958927155,
0.016112178564071655,
0.02232193388044834,
0.03913667052984238,
0.009686283767223358,
0.049087535589933395,
0.01493589486926794,
-0.004562551621347666,
0.013671874068677425,
0.030463768169283867,
-0.04106089845299721,
0.01814204640686512,
-0.01624518819153309,
-0.012125011533498764,
0.025878747925162315,
-0.07051995396614075,
0.05821701139211655,
-0.023681089282035828,
-0.009388275444507599,
0.009028500877320766,
-0.03909565135836601,
0.004557412583380938,
0.00097131566144526,
-0.01974485069513321,
0.020841065794229507,
-0.03740574046969414,
-0.031178534030914307,
0.010049816220998764,
0.028698459267616272,
-0.07223556190729141,
-0.006240426562726498,
0.023242922499775887,
0.00909513607621193,
-0.05159595236182213,
-0.02192961610853672,
0.01723114773631096,
-0.03233512490987778,
-0.014075583778321743,
0.0188469048589468,
0.06896081566810608,
0.02964329905807972,
0.0038859660271555185,
0.0006179036572575569,
0.07526420056819916,
0.06714055687189102,
-0.009131496772170067,
-0.012360788881778717,
0.04759815335273743,
-0.020497795194387436,
-0.026045024394989014,
0.012073309160768986,
0.057211097329854965,
-0.05229249596595764,
-0.00556310685351491,
-0.016245363280177116,
-0.03390337899327278,
0.0036962172016501427,
-0.017522113397717476,
-0.01966094970703125,
0.006848466116935015,
0.022152891382575035,
-0.015323562547564507,
-0.03089137375354767,
-0.009059708565473557,
0.012816950678825378,
0.004031438380479813,
0.01917840540409088,
0.0031108965631574392,
-0.009860743768513203,
-0.020241525024175644,
0.075471892952919,
0.015331202186644077,
-0.004777546040713787,
-0.019058413803577423,
0.08246010541915894,
0.011126681230962276,
-0.022172171622514725,
0.038558460772037506,
0.008942855522036552,
0.02333633042871952,
-0.010111070238053799,
-0.0004347714420873672,
0.034078776836395264,
-0.010776125825941563,
-0.04710490256547928,
-0.03141096234321594,
-0.02495688758790493,
-0.021681025624275208,
0.05152805894613266,
-0.011545081622898579,
0.06052364781498909,
-0.02249005064368248,
-0.027347370982170105,
-0.048388995230197906,
0.02003921940922737,
-0.08381102234125137,
-0.048139411956071854,
0.003624305361881852,
0.012015549466013908,
-0.07057900726795197,
-0.0093482481315732,
-0.01582399755716324,
0.008751099929213524,
-0.024305950850248337,
0.018824229016900063,
0.020317960530519485,
0.022293582558631897,
0.02512228488922119,
-0.030561862513422966,
-0.012539278715848923,
0.07734941691160202,
-0.003181209322065115,
0.05302827060222626,
-0.019594760611653328,
-0.019096270203590393,
0.043585941195487976,
0.0452004000544548,
0.0048216781578958035,
-0.044861968606710434,
-0.04025055840611458,
-0.044959213584661484,
-0.014555707573890686,
0.05372616648674011,
-0.007821564562618732,
0.02252107486128807,
-0.0033714822493493557,
-0.0009826580062508583,
0.01719665341079235,
0.029545901343226433,
0.0016161928651854396,
-0.0489468090236187,
-0.008872568607330322,
0.013397539965808392,
-0.05033786967396736,
0.04314933344721794,
0.04184264317154884,
0.009710210375487804,
0.024202726781368256,
-0.02131473645567894,
-0.01084616407752037,
-0.01189190149307251,
-0.010530136525630951,
-0.025306811556220055,
0.06584184616804123,
-0.021252218633890152,
0.016804680228233337,
0.0011735835578292608,
-0.010549100115895271,
0.12515418231487274,
0.06802477687597275,
-0.007553021889179945,
-0.07058289647102356,
0.0359545573592186,
-0.023772450163960457,
0.022437306120991707,
-0.07403302937746048,
0.020900264382362366,
0.011935250833630562,
0.032250091433525085,
0.0012025181204080582,
0.049104638397693634,
-0.0319693423807621,
0.0032657315023243427,
0.039558179676532745,
-0.03613949939608574,
-0.019168676808476448,
-0.015490141697227955,
0.0398385114967823,
0.01821398362517357,
0.005371067672967911,
-0.005298068281263113,
0.03335997834801674,
0.012330652214586735,
0.015894005075097084,
-0.003533868817612529,
-0.048761527985334396,
-0.021130142733454704,
-0.04128497466444969,
-0.021313535049557686,
0.011718539521098137,
0.01821049489080906,
-0.02714301273226738,
-0.0009308821754530072,
0.054597072303295135,
0.030287934467196465,
0.012842537835240364,
0.045108284801244736,
-0.0065606278367340565,
-0.020403554663062096,
0.01626840978860855,
0.03222060576081276,
0.03408006206154823,
0.005278063006699085,
-0.0339173823595047,
-0.009078080765902996,
0.05894144997000694,
-0.010837697423994541,
-0.003183710388839245,
-0.0115425493568182,
-0.02020559273660183,
0.0034126250538975,
-0.03756687790155411,
0.009482434019446373,
0.012182656675577164,
-0.0033666600938886404,
-0.03268352150917053,
-0.03485271707177162,
-0.009502868168056011,
0.028264345601201057,
0.03626897931098938,
0.019376352429389954,
-0.03424248844385147,
-0.00867676455527544,
0.021652957424521446,
-0.036872558295726776,
0.04447336494922638,
0.019701311364769936,
-0.01115969568490982,
0.018454857170581818,
-0.012147516943514347,
-0.0526118203997612,
0.012865141965448856,
-0.003824604209512472,
0.0014392986195161939,
0.016101807355880737,
-0.011861640959978104,
0.03215961903333664,
-0.02600806951522827,
-0.06125233694911003,
0.057965755462646484,
-0.018390938639640808,
-0.005317459348589182,
-0.020194336771965027,
-0.056925226002931595,
0.010067124851047993,
0.006388295441865921,
0.0015639205230399966,
0.005392015445977449,
-0.00457483995705843,
0.03479159623384476,
0.04114841669797897,
-0.027043497189879417,
-0.03842778503894806,
0.02646656706929207,
-0.0420621819794178,
-0.011412356980144978,
-0.0296256672590971,
0.003499681130051613,
-0.02292138896882534,
0.01862184889614582,
-0.01832621730864048,
0.019869906827807426,
0.015795961022377014,
-0.003978605382144451,
0.040820978581905365,
-0.02687443606555462,
0.02349008060991764,
0.012770647183060646,
-0.00868342537432909,
-0.025608936324715614,
-0.002569030039012432,
-0.026189494878053665,
-0.00501537648960948,
-0.01076933927834034,
0.008223984390497208,
-0.05235643312335014,
0.03678147867321968,
-0.03772251307964325,
0.02907492034137249,
-0.04275332763791084,
0.020182698965072632,
-0.02904851920902729,
0.020911136642098427,
0.011440493166446686,
-0.008526748046278954,
0.00014670426025986671,
0.031526919454336166,
-0.020575903356075287,
-0.018252957612276077,
0.010895788669586182,
-0.00897975079715252,
0.017093373462557793,
0.0014446881832554936,
0.019224466755986214,
0.0012878549750894308,
0.020391633734107018,
-0.027303926646709442,
-0.09220947325229645,
-0.020474549382925034,
-0.04959488660097122,
-0.08191949129104614,
0.03649315610527992,
0.03324133902788162,
0.029456665739417076,
0.036702122539281845,
-0.042606234550476074,
-0.007987701334059238,
0.06981704384088516,
-0.05632038041949272,
-0.02705979533493519,
0.007620203774422407,
-0.035645853728055954,
-0.0009626005194149911,
-0.022896677255630493,
-0.011029571294784546,
-0.0010359566658735275,
0.052417926490306854,
0.022503703832626343,
0.013144902884960175,
-0.02839866280555725,
-0.007290855050086975,
0.005404175724834204,
0.0032310811802744865,
0.024268323555588722,
-0.026444757357239723,
0.018892809748649597,
0.009047656320035458,
0.01969296857714653,
-0.04234037175774574,
0.02139338292181492,
0.04500444605946541,
0.016773220151662827,
-0.0592990443110466,
-0.0060218023136258125,
-0.014792113564908504,
0.026083074510097504,
0.03858380392193794,
-0.04857666417956352,
0.002069940557703376,
0.006862213835120201,
-0.017627237364649773,
0.0399344377219677,
-0.0436982586979866,
0.010312344878911972,
-0.025436675176024437,
-0.03950061276555061,
-0.006892675533890724,
0.08796529471874237,
0.014189106412231922,
0.015927942469716072,
-0.01955096423625946,
-0.02472933568060398,
-0.013783537782728672,
-0.04763809219002724,
0.0280764140188694,
0.04044397547841072,
0.02677225135266781,
-0.022323232144117355,
0.06367892026901245,
-0.00898638553917408,
-0.03977673873305321,
0.04070198908448219,
0.007965687662363052,
0.0005838894285261631,
-0.009547390043735504,
0.031320564448833466,
0.00595979206264019,
0.03249571472406387,
0.029233010485768318,
0.00006528136873384938,
-0.034559573978185654,
0.0026501400861889124,
0.02438262104988098,
0.023626180365681648,
-0.01334439031779766,
0.015156093053519726,
0.021139318123459816,
-0.0034453189000487328,
-0.01881416328251362,
0.01623711921274662,
-0.043662503361701965,
0.015612853690981865,
-0.012750162743031979,
-0.03309788927435875,
0.013046558946371078,
0.014300249516963959,
0.035389069467782974,
-0.029744291678071022,
0.013613706454634666,
0.04961800575256348,
-0.019692035391926765,
-0.03951851278543472,
0.029100827872753143,
-0.041814837604761124,
-0.023235855624079704,
0.01611773669719696,
0.011530661024153233,
0.012938019819557667,
-0.04344237968325615,
-0.010131041519343853,
0.018897727131843567,
0.016123367473483086,
-0.030790433287620544,
-0.0023715284187346697,
-0.03795318305492401,
0.030790245160460472,
0.00981677882373333,
0.010216102935373783,
-0.0639764592051506,
-0.05381631851196289,
0.02781819924712181,
-0.04261491820216179,
-0.0034702084958553314,
0.007854885421693325,
-0.037396229803562164,
0.022359395399689674,
-0.04891562461853027,
-0.009646352380514145,
0.003607966238632798,
0.042741529643535614,
0.017474761232733727,
-0.024616409093141556,
0.014785507693886757,
-0.000738832401111722,
0.0261769350618124,
-0.04664194956421852,
-0.002728191902860999,
0.009005566127598286,
0.007875627838075161,
0.003492790274322033,
0.027369527146220207,
-0.013532881624996662,
-0.012795657850801945,
0.030940502882003784,
0.0008376533514820039,
0.04325408861041069,
0.031520016491413116,
-0.024504926055669785,
0.03423623368144035,
-0.0002576152328401804,
0.020649904385209084,
0.07867574691772461,
-0.0031376497354358435,
0.017196521162986755,
0.03142041340470314,
0.013773933053016663,
-0.037087082862854004,
0.03784028813242912,
-0.011191565543413162,
-0.04481907933950424,
0.001496398588642478,
0.004237606190145016,
-0.0055854287929832935,
-0.044238556176424026,
-0.018633157014846802,
0.027482204139232635,
-0.029814181849360466,
0.02592291310429573,
0.022352023050189018,
-0.010698998346924782,
0.007861553691327572,
0.02918347902595997,
-0.0011366135440766811,
0.02461945079267025,
-0.007649386301636696,
0.00660289078950882,
0.038698021322488785,
0.025409646332263947,
0.012024536728858948,
0.02040897309780121,
0.015570848248898983,
-0.044042881578207016,
0.02886257879436016,
-0.01909484528005123,
0.031705934554338455,
-0.02835068106651306,
-0.020753715187311172,
0.01107567735016346,
0.01735864207148552,
-0.0209790151566267,
-0.011771216988563538,
-0.00013678423420060426,
0.07290127873420715,
-0.00473231403157115,
0.002389723202213645,
-0.004350585397332907,
0.0035176915116608143,
-0.03626301512122154,
0.02043020911514759,
-0.03633149713277817,
0.008990702219307423,
0.004776936490088701,
0.004278187640011311,
-0.03953128680586815,
-0.010105622000992298,
-0.014327902346849442,
-0.04799310863018036,
-0.012128045782446861,
0.06477008759975433,
-0.005047502461820841,
0.015290346927940845,
-0.03752199560403824,
-0.025685535743832588,
-0.04820389673113823,
0.022498508915305138,
0.035668376833200455,
0.022794099524617195,
-0.009929746389389038,
0.014295308850705624,
-0.01376941055059433,
0.04344530776143074,
-0.06738007813692093,
0.01054789312183857,
-0.011296553537249565,
0.024421222507953644,
-0.001660578534938395,
0.005912087392061949
] |
<p>I'm new to physics and am just going through some of the free online classes at World Science U, and after watching this video on the nature of the speed of light and its constancy, a question came to mind about photons. (Video: <a href="http://www.youtube.com/watch?v=fDm1PQgIq7U">YouTube Video</a>, <a href="http://www.worldscienceu.com/courses/1/elements/5H4am8">World Science U course</a>) </p>
<p>I know that photons don't have mass, but what happens when photons — even the photons from distant stars — reach us? Are we merely observing the occurrence of photons moving through space relative to us, or are we really being "bathed" in photons? I know that when I observe rain, I can both observe it from a distance but could also be immersed in it as well if in the path of that rain. But with distant starlight, are we just observing it or are the photons actually reaching and penetrating the earth around us? If they are penetrating, does science tell us what is actually happening on an atomic or sub-atomic level?</p>
| 9,633 |
[
0.001575273578055203,
-0.06398063898086548,
-0.010126035660505295,
-0.05109192803502083,
0.0255430955439806,
0.024608513340353966,
-0.041605185717344284,
-0.03429641202092171,
0.028998568654060364,
-0.023469718173146248,
0.014180835336446762,
0.07666094601154327,
-0.008306054398417473,
0.019960328936576843,
0.03069808892905712,
0.027352705597877502,
-0.02807500958442688,
-0.008342549204826355,
-0.015335727483034134,
-0.029843715950846672,
-0.0068134767934679985,
0.00169741443824023,
0.009111846797168255,
0.015480497851967812,
-0.023519638925790787,
0.023603759706020355,
-0.022838829085230827,
0.006698343902826309,
0.005185886286199093,
0.012159792706370354,
0.03660011664032936,
0.0025783174205571413,
-0.00029599692788906395,
0.005228633526712656,
0.01520297396928072,
0.0015817406820133328,
-0.05535023659467697,
-0.016525432467460632,
-0.006962901912629604,
0.015138453803956509,
-0.04373106732964516,
-0.03727900609374046,
0.0027004212606698275,
0.014290702529251575,
-0.05494686961174011,
0.0013128123246133327,
0.035591889172792435,
-0.012764344923198223,
0.09272658824920654,
-0.038709577172994614,
0.04615418240427971,
-0.004013936500996351,
0.03909824416041374,
0.013923270627856255,
-0.03592747077345848,
-0.018897362053394318,
0.0770450308918953,
0.058560799807310104,
-0.029735079035162926,
-0.008344393223524094,
-0.014083629474043846,
-0.004818679299205542,
-0.00965750403702259,
-0.04034845158457756,
-0.002136723604053259,
0.02246764302253723,
-0.02970520220696926,
0.0047745355404913425,
0.019969984889030457,
0.023126110434532166,
0.006458955816924572,
-0.024531293660402298,
0.04102049395442009,
0.024942276999354362,
-0.011021338403224945,
-0.03223470225930214,
0.035119347274303436,
-0.0031585698015987873,
0.06697103381156921,
0.007651126477867365,
-0.006897272076457739,
-0.0037651441525667906,
-0.017385708168148994,
0.02688070759177208,
0.015269484370946884,
-0.010209650732576847,
0.07761210948228836,
-0.0046475413255393505,
-0.041514862328767776,
0.02114180289208889,
0.0071907262317836285,
0.014942505396902561,
-0.020739585161209106,
0.023215649649500847,
0.027758387848734856,
0.02412674017250538,
-0.02067776769399643,
0.03279494866728783,
-0.000866694375872612,
0.00639097485691309,
0.003051179926842451,
0.0035046273842453957,
0.036357007920742035,
0.05263284593820572,
0.0014001749223098159,
-0.04971548914909363,
-0.014611913822591305,
0.010302938520908356,
-0.013735645450651646,
0.010669954121112823,
-0.05518295243382454,
0.015888990834355354,
0.029807982966303825,
0.013639869168400764,
0.03291578218340874,
-0.024464499205350876,
0.012529670260846615,
-0.01854844205081463,
0.08820687979459763,
0.08230601251125336,
0.04442712292075157,
-0.027513032779097557,
0.010520202107727528,
-0.020998872816562653,
-0.044792886823415756,
0.03272371366620064,
0.01984771527349949,
0.005283964332193136,
-0.058462101966142654,
0.009320922195911407,
-0.008283120580017567,
-0.0008421040256507695,
-0.009064099751412868,
-0.018514681607484818,
0.04794957488775253,
-0.02729441225528717,
-0.12479272484779358,
-0.06558440625667572,
0.02173462323844433,
0.08084011822938919,
-0.029521644115447998,
-0.07021106779575348,
0.0017559448024258018,
-0.005323463585227728,
0.09098675847053528,
0.010396690107882023,
0.00035367649979889393,
-0.010431051254272461,
0.031332287937402725,
-0.0012856180546805263,
-0.019216924905776978,
-0.010631137527525425,
-0.009352141059935093,
-0.005371694918721914,
0.03979704901576042,
-0.07102417200803757,
0.007431259378790855,
0.038606420159339905,
0.01856071688234806,
-0.03142475336790085,
0.08310116082429886,
-0.02189910039305687,
0.010899156332015991,
0.030730441212654114,
-0.02776993252336979,
-0.03528594225645065,
0.04576805606484413,
0.027118021622300148,
0.036148957908153534,
0.051861025393009186,
0.026432951912283897,
0.02319783717393875,
0.007068601902574301,
0.03154988959431648,
0.001959557179361582,
-0.027059465646743774,
0.00664675934240222,
-0.016620025038719177,
0.022054852917790413,
-0.042241547256708145,
-0.03149609640240669,
-0.0453718826174736,
0.015939438715577126,
0.0024047549813985825,
0.027517061680555344,
0.043618347495794296,
0.0042189485393464565,
-0.016271833330392838,
-0.020897727459669113,
-0.029091600328683853,
-0.009409972466528416,
-0.010223792865872383,
0.017508897930383682,
-0.010113543830811977,
0.0030413116328418255,
-0.007568303029984236,
0.006613244768232107,
-0.002750416286289692,
0.002296800957992673,
-0.019453341141343117,
-0.019672473892569542,
0.0572960264980793,
0.02210533618927002,
0.008048069663345814,
0.012586883269250393,
0.05240890756249428,
0.035855863243341446,
0.016425004228949547,
-0.023064926266670227,
-0.0020171909127384424,
-0.03836449235677719,
0.003935611806809902,
0.010418955236673355,
0.028366796672344208,
0.03417542576789856,
0.007549935486167669,
0.004964412190020084,
-0.01181661058217287,
-0.0204936433583498,
0.028174856677651405,
-0.01060058455914259,
0.07043928653001785,
0.021663568913936615,
-0.008076387457549572,
-0.002347778296098113,
0.023551559075713158,
0.0024958965368568897,
0.003711983095854521,
0.0012786908773705363,
-0.035115890204906464,
-0.06756981462240219,
-0.017375770956277847,
0.042901381850242615,
-0.01614035852253437,
-0.01564737595617771,
0.001567893079482019,
-0.0009540702449157834,
0.04656050354242325,
0.04725606366991997,
0.0174428541213274,
-0.03499559313058853,
-0.05122873932123184,
0.003505071857944131,
0.023598631843924522,
0.01702900230884552,
0.031067946925759315,
0.026853203773498535,
0.018310299143195152,
0.02683238312602043,
-0.015154206193983555,
0.002093990333378315,
0.02476235292851925,
-0.02787323109805584,
0.052249107509851456,
-0.012815405614674091,
-0.0366218276321888,
0.02994687482714653,
0.0033369422890245914,
0.0027765945997089148,
-0.010031281039118767,
-0.029403185471892357,
0.0007649013423360884,
-0.055859409272670746,
-0.00069273920962587,
0.0014111471828073263,
-0.010849122889339924,
-0.03398376330733299,
-0.01523996889591217,
0.020516231656074524,
-0.07150372862815857,
0.03462332859635353,
-0.020991718396544456,
-0.03133251518011093,
-0.038631804287433624,
-0.008155581541359425,
0.05846879258751869,
0.015284722670912743,
0.00875481590628624,
-0.04302505403757095,
-0.0650143101811409,
-0.0076572829857468605,
-0.05485374107956886,
-0.007901282981038094,
0.027382582426071167,
-0.012941353023052216,
0.03613785654306412,
-0.029424797743558884,
-0.005377762019634247,
0.05009014531970024,
-0.026378419250249863,
0.016996171325445175,
0.019535081461071968,
-0.011966503225266933,
-0.017086736857891083,
0.0034810968209058046,
0.027988985180854797,
-0.012688866816461086,
-0.011155566200613976,
0.02580253593623638,
0.049926575273275375,
-0.03230517357587814,
-0.028774041682481766,
-0.024359215050935745,
-0.035011567175388336,
-0.04879974573850632,
-0.026503676548600197,
-0.022297298535704613,
-0.007146727293729782,
-0.028117749840021133,
0.015518859960138798,
0.02571110799908638,
-0.06422678381204605,
0.004040182568132877,
-0.016624094918370247,
-0.05299687758088112,
0.029498444870114326,
0.0033297766931355,
-0.0008650938980281353,
-0.000060567777836695313,
-0.022025832906365395,
0.05135665461421013,
0.039637159556150436,
-0.026631677523255348,
-0.016019754111766815,
0.005535627715289593,
0.006153731606900692,
0.0036711725406348705,
0.025530720129609108,
0.028106097131967545,
0.006692526862025261,
-0.0075516775250434875,
0.00853133574128151,
0.0206800177693367,
0.028555549681186676,
0.011547812260687351,
-0.006059230305254459,
0.005060203839093447,
-0.014390379190444946,
-0.001037359586916864,
0.03318876028060913,
0.057842034846544266,
-0.04362595081329346,
0.008943283930420876,
-0.016236569732427597,
0.014169246889650822,
0.061387501657009125,
-0.01830022595822811,
0.0775890201330185,
0.005386792588979006,
-0.005340783391147852,
-0.040751244872808456,
0.01840202882885933,
0.012626076117157936,
-0.005865158513188362,
-0.009140248410403728,
-0.004575115628540516,
0.018946394324302673,
0.005377796478569508,
-0.0326346717774868,
0.0015572713455185294,
0.07069341093301773,
-0.015970302745699883,
-0.020574316382408142,
-0.005607670173048973,
0.002426269231364131,
0.020985977724194527,
-0.002647354733198881,
-0.006291871890425682,
0.05146072804927826,
0.03076760284602642,
0.0325997993350029,
-0.014509563334286213,
-0.01973794773221016,
-0.06665908545255661,
-0.03165075555443764,
0.00813208520412445,
-0.005130235571414232,
0.013899214565753937,
0.020319879055023193,
0.047807544469833374,
0.031236199662089348,
0.029324961826205254,
-0.00127216090913862,
-0.0159844271838665,
-0.0606217198073864,
0.005927508696913719,
-0.025033287703990936,
-0.016923272982239723,
-0.049028247594833374,
-0.004809010308235884,
-0.025185002014040947,
-0.043275218456983566,
-0.005845042876899242,
0.008589115925133228,
-0.026503900066018105,
-0.03682922571897507,
-0.020214872434735298,
-0.04164557158946991,
-0.054304130375385284,
-0.009774702601134777,
-0.002579285530373454,
0.04520343244075775,
-0.012866648845374584,
0.005540336947888136,
0.02250875160098076,
-0.016011660918593407,
0.006962740793824196,
0.0008828855934552848,
-0.006414677482098341,
0.017067449167370796,
0.03481558710336685,
0.05752693861722946,
-0.0006336316000670195,
-0.03239701688289642,
0.045194849371910095,
0.030669420957565308,
0.011774398386478424,
-0.0020174128003418446,
-0.04714898765087128,
-0.042935602366924286,
-0.0008603258174844086,
-0.015722405165433884,
0.0016136141493916512,
0.03735297918319702,
0.002045739209279418,
-0.0018896502442657948,
0.038583312183618546,
-0.020052121952176094,
-0.006346848327666521,
0.05765947327017784,
0.03515647351741791,
-0.02521488629281521,
-0.0174516923725605,
-0.07514713704586029,
-0.005689142271876335,
-0.015072857961058617,
0.012620874680578709,
0.029597336426377296,
0.01363295316696167,
0.012319841422140598,
0.0001136771243182011,
0.034364327788352966,
0.023237064480781555,
-0.025290798395872116,
-0.005062466952949762,
-0.027785681188106537,
-0.009057251736521721,
-0.02542160451412201,
0.0032298839651048183,
-0.01387473288923502,
0.03597111999988556,
0.05074658617377281,
-0.01631765067577362,
-0.01493142731487751,
-0.08870462328195572,
0.0031527786049991846,
0.05434322729706764,
0.04252677038311958,
-0.030742449685931206,
0.011633918620646,
-0.04211781173944473,
0.02177773043513298,
0.023956501856446266,
-0.009730372577905655,
0.055588576942682266,
-0.023092765361070633,
0.010015604086220264,
-0.0007050555432215333,
-0.025474512949585915,
-0.008506000973284245,
0.003148718737065792,
-0.004763553384691477,
-0.017773810774087906,
-0.0029820636846125126,
-0.013487785123288631,
-0.030493611469864845,
0.051497042179107666,
0.027233121916651726,
0.03279924765229225,
-0.013132881373167038,
-0.01678396575152874,
-0.0261384230107069,
-0.01572508178651333,
-0.0030895511154085398,
-0.08881073445081711,
-0.001505840802565217,
0.0279411431401968,
-0.0429985336959362,
0.04010531306266785,
0.015175579115748405,
-0.061198122799396515,
0.044582124799489975,
0.035438623279333115,
-0.02143637277185917,
-0.04633031040430069,
-0.06505061686038971,
0.040478747338056564,
0.026052163913846016,
0.005576154682785273,
0.022634724155068398,
0.012796612456440926,
-0.01212258916348219,
0.02454262226819992,
0.005621100310236216,
0.09216472506523132,
-0.009804901666939259,
0.028248019516468048,
-0.011035808362066746,
-0.013528534211218357,
-0.017653340473771095,
0.05036696791648865,
0.02129303105175495,
-0.010074648074805737,
0.00515525508671999,
-0.0500616580247879,
0.008110438473522663,
0.02538388967514038,
0.0067314403131604195,
0.0076853446662425995,
-0.06368047744035721,
0.015261524356901646,
-0.025625141337513924,
-0.02868070639669895,
-0.005258704535663128,
0.021220015361905098,
0.011098025366663933,
0.016903143376111984,
0.022492721676826477,
0.01392325758934021,
-0.04195752739906311,
-0.005906065925955772,
0.01964474655687809,
-0.06374044716358185,
0.044550925493240356,
-0.0024624865036457777,
-0.00019671324116643518,
0.03159322962164879,
-0.04744166508316994,
-0.02393169328570366,
0.018549852073192596,
-0.02175232395529747,
0.02191820740699768,
-0.05959688499569893,
0.005221415311098099,
0.017481040209531784,
0.004501593764871359,
-0.05922110006213188,
-0.04199456423521042,
0.00953050795942545,
0.005408455152064562,
-0.02522980608046055,
-0.021966956555843353,
0.020181166008114815,
-0.024693720042705536,
-0.016658348962664604,
-0.011100445874035358,
0.032767750322818756,
-0.04943569377064705,
-0.02629956416785717,
-0.020098477602005005,
0.020289966836571693,
0.035325583070516586,
-0.021518979221582413,
0.017969248816370964,
0.0018735812045633793,
0.019629107788205147,
-0.0235299039632082,
0.0032533013727515936,
0.07251343876123428,
-0.011521953158080578,
-0.05593350902199745,
-0.01968609355390072,
-0.01414897758513689,
0.022582130506634712,
-0.018907034769654274,
0.006909951567649841,
0.0762554407119751,
0.014431443065404892,
0.0020331216510385275,
-0.006365838460624218,
0.047781333327293396,
0.025223640725016594,
0.02443361096084118,
-0.00453208340331912,
0.004202508367598057,
-0.010748344473540783,
-0.040315788239240646,
0.04165768250823021,
0.006468159146606922,
0.020891588181257248,
0.0035137960221618414,
0.006299284752458334,
-0.028970474377274513,
0.0002464081044308841,
0.03721220791339874,
0.012088540010154247,
0.00027871481142938137,
-0.025931892916560173,
0.00749321049079299,
0.015224169939756393,
0.011763409711420536,
0.0013108754064887762,
0.007248720619827509,
-0.05650385841727257,
-0.01729387231171131,
0.09183083474636078,
-0.004296797793358564,
0.04431348666548729,
0.010962764732539654,
-0.016180342063307762,
-0.002008955692872405,
-0.03528580069541931,
-0.02318193018436432,
0.015179883688688278,
0.021296096965670586,
0.010858222842216492,
-0.05176418647170067,
-0.003513246076181531,
0.010394618846476078,
0.056187089532613754,
-0.048247769474983215,
0.01877911202609539,
0.0191898625344038,
0.014651927165687084,
0.038847316056489944,
-0.009518975391983986,
-0.032554373145103455,
0.0066431425511837006,
-0.049752358347177505,
-0.006743418052792549,
0.028680473566055298,
-0.016934536397457123,
0.05118044093251228,
0.013503307476639748,
0.024365458637475967,
-0.02818187139928341,
-0.01676708646118641,
-0.057736270129680634,
0.0058481739833951,
-0.023600660264492035,
0.04583486542105675,
-0.02938319928944111,
0.012504108250141144,
0.039266712963581085,
0.012936240062117577,
0.029095347970724106,
-0.000859439664054662,
-0.0711158812046051,
-0.041708655655384064,
-0.05563564598560333,
-0.033550769090652466,
0.0640588328242302,
-0.006939197890460491,
-0.03137488290667534,
0.02456214465200901,
-0.0413694754242897,
0.033122122287750244,
0.02832281030714512,
0.055911142379045486,
-0.009079579263925552,
0.039451632648706436,
-0.028372375294566154,
-0.0035186009481549263,
0.02295175939798355,
0.015398741699755192,
0.10656193643808365,
0.027445608749985695,
-0.010510657913982868,
-0.010176400654017925,
-0.03833753243088722,
-0.03685689717531204,
0.04935140907764435,
-0.02249719388782978,
-0.009017611853778362,
-0.041204892098903656,
0.024558408185839653,
-0.004903934895992279,
0.03405913710594177,
0.03664175048470497,
-0.0010165105341002345,
0.04871664568781853,
-0.024480804800987244,
-0.015363744460046291,
0.0422196127474308,
-0.0012870138743892312,
-0.025262489914894104,
0.036183301359415054,
-0.06041022017598152,
0.026241695508360863,
-0.011995352804660797,
0.0006358869140967727,
0.0033118457067757845,
-0.036754060536623,
0.019281907007098198,
-0.0003414668026380241,
-0.046909037977457047,
-0.0025221745017915964,
0.03989538922905922,
-0.031867820769548416,
-0.040229037404060364,
0.028996607288718224,
0.07881278544664383,
-0.006866362411528826,
0.02303951606154442,
-0.0002621515595819801,
0.00805736519396305,
-0.008783788420259953,
0.02197430469095707,
0.03014468215405941,
-0.040166109800338745,
0.0009543326450511813,
-0.02517741546034813,
0.033850688487291336,
-0.007262127008289099,
0.0006085414788685739,
-0.0015311718452721834,
-0.0006897879648022354,
-0.0011309038382023573,
-0.04972414672374725,
0.0139450803399086,
0.009449842385947704,
0.013330561108887196,
-0.004521150607615709,
-0.035298965871334076,
-0.009858532808721066,
-0.001519475830718875,
-0.007855374366044998,
0.02266482077538967,
0.011730922386050224,
0.03803706169128418,
0.014399236999452114,
0.013186768628656864,
0.022724710404872894,
-0.04096042364835739,
-0.0173654668033123,
-0.013113433495163918,
-0.0020836452022194862,
-0.032315511256456375,
-0.043236441910266876,
0.05910239368677139,
0.02801414020359516,
-0.00863723736256361,
0.02484235167503357,
0.001130624208599329,
-0.037233222275972366,
-0.026604443788528442,
0.009874342009425163,
-0.04740114137530327,
-0.04204024374485016,
-0.005368187557905912,
-0.01585422456264496,
0.018232112750411034,
-0.004840698558837175,
-0.027290930971503258,
-0.016535058617591858,
0.0416753925383091,
0.02617119811475277,
0.011111742816865444,
-0.02039993740618229,
-0.024445058777928352,
0.037673719227313995,
0.013071306981146336,
0.003017037408426404,
-0.020694704726338387,
0.03635852038860321,
0.018490247428417206,
-0.005378884728997946,
0.005748347379267216,
-0.004239644389599562,
-0.054860733449459076,
0.00326839042827487,
0.014608060009777546,
-0.01777663454413414,
-0.002294958336278796,
-0.00478327414020896,
-0.019669201225042343,
-0.0054010059684515,
-0.03234456852078438,
-0.03377366065979004,
0.007313574198633432,
-0.018469328060746193,
-0.022701390087604523,
-0.05423044413328171,
0.06903846561908722,
0.00885990634560585,
0.022344695404171944,
-0.02515527978539467,
0.018454130738973618,
-0.04091096669435501,
-0.012337966822087765,
0.002274148864671588,
-0.03657744452357292,
-0.0016409126110374928,
0.045016609132289886,
-0.0681372731924057,
-0.01628114841878414,
0.04560345038771629,
0.03584279865026474,
-0.011309043504297733,
0.0028257013764232397,
0.032484278082847595,
-0.04061594232916832,
0.05438901111483574,
-0.003928979393094778,
-0.018606487661600113,
0.05658360570669174,
-0.011348874308168888,
-0.051006365567445755,
0.045523788779973984,
-0.07455907016992569,
0.03584570810198784,
0.015449315309524536,
-0.015381187200546265,
-0.001756190089508891,
0.044514089822769165,
-0.01232336089015007,
0.023614943027496338,
-0.005705076735466719,
-0.041756730526685715,
-0.02755115181207657,
0.03142959251999855,
0.03641926497220993,
-0.038143936544656754,
-0.023135295137763023,
0.0606958232820034,
0.026185212656855583,
-0.009236226789653301,
0.037533316761255264,
-0.03884342312812805,
-0.06479379534721375,
-0.008013488724827766,
0.020553909242153168,
-0.014465800486505032,
-0.011043951846659184,
0.0426160991191864,
-0.01572854444384575,
0.05631815642118454,
0.003407721407711506,
-0.01580800861120224,
-0.10798043757677078,
0.021930886432528496,
0.004499620292335749,
-0.003908967133611441,
0.006689354311674833,
-0.04194510355591774,
-0.02033476158976555,
0.040055736899375916,
-0.07517444342374802,
0.048430707305669785,
-0.019897399470210075,
-0.024698898196220398,
-0.015346871688961983,
0.07330632954835892,
0.016744345426559448,
0.024703728035092354,
0.02563672512769699,
0.031505487859249115,
0.012149802409112453,
0.020333673804998398,
-0.0009917293209582567,
-0.03404708579182625,
-0.012974894605576992,
0.025880219414830208,
-0.00838914792984724,
0.03293049708008766,
0.08561067283153534,
0.002534021157771349,
0.022887570783495903,
0.029803531244397163,
-0.004148073494434357,
0.047819510102272034,
-0.023346059024333954,
-0.007806980051100254,
0.011265208013355732,
0.008280977606773376,
-0.0020954457577317953,
-0.017662160098552704,
0.005883628968149424,
0.03665262833237648,
0.012910425662994385,
0.04561450332403183,
-0.008839147165417671,
-0.04094447195529938,
-0.010810540989041328,
-0.034403324127197266,
-0.03207151219248772,
0.023883424699306488,
0.0014763610670343041,
0.01913473755121231,
0.013643404468894005,
0.06312188506126404,
-0.005557071417570114,
-0.014602686278522015,
-0.0013903307262808084,
-0.09158994257450104,
0.006547869648784399,
0.019769873470067978,
0.031071268022060394,
-0.023212052881717682,
0.0049948361702263355,
0.02106127142906189,
-0.023326069116592407,
-0.010297010652720928,
-0.006122009363025427,
-0.01085718348622322,
-0.023927390575408936,
-0.046582747250795364,
0.014370493590831757,
-0.004548126831650734,
0.0006530344835482538,
-0.0025720216799527407,
-0.04288582131266594,
0.04561715945601463,
-0.0007515032193623483,
-0.00226648454554379,
0.030911268666386604,
-0.0052156816236674786,
-0.026509488001465797,
-0.0759449303150177,
0.027678057551383972,
-0.02248661406338215,
0.04335080459713936,
-0.05926637351512909,
-0.014789261855185032,
-0.008462643250823021,
-0.00571422278881073,
0.056686192750930786,
0.006961204577237368,
0.019322600215673447,
0.022846762090921402,
-0.018759844824671745,
0.021333372220396996,
-0.0466252863407135,
-0.02119392715394497,
-0.010106269270181656,
-0.02487673982977867,
-0.032247189432382584,
-0.008499037474393845,
-0.012190486304461956,
0.04000363498926163,
0.016162464395165443,
0.007496645674109459,
0.036212921142578125,
0.0032229237258434296,
-0.03891991451382637,
0.02996964007616043,
0.007902823388576508,
0.013653705827891827,
0.02197282761335373,
0.016393760219216347,
0.0178696122020483,
0.05014655366539955,
-0.03228817507624626,
-0.008088851347565651,
0.034775979816913605,
-0.01783297210931778,
-0.0025029245298355818,
-0.007224002853035927,
-0.02650258131325245,
0.01385676022619009,
-0.05292617529630661,
-0.006802448537200689,
0.024030297994613647,
-0.044799406081438065,
-0.010211740620434284,
0.052861541509628296,
-0.005478749517351389,
0.028542688116431236,
0.025779837742447853,
0.04350670799612999,
0.029556775465607643,
0.0008328148978762329,
-0.04077475517988205,
0.050855305045843124,
0.012397277168929577,
-0.035475388169288635,
0.045675087720155716,
0.018039820715785027,
0.03519982844591141,
-0.015626009553670883,
0.0003216489276383072,
0.06380501389503479,
-0.023876231163740158,
-0.006076409015804529,
0.0049616675823926926,
0.017008695751428604,
-0.022897925227880478,
0.012036142870783806,
0.000011300313417450525,
0.06843827664852142,
-0.019458375871181488,
0.037977300584316254,
-0.014469222165644169,
-0.009972858242690563,
-0.004046468064188957,
0.02650543302297592,
-0.010937293991446495,
-0.0013681164709851146,
0.017482785508036613,
-0.029687408357858658,
-0.047675225883722305,
-0.020313911139965057,
0.03206981346011162,
-0.050944894552230835,
0.050057753920555115,
-0.041564565151929855,
-0.024031247943639755,
-0.001191608957014978,
-0.006417052820324898,
0.018752528354525566,
-0.025638621300458908,
0.03128480911254883,
-0.001056221197359264,
0.004574076738208532,
-0.000647866923827678,
0.03448459878563881,
-0.0019120951183140278,
0.040429867804050446,
-0.0881388708949089,
0.016211820766329765,
-0.029461322352290154,
0.021020401269197464,
-0.0085093779489398,
-0.07432235032320023
] |
<p>given a Hamiltonian and the semiclassical WKB partition function in units $ \hbar =2m=1 $</p>
<p>$ \Theta (t) = \frac{1}{2\pi} \iint dx dp exp(-tp^{2}-tV(x)) $</p>
<p>can i use this Theta function to evaluate the Funntional determinant ??</p>
<p>$ \zeta (s,z^{2}) \Gamma (s)= \int_{0}^{\infty}dt\Theta (t) exp(-tz^{2})$</p>
<p>$ \zeta (s,z^{2})= \sum_{n=0}^{\infty}(z^{2}+E_{n})^{-s}$</p>
<p>the functional determinant is evaluated as $ det(H+z^{2})=exp(- \partial _{s} \zeta (0,z^{2}))$</p>
<p>so we need only the Theta function which is $ \Theta (t)= \sum_{n}exp(-tE_{n})$ i have simply approximated this sum by an integral over phase space involving the Hamiltonian</p>
| 9,634 |
[
0.02073175273835659,
-0.05525725707411766,
-0.009142514318227768,
-0.009029688313603401,
0.05732274428009987,
-0.031537014991045,
-0.04873528331518173,
-0.04769770801067352,
0.021485550329089165,
-0.05114658176898956,
0.010517256334424019,
0.022459151223301888,
0.06701422482728958,
0.016581149771809578,
0.022131135687232018,
-0.017119476571679115,
-0.027542635798454285,
-0.015008918941020966,
-0.026186294853687286,
0.024250805377960205,
-0.010751939378678799,
0.04688350111246109,
0.008454181253910065,
-0.02891446463763714,
-0.030348584055900574,
-0.0026999181136488914,
0.034420985728502274,
-0.02666335552930832,
0.017778754234313965,
0.08124185353517532,
0.01073091197758913,
-0.014335649088025093,
0.026760902255773544,
0.022968392819166183,
0.004892467055469751,
0.012016206979751587,
-0.07882539927959442,
-0.03697861358523369,
0.0008038950618356466,
0.023727362975478172,
-0.055448226630687714,
-0.04632209986448288,
-0.032193347811698914,
0.045453719794750214,
0.010782950557768345,
0.009496633894741535,
-0.02105441316962242,
-0.007148991338908672,
0.021516967564821243,
-0.05229196697473526,
0.05766855552792549,
0.02589581348001957,
0.027257824316620827,
-0.018012356013059616,
-0.010348055511713028,
-0.035478800535202026,
0.03064873442053795,
0.07066433876752853,
0.016669239848852158,
-0.050655193626880646,
-0.018145345151424408,
-0.07414223253726959,
-0.012106801383197308,
-0.02984972484409809,
-0.01336726825684309,
-0.00036565211485140026,
0.048286788165569305,
-0.040251825004816055,
-0.019665958359837532,
-0.011502417735755444,
0.013654060661792755,
0.030738040804862976,
0.008311796002089977,
-0.04949856549501419,
0.014609037898480892,
-0.020594539120793343,
0.03318415582180023,
0.00024066212063189596,
0.02388463355600834,
0.021767938509583473,
-0.0005351337604224682,
0.007493881508708,
0.014017952606081963,
0.02760494127869606,
0.03637353330850601,
0.0018034020904451609,
0.07082884758710861,
-0.0134489880874753,
-0.017315054312348366,
0.04808446019887924,
-0.021277591586112976,
0.02395728789269924,
0.026497963815927505,
-0.03156847506761551,
-0.05826194956898689,
0.006000828463584185,
-0.002982798730954528,
0.0660848543047905,
-0.011792240664362907,
-0.025772131979465485,
-0.01880020834505558,
-0.04335636645555496,
-0.0029501805547624826,
0.10225643217563629,
-0.01972520351409912,
0.010194933973252773,
-0.005149461794644594,
-0.018191324546933174,
-0.00494273891672492,
-0.026247315108776093,
-0.05174984410405159,
0.038167793303728104,
0.005322317127138376,
-0.0023583369329571724,
-0.014633328653872013,
-0.0005774594028480351,
-0.05213436111807823,
0.0012499102158471942,
0.028981110081076622,
0.07729021459817886,
0.04395364224910736,
-0.03838423639535904,
0.013336023315787315,
-0.042887140065431595,
-0.05855005234479904,
0.0108347712084651,
0.03564569726586342,
-0.009908812120556831,
-0.028193552047014236,
-0.0013672782806679606,
0.05166881904006004,
-0.021097593009471893,
0.025779828429222107,
0.024561574682593346,
0.02223183959722519,
-0.0053190505132079124,
-0.045157164335250854,
-0.024265894666314125,
0.026220127940177917,
-0.038249753415584564,
0.015411109663546085,
-0.03912278637290001,
0.024128038436174393,
0.021470876410603523,
0.07543950527906418,
0.04080449789762497,
0.02885030210018158,
-0.0003878503921441734,
0.025127943605184555,
-0.0024343132972717285,
-0.043621696531772614,
-0.02267802134156227,
-0.006874130107462406,
-0.0318891815841198,
-0.019814832136034966,
-0.049350131303071976,
0.05496469512581825,
0.046535003930330276,
0.0193612240254879,
0.00002851507997547742,
0.06306695938110352,
-0.0012748274020850658,
-0.013452257961034775,
0.03468143567442894,
0.011907638981938362,
-0.031091108918190002,
0.05455423891544342,
0.009100591763854027,
0.01144847460091114,
0.009954533539712429,
0.005843153689056635,
0.006062234286218882,
-0.011940503492951393,
0.009796593338251114,
-0.012949093244969845,
-0.05918057635426521,
-0.02051025815308094,
0.009050801396369934,
0.04520973190665245,
-0.012736360542476177,
-0.030783122405409813,
-0.04304954782128334,
0.0023921122774481773,
0.017804788425564766,
0.007324144244194031,
0.0181986466050148,
0.009501926600933075,
-0.026837876066565514,
-0.01570408046245575,
-0.02942804992198944,
0.006115742493420839,
-0.02703985571861267,
0.021370811387896538,
0.008812818676233292,
-0.0258076973259449,
0.05875391885638237,
-0.019667282700538635,
0.04146607592701912,
0.027374666184186935,
-0.02923322655260563,
-0.013137055560946465,
0.024413909763097763,
-0.02416292019188404,
-0.02815009281039238,
0.0446319542825222,
0.01100075151771307,
0.06928509473800659,
-0.012150094844400883,
0.060908243060112,
-0.013474303297698498,
-0.04463169351220131,
-0.03609348088502884,
-0.025261864066123962,
0.042065154761075974,
0.01012325193732977,
-0.006988198962062597,
0.020558014512062073,
-0.015203581191599369,
0.001734134741127491,
0.004820466041564941,
-0.06760014593601227,
0.0649004578590393,
0.08802302926778793,
0.037445154041051865,
0.03925520181655884,
0.03666707128286362,
-0.0005986109608784318,
0.02729802206158638,
0.017616575583815575,
-0.013374879024922848,
-0.04652383551001549,
0.0010303950402885675,
0.049301356077194214,
0.05274462327361107,
-0.053541701287031174,
0.00036894207005389035,
0.04730189964175224,
0.005195508245378733,
0.021928709000349045,
-0.0018390454351902008,
-0.011843412183225155,
-0.0017823700327426195,
0.015836039558053017,
0.02831425331532955,
0.027398327365517616,
0.012364629656076431,
0.012144705280661583,
-0.007931575179100037,
-0.011147317476570606,
-0.001295735128223896,
-0.04219920560717583,
0.062499433755874634,
-0.012487737461924553,
-0.016215071082115173,
-0.011267813853919506,
-0.017552154138684273,
0.05403623729944229,
0.004241432063281536,
0.05988268554210663,
-0.019831018522381783,
0.0007401113980449736,
0.0028466179501265287,
-0.02801777422428131,
-0.012376428581774235,
0.05215306952595711,
-0.034964051097631454,
-0.021540291607379913,
-0.016162248328328133,
0.01460601668804884,
-0.038156066089868546,
0.007578609045594931,
-0.03187894821166992,
-0.012721127830445766,
-0.023290550336241722,
-0.01120106689631939,
0.017399469390511513,
0.018381690606474876,
-0.002183443633839488,
-0.0033456087112426758,
-0.04427938163280487,
-0.003684047143906355,
0.001655498519539833,
-0.011773781850934029,
0.046001989394426346,
-0.0874464213848114,
0.007830126211047173,
-0.03857351467013359,
0.011230903677642345,
0.04384709149599075,
0.011569743044674397,
0.005239496473222971,
-0.0022451519034802914,
-0.02424483746290207,
-0.042461149394512177,
-0.05251145362854004,
0.007412748411297798,
-0.0036813849583268166,
-0.08008517324924469,
0.008173338137567043,
-0.0032031740993261337,
0.012386509217321873,
-0.008145102299749851,
0.013005794957280159,
-0.01667524315416813,
-0.024164723232388496,
0.0018409456824883819,
0.009186302311718464,
0.04925472289323807,
-0.03535296767950058,
-0.007684069219976664,
0.007649879902601242,
-0.06061316654086113,
0.012370933778584003,
-0.1004885584115982,
-0.00027149016386829317,
0.019893823191523552,
-0.02361782267689705,
0.0332321971654892,
-0.010075465776026249,
-0.05682523176074028,
0.06525206565856934,
0.028979666531085968,
-0.007025602739304304,
-0.0026349371764808893,
-0.009035407565534115,
-0.02709706500172615,
-0.004287359304726124,
0.034573283046483994,
0.025413526222109795,
-0.0176274124532938,
0.04926968738436699,
0.018875684589147568,
0.00598016194999218,
0.05481291934847832,
-0.038791581988334656,
-0.018741628155112267,
0.06125633046030998,
0.014486233703792095,
-0.0036763385869562626,
0.05856405198574066,
-0.0010049081174656749,
-0.036863572895526886,
0.03155310079455376,
-0.013038871809840202,
-0.0017953525530174375,
0.013683365657925606,
-0.05768546462059021,
0.008871166966855526,
0.005770997144281864,
0.02452734485268593,
0.008562828414142132,
0.08023884147405624,
0.025941768661141396,
-0.03326451778411865,
-0.005031869746744633,
0.05677558854222298,
0.02933555655181408,
0.0020023267716169357,
0.02385389804840088,
0.05328665301203728,
0.04003596678376198,
-0.025386283174157143,
-0.009930000640451908,
0.009087040089070797,
0.002850352320820093,
0.010038125328719616,
-0.03771983087062836,
-0.0333169549703598,
0.010229267179965973,
0.04019535705447197,
0.024540992453694344,
-0.0284586139023304,
-0.03138348087668419,
-0.03462847322225571,
-0.05948169156908989,
0.0009151541744358838,
-0.032769400626420975,
0.05349668860435486,
-0.001893990091048181,
-0.003453846788033843,
0.0016757802804931998,
0.035227999091148376,
0.009066254831850529,
0.006984308827668428,
-0.06868255883455276,
0.014894012361764908,
-0.0004472699365578592,
-0.009236152283847332,
0.012947243638336658,
0.02266606129705906,
0.04665231332182884,
0.007594046648591757,
-0.04413587227463722,
0.008371156640350819,
-0.004457705654203892,
-0.03923648223280907,
-0.010717676021158695,
-0.02406211756169796,
-0.02740791067481041,
-0.01881680078804493,
0.036078307777643204,
0.04511938616633415,
-0.007993878796696663,
-0.005522951949387789,
0.05433805286884308,
-0.04574742913246155,
0.020774012431502342,
-0.027186550199985504,
0.01509189698845148,
-0.0033861547708511353,
0.022261319682002068,
0.03775111958384514,
0.008725582621991634,
-0.02871072292327881,
-0.003689801786094904,
-0.000402551784645766,
0.04959113523364067,
0.0511283241212368,
-0.011661951430141926,
0.004486860241740942,
-0.05335105210542679,
-0.011685151606798172,
0.00516507076099515,
0.06347829848527908,
-0.005364592187106609,
0.01018631923943758,
0.0437021404504776,
-0.019747421145439148,
0.002659402322024107,
0.03846095874905586,
0.036967091262340546,
0.00103306258097291,
-0.007855609990656376,
-0.03634610027074814,
0.005401767790317535,
0.00016761997540015727,
-0.0015254837926477194,
-0.007388893980532885,
0.002832904225215316,
-0.03921211510896683,
0.02820015512406826,
-0.023814426735043526,
0.03106425516307354,
-0.012514956295490265,
-0.007588658016175032,
0.01142522506415844,
0.05714697390794754,
0.01801248826086521,
0.004250471945852041,
0.017800545319914818,
0.0517260804772377,
0.009052861481904984,
-0.012105951085686684,
-0.0051916493102908134,
-0.05738788843154907,
-0.022164084017276764,
0.022913068532943726,
0.05678834021091461,
0.010367369279265404,
-0.007125453092157841,
-0.03281063959002495,
-0.0009429093333892524,
0.06028658524155617,
0.007758106105029583,
0.03609870746731758,
0.011186621151864529,
-0.006296096369624138,
-0.03277503326535225,
-0.03289612755179405,
-0.025277847424149513,
0.05952811986207962,
-0.03000342845916748,
0.023758407682180405,
-0.07207409292459488,
-0.02426021918654442,
-0.028976889327168465,
0.03408851847052574,
0.008205603808164597,
0.05956773832440376,
0.04736950621008873,
-0.023484591394662857,
-0.0042562722228467464,
0.019637422636151314,
-0.047400474548339844,
-0.057341210544109344,
0.004939632955938578,
0.015838561579585075,
0.0020369833800941706,
0.01829737424850464,
-0.04556601122021675,
-0.047843992710113525,
0.0009112914558500051,
-0.024772072210907936,
0.01192385982722044,
0.032112833112478256,
-0.019569795578718185,
0.0509440042078495,
0.05853743851184845,
-0.012647554278373718,
0.06257730722427368,
0.04561396315693855,
-0.014710277318954468,
0.013761579990386963,
0.004159670323133469,
0.011926536448299885,
-0.029279675334692,
-0.011358960531651974,
-0.03376481309533119,
-0.006162998266518116,
-0.028339646756649017,
0.004063402768224478,
-0.014949695207178593,
-0.005960918962955475,
-0.04083815589547157,
-0.0004972676979377866,
-0.00040013916441239417,
0.04053337499499321,
-0.005508830305188894,
-0.014496888965368271,
0.012890919111669064,
0.021908961236476898,
0.03671158477663994,
-0.03789816424250603,
0.003933602012693882,
-0.005507988389581442,
-0.0013664987636730075,
0.002454501809552312,
0.04003869742155075,
0.004456514026969671,
-0.004929501563310623,
0.0019813873805105686,
0.020324796438217163,
-0.020803898572921753,
0.012249666266143322,
-0.016294660046696663,
0.020763413980603218,
0.026308346539735794,
-0.04849487170577049,
-0.0315757691860199,
-0.014083071611821651,
-0.01724986732006073,
0.009417549706995487,
-0.06248272955417633,
0.018414827063679695,
0.021931147202849388,
-0.009942841716110706,
-0.0740799680352211,
-0.02028569020330906,
-0.00613353680819273,
-0.0011075785150751472,
-0.005820955615490675,
-0.029476424679160118,
0.0026098862290382385,
-0.06600502878427505,
-0.01106373779475689,
0.005785415880382061,
0.05904042720794678,
-0.029424134641885757,
0.034797556698322296,
0.009781379252672195,
0.020500103011727333,
0.04307539016008377,
0.019665369763970375,
-0.012774687260389328,
0.047627974301576614,
-0.060101479291915894,
-0.004825743380934,
-0.0004173518973402679,
0.039627332240343094,
-0.020679764449596405,
-0.010610618628561497,
0.021251900121569633,
-0.02069365791976452,
0.03520024195313454,
-0.008465607650578022,
-0.03705718740820885,
0.009054001420736313,
0.009656146168708801,
0.04436366632580757,
-0.014234604313969612,
-0.01630818471312523,
0.008589379489421844,
0.026436911895871162,
0.004824898671358824,
0.018498267978429794,
-0.07734207808971405,
-0.027205154299736023,
0.02068682201206684,
-0.012072054669260979,
-0.03941142186522484,
-0.004179965704679489,
0.042122792452573776,
-0.008612587116658688,
0.0045708403922617435,
0.030660763382911682,
-0.005897997412830591,
0.013390381820499897,
0.007359268143773079,
0.0063019003719091415,
0.0234722550958395,
-0.002689148997887969,
0.004441570024937391,
-0.03360816091299057,
-0.0654345378279686,
0.01693686656653881,
0.07340700924396515,
-0.009452472440898418,
0.015919754281640053,
0.007573950570076704,
0.005090811755508184,
-0.015360875986516476,
-0.012354071252048016,
-0.020199725404381752,
0.023417901247739792,
-0.020141469314694405,
0.021286623552441597,
-0.042183343321084976,
0.015388952568173409,
0.021672841161489487,
0.02471892163157463,
-0.04601626098155975,
0.008230652660131454,
0.004449151922017336,
-0.019767355173826218,
0.01858721487224102,
0.007745858747512102,
-0.0004106709675397724,
0.024751432240009308,
-0.003862751182168722,
0.04207633063197136,
-0.002307910704985261,
0.0072441091760993,
0.04026825353503227,
0.04289983585476875,
0.0032103850971907377,
-0.03798064589500427,
-0.01983063854277134,
-0.0019407739164307714,
0.06087086722254753,
0.023961538448929787,
0.012106048874557018,
0.044461119920015335,
0.009918185882270336,
0.05119509994983673,
0.03181813284754753,
0.01603744365274906,
-0.021433044224977493,
-0.04521600157022476,
0.004472740460187197,
-0.04997184872627258,
-0.06113969162106514,
0.012322966940701008,
-0.0018374430947005749,
-0.03724023699760437,
0.01961611583828926,
-0.0005133672966621816,
0.03194752708077431,
0.02436668984591961,
0.045781493186950684,
-0.013109036721289158,
0.07224462181329727,
0.0033062235452234745,
0.02161370776593685,
0.0035216445103287697,
0.017215201631188393,
0.13696131110191345,
0.03621077537536621,
0.010420918464660645,
-0.041476376354694366,
-0.0020315079018473625,
0.031052716076374054,
-0.016917642205953598,
-0.02454899623990059,
-0.011504997499287128,
-0.004806009586900473,
-0.025322899222373962,
-0.0060911476612091064,
0.08167308568954468,
0.013583526015281677,
-0.0274160485714674,
0.020289381965994835,
-0.045527298003435135,
-0.05359219014644623,
-0.0034839240834116936,
-0.0045599136501550674,
-0.004180888179689646,
0.02390054613351822,
-0.05620472505688667,
-0.024406924843788147,
-0.04117311164736748,
0.009338599629700184,
-0.05608557164669037,
-0.01441396027803421,
0.010953307151794434,
-0.01625312864780426,
-0.03656081110239029,
0.006650874856859446,
0.02905198559165001,
0.013298247940838337,
-0.020263686776161194,
0.0026448566932231188,
-0.008075123652815819,
0.013866824097931385,
0.06891966611146927,
0.06870511174201965,
0.03650049865245819,
-0.0014957787934690714,
0.0020829448476433754,
0.012525445781648159,
-0.04314563795924187,
-0.019978700205683708,
-0.009371845051646233,
0.05258805304765701,
-0.00011381027434254065,
-0.03185867518186569,
-0.0009322534315288067,
-0.03701884299516678,
0.02485233172774315,
-0.022967999801039696,
0.028020817786455154,
-0.04210215061903,
0.004699598997831345,
-0.050222303718328476,
0.0020752958953380585,
-0.007804343476891518,
0.029744213446974754,
0.018514230847358704,
-0.004070664756000042,
-0.013973452150821686,
-0.03361867368221283,
0.04028287157416344,
0.003339385846629739,
0.034504350274801254,
0.0023242556490004063,
-0.013672920875251293,
-0.0170633252710104,
-0.02199171856045723,
-0.060634929686784744,
-0.026746882125735283,
0.017958808690309525,
-0.028569797053933144,
0.05413053184747696,
0.010941545478999615,
0.02099006064236164,
-0.04603848606348038,
-0.1003783643245697,
0.010733546689152718,
-0.013782310299575329,
-0.010667933151125908,
-0.014077349565923214,
-0.015088791958987713,
0.023303497582674026,
0.019235802814364433,
-0.056519296020269394,
-0.00887602474540472,
0.012765880674123764,
0.05268823727965355,
0.014375404454767704,
-0.020387740805745125,
-0.010632457211613655,
-0.012476188130676746,
0.022200262174010277,
0.000559662061277777,
-0.027898307889699936,
0.013026248663663864,
0.01866854727268219,
0.003248318564146757,
-0.017330972477793694,
0.010563920252025127,
-0.02234579063951969,
-0.012151645496487617,
-0.0016827676445245743,
-0.027756692841649055,
-0.010111745446920395,
0.01605595089495182,
0.006615637801587582,
-0.0004997341311536729,
-0.012206445448100567,
-0.01801617257297039,
0.012960802763700485,
-0.015839871019124985,
0.0028033906128257513,
-0.04193535074591637,
-0.010988447815179825,
-0.045580729842185974,
0.0013804344926029444,
-0.024465149268507957,
0.0240816418081522,
-0.023022912442684174,
0.040182437747716904,
-0.015505876392126083,
0.016994992271065712,
0.006036200560629368,
0.041994474828243256,
-0.0008540806011296809,
-0.04040436074137688,
0.0392608679831028,
0.04296618327498436,
0.0038550342433154583,
-0.028078416362404823,
-0.02248091623187065,
-0.019801534712314606,
0.005430081393569708,
0.007344920188188553,
-0.01078872848302126,
0.022955479100346565,
-0.028743023052811623,
-0.04264689236879349,
0.012392374686896801,
-0.04275719076395035,
0.04110318049788475,
0.0386076457798481,
-0.012015515007078648,
-0.002468480495736003,
-0.012141965329647064,
0.006931991782039404,
-0.012801030650734901,
0.03157973289489746,
-0.027462396770715714,
-0.016303565353155136,
-0.025802399963140488,
0.0496080219745636,
-0.003644534619525075,
0.02891448698937893,
0.019336363300681114,
0.02170545607805252,
0.008744235150516033,
-0.021679945290088654,
0.004666843917220831,
0.007550829090178013,
0.02238466963171959,
0.02492859587073326,
-0.04742888733744621,
0.03801379352807999,
0.053569246083498,
-0.016469651833176613,
0.004064621403813362,
-0.02985113486647606,
-0.000019599438019213267,
-0.10295285284519196,
-0.035559289157390594,
-0.01212435495108366,
-0.015084960497915745,
0.07248082756996155,
-0.047685958445072174,
-0.008082489483058453,
0.004691787529736757,
-0.06999675929546356,
0.03487549349665642,
-0.009004837833344936,
0.0017105184961110353,
-0.022417651489377022,
0.01152878999710083,
-0.01279421802610159,
0.06774882227182388,
0.0362132266163826,
0.04563312605023384,
0.04591083154082298,
-0.040630970150232315,
-0.010974626056849957,
-0.02452935464680195,
-0.008308331482112408,
0.019196605309844017,
0.027051467448472977,
-0.025364810600876808,
0.06089106202125549,
-0.04223507642745972,
-0.028868699446320534,
-0.03245509788393974,
-0.02586626261472702,
0.016644654795527458,
-0.03669728338718414,
0.0011079831747338176,
-0.0025479306932538748,
0.060829490423202515,
0.04598143696784973,
-0.001529175671748817,
-0.0007752683013677597,
-0.004342152737081051,
-0.005209927912801504,
-0.009938145987689495,
-0.07532615214586258,
-0.008841284550726414,
0.002145098289474845,
0.0028721815906465054,
-0.05560188367962837,
0.0465066060423851,
0.00991585198789835,
-0.020981978625059128,
-0.023613840341567993,
-0.0004953378229402006,
0.013043633662164211,
-0.01337808184325695,
0.006844470277428627,
-0.026926225051283836,
-0.010944090783596039,
0.004725507460534573,
0.010691101662814617,
0.015856631100177765,
-0.009668368846178055,
0.0032944439444690943,
-0.07442072033882141,
0.02534474991261959,
0.010677794925868511,
-0.03486678749322891,
-0.0022816541604697704,
-0.003899180330336094,
0.008241185918450356,
0.01922272890806198,
-0.00358041119761765,
-0.008248398080468178,
-0.03027956746518612,
0.02068687602877617,
-0.026451976969838142,
0.02066720835864544,
-0.01657937839627266,
-0.003506077453494072,
0.010774723254144192,
-0.019735176116228104,
0.0002673861163202673,
0.005130080506205559,
-0.021612996235489845,
-0.005308268591761589,
0.022027507424354553,
0.02800259366631508,
0.01336495578289032,
0.0529509074985981,
-0.006784098222851753,
0.016299061477184296,
0.024815399199724197,
-0.004850104916840792,
0.026763731613755226,
-0.04685971513390541,
0.0014991540228947997,
-0.029794765636324883,
-0.01719576120376587,
0.005847290623933077,
0.013209962286055088,
0.0059924619272351265,
0.032641105353832245,
0.013360932469367981,
-0.025976670905947685,
0.012335199862718582,
-0.02162741869688034,
-0.04259088635444641,
0.046735815703868866,
-0.011782633140683174,
-0.021255746483802795,
0.06268864125013351,
-0.020571701228618622,
0.036287255585193634,
0.016512012109160423,
-0.04043935611844063,
-0.006967367138713598,
0.006093872245401144,
-0.061353716999292374,
-0.032533302903175354,
-0.013586420565843582,
-0.01131943054497242,
-0.03372737765312195,
-0.043615225702524185,
0.01637677103281021,
0.024508105590939522,
-0.028876375406980515,
-0.015487109310925007,
0.07631461322307587,
0.026683034375309944,
0.04374255985021591,
0.0242699533700943,
0.019151752814650536,
0.033397939056158066,
0.014478981494903564,
0.043135251849889755,
0.0418948158621788,
0.01770539954304695,
-0.016984643414616585,
-0.01472489070147276,
0.0022139837965369225,
-0.007683595176786184,
0.00126496865414083,
0.04594368487596512,
0.02192283421754837,
-0.037262674421072006,
0.020589562132954597,
0.026812130585312843,
-0.003017368959262967,
0.018410565331578255,
-0.0006513983244076371,
-0.05046685039997101,
0.10056988149881363,
-0.005954639054834843,
-0.018032601103186607,
-0.02657180465757847,
-0.02787846326828003,
-0.03593452647328377,
0.0045328326523303986,
0.05320259556174278,
0.06840039044618607,
-0.029051607474684715,
-0.017274189740419388,
-0.02202635630965233,
-0.0063430736772716045,
-0.014724084176123142,
-0.033163584768772125,
-0.005949502810835838,
-0.01384153962135315,
-0.029955437406897545,
0.0007549115689471364,
-0.047866590321063995,
-0.020667077973484993,
-0.04563088342547417,
-0.004862104542553425,
0.03196396306157112,
0.06027604267001152,
0.0009264980326406658,
0.0020906003192067146,
-0.014418966136872768,
0.06198267638683319,
-0.0016060838242992759,
-0.005545378662645817,
-0.0034788434859365225,
0.024973267689347267,
-0.022322451695799828,
-0.007872200571000576
] |
<p>Put the classical electron-emitting double-slit apparatus in a sealed box. At each slit there's a counter to check whether an electron has passed it or not, so had the apparatus been left in open, we would have observed dots pile after the two slits on the screen with no interference pattern. But now the apparatus is running in the sealed box, and the box is so designed that 1) an outside observer can't know anything inside the box unless he opens it. 2) the box destroys the counters just before you open it, leaving no information of their past recordings. My question is, will you see interference pattern after you open the box? Why or why not?</p>
<p>To quote Feynman:"You do add the amplitudes for the different indistinguishable alternatives inside the experiment... At the end of the process you may say that you 'don't want to look at the photon.' That's your bussiness... Nature does not know what you are looking at, and she behaves the way she's going to behave whether you bother to take down the data or not" Does this comment apply here? But which slit the electrons have passed does seem indistinguishable to an outside observer during or after the experiment. </p>
| 9,635 |
[
-0.0303452480584383,
-0.02464512549340725,
-0.00021994521375745535,
-0.026822974905371666,
-0.004304058384150267,
0.014724234119057655,
0.009376357309520245,
-0.014045404270291328,
-0.011269169859588146,
0.02747136913239956,
0.03807268291711807,
0.024888403713703156,
0.0038383363280445337,
-0.0008495979709550738,
0.0011001172242686152,
0.010931718163192272,
-0.016084356233477592,
-0.039563313126564026,
-0.006237119901925325,
-0.05948483571410179,
-0.031100695952773094,
0.02057921141386032,
0.015541971661150455,
-0.006371363066136837,
-0.05886000394821167,
0.029599178582429886,
-0.007697248365730047,
-0.018009165301918983,
0.05289062112569809,
0.043069466948509216,
-0.01513462420552969,
-0.007988308556377888,
0.0037929301615804434,
0.01625780016183853,
0.027875788509845734,
-0.020858336240053177,
-0.02526305615901947,
-0.040129516273736954,
0.02367488667368889,
0.00612588319927454,
0.006106936372816563,
0.007046809885650873,
-0.024755122140049934,
0.06169142946600914,
-0.01854984275996685,
0.02531524933874607,
0.0032065920531749725,
-0.03021133691072464,
0.0539163313806057,
-0.041050564497709274,
0.06183020398020744,
-0.038221679627895355,
0.01526655349880457,
0.027415238320827484,
-0.01874115876853466,
0.0026221589650958776,
0.1071661114692688,
0.06813732534646988,
-0.0072465441189706326,
-0.02615833654999733,
-0.030961861833930016,
-0.009391073137521744,
-0.010778447613120079,
-0.004352333024144173,
-0.036209385842084885,
0.034699201583862305,
0.019185857847332954,
-0.04581242799758911,
0.020129676908254623,
-0.013192736543715,
-0.002007798058912158,
0.015070009976625443,
0.046627726405858994,
0.003114009043201804,
0.01580994203686714,
-0.01431470736861229,
0.04401431977748871,
0.016957111656665802,
0.022294320166110992,
0.06718932092189789,
-0.0023466695565730333,
0.0212307870388031,
0.025911103934049606,
0.04691930487751961,
0.03449077159166336,
-0.018863052129745483,
0.07780997455120087,
-0.029038356617093086,
0.007429896388202906,
0.055954884737730026,
-0.012837654910981655,
0.026682820171117783,
0.03952251374721527,
-0.006893194280564785,
-0.035081665962934494,
0.01874801702797413,
-0.00790766067802906,
0.08648308366537094,
0.009830757044255733,
-0.009469259530305862,
0.005735569633543491,
-0.004220125265419483,
0.01123406458646059,
0.06952930241823196,
0.0007402899791486561,
-0.01628289185464382,
-0.05135433375835419,
0.0561068058013916,
0.00742568913847208,
-0.01174084935337305,
-0.02312389388680458,
0.009772317484021187,
0.006841880269348621,
0.018468700349330902,
0.006783741060644388,
-0.0092677753418684,
-0.012347676791250706,
0.0026880439836531878,
0.04671547934412956,
0.08896084874868393,
0.01959952525794506,
-0.017840426415205002,
0.01455250196158886,
-0.03646743297576904,
-0.07423187792301178,
-0.013656128197908401,
0.056239042431116104,
-0.01336255669593811,
-0.03248894587159157,
0.05353560671210289,
-0.005037506576627493,
0.0010192006593570113,
0.016184739768505096,
-0.0029796771705150604,
0.012860609218478203,
-0.0120131466537714,
-0.10496416687965393,
-0.06719540059566498,
0.021272454410791397,
-0.02455892227590084,
-0.01571408472955227,
-0.08675693720579147,
-0.004039420746266842,
0.028171811252832413,
0.08011255413293839,
-0.03351106122136116,
-0.02132266014814377,
-0.00010001786722568795,
0.015513963997364044,
0.003896139794960618,
-0.007623767014592886,
-0.0001309592043980956,
0.026775801554322243,
-0.027914144098758698,
-0.02073022723197937,
-0.03661804273724556,
0.032833799719810486,
0.019617648795247078,
0.0024787771981209517,
-0.027027543634176254,
0.0435786098241806,
-0.022997047752141953,
0.0356123186647892,
-0.003971464931964874,
-0.030626554042100906,
-0.04281779006123543,
0.10436102002859116,
0.009044729173183441,
0.031585950404405594,
0.010327892377972603,
0.025132814422249794,
0.03849496319890022,
-0.040576767176389694,
-0.004457064438611269,
0.00025536830071359873,
-0.016573727130889893,
-0.02201707847416401,
-0.0028656490612775087,
0.05117131024599075,
-0.009731674566864967,
0.008348740637302399,
-0.013631313107907772,
-0.014970378018915653,
0.003893535118550062,
-0.0016559355426579714,
0.0191941000521183,
0.0076189772225916386,
-0.02999422885477543,
-0.03293219581246376,
-0.060940299183130264,
-0.018913179636001587,
-0.08150176703929901,
0.002389236818999052,
0.030017370358109474,
-0.020003873854875565,
0.026400133967399597,
0.02068897895514965,
0.014990599825978279,
-0.01467217318713665,
-0.033325426280498505,
-0.016440611332654953,
0.02614704705774784,
0.008412607945501804,
-0.02619178220629692,
0.018084293231368065,
0.0357191227376461,
0.021322624757885933,
-0.01775456592440605,
0.04964004456996918,
-0.02247745171189308,
-0.021364327520132065,
0.013721028342843056,
-0.0026999316178262234,
0.03134140372276306,
0.00894385389983654,
0.025775494053959846,
0.026073170825839043,
0.022418148815631866,
0.0017522990237921476,
0.0011680497555062175,
-0.05388034135103226,
0.05292322114109993,
0.037762485444545746,
0.008648405782878399,
-0.0151972696185112,
-0.0003437805862631649,
0.00482976995408535,
0.01999870501458645,
-0.004542124457657337,
-0.012144943699240685,
-0.0338473841547966,
-0.020478807389736176,
0.0036155718844383955,
0.03142903000116348,
-0.008016721345484257,
0.07110931724309921,
0.01730557344853878,
-0.002480595838278532,
-0.0045595006085932255,
0.016579249873757362,
0.015260656364262104,
0.0007587859290651977,
-0.007218405604362488,
0.01761537976562977,
-0.010750364512205124,
0.01971961185336113,
0.036125317215919495,
0.010607535019516945,
-0.03339608758687973,
-0.023268096148967743,
-0.018861012533307076,
0.01595253497362137,
-0.01814418099820614,
0.017888719215989113,
-0.0251093041151762,
-0.012739535421133041,
0.01337294653058052,
-0.01650460809469223,
0.024452166631817818,
-0.024906283244490623,
0.006747780833393335,
-0.025987882167100906,
-0.07141950726509094,
-0.008929598145186901,
-0.01640636846423149,
-0.01587079092860222,
-0.05523478612303734,
-0.008612768724560738,
0.03309192508459091,
-0.05014974996447563,
0.010237331502139568,
-0.004694633185863495,
0.0176252294331789,
-0.02614016644656658,
0.027971671894192696,
0.02661316655576229,
0.0043162754736840725,
0.047257594764232635,
-0.05609946325421333,
-0.06341757625341415,
-0.03321103751659393,
-0.030369345098733902,
0.031107984483242035,
0.029581435024738312,
-0.054422277957201004,
-0.0011074159992858768,
-0.03240786865353584,
-0.04275538772344589,
0.04891180247068405,
-0.023435907438397408,
0.020470229908823967,
0.04528360068798065,
-0.009123653173446655,
-0.04994604364037514,
-0.034376051276922226,
0.0007969062426127493,
-0.015408641658723354,
0.006208677776157856,
-0.01468713954091072,
0.03484125807881355,
0.022898558527231216,
-0.013239570893347263,
-0.005776825360953808,
-0.040393054485321045,
-0.05923601612448692,
0.004533781204372644,
-0.01624523475766182,
0.0030764229595661163,
-0.03348935768008232,
-0.01687038503587246,
0.005172416102141142,
-0.03940151259303093,
0.0036866648588329554,
-0.06525485217571259,
-0.08315986394882202,
0.006365462671965361,
-0.007837205193936825,
0.007559974677860737,
-0.024814032018184662,
-0.0002800973306875676,
0.04482460767030716,
0.042955368757247925,
-0.039244722574949265,
-0.029662322252988815,
-0.008100924082100391,
-0.004101663827896118,
-0.012677323073148727,
-0.010136714205145836,
0.00790658500045538,
0.01417937595397234,
0.0326559878885746,
0.013000416569411755,
0.0283698420971632,
0.005790221504867077,
0.014530880376696587,
-0.0075663249008357525,
0.024494290351867676,
0.0030725339893251657,
-0.02363247610628605,
0.018615370616316795,
0.048093948513269424,
-0.0031417175196111202,
-0.0002053252828773111,
-0.020359598100185394,
0.024325435981154442,
0.029594125226140022,
-0.03631441295146942,
0.05399729683995247,
0.006103746127337217,
0.0476052463054657,
-0.004138025920838118,
0.039521146565675735,
0.010169162414968014,
0.018165862187743187,
-0.03916364163160324,
-0.024707064032554626,
0.038023706525564194,
-0.010388249531388283,
-0.009584692306816578,
0.04287625104188919,
0.0382964052259922,
0.013011708855628967,
-0.026484839618206024,
0.042031168937683105,
0.0001577862713020295,
0.044247474521398544,
-0.021047238260507584,
-0.03258068859577179,
0.04038345068693161,
0.0076301200315356255,
0.03229577839374542,
-0.0014930468751117587,
-0.04240918159484863,
-0.018047800287604332,
-0.031616874039173126,
-0.0036664435174316168,
0.014971274882555008,
0.03816710785031319,
0.019722431898117065,
0.029254529625177383,
0.04052875190973282,
-0.016668513417243958,
-0.019196607172489166,
-0.006458963733166456,
-0.06465553492307663,
0.011816829442977905,
-0.00972141046077013,
-0.03224964439868927,
-0.019248008728027344,
0.005769169889390469,
-0.004111528862267733,
-0.021174637600779533,
-0.03158710524439812,
0.022909335792064667,
-0.0019267715979367495,
-0.07081768661737442,
0.0007056758622638881,
-0.019086921587586403,
-0.018950825557112694,
-0.030240841209888458,
0.09482746571302414,
0.024920038878917694,
0.011157806031405926,
0.022562934085726738,
0.007815202698111534,
-0.05753307789564133,
0.020785892382264137,
0.043111078441143036,
-0.001391416066326201,
0.01733270473778248,
0.04249618947505951,
0.05188759043812752,
0.01226977538317442,
-0.04827405884861946,
0.009451175108551979,
0.027188951149582863,
0.03629104793071747,
0.008841874077916145,
-0.022849641740322113,
-0.02310122363269329,
0.015074502676725388,
-0.02521529793739319,
-0.013145687058568,
0.07433588802814484,
-0.029708554968237877,
0.006928722374141216,
0.030384916812181473,
0.013969175517559052,
-0.020825451239943504,
0.031218625605106354,
0.060565285384655,
0.03584780916571617,
-0.01643701270222664,
-0.04173249751329422,
-0.011448676697909832,
-0.044851791113615036,
-0.0029364805668592453,
-0.04916185513138771,
0.013055678457021713,
0.013086155988276005,
0.005915628746151924,
0.011561015620827675,
0.03757426142692566,
-0.0027806779835373163,
-0.013009322807192802,
-0.04911518841981888,
-0.004165619146078825,
-0.003108036471530795,
0.02300916612148285,
0.025104284286499023,
0.04501049220561981,
0.02491559460759163,
0.038911372423172,
-0.0071905492804944515,
-0.044059257954359055,
-0.007142522372305393,
0.03571630269289017,
0.05430904030799866,
0.002312161261215806,
-0.0033620151225477457,
-0.0541205033659935,
-0.01658235676586628,
0.06907106190919876,
-0.01339696440845728,
0.033889323472976685,
-0.04780380800366402,
-0.03100149892270565,
-0.03077775426208973,
-0.012451879680156708,
-0.01114253792911768,
-0.0013341127196326852,
0.002728620544075966,
0.027111997827887535,
-0.0060850828886032104,
-0.019392497837543488,
-0.03420337289571762,
0.007628616411238909,
0.02226034179329872,
0.0406411737203598,
-0.010573272593319416,
0.0294315367937088,
0.007063827011734247,
-0.017252527177333832,
-0.026548389345407486,
-0.07521793991327286,
0.056946612894535065,
-0.019547246396541595,
0.009861616417765617,
0.05027807131409645,
-0.026608742773532867,
-0.032812174409627914,
-0.008049518801271915,
-0.005098115652799606,
0.007866202853620052,
0.03007836826145649,
-0.023982703685760498,
0.05472845211625099,
-0.0014060812536627054,
0.003610999323427677,
0.031064463779330254,
-0.004525786731392145,
0.005849841516464949,
0.03475712612271309,
-0.008428466506302357,
0.04900789260864258,
-0.027542060241103172,
0.018823770806193352,
-0.0407254621386528,
0.025967229157686234,
-0.01957002282142639,
0.08431082218885422,
-0.008018401451408863,
0.02650497853755951,
-0.0027709531132131815,
-0.04555968940258026,
0.01817706786096096,
-0.006465058773756027,
-0.019626427441835403,
0.010880956426262856,
-0.048772815614938736,
0.018843283876776695,
-0.02236928418278694,
-0.033131200820207596,
-0.02113535813987255,
-0.04534591734409332,
0.02700481191277504,
0.04469490796327591,
0.003370181191712618,
0.03932083025574684,
-0.05095363035798073,
-0.029608719050884247,
0.022180594503879547,
-0.028893694281578064,
-0.008490276522934437,
-0.011809282936155796,
0.023894425481557846,
0.031037306413054466,
-0.06394948065280914,
-0.04298872873187065,
-0.0024601041804999113,
-0.0202169269323349,
0.017316240817308426,
-0.040820345282554626,
0.06898840516805649,
0.013662065379321575,
-0.007104685064405203,
-0.08961586654186249,
-0.06109100952744484,
0.001453721197322011,
0.006185766309499741,
-0.0174380075186491,
0.028564101085066795,
0.025792555883526802,
-0.0007357311551459134,
-0.04106085002422333,
-0.03192593902349472,
0.015082054771482944,
-0.012855598703026772,
-0.016941262409090996,
0.03536456078290939,
0.020306825637817383,
0.047366127371788025,
0.015665976330637932,
-0.007738057989627123,
-0.02869630791246891,
-0.023993991315364838,
-0.029158582910895348,
0.01011672057211399,
0.01230095885694027,
0.00644698366522789,
-0.051969755440950394,
-0.03058611787855625,
-0.007884599268436432,
0.038705501705408096,
-0.022026192396879196,
-0.0352381132543087,
0.015505357645452023,
-0.003279727650806308,
0.017079535871744156,
0.012621276080608368,
-0.006172736641019583,
-0.006204921752214432,
0.023069385439157486,
0.040383122861385345,
0.022578071802854538,
0.0017914010677486658,
-0.06123196333646774,
-0.016832120716571808,
-0.004212545696645975,
-0.008063097484409809,
0.0009783694986253977,
0.027863189578056335,
0.003744949819520116,
-0.03636227920651436,
-0.00005671559483744204,
-0.02622452937066555,
-0.006778839975595474,
-0.04225272312760353,
0.014409349299967289,
0.005073428153991699,
0.01360511314123869,
-0.04068312793970108,
-0.03686627000570297,
-0.02822842076420784,
-0.015110242180526257,
0.04972665384411812,
-0.023325743153691292,
0.04653863236308098,
-0.002543325535953045,
0.01706209033727646,
0.0007960399379953742,
-0.032501645386219025,
0.04609428718686104,
0.013583625666797161,
0.0009132506093010306,
0.029620390385389328,
-0.0428064726293087,
-0.005284749902784824,
0.04166321083903313,
0.06188109517097473,
0.0019566877745091915,
0.037558797746896744,
0.03482460230588913,
0.013646433129906654,
0.026116862893104553,
0.007071017287671566,
-0.03418002277612686,
0.01857008971273899,
-0.05848625674843788,
0.007725232280790806,
0.01043797843158245,
-0.012360239401459694,
0.03908008709549904,
0.015277021564543247,
0.0065606581047177315,
-0.024182897061109543,
-0.02726411446928978,
-0.08106149733066559,
0.010480272583663464,
-0.01678977906703949,
0.031237414106726646,
-0.010303246788680553,
0.001914377324283123,
0.025692271068692207,
0.022228198125958443,
-0.01029709167778492,
0.0021587174851447344,
-0.05233197286725044,
-0.07943687587976456,
-0.04328363761305809,
-0.01922060176730156,
0.08764297515153885,
0.007155535276979208,
-0.000018919028661912307,
0.018348578363656998,
-0.024836255237460136,
0.030033260583877563,
0.033957622945308685,
0.05925999581813812,
-0.011793329380452633,
0.013421542011201382,
-0.030658958479762077,
0.03510505333542824,
-0.049206990748643875,
0.026308121159672737,
0.11210648715496063,
0.0427391342818737,
0.005308610387146473,
-0.06057075411081314,
0.01499924249947071,
-0.01608705334365368,
0.04419819265604019,
-0.025479622185230255,
0.0259794220328331,
-0.015022254548966885,
0.00893218070268631,
0.015339655801653862,
0.048208579421043396,
0.038678377866744995,
0.004147375468164682,
0.03724629059433937,
-0.039771612733602524,
-0.04848532751202583,
0.013771978206932545,
0.03357291966676712,
0.01331341452896595,
-0.005226185545325279,
-0.030762765556573868,
0.0025424181949347258,
0.001472323085181415,
0.0090887900441885,
0.0016671119956299663,
-0.04814516007900238,
0.013386670500040054,
0.03618242219090462,
-0.04043290764093399,
-0.006415303330868483,
0.0368037186563015,
-0.0005337501643225551,
-0.0400802344083786,
0.0243653766810894,
0.010180591605603695,
-0.018089095130562782,
0.05973469465970993,
0.05044141784310341,
0.01816428080201149,
-0.0033264176454395056,
0.01603381149470806,
0.0036117956042289734,
-0.03959695249795914,
-0.001858963631093502,
0.017426500096917152,
0.04587390273809433,
-0.008777773007750511,
-0.0302647165954113,
-0.00285093835555017,
-0.04342085123062134,
0.038092173635959625,
-0.07767412811517715,
-0.02741861343383789,
-0.007891257293522358,
-0.013926658779382706,
-0.040880702435970306,
-0.008691567927598953,
-0.028652852401137352,
-0.0014821385266259313,
0.0031736514065414667,
-0.00938643142580986,
-0.0030333532486110926,
0.011834331788122654,
-0.023503532633185387,
0.0016598078655079007,
0.03318214789032936,
0.011848891153931618,
-0.011250041425228119,
-0.02875782735645771,
-0.02107435278594494,
-0.05217283219099045,
-0.00372716854326427,
-0.008922881446778774,
0.04168233647942543,
0.05565546825528145,
-0.02378975786268711,
-0.017785491421818733,
-0.023176275193691254,
-0.03215756267309189,
0.015035690739750862,
-0.024497786536812782,
0.0012183855287730694,
0.01356954500079155,
-0.004691455513238907,
0.04689503088593483,
0.0380883626639843,
0.003739347215741873,
-0.008577602915465832,
0.07399065047502518,
0.04468080401420593,
0.030300430953502655,
-0.03643249347805977,
-0.025666648522019386,
0.034189071506261826,
-0.0034156034234911203,
-0.008619030006229877,
-0.04578626528382301,
0.0007652999483980238,
-0.02489149197936058,
0.004190751351416111,
0.007023760117590427,
0.038053128868341446,
-0.018325239419937134,
-0.010343367233872414,
-0.017890529707074165,
-0.021646415814757347,
0.015001576393842697,
0.03651873394846916,
0.040200356394052505,
0.00029932562028989196,
-0.05618739500641823,
-0.04086213558912277,
0.004983207210898399,
-0.029352733865380287,
0.010907839983701706,
-0.027440719306468964,
0.005134389270097017,
-0.017887840047478676,
0.010789758525788784,
0.0193780567497015,
-0.019647402688860893,
-0.05002643167972565,
0.00023246530327014625,
0.001978132873773575,
-0.026351161301136017,
-0.021605143323540688,
0.05969256907701492,
0.0023054105695337057,
-0.06617320328950882,
0.002287481911480427,
0.02204451709985733,
-0.014368826523423195,
-0.029193980619311333,
-0.002456312533468008,
0.017280234023928642,
0.04584459215402603,
0.026391442865133286,
-0.020603947341442108,
0.027685483917593956,
-0.04303878918290138,
-0.048037003725767136,
0.041643209755420685,
0.0034539804328233004,
0.016440121456980705,
0.05839361995458603,
0.0016678411047905684,
0.006187926046550274,
0.03396352380514145,
-0.021001653745770454,
-0.03309620916843414,
0.03255194425582886,
-0.032260995358228683,
-0.003893532557412982,
-0.012753806076943874,
0.015519252978265285,
0.0026823903899639845,
-0.026115071028470993,
0.03305928781628609,
0.006316646002233028,
0.06502284854650497,
-0.003936483524739742,
-0.03674328699707985,
-0.016420498490333557,
0.021879643201828003,
-0.013695422559976578,
-0.037885088473558426,
-0.03199521824717522,
0.07362725585699081,
-0.034802451729774475,
0.018337510526180267,
0.027920907363295555,
-0.0085041718557477,
-0.10496555268764496,
0.028898151591420174,
-0.0066774883307516575,
0.04277373477816582,
0.00979791209101677,
-0.012465178035199642,
-0.000016801353922346607,
0.01830601692199707,
-0.09265268594026566,
-0.0035794274881482124,
0.0007915911846794188,
-0.04826692119240761,
-0.03577309846878052,
0.03369581699371338,
-0.05816161632537842,
0.030950991436839104,
0.037887826561927795,
-0.0009080555173568428,
0.009123919531702995,
-0.0026233394164592028,
-0.023038946092128754,
-0.0068381293676793575,
-0.048933982849121094,
0.02584407478570938,
0.025338495150208473,
0.005004678852856159,
0.08040095120668411,
-0.03493589162826538,
0.0024424958974123,
0.02410009317100048,
-0.008432724513113499,
0.01401682198047638,
-0.011130736209452152,
-0.011679062619805336,
0.03523667901754379,
0.013285237364470959,
0.01927000656723976,
0.034782975912094116,
0.01128856185823679,
0.01413998194038868,
0.03464745357632637,
-0.04243311658501625,
-0.005253307055681944,
0.0014647127827629447,
0.005218322388827801,
0.00927739031612873,
-0.042246315628290176,
0.003675189334899187,
0.004705853760242462,
0.010456276126205921,
-0.006935820449143648,
0.04076242819428444,
0.023064879700541496,
-0.0009668105631135404,
-0.02198587916791439,
-0.04282824322581291,
-0.017460063099861145,
0.0135953389108181,
0.05198536813259125,
-0.0362502783536911,
0.012968461029231548,
-0.0275412704795599,
-0.05872323736548424,
0.036374282091856,
0.03183615952730179,
0.014131749048829079,
-0.048880137503147125,
-0.047463368624448776,
-0.020646410062909126,
0.0073122289031744,
0.052855368703603745,
-0.0406138151884079,
-0.020402755588293076,
0.002935555763542652,
-0.0018447451293468475,
0.010457819327712059,
-0.007721274625509977,
-0.036658480763435364,
-0.03766706958413124,
-0.041887082159519196,
0.017666952684521675,
0.006824356969445944,
0.02551141194999218,
-0.035034243017435074,
-0.0015988287050276995,
-0.01987696811556816,
0.06185846030712128,
0.057499222457408905,
-0.0016765451291576028,
0.004600887652486563,
0.02591448277235031,
-0.029415160417556763,
0.017950257286429405,
-0.04120635986328125,
0.019580671563744545,
-0.011781668290495872,
0.017625072970986366,
-0.010839358903467655,
-0.007761812303215265,
0.013105570338666439,
0.02278905175626278,
0.01988382451236248,
0.01620890572667122,
-0.012655448168516159,
-0.007386279758065939,
-0.02164243347942829,
0.01860835961997509,
0.0035061482340097427,
0.01605953462421894,
0.07497259974479675,
0.00017696265422273427,
0.050594378262758255,
0.024368584156036377,
-0.026830323040485382,
-0.05095555633306503,
0.02804606780409813,
-0.028351163491606712,
-0.0019132746383547783,
0.0017742443596944213,
0.05006808415055275,
0.014038056135177612,
-0.001364596071653068,
0.0054304334335029125,
0.012748037464916706,
-0.03433731198310852,
-0.03345245495438576,
0.0531754307448864,
-0.004409447778016329,
0.02066737227141857,
-0.005877045448869467,
0.041604265570640564,
0.024756669998168945,
0.00965052843093872,
-0.004326110705733299,
0.047518812119960785,
0.0521722137928009,
0.006518040783703327,
0.04041412100195885,
0.045062363147735596,
-0.008738039061427116,
-0.015603596344590187,
-0.022359322756528854,
0.0401742123067379,
-0.014626163989305496,
0.0026559156831353903,
0.015118077397346497,
-0.0027086888439953327,
-0.0009153659921139479,
0.0033682032953947783,
-0.005382587667554617,
0.0464799590408802,
-0.03634897246956825,
0.025935957208275795,
-0.007687223143875599,
-0.014848227612674236,
-0.0408211350440979,
0.015587600879371166,
0.05382499471306801,
0.026620827615261078,
-0.004244193900376558,
-0.0015242304652929306,
-0.04275044426321983,
0.031045209616422653,
0.018225712701678276,
-0.08168955147266388,
-0.0009370716870762408,
-0.02752465382218361,
-0.011927144601941109,
-0.00951407477259636,
0.02172021195292473,
-0.03786895051598549,
-0.013855845667421818,
0.029635250568389893,
-0.01390815433114767,
-0.017015241086483,
0.010677393525838852,
-0.020597700029611588,
-0.03752598911523819,
0.06166115775704384,
-0.029220659285783768,
-0.016737550497055054,
-0.04390222206711769,
0.046274662017822266,
-0.006704673636704683,
-0.017391106113791466
] |
<p>I'm supposed to calculate the capacitance of an unknown capacitor in series, but I'm not sure exactly which equation to use.</p>
<p>I know the voltage across the resistor (Vr), voltage across the capacitor (Vc), the total voltage (V), the resistance value of the resistor (R), the frequency (f), and since I was using an oscilloscope, the change in time between Vr and V.
I know there's an equation that deals with these values (it includes natural number e), but I can't find it, and even if I had it I'm not exactly sure how I would rederive it to solve for the capacitance. How would I attempt this problem?</p>
| 9,636 |
[
-0.00580759858712554,
-0.02881384827196598,
-0.019572006538510323,
0.01830264739692211,
0.009907074272632599,
-0.01624520681798458,
-0.0196551363915205,
0.01765533909201622,
0.015798894688487053,
0.0040360912680625916,
0.00560795608907938,
0.081230528652668,
0.05846276506781578,
0.001440964755602181,
0.022930461913347244,
-0.005802675615996122,
-0.022558512166142464,
0.005426486954092979,
-0.02596711367368698,
-0.03888092190027237,
0.011033991351723671,
0.022097628563642502,
0.023897266015410423,
-0.009608701802790165,
-0.017704734578728676,
0.06508161127567291,
0.052647653967142105,
0.004484970588237047,
0.018193406984210014,
0.028263304382562637,
-0.014176332391798496,
-0.053510457277297974,
-0.004287648480385542,
0.034023918211460114,
0.04944126307964325,
0.022506525740027428,
-0.017830554395914078,
-0.05656122416257858,
-0.024560218676924706,
0.04674464091658592,
-0.0008529742481186986,
0.01156377512961626,
0.005573755130171776,
0.02444058656692505,
-0.011222071014344692,
-0.0029137483797967434,
0.013137727975845337,
0.010815943591296673,
0.027714719995856285,
-0.09598340839147568,
0.0960603803396225,
-0.019812779501080513,
0.06814588606357574,
0.0358259491622448,
-0.01580110937356949,
0.022579221054911613,
0.057012688368558884,
0.06563057750463486,
-0.015765804797410965,
-0.03256825730204582,
-0.01662398874759674,
-0.025164149701595306,
-0.040859099477529526,
-0.04177194833755493,
-0.024626342579722404,
0.04750235751271248,
0.009636213071644306,
-0.0016021718038246036,
0.0055270507000386715,
-0.020866278558969498,
0.026062285527586937,
0.019445382058620453,
0.030453333631157875,
-0.05182959884405136,
0.010070170275866985,
-0.02821199782192707,
-0.000229597048019059,
0.03527204319834709,
0.02201056480407715,
0.04189366102218628,
-0.04016248509287834,
0.008247639052569866,
0.04848185181617737,
0.020138857886195183,
0.02233302593231201,
-0.039100922644138336,
0.04276910796761513,
0.04072318598628044,
0.004456847906112671,
0.014938492327928543,
-0.018636716529726982,
0.03526540845632553,
0.040040064603090286,
-0.024431053549051285,
-0.03911847248673439,
0.02067459374666214,
-0.010499230585992336,
0.05900508165359497,
0.006327206734567881,
-0.03722463920712471,
0.052099213004112244,
-0.029236165806651115,
0.017093170434236526,
0.08385476469993591,
-0.01558848936110735,
-0.005742802284657955,
-0.008161339908838272,
0.004710162058472633,
0.01925922930240631,
-0.05379203334450722,
-0.03347311541438103,
0.03263406828045845,
-0.001200016587972641,
0.03415260463953018,
0.02958066202700138,
-0.00008131234790198505,
0.00034103530924767256,
0.0045824297703802586,
0.06950528174638748,
0.012797605246305466,
0.024125993251800537,
-0.03344419226050377,
0.023029306903481483,
-0.01614970900118351,
-0.05967944860458374,
0.01764802448451519,
-0.025694862008094788,
-0.0006259258952923119,
-0.01712389849126339,
0.041625846177339554,
-0.03010454773902893,
-0.04608599841594696,
0.0027057162951678038,
-0.01640401966869831,
0.022390145808458328,
-0.01885620690882206,
-0.06313858926296234,
-0.06837020814418793,
-0.004887001123279333,
-0.039181385189294815,
-0.03916311636567116,
-0.06869091838598251,
0.032696351408958435,
0.02436881512403488,
0.04077019542455673,
-0.00007374800043180585,
-0.010070566087961197,
-0.007365831173956394,
0.020742911845445633,
-0.0037075148429721594,
-0.010880236513912678,
-0.061226986348629,
0.01987609826028347,
0.013095558620989323,
0.003276983043178916,
-0.023539703339338303,
0.0031829937361180782,
0.05195377767086029,
0.0022974738385528326,
-0.005739955231547356,
0.07735317945480347,
0.021014198660850525,
-0.0450599230825901,
0.032425276935100555,
-0.007048637140542269,
-0.05443478003144264,
0.056999556720256805,
-0.006942965090274811,
0.001412881538271904,
0.03726808726787567,
0.004793285857886076,
0.021671896800398827,
0.010503636673092842,
-0.010332115925848484,
0.0884115919470787,
-0.015138049609959126,
-0.027708595618605614,
-0.018449101597070694,
0.011226575821638107,
0.02887146733701229,
-0.004917037207633257,
-0.0396035760641098,
0.01986493356525898,
0.001544891158118844,
0.042526088654994965,
0.05199526622891426,
0.007092935498803854,
-0.023555615916848183,
-0.024859443306922913,
-0.016250114887952805,
-0.02858324535191059,
-0.055908288806676865,
-0.0001673446677159518,
-0.0033621874172240496,
-0.01621238887310028,
0.016332300379872322,
0.021627923473715782,
0.036979224532842636,
-0.025420431047677994,
-0.03602597862482071,
-0.004360726568847895,
0.015992242842912674,
-0.014450964517891407,
-0.02164776623249054,
0.04740210995078087,
0.05113420635461807,
0.05386177450418472,
0.009815292432904243,
0.058753710240125656,
-0.03404064476490021,
-0.006721862126141787,
0.02214914560317993,
-0.022333480417728424,
0.04686012491583824,
-0.01145140826702118,
0.00766363088041544,
0.016203973442316055,
0.005664398893713951,
0.015551146119832993,
0.014360543340444565,
-0.0054533821530640125,
0.06153453141450882,
0.0820443406701088,
0.05276781693100929,
0.01216522604227066,
0.04673704504966736,
0.02853122167289257,
0.023303933441638947,
-0.013716336339712143,
-0.016853995621204376,
-0.0373271219432354,
0.009548086673021317,
0.012422092258930206,
0.005508300382643938,
-0.019449394196271896,
-0.007024445571005344,
0.06131356954574585,
0.031055137515068054,
0.05237874761223793,
0.037464797496795654,
0.003931442741304636,
-0.006285155192017555,
-0.026567410677671432,
-0.007257996592670679,
-0.019452199339866638,
0.0018420659471303225,
0.002570117823779583,
0.0374513640999794,
0.03039112687110901,
-0.015314542688429356,
-0.01273867767304182,
0.0065621607936918736,
0.02992992475628853,
0.028899386525154114,
0.017003875225782394,
-0.042639970779418945,
0.02797030657529831,
-0.045914046466350555,
0.00542244128882885,
0.01856462098658085,
-0.01299968734383583,
0.010931339114904404,
0.011760820634663105,
0.006429852452129126,
0.021208371967077255,
0.012056649662554264,
-0.026170330122113228,
-0.019646648317575455,
0.014554576016962528,
-0.024072084575891495,
0.023500794544816017,
-0.004672330804169178,
-0.01598895527422428,
-0.023519881069660187,
-0.02023165300488472,
0.0022156706545501947,
0.02180630713701248,
0.048426304012537,
-0.02279030717909336,
-0.031785037368535995,
0.005569114815443754,
-0.036273837089538574,
0.018706247210502625,
-0.01413161400705576,
-0.02984139695763588,
0.011767739430069923,
0.0006871617515571415,
-0.044289231300354004,
0.040885139256715775,
0.04407081753015518,
-0.04440956935286522,
0.03151232376694679,
-0.0057410746812820435,
-0.0861448347568512,
-0.03684627264738083,
-0.0009658611379563808,
0.04528680443763733,
-0.02749864012002945,
0.004243251867592335,
0.057338565587997437,
-0.006061705760657787,
-0.008547733537852764,
0.02413390576839447,
-0.025661269202828407,
-0.04040941968560219,
-0.008274059742689133,
-0.010254408232867718,
0.016984624788165092,
-0.0486895851790905,
0.0029728005174547434,
-0.001686640316620469,
-0.025270050391554832,
-0.01887470856308937,
-0.03565385937690735,
-0.07940604537725449,
0.02096274122595787,
-0.025798266753554344,
0.05651550367474556,
0.03613440319895744,
-0.03459485247731209,
0.05903825908899307,
-0.008036649785935879,
-0.0006721069221384823,
-0.004685122519731522,
-0.0029604050796478987,
-0.01118104811757803,
-0.015425973571836948,
-0.0007034156587906182,
0.049982793629169464,
-0.011606374755501747,
0.007179216481745243,
0.005684598349034786,
0.013944435864686966,
0.056189075112342834,
0.02080262266099453,
0.034828070551157,
0.021885717287659645,
0.006690493784844875,
-0.031213287264108658,
0.06284153461456299,
0.0004053679294884205,
-0.0165395624935627,
0.0143459876999259,
0.01576385088264942,
0.04595373570919037,
0.04679693281650543,
-0.022880826145410538,
-0.01896500773727894,
-0.013364581391215324,
-0.016918586567044258,
-0.04409629479050636,
0.023510947823524475,
-0.013570831157267094,
0.016316007822752,
-0.0015574661083519459,
0.0406639501452446,
0.04056259244680405,
-0.0165844839066267,
0.0009716589120216668,
0.046291857957839966,
0.02463645674288273,
0.0012275348417460918,
-0.04314412176609039,
0.005395004991441965,
-0.019222106784582138,
0.035586658865213394,
-0.031521882861852646,
-0.006543097551912069,
0.06182345747947693,
0.005013357847929001,
0.037776339799165726,
-0.004272602964192629,
-0.058876924216747284,
0.0013241558335721493,
-0.027105897665023804,
-0.011722726747393608,
-0.00801099557429552,
0.0633523017168045,
0.004743003286421299,
0.07115605473518372,
0.011205767281353474,
-0.016644075512886047,
0.034545380622148514,
0.00025456506409682333,
-0.07552948594093323,
0.04230857267975807,
-0.0067635029554367065,
-0.03535540774464607,
-0.021660737693309784,
0.026298580691218376,
0.028561493381857872,
0.000033992811950156465,
-0.013999391347169876,
-0.023698482662439346,
-0.009221178479492664,
-0.034536801278591156,
0.0374358631670475,
0.004798886366188526,
0.01760375313460827,
-0.033575329929590225,
0.022808970883488655,
0.012298672460019588,
-0.018267488107085228,
-0.008554384112358093,
0.04944218695163727,
-0.026382938027381897,
0.014820962212979794,
-0.010059761814773083,
-0.017381133511662483,
0.008155967108905315,
0.000171680047060363,
0.0038970729801803827,
0.004967640619724989,
-0.009723272174596786,
0.0005342793883755803,
-0.01702362298965454,
0.07471056282520294,
0.018770107999444008,
-0.04719507694244385,
-0.03503645956516266,
-0.04753598943352699,
0.005848838947713375,
-0.016427114605903625,
0.07303791493177414,
-0.01529841497540474,
0.016119446605443954,
0.04247795790433884,
-0.0037040456663817167,
-0.04069061949849129,
0.04984616860747337,
0.037343498319387436,
0.028982190415263176,
-0.010542388074100018,
-0.034319598227739334,
0.003317047841846943,
-0.047698698937892914,
0.009162847883999348,
0.02324257418513298,
0.03174664080142975,
-0.05226387828588486,
-0.008905477821826935,
0.028253544121980667,
0.0008078518440015614,
0.02410087361931801,
-0.010654253885149956,
0.009754707105457783,
0.021179761737585068,
0.0030796171631664038,
-0.03639800846576691,
0.008239559829235077,
0.0027592377737164497,
0.04685860499739647,
-0.004703236743807793,
-0.009268051944673061,
-0.10862278938293457,
-0.044288523495197296,
0.05359211191534996,
0.023336658254265785,
-0.03923491761088371,
-0.05112295597791672,
-0.0561956986784935,
-0.016238683834671974,
0.06233379989862442,
-0.05642465129494667,
-0.0024923267774283886,
0.009681608527898788,
0.007865422405302525,
-0.021855730563402176,
-0.0503365732729435,
-0.02171255834400654,
0.03621084615588188,
-0.014094492420554161,
0.026230191811919212,
-0.027684291824698448,
-0.022008009254932404,
-0.027283182367682457,
0.01084540132433176,
0.05248530954122543,
0.09312591701745987,
0.01936372183263302,
-0.021424010396003723,
0.0010211915941908956,
0.0285616647452116,
-0.02735433168709278,
-0.06139232963323593,
-0.003516034223139286,
-0.029380565509200096,
0.02895229123532772,
0.019189411774277687,
-0.014479142613708973,
-0.006279434077441692,
0.02437145635485649,
0.0033449435140937567,
0.015082404948771,
-0.0031593195162713528,
-0.00748014310374856,
0.05600918456912041,
0.04251490533351898,
-0.006270264275372028,
0.07456588000059128,
0.01793520897626877,
0.0030374997295439243,
0.01240202784538269,
-0.017200469970703125,
-0.003368095261976123,
-0.02617950178682804,
-0.02502298541367054,
-0.008284120820462704,
0.038202717900276184,
-0.0355265736579895,
0.024106308817863464,
-0.002690246095880866,
0.045033134520053864,
-0.03751545026898384,
-0.009121295996010303,
0.0026879634242504835,
0.007562145125120878,
-0.007704219315201044,
0.002745059784501791,
0.011995509266853333,
0.013658830896019936,
0.016711050644516945,
-0.027218133211135864,
0.0202023945748806,
0.02049369551241398,
0.02011343650519848,
0.0020537388045340776,
0.006847596727311611,
0.004176872316747904,
-0.04814600944519043,
-0.02245260588824749,
0.031636934727430344,
-0.06117106229066849,
0.045657865703105927,
-0.019695980474352837,
0.010060415603220463,
0.008407761342823505,
-0.027171539142727852,
-0.08552537113428116,
0.02616051398217678,
0.0011803761590272188,
0.050051357597112656,
-0.07053883373737335,
0.011771045625209808,
0.0022042386699467897,
-0.014144239947199821,
-0.05701544135808945,
-0.060908373445272446,
0.03324996680021286,
0.008433963172137737,
-0.0070984214544296265,
-0.011137258261442184,
0.023720281198620796,
0.008781579323112965,
-0.00521957827731967,
0.03986429050564766,
0.024604400619864464,
-0.019473155960440636,
-0.00567777780815959,
-0.022893495857715607,
-0.0073932199738919735,
0.034053631126880646,
0.03421198949217796,
0.019320614635944366,
-0.00284103793092072,
-0.051924314349889755,
-0.010695694014430046,
0.007856260985136032,
0.04052678868174553,
-0.03627762570977211,
-0.02533070556819439,
-0.011753023602068424,
-0.002857383107766509,
0.03844886273145676,
-0.02756664715707302,
0.0009618625626899302,
0.0225507952272892,
0.021926356479525566,
-0.0111148152500391,
-0.023012474179267883,
0.038364626467227936,
-0.026387469843029976,
0.006486798636615276,
0.0035523229744285345,
-0.016772057861089706,
-0.079961396753788,
0.014146466739475727,
-0.0058415718376636505,
0.0331542007625103,
-0.00586029002442956,
-0.02942679263651371,
0.048441167920827866,
0.007640224415808916,
0.00040002702735364437,
0.02352757379412651,
0.011003146879374981,
0.0009148394456133246,
-0.00890971627086401,
-0.022014902904629707,
0.023262696340680122,
0.007520172279328108,
-0.06471115350723267,
-0.0366242453455925,
-0.050211187452077866,
0.001988163683563471,
0.06787331402301788,
-0.018226340413093567,
0.05513514578342438,
0.015935933217406273,
0.004251564387232065,
0.008819321170449257,
0.001624044612981379,
-0.015764199197292328,
0.022287430241703987,
0.010530085302889347,
0.037136998027563095,
-0.008844639174640179,
0.008572977967560291,
-0.010583917610347271,
0.014008971862494946,
-0.00313241477124393,
0.01773257739841938,
0.028432147577404976,
0.022101368755102158,
0.01847539097070694,
-0.006646353751420975,
-0.030924132093787193,
0.024620478972792625,
-0.00009404520824318752,
0.03152919188141823,
0.007690848782658577,
-0.018929798156023026,
0.06251484155654907,
0.03387058898806572,
-0.001999194035306573,
-0.0268581360578537,
-0.023767083883285522,
-0.028591789305210114,
-0.011014018207788467,
0.015462963841855526,
0.0037943352945148945,
0.007960342802107334,
0.028850672766566277,
0.035635292530059814,
0.005038458853960037,
0.04680074006319046,
-0.049254391342401505,
-0.05704497545957565,
0.007848748005926609,
-0.011385641992092133,
-0.027597414329648018,
0.010654477402567863,
0.010440983809530735,
-0.02179841510951519,
0.019740834832191467,
-0.03521883487701416,
0.028704309836030006,
0.025811148807406425,
0.024573909118771553,
-0.016785362735390663,
0.061063557863235474,
-0.03036440536379814,
-0.007904188707470894,
-0.01665419340133667,
-0.014299354515969753,
0.0899871438741684,
0.030050477012991905,
0.002010666998103261,
-0.05738858878612518,
0.01437409408390522,
-0.009255913086235523,
0.024628836661577225,
-0.03266021981835365,
0.005704522132873535,
-0.02871057018637657,
0.0019825694616883993,
0.037226609885692596,
0.00799779873341322,
-0.00490938313305378,
0.033030956983566284,
0.03220198303461075,
-0.019962558522820473,
-0.007764083798974752,
-0.01514401100575924,
0.01799495704472065,
0.014208564534783363,
0.054461654275655746,
-0.025453658774495125,
0.04110563546419144,
-0.07179806381464005,
-0.05146011337637901,
-0.049475543200969696,
-0.0015111264074221253,
0.03994229435920715,
0.018351515755057335,
-0.03646337613463402,
0.04091028496623039,
0.03226715698838234,
-0.03458983078598976,
-0.014876233413815498,
0.016667328774929047,
0.024573655799031258,
0.0007697292603552341,
0.014399065636098385,
0.013957101851701736,
0.0022769549395889044,
-0.02829134464263916,
0.001573159359395504,
-0.012825578451156616,
-0.04859654977917671,
-0.003050836967304349,
-0.04785553738474846,
0.045429833233356476,
0.02007533609867096,
-0.007971919141709805,
0.017719320952892303,
0.014504547230899334,
-0.0012893497478216887,
-0.09524944424629211,
-0.0420985110104084,
-0.02302962727844715,
0.01419069617986679,
-0.03621348738670349,
-0.015609261579811573,
-0.057407982647418976,
0.035386838018894196,
-0.006598904263228178,
-0.009276548400521278,
-0.011072485707700253,
-0.009868016466498375,
-0.0031460821628570557,
-0.0037822595331817865,
0.01705828681588173,
-0.04836205393075943,
-0.0384831428527832,
0.025476541370153427,
-0.03239619359374046,
0.005033939611166716,
-0.028155382722616196,
0.009199690073728561,
0.02067757025361061,
0.030381539836525917,
-0.04940672591328621,
0.0038858794141560793,
0.010719306766986847,
-0.08906468003988266,
0.021220309659838676,
0.006254080682992935,
0.004352156538516283,
-0.05486442521214485,
0.016524869948625565,
0.020000316202640533,
0.042834579944610596,
-0.00009912680980050936,
0.03132978826761246,
0.014212405309081078,
-0.00398989487439394,
0.053759124130010605,
-0.03500988334417343,
-0.000533904938492924,
0.008651340380311012,
-0.052895352244377136,
0.014982271939516068,
-0.03228340297937393,
0.030410047620534897,
0.028773458674550056,
0.024683937430381775,
0.0041145761497318745,
0.012373504228889942,
-0.04370778426527977,
-0.0037283070851117373,
-0.03587162867188454,
-0.027948755770921707,
0.00789694581180811,
-0.03062843717634678,
0.033432040363550186,
0.0012504191836342216,
-0.00020937161752954125,
-0.040626224130392075,
0.0034857646096497774,
-0.013661710545420647,
0.02131863310933113,
-0.03858352452516556,
0.04385676234960556,
-0.03274804726243019,
0.022536132484674454,
-0.028068210929632187,
-0.004524040035903454,
-0.009468669071793556,
0.0023343837819993496,
0.02191527746617794,
0.0013735259417444468,
0.004096402786672115,
0.0305799450725317,
-0.02301621437072754,
0.01185036264359951,
0.020023440942168236,
0.029836315661668777,
0.005928322207182646,
-0.02784644439816475,
-0.006560072302818298,
0.007548908237367868,
0.028506632894277573,
-0.023234127089381218,
-0.030986366793513298,
0.049990858882665634,
-0.02396729774773121,
-0.01608176901936531,
0.003470236901193857,
0.02847495675086975,
0.044645436108112335,
0.019997434690594673,
-0.037416525185108185,
0.0004997469950467348,
0.03032376803457737,
-0.0074158632196486,
-0.012559629045426846,
-0.011018454097211361,
-0.030794622376561165,
0.0033946644980460405,
0.013322937302291393,
-0.010190144181251526,
-0.02208947390317917,
0.023441433906555176,
0.028651224449276924,
0.05564284324645996,
0.00399898923933506,
-0.018649479374289513,
0.02180461771786213,
-0.00009170333942165598,
0.005437491461634636,
0.04761839285492897,
-0.010372442193329334,
0.01549287885427475,
0.018378131091594696,
-0.021013222634792328,
0.01002333965152502,
0.01796586625277996,
-0.02092578448355198,
-0.07558561116456985,
-0.020473981276154518,
-0.015437756665050983,
0.018757376819849014,
0.029165567830204964,
-0.039565302431583405,
-0.028972407802939415,
0.017766330391168594,
-0.051208991557359695,
-0.028284292668104172,
-0.05316087231040001,
-0.021644961088895798,
0.000219773079152219,
-0.030772948637604713,
0.011589355766773224,
0.013580352999269962,
0.022162577137351036,
0.02577495016157627,
0.020556993782520294,
-0.024346373975276947,
0.00000766187167755561,
-0.06911575794219971,
0.029718149453401566,
0.037461135536432266,
0.012276933528482914,
-0.06177734583616257,
0.019901953637599945,
-0.04077307507395744,
0.010276596993207932,
0.031182462349534035,
0.0019960871431976557,
0.031803496181964874,
-0.013730446808040142,
0.02725164406001568,
-0.0014723512576892972,
0.07136943936347961,
-0.01425242330878973,
-0.04338635131716728,
-0.04920030012726784,
-0.014734074473381042,
-0.0033795256167650223,
0.021948546171188354,
-0.006522975862026215,
-0.0023667237255722284,
0.013932802714407444,
-0.012888569384813309,
-0.05595218017697334,
0.016930703073740005,
-0.01935409940779209,
-0.013052348978817463,
0.0006961110630072653,
-0.02268451452255249,
-0.0031429703813046217,
-0.038724545389413834,
0.010628141462802887,
-0.030009208247065544,
-0.014035375788807869,
0.04097336158156395,
-0.008387896232306957,
0.018315669149160385,
-0.027851715683937073,
-0.003934846259653568,
-0.03757188096642494,
0.029774924740195274,
0.040367692708969116,
-0.009750072844326496,
-0.09108085185289383,
-0.00484515680000186,
0.04460581764578819,
-0.03188664838671684,
0.006739165633916855,
-0.053353920578956604,
-0.017564719542860985,
0.016226552426815033,
0.011772014200687408,
-0.02946610562503338,
0.013712950050830841,
-0.04754452779889107,
-0.008430696092545986,
-0.03616758808493614,
0.04676253721117973,
0.0278791394084692,
-0.039771679788827896,
-0.03076840378344059,
-0.042398132383823395,
-0.01477463822811842,
0.020284244790673256,
0.0798472911119461,
-0.024506790563464165,
-0.04804256930947304,
0.002216627122834325,
-0.015020381659269333,
0.03267819806933403,
-0.08238429576158524,
0.00580053823068738,
0.04559437930583954,
-0.01849484071135521,
0.0005377447232604027,
0.0017327496316283941,
-0.018927784636616707,
-0.011005628854036331,
0.011981052346527576,
0.009890545159578323,
0.020370829850435257,
-0.008751972578465939,
-0.013230894692242146,
0.021172666922211647,
0.02454984374344349,
-0.0019041686318814754,
0.0778142586350441,
0.00032344640931114554,
-0.005801327060908079,
0.033019278198480606,
-0.002758160699158907,
-0.026327243074774742,
-0.009010106325149536,
-0.025977393612265587,
0.004890225827693939,
-0.006080446299165487,
0.001498967525549233,
0.0302064660936594,
-0.057885050773620605,
-0.041935183107852936,
0.03624587506055832,
-0.051480621099472046,
-0.016331704333424568,
0.08539526164531708,
-0.0397261306643486,
0.03308281674981117,
-0.020792881026864052,
0.0051906295120716095,
0.013770920224487782,
-0.013436808250844479,
0.0032503900583833456,
0.008835547603666782,
0.06004417687654495,
-0.021068328991532326,
0.013243097811937332,
0.04693559557199478,
-0.031697217375040054,
0.009036973118782043,
-0.008424087427556515,
0.020012391731142998,
-0.03792444244027138,
-0.02876873128116131,
-0.0008645468624308705,
-0.030721399933099747,
-0.0004640985280275345,
0.01849321834743023,
-0.061100371181964874,
0.0763237327337265,
-0.026730969548225403,
0.0021975866984575987,
0.018245358020067215,
-0.004140675533562899,
-0.020409468561410904,
0.013864164240658283,
-0.008711451664566994,
0.006931646261364222,
-0.033637482672929764,
0.036372411996126175,
-0.009974663145840168,
-0.0001725308975437656,
0.046001892536878586,
-0.08022065460681915,
0.020966988056898117,
0.008149770088493824,
-0.0000657836499158293,
-0.02668648771941662,
-0.0003644009993877262,
-0.055829450488090515,
-0.020327037200331688,
0.028402257710695267,
0.02808883599936962,
0.0028288147877901793,
-0.011614667251706123,
0.0014819973148405552,
0.0036455702502280474,
0.06445597112178802,
-0.074883371591568,
-0.017186908051371574,
-0.01771259307861328,
0.029485158622264862,
-0.0009155850857496262,
-0.009045652113854885
] |
<p>What's the difference between particle's helicity, spinor's helicity and chirality ?</p>
<p>I read a saying that right-handed spinor correspond to the left-handed positron, right-handed spinor correspond to the right-handed positron. </p>
<p>Why the particle's helicity is different from the spinor's? </p>
| 9,637 |
[
-0.03629340976476669,
-0.007112669292837381,
0.0052855731919407845,
-0.01391795463860035,
0.04640313982963562,
0.025059543550014496,
-0.020278889685869217,
-0.025813618674874306,
0.0035774277057498693,
-0.010380962863564491,
0.05650904402136803,
0.012653112411499023,
0.01441117748618126,
0.033957771956920624,
0.021816644817590714,
0.019044239073991776,
-0.004451974760740995,
-0.015613882802426815,
0.007054808549582958,
0.010668285191059113,
0.017047444358468056,
0.02486749365925789,
-0.0017784336814656854,
0.053569626063108444,
-0.006915289908647537,
0.033935558050870895,
0.045735374093055725,
0.013610968366265297,
0.03569363057613373,
0.032988905906677246,
-0.01589304208755493,
-0.0074871680699288845,
0.019796259701251984,
0.014077098108828068,
0.006359217222779989,
-0.04080463573336601,
-0.01046340074390173,
-0.028201987966895103,
-0.01634920760989189,
0.01675187423825264,
-0.02224051021039486,
-0.040070485323667526,
-0.0219433456659317,
0.06628280133008957,
-0.024221494793891907,
0.011998383328318596,
-0.012581318616867065,
-0.024511931464076042,
0.08828742802143097,
-0.08091196417808533,
0.053997114300727844,
0.01158152986317873,
0.033929284662008286,
-0.03234944865107536,
0.00783684104681015,
0.003936990164220333,
0.06321047246456146,
0.08128255605697632,
-0.01130085252225399,
-0.06033001095056534,
-0.003711448982357979,
-0.016736101359128952,
0.007048423867672682,
-0.03324588015675545,
-0.02744409814476967,
0.03906106948852539,
0.0011579543352127075,
-0.02130730077624321,
0.011388213373720646,
0.007324070204049349,
0.008516266010701656,
-0.015482781454920769,
0.02549925446510315,
0.004806156735867262,
0.0006284788832999766,
-0.05664215236902237,
-0.0008523493888787925,
0.030693408101797104,
0.02209516428411007,
0.010439281351864338,
0.0037914603017270565,
0.03395835682749748,
0.005708781071007252,
0.00167681067250669,
0.0030513987876474857,
-0.040162455290555954,
0.060943182557821274,
0.00094648078083992,
-0.012786269187927246,
0.04617772623896599,
-0.012913593091070652,
0.009526994079351425,
0.02629968337714672,
-0.0025361443404108286,
-0.03348241373896599,
0.0552225299179554,
0.004876785445958376,
0.00711465161293745,
0.001219203812070191,
-0.007110238075256348,
0.0016295877285301685,
-0.013770904392004013,
0.0259829293936491,
0.07582861185073853,
0.0076040164567530155,
-0.003993225283920765,
-0.023278849199414253,
0.021980639547109604,
-0.02599809318780899,
-0.02254202589392662,
-0.03627718985080719,
0.005743805319070816,
-0.01487670373171568,
0.012055592611432076,
-0.012921285815536976,
-0.02397890016436577,
0.0066203647293150425,
-0.004726485349237919,
0.036764223128557205,
0.07291112840175629,
0.03467341139912605,
-0.0208024550229311,
0.013066773302853107,
-0.0323302298784256,
-0.08937419205904007,
-0.008275405503809452,
0.04632354527711868,
0.02519337832927704,
-0.017660900950431824,
0.020200548693537712,
0.011529652401804924,
-0.016024844720959663,
0.013401973061263561,
0.007182064466178417,
0.012897731736302376,
-0.009944588877260685,
-0.1286015659570694,
-0.03871838003396988,
0.026252128183841705,
-0.03022972121834755,
-0.030041340738534927,
-0.0824061930179596,
0.00038683091406710446,
0.029755914583802223,
0.11949902027845383,
-0.004175430629402399,
0.009133603423833847,
0.01720147393643856,
0.03534002602100372,
0.010014115832746029,
0.00017007315182127059,
0.024624399840831757,
-0.014618473127484322,
-0.01355868298560381,
-0.017539232969284058,
-0.04071834683418274,
-0.008286257274448872,
0.02925526537001133,
-0.019700950011610985,
-0.014050079509615898,
0.05440038442611694,
-0.019605455920100212,
0.016063222661614418,
0.02537669613957405,
-0.017553776502609253,
-0.03397129848599434,
0.06726451218128204,
0.007657346781343222,
-0.007690987084060907,
0.038990337401628494,
-0.023699112236499786,
0.01261899620294571,
-0.01123918779194355,
0.038925159722566605,
0.05123336240649223,
-0.004250603727996349,
-0.05847189575433731,
-0.006732393987476826,
-0.0005090219783596694,
-0.03941919654607773,
-0.06869225949048996,
-0.03573131188750267,
-0.01927374117076397,
0.056049998849630356,
-0.021699225530028343,
0.03397945687174797,
0.0026792646385729313,
-0.030667370185256004,
0.00037278851959854364,
-0.05766315758228302,
-0.020555689930915833,
-0.0627024844288826,
-0.009403123520314693,
-0.017754031345248222,
-0.04282492771744728,
0.05117884650826454,
0.03547462448477745,
0.009237646125257015,
-0.036401886492967606,
-0.0023689628578722477,
-0.027541236951947212,
0.04142000898718834,
-0.003637966001406312,
0.02419491671025753,
0.00824031699448824,
0.06009881570935249,
0.03314266353845596,
-0.008958607912063599,
0.04328673332929611,
0.003792395582422614,
-0.042288925498723984,
0.02978881075978279,
0.023694612085819244,
-0.012546652927994728,
0.013454741798341274,
-0.006252688355743885,
0.016170285642147064,
-0.006934309843927622,
-0.021007446572184563,
0.04976079240441322,
-0.0054301004856824875,
0.05867605656385422,
0.028590165078639984,
-0.015375956892967224,
0.014109485782682896,
0.03920678794384003,
0.010006709024310112,
0.003542650258168578,
-0.04184785485267639,
0.005181967280805111,
-0.030150525271892548,
-0.002629062393680215,
0.04214828461408615,
0.029972217977046967,
-0.07407538592815399,
0.019505782052874565,
0.008772937580943108,
0.04196846857666969,
0.017170175909996033,
0.038701754063367844,
-0.022727057337760925,
-0.08758419752120972,
0.018492380157113075,
-0.029382191598415375,
-0.005178659688681364,
0.012490385212004185,
0.052237752825021744,
-0.0260838121175766,
0.02941094897687435,
0.004009549040347338,
-0.05640535429120064,
0.059530120342969894,
-0.03023955039680004,
-0.026217883452773094,
0.040376778692007065,
-0.053216468542814255,
0.010021129623055458,
-0.017350327223539352,
0.004901394713670015,
-0.006077922880649567,
-0.041194699704647064,
-0.029344892129302025,
-0.023725368082523346,
0.013208006508648396,
0.0006759338430128992,
0.006318668369203806,
-0.016970574855804443,
-0.019269118085503578,
0.01673569343984127,
-0.020606130361557007,
-0.0002755334135144949,
-0.00633678212761879,
-0.014200011268258095,
-0.009410255588591099,
-0.004114242270588875,
0.06490984559059143,
-0.00881308875977993,
0.030321097001433372,
0.00010681898857001215,
-0.01944771781563759,
0.046089861541986465,
-0.023060940206050873,
0.014009335078299046,
0.03445051237940788,
-0.019343232735991478,
0.04140105098485947,
-0.06195637583732605,
-0.031776364892721176,
0.009742897003889084,
-0.0024823977146297693,
0.002746230224147439,
0.001577311079017818,
-0.02741735428571701,
-0.04950840771198273,
-0.013428499922156334,
-0.004224962089210749,
0.05192771926522255,
-0.015647709369659424,
-0.001945781521499157,
0.0346108041703701,
-0.022011101245880127,
0.025186417624354362,
0.011793346144258976,
-0.026868605986237526,
-0.037586551159620285,
-0.007109818514436483,
-0.004456495866179466,
0.026226801797747612,
-0.01540283765643835,
0.005076316650956869,
0.03557724878191948,
-0.05793675780296326,
0.028007879853248596,
-0.019476618617773056,
-0.015675969421863556,
-0.011647416278719902,
-0.00864904560148716,
0.008581900037825108,
0.008597818203270435,
-0.026520483195781708,
0.0610681027173996,
0.013377373106777668,
-0.04790018871426582,
-0.02533193677663803,
0.0062465122900903225,
-0.04803105443716049,
-0.027713432908058167,
0.017622321844100952,
0.031080201268196106,
-0.0019446947844699025,
0.026254845783114433,
0.031415704637765884,
0.02662719413638115,
0.007329810876399279,
0.03458245098590851,
-0.012379557825624943,
-0.0051615238189697266,
0.004302255809307098,
-0.02454746700823307,
0.05531437695026398,
-0.0024612711276859045,
-0.021245917305350304,
0.014295993372797966,
0.018826130777597427,
0.004188212566077709,
0.0016858256421983242,
-0.030009988695383072,
0.07046017050743103,
-0.010357310995459557,
0.03973289206624031,
-0.01878548599779606,
0.04227180406451225,
-0.0011309996480122209,
-0.013767356984317303,
0.0010493530426174402,
-0.020685691386461258,
0.024543141946196556,
-0.0283137746155262,
-0.0007649029139429331,
0.04112042486667633,
0.023755861446261406,
-0.06270961463451385,
-0.02280086651444435,
-0.0029036863707005978,
-0.012886970303952694,
0.03868718445301056,
-0.03037206642329693,
-0.015692107379436493,
0.04674037918448448,
0.025205222889780998,
0.01878802850842476,
-0.006044188514351845,
-0.04456629604101181,
0.009809229522943497,
-0.06421486288309097,
0.05585981160402298,
-0.030678080394864082,
0.024642329663038254,
0.004217886831611395,
0.06904269009828568,
0.027243681252002716,
0.0069029550068080425,
-0.007004773709923029,
0.005351081490516663,
-0.08289601653814316,
0.04136180877685547,
-0.04949047788977623,
0.003772128839045763,
-0.036851342767477036,
-0.01527753658592701,
0.0117750633507967,
-0.03987086936831474,
-0.02582666464149952,
-0.03753763809800148,
-0.042019400745630264,
-0.014204973354935646,
0.07589387893676758,
-0.03414557874202728,
-0.040935441851615906,
-0.018348470330238342,
0.052483975887298584,
0.02281150408089161,
-0.004962750244885683,
0.023921431973576546,
0.04861517250537872,
-0.03895016387104988,
0.03833674266934395,
-0.0002743444056250155,
0.012257895432412624,
-0.00019283959409222007,
0.014167865738272667,
0.046500060707330704,
0.007078077178448439,
-0.010423671454191208,
0.0015203795628622174,
0.018674328923225403,
0.050411395728588104,
0.0008842905517667532,
-0.018377462401986122,
0.0013428513193503022,
-0.08592920005321503,
-0.01586693897843361,
-0.03390733525156975,
0.06822638213634491,
0.006384379230439663,
0.04272814095020294,
0.05337097868323326,
-0.022920215502381325,
-0.012155059725046158,
0.022278405725955963,
0.020095501095056534,
0.00882009044289589,
-0.022560760378837585,
-0.04355926439166069,
0.013424809090793133,
-0.01271219365298748,
-0.021137068048119545,
0.015212374739348888,
-0.03429751843214035,
-0.052557479590177536,
0.0006886555929668248,
0.0209344569593668,
-0.023856496438384056,
-0.026729434728622437,
0.00463213911280036,
-0.028990397229790688,
0.006888813804835081,
-0.009809997864067554,
0.006116813980042934,
-0.038724444806575775,
0.059524696320295334,
0.01207785401493311,
-0.009323522448539734,
-0.02353503182530403,
-0.04212019592523575,
-0.0022533724550157785,
0.031163247302174568,
0.045871492475271225,
-0.031078122556209564,
-0.029404405504465103,
-0.028043435886502266,
0.004039593040943146,
0.05547371506690979,
-0.05335460603237152,
0.024272816255688667,
-0.034082576632499695,
-0.004300086759030819,
-0.03015456721186638,
-0.024305418133735657,
-0.03918854519724846,
0.014978434890508652,
-0.009116197936236858,
0.007580410689115524,
-0.041277796030044556,
-0.007110385689884424,
-0.032450687140226364,
-0.009063942357897758,
0.025907495990395546,
0.02081240527331829,
0.01652824506163597,
0.05926680937409401,
0.0015186549862846732,
0.026254303753376007,
-0.004964854102581739,
-0.12013028562068939,
0.002521298825740814,
0.03235430270433426,
0.001517279539257288,
0.053980592638254166,
-0.04701273888349533,
-0.06623246520757675,
-0.0039496286772191525,
0.018139326944947243,
-0.013275560922920704,
0.00005776101170340553,
-0.08886165916919708,
0.018618548288941383,
0.028166459873318672,
-0.026079464703798294,
0.029569264501333237,
0.003169215517118573,
-0.03207821398973465,
-0.023323846980929375,
-0.021489448845386505,
0.025842642411589622,
-0.0467410646378994,
-0.0040489621460437775,
-0.02230152301490307,
-0.0013292330550029874,
-0.011779242195189,
0.07409403473138809,
-0.012234697118401527,
0.007236368954181671,
-0.014521860517561436,
-0.033628664910793304,
-0.030197873711586,
0.018384050577878952,
0.009835177101194859,
0.007858723402023315,
-0.009810018353164196,
-0.01010738592594862,
0.01861414685845375,
-0.009221674874424934,
-0.0016435094876214862,
0.0037624514661729336,
-0.019727475941181183,
0.03385859355330467,
0.0036707459948956966,
0.01837848499417305,
-0.03512188419699669,
-0.009286894463002682,
0.019729912281036377,
-0.06626439839601517,
0.02281494438648224,
0.00023201601288747042,
-0.04558731988072395,
0.016368431970477104,
-0.0715281292796135,
-0.05792151764035225,
0.0025158401113003492,
-0.01770978420972824,
-0.010981394909322262,
-0.04905551299452782,
0.038367029279470444,
-0.002480904571712017,
0.008301709778606892,
-0.05781479552388191,
-0.02388647384941578,
-0.014513068832457066,
-0.0058482857421040535,
-0.023330384865403175,
0.011109833605587482,
0.02135724574327469,
-0.018327195197343826,
-0.06523800641298294,
-0.0060266125947237015,
0.04443424195051193,
-0.023720160126686096,
-0.00917148683220148,
0.023773975670337677,
-0.003468026639893651,
0.034373003989458084,
-0.02047264575958252,
-0.024283695966005325,
-0.004964832682162523,
-0.03865532577037811,
0.004286675248295069,
-0.01049104891717434,
0.05945105850696564,
0.0019328779308125377,
-0.04894207790493965,
0.014095380902290344,
0.004048858303576708,
0.034002698957920074,
0.0072516389191150665,
0.011947284452617168,
0.04043005406856537,
0.03856346756219864,
-0.031779199838638306,
-0.018733009696006775,
0.02096838690340519,
0.027423018589615822,
0.02779543213546276,
0.007357437629252672,
0.002299400744959712,
-0.04573814198374748,
-0.04291992634534836,
0.032029811292886734,
0.0008260508184321225,
0.03043891303241253,
0.0074037229642271996,
0.031479936093091965,
-0.0324135385453701,
-0.00491380924358964,
0.022435232996940613,
-0.013293925672769547,
-0.005593347363173962,
-0.010396300815045834,
0.020815163850784302,
0.0066477213986217976,
0.019327504560351372,
0.0052061183378100395,
0.00116049125790596,
-0.0235343836247921,
0.026177220046520233,
0.055201634764671326,
0.0000065358403844584245,
0.05006265640258789,
0.023165538907051086,
-0.01296266634017229,
-0.015677519142627716,
-0.0166024062782526,
-0.004232333041727543,
-0.00027229159604758024,
-0.0010533385211601853,
0.04351605102419853,
-0.019272083416581154,
-0.0021608483511954546,
0.031769149005413055,
0.04456546530127525,
-0.048625554889440536,
0.007771920412778854,
0.045666538178920746,
-0.0012421105057001114,
0.005965644959360361,
-0.004007878713309765,
-0.04925471544265747,
0.015318905003368855,
-0.01717974804341793,
0.04288695007562637,
0.005024876445531845,
-0.006492550950497389,
0.04100356251001358,
-0.0034885003697127104,
0.014913919381797314,
-0.03741752728819847,
0.01679578423500061,
-0.03176400065422058,
-0.007597756572067738,
0.041622668504714966,
-0.01749250292778015,
-0.038305047899484634,
0.03876723721623421,
0.05778459087014198,
0.02610788866877556,
0.007741107139736414,
0.010832825675606728,
-0.06701656430959702,
-0.014497112482786179,
-0.030676301568746567,
-0.04576271027326584,
0.05439574271440506,
-0.021993538364768028,
-0.008060004562139511,
-0.006487588863819838,
-0.00022776371042709798,
-0.00026389164850115776,
0.027017975226044655,
0.03698045387864113,
-0.014544092118740082,
0.026653289794921875,
-0.028876949101686478,
0.026389149948954582,
0.0017585200257599354,
0.012272218242287636,
0.1125897616147995,
0.06499048322439194,
-0.00042303785448893905,
-0.05912867933511734,
0.037092626094818115,
-0.03865261748433113,
0.033989179879426956,
-0.013908877037465572,
0.02355363965034485,
-0.006894087418913841,
0.01825389452278614,
-0.0201104823499918,
0.01778869703412056,
0.0029332302510738373,
-0.006902069319039583,
0.04956502467393875,
-0.04744695872068405,
-0.0665571466088295,
-0.023887936025857925,
0.024334482848644257,
-0.015324616804718971,
0.04290590062737465,
-0.04941624402999878,
0.01615873910486698,
-0.02779238112270832,
0.028391867876052856,
-0.012873383238911629,
-0.061812784522771835,
0.020261723548173904,
-0.017005393281579018,
-0.04105662181973457,
-0.01824047602713108,
0.020216749981045723,
-0.028405847027897835,
-0.052533626556396484,
0.0181466992944479,
0.010095968842506409,
-0.02818257361650467,
0.025564514100551605,
0.01833464950323105,
0.02708299271762371,
-0.0011078548850491643,
0.04950430244207382,
0.026752367615699768,
-0.04677502065896988,
-0.007790168281644583,
-0.02610541135072708,
0.03937193751335144,
-0.007821709848940372,
0.02060195431113243,
-0.009441833943128586,
0.02429056540131569,
0.0030694096349179745,
-0.04905951768159866,
-0.014320301823318005,
0.00011100040865130723,
0.006665640976279974,
0.008415164425969124,
-0.0014526316663250327,
-0.0164471622556448,
0.017784271389245987,
-0.013392360880970955,
0.03610705956816673,
-0.0321296788752079,
-0.0005588529165834188,
0.043522629886865616,
0.003182615153491497,
0.029024485498666763,
-0.014453873038291931,
0.014941507019102573,
0.00314585049636662,
-0.0034745140001177788,
-0.04686181992292404,
0.026270421221852303,
0.034200944006443024,
0.021792825311422348,
0.01933031901717186,
0.008581208996474743,
-0.01136880274862051,
-0.005114342551678419,
-0.04550378397107124,
0.025699669495224953,
-0.011947428807616234,
-0.022437548264861107,
0.009020386263728142,
0.02538481540977955,
0.03451636806130409,
0.0643644854426384,
-0.028010813519358635,
0.02194175124168396,
-0.017927931621670723,
0.0020479196682572365,
0.00764431431889534,
-0.03146004304289818,
-0.007044164929538965,
0.04348686710000038,
-0.04573994129896164,
-0.020386062562465668,
-0.03354625776410103,
0.011490322649478912,
0.044888291507959366,
0.015053970739245415,
-0.03239733725786209,
0.029339220374822617,
-0.009034520946443081,
-0.030051644891500473,
0.022652894258499146,
0.005951052997261286,
-0.009036978706717491,
0.01901417225599289,
-0.006761027500033379,
-0.055111441761255264,
-0.04740893840789795,
-0.014545993879437447,
-0.03222339600324631,
0.03023398108780384,
0.021992260590195656,
-0.017743581905961037,
-0.023019272834062576,
-0.01850183680653572,
0.026455635204911232,
-0.00831072311848402,
-0.010521892458200455,
-0.08236418664455414,
0.02754562720656395,
-0.011263947933912277,
-0.016900241374969482,
-0.011433816514909267,
0.043682485818862915,
0.013497155159711838,
0.006949074100703001,
0.01742909476161003,
0.043141454458236694,
-0.00593927875161171,
-0.003549139481037855,
0.038758136332035065,
0.005638794042170048,
0.03763076290488243,
0.007151786237955093,
-0.02661069855093956,
0.04587544500827789,
-0.042745184153318405,
-0.04638395458459854,
0.027389226481318474,
0.00029054906917735934,
0.014400471933186054,
0.02244631201028824,
-0.01133233867585659,
0.0000728887171135284,
0.057776208966970444,
-0.023729316890239716,
-0.01714775152504444,
0.008574556559324265,
-0.04041861370205879,
-0.026962166652083397,
-0.04688677936792374,
0.006953634321689606,
0.013475869782269001,
-0.03713390976190567,
0.05148403346538544,
0.02822541445493698,
0.014273460954427719,
0.020536979660391808,
0.005651130340993404,
0.03668975830078125,
0.05209577456116676,
0.03290790319442749,
-0.010359874926507473,
0.013458319939672947,
0.02866494096815586,
-0.044203005731105804,
0.0388852022588253,
0.011223824694752693,
0.00019978692580480129,
-0.08844177424907684,
0.00012343340495135635,
0.016413984820246696,
-0.011513574048876762,
0.05281057208776474,
-0.03479443117976189,
0.009497920982539654,
0.032531991600990295,
-0.06679544597864151,
0.02049846760928631,
-0.030633218586444855,
-0.013983763754367828,
-0.005986491683870554,
-0.02352900616824627,
-0.01619027741253376,
0.09984509646892548,
0.024788573384284973,
0.05079265311360359,
-0.010765934363007545,
0.005996476858854294,
-0.03221561014652252,
-0.027257274836301804,
-0.03834286704659462,
0.04454832524061203,
-0.010050822049379349,
-0.03772683069109917,
0.0787520706653595,
-0.0016333640087395906,
-0.022609155625104904,
0.0404454842209816,
0.01954655349254608,
0.0021128859370946884,
-0.004621484316885471,
0.021030208095908165,
0.014753975905478,
0.01120713446289301,
-0.01732022687792778,
-0.00800652801990509,
-0.022298170253634453,
0.027576031163334846,
0.016548363491892815,
0.04526786133646965,
0.024365084245800972,
-0.01683122292160988,
-0.014817878603935242,
-0.00823994167149067,
0.01780594512820244,
0.04408854618668556,
-0.05659499019384384,
-0.03222533315420151,
-0.017359483987092972,
-0.004828513599932194,
0.024247949942946434,
-0.0228187907487154,
0.03324229270219803,
-0.03780995309352875,
0.008231018669903278,
0.01714378222823143,
-0.005185683723539114,
0.0032324111089110374,
0.03982217609882355,
-0.010885528288781643,
-0.020155226811766624,
0.0371549054980278,
0.027050474658608437,
0.012347924523055553,
0.008421773090958595,
0.026406655088067055,
0.03560713306069374,
0.027096174657344818,
0.0036333443131297827,
-0.04952288046479225,
-0.026494566351175308,
0.011326415464282036,
0.019159255549311638,
0.028699461370706558,
-0.01498423982411623,
-0.019899409264326096,
-0.01244218461215496,
-0.056300438940525055,
0.0319211408495903,
0.02876998856663704,
-0.010280409827828407,
-0.036151520907878876,
-0.034032586961984634,
-0.018786141648888588,
0.029504848644137383,
0.06138915941119194,
0.024441247805953026,
-0.03492506965994835,
0.005098295863717794,
0.009545085951685905,
0.012245153076946735,
-0.02683100476861,
-0.015148057602345943,
-0.015633655712008476,
-0.03881241753697395,
0.004182835575193167,
-0.013955999165773392,
-0.022125855088233948,
0.0593448281288147,
0.021389709785580635,
0.020832056179642677,
0.03167303279042244,
0.013406011275947094,
-0.040367837995290756,
0.038284093141555786,
-0.0013562811072915792,
-0.016150405630469322,
0.06218881532549858,
-0.00798438023775816,
0.020564990118145943,
0.008470935747027397,
-0.022377081215381622,
0.0033507521729916334,
-0.008731954731047153,
-0.04123071953654289,
-0.011080233380198479,
-0.01286360528320074,
-0.02809746004641056,
0.06679138541221619,
-0.038790952414274216,
-0.0034979123156517744,
0.03385011479258537,
-0.027718108147382736,
0.00608417484909296,
0.048003751784563065,
0.043140459805727005,
-0.0006570875411853194,
-0.0036494596861302853,
-0.00579524040222168,
0.012367337942123413,
-0.009629381820559502,
0.011213541962206364,
0.048186905682086945,
0.003987304400652647,
0.034491267055273056,
-0.012696296907961369,
0.03977091237902641,
0.00626495061442256,
0.02106110192835331,
0.020679159089922905,
0.0450763963162899,
0.01477919053286314,
-0.0036636474542319775,
0.014678385108709335,
-0.014690910466015339,
0.022967558354139328,
0.026085104793310165,
-0.02225549891591072,
0.07794461399316788,
-0.029280778020620346,
-0.01588054746389389,
-0.0013324362225830555,
-0.016311274841427803,
-0.01784675195813179,
-0.03644442930817604,
0.02317623607814312,
0.05111510306596756,
0.028485305607318878,
-0.058862339705228806,
-0.021457085385918617,
-0.02056996151804924,
0.03976993262767792,
-0.0643923208117485,
0.006215703207999468,
0.021713780239224434,
-0.015646271407604218,
-0.04674888402223587,
-0.011498748324811459,
0.0009805053705349565,
-0.011969443410634995,
0.015926547348499298,
0.04006871581077576,
0.032168589532375336,
-0.011496187187731266,
-0.02757555991411209,
-0.035304393619298935,
0.027948057278990746,
-0.07503046095371246,
-0.020366158336400986,
-0.02715805172920227,
0.015387055464088917,
-0.008336747996509075,
0.003786523127928376
] |
<p>In the late nineties Bender has started a research program on what is called PT symmetric QM, or non hermitian QM, in which he has shown that if the hamiltonian enjoys a PT symmetry then the spectrum is real even if the hamiltonian was not hermitian. Now a search for "PT symmetric" on the arxiv will return over 400 papers.</p>
<p>This relaxation of the hermiticity of the hamiltonian has led to new forms of hamiltonians that have been rejected before because they were non hermitian. It turns out that such PT symmetric hamiltonians can describe real physical systems.</p>
<p>Since this PT symmetric QM cannot be considered a generalization to conventional quantum mechanics I suppose in which observables are mathematically represented by hermitian operators, I find it intriguing that something like this can describe real physical systems. So how can one understand PT symmetric QM from first principles? I mean how does it fit in the grand picture, why it works? </p>
| 9,638 |
[
-0.0027033856604248285,
-0.052920106798410416,
0.025574078783392906,
-0.038764212280511856,
0.026494406163692474,
0.035171668976545334,
-0.016361799091100693,
-0.01265754085034132,
0.024449754506349564,
-0.07801873981952667,
0.010079784318804741,
-0.007588162552565336,
0.007341853342950344,
-0.003382135182619095,
0.014598853886127472,
0.01321022491902113,
0.007391307968646288,
-0.04815199598670006,
-0.03834512084722519,
-0.014571118168532848,
0.006050963420420885,
0.022447168827056885,
0.01187314186245203,
-0.0077967215329408646,
-0.014955568127334118,
0.020846063271164894,
0.007967176847159863,
0.0205629151314497,
0.015027401968836784,
0.04794028401374817,
-0.003797895507887006,
-0.01013087760657072,
-0.027606727555394173,
-0.0006236609187908471,
0.0194548387080431,
-0.004823680501431227,
-0.02405395172536373,
-0.04652884975075722,
0.02785084769129753,
0.005521079991012812,
-0.030933180823922157,
-0.007751015946269035,
-0.012339292094111443,
0.03826194629073143,
-0.04256739094853401,
0.006482827011495829,
0.011553704738616943,
0.016248133033514023,
0.04890340939164162,
-0.056922245770692825,
0.07433643937110901,
0.027440089732408524,
0.04406586289405823,
0.014096765778958797,
-0.02899290807545185,
0.009519146755337715,
0.05224727466702461,
0.07233759015798569,
-0.017164569348096848,
-0.0467020682990551,
-0.01373679656535387,
-0.021542368456721306,
-0.011034938506782055,
-0.01824006251990795,
-0.03248773515224457,
0.027028223499655724,
0.010447858832776546,
-0.03889220207929611,
0.01577848382294178,
0.003588478546589613,
-0.01524683553725481,
0.001346204779110849,
0.045164696872234344,
-0.01541490014642477,
0.015071537345647812,
-0.029138624668121338,
0.004310455173254013,
-0.0070156981237232685,
0.05276893824338913,
0.009728161618113518,
0.04249519482254982,
0.01980912871658802,
0.008163764141499996,
0.014349049888551235,
-0.032237399369478226,
0.0010210450273007154,
0.03063157945871353,
0.004863718990236521,
-0.008154043927788734,
0.0596705786883831,
0.01819017343223095,
0.031987786293029785,
0.04019475728273392,
-0.008875766769051552,
-0.021888012066483498,
-0.011332226917147636,
0.015190270729362965,
0.06017231568694115,
-0.015506032854318619,
-0.03399506211280823,
0.013228769414126873,
-0.01610308140516281,
-0.015900319442152977,
0.07950285822153091,
-0.028360635042190552,
-0.026241671293973923,
-0.015573837794363499,
0.02664559707045555,
0.011574952863156796,
0.00021481598378159106,
-0.04311160743236542,
0.006283362861722708,
-0.028200821951031685,
0.00865126308053732,
0.023992590606212616,
-0.03239109367132187,
-0.007446879521012306,
-0.02066298946738243,
0.05534815415740013,
0.08984608948230743,
-0.003991021774709225,
0.05144565925002098,
0.05472401902079582,
-0.04247875511646271,
-0.046158257871866226,
0.014071766287088394,
0.025634605437517166,
-0.0018735582707449794,
-0.0786595419049263,
-0.032455191016197205,
0.001446202746592462,
0.000009888162821880542,
-0.004336628597229719,
-0.01258515752851963,
0.04178984835743904,
-0.03323368728160858,
-0.12728776037693024,
-0.0579858236014843,
0.023545026779174805,
0.014970259740948677,
-0.033764712512493134,
-0.04012070968747139,
0.004790221806615591,
0.03735792636871338,
0.11305709183216095,
0.009486700408160686,
0.01929667219519615,
0.023546623066067696,
0.004861215129494667,
0.02304842323064804,
0.01148578803986311,
-0.010237242095172405,
0.040470611304044724,
-0.051245711743831635,
0.002648979192599654,
-0.058838967233896255,
0.0035574904177337885,
-0.026469983160495758,
0.005330737680196762,
-0.025681523606181145,
0.04323229566216469,
-0.02503439038991928,
-0.01885649375617504,
0.004284700844436884,
-0.01777411252260208,
0.008807935751974583,
0.07185985147953033,
0.039856694638729095,
-0.0243698600679636,
0.042959991842508316,
0.009425254538655281,
0.02267821691930294,
-0.011639860458672047,
0.03166748583316803,
-0.0034095048904418945,
-0.038961537182331085,
0.01443866640329361,
0.00045378622598946095,
0.02316121757030487,
0.010128435678780079,
-0.0032809630502015352,
-0.002496910747140646,
0.007931296713650227,
0.023122748360037804,
-0.02107895351946354,
0.042362626641988754,
0.013818211853504181,
0.024881454184651375,
0.05239146947860718,
-0.026662537828087807,
-0.015056092292070389,
-0.06940087676048279,
-0.0005939754191786051,
0.02469148300588131,
-0.03346922993659973,
0.03978944569826126,
0.04857570677995682,
-0.005636055953800678,
-0.014086104929447174,
-0.0152595154941082,
0.011898153461515903,
0.047974102199077606,
0.01452720072120428,
-0.0014942956622689962,
0.041522152721881866,
0.06398048996925354,
0.024091670289635658,
-0.021279271692037582,
0.009404642507433891,
-0.009650598280131817,
-0.04326625168323517,
0.004369017202407122,
-0.010020438581705093,
0.037759266793727875,
0.027465829625725746,
0.0068521746434271336,
-0.006312994752079248,
-0.044833920896053314,
-0.024974744766950607,
0.02478918619453907,
-0.040311623364686966,
0.03953804448246956,
0.009988127276301384,
0.02629013918340206,
0.01281913835555315,
0.047615766525268555,
0.001435175770893693,
0.012450287118554115,
0.02211286872625351,
-0.030260203406214714,
-0.04164093732833862,
0.023996343836188316,
0.034421343356370926,
0.04574545472860336,
-0.0341046005487442,
0.02948935329914093,
0.0023032191675156355,
0.05829677730798721,
0.04141352325677872,
-0.0009743409464135766,
-0.05016342177987099,
-0.004928945563733578,
0.02320130728185177,
0.0013483257498592138,
0.02655910700559616,
0.01273319125175476,
0.007912853732705116,
0.0029573836363852024,
0.007271174807101488,
-0.005840133875608444,
-0.03732508420944214,
0.04668799787759781,
-0.0023646224290132523,
0.006869092117995024,
0.011104666627943516,
-0.03436968848109245,
0.01813325844705105,
-0.029759038239717484,
0.013457679189741611,
0.033635463565588,
-0.00835370272397995,
-0.01302134059369564,
-0.04807770252227783,
-0.05086258798837662,
0.007732790429145098,
-0.017950300127267838,
-0.0020207231864333153,
-0.016995111480355263,
0.0160879697650671,
-0.003798948135226965,
-0.006497321184724569,
-0.03261693939566612,
-0.035860154777765274,
-0.009114528074860573,
-0.039859481155872345,
0.0016089974669739604,
0.026887934654951096,
0.04814889281988144,
-0.04852159321308136,
-0.03238320350646973,
0.007990009151399136,
-0.020598946139216423,
-0.00039596197893843055,
0.04341321811079979,
-0.06601663678884506,
0.02071564272046089,
-0.07881663739681244,
-0.01542526576668024,
0.001589609426446259,
0.02354065701365471,
0.026269465684890747,
-0.00299434014596045,
-0.01611500419676304,
-0.06331488490104675,
0.0002340252831345424,
-0.04140618070960045,
-0.023865222930908203,
-0.040766339749097824,
-0.0041526383720338345,
0.023922841995954514,
-0.003196222009137273,
-0.016587968915700912,
-0.020262354984879494,
-0.029552467167377472,
-0.044187214225530624,
-0.009600338526070118,
-0.0083438940346241,
-0.02327122911810875,
-0.03850647062063217,
0.020850690081715584,
0.0421682707965374,
-0.035894155502319336,
0.021053023636341095,
-0.0641675516963005,
-0.04982183873653412,
-0.026956310495734215,
-0.00009899472206598148,
0.007695493753999472,
0.024192024022340775,
-0.01603410392999649,
0.10486476868391037,
0.008835266344249249,
-0.02186916209757328,
-0.01984304003417492,
0.03024354577064514,
0.005980365443974733,
-0.03413913771510124,
0.029023323208093643,
0.0514131635427475,
-0.0034658859949558973,
0.04084205999970436,
0.022067861631512642,
0.007643790449947119,
0.014865946024656296,
0.04264164716005325,
-0.04731595143675804,
-0.006231049541383982,
-0.007897097617387772,
0.03822541981935501,
0.0327722430229187,
0.010754551738500595,
-0.04483921825885773,
0.02413998916745186,
-0.01107398234307766,
-0.003010458080098033,
0.010019158013164997,
-0.042946673929691315,
0.04892865940928459,
0.0005866092396900058,
0.03251250833272934,
-0.021040577441453934,
0.03848278522491455,
-0.05950365588068962,
-0.033217377960681915,
-0.029143791645765305,
0.057923685759305954,
-0.0014178944984450936,
0.0020405808463692665,
0.008125840686261654,
-0.0017843114910647273,
-0.004224760457873344,
-0.026306595653295517,
-0.006683101411908865,
0.015110474079847336,
-0.030888233333826065,
0.005458743777126074,
-0.030502494424581528,
-0.04294290393590927,
0.05043986067175865,
0.035463009029626846,
0.02668929658830166,
0.018520480021834373,
-0.020707007497549057,
-0.019300835207104683,
-0.02018928714096546,
-0.006075593177229166,
-0.0031876855064183474,
0.057790812104940414,
-0.013945339247584343,
0.05680027976632118,
0.012744881212711334,
0.010667353868484497,
0.006623097695410252,
0.0010586853604763746,
-0.028587570413947105,
0.061740756034851074,
-0.04650559276342392,
-0.0063102333806455135,
0.012076389975845814,
-0.01394870225340128,
-0.0043262518011033535,
-0.021085426211357117,
-0.028418097645044327,
-0.04096890613436699,
-0.022775182500481606,
-0.05691347271203995,
0.027430661022663116,
0.004225229844450951,
-0.050293438136577606,
-0.00992659293115139,
0.01951012760400772,
0.03779009357094765,
-0.013156461529433727,
0.007692995015531778,
0.021493948996067047,
-0.0496235117316246,
0.012492379173636436,
-0.039733219891786575,
0.01679277792572975,
0.02994302287697792,
0.012187053449451923,
0.02559083327651024,
0.0036250553093850613,
0.0018984450725838542,
-0.010849492624402046,
-0.006446628365665674,
0.10016817599534988,
0.010483119636774063,
0.006499591749161482,
0.02735031023621559,
-0.04332897067070007,
0.0023764430079609156,
0.022894328460097313,
0.02174742892384529,
0.012987257912755013,
0.013933579437434673,
0.032037295401096344,
0.009116747416555882,
-0.047892916947603226,
-0.0004280588182155043,
0.01674819365143776,
0.030088281258940697,
-0.014916909858584404,
-0.08705437183380127,
-0.007576388772577047,
-0.0012966442154720426,
-0.0033244581427425146,
-0.011477673426270485,
-0.020419040694832802,
0.005773905199021101,
0.05275065451860428,
0.0426509752869606,
-0.004257026128470898,
-0.026239637285470963,
0.013963495381176472,
-0.012584916315972805,
-0.003489721566438675,
-0.03641263023018837,
0.020926959812641144,
0.007205236237496138,
0.07188642770051956,
0.06830697506666183,
-0.009847516193985939,
0.006236691493541002,
-0.05650753155350685,
0.006942841690033674,
0.04240511357784271,
0.029522046446800232,
0.02499249204993248,
-0.029725631698966026,
-0.00982721522450447,
-0.013234898447990417,
0.07629389315843582,
-0.02938702702522278,
0.03633632883429527,
-0.01331929862499237,
-0.028774432837963104,
-0.04934389144182205,
-0.0421677865087986,
0.003558728378266096,
0.009633006528019905,
-0.015033554285764694,
-0.004944839980453253,
-0.04157986491918564,
0.0012051373487338424,
-0.05097413808107376,
0.02132573351264,
-0.001591634820215404,
0.03356144204735756,
-0.006197799928486347,
-0.007634948007762432,
-0.005415110383182764,
0.05042063817381859,
-0.02179601602256298,
-0.07452625036239624,
0.013042530976235867,
0.018127700313925743,
0.0013628615997731686,
0.031266577541828156,
-0.04061288759112358,
-0.05843978002667427,
0.001849160180427134,
-0.022608477622270584,
0.016309652477502823,
0.011898758821189404,
-0.017440084367990494,
0.02673296630382538,
0.039371307939291,
0.01013629138469696,
0.04656600207090378,
0.04187164828181267,
0.004192336928099394,
-0.023416342213749886,
-0.007367685902863741,
0.007976376451551914,
-0.020994560793042183,
0.028531072661280632,
-0.04224046692252159,
0.010024293325841427,
-0.03182616084814072,
0.0345882885158062,
-0.011149691417813301,
-0.019335567951202393,
0.008565232157707214,
-0.03036622144281864,
-0.0382419191300869,
0.04531760513782501,
-0.01644144020974636,
-0.00915328785777092,
0.014756633900105953,
0.053656455129384995,
0.03348064795136452,
-0.002991692628711462,
0.005235664080828428,
-0.02431579679250717,
-0.01224282756447792,
0.04746505245566368,
-0.003791116876527667,
0.08297201246023178,
-0.033528149127960205,
-0.02220853604376316,
0.010371506214141846,
-0.04837246611714363,
-0.0009738999069668353,
0.014786217361688614,
0.013075479306280613,
0.027736959978938103,
-0.08438165485858917,
-0.04163186252117157,
0.04030138999223709,
-0.03205983340740204,
0.027830902487039566,
-0.011838690377771854,
0.0035610490012913942,
0.023291973397135735,
0.00008334044832736254,
-0.05584966391324997,
-0.046373020857572556,
0.0210049357265234,
0.025484146550297737,
-0.01967032626271248,
-0.0213638748973608,
-0.013789410702884197,
0.005526111461222172,
0.004293856676667929,
0.03869375213980675,
0.04495101422071457,
-0.020439032465219498,
0.002454508328810334,
0.01490417867898941,
0.009797588922083378,
0.047605060040950775,
-0.030062375590205193,
0.03098507784307003,
0.008844209834933281,
-0.038604736328125,
0.029632609337568283,
0.007869060151278973,
0.05281287431716919,
-0.021718645468354225,
0.0024582017213106155,
-0.04862019419670105,
0.021568289026618004,
0.035648979246616364,
0.008941221050918102,
0.0018584753852337599,
0.02032504417002201,
-0.016899246722459793,
0.010859321802854538,
-0.04286041483283043,
0.0031505299266427755,
0.038592997938394547,
0.052959173917770386,
0.007147044409066439,
-0.019412893801927567,
-0.0220506489276886,
-0.04516040161252022,
0.03572072088718414,
-0.015193791128695011,
-0.027856256812810898,
-0.008090839721262455,
0.02380753494799137,
-0.0002468688180670142,
0.0016644754214212298,
0.027305088937282562,
-0.028467576950788498,
-0.011535914614796638,
-0.008578408509492874,
0.009265538305044174,
-0.024046000093221664,
0.00605622585862875,
-0.06001656502485275,
-0.05261024832725525,
-0.026767496019601822,
0.013596259988844395,
0.048281095921993256,
0.019949564710259438,
0.03004487417638302,
0.04205935448408127,
-0.021774381399154663,
-0.048295918852090836,
-0.0069035012274980545,
-0.01643184944987297,
-0.0011977778049185872,
0.014924012124538422,
0.025776565074920654,
-0.039356257766485214,
0.027177229523658752,
0.038800690323114395,
0.06133830174803734,
-0.022796569392085075,
-0.00681826937943697,
0.01952466368675232,
0.06165267154574394,
0.005577570293098688,
-0.011772392317652702,
-0.029334979131817818,
0.06292863935232162,
-0.014269575476646423,
0.0037386964540928602,
0.013227513059973717,
0.017222438007593155,
0.03321594372391701,
-0.017201170325279236,
0.01958487741649151,
-0.005560528952628374,
-0.0011041979305446148,
-0.050378601998090744,
0.057945188134908676,
0.005450766067951918,
0.008950385265052319,
-0.00960522424429655,
-0.015577241778373718,
0.034582484513521194,
-0.004765221383422613,
0.04432089626789093,
0.01783008687198162,
-0.05408642441034317,
-0.016455447301268578,
-0.025878485292196274,
-0.023151254281401634,
0.032936494797468185,
-0.024083366617560387,
-0.010980764403939247,
0.011014909483492374,
-0.022967010736465454,
0.0004196463560219854,
-0.013227386400103569,
0.002243672264739871,
-0.04567442461848259,
0.0013448706595227122,
-0.019212836399674416,
0.0164017416536808,
0.026619751006364822,
-0.023272164165973663,
0.129926860332489,
0.02030807174742222,
-0.001125537441112101,
-0.04459730535745621,
0.0053124683909118176,
0.011484552174806595,
0.03092673048377037,
0.03006698749959469,
0.02548965811729431,
-0.016385212540626526,
0.03046990931034088,
-0.020526988431811333,
0.031494736671447754,
0.03138838708400726,
-0.01576320268213749,
0.07591013610363007,
-0.0527200885117054,
-0.05905873700976372,
0.008331582881510258,
0.014654156751930714,
-0.019185487180948257,
-0.037495870143175125,
-0.041692741215229034,
0.014782886020839214,
-0.04381877928972244,
0.014513649977743626,
-0.017410920932888985,
-0.021448342129588127,
-0.007764687296003103,
0.006801453419029713,
-0.020115934312343597,
-0.0013464306248351932,
0.011468617245554924,
-0.005345269106328487,
-0.04023972153663635,
0.03178799897432327,
0.016480403020977974,
0.0013303104788064957,
0.0636708214879036,
0.005689452402293682,
-0.004537619650363922,
-0.03581136465072632,
0.007892247289419174,
0.005683567840605974,
-0.050236716866493225,
0.014766542240977287,
-0.009246849454939365,
0.045254748314619064,
-0.03720013424754143,
0.0006424784078262746,
0.015150446444749832,
-0.041817862540483475,
-0.021020306274294853,
-0.029410086572170258,
-0.0012646461836993694,
-0.016121473163366318,
0.024675535038113594,
-0.025364957749843597,
0.01394573226571083,
-0.01740320213139057,
0.004316964186728001,
0.0001359972229693085,
0.0249656829982996,
0.01148180104792118,
0.008760439231991768,
0.03346427157521248,
-0.003336520167067647,
0.03095504269003868,
-0.0027754907496273518,
-0.018053509294986725,
-0.05683661252260208,
-0.009775597602128983,
-0.04533861577510834,
-0.04751666262745857,
-0.0029542995616793633,
0.007979726418852806,
0.08139713108539581,
-0.00663582282140851,
0.008021572604775429,
-0.03106267936527729,
-0.04872274026274681,
-0.0011259117163717747,
-0.04342123493552208,
-0.005404131952673197,
-0.001268003135919571,
-0.017374126240611076,
0.02909719944000244,
0.07822659611701965,
-0.05793667957186699,
0.030133042484521866,
0.0315963514149189,
-0.028356904163956642,
0.034433335065841675,
-0.010589056648314,
0.023436281830072403,
0.019921306520700455,
-0.027886660769581795,
0.02109118178486824,
-0.02571941539645195,
-0.032356616109609604,
0.003584816586226225,
0.002266641240566969,
-0.015198767185211182,
0.047817036509513855,
-0.04548059403896332,
-0.03286674618721008,
0.025333192199468613,
-0.02884158305823803,
0.009520957246422768,
0.022373413667082787,
0.038974449038505554,
-0.08168847858905792,
-0.040906354784965515,
-0.010014318861067295,
-0.026211796328425407,
-0.0052168057300150394,
0.042238276451826096,
-0.03432007133960724,
-0.0317353829741478,
-0.02212592400610447,
0.04260551929473877,
-0.010029078461229801,
0.002686082851141691,
-0.03974844142794609,
0.028368795290589333,
-0.008815521374344826,
-0.015142246149480343,
-0.019200047478079796,
0.0038052734453231096,
0.005465228110551834,
-0.01958899013698101,
0.03500611335039139,
0.025921648368239403,
-0.059834565967321396,
0.008852444589138031,
0.03051215037703514,
-0.013122876174747944,
0.004780692979693413,
0.02108175680041313,
-0.016173826530575752,
0.033307209610939026,
-0.04340922087430954,
-0.0318133719265461,
0.022294798865914345,
-0.04112383723258972,
0.021104710176587105,
0.01296780165284872,
-0.02872498892247677,
0.015029432252049446,
-0.0199692752212286,
-0.023580972105264664,
-0.016761038452386856,
0.018739165738224983,
0.007928026840090752,
-0.0006536646978929639,
-0.013631660491228104,
0.030838215723633766,
-0.01154331024736166,
0.004116615280508995,
0.019462373107671738,
0.017606547102332115,
0.007117025554180145,
0.0072878273203969,
-0.009534613229334354,
-0.007206191308796406,
0.03818279504776001,
0.004788408987224102,
0.02335534431040287,
0.02070702612400055,
0.05694914609193802,
-0.05764387547969818,
0.0164791289716959,
0.015990812331438065,
0.01401512324810028,
-0.07943898439407349,
0.032950688153505325,
-0.0005426017451100051,
-0.029008684679865837,
0.059502582997083664,
-0.03558298200368881,
0.01920013315975666,
0.010096020065248013,
-0.09735102206468582,
0.019103972241282463,
-0.014894907362759113,
-0.03176964074373245,
-0.0026547422166913748,
0.03312646970152855,
-0.043011270463466644,
0.08443685621023178,
0.03153803572058678,
0.024163028225302696,
0.021339846774935722,
0.007665335666388273,
0.026077037677168846,
-0.01814328506588936,
-0.01291404478251934,
0.006251995451748371,
-0.03282792121171951,
0.02355697751045227,
0.03689304739236832,
-0.02533954754471779,
-0.01690935529768467,
0.03218265250325203,
-0.044572509825229645,
0.005653070751577616,
-0.016906073316931725,
-0.0017110693734139204,
0.009052864275872707,
0.02254577726125717,
0.027257928624749184,
-0.02702918089926243,
-0.03956175222992897,
0.006759266369044781,
0.057716429233551025,
0.08619505912065506,
-0.010534665547311306,
0.007418337743729353,
-0.022655963897705078,
-0.031391691416502,
-0.03204157575964928,
-0.0012002155417576432,
0.02290927991271019,
0.0013617342337965965,
0.01940714195370674,
-0.0010948810959234834,
-0.035869140177965164,
0.00034404461621306837,
0.04247118905186653,
-0.052437812089920044,
-0.0010879543842747808,
0.019421149045228958,
0.026648743078112602,
0.0005737364408560097,
0.021916646510362625,
-0.052891507744789124,
-0.028492797166109085,
0.01672256551682949,
0.0087428018450737,
-0.019553156569600105,
-0.06242816522717476,
-0.01568201184272766,
0.03580603748559952,
0.00826908741146326,
0.0038884172681719065,
-0.029760221019387245,
-0.016492845490574837,
0.028791913762688637,
0.0061669256538152695,
0.010176497511565685,
-0.016331953927874565,
-0.034326907247304916,
-0.019296694546937943,
-0.034470971673727036,
0.06731516867876053,
0.025793392211198807,
0.044764257967472076,
0.015310783870518208,
-0.04830171912908554,
0.006679900456219912,
0.006164168007671833,
0.04172707349061966,
0.013823323883116245,
-0.019215954467654228,
0.012272076681256294,
-0.03741968050599098,
0.010980142280459404,
-0.0270723644644022,
-0.004661853890866041,
-0.02305075339972973,
0.0022124256938695908,
-0.0007833386771380901,
-0.007321563549339771,
-0.0032838357146829367,
0.017450958490371704,
0.01340949721634388,
0.0032675149850547314,
-0.02312895841896534,
0.0021969338413327932,
-0.04735199734568596,
0.10078509896993637,
0.012001607567071915,
-0.015964914113283157,
0.07955607026815414,
0.007505201268941164,
0.03219202905893326,
0.022822218015789986,
-0.03820870444178581,
0.006126062944531441,
0.015516305342316628,
-0.03233964368700981,
-0.01947779767215252,
0.006631472613662481,
0.0013908491237089038,
0.019757235422730446,
-0.003830953035503626,
0.0010173757327720523,
0.01822955161333084,
-0.036727238446474075,
-0.04780374839901924,
0.018438048660755157,
0.003052108222618699,
0.024677282199263573,
0.030209273099899292,
0.011303501203656197,
0.008772913366556168,
0.010861046612262726,
0.029944084584712982,
0.045727621763944626,
0.00967678613960743,
0.010318980552256107,
0.02710830233991146,
0.01958431676030159,
-0.039322830736637115,
0.044139500707387924,
0.04029429703950882,
0.04446648806333542,
-0.04530179500579834,
-0.008595270104706287,
0.03292996436357498,
0.0034615148324519396,
0.01830953173339367,
-0.02165190316736698,
-0.016339734196662903,
0.09498143941164017,
-0.003837903030216694,
0.006593495607376099,
-0.009343430399894714,
0.01027711108326912,
-0.0014285137876868248,
-0.023176847025752068,
-0.0010515240719541907,
0.04191700741648674,
-0.032170169055461884,
-0.0015082526952028275,
-0.05276116728782654,
0.032665811479091644,
-0.02341320738196373,
-0.06134974956512451,
-0.000570505450014025,
0.0011117628309875727,
0.006454659625887871,
-0.015453117899596691,
-0.026614515110850334,
-0.003937208093702793,
-0.016097132116556168,
0.025629986077547073,
0.03315679728984833,
0.051705501973629,
0.002559749875217676,
-0.036658648401498795,
-0.05114973336458206,
0.043010398745536804,
-0.04394727200269699,
0.004511815961450338,
-0.03848494961857796,
-0.01863059587776661,
-0.040372900664806366,
-0.0022463807836174965
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.