question
stringlengths
37
38.8k
group_id
stringlengths
2
6
sentence_embeddings
listlengths
768
768
<p>I understand that the fundamental representation of $U(1)$ amounts to a multiplication by a phase factor, e.g. EM. I thought that when it is extended to higher dimensional representations, it would just become a phase factor times the identity matrix.</p> <p>Can someone explain where the hypercharge comes into the $U(1)$ generator matrices in $SU(2)\times U(1)$ model, e.g. $Y = -(1/2) I$ in $(2, -1/2)$ representation? I don't quite understand where the "$-1/2$" comes from.</p> <p>Where do all these hypercharges come from? What is the logic behind choosing a particular value like $-1/2$?</p> <p>Hope someone can clarify. </p>
g8339
[ 0.0072609358467161655, 0.057146891951560974, -0.026182038709521294, 0.012732723727822304, 0.04594440758228302, -0.02227853611111641, 0.032131705433130264, 0.04679315537214279, -0.07506720721721649, 0.005322088021785021, -0.07419538497924805, 0.025218671187758446, 0.046043701469898224, 0.04838915914297104, -0.007778293453156948, -0.0045129721984267235, 0.05074331909418106, 0.06545887887477875, 0.009752416051924229, -0.004979933612048626, -0.08363209664821625, 0.0029107655864208937, 0.001099458779208362, -0.06976382434368134, -0.008759601972997189, 0.016891254112124443, 0.09691307693719864, 0.017028629779815674, -0.007575304247438908, -0.021311327815055847, 0.013668052852153778, -0.02548256888985634, 0.05167170241475105, -0.049232617020606995, -0.03241346776485443, -0.0038304212503135204, 0.06585810333490372, 0.061190973967313766, 0.01734819822013378, 0.026325318962335587, 0.016214633360505104, -0.050710082054138184, -0.00966861192137003, 0.02233266271650791, -0.05044595152139664, 0.03394389897584915, -0.012216595001518726, -0.019526036456227303, -0.04571765661239624, 0.04951360821723938, 0.07269695401191711, 0.032018207013607025, 0.03292553871870041, -0.03672720119357109, 0.002444947836920619, 0.020692460238933563, -0.012259071692824364, 0.011174104176461697, 0.05352539196610451, 0.08452481031417847, 0.036338452249765396, 0.015919724479317665, 0.019148284569382668, 0.021692635491490364, 0.06656419485807419, -0.005258418619632721, 0.004300615284591913, 0.0022510334383696318, -0.0307990200817585, 0.02218385972082615, -0.03398794308304787, -0.07414186745882034, -0.0032609219197183847, -0.03365906700491905, 0.03254855424165726, -0.03515509516000748, 0.05144258216023445, 0.010653289034962654, 0.0035397664178162813, 0.0023018161300569773, 0.01785186678171158, -0.0029224599711596966, 0.08015470951795578, -0.01044908445328474, -0.0023884146939963102, -0.008814278990030289, -0.011207297444343567, 0.03017783910036087, 0.007596377283334732, -0.02747165784239769, -0.01909000612795353, 0.04961623251438141, 0.00782152358442545, 0.00998182874172926, -0.035337913781404495, -0.008472636342048645, -0.00832963827997446, 0.013290975242853165, -0.030610909685492516, -0.013256924226880074, -0.016942471265792847, 0.021056080237030983, 0.0640784502029419, 0.0018169352551922202, -0.05882968381047249, 0.05070735141634941, -0.0030689705163240433, -0.03670688346028328, 0.007815324701368809, -0.0414612777531147, -0.09325678646564484, 0.010474085807800293, -0.029196567833423615, -0.04719991981983185, -0.05221579968929291, 0.00032675956026650965, 0.06571641564369202, -0.0005557744298130274, -0.0118783637881279, -0.030910924077033997, 0.005445740185678005, -0.022988226264715195, 0.03019978292286396, 0.019521350041031837, 0.024412263184785843, 0.0003911539679393172, 0.030666468665003777, 0.052198685705661774, -0.043401725590229034, 0.03390202298760414, -0.020334307104349136, -0.04701356589794159, -0.018195563927292824, 0.008179053664207458, 0.09377861768007278, 0.043955035507678986, 0.026408085599541664, 0.02850913628935814, -0.016807017847895622, 0.03278368338942528, -0.039771031588315964, -0.04932066425681114, -0.00829898752272129, -0.056119292974472046, -0.016216805204749107, 0.027246376499533653, 0.01182957086712122, -0.08214440196752548, 0.016127755865454674, -0.012262904085218906, -0.0004879733605775982, 0.11190533638000488, -0.03129872679710388, -0.0363876074552536, 0.0002231429098173976, 0.014784369617700577, 0.07198372483253479, -0.06346182525157928, -0.0092904232442379, -0.03591221943497658, 0.025109028443694115, 0.0012088215444236994, 0.04269691929221153, -0.0002438578085275367, -0.0549611933529377, -0.05558934062719345, 0.03179877623915672, -0.03571590408682823, -0.032954148948192596, -0.020697204396128654, 0.03409985825419426, -0.001971720950677991, 0.014280700124800205, 0.013369233347475529, 0.03369561582803726, 0.004549854900687933, 0.02099464274942875, -0.04511426016688347, 0.052755799144506454, -0.006149573251605034, -0.0938480943441391, -0.02691466547548771, 0.019024569541215897, 0.002019106177613139, 0.004364826716482639, -0.014000625349581242, 0.0019856998696923256, 0.08283427357673645, -0.007399378344416618, 0.07174581289291382, -0.049957044422626495, 0.02552162855863571, 0.029978035017848015, 0.0033743162639439106, -0.024969089776277542, -0.009738975204527378, -0.009510722942650318, -0.03402375057339668, -0.0273688156157732, 0.037113673985004425, -0.02470712922513485, -0.005826993379741907, 0.008859412744641304, -0.02601558156311512, -0.033592816442251205, 0.07428289949893951, 0.018098480999469757, 0.040385618805885315, -0.0315440334379673, -0.024333899840712547, -0.0493774376809597, -0.012254780158400536, -0.013325079344213009, 0.01744607649743557, -0.007461230736225843, -0.02712145633995533, -0.022156251594424248, -0.057680316269397736, 0.003543209284543991, 0.01221406552940607, 0.012507881037890911, -0.05297228321433067, 0.055508602410554886, 0.032167643308639526, -0.03400655463337898, 0.028149068355560303, 0.0006257078493945301, 0.01991518959403038, 0.010376350954174995, 0.03301141411066055, -0.019293690100312233, 0.06480932235717773, -0.032883718609809875, -0.03130510449409485, -0.02128172665834427, -0.0032286287751048803, -0.04378701001405716, 0.05146729201078415, -0.006609917618334293, 0.030902182683348656, 0.04443608969449997, 0.029059601947665215, 0.015855731442570686, 0.02243683859705925, 0.004974439740180969, -0.03866753727197647, 0.024816961959004402, -0.0274509284645319, -0.06304579228162766, 0.05460549145936966, -0.0937461256980896, -0.02556329406797886, -0.017851246520876884, -0.03823689743876457, -0.04504780098795891, -0.02542128972709179, -0.004170211032032967, 0.021843336522579193, -0.05577593296766281, -0.03781299665570259, 0.004429057706147432, 0.017374763265252113, 0.013217024505138397, 0.004698196891695261, -0.05948794633150101, -0.04945448786020279, 0.014552118256688118, -0.028200186789035797, -0.01847396418452263, -0.034887295216321945, -0.01613922417163849, 0.049923066049814224, -0.019829723984003067, -0.01701343059539795, -0.021059231832623482, -0.08630339056253433, 0.014542103745043278, -0.014651129953563213, -0.023285504430532455, -0.03239055722951889, -0.012675061821937561, -0.059573691338300705, -0.032381653785705566, 0.020550519227981567, 0.005280246026813984, -0.03658917546272278, -0.006337013561278582, 0.06257275491952896, -0.011819074861705303, -0.019740981981158257, -0.006850509438663721, 0.019574791193008423, 0.020246582105755806, 0.00756409764289856, 0.0167076513171196, 0.0033140077721327543, 0.04643171653151512, -0.05607465282082558, -0.0062255715020000935, 0.06308545917272568, -0.021688545122742653, -0.029621034860610962, 0.03527529910206795, -0.03125583380460739, 0.0029240776784718037, 0.005909319967031479, -0.01259632408618927, -0.01004580594599247, -0.061316490173339844, 0.026798054575920105, -0.07325278967618942, 0.026083948090672493, -0.026982704177498817, -0.004143060650676489, -0.06618735194206238, -0.03089158423244953, 0.026513203978538513, -0.024838967248797417, -0.002062038518488407, -0.02987915463745594, -0.028065115213394165, -0.035556893795728683, 0.007813937962055206, 0.03997908905148506, -0.011373416520655155, 0.04323501139879227, -0.07496683299541473, 0.031424250453710556, -0.02279284968972206, -0.04971373826265335, 0.08121408522129059, -0.0005192584940232337, 0.006941872648894787, 0.02456524223089218, 0.009141534566879272, -0.038618579506874084, -0.04380005598068237, 0.013653861358761787, -0.002711071167141199, -0.0209648534655571, -0.04915686324238777, 0.06899018585681915, 0.030489472672343254, -0.013334582559764385, 0.028884314000606537, -0.06356198340654373, -0.030579473823308945, 0.016581788659095764, -0.03440851345658302, -0.07200190424919128, -0.03927217423915863, 0.08257710933685303, 0.02806396782398224, 0.002845075214281678, -0.029218461364507675, 0.022502392530441284, 0.011502845212817192, 0.039515361189842224, -0.01836557500064373, 0.04669303074479103, 0.030760811641812325, -0.002872172510251403, -0.010575124993920326, 0.0066215177066624165, 0.004123541992157698, 0.003975223284214735, -0.013863862492144108, 0.0360432043671608, 0.025747131556272507, 0.011184228584170341, 0.07384735345840454, 0.03286658972501755, -0.01424089353531599, 0.02541610784828663, -0.023008357733488083, -0.07923921197652817, 0.010326409712433815, 0.004246171098202467, 0.05183984339237213, 0.04436270147562027, 0.003042407101020217, -0.02671998366713524, 0.0455743782222271, -0.04090767353773117, -0.0011683510383591056, 0.011579719372093678, -0.02902890555560589, -0.015490035526454449, -0.01445506140589714, -0.04677816852927208, 0.029045606032013893, -0.019440973177552223, 0.03275255858898163, 0.04270679131150246, -0.01844083145260811, -0.033090900629758835, 0.0025104458909481764, -0.023901037871837616, -0.017465822398662567, -0.023904960602521896, 0.03627628833055496, -0.008655472658574581, 0.03035658597946167, 0.01846504770219326, 0.022766243666410446, 0.0221074428409338, 0.023390373215079308, -0.06978447735309601, 0.011016815900802612, -0.009427753277122974, -0.016058120876550674, 0.05178649723529816, 0.08256164938211441, -0.053872883319854736, 0.053866319358348846, 0.024240514263510704, 0.04940137639641762, 0.019253181293606758, 0.04529275372624397, -0.025159237906336784, 0.04273800924420357, 0.04734699800610542, -0.020706595852971077, 0.0008074184879660606, 0.005677693989127874, 0.026639265939593315, 0.004857020452618599, -0.04343133047223091, -0.031025350093841553, -0.01440868154168129, -0.010759240947663784, 0.05278656259179115, 0.012457875534892082, 0.05318756029009819, -0.07794252038002014, -0.05357758700847626, -0.043655700981616974, 0.06496679782867432, -0.06134263426065445, 0.03440530598163605, 0.05906839668750763, 0.020243441686034203, 0.041759442538022995, -0.01711614802479744, 0.01143112126737833, -0.04155851900577545, 0.00012967106886208057, 0.012789109721779823, 0.00372522184625268, -0.02028045430779457, -0.03661182150244713, 0.05329491198062897, -0.00896883849054575, -0.04010983183979988, 0.07455266267061234, -0.038676824420690536, -0.04135194793343544, 0.022049555554986, 0.042452797293663025, -0.014368770644068718, -0.023711932823061943, -0.022310877218842506, -0.0195911917835474, -0.00498025119304657, -0.010802476666867733, -0.06089073792099953, -0.056263018399477005, -0.02881738543510437, 0.02760397084057331, 0.028085999190807343, 0.04615398868918419, -0.046028342097997665, 0.007043271791189909, 0.0086165526881814, 0.06615754216909409, 0.005545143969357014, -0.019792430102825165, -0.02254118025302887, -0.022561227902770042, 0.01967090740799904, 0.03052227944135666, 0.03396926820278168, -0.015092048794031143, 0.017692001536488533, -0.02789308689534664, 0.01920747570693493, -0.03936227411031723, -0.05278921127319336, 0.006765629630535841, -0.026326613500714302, 0.0027398390229791403, 0.04655225947499275, -0.002588379429653287, 0.027331147342920303, 0.016036661341786385, -0.010389227420091629, 0.041743841022253036, -0.052389245480298996, -0.04031222313642502, -0.039042986929416656, -0.06622452288866043, 0.019719278439879417, 0.05621107295155525, 0.04720142483711243, 0.019418373703956604, 0.009550271555781364, 0.08562223613262177, -0.001449469942599535, -0.032551005482673645, -0.03265240415930748, 0.015792442485690117, 0.0011937504168599844, -0.015913477167487144, -0.010255089029669762, 0.01641097478568554, 0.022485367953777313, -0.008740593679249287, 0.014705152250826359, -0.029462222009897232, -0.0032305431086570024, 0.030039075762033463, 0.002742297947406769, 0.07751759886741638, -0.010724615305662155, 0.01871437020599842, 0.053248561918735504, -0.0008234843844547868, -0.12779635190963745, 0.021839283406734467, 0.0449482761323452, 0.009235427714884281, -0.017497865483164787, -0.009631376713514328, 0.007250843103975058, 0.05297395586967468, -0.00651969201862812, 0.011949565261602402, -0.012337143532931805, 0.0007365812780335546, 0.010671277530491352, -0.008962881751358509, -0.06284689158201218, 0.0509844571352005, 0.033089619129896164, -0.026334615424275398, 0.005368571262806654, 0.002531685633584857, 0.0017248737858608365, 0.02781793847680092, -0.019478878006339073, -0.024254243820905685, -0.00909009575843811, 0.029699373990297318, -0.05396609753370285, 0.014232422225177288, 0.06206957995891571, 0.04138513654470444, 0.02070624753832817, 0.017681384459137917, 0.021093662828207016, 0.011939230374991894, 0.03794442489743233, 0.029916152358055115, -0.02990749664604664, 0.06280846893787384, -0.01922738365828991, 0.03793234005570412, -0.04991111159324646, 0.045603808015584946, 0.09143341332674026, 0.0719623789191246, 0.027120547369122505, 0.05462075397372246, -0.017660602927207947, -0.02896888181567192, 0.041561394929885864, -0.008101430721580982, -0.02126663736999035, -0.002778020454570651, -0.013498833402991295, -0.046352874487638474, -0.043681565672159195, 0.03434722125530243, 0.00970643199980259, -0.04616856202483177, 0.0318712443113327, -0.015166272409260273, -0.03544025868177414, 0.02750631421804428, 0.00971447303891182, -0.04983190819621086, 0.006410703063011169, -0.018533237278461456, 0.02614569664001465, -0.008511007763445377, 0.01496102474629879, 0.02933337166905403, 0.05882972851395607, 0.019670331850647926, -0.09664055705070496, 0.04620348662137985, 0.01135924831032753, 0.0001584601850481704, -0.023983096703886986, 0.05096522346138954, 0.029692938551306725, -0.048945751041173935, -0.016686178743839264, -0.0023139766417443752, 0.027525899931788445, 0.025313466787338257, -0.01089079212397337, -0.041136566549539566, -0.015784310176968575, -0.03386756405234337, -0.06893374770879745, 0.0006103000487200916, 0.01893783174455166, 0.03676585108041763, 0.07483497262001038, 0.06226840242743492, 0.04978940635919571, 0.021643031388521194, -0.050888288766145706, 0.06958229094743729, 0.007225298788398504, 0.04320080578327179, 0.0023406599648296833, 0.055069487541913986, -0.01671508327126503, 0.01568889617919922, -0.030669137835502625, -0.05054633319377899, 0.06478635221719742, 0.017648274078965187, 0.020722001791000366, -0.06591830402612686, 0.04647018387913704, -0.022165941074490547, 0.03768536448478699, -0.011643985286355019, 0.012077825143933296, -0.0021774128545075655, -0.013741778209805489, 0.018667766824364662, -0.053387027233839035, 0.021443521603941917, -0.006133728660643101, -0.04788583889603615, 0.07661044597625732, 0.07353493571281433, 0.02983981743454933, -0.04048750922083855, 0.015014132484793663, -0.051685772836208344, -0.03854413330554962, -0.0053036874160170555, 0.05799151584506035, -0.007931613363325596, -0.02846960723400116, -0.05945800617337227, 0.021429393440485, 0.00432959059253335, 0.00029914191691204906, 0.007662596181035042, 0.020028574392199516, 0.005309087224304676, 0.005044237244874239, 0.0289059616625309, -0.0447932630777359, -0.02748582325875759, -0.046896860003471375, -0.019842471927404404, 0.003617050824686885, 0.019874632358551025, -0.04335629194974899, -0.07413306087255478, 0.04781852290034294, -0.029232293367385864, -0.03032528981566429, 0.01520361378788948, 0.00883191917091608, -0.023720191791653633, -0.03186527267098427, -0.022870304062962532, 0.01146012730896473, -0.005065146833658218, -0.0012661992805078626, -0.03740270435810089, 0.019543752074241638, 0.059892814606428146, 0.0005310887354426086, 0.05064104497432709, 0.02600995823740959, -0.05515272170305252, 0.0035138861276209354, -0.010139325633645058, 0.02436022274196148, -0.015436051413416862, 0.02919885888695717, -0.014438614249229431, -0.058668144047260284, -0.004267243668437004, 0.023489000275731087, 0.012373963370919228, 0.009116661734879017, 0.02074628323316574, -0.04681717976927757, -0.019804945215582848, -0.05992472544312477, -0.02818194031715393, 0.02911355346441269, 0.02049442008137703, -0.019081199541687965, 0.012794364243745804, -0.0011735016014426947, -0.003193288343027234, -0.04130357503890991, 0.0007770534139126539, 0.0271353367716074, -0.0019103564554825425, -0.07766982913017273, -0.036944422870874405, -0.0498046912252903, 0.008031579665839672, -0.07168854773044586, 0.0005566380568780005, 0.042020317167043686, -0.003942469134926796, 0.03511408343911171, 0.005570362787693739, 0.008219687268137932, -0.031594663858413696, 0.0444735586643219, -0.01725679822266102, 0.014705910347402096, -0.019035184755921364, -0.034203946590423584, -0.013999995775520802, 0.03299172595143318, -0.004510513041168451, -0.028347911313176155, 0.024831954389810562, 0.015628235414624214, -0.061773840337991714, -0.007866457104682922, -0.06684091687202454, 0.025531800463795662, -0.020959949120879173, -0.009834577329456806, -0.011556378565728664, -0.005428999662399292, 0.012605114839971066, 0.03681383654475212, 0.02748868428170681, -0.004950612783432007, 0.03267845883965492, -0.01811482012271881, -0.017727438360452652, -0.07874184846878052, -0.022040236741304398, -0.026191629469394684, 0.008651229552924633, 0.019875293597579002, 0.007260506507009268, -0.048659518361091614, 0.0026683202013373375, 0.013985015451908112 ]
<p>why do two observers measure the same order of events if we are inside the light cone?</p> <p>(e.g. if ds^2 > 0 time order is preserved according to the class mech book I am reading, but it doesn't give any proof of this) I assume there is some simple geometrical argument I am missing</p> <p>and analgously why do two observers measure possible different order of events if we are outside the light cone?</p>
g8340
[ 0.02054065465927124, 0.00995391234755516, 0.022796766832470894, -0.005415729712694883, 0.06603876501321793, 0.002683880738914013, -0.013811022974550724, 0.0020935791544616222, -0.052805762737989426, -0.04809103161096573, -0.009731587953865528, -0.02338228188455105, 0.03916194662451744, 0.027326378971338272, 0.013093139976263046, -0.02375323697924614, 0.010250181891024113, -0.007946611382067204, -0.002572454046458006, 0.01725192554295063, 0.02501048520207405, 0.024318642914295197, 0.012173397466540337, -0.029011132195591927, -0.02862064726650715, -0.05862695351243019, 0.07050981372594833, -0.0688515305519104, -0.05419059842824936, -0.015136818401515484, 0.049494534730911255, -0.009721104986965656, 0.050154466181993484, -0.04957074299454689, -0.03663099929690361, -0.040889088064432144, 0.027222011238336563, -0.04186026751995087, 0.03403019160032272, 0.0320776030421257, 0.031136712059378624, 0.03250912204384804, 0.022456351667642593, -0.10258091986179352, 0.05577727407217026, 0.011737445369362831, -0.06895963102579117, -0.02363155223429203, 0.0150160426273942, -0.015096363611519337, 0.000900288054253906, 0.03431558609008789, 0.047008950263261795, 0.004300287924706936, 0.050118155777454376, 0.060750268399715424, 0.002135594841092825, -0.024073250591754913, 0.08668269217014313, 0.03517184406518936, 0.01294498611241579, -0.0015310632297769189, 0.05805428698658943, 0.011922050267457962, 0.0006915308767929673, 0.00326857203617692, -0.0037546269595623016, 0.004091326147317886, -0.006591601297259331, -0.0200387854129076, -0.029220670461654663, -0.06026703119277954, -0.0028255970682948828, -0.031026428565382957, -0.005981133785098791, 0.007923251017928123, 0.03256978839635849, 0.003704749047756195, 0.02583717741072178, -0.009892702102661133, -0.11159626394510269, -0.02655925042927265, 0.011924823746085167, 0.03802253305912018, 0.03771790862083435, 0.0037695541977882385, 0.03659650683403015, -0.0568232387304306, 0.004341413266956806, 0.06946711987257004, 0.033059023320674896, -0.0659187063574791, 0.11844894289970398, 0.032231416553258896, -0.08245768398046494, -0.0008439451921731234, -0.07251386344432831, 0.07077942788600922, -0.02215571142733097, 0.040785450488328934, -0.060677457600831985, -0.004666643682867289, -0.024086354300379753, 0.05364084243774414, 0.034891288727521896, -0.028251219540834427, -0.014310411177575588, 0.012859436683356762, -0.057051483541727066, -0.0507953055202961, -0.00626828009262681, -0.027005337178707123, -0.056442540138959885, -0.0276859849691391, -0.01298034843057394, -0.019771212711930275, 0.08871098607778549, 0.013192237354815006, 0.013343251310288906, 0.07404392957687378, 0.05915209650993347, 0.005201477557420731, -0.03076286055147648, 0.039273519068956375, 0.02438790164887905, 0.02973957732319832, 0.0357237309217453, 0.013383938930928707, 0.03934655338525772, -0.007776676677167416, 0.00862392783164978, 0.022384028881788254, -0.006691372953355312, 0.042409732937812805, -0.04641587287187576, -0.006356825586408377, 0.021312739700078964, 0.028489068150520325, 0.06929755955934525, 0.003734634956344962, -0.03939992934465408, 0.05586837977170944, 0.020195556804537773, -0.05487186461687088, -0.002940627746284008, 0.03391958028078079, 0.006728637497872114, -0.029746994376182556, -0.03832371532917023, 0.012273665517568588, 0.002282818080857396, 0.055096518248319626, -0.01401450950652361, -0.011304832063615322, 0.01648143120110035, -0.006816002540290356, -0.015812790021300316, -0.03775518015027046, -0.011337952688336372, 0.03446308150887489, 0.09093141555786133, 0.002996566239744425, 0.038477666676044464, -0.010315476916730404, -0.048564065247774124, 0.04783882200717926, 0.017425518482923508, -0.11065743118524551, -0.02266426384449005, -0.12273213267326355, -0.07787913829088211, 0.004882979206740856, 0.002722442150115967, 0.07770725339651108, -0.018512489274144173, 0.05467069894075394, -0.02544725313782692, 0.0037780834827572107, -0.008954113349318504, 0.030542049556970596, -0.03175805136561394, 0.027783190831542015, -0.051956936717033386, -0.06464624404907227, -0.010095758363604546, -0.030680865049362183, 0.00791470892727375, 0.041967201977968216, -0.05466218292713165, 0.030498651787638664, 0.032055292278528214, -0.01989826373755932, -0.04117487370967865, 0.0676361694931984, 0.006386248394846916, -0.024546047672629356, -0.04489139840006828, 0.020845776423811913, -0.02958124876022339, 0.02025912143290043, 0.0066952770575881, -0.023391781374812126, -0.009514943696558475, -0.0006182669894769788, -0.022639159113168716, 0.029435647651553154, 0.006684299558401108, 0.02986360713839531, -0.01996137760579586, -0.030507301911711693, 0.022284355014562607, -0.008295468054711819, 0.028576871380209923, -0.01740189455449581, -0.03541038930416107, 0.019829068332910538, 0.05432909354567528, 0.034553300589323044, 0.03616964444518089, -0.0052770813927054405, -0.04463619738817215, -0.010384163819253445, 0.030065681785345078, -0.05769139155745506, -0.035130493342876434, 0.009131195023655891, 0.006501107942312956, 0.002338073682039976, 0.011853786185383797, 0.0288484375923872, -0.10434312373399734, 0.0009249627473764122, -0.020180488005280495, 0.004308713600039482, 0.04032321274280548, 0.023441554978489876, 0.012914898805320263, 0.03609592095017433, 0.0498650036752224, 0.011363989673554897, 0.0011310003465041518, -0.03585241362452507, -0.02700193226337433, 0.019462209194898605, 0.0007983368122950196, -0.04047394171357155, 0.06272756308317184, 0.03347014635801315, 0.03926045820116997, 0.03977429121732712, -0.009612089022994041, 0.008795233443379402, -0.02432418055832386, -0.040065947920084, -0.03455989062786102, -0.07351471483707428, 0.045018989592790604, 0.0314331129193306, -0.080388642847538, -0.057757534086704254, 0.0024825981818139553, -0.04135175421833992, 0.0015222136862576008, -0.08490963280200958, -0.0036755488254129887, -0.014686532318592072, 0.005338182207196951, 0.04122054576873779, 0.03144953027367592, -0.01624896563589573, -0.03027435764670372, 0.036862563341856, -0.0008670606766827404, 0.01582174375653267, -0.027184918522834778, 0.027559753507375717, -0.03196094185113907, -0.05926865339279175, 0.008945700712502003, 0.006380071397870779, 0.01599757932126522, -0.007080609444528818, -0.060701169073581696, -0.010646512731909752, 0.06969214230775833, -0.06163281947374344, 0.03487415611743927, -0.010954250581562519, 0.01468526292592287, -0.025666797533631325, -0.06662875413894653, 0.06932578980922699, 0.02795753814280033, 0.020792674273252487, 0.011011755093932152, 0.0039334590546786785, 0.016399459913372993, 0.03183620050549507, 0.031233662739396095, 0.018672600388526917, -0.03300292417407036, 0.005597088951617479, 0.006383343134075403, 0.01272527314722538, 0.06614512205123901, 0.020566212013363838, 0.0003179766936227679, -0.044430240988731384, -0.02351786382496357, 0.004171972628682852, 0.06848344206809998, -0.003700433997437358, -0.09509848058223724, -0.031042469665408134, 0.015774276107549667, 0.01199845876544714, -0.04791654273867607, 0.04644877463579178, -0.0705878734588623, -0.007256695069372654, -0.002635616809129715, 0.04417293146252632, -0.04778416454792023, -0.028383713215589523, 0.01372161228209734, -0.011842718347907066, -0.029158739373087883, 0.06273619085550308, -0.015810834243893623, -0.0011487333104014397, 0.015177884139120579, -0.0009485497139394283, 0.03822971507906914, -0.015939027070999146, 0.06490998715162277, -0.060707736760377884, -0.08146321028470993, 0.036977823823690414, 0.02567751333117485, -0.01720055565237999, 0.027731286361813545, 0.01306513138115406, -0.0803031399846077, 0.015316846780478954, 0.030736494809389114, -0.03248040750622749, 0.013054757378995419, 0.035517673939466476, 0.010741066187620163, -0.046967122703790665, 0.02721415087580681, -0.005900072865188122, 0.01698712818324566, 0.004253020975738764, -0.005751033313572407, 0.006687850225716829, 0.0008417830686084926, 0.01013856753706932, 0.01950637251138687, -0.032808106392621994, 0.017163828015327454, 0.012596101500093937, -0.01885233074426651, -0.010395805351436138, -0.007460855878889561, -0.013932906091213226, -0.03447350487112999, 0.05199669674038887, 0.03886939957737923, 0.017937753349542618, 0.0016592867905274034, 0.0008069819305092096, -0.03993939608335495, 0.004807270597666502, 0.04827765002846718, -0.06604144722223282, 0.057348527014255524, 0.0403905063867569, -0.046445250511169434, 0.0018271729350090027, 0.03396355360746384, 0.030686572194099426, 0.02191360853612423, -0.022075194865465164, 0.06637762486934662, 0.03282177075743675, 0.015850195661187172, -0.010921405628323555, -0.056378621608018875, -0.07911483943462372, 0.04815637320280075, -0.012758319266140461, -0.054199304431676865, -0.06390600651502609, 0.07944843918085098, -0.0047002569772303104, 0.040488798171281815, -0.018583860248327255, 0.013116111978888512, -0.04301948472857475, 0.0067986855283379555, -0.057290852069854736, 0.035169925540685654, -0.03582342341542244, -0.03352552279829979, 0.04521654546260834, 0.0039042141288518906, 0.01666480489075184, 0.03329326584935188, 0.0326288565993309, -0.011211664415895939, -0.01867133192718029, -0.013768281787633896, -0.05667021870613098, 0.036906685680150986, -0.03450121358036995, 0.015770014375448227, 0.02952868863940239, 0.05399465560913086, 0.007500678300857544, 0.020421234890818596, 0.04020656272768974, 0.0025412514805793762, -0.05111386254429817, -0.015854407101869583, 0.0618528388440609, 0.014964350499212742, -0.003336925758048892, -0.042086586356163025, -0.06092129275202751, -0.01159670576453209, 0.032097943127155304, 0.0077208601869642735, -0.001098242006264627, -0.04858504608273506, 0.03301137313246727, 0.005247036926448345, 0.08090934157371521, -0.02119147963821888, 0.0029054072219878435, 0.016615573316812515, 0.0029698896687477827, -0.010727167129516602, -0.025468692183494568, 0.044255588203668594, 0.007490689866244793, 0.01408910471946001, 0.022856412455439568, 0.0024528580252081156, 0.04015569016337395, 0.009074755944311619, 0.060311924666166306, 0.001765499240718782, -0.03455657884478569, 0.004568549804389477, 0.00408112071454525, 0.01850477047264576, 0.009784150868654251, -0.04985965043306351, 0.01066270936280489, -0.01905672810971737, -0.002505786716938019, 0.027083924040198326, 0.016191815957427025, 0.03688076138496399, 0.03755558654665947, -0.10660264641046524, 0.009620750322937965, -0.08508419990539551, -0.010011105798184872, 0.017888547852635384, 0.0021182915661484003, 0.005967444274574518, 0.010823703370988369, 0.033403705805540085, 0.03451799973845482, -0.06496351212263107, -0.003142094472423196, 0.015042751096189022, -0.030324194580316544, -0.06126037985086441, -0.020237091928720474, -0.0011433347826823592, -0.017136501148343086, -0.018646929413080215, 0.010698545724153519, -0.03682217001914978, -0.04354009032249451, 0.004318809136748314, -0.016613449901342392, -0.00023254142433870584, -0.016150936484336853, 0.019611289724707603, 0.019216902554035187, 0.018820585682988167, 0.01610030047595501, 0.033254873007535934, -0.024834467098116875, 0.01003503892570734, -0.06752892583608627, -0.0973205715417862, 0.006851600483059883, 0.024326933547854424, -0.02219739370048046, -0.020460007712244987, 0.08069872111082077, 0.0016246344894170761, -0.018162347376346588, -0.006478885654360056, -0.0025043999776244164, 0.013674316927790642, 0.02374175377190113, 0.013704019598662853, 0.05429491773247719, -0.003024619771167636, -0.019323982298374176, 0.050383638590574265, -0.0030797896906733513, -0.03387204930186272, -0.0572168231010437, -0.01025012880563736, 0.01663105934858322, 0.04124775528907776, -0.03660507872700691, 0.018145577982068062, -0.003367417259141803, -0.031001130118966103, -0.053340110927820206, 0.025366539135575294, -0.012926502153277397, 0.021102413535118103, 0.048484690487384796, 0.03116828016936779, -0.03705604746937752, -0.055238936096429825, -0.03655491769313812, 0.003188148606568575, -0.034160349518060684, 0.05017556995153427, 0.0008437193464487791, -0.0473591610789299, -0.010376800782978535, 0.015274845995008945, 0.057536885142326355, -0.007252142298966646, 0.013202064670622349, -0.029721448197960854, -0.02218875102698803, 0.024728087708353996, -0.013505914248526096, -0.004835066851228476, 0.039434611797332764, 0.0105822142213583, -0.006835821084678173, 0.003339325310662389, 0.0612749345600605, -0.041324373334646225, 0.017713073641061783, -0.04145907983183861, -0.027714166790246964, 0.06641491502523422, 0.049645356833934784, 0.012513112276792526, 0.019954094663262367, -0.03219910338521004, -0.029412444680929184, 0.03690258786082268, 0.015265743248164654, 0.0009509476949460804, 0.012913194485008717, 0.04676312208175659, -0.030009286478161812, 0.0026193447411060333, 0.0009455420076847076, 0.019429661333560944, -0.013390514068305492, 0.002500655362382531, -0.014854087494313717, -0.04037142172455788, -0.03372254595160484, -0.02345072664320469, 0.028391823172569275, 0.017297836020588875, -0.041877325624227524, -0.005125942174345255, 0.0503830648958683, -0.010413981042802334, 0.04480873420834541, 0.035355035215616226, -0.04324666038155556, -0.019099988043308258, -0.017878009006381035, -0.029030902311205864, -0.009708603844046593, -0.06444203108549118, 0.00243325624614954, -0.0009190900600515306, 0.044554293155670166, -0.0039026872254908085, 0.024107737466692924, 0.013371133245527744, -0.05030195787549019, 0.06943463534116745, -0.04161721467971802, 0.007519691251218319, 0.07452016323804855, -0.028954854235053062, 0.03317555785179138, 0.040951136499643326, -0.031115490943193436, -0.053580593317747116, 0.010516930371522903, 0.00462182704359293, 0.020412953570485115, -0.003209116403013468, -0.005315643735229969, -0.058378465473651886, -0.05455382540822029, -0.0424506850540638, 0.01610671356320381, 0.0448523573577404, 0.011951334774494171, -0.01856989413499832, -0.0017175241373479366, 0.022572891786694527, 0.055630989372730255, -0.017876094207167625, -0.024231456220149994, 0.04058747738599777, 0.08929727971553802, -0.02780788764357567, -0.020683392882347107, -0.0033338237553834915, 0.00879437942057848, 0.04710888862609863, 0.01056872308254242, -0.027297263965010643, 0.03697042912244797, 0.023607289418578148, 0.0024104840122163296, 0.04828183725476265, 0.06594420224428177, 0.051158733665943146, -0.03900709003210068, -0.009451836347579956, -0.034772615879774094, 0.04071963578462601, -0.054483816027641296, -0.030978603288531303, -0.01293807104229927, 0.0006871129735372961, 0.010872552171349525, 0.007457051891833544, -0.04564019292593002, -0.004843690898269415, -0.014698761515319347, 0.01350860483944416, -0.01044368464499712, 0.0012848643818870187, -0.04287603124976158, -0.05365835875272751, -0.012800034135580063, -0.05559414625167847, 0.026920627802610397, -0.0004526988777797669, -0.0014744368381798267, -0.006077101919800043, -0.0722384825348854, -0.04095255583524704, -0.011690150946378708, 0.0018333662301301956, -0.010382319800555706, -0.06285817921161652, -0.03619809076189995, -0.021894924342632294, 0.016187753528356552, 0.010792276822030544, 0.06255500018596649, 0.0034706061705946922, 0.03819996118545532, -0.00269073317758739, -0.00006968405068619177, 0.0456966757774353, -0.016482606530189514, -0.05854829400777817, 0.05606798082590103, 0.004628067370504141, -0.024573221802711487, 0.007815022021532059, -0.06916653364896774, -0.007699056528508663, 0.02959277480840683, 0.018782155588269234, -0.049861419945955276, 0.022790424525737762, -0.006390622351318598, 0.018771804869174957, 0.029739519581198692, -0.043435074388980865, -0.039677944034338, -0.001080256188288331, 0.006559460423886776, 0.03913039341568947, -0.0010899018961936235, 0.034575220197439194, -0.026204146444797516, -0.025168851017951965, 0.010344360023736954, 0.01050925999879837, 0.0031910163816064596, -0.019568422809243202, 0.04009605199098587, -0.015500216744840145, -0.021913863718509674, -0.01635921001434326, -0.028879785910248756, -0.08615510910749435, 0.014696446247398853, 0.049395374953746796, -0.011545001529157162, 0.01324829924851656, -0.06419957429170609, -0.004410519730299711, -0.062203556299209595, -0.015001567080616951, -0.020061364397406578, 0.0706680417060852, -0.00741136260330677, 0.010268761776387691, 0.015354973264038563, 0.06330959498882294, 0.005415069870650768, -0.0328659825026989, 0.05466434359550476, -0.000569011433981359, 0.0400942862033844, 0.02859802544116974, 0.028545308858156204, -0.020039066672325134, -0.005033835768699646, 0.03506685793399811, -0.026111656799912453, 0.010881993919610977, -0.0004074155876878649, 0.005434298887848854, -0.017986612394452095, -0.008964292705059052, -0.020508108660578728, 0.017727836966514587, -0.06410103291273117, 0.009384725242853165, 0.019294219091534615, -0.04604509845376015, 0.03394337370991707, 0.021671630442142487, -0.008534679189324379, 0.024084193632006645, -0.016605878248810768, 0.053018730133771896, 0.013498988002538681, 0.043253883719444275, 0.007875751703977585, -0.02824142575263977, 0.011525878682732582, -0.02858012542128563, -0.014448345638811588, -0.06347932666540146, 0.030363233759999275 ]
<p>In a common wood fire such as a campfire, is matter converted to energy or is it simply an exothermic chemical reaction and all the mass can be accounted for in the ash and soot?</p>
g8341
[ 0.06507246196269989, -0.019464408978819847, 0.00957055576145649, -0.036770258098840714, 0.005248061381280422, -0.027557486668229103, -0.02666395530104637, 0.07569871097803116, -0.007665990851819515, -0.03209485486149788, -0.014585432596504688, -0.04437806084752083, 0.03820696845650673, 0.043544698506593704, -0.006182203534990549, 0.00046099332394078374, 0.06545288860797882, -0.01786280795931816, -0.00045265108929015696, 0.0697145164012909, -0.0630287155508995, -0.04207397997379303, -0.03435744345188141, -0.02282879129052162, -0.03655024990439415, -0.03253175690770149, -0.03355494141578674, -0.017902733758091927, 0.005935813300311565, -0.00024506953195668757, 0.005196342710405588, 0.025618089362978935, -0.019189994782209396, 0.013816886581480503, -0.027791030704975128, -0.009862278588116169, -0.03345360979437828, -0.05081910640001297, 0.05206065624952316, 0.006405871361494064, -0.039614204317331314, 0.03427456319332123, -0.00524380337446928, 0.03231462463736534, -0.04326384514570236, 0.004827745258808136, -0.021249616518616676, -0.02336207404732704, -0.03402222320437431, 0.015235384926199913, -0.01809760183095932, -0.011339589953422546, 0.020755859091877937, 0.04009545221924782, 0.009075586684048176, 0.04054197296500206, 0.007905109785497189, -0.0402151495218277, 0.050493065267801285, 0.038685448467731476, -0.02739178203046322, 0.022958878427743912, 0.000799759232904762, -0.05428074300289154, 0.02557031251490116, 0.03210025280714035, -0.0466662235558033, 0.01691536232829094, 0.09683308005332947, -0.0005557224503718317, 0.029323536902666092, 0.037619899958372116, -0.029863616451621056, 0.027241770178079605, -0.04579721763730049, -0.017498092725872993, 0.01765325665473938, 0.04528620094060898, -0.051525332033634186, 0.03373875841498375, -0.06782186031341553, -0.011338330805301666, 0.044104982167482376, -0.04583726450800896, 0.01991480030119419, -0.031402722001075745, -0.04682493209838867, 0.006848631426692009, -0.0000519409695698414, 0.032035943120718, -0.0008876921492628753, 0.05864282697439194, 0.1210395097732544, 0.013355798088014126, -0.024950489401817322, 0.025033792480826378, 0.003171069547533989, 0.00649816170334816, -0.05373610183596611, 0.0061249081045389175, -0.047247886657714844, -0.049566421657800674, 0.0078181903809309, -0.043966248631477356, 0.03427349776029587, 0.005211804527789354, -0.05446536839008331, -0.02447294443845749, -0.09194806963205338, 0.0556778758764267, 0.03596513718366623, -0.003973312675952911, -0.07068376243114471, 0.022921865805983543, -0.02939261496067047, -0.00826201867312193, 0.04042550548911095, 0.011209101416170597, 0.050431881099939346, 0.038524385541677475, -0.0032735371496528387, 0.004013575613498688, -0.01796776056289673, 0.0004002965579275042, -0.03802884742617607, -0.012678596191108227, 0.02250981330871582, -0.019437916576862335, -0.03942747414112091, -0.011678977869451046, -0.03828660771250725, -0.027584480121731758, 0.0382121317088604, -0.003333086147904396, 0.07541860640048981, -0.045723263174295425, -0.0026200346183031797, 0.016445856541395187, -0.019125627353787422, -0.0036284911911934614, 0.0054234713315963745, 0.05024183169007301, -0.0007441905327141285, -0.014870508573949337, -0.051578670740127563, 0.06332053989171982, -0.03553236648440361, 0.07446736842393875, 0.02590370923280716, 0.05741278827190399, 0.018165290355682373, -0.017257483676075935, 0.03563546761870384, -0.012404409237205982, 0.07655874639749527, -0.017815973609685898, -0.02921242266893387, -0.032179538160562515, 0.01758257858455181, -0.03494851663708687, 0.06316100060939789, -0.023662636056542397, -0.008655824698507786, 0.021548818796873093, -0.07244676351547241, -0.015529227443039417, 0.025042276829481125, 0.0028646807186305523, 0.02252868376672268, -0.01753281243145466, -0.034787144511938095, 0.007065439131110907, -0.005916828755289316, 0.07857213914394379, -0.03498375043272972, -0.0013049773406237364, 0.07191598415374756, 0.03431195393204689, -0.02405925840139389, -0.057451460510492325, 0.014256437309086323, 0.04014968499541283, 0.0012697398196905851, -0.03740596026182175, 0.03319152072072029, -0.013570157811045647, 0.0030184113420546055, -0.014370488002896309, -0.012333904393017292, 0.011830827221274376, -0.038486137986183167, -0.06951577961444855, -0.01206045038998127, 0.015396010130643845, 0.07320193946361542, 0.029020486399531364, -0.026834914460778236, 0.0033321247901767492, -0.020824149250984192, -0.08634475618600845, 0.00639710295945406, 0.058692384511232376, -0.02564581297338009, -0.009150620549917221, 0.0889672189950943, 0.03833891078829765, 0.0032525290735065937, -0.0008527825702913105, -0.00917150266468525, -0.06580118834972382, -0.014679063111543655, 0.04777015000581741, -0.024847766384482384, 0.0027248268015682697, -0.03741142526268959, 0.02688509039580822, -0.0817517414689064, -0.018412917852401733, 0.0026154923252761364, -0.06462366878986359, 0.000584418245125562, 0.01444200985133648, 0.027005257084965706, -0.008736451156437397, -0.0026276211719959974, 0.007076537702232599, -0.007899636402726173, -0.031613051891326904, 0.02007671631872654, -0.015067334286868572, -0.004105500411242247, 0.02309432439506054, 0.012395240366458893, -0.030926508828997612, 0.017967771738767624, 0.06524638831615448, 0.002716484246775508, -0.027986522763967514, 0.03267884626984596, -0.037737324833869934, -0.015627499669790268, -0.03554815426468849, -0.016191817820072174, 0.01137594785541296, 0.041327349841594696, -0.057011742144823074, 0.012939025647938251, -0.017600206658244133, -0.018123850226402283, 0.009681682102382183, 0.005998621229082346, 0.06516694277524948, 0.012258750386536121, -0.014304319396615028, -0.036854088306427, 0.004054942633956671, -0.02729387953877449, 0.03018318861722946, -0.013460814021527767, -0.0023563525173813105, 0.027160651981830597, -0.02887117676436901, -0.059628453105688095, -0.0071935770101845264, -0.0070112887769937515, -0.05746486783027649, -0.04110478237271309, -0.07117681205272675, -0.05932950973510742, -0.03231208398938179, -0.04547882825136185, -0.00236506131477654, 0.033531755208969116, 0.0005132753867655993, -0.010957740247249603, -0.0008300489280372858, 0.0005466680158860981, -0.044231291860342026, 0.043250713497400284, -0.07807189971208572, -0.004290353506803513, 0.07449299842119217, -0.04121480509638786, 0.0808151513338089, -0.014380564913153648, 0.019358457997441292, -0.03257250413298607, 0.016838695853948593, 0.012491931207478046, -0.04229794442653656, 0.004402266815304756, -0.032444581389427185, 0.016989000141620636, 0.021785395219922066, -0.0024036988615989685, 0.03342331573367119, 0.10337753593921661, -0.039166003465652466, 0.03962570056319237, 0.029541585594415665, -0.041094932705163956, -0.041058801114559174, -0.006070725154131651, -0.031220663338899612, 0.00811433419585228, 0.08103034645318985, 0.016104798763990402, -0.0386023074388504, 0.0492652989923954, -0.048571839928627014, -0.03858655318617821, -0.02174329198896885, 0.014346037991344929, 0.04420237988233566, -0.07434060424566269, 0.007377891335636377, -0.02942488342523575, -0.02761503867805004, 0.04917561262845993, -0.02546698972582817, -0.05997077003121376, -0.017352702096104622, 0.0034815247636288404, -0.041665662080049515, -0.008137855678796768, -0.019368421286344528, 0.029210997745394707, -0.04342658072710037, -0.047567375004291534, -0.05552015081048012, -0.05344625934958458, -0.0073983254842460155, -0.06980668753385544, -0.0006488616927526891, -0.052787840366363525, 0.008432051166892052, -0.04023761302232742, -0.02355724200606346, 0.030312882736325264, 0.06243240460753441, 0.041770149022340775, 0.0028656460344791412, -0.06457942724227905, 0.014388523995876312, 0.010222900658845901, -0.018042346462607384, -0.037354566156864166, -0.021427636966109276, 0.00972319208085537, -0.03204423561692238, -0.0024494503159075975, -0.023124895989894867, 0.010528108105063438, 0.024406030774116516, -0.024905862286686897, 0.03529544919729233, -0.007890935055911541, 0.03224484995007515, -0.036554235965013504, 0.06828393042087555, 0.012929171323776245, -0.05860890820622444, 0.04239257797598839, -0.005790246184915304, 0.008662477135658264, -0.013644488528370857, -0.01449232455343008, -0.02912958711385727, 0.004224815405905247, -0.018868058919906616, 0.0510304756462574, 0.004425684921443462, -0.04185705631971359, 0.006153027527034283, 0.07170040160417557, 0.03177458420395851, 0.09218011796474457, 0.061029642820358276, -0.03079686313867569, -0.012532215565443039, 0.027544695883989334, -0.030786840245127678, -0.008067002519965172, 0.015444881282746792, -0.039196595549583435, 0.005259934812784195, -0.04693741723895073, 0.07196498662233353, 0.020366860553622246, 0.02005017176270485, -0.015533166006207466, -0.05284447968006134, -0.0337766669690609, -0.012323894537985325, -0.015102129429578781, -0.043178558349609375, 0.028705496340990067, -0.03505651280283928, 0.034415680915117264, 0.06661209464073181, -0.0009862182196229696, 0.050612933933734894, -0.0005868631415069103, -0.0624438151717186, 0.044350333511829376, 0.105852872133255, 0.037403881549835205, -0.050685226917266846, -0.006755675654858351, -0.04314101114869118, 0.05881960690021515, 0.018956469371914864, -0.008740123361349106, 0.008006373420357704, 0.02790035679936409, -0.06381813436746597, 0.06052320823073387, 0.04375632852315903, 0.016711965203285217, -0.007534963544458151, -0.01107640378177166, -0.0037540846969932318, -0.04041537642478943, 0.002389440080150962, 0.022428683936595917, 0.022769583389163017, 0.04601206257939339, 0.019484445452690125, 0.008089237846434116, 0.013089590705931187, 0.048260707408189774, -0.04839365556836128, 0.031652096658945084, -0.02664477564394474, -0.06884115934371948, 0.04038593918085098, -0.010408570058643818, 0.010243627242743969, 0.005909498315304518, 0.08308421075344086, 0.06600207090377808, 0.05151878669857979, 0.018609875813126564, -0.0038756029680371284, 0.005380498711019754, -0.006190050393342972, 0.007607887964695692, -0.035978808999061584, -0.029827231541275978, -0.08397594839334488, 0.006662184372544289, 0.012047956697642803, -0.05645710602402687, -0.05686274543404579, -0.0024944322649389505, 0.012289074249565601, -0.019400712102651596, 0.05435684695839882, -0.004594413563609123, 0.0905381590127945, -0.07057875394821167, -0.051954448223114014, 0.022259153425693512, 0.042509570717811584, -0.00721664447337389, 0.016636651009321213, -0.06692767143249512, -0.013940347358584404, 0.0307331383228302, 0.0817885473370552, 0.04779936373233795, -0.035239219665527344, -0.030774515122175217, -0.009002335369586945, 0.018216583877801895, -0.012862872332334518, -0.00042938312981277704, -0.024554269388318062, 0.0242305975407362, -0.0021227507386356592, 0.0005361502408050001, 0.050848305225372314, 0.009107856079936028, 0.000982934609055519, 0.041073013097047806, 0.024148983880877495, -0.0016694734804332256, 0.0323331281542778, -0.009903425350785255, -0.005041303113102913, 0.005228481255471706, 0.07198334485292435, -0.027426963672041893, -0.016154984012246132, 0.01783316396176815, 0.0338258296251297, -0.017752861604094505, -0.07176866382360458, -0.034042004495859146, -0.004411168862134218, 0.018053021281957626, -0.05160780996084213, 0.00758021604269743, 0.04158274829387665, 0.038081277161836624, 0.06083624064922333, 0.008061040192842484, -0.02946401573717594, -0.04377558082342148, 0.012579205445945263, 0.013026535511016846, -0.000794499006588012, -0.07223568111658096, 0.04200537130236626, 0.029372060671448708, -0.01783919148147106, -0.0015804710565134883, 0.044137753546237946, 0.027974393218755722, 0.0007005163352005184, -0.011075418442487717, -0.008723987266421318, 0.01624028943479061, 0.02513379417359829, -0.04524460807442665, 0.02309037558734417, -0.04254640266299248, -0.030576840043067932, 0.003767231944948435, 0.08914704620838165, 0.004460836295038462, -0.004765513818711042, -0.0036135066766291857, 0.017614692449569702, 0.004545596893876791, -0.00921196211129427, -0.07251746207475662, 0.04930708557367325, 0.01235185842961073, 0.05420105159282684, -0.0032761029433459044, -0.034773122519254684, 0.012039861641824245, 0.02781083434820175, 0.06659678369760513, 0.015667427331209183, 0.004073635209351778, -0.005638346076011658, 0.004134084563702345, -0.008173242211341858, -0.005625753663480282, 0.05992099642753601, 0.07969238609075546, -0.08043619990348816, 0.0009725046693347394, 0.0278801117092371, -0.032270222902297974, -0.02842784859240055, 0.010430125519633293, -0.03425279259681702, -0.03577171266078949, 0.048903025686740875, 0.02668275125324726, -0.007643059827387333, 0.07355593889951706, -0.023485830053687096, -0.01584707945585251, -0.06923697888851166, 0.004206499084830284, -0.046090297400951385, -0.008109411224722862, -0.007781248074024916, 0.029741838574409485, 0.010816320776939392, 0.002779061673209071, -0.008877629414200783, -0.028750130906701088, -0.007659214083105326, 0.010323611088097095, 0.009470561519265175, 0.042363010346889496, -0.05265252664685249, -0.01540242787450552, -0.0026925860438495874, -0.0019679595716297626, -0.05311955139040947, 0.019214266911149025, -0.025555556640028954, 0.00543870497494936, 0.028055164963006973, -0.02614259347319603, 0.06632062047719955, -0.04485821723937988, 0.0516175851225853, -0.01154885720461607, -0.020488154143095016, 0.0030773670878261328, -0.01816367730498314, 0.03245024010539055, 0.0007249981281347573, 0.00019986400729976594, 0.0644131749868393, -0.009056733921170235, -0.08394038677215576, 0.05078825727105141, -0.0015333166811615229, -0.006539614871144295, 0.027000373229384422, 0.03380371630191803, -0.008451972156763077, 0.00207402091473341, -0.04050981253385544, 0.013315343298017979, -0.0032979967072606087, -0.04719228297472, -0.009446854703128338, -0.03755006939172745, 0.008818745613098145, 0.0013265341985970736, -0.004738855175673962, 0.015492912381887436, 0.006388191133737564, 0.0574764646589756, -0.03081895038485527, 0.03125593811273575, 0.058936186134815216, -0.04774142801761627, 0.10590273141860962, 0.05764422193169594, -0.010224205441772938, -0.05381867662072182, 0.07881597429513931, -0.020630693063139915, -0.015712285414338112, -0.0054250736720860004, 0.004249859601259232, -0.010451601818203926, -0.006188420578837395, -0.023961398750543594, 0.01076007541269064, 0.019803745672106743, -0.02841351181268692, -0.021558115258812904, 0.030995173379778862, -0.0561232715845108, -0.03766212984919548, 0.043664831668138504, -0.05344843491911888, -0.037249792367219925, -0.050349634140729904, -0.047403484582901, -0.03131150081753731, -0.04086120426654816, 0.03712594136595726, -0.009761256165802479, 0.03146722912788391, -0.00462325057014823, 0.03254466876387596, 0.03372638672590256, 0.009355458430945873, -0.004469732288271189, -0.012246732600033283, 0.06473459303379059, -0.005291867069900036, 0.017972182482481003, 0.036795929074287415, 0.06107953563332558, 0.0080265486612916, -0.005763140507042408, -0.03788160905241966, 0.0210508331656456, -0.025211237370967865, -0.018925698474049568, -0.02557186782360077, -0.03396597132086754, -0.010422920808196068, 0.013757173903286457, 0.02607983537018299, 0.035868365317583084, -0.058147165924310684, 0.0367724783718586, 0.031161416321992874, 0.013527155853807926, 0.06474196910858154, 0.008879791013896465, 0.002647732850164175, -0.01150688249617815, 0.04641309380531311, 0.013742080889642239, 0.009298416785895824, -0.04598401486873627, 0.0139571288600564, 0.052473749965429306, -0.01902870088815689, -0.010228833183646202, -0.018527278676629066, 0.03722658008337021, -0.01056766603142023, 0.029404273256659508, -0.0439181886613369, 0.028018832206726074, 0.023989468812942505, -0.04176152125000954, 0.004081449005752802, -0.028348585590720177, 0.019961675629019737, -0.02293737605214119, 0.027142537757754326, -0.015465864911675453, -0.028206780552864075, 0.020697519183158875, 0.06017031893134117, -0.0006871421937830746, 0.004601754248142242, 0.06322582066059113, 0.004482373595237732, -0.02793332003057003, -0.01584266684949398, -0.00045359303476288915, 0.02372535690665245, 0.0004924267996102571, 0.018210990354418755, -0.07239250838756561, 0.01374854613095522, 0.07253163307905197, -0.002990562003105879, -0.027762427926063538, -0.05901720002293587, 0.03307430073618889, 0.006105608306825161, -0.00023853675520513207, 0.02149958163499832, 0.025981096550822258, 0.011046348139643669, 0.05145050957798958, -0.046032343059778214, 0.04708201810717583, -0.02687864936888218, -0.016943898051977158, 0.027361024171113968, -0.0062388284131884575, 0.030548827722668648, -0.01616223156452179, 0.0004385645152069628, -0.01717730611562729, -0.054100602865219116, -0.02316603995859623, 0.01853017322719097, -0.02374199405312538, -0.008267047815024853, 0.029185162857174873, -0.009064610116183758, -0.03021019883453846, -0.00707233976572752, 0.009532356634736061, -0.005560681689530611, -0.013473882339894772, 0.00238425238057971, -0.014401264488697052, 0.011965216137468815, -0.05731832608580589, 0.038388531655073166, -0.00830668956041336, -0.044669825583696365, 0.03286848962306976, -0.04209715500473976, 0.01226577814668417, 0.01838846132159233 ]
<p>Consider the following example:</p> <blockquote> <p><em>A bullet of mass 45g is fired at a speed of 220 m/s into a 5.0 kg sandbag hanging from a string from the ceiling. The sandbag absorbs the bullet and begins to swing. To what maximum vertical height will it rise? (Assuming negligent air resistance and heat loss due to friction)</em></p> </blockquote> <p>The way to solve this would be to calculate the kinetic energy of the bullet and then convert it to gravitational potential energy of the bullet + sandbag.</p> <p>$$E_{k} = \frac12 * 0.045\,{\rm kg} * (220\,{\rm m/s})^2=1089\,{\rm J}$$</p> <p>We could then find the gravitational potential energy here by substituting in $E_{p} = E_{k}$.</p> <p>But, what I'm curious about here is, what would be the speed immediately after the bullet impacts the sandbag? Either the kinetic energy, or the momentum could be conserved, but not both.</p> <p>$$P = 0.045\,{\rm kg} * 220 \,{\rm m/s} = 9.9 \,{\rm kg} \cdot \,{\rm m/s}$$</p> <p>Then we find the speed after the collision of the sandbag + bullet to be:</p> <p>$$9.9 \,{\rm kg} \cdot \,{\rm m/s} = 5.0\,{\rm kg} + 0.045\,{\rm kg} * X \,{\rm m/s}\to 1.96234 \,{\rm m/s} = X$$</p> <p>So if momentum is conserved then the kinetic energy would be:</p> <p>$$E_{k} = \frac12(5.0\,{\rm kg} + 0.045\,{\rm kg}) * (1.96324 \,{\rm m/s})^2=9.72\,{\rm J}$$</p> <p>Should this question specifically state whether momentum or energy was conserved? How can you tell which one will be conserved?</p>
g8342
[ 0.13335731625556946, -0.015859246253967285, 0.024244409054517746, 0.051802605390548706, 0.024477440863847733, 0.026828918606042862, 0.03773913159966469, 0.027887362986803055, -0.08771573007106781, 0.031048117205500603, -0.011333678849041462, -0.007733926177024841, 0.0040595256723463535, 0.019108949229121208, 0.022638196125626564, -0.03635192662477493, 0.09227573126554489, -0.006192866247147322, 0.02371508814394474, 0.0521341934800148, -0.0627349466085434, -0.028574824333190918, -0.015836885198950768, -0.03459709882736206, -0.02143239974975586, -0.0033707383554428816, 0.016910072416067123, 0.013531659729778767, -0.0764460414648056, 0.0038543485570698977, -0.005523292347788811, 0.030207578092813492, 0.008515615016222, -0.09143117070198059, -0.06454886496067047, 0.011712579987943172, 0.05839265137910843, -0.0335368849337101, 0.01265567634254694, 0.0009606678504496813, 0.04125877469778061, -0.05779256671667099, 0.00360751966945827, 0.003847224870696664, 0.00936031248420477, 0.021986499428749084, -0.018201828002929688, -0.02812541462481022, 0.002718389965593815, -0.013381331227719784, -0.022014126181602478, 0.06875248998403549, -0.0015245197573676705, 0.012496963143348694, 0.00683864951133728, 0.017125457525253296, 0.04824256896972656, -0.02319207228720188, -0.021133102476596832, 0.04502711072564125, -0.002389681525528431, -0.04108276218175888, -0.033604785799980164, -0.03763953223824501, 0.05411792919039726, -0.0614866241812706, -0.050168249756097794, 0.004356982186436653, 0.021988721564412117, -0.025157682597637177, 0.038387320935726166, 0.023325037211179733, -0.01809423789381981, -0.02190914936363697, -0.04179133102297783, -0.017602302134037018, 0.03775707632303238, 0.0014279360184445977, -0.007582766469568014, 0.024885274469852448, -0.056729935109615326, 0.0753074362874031, 0.048542432487010956, -0.0050699529238045216, 0.012164928019046783, -0.010140158236026764, -0.04458880424499512, 0.03687753528356552, -0.05633395165205002, 0.01886727288365364, 0.024264907464385033, -0.04952000454068184, 0.06875143200159073, 0.01264591421931982, -0.009748836047947407, 0.03145240247249603, -0.03263420611619949, 0.08621373027563095, 0.03662527725100517, -0.057768624275922775, 0.03753463551402092, -0.06458638608455658, -0.013623676262795925, 0.002544674789533019, -0.0007223946158774197, -0.00723942881450057, 0.024616682901978493, 0.013375815004110336, 0.0055188946425914764, -0.0487714484333992, 0.03963160887360573, -0.06472164392471313, -0.040580589324235916, -0.0495050847530365, -0.05925174802541733, -0.07614736258983612, 0.04007558152079582, 0.005031269509345293, -0.0188343096524477, 0.056263841688632965, 0.014432564377784729, 0.02895396761596203, 0.0025703422725200653, -0.008851374499499798, 0.015480085276067257, -0.011734341271221638, -0.018629511818289757, -0.015508068725466728, -0.006107795983552933, 0.005115229170769453, -0.018683917820453644, -0.025551654398441315, 0.07398694008588791, 0.03584609925746918, -0.015382166020572186, 0.016221053898334503, -0.00513153662905097, 0.08742256462574005, -0.023161273449659348, -0.012693616561591625, 0.01940511167049408, -0.030448244884610176, 0.04247337207198143, 0.0054804133251309395, -0.044244084507226944, 0.008864148519933224, -0.03348087891936302, 0.0348619781434536, 0.03188431262969971, 0.0019863825291395187, 0.0019245457369834185, 0.0467614009976387, -0.025342337787151337, -0.04745542258024216, 0.06868651509284973, 0.010772603563964367, 0.04870222136378288, 0.006084668915718794, 0.02055557258427143, 0.08455333858728409, 0.06678509712219238, -0.021480251103639603, 0.02634098194539547, -0.014101028442382812, -0.021030660718679428, 0.0022781752049922943, 0.024263547733426094, -0.055631645023822784, -0.02339860238134861, -0.03246714919805527, -0.050551775842905045, -0.04709510877728462, 0.013719812966883183, 0.026608778163790703, -0.03659846633672714, 0.019934814423322678, 0.04041542112827301, -0.07503259181976318, -0.04842124134302139, 0.008877367712557316, 0.0538635291159153, -0.01943240687251091, 0.07743523269891739, -0.010452905669808388, 0.024180874228477478, 0.029812712222337723, 0.062035512179136276, 0.05636414885520935, -0.02549058385193348, -0.04449867829680443, 0.006602495908737183, 0.008521206676959991, -0.05050092935562134, -0.030237287282943726, -0.05430825427174568, 0.03763657435774803, 0.041695285588502884, -0.008304941467940807, -0.060648683458566666, 0.022586720064282417, -0.03853074461221695, 0.06289075314998627, 0.025531332939863205, 0.03431977331638336, 0.026308689266443253, 0.027765527367591858, 0.012206640094518661, 0.015477401204407215, -0.004378181416541338, -0.0372154675424099, -0.028509538620710373, -0.012010651640594006, -0.03287265822291374, 0.029767634347081184, 0.01901564747095108, 0.025907576084136963, 0.018333232030272484, 0.09832582622766495, -0.051915254443883896, -0.008491729386150837, -0.04420106112957001, 0.019106021150946617, 0.00067382981069386, 0.0026431852020323277, -0.05505111441016197, -0.026846863329410553, -0.038490310311317444, -0.030519066378474236, -0.004654766526073217, 0.036285292357206345, -0.028016110882163048, 0.0410410612821579, -0.029895983636379242, -0.02842314913868904, 0.044085659086704254, 0.055084843188524246, 0.03364374488592148, -0.00340054533444345, 0.027075013145804405, -0.018644709140062332, 0.07019509375095367, -0.039708174765110016, 0.029357830062508583, -0.0003404364688321948, 0.05103735998272896, 0.002470501931384206, 0.02812073566019535, -0.010695081204175949, 0.004390910267829895, 0.012394120916724205, 0.009428206831216812, -0.00473645469173789, -0.057420969009399414, -0.004249011166393757, 0.025346048176288605, -0.015585741959512234, -0.024660874158143997, -0.035455625504255295, -0.08108730614185333, -0.057081688195466995, 0.009667295962572098, -0.037440620362758636, -0.05249052122235298, 0.026053624227643013, -0.0399746298789978, -0.04692275449633598, -0.023933175951242447, -0.0401340089738369, 0.015476190485060215, 0.005641992669552565, -0.02054036781191826, 0.0515044666826725, -0.0292582456022501, 0.025949055328965187, 0.029737289994955063, -0.05548436567187309, 0.023504363372921944, -0.03947416692972183, -0.0010948803974315524, -0.007139585912227631, -0.015672069042921066, 0.006803045980632305, -0.0455096960067749, 0.013118360191583633, 0.007395347114652395, -0.06437184661626816, -0.01519912201911211, 0.045833270996809006, 0.025315212085843086, -0.033970896154642105, -0.0536542609333992, 0.07415658980607986, 0.07738754153251648, 0.05949411168694496, -0.01257235649973154, 0.10468707233667374, 0.040092483162879944, -0.026965100318193436, -0.021867014467716217, -0.018505601212382317, -0.00022037397138774395, -0.03455525264143944, 0.004759141709655523, 0.048126012086868286, 0.02116159163415432, 0.016157664358615875, -0.05118399113416672, -0.027570899575948715, 0.024470362812280655, 0.0032314450945705175, -0.06909516453742981, 0.08333103358745575, -0.0010247546015307307, 0.0017412888118997216, -0.10059463977813721, -0.04191754758358002, 0.020421694964170456, -0.04039936512708664, -0.009192713536322117, -0.013905731029808521, -0.029819659888744354, -0.0262020081281662, 0.004467297345399857, 0.009818678721785545, -0.03483395278453827, 0.045112669467926025, -0.05336480587720871, 0.04614328593015671, -0.004405539948493242, -0.022483523935079575, -0.033496417105197906, 0.05520601198077202, 0.0338166207075119, -0.02816542610526085, 0.01261973101645708, -0.03606823831796646, -0.0031863374169915915, -0.02655603550374508, 0.0763336792588234, 0.024423498660326004, 0.006068012211471796, 0.04129170998930931, 0.008222769014537334, -0.012408391572535038, 0.0006435351679101586, 0.041290394961833954, 0.044977396726608276, -0.001918633934110403, -0.026165267452597618, -0.03701484575867653, 0.031207159161567688, -0.03029051423072815, -0.016277046874165535, 0.0041273715905845165, -0.025956502184271812, 0.0983310118317604, -0.036967743188142776, 0.07697965204715729, -0.034892886877059937, 0.02831096388399601, 0.023774953559041023, -0.005152174271643162, 0.007677079178392887, -0.008523437194526196, 0.008298737928271294, -0.0005517950630746782, -0.03701811283826828, -0.03283168002963066, -0.013872063718736172, 0.001959004206582904, 0.01783590391278267, 0.020345592871308327, -0.05596855282783508, 0.03869364783167839, 0.048572663217782974, 0.009569194167852402, 0.05415799841284752, -0.00473358016461134, -0.042560040950775146, -0.008301389403641224, 0.03725149482488632, -0.05651182308793068, -0.03388812392950058, 0.00809523556381464, 0.008823876269161701, 0.03940169885754585, -0.01766960322856903, 0.03417672589421272, 0.0822906345129013, -0.023386606946587563, 0.0023082857951521873, -0.018695611506700516, -0.02961127832531929, -0.014115950092673302, 0.015260457992553711, 0.0505201555788517, 0.04859121888875961, -0.011977319605648518, -0.012141061946749687, 0.017751071602106094, -0.0018368733581155539, 0.07183043658733368, -0.05713319033384323, -0.028562624007463455, 0.012667360715568066, 0.015180819667875767, 0.031918931752443314, -0.031669650226831436, -0.011875485070049763, -0.0010397646110504866, 0.05556657910346985, -0.030168447643518448, -0.03405226394534111, -0.013459204696118832, -0.04598787799477577, 0.006468115374445915, -0.03160373121500015, 0.054753709584474564, 0.027659401297569275, -0.03386913612484932, 0.04238038510084152, 0.030502621084451675, 0.005670709535479546, -0.037713561207056046, -0.005640351679176092, 0.05689381808042526, 0.07349713146686554, 0.013991515152156353, 0.012549669481813908, -0.01218758150935173, 0.026525652036070824, 0.013373643159866333, -0.004618458915501833, 0.011105411686003208, -0.0949738621711731, 0.05024411156773567, 0.017591292038559914, -0.020923228934407234, 0.028680428862571716, 0.049649130553007126, 0.06255543231964111, 0.04103272408246994, -0.016860106959939003, -0.030522551387548447, 0.003467258997261524, 0.0698779821395874, -0.017277082428336143, -0.030262958258390427, -0.006737883202731609, -0.03998364880681038, -0.04542328417301178, 0.007169504649937153, -0.0021974726114422083, 0.00047181115951389074, -0.018368979915976524, 0.021193478256464005, -0.07321283221244812, -0.025492912158370018, 0.019252927973866463, 0.025869371369481087, -0.040345434099435806, 0.012028070166707039, 0.02348668873310089, -0.016869526356458664, -0.007891434244811535, -0.04928695037961006, -0.011179921217262745, 0.029332583770155907, -0.00015812829951755702, -0.027765309438109398, 0.02895672246813774, -0.026851054280996323, -0.030542751774191856, 0.0236442219465971, -0.007428978104144335, 0.00937647745013237, -0.009432419203221798, 0.02722519263625145, 0.08805059641599655, -0.05714628845453262, -0.05319223552942276, 0.004196221008896828, -0.02834990806877613, 0.004360940307378769, 0.0519118532538414, 0.009712779894471169, -0.07136692106723785, -0.005938831716775894, 0.012132036499679089, -0.018127132207155228, 0.0359836146235466, 0.04651498794555664, -0.04957878589630127, -0.013108481653034687, 0.02092696726322174, -0.03462769463658333, 0.03320230171084404, -0.003459348576143384, 0.011786218732595444, -0.011592080816626549, -0.04840535297989845, -0.0403352826833725, 0.002354553434997797, 0.00677217124029994, -0.004210935439914465, 0.04495493322610855, 0.05007638782262802, 0.01986740157008171, -0.018199795857071877, 0.023982658982276917, -0.043534450232982635, 0.035985421389341354, 0.0071100196801126, -0.01910099759697914, -0.009900557808578014, -0.061440370976924896, 0.061456359922885895, 0.005979880224913359, -0.03301158547401428, -0.010621348395943642, 0.013799002394080162, 0.01793610118329525, 0.05919337645173073, 0.00909344106912613, 0.016557298600673676, -0.013987204059958458, -0.048914164304733276, -0.028396494686603546, -0.01570158638060093, 0.051104672253131866, 0.007798588369041681, -0.07081752270460129, -0.07617855072021484, -0.023435568436980247, -0.04697432368993759, -0.008632834069430828, -0.027394883334636688, -0.0063140857964754105, -0.016076909378170967, -0.005888023879379034, -0.06704159080982208, 0.003390370635315776, 0.055300816893577576, 0.0460815504193306, -0.009252000600099564, -0.003748473012819886, -0.0683644562959671, -0.009911398403346539, -0.008150337263941765, -0.060409240424633026, -0.018241971731185913, 0.04530613496899605, 0.004413073416799307, -0.015048758126795292, 0.0068147447891533375, 0.006611539516597986, 0.03738998621702194, -0.020290911197662354, 0.01243030559271574, -0.045241303741931915, 0.03019166924059391, 0.022916140034794807, 0.02360331453382969, 0.06118561699986458, 0.047569479793310165, -0.006001266185194254, -0.018855836242437363, -0.045056477189064026, 0.09765642136335373, 0.004958852659910917, -0.0018948152428492904, 0.011253309436142445, -0.017973683774471283, 0.018541326746344566, 0.03478430584073067, -0.034420445561409, -0.050878722220659256, -0.020700886845588684, -0.04032573848962784, -0.04995216429233551, 0.02333233691751957, -0.02083727717399597, 0.047167032957077026, -0.042781323194503784, -0.05463443323969841, 0.004775723442435265, -0.03416496887803078, -0.02788633666932583, 0.0273523461073637, 0.009422989562153816, 0.016013100743293762, 0.007072827313095331, -0.014149359427392483, 0.011194870807230473, -0.0034585639368742704, 0.030623959377408028, 0.012806873768568039, -0.01723969355225563, -0.0390891507267952, 0.030246317386627197, 0.04031713306903839, -0.031125899404287338, 0.007836497388780117, -0.03435075283050537, 0.03501109778881073, -0.0007792747346684337, -0.005620147567242384, 0.03743557631969452, -0.015090993605554104, -0.048438917845487595, -0.025683436542749405, 0.01149960421025753, 0.03106226958334446, 0.02354268729686737, -0.057007912546396255, 0.0016180631937459111, 0.03907649591565132, -0.005149435251951218, -0.0374159961938858, 0.00203451095148921, -0.006565934978425503, 0.011002490296959877, 0.030786260962486267, -0.07196297496557236, 0.04025352746248245, -0.02527214214205742, -0.04812142997980118, 0.0542101189494133, 0.06519899517297745, -0.0018022030126303434, 0.0031477969605475664, 0.017924459651112556, 0.01765751652419567, 0.030274970456957817, 0.027765830978751183, 0.05418452247977257, 0.0041253757663071156, 0.04109004884958267, -0.024905862286686897, 0.007567899767309427, 0.021715017035603523, 0.014112677425146103, 0.05367368087172508, 0.04968801513314247, -0.019352667033672333, -0.006769742351025343, 0.017830854281783104, -0.0013147112913429737, -0.004166866187006235, -0.05731634795665741, -0.059335898607969284, -0.01241297833621502, -0.04910185933113098, 0.015353557653725147, 0.009755297563970089, 0.0216120183467865, -0.004326079972088337, 0.05840978026390076, 0.048238229006528854, -0.051056429743766785, 0.00855394545942545, -0.08864866942167282, 0.01625482738018036, -0.06861153244972229, -0.06674379110336304, 0.030976638197898865, 0.02506837621331215, -0.06259999424219131, 0.03242478519678116, -0.009277630597352982, 0.008510221727192402, -0.05465370789170265, -0.06240608170628548, 0.010890302248299122, -0.02291909232735634, -0.0076393005438148975, 0.01674400269985199, -0.015323621220886707, -0.0475456677377224, -0.004812793806195259, 0.002394961193203926, 0.03278200328350067, -0.03766556829214096, -0.021440809592604637, 0.011498356238007545, 0.04994909465312958, -0.008721970021724701, 0.0055700973607599735, 0.02629215270280838, 0.012639163993299007, -0.024179184809327126, 0.0663631334900856, 0.07350827753543854, 0.0019476051675155759, -0.00450112484395504, -0.03637036681175232, 0.011834140866994858, 0.002063699997961521, -0.014259575866162777, 0.011041104793548584, -0.010176561772823334, 0.030774788931012154, 0.07084383815526962, 0.021662699058651924, -0.022869523614645004, 0.013712047599256039, -0.028025692328810692, -0.032341331243515015, -0.05244887247681618, 0.010308722965419292, -0.0025615738704800606, 0.011504050344228745, 0.022124268114566803, 0.01460275799036026, -0.016072025522589684, -0.013717330060899258, -0.030021093785762787, -0.022188078612089157, 0.011208758689463139, -0.026179810985922813, 0.014817793853580952, -0.0053178658708930016, -0.009007847867906094, -0.08226420730352402, -0.009454932063817978, -0.011220286600291729, -0.027712807059288025, -0.013324103318154812, -0.022045116871595383, -0.0013467122334986925, -0.008221977390348911, -0.02760300599038601, 0.00029765060753561556, -0.030851125717163086, 0.034802548587322235, 0.006756308022886515, 0.012198841199278831, -0.026599416509270668, 0.01205576304346323, 0.048128798604011536, -0.01722477190196514, -0.02844148501753807, 0.004193552769720554, 0.04020728915929794, -0.03143094852566719, -0.038536448031663895, 0.006262939888983965, 0.041075270622968674, 0.06238569691777229, 0.006755610927939415, 0.059649478644132614, 0.005207359790802002, 0.005103347357362509, 0.07161872088909149, -0.017494499683380127, -0.042979732155799866, -0.013708643615245819, -0.013950924389064312, -0.033405378460884094, -0.025845730677247047, -0.015595505014061928, 0.004234112333506346, -0.01836787723004818, -0.05691194906830788, 0.034599944949150085, -0.07151544839143753, 0.021969346329569817, 0.011746191419661045 ]
<p>The abstract Weyl Algebra $W_n$ is the *-algebra generated by a family of elements $U(u),V(v)$ with $u,v\in\mathbb{R}^n$ such that (Weyl relations) $$U(u)V(v)=V(v)U(u)e^{i u\cdot v}\ \ Commutation\ Relations$$ $$U(u+u')=U(u)U(u'),\qquad V(v+v')=V(v)V(v')$$ $$U(u)^*=U(-u),\qquad V(v)^*=V(-v)$$ It is a well known fact (Stone- von Neumann theorem) that all irreducible representations $\pi:W_n\rightarrow B(H)$ of this algebra such that $$s-\lim_{u\rightarrow 0}\pi(U(u))=U(0),\qquad s-\lim_{v\rightarrow 0}\pi(V(v))=V(0)$$ are unitary equivalent to the Schroedinger one: $$H\equiv L^2(\mathbb{R}^n)$$ $$\pi(U(u))\equiv e^{i\overline{u\cdot X}},\qquad \pi(V(v))\equiv e^{i\overline{v\cdot P}}$$ where $X,P$ are the usual position and momentum operators defined (and essentially self-adjoint) on the Schwartz space $S(\mathbb{R}^n)$. For this reason, this algebra is usually associated to the quantization of a spinless non relativistic particle in $\mathbb{R}^n$. But what happen if one considers a spinless particle confined in a subregion $K\subset\mathbb{R}^n$, for example a circle $S^1\subset\mathbb{R}^2$, a sphere $S^2\subset\mathbb{R}^n$ or a generic open subset? The state space could still be chosen as $L^2(K)$, but what about the associated Weyl Algebra? I think it can still be defined abstractly but, while the commutation relations must be conserved in some way, the parameters domain $(u,v)$ cannot still be taken as $\mathbb{R}^n\times\mathbb{R}^n$ otherwise we fall in the previous context.</p> <p>Is there some prescription for such a general situation? To be more precise: Given a bosonic particle confined in a sub region K, is it possibile to associate a family of abstract elements $U(u),V(v)$, $u,v$ belonging for example to some additive groups, such that the above Weyl properties are satisfied? </p>
g8343
[ -0.007047492545098066, -0.061632152646780014, -0.020719407126307487, -0.019003525376319885, 0.0342869758605957, -0.02107313647866249, 0.07592684030532837, 0.01261475682258606, 0.010343313217163086, 0.029939595609903336, -0.04697905108332634, 0.0992942601442337, -0.03529603034257889, 0.03809694945812225, -0.026385007426142693, 0.005600898526608944, 0.02842172607779503, 0.02403155528008938, 0.003756718710064888, -0.04768352955579758, -0.06029803305864334, 0.03201467543840408, -0.003206065855920315, 0.01478504203259945, -0.011285767890512943, -0.013352243229746819, 0.13450102508068085, -0.06430229544639587, -0.010285288095474243, 0.011884195730090141, 0.085667684674263, -0.025884145870804787, 0.04984202980995178, -0.07053735852241516, -0.010584093630313873, -0.06964784115552902, 0.049317866563797, 0.06240410357713699, 0.016587067395448685, -0.030518697574734688, 0.07084935158491135, -0.013566390611231327, 0.006855635903775692, -0.032141249626874924, -0.012368770316243172, -0.00015688360144849867, -0.013001884333789349, -0.01122395507991314, -0.004075611475855112, -0.01100931502878666, -0.05730309709906578, 0.021304819732904434, 0.0013574117328971624, 0.004112675320357084, 0.07916267216205597, -0.01545677613466978, -0.01708311215043068, -0.009358109906315804, 0.027299165725708008, 0.0721905454993248, 0.0034846311900764704, -0.007770170457661152, 0.02113904245197773, 0.046963442116975784, 0.05912911519408226, 0.028621867299079895, -0.02817258983850479, 0.027766847983002663, -0.04138300195336342, -0.013691478408873081, 0.03489144891500473, -0.03217070922255516, 0.03211183845996857, -0.004378350917249918, 0.020729104056954384, 0.0013465018710121512, -0.003978468477725983, 0.0279579758644104, 0.035968732088804245, 0.01805543154478073, -0.0892004445195198, 0.009448112919926643, 0.0022679029498249292, -0.02098701149225235, 0.02306484431028366, 0.0005094508524052799, 0.004670364782214165, -0.001311986125074327, -0.025996537879109383, -0.010499238967895508, 0.012942647561430931, -0.0696016326546669, 0.0715513750910759, 0.03214866295456886, 0.015559133142232895, 0.027562174946069717, -0.008907148614525795, 0.06359821557998657, -0.05107826739549637, -0.051474880427122116, -0.030682455748319626, 0.015294044278562069, 0.0287774745374918, -0.01500471867620945, 0.012939016334712505, 0.03588303551077843, 0.0320916585624218, -0.016356557607650757, 0.014244847930967808, 0.04972817003726959, -0.023044081404805183, -0.019870037212967873, -0.0006535729044117033, 0.01898817904293537, -0.07952733337879181, -0.00778992660343647, 0.028402311727404594, -0.02885878086090088, 0.039440494030714035, 0.047559015452861786, 0.031315963715314865, 0.036339107900857925, -0.005820728372782469, 0.01065006386488676, -0.007869591936469078, 0.016661694273352623, -0.015432476997375488, -0.006320348475128412, 0.04198300465941429, -0.034496430307626724, 0.006413101684302092, -0.07057922333478928, -0.007507080677896738, 0.10556831955909729, -0.0107494555413723, -0.04062496870756149, -0.02130209282040596, -0.006351816933602095, 0.02940870262682438, -0.007019014563411474, -0.051176976412534714, 0.05867619067430496, -0.042367398738861084, -0.04191485419869423, -0.025961941108107567, -0.0012647364055737853, 0.06760647892951965, -0.05899481102824211, -0.015552031807601452, 0.05799061432480812, -0.028789376839995384, 0.04915051534771919, -0.03856087476015091, -0.03268290311098099, 0.0029885072726756334, -0.03303267061710358, 0.03681648522615433, 0.0322171188890934, 0.050667159259319305, -0.007101302966475487, 0.02701806277036667, 0.03194238990545273, 0.07847780734300613, 0.006206032820045948, -0.033198896795511246, -0.039195481687784195, -0.014693456701934338, -0.05098378658294678, 0.018714889883995056, -0.04246341064572334, 0.019722305238246918, -0.010219356045126915, -0.02920268289744854, 0.06552208214998245, 0.04423215240240097, 0.024523092433810234, 0.0006531760445795953, -0.026980368420481682, 0.040227677673101425, 0.07049862295389175, -0.027414018288254738, -0.012796706520020962, 0.0435246117413044, -0.02134362980723381, 0.010715666227042675, 0.06323894113302231, -0.0401507243514061, 0.02895105630159378, -0.009983113966882229, -0.004173867870122194, -0.000994272530078888, 0.01930571347475052, 0.04570053890347481, -0.0005069297039881349, -0.01764439046382904, 0.03395051881670952, 0.010060329921543598, -0.03504897654056549, -0.0655316635966301, 0.0013381876051425934, 0.0361708365380764, 0.07524800300598145, 0.032555945217609406, -0.04894335940480232, 0.03808135166764259, -0.005863402970135212, 0.012053481303155422, 0.011989623308181763, 0.045759107917547226, -0.0012125461362302303, 0.07202828675508499, -0.010885796509683132, -0.025382591411471367, -0.0016099672066047788, -0.02609074115753174, -0.046782247722148895, 0.04308965802192688, -0.022564800456166267, 0.030465135350823402, 0.008459582924842834, -0.04901757836341858, -0.028539326041936874, 0.0619472898542881, -0.00855815690010786, 0.008661530911922455, 0.029869871214032173, -0.010000413283705711, -0.00013263730215840042, -0.00031410439987666905, 0.024799806997179985, -0.015619318000972271, -0.059902310371398926, 0.0432140976190567, -0.06031346321105957, -0.02093498781323433, 0.048538532108068466, -0.004296659026294947, 0.042142804712057114, 0.033913563936948776, 0.008721563033759594, 0.02157730795443058, -0.016008643433451653, -0.04253830760717392, 0.016943445429205894, 0.04892102628946304, -0.024303773418068886, 0.04872174188494682, -0.016258150339126587, -0.0013170019956305623, 0.043693460524082184, -0.043058063834905624, -0.07838907837867737, 0.011112545616924763, -0.06591832637786865, 0.00019303830049466342, 0.04945380613207817, 0.006595537066459656, -0.015451882965862751, 0.01994895562529564, -0.01611071266233921, -0.016241468489170074, -0.01572352834045887, -0.01937994919717312, 0.010806692764163017, -0.0004372235562186688, 0.00415857695043087, -0.00372027768753469, 0.043547622859478, 0.0392768457531929, -0.001506781904026866, -0.03534739464521408, 0.030841484665870667, 0.012144168838858604, 0.02121776156127453, -0.0053973873145878315, -0.0014037200016900897, -0.035662662237882614, 0.01955839991569519, -0.04623757302761078, 0.01703844964504242, -0.0041270204819738865, 0.047382764518260956, -0.010254031047224998, 0.026931311935186386, -0.007794615346938372, -0.06615205109119415, -0.025546107441186905, 0.032107703387737274, 0.022487236186861992, -0.03316938132047653, 0.015001446940004826, 0.03937980905175209, 0.03184656426310539, 0.06776060909032822, 0.037334803491830826, 0.02776440978050232, -0.034768231213092804, 0.005401131696999073, 0.03129363805055618, 0.10036573559045792, -0.03196004405617714, -0.024949293583631516, 0.028853630647063255, -0.023668257519602776, 0.018138106912374496, 0.01002182625234127, -0.05393947288393974, -0.06598734110593796, -0.04818575084209442, -0.01626848429441452, -0.0690891221165657, 0.019113725051283836, -0.017486095428466797, -0.0332975760102272, -0.012012505903840065, -0.01032629981637001, 0.005544660612940788, -0.03191414847970009, -0.006948512978851795, -0.025174427777528763, -0.027833234518766403, 0.0172104649245739, 0.07705561071634293, 0.01639828272163868, 0.04189261049032211, 0.06967282295227051, -0.060948289930820465, 0.04127223417162895, -0.028446080163121223, -0.026648320257663727, 0.01135562825948, -0.03729496896266937, 0.1032525822520256, 0.018811160698533058, -0.12807375192642212, -0.0388929583132267, -0.07317297160625458, -0.05411391705274582, 0.02475854754447937, -0.06660821288824081, -0.025924181565642357, -0.033022359013557434, 0.038450464606285095, 0.03253505378961563, -0.050549961626529694, 0.027891818434000015, -0.006144486367702484, -0.03649260103702545, 0.01786077208817005, 0.006485993042588234, -0.006811812985688448, 0.008534032851457596, 0.046623848378658295, 0.00010772253153845668, 0.024332335218787193, -0.025468258187174797, 0.03638096898794174, 0.04294857010245323, -0.023732028901576996, -0.04711400717496872, -0.02795621007680893, -0.026106758043169975, 0.002332981675863266, -0.02706790529191494, -0.02653871476650238, -0.04640548303723335, 0.04359273239970207, -0.07206622511148453, 0.01367671974003315, 0.04245838522911072, 0.008040020242333412, -0.02502661757171154, -0.06289993226528168, -0.016961006447672844, -0.0708104819059372, -0.051606435328722, 0.01669042557477951, -0.011213796213269234, -0.050452880561351776, -0.030233846977353096, 0.021783096715807915, 0.03005925565958023, 0.025161853060126305, 0.03327120095491409, -0.011132333427667618, 0.02618105337023735, -0.005723371170461178, 0.04343986511230469, -0.041222598403692245, 0.019148431718349457, 0.009095186367630959, 0.004145392682403326, 0.00758992088958621, -0.020115356892347336, 0.04499233141541481, 0.0026825338136404753, 0.03736786171793938, -0.03331417962908745, -0.02308807335793972, 0.00974801741540432, -0.049702949821949005, -0.030931850895285606, -0.014495816081762314, -0.012290296144783497, 0.025849798694252968, 0.03937237709760666, -0.0033972731325775385, -0.017580363899469376, 0.009184565395116806, -0.01704377681016922, 0.0032240324653685093, 0.004087226465344429, -0.010487549006938934, -0.03169798478484154, 0.01395046804100275, -0.04113603010773659, -0.03990505263209343, -0.02657921612262726, -0.0643153265118599, 0.025478091090917587, -0.0009116941946558654, -0.018473492935299873, 0.04288419336080551, -0.005264888051897287, 0.008800780400633812, -0.04826918616890907, -0.04427143186330795, -0.016816113144159317, 0.021828100085258484, 0.007057914976030588, 0.04614735394716263, 0.0015859196428209543, 0.009983668103814125, 0.010646982118487358, -0.07308697700500488, 0.001925310934893787, -0.08555150032043457, 0.035650093108415604, -0.01926836557686329, 0.047306790947914124, 0.049622777849435806, -0.024681411683559418, -0.01606827601790428, -0.016347890719771385, -0.0007503792876377702, 0.05001721531152725, -0.0210479237139225, 0.038102660328149796, 0.03743389621376991, -0.01789098046720028, -0.014237450435757637, 0.037454426288604736, 0.04625608026981354, -0.04319501295685768, 0.018427232280373573, -0.04671873152256012, -0.014086159877479076, -0.027788423001766205, 0.03613889589905739, -0.008370739407837391, -0.03629444167017937, -0.005188864190131426, -0.0268804170191288, 0.014746609143912792, 0.02068755030632019, -0.0042090448550879955, -0.1073499470949173, 0.043211933225393295, -0.05541203171014786, -0.0395769402384758, 0.056194767355918884, 0.019276190549135208, 0.06422591209411621, -0.02687453292310238, -0.0033635185100138187, 0.03771847486495972, -0.031389378011226654, 0.005109936930239201, -0.04722699522972107, -0.0511741004884243, 0.03525440767407417, 0.03310224786400795, -0.011914429254829884, 0.03430115059018135, 0.006242556497454643, 0.05931568145751953, -0.00766797224059701, -0.009060950018465519, -0.0010089274728670716, 0.010967516340315342, -0.005741340108215809, 0.010292819701135159, -0.019662121310830116, 0.04575127735733986, 0.03502024710178375, -0.036959122866392136, -0.030592110008001328, -0.05408370867371559, 0.005980907008051872, 0.042367395013570786, 0.00309938145801425, 0.05080883949995041, 0.07167059928178787, 0.03438109531998634, -0.011747393757104874, -0.008319389075040817, 0.05327814444899559, 0.01563362218439579, -0.009339590556919575, 0.005359287839382887, 0.013321883045136929, 0.028199443593621254, 0.02918967790901661, 0.0010444236686453223, 0.003942187875509262, 0.020433688536286354, -0.051254164427518845, -0.012209182605147362, -0.04989474639296532, 0.0028956460300832987, -0.028205610811710358, 0.0011866020504385233, 0.01989031210541725, -0.0029562998097389936, 0.005843709222972393, 0.041094787418842316, -0.03313412144780159, -0.046769265085458755, -0.05075128376483917, 0.0894230380654335, 0.020366154611110687, -0.04524766281247139, 0.02610141597688198, -0.006542491260915995, 0.03975745663046837, -0.09020793437957764, -0.016572168096899986, 0.01730457693338394, 0.06320495903491974, 0.016599483788013458, -0.025224551558494568, -0.08451153337955475, -0.004336288198828697, 0.004219369497150183, 0.009997841902077198, 0.03568331152200699, -0.0489884577691555, 0.06227754428982735, -0.020244410261511803, -0.044129833579063416, -0.024534478783607483, -0.029559031128883362, 0.014514983631670475, -0.015536237508058548, -0.008924979716539383, -0.023221151903271675, 0.009175517596304417, -0.011713443323969841, 0.02078365348279476, 0.012686685658991337, -0.03320370987057686, 0.04045076668262482, -0.01706233248114586, 0.035024672746658325, 0.016340438276529312, 0.03674095869064331, 0.035313136875629425, -0.014926683157682419, 0.03470490500330925, 0.03992340713739395, -0.04041232541203499, 0.003321608994156122, -0.017054572701454163, -0.020723294466733932, 0.02141622267663479, 0.00696474127471447, -0.01916445791721344, -0.01197430957108736, -0.04851314797997475, 0.016960231587290764, -0.004887210670858622, -0.00228246976621449, 0.002819281769916415, -0.11046285927295685, 0.008578323759138584, 0.03022325597703457, -0.0020250107627362013, 0.0013361773453652859, 0.04500765725970268, 0.036231864243745804, 0.030147654935717583, 0.05926567688584328, -0.05945828557014465, 0.030162768438458443, -0.026833103969693184, 0.03931881859898567, 0.06215668097138405, -0.014385882765054703, -0.056692060083150864, -0.019319623708724976, 0.045455314218997955, -0.01542809046804905, 0.04392596334218979, 0.021353889256715775, 0.00015928849461488426, 0.0634118989109993, -0.07678218930959702, -0.048580411821603775, 0.023584334179759026, -0.0030900759156793356, 0.021896617487072945, 0.009604675695300102, 0.02883831597864628, 0.014135169796645641, -0.0001556245842948556, -0.033402156084775925, 0.02649679034948349, -0.019119199365377426, -0.006651824340224266, -0.046927861869335175, -0.01059657335281372, 0.03659242019057274, 0.005744161084294319, -0.003763080108910799, -0.04347126558423042, 0.03440206125378609, 0.018708737567067146, 0.005174899473786354, 0.0099165178835392, 0.06357217580080032, 0.024350730702280998, 0.016703911125659943, 0.0050556594505906105, 0.00638597970828414, -0.017505479976534843, -0.008798850700259209, -0.02989359200000763, 0.007655913941562176, 0.031378403306007385, -0.0068888249807059765, -0.035186439752578735, 0.07811592519283295, 0.004513251129537821, 0.021307069808244705, -0.056828632950782776, -0.039106469601392746, 0.029186395928263664, -0.018247295171022415, -0.04736699163913727, 0.039740484207868576, 0.04722350835800171, 0.08404185622930527, -0.06459847837686539, -0.05254093185067177, -0.06424402445554733, -0.04697776585817337, 0.015441854484379292, 0.018007464706897736, -0.024906227365136147, 0.007687125820666552, -0.049726296216249466, 0.03690056502819061, -0.018420502543449402, 0.01110976655036211, -0.02183314599096775, 0.0337180569767952, 0.015543605200946331, 0.011896485462784767, 0.0418919138610363, -0.03414947912096977, -0.04659964144229889, -0.037056609988212585, -0.05452011153101921, -0.025158466771245003, -0.03449724614620209, -0.0014200457371771336, 0.035916395485401154, 0.054602500051259995, -0.02617787942290306, 0.004161431919783354, 0.030174460262060165, 0.039197735488414764, -0.028217168524861336, 0.019020672887563705, -0.08989007025957108, -0.017258448526263237, 0.016505658626556396, 0.006954163312911987, 0.011715699918568134, -0.020561756566166878, -0.004176461603492498, 0.024015698581933975, 0.07627816498279572, -0.005033631343394518, 0.011785630136728287, -0.016902849078178406, -0.010511355474591255, 0.04416291043162346, -0.023951612412929535, 0.0126836271956563, 0.008326358161866665, -0.005310547538101673, -0.031176205724477768, 0.008708086796104908, 0.007670104503631592, 0.003372220089659095, -0.030686724931001663, -0.031182166188955307, -0.021483207121491432, -0.004658844787627459, 0.014535070396959782, 0.020742466673254967, -0.003734394209459424, 0.0058321296237409115, 0.04815226420760155, -0.012638144195079803, -0.05071795731782913, 0.02234770357608795, -0.00825410895049572, -0.030914586037397385, 0.03783183917403221, -0.04108491167426109, -0.02013367973268032, -0.011637014336884022, 0.06674779951572418, -0.07369086891412735, -0.006623502355068922, -0.019252600148320198, 0.03687944635748863, 0.032312411814928055, -0.02474455162882805, -0.025925971567630768, -0.03682743385434151, 0.049436457455158234, -0.08317307382822037, 0.0005308375111781061, 0.03138622269034386, -0.06869178265333176, 0.005863435100764036, -0.011018767021596432, -0.06259363889694214, -0.04552675783634186, -0.019283821806311607, 0.025193197652697563, -0.02003224939107895, 0.01439718995243311, -0.0033640526235103607, -0.050700072199106216, -0.02106074057519436, -0.02525675669312477, -0.0127455685287714, 0.01647878997027874, -0.0058688693679869175, 0.051438119262456894, -0.0033898022957146168, -0.05037924274802208, 0.04997831583023071, 0.0018240829231217504, 0.042445674538612366, 0.038516927510499954, -0.014050404541194439, -0.007247727829962969, -0.017214151099324226, -0.02900417521595955, 0.004847338888794184, -0.052155230194330215, -0.005210052710026503, 0.007929864339530468 ]
<p>Given a system of two particles with spin up and down, I have troubles to understand the possible states of this system.</p> <p>I would have normally thought, that the possible states are the tensor products of the states of each particle with one of the other. This would have given us the states that are listed in Wikipedia under: substituting in the four basis states. So why do we define these new states(three with total spin $1$ and one with total spin $0$) that are given by triplet and singlet representations? So maybe you don't know what I am asking so I repeat my question: What is the meaning of these triplet and singlet states, because I would have thought that the four states listed above are the possible states of a system? The reference to what I am talking about: <a href="http://en.wikipedia.org/wiki/Triplet_state" rel="nofollow">wikipedia reference</a></p>
g8344
[ -0.036790959537029266, 0.037968963384628296, -0.01737751066684723, -0.012732096947729588, 0.06033572554588318, 0.04315786063671112, 0.06410574167966843, 0.07189049571752548, 0.034246839582920074, 0.003656218061223626, -0.08366455137729645, -0.027676492929458618, 0.05643897503614426, -0.06059396639466286, -0.03849129006266594, 0.004581286571919918, 0.07573352754116058, 0.053209882229566574, 0.019584814086556435, -0.03802413120865822, -0.010762958787381649, 0.024553336203098297, -0.03498624637722969, -0.0455089770257473, -0.009933015331625938, -0.01793467439711094, -0.023664632812142372, 0.006178848445415497, -0.03942814841866493, 0.03460844233632088, 0.02709341235458851, -0.00897362269461155, -0.024398311972618103, 0.006049082614481449, 0.08879819512367249, -0.04433342069387436, 0.10625440627336502, 0.013598615303635597, -0.03875914216041565, -0.04642612859606743, -0.009999093599617481, -0.008382346481084824, -0.005520525388419628, -0.07355671375989914, -0.01115062553435564, 0.03626261278986931, 0.025429893285036087, -0.02106376178562641, -0.039006419479846954, -0.0019585033878684044, 0.02503238432109356, -0.020627453923225403, 0.06648697704076767, 0.01810717210173607, 0.051023244857788086, -0.027798661962151527, 0.02507137507200241, -0.0333198644220829, 0.07373160868883133, 0.020996807143092155, -0.05639979988336563, 0.017121855169534683, 0.01292929146438837, -0.01462122704833746, 0.06443635374307632, -0.020672719925642014, 0.0078879464417696, 0.04841316491365433, 0.017936715856194496, 0.026621365919709206, 0.0020905330311506987, 0.001053937361575663, 0.01711495779454708, -0.04404091089963913, -0.019767403602600098, 0.02058222144842148, 0.002988256048411131, -0.010853155516088009, 0.04098061844706535, 0.05159973353147507, 0.0011118175461888313, -0.03133712336421013, 0.07622891664505005, -0.003009448992088437, 0.010783473029732704, 0.03185177966952324, 0.008154010400176048, 0.0041293371468782425, -0.028228439390659332, 0.06121298298239708, -0.02392973005771637, 0.011146925389766693, 0.08646363019943237, 0.008184797130525112, -0.016901236027479172, -0.022986827418208122, -0.0435975156724453, 0.012911449186503887, 0.00419516209512949, 0.027168549597263336, -0.057700265198946, 0.015056945383548737, 0.03584247827529907, -0.08092575520277023, 0.03461647033691406, 0.05850373953580856, 0.03880323842167854, 0.01623852550983429, -0.007421987131237984, -0.03332081064581871, -0.05240675061941147, 0.07705973833799362, 0.014078760519623756, -0.0027941344305872917, -0.10372460633516312, 0.00713077187538147, 0.005112963728606701, -0.04343061149120331, 0.020534919574856758, 0.017712321132421494, 0.01568962261080742, 0.030251318588852882, -0.03511983901262283, 0.12739525735378265, -0.014583575539290905, -0.006562071852385998, -0.032531194388866425, -0.010601401329040527, 0.037792790681123734, -0.03367435559630394, -0.007823361083865166, -0.012571058236062527, -0.00799509510397911, -0.025463169440627098, -0.007970773614943027, 0.012229238636791706, 0.009882915765047073, -0.029702572152018547, 0.003752838121727109, -0.02861609496176243, -0.0021739632356911898, -0.012681068852543831, -0.04765010625123978, -0.019828414544463158, 0.002857356797903776, -0.04507381096482277, 0.01715182699263096, -0.06667305529117584, -0.02749685011804104, 0.005933605600148439, 0.07599113136529922, 0.07452938705682755, 0.007785580586642027, -0.03846174106001854, 0.06661847233772278, -0.0413195826113224, 0.05969877913594246, 0.0297361109405756, -0.006712009198963642, -0.02588167041540146, 0.06350065767765045, -0.026020625606179237, -0.004383035935461521, 0.00927524734288454, -0.06051874905824661, 0.02473263628780842, 0.008238724432885647, -0.0686110407114029, -0.01561169233173132, -0.042505163699388504, 0.006153703201562166, 0.0005998247070237994, -0.026002895087003708, 0.013430602848529816, 0.0298774316906929, 0.02291496843099594, 0.00725539168342948, -0.030449412763118744, -0.002398650860413909, -0.002867778530344367, -0.061802223324775696, 0.050198256969451904, 0.014623845927417278, 0.08204451948404312, -0.016315476968884468, 0.022329410538077354, -0.0278298482298851, 0.0012534764828160405, -0.0395597442984581, 0.03204561024904251, -0.04492443799972534, 0.038466356694698334, 0.05470696836709976, 0.00048102313303388655, 0.021470457315444946, 0.020095733925700188, 0.0370832234621048, -0.02758493833243847, -0.03845600411295891, -0.007914552465081215, -0.02751937136054039, -0.003773211734369397, -0.021765053272247314, -0.009735098108649254, -0.010159109719097614, 0.036577921360731125, 0.0071292780339717865, 0.06841722130775452, 0.03247678652405739, 0.0029029420111328363, -0.009516668505966663, -0.016055945307016373, 0.013704306446015835, 0.029512688517570496, -0.0069618127308785915, -0.028955796733498573, 0.040209200233221054, -0.01935769058763981, -0.010009938850998878, -0.01569562777876854, -0.041293345391750336, -0.05656392127275467, 0.06634318083524704, 0.013476498425006866, -0.019274132326245308, 0.038314685225486755, -0.03870321437716484, -0.02108822576701641, -0.024241823703050613, 0.07351100444793701, -0.06022511422634125, -0.028015008196234703, -0.006855088286101818, -0.05307857692241669, 0.04548892751336098, 0.07302989810705185, -0.020464260131120682, -0.04871366173028946, -0.0032519567757844925, 0.003624616889283061, 0.008077815175056458, -0.0017351980786770582, 0.01599554717540741, 0.01642228104174137, 0.04206870123744011, -0.030190490186214447, 0.002127926331013441, 0.00032743753399699926, -0.03757496550679207, 0.06314563006162643, -0.027292944490909576, -0.0360502265393734, -0.03196846321225166, 0.01554457750171423, -0.0015002035070210695, -0.01698404550552368, 0.006285039242357016, 0.013152754865586758, -0.029577700421214104, -0.01671111397445202, -0.00645774370059371, -0.04295284301042557, -0.01961716264486313, 0.03726030886173248, -0.020173942670226097, 0.023927439004182816, 0.023985406383872032, -0.04876819998025894, -0.0005650362581945956, -0.0019411540124565363, -0.038428906351327896, 0.016476105898618698, 0.03046237863600254, -0.008936192840337753, -0.0484098345041275, -0.021740013733506203, 0.01159651204943657, 0.0209643617272377, -0.027947140857577324, -0.02731575258076191, -0.07431399077177048, 0.04876958206295967, 0.01928607188165188, -0.015600750222802162, 0.014047764241695404, -0.023313535377383232, -0.018192239105701447, 0.009796740487217903, -0.028916750103235245, 0.046531494706869125, -0.006990606430917978, 0.05252790078520775, 0.07202403992414474, -0.06484592705965042, -0.05642034485936165, -0.013350307010114193, -0.03737073391675949, -0.0847267359495163, -0.03996339067816734, 0.10368598252534866, -0.0016174871707335114, 0.007277274504303932, 0.06502538919448853, -0.03156280890107155, 0.07023845613002777, -0.012023506686091423, -0.05367620661854744, 0.01593957468867302, -0.037288352847099304, 0.012521719560027122, -0.09416933357715607, 0.052685678005218506, -0.007725693751126528, -0.014338020235300064, -0.014692051336169243, 0.011418239213526249, -0.06268474459648132, 0.011596301570534706, 0.03587964549660683, -0.026960378512740135, -0.03825801983475685, -0.01057188306003809, -0.009806184098124504, -0.012434865348041058, 0.06166333332657814, 0.01522511150687933, -0.06726863980293274, -0.024919800460338593, -0.04154791682958603, -0.015366043895483017, 0.04563085362315178, -0.05549769103527069, -0.0038648811168968678, -0.0014475438510999084, -0.04273911193013191, -0.012140979990363121, -0.052515771239995956, -0.011923180893063545, 0.005521485581994057, -0.055465150624513626, 0.030950935557484627, 0.010077609680593014, -0.011066235601902008, 0.0020362113136798143, 0.009457707405090332, 0.02447165921330452, -0.05457674711942673, -0.0018766323337331414, -0.014768650755286217, -0.024336237460374832, -0.02008005790412426, 0.032846566289663315, 0.045216359198093414, 0.031124809756875038, -0.04296336695551872, -0.01945844665169716, 0.043755676597356796, 0.03324362635612488, 0.009513451717793941, 0.05191050469875336, 0.020537856966257095, -0.04362231120467186, 0.011938796378672123, 0.028857151046395302, 0.020339230075478554, 0.0327526330947876, -0.024499818682670593, 0.007298790384083986, 0.02586629055440426, 0.006185081321746111, -0.03923825919628143, -0.03936728835105896, 0.0055086081847548485, -0.001970649231225252, 0.029214266687631607, -0.030369920656085014, 0.008647856302559376, -0.02577984519302845, -0.0879315435886383, 0.02181367762386799, 0.05610505864024162, -0.014763674698770046, 0.06711756438016891, 0.027575217187404633, 0.03475089743733406, 0.05541875585913658, -0.013174919411540031, 0.013739186339080334, -0.04448553919792175, 0.04884013161063194, 0.011470332741737366, -0.04797190800309181, -0.047661639750003815, 0.012840931303799152, 0.03072383441030979, 0.015009570866823196, 0.0284934900701046, -0.057542648166418076, -0.05049699917435646, 0.039873771369457245, -0.07514000684022903, -0.0814698114991188, -0.02839667722582817, -0.07054029405117035, 0.015286282636225224, 0.023839404806494713, 0.003088106168434024, -0.012568044476211071, 0.04650413990020752, -0.00641650753095746, -0.010536608286201954, 0.07250571995973587, 0.055745404213666916, 0.01757449097931385, 0.04672073572874069, 0.03711605817079544, -0.012008540332317352, -0.050456397235393524, -0.023492643609642982, 0.025962326675653458, 0.0036991890519857407, 0.045952923595905304, 0.031243236735463142, 0.02723940834403038, 0.00755491154268384, 0.04803500324487686, -0.03502510488033295, -0.02392200008034706, -0.009982905350625515, 0.0037514737341552973, 0.04060937836766243, 0.015311128459870815, 0.01615259423851967, -0.0009677367634139955, -0.01598915457725525, 0.003727165749296546, -0.020897677168250084, -0.013485454954206944, 0.03096180595457554, 0.021538570523262024, 0.04316842555999756, -0.0065692029893398285, -0.012969904579222202, -0.006343011744320393, -0.0221331175416708, 0.01046544499695301, -0.023845016956329346, 0.0025938572362065315, 0.03812275826931, -0.07106398791074753, -0.03969426825642586, -0.019893808290362358, -0.027798831462860107, -0.046510808169841766, 0.022566672414541245, 0.008073562756180763, -0.024841610342264175, -0.017172323539853096, -0.011503658257424831, 0.04009532555937767, -0.03103850968182087, 0.021030886098742485, -0.020521672442555428, -0.01830153726041317, -0.01387566514313221, 0.030008306726813316, -0.06166906654834747, 0.07135244458913803, -0.06264171004295349, -0.05224185436964035, 0.02287951111793518, -0.03267882764339447, 0.0006555391009896994, 0.01702156476676464, 0.036854010075330734, 0.016693176701664925, 0.00252695195376873, -0.02229578047990799, 0.02534419298171997, 0.02887261100113392, 0.004552436526864767, 0.007664038334041834, 0.025073615834116936, 0.012258011847734451, 0.011331900954246521, 0.025630803778767586, 0.041917912662029266, -0.02273750863969326, -0.0012836259556934237, -0.005678355228155851, 0.03576513007283211, 0.03167947381734848, -0.015130908228456974, 0.018003666773438454, 0.0032524641137570143, -0.010069661773741245, -0.06450416892766953, -0.03553960099816322, -0.032545771449804306, 0.02500787191092968, -0.014640239998698235, 0.020733987912535667, 0.06303273141384125, 0.05620435252785683, 0.011472737416625023, 0.037427399307489395, 0.08317320793867111, -0.0539807453751564, 0.041681572794914246, -0.02436901442706585, 0.027210908010601997, 0.04911614954471588, -0.013277320191264153, -0.004041563253849745, -0.02900109253823757, -0.035754960030317307, 0.01428385078907013, 0.04351402074098587, 0.016918634995818138, -0.006577811669558287, -0.0764639601111412, -0.025426190346479416, 0.027476243674755096, -0.08451792597770691, -0.020776644349098206, 0.014284311793744564, 0.004020403604954481, 0.011618752963840961, 0.01725049875676632, 0.046418461948633194, -0.00011319536133669317, 0.027177976444363594, 0.02288617007434368, 0.02452121116220951, 0.018770625814795494, -0.0061339884996414185, -0.05404622107744217, -0.05729498341679573, 0.08933429419994354, 0.044049184769392014, -0.03391620144248009, -0.08355676382780075, -0.03192407637834549, 0.05377109721302986, -0.02663956582546234, -0.03835687413811684, -0.0037482711486518383, -0.029442470520734787, -0.01723368465900421, -0.004109625704586506, -0.02767021767795086, -0.018197234719991684, -0.00415420439094305, -0.07725764065980911, 0.032353680580854416, 0.046357810497283936, -0.000478174100862816, 0.0003591213608160615, 0.021217836067080498, 0.0115575660020113, 0.005954358261078596, 0.006370537914335728, 0.01720314845442772, 0.034146059304475784, -0.01134162675589323, 0.02777162380516529, -0.02366640605032444, 0.0036728272680193186, -0.004921036772429943, -0.027363745495676994, 0.0247233584523201, -0.018550757318735123, 0.03782069683074951, 0.043424610048532486, -0.003893230576068163, 0.022143477573990822, -0.04262803867459297, 0.010128588415682316, -0.04982393607497215, -0.012828982435166836, -0.009249714203178883, 0.011617269366979599, 0.021560946479439735, -0.016109349206089973, -0.021255705505609512, 0.03639387711882591, -0.04610877484083176, -0.040406711399555206, -0.004746903199702501, 0.018977956846356392, 0.0004899212508462369, 0.019991936162114143, -0.018009742721915245, -0.015558681450784206, -0.013003786094486713, 0.006830078549683094, -0.012645835056900978, 0.0055150664411485195, -0.026277728378772736, -0.032721251249313354, 0.03549189120531082, -0.016663143411278725, 0.00442167092114687, -0.034711532294750214, -0.002703021513298154, 0.10303220897912979, -0.03718287870287895, -0.019692327827215195, -0.019311891868710518, 0.020806824788451195, 0.028386440128087997, -0.013311082497239113, -0.05901027470827103, 0.032677363604307175, 0.01906603015959263, -0.04780605435371399, -0.01750885508954525, 0.013436590321362019, -0.035455312579870224, 0.032130640000104904, 0.026404276490211487, -0.051762159913778305, 0.029577793553471565, -0.07670608162879944, 0.0470404215157032, 0.04076479375362396, -0.0097951116040349, 0.04345115274190903, -0.025236031040549278, 0.04910657927393913, 0.044377006590366364, -0.033503465354442596, -0.0016477677272632718, 0.04232281446456909, 0.030676158145070076, -0.018126165494322777, 0.01240463461726904, -0.009731238707900047, 0.07452709972858429, 0.05848699063062668, -0.01343042217195034, 0.0010643727146089077, 0.04567349702119827, 0.013400107622146606, -0.012177511118352413, -0.008709696121513844, 0.07742653042078018, -0.031497128307819366, -0.040349893271923065, 0.002082390710711479, 0.005651748739182949, -0.01823694258928299, -0.033422816544771194, 0.002924996893852949, -0.01346852257847786, -0.030693739652633667, 0.017414597794413567, 0.017517223954200745, 0.018439149484038353, -0.028357336297631264, -0.04823257401585579, -0.03533625602722168, -0.05413380637764931, 0.025753991678357124, -0.01934296451508999, 0.05386759713292122, 0.019575979560613632, -0.00944821909070015, 0.006448686122894287, -0.06330516934394836, -0.024590982124209404, -0.03797142952680588, -0.058667588979005814, 0.04145348444581032, -0.004556430038064718, -0.01709906943142414, 0.026121927425265312, 0.05539245158433914, 0.024937277659773827, -0.04033038392663002, -0.07957933843135834, 0.014520407654345036, -0.026869801804423332, -0.009956912137567997, -0.056082334369421005, -0.024745946750044823, 0.011447139084339142, 0.07888583838939667, -0.02902599237859249, 0.02531777322292328, 0.06733808666467667, 0.02495444566011429, 0.03342453017830849, 0.011478959582746029, -0.05491697043180466, 0.03435260429978371, 0.035439327359199524, -0.010130216367542744, 0.022302694618701935, -0.06850080192089081, 0.003677950007840991, 0.029035033658146858, -0.01839086040854454, 0.0009355380898341537, -0.004537284839898348, -0.019298642873764038, 0.014766045846045017, 0.001116706756874919, 0.02996583841741085, -0.039001207798719406, -0.044512514024972916, 0.003344152122735977, -0.013223487883806229, 0.057640984654426575, -0.026369718834757805, 0.0173192135989666, -0.016201825812458992, 0.007764444686472416, -0.035698890686035156, 0.007755234371870756, -0.016801347956061363, -0.0001816814037738368, -0.0367400236427784, -0.026669416576623917, -0.014758182689547539, -0.056772127747535706, 0.05638619884848595, 0.0795813649892807, 0.021723726764321327, 0.014234481379389763, -0.01792300119996071, 0.010342316702008247, -0.0885402262210846, 0.01880529522895813, 0.004630863666534424, 0.04339117556810379, -0.03731027990579605, 0.001378254615701735, 0.002235063351690769, 0.019801456481218338, -0.028336092829704285, -0.08376996964216232, 0.03371976688504219, -0.04942389205098152, -0.05010368302464485, -0.002135815331712365, 0.01047601830214262, 0.010170449502766132, 0.02454317919909954, -0.015464107505977154, -0.014687744900584221, -0.015867240726947784, 0.024373646825551987, 0.06016506254673004, 0.0012935104314237833, 0.03143022581934929, 0.0059002842754125595, 0.041573770344257355, 0.04510156437754631, 0.03587721660733223, -0.025062253698706627, 0.03524613380432129, -0.019454455003142357, -0.01980012096464634, -0.039433449506759644, -0.013882357627153397, -0.07040566951036453, 0.06743425875902176 ]
<p>I have seen on this site some questions regarding the nature of gravitational-force, and the ways in which it could be interpreted. Most of them mention that the space-time fabric came into existence due to the big-bang. But I cannot understand why it came into existence during the big-bang, and had no earlier existence. Also, how should I develop my notion regarding the form of a gravitational-singularity? My current concept holds it that a gravitational singularity, is a compact-clump of spatial and temporal curves, where laws of Classical Physics are rarely(?) valid. But more often, I "like" to compare a garvitational-singularity with a huge go-down of energy, that is longing to burst open, and thus, decrease its entropy, as well as energy. If in-any way my current-notion is to a-certain degree acceptable, would it then be correct for me to guess that "minute"(?)-fabrics of space-time come into existence whenever there is a conversion of matter into an equivalent amount of energy, according to Einstein's equation E=m.(c^2) ?</p> <hr> <p>Please take care of the fact that I am a high-school student-with a corresponding limited-knowledge on Physics, and especially, Quantum-Mechanics.</p>
g8345
[ 0.01630065217614174, 0.0358201265335083, 0.01035568118095398, -0.06009792909026146, -0.005496967118233442, 0.08816362172365189, 0.016276530921459198, 0.018672427162528038, -0.0690937489271164, -0.03956183046102524, 0.033866532146930695, -0.03619649261236191, 0.075493223965168, -0.004407885018736124, 0.022735435515642166, -0.0556049607694149, 0.04802418500185013, -0.007290761452168226, 0.01382185984402895, 0.03823508694767952, -0.0034091563429683447, 0.024717211723327637, 0.02883877418935299, -0.019238395616412163, 0.015497193671762943, -0.0015739501686766744, 0.046434249728918076, -0.014452895149588585, 0.011164232157170773, -0.032090310007333755, 0.04299390688538551, -0.0369928814470768, 0.02428271248936653, -0.08243309706449509, 0.023729639127850533, -0.005681341048330069, -0.01130507793277502, -0.02608558163046837, -0.021766439080238342, -0.005474552977830172, -0.015227524563670158, -0.061846036463975906, 0.02306433767080307, -0.057056427001953125, 0.017370600253343582, 0.005840434227138758, -0.00045161688467487693, -0.035415440797805786, 0.08489524573087692, -0.07877062261104584, 0.01104121282696724, 0.06185273453593254, 0.058558862656354904, -0.03217543661594391, 0.011552663519978523, 0.005085587035864592, 0.07667926698923111, -0.014787672087550163, 0.07538405060768127, 0.03798456862568855, -0.021023379638791084, 0.004645009059458971, -0.002837038366124034, 0.01659277081489563, 0.025536345317959785, 0.017750008031725883, -0.010966136120259762, -0.008859916590154171, 0.02460656128823757, -0.009951655752956867, 0.023815635591745377, -0.06660470366477966, 0.015241426415741444, 0.026862386614084244, -0.003335139714181423, 0.043471094220876694, -0.02459169179201126, -0.0044355494901537895, -0.006584192160516977, -0.013228684663772583, -0.00021769058366771787, 0.03933313488960266, 0.032473091036081314, -0.006453066132962704, 0.047822754830121994, -0.041455548256635666, -0.0432194359600544, -0.056595578789711, 0.040575433522462845, 0.02674289047718048, 0.0157894529402256, 0.030419155955314636, 0.061889711767435074, -0.0004932910087518394, -0.028582487255334854, -0.04210270196199417, 0.012105581350624561, 0.11371952295303345, -0.03508955240249634, 0.03318139538168907, -0.003658674657344818, -0.05131906643509865, 0.007503783330321312, -0.03558916598558426, -0.017887771129608154, -0.027867669239640236, -0.04473395273089409, -0.005076124332845211, -0.011885019950568676, 0.002717116381973028, -0.033302612602710724, 0.03947483375668526, -0.033070869743824005, 0.045555852353572845, -0.014524435624480247, 0.04437395557761192, 0.058963313698768616, -0.000458506285212934, -0.01510542444884777, 0.054844994097948074, -0.028107892721891403, -0.0011044812854379416, -0.0048238555900752544, 0.028390437364578247, -0.06940101832151413, -0.03247818350791931, -0.004701266996562481, -0.01195583026856184, -0.01941423863172531, -0.017765143886208534, 0.0160167645663023, -0.002803302137181163, -0.0003894553810823709, -0.01966666989028454, 0.0341145396232605, 0.020029820501804352, -0.0530792735517025, -0.017821233719587326, -0.0018639162881299853, 0.00900236051529646, -0.0144115025177598, -0.06829220056533813, -0.01833317242562771, -0.011303466744720936, -0.012507596053183079, 0.032852496951818466, -0.04803958162665367, 0.05086878687143326, 0.019603172317147255, -0.017114197835326195, -0.013690163381397724, 0.086081862449646, -0.08488070219755173, -0.10699629783630371, -0.033632032573223114, 0.0356513075530529, 0.002645603148266673, -0.00929032638669014, -0.041836537420749664, -0.005823788233101368, 0.07521072775125504, 0.02233053185045719, 0.05825455114245415, 0.006518603768199682, -0.013572309166193008, 0.0745028406381607, -0.0060014305636286736, -0.06123043969273567, 0.04120335355401039, -0.028060467913746834, -0.055924192070961, -0.03185637295246124, -0.001910259248688817, 0.04783123359084129, -0.023285239934921265, 0.007058333605527878, 0.011013912968337536, -0.03618313744664192, 0.0025932793505489826, -0.014781893230974674, -0.020206056535243988, -0.03620639443397522, 0.036794256418943405, -0.034560080617666245, 0.016122400760650635, -0.021745065227150917, 0.06332427263259888, 0.013481071218848228, -0.06736183166503906, 0.04707520827651024, -0.052309006452560425, -0.04889583960175514, -0.012429178692400455, 0.02004203014075756, 0.06097421050071716, 0.006190202198922634, 0.04928999021649361, 0.023892372846603394, -0.04043278470635414, 0.002405896782875061, -0.050434090197086334, 0.022510237991809845, 0.03172506019473076, 0.025229215621948242, 0.028208447620272636, 0.025513511151075363, 0.009759261272847652, 0.051604822278022766, 0.04085699841380119, -0.006968928501009941, 0.08484955877065659, -0.09268917888402939, 0.004957383964210749, -0.04102490842342377, -0.01637512631714344, 0.013500270433723927, -0.07731311768293381, -0.014165030792355537, 0.010395324788987637, 0.0570237897336483, 0.01101757399737835, 0.020592357963323593, 0.03982890397310257, 0.019156986847519875, 0.034334853291511536, -0.006877124309539795, -0.046540211886167526, -0.06274411827325821, -0.008236292749643326, -0.025239456444978714, -0.05510472506284714, 0.037126753479242325, -0.030641065910458565, 0.00763204600661993, 0.03222459554672241, 0.024136120453476906, 0.046695735305547714, -0.025026066228747368, 0.0010558172361925244, -0.03405488654971123, -0.009254218079149723, -0.028784465044736862, 0.07978619635105133, -0.03084043599665165, 0.06406580656766891, -0.02063567563891411, 0.036424487829208374, -0.0398382730782032, 0.0019380503799766302, 0.000934589363168925, 0.04003028944134712, -0.0797070860862732, -0.02337350696325302, 0.019752224907279015, -0.013008716516196728, -0.014448242262005806, 0.010404468514025211, 0.06751468032598495, -0.11001405864953995, -0.032145604491233826, 0.026082616299390793, -0.04007617011666298, -0.0021539852023124695, 0.06374894827604294, -0.023822177201509476, -0.00959969125688076, -0.05217672884464264, -0.01570301502943039, -0.05090920627117157, -0.012968964874744415, 0.0038893676828593016, 0.06255598366260529, 0.010181448422372341, 0.024638399481773376, -0.006629077717661858, 0.019134143367409706, -0.025173064321279526, 0.026266658678650856, 0.04072893038392067, -0.03721492365002632, -0.04660026729106903, 0.005789358634501696, -0.01597503013908863, 0.01268453523516655, -0.013184675946831703, -0.02375752292573452, 0.009204094298183918, 0.06227881461381912, 0.04369073361158371, -0.012871067970991135, -0.03524208813905716, 0.021884797140955925, -0.005054805893450975, 0.0005188059294596314, -0.03920476883649826, 0.04518289119005203, -0.06499823182821274, 0.031913336366415024, -0.017181018367409706, -0.015007068403065205, 0.00027824705466628075, -0.0025724295992404222, 0.01823197305202484, 0.00922287069261074, -0.028668630868196487, 0.040929850190877914, 0.0014058556407690048, -0.03455517068505287, -0.0577172189950943, -0.04538603872060776, -0.03127479925751686, 0.05225808173418045, 0.047282882034778595, -0.004674545489251614, -0.02262382209300995, -0.013297461904585361, 0.0009628923726268113, -0.02120337262749672, -0.0022480622865259647, 0.00584412319585681, 0.013412406668066978, -0.00563765550032258, 0.016879884526133537, -0.07774066925048828, 0.02558906190097332, 0.053613871335983276, -0.08625739067792892, -0.036406584084033966, 0.008434800431132317, 0.000958614400587976, -0.015420249663293362, -0.081169992685318, -0.044645071029663086, 0.0022585673723369837, -0.03772652521729469, -0.019680486992001534, -0.005463064182549715, 0.0012247540289536119, 0.04079393297433853, 0.034499991685152054, 0.00737766595557332, 0.02913418598473072, 0.009932996705174446, 0.04189707711338997, -0.00010365003981860355, 0.03981856629252434, -0.01706942915916443, 0.04149681702256203, -0.013436337932944298, 0.015445644967257977, 0.013161311857402325, -0.02402511052787304, 0.06709709018468857, -0.04481644928455353, -0.00021713049500249326, 0.01189185306429863, -0.016883859410881996, 0.01020187046378851, 0.05237342044711113, -0.07268720120191574, 0.01332234125584364, -0.022927068173885345, 0.015583583153784275, 0.09528876841068268, 0.021719923242926598, -0.08031683415174484, 0.03787476569414139, 0.0011459107045084238, -0.027292076498270035, 0.015180117450654507, 0.06434934586286545, -0.01800890453159809, -0.0011266156798228621, -0.003527591470628977, 0.03385303169488907, -0.026536062359809875, -0.004318603314459324, 0.01416084449738264, 0.020569872111082077, -0.04562399908900261, 0.029654676094651222, 0.011213446035981178, 0.024796323850750923, 0.022151928395032883, 0.04190541058778763, 0.012997468933463097, -0.06117695942521095, -0.031969450414180756, 0.024123765528202057, -0.0261111818253994, 0.00915189366787672, -0.04451296851038933, 0.017216401174664497, -0.08024051785469055, 0.0009749070159159601, 0.02044655755162239, 0.036901041865348816, 0.019121337682008743, -0.01974167488515377, 0.006554559338837862, 0.023848017677664757, 0.030453650280833244, -0.010177251882851124, 0.0024843488354235888, 0.03868989273905754, -0.01702822372317314, 0.01520507037639618, -0.05698024481534958, -0.005274943076074123, -0.08441103249788284, 0.04553883895277977, -0.012279694899916649, -0.029686948284506798, -0.10578157752752304, -0.03800637274980545, -0.037715472280979156, 0.003162939101457596, -0.028129875659942627, 0.0608033761382103, 0.04394062981009483, 0.03870212659239769, 0.01731044612824917, -0.008339852094650269, -0.029895057901740074, -0.04093532636761665, 0.08112840354442596, 0.060844872146844864, -0.003464854322373867, -0.013727115467190742, 0.02229859121143818, 0.020444832742214203, 0.012589255347847939, 0.03441647067666054, 0.042275432497262955, -0.020635949447751045, 0.005038504023104906, 0.02133001945912838, 0.007329051848500967, 0.014951216988265514, 0.03641142696142197, 0.09716370701789856, -0.020885352045297623, 0.03288329020142555, 0.02369658090174198, -0.006573605351150036, 0.019938673824071884, -0.04075198993086815, -0.03441305831074715, -0.02813655696809292, -0.039472147822380066, -0.0019405573839321733, 0.0014716002624481916, -0.0024731263983994722, -0.015755528584122658, -0.027758628129959106, 0.04743264243006706, -0.021151378750801086, 0.005816088989377022, -0.007769543211907148, 0.003867544699460268, -0.009022181853652, -0.01657749153673649, -0.022780565544962883, 0.05417085438966751, 0.008158357813954353, -0.03462544083595276, -0.05639950558543205, 0.010312569327652454, -0.014584868215024471, -0.05142016336321831, -0.05553022772073746, 0.01862861029803753, 0.03493953496217728, -0.01996379718184471, -0.010447985492646694, 0.026104556396603584, -0.0025224348064512014, -0.07067831605672836, 0.01373250037431717, 0.03972899168729782, -0.0176503024995327, 0.03409108147025108, 0.010834287852048874, -0.0031091647688299417, 0.003706678282469511, 0.0014732915442436934, 0.015458153560757637, 0.017580900341272354, 0.0123595567420125, 0.02357216365635395, -0.03401237353682518, -0.032483719289302826, 0.022830547764897346, -0.0014455398777499795, 0.06350012123584747, -0.006817677058279514, 0.026147417724132538, -0.008843929506838322, -0.02749837189912796, -0.02311224490404129, -0.08909983187913895, 0.06206594780087471, 0.017047062516212463, 0.03785087913274765, 0.010230517946183681, 0.04854987561702728, -0.006804719101637602, -0.02794770896434784, -0.02062607929110527, 0.07108946889638901, -0.027490682899951935, 0.0491463765501976, -0.018248600885272026, 0.038728419691324234, 0.016052642837166786, -0.028850039467215538, 0.05056917294859886, 0.0008155469549819827, 0.036313410848379135, 0.0003087757504545152, -0.0419289655983448, 0.02096482366323471, 0.030168941244482994, 0.02432028204202652, 0.02415369264781475, 0.04567263275384903, -0.00917661003768444, 0.00048592110397294164, 0.06191548332571983, -0.04019008204340935, -0.023177457973361015, 0.02307373844087124, -0.005910211708396673, 0.0012835778761655092, -0.03700396046042442, 0.018470071256160736, 0.07343479990959167, 0.02306239865720272, 0.03592950850725174, -0.0824829638004303, -0.07724864780902863, 0.011936306953430176, -0.028774237260222435, -0.012089231982827187, -0.016842622309923172, 0.026208749040961266, -0.03181787580251694, -0.0037081600166857243, 0.036889608949422836, -0.023271938785910606, -0.03874889388680458, -0.047370824962854385, 0.02871393784880638, 0.041949037462472916, -0.007952375337481499, 0.02929070219397545, 0.019138311967253685, -0.05335032567381859, -0.044925231486558914, -0.005264638923108578, 0.04919528216123581, 0.015981711447238922, -0.013464285992085934, -0.02635195106267929, 0.007400889415293932, 0.02092771790921688, 0.024354087188839912, -0.07828571647405624, 0.06654123961925507, 0.0373883955180645, 0.006179966032505035, 0.03680238872766495, 0.05407899618148804, -0.010468874126672745, -0.009093648754060268, -0.07869165390729904, 0.034320175647735596, -0.04102042689919472, -0.029426323249936104, 0.005242046434432268, 0.03618374466896057, 0.00539280055090785, 0.07830672711133957, -0.026242345571517944, 0.010092961601912975, 0.03148139640688896, -0.06371063739061356, -0.002308949828147888, -0.015946870669722557, -0.011233235709369183, -0.007663914002478123, 0.027915723621845245, 0.04213794320821762, -0.02880392037332058, -0.01723296567797661, 0.031869132071733475, 0.020355399698019028, -0.03414255008101463, -0.06548058241605759, -0.007664843928068876, -0.05747876688838005, -0.002905236789956689, 0.02520011179149151, 0.0091093759983778, 0.05468118190765381, 0.04394989833235741, 0.0028082134667783976, 0.025267180055379868, 0.01612953469157219, 0.032220177352428436, 0.047746166586875916, 0.002079678699374199, -0.08310963213443756, -0.010335265658795834, 0.030375534668564796, -0.02829400822520256, 0.03820236027240753, 0.006103314459323883, 0.03777230903506279, -0.01555362343788147, 0.03418862074613571, 0.04181516170501709, 0.041902899742126465, -0.0037115493323653936, 0.024775095283985138, 0.013065464794635773, -0.0712859109044075, 0.07668622583150864, 0.00570359081029892, -0.02982630766928196, -0.0063870451413095, -0.03170056641101837, 0.001423345529474318, 0.02364875003695488, -0.023404737934470177, 0.047500140964984894, -0.0101966243237257, 0.011313122697174549, 0.019471118226647377, 0.004479247611016035, 0.005915282294154167, 0.018438437953591347, 0.013997670263051987, -0.004285134375095367, -0.01359870471060276, 0.010211452841758728, -0.02355995401740074, 0.017189571633934975, 0.00774349132552743, -0.017538655549287796, -0.025758646428585052, -0.03755630552768707, -0.0027010587509721518, -0.0021056917030364275, -0.009079347364604473, -0.01843367889523506, -0.0557449534535408, -0.018842585384845734, 0.01837742328643799, -0.11275859922170639, -0.031151074916124344, -0.04029164835810661, 0.028975138440728188, 0.01403985358774662, -0.06690636277198792, 0.052855201065540314, 0.07083363085985184, -0.022470884025096893, 0.0018644232768565416, -0.032195910811424255, 0.008458975702524185, -0.011376187205314636, -0.029940923675894737, -0.0676875039935112, -0.04621443152427673, -0.03749031573534012, -0.054122041910886765, -0.004147605504840612, 0.04216485470533371, 0.005231952294707298, -0.04892490804195404, 0.07431301474571228, 0.025470176711678505, 0.04928554221987724, -0.05855308100581169, 0.009795748628675938, 0.014984511770308018, 0.026302054524421692, -0.051626820117235184, 0.005841063801199198, -0.05091022327542305, 0.015470070764422417, -0.04456080496311188, 0.024421164765954018, 0.03258568421006203, -0.06778908520936966, 0.04167087748646736, 0.025430116802453995, 0.00010475867748027667, -0.02331302873790264, 0.015758788213133812, -0.0026682280004024506, -0.06842787563800812, -0.048287320882081985, 0.0389125794172287, 0.04878653958439827, 0.003759089158847928, -0.019859926775097847, -0.07292584329843521, 0.018916994333267212, -0.03127060458064079, -0.0001735696423565969, -0.024420714005827904, 0.02159304730594158, 0.03170621022582054, 0.000010908501280937344, -0.04194924235343933, 0.018182797357439995, -0.008039870299398899, -0.038368020206689835, -0.01758226752281189, -0.026696618646383286, -0.003188806353136897, -0.0305535476654768, -0.02339659072458744, 0.03246485814452171, -0.01642940193414688, -0.03766591474413872, 0.012537696398794651, -0.011295679025352001, -0.026540346443653107, -0.037225089967250824, 0.014426704496145248, -0.008123519830405712, -0.024434620514512062, 0.01471880916506052, 0.024602403864264488, -0.037272870540618896, 0.04273863136768341, 0.002960382727906108, -0.03371019288897514, -0.036210618913173676, 0.012068876065313816, 0.009091908112168312, -0.03458892181515694, -0.031236208975315094, -0.027195503935217857, 0.028744254261255264, 0.053558349609375, -0.02585451491177082, 0.02294246479868889, 0.019168617203831673, 0.0035192721989005804, -0.0030263985972851515, 0.02784017100930214, -0.03854477033019066, 0.04048560932278633, 0.009133679792284966, 0.026967328041791916, -0.0115805109962821, -0.013777277432382107, 0.011265595443546772, -0.008617129176855087, 0.019846836104989052, -0.006025075912475586, 0.03448401391506195, 0.07546576112508774, -0.01107665617018938 ]
<p>My question is, <em>can the (classical) Lagrangian be thought of as a metric</em>? That is, is there a meaningful sense in which we can think of the <em>least-action</em> path from the initial to the final configuration as being the <em>shortest</em> one? Then the equations of motion would be geodesics - not in physical space, but in phase space, with the metric defined by the Lagrangian. Below is a slightly expanded outline of this idea, outlining why I think it might make sense.</p> <p>(Classical) Lagrangian mechanics is derived by assuming the system takes the path of minimum action from its initial state to its final one. In the formalism of classical mechanics we normally write time $t$ as a special type of coordinate, quite distinct from the other (generalised) coordinates $\mathbf{q}$. </p> <p>However, if we want we can lump these together into a single set of "generalised space-time coordinates" $\mathbf{r} = (t, q_0, q_1, \dots)$, to be considered a vector space of dimension $1+n$, where $n$ is the number of degrees of freedom. Then the action is just a function of curves in $\mathbf{r}$-space, and the equations of motion are determined by choosing the least-action path between two points, $\mathbf{r_0}$ and $\mathbf{r_1}$. In this picture, $L$ depends upon the position and direction of the curve at each point along it, and the action is obtained by a line integral along the curve.</p> <p>This has a pleasingly geometrical feel, and so my question is, is there a meaningful sense in which I can think of the least-action path as being the <em>shortest</em> path, with the Lagrangian playing the role of a metric on $\mathbf{r}$-space? Or is there some technical reason why $L$ can't be thought of as a metric in this sense?</p> <p>Note that this isn't in general the same as a metric defined on space-time. For an $m$-particle system in $3+1$ space-time, $\mathbf{r}$ will have $3m+1$ dimensions, rather than 4. I'm interested in the notion of a metric in $\mathbf{r}$-space defined by $L$, rather than the more usual picture of $L$ being defined in terms of a metric on space-time.</p>
g8346
[ 0.07282698899507523, -0.001063054078258574, -0.009587492793798447, -0.002842782996594906, 0.03724910318851471, -0.020058369264006615, 0.04893943667411804, -0.01622728817164898, -0.053010910749435425, -0.03145148605108261, 0.059061020612716675, 0.00026878566131927073, 0.025672707706689835, -0.0510612316429615, -0.04824942722916603, -0.017823003232479095, 0.05087687447667122, -0.02580612152814865, 0.03807314485311508, 0.0038791971746832132, 0.05294262245297432, 0.01699318364262581, 0.05169333890080452, -0.012265129014849663, 0.0008460135431960225, 0.004525430034846067, 0.09450080245733261, -0.04736511409282684, -0.05952150747179985, -0.001948527991771698, -0.01218771655112505, 0.002046280074864626, 0.03679460659623146, -0.03511297330260277, -0.03078889288008213, -0.050262805074453354, 0.03019607625901699, -0.009154283441603184, 0.025732560083270073, -0.006960673723369837, 0.005610184744000435, -0.06215166673064232, 0.10327181220054626, 0.03729157894849777, 0.046454526484012604, -0.010418313555419445, 0.03741434961557388, 0.012098710052669048, 0.035650160163640976, -0.004219428636133671, -0.018939940258860588, -0.0032084835693240166, -0.07122208178043365, -0.02947087399661541, -0.028564397245645523, 0.007585680577903986, 0.027810391038656235, 0.007048654370009899, 0.005563841201364994, 0.017847193405032158, -0.016522815451025963, -0.005410987418144941, -0.01652715913951397, 0.02834700234234333, 0.028881048783659935, -0.013834920711815357, -0.05929400026798248, -0.07291999459266663, 0.03712891787290573, -0.04996492341160774, -0.004924425855278969, -0.06743630021810532, -0.021143974736332893, -0.055615946650505066, -0.012208190746605396, 0.0795077532529831, -0.03030598908662796, 0.014767595566809177, 0.03702158108353615, -0.05126567929983139, -0.02857729233801365, 0.015475578606128693, 0.02163217030465603, 0.019658643752336502, 0.10045867413282394, 0.02143632061779499, 0.007235238328576088, -0.03982750326395035, -0.022643670439720154, -0.021119577810168266, 0.013180609792470932, -0.006402532570064068, 0.06874850392341614, -0.01867331750690937, -0.0492861270904541, -0.0026009324938058853, 0.020870324224233627, 0.03235291689634323, 0.01645459048449993, 0.009371954947710037, -0.008282288908958435, 0.009289540350437164, -0.015587680973112583, -0.04637879133224487, 0.0019989446736872196, -0.004775581881403923, 0.0036054726224392653, 0.03175980597734451, 0.010262894444167614, -0.04898837208747864, 0.021060530096292496, 0.0026831908617168665, 0.011991996318101883, -0.0305654127150774, -0.04887225106358528, 0.004664208739995956, 0.01492240559309721, 0.0005383899551816285, 0.042899731546640396, 0.06296045333147049, 0.011353393085300922, 0.020741550251841545, 0.023144278675317764, 0.053387805819511414, -0.01480240747332573, 0.007906011305749416, -0.022241558879613876, 0.008711664006114006, 0.010079904459416866, 0.02965988963842392, 0.014480448327958584, 0.09086062759160995, -0.036177858710289, -0.012651268392801285, -0.08382517099380493, 0.039221253246068954, -0.03593601658940315, -0.009516517631709576, -0.01163982693105936, 0.054679024964571, -0.048679132014513016, -0.0087201539427042, 0.01730279065668583, -0.07216553390026093, -0.0681377425789833, 0.11730910837650299, -0.06836073845624924, -0.016316315159201622, 0.01673487201333046, 0.03702225536108017, -0.04261341318488121, 0.037829477339982986, 0.014924976043403149, -0.007796828169375658, 0.056778162717819214, 0.007557190489023924, 0.005328029859811068, 0.03574030101299286, -0.024043701589107513, -0.0691540390253067, 0.06072346121072769, 0.012311852537095547, 0.06606205552816391, -0.003327435115352273, -0.03474156931042671, 0.0005572916124947369, -0.018802335485816002, -0.03269663825631142, 0.05644282326102257, -0.10052389651536942, -0.03587925061583519, -0.08071238547563553, -0.018900146707892418, 0.015345333144068718, -0.03341403976082802, 0.022212710231542587, 0.008975610136985779, -0.05270775407552719, -0.03528086096048355, 0.0002476340450812131, -0.057304415851831436, 0.01072603464126587, -0.01838742196559906, -0.018777422606945038, -0.03651943430304527, 0.009246831759810448, 0.0507156066596508, -0.002481789793819189, 0.004895531572401524, -0.00567252142354846, -0.01375687588006258, 0.0009540581377223134, 0.013000953011214733, 0.009321704506874084, -0.016726771369576454, -0.007010601460933685, 0.02891438826918602, -0.003992331214249134, 0.0020933484192937613, 0.01726687140762806, 0.023546159267425537, 0.05060962960124016, 0.017231207340955734, 0.008560603484511375, 0.005082906223833561, -0.013555742800235748, -0.0055686105042696, -0.00875563733279705, 0.01751796156167984, -0.051405489444732666, 0.09249875694513321, 0.0010838484158739448, 0.03078315034508705, -0.0447053499519825, -0.05420217663049698, -0.05055921524763107, 0.011508326977491379, -0.02100236341357231, 0.0017923732521012425, 0.011921144090592861, -0.014353289268910885, -0.02456357143819332, 0.051671285182237625, -0.03690064698457718, 0.0033913282677531242, 0.014807642437517643, -0.010594096966087818, -0.010538025759160519, 0.032805413007736206, 0.008679705671966076, -0.054801300168037415, 0.011872317641973495, 0.011318393982946873, -0.009738828986883163, 0.056873954832553864, 0.006517419125884771, -0.022799672558903694, -0.023713264614343643, 0.046344999223947525, 0.053036995232105255, 0.051887452602386475, -0.027059393003582954, -0.00006619139458052814, 0.017789248377084732, 0.0727844163775444, 0.009133242070674896, 0.034233223646879196, 0.03563922271132469, -0.03551853448152542, -0.0177228432148695, -0.030262814834713936, -0.02409680373966694, -0.031002037227153778, -0.05442675203084946, 0.02274160459637642, -0.007899029180407524, -0.028996478766202927, 0.03655421361327171, -0.04408153519034386, -0.013402912765741348, -0.0020718576852232218, 0.024907898157835007, -0.028811393305659294, 0.07942287623882294, -0.022650359198451042, -0.007901613600552082, 0.014100276865065098, -0.016932422295212746, -0.027307694777846336, -0.008878357708454132, -0.0011675800196826458, 0.057764358818531036, 0.002607376081869006, 0.012386517599225044, -0.042106978595256805, -0.006661958061158657, -0.01114353071898222, -0.03365889564156532, 0.0014311694540083408, -0.022234568372368813, 0.044749461114406586, -0.052774395793676376, -0.04487008601427078, 0.01982683688402176, 0.013531163334846497, -0.05975699797272682, 0.009902319870889187, 0.018951822072267532, -0.03337172046303749, 0.038218528032302856, -0.006472516339272261, 0.017905382439494133, 0.03089282661676407, -0.05373648181557655, -0.03810545802116394, 0.02611534297466278, -0.07076889276504517, -0.017200656235218048, -0.021654125303030014, -0.01913478597998619, -0.042909055948257446, -0.032044317573308945, -0.008937519043684006, 0.026466872543096542, -0.04742671921849251, -0.0063591510988771915, -0.04418021813035011, -0.05843688175082207, -0.02049771137535572, 0.0002323711378267035, 0.008410044945776463, 0.07942245155572891, -0.04051028564572334, -0.0037155149038881063, -0.07214266806840897, -0.026631075888872147, -0.02918217144906521, -0.027595411986112595, -0.009265827015042305, 0.023862237110733986, -0.04140250012278557, -0.08738367259502411, -0.041468508541584015, -0.03556583449244499, 0.02883072942495346, 0.029569676145911217, 0.02298796735703945, -0.05104092136025429, -0.028029674664139748, 0.022898346185684204, 0.010225248523056507, -0.040069520473480225, -0.0032341317273676395, 0.03570067882537842, -0.00715396786108613, -0.060780420899391174, -0.03599800169467926, -0.007348859217017889, 0.06558500230312347, -0.018396642059087753, -0.00035566731821745634, -0.012818049639463425, -0.015912652015686035, 0.04721604660153389, 0.0720096006989479, 0.004545851610600948, 0.004758500959724188, 0.04684792086482048, 0.016696175560355186, -0.005957506597042084, -0.026493048295378685, -0.0928022488951683, -0.009630095213651657, -0.05117645487189293, -0.028826503083109856, -0.008384397253394127, 0.009420214220881462, 0.051741983741521835, 0.05345487222075462, -0.014155755750834942, -0.045967038720846176, 0.009747826494276524, -0.0784521996974945, 0.03035527840256691, 0.027311749756336212, 0.0020501306280493736, -0.019279174506664276, -0.014080287888646126, 0.025654751807451248, -0.02833259478211403, 0.07775450497865677, -0.033759716898202896, -0.010188027285039425, 0.054692067205905914, 0.03877998888492584, 0.004519098903983831, -0.012703748419880867, -0.005600556265562773, -0.04576466605067253, 0.0020419384818524122, -0.0024250578135252, 0.036012306809425354, 0.055462270975112915, 0.053124018013477325, 0.020320270210504532, 0.03317881375551224, -0.04001484811306, -0.003013030393049121, -0.00511291716247797, -0.0028928860556334257, -0.004029233939945698, -0.028040137141942978, -0.02153625711798668, 0.006143786944448948, 0.01456955075263977, 0.06408292055130005, 0.05588613077998161, -0.012079154141247272, -0.018832316622138023, 0.012539601884782314, -0.0172688290476799, 0.03439457714557648, 0.00833545159548521, 0.038399532437324524, 0.045149464160203934, -0.01588795706629753, 0.01802799478173256, 0.005023411475121975, 0.01842084527015686, -0.07630100846290588, 0.006120946258306503, -0.011675597168505192, 0.026738131418824196, -0.06525462120771408, -0.001591130392625928, 0.03923308849334717, -0.06730449944734573, -0.04999919235706329, -0.038665637373924255, 0.03047381341457367, 0.036612819880247116, 0.04556586965918541, 0.008765165694057941, -0.04691712558269501, 0.0025825826451182365, 0.04138854518532753, 0.10528413206338882, 0.029267381876707077, -0.05175194889307022, -0.04610394686460495, -0.028254585340619087, -0.0369315966963768, 0.061021801084280014, 0.008146273903548717, -0.03890933468937874, -0.011584685184061527, -0.025235047563910484, 0.007788923103362322, 0.052127156406641006, 0.04110627993941307, 0.03538445755839348, 0.034019697457551956, 0.048368342220783234, -0.02283206582069397, -0.019747862592339516, 0.002077752724289894, 0.021980494260787964, -0.07185035198926926, -0.06683721393346786, -0.0458461195230484, 0.054195284843444824, 0.0380193330347538, -0.037197306752204895, -0.026921141892671585, -0.000014717225894855801, 0.021828778088092804, 0.005288437940180302, 0.014697901904582977, 0.004936096724122763, -0.0005993784288875759, 0.005148376803845167, -0.038902465254068375, 0.032226379960775375, 0.03568646311759949, 0.048199404031038284, -0.02550927735865116, -0.048836007714271545, 0.029804322868585587, -0.04892906919121742, -0.014602867886424065, 0.03662688285112381, 0.02226862870156765, 0.04378953576087952, -0.02309115044772625, -0.007551546674221754, 0.0011675048153847456, 0.001981021137908101, 0.02956181764602661, -0.009796074591577053, 0.0007659396505914629, 0.0015711461892351508, -0.027040794491767883, -0.013839843682944775, 0.010491558350622654, -0.013149872422218323, 0.027922168374061584, 0.014871149323880672, -0.04512687399983406, -0.028283577412366867, 0.019567985087633133, 0.0310555137693882, -0.03072013333439827, 0.014695178717374802, 0.020700136199593544, -0.017886223271489143, -0.008636641316115856, -0.01431349292397499, 0.011945502832531929, -0.013670960441231728, 0.005100555252283812, -0.09268665313720703, 0.03511068969964981, 0.01449357345700264, -0.011651427485048771, 0.0404493473470211, 0.031524185091257095, 0.008381921797990799, -0.0034487212542444468, -0.09161000698804855, 0.031101075932383537, 0.03149964287877083, 0.03276330977678299, -0.05585622787475586, 0.059682514518499374, -0.026982221752405167, -0.06266722083091736, -0.045096755027770996, 0.033306945115327835, 0.042568936944007874, -0.0007644252618774772, -0.01816973276436329, 0.01713624596595764, 0.03680511936545372, -0.06807240843772888, 0.026354486122727394, 0.011038759723305702, -0.009685219265520573, -0.00019492949650157243, 0.0073231798596680164, 0.0717526227235794, 0.01627492718398571, 0.029266446828842163, 0.007866286672651768, 0.020656684413552284, -0.033313099294900894, -0.0014514768263325095, 0.015750855207443237, 0.027185993269085884, 0.07722029089927673, -0.03688773885369301, -0.07326769083738327, -0.10151544958353043, 0.018052183091640472, -0.011256935074925423, -0.015311955474317074, 0.005697396583855152, 0.0052592274732887745, -0.029061995446681976, -0.010046599432826042, -0.019991902634501457, -0.03313922509551048, 0.006468312349170446, -0.017869506031274796, -0.012481968849897385, -0.07143279910087585, 0.03818507120013237, -0.006834486965090036, 0.01199533324688673, 0.03976532816886902, -0.029445482417941093, 0.058581214398145676, -0.012108996510505676, 0.024234795942902565, -0.004035511985421181, 0.005346760153770447, 0.02038605324923992, 0.012847727164626122, -0.01849221996963024, 0.054361432790756226, 0.02897479385137558, 0.006077984813600779, -0.005089927930384874, 0.00042520766146481037, 0.030541928485035896, 0.0393056757748127, -0.02078084647655487, -0.013559318147599697, -0.03449864685535431, -0.08875808119773865, 0.05408908426761627, -0.02119489386677742, 0.04163096472620964, 0.009611531160771847, -0.06716348230838776, -0.035080574452877045, 0.034100521355867386, -0.02888970449566841, -0.06085432693362236, -0.03838304430246353, 0.0492294579744339, 0.0286953654140234, -0.020420363172888756, -0.051537055522203445, 0.07729725539684296, 0.038638871163129807, 0.032863110303878784, -0.015715064480900764, 0.006507343612611294, -0.02990046516060829, 0.07540804892778397, 0.01534799300134182, 0.10023584961891174, -0.02481512352824211, -0.012836342677474022, -0.032509252429008484, 0.0859496220946312, -0.011752717196941376, -0.006281506270170212, 0.028285400941967964, -0.0614500492811203, 0.01457988377660513, 0.02336309663951397, -0.05064896494150162, 0.04243640601634979, 0.0172016229480505, -0.04920370876789093, 0.010917041450738907, -0.007210239768028259, -0.0147705702111125, -0.05488906428217888, -0.016267072409391403, 0.06435208022594452, -0.03600051999092102, -0.02956104651093483, -0.03145691752433777, 0.01614757440984249, 0.00684564420953393, 0.03815515339374542, -0.02103821560740471, 0.01811075396835804, 0.021259095519781113, -0.004829901736229658, 0.015858257189393044, 0.06157221272587776, 0.011436425149440765, 0.001771910348907113, -0.06458103656768799, 0.04882354661822319, 0.042371150106191635, -0.010179649107158184, 0.013935769908130169, -0.03806808963418007, 0.02711351402103901, 0.013101872056722641, -0.07468358427286148, 0.0007361285388469696, -0.018819207325577736, 0.015311273746192455, -0.032364990562200546, -0.010669481009244919, 0.017462819814682007, 0.018331095576286316, -0.02310727722942829, 0.010440320707857609, 0.004585532005876303, -0.03179893270134926, -0.03311682492494583, 0.02747146412730217, 0.0018074430990964174, -0.05470006540417671, -0.035605136305093765, 0.026934023946523666, -0.015473552979528904, -0.02155817486345768, 0.012340054847300053, 0.045739565044641495, -0.020641077309846878, -0.004030823707580566, -0.015908222645521164, 0.003093978390097618, -0.024848949164152145, -0.03553568944334984, -0.00011720960901584476, 0.04824880138039589, 0.03572491183876991, 0.05115238204598427, 0.05523890629410744, 0.01482864934951067, 0.005494400393217802, 0.06151964142918587, 0.03160474821925163, 0.026919228956103325, 0.036482084542512894, -0.018048550933599472, -0.04911785200238228, -0.015279260464012623, 0.06648537516593933, -0.01781439408659935, -0.062394436448812485, -0.03802041709423065, -0.027597514912486076, 0.013580577448010445, -0.031129978597164154, 0.0030988070648163557, 0.009059939533472061, -0.021790284663438797, 0.06741511076688766, 0.049482136964797974, -0.01858222484588623, -0.0009256252087652683, 0.03902279585599899, -0.05960041657090187, -0.04459017887711525, 0.044463787227869034, 0.027837403118610382, 0.005131258629262447, 0.007983243092894554, 0.022759243845939636, -0.06531178206205368, 0.047386035323143005, -0.04515312612056732, 0.03924790024757385, -0.043370265513658524, 0.060104530304670334, 0.018334675580263138, 0.027378888800740242, -0.023948220536112785, 0.012753373943269253, 0.015361689031124115, -0.006720380391925573, 0.005813173018395901, 0.013775108382105827, -0.005236366298049688, -0.06595593690872192, 0.009310097433626652, 0.024306515231728554, 0.007172388024628162, -0.058493372052907944, 0.043330904096364975, -0.034163400530815125, -0.004359761718660593, -0.049791526049375534, -0.009419634006917477, 0.06802831590175629, -0.020538927987217903, -0.00641007162630558, -0.04725122079253197, 0.014525888487696648, 0.024545788764953613, 0.03199046477675438, -0.027064701542258263, -0.03776746988296509, 0.008409530855715275, 0.0267806313931942, 0.004094836302101612, -0.018260125070810318, 0.0470162034034729, 0.0029798662289977074, -0.0220393855124712, 0.006373241078108549, 0.027557192370295525, 0.05172856152057648, 0.04312119260430336, -0.004189288709312677, 0.027784062549471855, -0.006423666141927242, -0.004865988157689571, -0.009866086766123772, 0.014428759925067425, -0.000402587465941906, 0.01034361682832241, -0.012938485480844975, 0.048553358763456345, -0.02754286862909794, -0.07380082458257675, 0.04717988520860672, 0.0392257422208786, 0.02539408765733242 ]
<p>I know perfectly well how to derive the magnitude of the electric field near a conductor, $$E = \frac{\sigma}{\varepsilon_0}$$ and near a sheet of charge, $$ E = \frac{\sigma}{2\varepsilon_0} .$$</p> <p>In fact, I can explain with clarity each step of the derivation and I understand why is one two times larger than the other. But here's what bothers me...</p> <p>When I try to think about it <em>purely</em> intuitively (whatever the heck that actually means), I find it difficult to accept that a planar charge distribution with the same surface density can produce a different field.</p> <p>Why should it <em>care</em> whether there's a conductor behind it or not... ?</p> <p>I repeat, I understand Gauss' law and everything formally required, but I want to understand where my intuition went wrong.</p> <p><strong>EDIT:</strong> <em>Thanks to you people, I developed my own intuition to deal with this problem, and I'm happy with it, you can see it posted as an answer!</em></p>
g8347
[ 0.029289599508047104, 0.014479227364063263, -0.027302362024784088, 0.00211218255572021, 0.04205609858036041, 0.09061283618211746, 0.0029370414558798075, 0.02464228868484497, -0.03056199662387371, -0.01778300479054451, -0.036846060305833817, 0.00010475322778802365, 0.03087378665804863, 0.015519734472036362, 0.020255764946341515, -0.0002519997942727059, 0.048960380256175995, -0.02030281536281109, 0.06832051277160645, 0.018007434904575348, -0.09230682253837585, -0.051931485533714294, 0.03293837606906891, -0.012726221233606339, -0.025879280641674995, -0.02105710469186306, 0.00018271520093549043, 0.00862039253115654, 0.03672415390610695, -0.06599476933479309, -0.024215126410126686, 0.0765540674328804, 0.08078321814537048, -0.009736398234963417, -0.04985867440700531, -0.012711203657090664, 0.030777137726545334, 0.008426171727478504, 0.00618557445704937, -0.0033848751336336136, 0.023826217278838158, -0.03122483752667904, 0.03600787743926048, -0.009207895956933498, -0.04081296548247337, -0.016090020537376404, -0.04937975853681564, 0.017893783748149872, 0.023619595915079117, -0.06384047865867615, -0.020946796983480453, 0.0419321171939373, 0.03715811297297478, 0.014233860187232494, 0.029498586431145668, 0.005839889869093895, 0.0015094686532393098, -0.009096196852624416, 0.034063536673784256, 0.026761842891573906, 0.005793867167085409, 0.01752946525812149, -0.05710114538669586, 0.031235363334417343, 0.020401908084750175, 0.04894102364778519, -0.027924906462430954, -0.011364647187292576, 0.020718272775411606, 0.012860382907092571, -0.022046342492103577, -0.02750823274254799, -0.015412170439958572, -0.03422832861542702, -0.031494248658418655, -0.0003953232953790575, 0.015800021588802338, 0.03749288618564606, 0.039636895060539246, -0.014484904706478119, 0.018860897049307823, 0.0036520243156701326, 0.020812449976801872, 0.029937811195850372, 0.08292452245950699, -0.05064012110233307, 0.0231203380972147, 0.016055943444371223, -0.0003895685658790171, -0.029592661187052727, -0.0017052178736776114, 0.024407047778367996, 0.05154258757829666, 0.0030379672534763813, -0.037304412573575974, -0.06888442486524582, 0.016341593116521835, 0.012297175824642181, -0.013555891811847687, -0.012529651634395123, -0.03191976994276047, 0.015968114137649536, 0.00032115104841068387, 0.047355856746435165, -0.025288650766015053, 0.06616449356079102, 0.03667456656694412, 0.044179972261190414, 0.04756689444184303, -0.012270915322005749, 0.007230359595268965, -0.012341877445578575, -0.04814167693257332, -0.0421791598200798, 0.004617469850927591, 0.010603652335703373, 0.05229008570313454, -0.04254797846078873, -0.04229481518268585, 0.05733397975564003, -0.015732761472463608, -0.023362282663583755, 0.0479007214307785, -0.02011103369295597, -0.009667427279055119, -0.0044758133590221405, 0.01893160305917263, 0.03633711859583855, 0.027754273265600204, 0.002834388054907322, 0.013295748271048069, -0.014056994579732418, 0.003850106615573168, -0.011720641516149044, 0.018219998106360435, 0.06369106471538544, -0.0826827734708786, 0.0033309105783700943, -0.019842421635985374, 0.01300634816288948, 0.014231855981051922, -0.010421795770525932, -0.016519878059625626, -0.03362493962049484, -0.03580250218510628, 0.01377936452627182, -0.055752869695425034, -0.04017181694507599, 0.060819536447525024, -0.048530835658311844, 0.04527512565255165, 0.05822141841053963, -0.030258003622293472, -0.013379490934312344, 0.03978670388460159, 0.03636704385280609, 0.041133806109428406, -0.05594082549214363, -0.025668757036328316, -0.04217018559575081, 0.02485753409564495, -0.023476263508200645, 0.008646490052342415, 0.01142560038715601, 0.022456634789705276, 0.005345185287296772, 0.03275860846042633, -0.06046753376722336, -0.000257601699559018, -0.05988486856222153, 0.00357737741433084, -0.017752299085259438, 0.052325379103422165, 0.048382408916950226, 0.0023715791758149862, 0.07341963797807693, 0.0033393462654203176, -0.012843579985201359, 0.10460127890110016, 0.06912170350551605, -0.044349223375320435, 0.01616162620484829, 0.000010000991096603684, -0.01307148952037096, 0.020188618451356888, -0.008819670416414738, -0.04956688731908798, 0.023336326703429222, -0.02507232502102852, 0.028545651584863663, -0.03776606544852257, -0.022790517657995224, -0.04710651934146881, 0.0703255757689476, -0.017775634303689003, 0.028760310262441635, 0.03545030951499939, -0.06004618853330612, -0.04766218736767769, -0.04012950137257576, -0.06075017899274826, 0.04293765872716904, 0.023098336532711983, -0.012623256072402, 0.005158678628504276, 0.021221652626991272, -0.017697159200906754, -0.06966876983642578, 0.05320359021425247, 0.012723269872367382, -0.034522637724876404, -0.0807717815041542, 0.004589315503835678, 0.07611767202615738, 0.007706811185926199, -0.06695310771465302, -0.049915850162506104, 0.004168160259723663, -0.052227962762117386, 0.059406399726867676, -0.035295795649290085, -0.00798786710947752, 0.09796463698148727, -0.02023867703974247, -0.06584171205759048, 0.04221222549676895, 0.009533907286822796, 0.005358463618904352, -0.04532724246382713, -0.00658873375505209, -0.045742835849523544, 0.012428347021341324, 0.018949419260025024, 0.03765597194433212, -0.008600033819675446, 0.028769249096512794, -0.015024324879050255, -0.04460543021559715, 0.04669840261340141, -0.03201089799404144, -0.01526241097599268, -0.019606556743383408, 0.028702301904559135, 0.03759691119194031, 0.03931247070431709, 0.02542317658662796, 0.044575851410627365, 0.03479543328285217, -0.025059130042791367, -0.018622547388076782, -0.007270082365721464, 0.019406171515583992, 0.022685041651129723, 0.018032832071185112, 0.013179049827158451, -0.023097921162843704, -0.016221778467297554, 0.023835020139813423, 0.03242428973317146, -0.024945011362433434, -0.04526734724640846, -0.054579444229602814, 0.05731146037578583, 0.05528901144862175, -0.043755993247032166, 0.0031665510032325983, -0.026594793424010277, 0.015171036124229431, 0.07528293132781982, -0.04388125240802765, -0.0066614518873393536, 0.08407097309827805, -0.027777206152677536, 0.012924022041261196, 0.034105073660612106, -0.0289422906935215, 0.01117702480405569, -0.010114015080034733, 0.061431754380464554, -0.01166178472340107, 0.014600551687180996, -0.018197955563664436, -0.010175020433962345, 0.009767686948180199, 0.06852295249700546, -0.06664276868104935, 0.030860545113682747, 0.009999653324484825, 0.00521535100415349, -0.005879429634660482, -0.007577293086796999, 0.018402745947241783, 0.04434066638350487, -0.02988050878047943, 0.0263847466558218, -0.008150959387421608, -0.007659279275685549, -0.07993277907371521, -0.04120992496609688, -0.004512366838753223, 0.033162035048007965, -0.04108792915940285, -0.0059274486266076565, 0.016326304525136948, 0.05913062393665314, 0.007363373413681984, -0.013622994534671307, -0.05228051170706749, 0.04395425692200661, -0.011442535556852818, -0.0018769713351503015, -0.009033262729644775, 0.01844927668571472, -0.06989654153585434, -0.04621138423681259, 0.016001058742403984, -0.02098992094397545, 0.0020825983956456184, -0.020175455138087273, -0.010137525387108326, -0.002732803113758564, 0.015173417516052723, -0.017224812880158424, -0.022375911474227905, -0.018061282113194466, 0.00488300621509552, -0.07692935317754745, 0.04681811109185219, -0.0037961499765515327, -0.025013143196702003, 0.012025007978081703, 0.008877908810973167, 0.022582797333598137, -0.04908306151628494, 0.012441001832485199, -0.07012870162725449, -0.005669087171554565, 0.08147679269313812, 0.04446679353713989, -0.02199862338602543, -0.030191803351044655, -0.012483912520110607, -0.07485578954219818, -0.04364827275276184, -0.05106670409440994, 0.01276706624776125, -0.010658659972250462, -0.012965180911123753, 0.02382156066596508, -0.05901933088898659, 0.0033958700951188803, -0.030094895511865616, 0.00895810965448618, 0.06296900659799576, -0.04923194646835327, 0.025776904076337814, 0.007588054519146681, 0.001406150870025158, 0.0010305081959813833, 0.025558633729815483, 0.04379142075777054, -0.03934475779533386, -0.02650478295981884, -0.030277058482170105, 0.016128752380609512, -0.025834383442997932, -0.007475301623344421, 0.06150880083441734, -0.03844086080789566, -0.02103523351252079, 0.014346097595989704, 0.0023280761670321226, 0.017647571861743927, 0.04654322564601898, 0.03957297280430794, -0.024526095017790794, 0.037273842841386795, 0.025255007669329643, 0.0070537421852350235, -0.011881846003234386, 0.08196621388196945, 0.0635538324713707, -0.023918552324175835, -0.025872791185975075, 0.008437858894467354, -0.03234288468956947, -0.03972965478897095, 0.028285617008805275, 0.018363073468208313, -0.04629558324813843, -0.03751744329929352, -0.034160200506448746, -0.03499762713909149, 0.015408261679112911, -0.03940471261739731, -0.0401228666305542, 0.031028740108013153, 0.004634441342204809, -0.014859425835311413, 0.02661333978176117, 0.024808524176478386, 0.02526669390499592, 0.03579661250114441, 0.004105739761143923, -0.03956560045480728, -0.0252719484269619, 0.017682824283838272, -0.049537770450115204, 0.015248093754053116, -0.01807987131178379, -0.004028871189802885, -0.029836945235729218, -0.0334034338593483, -0.072537362575531, 0.044162552803754807, 0.04412715137004852, 0.02640354074537754, 0.030257925391197205, 0.04180417209863663, 0.008013864979147911, 0.030891090631484985, 0.02393246255815029, 0.06131328269839287, -0.0820361077785492, 0.006772648077458143, 0.10476423054933548, 0.06128726527094841, -0.015524493530392647, 0.030220413580536842, -0.008321049623191357, 0.0030779154039919376, 0.06771805882453918, -0.02965412475168705, -0.030945291742682457, -0.1109478771686554, 0.0423537939786911, -0.09088197350502014, 0.0668376162648201, -0.031580470502376556, 0.05966010317206383, 0.05628151074051857, 0.0019158899085596204, 0.026612063869833946, -0.006812884006649256, 0.03338615223765373, -0.009494537487626076, -0.07088666409254074, -0.01395393256098032, 0.0012695026816800237, -0.025920787826180458, -0.047251809388399124, 0.010529713705182076, -0.011635671369731426, -0.03744097426533699, 0.021815307438373566, 0.011681502684950829, 0.012538230046629906, -0.005855331663042307, -0.0019137011840939522, -0.03269519656896591, -0.04200303182005882, -0.0002068827161565423, -0.037616025656461716, 0.019526703283190727, 0.038389455527067184, -0.020209409296512604, -0.0856231078505516, 0.009277489967644215, 0.025777816772460938, -0.059300608932971954, -0.0050149643793702126, 0.030021468177437782, 0.009142978116869926, -0.05628921091556549, 0.05476965010166168, 0.0329708568751812, 0.03188647702336311, -0.011611818335950375, -0.0945785865187645, -0.06325183063745499, -0.07188982516527176, -0.008797122165560722, 0.024071717634797096, 0.013244329020380974, -0.03223966062068939, 0.036175016313791275, -0.008292528800666332, 0.036912739276885986, -0.017689423635601997, -0.05339565873146057, -0.0019530659774318337, 0.009324328042566776, -0.03710007295012474, 0.027124527841806412, -0.01559697836637497, -0.01734217256307602, 0.03949112445116043, 0.014810767956078053, 0.0018351816106587648, -0.00626708660274744, -0.0073862881399691105, -0.013150214217603207, -0.04298556223511696, 0.06016248092055321, 0.014119483530521393, 0.08093983680009842, 0.03634479269385338, -0.05339215323328972, 0.015607660636305809, -0.0023812062572687864, -0.00790468044579029, 0.01232908759266138, 0.042424678802490234, -0.058592528104782104, 0.022833185270428658, 0.006440567784011364, -0.03359442576766014, 0.022061830386519432, -0.038368675857782364, -0.00882564578205347, 0.05733751133084297, 0.010515570640563965, 0.00229323236271739, -0.03163706138730049, -0.046506889164447784, -0.006608803290873766, -0.024954823777079582, -0.11420466005802155, -0.0011972301872447133, 0.0030168022494763136, 0.0018138488521799445, 0.030960235744714737, -0.02740163542330265, -0.017733996734023094, -0.006219209171831608, -0.03356380760669708, 0.016653547063469887, -0.001132217119447887, -0.0202584620565176, -0.023138169199228287, 0.03095528855919838, -0.0043921638280153275, 0.025301698595285416, 0.04437250271439552, -0.0269362423568964, -0.012349267490208149, -0.03130150958895683, 0.0018436698010191321, 0.08955951035022736, 0.008518101647496223, 0.001394755090586841, 0.034496646374464035, -0.011731511913239956, -0.010141649283468723, 0.018067464232444763, 0.05278228223323822, -0.0030943909659981728, -0.016756001859903336, -0.03536584973335266, 0.002809931291267276, 0.010598750784993172, -0.020052148029208183, -0.02405613474547863, -0.008789549581706524, 0.057714033871889114, -0.02108541503548622, 0.030530042946338654, 0.039330802857875824, 0.029766064137220383, 0.06312420964241028, 0.006949454080313444, 0.02557622827589512, 0.06295894086360931, 0.006100633647292852, 0.011562485247850418, 0.0012570084072649479, 0.0015256224432960153, -0.0015178106259554625, 0.0012327042641118169, 0.0047444370575249195, 0.010960428044199944, -0.032340336591005325, 0.03549580276012421, -0.005989378783851862, -0.0115479975938797, -0.0002362111263209954, -0.031546104699373245, -0.051757730543613434, 0.11377589404582977, -0.03173654526472092, -0.027767576277256012, -0.010784314945340157, 0.06935068964958191, -0.027095859870314598, -0.04626593738794327, -0.007362305652350187, 0.00818632636219263, -0.03377414867281914, -0.030847780406475067, 0.02894730307161808, 0.06592351943254471, 0.0017009030561894178, 0.02384144440293312, 0.021282784640789032, 0.08304724842309952, 0.007123834919184446, 0.037886809557676315, 0.006585085764527321, -0.05828418582677841, -0.009993568994104862, -0.024122051894664764, 0.02386770024895668, -0.03672807291150093, -0.03859197348356247, 0.024269064888358116, 0.018178123980760574, -0.001216571545228362, 0.06525809317827225, -0.010464678518474102, -0.00218453467823565, 0.03599606454372406, 0.011111631989479065, 0.001206771470606327, 0.002460844349116087, 0.023784050717949867, 0.029981648549437523, 0.03905496746301651, 0.030581573024392128, 0.059298690408468246, -0.008467629551887512, -0.007460601627826691, 0.026655202731490135, -0.040250420570373535, 0.08558385074138641, 0.002357236575335264, 0.013366730883717537, -0.00792615581303835, -0.019543783739209175, 0.020825296640396118, 0.027002908289432526, -0.05624651908874512, -0.021901972591876984, 0.05601458251476288, 0.023886816576123238, -0.061745621263980865, -0.07553770393133163, 0.014711144380271435, -0.00731047336012125, -0.06034337356686592, 0.062248777598142624, 0.029137087985873222, 0.041999440640211105, 0.028857508674263954, -0.03770739212632179, -0.004836518783122301, -0.0020608974155038595, -0.0032823968213051558, 0.0011711351107805967, 0.008577665314078331, -0.03217536211013794, -0.03501644730567932, 0.03543650731444359, 0.0029502050019800663, -0.016733244061470032, -0.011071360670030117, -0.003986091818660498, -0.0023109435569494963, -0.048314210027456284, -0.03925856947898865, -0.04564833268523216, -0.013163808733224869, -0.08169075101613998, -0.03709018602967262, -0.004337094258517027, -0.004762585740536451, -0.018568452447652817, -0.011520936153829098, 0.05438020080327988, -0.0069254604168236256, -0.033569905906915665, 0.010923300869762897, 0.0020196905825287104, -0.0319850817322731, -0.01707061193883419, 0.0037731733173131943, 0.006277725100517273, -0.07288477569818497, -0.022919701412320137, -0.0018302976386621594, 0.01696586050093174, 0.029896387830376625, -0.02021934650838375, 0.017277579754590988, -0.01780831441283226, 0.025439759716391563, 0.044907256960868835, 0.010815205983817577, 0.00973295234143734, 0.062221795320510864, 0.022766338661313057, 0.01935727149248123, 0.0060667251236736774, 0.01410747691988945, -0.057148277759552, 0.027811190113425255, -0.027519717812538147, -0.023023521527647972, 0.03425160050392151, -0.07570198178291321, -0.05383799970149994, 0.005000699311494827, 0.0018385451985523105, 0.014148576185107231, 0.017392918467521667, 0.05641897767782211, -0.004613406490534544, -0.04301377013325691, 0.024306561797857285, -0.004600813612341881, -0.00098160351626575, -0.02555391751229763, -0.010964728891849518, -0.029591623693704605, -0.01825346052646637, -0.0025479861069470644, -0.0009650179999880493, 0.008124507032334805, 0.00042887486051768064, 0.0493902862071991, -0.000583476503379643, -0.05896160751581192, 0.02086408995091915, -0.0029035566840320826, 0.006301486864686012, -0.07180164754390717, -0.008658591657876968, 0.018138915300369263, 0.028341062366962433, 0.05742282047867775, -0.059479378163814545, 0.002740825293585658, -0.040898650884628296, 0.0032246664632111788, -0.05481437221169472, -0.04340644180774689, 0.022265389561653137, -0.016156906262040138, 0.03569870814681053, 0.030917907133698463, -0.03647667542099953, -0.027027945965528488, 0.0015958779258653522, -0.07446794211864471, 0.01305931806564331, 0.04991873353719711, -0.045436568558216095, 0.055982425808906555, -0.002244542120024562, 0.04275820776820183, 0.029320083558559418, -0.004389424342662096, -0.04290641099214554, -0.047539547085762024, 0.019476022571325302, -0.03191198408603668, -0.05416898429393768, -0.0250130295753479, -0.005236828699707985 ]
<p>I've been wondering: </p> <p>Are there, still, some advantages, for current research, to study Newtonian gravity? I mean, not experimentally, where Newton gravity is a very good approximation to everyday phenomenon or, even, to the solar system (aside some perihelion problems, gravitational lensing, etc...) but to some study of General Relativity or some approximation to the Einstein field equations where knowing the Newton potential is needed.</p>
g8348
[ 0.009785090573132038, 0.04962747171521187, 0.028661051765084267, -0.028681153431534767, -0.02193714678287506, 0.016545278951525688, 0.004994906485080719, -0.02495320327579975, -0.020946523174643517, -0.033482443541288376, 0.09403544664382935, -0.021905357018113136, 0.028374256566166878, 0.010608901269733906, -0.02792396955192089, -0.010831063613295555, 0.02158038318157196, -0.035101212561130524, 0.014945060946047306, -0.024382269009947777, 0.018282560631632805, 0.015551295131444931, 0.029256515204906464, 0.008516797795891762, -0.01738460175693035, 0.019719038158655167, 0.0015316506614908576, 0.006566253490746021, -0.032101016491651535, 0.0263519324362278, 0.02218611165881157, -0.05733067914843559, 0.0743517130613327, -0.035018984228372574, -0.029099291190505028, 0.00943570863455534, 0.021273626014590263, 0.04512182995676994, 0.022670801728963852, -0.07083813101053238, 0.017679009586572647, -0.03551896661520004, -0.03397717699408531, 0.030441856011748314, 0.027824323624372482, -0.041882555931806564, -0.014219816774129868, -0.04828482121229172, 0.09336765110492706, -0.0691491886973381, -0.0029005026444792747, 0.02745181880891323, -0.013450182043015957, 0.028522420674562454, 0.04772679880261421, 0.023196537047624588, 0.018592925742268562, 0.028850439935922623, 0.022213082760572433, -0.060488224029541016, 0.009344247169792652, 0.042436450719833374, 0.02071375772356987, -0.07051361352205276, -0.02072913944721222, 0.012702932581305504, -0.06584890931844711, -0.0264141708612442, -0.023105474188923836, 0.02554643154144287, 0.055887434631586075, -0.028666673228144646, -0.016677126288414, -0.01969010755419731, -0.03293362632393837, 0.007801481988281012, -0.002050474751740694, -0.022389378398656845, -0.021069837734103203, -0.0012948012445122004, 0.06671706587076187, -0.011608212254941463, -0.020041894167661667, 0.006534281186759472, 0.08836700767278671, -0.015671683475375175, 0.02638908103108406, 0.026410022750496864, -0.020680468529462814, 0.04625658318400383, 0.03342280164361, 0.04777968302369118, 0.06100970506668091, 0.03380144387483597, -0.012244055047631264, 0.06763108819723129, 0.014129108749330044, 0.02958010882139206, 0.0448976531624794, 0.05676000565290451, 0.027129342779517174, 0.004857731983065605, 0.034045394510030746, 0.039856817573308945, 0.051670465618371964, 0.0689694881439209, 0.061102837324142456, 0.06627852469682693, -0.0019555133767426014, -0.028869276866316795, -0.040051113814115524, -0.003857924835756421, 0.039626412093639374, -0.009142494760453701, -0.1042070984840393, -0.056704018265008926, -0.017529457807540894, -0.05677221715450287, -0.006967817433178425, 0.08250205218791962, -0.0797354057431221, 0.09140272438526154, 0.0050045885145664215, 0.05135740339756012, -0.0412527397274971, 0.008038248866796494, 0.015404715202748775, -0.010496879927814007, 0.033904582262039185, -0.02945416420698166, 0.003428293392062187, -0.024156715720891953, -0.027606848627328873, -0.0014729977119714022, 0.006599427200853825, 0.015466020442545414, -0.042171329259872437, 0.0008915737853385508, 0.019786130636930466, -0.008796723559498787, -0.019876068457961082, -0.026853550225496292, -0.019256915897130966, 0.05079422518610954, -0.014542513526976109, 0.01735924743115902, -0.03631700947880745, 0.0700366273522377, 0.00547010125592351, 0.004535909742116928, -0.003987267147749662, 0.07435786724090576, 0.07605668902397156, -0.08652175962924957, -0.0002981046272907406, -0.0006867263582535088, -0.04916396737098694, -0.025920867919921875, 0.011170518584549427, 0.04307767376303673, 0.020803287625312805, 0.02102857641875744, -0.036063119769096375, 0.015374233014881611, -0.03898155689239502, 0.05005580559372902, -0.04781949892640114, -0.08637670427560806, 0.037388063967227936, -0.035293444991111755, -0.049246646463871, -0.029511447995901108, 0.018367595970630646, 0.03693253546953201, -0.016812769696116447, -0.05522371456027031, 0.05340643972158432, -0.027086997404694557, -0.012337220832705498, 0.019465846940875053, 0.011240520514547825, -0.0376981645822525, -0.0010317231062799692, 0.025952672585844994, -0.04288696497678757, -0.009256679564714432, 0.02809751406311989, -0.018544597551226616, -0.05931932106614113, 0.04505603387951851, -0.05887281149625778, -0.06541653722524643, -0.054587263613939285, 0.028510572388768196, -0.06210489198565483, -0.0019923695363104343, 0.033443767577409744, 0.012743387371301651, -0.04244744032621384, 0.07688311487436295, -0.044114358723163605, 0.04032278433442116, -0.008240744471549988, -0.003525682957842946, 0.004650418646633625, -0.029454704374074936, 0.011655837297439575, 0.0019534302409738302, 0.029207943007349968, -0.0011066673323512077, 0.03313418850302696, -0.028500767424702644, 0.07232616096735, 0.020902611315250397, -0.00592632032930851, -0.020708808675408363, -0.03882383182644844, 0.04111386090517044, -0.005442135967314243, 0.06733182072639465, 0.008791417814791203, 0.0021406179293990135, 0.019226545467972755, 0.06831292808055878, 0.01108520943671465, -0.030262399464845657, -0.06305650621652603, 0.014066435396671295, -0.009797953069210052, 0.026477431878447533, -0.06211155652999878, 0.021519286558032036, 0.017352141439914703, 0.014220722950994968, 0.03767084330320358, 0.013130403123795986, 0.019012831151485443, -0.06182299926877022, 0.044186417013406754, 0.001885087345726788, 0.03671008348464966, -0.016917146742343903, -0.03281538188457489, -0.022946598008275032, 0.04264404624700546, -0.0016805226914584637, 0.024331772699952126, -0.009663887321949005, -0.010804673656821251, -0.03015202097594738, -0.005818030331283808, 0.006211405154317617, -0.01882288232445717, -0.031194651499390602, 0.004770608618855476, 0.030604103580117226, -0.0010660100961104035, 0.03787219896912575, -0.02442176640033722, -0.016257427632808685, 0.015779059380292892, -0.05740392580628395, 0.040500592440366745, 0.05374963581562042, 0.015266905538737774, 0.04786527156829834, -0.02870302088558674, 0.01911773718893528, -0.001980871893465519, -0.015536143444478512, -0.041103608906269073, -0.0067135924473404884, -0.002829925389960408, 0.03472811356186867, -0.03292876109480858, -0.004066276829689741, 0.015244491398334503, 0.012955193407833576, -0.003384205512702465, -0.046044908463954926, 0.018709849566221237, -0.036170970648527145, -0.013096898794174194, 0.003200280712917447, 0.009308594278991222, -0.08960682898759842, 0.01110038347542286, -0.06245890259742737, 0.01870330050587654, 0.004740791395306587, 0.07645323127508163, 0.08147118240594864, 0.004449451342225075, 0.060364730656147, -0.05756986141204834, -0.012546379119157791, -0.004067531321197748, -0.028261523693799973, -0.033511850982904434, -0.045564137399196625, -0.03465178236365318, 0.043844301253557205, 0.018293730914592743, 0.08012896031141281, 0.009058427065610886, -0.01716586947441101, -0.06951317936182022, -0.05663725733757019, -0.052683353424072266, -0.02796790562570095, 0.033436667174100876, 0.071017786860466, -0.024361075833439827, 0.031162133440375328, -0.011444250121712685, -0.03260795772075653, 0.04754270240664482, -0.014269708655774593, 0.013236857950687408, -0.025174004957079887, 0.056598275899887085, -0.019046219065785408, 0.026336340233683586, -0.06356103718280792, 0.017418373376131058, 0.039192043244838715, -0.0423547588288784, -0.03733344376087189, -0.04265386983752251, 0.042846910655498505, 0.02722085826098919, -0.05827818810939789, -0.04376296326518059, 0.03444330766797066, -0.054087039083242416, -0.026566674932837486, -0.027838662266731262, 0.005168324802070856, 0.051695745438337326, -0.024290237575769424, 0.013212356716394424, 0.03832491487264633, -0.04178452119231224, -0.007544080726802349, -0.017065566033124924, 0.010036650113761425, 0.006240770686417818, 0.013298938050866127, -0.02531019225716591, -0.03981800377368927, -0.007711260579526424, -0.02332049049437046, 0.020212944597005844, -0.029554633423686028, -0.011661273427307606, 0.020951077342033386, 0.02537449263036251, 0.009977900423109531, 0.006643084343522787, -0.012085889466106892, -0.07099627703428268, -0.0017160011921077967, -0.003591765882447362, 0.03273933753371239, 0.04189369082450867, 0.014500275254249573, 0.02943773940205574, -0.0348333939909935, -0.059231407940387726, -0.020591644570231438, 0.030605696141719818, 0.06080162897706032, 0.03371073678135872, -0.006909003481268883, -0.013795102015137672, -0.03659268841147423, -0.042820043861866, 0.011007262393832207, 0.055673521012067795, -0.03183770552277565, 0.04985862970352173, 0.03198762983083725, -0.0319986529648304, 0.008068938739597797, 0.02387504279613495, -0.02406635880470276, -0.06318964064121246, -0.019350603222846985, 0.033234383910894394, 0.0014352276921272278, 0.01188770029693842, -0.034029919654130936, -0.05629143863916397, -0.012186886742711067, -0.06944121420383453, -0.02741808257997036, -0.03842438384890556, -0.013786310330033302, 0.04043278098106384, -0.003774101845920086, 0.013562078587710857, -0.04022209718823433, -0.012472767382860184, 0.047615233808755875, -0.03623788431286812, -0.048267047852277756, 0.00938441138714552, -0.01372621115297079, -0.08561477810144424, 0.01568920537829399, 0.06786644458770752, -0.004696195013821125, 0.0017345366068184376, -0.029269414022564888, -0.012005150318145752, -0.04942237213253975, -0.045680463314056396, -0.02376122958958149, 0.05544444918632507, 0.033984191715717316, 0.020695365965366364, 0.04473315551877022, -0.029902668669819832, 0.007265245541930199, -0.04411325976252556, 0.03207121044397354, 0.03171573206782341, -0.021625712513923645, -0.02885986492037773, 0.014984913170337677, 0.045495517551898956, 0.016217699274420738, 0.012393551878631115, -0.0414586067199707, -0.007782595697790384, 0.06806571781635284, -0.0487607941031456, -0.003323109820485115, -0.03209228441119194, 0.0035310471430420876, 0.09339713305234909, 0.06623560935258865, 0.00801066029816866, 0.02245337888598442, -0.014149936847388744, 0.04075733944773674, -0.00559135852381587, 0.0059222206473350525, -0.031642790883779526, 0.0028725324664264917, -0.05065363273024559, -0.015543381683528423, 0.020313622429966927, -0.008982550352811813, -0.032366443425416946, 0.003394167870283127, 0.0033012789208441973, -0.023549504578113556, 0.029688334092497826, 0.05667494609951973, -0.035158053040504456, -0.008458392694592476, 0.018682606518268585, 0.0635204091668129, 0.008597586303949356, -0.006176268681883812, -0.08811310678720474, -0.017733635380864143, -0.032692812383174896, -0.07221055775880814, -0.026950187981128693, -0.04652851074934006, 0.039523184299468994, -0.03290463238954544, -0.01909356378018856, -0.03408345207571983, -0.030966728925704956, -0.004007674288004637, -0.0023153629153966904, 0.010911345481872559, -0.05566869303584099, -0.026601146906614304, 0.07219844311475754, 0.03033767081797123, -0.006625742185860872, -0.01573353447020054, -0.06349128484725952, 0.02455032989382744, -0.0616614893078804, -0.05649365484714508, 0.014980040490627289, -0.007287598680704832, 0.025744661688804626, -0.030554668977856636, -0.0056822155602276325, 0.022224517539143562, -0.014098376035690308, 0.043054789304733276, 0.00014334195293486118, -0.038086652755737305, -0.04066570848226547, 0.059673845767974854, -0.030711568892002106, -0.027165932580828667, -0.01624492183327675, 0.0316646434366703, -0.017116215080022812, -0.03493015095591545, -0.04837470129132271, 0.06982922554016113, -0.001727652852423489, -0.005919128190726042, -0.01594121940433979, 0.0437905453145504, 0.05521417409181595, 0.009824604727327824, 0.028113625943660736, -0.048591867089271545, -0.061722636222839355, -0.07138145714998245, -0.002927136607468128, -0.019375590607523918, 0.07008569687604904, 0.03682130575180054, 0.08884824067354202, 0.021536309272050858, -0.00012786363367922604, -0.0059857117012143135, -0.0163995623588562, -0.05173666030168533, 0.023649752140045166, 0.008024479262530804, 0.10658973455429077, 0.02362404204905033, 0.01277534756809473, 0.00793829932808876, -0.02865489572286606, 0.0024397303350269794, 0.022342801094055176, -0.05525656417012215, -0.06925861537456512, -0.025474296882748604, 0.016110172495245934, 0.016626974567770958, 0.015524252317845821, 0.04709627106785774, 0.023770365864038467, 0.0673244372010231, 0.021435486152768135, -0.09240997582674026, -0.03266303613781929, -0.020578190684318542, -0.0032456456683576107, -0.019665392115712166, -0.05943157523870468, -0.01905309408903122, 0.005699790548533201, -0.06418062746524811, 0.023394953459501266, 0.027645209804177284, -0.0013361298479139805, 0.0028823555912822485, -0.04201824218034744, -0.06750340014696121, -0.02808217890560627, 0.05295659229159355, 0.04256913810968399, -0.038589585572481155, 0.03034149296581745, -0.009386703372001648, -0.06992270052433014, 0.023947400972247124, 0.037809912115335464, 0.04611407592892647, 0.055067479610443115, -0.02613167278468609, 0.0007091244915500283, 0.015356994234025478, 0.017593329772353172, -0.02900158241391182, -0.014444689266383648, -0.026867307722568512, 0.05350600928068161, -0.07442237436771393, 0.009744602255523205, 0.007941840216517448, -0.04020383954048157, -0.019757963716983795, 0.04054202139377594, -0.08365132659673691, -0.04224518686532974, -0.017951438203454018, 0.011342576704919338, -0.008927745744585991, 0.008437879383563995, 0.0027014680672436953, 0.010771742090582848, -0.009383521042764187, -0.0305048618465662, 0.0247099120169878, 0.042826589196920395, 0.0010524459648877382, 0.0698300153017044, -0.00925034936517477, -0.0005482707638293505, 0.0038929886650294065, -0.04387835040688515, 0.00838901475071907, 0.02112370915710926, 0.020038479939103127, -0.015087982639670372, 0.03579273819923401, -0.029055766761302948, 0.01174148079007864, 0.022698627784848213, -0.0261948574334383, 0.058514513075351715, -0.045934710651636124, 0.009825516492128372, -0.005225363653153181, -0.012696057558059692, -0.015001608990132809, 0.03468820080161095, -0.04920483008027077, -0.018064800649881363, 0.005695470608770847, -0.0381271056830883, 0.03925319388508797, 0.02878301963210106, 0.02264638990163803, 0.021759413182735443, 0.03188004717230797, -0.023820333182811737, 0.0314779095351696, 0.027324751019477844, 0.05162165313959122, -0.0019457269227132201, 0.0014875407796353102, 0.0009710984886623919, 0.003289658110588789, -0.02064524032175541, -0.006907276343554258, 0.006487441714853048, -0.019266648218035698, -0.0386367030441761, 0.006745081394910812, -0.0020456367637962103, 0.020557524636387825, -0.04299413040280342, 0.00817599706351757, -0.010047792457044125, -0.05022577941417694, -0.010299558751285076, 0.0024947072379291058, -0.00021683474187739193, 0.03177294507622719, 0.02489303983747959, 0.006106031127274036, 0.02489527314901352, -0.07555831968784332, 0.01825224980711937, -0.008372223936021328, -0.019223203882575035, 0.020852884277701378, -0.0067018368281424046, 0.016681883484125137, 0.006059042643755674, 0.00416497141122818, 0.0016942794900387526, 0.023188777267932892, 0.05541680380702019, 0.013050811365246773, -0.03712671250104904, -0.016469644382596016, -0.01713922619819641, 0.005169915501028299, -0.012904179282486439, -0.05039548501372337, -0.007907629013061523, -0.008726083673536777, -0.008607471361756325, 0.05916842073202133, 0.028479428961873055, 0.07091079652309418, -0.019879313185811043, 0.04518468677997589, -0.005869259592145681, -0.008243300020694733, -0.008795726113021374, -0.04342130944132805, 0.023264411836862564, 0.025877337902784348, -0.03656185418367386, -0.026218079030513763, 0.04809477925300598, -0.004018653649836779, 0.019966403022408485, 0.03664570301771164, 0.07948793470859528, -0.012007011100649834, -0.042048823088407516, -0.0183941051363945, 0.014362096786499023, -0.049056343734264374, -0.006606300827115774, -0.007359130308032036, -0.029688116163015366, -0.060095664113759995, -0.037731535732746124, 0.05043454095721245, -0.002619456499814987, 0.01265868078917265, 0.029047904536128044, -0.019097669050097466, 0.021428147330880165, 0.005504155065864325, -0.021735910326242447, -0.02733529545366764, 0.02483338862657547, -0.010701777413487434, 0.008834972977638245, -0.03296490013599396, 0.035422373563051224, -0.04286335036158562, -0.06942589581012726, 0.012652864679694176, -0.04219786822795868, -0.060682475566864014, -0.016336113214492798, -0.04017546400427818, 0.01862339675426483, 0.022192737087607384, 0.02306090109050274, -0.048950158059597015, -0.019236069172620773, 0.022198686376214027, 0.04211150482296944, -0.03446746617555618, -0.009078605100512505, 0.039490409195423126, 0.010155691765248775, -0.030221037566661835, 0.032099369913339615, 0.01433962769806385, 0.06896788626909256, -0.0032320301979780197, -0.004965931177139282, 0.04565747082233429, 0.059050727635622025, 0.031437214463949203, -0.04472934082150459, 0.08013582974672318, 0.007259144447743893, 0.032022688537836075, -0.0059212930500507355, -0.02406802773475647, 0.028551027178764343, 0.008227749727666378, 0.03257060796022415, -0.025690654292702675, 0.03863123431801796, 0.03659658879041672, 0.03533913567662239, -0.020882099866867065, 0.0007634338107891381, -0.01628653146326542, 0.005368160083889961, 0.013928888365626335 ]
<p>How can we construct a <a href="http://en.wikipedia.org/wiki/Tauc_plot" rel="nofollow">tauc plot</a> using data from the transmission spectra? How does one calculate the absorption coefficient for plotting tauc plots? </p>
g8349
[ -0.023257475346326828, -0.00588265573605895, -0.011941269971430302, -0.09862825274467468, 0.035839956253767014, -0.01712149567902088, -0.0074766878969967365, -0.004020518623292446, -0.026537416502833366, -0.037595998495817184, 0.024242635816335678, 0.021226560696959496, 0.05632041394710541, 0.012331166304647923, 0.019888456910848618, -0.042424604296684265, 0.07795808464288712, 0.03449929878115654, 0.02920607477426529, 0.005614122375845909, -0.008868291974067688, -0.024080514907836914, 0.02370450831949711, -0.03834926337003708, -0.014260976575314999, 0.0037294672802090645, 0.018145740032196045, 0.02006208337843418, -0.026087503880262375, -0.03649643808603287, -0.014301285147666931, 0.04580574855208397, -0.020764874294400215, 0.0038210470229387283, -0.03767123818397522, 0.004637996666133404, -0.01969054900109768, 0.028835151344537735, -0.04047432169318199, 0.015204889699816704, -0.052785784006118774, 0.005401593167334795, 0.028476890176534653, 0.02827194519340992, -0.0031132125295698643, -0.03927358239889145, 0.013849491253495216, -0.026723889634013176, -0.056882962584495544, -0.029029177501797676, -0.00840405561029911, 0.010450168512761593, 0.009378042072057724, 0.024376876652240753, 0.018669534474611282, 0.013494831509888172, 0.020324954763054848, -0.07140206545591354, 0.02588885836303234, -0.036591850221157074, -0.038383763283491135, 0.0508011057972908, 0.028155118227005005, -0.032438814640045166, 0.026166394352912903, 0.01623919978737831, -0.04467935860157013, -0.006778851617127657, -0.03397239372134209, -0.03365277871489525, 0.0519280768930912, 0.017452504485845566, -0.035166993737220764, -0.049237869679927826, 0.003253416158258915, -0.019166631624102592, -0.002278673928231001, -0.009923416189849377, 0.01841176487505436, 0.07526209950447083, 0.011887538246810436, -0.0041697220876812935, -0.01136441808193922, 0.042311377823352814, 0.021514341235160828, -0.0064066024497151375, 0.027044663205742836, -0.002163317985832691, 0.045704036951065063, -0.005274828523397446, 0.04676191136240959, 0.0898103341460228, -0.030369846150279045, -0.004805909004062414, 0.05769386887550354, -0.017032770439982414, -0.04031125828623772, -0.004068817012012005, -0.09060979634523392, -0.05342593044042587, -0.02171057090163231, 0.012473056092858315, -0.020641451701521873, -0.005026286002248526, 0.008673581294715405, -0.0010196695802733302, 0.032505858689546585, -0.03981051966547966, 0.021782072260975838, 0.01779301092028618, -0.06396126002073288, 0.03560180217027664, -0.019271686673164368, -0.019755421206355095, 0.04135429114103317, -0.0926285907626152, 0.045702047646045685, 0.01709318347275257, -0.04883389547467232, 0.009462481364607811, 0.02147473581135273, 0.05956798791885376, 0.04281776398420334, 0.028047582134604454, 0.0007029192056506872, 0.026250628754496574, 0.02709129825234413, 0.03465912491083145, 0.017896590754389763, -0.01872304640710354, 0.012246751226484776, -0.02900419943034649, -0.012743125669658184, 0.0849420502781868, 0.030113432556390762, 0.03795471042394638, 0.05029752850532532, 0.06536131352186203, -0.06854616850614548, -0.03007420338690281, 0.015292820520699024, -0.023865394294261932, -0.018321800976991653, -0.06527342647314072, -0.029576214030385017, 0.0054737841710448265, -0.02626059390604496, -0.01608029380440712, 0.011791292577981949, -0.051915109157562256, 0.055552899837493896, 0.04168933629989624, 0.016063177958130836, 0.02929394133388996, -0.00047004997031763196, -0.031943608075380325, 0.0455855131149292, -0.0478103943169117, -0.009464994072914124, 0.03192197531461716, -0.001039706519804895, -0.025248784571886063, 0.03753472864627838, -0.04409816861152649, -0.013234194368124008, -0.006865435279905796, -0.03857579082250595, -0.017649607732892036, -0.01532215066254139, -0.11761545389890671, -0.006994391325861216, 0.0669921487569809, 0.021350860595703125, 0.02385786548256874, -0.03850269317626953, 0.04373969882726669, -0.04851910099387169, 0.04358280450105667, 0.019208552315831184, 0.0789836198091507, 0.009399393573403358, -0.002239519264549017, 0.030143650248646736, -0.03504513204097748, -0.015311526134610176, -0.07589227706193924, 0.01689787209033966, -0.060954198241233826, -0.07547061890363693, 0.05233760178089142, -0.015448923222720623, -0.005960546433925629, -0.03171830251812935, -0.006706027779728174, -0.00955983903259039, 0.011061389930546284, 0.05250046029686928, 0.00603088503703475, -0.024678092449903488, 0.022503221407532692, 0.04729898273944855, 0.0213030818849802, 0.04086889326572418, 0.022054579108953476, 0.019719257950782776, -0.05148232355713844, -0.017661092802882195, -0.03580211102962494, 0.03747057542204857, -0.030999867245554924, -0.015975723043084145, -0.05416715890169144, -0.04339936375617981, -0.030140681192278862, -0.009157227352261543, 0.0005607428611256182, 0.00528563791885972, -0.011068256571888924, 0.013375625014305115, -0.011772213503718376, -0.019117513671517372, 0.05565764009952545, -0.04777977615594864, 0.050022613257169724, -0.013964067213237286, 0.008459948003292084, 0.05411349982023239, -0.009063472039997578, -0.008891231380403042, -0.004066856112331152, 0.001984365750104189, -0.027404839172959328, -0.02696920931339264, -0.04359753057360649, -0.003805481595918536, -0.001367771066725254, -0.013511347584426403, 0.034238051623106, -0.03657880425453186, 0.03293309360742569, 0.006126424763351679, -0.04278699681162834, -0.002609519986435771, 0.03874766081571579, -0.010582459159195423, 0.005754292011260986, -0.00413286779075861, -0.05270173400640488, -0.08840034157037735, -0.0034904079511761665, -0.01920359954237938, 0.04496359825134277, 0.04643479362130165, 0.06432708352804184, -0.0335121750831604, -0.05652279406785965, -0.028790438547730446, 0.006034465041011572, -0.012648381292819977, -0.03925830498337746, 0.005867679137736559, 0.012968025170266628, 0.02483615279197693, -0.09467256814241409, -0.05888332426548004, 0.019690122455358505, -0.011786543764173985, -0.04951635003089905, 0.0063276211731135845, -0.028639432042837143, -0.05301329866051674, 0.01629951037466526, 0.051665596663951874, -0.01173319760710001, 0.0044763595797121525, -0.04129906743764877, 0.0780530646443367, 0.014381266199052334, -0.02837401255965233, -0.056587547063827515, -0.00700374273583293, 0.011866421438753605, 0.008074545301496983, 0.0581926554441452, 0.03647764399647713, -0.008244995027780533, 0.008314145728945732, 0.018178792670369148, -0.024223407730460167, -0.02125203236937523, 0.028610508888959885, -0.004472892731428146, -0.0036444321740418673, 0.049774039536714554, -0.08134143799543381, 0.036874786019325256, 0.09764433652162552, -0.021823495626449585, 0.03897114843130112, 0.0387277789413929, 0.015638288110494614, 0.031364183872938156, 0.011623828671872616, -0.01790221594274044, -0.03872692212462425, -0.014008593745529652, -0.007081850431859493, -0.0701347216963768, 0.006638607941567898, 0.06814880669116974, -0.025485442951321602, -0.039557334035634995, 0.007003347389400005, -0.024036196991801262, -0.016680840402841568, 0.013076134957373142, 0.03802833333611488, -0.04337189346551895, 0.04289984330534935, 0.04005050286650658, 0.024220557883381844, -0.057866279035806656, 0.01878887414932251, -0.003373929299414158, -0.0004239428963046521, -0.04655032604932785, -0.030749743804335594, -0.00861475057899952, -0.022496594116091728, -0.05929996445775032, -0.000442942779045552, 0.027714984491467476, 0.04342028871178627, -0.010887280106544495, -0.02173064835369587, 0.0020818777848035097, -0.027877088636159897, 0.01477314904332161, -0.07466280460357666, 0.0058792829513549805, -0.07601948827505112, -0.07223490625619888, -0.05597662553191185, -0.05542049556970596, -0.05149606987833977, -0.0075231073424220085, 0.001135579776018858, 0.0599590428173542, -0.04261232540011406, -0.06552713364362717, -0.007699130568653345, 0.009450048208236694, -0.06416627764701843, -0.058674998581409454, -0.009739075787365437, -0.028997216373682022, 0.028408417478203773, 0.0077865514904260635, 0.03573514148592949, -0.01939716376364231, 0.03874817490577698, -0.019173486158251762, 0.023382868617773056, -0.0106167858466506, -0.0021015466190874577, -0.0032568927854299545, -0.02419009990990162, 0.07548683881759644, 0.0704573318362236, 0.0566701740026474, 0.00523980101570487, 0.02558511681854725, 0.016956157982349396, -0.003948430996388197, -0.008283845148980618, 0.0033423237036913633, -0.023245064541697502, 0.016463283449411392, -0.010713264346122742, 0.09490436315536499, -0.03387092798948288, 0.019526928663253784, 0.00008519605034962296, -0.033853840082883835, 0.04205440729856491, -0.012114974670112133, 0.033221904188394547, 0.013990365900099277, -0.019139619544148445, -0.04783264920115471, -0.017754117026925087, -0.08888765424489975, -0.00015589507529512048, -0.03621242567896843, -0.020109867677092552, -0.0907052531838417, 0.016591332852840424, 0.021579086780548096, -0.042473260313272476, 0.07236211746931076, 0.015543683432042599, 0.0031808833591639996, 0.017850181087851524, -0.008187455125153065, 0.00099032127764076, 0.04891311004757881, -0.02679029107093811, -0.08628875017166138, 0.033598337322473526, -0.04104334115982056, -0.009403305128216743, -0.020403893664479256, -0.0187632218003273, -0.03825248405337334, 0.017198529094457626, 0.04861435294151306, -0.002104467712342739, -0.03520838916301727, 0.0010653819190338254, 0.009729048237204552, -0.06370174139738083, -0.029752377420663834, 0.0318310521543026, 0.03226112946867943, -0.03005564585328102, -0.007063673809170723, -0.011445386335253716, -0.023687418550252914, 0.03906842693686485, -0.0009854229865595698, 0.023790979757905006, -0.018872428685426712, -0.01394057460129261, 0.029626261442899704, -0.07680725306272507, -0.03491061553359032, -0.024530183523893356, -0.0421190969645977, 0.036048319190740585, -0.017449604347348213, -0.017304209992289543, -0.06641030311584473, -0.020159613341093063, -0.004124617204070091, -0.03520439192652702, 0.040609586983919144, -0.029309406876564026, -0.0033371606841683388, -0.017373722046613693, 0.03565004840493202, -0.02104410156607628, 0.03878587856888771, 0.0050946916453540325, 0.015158433467149734, -0.012485085055232048, 0.051735471934080124, 0.014199638739228249, 0.04557400569319725, 0.05174320191144943, -0.005075670778751373, -0.040522996336221695, -0.014168954454362392, -0.000593933742493391, -0.06809534877538681, 0.015306596644222736, 0.002719003474339843, 0.008084271103143692, 0.03046221099793911, -0.008820443414151669, -0.017115158960223198, -0.033766649663448334, -0.02584587037563324, 0.02150743454694748, -0.01808183267712593, -0.00255860248580575, -0.031519826501607895, 0.015318312682211399, 0.018321974202990532, -0.029701415449380875, -0.04233456030488014, 0.021051965653896332, 0.047596052289009094, 0.0460951030254364, 0.01987447962164879, 0.05290256068110466, 0.046401191502809525, -0.04251987114548683, 0.010250012390315533, -0.02218899503350258, -0.022560784593224525, -0.06546062976121902, 0.03091232292354107, -0.001785977859981358, -0.008417511358857155, -0.004183263052254915, -0.10849326848983765, 0.07319043576717377, -0.044827595353126526, 0.037479251623153687, 0.0008911925251595676, 0.024483174085617065, 0.0647110641002655, -0.06527912616729736, 0.05048466473817825, 0.026419885456562042, -0.00033619723399169743, 0.01766708865761757, -0.030083846300840378, 0.012299716472625732, 0.04166644811630249, 0.04906244948506355, -0.012361474335193634, 0.05280168354511261, -0.051827140152454376, 0.003396562533453107, 0.030708134174346924, -0.05893964692950249, 0.05289619043469429, -0.044697873294353485, -0.0626777708530426, -0.06282863020896912, 0.056824941188097, -0.02504456415772438, 0.092624232172966, 0.04884620010852814, -0.040939465165138245, -0.01346407551318407, -0.0051323408260941505, 0.03736031800508499, -0.009586134925484657, -0.0013615451753139496, 0.020758353173732758, -0.005596131552010775, 0.023531625047326088, 0.07336540520191193, 0.0170645359903574, 0.015587184578180313, -0.03657560795545578, 0.018272414803504944, 0.04702332615852356, -0.0010565264383330941, 0.011529364623129368, 0.008001300506293774, 0.05567963421344757, 0.01705634593963623, -0.011854189448058605, 0.011661640368402004, 0.020361274480819702, 0.020187992602586746, 0.003962743561714888, 0.015379736199975014, 0.008105015382170677, 0.08025389909744263, -0.019776619970798492, 0.015669509768486023, 0.006873025093227625, 0.06419684737920761, -0.007346106693148613, 0.000617984973359853, 0.008554388768970966, 0.03432613983750343, 0.028487613424658775, -0.012648596428334713, 0.0761750191450119, 0.02520723268389702, -0.020668743178248405, 0.010609335266053677, 0.013824369758367538, 0.026090102270245552, -0.023400282487273216, 0.0012089281808584929, -0.024625582620501518, -0.011893212795257568, 0.03454203903675079, 0.03495296090841293, 0.07015914469957352, 0.01895412988960743, 0.017324984073638916, 0.00578473461791873, 0.005676665809005499, 0.03544997051358223, 0.017881320789456367, 0.038421373814344406, -0.022101232782006264, -0.02321266382932663, -0.000277688232017681, -0.0226439218968153, -0.008043544366955757, 0.03645062446594238, -0.01495426520705223, -0.007345650810748339, -0.008779033087193966, 0.008597820065915585, -0.05558847263455391, 0.04592137038707733, 0.02676377259194851, -0.06830596178770065, 0.04509206488728523, -0.0013925312086939812, -0.005925011821091175, 0.02317844144999981, -0.0018429849296808243, 0.04888342693448067, -0.0409301295876503, 0.022978322580456734, -0.07829543203115463, 0.03480542078614235, -0.008355848491191864, -0.008440721780061722, -0.061558373272418976, -0.02501121535897255, 0.06287389993667603, -0.004675765056163073, 0.00872178003191948, -0.0006183138466440141, -0.023516187444329262, -0.009341667406260967, 0.02984757162630558, -0.008348003961145878, 0.05744100362062454, 0.008240851573646069, -0.06938645243644714, 0.026640545576810837, 0.0014832582091912627, -0.04043061286211014, 0.04690674692392349, 0.001270813518203795, 0.002666066400706768, 0.013926543295383453, -0.014793609268963337, -0.002957260701805353, 0.008427917025983334, 0.052426569163799286, -0.02242758683860302, 0.0182646457105875, 0.08625036478042603, -0.04293359816074371, 0.03429928049445152, 0.03475618362426758, 0.08060130476951599, -0.02199975773692131, 0.029199356213212013, 0.042009901255369186, -0.035470135509967804, -0.01711152493953705, 0.05401064455509186, 0.037640150636434555, 0.02345988340675831, -0.06893277168273926, -0.02791013941168785, 0.04674677923321724, -0.009494866244494915, -0.0021133525297045708, 0.012976503930985928, 0.06490615755319595, 0.0008730104891583323, 0.004197555594146252, 0.04647083207964897, 0.010710090398788452, 0.00836120918393135, 0.012336937710642815, -0.06224776431918144, 0.042312443256378174, -0.02787408046424389, 0.06622461974620819, 0.06685701012611389, 0.079078808426857, -0.03568291291594505, 0.04728414863348007, -0.02561667002737522, -0.01086403988301754, 0.006318767089396715, 0.023286161944270134, -0.039656322449445724, -0.03813662752509117, -0.06503719091415405, 0.03609396144747734, 0.02024233527481556, -0.021976681426167488, 0.011557922698557377, -0.06457361578941345, -0.033870629966259, 0.028732309117913246, -0.029884811490774155, -0.0015637387987226248, -0.016871877014636993, -0.04339955747127533, -0.009797350503504276, -0.025486227124929428, 0.011856256052851677, -0.0032264036126434803, 0.028509482741355896, -0.03358817845582962, -0.05191626772284508, 0.03262817859649658, -0.000049921683967113495, -0.02441324107348919, -0.03702804818749428, -0.019742434844374657, -0.017052406445145607, 0.00249210256151855, -0.027583429589867592, 0.009555584751069546, -0.03667289391160011, 0.05745236575603485, -0.02859313227236271, 0.012854008004069328, -0.048360757529735565, -0.045932117849588394, 0.005671368911862373, 0.026489943265914917, 0.058730512857437134, 0.017952444031834602, 0.04751119017601013, -0.0130666084587574, -0.006881765089929104, -0.01778634637594223, 0.008654655888676643, -0.028209730982780457, -0.04107121378183365, -0.04586257413029671, -0.031370412558317184, 0.01812116988003254, -0.0041977157816290855, 0.02428213134407997, 0.00607489375397563, -0.019112251698970795, 0.03934188932180405, 0.013208980672061443, 0.037117186933755875, -0.02658773958683014, 0.10304609686136246, -0.05339571461081505, -0.044982705265283585, -0.0360800102353096, -0.009532120078802109, -0.002207160694524646, -0.01629033125936985, -0.006612308323383331, 0.05193423852324486, 0.009184569120407104, -0.013791211880743504, -0.04549429938197136, -0.004916028585284948, -0.03809739276766777, -0.011493073776364326, -0.01148375403136015, 0.025722676888108253, 0.08970117568969727, -0.003952986095100641, 0.016703808680176735, 0.014797823503613472, 0.009938684292137623, 0.03436923027038574, 0.004455622751265764, -0.005131378769874573, 0.010459933429956436, 0.02196040377020836, 0.01925666071474552, 0.025692248716950417, 0.05444309115409851, -0.017093433067202568, -0.02364562824368477, 0.05746115744113922, -0.021736854687333107, 0.03108229488134384, -0.02574293129146099, 0.008002831600606441 ]
<ol> <li><p>Mathematically, (by mathematically I means by equations) what is path of light in the accelerating elevator?</p></li> <li><p>What is the difference between an ordinary derivative and covariant derivative (which is used in curved geodesic)?</p></li> </ol>
g8350
[ 0.06851675361394882, 0.06916235387325287, -0.029527943581342697, 0.02290605567395687, 0.0385570265352726, 0.0272191371768713, 0.048521738499403, -0.0522608645260334, -0.05916591361165047, -0.0019971393048763275, 0.006266401614993811, -0.023064130917191505, 0.09715365618467331, 0.015082431957125664, -0.014225039631128311, -0.013522839173674583, 0.036491088569164276, 0.009815027005970478, 0.060238081961870193, -0.029153700917959213, 0.02260890044271946, 0.05215327441692352, -0.005828918889164925, -0.05375099182128906, 0.058525677770376205, 0.012627553194761276, -0.00626995088532567, -0.042551860213279724, -0.0982428565621376, -0.001622669631615281, 0.017538951709866524, -0.019539611414074898, 0.08404587209224701, -0.02840900607407093, -0.03983543813228607, 0.0014444143744185567, 0.04137606918811798, 0.04516100883483887, 0.0730319544672966, 0.007328196428716183, 0.04029354825615883, 0.010113045573234558, 0.056447770446538925, 0.03436588868498802, 0.007995249703526497, -0.005487882997840643, -0.04347396269440651, 0.03282545879483223, 0.048813216388225555, 0.011460886336863041, -0.0321224145591259, 0.029382992535829544, -0.015888599678874016, -0.02831714041531086, -0.033174723386764526, 0.029800180345773697, 0.01479760929942131, -0.00042956898687407374, 0.0010975354816764593, 0.06310943514108658, -0.017314225435256958, -0.03779048100113869, 0.05861058458685875, 0.014066214673221111, 0.09730500727891922, -0.02246115356683731, -0.00156543985940516, -0.04857770353555679, 0.04400382936000824, -0.05146445333957672, 0.06789897382259369, -0.06504746526479721, 0.034543879330158234, -0.05549793690443039, -0.0629703626036644, -0.05593344196677208, 0.036191437393426895, -0.005450707860291004, -0.008462333120405674, -0.006185288541018963, -0.03283362835645676, 0.02238040789961815, 0.0007034372538328171, -0.02523154765367508, 0.03544198349118233, 0.037574172019958496, -0.012157768942415714, 0.04836663976311684, 0.0021030434872955084, -0.004066329915076494, 0.029490182176232338, -0.038647327572107315, 0.04643608629703522, 0.03174258768558502, -0.07051915675401688, -0.037403542548418045, -0.029488040134310722, 0.0339713953435421, 0.019387241452932358, -0.009058783762156963, 0.0005661281757056713, -0.029058845713734627, -0.014678466133773327, 0.0329962782561779, 0.011206588707864285, -0.03549632802605629, -0.0056671397760510445, -0.017612343654036522, 0.04264760762453079, -0.04615183174610138, 0.011980396695435047, -0.03800849989056587, -0.03124462440609932, -0.07920053601264954, 0.010706901550292969, -0.005725323688238859, 0.03177255764603615, 0.023008940741419792, -0.034689076244831085, 0.03932849317789078, 0.03140854462981224, 0.04241273179650307, -0.007444876711815596, 0.013352558016777039, 0.050090860575437546, 0.029749559238553047, 0.034148331731557846, -0.02692755125463009, 0.00299840047955513, -0.008603053167462349, 0.05418198183178902, 0.01379198394715786, -0.053716741502285004, 0.020251549780368805, -0.047604359686374664, 0.01109806727617979, -0.0342579260468483, -0.012414145283401012, -0.020864412188529968, -0.035710226744413376, -0.026179837062954903, -0.05782107263803482, 0.018637945875525475, -0.0011158144334331155, -0.03662475571036339, 0.05562729388475418, 0.024659009650349617, 0.016441315412521362, 0.03151848167181015, 0.0336429588496685, -0.01722273975610733, 0.06661759316921234, 0.008991992101073265, -0.06730864942073822, 0.020916476845741272, -0.006291291676461697, 0.030123243108391762, 0.05732537806034088, -0.029978320002555847, -0.010452463291585445, 0.025019949302077293, 0.015163171105086803, 0.017852934077382088, -0.028044208884239197, -0.04702818766236305, -0.030513934791088104, -0.02627304196357727, -0.05084953084588051, 0.021462135016918182, -0.023211656138300896, -0.02689977176487446, -0.0016691366909071803, 0.04920994117856026, 0.01945350132882595, 0.014324614778161049, 0.03511283919215202, 0.021912820637226105, -0.03757159411907196, -0.003146945498883724, -0.01568073034286499, -0.009407417848706245, -0.029661597684025764, -0.0039724078960716724, -0.035332899540662766, -0.045483335852622986, -0.03561367467045784, -0.03845486417412758, -0.05290031060576439, -0.05205962061882019, -0.0032175828237086535, -0.0020034725312143564, -0.028851870447397232, -0.036714017391204834, 0.08009997755289078, -0.038259103894233704, -0.021987371146678925, -0.004989375825971365, -0.021496500819921494, -0.029630664736032486, 0.04890628159046173, 0.035177718847990036, 0.07078772038221359, 0.05410558357834816, -0.008381425403058529, -0.014771648682653904, 0.033734142780303955, -0.018190374597907066, -0.01790979504585266, 0.0009785136207938194, -0.029452841728925705, 0.0469207726418972, 0.013940120115876198, 0.08064263314008713, -0.0031201099045574665, 0.008903318084776402, -0.011293556541204453, -0.007980333641171455, -0.008207576349377632, 0.004955974407494068, -0.02818157523870468, 0.022482018917798996, -0.014086365699768066, 0.006524983327835798, -0.07116986066102982, 0.006406362634152174, 0.025548860430717468, -0.08014137297868729, -0.03505661338567734, 0.04354614391922951, 0.020118776708841324, -0.0760444924235344, -0.04406486079096794, -0.03790448606014252, -0.008362402208149433, 0.05867576599121094, 0.01963798515498638, -0.04127127677202225, 0.01972603052854538, 0.055283475667238235, 0.09346862882375717, 0.03751678019762039, -0.021904747933149338, 0.01771906577050686, 0.002592513570562005, -0.03779065981507301, -0.03657897934317589, 0.06956399977207184, 0.04836946353316307, -0.010275916196405888, -0.018160909414291382, 0.015722988173365593, -0.0509258508682251, -0.04216834902763367, 0.05536191165447235, 0.011785954236984253, -0.023956600576639175, -0.03217120096087456, 0.00901929009705782, -0.015564309433102608, 0.03316894918680191, -0.019134528934955597, -0.009971859864890575, 0.01529884897172451, 0.00043873919639736414, -0.017676061019301414, 0.005685688927769661, -0.00048730490379966795, -0.005275988485664129, 0.04151509329676628, -0.027522670105099678, 0.05479414761066437, 0.07044144719839096, -0.07450561225414276, 0.036996111273765564, 0.010361384600400925, -0.008119109086692333, -0.030802560970187187, -0.016394557431340218, -0.0023445880506187677, -0.032930485904216766, 0.057145021855831146, -0.05676549673080444, -0.033497054129838943, 0.006804062053561211, 0.017165521159768105, -0.029094090685248375, 0.037540119141340256, 0.020582817494869232, -0.025491859763860703, 0.042416710406541824, -0.06638297438621521, -0.02577180601656437, -0.03628012537956238, -0.06561767309904099, -0.02836449258029461, -0.0009716282365843654, -0.0019913003779947758, 0.026344003155827522, 0.017033308744430542, -0.018493881449103355, 0.013742097653448582, -0.05667303502559662, 0.03468483313918114, -0.024118799716234207, -0.023374589160084724, 0.010542400181293488, 0.0010625708382576704, -0.05066667124629021, -0.015489386394619942, 0.03926948830485344, 0.004786801990121603, 0.016041988506913185, 0.01441881712526083, -0.02332187443971634, -0.004945461638271809, -0.01287507452070713, -0.0018195600714534521, -0.03170507401227951, 0.06384468078613281, 0.04321281239390373, -0.05554080754518509, -0.04742889478802681, -0.08017923682928085, -0.006661455612629652, -0.004952149465680122, 0.0009689692524261773, 0.023950859904289246, 0.010521512478590012, 0.004492226988077164, -0.0716717541217804, 0.005811590701341629, -0.007012433372437954, 0.001745828427374363, 0.00906184408813715, 0.030073439702391624, -0.06204031780362129, -0.05323952063918114, 0.036642298102378845, 0.04992294684052467, 0.0027146039064973593, 0.007540159858763218, 0.002219043904915452, -0.08138024061918259, -0.006649157032370567, -0.02855873852968216, -0.03826243430376053, 0.025153955444693565, 0.04513698071241379, 0.027139246463775635, -0.04511401057243347, 0.0676283985376358, -0.05441323667764664, 0.02838023193180561, -0.038308531045913696, -0.022798879072070122, 0.017890959978103638, 0.0319945365190506, 0.03971341997385025, 0.007819087244570255, 0.0414775125682354, 0.0030890372581779957, 0.013259872794151306, -0.019943609833717346, 0.0612659752368927, 0.013823469169437885, 0.015577943995594978, 0.000410718988860026, 0.03465178981423378, -0.08999768644571304, -0.040690455585718155, 0.01041463389992714, 0.03412371501326561, -0.0011298246681690216, -0.017678363248705864, 0.03144938871264458, -0.005655139684677124, -0.0038873006124049425, -0.014823447912931442, -0.04485735297203064, -0.01854340359568596, 0.0053197587840259075, -0.0004417146265041083, 0.06139002740383148, -0.00025768877821974456, 0.026134822517633438, -0.007461442146450281, -0.06430873274803162, -0.03825626149773598, 0.03651046380400658, -0.01830732636153698, 0.044524919241666794, -0.04332832992076874, -0.01961473561823368, 0.015401627868413925, 0.02702016569674015, -0.006050434894859791, 0.023805372416973114, 0.037619344890117645, -0.040962863713502884, 0.003077482571825385, -0.009646788239479065, 0.041165221482515335, 0.04073689505457878, 0.02728472463786602, -0.03505079820752144, 0.02160421758890152, 0.05034823343157768, -0.052053578197956085, -0.00003982759153586812, 0.03541838750243187, 0.052764080464839935, -0.04058696702122688, 0.006493010092526674, -0.03841913491487503, 0.052317336201667786, 0.001811567577533424, 0.049852155148983, 0.006858688313513994, -0.009921912103891373, 0.033644452691078186, 0.059497419744729996, 0.012835178524255753, 0.018071847036480904, -0.014494013972580433, 0.009723440743982792, 0.04605751112103462, 0.039310652762651443, -0.002920824335888028, -0.05836045742034912, -0.06533854454755783, -0.016080884262919426, 0.03077705018222332, -0.002727409126237035, 0.023267876356840134, -0.0633024349808693, 0.05410481616854668, 0.0080948481336236, 0.06988818198442459, 0.004491504281759262, 0.013082199729979038, 0.058007676154375076, -0.012751174159348011, 0.017810000106692314, -0.013449996709823608, 0.037204429507255554, 0.055534783750772476, -0.01595812849700451, -0.08521263301372528, -0.03599780052900314, 0.0018212177092209458, -0.004811588674783707, 0.03843333199620247, 0.0005567448679357767, 0.038392964750528336, 0.011347953230142593, -0.02242695912718773, -0.06471666693687439, -0.013298066332936287, 0.026601653546094894, 0.054968006908893585, -0.011851085349917412, 0.006819906644523144, -0.037756387144327164, -0.04421557858586311, -0.01153675839304924, -0.05321335047483444, -0.08993522077798843, -0.007964806631207466, 0.015350526198744774, -0.005694684572517872, -0.013029082678258419, 0.012189384549856186, 0.020560462027788162, 0.010951690375804901, 0.016541091725230217, 0.018259160220623016, 0.016397977247834206, 0.04540816694498062, -0.041080232709646225, -0.05175025388598442, -0.050727639347314835, -0.038668498396873474, -0.020190326496958733, -0.04331658408045769, -0.03663387522101402, -0.01441084872931242, 0.00884185079485178, -0.0206140149384737, 0.023348761722445488, -0.061682648956775665, 0.06501055508852005, 0.012548936530947685, 0.021895628422498703, -0.014874284155666828, -0.06097104772925377, -0.0019916957244277, 0.020845569670200348, 0.0070641846396028996, 0.016604481264948845, -0.029914112761616707, -0.12120511382818222, 0.01048397459089756, -0.02224588952958584, -0.01231718622148037, 0.022363917902112007, 0.004031051881611347, 0.039438944309949875, 0.005342745687812567, -0.024232905358076096, 0.0416402705013752, 0.011929775588214397, -0.032015737146139145, 0.0039017233066260815, 0.027116194367408752, 0.010207698680460453, 0.010611122474074364, -0.02714618481695652, 0.052697449922561646, 0.0016397750005126, -0.09210268408060074, 0.009864941239356995, -0.005323188379406929, 0.030490299686789513, -0.011605599895119667, 0.06027987226843834, 0.0010805075289681554, -0.030678192153573036, -0.03405728563666344, 0.010474101640284061, 0.006778012961149216, 0.0033625622745603323, 0.013369858264923096, 0.03578508645296097, -0.05158379301428795, -0.03289934620261192, -0.028191499412059784, 0.05489889159798622, 0.01609046570956707, 0.013956643640995026, -0.005704727955162525, -0.09696035087108612, -0.046757590025663376, 0.0022145016118884087, 0.08980947732925415, -0.004181194119155407, 0.014026510529220104, -0.04630469158291817, 0.01704036258161068, 0.041086338460445404, -0.04940014332532883, -0.04406527802348137, -0.05304426699876785, 0.042104147374629974, 0.03513585776090622, -0.04363267496228218, 0.01752426289021969, 0.022094013169407845, 0.008747292682528496, -0.05831245332956314, -0.028525806963443756, 0.029293227940797806, 0.0017916205106303096, -0.0010767847998067737, -0.06583407521247864, -0.018143180757761, -0.05705190449953079, 0.018378164619207382, 0.023092493414878845, 0.058018557727336884, 0.031259771436452866, -0.002825680887326598, -0.0036248823162168264, 0.006380281876772642, 0.05165690556168556, 0.021842291578650475, 0.022695470601320267, -0.05544494464993477, -0.05134851858019829, -0.06375197321176529, -0.002876548795029521, -0.015452632680535316, 0.0219101645052433, 0.010123275220394135, -0.03649113327264786, -0.03091134876012802, -0.01739254966378212, -0.06576191633939743, -0.016300199553370476, 0.06069858744740486, -0.03876461833715439, -0.03413093090057373, 0.0062080309726297855, -0.030034692957997322, -0.02942430041730404, -0.02110310085117817, 0.0029817780014127493, -0.024561163038015366, 0.06588798016309738, 0.03588620945811272, -0.01759623922407627, 0.008928903378546238, 0.05225035175681114, 0.03945841267704964, 0.007980631664395332, 0.047812871634960175, -0.010025521740317345, -0.014579420909285545, 0.007223010994493961, 0.020510578528046608, -0.04372597113251686, 0.04716718941926956, 0.0645698830485344, -0.0012574910651892424, 0.008750728331506252, -0.025516267865896225, 0.03891034796833992, -0.03374674916267395, 0.012254789471626282, 0.04277336597442627, -0.048931192606687546, 0.03451637923717499, -0.011372992768883705, -0.01863124780356884, 0.0031071677803993225, 0.01757531426846981, 0.02230246737599373, -0.028336510062217712, 0.03090333752334118, -0.0025219495873898268, -0.000965869752690196, 0.008431075140833855, 0.009932163171470165, -0.013933291658759117, 0.02485751546919346, 0.022804128006100655, 0.044380925595760345, -0.008981714025139809, 0.02876598760485649, 0.03594339266419411, 0.01917789690196514, 0.017816273495554924, 0.05908030644059181, 0.006618991028517485, 0.027445564046502113, -0.04424351081252098, 0.021031562238931656, -0.040291279554367065, -0.025176437571644783, -0.008361242711544037, -0.01906132884323597, 0.009185579605400562, -0.021222194656729698, -0.013967516832053661, 0.001576036331243813, -0.06356579065322876, 0.03591582179069519, -0.005700763780623674, 0.020432446151971817, -0.01656571589410305, -0.06573238968849182, -0.019231125712394714, 0.041612621396780014, -0.006186098791658878, 0.019355710595846176, -0.0016443125205114484, 0.02243512123823166, 0.010304647497832775, -0.018378114327788353, -0.0048000384122133255, 0.08048103004693985, 0.011100288480520248, -0.029931843280792236, 0.004096220247447491, 0.07629922777414322, -0.002760143019258976, 0.029417866840958595, -0.07418739795684814, 0.0008851799066178501, -0.008179680444300175, 0.0071528274565935135, 0.004887165501713753, 0.06325000524520874, 0.005255789030343294, -0.05288657918572426, -0.010415320284664631, 0.028291964903473854, -0.00489388033747673, -0.05644688755273819, -0.016179151833057404, -0.05114694684743881, -0.06156199797987938, 0.02034018561244011, -0.04786396026611328, -0.025082087144255638, -0.004247283563017845, 0.029331788420677185, -0.030857974663376808, 0.11065404117107391, 0.00924602523446083, 0.05600026249885559, -0.012654639780521393, -0.0003628966514952481, 0.012263905256986618, 0.012414053082466125, -0.03687141090631485, -0.028197744861245155, 0.0027583949267864227, -0.0004349224327597767, -0.016217034310102463, 0.044343139976263046, -0.006787756457924843, 0.03794700279831886, 0.009767517447471619, 0.06710787117481232, -0.0011203904869034886, 0.04251869022846222, 0.01808372139930725, 0.00838267058134079, -0.06633114814758301, 0.016908567398786545, -0.005634504836052656, 0.0033996361307799816, 0.005266882944852114, -0.07621224969625473, 0.022109856829047203, 0.002874700352549553, -0.006951242685317993, -0.042855773121118546, -0.0506998673081398, -0.040793780237436295, 0.008188607171177864, 0.0052056685090065, 0.024115784093737602, 0.05213446542620659, -0.05877099558711052, 0.028010275214910507, -0.033072084188461304, -0.0021504852920770645, 0.04337599501013756, 0.004890889395028353, 0.03108573704957962, -0.06349722295999527, -0.0020538654644042253, -0.009878718294203281, -0.008891636505723, 0.061627503484487534, 0.003558497875928879, 0.01880621165037155, 0.0185651034116745, -0.0030547496862709522, 0.03569124639034271, 0.0586259588599205, -0.045274440199136734, 0.04593881592154503, 0.02147110179066658, -0.03854382783174515, -0.04497157037258148, -0.033194396644830704, 0.06328096240758896, -0.02692071907222271, -0.024434298276901245, -0.055284418165683746, 0.010614139959216118, -0.04808908328413963, -0.01802677847445011, -0.053165435791015625, -0.024777056649327278, 0.0317143090069294 ]
<p>I have read about the application of railguns and other ground powered launch, where there is no need to carry any propellant in the rocket.</p> <p>I am wondering, to <strong>what velocity should the vehicle achieve to enter into the orbit of earth?</strong> I know the orbital velocity and escape velocity calculations and their values too. I want to know the practical velocity needed, <strong><em>by accounting for the atmospheric resistance</em></strong>. </p> <p>Will the rocket enter into an orbit when launched at any angle? Or <em>is there a range of angle of launch</em> to achieve orbit?</p>
g8351
[ -0.010859191417694092, 0.04738186299800873, 0.005272848531603813, 0.0363205224275589, -0.00127418281044811, 0.006407658103853464, -0.004631971940398216, -0.0031948748510330915, -0.07343891263008118, -0.02972266636788845, 0.009685037657618523, 0.013101915828883648, 0.043720271438360214, -0.006130457855761051, 0.034311626106500626, -0.0005848849541507661, 0.10067048668861389, -0.06429992616176605, 0.04952888563275337, 0.053660690784454346, 0.018793543800711632, -0.035784751176834106, -0.016346778720617294, 0.021962845697999, 0.0034412292297929525, -0.006997557822614908, 0.021803230047225952, -0.07430656254291534, -0.051203954964876175, 0.018293272703886032, 0.005757526028901339, -0.03525876626372337, 0.013152250088751316, -0.04691072925925255, -0.06504900008440018, -0.026004156097769737, -0.03310057520866394, 0.021679643541574478, 0.019093913957476616, -0.06114168465137482, -0.008271291851997375, -0.04842366278171539, -0.06459331512451172, 0.024464232847094536, 0.012473855167627335, 0.013818996958434582, -0.019784489646553993, -0.049760427325963974, 0.004504010546952486, -0.013578945770859718, -0.031074898317456245, -0.0014947077725082636, -0.031687453389167786, -0.08854140341281891, -0.02952101267874241, -0.0009877184638753533, -0.043955810368061066, -0.02484602853655815, 0.01505668181926012, -0.05296912044286728, 0.04136522114276886, -0.03301379084587097, -0.029148967936635017, -0.03511267155408859, 0.03309464082121849, -0.007170687895268202, -0.052511412650346756, 0.03886793553829193, 0.03700019419193268, 0.04870769754052162, 0.030660375952720642, -0.03513871878385544, -0.06679313629865646, -0.07398167997598648, -0.00684649171307683, -0.027815233916044235, 0.020428622141480446, -0.0411943644285202, 0.003867045044898987, 0.0039363885298371315, 0.02225670777261257, 0.005163058638572693, 0.017667466774582863, -0.01360727846622467, -0.005478399805724621, -0.026988903060555458, 0.017257437109947205, -0.01024885755032301, 0.01830984838306904, -0.025273360311985016, 0.019832398742437363, 0.03454015031456947, 0.03084387816488743, 0.05603776127099991, -0.002361380262300372, -0.019458459690213203, -0.07676169276237488, 0.09180223941802979, 0.009660501033067703, 0.022540461272001266, -0.004910734482109547, -0.035210322588682175, -0.03147383779287338, -0.04300453141331673, 0.033020153641700745, 0.005791014526039362, 0.04015070199966431, 0.026911890134215355, 0.042265910655260086, -0.05323311686515808, 0.006100154016166925, -0.016104573383927345, -0.0044252583757042885, 0.012202177196741104, 0.005751054268330336, 0.04057467356324196, 0.041141487658023834, -0.057734932750463486, 0.036889251321554184, 0.03713779151439667, 0.05185422673821449, 0.035328954458236694, 0.010910826735198498, 0.054918739944696426, -0.028086157515645027, -0.027899235486984253, -0.03747676685452461, -0.07483387738466263, 0.021109160035848618, 0.031530316919088364, -0.0383664071559906, -0.04195880889892578, -0.014128850772976875, -0.042629603296518326, 0.0040645720437169075, 0.026266925036907196, 0.018417000770568848, -0.06616371870040894, -0.01697382517158985, 0.0054351952858269215, 0.01533978246152401, 0.033803995698690414, 0.05132797732949257, 0.040687184780836105, -0.05446049943566322, 0.021987132728099823, 0.01392220240086317, 0.067659892141819, 0.015546750277280807, 0.04409487172961235, 0.015405348502099514, 0.0712193176150322, 0.026186294853687286, 0.027737975120544434, -0.016767485067248344, -0.033019497990608215, 0.048095814883708954, 0.03517887741327286, 0.01665104739367962, -0.030190199613571167, 0.050604116171598434, 0.02476811222732067, -0.018352556973695755, 0.008239989168941975, -0.07020840048789978, 0.009757950901985168, 0.009047023020684719, -0.06384578347206116, -0.0016657233936712146, -0.006605950184166431, -0.0012147254310548306, -0.03494371473789215, -0.020590560510754585, 0.03568834066390991, -0.09050910174846649, -0.017618488520383835, 0.08810046315193176, 0.06414636224508286, 0.03163278102874756, -0.037691693753004074, 0.031179413199424744, -0.05133404582738876, 0.0191746074706316, -0.008491737768054008, -0.0776975005865097, -0.06277822703123093, 0.010453945957124233, 0.002426090883091092, -0.040876831859350204, 0.05925573781132698, -0.017988624051213264, 0.008581852540373802, -0.03450478985905647, 0.0023371458519250154, -0.023137716576457024, -0.02158736251294613, 0.022899145260453224, 0.008558867499232292, -0.04667661339044571, 0.011969723738729954, 0.04141337797045708, 0.06403473019599915, 0.030490269884467125, -0.00874993298202753, 0.00907332543283701, -0.03707542270421982, 0.0031752977520227432, 0.03328507021069527, 0.02129395492374897, 0.021320782601833344, 0.055668819695711136, -0.01715114153921604, 0.005008121486753225, 0.0496523380279541, 0.0618988536298275, 0.057455480098724365, -0.0010003193747252226, 0.018583092838525772, 0.00897269044071436, 0.015409679152071476, -0.004790925886482, -0.005198636092245579, 0.003052277024835348, 0.01859322190284729, -0.0019227814627811313, 0.037735067307949066, -0.07101520150899887, 0.026904480531811714, 0.10453201085329056, -0.02797514572739601, 0.007362060714513063, -0.032139264047145844, -0.029803691431879997, -0.07864910364151001, 0.026848090812563896, -0.0056892093271017075, 0.023607291281223297, -0.02235330082476139, -0.0313245989382267, 0.004956905264407396, 0.01582048274576664, -0.03467963635921478, -0.0001799605379346758, -0.014178293757140636, 0.03531842678785324, -0.09064415842294693, 0.03858259320259094, 0.04569720849394798, -0.03647204115986824, -0.013474679552018642, 0.02772372029721737, 0.013915701769292355, -0.04793348163366318, -0.0032182426657527685, -0.08252395689487457, 0.025106651708483696, -0.021921055391430855, -0.00950108002871275, -0.061922814697027206, -0.006787479389458895, -0.05536473169922829, -0.014825677499175072, 0.019400229677557945, 0.012235707603394985, -0.04327749088406563, 0.04476049914956093, -0.05828186869621277, -0.012068945914506912, 0.012885641306638718, -0.02160974219441414, -0.04509231075644493, 0.0051898714154958725, -0.013237853534519672, 0.02919173426926136, 0.02672789804637432, -0.016284575685858727, 0.034097056835889816, -0.03754599392414093, 0.0009420116548426449, 0.04871678352355957, 0.01476558018475771, -0.05905602127313614, -0.026590345427393913, 0.021496327593922615, 0.012986564077436924, -0.01626305840909481, 0.06584189087152481, 0.06767001003026962, 0.03643789887428284, -0.03660992532968521, 0.0009992066770792007, 0.026612743735313416, -0.006209681276232004, 0.00600798474624753, -0.011266425251960754, 0.01813637837767601, 0.04001404345035553, 0.0022201333194971085, 0.01999787800014019, -0.0846140906214714, 0.018745947629213333, -0.03984910249710083, 0.015718959271907806, -0.018510805442929268, -0.07342806458473206, 0.040960460901260376, -0.0029244013130664825, 0.0024455152451992035, -0.018759071826934814, -0.024386439472436905, 0.019782520830631256, 0.03751092776656151, 0.017140116542577744, 0.02966238185763359, -0.023200204595923424, -0.006537874694913626, -0.01173484418541193, 0.015575545839965343, 0.007028142921626568, 0.02425609529018402, -0.03868650645017624, -0.09580610692501068, -0.012068210169672966, 0.021863680332899094, -0.035034116357564926, 0.00821803417056799, -0.0027403580024838448, -0.013562661595642567, 0.014257439412176609, -0.012037355452775955, 0.009665777906775475, 0.12439651787281036, -0.028307843953371048, -0.01600073091685772, -0.005569098051637411, 0.04752648249268532, 0.037632185965776443, 0.03355937823653221, 0.003899485571309924, 0.01751028187572956, -0.0021002492867410183, -0.02860555797815323, -0.01232936792075634, -0.015825346112251282, -0.0012164758518338203, -0.03705016151070595, 0.02886555902659893, 0.01925245113670826, -0.035738468170166016, -0.04369184002280235, 0.04670551046729088, -0.02493421733379364, 0.004142696037888527, -0.03511613979935646, -0.056735169142484665, 0.0228712297976017, -0.021852578967809677, 0.1020747572183609, 0.01439754944294691, 0.0028466791845858097, 0.0018114703707396984, -0.005910532549023628, -0.01847168803215027, 0.038957685232162476, 0.02200063318014145, -0.04769507795572281, -0.06381787359714508, 0.009423264302313328, -0.014314001426100731, -0.026332184672355652, -0.006471999455243349, -0.08306976407766342, -0.0038528305012732744, -0.02830212563276291, 0.045730169862508774, -0.002646051812916994, 0.03801504895091057, 0.011692016385495663, -0.0954417735338211, 0.02514253370463848, 0.04615943133831024, 0.019211063161492348, -0.010645769536495209, 0.029605040326714516, 0.034001171588897705, -0.01747038960456848, -0.03348562493920326, 0.060172080993652344, -0.003655156120657921, 0.007357730995863676, 0.022918779402971268, -0.05967932939529419, -0.008355000987648964, 0.01769302412867546, 0.020826907828450203, -0.005931801628321409, -0.006999110337346792, -0.01815374754369259, -0.008702356368303299, 0.055761512368917465, 0.028137141838669777, 0.00626545213162899, -0.005147199612110853, 0.026807276532053947, 0.0204811692237854, 0.025088444352149963, -0.0015220092609524727, 0.019606828689575195, -0.028823409229516983, -0.013414186425507069, 0.04077112674713135, 0.030285388231277466, -0.037953734397888184, -0.012110664509236813, -0.002440069569274783, -0.015596778132021427, -0.01762242801487446, 0.013689122162759304, -0.032824061810970306, -0.014655063860118389, -0.012574427761137486, 0.017322391271591187, -0.0035242147278040648, -0.047616321593523026, 0.009951012209057808, 0.03304246813058853, 0.02997715026140213, 0.006952924653887749, 0.06986048817634583, -0.00978152360767126, 0.020219413563609123, -0.00654462119564414, -0.031177328899502754, 0.040596865117549896, -0.05057967081665993, 0.05761951580643654, 0.008020400069653988, 0.0722692608833313, 0.01859964430332184, 0.02898195944726467, 0.018000086769461632, 0.04284811392426491, 0.00472980085760355, 0.025229910388588905, -0.010116453282535076, 0.05110439658164978, 0.03146875277161598, 0.017607353627681732, -0.015476531349122524, -0.03669210523366928, 0.02639036998152733, -0.021420273929834366, 0.014506090432405472, 0.03023136407136917, -0.08025998622179031, 0.024956073611974716, -0.05784325674176216, -0.05147840455174446, -0.009967854246497154, -0.0042151594534516335, -0.01908094808459282, -0.027812957763671875, 0.03844325244426727, -0.019448164850473404, 0.02345338463783264, -0.06278704851865768, -0.034111570566892624, 0.029325537383556366, -0.013020193204283714, -0.00869765318930149, -0.01692296750843525, -0.06168432533740997, 0.06624327600002289, 0.02924407087266445, -0.10669279843568802, -0.005475697107613087, 0.002838722663000226, -0.04555993154644966, 0.06285069137811661, -0.02274332009255886, -0.019722862169146538, 0.006259765941649675, -0.033463362604379654, 0.024925127625465393, -0.0001892559666885063, -0.02614079974591732, 0.01665654219686985, -0.05995152145624161, 0.05262264609336853, -0.01933644898235798, -0.05704798921942711, 0.02118879370391369, -0.0271199531853199, -0.009682627394795418, -0.018424971029162407, 0.03691960498690605, 0.050624456256628036, -0.04090153053402901, 0.003308685263618827, -0.004479228053241968, -0.04999261349439621, -0.03835393860936165, 0.031077036634087563, 0.04357802867889404, -0.04055732488632202, 0.030605947598814964, 0.05889518931508064, -0.018537120893597603, -0.03914639353752136, -0.003184315050020814, 0.010837569832801819, 0.02284860797226429, -0.026616154238581657, -0.016370179131627083, -0.02530890330672264, -0.08202477544546127, 0.0007802912150509655, 0.04258367046713829, 0.0024216945748776197, 0.01754097081720829, 0.052576031535863876, -0.06620796024799347, 0.06658917665481567, 0.011990928091108799, 0.0015675469767302275, -0.004346739035099745, -0.040729962289333344, 0.035739339888095856, 0.010463193990290165, 0.054364170879125595, -0.03816971927881241, -0.002585415728390217, -0.0220504030585289, -0.005113673862069845, -0.033466748893260956, -0.055649008601903915, -0.012444990687072277, 0.014364030212163925, 0.020992714911699295, -0.08620400726795197, -0.0546613447368145, 0.03962751850485802, 0.009280561469495296, 0.03742991387844086, 0.011075271293520927, 0.04070098698139191, -0.027415160089731216, 0.046717215329408646, 0.010971461422741413, -0.04685250297188759, -0.022441450506448746, 0.02432861551642418, -0.020311495289206505, -0.08142699301242828, -0.03891870379447937, 0.02927050180733204, 0.01456357166171074, 0.06355009227991104, 0.006500565446913242, -0.042265020310878754, 0.03339020162820816, 0.0409528911113739, 0.047091204673051834, 0.018140457570552826, 0.0016712407814338803, 0.01550608966499567, 0.03342941030859947, -0.03722584620118141, 0.05274519696831703, -0.005076546221971512, -0.0021025242749601603, -0.006940578576177359, -0.014215677976608276, -0.025592686608433723, 0.06285440921783447, -0.023107370361685753, -0.021332165226340294, -0.0017851956654340029, -0.002435758477076888, 0.01991932839155197, 0.046896521002054214, 0.01641886867582798, 0.038656383752822876, -0.012896087020635605, -0.027964526787400246, 0.006628601811826229, -0.028914164751768112, -0.08986509591341019, -0.022679319605231285, -0.03741490840911865, -0.009573215618729591, 0.04025433957576752, -0.0013784982729703188, -0.04431743174791336, -0.05236157029867172, -0.006693942937999964, -0.02928977832198143, -0.00021507822384592146, 0.05387357249855995, 0.06518365442752838, 0.031392212957143784, 0.02426677942276001, -0.003308291779831052, 0.011347598396241665, 0.024079792201519012, 0.03395838662981987, 0.03570791706442833, -0.007801505737006664, 0.052922237664461136, 0.0029977078083902597, 0.041761260479688644, 0.055707596242427826, 0.02398734539747238, -0.020821860060095787, -0.06339780241250992, 0.014699826017022133, -0.02931760996580124, -0.02075701579451561, 0.025659991428256035, -0.013248860836029053, 0.011795973405241966, 0.03314086049795151, 0.025042494758963585, 0.0038280305452644825, 0.001131655415520072, 0.05207006260752678, -0.014161938801407814, 0.023849042132496834, 0.0025470880791544914, -0.024944715201854706, 0.0027723524253815413, 0.004703977610915899, -0.0638464093208313, -0.02804814837872982, 0.03108462318778038, 0.021819785237312317, 0.02191169559955597, 0.02194979228079319, -0.03957226872444153, 0.010736171156167984, 0.009846591390669346, 0.01946614496409893, -0.009698107838630676, 0.041074469685554504, -0.06359873712062836, 0.019183989614248276, -0.007304163184016943, -0.04515254124999046, 0.011300607584416866, -0.04129139333963394, -0.05429016426205635, -0.10319330543279648, -0.06255330890417099, -0.017880544066429138, 0.01248236559331417, 0.048029202967882156, -0.01954357884824276, 0.02792685478925705, -0.022822009399533272, 0.006755027920007706, 0.028379173949360847, -0.0011590550420805812, 0.042789001017808914, -0.038323286920785904, 0.03530226647853851, 0.027093414217233658, -0.028880972415208817, 0.030529621988534927, -0.03974736109375954, 0.017648519948124886, 0.018714679405093193, 0.014238373376429081, -0.04320106655359268, 0.009340595453977585, -0.049763698130846024, -0.015026026405394077, -0.019951149821281433, 0.03489004075527191, -0.005579945165663958, -0.02513977885246277, -0.03948545455932617, 0.024854088202118874, 0.009969045408070087, 0.0874197855591774, 0.013880626298487186, 0.0023549343459308147, 0.04486817866563797, 0.0001341881143162027, 0.010987880639731884, -0.08381830900907516, 0.019553381949663162, 0.07692772150039673, 0.07848662883043289, -0.03339500352740288, 0.02406511828303337, -0.024379471316933632, -0.05055052787065506, 0.015087363310158253, 0.05401639640331268, -0.0011836723424494267, -0.009712735190987587, 0.03246169164776802, -0.017557526007294655, 0.010065305046737194, 0.010747975669801235, 0.03548986092209816, 0.05322040244936943, -0.007018373813480139, -0.08420966565608978, 0.01896701008081436, 0.028393281623721123, -0.005862658377736807, 0.04214907065033913, 0.004772941581904888, -0.030087493360042572, 0.0026749013923108578, 0.018140656873583794, 0.03065013699233532, 0.01349901594221592, -0.008887719362974167, 0.02517779730260372, -0.016851240769028664, 0.033582061529159546, -0.0011017246870324016, 0.012514273636043072, -0.02688058838248253, -0.04709075763821602, -0.01359479408711195, 0.034873753786087036, -0.05867095664143562, 0.05765664950013161, -0.042609985917806625, -0.024014879018068314, 0.0898890420794487, -0.02878611348569393, -0.005432315170764923, -0.011388164944946766, -0.01591855101287365, 0.009569826535880566, 0.047680988907814026, -0.002501676557585597, 0.022383984178304672, -0.052688051015138626, 0.03307211771607399, 0.03820163756608963, 0.0398491695523262, -0.011388707906007767, 0.061787717044353485, -0.014057277701795101, 0.002739210845902562, 0.09517044574022293, 0.03917170315980911, 0.005983034148812294, 0.020267270505428314, -0.042011722922325134, -0.06491544842720032, -0.012329456396400928, -0.03634613752365112, -0.028596991673111916, -0.030584895983338356, -0.005019562318921089, 0.018975304439663887, 0.02167864888906479, -0.022441795095801353, -0.016566621139645576, -0.05135731026530266, -0.04103478789329529, -0.0038542794063687325 ]
<p>I'd like to know if the sign in front of a kinetic term in QFT important. For the scalar field we conventionally write (in the $ + --- $ metric), \begin{equation} {\cal L} _{ kin} = \frac{1}{2} \partial _\mu \phi \partial ^\mu \phi \end{equation} Based on the answer given <a href="http://physics.stackexchange.com/questions/99252/meaning-of-kinetic-part-in-the-lagrangian-density">here</a>, this makes perfect sense since we want to have positive kinetic energy $\propto \dot{\phi}^2$. So would the Hamiltonian with a negative in front of the kinetic term be unbounded?</p> <p>Does this logic extend to the Dirac Lagrangian typically given by, \begin{equation} \bar{\psi} i \partial _\mu \gamma ^\mu \psi \quad ? \end{equation} i.e., would having a negative in front of the Dirac Lagrangian make the Hamiltonian unbounded?</p>
g8352
[ 0.049655236303806305, 0.03198898583650589, -0.011884533800184727, -0.07498553395271301, 0.041807129979133606, -0.02198045514523983, 0.06314446777105331, 0.03796657174825668, -0.052165061235427856, -0.019948456436395645, 0.03461693227291107, 0.05330837890505791, 0.004098298028111458, 0.008433961309492588, 0.029083894565701485, 0.021008264273405075, 0.05518324300646782, -0.015081695280969143, 0.026714731007814407, 0.03191560134291649, -0.05907271429896355, 0.03323342278599739, -0.01718061789870262, -0.022704044356942177, 0.06690458953380585, -0.0541173554956913, 0.04350068420171738, -0.04869522899389267, -0.03241515904664993, -0.04451749101281166, 0.008028204552829266, 0.01828004978597164, -0.02425607293844223, -0.04997141286730766, -0.044902704656124115, 0.024163853377103806, 0.06580883264541626, 0.040131423622369766, -0.02042047120630741, -0.04299671947956085, 0.01715582236647606, -0.04158703237771988, 0.01635672152042389, -0.024887941777706146, 0.0012271697632968426, 0.04156406968832016, -0.026129476726055145, 0.03540623560547829, -0.0011511329794302583, 0.026586471125483513, 0.0031104811932891607, 0.05060876905918121, -0.06522423774003983, -0.0044220006093382835, -0.03714689984917641, 0.10213802754878998, 0.08168794959783554, -0.01884598284959793, 0.006371710915118456, 0.006666157394647598, 0.060788895934820175, -0.02702363021671772, 0.008973573334515095, -0.033908210694789886, 0.02282307855784893, -0.04402758926153183, -0.03507327288389206, 0.011038300581276417, -0.024997510015964508, 0.012121233157813549, -0.04742252826690674, -0.018497692421078682, 0.01449093408882618, -0.0073198904283344746, 0.056071970611810684, 0.0825638473033905, -0.018743455410003662, -0.006913481280207634, 0.04684532806277275, -0.05422889068722725, -0.06995269656181335, -0.07143029570579529, 0.018809396773576736, 0.03229129686951637, 0.07512055337429047, 0.020685657858848572, 0.012758957222104073, -0.008994616568088531, -0.04994840547442436, 0.06957964599132538, 0.03871053829789162, -0.008534166030585766, 0.04310883954167366, -0.019233902916312218, -0.0071471622213721275, 0.011052153073251247, -0.012905719690024853, 0.012497317045927048, -0.05288858711719513, -0.02231045439839363, -0.021703312173485756, 0.004920328035950661, 0.0226039569824934, -0.013299733400344849, -0.042181406170129776, -0.046220310032367706, -0.02240511029958725, -0.03466860204935074, 0.022160641849040985, -0.011944347061216831, -0.013818089850246906, 0.020382747054100037, 0.006062979344278574, -0.041320979595184326, -0.04389764368534088, -0.018687225878238678, 0.03641674667596817, -0.024440599605441093, -0.005839186254888773, 0.06118564307689667, -0.046329814940690994, 0.0679578110575676, 0.052772123366594315, 0.0007827060180716217, 0.02067052386701107, -0.023410368710756302, -0.029407944530248642, 0.01683899573981762, 0.015521285124123096, -0.010125094093382359, 0.05398951843380928, 0.025338342413306236, 0.0026651271618902683, 0.007103432901203632, -0.04328835383057594, 0.058241166174411774, 0.0014660628512501717, 0.05124029517173767, 0.021694989874958992, -0.00641134986653924, -0.011046940460801125, -0.03723645210266113, 0.065614253282547, -0.028747165575623512, -0.06445641815662384, -0.008158119395375252, 0.03368252143263817, -0.025190314278006554, -0.012606303207576275, -0.028013739734888077, -0.015444610267877579, 0.016020402312278748, -0.014932946301996708, 0.02940749004483223, 0.06952330470085144, 0.014000620692968369, 0.015944823622703552, 0.01797739416360855, 0.001848745858296752, -0.01105180848389864, 0.029289765283465385, 0.019119566306471825, 0.05726761743426323, 0.026530176401138306, -0.004920940846204758, -0.009461350739002228, 0.022916775196790695, 0.029865212738513947, 0.0048650214448571205, -0.009754105471074581, -0.023602301254868507, 0.011817269027233124, -0.027782557532191277, -0.0005143553717061877, -0.02398563176393509, 0.017714036628603935, -0.04982950538396835, 0.07497089356184006, 0.008899942971765995, 0.030523473396897316, -0.08079743385314941, -0.04982137307524681, 0.022816019132733345, -0.05346805974841118, -0.010957411490380764, -0.015180825255811214, -0.009977951645851135, 0.09902447462081909, -0.05245954170823097, 0.020414378494024277, 0.008799474686384201, -0.014971546828746796, -0.03297491371631622, 0.05104099586606026, -0.021684367209672928, 0.008420711383223534, 0.015725651755928993, -0.06008545309305191, 0.05537228658795357, 0.0056157950311899185, -0.03176221251487732, 0.05796156823635101, -0.017752740532159805, 0.0020891570020467043, 0.03298700228333473, -0.03622160106897354, -0.003014977090060711, 0.01993369311094284, 0.063381627202034, -0.056318726390600204, -0.020315302535891533, -0.06657417863607407, 0.006911122240126133, 0.10392692685127258, 0.03008655644953251, -0.03986327350139618, -0.012736469507217407, 0.03994739428162575, -0.004018375184386969, 0.020078344270586967, -0.04733746871352196, 0.002035753335803747, 0.04343739151954651, -0.019164880737662315, -0.045072369277477264, 0.004125599283725023, -0.011217951774597168, -0.031142324209213257, -0.056137874722480774, 0.061478834599256516, -0.08239668607711792, 0.028676141053438187, -0.04703061282634735, 0.0035590531770139933, 0.04185190424323082, 0.015852458775043488, 0.024800138548016548, -0.010966381058096886, 0.02263782173395157, 0.03858296200633049, 0.012402048334479332, -0.02437024749815464, -0.006854901555925608, 0.00023147692263592035, 0.0744175985455513, -0.019321883097290993, 0.034040141850709915, 0.012946903705596924, -0.08808166533708572, 0.043461672961711884, 0.030135709792375565, 0.03523143008351326, -0.027445748448371887, -0.008355813100934029, -0.02833729237318039, -0.014124639332294464, -0.024311525747179985, -0.02006741240620613, -0.01690545119345188, -0.055634964257478714, 0.06708620488643646, -0.025837579742074013, -0.0818001851439476, -0.004833382088690996, -0.013265402987599373, 0.037405967712402344, -0.02250589430332184, 0.06089283525943756, 0.028494665399193764, 0.031934648752212524, -0.023285258561372757, 0.06155581399798393, 0.0263307373970747, -0.0010033383732661605, 0.02071520872414112, -0.03812282159924507, -0.006525721866637468, -0.06906462460756302, 0.0023420772049576044, -0.004865359049290419, 0.0022722387220710516, -0.03284415602684021, -0.0021221176721155643, 0.03539322316646576, -0.00556018203496933, -0.035429053008556366, 0.016128771007061005, 0.02012988179922104, 0.020485833287239075, 0.01143682561814785, 0.03552239015698433, 0.04174714535474777, 0.0326121486723423, 0.01266829390078783, -0.0035500426311045885, -0.025180742144584656, -0.010683859698474407, -0.049247853457927704, 0.019850777462124825, 0.015474445186555386, 0.01085845846682787, -0.042993247509002686, 0.0008651188691146672, 0.038419898599386215, 0.023637084290385246, 0.006762694101780653, -0.050862912088632584, -0.029410470277071, 0.029729019850492477, -0.03142552822828293, -0.04504704102873802, 0.0643080323934555, 0.049433425068855286, -0.04195044934749603, -0.05158316344022751, 0.01240786723792553, -0.020239580422639847, -0.012693095952272415, -0.003966655116528273, -0.019155029207468033, 0.014059608802199364, -0.04619523882865906, 0.022367335855960846, 0.06181401014328003, 0.06144706904888153, 0.013384077697992325, -0.0029550488106906414, 0.011041000485420227, -0.008936387486755848, -0.0026791165582835674, 0.016807638108730316, -0.005793808493763208, 0.02481880597770214, 0.037383247166872025, -0.023423118516802788, 0.003801413346081972, -0.06356219202280045, 0.0068916333839297295, 0.010608192533254623, 0.029442807659506798, -0.04333959519863129, 0.014338767156004906, -0.01742945797741413, 0.06849272549152374, 0.0007700126152485609, -0.05475592240691185, 0.0035238824784755707, 0.04299730435013771, -0.011353381909430027, -0.0022419493179768324, -0.03174002841114998, -0.042057231068611145, -0.01377602107822895, 0.041812505573034286, 0.001424149377271533, 0.008082040585577488, 0.08356877416372299, 0.03425232321023941, 0.02001260779798031, 0.0118073346093297, -0.039408326148986816, -0.023803725838661194, 0.024440716952085495, 0.053015705198049545, -0.010160413570702076, 0.0029114256612956524, -0.01527335587888956, -0.025440922006964684, -0.02623087354004383, -0.014864439144730568, 0.032795753329992294, 0.0038513995241373777, -0.0031659759115427732, 0.040930718183517456, -0.0024079710710793734, 0.01319933868944645, -0.009706489741802216, 0.0075464509427547455, 0.006513663101941347, 0.01321998331695795, -0.018193742260336876, 0.02304694429039955, 0.009249372407793999, 0.02663474902510643, 0.0006191967404447496, 0.04474731907248497, -0.07314620912075043, -0.029437538236379623, 0.03448229283094406, 0.003619868541136384, -0.05043337866663933, -0.0032201390713453293, -0.05572072044014931, 0.01211436279118061, 0.02027157135307789, -0.011469276621937752, 0.0365043580532074, 0.0011859649093821645, 0.0021631987765431404, 0.054899897426366806, -0.06020309403538704, 0.025517651811242104, 0.04738406091928482, 0.020253857597708702, 0.008654562756419182, -0.03279681131243706, -0.012331749312579632, -0.0007104356773197651, 0.024790028110146523, -0.06888660788536072, -0.026461530476808548, -0.07645197212696075, 0.005224369466304779, -0.049950629472732544, -0.007656042464077473, 0.018111931160092354, -0.023823190480470657, -0.0767289474606514, -0.007436529267579317, -0.018963972106575966, 0.07597031444311142, 0.04720189794898033, 0.0658365860581398, 0.0086493119597435, 0.016374314203858376, 0.02620193362236023, 0.11840382218360901, 0.0324699766933918, -0.08877179026603699, -0.027784494683146477, -0.051567450165748596, 0.026107167825102806, -0.0080712353810668, -0.017557324841618538, -0.03412530943751335, -0.005744887515902519, -0.08869824558496475, 0.018620463088154793, -0.026938291266560555, 0.026230478659272194, 0.05253581330180168, 0.0034184339456260204, -0.002041257917881012, -0.020033497363328934, 0.005795411299914122, 0.024889439344406128, -0.011899346485733986, -0.06659084558486938, -0.05108572542667389, -0.03672020137310028, -0.01386119332164526, 0.06689287722110748, -0.03095990978181362, -0.02442670613527298, 0.04916439577937126, 0.00242481823079288, -0.053271908313035965, -0.002660692436620593, 0.008712120354175568, 0.02522415667772293, -0.017298966646194458, -0.008962148800492287, 0.02559714950621128, 0.01375930942595005, 0.03483525291085243, -0.054994747042655945, -0.007882592268288136, 0.048714280128479004, -0.04761543869972229, 0.013792677782475948, 0.003223329782485962, 0.00889576505869627, -0.004148319363594055, -0.03890680894255638, -0.08842622488737106, -0.018795659765601158, 0.028776459395885468, 0.004994072485715151, -0.03696427866816521, -0.05213458836078644, 0.0021065629553049803, 0.012716883793473244, 0.020874524489045143, -0.014248233288526535, -0.008207516744732857, 0.029700743034482002, -0.002523464150726795, -0.015087890438735485, -0.0061022513546049595, -0.02975090593099594, 0.047186847776174545, 0.04209522157907486, 0.007948664017021656, 0.09583508968353271, 0.005447282921522856, 0.01939009130001068, 0.004663131665438414, 0.020435262471437454, 0.033547744154930115, -0.009551444090902805, -0.04555351659655571, 0.011487024836242199, 0.0037286055739969015, -0.05325334146618843, -0.005374119151383638, 0.061707403510808945, 0.05708838254213333, -0.021238604560494423, -0.03932873532176018, -0.015387267805635929, 0.0008210089290514588, 0.013002588413655758, -0.014812830835580826, -0.00993112288415432, 0.01643981784582138, -0.04492281377315521, -0.017018135637044907, -0.0525888167321682, -0.020798031240701675, -0.014148262329399586, -0.005785183049738407, 0.016334205865859985, 0.013273369520902634, -0.013779164291918278, 0.023864591494202614, 0.012156396172940731, -0.02642393484711647, -0.043166812509298325, -0.06623172014951706, 0.038411032408475876, 0.03753945231437683, 0.012489493936300278, 0.0028191402088850737, 0.02525952272117138, 0.0008187743951566517, -0.057913441210985184, -0.0017522411653771996, 0.023690931499004364, 0.015908677130937576, 0.030429143458604813, -0.004675007425248623, -0.05180896818637848, -0.052139222621917725, 0.031321652233600616, -0.04797522351145744, 0.008435777388513088, -0.027938928455114365, -0.015405574813485146, -0.005534161347895861, -0.11241689324378967, 0.022683734074234962, -0.029965411871671677, -0.005647546611726284, -0.005939142312854528, -0.014200879260897636, 0.006668903864920139, -0.005612313747406006, 0.0016058541368693113, -0.02569406107068062, -0.021436050534248352, 0.01643197238445282, -0.047807082533836365, 0.04505350440740585, 0.009556921198964119, 0.023693609982728958, 0.007274208590388298, 0.007191205397248268, -0.03597540408372879, 0.08503033965826035, -0.016376707702875137, 0.04808806627988815, 0.004528915975242853, -0.04994606226682663, 0.016649696975946426, 0.06678757816553116, 0.035144172608852386, 0.000670965644530952, -0.03516676276922226, -0.05623898282647133, 0.04289424791932106, -0.030111460015177727, 0.056810252368450165, -0.008736659772694111, -0.13610774278640747, -0.0221441388130188, -0.003298001829534769, -0.009776467457413673, -0.0017733409767970443, 0.015490666963160038, 0.022021209821105003, 0.04209786653518677, -0.005510543007403612, -0.02192750945687294, 0.014078187756240368, -0.0388706810772419, 0.01955169066786766, -0.033539850264787674, -0.045098841190338135, -0.04162377491593361, 0.02586541138589382, 0.01448843814432621, -0.007229271344840527, -0.025932272896170616, -0.02116798236966133, 0.005762765184044838, 0.0068104881793260574, -0.01038843858987093, 0.028115706518292427, 0.03089381381869316, 0.054394956678152084, 0.0018162811174988747, -0.02541431598365307, 0.0332283116877079, -0.01818488910794258, 0.01951705478131771, -0.0563957579433918, 0.054234229028224945, 0.04650266468524933, -0.0508323572576046, 0.003140058135613799, 0.047921322286129, -0.0030633879359811544, -0.012599342502653599, 0.011378860101103783, 0.0397934727370739, 0.05092773586511612, -0.05904654413461685, 0.03294053301215172, -0.004841610789299011, -0.012439696118235588, 0.07918434590101242, 0.02464914880692959, -0.09634748846292496, 0.026894280686974525, 0.04451146721839905, -0.022113533690571785, -0.06801553815603256, 0.03284294530749321, 0.07557115703821182, -0.05043860152363777, -0.007019356824457645, 0.010793667286634445, 0.03529230132699013, -0.03686578571796417, -0.04896792396903038, -0.005636613350361586, 0.031042782589793205, 0.008513911627233028, -0.07996214926242828, -0.03222760930657387, 0.03040851466357708, -0.018899070098996162, -0.05055750906467438, 0.05343017354607582, -0.01367987785488367, 0.0028252832125872374, -0.002281172201037407, 0.03958829119801521, -0.0279744490981102, -0.03524196892976761, 0.025187622755765915, -0.02313920669257641, 0.001183921005576849, 0.028499288484454155, 0.022254375740885735, 0.024705616757273674, 0.0029367159586399794, 0.01709095761179924, 0.02420836128294468, 0.012277056463062763, 0.02520422264933586, -0.011351996101439, -0.024871226400136948, -0.014669633470475674, -0.025680961087346077, 0.03731849044561386, -0.007493614684790373, 0.04714548960328102, 0.013635775074362755, 0.013733111321926117, -0.018208596855401993, -0.0006739416858181357, -0.02953564189374447, -0.021901370957493782, -0.052984464913606644, -0.010232798755168915, 0.016346953809261322, -0.047361377626657486, -0.051696889102458954, 0.053862571716308594, 0.003072938183322549, -0.014213498681783676, -0.020082984119653702, -0.03385962173342705, 0.006982922088354826, 0.002201573457568884, 0.05852063000202179, 0.08269745856523514, -0.02059624344110489, 0.010518675670027733, -0.017487457022070885, -0.0046773324720561504, -0.007012758869677782, 0.03885173425078392, 0.04912729561328888, 0.01743418164551258, 0.05154675245285034, -0.02291097678244114, -0.07995296269655228, 0.013979088515043259, 0.006330386269837618, -0.005200009793043137, -0.028536610305309296, 0.01509217731654644, 0.06170272454619408, -0.02905893698334694, -0.015141699463129044, -0.027683677151799202, 0.0390043668448925, -0.05518313869833946, -0.004623134154826403, 0.06254437565803528, -0.0826176255941391, -0.04943503439426422, -0.008139681071043015, 0.007672285661101341, -0.05261717364192009, 0.008956639096140862, -0.0021127955988049507, 0.008250568993389606, -0.020652219653129578, -0.01563822291791439, -0.020775258541107178, 0.04247846454381943, -0.06252516806125641, 0.039634205400943756, -0.009410388767719269, -0.01879276894032955, 0.09292443841695786, 0.009633470326662064, -0.047950372099876404, -0.08455344289541245, 0.004966286011040211, -0.0027411661576479673, -0.03228823468089104, -0.014657142572104931, 0.001971067627891898, 0.007625512778759003, 0.05390375107526779, -0.009889143519103527, 0.02709948644042015, 0.05768266320228577, -0.021052338182926178, 0.011125042103230953, 0.004065268207341433, -0.013397843576967716, -0.02371043898165226, -0.001215531607158482, 0.013566756621003151, 0.017674092203378677, 0.013270160183310509, -0.035677675157785416, 0.013422149233520031, -0.05193458870053291, -0.0041184076108038425, -0.039998799562454224, 0.014837040565907955, -0.014689077623188496 ]
<p>What happens when the photon which hits a metal surface has energy equal to the work function of that surface? $$\phi = hf$$ I realise the emitted electron will have no kinetic energy after escape, but then what does it do? Hover above the surface? Or does it have momentum from escaping? I also don't understand what the work function is caused by - is it the electrostatic attraction between nuclei and the electrons?</p>
g8353
[ 0.002332605654373765, 0.04999499022960663, 0.011601000092923641, 0.028269652277231216, 0.03800135850906372, 0.03581353276968002, 0.06150399520993233, 0.019911576062440872, -0.03857680410146713, -0.0035033943131566048, -0.046707332134246826, 0.048524338752031326, 0.0026451984886080027, -0.04528263583779335, -0.00280889798887074, 0.02937920391559601, 0.041251327842473984, 0.009221783839166164, 0.03505769371986389, 0.053345970809459686, -0.04145854711532593, 0.047338973730802536, -0.05016221106052399, -0.05052637308835983, 0.03262370452284813, 0.00994402077049017, -0.03496798872947693, -0.04997466132044792, 0.02972947247326374, 0.017424000427126884, -0.04304259642958641, 0.029573021456599236, 0.04640566557645798, -0.03344913199543953, -0.056086212396621704, 0.016824092715978622, 0.061749204993247986, 0.045310646295547485, 0.010306191630661488, 0.01084114983677864, -0.016551269218325615, -0.03612470626831055, -0.016643239185214043, -0.010814507491886616, 0.047519635409116745, -0.007325337268412113, -0.027928132563829422, -0.01624344289302826, -0.010748237371444702, 0.009255980141460896, -0.0011636759154498577, 0.04403975233435631, 0.014080818742513657, -0.005112315993756056, 0.019849024713039398, 0.005319532472640276, 0.023542029783129692, -0.02878912165760994, 0.0977853536605835, 0.02066108211874962, 0.02026180550456047, 0.05327649042010307, 0.006635649129748344, -0.006873756181448698, 0.06342064589262009, -0.034276332706213, -0.0021537081338465214, 0.017566144466400146, -0.009344982914626598, 0.005786345340311527, -0.02865426056087017, 0.02854090742766857, -0.04955321177840233, -0.01391658280044794, 0.023274945095181465, 0.015914244577288628, 0.03285418078303337, -0.08368608355522156, -0.015023400075733662, 0.04248704016208649, 0.006448111496865749, -0.0694970041513443, 0.0019363260362297297, -0.0008753512520343065, 0.04550536349415779, 0.004364742897450924, -0.011529829353094101, -0.015867719426751137, -0.02151864394545555, -0.04481184855103493, 0.04395270347595215, -0.011487362906336784, 0.036767955869436264, -0.004272604361176491, -0.05816575884819031, -0.0036897952668368816, -0.0047593312337994576, 0.020660651847720146, -0.024893412366509438, -0.04216952994465828, -0.016608763486146927, -0.05706338956952095, 0.013586866669356823, 0.01608368009328842, 0.03210127726197243, -0.006111668888479471, 0.008722174912691116, -0.047427091747522354, 0.016886744648218155, 0.03752661496400833, -0.000021731004380853847, -0.018588250502943993, -0.02001888118684292, -0.0838855728507042, -0.0004093714524060488, -0.021860376000404358, 0.016885336488485336, -0.08773334324359894, -0.03624631091952324, 0.06537497043609619, 0.046402812004089355, -0.0025184752885252237, 0.006960708647966385, 0.011046730913221836, 0.01868254877626896, 0.01201093290001154, -0.032781779766082764, -0.008111762814223766, -0.027732722461223602, -0.004728982225060463, 0.03586473688483238, 0.05552108958363533, -0.07692351192235947, 0.06182386353611946, 0.03930984437465668, 0.014526458457112312, 0.01001050230115652, 0.013688103295862675, 0.002971688285470009, -0.03765455260872841, 0.06878680735826492, -0.016814744099974632, -0.01892782561480999, -0.013604890555143356, -0.0731314942240715, -0.03043399751186371, -0.03605915233492851, 0.014691912569105625, 0.036181192845106125, 0.012061397545039654, 0.01870296522974968, 0.0762719139456749, -0.018350858241319656, -0.02456466481089592, 0.042804520577192307, -0.06928270310163498, 0.05450852960348129, 0.0014238620642572641, 0.007181305438280106, 0.01332966797053814, 0.08710435032844543, -0.038306813687086105, 0.045036401599645615, -0.008517433889210224, -0.03660358861088753, -0.00839968491345644, 0.004402741324156523, -0.08528845757246017, -0.0255487859249115, -0.037932418286800385, -0.0022147914860397577, -0.014026602730154991, -0.025104373693466187, -0.0011776888277381659, -0.058453187346458435, 0.024803845211863518, -0.032684460282325745, 0.028430573642253876, 0.014298947528004646, 0.05701638013124466, 0.010435239411890507, -0.052349723875522614, 0.07792745530605316, -0.012504031881690025, 0.004947497509419918, 0.021803446114063263, -0.03301398828625679, 0.02142428793013096, -0.0554211251437664, 0.03960100933909416, -0.043101660907268524, -0.00890690553933382, 0.03865236043930054, -0.02517884224653244, -0.03706363961100578, -0.027628842741250992, -0.01796586439013481, -0.03922615945339203, -0.011064833961427212, -0.06675542145967484, -0.022816818207502365, 0.06580585986375809, -0.0572488009929657, -0.014715001918375492, 0.0031594261527061462, 0.023733822628855705, 0.012327030301094055, -0.02085176296532154, 0.017618779093027115, -0.0028227465227246284, 0.0262819305062294, -0.021088767796754837, 0.004311190452426672, 0.03914854675531387, 0.01259095873683691, 0.009520660154521465, -0.06405088305473328, 0.002524442272260785, 0.03251345083117485, 0.0026771388947963715, 0.014134631492197514, -0.022956697270274162, 0.020277580246329308, 0.017313746735453606, -0.002270158613100648, 0.036347005516290665, -0.03236893564462662, -0.02729189395904541, -0.01213697250932455, 0.06968962401151657, -0.03662780672311783, 0.01865057274699211, -0.01886790432035923, 0.0037399937864392996, -0.01060689426958561, 0.03609943389892578, -0.007045319769531488, 0.042585693299770355, -0.007043624296784401, -0.005134533159434795, -0.012808526866137981, -0.016904568299651146, -0.07494834065437317, -0.03186206519603729, 0.016216343268752098, -0.029370350763201714, 0.02541215904057026, 0.010949653573334217, -0.017347319051623344, -0.016470899805426598, 0.08132905513048172, -0.01065476331859827, -0.0203030277043581, 0.050672322511672974, -0.03092167153954506, -0.06690812855958939, -0.07417949289083481, 0.022444967180490494, -0.07873496413230896, -0.0620400570333004, -0.00008272068953374401, -0.023476367816329002, -0.024641433730721474, 0.01671907678246498, -0.02414156310260296, -0.02781052701175213, -0.018551958724856377, 0.03578651696443558, 0.008909295313060284, -0.05750788375735283, -0.012690658681094646, 0.06636307388544083, -0.024438975378870964, 0.031459271907806396, 0.010443403385579586, -0.06553737819194794, -0.01566906087100506, -0.025637632235884666, 0.014652458019554615, -0.05602423474192619, -0.0279353279620409, -0.015466625802218914, -0.06376434862613678, -0.02769230492413044, -0.022312138229608536, -0.0538143664598465, 0.009633022360503674, 0.007798873819410801, 0.018824229016900063, -0.05124599114060402, -0.025149617344141006, -0.0076010930351912975, 0.01764071360230446, 0.028503257781267166, -0.04500843212008476, 0.027065947651863098, 0.041036706417798996, 0.02723938785493374, -0.06688377261161804, 0.07308104634284973, -0.001786971464753151, -0.023270729929208755, -0.02441929467022419, -0.023076076060533524, -0.023509325459599495, 0.047092895954847336, -0.0353209413588047, -0.01598537154495716, -0.059892527759075165, 0.010953194461762905, -0.0382545180618763, 0.07324959337711334, 0.01211309153586626, 0.001450277166441083, -0.01454913429915905, -0.003294587368145585, -0.0018111735116690397, -0.010304233059287071, -0.045420870184898376, 0.042640674859285355, -0.019075848162174225, -0.013735786080360413, -0.004356556572020054, 0.014188927598297596, 0.019914932548999786, 0.026605337858200073, -0.03604789823293686, -0.02065568044781685, 0.004480179399251938, 0.007503356318920851, 0.04239200800657272, 0.03889741376042366, -0.05159883201122284, -0.02508467435836792, 0.02144239842891693, 0.00341065414249897, 0.00020648942154366523, 0.06901567429304123, 0.024117417633533478, 0.06285658478736877, 0.027618100866675377, 0.04306130111217499, -0.04235590994358063, 0.017617840319871902, 0.0463874377310276, -0.0166646558791399, 0.016545673832297325, -0.04830543324351311, 0.004055137746036053, -0.006904487032443285, 0.0631571114063263, -0.007093379739671946, -0.0012457326520234346, 0.03177974373102188, 0.015243452973663807, 0.025914637371897697, -0.018690628930926323, 0.017471738159656525, 0.031811460852622986, -0.019274935126304626, -0.006414067465811968, -0.020770391449332237, 0.07856637984514236, 0.00587529456242919, -0.051442522555589676, -0.020608242601156235, -0.0009745854767970741, 0.06938086450099945, 0.0012683536624535918, -0.036731261759996414, 0.01048992108553648, 0.01819595880806446, 0.02983510121703148, 0.03505587950348854, -0.06624355167150497, 0.011187715455889702, 0.0077947149984538555, -0.03488950803875923, -0.06213415414094925, -0.017769718542695045, -0.024872032925486565, 0.012666476890444756, 0.0215439610183239, 0.02078242599964142, 0.043023593723773956, 0.022470487281680107, -0.05403894558548927, 0.0033535936381667852, 0.006082372274249792, -0.0022523447405546904, -0.036854442209005356, -0.039497919380664825, -0.026387905701994896, 0.04185670241713524, 0.028859088197350502, -0.033987317234277725, 0.06426519900560379, -0.03410407155752182, 0.030141271650791168, -0.027784738689661026, 0.02606586366891861, 0.03351569175720215, -0.0880824401974678, 0.006352107040584087, 0.04685067757964134, 0.013879125937819481, 0.030646974220871925, -0.030616533011198044, -0.03914159908890724, -0.0337204672396183, -0.03886355087161064, 0.0038874505553394556, -0.0129852918908, 0.009280575439333916, 0.005539359524846077, -0.022710638120770454, -0.017422905191779137, 0.03770745173096657, -0.023565080016851425, 0.0016897927271202207, -0.032624464482069016, 0.0160182174295187, 0.12689049541950226, 0.007163513917475939, 0.001607534708455205, 0.029265128076076508, 0.021154366433620453, 0.02139901928603649, 0.01658220775425434, -0.04577845335006714, 0.0184920746833086, 0.04674204811453819, -0.004834548570215702, -0.015414882451295853, -0.07092732936143875, 0.06929907202720642, -0.04781154915690422, 0.03975926712155342, 0.004651860799640417, 0.05173399671912193, 0.10308399051427841, 0.034588124603033066, -0.00827910378575325, 0.05558735877275467, 0.003034678753465414, 0.0334814079105854, -0.026822417974472046, -0.0687955841422081, -0.0045398324728012085, -0.021558664739131927, -0.05550628900527954, -0.027626100927591324, -0.03811531141400337, 0.00010637829836923629, 0.0059273201040923595, -0.002543465467169881, -0.010436108335852623, -0.013451329432427883, 0.008628473617136478, 0.022713782265782356, -0.04036237671971321, -0.04546802490949631, -0.0016273842193186283, 0.002395804738625884, 0.00048647329094819725, -0.0507957749068737, -0.08065708726644516, 0.008204329758882523, -0.06530537456274033, 0.03392825275659561, 0.018837179988622665, 0.02605390176177025, 0.06348730623722076, -0.023288942873477936, -0.017139576375484467, -0.03441224992275238, 0.008357096463441849, 0.022676674649119377, 0.03481505438685417, -0.01049125101417303, 0.05509714037179947, 0.009313230402767658, 0.009770580567419529, 0.026689739897847176, -0.0032940299715846777, -0.002247265074402094, -0.06433888524770737, 0.04899343103170395, -0.011114709079265594, -0.04675716534256935, 0.01664419285953045, 0.02436523698270321, -0.007666878402233124, -0.004939407575875521, -0.02269825153052807, 0.022264432162046432, -0.02037290297448635, 0.052762873470783234, 0.03531219810247421, 0.03389521315693855, -0.04003888741135597, -0.03917086124420166, -0.059038612991571426, 0.04400371387600899, 0.03573881462216377, 0.026274072006344795, 0.03427378833293915, -0.04367804527282715, 0.045770030468702316, -0.02898227795958519, -0.05138610303401947, -0.00658169761300087, 0.014050645753741264, 0.02530394122004509, 0.005469041410833597, -0.012978230603039265, -0.027454663068056107, 0.019791129976511, -0.0031681100372225046, 0.060381267219781876, 0.006193982902914286, 0.022837813943624496, 0.0061997463926672935, -0.041778381913900375, 0.06576584279537201, -0.018687445670366287, -0.025064757093787193, 0.011250942014157772, 0.03882668912410736, 0.08814319968223572, 0.02976333536207676, 0.005931287072598934, 0.006811316590756178, 0.04089464992284775, 0.025751754641532898, -0.02668021060526371, 0.031380586326122284, -0.00403609499335289, 0.008328248746693134, 0.04039803519845009, -0.01685354672372341, -0.04113128036260605, 0.024086831137537956, 0.05130245164036751, 0.03044150397181511, -0.020638328045606613, 0.03465326875448227, -0.010384623892605305, 0.04214299097657204, -0.05524849519133568, 0.0051278951577842236, 0.03719015792012215, 0.055198490619659424, 0.04623640701174736, 0.001809402136132121, 0.06704551726579666, 0.04757287725806236, -0.0102788545191288, 0.00942821241915226, -0.060933250933885574, 0.08044104278087616, 0.04380610212683678, 0.03554148972034454, 0.020253553986549377, 0.08324532210826874, 0.0004762191092595458, -0.030802350491285324, 0.020112276077270508, -0.018005630001425743, -0.05122390016913414, 0.027293549850583076, 0.015652203932404518, 0.0014052476035431027, -0.0043172575533390045, -0.04375153407454491, 0.08319465816020966, -0.04296346381306648, -0.019130850210785866, -0.09377404302358627, -0.007538790348917246, 0.04077424854040146, 0.024814961478114128, 0.04559884965419769, -0.02540474385023117, -0.030493028461933136, 0.027584927156567574, -0.033484913408756256, -0.04676363989710808, 0.09086975455284119, -0.0049354606308043, -0.03717460110783577, -0.004083991050720215, 0.032025501132011414, 0.03511098027229309, -0.0178365595638752, 0.0053144837729632854, -0.021044908091425896, 0.006207541562616825, -0.012251993641257286, 0.04892164096236229, 0.04133550450205803, 0.011357014067471027, 0.04524517431855202, -0.06466803699731827, 0.04835660755634308, 0.02666102908551693, -0.012014427222311497, -0.0023570270277559757, -0.05124623700976372, -0.007994771003723145, -0.06314394623041153, 0.02319788932800293, -0.019641272723674774, -0.036711178719997406, -0.016357114538550377, -0.023482417687773705, 0.04427742213010788, 0.013638234697282314, -0.009318346157670021, -0.010806025005877018, -0.007269706577062607, -0.02798052877187729, 0.0616411454975605, -0.050850387662649155, 0.03909871727228165, 0.003086874959990382, -0.008355174213647842, 0.05615130066871643, 0.028638675808906555, 0.01052040234208107, -0.014589832164347172, 0.04799969494342804, -0.0075315264984965324, 0.03615869581699371, -0.07666564732789993, 0.0200178325176239, 0.006669775117188692, -0.037787359207868576, 0.022379815578460693, 0.03378088027238846, -0.005641433410346508, 0.0061533572152256966, 0.06330320984125137, -0.014676417224109173, -0.10270441323518753, 0.013704942539334297, -0.042586520314216614, -0.025931956246495247, -0.06945507973432541, 0.02076762728393078, -0.04552077129483223, -0.06627728044986725, -0.017203837633132935, 0.030090713873505592, 0.03127399832010269, 0.0020366155076771975, -0.04772867634892464, 0.013394096866250038, -0.0625624731183052, -0.0013270414201542735, -0.0278562493622303, -0.026815170422196388, 0.01944606937468052, 0.011951211839914322, 0.016972027719020844, 0.05066673830151558, 0.016366248950362206, -0.052410226315259933, -0.02464645355939865, -0.013391449116170406, -0.0306649599224329, -0.03308169171214104, -0.0481901615858078, 0.013417179696261883, -0.03792881965637207, 0.05421832576394081, -0.01827479526400566, 0.03619455546140671, -0.04701774939894676, -0.015200548805296421, -0.021425850689411163, 0.037858907133340836, 0.0026890872977674007, -0.02335388772189617, 0.013047249056398869, -0.024981530383229256, -0.052511367946863174, 0.015066363848745823, -0.029645346105098724, 0.05165354534983635, 0.03948062285780907, -0.024227073416113853, 0.038115229457616806, -0.03598639369010925, -0.02578030340373516, -0.010045228525996208, 0.04583568871021271, -0.0018719786312431097, 0.05283699557185173, 0.024825479835271835, 0.005746873561292887, -0.023470669984817505, 0.018246794119477272, -0.04454925283789635, 0.011402364820241928, 0.07556509971618652, 0.002380711492151022, -0.04644184932112694, -0.04425491392612457, -0.02000661939382553, 0.04271137714385986, 0.01227605901658535, -0.010240555740892887, -0.013719900511205196, 0.01654822565615177, -0.0008517541573382914, -0.033897850662469864, 0.04199651628732681, 0.0633547455072403, -0.02810196578502655, 0.01825745962560177, 0.02425716258585453, -0.037243399769067764, -0.019724760204553604, 0.019325757399201393, 0.02429894357919693, -0.03681929409503937, -0.04281206429004669, 0.020385777577757835, -0.022034844383597374, -0.046097282320261, 0.01500382274389267, -0.023048043251037598, -0.039968911558389664, -0.04147288575768471, -0.04223313555121422, 0.048323675990104675, -0.0076996381394565105, 0.029075318947434425, -0.03439078480005264, 0.03150487691164017, -0.059282876551151276, -0.005354402121156454, -0.011779624037444592, -0.006454993970692158, -0.03389771282672882, 0.023879939690232277, -0.01266472227871418, 0.034163009375333786, 0.00407157838344574, -0.006277795415371656, 0.044356223195791245, -0.025027062743902206, 0.059708040207624435, 0.07546170055866241, -0.11146645247936249, 0.0030807070434093475, 0.0007216075900942087, -0.008420316502451897, 0.02264801412820816, 0.010101881809532642, -0.05231190100312233, -0.038323186337947845, -0.02811400406062603, 0.00006703518738504499, -0.0681125596165657, 0.027474340051412582, 0.025076963007450104 ]
<p>The annihilation and creation operators are given below $$ \hat a|n\rangle=\sqrt{n}|n-1\rangle\qquad\text{and}\qquad\hat a^\dagger|n\rangle=\sqrt{n+1}|n+1\rangle $$</p> <p>Now I know the operator a^ is not Hermitian but as to why I'm a little confused. Is it because they 'create' and 'annihilate' photons hence they're not hermitian? I don't think that explanation would be good for an exam if this question was asked though...</p>
g8354
[ -0.01830575428903103, -0.04527046158909798, -0.0160819124430418, 0.031331177800893784, 0.06663020700216293, -0.0012552946573123336, 0.04620715603232384, 0.016069181263446808, 0.0009379637776874006, 0.05553862452507019, -0.039888445287942886, 0.033774200826883316, 0.023668203502893448, -0.00034437692374922335, -0.00783019419759512, 0.004172199405729771, 0.029455553740262985, 0.0317525751888752, 0.02165013551712036, 0.02516174502670765, -0.08195198327302933, -0.0157026220113039, 0.016858119517564774, -0.06140315532684326, 0.09258167445659637, -0.043611057102680206, -0.006544506177306175, -0.01262813713401556, -0.05078846961259842, -0.03998374938964844, 0.06795206665992737, 0.03932705149054527, 0.030191611498594284, 0.008907105773687363, 0.0018336698412895203, 0.016753345727920532, 0.10169161856174469, 0.003963405266404152, 0.030766189098358154, -0.014546393416821957, -0.006505193654447794, -0.012303084135055542, 0.028314407914876938, -0.044491857290267944, -0.01679162308573723, 0.006785213481634855, 0.025310121476650238, 0.022335391491651535, 0.0032207982148975134, 0.023911848664283752, -0.012940503656864166, -0.02434646524488926, 0.07333287596702576, -0.0365583561360836, 0.017036210745573044, 0.04317309334874153, -0.02819686010479927, 0.0006152649293653667, 0.04381050541996956, 0.013087458908557892, -0.03437348082661629, -0.023364752531051636, 0.032376836985349655, 0.04095415398478508, 0.04020850732922554, -0.030376212671399117, 0.0680619403719902, -0.02727135270833969, 0.026185406371951103, 0.019431130960583687, 0.03716538846492767, -0.02401774376630783, -0.0030310458969324827, 0.03245394304394722, 0.056552257388830185, 0.02049744315445423, 0.036995694041252136, -0.023602841421961784, -0.03053237870335579, 0.04050454497337341, -0.018020011484622955, -0.030141638591885567, 0.01409320067614317, 0.010450957342982292, 0.03697766736149788, 0.012456288561224937, -0.02105920948088169, -0.0016146480338647962, 0.007821338251233101, 0.05262633040547371, 0.01328665018081665, -0.01195701863616705, 0.05501054599881172, 0.08599451929330826, -0.024917399510741234, -0.009386218152940273, -0.04716549813747406, 0.06623266637325287, -0.009326272644102573, 0.04070920869708061, 0.01459706760942936, 0.007361855357885361, 0.028592616319656372, -0.01215105690062046, 0.020199434831738472, 0.0059156413190066814, -0.010674605146050453, -0.05989557132124901, -0.0005237844306975603, 0.01619398593902588, -0.05389605835080147, 0.014117131009697914, -0.0468718595802784, -0.018994266167283058, 0.02104652300477028, -0.00258912262506783, 0.021682772785425186, -0.041912902146577835, 0.026694772765040398, 0.08862897753715515, 0.02218577079474926, 0.04174506291747093, -0.021421125158667564, -0.00872744619846344, 0.041652530431747437, 0.022098474204540253, -0.0011165014002472162, 0.04658868908882141, 0.06264885514974594, 0.0067201294004917145, 0.05138291418552399, 0.007032791152596474, -0.0293398667126894, 0.058020152151584625, 0.0520150400698185, 0.04042124003171921, -0.009616289287805557, 0.014677370898425579, 0.039910025894641876, -0.08575054258108139, -0.011160345748066902, 0.03294350579380989, 0.0008472959161736071, 0.013501349836587906, -0.028248578310012817, -0.01290286984294653, 0.036518074572086334, -0.05530542880296707, -0.0395742766559124, 0.1097044125199318, 0.06166980415582657, 0.03041713498532772, 0.022670796141028404, -0.030649473890662193, 0.015680482611060143, 0.002843390917405486, 0.0540299117565155, -0.04083113372325897, -0.0627099797129631, -0.01911579631268978, 0.014836674556136131, 0.002372539369389415, 0.014703127555549145, 0.0427282452583313, -0.04048633575439453, 0.014179173856973648, 0.0059568267315626144, -0.10812874883413315, -0.010628854855895042, -0.03518332168459892, 0.03761905059218407, 0.041045624762773514, 0.038478441536426544, 0.05532005801796913, -0.02645662985742092, 0.04783192276954651, -0.0376347154378891, 0.04698340222239494, 0.022286763414740562, 0.008045121096074581, -0.00651931669563055, 0.00896230898797512, 0.029337402433156967, -0.038460537791252136, 0.043672289699316025, -0.03716609627008438, -0.03454432263970375, 0.0005112146609462798, -0.07134819030761719, 0.0002525919408071786, 0.021971208974719048, 0.0006637303740717471, 0.004761553835123777, 0.03874905779957771, 0.029431404545903206, -0.004736199975013733, -0.008329087868332863, -0.022295711562037468, 0.011830865405499935, 0.03580043837428093, -0.002079225378111005, 0.03124760277569294, -0.01797674037516117, -0.06293798983097076, -0.017809109762310982, -0.006028633564710617, -0.0066894288174808025, -0.02605249173939228, 0.025577304884791374, 0.011812248267233372, -0.004008599556982517, -0.06248669698834419, 0.01824270375072956, 0.008557825349271297, 0.01940276473760605, -0.02702045626938343, 0.022118890658020973, 0.023628121241927147, 0.0027575993444770575, -0.003665997413918376, -0.030692083761096, 0.004365677945315838, -0.01781824603676796, -0.028364555910229683, 0.024421019479632378, 0.03164563700556755, -0.06265027076005936, -0.025151683017611504, -0.00016162602696567774, 0.004349329974502325, -0.019497815519571304, -0.02634943649172783, -0.012115221470594406, -0.04587472975254059, 0.019834032282233238, 0.014801404438912868, 0.028977345675230026, 0.028890691697597504, 0.025810403749346733, 0.005931209307163954, -0.032714858651161194, 0.010225264355540276, 0.011720999144017696, 0.025856977328658104, -0.009729827754199505, -0.04757682606577873, 0.027046585455536842, -0.04747677221894264, -0.05632202327251434, 0.036372456699609756, 0.01884903572499752, -0.03619907796382904, -0.004733985755592585, 0.017881762236356735, 0.001793170114979148, -0.008545665070414543, -0.0012741790851578116, 0.03859834000468254, -0.03568323329091072, -0.001891166903078556, -0.05866466090083122, 0.03367830067873001, -0.0759052187204361, -0.011443773284554482, -0.03126893565058708, -0.01162703800946474, -0.022081585600972176, 0.012373954057693481, 0.05225987359881401, 0.0023918200749903917, -0.05371072143316269, 0.04397851973772049, 0.05285158380866051, 0.010472012683749199, 0.005019309464842081, -0.03241855278611183, 0.013806548900902271, 0.040225330740213394, 0.007478237617760897, -0.02584490366280079, -0.020121080800890923, -0.02187493070960045, -0.09896361827850342, 0.034342195838689804, 0.013327887281775475, -0.08122868090867996, 0.013287761248648167, 0.02003679797053337, -0.04930562525987625, -0.0004146152641624212, -0.05432130768895149, -0.006660811137408018, -0.055810682475566864, -0.04751091077923775, -0.012862419709563255, -0.05657251179218292, -0.05531703308224678, -0.021218713372945786, -0.009278674609959126, 0.05063830316066742, 0.008235241286456585, -0.03054818883538246, -0.008910134434700012, -0.008291907608509064, 0.015628239139914513, -0.025822807103395462, -0.01895882748067379, -0.09746972471475601, -0.03545226529240608, 0.021213846281170845, 0.02828153222799301, 0.04087500646710396, -0.010832737199962139, -0.017932401970028877, 0.026114962995052338, -0.004575270228087902, -0.11903709918260574, -0.026113154366612434, 0.05009501427412033, 0.009913329966366291, -0.09490976482629776, -0.0193568654358387, 0.024812670424580574, -0.014358163811266422, 0.054112713783979416, 0.023005222901701927, -0.06226172298192978, 0.06503569334745407, 0.04056505113840103, -0.06892555207014084, 0.015394643880426884, -0.02223731204867363, 0.031695324927568436, -0.017846526578068733, -0.021824760362505913, -0.03132049739360809, -0.01396702229976654, 0.011464142240583897, 0.0008034901693463326, 0.008572926744818687, 0.014084120281040668, 0.011791952885687351, -0.02178044244647026, -0.0044243186712265015, -0.01132842618972063, 0.030313868075609207, -0.0035681999288499355, -0.013308432884514332, 0.015375702641904354, -0.022163046523928642, 0.002886011963710189, -0.035399388521909714, 0.06323233246803284, -0.015249445103108883, -0.04950353130698204, 0.023150285705924034, 0.01396824512630701, 0.030857224017381668, 0.03354021906852722, -0.06517589092254639, -0.009055212140083313, 0.006497940514236689, 0.032363906502723694, 0.005785294342786074, 0.011360550299286842, 0.018810510635375977, -0.027660153806209564, 0.0008736890158616006, -0.01131769735366106, 0.016284774988889694, 0.04480742663145065, 0.017013918608427048, 0.003090593731030822, -0.021593496203422546, -0.018783599138259888, -0.016525402665138245, -0.011970644816756248, -0.019942298531532288, -0.013005171902477741, 0.0016940723871812224, -0.034956011921167374, -0.033775653690099716, 0.02013520337641239, 0.018217923119664192, 0.023673804476857185, 0.08900626748800278, 0.00993319507688284, -0.008171494118869305, 0.00942415650933981, -0.09693478047847748, 0.017653249204158783, -0.0655110627412796, -0.04060641676187515, -0.004481411073356867, 0.006111414171755314, 0.03033311478793621, -0.010411333292722702, -0.08414322882890701, -0.028837909922003746, 0.03422951325774193, -0.016690891236066818, -0.03898758068680763, 0.03023379109799862, -0.03872969374060631, 0.03902796655893326, 0.0009656926267780364, 0.07266059517860413, -0.023212090134620667, 0.015818780288100243, -0.028424017131328583, -0.0496785044670105, 0.023872053250670433, 0.001224758569151163, -0.05048036575317383, 0.046750959008932114, 0.020073164254426956, 0.03597469627857208, -0.026642655953764915, -0.04615608602762222, -0.03018810600042343, -0.009930938482284546, -0.03043217398226261, 0.056707292795181274, 0.01203420851379633, -0.004712129943072796, 0.026449261233210564, -0.003868133993819356, -0.04510785639286041, 0.06807569414377213, -0.01565934531390667, 0.029618432745337486, -0.00675489054992795, 0.008854983374476433, 0.03710009157657623, -0.046729676425457, -0.0010531145380809903, -0.0069229695945978165, 0.04183105379343033, 0.0069288210943341255, 0.009761528111994267, 0.054324354976415634, -0.054610636085271835, 0.047990068793296814, -0.04064890369772911, 0.06516508013010025, 0.006423023995012045, -0.004263385199010372, -0.0591571219265461, -0.033776771277189255, -0.014990704134106636, -0.01579838991165161, -0.001784785883501172, 0.017141126096248627, -0.07009696960449219, 0.03965073078870773, -0.009237623773515224, -0.025690283626317978, 0.0028366995975375175, 0.033576320856809616, 0.04182687774300575, -0.04691179096698761, -0.017416078597307205, 0.02781159244477749, -0.00720045855268836, 0.04202526435256004, -0.006297908257693052, -0.024280013516545296, 0.03507218509912491, -0.05169166252017021, -0.05776713043451309, 0.022810310125350952, -0.007700252812355757, -0.00750787602737546, -0.036309290677309036, -0.04774618521332741, -0.07147053629159927, 0.028495939448475838, 0.006014987826347351, -0.04327359050512314, 0.006379523780196905, 0.03926696255803108, -0.025429530069231987, -0.020478254184126854, 0.003766607725992799, -0.005980097223073244, 0.04225439950823784, 0.011177551932632923, -0.05212642624974251, -0.014065923169255257, -0.02435125596821308, -0.024157503619790077, -0.08380700647830963, 0.015390812419354916, -0.01476000715047121, 0.018515286967158318, -0.016610754653811455, 0.026003185659646988, -0.01199301052838564, -0.013133895583450794, 0.010862809605896473, -0.016055990010499954, -0.01845291070640087, -0.05502137541770935, 0.03396795317530632, 0.00511869415640831, 0.007326914928853512, 0.08483016490936279, -0.02173447236418724, 0.0559682622551918, -0.011971361003816128, 0.02178858034312725, -0.023709019646048546, 0.07033021748065948, -0.04526417329907417, 0.0633942186832428, 0.04271495342254639, -0.017606424167752266, 0.03941570967435837, -0.04403514787554741, -0.047370634973049164, 0.010730787180364132, 0.029710762202739716, 0.011031534522771835, -0.01694304309785366, 0.09826426208019257, 0.017424341291189194, -0.0634295716881752, -0.06518083065748215, 0.05831420421600342, 0.07892069965600967, 0.009099914692342281, 0.04826001450419426, 0.0437132902443409, -0.0345936119556427, -0.007537304423749447, -0.073295958340168, -0.015285762958228588, 0.00910393986850977, 0.01784944161772728, -0.04333488270640373, 0.03947770223021507, -0.003955869935452938, -0.0279090516269207, 0.10287271440029144, -0.0003133798891212791, 0.02332463674247265, -0.026750432327389717, -0.016468677669763565, -0.01916818879544735, -0.0074945902451872826, -0.05687275156378746, -0.006177625618875027, 0.006037900224328041, -0.0250005554407835, 0.01390127744525671, 0.022894984111189842, -0.00014607181947212666, -0.01530070323497057, -0.07867119461297989, -0.04735015705227852, 0.051336869597435, 0.04849821329116821, 0.014819307252764702, -0.007160552777349949, 0.011292160488665104, -0.05366538465023041, 0.00777283962816, 0.0066891866736114025, 0.03815669193863869, 0.04942231625318527, 0.02464340440928936, 0.06532873958349228, 0.010267198085784912, 0.007475908380001783, 0.009048671461641788, 0.051476702094078064, 0.018295710906386375, -0.021843669936060905, -0.036516446620225906, 0.009246207773685455, 0.02813861332833767, -0.0008964503067545593, 0.013684285804629326, -0.0452718622982502, 0.015543458983302116, 0.011335530318319798, -0.020576464012265205, 0.042814046144485474, 0.07237701863050461, 0.07335080951452255, -0.025153890252113342, -0.012537560425698757, -0.029582787305116653, -0.01845618151128292, -0.007574018090963364, 0.0426572822034359, 0.030556637793779373, 0.0022087786346673965, -0.02035745233297348, -0.05560814589262009, 0.007657461334019899, 0.0016569924773648381, 0.054867781698703766, 0.02745811827480793, -0.009131036698818207, 0.07708725333213806, -0.056882962584495544, 0.037072986364364624, -0.025449732318520546, 0.033627960830926895, -0.033173974603414536, 0.037417806684970856, -0.05344054102897644, 0.03660460188984871, 0.017763087525963783, -0.033096011728048325, -0.06159508228302002, 0.07874749600887299, -0.007183674722909927, 0.009950514882802963, 0.07084784656763077, -0.0087124640122056, -0.009663572534918785, -0.023991713300347328, 0.040269650518894196, 0.09799358248710632, -0.01800723373889923, 0.020762696862220764, -0.015181522816419601, -0.02585707977414131, -0.03215484693646431, -0.03531946241855621, -0.016171058639883995, -0.0007663502474315464, 0.001993661979213357, 0.08561472594738007, -0.03536098822951317, 0.03444725647568703, -0.03533114120364189, 0.02933943085372448, 0.0004436245944816619, 0.046442195773124695, 0.1145809069275856, -0.06222056970000267, -0.034634996205568314, 0.021486759185791016, 0.019938349723815918, -0.017578471451997757, -0.02632119134068489, 0.032536350190639496, -0.03445736691355705, 0.04939098656177521, -0.008779442869126797, -0.023123260587453842, 0.009083441458642483, -0.006265711039304733, -0.024402407929301262, -0.0052981507033109665, -0.0484868623316288, -0.04559178650379181, -0.021646063774824142, 0.009510878473520279, -0.030149787664413452, 0.011127687990665436, 0.027549609541893005, 0.011716563254594803, -0.011876644566655159, 0.0022003529593348503, -0.005719525273889303, 0.012791281566023827, -0.017445415258407593, -0.019489474594593048, -0.025401920080184937, -0.03237605839967728, -0.032476723194122314, 0.015250512398779392, 0.02679019421339035, 0.04022793099284172, -0.04034707695245743, -0.05451296642422676, -0.01821603812277317, -0.02549765817821026, -0.02474716678261757, -0.037079811096191406, 0.02308310568332672, 0.0221908800303936, -0.01960335671901703, 0.0016076912870630622, 0.05033168941736221, -0.02225043997168541, -0.021170172840356827, -0.05674540996551514, 0.0029928325675427914, 0.04480062052607536, 0.03001699410378933, -0.049375977367162704, 0.011896291747689247, 0.056596022099256516, -0.03314846754074097, 0.01046660728752613, -0.008363292552530766, -0.005179204978048801, -0.007419925183057785, -0.061279941350221634, -0.003535639960318804, 0.038013946264982224, 0.021537594497203827, -0.012267007492482662, 0.03112800419330597, -0.021350068971514702, -0.027493327856063843, -0.0020198212005198, 0.008253165520727634, 0.001258825184777379, -0.00343168037943542, -0.038999032229185104, -0.03321864455938339, 0.04666140303015709, 0.024046652019023895, -0.04829464107751846, -0.012251211330294609, -0.01830098032951355, -0.047775402665138245, -0.02672935649752617, 0.003133355174213648, -0.021121235564351082, 0.013756618835031986, 0.02730534039437771, -0.025243746116757393, -0.045237742364406586, -0.02695567160844803, -0.009842876344919205, -0.09863495081663132, -0.02466970682144165, 0.005391097627580166, -0.0366116538643837, 0.018123963847756386, 0.017743172124028206, 0.08842205256223679, -0.01924130693078041, -0.006986348889768124, -0.04307200014591217, 0.04590374603867531, -0.02632351592183113, -0.023684190586209297, -0.06273955851793289, -0.023324018344283104, 0.023626046255230904, -0.026216184720396996, -0.05736593157052994, -0.011069816537201405, 0.052751749753952026, 0.0053502521477639675, 0.028109684586524963, 0.07328200340270996, -0.03864491358399391, 0.055529624223709106, 0.048170510679483414, 0.017670737579464912, -0.03350688889622688, -0.010406404733657837, -0.01568622700870037, -0.04045892134308815, -0.01077223476022482, -0.008447683416306973, -0.014636664651334286, -0.0043838899582624435, -0.06424960494041443 ]
<p>When I learn QFT, I am bothered by many problems in complex analysis.</p> <p>1) $$\frac{1}{x-x_0+i\epsilon}=P\frac{1}{x-x_0}-i\pi\delta(x-x_0)$$</p> <p>I can't understand why $1/x$ can have a principal value because it's not a multivalued function. I'm very confused. And when I learned the complex analysis, I've not watched <a href="http://en.wikipedia.org/wiki/Sokhotski%E2%80%93Plemelj_theorem" rel="nofollow">this formula</a>, can anybody tell me where I can find this formula's proof.</p> <p>2) $$\frac{d}{dx}\ln(x+i\epsilon)=P\frac{1}{x}-i\pi\delta(x)$$</p> <p>3) And I also find this formula. Seemingly $f(x)$ has a branch cut, then $$f(z)=\frac{1}{\pi}\int_Z^{\infty}dz^{\prime}\frac{{\rm Im} f(z^{\prime})}{z^{\prime}-z}$$ Can anyone can tell the whole theorem and its proof, and what it wants to express. <img src="http://i.stack.imgur.com/oK0o1.png" alt="enter image description here"></p> <p>Now I am very confused by these formula, because I haven't read it in any complex analysis book and never been taught how to handle an integral with branch cut. Can anyone give me the whole proof and where I can consult. </p>
g8355
[ -0.01051099132746458, 0.012556304223835468, -0.009057929739356041, 0.0003373695071786642, 0.032511670142412186, -0.028034519404172897, 0.04056544229388237, 0.014868741855025291, 0.006061199586838484, -0.0498645044863224, -0.04582272469997406, 0.029675157740712166, -0.007639501243829727, -0.01682458259165287, -0.0051161847077310085, -0.03059210255742073, -0.0462150052189827, 0.03398603945970535, -0.021092716604471207, -0.020034311339259148, -0.0057395813055336475, 0.007469542790204287, 0.021533897146582603, -0.06428192555904388, 0.04812777414917946, -0.052591100335121155, 0.009206286631524563, 0.03498977795243263, -0.059581320732831955, 0.005055557005107403, 0.004927944857627153, 0.0377424880862236, 0.022012801840901375, 0.0697401612997055, -0.002747416729107499, -0.0750289186835289, 0.00724823260679841, 0.048129063099622726, 0.049148838967084885, -0.05938858538866043, -0.04395328834652901, -0.008799022994935513, 0.0502345971763134, -0.046680767089128494, -0.028741342946887016, -0.013288600370287895, -0.008105887100100517, -0.023459136486053467, -0.005525936372578144, -0.013566328212618828, 0.024010974913835526, 0.002275192877277732, 0.10508526116609573, 0.01490733865648508, -0.07347183674573898, 0.0032010506838560104, -0.011764656752347946, -0.0312749482691288, 0.0470992848277092, 0.0017450980376452208, -0.008549918420612812, -0.04692769795656204, 0.0355856716632843, 0.009542670100927353, 0.0037657301872968674, -0.022166967391967773, 0.04036366194486618, -0.04059837386012077, -0.05874423682689667, 0.020435187965631485, -0.01655900664627552, -0.058504633605480194, 0.03197226673364639, -0.025987882167100906, -0.05668051540851593, 0.020006874576210976, 0.005039150360971689, -0.018953152000904083, -0.002527841366827488, -0.008532941341400146, -0.0078028407879173756, 0.027842367067933083, -0.03640810027718544, 0.04226920008659363, -0.015708569437265396, -0.03207363188266754, 0.027365470305085182, -0.075738824903965, 0.007465694565325975, -0.02256975695490837, -0.01833353377878666, 0.0038914724718779325, -0.018878085538744926, -0.04814605414867401, 0.019285282120108604, -0.0004261147405486554, -0.0006513672415167093, 0.04428325966000557, -0.039237577468156815, -0.009989640675485134, 0.01230473443865776, 0.06160460785031319, 0.06345348805189133, -0.0065695918165147305, -0.040306173264980316, -0.033950041979551315, 0.031872935593128204, 0.005659408867359161, -0.04210412874817848, 0.02672548219561577, -0.01568657159805298, -0.0004243125149514526, -0.06268276274204254, -0.04112006723880768, 0.05369891598820686, 0.026754209771752357, 0.0023349588736891747, -0.013337841257452965, 0.019811619073152542, -0.010060204192996025, -0.007082149852067232, -0.014261605218052864, 0.12690338492393494, 0.039320167154073715, -0.022226877510547638, -0.018219007179141045, 0.002842356450855732, 0.02837330475449562, 0.02069167047739029, -0.01904260739684105, 0.015258358791470528, -0.0005547130131162703, 0.025160344317555428, -0.0023915483616292477, -0.028893841430544853, -0.004372770898044109, -0.05173632502555847, -0.002830083016306162, 0.006930256262421608, -0.015600234270095825, -0.027602223679423332, 0.0028197728097438812, -0.04005608335137367, -0.03052898310124874, 0.028825730085372925, 0.030439112335443497, -0.04920011758804321, 0.002949254820123315, -0.021961063146591187, -0.011211958713829517, 0.058468252420425415, 0.04465735703706741, -0.03037133254110813, 0.01599285937845707, 0.044805511832237244, 0.018568450585007668, 0.034112464636564255, 0.03318804129958153, -0.0230727419257164, -0.007806930225342512, -0.027337802574038506, 0.060093991458415985, -0.00025667110458016396, 0.01676921173930168, -0.005129808560013771, -0.037465669214725494, -0.020579220727086067, -0.07618251442909241, -0.010688473470509052, -0.07164599746465683, -0.0007938736816868186, 0.09544635564088821, 0.061891745775938034, -0.0011893388582393527, 0.05531860515475273, 0.03034893050789833, -0.010600456036627293, -0.02037186734378338, 0.03962896019220352, 0.047160424292087555, -0.04990624636411667, 0.009008820168673992, -0.05021784454584122, -0.04148808866739273, -0.027783101424574852, 0.017878573387861252, 0.008548087440431118, -0.010685001499950886, 0.004729891195893288, 0.007954102009534836, -0.03476211428642273, 0.03714185953140259, 0.058644674718379974, 0.03338278457522392, 0.03288339823484421, 0.005583657883107662, -0.022265026345849037, -0.0739578902721405, 0.01814478449523449, 0.008894949220120907, 0.03021920472383499, 0.02158418670296669, -0.02389516681432724, -0.036158014088869095, 0.025899816304445267, -0.011093498207628727, -0.008627062663435936, 0.0015761309769004583, -0.002998705953359604, 0.02192774787545204, -0.06345689296722412, -0.08773557096719742, -0.012089107185602188, 0.039956290274858475, 0.011724850162863731, -0.03996654972434044, 0.038864150643348694, -0.002864635083824396, -0.002025421243160963, 0.00019751462968997657, 0.0045912559144198895, -0.030311577022075653, 0.035725753754377365, -0.01369360089302063, 0.015854880213737488, 0.03855309635400772, 0.04036138951778412, -0.05025990307331085, -0.018405793234705925, 0.053277771919965744, -0.07607401907444, 0.007880606688559055, -0.02141910418868065, 0.04847979545593262, -0.0071650901809334755, 0.016122862696647644, 0.0007116927881725132, -0.03463685140013695, 0.012486957013607025, 0.03386874124407768, -0.02851821854710579, -0.0365101620554924, -0.019107727333903313, 0.02185572125017643, 0.03809844329953194, -0.007596930488944054, 0.01835416816174984, 0.04216180741786957, -0.011127816513180733, -0.005529860500246286, -0.021226538345217705, 0.005734483245760202, 0.02330821380019188, 0.04262474179267883, -0.05748594552278519, -0.07887519150972366, 0.03226330503821373, -0.007508944254368544, 0.05360253527760506, 0.03159690648317337, -0.013863421976566315, -0.02450966276228428, -0.021480513736605644, 0.015681860968470573, -0.05274069681763649, 0.037058036774396896, 0.007244242820888758, -0.0037856954149901867, -0.018012594431638718, 0.004229951184242964, -0.023036137223243713, 0.05752817541360855, 0.050681788474321365, 0.09339572489261627, -0.013745072297751904, -0.024665428325533867, 0.013075372204184532, -0.0035572857595980167, 0.013049931265413761, 0.0057450407184660435, -0.009047119878232479, -0.017539534717798233, -0.009607668966054916, 0.06720180809497833, 0.015868257731199265, 0.0048645916394889355, 0.021133124828338623, 0.03714246302843094, -0.027933470904827118, -0.06243467703461647, -0.02810584008693695, -0.01054131705313921, -0.04659901559352875, -0.08256512880325317, -0.0034059728495776653, -0.019051479175686836, 0.0059453221037983894, -0.02001895010471344, 0.025928817689418793, 0.018428193405270576, 0.019301943480968475, -0.001942602451890707, 0.06388375908136368, 0.01565375179052353, 0.0696648433804512, -0.014849069528281689, 0.04455594718456268, 0.018450560048222542, -0.04489218071103096, 0.033311691135168076, 0.04698339104652405, -0.02322559803724289, 0.01639038696885109, -0.04719814285635948, -0.017645755782723427, -0.025090040639042854, -0.0026138678658753633, -0.024383239448070526, 0.03448403626680374, -0.0017444073455408216, -0.022434638813138008, -0.02074757032096386, -0.039317697286605835, 0.0076326229609549046, 0.021152636036276817, -0.0054108258336782455, -0.06049901992082596, 0.044277094304561615, 0.005873421672731638, 0.0213263388723135, 0.04123818501830101, 0.013412632048130035, -0.018464474007487297, 0.019444193691015244, -0.02093498595058918, -0.02965746633708477, 0.0015750325983390212, 0.05824131518602371, 0.06749356538057327, -0.01838706247508526, -0.03504831716418266, -0.038244280964136124, -0.04089215025305748, -0.02725980244576931, 0.0066376253962516785, -0.0390416644513607, 0.03753219544887543, 0.059225812554359436, 0.05369347333908081, 0.004442935809493065, -0.03263401240110397, -0.03858499228954315, -0.029677560552954674, -0.009252766147255898, 0.005789447575807571, 0.021506793797016144, 0.012303752824664116, 0.03580296039581299, -0.006099669262766838, -0.002155640162527561, 0.05678972601890564, -0.04823590815067291, 0.023719409480690956, 0.0237180944532156, 0.025857077911496162, -0.05919359251856804, 0.050198934972286224, -0.014134391210973263, -0.018764222040772438, -0.01529207918792963, 0.019143709912896156, 0.009402629919350147, 0.029161512851715088, 0.021858619526028633, -0.044399674981832504, -0.08408340811729431, -0.05023277923464775, 0.02858354151248932, -0.013205129653215408, 0.039987992495298386, 0.05475297570228577, 0.021949972957372665, 0.07480931282043457, 0.0481281504034996, 0.010645052418112755, 0.019091371446847916, 0.026848694309592247, -0.02765716426074505, 0.09728331118822098, 0.009438736364245415, 0.003447458613663912, -0.016486434265971184, -0.05515145882964134, 0.05946800112724304, -0.0036317778285592794, -0.02587777003645897, -0.005726061761379242, -0.03441433981060982, -0.08976319432258606, 0.030656255781650543, -0.02006722427904606, -0.018122833222150803, 0.027153408154845238, 0.00285162590444088, -0.008818631060421467, 0.0014488277956843376, -0.011100917123258114, 0.03277522698044777, 0.09724948555231094, -0.07077980041503906, 0.0080260019749403, -0.018313471227884293, 0.03387131914496422, -0.018970448523759842, -0.04340001940727234, -0.03291334584355354, 0.08118844777345657, -0.04533093422651291, 0.042304717004299164, -0.07795442640781403, 0.03247755765914917, -0.006497291382402182, -0.03397294878959656, -0.038685142993927, 0.07132477313280106, 0.06799469888210297, 0.04818691685795784, -0.034693751484155655, 0.00023790693376213312, 0.012142270803451538, -0.022264419123530388, 0.03416973352432251, -0.008687636815011501, 0.0490904226899147, -0.058533716946840286, 0.039742279797792435, -0.08366364985704422, 0.011757077649235725, -0.04387712478637695, -0.006026259157806635, 0.015676138922572136, 0.029352489858865738, -0.033276259899139404, 0.03038262389600277, 0.054109469056129456, -0.008175831288099289, -0.05941886082291603, -0.025267187505960464, 0.024745065718889236, -0.04091186821460724, 0.01184073556214571, 0.02197805605828762, -0.0023838747292757034, 0.01059340313076973, 0.01161436177790165, -0.020019415766000748, -0.01098850928246975, -0.05670524761080742, -0.03566409647464752, 0.031087808310985565, -0.00140494538936764, -0.02279278077185154, 0.012219052761793137, 0.005633693654090166, 0.07113513350486755, 0.0002105166931869462, -0.04725685715675354, -0.0023977525997906923, -0.0003043254546355456, 0.019707603380084038, 0.041243504732847214, 0.055528298020362854, 0.06708791851997375, -0.019853830337524414, -0.01859569363296032, -0.05941560119390488, 0.02860405668616295, 0.027149531990289688, -0.00034137043985538185, -0.04183057323098183, 0.031139211729168892, -0.03283129259943962, -0.034196071326732635, -0.009741559624671936, 0.024591509252786636, -0.032192204147577286, 0.003910981584340334, -0.06772056221961975, -0.022602194920182228, -0.0016194344498217106, 0.054499875754117966, 0.05740375444293022, 0.07974972575902939, -0.02168877422809601, -0.026454785838723183, -0.009423840790987015, -0.02473779395222664, 0.01892797090113163, 0.040447767823934555, -0.03028874844312668, -0.01654806174337864, 0.021524904295802116, -0.01175300870090723, -0.03321072831749916, 0.043011151254177094, 0.04256812110543251, 0.0045225913636386395, -0.006599524524062872, -0.023261448368430138, 0.028029415756464005, -0.0004597964871209115, -0.030270909890532494, -0.010355163365602493, -0.03710618242621422, 0.008835515938699245, -0.012024433352053165, -0.07830312848091125, -0.05462057143449783, -0.038590993732213974, -0.0355515256524086, 0.032599881291389465, 0.024059342220425606, -0.08166468143463135, -0.0028481106273829937, 0.0254780612885952, 0.006974761839956045, -0.023614728823304176, -0.07999242097139359, -0.027877280488610268, 0.04648710414767265, -0.014420787803828716, -0.008862345479428768, -0.024122891947627068, -0.009664350189268589, 0.022980069741606712, 0.0543876551091671, -0.05277810990810394, 0.017962314188480377, 0.015317268669605255, 0.011288179084658623, 0.048638373613357544, 0.02861963026225567, -0.011418748646974564, 0.05030097812414169, -0.07200302928686142, 0.009950296021997929, 0.02318957820534706, 0.02531689777970314, 0.034865204244852066, -0.03779325634241104, 0.048470981419086456, -0.01309578400105238, -0.06927932053804398, -0.05898548290133476, 0.004165461286902428, 0.043634966015815735, 0.019601741805672646, -0.030651966109871864, -0.0436132550239563, -0.02453409694135189, -0.0631660521030426, -0.0649566501379013, -0.005951392464339733, -0.0615910068154335, 0.011597425676882267, -0.08964680135250092, 0.015460104681551456, -0.007507606875151396, -0.04220488667488098, -0.04491625726222992, -0.010026170872151852, 0.02097019925713539, 0.010646315291523933, 0.08027483522891998, 0.06020231917500496, 0.0817277804017067, -0.05127915367484093, -0.010102498345077038, -0.0048913247883319855, 0.005216384772211313, -0.03985276073217392, 0.07348251342773438, 0.056414056569337845, -0.01050598081201315, -0.02372954785823822, 0.029419146478176117, -0.02085886523127556, -0.0014629404759034514, 0.01964995637536049, 0.004834390711039305, -0.0599382184445858, 0.0325060598552227, -0.04041484370827675, 0.0006112057017162442, 0.01008446142077446, 0.004413791932165623, 0.06971131265163422, 0.025736108422279358, 0.05250716954469681, -0.09433747082948685, 0.01610049232840538, 0.025451941415667534, -0.004422124940901995, -0.03951442241668701, 0.030014630407094955, 0.03539388254284859, 0.018902786076068878, -0.059100907295942307, -0.02066054195165634, 0.045696597546339035, 0.04258323460817337, 0.0319177620112896, -0.011768931522965431, -0.013905772008001804, 0.004834562540054321, -0.004437811207026243, 0.019061874598264694, -0.002634169766679406, 0.041279856115579605, 0.010549425147473812, 0.03483571484684944, -0.03030703403055668, 0.00513233058154583, -0.023660991340875626, 0.05639904364943504, 0.05200716480612755, 0.010883254930377007, -0.007444283459335566, -0.02286943420767784, -0.009360031224787235, -0.012029622681438923, 0.02585018053650856, -0.024487504735589027, -0.011883997358381748, -0.03302602469921112, -0.022390015423297882, -0.016388865187764168, 0.029188573360443115, 0.05617916211485863, 0.05832461640238762, -0.041372042149305344, 0.0896415114402771, 0.021423278376460075, -0.0008865415584295988, -0.07987827062606812, -0.011428101919591427, -0.007033674977719784, -0.008945277892053127, -0.09112190455198288, -0.012803396210074425, 0.06842911243438721, 0.04470068961381912, 0.026942072436213493, 0.011728710494935513, -0.011761011555790901, -0.04600254446268082, 0.09063685685396194, 0.005584415048360825, -0.04357927292585373, -0.05314910411834717, -0.013829674571752548, 0.030949709936976433, -0.006557909771800041, 0.030230557546019554, -0.011647701263427734, 0.08340419828891754, 0.04408293962478638, -0.017346609383821487, -0.024536633864045143, -0.022476430982351303, -0.04122504964470863, -0.009051171131432056, -0.010305799543857574, 0.015310728922486305, 0.027995329350233078, 0.017008034512400627, 0.029073193669319153, 0.025232825428247452, -0.01953483372926712, 0.02075781859457493, -0.023162705823779106, 0.0318596325814724, -0.006062713451683521, -0.03427505865693092, -0.03179027885198593, -0.025970956310629845, -0.006490382365882397, -0.008195054717361927, 0.02581547386944294, 0.04794758930802345, -0.035595349967479706, -0.06206514686346054, 0.0692509189248085, 0.00586295360699296, 0.0032660681754350662, -0.019906852394342422, -0.007188292685896158, 0.05368722230195999, 0.03754886984825134, 0.06031117960810661, 0.049677472561597824, -0.016716880723834038, 0.0035179180558770895, 0.009176385588943958, -0.024091416969895363, 0.034725919365882874, 0.019379863515496254, 0.031147219240665436, -0.012527147307991982, 0.019969115033745766, 0.01325197797268629, -0.005181227345019579, -0.012321481481194496, -0.024645686149597168, 0.022805936634540558, -0.043341394513845444, -0.03129612281918526, 0.07630861550569534, -0.02758960798382759, -0.00681473920121789, 0.04694043844938278, -0.026246873661875725, -0.02003532461822033, -0.04084089770913124, -0.012859898619353771, 0.007352420594543219, -0.046631790697574615, -0.02816903404891491, -0.0006568445824086666, 0.06861987709999084, -0.009746297262609005, 0.0069148950278759, -0.030761301517486572, -0.003417369443923235, -0.021533269435167313, 0.003927984274923801, 0.013794093392789364, -0.03268419951200485, -0.028285397216677666, 0.015229861252009869, 0.023434339091181755, -0.018732422962784767, 0.003761880099773407, 0.01769200526177883, -0.01811160519719124, -0.0134836221113801, -0.008081961423158646, 0.012522459961473942, 0.04154393821954727, 0.005155274644494057, -0.034829750657081604, -0.006852850783616304, -0.06887272000312805, 0.04020632058382034, 0.0483701191842556, -0.03870552405714989, -0.0063324314542114735, 0.018348585814237595, 0.03469674661755562, -0.02527019754052162, -0.03368828445672989, -0.023115303367376328, -0.049911968410015106, 0.07062232494354248, -0.03822653368115425, -0.048265185207128525, -0.006357479374855757, -0.007006928790360689 ]
<p>Consider the 3-dimensional Minkowski space $$ ds^2=dt'^2-dr'^2-r'^2d\phi'^2 $$</p> <p>Now we transform it into a rotating frame: $$ t'=t,r'=r,\phi'=\phi+\omega t $$</p> <p>Then the metric becomes $$ ds^2=(1-r^2\omega^2)dt^2-dr^2-2\omega r^2d\phi dt-r^2 d\phi^2 $$</p> <p>Consider a static observer in the rotating frame with coordinate $(r,\phi)=(R,0)$. Could anyone show me how to compute the 4-acceleration of this observer?</p> <p>I am expecting the answer to be $(0,-\omega^2 R,0)$ based on my knowledge of Newtonian mechanics. But my calculation does not give this.</p> <p>I have calculated the 4-velocity to be $$ u=\left(\frac{1}{\sqrt{1-R^2\omega^2}},0,0\right) $$</p> <p>Then I use the formula $$ a^\mu=u^\nu\nabla_\nu u^\mu=u^t\nabla_tu^\mu=u^t(\partial_tu^\mu+\Gamma^\mu_{t\alpha}u^\alpha)=u^tu^\alpha\Gamma^\mu_{t\alpha} $$ Then it turns out only $\alpha=t,\mu=r$ is meaningful, and $$ a^r=-\frac{2R\omega^2}{1-R^2\omega^2}R^2(1-2\omega^2R^2) $$ which I think is definitely wrong...</p>
g8356
[ 0.0021246972028166056, 0.03988596424460411, -0.012499770149588585, -0.035481736063957214, -0.007565710227936506, -0.0004955484764650464, 0.08514248579740524, 0.04172966629266739, -0.04978403449058533, 0.005118433851748705, -0.015505217015743256, -0.003290618536993861, 0.0010751052759587765, -0.03584998846054077, 0.023568045347929, -0.0012625009985640645, 0.029714403674006462, 0.008686678484082222, 0.012663875706493855, -0.026624877005815506, 0.029251381754875183, -0.028843266889452934, 0.024013672024011612, -0.026381436735391617, 0.0544012077152729, -0.02711065486073494, 0.002882343716919422, 0.006412680260837078, -0.07399667054414749, 0.022188307717442513, 0.04741065204143524, 0.013317141681909561, 0.003960085101425648, -0.009456174448132515, 0.024853860959410667, 0.0014425539411604404, 0.043850045651197433, -0.030926376581192017, -0.00904123205691576, -0.001226128893904388, -0.05329422652721405, -0.02526991069316864, -0.004761329386383295, 0.055028967559337616, 0.06417123228311539, -0.028688350692391396, 0.00615847110748291, 0.018164901062846184, -0.01583692617714405, 0.027404500171542168, -0.016249077394604683, 0.02192698046565056, 0.05071399360895157, 0.014081246219575405, -0.005486919544637203, 0.0687611922621727, -0.02484481781721115, -0.049145519733428955, 0.04389087110757828, 0.05707395076751709, -0.03666751831769943, -0.10226660221815109, -0.005452517420053482, -0.018707500770688057, 0.04803040996193886, -0.009454580023884773, 0.018690750002861023, 0.00910837110131979, -0.0014782750513404608, -0.0033128380309790373, 0.019740600138902664, -0.004964257590472698, 0.007895935326814651, 0.007658787537366152, 0.005923899821937084, 0.005046201404184103, -0.045760512351989746, -0.029608633369207382, -0.028065897524356842, -0.031042028218507767, -0.0009490922675468028, 0.01358417235314846, 0.030908966436982155, -0.003174111945554614, 0.020793724805116653, 0.013545588590204716, 0.023153379559516907, 0.05861184373497963, -0.02041749283671379, -0.006415193900465965, 0.02557063102722168, 0.0006122700870037079, 0.05759904533624649, -0.020427918061614037, 0.015252347104251385, 0.026849830523133278, -0.060375817120075226, 0.04598298668861389, 0.017894823104143143, -0.019639043137431145, -0.03178773820400238, -0.0019029432442039251, 0.015245793387293816, 0.018518080934882164, 0.04495511204004288, -0.004071712028235197, 0.0195620134472847, 0.03304312005639076, 0.013899534940719604, -0.03862808272242546, -0.030390378087759018, -0.0413053072988987, 0.04197033494710922, -0.020090753212571144, -0.04099659621715546, -0.059383828192949295, 0.030940962955355644, 0.01310380082577467, 0.0008992051589302719, 0.0750124454498291, 0.022271620109677315, 0.05141598731279373, 0.0005430342862382531, 0.12085911631584167, 0.030932921916246414, 0.008518524467945099, -0.06998059898614883, 0.018576933071017265, 0.03863378241658211, 0.0076697287149727345, 0.03694524988532066, 0.014557546935975552, 0.07466558367013931, -0.008303585462272167, -0.023418668657541275, 0.03390999510884285, -0.01927216723561287, -0.025062082335352898, -0.01062643714249134, 0.05187852680683136, 0.020317889750003815, -0.04390590637922287, 0.008762488141655922, 0.007137723732739687, -0.07580390572547913, 0.05030669644474983, -0.0030509403441101313, -0.034250304102897644, 0.04171542078256607, 0.05796656012535095, 0.03369565308094025, 0.08464910835027695, -0.02469457872211933, 0.02622799202799797, 0.04714801162481308, 0.013498284853994846, 0.013176299631595612, -0.0033344142138957977, -0.006385818123817444, 0.025433486327528954, 0.09456290304660797, 0.020716901868581772, 0.06401748955249786, -0.006482193246483803, -0.09566502273082733, 0.020638057962059975, 0.017948534339666367, -0.03484102711081505, 0.03077595680952072, -0.09404075890779495, -0.044515468180179596, -0.017303016036748886, 0.04605408012866974, -0.008384292013943195, -0.06699567288160324, 0.003882867284119129, -0.04043309763073921, -0.04605824500322342, -0.062104515731334686, 0.023661674931645393, 0.029468117281794548, -0.050453897565603256, 0.0518449991941452, -0.03538252040743828, -0.0015545226633548737, -0.02404254674911499, 0.028220592066645622, 0.012059010565280914, 0.014439621940255165, 0.015000204555690289, 0.016231704503297806, -0.02444705367088318, 0.06653069704771042, 0.042735278606414795, 0.016818460077047348, 0.03580839931964874, -0.02835189737379551, -0.0468311570584774, 0.01804482750594616, 0.042645204812288284, -0.013323609717190266, -0.024093013256788254, 0.05365060642361641, -0.01014404371380806, 0.010447095148265362, -0.011124876327812672, 0.0035805143415927887, 0.007488347124308348, 0.010746346786618233, 0.03388722240924835, -0.006105734501034021, -0.040351007133722305, -0.04548819735646248, 0.012320158071815968, 0.004650868009775877, 0.009790520183742046, 0.024685660377144814, 0.016336992383003235, -0.04064035043120384, 0.022728968411684036, -0.038533538579940796, -0.016384059563279152, 0.02697431668639183, 0.00650889752432704, -0.03009805642068386, -0.016103364527225494, -0.050655100494623184, 0.008345822803676128, 0.037981532514095306, 0.0021286923438310623, -0.037375595420598984, 0.017937002703547478, -0.01273494865745306, 0.0723230168223381, 0.06109314411878586, 0.04675770923495293, -0.060453854501247406, 0.01918756403028965, 0.04403531178832054, 0.0032899887301027775, 0.015738602727651596, 0.03971060737967491, -0.011318868957459927, -0.07043644040822983, 0.04665060713887215, -0.010163203813135624, 0.08403200656175613, 0.03805844858288765, -0.0014298915630206466, -0.024210389703512192, 0.01650421693921089, -0.010962879285216331, 0.009401221759617329, -0.02456158958375454, -0.015485704876482487, 0.00212648743763566, -0.02509450726211071, 0.02363511733710766, -0.06518057733774185, -0.07275109738111496, 0.026850640773773193, -0.009134482592344284, -0.01623629219830036, 0.01426722202450037, -0.05042067915201187, 0.013350196182727814, 0.002286780159920454, 0.04498414322733879, 0.003591724205762148, 0.05364010110497475, -0.00850309245288372, 0.025760581716895103, 0.004682779312133789, 0.06611456722021103, -0.09375853091478348, -0.019387545064091682, 0.014851794578135014, 0.006106958724558353, -0.032355740666389465, 0.017232052981853485, 0.010372675955295563, 0.007112502120435238, -0.03838605433702469, 0.0009495990234427154, 0.014246282167732716, -0.09006870537996292, -0.023574206978082657, 0.027595918625593185, -0.012830628082156181, -0.024677323177456856, -0.004752610344439745, 0.028597814962267876, -0.01269683986902237, -0.02061128430068493, -0.00990427564829588, 0.028379783034324646, 0.0017102576093748212, -0.014645184390246868, 0.016982760280370712, 0.04576215520501137, -0.03293582424521446, -0.03045758418738842, 0.020657921209931374, -0.02204148843884468, -0.02201637625694275, -0.037643637508153915, -0.03374893590807915, -0.06688515096902847, -0.006248310208320618, -0.0022464864887297153, -0.03962060436606407, -0.02630082331597805, -0.027705585584044456, -0.03797334432601929, -0.034968651831150055, -0.08159450441598892, 0.01618853770196438, -0.020627643913030624, 0.005821568425744772, 0.00004137177165830508, 0.004100395832210779, -0.057265955954790115, -0.06567900627851486, 0.02182738296687603, 0.039516154676675797, 0.02207629382610321, -0.00014298463065642864, 0.01129829604178667, -0.05043388530611992, -0.04371606558561325, 0.032533224672079086, -0.022428244352340698, -0.007844062522053719, 0.017516043037176132, -0.06003936380147934, -0.02938421070575714, -0.053247321397066116, 0.055474601686000824, 0.03700040280818939, -0.06763803958892822, -0.017845673486590385, -0.020255884155631065, -0.03638368099927902, -0.011222378350794315, 0.002047369023784995, -0.023351578041911125, -0.01651468127965927, 0.0026071981992572546, 0.013408521190285683, -0.046653326600790024, 0.026234904304146767, -0.028530588373541832, 0.024301666766405106, 0.0038645935710519552, 0.00002573313940956723, 0.04295339062809944, 0.03362012282013893, 0.02591879665851593, 0.005374235566705465, -0.024431340396404266, -0.012776664458215237, -0.03201639652252197, -0.03982557728886604, 0.0030843110289424658, 0.0006905561313033104, -0.015264350920915604, -0.0010039156768471003, 0.030636925250291824, -0.008513707667589188, -0.028025304898619652, 0.027761129662394524, -0.05141008272767067, 0.012760561890900135, -0.012434703297913074, 0.0037242800462991, -0.07182971388101578, -0.019146965816617012, -0.0016054378356784582, 0.006841903552412987, 0.03658582270145416, 0.05119067803025246, -0.024589134380221367, -0.05159866809844971, 0.04744894802570343, 0.019641991704702377, 0.05059127137064934, -0.008783252909779549, -0.04429945722222328, -0.006691246293485165, -0.053524259477853775, 0.031649958342313766, -0.021466057747602463, 0.01005059015005827, -0.0483112707734108, 0.054589226841926575, -0.08332043141126633, 0.024798965081572533, 0.011586704291403294, -0.044761478900909424, 0.0074053374119102955, -0.02512110024690628, -0.01928010769188404, 0.03978893533349037, -0.0019103955710306764, -0.04258004203438759, 0.02410060353577137, 0.006382778752595186, 0.020709199830889702, 0.05029897391796112, 0.037281643599271774, 0.01606025919318199, 0.059483852237463, 0.0342981182038784, -0.06677744537591934, 0.00033733571763150394, 0.019027918577194214, -0.016863912343978882, 0.017598602920770645, -0.034537702798843384, 0.02118137665092945, 0.00695415074005723, 0.015533683821558952, -0.0037972722202539444, -0.053206611424684525, -0.0009764587739482522, 0.0699712410569191, 0.10235254466533661, -0.006324527785181999, -0.020597096532583237, -0.020924845710396767, 0.04237092658877373, -0.005103350151330233, -0.0049392906948924065, 0.03190005198121071, -0.012451943010091782, 0.02671085111796856, 0.020597556605935097, 0.01707003265619278, 0.03374924510717392, 0.015317278914153576, -0.0059540849179029465, 0.016835695132613182, 0.041201673448085785, -0.04310357943177223, -0.047251664102077484, 0.04112028330564499, -0.007246340159326792, -0.04441741108894348, 0.021723754703998566, 0.06521786004304886, 0.0054794359020888805, 0.01806049607694149, 0.015371053479611874, 0.01044466532766819, 0.03766552731394768, 0.027826085686683655, -0.039318934082984924, 0.004775994457304478, -0.047343410551548004, -0.004826935939490795, -0.078470379114151, -0.03826480731368065, 0.013735625892877579, -0.003745690453797579, 0.03394971787929535, 0.03856572136282921, -0.06037958711385727, 0.045490462332963943, -0.0756378099322319, -0.0428343191742897, -0.008247002959251404, 0.001131442841142416, -0.0561320036649704, -0.033923495560884476, -0.017984747886657715, 0.04390600696206093, -0.01846642792224884, 0.03581414371728897, 0.039418090134859085, -0.036022331565618515, 0.020295951515436172, -0.0006593505386263132, 0.023159829899668694, -0.02835092879831791, 0.04140417277812958, 0.0233946293592453, -0.05336614325642586, 0.004380601923912764, -0.01989220455288887, 0.006172721739858389, -0.01509819459170103, 0.029013676568865776, -0.03610418736934662, -0.06248610094189644, -0.017625555396080017, 0.11829426884651184, 0.024927938356995583, -0.06562437862157822, -0.030582157894968987, -0.009555121883749962, -0.10039664059877396, -0.023346463218331337, 0.03180807828903198, -0.030402574688196182, 0.009361648000776768, 0.06730146706104279, 0.0828750804066658, -0.029986049979925156, 0.0007681867573410273, 0.10204612463712692, -0.014520909637212753, 0.00016634447092656046, 0.01835101842880249, 0.015800487250089645, 0.010084730572998524, -0.025478506460785866, 0.04491114616394043, -0.0026575985830277205, -0.004392382223159075, -0.07276855409145355, 0.03502007946372032, 0.014480991289019585, 0.029359815642237663, 0.012041627429425716, -0.02422003634274006, 0.06003765016794205, 0.008720406331121922, -0.0235870573669672, -0.022819675505161285, -0.006828800309449434, 0.014693393371999264, -0.04318062961101532, 0.0075564756989479065, 0.007238520309329033, 0.02550981193780899, -0.007541654631495476, 0.0035585497971624136, -0.009006300941109657, 0.05828612670302391, 0.003336722496896982, -0.05172183737158775, -0.02510884590446949, -0.0027928382623940706, 0.03731144964694977, -0.08446954190731049, 0.02612033672630787, -0.013974975794553757, 0.003209529910236597, 0.025228803977370262, -0.043501030653715134, -0.039589881896972656, 0.036380089819431305, 0.030429072678089142, -0.061363160610198975, 0.005352271720767021, 0.03350361809134483, 0.020737359300255775, 0.004664802458137274, -0.05789134278893471, -0.03530902788043022, 0.03994002565741539, -0.023426447063684464, 0.029952967539429665, 0.006957679521292448, -0.005038796458393335, -0.0018822994315996766, 0.004303599242120981, -0.0352729894220829, 0.04357299208641052, -0.02319391258060932, -0.0029354547150433064, 0.02229251340031624, 0.003153088502585888, 0.01905941590666771, 0.031048910692334175, 0.05505462735891342, 0.011271776631474495, -0.010417620651423931, -0.06725046783685684, 0.016081681475043297, -0.013292646035552025, 0.04166131466627121, 0.06510473042726517, -0.03068671002984047, -0.039137501269578934, 0.05178689584136009, 0.006420550402253866, 0.002558664884418249, -0.03274351730942726, -0.006830049213021994, -0.07933269441127777, 0.04423725977540016, -0.01144806295633316, -0.046621572226285934, -0.039068881422281265, -0.018844081088900566, -0.007171959616243839, -0.017886431887745857, -0.022077618166804314, 0.0014551487984135747, 0.02418692782521248, 0.0018051385413855314, 0.016743965446949005, -0.03061504289507866, 0.00981409102678299, 0.0013154450571164489, -0.08148150891065598, -0.04806455597281456, 0.03062794916331768, -0.012736361473798752, -0.04257805272936821, 0.06361330300569534, 0.023046009242534637, 0.09309089183807373, -0.010540145449340343, -0.02776886522769928, 0.0005389259313233197, 0.013511868193745613, 0.02039623260498047, -0.016489919275045395, 0.10719767957925797, -0.010646263137459755, -0.021847262978553772, -0.06648512929677963, 0.032019391655921936, 0.009814806282520294, -0.018420789390802383, -0.026894988492131233, 0.036555636674165726, -0.010542728006839752, 0.0391700379550457, -0.08710186928510666, -0.05414269492030144, 0.03004305623471737, 0.052732616662979126, 0.010172110050916672, -0.026078863069415092, 0.04692244529724121, -0.02431466057896614, 0.08200858533382416, 0.00754841323941946, 0.017050979658961296, -0.05063285678625107, -0.0539778470993042, -0.06159403547644615, -0.04803959280252457, -0.009059992618858814, 0.043692249804735184, -0.08931304514408112, 0.009523802436888218, 0.0005685542128048837, -0.02755727432668209, 0.005167014896869659, 0.05558714270591736, -0.044924601912498474, -0.02234650030732155, -0.0003865472099278122, 0.018668226897716522, 0.03346856310963631, -0.03042302466928959, 0.02375110611319542, -0.030425379052758217, -0.014070339500904083, 0.01681363582611084, -0.03294036164879799, -0.009352900087833405, -0.01895337738096714, 0.019392510876059532, 0.019663456827402115, -0.02344522811472416, 0.047006309032440186, 0.02386249415576458, -0.046165287494659424, 0.051156360656023026, 0.010363221168518066, 0.0005990087520331144, -0.022520052269101143, 0.014602206647396088, 0.00553846312686801, 0.00343043589964509, -0.06846751272678375, 0.04587612673640251, -0.01788574457168579, 0.02172432653605938, -0.02002369426190853, 0.03604968264698982, 0.04861942678689957, -0.05801940709352493, 0.00741798710078001, 0.019813749939203262, -0.006574338302016258, 0.06459152698516846, 0.006780609954148531, -0.04999528452754021, -0.04291849583387375, -0.011006630957126617, 0.040547534823417664, 0.011371633037924767, -0.03499140217900276, -0.013997315429151058, 0.011781510896980762, -0.044807542115449905, 0.03193282335996628, 0.035882044583559036, 0.008864890784025192, 0.0015408030012622476, -0.034933239221572876, -0.05536770075559616, 0.025144459679722786, 0.0422084666788578, 0.022738995030522346, 0.002542242407798767, -0.04236292466521263, -0.03597642108798027, 0.004379383288323879, -0.024972282350063324, -0.03996764495968819, 0.04492862895131111, 0.010176802054047585, -0.057264186441898346, -0.03463387489318848, -0.012254444882273674, -0.0232960544526577, -0.05027018114924431, -0.029856285080313683, 0.0020029970910400152, -0.03404489904642105, -0.03418717160820961, 0.0808701142668724, -0.03988971561193466, -0.02583976648747921, 0.04833126813173294, -0.03252480551600456, 0.04610517621040344, -0.006316241808235645, 0.036838144063949585, -0.018295716494321823, 0.0014638680731877685, 0.04725873842835426, 0.04929152503609657, 0.01665695756673813, -0.06628783792257309, 0.019375519827008247, 0.0017652401002123952, 0.0012091562384739518, -0.05754077062010765, 0.00974762998521328, 0.037645336240530014, 0.04724656417965889, -0.0726926401257515, 0.0344073660671711, 0.06809365004301071, 0.00219947868026793, -0.06485775858163834, 0.044598691165447235, -0.03133152425289154, 0.01132157351821661, -0.024271801114082336, 0.021732021123170853, 0.004388192668557167, 0.012535396963357925, -0.006104731000959873, -0.01280435360968113, -0.01936645619571209, 0.013333906419575214, -0.05477874353528023, -0.02562079019844532, 0.03226925805211067 ]
<p>I have studied from Griffiths, the relativistic form of momentum is $$p = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} m_0v$$ </p> <p>Now when I evaluate the momentum for photon, I just insert $v=c$ and $m_0=0$ and I get $p= 0/0$. How does it make sense? </p> <p>Can you tell me that where I am wrong?</p>
g195
[ 0.03059096820652485, -0.034972961992025375, -0.006770215928554535, -0.02187214605510235, 0.09285639226436615, 0.03703801706433296, 0.023698942735791206, 0.012704700231552124, -0.02129882574081421, -0.010920966044068336, 0.009308296255767345, -0.03643481433391571, -0.031184343621134758, 0.004530983045697212, 0.008608438074588776, 0.0034673542249947786, 0.035745732486248016, 0.03431013599038124, 0.002443851437419653, 0.004421695601195097, -0.06336834281682968, -0.05359327048063278, 0.030193807557225227, -0.047184571623802185, -0.0024966001510620117, 0.020836587995290756, -0.0009074701811186969, 0.008583534508943558, -0.029951896518468857, 0.0285881906747818, 0.05721311643719673, 0.00924464501440525, 0.04602038115262985, -0.03812513127923012, -0.012096918188035488, -0.007194033358246088, 0.0831691101193428, 0.023854656144976616, 0.0118175083771348, 0.03173227235674858, 0.008733851835131645, -0.0184315275400877, -0.018693707883358, -0.0017191318329423666, -0.02712881565093994, -0.014447133988142014, -0.015174513682723045, 0.021955085918307304, -0.020102856680750847, 0.00445941835641861, 0.02300833910703659, 0.02883845567703247, 0.03784127160906792, -0.0000691791792633012, 0.07655064016580582, 0.0535193607211113, -0.020093953236937523, -0.02504653111100197, 0.037677038460969925, 0.0407591350376606, -0.014761590398848057, -0.0423412062227726, -0.0028694120701402426, 0.024314746260643005, 0.03696190565824509, -0.01589949242770672, -0.016720106825232506, -0.039240818470716476, -0.008544093929231167, -0.000989640480838716, -0.009623765014111996, -0.06283704936504364, 0.01112124603241682, 0.0037624684628099203, -0.0005082906573079526, -0.028013283386826515, -0.02900436520576477, -0.01992526650428772, 0.0058706896379590034, -0.023271648213267326, 0.007301239296793938, -0.03479871153831482, 0.07923684269189835, -0.052389372140169144, 0.03857935592532158, -0.05026629939675331, 0.01809185929596424, -0.010195175185799599, -0.0560886487364769, -0.03965901583433151, 0.048606786876916885, -0.049172211438417435, 0.061843134462833405, 0.012201852165162563, -0.02823828160762787, -0.03995656594634056, -0.04029850289225578, 0.050658177584409714, -0.023431502282619476, -0.016377432271838188, -0.03361401706933975, 0.05583994835615158, -0.0014920167159289122, 0.02519902214407921, -0.007330930791795254, -0.01955551840364933, -0.07592801749706268, 0.019130675122141838, -0.009351043961942196, -0.06703422963619232, -0.06621512025594711, -0.012718035839498043, 0.0183916836977005, -0.020318880677223206, -0.09614819288253784, -0.04217350855469704, 0.09156632423400879, -0.0593792162835598, 0.005075847264379263, 0.09491503983736038, 0.06777148693799973, 0.05101928487420082, 0.011910907924175262, 0.1009359136223793, 0.009948640130460262, -0.010487494990229607, -0.022513343021273613, 0.010057110339403152, 0.03938005864620209, -0.004707784857600927, 0.008330600336194038, -0.016002286225557327, -0.0035366984084248543, -0.018073944374918938, 0.031716037541627884, 0.004962112754583359, -0.0298644807189703, 0.009529025293886662, -0.0067395796068012714, -0.008336206898093224, 0.0441310852766037, -0.04091138765215874, 0.0319807268679142, -0.033400971442461014, -0.022774307057261467, -0.02285543829202652, 0.003485986264422536, -0.016294235363602638, 0.018283696845173836, 0.015187217853963375, 0.03358635678887367, 0.05877046287059784, -0.040439072996377945, 0.037728019058704376, 0.02252168580889702, 0.02602030336856842, 0.049030695110559464, 0.029475117102265358, -0.015136159025132656, 0.02171568013727665, 0.06301122903823853, 0.052283793687820435, 0.04616222530603409, -0.04621987044811249, -0.05021616071462631, 0.034261178225278854, 0.03517763316631317, -0.10187368094921112, -0.07929478585720062, -0.05199725925922394, 0.010016058571636677, -0.014854910783469677, -0.010381132364273071, 0.020344965159893036, 0.002646614331752062, 0.014564020559191704, -0.023999445140361786, 0.021293580532073975, 0.015390323475003242, 0.04228779301047325, 0.002095720963552594, -0.024317750707268715, 0.05299403518438339, -0.003914864268153906, 0.013868844136595726, 0.008187123574316502, 0.02263956516981125, 0.059425607323646545, -0.05878353863954544, -0.022007256746292114, -0.017197968438267708, 0.048170916736125946, -0.026602469384670258, 0.034032732248306274, 0.009476354345679283, 0.03739986941218376, -0.05623606964945793, -0.03539648279547691, 0.004613802768290043, 0.09568393230438232, -0.0035799334291368723, 0.044288452714681625, 0.037904929369688034, 0.03929157182574272, 0.04039056971669197, -0.00494980625808239, 0.025598231703042984, -0.03179396688938141, 0.021332090720534325, 0.04665858671069145, 0.06118960306048393, -0.10667869448661804, 0.0019528308184817433, 0.04957897588610649, 0.00025197159266099334, -0.025075986981391907, 0.055283818393945694, 0.0026213941164314747, -0.003701769048348069, -0.008494235575199127, -0.029884537681937218, -0.009705470874905586, 0.01070175040513277, 0.0005145987961441278, -0.02311575412750244, 0.024450160562992096, -0.035162102431058884, 0.01410831417888403, 0.052370548248291016, 0.0490763783454895, -0.015528799965977669, 0.03156604245305061, -0.03159200772643089, 0.010217582806944847, 0.01991172321140766, 0.008701041340827942, -0.051478225737810135, -0.012818589806556702, -0.010483144782483578, 0.009646087884902954, 0.0028294643852859735, -0.02259855903685093, 0.006416235584765673, -0.009326445870101452, 0.03228165581822395, -0.026640381664037704, 0.07287279516458511, 0.016284137964248657, -0.029010849073529243, -0.023662151768803596, 0.0430673211812973, -0.017448773607611656, -0.013992645777761936, -0.013857471756637096, -0.001646071788854897, -0.0009491072851233184, -0.011376538313925266, 0.059170473366975784, -0.09763728082180023, -0.008168471045792103, -0.03029475174844265, -0.015340331941843033, -0.06851550191640854, 0.03458285331726074, -0.0537603534758091, 0.024090660735964775, 0.014641753397881985, 0.056111469864845276, 0.07734580338001251, -0.042824868112802505, 0.011090980842709541, 0.08391458541154861, 0.023611055687069893, 0.01903510093688965, 0.019398726522922516, -0.04152935743331909, 0.017428306862711906, -0.031022312119603157, 0.026959046721458435, -0.04753626510500908, -0.04922281578183174, 0.04504133015871048, -0.060520827770233154, -0.026106638833880424, 0.011445200070738792, -0.11552530527114868, 0.034765131771564484, 0.01799137145280838, -0.022361161187291145, -0.019001297652721405, 0.028846316039562225, 0.04110760986804962, 0.015470669604837894, -0.011568212881684303, 0.05647798627614975, 0.03716178610920906, 0.06730138510465622, -0.0631827861070633, -0.0293789841234684, 0.034949447959661484, 0.0017912532202899456, 0.00836564227938652, -0.031198957934975624, -0.043651022017002106, 0.009256790392100811, -0.009316405281424522, -0.029633531346917152, -0.020061057060956955, -0.006134909577667713, 0.021799450740218163, -0.06925634294748306, 0.09837085008621216, -0.009079400449991226, -0.014426503330469131, -0.018079865723848343, -0.01866508089005947, -0.023196488618850708, 0.0047882311046123505, -0.01568225398659706, 0.006059964187443256, -0.037409089505672455, -0.02976827323436737, 0.02726627327501774, -0.029090777039527893, 0.06003837287425995, -0.004089335910975933, -0.05537845939397812, -0.030929112806916237, -0.055366434156894684, -0.02116665430366993, 0.044163063168525696, -0.008880235254764557, -0.0058031240478158, -0.022225793451070786, -0.012839099392294884, -0.04781436175107956, -0.0362435020506382, 0.04266433045268059, 0.019206032156944275, -0.010492539033293724, -0.009847816079854965, 0.0007788939983583987, -0.03669292852282524, 0.09094598144292831, 0.006303839385509491, -0.017179707065224648, 0.020078491419553757, 0.03722961246967316, -0.011946847662329674, -0.046989358961582184, -0.03643296658992767, -0.002422167221084237, 0.047511063516139984, -0.02142016962170601, 0.0052322689443826675, 0.03380648046731949, -0.04135353863239288, 0.07935016602277756, 0.03743695467710495, -0.018896276131272316, 0.0018703043460845947, -0.0006545134237967432, 0.0075112865306437016, -0.03181598335504532, -0.020570363849401474, -0.01743212342262268, -0.041840072721242905, 0.03559719771146774, 0.009154490195214748, -0.0039133899845182896, -0.007932808250188828, -0.04232388362288475, 0.009020046330988407, 0.0352417416870594, -0.031398266553878784, -0.03392139449715614, 0.004335543606430292, -0.03301816061139107, 0.031160010024905205, 0.031274568289518356, -0.01309879682958126, 0.008683710359036922, -0.019750963896512985, 0.0217882189899683, -0.04230840131640434, 0.020844824612140656, -0.03387782722711563, 0.005582818295806646, 0.004086767788976431, -0.012598617002367973, 0.03563794866204262, -0.04951762408018112, -0.02258589304983616, 0.0321890190243721, 0.007666326593607664, -0.00523209385573864, 0.06052751466631889, -0.04365972802042961, -0.02012353390455246, 0.025212276726961136, -0.014847955666482449, 0.024275384843349457, 0.012745068408548832, -0.018265753984451294, -0.0099589629098773, 0.05450640991330147, 0.03615746274590492, -0.03194243088364601, -0.032558318227529526, 0.02446632646024227, -0.003682746086269617, -0.031185170635581017, 0.03894462436437607, -0.08040381222963333, 0.04626784101128578, -0.0007552175084128976, -0.00075325439684093, -0.06359902024269104, 0.0022674084175378084, 0.02203032188117504, 0.014594366773962975, 0.010175774805247784, 0.07217514514923096, -0.03019392117857933, 0.020088322460651398, 0.05998725816607475, 0.045437026768922806, 0.032095447182655334, 0.04249893128871918, -0.01303290668874979, 0.025241736322641373, -0.004660491831600666, -0.0036559440195560455, 0.009626857936382294, -0.05416471138596535, 0.06163276359438896, 0.007529336027801037, 0.008212666027247906, 0.0013122163945809007, 0.046693239361047745, 0.06581258773803711, 0.0070691644214093685, 0.018014289438724518, -0.031510233879089355, 0.012837784364819527, 0.04215225204825401, -0.00561485905200243, -0.023818811401724815, -0.019505418837070465, -0.03360908478498459, -0.019092485308647156, -0.02666633576154709, -0.017405418679118156, -0.06474235653877258, 0.054235588759183884, 0.031648095697164536, -0.059962447732686996, 0.041327301412820816, 0.032156601548194885, 0.02054620534181595, -0.06689286231994629, -0.0035596222151070833, 0.041884344071149826, -0.02840515971183777, 0.07925402373075485, 0.020642336457967758, -0.08662180602550507, 0.03446785360574722, -0.0230601467192173, -0.051638901233673096, -0.015528528019785881, -0.06278232485055923, 0.015029228292405605, -0.04201853647828102, 0.027674157172441483, -0.0030963995959609747, 0.0018982719630002975, 0.0022935369051992893, 0.03992640599608421, -0.029827069491147995, -0.027174530550837517, 0.010638004168868065, 0.019980696961283684, -0.021803712472319603, 0.0009264365653507411, -0.0016220181714743376, -0.04991039261221886, 0.02425442263484001, 0.007017376367002726, -0.02839420922100544, 0.02995814010500908, 0.06119261682033539, -0.07390930503606796, -0.03751807659864426, 0.07352705299854279, 0.03963533788919449, 0.019442161545157433, -0.024285240098834038, 0.037957653403282166, -0.03073006682097912, -0.12251173704862595, 0.00610346719622612, -0.01872451975941658, 0.01327002327889204, 0.021015724167227745, 0.01351118739694357, 0.03915081545710564, 0.006370535586029291, 0.007531384006142616, 0.013892103917896748, 0.022686120122671127, 0.019474543631076813, 0.027308396995067596, -0.033687952905893326, 0.03802485764026642, -0.01778772473335266, 0.024130554869771004, -0.014730979688465595, -0.021339016035199165, 0.0015988681698217988, 0.029465125873684883, -0.01745639555156231, 0.010590101592242718, -0.06161736324429512, 0.02676178514957428, -0.021989768370985985, -0.05773980915546417, -0.09482517093420029, 0.018870368599891663, -0.004712825641036034, -0.003870194312185049, -0.02881576679646969, 0.0580131821334362, -0.010715116746723652, -0.0193412397056818, -0.04236108809709549, 0.014526826329529285, 0.021897438913583755, 0.017338771373033524, -0.06789758801460266, -0.06850849092006683, -0.02464371733367443, -0.04029935598373413, 0.0756235122680664, -0.056394632905721664, 0.017313579097390175, 0.013323345221579075, 0.0010570136364549398, 0.015743114054203033, -0.0595242865383625, -0.008592568337917328, -0.00012804595462512225, -0.023835834115743637, -0.038358986377716064, 0.0035256536211818457, -0.005096948239952326, -0.016516733914613724, -0.017135847359895706, -0.01403567474335432, 0.009634674526751041, 0.027936160564422607, -0.013798157684504986, 0.029468318447470665, -0.030353708192706108, -0.00006272348400671035, -0.023004833608865738, -0.017764898017048836, -0.051104556769132614, 0.013863703235983849, 0.03614795207977295, -0.02938447706401348, 0.04927627369761467, -0.00337019725702703, -0.005965162999927998, -0.006245287135243416, -0.0025076388847082853, 0.04196104407310486, -0.03667490556836128, -0.018733344972133636, -0.055766575038433075, 0.034512948244810104, 0.038450613617897034, 0.054561417549848557, -0.02524934895336628, -0.01946611888706684, 0.07263711839914322, -0.03253725543618202, -0.035527121275663376, 0.0372055284678936, 0.06352376937866211, -0.011926084756851196, 0.04776972904801369, -0.0343824103474617, -0.05381090193986893, -0.008197127841413021, 0.00908718816936016, 0.03064463473856449, -0.038946811109781265, -0.00048674287972971797, 0.03478559851646423, 0.03489503636956215, 0.018901990726590157, -0.0024175113067030907, 0.02784515917301178, 0.01924053393304348, 0.043142933398485184, -0.009025050327181816, -0.013850755989551544, -0.004128511995077133, 0.03200455382466316, -0.021723546087741852, 0.04233609512448311, -0.007321447599679232, -0.06169763579964638, 0.06125645712018013, -0.024511346593499184, -0.03801985830068588, 0.045972246676683426, 0.041267868131399155, -0.004010114818811417, 0.052303820848464966, -0.052241530269384384, -0.019741512835025787, 0.0032901521772146225, 0.0796712264418602, 0.0416158027946949, -0.03190227970480919, 0.08252546936273575, 0.032543860375881195, -0.03418397530913353, -0.011320107616484165, -0.03976104408502579, 0.000893755757715553, 0.022120842710137367, 0.029413629323244095, 0.03957165405154228, -0.03730323910713196, -0.0012881058501079679, 0.01587255485355854, -0.0009561008191667497, 0.03001890704035759, 0.004858306609094143, 0.05716109648346901, -0.0073371995240449905, -0.000049608108383836225, 0.04063665121793747, -0.006509764585644007, -0.01481859665364027, -0.09197589755058289, 0.02557244524359703, -0.019298957660794258, 0.009859866462647915, 0.012373481877148151, 0.014549368992447853, 0.006240752525627613, -0.004158139694482088, -0.02242494933307171, 0.06523337215185165, 0.008328381925821304, -0.05322727560997009, 0.009566083550453186, -0.030530419200658798, 0.003184037283062935, 0.012344119139015675, 0.005829844158142805, 0.03168672323226929, 0.012132727541029453, -0.027659596875309944, 0.06620465964078903, -0.055239543318748474, -0.012279795482754707, -0.03121151402592659, -0.041959356516599655, -0.03474012762308121, 0.008557370863854885, 0.0023909572046250105, -0.05980120971798897, 0.029804598540067673, -0.06250664591789246, 0.0098047386854887, -0.028860323131084442, 0.06624433398246765, -0.04817067086696625, 0.02922293171286583, 0.0006448470521718264, -0.03007042035460472, -0.025776246562600136, -0.03125017508864403, -0.027510937303304672, 0.00643271766602993, 0.0055554891005158424, 0.005912289023399353, -0.0055661327205598354, -0.014375639148056507, -0.009469940327107906, 0.004193979315459728, 0.032391153275966644, 0.013414974324405193, -0.011006880551576614, 0.019669802859425545, -0.0027143750339746475, -0.06331688910722733, -0.013533244840800762, 0.012715458869934082, 0.0087207593023777, 0.007025969214737415, 0.02165457420051098, -0.04123316705226898, -0.022062333300709724, -0.013519557192921638, 0.019354207441210747, -0.023829268291592598, 0.002590083284303546, 0.013138980604708195, 0.020997123792767525, -0.025040704756975174, -0.0660741776227951, 0.03642739728093147, 0.014433550648391247, -0.06789331138134003, -0.052600353956222534, -0.05526378005743027, -0.004545401781797409, -0.028674252331256866, -0.01447602454572916, -0.05797608196735382, -0.0455692894756794, -0.0012258694041520357, 0.009218400344252586, 0.020012419670820236, -0.0425526425242424, 0.008488697931170464, -0.09423240274190903, 0.01849808730185032, 0.01106135081499815, 0.02451247349381447, 0.022694362327456474, -0.048743829131126404, 0.02404487133026123, 0.025006966665387154, 0.00995096005499363, -0.08983832597732544, 0.005937009118497372, 0.051406923681497574, 0.006672865245491266, -0.023705463856458664, 0.0007208093302324414, 0.03654405102133751, 0.030129801481962204, -0.024528868496418, 0.04451742023229599, 0.053524162620306015, 0.01366117037832737, 0.016130812466144562, 0.07621864974498749, -0.05668605864048004, 0.02420707792043686, 0.022015349939465523, -0.00866150576621294, -0.010090721771121025, 0.01935306005179882, -0.01560556422919035, -0.06284843385219574, 0.04578389972448349, 0.012461140751838684, -0.046243082731962204, -0.005401994567364454, -0.003199300728738308 ]
<p>I am attempting to validate an accelerometer. I have a triaxial accelerometer and placed it on a wheel which goes at various frequencies from 1 to 3 Hz. Am I right in thinking that I would expect the acceleration in <em>z</em> to be 1g?</p> <p>Then in the <em>x</em> and <em>y</em> plane I would expect a read out of acceleration in $X(t) = -2\pi fr\cos{(2\pi f t)}$ and acceleration in $Y(t) = -2\pi fr\sin{(2\pi f t)}$ where $r$ is the radius of the wheel and $f$ is frequency.</p> <p>How can I compare these with my readout from the sensor, and what is the best way to report accuracy? I'm confused as surely I will need to quite accurately time align the two traces.</p>
g8357
[ 0.061846476048231125, -0.017477814108133316, 0.0035632597282528877, 0.031105993315577507, 0.06795601546764374, -0.01387875434011221, 0.06429943442344666, -0.011812793090939522, -0.021912191063165665, 0.0252019502222538, 0.046211421489715576, 0.039885103702545166, -0.011674229055643082, 0.008426094427704811, 0.032409828156232834, -0.045830126851797104, 0.04513666406273842, 0.034095361828804016, 0.04994441568851471, -0.016707325354218483, 0.04881027340888977, 0.010643639601767063, -0.06766297668218613, -0.024943962693214417, 0.031412508338689804, -0.014528857544064522, 0.028759170323610306, -0.051789648830890656, -0.07023546099662781, -0.015048157423734665, 0.04630181938409805, -0.017643766477704048, 0.04391196370124817, 0.0014836899936199188, 0.010809987783432007, 0.003017695154994726, -0.003854087321087718, 0.05353475362062454, -0.0011478589149191976, -0.00472912285476923, 0.007940316572785378, -0.0195175688713789, 0.04892163351178169, 0.0006481822929345071, 0.03679759055376053, 0.0334790013730526, -0.018518853932619095, 0.051564980298280716, 0.021290099248290062, 0.028497641906142235, -0.09506765753030777, 0.004719266202300787, 0.03243398293852806, 0.05513381212949753, -0.003348895348608494, 0.073773093521595, -0.008291507139801979, 0.0153949074447155, -0.040018629282712936, 0.011742480099201202, -0.05260709673166275, -0.04412711039185524, -0.03416664898395538, -0.042860835790634155, 0.024607831612229347, 0.015120409429073334, -0.012293973006308079, 0.0017804325325414538, -0.009156295098364353, -0.015491285361349583, -0.0034302917774766684, 0.0020726637449115515, 0.005369515623897314, -0.040943048894405365, -0.07861965894699097, 0.009708122350275517, 0.01982325315475464, -0.03337377309799194, 0.013270503841340542, 0.06255301088094711, -0.05466800928115845, 0.030765464529395103, -0.008579812943935394, 0.029148265719413757, 0.03594714030623436, -0.03040085919201374, 0.01212664321064949, 0.0389481820166111, -0.015459270216524601, 0.047387585043907166, 0.07541158050298691, -0.0178713146597147, 0.04724481701850891, 0.015100713819265366, 0.0030315620824694633, 0.003946913406252861, -0.07373994588851929, 0.07112812250852585, 0.03248539939522743, 0.03865857422351837, -0.003564206650480628, 0.055160023272037506, 0.027954338118433952, -0.026250546798110008, 0.032323550432920456, -0.023292699828743935, 0.022533392533659935, -0.011797692626714706, 0.024476541206240654, -0.04813896119594574, -0.02769903838634491, -0.016480227932333946, 0.0017026807181537151, -0.07925789803266525, -0.04123096540570259, 0.023910662159323692, 0.04097442328929901, 0.024708406999707222, 0.021131005138158798, 0.006271691992878914, 0.007323611062020063, -0.03144228830933571, 0.0004710594657808542, 0.1012507975101471, -0.02534923516213894, -0.05242645740509033, -0.012944400310516357, -0.01200480293482542, 0.042699024081230164, -0.027179483324289322, -0.0095812464132905, 0.008897977881133556, 0.060709573328495026, 0.0005422868998721242, -0.05078297480940819, 0.01173064112663269, 0.05013623461127281, -0.014575465582311153, -0.028053205460309982, 0.03004935383796692, -0.03128397464752197, -0.06641760468482971, 0.03813245892524719, -0.07246449589729309, -0.009923955425620079, 0.022097207605838776, -0.03309078887104988, -0.030726151540875435, 0.05189449340105057, 0.0507422536611557, 0.022234924137592316, 0.08245552331209183, 0.01661638543009758, -0.035058993846178055, 0.0030203310307115316, -0.012319818139076233, 0.03415603190660477, -0.05008575692772865, 0.02113996632397175, 0.05994139611721039, 0.02351468801498413, -0.017876407131552696, 0.043193526566028595, 0.05155256390571594, -0.060371413826942444, -0.03373527526855469, -0.02620025724172592, -0.09279882162809372, 0.03302853927016258, -0.006597838364541531, -0.011444425210356712, 0.02499552071094513, 0.0419248528778553, -0.05786772072315216, -0.037240032106637955, 0.01565016619861126, -0.002516145585104823, -0.045729123055934906, 0.055274710059165955, 0.019599201157689095, 0.026630939915776253, 0.0174463652074337, 0.00463293818756938, 0.023754850029945374, -0.013544267043471336, -0.042237672954797745, 0.048147574067115784, -0.06925518065690994, -0.05451779067516327, 0.0349113792181015, 0.0011632471578195691, -0.049549926072359085, -0.030336134135723114, -0.0061288452707231045, -0.05256367102265358, -0.0023325257934629917, -0.007884752005338669, -0.041355181485414505, 0.0029008889105170965, 0.060507919639348984, 0.03701820597052574, 0.009073788300156593, 0.03165196627378464, 0.049121033400297165, 0.05420192703604698, -0.04856273531913757, -0.002225111471489072, -0.05346470698714256, -0.03273552656173706, 0.037910107523202896, -0.028525181114673615, 0.10277239978313446, -0.01577652618288994, 0.04614901542663574, 0.0441431999206543, -0.03855009004473686, 0.08086364716291428, 0.03333193436264992, 0.04705660417675972, 0.0022873072884976864, -0.03291819989681244, -0.07620274275541306, 0.10429542511701584, -0.08820948749780655, -0.011771718971431255, -0.02561437152326107, -0.0023489720188081264, -0.009259248152375221, 0.0016499502817168832, -0.0008935296209529042, -0.017998691648244858, -0.0019431725377216935, -0.002394083421677351, -0.021709155291318893, 0.009856165386736393, 0.026201369240880013, -0.020599571987986565, 0.003093983978033066, 0.05238814279437065, 0.004324995446950197, 0.024965709075331688, 0.0006378611433319747, -0.015479251742362976, -0.04432220011949539, 0.02799508161842823, -0.01629696972668171, 0.10511136800050735, 0.02111126109957695, -0.007235449738800526, -0.0034891157411038876, -0.0317951999604702, 0.001870170934125781, -0.058918606489896774, 0.004266049712896347, -0.062457576394081116, 0.005830343347042799, 0.003412857186049223, -0.029359063133597374, -0.043535176664590836, 0.0289604514837265, -0.02172880992293358, 0.0052312221378088, 0.011702151969075203, -0.006257638800889254, -0.005790008697658777, -0.0851062685251236, 0.004810357466340065, -0.020718982443213463, -0.010437392629683018, -0.0720825344324112, 0.009295620955526829, -0.002682250691577792, 0.026134749874472618, 0.05743831396102905, 0.015916557982563972, -0.02747335098683834, -0.05077892169356346, -0.022405555471777916, 0.033241163939237595, 0.006919923238456249, -0.06373022496700287, -0.011336318217217922, -0.0036211388651281595, 0.016643475741147995, 0.013450613245368004, 0.030404595658183098, 0.021313287317752838, 0.017390044406056404, -0.018995195627212524, 0.0413203090429306, -0.045117393136024475, 0.008170253597199917, 0.016281280666589737, -0.03427155688405037, -0.032512739300727844, 0.04367398843169212, 0.03996171057224274, -0.02904181368649006, 0.0717320591211319, 0.015163350850343704, 0.006747864186763763, 0.012677361257374287, -0.019221678376197815, -0.0199554692953825, -0.016977347433567047, -0.06604371219873428, -0.01692361943423748, -0.001209764275699854, 0.038024961948394775, 0.015785779803991318, -0.027209384366869926, -0.03615627437829971, -0.006500376854091883, -0.046892594546079636, -0.036599915474653244, -0.03969636559486389, -0.031070321798324585, -0.005287184379994869, -0.021728750318288803, 0.04485385864973068, -0.013128062710165977, -0.05853784456849098, 0.007451511453837156, -0.026887496933341026, 0.0030700776260346174, -0.005834366660565138, 0.024641860276460648, 0.00035905034746974707, -0.04868694022297859, -0.014732779003679752, -0.0059380135498940945, 0.012770366854965687, 0.0008054802310653031, 0.0032527733128517866, 0.005360393784940243, -0.049262743443250656, -0.016838110983371735, 0.020553503185510635, -0.010713965632021427, 0.01369859091937542, -0.021597091108560562, 0.027721568942070007, 0.004873581230640411, -0.04880097508430481, 0.013325972482562065, 0.023440606892108917, -0.0035446190740913153, 0.03154395893216133, -0.01669321209192276, -0.09508749842643738, 0.0036859908141195774, -0.03370817378163338, 0.0013647383311763406, -0.0043487646616995335, -0.019291630014777184, 0.016629664227366447, 0.025943417102098465, 0.010214058682322502, -0.03001195378601551, -0.0029582420829683542, 0.020264990627765656, 0.021669499576091766, -0.058161184191703796, -0.03143975883722305, 0.021858762949705124, -0.018871812149882317, -0.0006412430084310472, 0.07495616376399994, 0.004193746019154787, 0.02120991423726082, -0.012756186537444592, -0.030844997614622116, 0.018187018111348152, 0.0018853979418054223, 0.021658308804035187, -0.06779152154922485, -0.009738289751112461, 0.01676918938755989, 0.021709831431508064, 0.04179839789867401, 0.0014046997530385852, 0.017431264743208885, 0.013571376912295818, -0.018004437908530235, 0.018289459869265556, -0.037300240248441696, 0.009810912422835827, 0.005127668846398592, -0.0032951277680695057, -0.01981927827000618, -0.003072277642786503, -0.07050240784883499, -0.049139004200696945, 0.023984381929039955, 0.0189660731703043, -0.11646293848752975, 0.04684525728225708, -0.02083347737789154, -0.01431612204760313, 0.06120872125029564, -0.009803968481719494, 0.035060565918684006, -0.016021378338336945, 0.012576671317219734, -0.04618653282523155, 0.025181010365486145, 0.02187364734709263, 0.026329146698117256, 0.028652120381593704, 0.0018263458041474223, -0.020780028775334358, 0.015673315152525902, 0.04401588439941406, -0.02909250557422638, 0.048370156437158585, 0.026075998321175575, 0.05633113160729408, -0.05596717819571495, -0.034728121012449265, -0.012225756421685219, 0.03422367945313454, 0.08164290338754654, 0.05981370061635971, -0.08289710432291031, 0.006299602333456278, 0.04618272930383682, -0.016130702570080757, -0.03460871800780296, 0.03552226349711418, 0.04246874526143074, 0.040829699486494064, -0.00839851051568985, 0.027971990406513214, 0.01759427599608898, -0.025161897763609886, 0.02832566201686859, 0.0021137872245162725, 0.05574773624539375, 0.046387217938899994, 0.01907435432076454, -0.016727004200220108, 0.003372151404619217, -0.0035209294874221087, -0.001542974030598998, -0.039556194096803665, 0.03666619211435318, -0.055968958884477615, 0.009330742061138153, 0.026692215353250504, 0.04043680429458618, -0.04913165047764778, -0.014808646403253078, -0.0182321947067976, 0.018475228920578957, -0.004072946030646563, 0.02375863492488861, 0.010809674859046936, 0.014463693834841251, 0.0039074295200407505, -0.02562851645052433, -0.03470565006136894, -0.006827463395893574, -0.07509654015302658, -0.031567759811878204, 0.01823311857879162, -0.03176480904221535, -0.026307787746191025, 0.009256529621779919, -0.0386669859290123, 0.00910136103630066, 0.028601253405213356, -0.05294433981180191, 0.016679970547556877, -0.00909669790416956, 0.036330025643110275, 0.053965598344802856, 0.014761017635464668, 0.01736459508538246, -0.0495450422167778, -0.03360123187303543, -0.041111063212156296, 0.024702953174710274, 0.03376525640487671, 0.004050291143357754, 0.021137522533535957, 0.024770192801952362, -0.004475987982004881, -0.014103722758591175, 0.04025162011384964, 0.03766125068068504, 0.08224490284919739, 0.05062422528862953, 0.01073652133345604, -0.05417245253920555, -0.044058043509721756, 0.03529725223779678, 0.0016407596413046122, -0.09097272157669067, -0.05150502175092697, -0.025728419423103333, -0.07285414636135101, 0.07085254788398743, 0.005951110273599625, 0.003147005569189787, -0.015725383535027504, 0.061744194477796555, 0.043871503323316574, -0.06033770740032196, 0.011262316256761551, 0.0501401424407959, -0.009680521674454212, 0.061559829860925674, 0.0008239995804615319, -0.0069123804569244385, -0.026440583169460297, -0.014747715555131435, 0.053794071078300476, 0.04029720649123192, 0.00418380182236433, -0.008360331878066063, 0.035606324672698975, 0.021591728553175926, 0.03806950896978378, -0.04460236802697182, -0.014655765146017075, 0.012193748727440834, 0.011278954334557056, -0.015132556669414043, 0.011166591197252274, -0.04542931914329529, -0.018549950793385506, -0.0041783456690609455, -0.010427108034491539, 0.016583489254117012, 0.0004780815215781331, -0.01104382798075676, 0.020578255876898766, -0.05893729254603386, 0.03408532589673996, -0.006322700064629316, -0.09107954800128937, -0.017670519649982452, 0.0000763215430197306, 0.020618697628378868, -0.0948842391371727, 0.011621694080531597, -0.029367594048380852, 0.0285840705037117, 0.036568690091371536, -0.01340589951723814, 0.01721983216702938, 0.011860105209052563, -0.009315500035881996, -0.04135775566101074, -0.009007479064166546, 0.059408172965049744, -0.007984788157045841, -0.011360731907188892, -0.03921141475439072, -0.011627579107880592, 0.012610867619514465, -0.03086463175714016, 0.05268411710858345, -0.020474931225180626, 0.013250202871859074, 0.01172354444861412, 0.0439106784760952, 0.02179623395204544, -0.01780087687075138, -0.02963119186460972, 0.006174250040203333, -0.06831901520490646, -0.03784911334514618, 0.03405633941292763, 0.007367821875959635, 0.04927762597799301, -0.027710890397429466, 0.05576236918568611, -0.016457976773381233, 0.0003178379265591502, 0.0058639864437282085, 0.014366482384502888, 0.00008275889558717608, 0.020731495693325996, -0.03145976737141609, -0.023408696055412292, -0.04565304145216942, -0.02370869740843773, 0.006561196409165859, -0.07517923414707184, -0.03972870856523514, -0.04949091374874115, 0.0029502813704311848, 0.03690722957253456, -0.036481186747550964, -0.07837779819965363, 0.0137705123052001, 0.04637397453188896, 0.016772856935858727, 0.027531079947948456, 0.02695116028189659, -0.014393742196261883, 0.03910507634282112, -0.05242873355746269, -0.005311372224241495, -0.061337150633335114, 0.009538351558148861, 0.0027199569158256054, 0.053789179772138596, -0.05780128762125969, -0.013763894326984882, 0.008396118879318237, 0.011350416578352451, 0.11125659942626953, -0.025330521166324615, 0.057708267122507095, 0.026399971917271614, -0.05456322804093361, -0.00007293007365660742, -0.021248657256364822, 0.061198052018880844, 0.02854694053530693, -0.0075625828467309475, -0.005047422833740711, -0.013948744162917137, -0.025733087211847305, 0.006774181965738535, -0.03922545164823532, 0.01634281501173973, -0.008593227714300156, -0.014479618519544601, 0.027850966900587082, -0.021575001999735832, 0.03628088906407356, 0.026787227019667625, 0.0267268568277359, 0.00982438214123249, -0.03116140142083168, 0.021867867559194565, 0.04564506933093071, -0.00636792229488492, 0.07088090479373932, 0.029238013550639153, 0.015842273831367493, -0.056150633841753006, -0.044538464397192, 0.010286571457982063, 0.010944928042590618, -0.03092561662197113, 0.03185160458087921, -0.00049984036013484, -0.05433976650238037, 0.04738916829228401, 0.0360182449221611, 0.004364509601145983, 0.009039230644702911, -0.0034293453209102154, 0.03875745087862015, 0.014955705031752586, -0.03595001995563507, -0.013231797143816948, -0.04763041064143181, -0.012768587097525597, -0.022635526955127716, -0.06194830685853958, -0.002551945159211755, -0.05551483482122421, -0.06259772181510925, 0.011991995386779308, -0.04016094282269478, 0.005509956274181604, -0.030457772314548492, -0.028674952685832977, 0.006931769195944071, -0.002506283111870289, 0.052348993718624115, -0.07906932383775711, -0.04038253799080849, -0.01434374786913395, 0.026568196713924408, -0.0250407662242651, -0.033264994621276855, 0.007108962628990412, 0.037541463971138, -0.012740102596580982, 0.08639897406101227, -0.013882084749639034, -0.023361369967460632, -0.010075083002448082, -0.024447742849588394, -0.06283736228942871, -0.003401006106287241, 0.010002871975302696, -0.03769607096910477, 0.0037036987487226725, -0.03322647511959076, -0.0033695923630148172, 0.05096108838915825, 0.012166585773229599, 0.050713423639535904, 0.0402497798204422, 0.019645195454359055, 0.034813567996025085, 0.03981625288724899, 0.012112517841160297, 0.017922310158610344, -0.010246888734400272, 0.049792997539043427, 0.059339188039302826, -0.014956127852201462, -0.009657303802669048, 0.027839472517371178, -0.00956249050796032, 0.02509840577840805, 0.004694332834333181, 0.04936341941356659, -0.026068713515996933, -0.029170295223593712, -0.044215649366378784, -0.014001882635056973, -0.06029811128973961, 0.008788127452135086, 0.03189237415790558, -0.04671555757522583, 0.05172138661146164, -0.034187138080596924, -0.0491328164935112, 0.05131949484348297, 0.035135164856910706, -0.0059156958013772964, -0.003953029867261648, -0.002792972605675459, -0.024553602561354637, 0.08784396201372147, -0.049311015754938126, -0.0034476995933800936, 0.06855662167072296, 0.013701681047677994, -0.07894976437091827, 0.03173721209168434, 0.01952729932963848, 0.03588201850652695, -0.02167241834104061, 0.02123469114303589, -0.020611397922039032, -0.014579840004444122, -0.002547709969803691, 0.001901926239952445, 0.025428911671042442, -0.06603348255157471, -0.017633112147450447, 0.01911739446222782, -0.04613892361521721, 0.0430014543235302, -0.006316772196441889, 0.0014500390971079469, 0.0022138275671750307, -0.026606516912579536, -0.009549282491207123, -0.037646252661943436, -0.007899482734501362, -0.006450427696108818, -0.044672928750514984, -0.04408331215381622, -0.04296198487281799, -0.04272846877574921, -0.054339807480573654, 0.028075914829969406 ]
<p>Let $\psi (x,y,z)$ be a scalar field. I found the following statement in Morse &amp; Feshbach Methods of Theoretical Physics:</p> <blockquote> <p>The limiting value of the difference between $\psi$ at a point and the average value of $\psi$ at neighboring points is $-\frac{1}{6}(dxdydz)^2\nabla ^2\psi$</p> </blockquote> <p>By taking a small sphere centered at the point of radius $r$, I was able to show that the difference between $\psi$ at a point and the average value of $\psi$ at neighboring points equals $-\frac{1}{6}r^2\nabla ^2\psi$. But I have not been able to get the expression given in the book. Thanks.</p> <p>Edit: To obtain $-\frac{1}{6}r^2\nabla ^2\psi$ I first expanded $\psi$ in a Taylor series up to quadratic terms about the point in question. Then I integrated $\psi$ (rather, its Taylor expansion up to quadratic terms) over the surface of a small sphere of radius $r$ centered at the given point and divided this by the surface are of the sphere (this gives the average value of $\psi$ in the sphere). Subtracting this average from the value of $\psi$ at the center of the sphere gives the result $-\frac{1}{6}r^2\nabla ^2\psi$.</p>
g8358
[ 0.035144973546266556, -0.0033672982826828957, -0.018869834020733833, -0.02130011096596718, 0.009617073461413383, 0.012805364094674587, 0.05383403226733208, -0.031028755009174347, -0.036521799862384796, -0.015295685268938541, 0.01977219246327877, 0.05914350599050522, 0.04200699180364609, -0.0006090477691031992, 0.012351075187325478, 0.0021457576658576727, -0.010806947015225887, -0.036070287227630615, -0.019385498017072678, 0.022146958857774734, -0.05020065978169441, -0.002811270300298929, 0.021959824487566948, -0.03479166328907013, 0.0016213118797168136, -0.0075967139564454556, 0.030868878588080406, 0.0264299176633358, -0.03564115986227989, 0.023890098556876183, -0.01598917692899704, 0.003467824310064316, 0.06558461487293243, -0.015318237245082855, -0.044996894896030426, -0.036723896861076355, 0.03638146445155144, 0.06413767486810684, -0.00679078558459878, -0.04022448882460594, 0.04279308021068573, -0.04252490773797035, 0.017523739486932755, 0.024736780673265457, 0.011759823188185692, -0.031308941543102264, -0.03514156490564346, 0.01970844343304634, 0.00634417962282896, -0.0013214226346462965, 0.018352147191762924, 0.01636003516614437, 0.03157953545451164, -0.0005532808136194944, 0.002638690872117877, 0.0581371933221817, 0.02772112376987934, -0.054612014442682266, 0.043255262076854706, 0.05265346169471741, -0.006893903482705355, 0.013051173649728298, -0.02565283328294754, 0.012898599728941917, 0.0068195052444934845, -0.011411839164793491, -0.07701805233955383, -0.03948034346103668, -0.011681214906275272, -0.03137509152293205, 0.010566584765911102, -0.07508325576782227, -0.016617748886346817, -0.03903137519955635, -0.12059143930673599, 0.03753174468874931, -0.01705224998295307, -0.001719737658277154, 0.03404931724071503, -0.0014657791471108794, 0.0020822270307689905, -0.02557145245373249, 0.05325612798333168, 0.010064867325127125, 0.014568000100553036, -0.015399003401398659, -0.01630008965730667, -0.011647489853203297, -0.04041343927383423, 0.007013286929577589, 0.04102974385023117, 0.05847664549946785, 0.022014392539858818, -0.025077231228351593, 0.024311956018209457, 0.02558000572025776, 0.0050948564894497395, -0.00689030671492219, -0.02357557602226734, -0.023420730605721474, -0.0022793435491621494, 0.05445069819688797, 0.041881855577230453, 0.045264557003974915, -0.00460088299587369, -0.06675524264574051, 0.025038953870534897, 0.012328125536441803, 0.026710670441389084, 0.0032436740584671497, -0.03336460143327713, -0.02633332461118698, -0.051515866070985794, -0.02537594363093376, -0.03429749608039856, -0.025430120527744293, 0.05256093665957451, 0.033658239990472794, -0.03413785994052887, 0.02332278899848461, 0.00009391395724378526, 0.017061252146959305, 0.027316980063915253, 0.02384081855416298, -0.01476161926984787, -0.011401794850826263, 0.02995724231004715, -0.019839242100715637, 0.005073024425655603, -0.010493061505258083, -0.0010175444185733795, -0.02557286061346531, 0.013222637586295605, -0.022839806973934174, -0.07388292253017426, -0.010317832231521606, -0.014327552169561386, -0.014011099934577942, -0.00292780390009284, -0.03519311547279358, -0.0013027708046138287, -0.04082978889346123, 0.00921420194208622, -0.027328908443450928, -0.07077980041503906, 0.009513616561889648, 0.01318907830864191, -0.07257197052240372, 0.04790417477488518, -0.038011740893125534, 0.08516977727413177, 0.07417571544647217, -0.04118908941745758, 0.0601792186498642, -0.021395450457930565, 0.008600100874900818, -0.024001844227313995, 0.04670754820108414, 0.04381883516907692, 0.027168195694684982, -0.0611824207007885, 0.00854183267802, 0.02946341782808304, 0.039846595376729965, -0.04502590745687485, 0.028790924698114395, 0.01935708522796631, -0.047531165182590485, -0.036641355603933334, -0.049017224460840225, -0.030339011922478676, -0.00308530917391181, 0.012988895177841187, -0.03852935880422592, 0.00557442381978035, 0.038021937012672424, -0.04919535666704178, -0.05293998867273331, -0.008959617465734482, 0.08176399767398834, 0.03876865655183792, -0.05578763782978058, 0.020383577793836594, -0.014369585551321507, 0.01700894720852375, 0.005034038797020912, -0.04382181540131569, -0.038388028740882874, -0.02720353752374649, -0.02028774656355381, -0.03070477396249771, 0.004106274340301752, -0.0260342825204134, 0.07271431386470795, 0.0173939298838377, 0.03713110834360123, 0.10601215809583664, -0.01634138450026512, -0.02410653792321682, 0.02985900640487671, 0.01991628296673298, 0.06055990979075432, 0.001108841155655682, 0.024056660011410713, 0.028988050296902657, 0.03718716278672218, -0.05613505095243454, -0.029536670073866844, 0.017466828227043152, 0.019866975024342537, -0.03807833790779114, -0.05464135482907295, 0.030704492703080177, 0.04231889545917511, -0.0014095230726525187, -0.023856474086642265, 0.012131769210100174, 0.04079678654670715, 0.04974770545959473, -0.001926740980707109, 0.009593985043466091, 0.034606773406267166, 0.024296509101986885, 0.016520893201231956, 0.046838320791721344, 0.05550902336835861, 0.02391820400953293, 0.017303811386227608, 0.008549602702260017, 0.05135173350572586, -0.13729625940322876, -0.03729770705103874, -0.025180742144584656, 0.007728903088718653, 0.022059857845306396, 0.01470209565013647, -0.05714663490653038, 0.028978632763028145, 0.03163057565689087, -0.022024642676115036, 0.012316595762968063, -0.06333959847688675, -0.035449687391519547, 0.05508394539356232, -0.012972292490303516, 0.03230266273021698, 0.004307165276259184, -0.04437774047255516, -0.018570225685834885, 0.006858304608613253, 0.04359232634305954, 0.017470482736825943, 0.015030068345367908, 0.00900194700807333, 0.02863738127052784, -0.026692107319831848, -0.020355286076664925, 0.00018018622358795255, -0.0005781942163594067, -0.08127620816230774, -0.07593639194965363, -0.062135327607393265, 0.04780586436390877, 0.01756633259356022, -0.02253425307571888, 0.028672466054558754, -0.0002613577526062727, 0.02728651650249958, -0.01572592929005623, -0.011228741146624088, -0.03849078714847565, 0.025512734428048134, 0.065910704433918, 0.11018425971269608, -0.041407905519008636, -0.0075009665451943874, 0.011816106736660004, 0.009596907533705235, 0.020880866795778275, 0.0018156793667003512, -0.07219847291707993, -0.03804232180118561, -0.049399856477975845, 0.09860369563102722, 0.06080261990427971, -0.06423431634902954, 0.08034545928239822, 0.0022798110730946064, -0.031039651483297348, -0.010519982315599918, -0.021405037492513657, 0.041841089725494385, 0.007635497022420168, 0.03487445414066315, 0.04233089089393616, 0.06578272581100464, 0.0044497414492070675, -0.05754198506474495, 0.02655549719929695, 0.05957300588488579, 0.044372182339429855, -0.017688389867544174, -0.013107704930007458, 0.00007225354056572542, 0.0683714747428894, -0.015018271282315254, -0.027203623205423355, -0.03374208137392998, 0.0038263495080173016, 0.01512117963284254, 0.01792844757437706, 0.014996646903455257, -0.015687813982367516, 0.005398258101195097, -0.08480363339185715, 0.03551602363586426, 0.049858856946229935, 0.021076427772641182, 0.0023723714984953403, 0.03580709174275398, 0.010192755609750748, 0.030127283185720444, 0.007080838084220886, 0.04400663450360298, -0.010538826696574688, 0.010067793540656567, -0.059281423687934875, 0.043688610196113586, -0.03563275560736656, 0.006692441180348396, -0.007298961281776428, 0.012263227254152298, -0.030059952288866043, -0.05339861661195755, -0.06425786018371582, -0.05676234886050224, -0.04258594661951065, 0.02429923787713051, 0.02635785937309265, -0.026182692497968674, -0.01947059854865074, 0.016586879268288612, -0.04067283868789673, -0.04542078077793121, 0.0030120552983134985, -0.01837245374917984, -0.044864196330308914, 0.030402813106775284, 0.0350165031850338, -0.01945490762591362, -0.01300871279090643, 0.03151293098926544, 0.016109716147184372, 0.0042370883747935295, 0.03848462179303169, -0.004192149266600609, 0.011603474617004395, -0.019816609099507332, -0.0006358175887726247, 0.005091315601021051, 0.04451245442032814, -0.01011891383677721, 0.026607779785990715, -0.027483461424708366, -0.0072758677415549755, -0.016369501128792763, 0.060468994081020355, 0.06777840107679367, -0.04938293248414993, -0.04991195723414421, -0.004566505551338196, -0.06694778800010681, 0.03906320407986641, 0.028455307707190514, -0.0012185629457235336, -0.08166470378637314, -0.003868594067171216, -0.026456326246261597, 0.026153365150094032, 0.012110703624784946, 0.00285693840123713, 0.058570168912410736, -0.06923394650220871, -0.023275071755051613, 0.0002785183605737984, 0.0051763663068413734, -0.007015498820692301, 0.015043728984892368, 0.06782365590333939, -0.009246370755136013, -0.025743061676621437, -0.06272819638252258, -0.03163408488035202, 0.06289408355951309, 0.01562453992664814, 0.049798499792814255, 0.02612757682800293, 0.019004303961992264, -0.011003775522112846, 0.07005223631858826, 0.011295069009065628, -0.01677062176167965, -0.012709368020296097, -0.0026310612447559834, -0.02055312879383564, -0.05395088717341423, 0.052574582397937775, -0.0030458674300462008, 0.0005689327954314649, -0.013142367824912071, -0.011530558578670025, -0.046777937561273575, 0.014655893668532372, -0.07589644193649292, 0.01728738471865654, -0.005944692995399237, 0.03717469424009323, -0.031383395195007324, 0.04539371654391289, -0.011045236140489578, 0.010205470956861973, -0.0010483994847163558, -0.030540281906723976, -0.03595663234591484, 0.04195214807987213, 0.04036608338356018, 0.012623459100723267, 0.07066919654607773, -0.03458932414650917, 0.013370458036661148, -0.018260061740875244, 0.02401149831712246, -0.04101003706455231, -0.007673768792301416, -0.026447687298059464, -0.044063225388526917, -0.05089601129293442, 0.0010670360643416643, 0.019674623385071754, 0.05491938441991806, 0.0025297109968960285, 0.0026168336626142263, 0.03309788554906845, 0.0006700875819660723, 0.0385340116918087, 0.01394337136298418, -0.062031470239162445, -0.014642423018813133, 0.06435440480709076, -0.003990857396274805, -0.016801513731479645, -0.008697418496012688, 0.055724289268255234, -0.0011806604452431202, 0.009689189493656158, -0.07567346841096878, -0.007056165486574173, 0.01768949069082737, -0.004958236590027809, 0.007798715494573116, 0.0383511520922184, -0.010055075399577618, -0.02924770675599575, -0.017096729949116707, 0.03667622432112694, 0.04375103861093521, -0.11302736401557922, -0.008622173219919205, -0.02826126106083393, -0.005608153063803911, -0.029108064249157906, 0.027461236342787743, 0.008657633326947689, -0.05031925067305565, -0.010130847804248333, -0.0010775140253826976, -0.011306371539831161, -0.0020398434717208147, 0.03566178306937218, -0.042638882994651794, -0.004409689921885729, -0.027648387476801872, -0.010184579528868198, 0.08236204832792282, 0.008245307020843029, 0.03282231464982033, -0.032160740345716476, -0.004347384441643953, -0.02944129705429077, -0.01890084333717823, 0.0004024538502562791, 0.07819534093141556, 0.002382672391831875, 0.017808737233281136, -0.010352634824812412, 0.008623097091913223, 0.04517702758312225, -0.03225640207529068, -0.04403436928987503, -0.0003155619779136032, -0.02144494839012623, 0.040812842547893524, -0.026353470981121063, 0.023605408146977425, 0.023658208549022675, 0.03441324457526207, 0.051093146204948425, 0.015205140225589275, 0.031044676899909973, 0.01058918982744217, -0.01649259403347969, -0.028455032035708427, 0.06993302702903748, -0.021375354379415512, -0.026619870215654373, -0.013895168900489807, -0.00646597146987915, 0.05931772664189339, -0.05412277579307556, -0.05378907918930054, 0.08036448061466217, -0.01767582818865776, 0.011729278601706028, -0.024032417684793472, 0.024763591587543488, 0.025069361552596092, 0.0019566260743886232, -0.02356116473674774, -0.021351445466279984, -0.018455781042575836, -0.018293485045433044, -0.0028708218596875668, -0.07801882177591324, 0.048312924802303314, 0.07309182733297348, 0.0005311390850692987, -0.044988781213760376, -0.03114910051226616, 0.04203173518180847, -0.002744241151958704, -0.023213353008031845, -0.003127577481791377, -0.017113761976361275, -0.024540182203054428, -0.0645081028342247, 0.00846787914633751, -0.019602779299020767, 0.03106997162103653, 0.013182633556425571, 0.022230787202715874, -0.013208365067839622, -0.030011188238859177, -0.05403955280780792, -0.06528329104185104, 0.017863621935248375, 0.012518838979303837, -0.008969775401055813, 0.018018905073404312, 0.011602165177464485, 0.006124448496848345, -0.0039664870128035545, -0.06736651808023453, 0.0013448261888697743, -0.0006913939141668379, -0.0015009046765044332, -0.08236446976661682, -0.052428461611270905, -0.04175936058163643, 0.05261396989226341, -0.027426619082689285, 0.04547417163848877, 0.01998108997941017, 0.011822094209492207, 0.03407180681824684, 0.0673668161034584, 0.017645616084337234, 0.010769329965114594, -0.01594998687505722, 0.01873650588095188, 0.06072703376412392, -0.035494495183229446, 0.02977157197892666, -0.016424398869276047, -0.03890172764658928, 0.013632058165967464, 0.023276928812265396, -0.05130097270011902, 0.023111790418624878, 0.022001754492521286, -0.0009797813836485147, 0.0364706851541996, -0.019306248053908348, -0.04427829012274742, 0.060638055205345154, -0.002899633953347802, -0.04687337577342987, 0.0018868210026994348, -0.02614452876150608, -0.02291465550661087, 0.004902875516563654, 0.05212409421801567, -0.021969148889183998, 0.07316315919160843, -0.040438562631607056, 0.011625939980149269, 0.008957887068390846, -0.06479844450950623, -0.043423768132925034, -0.033007800579071045, 0.04892429709434509, 0.001108394586481154, 0.04659847170114517, 0.032858144491910934, 0.013598056510090828, 0.031053883954882622, -0.06731633096933365, 0.06064566969871521, 0.016238035634160042, -0.07069674879312515, 0.0003994355211034417, 0.05129534751176834, 0.02785451151430607, -0.04374300315976143, -0.04799537733197212, 0.06525866687297821, 0.018156368285417557, -0.032963383942842484, 0.002751499181613326, 0.028419559821486473, -0.013241891749203205, 0.043750353157520294, -0.028354119509458542, -0.033143579959869385, 0.024084294214844704, -0.05543002858757973, 0.051534902304410934, -0.048377517610788345, 0.03464335575699806, 0.032714009284973145, 0.013554157689213753, 0.005710495635867119, 0.014605699107050896, 0.021386953070759773, 0.018701782450079918, -0.04559789225459099, -0.027188025414943695, 0.013927530497312546, 0.052712537348270416, -0.06915950030088425, 0.054245878010988235, 0.038833245635032654, 0.03074614703655243, -0.024540124461054802, -0.04154874384403229, -0.02044610120356083, -0.045386508107185364, 0.0017218864522874355, 0.03202906623482704, -0.02029990963637829, -0.0366646870970726, -0.01250832062214613, -0.017220746725797653, 0.013983352109789848, 0.056473493576049805, -0.028318054974079132, 0.10336872190237045, -0.004861265420913696, -0.007497943472117186, -0.0024727629497647285, -0.04799589514732361, -0.009119129739701748, -0.026326728984713554, -0.07709798216819763, -0.0030027898028492928, 0.010661386884748936, 0.021723154932260513, 0.042270660400390625, 0.010689187794923782, -0.017547858878970146, -0.03264616057276726, 0.011319993995130062, 0.008329697884619236, -0.025774279609322548, -0.04480103775858879, -0.04974263533949852, 0.01791778951883316, -0.030498458072543144, -0.03893811255693436, 0.008360217325389385, -0.0065768868662416935, -0.015173347666859627, -0.01510646566748619, 0.031762801110744476, 0.02843901515007019, -0.0029283124022185802, -0.037397127598524094, 0.025503333657979965, 0.08944563567638397, -0.005138230975717306, 0.005418659653514624, 0.041726913303136826, -0.06484164297580719, -0.00597835797816515, 0.029482554644346237, 0.014730529859662056, -0.025772465392947197, 0.004221739247441292, 0.027288367971777916, -0.008599717170000076, -0.03702022507786751, 0.028360586613416672, -0.0008024630951695144, 0.027796678245067596, 0.02061534859240055, 0.04585906118154526, 0.004379977472126484, 0.017448654398322105, -0.019101567566394806, 0.01678583212196827, -0.0374392606317997, 0.013331732712686062, -0.02605878747999668, -0.00952154491096735, -0.09927438944578171, -0.036458030343055725, -0.043222781270742416, -0.0037453658878803253, -0.027558576315641403, 0.03873898461461067, -0.015397206880152225, -0.024921119213104248, -0.006803853437304497, -0.03098798729479313, 0.0007967950077727437, -0.07681561261415482, 0.03269810229539871, -0.0040772161446511745, 0.0164423156529665, -0.002941862214356661, -0.00610074307769537, 0.007477675564587116, 0.02048710361123085, 0.039662886410951614, 0.02932608127593994, -0.040483616292476654, 0.03816121444106102, -0.014254535548388958, 0.05614558979868889, 0.08731690049171448, 0.005534751806408167, -0.00414062337949872, 0.023091096431016922, -0.022358400747179985, 0.022702626883983612, 0.031963054090738297, -0.05337921902537346, -0.031465835869312286, -0.013782012276351452, -0.010473640635609627, -0.04884196072816849, -0.031594354659318924, -0.01989990472793579, -0.02102530188858509, 0.02297843061387539, 0.0077276770025491714, -0.04507435858249664, 0.0019428051309660077, 0.04536663368344307 ]
<p>I'm trying to relate the concept of entropy to keeping my room clean as suggested by my high school teacher ~1993...</p> <p>Comparing the two scenarios:</p> <ol> <li><p>Every day I come home and throw an empty can on the floor and every night before bed I pick it up and throw it in the trash.</p></li> <li><p>Every day I come home and throw an empty can on the floor and every six months I bag them all up at once.</p></li> </ol> <p>So to me it's obviously more efficient to let entropy run its course and then undo it in a "batch" as opposed to constantly undoing it.</p> <p>Is that right though? I'm thinking since entropy is related to energy, then is has to be conserved and the same amount of effort should be required to keep a room clean than to clean it after its become horribly messy.</p>
g8359
[ 0.019493747502565384, -0.006034302059561014, 0.009444638155400753, -0.012042278423905373, 0.015749700367450714, -0.04759439826011658, 0.05664703622460365, 0.0423804447054863, -0.02921409346163273, -0.009197385981678963, 0.016968529671430588, -0.020306801423430443, 0.03728144243359566, 0.03211637958884239, -0.003518190234899521, -0.005814102478325367, 0.05149674788117409, -0.009438115172088146, -0.030712783336639404, 0.050818849354982376, 0.008936877362430096, -0.01364045962691307, 0.008094912394881248, -0.08334912359714508, -0.07478446513414383, 0.007846451364457607, -0.03863069787621498, -0.015062644146382809, -0.029148269444704056, -0.019976332783699036, 0.005195438861846924, 0.028053952381014824, -0.003227161942049861, -0.08145653456449509, -0.06866674870252609, -0.0023903322871774435, 0.028281740844249725, 0.02044457010924816, 0.006827726028859615, -0.05050767958164215, 0.04448341578245163, 0.04098495468497276, 0.012750918045639992, -0.06046483293175697, -0.0032863037195056677, 0.03278860077261925, -0.008756392635405064, 0.010491909459233284, -0.010759553872048855, -0.02015151083469391, -0.017683032900094986, -0.02032206952571869, -0.018620800226926804, 0.0611412338912487, -0.0011673944536596537, 0.028427794575691223, 0.03192253038287163, -0.038741763681173325, 0.04230440407991409, 0.010462919250130653, 0.02382006123661995, -0.0017392485169693828, -0.053303204476833344, 0.0387883223593235, -0.023167608305811882, 0.012857932597398758, 0.033438168466091156, -0.0003814969095401466, 0.0711023285984993, -0.01002538576722145, -0.008888984099030495, 0.0017835504841059446, -0.0003146707022096962, -0.039923544973134995, -0.0005286895320750773, 0.07835333794355392, 0.031293127685785294, 0.012037739157676697, 0.05321849137544632, 0.021656299009919167, -0.06848837435245514, -0.07664214819669724, 0.043111402541399, 0.0025150205474346876, 0.041083913296461105, 0.012291551567614079, -0.007726408541202545, -0.06389699131250381, 0.03570295125246048, 0.045402318239212036, 0.032462820410728455, -0.0641656219959259, 0.01905853860080242, 0.03318608179688454, -0.08948652446269989, 0.028397032991051674, 0.011415651068091393, 0.021120626479387283, 0.010908746160566807, 0.06430911272764206, -0.058205343782901764, -0.10105841606855392, 0.0062897708266973495, 0.005990177858620882, 0.007888225838541985, -0.011973649263381958, -0.01543300412595272, -0.004203761927783489, -0.0705857202410698, 0.03524945676326752, 0.003032510867342353, 0.015035087242722511, -0.03313177451491356, 0.023672549054026604, 0.0002714062575250864, 0.015935488045215607, 0.13989457488059998, -0.00010574458428891376, -0.0002572490193415433, 0.01710277423262596, 0.013625318184494972, 0.04814570024609566, 0.014768086373806, -0.04941023141145706, 0.03955572098493576, -0.006091944873332977, 0.05324382334947586, 0.021897675469517708, 0.055516570806503296, 0.05581041797995567, -0.03377959877252579, -0.01925000175833702, -0.05610712245106697, -0.012678573839366436, 0.03779951483011246, 0.003234390402212739, -0.029967408627271652, -0.011044344864785671, 0.02474229224026203, -0.03163215145468712, 0.06955624371767044, 0.021567773073911667, 0.007855948992073536, 0.023099999874830246, -0.04993225261569023, 0.040317416191101074, -0.022196339443325996, -0.03450465574860573, 0.00478766206651926, -0.005079189781099558, 0.0055711530148983, -0.011628171429038048, -0.025912292301654816, -0.07528190314769745, 0.017519133165478706, -0.010644050315022469, 0.05934242531657219, -0.009025152772665024, 0.05272935703396797, 0.015367229469120502, 0.00729219289496541, -0.02575400471687317, 0.022006532177329063, -0.022289814427495003, -0.04553091153502464, -0.02447395771741867, 0.025274520739912987, -0.057353489100933075, -0.007993362843990326, -0.044196780771017075, -0.04561067000031471, 0.004433772061020136, 0.01843905635178089, 0.056031953543424606, -0.0044836499728262424, 0.009385812096297741, 0.007510400377213955, -0.01097293570637703, 0.01067656185477972, -0.05304199084639549, 0.012437012046575546, 0.021545222029089928, 0.03912684693932533, -0.03334680572152138, 0.04254039376974106, -0.0006782682612538338, 0.007245867978781462, 0.02084333822131157, -0.08668361604213715, -0.02978772297501564, 0.053167957812547684, 0.005667613819241524, -0.027204841375350952, 0.041442062705755234, 0.02951677516102791, -0.0042337398044764996, -0.03144468367099762, -0.021020403131842613, -0.06647322326898575, -0.04197939857840538, -0.02060915343463421, -0.07688156515359879, 0.04847312718629837, 0.005590112414211035, -0.043196339160203934, 0.020777596160769463, -0.020280035212635994, 0.00843995250761509, -0.006729606073349714, -0.03053118847310543, -0.009053083136677742, 0.002373521914705634, 0.0020624238532036543, 0.01999310776591301, 0.020482350140810013, -0.007100444752722979, -0.02537374012172222, 0.04636134207248688, -0.03472457826137543, -0.014227738603949547, -0.014111162163317204, -0.031287260353565216, 0.06265410780906677, -0.002390130190178752, -0.014834083616733551, -0.0011489735916256905, -0.009483193047344685, -0.02379404753446579, -0.03149821609258652, 0.015434589236974716, 0.004483425989747047, 0.02117251046001911, 0.021588299423456192, -0.05255036801099777, 0.003115707775577903, 0.09810683876276016, 0.033459097146987915, 0.03257959336042404, -0.009872330352663994, -0.026751698926091194, -0.015182677656412125, 0.01584765873849392, -0.04046617075800896, -0.009266369976103306, 0.029818352311849594, -0.030583783984184265, 0.008694082498550415, -0.03804364055395126, 0.014703023247420788, -0.005683550611138344, -0.0063441903330385685, 0.020960941910743713, -0.03776504471898079, -0.02680899202823639, 0.0089664151892066, -0.038848698139190674, 0.03410053625702858, -0.004696333315223455, 0.017194731160998344, 0.03383082523941994, 0.01593717932701111, -0.0494137778878212, -0.04077881574630737, 0.004244660492986441, 0.013715149834752083, -0.018839210271835327, -0.04469366371631622, -0.010309016332030296, 0.041379414498806, 0.009299186989665031, 0.0687103122472763, 0.0044091022573411465, 0.006445400416851044, -0.012229659594595432, 0.011310317553579807, 0.0006356368539854884, 0.03411618992686272, -0.012398534454405308, 0.027403781190514565, 0.010484267957508564, 0.03327830508351326, 0.007656000088900328, -0.06040779501199722, 0.01611715741455555, 0.07452701777219772, -0.025403128936886787, 0.020635785534977913, -0.020838165655732155, -0.022470014169812202, 0.035194095224142075, -0.012320385314524174, 0.05439499393105507, 0.01825234480202198, 0.01689673401415348, -0.003163619665428996, 0.04220971092581749, 0.026896243914961815, -0.05456119030714035, -0.01614980585873127, 0.010849220678210258, 0.0320156030356884, 0.041767533868551254, -0.0034101782366633415, -0.0035995380021631718, 0.002761577256023884, 0.020097555592656136, -0.09293569624423981, -0.013144511729478836, -0.012189962901175022, -0.020745955407619476, -0.0029843803495168686, 0.03755035251379013, -0.0556633435189724, 0.0560607947409153, -0.01646704599261284, -0.04193384572863579, 0.025342745706439018, -0.05803524702787399, 0.01878339983522892, 0.011479442939162254, 0.012844318524003029, 0.03345268964767456, 0.06517750024795532, 0.007272311951965094, -0.007880003191530704, 0.03977381810545921, -0.060063671320676804, 0.016744157299399376, -0.023958491161465645, 0.014923146925866604, 0.002594804158434272, 0.028401877731084824, -0.007797034922987223, -0.009350958280265331, -0.06828323751688004, -0.051145292818546295, -0.06834367662668228, -0.0677875205874443, -0.03746075555682182, 0.040214959532022476, -0.0019864921923726797, 0.061685480177402496, -0.002833912381902337, -0.028428373858332634, -0.011334012262523174, 0.0198247991502285, -0.00030632526613771915, -0.04750936105847359, -0.039363887161016464, 0.007604155223816633, 0.030683984979987144, -0.03021932765841484, 0.0037156378384679556, 0.008741561323404312, -0.01916869357228279, -0.020478643476963043, -0.024195699021220207, 0.044976040720939636, 0.03880380094051361, 0.010684391483664513, -0.08715175092220306, -0.04084986448287964, -0.005317071918398142, -0.025249017402529716, -0.03957899287343025, 0.029448509216308594, -0.019361793994903564, 0.03520453721284866, -0.03694148361682892, 0.02386690489947796, -0.048024699091911316, 0.02393205091357231, -0.019392304122447968, -0.005261968355625868, 0.025974811986088753, 0.0371963195502758, 0.1002652570605278, 0.025565961375832558, -0.041057247668504715, -0.004033702425658703, 0.04156965762376785, -0.025705449283123016, -0.06286314874887466, -0.08333243429660797, -0.026354115456342697, 0.01209215633571148, 0.0047407313250005245, 0.011237581260502338, -0.038645610213279724, -0.023887677118182182, -0.025073185563087463, 0.05106571316719055, 0.01443022396415472, -0.019109806045889854, -0.003120885696262121, 0.07149875909090042, 0.013551630079746246, 0.010139280930161476, -0.042379528284072876, 0.05567095801234245, 0.030555833131074905, -0.012359699234366417, 0.0027235031593590975, -0.006342045962810516, -0.009350570850074291, -0.00007157371146604419, -0.023022793233394623, -0.05807524919509888, -0.032418522983789444, -0.01752937026321888, 0.03284866362810135, 0.026925262063741684, -0.04477711021900177, 0.0169554241001606, -0.029644131660461426, -0.01126962061971426, -0.015790702775120735, 0.018360953778028488, -0.0015119343297556043, 0.0535019114613533, 0.014937133528292179, 0.0007204660214483738, -0.02839669957756996, 0.004121751058846712, 0.01768128201365471, 0.04663287475705147, 0.043209269642829895, 0.05602816492319107, -0.027663573622703552, -0.10037700831890106, 0.02050933428108692, 0.0415656641125679, -0.027674727141857147, 0.013958635739982128, -0.03323807567358017, 0.01952146366238594, -0.0017067617736756802, 0.06968645751476288, 0.03475961461663246, -0.0038028894923627377, 0.017973797395825386, -0.011412101797759533, -0.031906068325042725, 0.016159093007445335, -0.042895395308732986, -0.0005039570387452841, -0.00933525338768959, -0.04870862141251564, 0.0227687768638134, -0.08208273351192474, -0.028097914531826973, 0.052549809217453, 0.036503780633211136, -0.04828938469290733, -0.024037793278694153, -0.002724685939028859, -0.0618191622197628, 0.035793203860521317, -0.0385625995695591, 0.01726953499019146, -0.014395245350897312, 0.010621857829391956, 0.07626780867576599, -0.005113648250699043, 0.00017175952962134033, 0.013710582628846169, -0.05472354590892792, -0.021856797859072685, -0.055520497262477875, -0.0020983226131647825, 0.01950742118060589, -0.015730028972029686, -0.02918199449777603, 0.07353430241346359, 0.061791133135557175, -0.042007461190223694, 0.007389615755528212, 0.05266241356730461, -0.00933123379945755, 0.015260719694197178, -0.06383547931909561, 0.002350590657442808, 0.03005450963973999, 0.0162119772285223, 0.021651459857821465, -0.03158970922231674, -0.017464445903897285, -0.030642377212643623, 0.01894126459956169, 0.021222896873950958, -0.01691332831978798, 0.0884571373462677, 0.08018842339515686, -0.014877348206937313, 0.027822470292448997, 0.002120227785781026, -0.0030310158617794514, 0.012807955965399742, -0.045548126101493835, -0.03557581827044487, -0.040958818048238754, 0.043920088559389114, -0.06074906885623932, -0.031514972448349, -0.043124258518218994, 0.01887025684118271, -0.017599226906895638, 0.0151244280859828, -0.04738706350326538, 0.012491848319768906, -0.012940042652189732, 0.008092386648058891, -0.04113767296075821, 0.06765927374362946, 0.08134590834379196, -0.0375438891351223, 0.0038774083368480206, 0.013647557236254215, -0.0173640176653862, -0.028799738734960556, 0.015245526097714901, 0.08240906894207001, -0.005016735754907131, -0.024367913603782654, -0.004563487600535154, 0.03176598995923996, -0.056125301867723465, 0.02484213188290596, 0.006535323336720467, 0.02335149236023426, 0.0515776164829731, -0.012764264829456806, -0.005276235286146402, 0.053953442722558975, -0.03157336637377739, 0.004040381405502558, -0.040718864649534225, 0.09669588506221771, -0.003575629787519574, 0.013780944980680943, -0.028862925246357918, -0.03444632515311241, -0.032923322170972824, 0.03054223023355007, -0.008684187196195126, -0.05280056595802307, -0.02950742281973362, -0.08373984694480896, -0.004750479478389025, -0.018852224573493004, -0.025056535378098488, -0.010505631566047668, -0.010600609704852104, -0.030764514580368996, 0.001786722568795085, -0.010109390132129192, 0.04515453428030014, -0.0392586924135685, 0.03362196311354637, 0.03200496733188629, 0.013039485551416874, 0.06998848170042038, 0.04404313117265701, -0.019751673564314842, 0.09771733731031418, -0.025672266259789467, 0.056537121534347534, 0.00746605359017849, 0.020383115857839584, 0.11475833505392075, 0.06582541018724442, 0.010569502599537373, 0.020211759954690933, 0.0129152936860919, -0.042241211980581284, -0.01165874395519495, -0.02392197959125042, -0.080045685172081, 0.0013705049641430378, -0.007530919276177883, -0.0015698575880378485, -0.07279634475708008, 0.03882575407624245, -0.025029227137565613, -0.010282717645168304, 0.0038085763808339834, -0.0231492817401886, 0.027635715901851654, 0.036063384264707565, -0.000007008473403402604, -0.04522484913468361, -0.010488227941095829, -0.021557165309786797, 0.015746891498565674, -0.008523653261363506, 0.05940138176083565, -0.03927017003297806, -0.06608131527900696, -0.028513746336102486, -0.03911888226866722, -0.04060785099864006, 0.010457493364810944, 0.02085345983505249, -0.033495351672172546, 0.008229241706430912, 0.07228341698646545, -0.004845554940402508, 0.061190176755189896, -0.023605166003108025, -0.0017152634682133794, -0.09559663385152817, 0.05352140590548515, 0.026658345013856888, 0.014545571058988571, -0.011811654083430767, -0.021021690219640732, -0.05039609968662262, 0.04550763592123985, 0.06000896170735359, 0.030458102002739906, 0.014227448962628841, 0.0415540486574173, 0.0268910713493824, -0.010916179977357388, 0.046949103474617004, 0.05644981190562248, 0.01391949225217104, -0.005665143020451069, 0.0171885397285223, 0.04648987576365471, -0.04619086533784866, -0.024791384115815163, -0.015253427438437939, 0.06771539896726608, -0.0025442366022616625, -0.043337903916835785, -0.10205280780792236, 0.03157029300928116, -0.0010736699914559722, 0.017070366069674492, -0.018704118207097054, 0.0015995922731235623, 0.03369290754199028, 0.023263201117515564, -0.03723624721169472, 0.041051771491765976, 0.03537863492965698, -0.03953732177615166, -0.02175687439739704, -0.032555751502513885, 0.013580719009041786, -0.023924190551042557, -0.04327237606048584, -0.06800264865159988, -0.027911661192774773, 0.02098792791366577, -0.039889201521873474, 0.04369452968239784, 0.004836591426283121, -0.03815819323062897, 0.041102416813373566, -0.00044142288970761, 0.011291120201349258, 0.046745993196964264, 0.0006044237525202334, -0.02212071418762207, 0.05588097870349884, 0.02035664953291416, 0.04333314299583435, -0.035622864961624146, 0.03867182508111, -0.04536878690123558, -0.054317742586135864, -0.0365518257021904, 0.017836464568972588, 0.03981373831629753, 0.02350577525794506, -0.02357175014913082, 0.005769586656242609, 0.036731552332639694, 0.031042352318763733, -0.07143699377775192, 0.010630794800817966, -0.03881598263978958, -0.033981285989284515, 0.05422279238700867, -0.055113695561885834, 0.01304607093334198, 0.0024454286321997643, -0.07814310491085052, -0.019420059397816658, 0.03262920677661896, 0.006946606561541557, -0.01921236328780651, -0.017881236970424652, 0.035927914083004, 0.08111397922039032, -0.024977916851639748, 0.03082919679582119, -0.01697266288101673, -0.0019863927736878395, 0.007434473372995853, 0.034687984734773636, 0.00006971175025682896, 0.025936322286725044, 0.016824716702103615, -0.04271518811583519, 0.015754027292132378, 0.015693476423621178, 0.03691285103559494, -0.023798642680048943, -0.025557370856404305, 0.03287563472986221, 0.03492828458547592, -0.006710692774504423, 0.0012148628011345863, -0.010730654001235962, -0.02728232555091381, 0.024300845339894295, 0.039269596338272095, -0.012656116858124733, 0.0359262190759182, -0.049289122223854065, 0.03736291453242302, -0.014038057997822762, 0.03682674095034599, 0.025455765426158905, -0.03404552489519119, -0.006687838118523359, -0.009387575089931488, -0.01041875034570694, -0.028082646429538727, 0.018937354907393456, -0.007038052659481764, 0.0461580790579319, 0.054410386830568314, 0.06630364805459976, 0.04817909747362137, -0.026849258691072464, -0.036994703114032745, 0.02791527658700943, 0.021321360021829605, 0.002866393653675914, -0.01028263010084629, 0.0017155110836029053, -0.019033407792448997, -0.05448611453175545, -0.05354209989309311, 0.03476792201399803, 0.004926248453557491, -0.03711886331439018, -0.05959463119506836, -0.027398018166422844, -0.0017542806454002857, 0.04120603948831558, -0.0027361223474144936, -0.008755584247410297, -0.009915689006447792, 0.026064123958349228, 0.026571223512291908, -0.049543190747499466, -0.004709231201559305, -0.022281641140580177, -0.004732506349682808, -0.0022926810197532177, -0.02995617501437664, 0.010748989880084991, -0.028036044910550117 ]
<p>I suppose this is also an English question, but I'll ask it here first.</p> <p>Why does the milli- prefix mean 1/1000 when it sounds so much like million? According to the internet, this dates back to the 18-19th centuries. Did it make more sense back then? Are we stubbornly holding on to meanings from borrowed prefix's languages (such as milli meaning 1000 in Latin)?</p> <p>Not that I'm qualified in any way to make this kind of statement, but if I were able to rename our unit prefixes, I would shift everything from milli- to femto- down 3 orders of magnitude and eliminate atto-. The resulting pairs would be:</p> <pre><code>thousand- kilo (placeholder) million- mega milli billion- giga micro trillion- terra nano quadrillion- peta pico quintillion- exa femto sextillion- zetta zepto ... </code></pre> <p>Which to me, sounds better. But I suppose I answered my own question by saying that since they are the units everyone uses, social inertia prevents us from changing. Would this be correct?</p>
g8360
[ 0.0381893664598465, 0.031176673248410225, 0.013098161667585373, 0.022096022963523865, 0.05255229026079178, 0.008945822715759277, 0.014389553107321262, 0.054442502558231354, -0.0004789138329215348, 0.019416319206357002, -0.03224754333496094, 0.018093464896082878, 0.033325258642435074, 0.023640550673007965, -0.005527607165277004, -0.023650582879781723, 0.0940566137433052, 0.021648431196808815, 0.013825299218297005, 0.08925978094339371, 0.013113288208842278, 0.0071936375461518764, -0.0019335777033120394, -0.01734323240816593, -0.051943615078926086, -0.01676134206354618, 0.07343161106109619, -0.01740850694477558, 0.01643429324030876, -0.03961414471268654, 0.06370735168457031, -0.002198936650529504, 0.017101744189858437, -0.021312030032277107, -0.011182483285665512, -0.026698974892497063, 0.019695166498422623, -0.009498397819697857, 0.003718882566317916, 0.03136157989501953, 0.040277209132909775, -0.029171552509069443, 0.06440015882253647, -0.03345080092549324, 0.03952271491289139, 0.02330838143825531, -0.0006190093699842691, -0.03747883811593056, 0.07115274667739868, -0.03889928385615349, 0.015337198972702026, -0.027605727314949036, 0.030964801087975502, 0.10106554627418518, 0.018465355038642883, 0.0536215640604496, 0.020633762702345848, 0.011472531594336033, 0.030411867424845695, 0.08744870871305466, 0.004549954552203417, -0.04884963110089302, 0.04092661663889885, 0.008431853726506233, 0.05750684812664986, -0.024364756420254707, -0.07187024503946304, -0.0029997120145708323, 0.06527610123157501, 0.036157578229904175, 0.015363146550953388, -0.018208155408501625, -0.0004553377802949399, 0.046935394406318665, -0.0554124116897583, 0.02243000641465187, -0.06859107315540314, -0.02820422500371933, 0.0901343822479248, -0.038828879594802856, 0.03240406513214111, 0.007630626671016216, 0.0795881450176239, 0.00771302031353116, 0.03247697651386261, 0.014537094160914421, -0.0466180145740509, 0.013812193647027016, -0.041210517287254333, 0.04132987931370735, -0.031913887709379196, -0.06592215597629547, 0.0346134789288044, 0.0321061871945858, -0.015786075964570045, -0.011224453337490559, -0.057431284338235855, 0.005769637413322926, 0.033562663942575455, 0.05714990943670273, 0.014851909130811691, 0.009422309696674347, 0.0471217967569828, 0.02740505151450634, -0.05453832447528839, 0.018527202308177948, 0.0020687468349933624, -0.023795150220394135, -0.016494346782565117, 0.012910875491797924, -0.002766853664070368, 0.013397245667874813, -0.0086368378251791, -0.04001926630735397, -0.04612968489527702, 0.028082560747861862, 0.07056982070207596, 0.016461718827486038, -0.04435630515217781, 0.04614274948835373, -0.05297179892659187, -0.07093499600887299, -0.01791108213365078, 0.012090247124433517, -0.030343307182192802, -0.08283474296331406, -0.03189067170023918, 0.054428018629550934, 0.02024022862315178, -0.06716281175613403, -0.02143857255578041, 0.054501958191394806, -0.039423298090696335, -0.007789183408021927, -0.014797347597777843, -0.008439979515969753, 0.0027563932817429304, -0.05306601896882057, 0.054255612194538116, -0.012912731617689133, 0.0009363467688672245, -0.009794325567781925, 0.018768267706036568, -0.03395995497703552, -0.004762731492519379, 0.03978925198316574, -0.051657479256391525, -0.05365036055445671, 0.030009325593709946, 0.037146855145692825, 0.021845359355211258, 0.03931984677910805, 0.023618001490831375, -0.04464452341198921, 0.013439719565212727, 0.0017478687223047018, -0.003078990848734975, 0.02797694131731987, -0.03823399171233177, -0.016757352277636528, -0.02399810217320919, -0.031650107353925705, -0.025679610669612885, 0.031307753175497055, -0.07919815927743912, -0.032150302082300186, -0.03749675303697586, -0.03835028037428856, -0.015252825804054737, 0.006615752819925547, -0.03377464786171913, -0.01146460510790348, 0.0029744559433311224, 0.025797346606850624, -0.01622541807591915, 0.03614126890897751, 0.01660877652466297, -0.013270918279886246, -0.042646050453186035, -0.018111007288098335, 0.025188563391566277, 0.004651636350899935, 0.018103135749697685, 0.014359410852193832, -0.004674549680203199, -0.035481709986925125, 0.023279476910829544, 0.07820364087820053, -0.03954179584980011, 0.05134248360991478, -0.008789693005383015, 0.004585414193570614, 0.0015382295241579413, 0.05644898861646652, -0.029742877930402756, -0.024571266025304794, -0.003845859318971634, 0.003816347336396575, -0.04553816094994545, -0.01659935712814331, -0.002073814859613776, 0.0050562163814902306, -0.028083408251404762, 0.00270322198048234, 0.03856575861573219, -0.06259322166442871, -0.008087181486189365, 0.018954679369926453, 0.013555108569562435, -0.03757721185684204, 0.02729753591120243, -0.061704520136117935, -0.07293448597192764, -0.0021893749944865704, -0.07022877037525177, -0.01104340422898531, 0.05007366091012955, -0.0104509387165308, 0.053318556398153305, -0.020597053691744804, -0.021193644031882286, -0.03146170452237129, 0.04718071594834328, 0.014519928954541683, -0.011171551421284676, -0.036357175558805466, 0.0026077493093907833, -0.03374513238668442, -0.03568754717707634, 0.040909212082624435, -0.06605613231658936, 0.022083548828959465, -0.03743574395775795, 0.023281598463654518, -0.011434606276452541, 0.05860245227813721, 0.0061289044097065926, 0.0077505894005298615, 0.005480379797518253, -0.005105352960526943, 0.033182770013809204, -0.005148365627974272, 0.02825562097132206, 0.01149268914014101, -0.05140851438045502, -0.050796642899513245, -0.0014148848131299019, 0.012489206157624722, -0.02779039926826954, 0.024970022961497307, -0.0678381398320198, -0.04306662455201149, -0.07835812866687775, -0.014888384379446507, 0.051759932190179825, 0.013473378494381905, -0.015846390277147293, 0.02251855842769146, -0.0012288171565160155, 0.07904680073261261, 0.03402584418654442, -0.03168204054236412, -0.018758313730359077, -0.022213388234376907, 0.07912862300872803, 0.0006673452444374561, 0.0011977932881563902, 0.02705141343176365, 0.05050919950008392, 0.026747750118374825, 0.03517550230026245, 0.010684533044695854, 0.06721022725105286, -0.009286942891776562, -0.015381546691060066, -0.047321174293756485, -0.03300570696592331, -0.023579007014632225, 0.029976382851600647, -0.011711075901985168, -0.05099202319979668, 0.05018573999404907, -0.05408431217074394, -0.032086651772260666, 0.060553211718797684, -0.022059230133891106, 0.0030383504927158356, -0.017082219943404198, 0.0015987048391252756, -0.009954997338354588, -0.005842401180416346, -0.009863249957561493, 0.020484687760472298, -0.02419503964483738, 0.021215345710515976, -0.0039353747852146626, -0.016557343304157257, -0.02749541588127613, -0.01835712417960167, -0.022111549973487854, 0.08027210831642151, 0.03187151998281479, 0.044262081384658813, 0.017173083499073982, -0.012124516069889069, 0.039547745138406754, -0.010621161200106144, 0.008473767898976803, -0.022968759760260582, -0.08923549205064774, 0.018533917143940926, 0.10764484107494354, -0.005583825521171093, -0.006752477493137121, -0.08046496659517288, 0.023759758099913597, -0.027422795072197914, 0.029997123405337334, -0.02261645905673504, 0.0047429148107767105, -0.047194138169288635, -0.02005116455256939, 0.019467834383249283, -0.03788764402270317, -0.019298702478408813, 0.027662932872772217, -0.028913572430610657, -0.0378868542611599, -0.04798349365592003, -0.0508158914744854, -0.03424710035324097, -0.03766043484210968, -0.0003791202325373888, -0.0015675059985369444, -0.0614871010184288, -0.04864422604441643, -0.021844077855348587, -0.008199261501431465, 0.050335146486759186, 0.0048083835281431675, 0.029437929391860962, 0.047869570553302765, -0.019072052091360092, 0.04064969718456268, 0.05747966468334198, 0.05745435506105423, 0.050277091562747955, -0.020932121202349663, -0.045737411826848984, 0.031093671917915344, -0.026154542341828346, 0.014299828559160233, -0.0033698698971420527, -0.0011937535600736737, 0.05877559632062912, 0.01186919305473566, 0.006135010160505772, 0.0269134733825922, -0.00021639207261614501, -0.03274712339043617, 0.039397962391376495, 0.0029104831628501415, 0.06858083605766296, 0.04659964144229889, 0.011363423429429531, 0.03595912829041481, -0.020865174010396004, 0.00060940784169361, -0.0099983224645257, -0.0363832525908947, -0.07312587648630142, -0.02707178331911564, -0.0307947788387537, 0.014392352662980556, -0.05610579624772072, 0.01643248274922371, 0.02645236626267433, 0.026911357417702675, -0.05382514372467995, 0.00280297314748168, 0.014338448643684387, -0.05349234119057655, 0.002088262466713786, -0.07370615750551224, 0.0033327643759548664, -0.014483975246548653, 0.04313585162162781, 0.008586311712861061, 0.001715946476906538, 0.0021757720969617367, 0.015573556534945965, -0.03921765461564064, 0.049794942140579224, -0.06553071737289429, -0.013034033589065075, -0.013865210115909576, 0.014589015394449234, -0.09491857886314392, 0.0006604345981031656, 0.029874786734580994, -0.040161941200494766, -0.01869424805045128, 0.06349615007638931, -0.05271070450544357, 0.04029103368520737, -0.029428739100694656, 0.013013812713325024, -0.01522503700107336, -0.0015100837917998433, -0.01889694482088089, -0.00304830982349813, 0.0522429458796978, 0.008086570538580418, -0.031286533921957016, 0.04063810035586357, 0.044189631938934326, 0.014276926405727863, -0.02962498739361763, -0.0005589817883446813, 0.04855780303478241, 0.0342642180621624, 0.018885353580117226, -0.01890711300075054, -0.029398789629340172, 0.024481041356921196, 0.03431696817278862, 0.03441304340958595, 0.022361060604453087, 0.00926794484257698, 0.03029470518231392, 0.044430095702409744, 0.05552198365330696, 0.03558492660522461, -0.017788304015994072, -0.014892677776515484, -0.06072438508272171, 0.015680067241191864, -0.031981468200683594, 0.03214101865887642, 0.012434589676558971, 0.0845952257514, -0.009300313889980316, -0.08292698860168457, 0.03327595070004463, 0.0015782719710841775, -0.018924791365861893, 0.03193076699972153, 0.03813037648797035, -0.01993991993367672, -0.0037122960202395916, -0.029666997492313385, 0.018620774149894714, 0.014658880420029163, -0.02865983545780182, 0.05959796905517578, 0.010388248600065708, -0.008031636476516724, -0.026267578825354576, 0.02174816094338894, 0.02227824553847313, -0.03194326162338257, 0.014799505472183228, -0.0675925761461258, 0.0633826032280922, 0.08864887058734894, 0.03854085132479668, -0.07173550873994827, -0.05821409448981285, -0.03021731786429882, 0.0185733363032341, -0.014391953125596046, -0.0018029266502708197, -0.0231131911277771, 0.045455556362867355, 0.0850570797920227, 0.048794373869895935, -0.040457699447870255, -0.04749450832605362, -0.03149893134832382, -0.08556331694126129, -0.024907365441322327, -0.007567987777292728, -0.015045259147882462, -0.017774799838662148, -0.008255686610937119, 0.04605802148580551, -0.009495370090007782, 0.017819561064243317, -0.006205803714692593, 0.0014824394602328539, 0.08601824194192886, -0.009120051749050617, 0.03796977549791336, -0.035066619515419006, -0.029216794297099113, -0.036394789814949036, -0.009982170537114143, -0.05488971620798111, 0.03251844272017479, -0.026897136121988297, -0.06292621046304703, 0.06425982713699341, -0.02659916877746582, -0.02197241224348545, 0.05790024250745773, 0.0031982162036001682, 0.04184477776288986, 0.018925484269857407, -0.013780851848423481, 0.03057710826396942, 0.0671100988984108, 0.011627939529716969, 0.02319742552936077, 0.03234363719820976, 0.032751526683568954, -0.04675256833434105, 0.03062143363058567, -0.004196377005428076, 0.003952890634536743, -0.039701975882053375, -0.041680388152599335, -0.06245530769228935, 0.06751307845115662, -0.013899006880819798, -0.037591755390167236, 0.0061963205225765705, 0.031429972499608994, -0.052338194102048874, 0.024119429290294647, 0.00553949223831296, -0.032957445830106735, 0.01082915160804987, 0.021289369091391563, -0.02948407270014286, -0.04938436299562454, 0.020246412605047226, -0.005233949050307274, -0.01350374799221754, 0.006954419892281294, 0.00715950783342123, 0.016249997541308403, -0.0038435556925833225, 0.00022073544096201658, 0.04679064452648163, -0.012889305129647255, -0.029393794015049934, 0.04832395911216736, 0.01115973386913538, -0.06278558075428009, 0.017591362819075584, 0.04269150644540787, -0.008189630694687366, 0.009853998199105263, -0.0376465767621994, -0.0029574690852314234, 0.04798922315239906, 0.0160030797123909, 0.018540645018219948, -0.05455625057220459, -0.049155157059431076, -0.006113272625952959, -0.012690669856965542, -0.0002787903940770775, -0.03757750615477562, 0.07517111301422119, -0.09488648176193237, -0.01936456747353077, -0.01102839782834053, 0.025617346167564392, 0.02214231714606285, 0.05776476860046387, -0.006642058491706848, 0.003740462940186262, -0.04927419498562813, -0.010997667908668518, 0.019337182864546776, -0.010943859815597534, 0.017630690708756447, -0.04085894301533699, 0.0051081618294119835, -0.040379270911216736, -0.0449848547577858, -0.08676891028881073, -0.022338207811117172, -0.004754798486828804, -0.006259955000132322, 0.01879570446908474, 0.013907489366829395, -0.008434765972197056, 0.0005588839994743466, 0.006028648931533098, -0.013201367110013962, -0.0344214104115963, -0.005557538941502571, -0.03622346743941307, -0.006625581998378038, -0.045623064041137695, 0.013816876336932182, -0.021017784252762794, -0.041023317724466324, 0.025059808045625687, -0.017095649614930153, 0.00838613510131836, -0.006657732184976339, 0.054338835179805756, 0.04855628311634064, -0.03518000245094299, 0.060593146830797195, 0.02229340746998787, 0.05297158658504486, 0.05448509380221367, -0.017185645177960396, -0.03472885861992836, 0.0009753714548423886, -0.023103253915905952, -0.02001424878835678, -0.0181244146078825, 0.05710400640964508, -0.022320130839943886, -0.003042033640667796, -0.004575806669890881, 0.006271864753216505, 0.0013934429734945297, -0.021403897553682327, 0.01493204478174448, -0.010596576146781445, 0.005411155056208372, 0.026137204840779305, 0.041772518306970596, 0.024464476853609085, -0.05971800535917282, -0.018283793702721596, -0.02221061661839485, 0.011541721411049366, -0.016766319051384926, -0.022254914045333862, -0.000490478181745857, -0.0014010309241712093, 0.0335455983877182, 0.026682058349251747, 0.012206930667161942, -0.047231484204530716, 0.0023269879166036844, 0.011051745153963566, 0.006118857767432928, -0.014621402136981487, -0.009049680083990097, 0.05732087045907974, 0.025354180485010147, -0.013478239066898823, -0.0064832172356545925, -0.00007354931585723534, -0.054838839918375015, 0.08763805776834488, -0.011185439303517342, 0.052311528474092484, 0.010429165326058865, 0.034677255898714066, 0.012485324405133724, -0.021950654685497284, 0.0298480037599802, -0.00011496114893816411, -0.004194461740553379, 0.04008576646447182, 0.03914261981844902, 0.047985706478357315, 0.03725656121969223, -0.05728890746831894, 0.03036644123494625, -0.0018952422542497516, 0.024660566821694374, 0.029467258602380753, -0.04064849764108658, -0.028029857203364372, -0.011908777058124542, 0.027432642877101898, -0.011649558320641518, -0.022846370935440063, -0.05961883068084717, -0.013886638917028904, 0.04881993308663368, 0.01827208325266838, 0.025804579257965088, -0.054333485662937164, -0.021251510828733444, -0.03373080864548683, -0.048500169068574905, 0.034714728593826294, 0.004263799171894789, -0.01782730594277382, 0.0086970841512084, -0.027404941618442535, 0.014792677946388721, 0.06547337770462036, -0.029658634215593338, -0.0027167368680238724, 0.013644561171531677, -0.02586747705936432, 0.03642928972840309, 0.006222086492925882, 0.044242601841688156, -0.04220239818096161, 0.0795639306306839, 0.02902178280055523, -0.006758042145520449, 0.019534854218363762, 0.0051614996045827866, 0.11158468574285507, -0.019644485786557198, -0.007142212241888046, -0.02431035414338112, -0.0055521409958601, 0.012797562405467033, -0.0022212876938283443, 0.009817525744438171, -0.007326195482164621, -0.0019784579053521156, -0.021065564826130867, -0.0403381809592247, -0.06434766203165054, -0.008217357099056244, 0.042980797588825226, -0.0074296067468822, -0.08155118674039841, -0.0019216981017962098, 0.004690864589065313, 0.02295178361237049, 0.0019020165782421827, -0.06327766180038452, -0.011984340846538544, -0.044910646975040436, -0.03521037474274635, -0.05557088181376457, -0.004532972816377878, -0.0033951341174542904, 0.014095650054514408, -0.04804644361138344, -0.02554040029644966, -0.08350559324026108, 0.009873856790363789, -0.0099791893735528, -0.018470177426934242, -0.0013273576041683555, 0.036835476756095886, 0.007792673073709011, -0.013363536447286606, 0.0001361941103823483, 0.04454071819782257, -0.06385190039873123, -0.05384764075279236, -0.03701533004641533, -0.009782182984054089, -0.06152193248271942, 0.017857806757092476, 0.0211136806756258, 0.0174765195697546, 0.04398362338542938, 0.03820432722568512, 0.025687195360660553, -0.08459534496068954, -0.01466267742216587, -0.010820201598107815, 0.015755435451865196, -0.015392742119729519, 0.020009707659482956, -0.03612290695309639, -0.022432969883084297, -0.00404181657359004 ]
<p>I took an empty clear sphere with radius r, put some weight inside this sphere, and put in into the water. I calculate the buoyancy force as:</p> <p>Volume of the sphere = Volume of the water displaced (Vdisplaced) = (4/3)<em>pi</em>(r^3); Weight of the displaced water = Buoyancy force (B) = Vdisplaced * density of water; Wtotal= Wsphere + Wweight;</p> <p>Then, the sphere will float when Buoyancy (B) > Wtotal, otherwise it will sink. I assume that I am right so far?? So the air inside the sphere will affect sphere's ability to float. My confusion is that I assume that I have already considered this effect during the aforementioned calculations (since density of the sphere itself is low). Is that right? Please note that the sphere is not flexible. </p>
g8361
[ 0.017430828884243965, 0.021104080602526665, 0.00962917786091566, 0.00934319943189621, 0.007735168561339378, 0.08998111635446548, 0.07492522895336151, 0.0009376236121170223, -0.051116932183504105, -0.019278664141893387, 0.0029239857103675604, 0.06987730413675308, -0.005534270778298378, -0.00034183223033323884, -0.022417573258280754, 0.08952310681343079, 0.049768224358558655, -0.012735861353576183, 0.0025366167537868023, 0.0011365421814844012, -0.002689300337806344, -0.013019714504480362, -0.04132897034287453, -0.0008162923040799797, -0.054125770926475525, 0.00993560254573822, 0.03808213025331497, 0.04789896681904793, -0.031591277569532394, 0.011096970178186893, 0.009405318647623062, 0.04907283931970596, -0.0361720472574234, -0.04404696822166443, -0.021689651533961296, 0.008507349528372288, 0.0348454974591732, -0.004930910188704729, 0.005020814947783947, -0.04457056522369385, 0.029156984761357307, 0.02012883685529232, 0.02710658684372902, 0.03120492585003376, -0.04468479007482529, 0.010073999874293804, 0.0039116861298680305, 0.03617392107844353, -0.03004453517496586, -0.10421508550643921, -0.015094163827598095, -0.014135884121060371, -0.05810396000742912, -0.02258671447634697, -0.023668067529797554, -0.0008321331115439534, 0.02529873140156269, -0.0313822366297245, -0.006758205126971006, 0.03475663810968399, 0.011161609552800655, 0.019968507811427116, -0.03445319086313248, 0.020834947004914284, 0.028105027973651886, 0.003096454543992877, -0.061931729316711426, -0.06098998710513115, -0.011576238088309765, -0.0007221564301289618, 0.022528257220983505, -0.002575986785814166, -0.03301900997757912, -0.10059195011854172, -0.07677924633026123, 0.026560718193650246, -0.00034509552642703056, 0.0021131790708750486, 0.04715053737163544, -0.03407517075538635, -0.02006113901734352, -0.00805843248963356, 0.0497877337038517, 0.014903544448316097, 0.04783809557557106, -0.011611740104854107, -0.034709274768829346, -0.02182953990995884, 0.019889619201421738, -0.022499026730656624, -0.008646409027278423, -0.046243902295827866, 0.07554500550031662, 0.03587791696190834, -0.008490738458931446, -0.05046950653195381, -0.0030712787993252277, 0.026792436838150024, -0.05626779422163963, 0.029886966571211815, -0.0029542145784944296, -0.013905818574130535, 0.033898040652275085, -0.014369424432516098, -0.004294003825634718, 0.013378167524933815, 0.10036633163690567, 0.051652662456035614, 0.010373853147029877, 0.0018706477712839842, -0.04405665770173073, -0.06786955893039703, 0.02401120401918888, 0.007074352819472551, -0.04709860309958458, -0.06620820611715317, 0.03160398080945015, -0.0008427514112554491, 0.002747800201177597, 0.02282555215060711, -0.009639812633395195, 0.05513053014874458, 0.08424297720193863, 0.04307829961180687, -0.009512833319604397, -0.04944704473018646, -0.022165795788168907, 0.02132369764149189, 0.02478964626789093, -0.039651770144701004, 0.04690602421760559, -0.003735665464773774, -0.040686313062906265, 0.035555511713027954, -0.0013939115451648831, -0.0545305497944355, -0.014746231026947498, -0.03689536824822426, -0.00686541898176074, -0.04485531896352768, 0.020068354904651642, 0.0324462354183197, 0.03381301090121269, -0.02628590166568756, -0.045705076307058334, -0.020406551659107208, 0.03309497982263565, -0.02451634779572487, -0.003823992796242237, 0.006534578278660774, 0.03281677886843681, 0.0351056307554245, 0.01130638550966978, -0.03341589495539665, 0.05721547082066536, -0.04987696185708046, 0.06120755150914192, -0.005330678541213274, 0.03851843997836113, 0.021129203960299492, 0.06144217774271965, 0.09170568734407425, 0.0483064278960228, 0.03931308537721634, -0.04676147177815437, 0.08201397955417633, 0.00838007964193821, -0.04900643974542618, -0.05328276753425598, -0.05879305303096771, -0.04345337301492691, -0.03383003547787666, -0.030487066134810448, 0.04020468145608902, 0.014759328216314316, -0.03968074917793274, 0.06439720094203949, 0.0032153462525457144, 0.001167338341474533, 0.06266055256128311, -0.017093366011977196, 0.004954387899488211, -0.014749333262443542, -0.018708467483520508, -0.051350608468055725, 0.01784035749733448, 0.0653427317738533, -0.020920254290103912, -0.060416266322135925, 0.010544275864958763, -0.033037278801202774, 0.05708806589245796, -0.01947821117937565, 0.042718466371297836, -0.013030468486249447, -0.017271149903535843, 0.08803621679544449, -0.0016784877516329288, -0.020595833659172058, 0.03774973005056381, -0.00615824107080698, 0.006509488448500633, 0.04977972432971001, 0.021890662610530853, 0.02814301662147045, -0.0052331374026834965, 0.003664596239104867, -0.009937404654920101, 0.02026321552693844, -0.006344061344861984, 0.05158911272883415, -0.013065638020634651, 0.05174650624394417, -0.03601919487118721, 0.05539819598197937, 0.08253754675388336, -0.07734216749668121, 0.0659710168838501, -0.032107654958963394, -0.020114107057452202, -0.02205042354762554, 0.017921052873134613, 0.002907105255872011, 0.012896138243377209, -0.0413714274764061, 0.012453236617147923, -0.04358617216348648, -0.05054324492812157, 0.012289663776755333, -0.005077690351754427, 0.0013737424742430449, -0.04289308935403824, 0.03982320427894592, -0.016967466101050377, 0.027061333879828453, 0.08968602865934372, -0.03623087704181671, 0.013187665492296219, 0.03089258074760437, 0.018773553892970085, -0.000040681792597752064, 0.0029711134266108274, -0.01662690006196499, -0.030702073127031326, 0.02295798249542713, -0.037167031317949295, -0.01976226642727852, -0.04576845094561577, 0.03177834674715996, 0.03608310595154762, 0.012654984369874, 0.017324546352028847, 0.01464155875146389, 0.02640371024608612, -0.007771690841764212, 0.053185559809207916, -0.08428039401769638, -0.015954792499542236, -0.0063518197275698185, -0.024874132126569748, 0.013788827694952488, -0.03274999186396599, -0.019598338752985, 0.018463367596268654, -0.08377134054899216, -0.018403908237814903, -0.06008022278547287, 0.03549053147435188, 0.10333985835313797, 0.015960996970534325, -0.014678851701319218, 0.04043617099523544, 0.05222775787115097, 0.0934177041053772, 0.026070183143019676, 0.0027024068403989077, -0.0584496445953846, 0.036910347640514374, 0.04121067374944687, 0.02754802815616131, -0.01194905024021864, 0.026545658707618713, -0.07540350407361984, 0.06998464465141296, 0.0432005412876606, -0.03718749061226845, 0.0024103582836687565, -0.0019041979685425758, -0.01623888872563839, -0.04916762188076973, 0.029963981360197067, 0.04153861477971077, -0.0012555629946291447, -0.015457401983439922, 0.0450674407184124, 0.038383256644010544, 0.04064362496137619, 0.0040094200521707535, -0.019617600366473198, 0.07753239572048187, -0.01742596924304962, 0.006925807800143957, 0.03549668565392494, 0.010926337912678719, -0.03281287103891373, 0.03220289200544357, -0.008517351932823658, -0.06257915496826172, -0.014976819977164268, -0.00019041512859985232, -0.07608768343925476, 0.04676716402173042, -0.07293252646923065, -0.044457726180553436, -0.03067316673696041, -0.028199689462780952, -0.0184385534375906, -0.02521689422428608, -0.03659897670149803, 0.012505963444709778, 0.0022065481171011925, 0.004735162481665611, -0.012962148524820805, 0.014253023080527782, 0.006539580877870321, 0.033033162355422974, -0.00911774206906557, -0.03859782591462135, -0.04833471402525902, -0.020551621913909912, -0.011590278707444668, 0.0017698659794405103, -0.03213595971465111, -0.030058125033974648, -0.05825594440102577, 0.018593549728393555, 0.026663657277822495, 0.01376494113355875, -0.02094314433634281, 0.002924347762018442, 0.011975900270044804, -0.0939958393573761, 0.02520083822309971, -0.03806668519973755, -0.034035343676805496, 0.00416386965662241, 0.003956619184464216, -0.0017674528062343597, -0.011637561954557896, 0.012917572632431984, 0.059320852160453796, -0.033341363072395325, 0.0417131632566452, -0.06629734486341476, 0.03455052152276039, 0.008701665326952934, 0.058293286710977554, 0.007161778397858143, -0.028706351295113564, 0.01141306385397911, -0.019014941528439522, -0.058884602040052414, 0.018515991047024727, 0.05053245276212692, -0.0650818794965744, -0.020214281976222992, -0.0017841586377471685, 0.034159641712903976, -0.05258336663246155, -0.014984051696956158, -0.008276459760963917, -0.052009012550115585, -0.028967691585421562, -0.004641630686819553, 0.04352105036377907, -0.019923990592360497, 0.06546781212091446, 0.0077432687394320965, -0.0014144708402454853, -0.012396764941513538, 0.08359450846910477, 0.011421232484281063, -0.000844060443341732, -0.009216723032295704, -0.016886454075574875, 0.05561027303338051, -0.04378136247396469, 0.007967143319547176, 0.0025945953093469143, -0.03534391149878502, -0.07234895974397659, -0.02356421947479248, 0.004692479502409697, 0.03816483914852142, 0.04250364378094673, -0.02234678901731968, -0.013100221753120422, -0.024339841678738594, -0.030979108065366745, -0.010238057933747768, -0.004966139793395996, -0.003919415641576052, -0.03729061782360077, 0.023092323914170265, 0.03437044471502304, 0.03790571168065071, 0.0656152218580246, -0.06397352367639542, -0.03953640162944794, -0.027018986642360687, 0.05526353046298027, 0.02744254469871521, -0.05189874768257141, -0.047918226569890976, -0.05503762140870094, 0.0009896300034597516, -0.01599252223968506, 0.04789242893457413, -0.04793273285031319, 0.01818983256816864, 0.01334230974316597, 0.020675871521234512, -0.033261191099882126, -0.016484949737787247, -0.04272467643022537, -0.008974827826023102, 0.00753438426181674, -0.014357080683112144, 0.05744786560535431, -0.04845971614122391, -0.028546476736664772, 0.026565873995423317, 0.02909008227288723, 0.02384444698691368, 0.008342013694345951, 0.0614168681204319, 0.032082851976156235, 0.006275502499192953, -0.017055777832865715, -0.014081347733736038, 0.025820918381214142, 0.02387460693717003, -0.05048568174242973, -0.03906629607081413, 0.015344233252108097, 0.006229712162166834, -0.04431845247745514, -0.020634887740015984, 0.05515889823436737, 0.012593179009854794, -0.004426838364452124, -0.04410843551158905, 0.057131826877593994, -0.028198622167110443, -0.03859714791178703, 0.027934296056628227, -0.03125317394733429, 0.0002636805293150246, -0.06979182362556458, -0.006490394938737154, -0.04768699035048485, -0.021512268111109734, -0.018178196623921394, 0.006409822963178158, 0.01855129934847355, -0.01586771570146084, 0.011492583900690079, 0.011435732245445251, 0.012560755014419556, -0.005100876558572054, 0.015018506906926632, 0.018144167959690094, 0.04383731633424759, 0.03924254700541496, -0.005092750769108534, 0.04912140592932701, 0.008962934836745262, -0.05091739445924759, 0.07488135248422623, -0.043993301689624786, 0.0006759524112567306, -0.022621508687734604, -0.006064369343221188, 0.040387850254774094, -0.020107580348849297, 0.04366433620452881, 0.006316098850220442, 0.04495738446712494, 0.004192433785647154, 0.02603042870759964, -0.03463197499513626, -0.004540745634585619, -0.04517679661512375, 0.01722228340804577, 0.002927982248365879, 0.026818981394171715, -0.02038606069982052, 0.0035781420301645994, -0.04600629583001137, 0.01182823721319437, -0.0015100387390702963, -0.03526465594768524, 0.0680856704711914, -0.0027173308189958334, -0.03167771175503731, 0.0062549118883907795, 0.007338397204875946, 0.04251469299197197, 0.04463902488350868, 0.021639656275510788, -0.0028079228941351175, 0.0217392910271883, 0.002336999401450157, -0.015713009983301163, 0.019216090440750122, -0.031440626829862595, 0.013263257220387459, 0.009610763750970364, 0.005862602032721043, 0.03288188576698303, 0.02573331631720066, -0.026777369901537895, 0.017592424526810646, 0.009987160563468933, -0.001427762326784432, 0.0108517836779356, -0.03742152079939842, -0.042467519640922546, 0.015300732105970383, 0.0395684577524662, -0.006954859476536512, 0.023993317037820816, 0.06452230364084244, -0.009846017695963383, -0.00006681953527731821, -0.045099008828401566, -0.0021505968179553747, -0.043202824890613556, 0.08066775649785995, -0.003880184143781662, -0.012447305954992771, 0.008784311823546886, 0.008665700443089008, 0.02643953450024128, -0.005975906737148762, 0.013216547667980194, -0.04975515604019165, -0.019240852445364, 0.09287107735872269, -0.011964029632508755, -0.011551517993211746, 0.013366114348173141, -0.06556568294763565, 0.029729323461651802, -0.024864928796887398, -0.005583043675869703, -0.01945457048714161, -0.01574113592505455, -0.017048299312591553, -0.012518920935690403, 0.011624107137322426, 0.030450068414211273, -0.008385189808905125, -0.03599226474761963, 0.016375327482819557, -0.01822851225733757, -0.0018346485449001193, 0.04611048847436905, 0.024181734770536423, 0.03558029234409332, -0.06330616027116776, -0.03952962905168533, 0.0358503982424736, -0.06317662447690964, 0.04834473505616188, 0.04728444293141365, 0.011392398737370968, 0.033036600798368454, -0.007295430172234774, 0.012880148366093636, 0.034952640533447266, -0.034116193652153015, 0.059400904923677444, -0.08896400779485703, 0.01678599789738655, 0.026300089433789253, -0.06920371949672699, -0.04228843003511429, 0.008605031296610832, -0.0560106597840786, -0.018987875431776047, -0.024955367669463158, 0.006655080243945122, -0.04307345673441887, -0.024775933474302292, 0.006264441180974245, -0.01531597413122654, 0.0021387436427176, -0.01687484420835972, -0.006910192780196667, 0.04773490130901337, 0.0030435642693191767, 0.01896391063928604, -0.07137731462717056, 0.009232706390321255, -0.04350464791059494, 0.013486405834555626, -0.027493895962834358, -0.012089652940630913, -0.0026685611810535192, -0.0672227069735527, 0.023030372336506844, 0.07098940759897232, -0.023027606308460236, 0.008325590752065182, -0.0713631883263588, 0.08346695452928543, -0.005383357405662537, -0.01894049346446991, -0.01509144064038992, -0.03381311893463135, -0.056968286633491516, 0.004899711348116398, -0.07426910102367401, 0.07468915730714798, 0.044791508466005325, -0.03903566673398018, -0.0048620253801345825, -0.013472333550453186, 0.008375100791454315, 0.006658317521214485, -0.051815517246723175, 0.05820603668689728, 0.0017670681700110435, -0.0006738505326211452, 0.046809032559394836, -0.0011970995692536235, 0.038410503417253494, 0.01112847588956356, 0.008038216270506382, -0.024163363501429558, 0.032517094165086746, -0.02294572815299034, 0.019912905991077423, -0.04218097776174545, 0.039766550064086914, 0.036270592361688614, 0.011903426609933376, -0.020617587491869926, 0.0027203711215406656, 0.04357477277517319, 0.00933171808719635, 0.014829910360276699, 0.0473455935716629, -0.009141195565462112, -0.03303315117955208, -0.061058416962623596, -0.004340083803981543, -0.019346414133906364, 0.011197744868695736, -0.029162408784031868, 0.0015055326512083411, -0.03758874908089638, 0.03231607377529144, -0.014265351928770542, 0.02998410165309906, -0.010015794076025486, -0.0395699143409729, 0.03200880438089371, -0.013072758913040161, -0.013840924948453903, -0.03616810962557793, -0.03886985033750534, -0.00021640541672240943, 0.007180086337029934, 0.021493174135684967, -0.0377538725733757, 0.005625793244689703, 0.030613547191023827, 0.06614311039447784, -0.038917314261198044, 0.020290544256567955, -0.06081554666161537, 0.058476220816373825, -0.0638127252459526, 0.014203638769686222, -0.03309663012623787, -0.0035755608696490526, 0.021776210516691208, 0.005627364385873079, 0.020966852083802223, 0.029570570215582848, -0.031061062589287758, 0.050129808485507965, -0.048498719930648804, 0.02757588028907776, 0.10858405381441116, -0.008887485601007938, 0.057859960943460464, 0.01847044937312603, -0.009315340779721737, -0.00821629911661148, -0.025545964017510414, -0.022684333845973015, 0.023784328252077103, -0.022412467747926712, -0.007879791781306267, 0.02020074799656868, 0.006794079672545195, -0.03948256000876427, 0.05782362073659897, -0.007732890546321869, 0.02439180575311184, -0.05951767414808273, -0.008683697320520878, -0.02779858373105526, -0.022183984518051147, -0.019816314801573753, -0.02617831900715828, -0.025019124150276184, -0.025681832805275917, 0.024216532707214355, 0.02695111371576786, -0.07620064914226532, -0.030965469777584076, -0.044087495654821396, -0.06276535242795944, 0.016774427145719528, -0.0024425871670246124, 0.018843546509742737, -0.022498924285173416, -0.04249976575374603, -0.029715539887547493, -0.031874317675828934, 0.06662052124738693, 0.03390306979417801, 0.03907981887459755, 0.004887241404503584, 0.03938564658164978, 0.005446595139801502, -0.003829906228929758, 0.028310975059866905, 0.03314508497714996, -0.041657455265522, 0.0370844267308712, -0.010085889138281345, -0.017720434814691544, 0.009250983595848083, 0.06856976449489594, -0.02263854630291462, 0.01035876665264368, 0.012835055589675903, 0.008833915926516056, -0.0027099871076643467, -0.005462812725454569, -0.04360399767756462, -0.03900245204567909, -0.007108618970960379, 0.015511423349380493, -0.05873434618115425, -0.05406367778778076, -0.01750977151095867, 0.017034633085131645, 0.03345967456698418, -0.008129969239234924, -0.0011237075086683035, -0.004781872034072876, 0.07233978807926178 ]
<p>Could anyone suggest where can I find absorption spectra &amp; refractive index of Glycerol?</p> <p>I am specifically interested in UV range, 200-400nm, everything I was able to find out was for standard conditions only...</p> <p>Is there any software which can get these parameters through simulation?</p>
g8362
[ -0.013898897916078568, -0.006000618450343609, 0.01130847167223692, 0.016116494312882423, -0.01788792572915554, 0.00611763633787632, 0.012786353006958961, 0.0018362401751801372, -0.05722816288471222, 0.004011767916381359, 0.05762048065662384, 0.015945862978696823, 0.054199185222387314, 0.00007386886863969266, 0.05272675305604935, -0.0004389306122902781, 0.003485561115667224, 0.023709066212177277, -0.015011582523584366, 0.029301533475518227, -0.05060546100139618, -0.02507983334362507, -0.06356766819953918, -0.027345551177859306, -0.05897078663110733, 0.0668306052684784, -0.02100873738527298, 0.037868425250053406, -0.032054878771305084, 0.010799162089824677, -0.053669918328523636, -0.00024399117683060467, -0.02135603502392769, 0.003307717153802514, 0.029628178104758263, 0.020436173304915428, 0.038030173629522324, 0.00826273299753666, 0.039387062191963196, -0.025428425520658493, 0.006516557652503252, 0.027981311082839966, 0.017899805679917336, 0.0819927230477333, 0.039942897856235504, 0.012865042313933372, 0.0014251158572733402, -0.012358381412923336, 0.007429057732224464, -0.04196729511022568, 0.02862413041293621, 0.042061127722263336, 0.044822417199611664, 0.013126001693308353, -0.012381641194224358, 0.013977973721921444, -0.06135588139295578, 0.0013725901953876019, 0.007909996435046196, -0.01791098713874817, 0.018574338406324387, 0.030275745317339897, 0.015667017549276352, 0.008121395483613014, -0.021860415115952492, -0.01147489994764328, 0.019925350323319435, -0.028744226321578026, 0.023133208975195885, -0.02360299415886402, 0.06548918783664703, 0.01973791792988777, 0.019542982801795006, 0.021946655586361885, 0.009593939408659935, -0.04605864733457565, -0.031762827187776566, -0.015565038658678532, 0.0027209834661334753, 0.04706665500998497, -0.03397072106599808, 0.0028513753786683083, -0.011904008686542511, -0.02126246877014637, -0.036855489015579224, -0.01637490838766098, -0.019398372620344162, 0.028781382367014885, 0.0428667813539505, 0.012466492131352425, 0.013899663463234901, 0.029017919674515724, 0.03366927057504654, 0.007082815747708082, 0.08098385483026505, 0.01338848564773798, -0.042701300233602524, 0.0580265149474144, -0.004342539701610804, -0.06169596314430237, 0.0060138399712741375, -0.022758247330784798, 0.015568657778203487, 0.030507182702422142, -0.01553348544985056, -0.01066777016967535, 0.018495265394449234, -0.03921176865696907, 0.0018960174638777971, 0.00549990963190794, -0.02327350154519081, 0.0097916629165411, -0.004283362999558449, -0.03720678761601448, -0.02878718450665474, -0.027071969583630562, 0.04113007336854935, -0.018721122294664383, 0.017440032213926315, 0.04242851585149765, 0.04902588948607445, 0.06316979974508286, 0.009612839668989182, 0.04862704500555992, 0.05628863722085953, 0.03075234405696392, 0.04500735178589821, -0.007549910340458155, 0.01659577526152134, 0.032467421144247055, 0.004387421067804098, -0.06753335893154144, -0.050004713237285614, 0.029349032789468765, 0.023493263870477676, -0.010392839089035988, 0.034917764365673065, 0.012041337788105011, -0.052390266209840775, -0.027536572888493538, 0.006946614943444729, 0.038587454706430435, -0.023916704580187798, -0.03941712528467178, 0.003520122030749917, -0.06371143460273743, -0.01763877458870411, -0.003574791830033064, 0.009884512051939964, -0.052341364324092865, 0.023961327970027924, 0.010785573162138462, 0.0914299413561821, 0.0015170122496783733, 0.001185392844490707, -0.038304876536130905, -0.031019482761621475, 0.0021739311050623655, 0.0375182069838047, 0.037383053451776505, 0.0007786150090396404, -0.02558639831840992, 0.024542387574911118, -0.0019529000855982304, -0.07279152423143387, 0.010692725889384747, -0.012996207922697067, -0.013288002461194992, 0.06825076788663864, -0.046544112265110016, -0.03473197668790817, -0.02435866929590702, 0.0589929036796093, 0.025207355618476868, 0.0222379919141531, 0.04431478679180145, 0.030264373868703842, 0.021483369171619415, -0.014323282055556774, 0.05201385170221329, -0.005678319372236729, -0.013218005187809467, 0.030900148674845695, -0.06906583905220032, 0.020642442628741264, -0.03928714245557785, 0.011447951197624207, -0.051709044724702835, -0.042762260884046555, 0.013025214895606041, 0.000859743682667613, 0.03839937970042229, 0.031470682471990585, -0.01383236050605774, 0.03944190964102745, 0.02041301503777504, 0.03662976622581482, -0.05660533159971237, -0.06284242868423462, 0.04533827677369118, -0.07448986172676086, -0.004086264409124851, -0.00906975194811821, 0.04703216999769211, -0.026046816259622574, -0.020387496799230576, 0.0218216460198164, 0.015684964135289192, 0.015291709452867508, -0.04737601801753044, -0.058042798191308975, 0.014973308891057968, -0.04164942353963852, -0.026242302730679512, 0.008638872765004635, 0.06265095621347427, -0.04947488754987717, 0.01782996766269207, 0.02456161379814148, 0.0002455763751640916, 0.00924738496541977, 0.01486115250736475, 0.002229265868663788, 0.09962556511163712, -0.01577545329928398, -0.008453572168946266, -0.035852231085300446, 0.0856056809425354, 0.10029181838035583, -0.006808261852711439, -0.03564442694187164, -0.022466711699962616, 0.023097509518265724, -0.05334900692105293, -0.017924489453434944, 0.050525713711977005, -0.1071547269821167, -0.027602456510066986, -0.010803140699863434, -0.043920744210481644, 0.0060695926658809185, 0.02153540775179863, -0.03184697777032852, 0.01919899880886078, -0.06312167644500732, 0.04071744903922081, 0.034488607197999954, -0.0075729480013251305, 0.04333284869790077, 0.018490148708224297, -0.0121093625202775, 0.04316846281290054, 0.01690489985048771, 0.04066121205687523, -0.017921600490808487, 0.020624248310923576, -0.03728875517845154, -0.027411872521042824, 0.028453929349780083, 0.014863523654639721, -0.04693493992090225, 0.018720686435699463, 0.02933819219470024, -0.0017217760905623436, 0.0038767969235777855, 0.015020926482975483, -0.037908319383859634, -0.024674754589796066, 0.005476063117384911, -0.023024126887321472, 0.038226693868637085, -0.03914034366607666, -0.009188652969896793, -0.0016672525089234114, 0.024894336238503456, -0.007154890336096287, 0.008954279124736786, 0.0068973456509411335, 0.004632174968719482, -0.00735133420675993, -0.06372769176959991, -0.08314482122659683, 0.017356330528855324, 0.021522467955946922, 0.0027230288833379745, 0.03520645946264267, 0.020829733461141586, 0.061599310487508774, 0.04751124605536461, -0.06296250224113464, -0.0033434578217566013, 0.007473190315067768, -0.02093052677810192, 0.017320189625024796, -0.10413448512554169, 0.05511559918522835, 0.037227313965559006, 0.024393703788518906, 0.008827627636492252, 0.06785159558057785, 0.011671248823404312, -0.057753294706344604, 0.003520395141094923, 0.013796859420835972, -0.09042110294103622, -0.030796300619840622, -0.08684676140546799, -0.03644431009888649, 0.021175365895032883, 0.07449065148830414, -0.01897062361240387, -0.03406118229031563, -0.05988746136426926, 0.04147345572710037, 0.05122359097003937, 0.00978535134345293, -0.011911647394299507, -0.044552162289619446, -0.03263503685593605, -0.015867769718170166, 0.01934926211833954, -0.04045036807656288, 0.01660270430147648, 0.020255468785762787, -0.004084683023393154, 0.006062294822186232, -0.03604290634393692, -0.014156721532344818, 0.008442271500825882, -0.07188617438077927, 0.008120384998619556, 0.01049256045371294, -0.012710469774901867, 0.0830870270729065, -0.033144161105155945, 0.005597786512225866, -0.07405868917703629, -0.026664553210139275, 0.005558377597481012, -0.022456973791122437, 0.017129555344581604, -0.03368150442838669, 0.008482960984110832, -0.048092346638441086, -0.05508077144622803, -0.08891977369785309, -0.03565541282296181, 0.009421284310519695, 0.0010475359158590436, -0.014893380925059319, 0.049876291304826736, -0.000410818203818053, -0.04618162289261818, -0.029333654791116714, -0.021302109584212303, 0.012016970664262772, 0.039552200585603714, -0.0010248555336147547, 0.033659204840660095, -0.013484353199601173, -0.01766141876578331, -0.01649555191397667, 0.04400942474603653, -0.04961109533905983, -0.016891811043024063, -0.005475933663547039, 0.058419860899448395, 0.035535652190446854, 0.02374184876680374, 0.044042374938726425, 0.019061144441366196, 0.013189159333705902, 0.028115013614296913, 0.0037654221523553133, -0.03743010759353638, -0.026886966079473495, 0.02787085808813572, 0.00816689059138298, 0.008463609032332897, 0.05730877444148064, -0.04043351113796234, -0.010342909954488277, 0.06438930332660675, 0.023414529860019684, -0.018467776477336884, -0.07651899009943008, 0.01957906223833561, -0.0042547485791146755, -0.022785453125834465, -0.020002854987978935, -0.008170872926712036, -0.07600414007902145, -0.033756323158741, 0.008955031633377075, 0.012923658825457096, -0.009999523870646954, 0.008496281690895557, -0.0300662349909544, -0.08025453239679337, 0.04680442810058594, 0.0021069995127618313, -0.0034445994533598423, -0.01322141382843256, 0.04325876384973526, -0.011724715121090412, 0.03346293419599533, -0.033958710730075836, -0.02716398797929287, -0.016694853082299232, 0.040778011083602905, 0.027372220531105995, 0.003775188932195306, 0.001962044509127736, -0.07233991473913193, 0.0010050937999039888, 0.05993439257144928, 0.024965617805719376, -0.03653935715556145, 0.03719513863325119, 0.013266775757074356, -0.029682841151952744, -0.016601109877228737, -0.041142210364341736, -0.0479079931974411, -0.06356821209192276, 0.06395033001899719, 0.053272806107997894, -0.026032034307718277, -0.01139280665665865, -0.029551275074481964, 0.04329632222652435, -0.05262076109647751, -0.009744678623974323, 0.021613428369164467, 0.009059621952474117, 0.051865823566913605, -0.012566693127155304, -0.04629605636000633, 0.04255208745598793, -0.01992756687104702, 0.03249716758728027, -0.014640090987086296, 0.07862123847007751, -0.04775422438979149, -0.045010656118392944, 0.026727503165602684, -0.04958764836192131, 0.013590201735496521, -0.03928187116980553, 0.01773100532591343, 0.0106855109333992, -0.04220331832766533, -0.02864377200603485, 0.006433066911995411, -0.018412811681628227, -0.008617541752755642, -0.03678864985704422, 0.01644163206219673, 0.041211530566215515, 0.011071017012000084, -0.02774529717862606, 0.0501166507601738, -0.010912196710705757, -0.020323876291513443, -0.01909048669040203, -0.002741963369771838, -0.022084984928369522, 0.04874806106090546, 0.02163432538509369, -0.012030319310724735, -0.013368497602641582, -0.018933512270450592, 0.06975837051868439, -0.057898424565792084, 0.02400859445333481, -0.021743550896644592, -0.04010096564888954, -0.027054844424128532, -0.014047074131667614, -0.008506734855473042, -0.037070319056510925, 0.0901932492852211, 0.06241096183657646, 0.05403372272849083, 0.011333364993333817, 0.022419672459363937, -0.02060757577419281, 0.04053933173418045, -0.0058913701213896275, -0.017276844009757042, -0.01294646505266428, -0.015782171860337257, 0.01216848660260439, -0.028069540858268738, 0.012275506742298603, -0.042956091463565826, 0.019978486001491547, -0.03938965126872063, -0.04645771160721779, 0.02993352897465229, 0.0022749414201825857, -0.038825005292892456, 0.00479412404820323, -0.009184008464217186, 0.03622373193502426, 0.02620689570903778, 0.056182894855737686, 0.02469550259411335, 0.019142819568514824, 0.03416256234049797, -0.010222796350717545, 0.012412709183990955, 0.02923307940363884, 0.037647418677806854, -0.033231623470783234, 0.01484950352460146, 0.004846432711929083, 0.09545698016881943, 0.007833760231733322, -0.05809139460325241, -0.041607193648815155, 0.0105429170653224, 0.00677458243444562, 0.036901768296957016, -0.01025615818798542, 0.04838747903704643, -0.002635003300383687, -0.02151196449995041, 0.05275142937898636, -0.041828807443380356, -0.010759247466921806, 0.00823232438415289, -0.034211814403533936, -0.08097877353429794, 0.08391762524843216, -0.03294879198074341, -0.053269609808921814, -0.0006419534329324961, -0.022656727582216263, 0.019872454926371574, -0.011971605941653252, 0.051533423364162445, -0.03246667981147766, 0.01932498626410961, -0.029259420931339264, 0.004650986287742853, 0.03125891461968422, 0.015819896012544632, 0.005321105010807514, 0.006473949179053307, 0.05592400208115578, -0.022358819842338562, 0.07072354853153229, 0.03383607789874077, 0.0245166327804327, 0.03019171580672264, -0.027145100757479668, 0.004900872707366943, -0.0032083182595670223, 0.02841717191040516, 0.03726082295179367, 0.06747918576002121, -0.020726202055811882, 0.029612362384796143, 0.008956262841820717, -0.03001837618649006, 0.003925117664039135, 0.015528039075434208, 0.024543238803744316, 0.0469498373568058, -0.06811758130788803, -0.07055240869522095, 0.025038009509444237, 0.011878855526447296, 0.09299515932798386, 0.030957330018281937, 0.019577382132411003, 0.010091911070048809, 0.014352294616401196, -0.04898736625909805, 0.025208985432982445, 0.015532254241406918, -0.016220686957240105, -0.010739421471953392, -0.06745922565460205, -0.04868330806493759, 0.03653957322239876, -0.0033119881991297007, -0.008234858512878418, -0.04876560717821121, 0.038750726729631424, -0.010430419817566872, -0.003448938252404332, -0.05616150423884392, 0.06350336223840714, -0.017247283831238747, -0.010091989301145077, 0.04188718646764755, -0.04452315717935562, -0.0072230021469295025, 0.0037336398381739855, -0.030726034194231033, 0.056754641234874725, -0.06773562729358673, 0.0014277213485911489, -0.06985178589820862, -0.0641026571393013, 0.0024367135483771563, 0.04712734743952751, 0.0010364687768742442, -0.012780007906258106, -0.02430018037557602, -0.00436005974188447, 0.005756236147135496, -0.022551188245415688, -0.05371404439210892, -0.040718596428632736, 0.019345983862876892, 0.023061441257596016, 0.02950589917600155, 0.010553549975156784, -0.03273436054587364, 0.04059319198131561, -0.04882374405860901, 0.023517876863479614, 0.05867500230669975, -0.04020646959543228, 0.014767413958907127, 0.012073185294866562, -0.014415297657251358, 0.09062765538692474, -0.00753332395106554, 0.04063912481069565, -0.0173004362732172, 0.06436538696289062, 0.0013448951067402959, -0.06561700254678726, -0.0029472270980477333, 0.0035178973339498043, 0.006883900612592697, 0.008948957547545433, -0.06571298837661743, 0.02189510315656662, 0.006181527394801378, 0.05262846127152443, 0.017606016248464584, 0.01571490429341793, -0.021004289388656616, 0.031984541565179825, 0.0014987974427640438, 0.043747153133153915, -0.054974913597106934, -0.00014019582886248827, -0.0021593021228909492, 0.010280339047312737, 0.060500241816043854, -0.02561003528535366, 0.019927315413951874, 0.017449483275413513, -0.03964588791131973, -0.029976539313793182, -0.037714507430791855, -0.02659609727561474, -0.03598026558756828, -0.0307588092982769, 0.044096723198890686, 0.03810666874051094, -0.026598375290632248, -0.004494218155741692, -0.008754282258450985, -0.02889750525355339, -0.015199374407529831, -0.006996577139943838, -0.044153790920972824, -0.02953985705971718, -0.004744756501168013, -0.08558148890733719, 0.029636289924383163, -0.02634129673242569, -0.018788186833262444, 0.00041649368358775973, 0.06095641106367111, 0.017338596284389496, 0.030538398772478104, -0.037467796355485916, 0.0033283354714512825, -0.007394908461719751, 0.028309622779488564, -0.026350272819399834, 0.0021791846957057714, -0.06852732598781586, 0.0007690670900046825, -0.01708918809890747, -0.08966939151287079, 0.00581159396097064, -0.06805697083473206, -0.000930731010157615, 0.039438825100660324, 0.010263181291520596, -0.028955280780792236, 0.04415299370884895, -0.03259080648422241, -0.028686750680208206, -0.022449588403105736, -0.04707818105816841, -0.01966991275548935, -0.014913362450897694, 0.005431794095784426, 0.06157880648970604, -0.010398251935839653, 0.036217041313648224, 0.02544180117547512, 0.007695028558373451, 0.04611723870038986, -0.003658524015918374, -0.02929762192070484, -0.06773840636014938, -0.04288404434919357, -0.06564993411302567, 0.0195684265345335, -0.01629342883825302, -0.04539940506219864, 0.023608826100826263, -0.006817793473601341, 0.004480244591832161, -0.05515711382031441, 0.005404174793511629, 0.06606661528348923, 0.03820066154003143, 0.021425889804959297, -0.0140362698584795, -0.03163124993443489, -0.07337450236082077, -0.06564338505268097, 0.0026963523123413324, 0.0742557942867279, 0.023567797616124153, -0.042567383497953415, 0.005981221795082092, 0.07644732296466827, 0.04539908096194267, -0.018076833337545395, -0.014454884454607964, 0.02265346050262451, -0.0014244933845475316, -0.06065340340137482, 0.012831754982471466, -0.03492637351155281, -0.0013083780650049448, -0.04411575570702553, -0.045709189027547836, 0.01747986301779747, 0.05000162124633789, 0.006968569941818714, 0.03169364854693413, -0.01934727095067501, 0.0721929594874382, -0.00827146414667368, -0.03996938467025757, 0.0036203903146088123, 0.041036419570446014, -0.02972792275249958, 0.011917181313037872, 0.06445910781621933, 0.011835461482405663, -0.01868031919002533, 0.03302300348877907, 0.014085005037486553 ]
<p>When a Electron gets promoted to the conduction band from valence band (In generation) lets say for example in Silicon at room temperature.</p> <p>Is there any way to determine (on average) how long it will last before falling back down in the hole it just left.</p> <p>What about with a Voltage Applied?</p> <p>Thanks</p>
g8363
[ 0.015802666544914246, -0.0014204184990376234, -0.01027810387313366, -0.03070582076907158, 0.045232564210891724, 0.0019002369372174144, 0.03161599859595299, -0.022995295003056526, 0.0075840577483177185, 0.03424897789955139, -0.026584114879369736, 0.13132159411907196, 0.011538738384842873, 0.04774252697825432, -0.01198914460837841, -0.06325586140155792, 0.028673583641648293, -0.018143227323889732, 0.03728323057293892, -0.02925521321594715, 0.004746804479509592, -0.018987154588103294, -0.03245376795530319, -0.04122842103242874, -0.008668770082294941, 0.017163705080747604, 0.0024571281392127275, 0.02443683333694935, 0.0052157496102154255, -0.005287356209009886, -0.032230451703071594, 0.042402755469083786, 0.05145002901554108, 0.01782648079097271, 0.007584469858556986, -0.022672703489661217, 0.008187728002667427, -0.010686888359487057, 0.020202258601784706, 0.014842716977000237, 0.04361642524600029, -0.07675282657146454, 0.031486086547374725, 0.0328255258500576, 0.002263300586491823, -0.006820647045969963, -0.046609893441200256, 0.020666923373937607, 0.021207090467214584, -0.0002189388615079224, -0.031922001391649246, 0.04385646805167198, 0.012099821120500565, 0.024673564359545708, -0.01764599233865738, -0.05769051983952522, -0.03659052029252052, -0.03198658302426338, 0.041816260665655136, 0.02948918752372265, -0.05517331510782242, 0.050642360001802444, -0.01903853751718998, -0.0013660447439178824, 0.05074521526694298, 0.02278883010149002, -0.061420079320669174, -0.0074040815234184265, -0.06996467709541321, 0.01745583303272724, -0.011365022510290146, -0.01616816036403179, 0.01927725039422512, -0.0034677376970648766, 0.0117451511323452, -0.0015810830518603325, -0.054749201983213425, 0.014699695631861687, 0.0548095703125, 0.0424763560295105, 0.008428073488175869, -0.038122162222862244, -0.0029997064266353846, 0.011269338428974152, 0.02043551579117775, 0.009881528094410896, 0.02241230197250843, 0.02946137823164463, -0.009167853742837906, 0.008972017094492912, 0.03175608068704605, -0.04121029004454613, 0.014728152193129063, -0.0036959510762244463, -0.00987122394144535, 0.015773415565490723, -0.025638312101364136, 0.026811661198735237, -0.0183907151222229, -0.03444858640432358, 0.01739364303648472, -0.03826171159744263, 0.029430855065584183, -0.037328820675611496, -0.027469715103507042, 0.02457498572766781, 0.006162744015455246, 0.009669098071753979, 0.05046701431274414, -0.023387141525745392, 0.009987576864659786, -0.03970503434538841, -0.07571641355752945, 0.02787424810230732, -0.07624679803848267, 0.007207662798464298, 0.02256287820637226, -0.05375676602125168, -0.03456490859389305, 0.0020837702322751284, -0.0270900409668684, 0.0204647034406662, -0.013892988674342632, 0.0180410947650671, 0.0226847305893898, 0.04343933239579201, 0.015092426910996437, 0.0031198852229863405, -0.041842538863420486, 0.03348039090633392, -0.0612565279006958, 0.0037339890841394663, 0.031011683866381645, 0.04827675223350525, 0.03854799270629883, -0.03427550941705704, 0.0685710608959198, 0.005038836970925331, 0.00500785605981946, -0.0011976462556049228, 0.00656857481226325, -0.05145664140582085, -0.0053437333554029465, -0.04817242920398712, -0.032802604138851166, -0.004246953409165144, 0.03025733307003975, 0.002345335204154253, 0.06167733296751976, 0.05361673980951309, 0.008802213706076145, 0.02993658371269703, -0.00009979168680729344, -0.11070260405540466, 0.0359610877931118, -0.05278408154845238, -0.007814555428922176, -0.014740628190338612, 0.010288634337484837, -0.022357312962412834, 0.04888138920068741, -0.04511846974492073, -0.013872475363314152, 0.00986930076032877, -0.058905601501464844, -0.05528203770518303, -0.0242962334305048, -0.021046195179224014, -0.01688324101269245, -0.05482693016529083, 0.017827199772000313, 0.013537252321839333, 0.06555882841348648, 0.008442840538918972, -0.01212063618004322, 0.037988901138305664, -0.03636547550559044, -0.035838980227708817, 0.04355160519480705, -0.010554984211921692, -0.01377233024686575, 0.0026886712294071913, 0.02912643924355507, -0.01355280913412571, -0.0006708108121529222, -0.03148004412651062, -0.0152275450527668, -0.006100857630372047, -0.07526212185621262, -0.027169624343514442, 0.0513540618121624, -0.011396742425858974, 0.030504051595926285, 0.009683477692306042, -0.07343577593564987, -0.03482834994792938, 0.05627255141735077, -0.04205787926912308, -0.012483826838433743, -0.04012095555663109, -0.0029142575804144144, 0.0009296705247834325, 0.036710675805807114, 0.0075934710912406445, 0.04596155509352684, -0.015041235834360123, 0.010123358108103275, -0.01672663539648056, -0.037375591695308685, 0.013630172237753868, 0.009754698723554611, 0.07376516610383987, -0.013792390003800392, 0.05839792639017105, -0.0059533934108912945, -0.005942207295447588, 0.004379844758659601, 0.04869699478149414, 0.008031319826841354, 0.022480273619294167, -0.05576089397072792, -0.01339788269251585, 0.02374044433236122, -0.011337154544889927, -0.023011868819594383, -0.0058091869577765465, 0.007237892597913742, 0.0799030289053917, -0.03874117136001587, 0.007937481626868248, -0.03989897295832634, 0.030496014282107353, -0.05818584933876991, -0.045022979378700256, 0.028144970536231995, 0.030400317162275314, -0.026989877223968506, -0.0349908284842968, -0.038675885647535324, -0.03252192586660385, 0.007209153845906258, -0.01069062389433384, -0.02959463559091091, 0.031048674136400223, -0.01556322444230318, -0.061641447246074677, 0.028378672897815704, -0.0042044175788760185, 0.012353497557342052, -0.02855900302529335, 0.010120436549186707, 0.0015651588328182697, -0.014560366049408913, 0.035954754799604416, -0.06197449564933777, 0.009775356389582157, -0.02289518527686596, 0.030734404921531677, 0.007828021422028542, -0.018493253737688065, -0.03901652991771698, 0.027824845165014267, 0.01745676063001156, -0.011341402307152748, 0.018925117328763008, -0.05795211344957352, 0.013147969730198383, -0.04647074639797211, -0.001918235095217824, 0.012470819056034088, 0.01593524031341076, 0.07462207227945328, 0.022547274827957153, 0.06316546350717545, 0.03584757074713707, -0.07862301915884018, -0.0012111299438402057, 0.006892083212733269, 0.02815094403922558, -0.06132249906659126, 0.011733008548617363, -0.04941016808152199, -0.07207123190164566, 0.0021708470303565264, -0.01963811367750168, -0.03255930170416832, 0.05144813656806946, -0.009018990211188793, -0.037364888936281204, 0.050758782774209976, -0.04046034440398216, -0.02707766741514206, 0.04157698526978493, 0.060757506638765335, 0.01456777285784483, 0.01506761834025383, 0.10175419598817825, -0.005520853213965893, -0.03787125647068024, 0.03277723863720894, 0.031247852370142937, -0.04388095811009407, -0.04702579975128174, 0.015205158852040768, 0.02060738019645214, 0.004000002518296242, -0.03610384091734886, 0.03546234592795372, 0.019241938367486, -0.05423114076256752, -0.05033314973115921, 0.03008752502501011, 0.0005306658567860723, -0.009331849403679371, -0.05834822356700897, -0.030753396451473236, -0.023130664601922035, 0.04568476974964142, -0.010029916651546955, -0.006418666336685419, -0.004868543706834316, -0.010359813459217548, 0.05223572254180908, 0.030218759551644325, 0.03049395978450775, 0.027599768713116646, -0.06692703068256378, -0.003155759070068598, -0.020615268498659134, -0.023977799341082573, 0.005735618527978659, 0.0064216675236821175, -0.030972151085734367, -0.03252284601330757, 0.05648455396294594, -0.010693991556763649, 0.036351729184389114, 0.03008694387972355, -0.04679172486066818, 0.06185102090239525, 0.023270513862371445, -0.015306700952351093, -0.03841421380639076, 0.01697354204952717, 0.03788420185446739, -0.014152836985886097, -0.041054826229810715, 0.02820766717195511, -0.01821070723235607, -0.046979691833257675, 0.01263356301933527, -0.03449557349085808, -0.006349814590066671, 0.043236467987298965, -0.040328167378902435, 0.009184887632727623, -0.04279215261340141, 0.01097164861857891, -0.06815201789140701, -0.012140707112848759, -0.015556528232991695, -0.0529647096991539, 0.05063043534755707, -0.04136800020933151, -0.04093126207590103, -0.009981040842831135, -0.002997357863932848, 0.10727216303348541, 0.07764987647533417, -0.06699952483177185, -0.0667283684015274, 0.034158993512392044, 0.0021496829576790333, -0.02572227641940117, -0.034738410264253616, -0.039036981761455536, -0.0026788816321641207, 0.02504543960094452, -0.03281561657786369, 0.05586624890565872, -0.028172854334115982, -0.02623683772981167, 0.05935006961226463, -0.02954118326306343, -0.0269305519759655, -0.03349297493696213, -0.030162671580910683, 0.03243809565901756, 0.01814090460538864, -0.046757299453020096, -0.03117845579981804, -0.007149327080696821, 0.0022420857567340136, 0.017152998596429825, 0.03038102760910988, -0.04061984270811081, 0.05303100496530533, 0.022371996194124222, 0.0872626081109047, -0.02918115444481373, 0.022804202511906624, 0.013689492829144001, 0.007409633602946997, 0.025751860812306404, 0.08149600028991699, -0.00028804107569158077, 0.06454814225435257, -0.02459859661757946, -0.02624398283660412, -0.06154029443860054, -0.08177875727415085, -0.016130788251757622, -0.008362038992345333, 0.0038523871917277575, 0.006466605234891176, -0.03870100528001785, 0.057368047535419464, 0.02136525698006153, 0.0058775548823177814, 0.012405388057231903, 0.029750535264611244, 0.05700434371829033, 0.09322269260883331, 0.002349168760702014, 0.020512212067842484, 0.07360368221998215, -0.016488967463374138, -0.04859313741326332, 0.015938714146614075, -0.02852346934378147, 0.011139538139104843, -0.010058165527880192, -0.04196804761886597, -0.023283012211322784, -0.04427969083189964, 0.06251201033592224, -0.009057671763002872, 0.009615015238523483, -0.005793141201138496, 0.059698686003685, 0.0641184076666832, -0.04861796274781227, 0.057283733040094376, 0.035540297627449036, -0.06238890066742897, 0.08569655567407608, -0.011084391735494137, 0.007752599194645882, 0.06580737978219986, -0.02405676059424877, -0.008392923511564732, 0.016974834725260735, 0.002809704514220357, -0.04001782834529877, 0.020733477547764778, 0.00790196843445301, -0.05461685359477997, 0.013699814677238464, 0.003402691101655364, 0.04037562012672424, -0.060635991394519806, -0.04967992380261421, -0.039512716233730316, 0.005343808326870203, -0.05347853899002075, -0.050796423107385635, 0.07055259495973587, -0.00519917905330658, -0.040280699729919434, 0.0163298137485981, 0.027897832915186882, 0.004077431280165911, 0.05428542196750641, 0.021357974037528038, 0.05211670696735382, -0.030909251421689987, 0.040177635848522186, 0.004387561231851578, 0.04344223439693451, -0.06461600959300995, -0.048534609377384186, -0.04921910911798477, -0.02707773447036743, 0.011384941637516022, -0.006435189861804247, -0.0034564142115414143, -0.040693558752536774, 0.03642687946557999, 0.024065591394901276, -0.0669822171330452, 0.02381964400410652, 0.007173016667366028, 0.00883537344634533, -0.029823388904333115, -0.05281858146190643, -0.040367964655160904, 0.010033481754362583, 0.021553197875618935, -0.030707689002156258, -0.02889062464237213, 0.025371521711349487, 0.014042100869119167, 0.032126784324645996, 0.01654212176799774, -0.01953972317278385, 0.054446395486593246, 0.0006837706314399838, -0.028380490839481354, -0.010021941736340523, -0.002512498991563916, -0.018439000472426414, 0.041642703115940094, 0.016556866466999054, 0.02212829329073429, 0.012874371372163296, -0.030619129538536072, -0.06887803226709366, 0.06193561479449272, -0.022324835881590843, -0.021020717918872833, 0.01866774633526802, 0.012987637892365456, 0.07379297912120819, 0.01922653615474701, 0.029135771095752716, -0.029096480458974838, -0.07117427885532379, -0.0550324022769928, 0.07290138304233551, -0.04834458604454994, 0.0862283855676651, -0.020016679540276527, -0.008026417344808578, -0.04711128771305084, 0.005751056596636772, 0.006442403886467218, 0.016674045473337173, 0.04740676283836365, -0.017700446769595146, -0.015012550167739391, -0.012387036345899105, -0.03164660558104515, 0.055728863924741745, 0.04386197030544281, 0.0646030530333519, -0.06733006983995438, -0.07587648183107376, 0.07514504343271255, 0.019056174904108047, 0.003097975393757224, 0.0359533317387104, 0.083777517080307, -0.02724909968674183, 0.007430276833474636, 0.0066796038299798965, 0.021943887695670128, 0.03645860031247139, -0.042714644223451614, -0.037918124347925186, -0.011566567234694958, 0.048619017004966736, -0.006505206227302551, 0.045234888792037964, 0.019184919074177742, 0.028532274067401886, 0.025938410311937332, -0.030821191146969795, -0.017740469425916672, 0.06998699903488159, 0.05794554203748703, 0.03779716417193413, -0.06250982731580734, -0.01773865520954132, -0.037417393177747726, -0.02910695970058441, 0.008456981740891933, 0.016149966046214104, -0.02810867689549923, -0.012459770776331425, -0.01456108596175909, 0.008340694941580296, 0.00624359305948019, 0.012511640787124634, 0.004757493734359741, -0.04920964315533638, -0.015162061899900436, 0.0403931587934494, -0.010653268545866013, 0.03042609617114067, 0.006714159157127142, -0.005853018723428249, 0.0218804944306612, 0.033135220408439636, 0.03643671050667763, -0.027411293238401413, 0.015815846621990204, -0.017022421583533287, -0.06798752397298813, 0.04855138435959816, 0.05782276764512062, 0.07426366209983826, 0.026233870536088943, 0.031406499445438385, 0.007865539751946926, 0.02958695963025093, -0.0013420997420325875, -0.019473912194371223, 0.04963727295398712, 0.006240352988243103, -0.02129478007555008, -0.009362434037029743, -0.014469201676547527, 0.0748286247253418, 0.0028776670806109905, 0.009629804641008377, -0.003563123755156994, 0.030011091381311417, 0.06713590770959854, -0.0011445865966379642, 0.027173791080713272, -0.04810290411114693, 0.034237951040267944, -0.04572807997465134, 0.0029912095051258802, 0.024688001722097397, 0.11324243992567062, 0.011132731102406979, -0.0018092903774231672, 0.04957754537463188, -0.02947913110256195, 0.008826969191432, 0.006727736908942461, -0.036581769585609436, -0.006141077261418104, 0.01795504428446293, 0.05500679835677147, 0.008961057290434837, -0.049320921301841736, -0.026045044884085655, 0.03746354952454567, 0.002976073417812586, -0.017579156905412674, 0.03023984469473362, 0.045402225106954575, -0.024035485461354256, 0.012569843791425228, 0.015705782920122147, 0.010662034153938293, 0.0012173103168606758, -0.046922750771045685, 0.04918576776981354, -0.020271070301532745, -0.0028690656181424856, 0.0595361553132534, -0.016727499663829803, 0.015802083536982536, 0.0032534862402826548, 0.012860243208706379, -0.009833953343331814, -0.026380550116300583, 0.021799184381961823, -0.07282258570194244, 0.0401780866086483, -0.005019462667405605, -0.00529908761382103, 0.020049860700964928, -0.028647754341363907, -0.07975918054580688, -0.0020439797081053257, -0.03511102870106697, 0.017741506919264793, -0.05895542353391647, 0.007728938013315201, 0.00527933519333601, 0.0028577730990946293, -0.024784447625279427, -0.019730957224965096, 0.03706372529268265, -0.04902290925383568, -0.04288559406995773, -0.019820254296064377, -0.02786833792924881, 0.018864693120121956, -0.07053866237401962, -0.02334715612232685, 0.02962648868560791, -0.06401093304157257, -0.006387230008840561, -0.02249906398355961, 0.03634737804532051, -0.013875029049813747, 0.0007565694395452738, 0.03156517073512077, -0.07256211340427399, -0.023767676204442978, 0.022356580942869186, 0.0003623003722168505, 0.013135409913957119, 0.0060239629819989204, 0.030648913234472275, 0.027137016877532005, 0.0654170885682106, 0.036799024790525436, -0.05042846128344536, 0.00041136989602819085, 0.0026431025471538305, -0.05892402306199074, -0.05224844813346863, -0.04580940306186676, -0.05097237229347229, 0.006397494580596685, 0.010235575959086418, -0.004817096516489983, 0.05120091140270233, -0.014694441109895706, -0.02041018009185791, -0.008522724732756615, 0.007749688811600208, -0.029206233099102974, 0.03832016885280609, -0.02263474278151989, -0.005779421888291836, 0.021449493244290352, 0.03163916990160942, 0.004992512986063957, -0.021806377917528152, 0.02031538635492325, 0.017197920009493828, -0.02145523950457573, -0.014298795722424984, 0.0027317351195961237, 0.012132825329899788, 0.007791755720973015, -0.0022007992956787348, 0.014487497508525848, 0.0168421883136034, 0.07286594063043594, 0.048390813171863556, -0.03496893495321274, 0.025572016835212708, -0.010335609316825867, 0.00770770525559783, 0.009551425464451313, 0.004798680543899536, 0.045586828142404556, -0.013011583127081394, -0.019692597910761833, 0.0006989890243858099, 0.029116712510585785, -0.018109137192368507, -0.019164633005857468, -0.051601190119981766, -0.00004405950312502682, 0.023124998435378075, 0.02780435048043728, -0.014987741596996784, -0.03433870151638985, -0.08094081282615662, -0.020920302718877792, -0.013575746677815914, -0.03320469334721565, -0.00044501383672468364, 0.021621285006403923, -0.05388457700610161, 0.02811911515891552, -0.0538482628762722, 0.0021321417298167944, -0.0754193514585495 ]
<p>So we can define a particle by defining its kinetic and potential energy, knowing that we can get a wavefunction describing a particle.</p> <p>But the kinetic energy involves motion, and motion can be described in many different frames of reference as different quantities, so is the Hamiltionian not uniquely defined?</p> <p>I mean, is the quantum state than dependant on in which frame of reference you look at the particle? Or it is just taken as a velocity in the Earths frame of reference as we cannot extract the energy contained in the velocity due to rotational motion around the Sun and the center of Galaxy?</p> <p>And also what is the same case with temperature? I found some things about it but I don't fully understand I think. relevant: <a href="http://en.wikipedia.org/wiki/Unruh_effect" rel="nofollow">Unruh effect</a></p> <p>I searched over the physics stackexchange and read about the energy in different frames of reference and the temperature and so on, and well I still don't feel that I understand it, but the main question is: <strong>isn't the wavefunction absolute description of the state of the particle?</strong></p>
g8364
[ 0.049858804792165756, 0.021543854847550392, -0.00600631395354867, -0.028382429853081703, 0.04560123756527901, -0.041004106402397156, 0.052645742893218994, 0.062459491193294525, -0.001394426915794611, -0.007224909029901028, 0.007307799067348242, 0.002193230437114835, 0.03622105345129967, 0.0067746080458164215, -0.03678096830844879, -0.030339838936924934, 0.09107766300439835, 0.027734631672501564, 0.04530639573931694, 0.06395717710256577, -0.03932392969727516, 0.06022091209888458, -0.003483058651909232, -0.01806945540010929, -0.008433832786977291, -0.030835863202810287, -0.01000111736357212, -0.07723447680473328, -0.04262673854827881, 0.006357994861900806, 0.0243073720484972, -0.023313798010349274, 0.0033695956226438284, -0.012105249799787998, 0.006150948815047741, 0.009658697992563248, 0.08387800306081772, 0.020547941327095032, -0.0077508497051894665, -0.004743667319417, -0.03777962550520897, 0.021346736699342728, -0.011278068646788597, -0.016002578660845757, 0.016515308991074562, 0.05407853424549103, 0.013934837654232979, -0.03655306249856949, -0.004547568503767252, -0.018082253634929657, -0.03420192003250122, 0.02781916968524456, 0.005516322795301676, 0.01308362279087305, 0.0477612167596817, 0.008845092728734016, -0.014723978005349636, 0.009675538167357445, 0.06553144752979279, 0.047346632927656174, 0.07176057994365692, 0.02842099592089653, 0.03469763323664665, 0.0006266764248721302, 0.004413802642375231, -0.015349674969911575, -0.049797624349594116, -0.004882119130343199, -0.03970830515027046, -0.0017769711557775736, -0.0026553194038569927, -0.05877966806292534, -0.09192512929439545, -0.019822491332888603, 0.018826931715011597, 0.031261492520570755, -0.029063327237963676, -0.04629134014248848, 0.010400102473795414, 0.057747118175029755, -0.07255396991968155, 0.010321405716240406, 0.07153663039207458, -0.011366245336830616, 0.07617389410734177, -0.025887496769428253, 0.002306798007339239, 0.04528781399130821, 0.0028858191799372435, 0.02964496985077858, -0.012954393401741982, -0.021219804883003235, 0.08304695785045624, 0.04698114097118378, -0.019883276894688606, -0.019471431151032448, -0.0671728253364563, 0.04449361935257912, -0.0012288994621485472, 0.04236087203025818, -0.07230361551046371, -0.00954717118293047, 0.011198651976883411, -0.015546761453151703, 0.03997192531824112, -0.00664009852334857, 0.0003214165917597711, 0.029359465464949608, -0.013316678814589977, -0.033473774790763855, -0.0611337311565876, -0.014822974801063538, 0.023299146443605423, 0.013127333484590054, -0.06731802225112915, -0.00200735148973763, 0.05633876845240593, -0.019383801147341728, -0.023836076259613037, 0.034522321075201035, 0.012200212106108665, 0.06347525864839554, 0.022906998172402382, 0.09835153818130493, -0.04063200578093529, 0.007795193698257208, 0.018392739817500114, 0.0107410978525877, -0.031024662777781487, -0.008898287080228329, 0.03241059184074402, -0.011216897517442703, 0.014898376539349556, 0.015620974823832512, -0.012230092659592628, -0.02062067948281765, 0.03693932667374611, 0.03048606775701046, -0.03530409187078476, 0.056373994797468185, 0.0005370699800550938, -0.014089901931583881, -0.00024347084399778396, -0.056066058576107025, -0.03644859418272972, -0.0031481804326176643, -0.02290494181215763, 0.009812585078179836, 0.05668877065181732, 0.035210222005844116, 0.02872724086046219, 0.04236144945025444, -0.03491799160838127, -0.011064235121011734, 0.07519487291574478, -0.013731067068874836, 0.026412129402160645, 0.0258321650326252, -0.04405420646071434, -0.012894046492874622, 0.06106410175561905, -0.020821290090680122, 0.06390169262886047, -0.028747830539941788, -0.04315439984202385, -0.04467572271823883, -0.023693745955824852, -0.0003579604672268033, 0.045967452228069305, -0.05573815107345581, -0.037364862859249115, 0.004274153150618076, -0.014742666855454445, 0.031243789941072464, -0.04285828024148941, 0.017102550715208054, 0.01323686633259058, -0.0066171553917229176, 0.0040385527536273, 0.007491863798350096, -0.01249354425817728, -0.03746375814080238, -0.006235397420823574, -0.05222697556018829, -0.0347132571041584, 0.0511479526758194, 0.02862348034977913, 0.04150290787220001, -0.04536830633878708, 0.028842201456427574, -0.06540211290121078, -0.015607811510562897, 0.012832023203372955, 0.017182372510433197, -0.035071421414613724, -0.02128782868385315, -0.01747780293226242, -0.07507818937301636, -0.04798886924982071, -0.010928917676210403, -0.0026067036669701338, 0.06816050410270691, -0.018413882702589035, 0.006689000409096479, 0.06655432283878326, 0.0020411352161318064, 0.02083764225244522, 0.03910252824425697, -0.02309305965900421, -0.02347363531589508, 0.04966285824775696, -0.01955307461321354, 0.01230795681476593, 0.04993933066725731, 0.01603725552558899, -0.03391142562031746, -0.0005158075946383178, -0.04554913192987442, -0.021809980273246765, -0.00005092003630124964, -0.031524572521448135, 0.007670426741242409, 0.053086988627910614, -0.020142287015914917, -0.04810066521167755, 0.01653703860938549, -0.11565013974905014, -0.012546244077384472, -0.009736686013638973, 0.06883133947849274, -0.0616607591509819, -0.01104471180588007, -0.02794775366783142, 0.017162106931209564, 0.005959187634289265, 0.020211070775985718, 0.011933737434446812, -0.03296183422207832, 0.03272652253508568, 0.0280714500695467, -0.03540860116481781, -0.030774610117077827, -0.031173434108495712, -0.0006055667181499302, 0.007203058339655399, -0.037481777369976044, 0.02296268753707409, -0.03988664969801903, -0.013965598307549953, -0.018636446446180344, -0.02737976610660553, -0.010605404153466225, -0.037614606320858, -0.027815435081720352, 0.0032735189888626337, -0.014681507833302021, -0.04181012138724327, 0.051950305700302124, -0.051302727311849594, -0.022785766050219536, 0.027288923040032387, -0.0035482451785355806, -0.027901876717805862, 0.01673159748315811, 0.06083913519978523, 0.04078701511025429, -0.0003697368083521724, 0.026596056297421455, -0.0636369064450264, -0.05089337006211281, -0.0020373142324388027, 0.08026336133480072, 0.006151421926915646, 0.02547391876578331, -0.03863301873207092, -0.007929927669465542, -0.030224882066249847, -0.032227449119091034, 0.005064261145889759, -0.052549123764038086, -0.03910129889845848, 0.050041843205690384, -0.04640097916126251, 0.02756957896053791, 0.012507048435509205, -0.10161107033491135, -0.007052504923194647, 0.01588370092213154, -0.020195169374346733, -0.05038962885737419, 0.0024959330912679434, 0.054794784635305405, 0.005957386456429958, 0.019433677196502686, -0.03170880302786827, 0.014966463670134544, -0.00984168704599142, -0.053411815315485, -0.011392234824597836, 0.05972569063305855, 0.025919580832123756, -0.044643376022577286, -0.027501190081238747, 0.02844199538230896, 0.06905347853899002, 0.04179177060723305, -0.044033799320459366, -0.05654585734009743, -0.011426366865634918, 0.006389910355210304, -0.03609614446759224, 0.04858256131410599, 0.006677235011011362, 0.011378060095012188, -0.05101865530014038, -0.010466978885233402, -0.04883843660354614, -0.03892143443226814, 0.03208552673459053, 0.014590821228921413, -0.019950702786445618, -0.031198004260659218, 0.003903060220181942, -0.0071036857552826405, 0.03275113180279732, 0.02078775316476822, -0.014780760742723942, -0.011209782212972641, -0.04560775309801102, -0.03835782781243324, -0.0052464911714196205, -0.0050321780145168304, 0.008859502151608467, -0.029750116169452667, -0.027622750028967857, -0.0395674854516983, -0.06890056282281876, -0.03767584264278412, 0.0964788869023323, -0.017698951065540314, 0.022696014493703842, 0.010134929791092873, 0.010810918174684048, 0.020418962463736534, -0.008959585800766945, 0.030429933220148087, -0.0069288224913179874, -0.0299801267683506, -0.0030825487338006496, 0.015101691707968712, 0.025987273082137108, 0.041825760155916214, -0.0368243083357811, 0.0054211243987083435, 0.0033638577442616224, -0.004666762426495552, 0.05613439157605171, 0.05530065670609474, -0.010838651098310947, 0.0017273607663810253, 0.039024028927087784, -0.03568875417113304, 0.009762782603502274, 0.054667335003614426, -0.0029504355043172836, 0.004495569504797459, 0.0011475079227238894, -0.01220076996833086, -0.0030292405281215906, -0.04284439980983734, -0.019203687086701393, -0.08009380102157593, -0.032417312264442444, -0.0510968416929245, 0.024879368022084236, -0.00011802057269960642, 0.013816140592098236, -0.02960822731256485, -0.05944806709885597, 0.005229586735367775, 0.014795792289078236, -0.023696092888712883, 0.05077308043837547, 0.06209748610854149, 0.06499666720628738, -0.008916197344660759, -0.04788742586970329, 0.01851864904165268, -0.0034852188546210527, 0.013575089164078236, 0.03050469048321247, -0.09629558026790619, -0.012547346763312817, -0.0546594001352787, 0.057526543736457825, 0.01940746419131756, 0.04279935732483864, -0.025788232684135437, 0.016339870169758797, 0.05306810885667801, -0.03924252465367317, -0.009167168289422989, -0.02394665777683258, -0.01811506226658821, -0.009226489812135696, 0.012221709825098515, 0.06144220754504204, -0.08963323384523392, -0.03865957260131836, -0.04907796531915665, -0.014113162644207478, 0.026843946427106857, 0.04144914820790291, -0.0630343034863472, 0.004397881682962179, -0.00004014751175418496, -0.012659207917749882, -0.038847777992486954, 0.03270328789949417, 0.0020012168679386377, 0.039750661700963974, 0.07509394735097885, 0.04584505781531334, 0.02246646024286747, 0.0426161102950573, 0.06963176280260086, 0.014519660733640194, 0.006545979529619217, -0.04253089800477028, -0.02000499702990055, 0.028262872248888016, 0.0038850181736052036, 0.04573819786310196, 0.026189858093857765, -0.013272157870233059, 0.026902640238404274, -0.03958494961261749, -0.004311555065214634, 0.03477427735924721, 0.011634423397481441, 0.06282506138086319, 0.03900156170129776, 0.0019627592992037535, 0.006308056879788637, 0.01814667135477066, 0.030675575137138367, -0.02688377909362316, -0.06090526282787323, -0.04964522644877434, -0.06497703492641449, -0.04097192361950874, 0.05836373567581177, -0.04453881084918976, -0.05034886673092842, 0.012518465518951416, -0.00011383509263396263, -0.056283868849277496, 0.04837268963456154, -0.02212156355381012, 0.008442499674856663, -0.12286102771759033, 0.01012932974845171, 0.014925764873623848, 0.022035596892237663, -0.007817678153514862, -0.0028412833344191313, -0.06330404430627823, 0.01731988601386547, -0.07902348786592484, 0.05184124782681465, 0.03871463984251022, 0.0010229757754132152, 0.008978763595223427, -0.0021515514235943556, 0.052371151745319366, -0.004951929207891226, 0.056454017758369446, -0.04557541385293007, -0.01785041019320488, -0.045595139265060425, -0.007498379796743393, 0.009663139469921589, 0.05070055276155472, 0.002961884019896388, -0.001964290626347065, 0.0466572530567646, -0.017381593585014343, -0.005928685422986746, -0.06425849348306656, -0.011343374848365784, -0.0032177141401916742, -0.023890085518360138, 0.02006014809012413, 0.03630750998854637, 0.05694901570677757, 0.02544526383280754, -0.0023823773954063654, -0.01824554055929184, -0.0023467629216611385, 0.02558027021586895, -0.02118542604148388, -0.009575434029102325, -0.008950968272984028, 0.037135206162929535, -0.002364136278629303, 0.04728972539305687, 0.11655320972204208, -0.02429702877998352, -0.014140961691737175, -0.03511032089591026, 0.02687135897576809, 0.00466538779437542, -0.03894119709730148, -0.018058745190501213, 0.020190859213471413, 0.02571825310587883, 0.0065064141526818275, 0.028874652460217476, 0.013377219438552856, -0.04434986785054207, -0.0000531095101905521, 0.04879561439156532, 0.033706411719322205, -0.01241680234670639, 0.008874881081283092, -0.021760188043117523, -0.01524330209940672, -0.016508331522345543, -0.01319899782538414, 0.06545563787221909, 0.042227454483509064, 0.008313193917274475, 0.04123145341873169, 0.0538816899061203, 0.0007324437610805035, -0.05356966331601143, -0.013377186842262745, -0.010469523258507252, 0.026579348370432854, 0.0047747474163770676, -0.027896735817193985, 0.003950263373553753, 0.020638078451156616, 0.03321922570466995, 0.016322515904903412, -0.00010893613216467202, -0.02913762256503105, 0.05074732378125191, 0.038227200508117676, -0.027721017599105835, -0.02952323853969574, 0.02732814848423004, -0.031077822670340538, -0.04585716128349304, 0.006364436354488134, 0.010102488100528717, 0.03931794688105583, -0.062059834599494934, -0.01851370371878147, -0.024032851681113243, 0.024116545915603638, 0.02896358072757721, 0.05453215539455414, -0.01159314252436161, 0.03645693138241768, -0.00715096527710557, -0.024645453318953514, -0.011552800424396992, 0.023692142218351364, 0.01661948300898075, 0.014096567407250404, -0.013321482576429844, -0.03552515432238579, -0.05045866221189499, -0.004293049219995737, 0.012555941939353943, -0.05168711394071579, 0.020420432090759277, -0.06265421211719513, 0.016144737601280212, -0.035614509135484695, -0.006898633670061827, 0.03821853548288345, -0.028565386310219765, -0.01401150319725275, 0.0013560272054746747, -0.01787693239748478, 0.03175506740808487, 0.023302553221583366, 0.03970038518309593, 0.01850929483771324, -0.016394339501857758, -0.007664738688617945, 0.005020740441977978, -0.05890647694468498, 0.0034760020207613707, -0.005473738070577383, -0.05582272633910179, -0.053302962332963943, 0.014527665451169014, 0.022933803498744965, -0.012624990195035934, -0.015827393159270287, -0.05074315890669823, 0.045113250613212585, 0.04002206027507782, -0.013940950855612755, 0.00003168944385834038, 0.010400121100246906, 0.058532215654850006, -0.04656968265771866, 0.011029897257685661, 0.016940390691161156, -0.021446343511343002, -0.030149681493639946, -0.07033021748065948, -0.03552258387207985, 0.001127137104049325, -0.028583914041519165, -0.052857354283332825, 0.025518318638205528, 0.016693055629730225, 0.005969707388430834, -0.0030702415388077497, 0.11738733947277069, 0.07028232514858246, -0.08566316217184067, 0.06665723025798798, 0.04406969994306564, -0.06071159243583679, 0.05541618540883064, 0.0014846918638795614, -0.03389711305499077, 0.08501734584569931, -0.012858506292104721, 0.016634108498692513, -0.06490002572536469, 0.006672876887023449, 0.014028938487172127, 0.003395069157704711, -0.04401908069849014, 0.00943309348076582, 0.06881273537874222, 0.0016100377542898059, -0.07727956771850586, -0.03671018034219742, -0.0027173489797860384, -0.015803810209035873, -0.06908702105283737, 0.0107152434065938, -0.04641817882657051, -0.025952013209462166, -0.022430982440710068, 0.06684570759534836, 0.04302067682147026, 0.04558894410729408, 0.02352575771510601, 0.007924300618469715, 0.014987201429903507, -0.05663884058594704, -0.02697024680674076, 0.010879265144467354, 0.0015415912494063377, 0.02244514599442482, 0.02196292020380497, 0.048470791429281235, 0.007113770116120577, -0.06511583179235458, -0.015389755368232727, -0.012863826006650925, 0.04947471618652344, -0.021773047745227814, -0.04271521791815758, 0.000312054471578449, -0.0008272012346424162, 0.007461123168468475, -0.04017377272248268, 0.06983272731304169, -0.007224540691822767, -0.03612449765205383, -0.004778008442372084, 0.06138361990451813, 0.03804435208439827, 0.005046918988227844, -0.012014235369861126, -0.0023951081093400717, -0.015562585555016994, -0.03185361623764038, 0.047939613461494446, -0.010261057876050472, -0.01145219150930643, 0.019801216199994087, 0.042419835925102234, -0.04175566881895065, -0.019016996026039124, 0.032084837555885315, 0.10726913809776306, 0.03094794973731041, 0.044060833752155304, 0.017937015742063522, 0.014789987355470657, 0.002233916660770774, 0.006107226014137268, 0.017524102702736855, 0.03275298699736595, 0.015534874051809311, -0.015409561805427074, 0.0015657262410968542, -0.05948057770729065, 0.031030435115098953, 0.011090517044067383, 0.036487236618995667, -0.015677044168114662, 0.016350997611880302, 0.001196126569993794, -0.019896235316991806, 0.002748789731413126, 0.013012703508138657, 0.03941942751407623, -0.04111987352371216, 0.014281118288636208, -0.012568716891109943, 0.021992681547999382, -0.022735852748155594, 0.023922668769955635, -0.008730637840926647, -0.007937181740999222, 0.001298653893172741, 0.018914027139544487, -0.018135830760002136, -0.02670462615787983, 0.05362508073449135, -0.007469594944268465, 0.01851612888276577, -0.03408901393413544, 0.017408249899744987, -0.010142290964722633, -0.011208816431462765, 0.028126301243901253, 0.016315534710884094, -0.02423020638525486, -0.0513647124171257, -0.01976478099822998, -0.03572501242160797, -0.056905895471572876, -0.03789350762963295, -0.0366167351603508, 0.01006526593118906, 0.04771457239985466, -0.0029255987610667944, -0.04237494617700577, 0.03946961089968681, -0.044519681483507156, 0.02615678496658802, 0.034353405237197876, -0.04673101752996445, 0.0012395537924021482, -0.008078357204794884, 0.02821265533566475, 0.031407132744789124, -0.0006514099659398198, -0.044680725783109665, 0.054916854947805405, -0.05001629889011383, 0.007261686492711306, -0.015268892049789429, 0.005329176317900419, 0.02411288395524025 ]
<p>A while ago, during my introductory physics course, my professor purposefully neglected to tell us about the existence of the anti-electron neutrino in beta decay; he made it an assignment(on our honor) to propose a theory to explain where the missing energy ran off to. Since I was not very experienced at the time, I did not come to the conclusion that the culprit had to be neutral (to conserve charge), but I was aware of basic particle collisions and how scientists smashed particles together in order to observe smaller, more basic ones. Consequently, I came to the conclusion that when the electron broke away from the nucleus, particle fragments (where the electron broke off) were released as well (so, a bit like detritus which would have accounted for the deviation in the missing energy, as a different number of particles could have broken off each time). Now, clearly, I had an advantage over Pauli (since I was aware of particle diversity, and the separable nature of baryons), yet I am still not certain exactly how he was able to narrow his choices down to a single particle (especially since he was decades away from being able to detect such an elusive creature). How would you have come to such a conclusion (if possible, perhaps another response besides Occam's Razor)?</p>
g8365
[ 0.06330365687608719, 0.0005904368590563536, 0.011792566627264023, -0.025679413229227066, 0.08546093106269836, 0.03617352619767189, 0.007320616394281387, 0.03853890299797058, -0.016579361632466316, -0.029585914686322212, -0.013003973290324211, 0.023693831637501717, 0.05128288269042969, 0.02412118762731552, 0.015028009191155434, -0.03442205488681793, 0.05215473473072052, -0.040540508925914764, 0.012243621982634068, -0.000006399313406291185, 0.011194822378456593, -0.010572945699095726, 0.014830171130597591, -0.011898201890289783, -0.015038765035569668, -0.03938278555870056, -0.026437103748321533, 0.0182624701410532, -0.038898397237062454, -0.037000883370637894, 0.00020062807016074657, -0.024476509541273117, 0.035735372453927994, -0.05709296464920044, -0.05564415082335472, 0.0045530833303928375, 0.027044858783483505, 0.06291263550519943, 0.034514814615249634, -0.02100771851837635, 0.0002921269915532321, -0.041841570287942886, -0.024621406570076942, -0.014701210893690586, 0.05652961879968643, 0.03947531431913376, -0.019341247156262398, -0.025293705984950066, -0.02518940530717373, 0.013172825798392296, 0.05821467563509941, -0.005461648106575012, 0.01843799650669098, 0.030625654384493828, 0.007555972319096327, -0.005371977109462023, 0.022970397025346756, -0.002183543751016259, 0.09570025652647018, -0.011500398628413677, 0.04660665616393089, -0.0039504352025687695, -0.015505309216678143, -0.025322681292891502, 0.04486102983355522, -0.05639265850186348, -0.04535657912492752, 0.07349714636802673, -0.040718138217926025, -0.031189071014523506, 0.017054380849003792, -0.05499035865068436, -0.01169058308005333, -0.044809743762016296, -0.026012999936938286, -0.00046904408372938633, -0.02970024384558201, -0.011970874853432178, 0.023333631455898285, -0.02701544016599655, -0.024047762155532837, 0.023979002609848976, 0.02792838029563427, -0.003827568842098117, 0.11437860131263733, -0.014465679414570332, -0.0048143016174435616, 0.019831426441669464, -0.0012595121515914798, 0.013533818535506725, -0.005999638233333826, -0.01782093197107315, 0.02956126630306244, -0.04009097442030907, 0.028137708082795143, -0.007454322651028633, -0.008040091022849083, 0.014068486168980598, -0.02660612016916275, 0.019867153838276863, 0.0046201967634260654, -0.05077901855111122, -0.00998847559094429, -0.04688414931297302, 0.03241277113556862, -0.03770216181874275, 0.031733494251966476, -0.045918338000774384, 0.045693110674619675, 0.04456738755106926, 0.01664440520107746, -0.03158792108297348, -0.04414854198694229, -0.038863640278577805, 0.05915454030036926, -0.010398908518254757, 0.08804392069578171, -0.0778304859995842, -0.02622610703110695, 0.06060457229614258, -0.10049189627170563, 0.029547197744250298, -0.03664378076791763, 0.059970125555992126, -0.03932512551546097, 0.0044976938515901566, -0.028339968994259834, -0.023761413991451263, 0.009004252031445503, 0.024256886914372444, -0.04964727163314819, -0.02078661136329174, 0.030022691935300827, 0.04289008677005768, 0.03660682588815689, 0.016135403886437416, -0.004568933974951506, -0.000814019818790257, -0.015286854468286037, -0.03211226686835289, 0.027553241699934006, 0.007045400328934193, -0.06200224533677101, 0.025898749008774757, -0.006291006226092577, 0.020250970497727394, -0.040439918637275696, -0.00006098969970480539, -0.03595450147986412, 0.09721802920103073, 0.013422351330518723, 0.012819493189454079, -0.02931166999042034, -0.007810230366885662, 0.06302393227815628, -0.03073125332593918, 0.04670458659529686, 0.008352137170732021, -0.07457606494426727, -0.026992686092853546, 0.052786555141210556, -0.010003248229622841, -0.05252775177359581, -0.02081197313964367, -0.018523214384913445, -0.0015209645498543978, 0.03416677564382553, -0.0220837090164423, 0.07315859198570251, 0.004631016869097948, -0.08612779527902603, -0.020876964554190636, 0.03798038512468338, 0.005589261185377836, -0.003045429941266775, 0.10774774849414825, -0.013108541257679462, -0.06457594782114029, -0.011911062523722649, 0.027055272832512856, 0.0113604124635458, 0.011870033107697964, 0.014466614462435246, 0.03725820407271385, 0.08810077607631683, -0.02455948479473591, -0.0077568236738443375, 0.05507243797183037, 0.03037348762154579, -0.020560476928949356, 0.012330242432653904, -0.05158533900976181, 0.011334347538650036, -0.01320506539195776, 0.00397185143083334, -0.031696390360593796, 0.012177292257547379, -0.05793088302016258, -0.01019093208014965, 0.030869895592331886, -0.03955540060997009, 0.07111144065856934, 0.0014381224755197763, -0.008157534524798393, 0.04662810266017914, -0.06486518681049347, 0.011575879529118538, -0.02922983467578888, 0.027609648182988167, -0.04161936789751053, -0.010317337699234486, 0.020849158987402916, -0.020481165498495102, 0.001884535187855363, -0.06611370295286179, -0.03420644626021385, -0.021455783396959305, 0.03314526751637459, 0.013324369676411152, 0.0017794861923903227, -0.07600122690200806, -0.024069499224424362, -0.001555956550873816, 0.0011039059609174728, 0.022730521857738495, 0.08797941356897354, -0.009816776029765606, -0.046553049236536026, -0.06189638748764992, 0.014549667946994305, -0.08619554340839386, 0.015946200117468834, -0.04663772135972977, -0.02777346968650818, 0.005764617118984461, 0.03557922691106796, 0.0011875753989443183, -0.0005046710139140487, 0.00929484236985445, -0.02027158997952938, 0.008262943476438522, -0.048094362020492554, -0.06993035227060318, -0.018313629552721977, 0.03833882138133049, -0.008152810856699944, 0.07429700344800949, -0.028278246521949768, -0.02549595944583416, -0.045526258647441864, -0.037054672837257385, 0.02088915929198265, -0.034337207674980164, 0.024769965559244156, 0.02695508301258087, -0.0335589200258255, 0.050762977451086044, -0.00730116618797183, -0.025817863643169403, 0.00030944054014980793, -0.0073289587162435055, -0.037611350417137146, -0.006675326731055975, 0.051155827939510345, -0.013373713940382004, 0.0006685839616693556, -0.005803010892122984, -0.03468900918960571, -0.029428496956825256, -0.012092704884707928, -0.009294542483985424, 0.058188144117593765, -0.010409904643893242, 0.014138895086944103, 0.01690186932682991, 0.010996067896485329, 0.002649388276040554, 0.024760788306593895, 0.012530479580163956, 0.017556916922330856, -0.02719675935804844, 0.08171259611845016, -0.045524146407842636, -0.05283492058515549, 0.04875914379954338, -0.03154306858778, 0.014795629307627678, -0.009028049185872078, 0.026522425934672356, 0.0008924043504521251, -0.03318602591753006, 0.007409765385091305, 0.046069711446762085, -0.011325816623866558, -0.02188180759549141, -0.009158636443316936, 0.04538476839661598, 0.007642096374183893, -0.027568098157644272, 0.001257202704437077, 0.027884742245078087, 0.015730196610093117, -0.04299886152148247, -0.021375427022576332, 0.020476069301366806, -0.00810946710407734, -0.04889138042926788, 0.024903522804379463, -0.051630038768053055, -0.01412468682974577, -0.029020117595791817, -0.00795777514576912, 0.08281362056732178, -0.043312061578035355, -0.0007128200377337635, -0.011170917190611362, -0.05276312306523323, 0.004478422924876213, 0.02600344456732273, 0.031034285202622414, -0.010303623974323273, 0.014744721353054047, 0.0644274652004242, -0.040998414158821106, 0.02530534565448761, 0.014002456329762936, -0.07856307923793793, 0.023040389642119408, -0.01956269145011902, 0.03354622796177864, -0.022327207028865814, -0.053739283233881, -0.015152065083384514, 0.008636211045086384, -0.045078013092279434, 0.0018577356822788715, 0.011347164399921894, 0.03540823981165886, 0.056869395077228546, 0.025027884170413017, -0.010553436353802681, 0.01592150703072548, 0.005850206594914198, -0.0038193203508853912, 0.01603100448846817, -0.01764528639614582, 0.009343995712697506, 0.039831459522247314, 0.028212929144501686, 0.026999376714229584, 0.02732500247657299, 0.0030292717274278402, -0.03380770981311798, 0.009587150067090988, 0.0005683034542016685, 0.003179535735398531, -0.013432345353066921, 0.014899241738021374, 0.008977552875876427, 0.015158924274146557, 0.02017824910581112, -0.04393834248185158, 0.03475644811987877, -0.02653428539633751, -0.013052016496658325, -0.023941490799188614, -0.037334591150283813, 0.02336248941719532, 0.023396819829940796, -0.068239226937294, 0.0005584636237472296, 0.012185897678136826, -0.014469142071902752, 0.07361197471618652, -0.030541865155100822, -0.008008146658539772, 0.05054739862680435, 0.07835804671049118, -0.052919287234544754, 0.04394063726067543, -0.024856775999069214, 0.014429116621613503, 0.019550688564777374, -0.005346795078366995, 0.020000996068120003, -0.0005397698259912431, -0.04758646711707115, -0.010522075928747654, -0.07009577751159668, -0.051371801644563675, 0.008306753821671009, -0.0017049163579940796, -0.04786583036184311, -0.0294824056327343, 0.006846181582659483, -0.003824226325377822, 0.00667456304654479, -0.01003672182559967, 0.037524282932281494, 0.07587137073278427, -0.053185008466243744, 0.049528397619724274, 0.022935718297958374, -0.06798341125249863, 0.03866247087717056, 0.01481309998780489, 0.012497330084443092, 0.0017820877255871892, -0.025372492149472237, -0.0485120564699173, -0.05731552094221115, 0.032148800790309906, -0.02557539753615856, -0.05238697677850723, -0.05418657884001732, -0.017690539360046387, 0.06693383306264877, 0.024190926924347878, 0.02075107954442501, 0.018936462700366974, 0.007385967765003443, -0.0018773790216073394, -0.09889093786478043, -0.02591048553586006, 0.013344399631023407, 0.06134624406695366, -0.010746021755039692, 0.0232962965965271, -0.035104356706142426, -0.03185084089636803, 0.001205229084007442, 0.01626056618988514, -0.034841734915971756, -0.021526776254177094, -0.0019167448626831174, -0.01193549856543541, 0.025183511897921562, 0.07317698746919632, -0.029414067044854164, 0.0782717913389206, 0.04204742982983589, -0.0225844606757164, 0.04836457222700119, -0.03087596595287323, -0.008498143404722214, 0.03528600186109543, 0.04468216747045517, -0.019999440759420395, -0.01588626019656658, 0.01787392981350422, -0.0019436965230852365, 0.008923362009227276, -0.05353084206581116, 0.024865038692951202, -0.011358993127942085, -0.030403658747673035, -0.01726829819381237, -0.009804479777812958, -0.002618843922391534, 0.09797445684671402, -0.036410603672266006, -0.0507284440100193, 0.0019432855769991875, 0.0356542207300663, 0.023226497694849968, -0.013776231557130814, 0.015634361654520035, -0.0057840002700686455, -0.006249941885471344, -0.0013624165439978242, -0.05208051949739456, 0.07659091055393219, 0.05125036835670471, -0.06504233181476593, -0.024831382557749748, 0.008461609482765198, -0.028215156868100166, 0.00015174208965618163, 0.03609556332230568, 0.024371977895498276, -0.035905078053474426, -0.02422855794429779, 0.014531329274177551, -0.05204535275697708, -0.053962886333465576, 0.046504128724336624, -0.08955361694097519, -0.027817409485578537, -0.0037576891481876373, -0.05550691485404968, 0.04798973724246025, 0.05462852492928505, 0.04305564612150192, -0.017704086378216743, -0.005194391123950481, -0.05077255144715309, 0.06577837467193604, 0.07723690569400787, 0.0031199026852846146, 0.021330777555704117, -0.0518697127699852, 0.03441905230283737, -0.003621249459683895, 0.004706236533820629, 0.00798286683857441, 0.05081164091825485, 0.045174725353717804, -0.03331296890974045, -0.023118147626519203, -0.03132500499486923, 0.026311885565519333, -0.01575901359319687, 0.00028372436645440757, -0.014408040791749954, 0.013529867865145206, 0.05074587091803551, -0.03919203579425812, 0.019928066059947014, 0.008951683528721333, -0.02771754376590252, 0.015023305080831051, 0.04235402122139931, 0.03173181414604187, -0.006915646605193615, 0.031094349920749664, -0.07090199738740921, -0.05761612951755524, -0.028857944533228874, -0.06332343816757202, -0.04923160374164581, 0.036109644919633865, -0.016366012394428253, -0.017809733748435974, 0.07624876499176025, -0.005073451902717352, -0.029191719368100166, -0.015876946970820427, 0.0556156300008297, 0.02026403695344925, -0.005323339719325304, -0.03246079757809639, 0.018514901399612427, 0.07556897401809692, 0.03586596995592117, -0.059403710067272186, -0.021588338539004326, -0.020930515602231026, 0.02603466995060444, 0.019995735958218575, -0.02648269757628441, -0.023311423137784004, 0.028902675956487656, 0.0208729337900877, 0.002934745978564024, -0.011435763910412788, 0.010673262178897858, 0.029162919148802757, -0.013232959434390068, -0.07670951634645462, -0.049341801553964615, -0.04190334677696228, -0.029290834441781044, 0.024863511323928833, 0.05823798105120659, 0.012191785499453545, -0.018468672409653664, -0.008883937261998653, -0.07299958169460297, -0.002896704711019993, -0.004520678427070379, 0.021770361810922623, 0.013646635226905346, -0.0005717293825000525, 0.025650247931480408, -0.010129683651030064, 0.03826082497835159, -0.04756493866443634, 0.021006539463996887, -0.03896788880228996, 0.0054132938385009766, 0.021821757778525352, -0.05161261558532715, 0.016138264909386635, 0.031302325427532196, -0.047885384410619736, 0.06300146132707596, -0.008830484002828598, 0.015642179176211357, 0.04299957677721977, 0.02911636233329773, 0.047091614454984665, -0.03276059404015541, 0.002226500539109111, -0.01764480024576187, -0.059430476278066635, 0.01229421328753233, -0.0018091994570568204, -0.06714454293251038, -0.07220964133739471, 0.059881050139665604, -0.03711557388305664, -0.002062092535197735, -0.01293778233230114, 0.01863289065659046, 0.07192609459161758, 0.04384122043848038, 0.0478505976498127, 0.0011176433181390166, 0.012770958244800568, -0.02310781739652157, -0.07135716080665588, 0.033423569053411484, -0.026512511074543, 0.028590265661478043, -0.011813952587544918, 0.013015219010412693, -0.0044390968978405, 0.02046898379921913, -0.02890205942094326, 0.06646348536014557, 0.04060369357466698, -0.007886255159974098, 0.0143350251019001, -0.005022631026804447, 0.03287086635828018, 0.03074483945965767, -0.018341852352023125, -0.01235413458198309, 0.07856438308954239, 0.006184710189700127, -0.004888656083494425, 0.020344510674476624, 0.022446997463703156, 0.03620237857103348, -0.059946209192276, -0.011602974496781826, 0.037140101194381714, -0.0008188241627067327, -0.030244257301092148, 0.00563144451007247, -0.007972470484673977, -0.007600392680615187, 0.036663711071014404, 0.008736991323530674, -0.06453252583742142, 0.04612528532743454, 0.040365736931562424, 0.044699933379888535, 0.0063765947706997395, -0.037045709788799286, 0.010178432799875736, -0.012740790843963623, 0.026042519137263298, 0.013453415594995022, -0.013625493273139, 0.012702911160886288, -0.005117988679558039, 0.02795018069446087, 0.0817028135061264, -0.06543031334877014, -0.04267600178718567, -0.042081430554389954, 0.03236246481537819, -0.015811948105692863, 0.0234591756016016, -0.02699379064142704, -0.03568873181939125, -0.012477773241698742, -0.0075441268272697926, -0.01560234185308218, -0.00045782275265082717, -0.005045415833592415, -0.06579715013504028, -0.01302964985370636, -0.005117885768413544, -0.052112869918346405, 0.04031166061758995, -0.018704663962125778, -0.0167220588773489, -0.03613801673054695, 0.025408968329429626, 0.041318271309137344, 0.01629684492945671, 0.014895285479724407, -0.035389918833971024, 0.0035728204529732466, -0.10380566865205765, 0.044340189546346664, -0.020036397501826286, 0.08052517473697662, -0.03597898781299591, 0.03612103313207626, 0.04514358565211296, -0.036280833184719086, -0.045108549296855927, -0.01563669927418232, 0.03060140833258629, 0.016190417110919952, 0.06469760835170746, 0.006189051549881697, 0.011872447095811367, -0.012395034544169903, 0.03143561631441116, 0.019698869436979294, 0.01514015905559063, 0.0265511404722929, 0.04083253815770149, -0.037378959357738495, -0.04240074381232262, 0.011854737065732479, -0.005068744532763958, 0.019064342603087425, 0.0008382845553569496, 0.03577899560332298, 0.060799889266490936, 0.003278840333223343, -0.049173008650541306, 0.025927279144525528, 0.06157192215323448, 0.039947088807821274, 0.017994336783885956, 0.04072701930999756, -0.016367679461836815, -0.012877480126917362, 0.033566150814294815, -0.034181494265794754, -0.012475084513425827, 0.019931068643927574, 0.009050203487277031, 0.029797883704304695, -0.02961764857172966, 0.017277680337429047, 0.0003336846421007067, -0.006539694499224424, -0.042079564183950424, 0.027932044118642807, 0.001987651688978076, 0.012291254475712776, -0.04784092307090759, -0.021445101127028465, -0.04032054543495178, 0.01789650321006775, -0.00660310173407197, -0.014710021205246449, -0.02155928686261177, -0.04612671583890915, -0.01720649003982544, 0.013024816289544106, 0.03136919438838959, 0.003375903470441699, -0.04577150568366051, 0.01757010444998741, -0.04936422035098076, 0.040670331567525864, 0.1070408746600151, -0.08514215797185898, 0.026088980957865715, -0.03162771090865135, -0.006042539607733488, 0.030044468119740486, -0.03989522159099579, -0.014025979675352573, 0.02144954912364483, 0.007009801920503378, -0.0032256983686238527, -0.01930953562259674, 0.0169829074293375, 0.00016040998161770403 ]
<p>Does it make sense to say that the quantum field of a photon is exactly proportional to the photon's electromagnetic field?</p> <p>\begin{align} \bar{\Psi} = \dfrac{\bar{E}+i\bar{B}}{\sqrt{\int (E^2+B^2)dV}} \end{align}</p>
g8366
[ 0.009885778650641441, 0.012048906646668911, -0.00572606548666954, -0.02413150668144226, 0.06259773671627045, 0.043491579592227936, 0.0413527712225914, 0.0057257129810750484, -0.008756263181567192, 0.037789616733789444, 0.028324227780103683, 0.01505262777209282, -0.03549732267856598, -0.03849835321307182, -0.021982958540320396, 0.021461818367242813, 0.09217754751443863, 0.013757322914898396, 0.023475391790270805, 0.004680671263486147, -0.05532409995794296, -0.023864643648266792, -0.01704634167253971, -0.05742194876074791, 0.03407061845064163, -0.03311729058623314, 0.06773443520069122, -0.03998597338795662, -0.006481810472905636, -0.03627919778227806, -0.017889684066176414, 0.013809001073241234, 0.07114455103874207, 0.010989291593432426, -0.015455526299774647, 0.0003735657373908907, 0.022654801607131958, 0.11339202523231506, 0.0021488999482244253, 0.030906926840543747, 0.06221974268555641, -0.03395116329193115, -0.025835871696472168, -0.027941599488258362, 0.0038954485207796097, -0.0015053946990519762, 0.0014808080159127712, 0.07850057631731033, -0.04102467745542526, -0.004693922586739063, -0.024663813412189484, -0.01760472171008587, 0.024299409240484238, 0.012064727954566479, 0.045522540807724, 0.07303425669670105, 0.03757436200976372, -0.01670946553349495, 0.02610194683074951, 0.01783742569386959, 0.03967216983437538, -0.04175277799367905, 0.019508348777890205, 0.04533328488469124, 0.02209845930337906, -0.017055781558156013, -0.034861695021390915, -0.041620176285505295, -0.014376585371792316, 0.01470243651419878, -0.04904256761074066, -0.046049218624830246, -0.019794248044490814, 0.04520021751523018, -0.011326572857797146, -0.00857530441135168, -0.02420741133391857, -0.04291921481490135, 0.017594821751117706, -0.007415164727717638, 0.006544232368469238, -0.044744495302438736, 0.0241722222417593, 0.03478098660707474, 0.043712325394153595, -0.03592267259955406, 0.009651517495512962, -0.022213194519281387, -0.01956716738641262, 0.005760695319622755, 0.010272026993334293, 0.007413072511553764, 0.10415322333574295, 0.04732401669025421, -0.021639734506607056, -0.08534838259220123, 0.008077283389866352, 0.03481113538146019, -0.0014599798014387488, 0.017821693792939186, -0.018925374373793602, 0.0526108480989933, 0.028606850653886795, 0.021823260933160782, -0.055002156645059586, -0.002022980945184827, 0.015016655437648296, 0.006051788572221994, -0.004840748850256205, -0.020264245569705963, -0.06929558515548706, -0.007852250710129738, -0.04758601263165474, -0.05797441303730011, -0.06417422741651535, -0.014740278013050556, 0.01831122487783432, -0.0778801366686821, 0.0037977274041622877, 0.07902241498231888, 0.08098778128623962, 0.023205392062664032, 0.042552635073661804, 0.026476318016648293, 0.0007658022223040462, -0.006969232112169266, -0.03483693674206734, 0.035014957189559937, 0.029453380033373833, -0.02106337994337082, 0.0693386048078537, 0.00029722379986196756, 0.013158517889678478, -0.010357826016843319, -0.03675369173288345, 0.024425840005278587, 0.045646511018276215, -0.00941778440028429, -0.0011569085763767362, 0.014939735643565655, -0.037804555147886276, 0.0016691688215360045, 0.017886316403746605, -0.037830401211977005, -0.05208877846598625, 0.03590865433216095, -0.01490421500056982, -0.007737255189567804, 0.07084387540817261, 0.05435512587428093, 0.021767377853393555, 0.0010195565409958363, -0.025926686823368073, -0.04069457948207855, 0.03376089781522751, -0.013179227709770203, 0.06704183667898178, -0.019122811034321785, -0.04992573335766792, 0.025290241464972496, 0.04815388470888138, 0.0298155527561903, 0.04484551399946213, -0.04306209832429886, -0.02379441447556019, -0.04076506197452545, 0.0009216590551659465, -0.029986519366502762, -0.011617095209658146, -0.05723003298044205, 0.02450304850935936, 0.014058832079172134, -0.012907016091048717, 0.02200748398900032, -0.06419983506202698, 0.07967029511928558, -0.009996666572988033, 0.030495019629597664, 0.0375177375972271, 0.0013151457533240318, 0.005141028668731451, 0.01842113956809044, 0.08663962036371231, -0.02970960922539234, -0.03743480518460274, -0.03603493049740791, 0.004213608801364899, 0.028594451025128365, -0.050399888306856155, -0.019917281344532967, 0.004982050508260727, 0.034966450184583664, -0.008828197605907917, 0.08013434708118439, -0.04925710707902908, 0.016591208055615425, -0.0017876951023936272, -0.010569257661700249, -0.003481070976704359, 0.042342234402894974, -0.005634400062263012, 0.07559359073638916, -0.017936117947101593, -0.013022656552493572, 0.053059957921504974, -0.012046621181070805, 0.005272113252431154, -0.03433142229914665, 0.048408880829811096, 0.04463896527886391, 0.018749600276350975, 0.012914258986711502, 0.019284546375274658, 0.025877851992845535, -0.025515982881188393, -0.02400229126214981, -0.014248314313590527, -0.006549648474901915, -0.048545707017183304, 0.07504499703645706, -0.054608747363090515, -0.011429408565163612, 0.038678672164678574, -0.04403242468833923, -0.034264180809259415, -0.014921274967491627, -0.0656604990363121, 0.02626541070640087, -0.038033582270145416, 0.010612346231937408, -0.019640523940324783, 0.029288366436958313, 0.0008204364567063749, 0.020803922787308693, 0.04501665011048317, 0.044390834867954254, -0.015564375557005405, -0.0012526524951681495, 0.02278895676136017, 0.016095751896500587, 0.05613576993346214, -0.03889351710677147, 0.004915757104754448, 0.03902552276849747, -0.018268374726176262, 0.02493133768439293, 0.09298764914274216, -0.01647123508155346, -0.048725325614213943, 0.026031294837594032, 0.02542802132666111, -0.06321579217910767, -0.008705402724444866, 0.01854024827480316, -0.0028904853388667107, -0.024041730910539627, -0.01980869472026825, 0.02030603401362896, -0.02620130591094494, 0.00318694906309247, -0.01396249234676361, -0.07629986107349396, -0.050201281905174255, 0.00020806796965189278, 0.006340959575027227, 0.0048276805318892, 0.00899395439773798, 0.010395411401987076, 0.07201001793146133, -0.017340047284960747, 0.020943481475114822, 0.05439862981438637, -0.005637125112116337, -0.01699071191251278, 0.01627502031624317, -0.03456496819853783, 0.004111857153475285, -0.02939675934612751, -0.019224368035793304, -0.045442886650562286, -0.026822295039892197, 0.021450530737638474, -0.05118745565414429, -0.009421032853424549, 0.0647997036576271, -0.06876000016927719, 0.02073536068201065, -0.027266914024949074, -0.009794950485229492, 0.008512335829436779, 0.011518859304487705, -0.024887993931770325, 0.0011543979635462165, 0.03738708049058914, 0.010782609693706036, 0.05045362189412117, 0.05392972007393837, -0.02170121856033802, -0.038416583091020584, 0.08034984022378922, -0.01855980046093464, 0.03956468030810356, -0.023371580988168716, -0.014140747487545013, 0.02911446802318096, 0.014514844864606857, -0.04357985034584999, -0.0297798290848732, 0.019258061423897743, 0.0338110476732254, -0.047041792422533035, 0.03366226330399513, 0.017554687336087227, 0.02397199720144272, -0.06671159714460373, 0.031440384685993195, 0.011421252973377705, 0.002408265834674239, -0.03291040286421776, 0.04270348697900772, -0.02571922354400158, -0.003145290771499276, 0.003176150843501091, 0.014276581816375256, 0.07871124148368835, 0.04624335840344429, -0.0018824802245944738, 0.04078105837106705, -0.022804297506809235, 0.006091458722949028, -0.04142133891582489, -0.01721448451280594, -0.02108040638267994, 0.0560101754963398, -0.01756175607442856, 0.01072442065924406, -0.018321793526411057, -0.006271690130233765, -0.032863155007362366, 0.008124538697302341, 0.02845602296292782, -0.044738855212926865, -0.024619968608021736, 0.011567926034331322, -0.012816949747502804, -0.011334630660712719, 0.052428461611270905, -0.04402683302760124, 0.03199850395321846, -0.0010366578353568912, -0.06318378448486328, -0.00592420157045126, -0.0170235987752676, 0.01947895996272564, -0.01873377338051796, 0.028652969747781754, 0.04287906363606453, 0.06071970611810684, 0.02593102678656578, -0.05028834566473961, 0.014795270748436451, 0.009912890382111073, 0.06536722928285599, -0.03936563804745674, -0.058156512677669525, -0.01932884380221367, -0.048040393739938736, -0.010219357907772064, -0.02853226847946644, 0.01092323288321495, -0.03479085862636566, -0.006054520606994629, -0.00545708741992712, 0.05264978110790253, -0.030074795708060265, -0.09945523738861084, 0.02268301323056221, -0.06243942305445671, -0.05884119123220444, -0.045277588069438934, -0.04002811387181282, 0.03013259917497635, -0.00009029519424075261, 0.03440903499722481, 0.017994819208979607, -0.0164595078676939, 0.006879455875605345, -0.03291666507720947, 0.03610512241721153, 0.0534014031291008, -0.025141356512904167, -0.01770257018506527, -0.05525616556406021, 0.05678485706448555, -0.012901331298053265, 0.051687613129615784, 0.046188414096832275, -0.0008468475425615907, -0.047906551510095596, -0.00969342328608036, 0.01921415701508522, -0.011602153070271015, 0.04079727083444595, 0.05041427165269852, -0.05328969657421112, 0.005304546561092138, 0.01421566866338253, -0.024230003356933594, 0.02803078666329384, -0.04371662437915802, -0.0011726852972060442, -0.02105923742055893, 0.00030509501812048256, -0.032574430108070374, 0.04050082713365555, 0.06568093597888947, -0.00005351222353056073, -0.01818687841296196, 0.05409138277173042, -0.0212848000228405, 0.013460406102240086, -0.026827827095985413, 0.08647384494543076, -0.048474665731191635, 0.04853188246488571, 0.060744646936655045, 0.03924719616770744, 0.032712094485759735, 0.013555648736655712, -0.0010787224164232612, -0.001791359856724739, 0.0696597546339035, 0.023406697437167168, 0.04759839177131653, -0.059569649398326874, 0.026217645034193993, -0.06021043285727501, 0.005246944725513458, 0.04742463678121567, -0.0017624467145651579, 0.02734631858766079, -0.03171379491686821, -0.01222875714302063, -0.0552695207297802, -0.024873685091733932, 0.04293215274810791, -0.03155340254306793, -0.09660312533378601, -0.05078421160578728, -0.033286016434431076, 0.007754183374345303, 0.028630482032895088, -0.0035619507543742657, 0.00023547634191345423, -0.03361530974507332, -0.03302439674735069, 0.03504336252808571, 0.051847632974386215, 0.034844618290662766, 0.010001380927860737, -0.07278774678707123, -0.0020143541041761637, 0.014297688379883766, 0.005479911342263222, 0.041122183203697205, -0.012178831733763218, -0.06632709503173828, 0.019465917721390724, -0.07771974056959152, -0.017367612570524216, 0.0227004736661911, -0.03928642347455025, 0.013696356676518917, -0.02248922362923622, 0.026997050270438194, -0.013506155461072922, -0.014594759792089462, -0.022511836141347885, 0.0038358529563993216, -0.03879605233669281, -0.002194239990785718, -0.054091278463602066, 0.014978064224123955, 0.018075382336974144, -0.018288005143404007, 0.008035024628043175, -0.023863328620791435, 0.003914232831448317, -0.03486521169543266, -0.05533464998006821, -0.01402398943901062, 0.03383338451385498, -0.026764793321490288, -0.009740388952195644, 0.0005001441459171474, 0.01504365261644125, 0.008357557468116283, 0.007130666635930538, 0.0481780543923378, 0.019737552851438522, -0.030278176069259644, 0.07582807540893555, -0.048766955733299255, 0.016095377504825592, -0.04374312981963158, 0.013975199311971664, 0.032426975667476654, 0.025946680456399918, 0.00899116788059473, 0.013390796259045601, -0.007349839434027672, -0.044041115790605545, 0.040041640400886536, -0.004585532937198877, 0.0236949659883976, -0.026266755536198616, -0.019152648746967316, -0.003604863304644823, 0.006768789608031511, -0.01808936893939972, 0.07873339205980301, 0.06408669054508209, -0.03905726969242096, -0.02509216219186783, 0.043169401586055756, 0.008576757274568081, -0.04120561107993126, -0.00793501827865839, 0.026250071823596954, 0.02139095962047577, 0.016941139474511147, 0.040052879601716995, 0.015388376079499722, 0.014045905321836472, 0.0026904018595814705, -0.040114592760801315, 0.019903816282749176, 0.0029209221247583628, 0.033102523535490036, 0.03626188635826111, -0.06508603692054749, 0.009713488630950451, 0.01673961989581585, 0.04360881820321083, 0.0032737634610384703, 0.007441712077707052, -0.018741384148597717, -0.03319608047604561, 0.031067954376339912, -0.02218497358262539, 0.0029660039581358433, 0.0038414865266531706, -0.0384017713367939, 0.006733468268066645, 0.00044137719669379294, 0.033104464411735535, 0.012295699678361416, 0.009380700066685677, 0.009167489595711231, -0.02947596274316311, 0.06196253001689911, -0.00871763564646244, -0.05266101658344269, -0.004898790270090103, -0.03176477551460266, -0.02313276380300522, -0.025181589648127556, -0.03027494065463543, -0.0207891333848238, -0.013361756689846516, -0.010507273487746716, -0.02000928483903408, -0.014304818585515022, 0.005349434446543455, -0.006773392204195261, 0.08671749383211136, -0.026485634967684746, -0.016618285328149796, -0.053483106195926666, -0.008088696748018265, 0.01990680582821369, 0.005100136157125235, 0.004173277411609888, -0.09289100021123886, -0.02227681688964367, 0.03751762583851814, -0.05902240052819252, 0.007443172857165337, 0.0862911194562912, 0.007332155015319586, -0.04813159629702568, -0.016287226229906082, -0.05066844820976257, 0.017181606963276863, -0.012969350442290306, -0.04479050263762474, 0.045281510800123215, -0.018046731129288673, -0.028462905436754227, 0.025630183517932892, 0.023038987070322037, -0.029615582898259163, -0.00856296718120575, 0.017955485731363297, 0.039888858795166016, 0.014052328653633595, -0.05383817479014397, -0.0008424247498624027, -0.030410511419177055, 0.011975003406405449, 0.01944725215435028, -0.026792265474796295, -0.008321010507643223, -0.013427489437162876, -0.014769061468541622, -0.06733085215091705, 0.022722849622368813, 0.06259346008300781, -0.057150039821863174, 0.038511164486408234, -0.0017701521283015609, -0.02274572104215622, -0.031019533053040504, -0.04938967898488045, 0.031911700963974, 0.08590724319219589, -0.013166134245693684, 0.025451913475990295, 0.010411704890429974, -0.037800297141075134, -0.01932128332555294, -0.017545392736792564, -0.054788827896118164, 0.002946159103885293, 0.009695577435195446, 0.014434429816901684, -0.06550974398851395, -0.02391107939183712, 0.035302020609378815, 0.00915443804115057, -0.037156909704208374, 0.038915857672691345, 0.06518792361021042, 0.04333095997571945, -0.09575894474983215, 0.0581694133579731, -0.03639408200979233, 0.01767757534980774, -0.07833895832300186, 0.05013936012983322, 0.033721521496772766, 0.06767325848340988, -0.02583407796919346, 0.003840586170554161, -0.030169714242219925, 0.03776741027832031, 0.007918467745184898, 0.02224315144121647, -0.012958194129168987, -0.11605457961559296, 0.017277752980589867, -0.060628458857536316, -0.03361578285694122, 0.023572485893964767, 0.0014655038248747587, 0.006779863033443689, 0.022977428510785103, -0.051649972796440125, 0.023725254461169243, -0.045590974390506744, 0.012216703034937382, -0.04011029377579689, -0.057151950895786285, -0.0025355706457048655, -0.012300686910748482, 0.04805123805999756, -0.030360432341694832, 0.017666248604655266, -0.034034013748168945, 0.02657419443130493, -0.018736908212304115, 0.032134007662534714, -0.0036688395775854588, -0.05787448585033417, -0.0437091663479805, 0.02051130123436451, 0.013086901977658272, -0.04222143068909645, 0.022450104355812073, 0.0219133198261261, -0.040039099752902985, -0.027014080435037613, -0.015597394667565823, 0.005913214758038521, 0.0032453201711177826, -0.008708462119102478, 0.0470108762383461, 0.010134289972484112, 0.026154354214668274, 0.034084662795066833, 0.008338883519172668, -0.015016832388937473, -0.0008774506859481335, -0.02690097875893116, 0.0022266258019953966, 0.02356712520122528, 0.002850001212209463, 0.0015684135723859072, -0.021060418337583542, 0.0013514346210286021, 0.054862938821315765, 0.0061690593138337135, 0.039769452065229416, 0.033836349844932556, 0.013585024513304234, 0.001967162825167179, -0.06455088406801224, 0.052522383630275726, -0.00041830178815871477, -0.059113215655088425, -0.008012688718736172, 0.02160370722413063, -0.0023632911033928394, -0.01975097320973873, 0.02313202992081642, 0.001655662665143609, -0.00960222352296114, -0.042147837579250336, 0.02063162252306938, -0.048476509749889374, 0.012034901417791843, -0.019946595653891563, -0.031437430530786514, -0.005454625468701124, -0.01862158626317978, 0.0234217569231987, -0.01907552406191826, 0.02109702304005623, 0.022686950862407684, 0.01303846761584282, 0.04252097010612488, -0.046851612627506256, -0.045371636748313904, -0.03024071268737316, -0.001833306159824133, -0.04956525191664696, -0.021052161231637, 0.01580614224076271, 0.01915251649916172, -0.020289434120059013, -0.017715254798531532, 0.06500903517007828, -0.006289436016231775, 0.09504877030849457, 0.11696434766054153, -0.07734332233667374, 0.03481966629624367, -0.01720474101603031, 0.016877559944987297, 0.04086510092020035, -0.023709869012236595, -0.08106303215026855, 0.005566223990172148, -0.022519275546073914, -0.04143071547150612, -0.029755868017673492, 0.011434697546064854, 0.004168202634900808 ]
<p>I've been studying Bagger &amp; Giannakis paper on the SuperHiggs Mechanism found <a href="http://arxiv.org/abs/hep-th/0502107v1" rel="nofollow">here</a>. </p> <p>The paper shows how SUSY is broken by a $B_{\mu\nu}$ gauge field background restricted to $T^3$ in $M^7\times T^3$ Compactification of the heterotic string.</p> <p><em>My question is, have these results been generalised to different Backgrounds and/or Compactifications (Perhaps even Calabi Yau 3-folds)?</em> </p> <p>So far my search has shown up no results, any pointers in the right direction are greatly appreciated, Thanks!</p>
g8367
[ 0.0553073026239872, 0.09023351222276688, -0.013484922237694263, -0.03785309940576553, -0.0035902017261832952, -0.0029432144947350025, 0.042912326753139496, 0.029622703790664673, 0.0010435165604576468, -0.010130166076123714, -0.025270510464906693, -0.0239998921751976, -0.0014537324896082282, 0.07048655301332474, -0.007284150924533606, 0.009523642249405384, 0.024357061833143234, 0.028401074931025505, 0.003807228058576584, -0.017619885504245758, -0.04661695659160614, 0.0039039338007569313, -0.007195260841399431, -0.02830372005701065, -0.012210192158818245, -0.03131253644824028, 0.05137094855308533, -0.0231653843075037, -0.0013612007023766637, -0.026790110394358635, 0.06672346591949463, -0.05880509316921234, 0.039926063269376755, -0.06291904300451279, 0.034004129469394684, -0.0027266493998467922, 0.044248610734939575, 0.005015953443944454, 0.02012493833899498, 0.03824079781770706, 0.012565825134515762, -0.02243589051067829, 0.006678312551230192, 0.013469967991113663, -0.038773685693740845, 0.005041136872023344, -0.019287390634417534, 0.009387457743287086, 0.009474811144173145, -0.02232278138399124, 0.03728773444890976, 0.04636778682470322, 0.0378166064620018, -0.0625225380063057, -0.011579426005482674, 0.052066124975681305, 0.024207644164562225, -0.034991323947906494, 0.056146275252103806, 0.027967097237706184, 0.014583793468773365, -0.014173978939652443, 0.017744658514857292, 0.01606268621981144, 0.052394669502973557, 0.00905950553715229, -0.025533894076943398, -0.010315845720469952, -0.041116707026958466, -0.03314528241753578, 0.005091346334666014, -0.042106665670871735, 0.01974322460591793, -0.014554514549672604, -0.005993206985294819, 0.031031232327222824, -0.03789982944726944, -0.02972712554037571, -0.06770088523626328, 0.027865204960107803, -0.07326646149158478, -0.02944842167198658, 0.022212335839867592, 0.02962161786854267, 0.059881825000047684, -0.11482299119234085, 0.01085403747856617, 0.07053527981042862, -0.04820144549012184, -0.018970057368278503, 0.004748033359646797, 0.028734244406223297, -0.04422954097390175, -0.06302522122859955, 0.0045898305252194405, 0.0509728379547596, 0.010956093668937683, 0.062016986310482025, -0.08951668441295624, -0.041374146938323975, -0.009343747980892658, 0.0377991609275341, 0.049966052174568176, 0.04599946737289429, -0.04862081632018089, 0.03153705224394798, 0.03132699429988861, -0.0254521407186985, 0.0196714885532856, -0.014508049935102463, -0.03738102689385414, 0.033928338438272476, -0.015792984515428543, -0.016492346301674843, -0.02789268270134926, -0.022541619837284088, -0.038978591561317444, 0.04298144951462746, -0.03225211799144745, -0.02787592262029648, -0.03728873282670975, 0.0038086245767772198, -0.007183104287832975, -0.05469985678792, -0.09210378676652908, 0.005114465020596981, -0.022363189607858658, 0.009597450494766235, 0.010603101924061775, 0.0015787212178111076, 0.02609861269593239, -0.0573277585208416, 0.029500208795070648, 0.02097262628376484, 0.030389927327632904, 0.08652433753013611, 0.005357063375413418, -0.019445033743977547, 0.01878872886300087, -0.0051512629725039005, -0.03712978586554527, -0.03808159753680229, -0.0035273507237434387, -0.005126893054693937, 0.02389655075967312, -0.041937001049518585, 0.035194024443626404, -0.0014416322810575366, -0.045504312962293625, 0.03052143007516861, 0.02155112288892269, 0.11673867702484131, 0.03860867768526077, -0.01513131894171238, 0.021076582372188568, -0.0013204870047047734, 0.027192961424589157, 0.023991713300347328, -0.002431226195767522, -0.035488151013851166, -0.01359243132174015, -0.014979807659983635, 0.023487644270062447, 0.01647276058793068, -0.0627136379480362, 0.05786222219467163, 0.001365234493277967, -0.0030706319957971573, 0.003697318257763982, -0.020350370556116104, -0.08705081045627594, 0.017513295635581017, 0.011784682050347328, 0.006870790384709835, -0.06505133211612701, 0.06802698969841003, 0.012283863499760628, -0.045159097760915756, 0.029647519811987877, 0.011779073625802994, -0.019302960485219955, -0.04554707556962967, -0.015287031419575214, -0.047960951924324036, 0.015958458185195923, -0.007975286804139614, 0.0033779554069042206, 0.0051514082588255405, 0.00003917020876542665, 0.014112099073827267, -0.013864307664334774, 0.016156962141394615, 0.020949136465787888, 0.016613012179732323, -0.02891417406499386, 0.01906071975827217, 0.037096451967954636, 0.004305826034396887, 0.019150204956531525, -0.006689796689897776, -0.01303117722272873, 0.02508441172540188, 0.032056912779808044, -0.021037591621279716, -0.002114272676408291, 0.0023073970805853605, -0.006964702159166336, 0.028188318014144897, -0.004084298852831125, -0.0219169519841671, -0.09176263958215714, -0.025935593992471695, 0.03259330987930298, 0.008916082791984081, -0.04769664630293846, -0.038899194449186325, 0.023303303867578506, 0.009338952600955963, 0.019544417038559914, 0.011469986289739609, -0.012884195894002914, -0.002347968751564622, 0.031876109540462494, -0.01077584084123373, -0.00003560904224286787, 0.007209506817162037, 0.02015102095901966, -0.007127007469534874, 0.014940556138753891, -0.030188046395778656, -0.04321816936135292, -0.004002031870186329, 0.007524210028350353, -0.07893232256174088, -0.005371074192225933, -0.02508356235921383, -0.023232335224747658, -0.01919771544635296, 0.06171566992998123, 0.031901247799396515, 0.04825593903660774, 0.05999713018536568, 0.02184719406068325, 0.02093249373137951, 0.04909135773777962, -0.007282949984073639, 0.04175596311688423, -0.02837396040558815, 0.009275790303945541, 0.03613186255097389, -0.016527468338608742, -0.022968288511037827, 0.011457025073468685, 0.010184615850448608, -0.03740258142352104, -0.032820288091897964, 0.037897542119026184, -0.027907997369766235, 0.00126472522970289, -0.0019256697269156575, 0.03872216120362282, 0.02526029758155346, 0.03240054100751877, -0.0052208309061825275, -0.0216792281717062, -0.005288057029247284, 0.052070531994104385, -0.060527559369802475, -0.05277789384126663, -0.03144296258687973, -0.05499850586056709, 0.02864784561097622, 0.02865593694150448, 0.006653647869825363, -0.013063143938779831, -0.007813464850187302, -0.014869559556245804, 0.028865637257695198, -0.03287571668624878, -0.06537023186683655, -0.021517589688301086, 0.015250594355165958, -0.004145394545048475, -0.05037693679332733, -0.006877195555716753, -0.020421797409653664, -0.035205356776714325, -0.02879789099097252, -0.03184707835316658, 0.07458363473415375, -0.01666424423456192, -0.017043154686689377, 0.07195315510034561, 0.028719769790768623, 0.0014801827492192388, 0.04325130209326744, -0.020359458401799202, -0.03220605477690697, -0.017760803923010826, 0.01956571452319622, 0.000964333419688046, 0.03433184325695038, -0.0077630383893847466, 0.021523181349039078, -0.003309390274807811, -0.0177383404225111, -0.05385546386241913, -0.0281330905854702, -0.005167654249817133, -0.033998750150203705, -0.0692327469587326, -0.0185602568089962, 0.05983970686793327, -0.01477040071040392, 0.02612420916557312, -0.026251984760165215, 0.028632400557398796, 0.009072361513972282, 0.005255161318928003, 0.01859840750694275, -0.046331435441970825, 0.010254723951220512, 0.0049938028678298, -0.027921035885810852, 0.03146277740597725, 0.06858685612678528, -0.009712910279631615, 0.020322294905781746, -0.008262459188699722, -0.017526976764202118, -0.02083885669708252, -0.076170913875103, 0.008259400725364685, -0.010448707267642021, -0.08382641524076462, 0.010270815342664719, -0.012245912104845047, 0.05158865451812744, 0.042676497250795364, 0.017567001283168793, -0.03328326344490051, 0.0319981649518013, -0.04913300648331642, -0.012876865454018116, 0.027048340067267418, 0.03515462577342987, -0.030299119651317596, -0.026495778933167458, 0.06723567098379135, 0.025917984545230865, -0.03293418139219284, 0.047526948153972626, 0.03881499171257019, -0.011822753585875034, 0.004300921224057674, 0.06424937397241592, -0.02020750753581524, 0.05442018806934357, 0.004361727740615606, -0.03329702839255333, 0.00157631142064929, 0.05603880062699318, 0.02188269980251789, -0.049783263355493546, 0.01957590878009796, -0.009216513484716415, -0.013016779907047749, -0.029139984399080276, 0.04397711157798767, 0.004558127373456955, 0.016088061034679413, -0.006738715805113316, 0.028187325224280357, 0.026357021182775497, -0.0030754448380321264, -0.01746433600783348, 0.0341745987534523, 0.010383930057287216, 0.009328502230346203, -0.03131555765867233, 0.006019570864737034, 0.03505169600248337, 0.05413183942437172, 0.01613520085811615, 0.006491517182439566, 0.046168647706508636, -0.017568426206707954, 0.0035847320687025785, -0.06200658157467842, -0.003028264967724681, -0.04158409684896469, 0.05045413598418236, -0.061108943074941635, -0.005395685322582722, -0.0436738058924675, -0.01205134205520153, -0.017094435170292854, -0.03748700022697449, -0.037529513239860535, -0.013845046982169151, -0.002157052746042609, 0.0006061455351300538, -0.007494842633605003, -0.04037865623831749, -0.07833881676197052, -0.030047502368688583, 0.053964223712682724, 0.018114624544978142, 0.014353918842971325, -0.05271865800023079, 0.03582462668418884, 0.01724587194621563, -0.04641082510352135, -0.06819171458482742, 0.06582792103290558, -0.06592365354299545, -0.013564270921051502, -0.034063056111335754, -0.0032530289608985186, -0.05471542477607727, 0.04277238994836807, 0.004464870318770409, -0.02906578965485096, 0.0004961720551364124, -0.03994869068264961, 0.07917121797800064, 0.01187228225171566, -0.007382442243397236, 0.004492610227316618, -0.025624632835388184, 0.08409158140420914, 0.004320209845900536, -0.032004088163375854, 0.038776036351919174, -0.051099952310323715, -0.022110460326075554, -0.030862120911478996, -0.04639347270131111, -0.032712243497371674, -0.005297163035720587, 0.1016499400138855, 0.003937509376555681, 0.018814336508512497, -0.018114907667040825, -0.0020853860769420862, -0.0016441305633634329, -0.018096959218382835, -0.0044673653319478035, -0.041802700608968735, -0.0428481288254261, -0.04458049312233925, 0.03415965288877487, -0.0316622368991375, 0.014223857782781124, -0.007023433223366737, -0.026975009590387344, -0.018936609849333763, 0.015629056841135025, 0.04863850399851799, -0.050489649176597595, -0.0036707210820168257, -0.04944448918104172, 0.024941354990005493, 0.03338669240474701, 0.01988927088677883, 0.0010340262670069933, -0.09166816622018814, 0.05558685585856438, 0.017965665087103844, -0.007648270111531019, 0.01811819151043892, -0.024922050535678864, -0.006811089813709259, -0.03636030852794647, -0.003473670920357108, -0.008894127793610096, -0.05037946626543999, 0.03306523337960243, -0.023281307891011238, -0.02428228035569191, 0.01276624109596014, -0.0101894186809659, -0.015904363244771957, 0.018785178661346436, -0.02506091259419918, 0.045442499220371246, -0.07152041792869568, -0.006300895009189844, -0.04407623037695885, -0.07388555258512497, 0.001921152463182807, -0.03368737921118736, 0.0564008392393589, -0.03829681873321533, -0.018828654661774635, -0.0045644487254321575, 0.06788119673728943, 0.0009793642675504088, -0.05830445885658264, 0.0120810242369771, -0.0028507704846560955, -0.002268341602757573, 0.009365028701722622, 0.0682390108704567, 0.01528521254658699, 0.05234524607658386, 0.07061346620321274, -0.027447305619716644, 0.0026895503979176283, -0.06318715214729309, -0.02953086420893669, -0.003118292661383748, -0.06010372191667557, -0.04415101930499077, -0.00017998687690123916, 0.04799952358007431, -0.0003542244667187333, 0.04954109713435173, -0.0012162452330812812, -0.0357527993619442, -0.031111758202314377, 0.03228643909096718, 0.02642207220196724, -0.00673714792355895, 0.06167318671941757, 0.06752200424671173, -0.09134732931852341, -0.04281168803572655, 0.057257939130067825, 0.002515900181606412, 0.008510109037160873, -0.031839415431022644, 0.09547214955091476, 0.01935209333896637, 0.0775686502456665, 0.00917016714811325, 0.015063652768731117, 0.004389388021081686, -0.034300994127988815, 0.019874688237905502, 0.016559001058340073, -0.08689665049314499, 0.034436892718076706, -0.014431316405534744, -0.02606959268450737, -0.003345315810292959, -0.05085553601384163, 0.024462683126330376, 0.021803447976708412, -0.07323121279478073, 0.0022711383644491434, 0.003544345498085022, 0.01270606741309166, 0.02147216722369194, -0.01573915034532547, 0.02319624274969101, -0.047473885118961334, -0.04608958587050438, -0.027168165892362595, 0.03658982738852501, -0.011894757859408855, -0.017886316403746605, 0.03303513675928116, 0.014627941884100437, 0.037987321615219116, -0.006960795260965824, -0.017721382901072502, -0.03113555908203125, 0.055742185562849045, 0.0216206107288599, -0.021969107910990715, 0.052951879799366, 0.037100695073604584, 0.04539516940712929, -0.035239141434431076, 0.018737472593784332, 0.044365379959344864, -0.04914672300219536, -0.038018740713596344, 0.023531269282102585, 0.026033906266093254, 0.0015615952434018254, 0.036881640553474426, -0.024441000074148178, -0.03371229022741318, 0.05237770453095436, -0.04711699113249779, 0.032583288848400116, 0.04192577674984932, 0.019924689084291458, 0.02162589132785797, 0.013017931021749973, -0.01617124117910862, 0.05614747852087021, 0.032677557319402695, 0.024242430925369263, 0.001804098952561617, -0.003950399812310934, -0.05759274214506149, 0.010643068701028824, -0.008787369355559349, 0.034395113587379456, 0.07547207921743393, -0.058776676654815674, -0.000904182146769017, 0.12629131972789764, 0.030958889052271843, 0.02439962327480316, -0.023496737703680992, -0.002830354031175375, 0.0017892173491418362, -0.019202379509806633, -0.014795784838497639, 0.03677958995103836, 0.009374229237437248, -0.07170199602842331, 0.004994452465325594, 0.015498388558626175, 0.044770848006010056, -0.03204423934221268, 0.07047190517187119, 0.01197437010705471, -0.02595861814916134, -0.013108721002936363, -0.011476474814116955, 0.022355204448103905, 0.011761137284338474, 0.027449827641248703, 0.011629661545157433, 0.001321899821050465, 0.06676074117422104, 0.00403945567086339, -0.014432300813496113, 0.030111540108919144, 0.022838320583105087, 0.03141896799206734, 0.029485050588846207, 0.05387502163648605, 0.01191923301666975, -0.039130039513111115, 0.0075968848541378975, 0.027828864753246307, 0.03662549704313278, -0.09230822324752808, 0.06507789343595505, 0.029306689277291298, -0.010940540581941605, 0.027538498863577843, 0.010193336755037308, -0.03257418051362038, 0.0379909873008728, 0.03053157404065132, -0.04612255468964577, 0.02208828553557396, 0.002881020773202181, -0.06922242045402527, -0.018987825140357018, -0.07114481925964355, 0.006463357247412205, -0.06382181495428085, -0.01749558188021183, 0.007696697022765875, 0.04689794033765793, -0.042988862842321396, 0.008924967609345913, 0.06643962860107422, -0.015133087523281574, -0.007472516503185034, 0.02055346593260765, 0.024115489795804024, 0.014323112554848194, -0.04550716653466225, -0.025851193815469742, 0.021520789712667465, -0.011138662695884705, -0.031445957720279694, 0.007525145076215267, 0.03942365199327469, -0.011479020118713379, -0.030248038470745087, 0.09115266799926758, 0.008963417261838913, 0.00904810894280672, -0.003683239221572876, -0.002748684026300907, 0.03001152165234089, -0.004896367434412241, -0.030473729595541954, 0.0093925716355443, 0.04006921127438545, 0.07799452543258667, -0.021920278668403625, -0.016186058521270752, -0.02563280425965786, 0.01698705367743969, -0.017408860847353935, -0.01939876191318035, 0.04864014312624931, 0.008782697841525078, -0.0188782699406147, -0.016873687505722046, -0.003151619341224432, -0.04243093729019165, -0.04979925602674484, 0.025682421401143074, 0.030258601531386375, -0.05464641749858856, -0.014889974147081375, -0.01928681880235672, 0.00898126233369112, -0.022003812715411186, 0.04875485226511955, -0.03854626789689064, -0.015101222321391106, 0.0862547755241394, -0.019708221778273582, -0.08183164149522781, -0.010077162645757198, 0.023941438645124435, -0.029992541298270226, -0.034849509596824646, 0.022798262536525726, -0.025029368698596954, -0.008907195180654526, 0.027482327073812485, -0.03835447505116463, -0.01123100332915783, -0.002189323306083679, 0.03729134798049927, 0.05923444777727127, -0.022571584209799767, -0.01875550113618374, 0.03412764519453049, -0.08215788751840591, -0.023965200409293175, -0.004302756395190954, 0.020513981580734253, -0.0625249445438385, 0.05280867591500282, -0.024172214791178703, -0.06200852245092392, -0.04576624929904938, -0.0008657932630740106, -0.014166158623993397, 0.013601088896393776, 0.0486692450940609, -0.06442251801490784, -0.012599723413586617, -0.06323084235191345, -0.042298827320337296, 0.07317382097244263, 0.005444630980491638, -0.0036092912778258324, 0.0614967867732048, 0.059715524315834045, -0.003992983605712652, 0.02163553424179554, -0.015823157504200935, 0.03149740770459175, -0.021967964246869087, -0.02187572792172432, -0.006339056883007288, -0.0032335196156054735, -0.004406808875501156, 0.021433237940073013, 0.015208392404019833, 0.07630174607038498, 0.011297416873276234 ]
<p>Let's say I've got an Earth-like planet with no atmosphere: it's just a barren ball of rock. I want to live there, but I don't like domes, so instead I'm just going to dig a big hole and let gravity keep the air in.</p> <p>How deep a hole do I need?</p> <p>According to a chart I found, the density of the atmosphere drops to pretty much zero by about 50km, at the top of the stratosphere. But 'pretty much zero' is not zero; the mesosphere beyond that extends up to about 80km and while vanishingly thin is responsible for dealing with most meteors.</p> <p>If my hole is a mere 50km deep, then, some of my air is going to diffuse out of the hole and onto the planet's surface. But the surface of my planet is largely flat; there's nowhere for the air to <em>go</em>, so it's just going to hang around and form a dynamic equilibrium. (Unlike, say, if I built a 50km wall and tried to keep the air inside. Air would leak over the top of the wall, fall down into the vacuum on the other side, and be lost forever. Which is why the Ringworld had walls 1000km high.)</p> <p>So I don't really know how shallow a hole I can get away with. I <em>can</em> replace the air, but I would like it to go without maintenance for at least small geological timescales. Any advice before I start up the earth-moving equipment?</p> <p>(Yes, it's SF worldbuilding.)</p>
g8368
[ -0.008261095732450485, 0.039074525237083435, -0.007216148544102907, 0.011690453626215458, -0.021774470806121826, 0.08723677694797516, 0.034744374454021454, -0.004687685053795576, -0.04301080480217934, -0.043615005910396576, 0.005556275602430105, -0.008336697705090046, 0.014030144549906254, -0.02613307721912861, -0.02792002633213997, 0.017256950959563255, -0.00047671658103354275, -0.022495899349451065, 0.03513668477535248, -0.016072312369942665, 0.0402098223567009, -0.034722134470939636, 0.0373416543006897, 0.004860362969338894, -0.028686244040727615, -0.05103447660803795, 0.025218961760401726, -0.03397025167942047, -0.02804132178425789, 0.00028323789592832327, 0.025874635204672813, 0.014086269773542881, 0.03351480886340141, 0.0193189587444067, -0.014368211850523949, -0.03894641250371933, 0.04849909618496895, 0.05350673198699951, 0.025680121034383774, -0.0725196972489357, 0.01926971785724163, -0.1238371729850769, 0.06188877671957016, 0.012478009797632694, 0.02693929336965084, -0.006257419008761644, -0.039291370660066605, -0.03952164202928543, 0.015068885870277882, -0.04929462447762489, -0.02543492615222931, 0.040172647684812546, -0.010702977888286114, -0.0397501066327095, -0.0535050630569458, -0.020077664405107498, -0.03476889058947563, -0.038278695195913315, 0.03173801675438881, -0.004924144595861435, -0.04896616190671921, -0.0406024195253849, 0.011812068521976471, 0.004978870507329702, -0.014265832491219044, 0.0934484675526619, -0.03402336686849594, -0.02335408702492714, -0.017184890806674957, -0.0015511480160057545, 0.009388160891830921, -0.0004900623462162912, -0.01902012899518013, -0.010494659654796124, -0.044823065400123596, 0.07007709890604019, -0.03947170078754425, 0.05218625068664551, 0.1171465590596199, 0.0003188061818946153, -0.02566276490688324, 0.029169883579015732, 0.05538610368967056, -0.04797501489520073, 0.008915485814213753, 0.008664732798933983, 0.02359675243496895, -0.07131386548280716, 0.033854130655527115, 0.026845913380384445, -0.007685898803174496, -0.01005647610872984, 0.028061673045158386, -0.027035126462578773, 0.06838805228471756, 0.010779835283756256, -0.01563156582415104, 0.07284332066774368, -0.05104450136423111, -0.03400709480047226, -0.00047659582924097776, -0.06460556387901306, -0.04366087540984154, 0.0027568372897803783, -0.006876547355204821, 0.0059811705723404884, 0.01973000355064869, 0.025899598374962807, 0.047620877623558044, 0.02620527520775795, 0.035101503133773804, 0.00485514709725976, -0.06717714667320251, -0.07130041718482971, 0.012658277526497841, -0.02104906737804413, -0.020480822771787643, 0.01998007483780384, 0.023285290226340294, 0.08334770053625107, 0.047286830842494965, 0.06165991351008415, 0.019528238102793694, -0.014966901391744614, -0.02474161982536316, -0.026794331148266792, 0.005575322546064854, 0.02124735899269581, 0.02483786828815937, -0.010507878847420216, -0.026492072269320488, -0.003538426011800766, -0.029295528307557106, 0.012499801814556122, -0.06441091001033783, 0.02077312208712101, -0.06585763394832611, -0.013662513345479965, -0.019524475559592247, -0.021534785628318787, -0.005019346717745066, 0.02850441075861454, 0.03029755689203739, -0.002022997010499239, -0.05226341634988785, 0.00010849672980839387, 0.001596983871422708, 0.015086738392710686, 0.06627851724624634, -0.03450315073132515, -0.014162120409309864, 0.03709845989942551, 0.001283074263483286, 0.016861429437994957, 0.036676257848739624, 0.08225572109222412, 0.034351229667663574, -0.005587957799434662, 0.04132533445954323, -0.027071664109826088, 0.02351723425090313, 0.03874380886554718, 0.0765378400683403, 0.026690863072872162, -0.07667553424835205, 0.009424634277820587, -0.025626707822084427, -0.022231057286262512, -0.021980416029691696, 0.013753640465438366, -0.008788962848484516, -0.013888949528336525, 0.054006289690732956, 0.05976087972521782, -0.08937651664018631, -0.04829525202512741, 0.05063677951693535, -0.04674632474780083, -0.03495316952466965, 0.016909189522266388, 0.08041549474000931, -0.0019127645064145327, -0.00701531209051609, -0.056169673800468445, 0.028029141947627068, 0.004847744479775429, 0.035980965942144394, -0.056523747742176056, -0.02619306556880474, -0.04039844125509262, 0.05990062654018402, -0.018003476783633232, 0.008684840984642506, 0.0914590135216713, -0.016218174248933792, 0.00752604054287076, 0.02713673748075962, -0.009751505218446255, -0.00912745762616396, 0.04526614025235176, 0.00557048199698329, 0.04489883780479431, 0.05904509499669075, 0.009443875402212143, 0.00716610811650753, 0.011299844831228256, -0.024056198075413704, 0.020748460665345192, -0.051096055656671524, 0.008163368329405785, 0.04087585210800171, -0.020120613276958466, 0.009328135289251804, 0.03220011666417122, 0.03793700411915779, 0.026914097368717194, -0.06832045316696167, 0.04646747186779976, -0.010890992358326912, -0.04721487686038017, 0.009405647404491901, -0.0029222052544355392, 0.025662004947662354, -0.057373519986867905, 0.0047028264962136745, -0.04025094956159592, -0.00966101698577404, 0.04621417075395584, 0.038784921169281006, -0.02061336860060692, 0.021333789452910423, -0.004640943370759487, -0.0015588457463309169, -0.03183125704526901, 0.04219286888837814, 0.06197093799710274, 0.03246515616774559, -0.014613546431064606, -0.03876596689224243, 0.03639395907521248, 0.011284750886261463, -0.0249377079308033, -0.06591389328241348, 0.005281365010887384, 0.055754486471414566, -0.0450025238096714, -0.07566624134778976, 0.025556443259119987, -0.0038471927400678396, 0.028224345296621323, 0.039450082927942276, -0.03772623836994171, -0.02634303830564022, -0.0051600136794149876, -0.05149712786078453, -0.019006121903657913, 0.014559084549546242, 0.006055893842130899, -0.027886265888810158, -0.007091047707945108, 0.015967700630426407, -0.061269212514162064, 0.009485344402492046, 0.029301991686224937, -0.04177848622202873, 0.0037735458463430405, -0.030470967292785645, 0.07809223234653473, -0.003912174142897129, 0.027346357703208923, 0.04441380128264427, -0.004050679970532656, 0.008555491454899311, 0.004869580734521151, 0.016728485003113747, 0.021901341155171394, 0.054668039083480835, 0.01624206081032753, 0.011551967822015285, 0.007696064654737711, 0.060224227607250214, -0.014367946423590183, -0.0018345045391470194, 0.040063776075839996, 0.05468670651316643, -0.07183162868022919, -0.004190475679934025, 0.02423781156539917, -0.02566004917025566, 0.027670055627822876, 0.03105277381837368, 0.000057690576795721427, 0.03519098460674286, 0.0791209414601326, 0.038926925510168076, 0.03642204776406288, -0.03993413224816322, 0.016326921060681343, 0.00925853755325079, 0.012984314002096653, 0.01025811955332756, -0.012877081520855427, 0.043253883719444275, 0.030385278165340424, 0.0034445489291101694, 0.017517048865556717, -0.03590386360883713, 0.015447651967406273, -0.049287233501672745, -0.004432755056768656, 0.031294237822294235, 0.04615160822868347, -0.0018823195714503527, 0.0029541808180510998, -0.026402806863188744, 0.0197049118578434, -0.03570083528757095, -0.04932716488838196, 0.02809067629277706, 0.020545773208141327, 0.021476589143276215, -0.03248712420463562, 0.026307929307222366, 0.023372767493128777, -0.01020341832190752, 0.08167003840208054, -0.039540987461805344, -0.04226963594555855, -0.05060951039195061, 0.0523923896253109, 0.014294271357357502, 0.009228105656802654, -0.05268527939915657, 0.00006905941700097173, -0.047451451420784, -0.003931127488613129, 0.07278548181056976, -0.03495605289936066, -0.011727170087397099, -0.003325248137116432, -0.04633144289255142, -0.013139559887349606, 0.0041085220873355865, -0.013644053600728512, 0.000736885704100132, -0.016854092478752136, 0.007854938507080078, 0.031536828726530075, -0.07834479957818985, -0.04239602014422417, 0.043713849037885666, -0.07511518150568008, 0.0066301519982516766, -0.02454199641942978, -0.05085834488272667, 0.047888025641441345, 0.056033648550510406, 0.0019232083577662706, 0.007902311161160469, -0.021947892382740974, 0.008515826426446438, 0.010129117406904697, -0.0009666724363341928, 0.02346753515303135, 0.01629525236785412, 0.009947559796273708, -0.08040416240692139, -0.03297333046793938, -0.013202431611716747, 0.009481525048613548, 0.0018817149102687836, -0.03899112343788147, -0.030524732545018196, 0.03797823563218117, -0.010434034280478954, -0.07159116864204407, 0.030962439253926277, 0.006653910037130117, 0.00447040144354105, 0.04011000692844391, 0.020198285579681396, -0.004133919253945351, -0.06158304214477539, -0.04420342296361923, -0.00776465842500329, 0.03394840285181999, -0.02540159784257412, -0.022474566474556923, 0.033539868891239166, 0.013902670703828335, -0.0023367730900645256, -0.053016748279333115, -0.023444483056664467, -0.014890152961015701, 0.04262656718492508, -0.03928457945585251, 0.005251993425190449, -0.017563043162226677, -0.03760550916194916, 0.006738244090229273, 0.07493859529495239, 0.026655005291104317, 0.03266375884413719, 0.004529331810772419, 0.015867825597524643, -0.0603533610701561, 0.005400409456342459, -0.000995361595414579, -0.00765845226123929, -0.016866808757185936, 0.028075028210878372, -0.006541850045323372, -0.018558111041784286, -0.017416059970855713, 0.00213720859028399, -0.0838983803987503, -0.007511398755013943, -0.03288683667778969, 0.03163108602166176, 0.04097235947847366, -0.04069601371884346, 0.07878459244966507, -0.016104040667414665, -0.05234897881746292, 0.015176421031355858, 0.05184005945920944, -0.003596328431740403, -0.03888080269098282, -0.022120989859104156, 0.01734202913939953, -0.04015935957431793, -0.024811752140522003, -0.024848666042089462, -0.05095330625772476, -0.0023177440743893385, 0.04794280230998993, -0.04151403531432152, -0.04581305384635925, -0.02039911039173603, 0.010836438275873661, 0.010947861708700657, -0.002544327173382044, -0.0062706652097404, -0.02267550863325596, -0.012397130019962788, 0.02441312186419964, -0.03280302509665489, -0.011970764957368374, 0.009536677040159702, -0.0037171810399740934, -0.02389463409781456, -0.027371542528271675, 0.04026566818356514, -0.038017116487026215, -0.024326132610440254, 0.05134276673197746, 0.015878567472100258, 0.032216086983680725, -0.011486594565212727, 0.016178876161575317, -0.045572180300951004, 0.03434791788458824, -0.02350311167538166, 0.030201178044080734, -0.02075151540338993, -0.052896153181791306, -0.043104130774736404, 0.01541801169514656, 0.007625087630003691, -0.05016708746552467, 0.025120262056589127, -0.00014976528473198414, -0.0056577762588858604, 0.09071992337703705, -0.05143704637885094, 0.08121717721223831, 0.048582836985588074, -0.0529361329972744, 0.014898466877639294, -0.0027036392129957676, -0.02446315623819828, 0.01998140662908554, -0.0036633340641856194, 0.08126625418663025, 0.009049576707184315, -0.010490628890693188, -0.04576774314045906, -0.0384112186729908, 0.008880899287760258, 0.0297892764210701, -0.03857317566871643, 0.024707624688744545, -0.02065933495759964, 0.03510487824678421, -0.07595081627368927, -0.008636520244181156, 0.044691190123558044, -0.027674606069922447, -0.039915841072797775, 0.014702318236231804, -0.03537781909108162, 0.019475745037198067, 0.013941287063062191, -0.03281661868095398, -0.02018967643380165, -0.01215751189738512, -0.008421603590250015, 0.046955984085798264, 0.04728079214692116, 0.0752711296081543, -0.029000544920563698, -0.04089640453457832, -0.02264036424458027, 0.04592607542872429, 0.05257067829370499, -0.08449935913085938, 0.012614995241165161, 0.023501921445131302, -0.05092419683933258, 0.0038014091551303864, 0.017459364607930183, -0.06426285207271576, 0.05077981948852539, 0.006349076051265001, 0.01637096330523491, 0.017624538391828537, -0.06853275746107101, -0.039010051637887955, -0.027417480945587158, 0.026040518656373024, 0.010061567649245262, -0.026302870362997055, -0.004973510280251503, -0.07915860414505005, -0.027254385873675346, 0.029276864603161812, 0.0022981094662100077, 0.0029919713269919157, 0.03673217073082924, -0.07795939594507217, -0.0011173884849995375, -0.0012869921047240496, 0.016363952308893204, 0.010379243642091751, -0.04242251440882683, -0.0809459239244461, 0.006314572878181934, 0.08510351181030273, 0.10980027914047241, -0.01426520012319088, -0.030590450391173363, -0.03119274601340294, -0.03700451925396919, 0.042910896241664886, 0.016982581466436386, -0.014141207560896873, -0.009780144318938255, 0.04126138612627983, 0.000529997400008142, -0.07811100780963898, 0.03625674545764923, 0.05867421627044678, -0.010685447603464127, -0.005409426521509886, -0.014663171023130417, -0.006495963782072067, -0.061618365347385406, -0.023335592821240425, 0.08487890660762787, -0.017252979800105095, -0.022543996572494507, 0.003862411016598344, -0.0641380250453949, -0.005098576657474041, -0.002336856909096241, -0.03558637201786041, -0.03707209601998329, 0.02731877937912941, 0.007897820323705673, 0.03945464268326759, -0.014467179775238037, -0.018192924559116364, 0.0889686867594719, -0.030016537755727768, 0.010700708255171776, 0.03469368815422058, 0.024375075474381447, -0.028933238238096237, -0.0004004439106211066, 0.046200115233659744, 0.012068897485733032, 0.031279854476451874, 0.02415718138217926, 0.016605883836746216, -0.006494775414466858, -0.009679713286459446, 0.004079230595380068, -0.05885731801390648, 0.013517646118998528, -0.024422699585556984, -0.0021521232556551695, 0.06473258882761002, 0.0030097069684416056, -0.019295673817396164, 0.04041525721549988, 0.02915840968489647, -0.01674068160355091, 0.07608494907617569, -0.0013360471930354834, -0.0019877979066222906, -0.00242292950861156, 0.043317392468452454, 0.03514932841062546, -0.022501284256577492, 0.015292171388864517, -0.0078369015827775, 0.04539910703897476, 0.032952770590782166, 0.041695427149534225, -0.03966705873608589, -0.04806600138545036, 0.011271960102021694, -0.028400244191288948, -0.02433052286505699, -0.0003506175125949085, -0.0272451750934124, 0.05549322068691254, 0.029411112889647484, 0.019752465188503265, -0.02109615132212639, -0.03446874022483826, 0.057813700288534164, -0.04961688816547394, -0.014674216508865356, -0.015018120408058167, 0.04091038927435875, -0.0015132708940654993, 0.016549766063690186, 0.011922703124582767, -0.021379943937063217, 0.03308304771780968, -0.04759419336915016, 0.006609922740608454, 0.06360211968421936, -0.021511241793632507, -0.042360179126262665, -0.0481182262301445, 0.0026149058248847723, 0.005686488933861256, -0.009090430103242397, -0.017758389934897423, -0.04690132662653923, -0.029034951701760292, -0.008371325209736824, -0.001968786818906665, 0.0548827238380909, -0.026645183563232422, -0.032264236360788345, 0.02437085472047329, -0.02888798713684082, 0.0636712983250618, -0.02922065556049347, 0.050892267376184464, -0.049912601709365845, -0.0032936842180788517, 0.018511394038796425, 0.03641963750123978, 0.013947063125669956, -0.011289548128843307, 0.0027798344381153584, 0.021290438249707222, 0.024319354444742203, -0.061496369540691376, 0.01325211115181446, 0.022349853068590164, 0.03283103555440903, 0.006474677938967943, 0.0246878731995821, -0.04533877596259117, 0.012494771741330624, 0.05364147573709488, 0.017285006120800972, -0.004540791269391775, -0.021905379369854927, -0.025793252512812614, 0.033783335238695145, -0.06164577230811119, 0.010812205262482166, -0.0158355962485075, -0.035097915679216385, -0.030735095962882042, 0.09012067317962646, 0.02543354593217373, -0.03742103651165962, -0.008160870522260666, 0.004179653711616993, 0.023359498009085655, -0.03749893605709076, 0.047865767031908035, -0.088225357234478, 0.0007837205776013434, 0.02651740424335003, -0.016674473881721497, -0.0714791864156723, 0.0006793873617425561, 0.011227814480662346, 0.01644684374332428, 0.022713566198945045, -0.04235955327749252, 0.03659006580710411, 0.034612152725458145, 0.02336975745856762, -0.002723457058891654, 0.0013953227316960692, -0.021203964948654175, -0.01842654123902321, -0.030448416247963905, 0.00756341265514493, 0.04538096860051155, -0.006138937082141638, -0.0823739543557167, 0.0032516655046492815, 0.019005630165338516, -0.007584842387586832, -0.020153531804680824, 0.06380365788936615, 0.004605101887136698, -0.020747022703289986, 0.015742965042591095, -0.027814095839858055, 0.04418209567666054, -0.015093672089278698, 0.00806603953242302, 0.009890438057482243, 0.04291388764977455, -0.04123375564813614, -0.008039797656238079, -0.006185225211083889, -0.06118695065379143, -0.000008381059160456061, -0.028317421674728394, 0.009100239723920822, -0.010224510915577412, 0.029506128281354904, 0.02113279514014721, 0.05876912176609039, -0.020173927769064903, 0.0349641889333725, 0.028291005641222, 0.008556281216442585, -0.049820590764284134, -0.027028700336813927, 0.005119473207741976, -0.03839736059308052, -0.04866940528154373, -0.026746520772576332, -0.012728601694107056, -0.04163670539855957, 0.03875165060162544, -0.03267373889684677, 0.009649948216974735, -0.0009811053751036525, 0.02327854558825493, -0.028978539630770683, -0.029588211327791214, -0.006109414156526327, 0.06248586252331734, 0.019670961424708366 ]
<p>I do not remember when, but a while a ago I was told that for a spring with stiffness $k$ and a mass $m$, the equation $-kx = ma$ never holds. (assume a horizontal spring)</p> <p>So if I was given a problem like this:</p> <blockquote> <p>You pull a mass $m$ attached to a spring with stiffness $k$ to the right of the equilibrium point $x = 5\text{ m}$ of the spring and you let it go, what is the acceleration of the mass?</p> </blockquote> <p>Then is this question meaningless (or any other that is similar)? I forgot what the real question is like, but I have seem such a method was used to tackle these problems? As such an attempt to write $-kx = ma$?</p> <p>Could someone please jog my memory? I realize I am asking you guys to 'read my mind', but please bear with me.</p>
g8369
[ 0.08650653809309006, 0.05431438609957695, 0.02259928546845913, 0.019343391060829163, 0.034654345363378525, -0.029623787850141525, 0.01171932928264141, 0.015914766117930412, -0.04911596700549126, -0.020833266898989677, -0.05578358471393585, -0.0023050978779792786, 0.03698372468352318, -0.0032868103589862585, 0.00286242738366127, -0.01995140127837658, 0.050874993205070496, -0.010209208354353905, -0.016095822677016258, 0.030950497835874557, 0.00810301210731268, 0.026933060958981514, -0.008663342334330082, -0.010312970727682114, 0.026368126273155212, 0.026245085522532463, 0.0070423646830022335, -0.020510025322437286, -0.08280672132968903, -0.011784270405769348, -0.011116391979157925, -0.04096069931983948, 0.024679480120539665, -0.02801681123673916, -0.09322097152471542, -0.052906665951013565, 0.048555392771959305, -0.026458600535988808, 0.005949269514530897, -0.019794633612036705, 0.087486632168293, -0.03263527899980545, 0.025034548714756966, 0.04742620512843132, 0.050314150750637054, 0.014336258172988892, 0.0011598828714340925, 0.014800972305238247, -0.029365969821810722, -0.016227522864937782, -0.02823692001402378, 0.02666846662759781, 0.05947482958436012, -0.052688684314489365, -0.03742438927292824, 0.06284796446561813, 0.05981609225273132, 0.0036216452717781067, 0.08436006307601929, 0.056701503694057465, -0.04674385115504265, -0.06438392400741577, 0.0291888527572155, -0.07831805944442749, 0.07918339222669601, -0.024417348206043243, -0.0016609554877504706, 0.029176080599427223, -0.017702948302030563, 0.007296218536794186, -0.0021688309498131275, -0.022614216431975365, 0.02413156069815159, -0.04148086532950401, -0.01776411198079586, 0.022732539102435112, -0.011191344819962978, 0.022175826132297516, -0.0009248732822015882, -0.03339625895023346, -0.0011945638107135892, 0.018886420875787735, 0.015702564269304276, 0.011538981460034847, 0.04787777364253998, 0.026618825271725655, 0.02159203216433525, 0.040824998170137405, -0.04071683809161186, 0.01902599260210991, 0.01873728819191456, -0.006870033219456673, 0.012588931247591972, 0.013920002616941929, -0.039121467620134354, -0.024231428280472755, -0.019609764218330383, 0.05994580313563347, -0.0027977507561445236, -0.019145354628562927, -0.017836442217230797, -0.018802383914589882, -0.011514480225741863, -0.011965123936533928, -0.02506466582417488, -0.016942480579018593, 0.01933412440121174, 0.03536687046289444, -0.016536513343453407, -0.025753764435648918, -0.0037117176689207554, -0.015227371826767921, -0.026342887431383133, -0.025989487767219543, -0.06728039681911469, -0.06770358234643936, 0.0578869953751564, 0.029241841286420822, 0.0036662316415458918, 0.021551543846726418, -0.04009102284908295, 0.012646641582250595, 0.007898264564573765, 0.03589923679828644, 0.027487752959132195, -0.0620102621614933, 0.01821529120206833, 0.034316979348659515, -0.022267265245318413, -0.05473968759179115, -0.02631440758705139, -0.02478381060063839, 0.04533854499459267, -0.012064474634826183, -0.011764817871153355, 0.06346801668405533, -0.024430222809314728, -0.0030590191017836332, 0.017461908981204033, 0.029660657048225403, -0.014458145014941692, -0.049547478556632996, -0.062321677803993225, 0.026994405314326286, -0.049912914633750916, 0.07350815087556839, -0.007008966524153948, -0.0460086390376091, 0.03024614043533802, 0.03804551437497139, -0.015624049119651318, 0.05062370002269745, -0.05380035936832428, -0.018500810489058495, 0.08554474264383316, 0.004737708251923323, 0.01039107795804739, -0.019847938790917397, 0.024232149124145508, -0.022331826388835907, 0.035366564989089966, -0.013509592041373253, 0.018428528681397438, -0.013700691051781178, -0.0681476891040802, -0.02935730293393135, -0.04589594155550003, -0.012969727627933025, 0.012918214313685894, -0.06593520939350128, -0.057396288961172104, 0.002291752491146326, 0.0662381500005722, 0.0737713873386383, 0.0018235581228509545, -0.009703515097498894, 0.01799282431602478, -0.026684612035751343, 0.03227907419204712, 0.012449696660041809, -0.012017318047583103, 0.015055009163916111, 0.043912459164857864, -0.038854651153087616, -0.02629760466516018, 0.003716820850968361, 0.0023718569427728653, 0.030867481604218483, -0.023398593068122864, -0.0463143028318882, -0.019505200907588005, -0.053134769201278687, 0.013647167012095451, 0.08795195817947388, -0.009866680018603802, -0.02877366729080677, 0.024684110656380653, -0.014419619925320148, -0.028156306594610214, 0.010351045057177544, 0.003949332050979137, 0.061465125530958176, 0.01948181353509426, 0.002958809956908226, -0.00497437734156847, -0.044035520404577255, -0.010700825601816177, -0.052941687405109406, 0.06227052956819534, -0.033801592886447906, 0.016503872349858284, 0.006267524790018797, 0.002919991035014391, 0.052541714161634445, -0.03503868356347084, -0.0652691125869751, 0.017281396314501762, -0.012520271353423595, 0.08472155779600143, 0.01789645291864872, -0.057528071105480194, -0.06189882010221481, 0.007182936649769545, -0.005911447573453188, -0.0649443194270134, -0.04971233382821083, 0.0029081490356475115, -0.031055791303515434, 0.002014358062297106, -0.007408417295664549, -0.022001225501298904, 0.0510227307677269, -0.014266557060182095, 0.0012057408457621932, 0.049792129546403885, 0.06798973679542542, -0.025351393967866898, 0.048469316214323044, -0.043027639389038086, 0.007400867063552141, 0.041092488914728165, -0.002891870215535164, -0.014833486638963223, -0.008317545056343079, -0.0014438806101679802, 0.0015908520435914397, 0.08184359222650528, 0.020800258964300156, 0.047444652765989304, 0.03310972452163696, -0.02656811848282814, -0.020388394594192505, 0.013917328789830208, -0.006446437444537878, 0.0469810776412487, -0.0043842424638569355, -0.044220298528671265, -0.02389463409781456, -0.0004943536478094757, 0.005992154590785503, 0.010347824543714523, -0.03801276534795761, 0.029819417744874954, -0.012389352545142174, -0.10195577889680862, -0.049715571105480194, -0.028561949729919434, -0.025012528523802757, 0.019832802936434746, 0.040776629000902176, -0.016200212761759758, 0.03601885959506035, 0.03868331387639046, 0.09892752766609192, -0.02164074219763279, -0.03960642218589783, -0.006643236614763737, -0.01891579106450081, 0.01804219000041485, -0.018212463706731796, 0.028897784650325775, -0.034685418009757996, -0.03853897005319595, -0.0036901934072375298, 0.008758320473134518, -0.002908040303736925, -0.026001613587141037, 0.039204880595207214, -0.002559696091338992, -0.013331159949302673, -0.047373320907354355, 0.01471694651991129, 0.07022352516651154, 0.03695904463529587, -0.0171500314027071, 0.1031217873096466, -0.07647297531366348, -0.08533995598554611, -0.046370211988687515, 0.029692145064473152, -0.005676185246556997, -0.034545302391052246, 0.022236283868551254, -0.004525169730186462, -0.009185337461531162, 0.00953960046172142, 0.003359055146574974, -0.05198397859930992, 0.057352062314748764, -0.0002552167570684105, -0.028690451756119728, 0.07189684361219406, 0.06502188742160797, -0.008037207648158073, -0.08614235371351242, -0.0013815094716846943, 0.031651344150304794, -0.048089444637298584, 0.037167251110076904, -0.04410827159881592, -0.017999982461333275, -0.055624619126319885, 0.05386749655008316, 0.03343930095434189, -0.016967881470918655, 0.029495440423488617, -0.04873459413647652, 0.04389221966266632, -0.034353870898485184, -0.036423541605472565, 0.014540690928697586, 0.01406892854720354, -0.01766427978873253, -0.013644842430949211, -0.028429074212908745, -0.06044432893395424, 0.012433917261660099, 0.013423397205770016, 0.014362583868205547, 0.02235090732574463, -0.007441719062626362, -0.020692849531769753, -0.016454486176371574, 0.041331999003887177, -0.01860123872756958, 0.021440664306282997, 0.014084178023040295, 0.0013967237900942564, 0.046887967735528946, -0.023196492344141006, 0.014981632120907307, -0.013135687448084354, -0.016749028116464615, -0.03312388435006142, 0.02090543694794178, 0.026457512751221657, 0.03868713974952698, 0.0064717731438577175, -0.035695455968379974, 0.014784295111894608, 0.01621559076011181, 0.0036341939121484756, 0.006835106294602156, 0.0020910287275910378, -0.0003815978125203401, -0.025349203497171402, -0.04000674560666084, 0.0688643679022789, -0.03927646577358246, -0.0401594452559948, -0.010352237150073051, -0.061371661722660065, 0.006746454164385796, -0.022128881886601448, -0.008528134785592556, -0.03133806586265564, -0.031233293935656548, 0.03854387253522873, -0.0019543985836207867, -0.0012989320093765855, 0.0236103143543005, 0.017380889505147934, -0.025435788556933403, 0.006029236596077681, -0.010226761922240257, 0.023776859045028687, -0.0484808124601841, -0.002058636397123337, 0.04172499105334282, -0.06474139541387558, 0.021441709250211716, 0.009505447000265121, -0.056195080280303955, 0.026339836418628693, 0.045053791254758835, 0.012063794769346714, 0.00819968618452549, -0.043632835149765015, -0.020478084683418274, 0.01196793932467699, -0.02343589812517166, 0.010047748684883118, -0.001814579009078443, 0.0017663170583546162, -0.02850559912621975, 0.06671082973480225, 0.015999142080545425, -0.015339192934334278, 0.02063361555337906, 0.0019368387293070555, 0.04088940471410751, -0.045572806149721146, -0.046459026634693146, -0.0014601110015064478, 0.025296522304415703, -0.03629765287041664, 0.03758590295910835, 0.019691364839673042, -0.012992695905268192, -0.01834423653781414, 0.03094971925020218, 0.037222422659397125, -0.07694189250469208, -0.022617803886532784, 0.035152338445186615, 0.08814795315265656, -0.014646078459918499, -0.03939191251993179, -0.00315354042686522, -0.011843129061162472, -0.022045521065592766, 0.0016314374515786767, 0.029436394572257996, 0.005579298362135887, 0.014463769271969795, 0.05152284353971481, -0.014342477545142174, 0.03967615216970444, -0.01839229092001915, 0.012525711208581924, -0.0040481919422745705, -0.008954492397606373, 0.00786165613681078, 0.038052622228860855, -0.07837186008691788, 0.0013760667061433196, 0.024086033925414085, 0.03969227522611618, -0.02937004156410694, -0.0020125629380345345, -0.05930357798933983, -0.01881856843829155, 0.010039805434644222, -0.027361217886209488, 0.025228332728147507, -0.002755508990958333, -0.02191160060465336, 0.004987176042050123, 0.023291392251849174, 0.02356385998427868, 0.02063106559216976, -0.06943195313215256, 0.057679183781147, 0.03648412227630615, 0.03079412318766117, -0.07217402011156082, 0.01726629212498665, 0.0042308904230594635, -0.07260482013225555, 0.013454707339406013, 0.009762502275407314, -0.01254898589104414, -0.025031331926584244, 0.031017910689115524, 0.038920510560274124, 0.022187024354934692, 0.0024428111501038074, 0.011012665927410126, 0.04494683817028999, -0.0296217892318964, -0.027303066104650497, -0.02950279600918293, -0.03337115794420242, -0.00269832625053823, 0.03191805258393288, 0.03487043455243111, -0.025437109172344208, 0.009549370035529137, 0.02484271675348282, -0.01948367990553379, 0.04974794387817383, 0.06360317766666412, -0.07489892095327377, -0.04277407377958298, -0.0006624326924793422, -0.013856649398803711, -0.03966934233903885, 0.008723187260329723, 0.0031276352237910032, -0.03756055608391762, -0.04236852005124092, -0.022431932389736176, 0.024350762367248535, 0.04080367460846901, 0.00923076830804348, 0.0016713773366063833, -0.016512878239154816, 0.006063804496079683, 0.01056708861142397, 0.01376357488334179, 0.07247573137283325, 0.029535837471485138, 0.02747739478945732, 0.07035446166992188, 0.008048567920923233, -0.010346636176109314, 0.01235027052462101, 0.018449118360877037, -0.010664481669664383, -0.06839834153652191, 0.059666216373443604, 0.0120254410430789, 0.01509121060371399, 0.013628602959215641, 0.010637051425874233, -0.01197302620857954, -0.016180790960788727, -0.001697822823189199, -0.05169712379574776, 0.044588033109903336, -0.006101202219724655, -0.035785142332315445, -0.017615005373954773, 0.0027066892944276333, 0.017821183428168297, -0.050703052431344986, 0.00937922578305006, 0.01003541611135006, -0.003594545414671302, -0.01907358504831791, -0.046326227486133575, 0.005682757124304771, 0.050209853798151016, 0.040676750242710114, 0.003274572780355811, 0.02643498219549656, -0.03101106733083725, -0.06549832224845886, 0.03670433908700943, -0.017734263092279434, -0.06164117157459259, 0.05175160616636276, -0.016109617426991463, 0.009170305915176868, -0.0049665868282318115, 0.05678389221429825, -0.0014695227146148682, -0.0268379095941782, -0.008937055245041847, 0.03405996412038803, 0.023835767060518265, -0.0031911474652588367, 0.07040676474571228, 0.016416870057582855, 0.031483061611652374, -0.048779066652059555, 0.016245460137724876, -0.053887173533439636, 0.053397923707962036, 0.005206694360822439, 0.00509487884119153, 0.034991245716810226, 0.014013197273015976, 0.06080717593431473, -0.006668694317340851, 0.03003150038421154, -0.06317578256130219, 0.007129186764359474, -0.009973524138331413, 0.07228581607341766, -0.0209514070302248, 0.01592126674950123, 0.05428175628185272, -0.04779241606593132, -0.005781929474323988, -0.033341020345687866, -0.03026042878627777, 0.02263927273452282, 0.02172166481614113, -0.00626814179122448, -0.06508351117372513, 0.022013163194060326, -0.059707533568143845, 0.05544779822230339, -0.030485190451145172, 0.018635405227541924, -0.004212681669741869, -0.007661430165171623, -0.016662823036313057, -0.0008356353500857949, 0.03897766023874283, 0.0552443265914917, 0.06542149931192398, -0.0324840322136879, 0.010544952005147934, -0.041615989059209824, -0.04551738128066063, 0.03405128791928291, -0.04086476191878319, -0.06041998416185379, -0.061071522533893585, 0.054648108780384064, -0.0003798271354753524, 0.009431160055100918, 0.027064591646194458, 0.0015235861064866185, 0.050307732075452805, 0.0281461663544178, -0.0460994653403759, -0.026367943733930588, 0.008755412884056568, 0.030371520668268204, 0.05282803252339363, -0.06801417469978333, 0.03060876578092575, -0.0017120811389759183, -0.01125257182866335, -0.0035801806952804327, -0.010747049935162067, 0.021689560264348984, 0.02189028635621071, -0.03669297322630882, -0.04272841662168503, -0.015016958117485046, 0.016953079029917717, 0.09341280907392502, -0.02850504405796528, 0.062224943190813065, 0.05800851434469223, 0.09413082152605057, -0.027592185884714127, 0.04134468361735344, -0.048194825649261475, 0.0062673212960362434, -0.06112346425652504, -0.05492686852812767, 0.06435829401016235, 0.020486820489168167, -0.06162749230861664, -0.055312786251306534, -0.01961541920900345, 0.013548867776989937, -0.06244466081261635, -0.0037210320588201284, 0.024353867396712303, -0.011032258160412312, -0.017715279012918472, -0.014907928183674812, 0.040190279483795166, -0.033207643777132034, -0.04575981944799423, -0.012034271843731403, 0.07176584005355835, 0.0016699036350473762, 0.004809146281331778, 0.032917123287916183, 0.0016586693236604333, 0.07275757938623428, 0.03653302416205406, 0.027489401400089264, 0.02335672453045845, -0.02242385409772396, 0.003038993803784251, 0.03365534543991089, 0.008163239806890488, 0.011461662128567696, -0.007017967756837606, 0.016865890473127365, 0.006514227017760277, -0.02009267918765545, -0.049651581794023514, 0.007579820696264505, -0.03663386404514313, -0.009432212449610233, -0.020598962903022766, 0.016367021948099136, -0.025697357952594757, -0.0064089056104421616, -0.009770781733095646, 0.02423746883869171, -0.003973796032369137, 0.04375921189785004, 0.029167838394641876, -0.042573366314172745, -0.021499760448932648, -0.04891769215464592, -0.04903155565261841, 0.041946616023778915, 0.03213810175657272, -0.0311809703707695, 0.020830556750297546, 0.019786009564995766, -0.01599048264324665, 0.06453172862529755, 0.03282292187213898, 0.04505124315619469, -0.04478442668914795, -0.013669326901435852, -0.03345460444688797, 0.059391725808382034, 0.031006349250674248, -0.0035027249250561, 0.02429218962788582, -0.010264616459608078, -0.02164710871875286, -0.0341254360973835, -0.023453855887055397, 0.032693177461624146, 0.06471912562847137, -0.06649605184793472, -0.036778733134269714, 0.01826186664402485, 0.017143437638878822, -0.085386261343956, -0.0026466590352356434, 0.020292233675718307, -0.011348088271915913, 0.03313036262989044, -0.04716238006949425, -0.02551615983247757, -0.01592964679002762, -0.04894664138555527, 0.014771644957363605, 0.05451535806059837, 0.0061075640842318535, 0.027508357539772987, 0.0008700400358065963, -0.029919199645519257, -0.02080836519598961, 0.018067190423607826, -0.0405615009367466, -0.07894867658615112, -0.007700939197093248, 0.009161125868558884, 0.0648297369480133, -0.02576819807291031, -0.01364952977746725, 0.057526666671037674, 0.08961710333824158, -0.055263880640268326, 0.0735553652048111, -0.0036608886439353228, -0.05804629623889923, 0.008815434761345387, -0.03506631404161453, -0.05674605071544647, -0.008432465605437756, -0.021595824509859085, 0.010394440963864326, 0.023665498942136765, -0.03736908361315727, -0.004158526659011841, -0.016165146604180336, -0.06835128366947174, 0.0065097501501441, -0.025197438895702362, -0.0032886615954339504, -0.0007603159174323082 ]
<p>Considering how low the power density is at the sun's core, I seem not to be able to expect what would happen to matter in case it was thrown inside the sun's core. For example, let's assume an Earth-like planet is placed at the center of the Sun's core, and with the power density of 276.5 $watts$/$m^3$ which is very low to even raise the temperature of the Earth by any noticeable degree. That was one thought. The other thought was that, the temperature in the core is already 15 million degrees K, so any matter there should get close to this temperature quickly enough.</p> <p>So now I'm very confused, like will the planet stay there intact for thousands or even millions of years until it has accumulated enough energy to melt or vaporize ? Or there are other types of energy absorption the planet would experience and thus have a shorter time staying as one piece in the core ?</p> <p>Just for trying to get a practical and numerical answer to this question, let it be : how long can the Earth as a whole survive in the core of the sun ? </p>
g8370
[ 0.038220006972551346, 0.040960174053907394, 0.028422269970178604, -0.026754282414913177, -0.009778963401913643, -0.005781996063888073, -0.01911603845655918, 0.020634358748793602, 0.013608710840344429, -0.010884463787078857, 0.014083866961300373, 0.018720952793955803, -0.027333855628967285, -0.0324387401342392, 0.029017778113484383, -0.007931600324809551, 0.020844867452979088, -0.009481496177613735, 0.09538248926401138, 0.041719965636730194, -0.026269584894180298, -0.08095985651016235, 0.03635662421584129, -0.02036718837916851, -0.08422674238681793, 0.006456287577748299, 0.03782714903354645, 0.00354341440834105, -0.013375123031437397, -0.025697311386466026, 0.014408099465072155, 0.021349750459194183, 0.010583976283669472, -0.024674970656633377, -0.005088150035589933, -0.08045978099107742, 0.026015594601631165, -0.03629656881093979, 0.023631831631064415, -0.025126799941062927, -0.01036615576595068, -0.04732474684715271, 0.03176272287964821, -0.014402869157493114, 0.03909441456198692, 0.03514258563518524, -0.016265250742435455, -0.046889837831258774, 0.04819461703300476, -0.049809373915195465, -0.0060944450087845325, -0.008806285448372364, 0.03339884802699089, 0.014043573290109634, 0.027103794738650322, -0.0419497936964035, 0.04429953172802925, -0.023644814267754555, -0.021330872550606728, -0.015978045761585236, 0.015004737302660942, -0.04834030568599701, 0.003109848592430353, 0.0051589785143733025, 0.022898122668266296, -0.0034821697045117617, -0.06451426446437836, 0.019036034122109413, -0.006157230585813522, -0.02837367355823517, 0.02745477296411991, -0.03714597225189209, -0.09459585696458817, -0.06155173480510712, 0.05240631476044655, -0.011713840998709202, 0.006812925450503826, 0.002891795476898551, 0.07129194587469101, 0.11632007360458374, -0.00030802289256826043, 0.0004749493964482099, 0.04046730324625969, -0.018287651240825653, 0.06065374240279198, -0.05132757127285004, -0.029123254120349884, -0.0152824642136693, -0.037085991352796555, 0.005377775989472866, 0.03374318778514862, 0.0032109932508319616, 0.021089816465973854, -0.05601489543914795, 0.019930075854063034, 0.01730705238878727, 0.002963949693366885, 0.029549727216362953, -0.07953092455863953, 0.034858301281929016, 0.0003574952424969524, -0.04986465349793434, -0.011911842972040176, -0.019850175827741623, -0.017934400588274002, 0.01842782087624073, -0.0037373581435531378, -0.010930919088423252, -0.03698689490556717, -0.014334864914417267, 0.020486431196331978, -0.011701314710080624, 0.009362204000353813, 0.010611491277813911, -0.07237807661294937, -0.02099534124135971, 0.06640420109033585, -0.0027603493072092533, 0.06490860134363174, -0.0055814217776060104, 0.06502328813076019, 0.06369643658399582, -0.02686530537903309, 0.07105808705091476, 0.020094316452741623, -0.018763499334454536, 0.04631032422184944, -0.025357550010085106, -0.010566958226263523, -0.002044191351160407, -0.026115305721759796, -0.009691263549029827, -0.0889802947640419, -0.025225849822163582, 0.052950937300920486, 0.011783582158386707, -0.00414331303909421, 0.013955333270132542, -0.008154328912496567, -0.008975730277597904, 0.007484332658350468, 0.02688678912818432, 0.027900200337171555, 0.02213886007666588, -0.042468126863241196, 0.011802196502685547, -0.023412808775901794, -0.017445214092731476, -0.004777817055583, 0.026612257584929466, 0.05129587650299072, 0.02224317379295826, 0.016506751999258995, -0.05618071183562279, 0.0627797394990921, 0.02569156140089035, 0.03846428170800209, -0.021572589874267578, 0.03895387426018715, -0.007974999025464058, 0.022875113412737846, -0.010221393778920174, 0.020030461251735687, 0.006646019872277975, -0.06476849317550659, 0.02544287219643593, -0.016949323937296867, -0.054079554975032806, -0.0028950474224984646, -0.041850391775369644, -0.016348058357834816, 0.004816150758415461, 0.004179336130619049, 0.07915963232517242, -0.01087536197155714, -0.004898950457572937, 0.039697419852018356, -0.02136126533150673, -0.04542415589094162, -0.018020473420619965, -0.025062784552574158, -0.0077101197093725204, -0.0386974923312664, -0.01675952784717083, 0.000687741965521127, -0.009998347610235214, 0.0618562251329422, 0.006479138974100351, -0.013018927536904812, 0.017037613317370415, -0.04503577575087547, -0.04439564794301987, 0.010172685608267784, 0.05493287742137909, 0.02040393464267254, -0.03544345870614052, 0.011995040811598301, -0.03254258632659912, -0.05542227253317833, -0.00550492201000452, 0.04525761306285858, 0.0050776321440935135, 0.018094610422849655, 0.02195793204009533, 0.02154744230210781, 0.00123418471775949, 0.012418529018759727, 0.016795098781585693, 0.018233485519886017, -0.033218350261449814, 0.07320239394903183, -0.052947305142879486, -0.023380326107144356, 0.04685329273343086, 0.0037299664691090584, 0.06294326484203339, -0.07013317197561264, 0.04936394840478897, 0.03295183926820755, -0.02646026760339737, -0.03392719849944115, 0.042451195418834686, 0.02330593764781952, -0.0421382337808609, -0.00841426383703947, 0.035068389028310776, -0.05331099033355713, 0.012197066098451614, 0.03760528936982155, 0.01846296526491642, -0.08274025470018387, -0.000460000621387735, -0.017538994550704956, 0.015619916841387749, -0.03148231282830238, 0.05273040384054184, -0.014769808389246464, -0.036008041352033615, -0.01759023219347, -0.0025283456780016422, -0.03569726645946503, 0.04686414450407028, -0.024342117831110954, 0.010617987252771854, 0.040942635387182236, -0.05581973120570183, -0.02595699578523636, 0.028760846704244614, 0.023301463574171066, 0.045262761414051056, 0.016848249360919, -0.017512332648038864, -0.04614286124706268, 0.0013009576359763741, -0.02299477346241474, -0.05569180101156235, -0.03407479450106621, 0.00300490390509367, -0.03515687957406044, -0.11266157031059265, -0.00822290126234293, -0.049779824912548065, -0.018661638721823692, 0.0031493804417550564, -0.019126737490296364, -0.011142861098051071, 0.003436170518398285, -0.0356963686645031, 0.05415035039186478, 0.019002640619874, -0.020142102614045143, 0.051420386880636215, -0.011608193628489971, 0.09290055930614471, 0.027726057916879654, -0.00861928891390562, -0.011718844063580036, -0.035577625036239624, 0.010979272425174713, -0.05493314936757088, -0.0070904698222875595, -0.005300649907439947, -0.03804982826113701, 0.09186635911464691, 0.00149967719335109, -0.06932322680950165, -0.062931589782238, 0.06910200417041779, 0.017118167132139206, -0.043234579265117645, 0.014837754890322685, 0.019724003970623016, 0.058077745139598846, 0.020801441743969917, 0.034811653196811676, 0.01604057289659977, 0.018026357516646385, -0.028965001925826073, -0.04961840435862541, 0.016780801117420197, 0.035835787653923035, -0.04665252938866615, -0.0026520390529185534, 0.03619927540421486, -0.03435197472572327, 0.022698786109685898, -0.06588118523359299, -0.0445144921541214, 0.0339336059987545, -0.03945915400981903, 0.03354864567518234, 0.09014081954956055, -0.05306775122880936, 0.012337774969637394, -0.025280551984906197, -0.014168282970786095, -0.06293435394763947, 0.01790730655193329, 0.06603210419416428, -0.023875175043940544, 0.013440653681755066, 0.019133590161800385, -0.01118997298181057, 0.013072964735329151, -0.004833129700273275, 0.08013150095939636, -0.05496615171432495, -0.04568798094987869, 0.013103009201586246, -0.021784216165542603, -0.037980370223522186, -0.018956568092107773, -0.05730060860514641, 0.015701700001955032, -0.013454585336148739, 0.02261737547814846, -0.03254147619009018, 0.02496700920164585, 0.01794627122581005, 0.06285671889781952, 0.012386719696223736, -0.006742097437381744, -0.032524868845939636, 0.02142638899385929, 0.05313872545957565, -0.008444012142717838, 0.016931649297475815, -0.07006072998046875, -0.0361286997795105, 0.004644858185201883, 0.07120818644762039, -0.0929732695221901, -0.015174692496657372, -0.038680534809827805, -0.0931071937084198, 0.014966650865972042, -0.021738138049840927, 0.019588744267821312, -0.006115700583904982, -0.016231220215559006, 0.04760061204433441, -0.008788056671619415, 0.1109807938337326, 0.006703285034745932, -0.011801942251622677, 0.01877450756728649, -0.01729714870452881, -0.008018666878342628, 0.04305650293827057, 0.04207482188940048, 0.02510802261531353, -0.005589581094682217, -0.013212217949330807, 0.011916721239686012, 0.01863151229918003, -0.07582559436559677, 0.0819346234202385, 0.03782261908054352, -0.0001614644716028124, 0.028458021581172943, 0.06733192503452301, 0.0034208493307232857, 0.023327771574258804, -0.03996947780251503, 0.007588477805256844, 0.06584130227565765, 0.023570705205202103, -0.03108402155339718, 0.0010395435383543372, 0.05558483675122261, 0.03016158938407898, -0.10176960378885269, 0.014742100611329079, -0.022084953263401985, 0.020520709455013275, -0.028958333656191826, -0.016978774219751358, -0.027239220216870308, 0.004450247623026371, 0.031418513506650925, -0.006254622712731361, 0.016566241160035133, 0.004564134869724512, -0.05954032391309738, 0.11155623942613602, 0.023960452526807785, 0.006872271187603474, -0.050998102873563766, -0.0629984438419342, -0.05780857056379318, 0.04588749632239342, 0.020517433062195778, -0.029496727511286736, -0.005325146950781345, -0.005425933748483658, -0.04580991715192795, 0.002915657591074705, -0.02530520409345627, 0.01779283955693245, 0.01018483005464077, 0.006215271539986134, -0.0014992564683780074, -0.0492999292910099, -0.01352938637137413, 0.006734840571880341, -0.008577689528465271, 0.007394181098788977, -0.03002559207379818, 0.009079993702471256, 0.05187302827835083, 0.0024033356457948685, 0.014331493526697159, 0.04293004795908928, -0.05482478439807892, 0.023367399349808693, -0.005535317584872246, -0.047714389860630035, 0.00007280986028490588, 0.018698567524552345, 0.030265092849731445, 0.03341114893555641, 0.01143819373100996, 0.060277510434389114, 0.03425851836800575, -0.02665252797305584, 0.01510042604058981, 0.034008074551820755, 0.011874571442604065, 0.022033674642443657, -0.049665600061416626, -0.030252324417233467, -0.0061240652576088905, -0.04496714100241661, -0.0420302115380764, -0.05225121229887009, 0.0010502181248739362, -0.027919432148337364, -0.03800461068749428, 0.005712414626032114, 0.08384018391370773, -0.09493573009967804, -0.011500854976475239, -0.02984561212360859, 0.011148384772241116, 0.017861802130937576, -0.025916660204529762, 0.010778761468827724, 0.027356980368494987, -0.014463328756392002, 0.005557557567954063, -0.01510336808860302, -0.003245013765990734, 0.032634761184453964, -0.011587192304432392, 0.03999202698469162, 0.023021891713142395, -0.019233791157603264, -0.0773245245218277, 0.051710087805986404, -0.03222250938415527, 0.002399842254817486, 0.0029803463257849216, -0.02706662379205227, 0.06161842867732048, -0.0035000599455088377, 0.04069548100233078, -0.055155277252197266, 0.018925249576568604, -0.02236407995223999, 0.043751172721385956, -0.012354248203337193, -0.007405802141875029, 0.057545583695173264, -0.020389528945088387, 0.019907524809241295, 0.03892810642719269, -0.01578187383711338, -0.07669343799352646, 0.001558253774419427, -0.011301021091639996, -0.015170342288911343, 0.00538483215495944, -0.007866204716265202, 0.005165811162441969, 0.009181736037135124, 0.034194864332675934, 0.010730350390076637, 0.028073515743017197, 0.0021558317821472883, 0.035261120647192, 0.037607911974191666, 0.06210280582308769, -0.07273060828447342, 0.031963661313056946, -0.004856585990637541, -0.017542891204357147, -0.04119592905044556, 0.04873495176434517, 0.03856664523482323, -0.008541739545762539, 0.02751336432993412, 0.024877168238162994, -0.01271748822182417, 0.035993847995996475, 0.0655493289232254, 0.013266007415950298, -0.03962869569659233, -0.016699155792593956, 0.02043008804321289, 0.00845562294125557, 0.04803451523184776, 0.002709269756451249, 0.003244497114792466, -0.03796835616230965, -0.05459055304527283, 0.00855585839599371, -0.0462043322622776, 0.008929676376283169, 0.08147909492254257, -0.002799359615892172, 0.004804051015526056, -0.034067798405885696, -0.021951138973236084, 0.003909238614141941, -0.0030939120333641768, 0.02766948938369751, -0.03171931952238083, 0.02994142845273018, 0.044271789491176605, 0.03972276672720909, -0.006351139862090349, 0.019927261397242546, 0.003354316111654043, -0.010907868854701519, 0.07346226274967194, 0.0029743302147835493, 0.05360938236117363, -0.003173642326146364, 0.052811264991760254, -0.0676555261015892, -0.020797045901417732, 0.03180982545018196, 0.03691953048110008, -0.04101260378956795, -0.02552993781864643, -0.03863169997930527, 0.03931835666298866, -0.09957461804151535, 0.05132041499018669, 0.042598336935043335, 0.06837381422519684, -0.07775933295488358, 0.042152296751737595, -0.017607195302844048, 0.027563199400901794, -0.025764593854546547, -0.03020692989230156, -0.006318201310932636, 0.00492152338847518, -0.05723433196544647, 0.03242749720811844, -0.021963490173220634, 0.00519583560526371, -0.024717511609196663, 0.04401804134249687, 0.03637227043509483, -0.05636376515030861, 0.014314038679003716, 0.043348830193281174, -0.045197486877441406, 0.03079751320183277, 0.012337939813733101, 0.002057052915915847, 0.021796323359012604, -0.010501731187105179, 0.0016145665431395173, -0.004729407373815775, -0.04032692313194275, -0.010975604876875877, 0.03564342483878136, 0.010731528513133526, 0.0433674156665802, 0.05252714082598686, -0.04464833810925484, 0.03434961289167404, -0.028502248227596283, 0.03882195055484772, 0.009277379140257835, -0.025995558127760887, 0.040221914649009705, -0.001378611079417169, 0.008143396116793156, 0.04338303953409195, -0.016615135595202446, 0.004870356060564518, -0.030732208862900734, 0.029048951342701912, -0.03472813963890076, 0.03951729089021683, -0.0027377400547266006, -0.03033086284995079, -0.041557855904102325, -0.042169906198978424, -0.09478779137134552, 0.007551607210189104, 0.030267097055912018, -0.02657892182469368, 0.05759480595588684, 0.06828216463327408, -0.028676260262727737, 0.00005451917968457565, -0.016850383952260017, 0.048682987689971924, -0.02607719972729683, 0.045923203229904175, 0.023592621088027954, -0.03587701544165611, -0.025142718106508255, -0.01688944175839424, -0.01965700462460518, 0.0075609381310641766, -0.0487484447658062, 0.02237197943031788, -0.0025467602536082268, -0.06729431450366974, 0.04881630092859268, -0.019276166334748268, -0.024438519030809402, 0.014669752679765224, -0.020394887775182724, -0.014032130129635334, -0.02518145553767681, -0.04241427034139633, -0.02754700928926468, 0.007411963772028685, 0.014968084171414375, -0.029388414695858955, -0.01391645148396492, -0.030148442834615707, -0.04284108430147171, 0.007186948321759701, -0.002995914313942194, -0.008684962056577206, -0.0011928878957405686, 0.032465025782585144, 0.031082607805728912, 0.08607219159603119, -0.07845202833414078, 0.012579284608364105, -0.022399578243494034, -0.006152813322842121, 0.02274213917553425, -0.020183518528938293, -0.038517482578754425, 0.028532715514302254, -0.007863991893827915, -0.009469461627304554, -0.022038375958800316, 0.07413974404335022, 0.04097019135951996, -0.022294115275144577, -0.020624350756406784, 0.015199397690594196, 0.008042611181735992, 0.040860388427972794, 0.024776466190814972, -0.007196289952844381, 0.0004951745504513383, -0.027923664078116417, 0.03393545374274254, 0.0035371906124055386, 0.050684165209531784, -0.005985323805361986, 0.04623517394065857, -0.04010400548577309, 0.0035347784869372845, 0.03781002014875412, -0.016140297055244446, -0.002061908133327961, -0.0008116774260997772, -0.04219290614128113, 0.01204877719283104, 0.024684086441993713, -0.04088125005364418, -0.0013883172068744898, 0.04619944468140602, -0.04640712961554527, 0.016486799344420433, -0.059892475605010986, 0.048714399337768555, 0.057983528822660446, -0.016745340079069138, 0.02422175742685795, 0.01765519194304943, 0.07000528275966644, -0.013923303224146366, -0.004544740077108145, -0.04142898693680763, -0.0159298162907362, 0.019170911982655525, -0.03891624137759209, -0.003080881666392088, 0.04441821575164795, -0.05212371423840523, 0.026186522096395493, -0.030361320823431015, -0.006676896940916777, 0.02300638146698475, 0.007634137291461229, -0.03735143318772316, -0.015294124372303486, 0.01210656389594078, -0.02014596201479435, -0.02965298853814602, 0.02774137444794178, -0.024266541004180908, 0.031253837049007416, -0.02824818342924118, 0.023558588698506355, 0.01448441669344902, -0.045407962054014206, -0.02683565951883793, -0.008991973474621773, 0.015442599542438984, -0.014835556969046593, 0.05724235624074936, -0.04897404462099075, 0.022651683539152145, 0.013416474685072899, -0.04207636043429375, -0.028634335845708847, -0.021258840337395668, -0.0063178217969834805, -0.019464578479528427, 0.001000650110654533, 0.0023535392247140408, 0.0038453659508377314, -0.05149562284350395, -0.01753891631960869, -0.03489166125655174, -0.013727799989283085, -0.012187587097287178, 0.003139520762488246, -0.025269320234656334, 0.026500558480620384, 0.00942638423293829, 0.014160249382257462, -0.05092983320355415 ]
<p>WHAT I KNOW: </p> <p>classical computers store information in bits which can either be 0 or 1, but in quantum computer the qubit can store 0 , 1 or a state that is the superposition of these two states. Now when we make a "measurement" (to determine the state of qubit), it changes the state of qubit, collapsing it from its superposition of 0 and 1 to the specific state consistent with the measurement result.</p> <p>MY QUESTION:</p> <p>If, from measurement of a qubit we obtain only a single bit of information (0 or 1 beacuse the qubit collapses to either of the states) then how is a qubit better than a classical bit..... since ultimately we are only able to get either 0 or 1 from either classical or quantum bit.</p> <p>[I hope that i have made the question clear enough to convey what i think].</p> <p>To those who answer this please try to explain with an example if you can.</p>
g8371
[ 0.005668359808623791, 0.044468045234680176, 0.00869126245379448, -0.027584819123148918, -0.017715569585561752, 0.038765572011470795, 0.02728503756225109, 0.028808120638132095, -0.04008395969867706, -0.04064108431339264, -0.014245664700865746, 0.007771719247102737, 0.006099293939769268, 0.012478034012019634, -0.0038881052751094103, 0.004558458924293518, 0.009075392037630081, -0.00446234829723835, 0.09379381686449051, 0.025442838668823242, 0.03445253148674965, -0.006428179331123829, -0.025219717994332314, 0.03039761818945408, -0.08289391547441483, -0.04963883012533188, 0.03542977198958397, 0.0014379656640812755, -0.06333009898662567, 0.004767244216054678, -0.0278305783867836, -0.02551727369427681, 0.009351115673780441, -0.009783369489014149, -0.0015771369216963649, -0.05096832290291786, -0.029155097901821136, -0.04872562363743782, 0.011556745506823063, -0.027934538200497627, 0.00966239906847477, -0.024174483492970467, -0.0018453417578712106, -0.029891362413764, -0.017827466130256653, 0.004441252443939447, 0.05342995747923851, -0.02049355022609234, 0.021178847178816795, -0.03673546761274338, 0.022408420220017433, -0.02957049198448658, 0.031790703535079956, 0.054109636694192886, 0.040155380964279175, 0.07413725554943085, -0.005897288676351309, -0.013212157413363457, 0.058867648243904114, -0.024870740249753, -0.030154328793287277, -0.017765922471880913, 0.02201213128864765, 0.0033945629838854074, 0.045685332268476486, 0.03498247265815735, -0.0245406124740839, 0.05382906645536423, 0.002230736194178462, 0.012299911119043827, -0.004502624273300171, -0.041033562272787094, 0.0002506780147086829, -0.0237593837082386, 0.026261258870363235, 0.04182641580700874, 0.019995572045445442, -0.056645382195711136, -0.012312610633671284, 0.03210858255624771, -0.014223366975784302, -0.0373595654964447, 0.013366031460464, 0.03475948050618172, 0.01942405104637146, 0.05226227641105652, -0.047204528003931046, -0.01739567518234253, -0.009610521607100964, 0.05805326998233795, -0.056554775685071945, -0.05464017391204834, 0.06750643253326416, 0.07532121986150742, -0.0428854376077652, -0.017655985429883003, -0.000007474292488041101, 0.02213464118540287, -0.01668097823858261, 0.014297987334430218, 0.029831545427441597, -0.045879874378442764, 0.006676113698631525, -0.01050996221601963, -0.016861431300640106, -0.017314136028289795, -0.03690020367503166, -0.027182193472981453, -0.04213917627930641, 0.013530944474041462, -0.03458445891737938, -0.020857997238636017, -0.010117659345269203, 0.0155542753636837, -0.03356596454977989, 0.08685383200645447, 0.0539419949054718, -0.019349118694663048, -0.049331214278936386, -0.009233235381543636, -0.011666123755276203, 0.05638957768678665, 0.052379392087459564, 0.006272007245570421, 0.030335014685988426, 0.030232425779104233, -0.025456584990024567, 0.047408733516931534, 0.02772989124059677, 0.06865793466567993, -0.0014231393579393625, 0.03184996545314789, 0.01941012218594551, 0.011439383961260319, 0.005489405244588852, 0.004901213571429253, -0.011088143102824688, 0.004400084726512432, 0.015368323773145676, -0.020651457831263542, -0.007261588238179684, -0.00226474367082119, -0.006897956132888794, -0.0024676418397575617, 0.04242875427007675, -0.05371091887354851, 0.014480958692729473, 0.02706219255924225, -0.06476397812366486, 0.05196830630302429, 0.0019138605566695333, -0.01579080894589424, 0.01598365418612957, -0.05233566462993622, 0.040235571563243866, 0.004361745435744524, 0.09724941849708557, 0.020787011831998825, -0.01654619723558426, 0.02092716097831726, 0.054968155920505524, 0.010201588273048401, 0.00906562339514494, 0.03719322755932808, -0.030111784115433693, -0.012542550452053547, -0.011410722509026527, -0.030510980635881424, 0.05155758559703827, -0.0259927399456501, 0.05568230152130127, -0.01310778222978115, -0.06553010642528534, 0.07389237731695175, -0.033783767372369766, 0.023546703159809113, 0.037597399204969406, 0.05342483893036842, 0.05242808163166046, -0.02536337450146675, -0.039391208440065384, 0.04104595631361008, 0.01953585259616375, -0.010674083605408669, -0.008542817085981369, 0.004227780271321535, 0.009108339436352253, 0.046697963029146194, -0.05145995691418648, -0.03134625777602196, -0.07239054888486862, -0.05827024579048157, 0.007952718995511532, -0.0052175940945744514, -0.0032275391276925802, -0.035785723477602005, 0.012177986092865467, -0.054077159613370895, -0.004311283119022846, 0.010133364237844944, -0.017238358035683632, 0.012468673288822174, -0.007544316817075014, -0.014670305885374546, -0.007235157769173384, -0.009705987758934498, -0.012335393577814102, 0.011577495373785496, -0.004658044315874577, -0.012609296478331089, -0.010835760273039341, 0.05213624984025955, 0.006564871873706579, -0.004896052647382021, 0.01721207983791828, -0.049190010875463486, 0.02583514153957367, -0.03423023223876953, -0.015069901011884212, -0.02761303074657917, -0.025587402284145355, -0.06041906028985977, 0.07509589195251465, -0.01312393881380558, 0.0005687972879968584, 0.05950768291950226, -0.010639757849276066, -0.015284805558621883, -0.032777708023786545, 0.059142787009477615, -0.09484249353408813, -0.012087145820260048, -0.028968334197998047, 0.012892345897853374, 0.009133449755609035, 0.09128481149673462, 0.014131641015410423, 0.01649523712694645, 0.055665016174316406, -0.0020967426244169474, 0.044641416519880295, 0.009980681352317333, -0.05359720066189766, -0.03456300124526024, -0.040024977177381516, -0.017295535653829575, 0.023711085319519043, 0.031006744131445885, 0.028188657015562057, 0.023083550855517387, -0.07746834307909012, -0.023718679323792458, -0.02203359454870224, -0.05832666903734207, 0.004622177686542273, -0.017513245344161987, 0.06055550277233124, 0.02396923117339611, -0.039317402988672256, -0.011626344174146652, -0.03560479357838631, 0.05194564908742905, -0.03799236938357353, 0.008750098757445812, 0.047209277749061584, -0.01141341868788004, -0.007125510834157467, -0.021820848807692528, -0.02796550840139389, -0.017710749059915543, -0.030548885464668274, 0.03303578495979309, -0.009871103800833225, -0.005641112104058266, 0.0018550098175182939, -0.08384951949119568, -0.011355366557836533, 0.004922561813145876, 0.048752181231975555, -0.060223538428545, -0.04519793018698692, -0.011175449937582016, -0.049569446593523026, -0.05354967340826988, 0.0005789120914414525, -0.0136650912463665, -0.011970947496592999, 0.00973928440362215, 0.035186517983675, 0.026193508878350258, -0.019271457567811012, 0.0373593345284462, 0.051666535437107086, -0.018402131274342537, 0.006856665015220642, 0.04034140706062317, -0.026016974821686745, -0.01632956974208355, -0.0051416256465017796, 0.06922542303800583, -0.06574289500713348, 0.025473833084106445, -0.013044224120676517, -0.006531430874019861, 0.027114475145936012, 0.028935331851243973, -0.05619803071022034, -0.023646345362067223, -0.04096669703722, -0.03637663647532463, -0.02486872673034668, 0.030519282445311546, 0.01829075813293457, -0.03707737848162651, 0.010588422417640686, -0.027679353952407837, -0.030556943267583847, 0.04907837137579918, -0.028480127453804016, 0.017787029966711998, -0.042941395193338394, -0.029882516711950302, -0.005643220152705908, -0.015850193798542023, 0.06908931583166122, -0.012919958680868149, -0.057880159467458725, 0.03590422868728638, -0.038999248296022415, -0.03476971387863159, -0.0017033970216289163, 0.018570957705378532, -0.011680059134960175, -0.005815866403281689, -0.03235480561852455, -0.07143809646368027, -0.032544586807489395, -0.014763809740543365, 0.013809723779559135, 0.026569848880171776, 0.022537751123309135, 0.01796647533774376, 0.00454485509544611, 0.00574836041778326, 0.046806689351797104, 0.016834218055009842, 0.013204558752477169, 0.010331208817660809, 0.015704989433288574, -0.009746651165187359, 0.02540389634668827, 0.017392512410879135, 0.015236806124448776, 0.003291481174528599, -0.010590110905468464, 0.058466628193855286, -0.04681485891342163, 0.03258952125906944, 0.017020603641867638, 0.010901503264904022, 0.03445761278271675, -0.02724955417215824, 0.04937755689024925, -0.025319352746009827, -0.03770097717642784, -0.0059196725487709045, -0.00799501221626997, 0.004067836329340935, 0.004706865642219782, 0.003375951200723648, -0.04034998267889023, -0.00778916897252202, 0.025555649772286415, -0.029079442843794823, 0.06504439562559128, -0.06990936398506165, 0.015332045964896679, -0.00233733793720603, 0.029918571934103966, -0.002650435082614422, 0.02854415960609913, -0.01097266748547554, 0.01704827882349491, -0.04021216928958893, 0.003072507679462433, -0.04583653435111046, -0.013032905757427216, -0.023032641038298607, -0.018053917214274406, -0.005015088710933924, 0.034247323870658875, -0.0785980373620987, -0.02432970702648163, 0.03131001442670822, -0.009756323881447315, 0.1066145971417427, 0.011235550045967102, -0.04497796297073364, -0.012990987859666348, 0.040061067789793015, -0.03682318702340126, 0.02055094577372074, 0.022219043225049973, -0.0005514476797543466, 0.018318360671401024, -0.03813251107931137, 0.038956418633461, -0.008718176744878292, -0.016458647325634956, -0.020766422152519226, 0.017302624881267548, -0.0073017398826777935, 0.016361143440008163, -0.05100884288549423, 0.028156092390418053, 0.10053574293851852, 0.02842716872692108, 0.015663867816329002, 0.032444823533296585, 0.009104725904762745, -0.006106519605964422, 0.009571355767548084, 0.015240446664392948, -0.04078437015414238, -0.021953778341412544, 0.04236004501581192, -0.005764567293226719, -0.017291197553277016, 0.032534800469875336, 0.023420579731464386, 0.07165411114692688, -0.006720928940922022, 0.09073439240455627, 0.06304196268320084, -0.0213762316852808, 0.023964229971170425, -0.025938551872968674, 0.07362961769104004, -0.0015987401129677892, 0.0007389851962216198, 0.06801474094390869, -0.02377660758793354, -0.045049648731946945, -0.04627780243754387, -0.017284926027059555, 0.02523159608244896, -0.036373019218444824, 0.00700675742700696, -0.03459925204515457, -0.061153847724199295, -0.003838653676211834, 0.058922890573740005, 0.011830268427729607, -0.08909262716770172, -0.012395820580422878, -0.02527819201350212, -0.0012887498596683145, 0.030945496633648872, 0.03892090916633606, 0.08114633709192276, -0.02855638600885868, 0.0011875297641381621, -0.011800880543887615, 0.03960246965289116, 0.019467240199446678, -0.02422459051012993, -0.04762238264083862, 0.03892476484179497, -0.08550228923559189, -0.021017301827669144, 0.004794743377715349, -0.0034682543482631445, -0.007596493232995272, -0.022721845656633377, 0.03289934992790222, -0.00220865267328918, -0.06965471804141998, -0.05208561196923256, 0.036790717393159866, -0.055139992386102676, -0.022044507786631584, 0.06372110545635223, 0.01823681965470314, -0.0069620562717318535, 0.014366060495376587, -0.004147430416196585, -0.017395885661244392, -0.05375664308667183, -0.0034425235353410244, -0.044808655977249146, 0.055261172354221344, 0.0021124558988958597, 0.09352070093154907, 0.0005736736347898841, 0.00794706679880619, -0.07549028843641281, -0.013476530089974403, -0.007177713792771101, -0.02148030884563923, 0.029419364407658577, -0.05753855034708977, 0.06918109208345413, 0.007490986026823521, 0.0681758001446724, -0.02246001735329628, 0.0239725261926651, 0.01594221591949463, 0.004504516255110502, -0.031609125435352325, 0.016083387657999992, -0.0398835726082325, -0.010733761824667454, -0.06343995779752731, 0.04411158710718155, 0.013367989100515842, 0.014118034392595291, 0.020787538960576057, 0.0004502875090111047, -0.0181648600846529, -0.02484102174639702, -0.032047100365161896, 0.07243335992097855, 0.00860755518078804, 0.0373995266854763, -0.024223538115620613, 0.014258991926908493, -0.10065001249313354, -0.06843672692775726, 0.0705837532877922, 0.0020952755585312843, 0.07562417536973953, 0.05835673585534096, 0.026116814464330673, 0.013292309828102589, 0.010231120511889458, 0.018738310784101486, -0.02445675991475582, -0.034632742404937744, 0.022777939215302467, 0.07415559142827988, -0.024296265095472336, 0.01644027791917324, 0.00020928696903865784, 0.0886351466178894, 0.03954721614718437, -0.05380546674132347, -0.0530126728117466, -0.02290390431880951, 0.009416292421519756, -0.006123169790953398, 0.004492112901061773, 0.01425174716860056, -0.029865702614188194, 0.054261866956949234, 0.022236809134483337, 0.02397250011563301, 0.011580527760088444, 0.020932015031576157, -0.022012285888195038, 0.005517435260117054, -0.017581511288881302, 0.044139280915260315, 0.04547179490327835, 0.029086753726005554, 0.06444969028234482, -0.015461190603673458, 0.00520635861903429, 0.0034284682478755713, 0.02697053551673889, 0.02178041636943817, -0.01865147426724434, 0.012751760892570019, -0.012351938523352146, -0.016876094043254852, -0.007646211888641119, 0.03976243734359741, -0.04487462341785431, -0.08979975432157516, -0.012040098197758198, -0.011823357082903385, 0.0183991938829422, -0.01645331270992756, 0.02585749886929989, 0.014263076707720757, 0.0392085500061512, 0.038146503269672394, -0.04145542532205582, 0.049435924738645554, 0.022472389042377472, 0.07347560673952103, -0.015489572659134865, 0.03427916392683983, 0.006507301237434149, -0.05212225019931793, 0.002651575021445751, 0.006792281288653612, -0.012149736285209656, -0.050656866282224655, -0.021191496402025223, -0.03288809582591057, -0.016437863931059837, 0.0019279404077678919, 0.06393096596002579, -0.01500353217124939, -0.0025989406276494265, 0.024729445576667786, -0.03427504748106003, -0.005134914070367813, 0.018349023535847664, -0.05064438283443451, -0.029615003615617752, 0.0005535552045330405, -0.009308191947638988, 0.01058329176157713, 0.03699597716331482, -0.05055531859397888, 0.00763589795678854, -0.03631975129246712, -0.042114462703466415, 0.026789303869009018, -0.005731137469410896, -0.03613026812672615, -0.007840301841497421, -0.05682672560214996, 0.020854288712143898, 0.0866033136844635, 0.0109180873259902, 0.053157929331064224, 0.058165714144706726, 0.07134654372930527, 0.007896693423390388, 0.047198664397001266, 0.047536756843328476, 0.0745995044708252, -0.018025586381554604, 0.0015717686619609594, -0.06322777271270752, 0.022635342553257942, -0.004495604429394007, 0.014500431716442108, 0.0639519989490509, 0.00008700211037648842, 0.014590603299438953, 0.014403748326003551, -0.04288606718182564, 0.01114405132830143, 0.009380507282912731, 0.03311493620276451, -0.07234679907560349, -0.015946034342050552, -0.017629144713282585, 0.021206337958574295, -0.008345535025000572, -0.02503189630806446, 0.01593673601746559, 0.009525693953037262, 0.028959820047020912, 0.0285209771245718, 0.029688771814107895, -0.1043260470032692, -0.04457053542137146, -0.057304497808218, -0.018654394894838333, -0.001869435072876513, 0.04765640199184418, -0.02464650757610798, -0.02040487714111805, -0.041028402745723724, -0.015568935312330723, -0.06472386419773102, -0.0070358808152377605, -0.05946487933397293, 0.02854476310312748, -0.029014775529503822, 0.06337493658065796, -0.007627618499100208, -0.031294967979192734, -0.0022365169133991003, -0.07842675596475601, -0.02653753198683262, -0.03174879401922226, 0.043379999697208405, 0.029987448826432228, 0.016442393884062767, -0.05623169243335724, 0.0415029376745224, -0.0030801205430179834, -0.0020141268614679575, 0.006450470071285963, -0.040614888072013855, 0.07629911601543427, -0.07144728302955627, -0.014715033583343029, -0.039448149502277374, -0.05967742204666138, 0.03582470118999481, 0.02678389474749565, -0.0018136402359232306, 0.0046220868825912476, -0.0025427336804568768, 0.01608554646372795, -0.0359254814684391, -0.001031982246786356, 0.03969812020659447, 0.05881455913186073, 0.010299420915544033, -0.02768435701727867, 0.0026310395915061235, -0.04103626310825348, 0.008082697167992592, 0.028284117579460144, -0.039922814816236496, 0.041235439479351044, -0.000008019484994292725, 0.03719049692153931, -0.03048480488359928, -0.04583844169974327, 0.07002514600753784, 0.014877785928547382, -0.01895766891539097, -0.008719775825738907, -0.057374242693185806, -0.0023963130079209805, -0.013221733272075653, -0.06061462312936783, -0.055461253970861435, 0.029043788090348244, 0.029102163389325142, 0.0077615706250071526, 0.020113958045840263, 0.039748210459947586, -0.044024091213941574, -0.02355642057955265, -0.012434002943336964, -0.01084655337035656, 0.05581148341298103, -0.03217411786317825, -0.00037982576759532094, -0.05187688395380974, 0.04262809827923775, -0.0051103937439620495, 0.006826526019722223, -0.025906408205628395, -0.04935828968882561, -0.004708162043243647, -0.08857151120901108, -0.025005372241139412, 0.0058013699017465115, -0.008092421106994152, -0.05269983783364296, -0.0159393809735775, -0.07557227462530136, 0.011861387640237808, 0.03631918132305145, 0.014804051257669926, 0.02472783997654915, -0.011350623331964016, 0.0055351764895021915, -0.01522576529532671, 0.0351899079978466, 0.03854051232337952, 0.030968572944402695, -0.029465988278388977, -0.021841486915946007, -0.07967179268598557, 0.006542921997606754, 0.0016771518858149648, -0.0064901327714324 ]
<p>This assignment is about the one dimensional harmonic oscillator (HO). The hamiltonian is just as you know from the HO, same goes for the energies, but I get that the wavefunction of the particle, at $t = 0$, is given by:</p> <p>$\psi \left( x,\,\,t=0 \right)=A\left( {{\phi }_{0}}\left( x \right)+2i{{\phi }_{2}}\left( x \right) \right)$</p> <p>Now I have to calculate A, so that $\psi$ is normalized.</p> <p>My question is, what is ${{\phi }_{0}}\left( x \right)$ and ${{\phi }_{2}}\left( x \right)$ given by ?</p> <p>Otherwise I guess is just doing the usual:</p> <p>$\int_{-\infty }^{\infty }{{{\left| \Psi \left( x,\,\,t \right) \right|}^{2}}}dx=1$</p> <p>To figure out A.</p>
g8372
[ 0.02976306714117527, -0.034763310104608536, -0.023138880729675293, -0.07273220270872116, 0.04452250525355339, -0.02404676005244255, 0.04504074528813362, 0.05799861252307892, -0.02171962708234787, 0.015646526589989662, -0.021811673417687416, 0.04318665340542793, -0.06434852629899979, 0.032297492027282715, 0.05718439444899559, 0.004958589095622301, 0.03685696795582771, 0.056666020303964615, 0.011023475788533688, -0.027252057567238808, -0.017155887559056282, 0.020277440547943115, -0.03782583028078079, -0.02836346998810768, 0.0454978384077549, -0.023623386397957802, -0.03981119766831398, -0.029502445831894875, -0.001349920523352921, -0.0054860287345945835, -0.00935904961079359, 0.046665579080581665, 0.05253414437174797, -0.04756598174571991, -0.05062340572476387, 0.08301375061273575, 0.09714701026678085, -0.015511487610638142, 0.02311452478170395, 0.0007070638239383698, -0.0024220733903348446, -0.07280468195676804, 0.007192203775048256, -0.02782132476568222, -0.000044244869059184566, 0.034579046070575714, -0.0013898491160944104, 0.048207491636276245, -0.025569049641489983, -0.017325598746538162, 0.04455258324742317, 0.016267264261841774, 0.05477887764573097, 0.04652649164199829, 0.02310248091816902, 0.04908216744661331, 0.029462743550539017, -0.05326201394200325, 0.05948769673705101, 0.07687173038721085, -0.004662076942622662, 0.039393872022628784, 0.0320558175444603, 0.016516398638486862, 0.030710337683558464, -0.01201473455876112, 0.01368203666061163, -0.03309301286935806, -0.04148990288376808, 0.0019612654577940702, -0.003478431375697255, -0.09336859732866287, -0.011323636397719383, -0.012866407632827759, -0.051366306841373444, 0.007208398077636957, 0.01495425682514906, -0.04747399687767029, -0.008142379112541676, -0.0068758283741772175, -0.016385847702622414, -0.08010320365428925, 0.06373025476932526, -0.007836445234715939, 0.039385341107845306, 0.022967444732785225, 0.01641951873898506, 0.007382489275187254, -0.04672329127788544, 0.03490834683179855, 0.006827166769653559, -0.009194092825055122, 0.029969722032546997, -0.01979963853955269, 0.029759587720036507, 0.01948959194123745, -0.07018343359231949, 0.03855770081281662, -0.03394399210810661, -0.011457778513431549, -0.024562720209360123, 0.015503640286624432, 0.043867241591215134, -0.03568778187036514, 0.011414577253162861, 0.061841800808906555, -0.0019108770648017526, 0.03377416357398033, -0.01843920536339283, -0.028491182252764702, -0.025908377021551132, 0.013702201656997204, 0.04047256335616112, -0.07276609539985657, -0.026976916939020157, -0.07254303246736526, 0.07605298608541489, -0.05168880522251129, 0.012843621894717216, 0.030937453731894493, -0.008762934245169163, -0.0034245196729898453, 0.05602555349469185, 0.0606636181473732, 0.037909939885139465, 0.03080020844936371, -0.02857254631817341, 0.011620082892477512, 0.002298009814694524, -0.01355139072984457, -0.016112303361296654, -0.011462411843240261, 0.005117539316415787, 0.03150547668337822, 0.010828605853021145, 0.021216023713350296, 0.004813456907868385, 0.0010865526273846626, 0.020307596772909164, 0.01139876153320074, 0.010349910706281662, -0.028796114027500153, 0.023269224911928177, -0.005865725222975016, -0.03820071369409561, 0.02573278918862343, 0.08209871500730515, -0.08846887201070786, 0.0044556171633303165, -0.005833467002958059, -0.010693416930735111, 0.060024991631507874, -0.0026394594460725784, 0.0109748225659132, -0.01774507574737072, -0.027744045481085777, 0.05074463412165642, 0.008218681439757347, -0.05442804843187332, 0.017853764817118645, 0.01186241302639246, 0.034544169902801514, 0.039567578583955765, -0.003966982010751963, -0.05426297336816788, 0.031785134226083755, 0.01710796356201172, -0.052269890904426575, 0.029119452461600304, -0.019476840272545815, 0.03590726479887962, -0.031137118116021156, -0.0019433560082688928, 0.005111590959131718, -0.020275255665183067, 0.06930799037218094, -0.040308792144060135, -0.0333528034389019, 0.04833732172846794, 0.07020484656095505, 0.03771521896123886, -0.04227868467569351, 0.02616652101278305, -0.0395292192697525, -0.04512817785143852, -0.019652483984827995, 0.0005150185315869749, 0.006640662904828787, -0.07027433812618256, 0.004912779200822115, -0.022780753672122955, 0.024521417915821075, 0.06806503236293793, 0.059206634759902954, -0.04095727577805519, 0.028584811836481094, 0.027442295104265213, -0.06837216764688492, -0.07071971148252487, -0.028211437165737152, 0.0011832958552986383, 0.039948318153619766, 0.05253956466913223, -0.012955693528056145, 0.041089680045843124, 0.009725443087518215, 0.049970027059316635, 0.023258699104189873, -0.00998535007238388, 0.0038480693474411964, -0.03629105165600777, -0.04874708503484726, -0.006499484647065401, 0.011956672184169292, -0.010417137295007706, -0.03363804891705513, -0.023500170558691025, -0.016119670122861862, -0.05970209836959839, -0.01235717162489891, 0.0032117757946252823, 0.009650998748838902, 0.06665939837694168, -0.015991387888789177, -0.016533827409148216, 0.0459899976849556, -0.026406848803162575, -0.006231804843991995, -0.02775673195719719, 0.012661655433475971, -0.025413352996110916, -0.016594160348176956, 0.006015140097588301, -0.0010104645043611526, -0.010079900734126568, 0.0452720932662487, -0.047038376331329346, 0.0030168651137501, 0.009208142757415771, 0.038767214864492416, -0.011811072006821632, 0.02394000068306923, 0.02349337749183178, -0.02037246711552143, 0.019416218623518944, 0.007634527049958706, 0.019594691693782806, -0.013162377290427685, -0.04346892982721329, -0.009148008190095425, 0.00015899910067673773, 0.031025366857647896, -0.01666441187262535, 0.002788134617730975, -0.03859829530119896, -0.05758894979953766, -0.009030690416693687, -0.006809907965362072, -0.016019631177186966, -0.07827315479516983, -0.032774992287158966, -0.008456450887024403, 0.0003005792386829853, 0.03381526842713356, -0.049800626933574677, -0.005287233740091324, 0.027509761974215508, 0.022862691432237625, 0.012764210812747478, -0.04807394742965698, 0.02923659235239029, 0.05730437859892845, 0.017793938517570496, 0.0650859847664833, -0.009417318738996983, -0.04934443533420563, -0.009862841106951237, -0.00937910471111536, 0.05013382434844971, -0.024027932435274124, -0.0036283284425735474, 0.013938872143626213, -0.04860642924904823, 0.04818255081772804, -0.014988528564572334, -0.06502892076969147, 0.002977738156914711, 0.05283224955201149, 0.005119847133755684, -0.057448893785476685, 0.011047441512346268, 0.005810968112200499, 0.0066578262485563755, 0.012681238353252411, 0.007597600109875202, 0.01647806167602539, 0.09237969666719437, -0.028220159932971, -0.001064966432750225, 0.09119672328233719, -0.019330106675624847, -0.003368541831150651, 0.028994549065828323, -0.041200436651706696, 0.0376683734357357, -0.005242557730525732, -0.03952116146683693, -0.011999555863440037, -0.02256867289543152, 0.026231467723846436, 0.011536180041730404, 0.030395066365599632, 0.03763778507709503, -0.0027503978926688433, -0.0024292992893606424, 0.012840334326028824, -0.09827060997486115, -0.08477147668600082, -0.020351935178041458, -0.03741909936070442, -0.03748464211821556, -0.04458228126168251, -0.0032875847537070513, 0.021938743069767952, 0.022435912862420082, 0.00019387378415558487, -0.08102694898843765, -0.013569865375757217, -0.05123387649655342, -0.023136982694268227, 0.015089320950210094, -0.008998258039355278, -0.03710174560546875, 0.014198964461684227, -0.032621897757053375, -0.035779956728219986, -0.029213519766926765, 0.04345899447798729, 0.05392350256443024, 0.06274151802062988, 0.016159337013959885, 0.013814895413815975, 0.021458301693201065, -0.0006498436559922993, 0.01332246232777834, -0.06630020588636398, -0.04502546787261963, 0.041325170546770096, -0.0057832240127027035, -0.002957492833957076, -0.008857594802975655, -0.012208388186991215, 0.01323959231376648, 0.021640963852405548, 0.03452630341053009, 0.002059110440313816, 0.029193537309765816, 0.06448210775852203, 0.004838449414819479, 0.015939410775899887, -0.017931317910552025, -0.06645096838474274, 0.01890125498175621, 0.06797882169485092, 0.01106712594628334, -0.03984825685620308, -0.015508248470723629, 0.01506136916577816, -0.002062139566987753, -0.06392081826925278, -0.009565865620970726, 0.0017574627418071032, 0.04221194237470627, -0.007431936450302601, -0.03136701136827469, -0.020368264988064766, -0.035416387021541595, -0.06129072234034538, 0.004455027636140585, 0.007492233999073505, -0.03605714812874794, -0.01002887636423111, 0.0009890616638585925, -0.03194762021303177, 0.07308393716812134, 0.001989031909033656, -0.03004283644258976, 0.0012030326761305332, 0.00563086336478591, -0.016494711861014366, 0.01917135715484619, -0.057863082736730576, -0.019622568041086197, 0.010903751477599144, -0.0021023722365498543, 0.027215152978897095, 0.032249804586172104, -0.014880308881402016, -0.08998224139213562, 0.05512543022632599, -0.031291600316762924, -0.05463895946741104, 0.03754579275846481, -0.028627978637814522, 0.019763903692364693, 0.05899859219789505, 0.05432353541254997, -0.027357373386621475, 0.03866122290492058, -0.05801144242286682, -0.015843717381358147, -0.00850171223282814, 0.04282262548804283, -0.028389636427164078, 0.002292365301400423, 0.01845810003578663, 0.047096457332372665, -0.036157116293907166, -0.002637736964970827, 0.01857057213783264, 0.0075844936072826385, -0.000422875105869025, 0.01832159049808979, -0.026892509311437607, -0.00558618176728487, 0.020297901704907417, 0.05712760239839554, 0.008365636691451073, -0.03906489536166191, -0.06217855215072632, 0.039424411952495575, 0.01920018158853054, 0.029952233657240868, -0.004230482038110495, -0.06724127382040024, -0.014976204372942448, -0.044217415153980255, 0.002298266626894474, -0.007362667005509138, -0.0036720025818794966, 0.05219641327857971, 0.01278025470674038, -0.01575203239917755, -0.004673715680837631, -0.0029012388549745083, -0.019172560423612595, -0.033398065716028214, -0.08822920173406601, -0.03261448070406914, -0.02988206222653389, 0.07012349367141724, 0.04588146507740021, -0.009138408116996288, -0.03760017082095146, 0.01629018597304821, -0.051128316670656204, -0.06710026413202286, 0.021928003057837486, -0.01379049476236105, 0.013837804086506367, -0.08622828125953674, -0.06691830605268478, -0.028651513159275055, -0.027697693556547165, 0.00006966044020373374, -0.007338948547840118, -0.07064267992973328, 0.038033921271562576, -0.04854772239923477, 0.021249687299132347, 0.04177742823958397, -0.06893197447061539, 0.037945352494716644, -0.04766688868403435, -0.008539717644453049, -0.028925476595759392, 0.0032737641595304012, -0.05454835295677185, 0.03605525195598602, -0.009831310249865055, -0.008168351836502552, -0.02279569022357464, 0.026654673740267754, 0.055204473435878754, -0.02979934774339199, -0.015510139986872673, -0.008234011009335518, -0.04631705582141876, 0.016050903126597404, 0.007220948580652475, -0.0030468469485640526, 0.04888753592967987, 0.042173225432634354, 0.024916894733905792, 0.02236722595989704, 0.009453153237700462, -0.01077608484774828, -0.018080689013004303, -0.0008485381258651614, -0.006619982421398163, -0.042013976722955704, 0.025296775624155998, -0.044909100979566574, 0.0014875954948365688, -0.011158968321979046, 0.03072575479745865, 0.06823046505451202, 0.030482841655611992, -0.02395384944975376, -0.010021494701504707, 0.004563498310744762, 0.0015817009843885899, 0.033598821610212326, 0.032295290380716324, 0.018242552876472473, -0.015333372168242931, -0.04053191468119621, 0.04034164920449257, -0.0002931168710347265, -0.005360473413020372, 0.05098981782793999, 0.03367140144109726, 0.023027610033750534, -0.06870080530643463, 0.030245879665017128, 0.026169713586568832, -0.021160777658224106, -0.05271882563829422, -0.027362369000911713, 0.0314909927546978, 0.01437298208475113, 0.01649720035493374, 0.03382460027933121, 0.02063538134098053, -0.003398263594135642, 0.03940003365278244, -0.04502708092331886, 0.008801620453596115, 0.011624387465417385, 0.018743768334388733, -0.01684596948325634, -0.013768140226602554, 0.030428403988480568, 0.011790914461016655, -0.03191555291414261, 0.01319118496030569, -0.027455180883407593, 0.027394890785217285, -0.029345791786909103, -0.01059590931981802, -0.05660610273480415, -0.02692646160721779, 0.017387229949235916, -0.037035055458545685, 0.031259916722774506, -0.01991443522274494, 0.028568005189299583, -0.030499428510665894, 0.008297535590827465, -0.008437315933406353, 0.03894776478409767, -0.0512460432946682, 0.015047111548483372, -0.03437596559524536, -0.0037117155734449625, 0.01873623952269554, -0.012709863483905792, -0.0339081697165966, 0.018111418932676315, -0.021564189344644547, -0.0341683030128479, -0.0005995557876303792, 0.03430253267288208, 0.04008373245596886, 0.07585316896438599, 0.04517649859189987, 0.00820098351687193, -0.015544743277132511, -0.025638453662395477, 0.00607646256685257, 0.002818369772285223, 0.02880231663584709, 0.03487982973456383, -0.06422539800405502, -0.04027819260954857, 0.09223711490631104, 0.004436344373971224, -0.06507392972707748, 0.08562396466732025, 0.02274077758193016, -0.017635919153690338, -0.01093898992985487, -0.01562599465250969, -0.02121318131685257, 0.012689747847616673, 0.05584589019417763, -0.004166401922702789, -0.04982737451791763, -0.00400608079507947, 0.04632896929979324, 0.02836710214614868, 0.012940023094415665, 0.041143130511045456, -0.00607952568680048, 0.000579496962018311, 0.03638004884123802, -0.06426355242729187, 0.006421913392841816, -0.06029680743813515, 0.05843554809689522, 0.027821915224194527, 0.0067412154749035835, -0.016982927918434143, -0.008958142250776291, 0.011349134147167206, -0.05084536597132683, 0.05154122784733772, 0.05202304944396019, 0.04364448040723801, 0.025676198303699493, 0.030549481511116028, 0.016392283141613007, -0.039268434047698975, 0.012257098220288754, 0.07655064761638641, -0.0021615512669086456, -0.012228306382894516, -0.05223473161458969, 0.03884544223546982, 0.0215810127556324, 0.015834102407097816, 0.012461992911994457, -0.0201994888484478, 0.08586947619915009, -0.024493860080838203, -0.04987189546227455, -0.06636625528335571, 0.00377654773183167, -0.011155476793646812, 0.08771925419569016, 0.0029227500781416893, 0.0485263355076313, 0.01915579102933407, -0.045113835483789444, -0.1149255558848381, 0.03449101001024246, 0.059172168374061584, -0.006192443426698446, -0.11877895146608353, -0.011179538443684578, -0.011994574218988419, -0.006427616346627474, -0.029445243999361992, 0.022640427574515343, -0.03617698326706886, -0.012477867305278778, 0.03774499520659447, 0.021845918148756027, 0.01679007150232792, -0.013794969767332077, 0.022345148026943207, -0.036413952708244324, 0.02884680964052677, 0.02213703840970993, 0.009687545709311962, 0.08425641804933548, -0.00003334685243316926, -0.016867518424987793, 0.007341108750551939, -0.060220908373594284, -0.0017792811850085855, 0.003784140106290579, -0.06005339324474335, 0.017864113673567772, 0.017388643696904182, 0.015330102294683456, 0.042959775775671005, 0.05549338459968567, -0.02631525509059429, -0.04800408333539963, -0.0036108708009123802, -0.01463226042687893, -0.009266208857297897, -0.007965033873915672, -0.00006283338007051498, -0.011046555824577808, -0.0048426971770823, -0.03264062851667404, -0.024669185280799866, 0.06231363117694855, 0.0031655977945774794, 0.010770978406071663, 0.007165636867284775, -0.03737565502524376, -0.012892307713627815, 0.04799610376358032, 0.029429953545331955, 0.04993981122970581, 0.028822533786296844, 0.031235594302415848, 0.02320733852684498, -0.05298333615064621, 0.000759767135605216, 0.011562495492398739, -0.04265834391117096, -0.02519937790930271, 0.00899738073348999, -0.05843121558427811, -0.010788599029183388, 0.0032045533880591393, 0.04550476744771004, -0.011742754839360714, 0.008361633867025375, 0.005168527830392122, 0.04100707173347473, 0.022927559912204742, -0.03417229279875755, 0.03617091849446297, 0.06807681918144226, -0.05373650789260864, -0.03312230110168457, 0.04026779904961586, -0.049520619213581085, -0.041291914880275726, 0.0031653011683374643, 0.017245566472411156, -0.05015277862548828, 0.008852813392877579, 0.02629241533577442, 0.01903032884001732, -0.049032747745513916, 0.01214138139039278, -0.015585184097290039, 0.029302505776286125, -0.011451865546405315, -0.03456506505608559, -0.014991597272455692, -0.03112208843231201, -0.010639546439051628, 0.03136320412158966, 0.011016512289643288, -0.046760134398937225, 0.013476221822202206, -0.04740298539400101, -0.01890549436211586, -0.0016065345844253898, -0.049950599670410156, 0.014122946187853813, 0.08981417864561081, -0.05399898439645767, -0.021636193618178368, 0.05151413381099701, -0.004946326371282339, 0.07438108325004578, 0.0030707765836268663, -0.09928811341524124, 0.01413127314299345, 0.0044854385778307915, 0.0469929575920105, -0.004359397571533918, 0.012549998238682747, -0.02126242034137249, 0.03371581807732582, -0.010350063443183899, 0.02875293232500553, -0.044813238084316254, 0.004799870308488607, 0.020422037690877914 ]
<p>If two balls collide (elastically) and there is no friction between them, will their angular momentum change after the collision?</p>
g8373
[ 0.07868107408285141, -0.030313577502965927, 0.02984905242919922, -0.04530424252152443, 0.04503243789076805, 0.037994757294654846, -0.003788850037381053, -0.011767051182687283, -0.0021533891558647156, -0.030582807958126068, -0.028018899261951447, -0.06280339509248734, -0.0017577280523255467, -0.11921558529138565, -0.0051792156882584095, 0.014052790589630604, 0.053896982222795486, -0.03392891213297844, -0.034540917724370956, 0.009777645580470562, -0.062294505536556244, -0.014362193644046783, 0.01414341852068901, -0.036089830100536346, -0.010206309147179127, -0.05830395594239235, -0.02734927088022232, -0.009108350612223148, -0.03664015978574753, 0.04255137965083122, 0.06549464166164398, -0.017038414254784584, 0.020893622189760208, -0.0915207639336586, -0.024258287623524666, -0.03188936039805412, 0.03981493413448334, -0.05534868687391281, -0.033398520201444626, -0.0045403484255075455, 0.06209959834814072, 0.024348242208361626, 0.0017190638463944197, -0.03495323657989502, -0.02584454044699669, -0.022192757576704025, 0.02326948009431362, 0.0442458875477314, -0.0036890420597046614, 0.036385100334882736, -0.004286188632249832, 0.07779183238744736, -0.02021845616400242, 0.004029866307973862, -0.014009274542331696, 0.030582675710320473, 0.05350717157125473, 0.011382417753338814, 0.05793595686554909, 0.02790972776710987, -0.06100470945239067, -0.03404487296938896, -0.014536802656948566, -0.02770303189754486, 0.03373199701309204, -0.058530792593955994, -0.028945744037628174, -0.017491720616817474, 0.034758515655994415, 0.0015627364628016949, 0.012652434408664703, 0.028124472126364708, -0.008804736658930779, 0.010269640944898129, -0.032049283385276794, -0.015268448740243912, 0.04411621019244194, -0.03599276766180992, -0.020180998370051384, -0.021127164363861084, -0.059560831636190414, 0.04130421578884125, 0.059630680829286575, -0.03631163761019707, 0.045819301158189774, -0.025023067370057106, 0.031036382541060448, -0.028776811435818672, -0.037004198879003525, 0.01265980675816536, 0.0833839401602745, -0.04379858076572418, -0.001921433606185019, 0.030622897669672966, -0.016454387456178665, -0.027368316426873207, -0.05749102681875229, 0.05579667538404465, 0.033378925174474716, 0.02467057667672634, -0.039614345878362656, -0.005130233708769083, 0.038697510957717896, -0.01832837052643299, 0.03335901349782944, -0.012055613100528717, 0.026981817558407784, 0.022368451580405235, -0.006918313447386026, -0.022793695330619812, 0.000012545868230517954, -0.05961373448371887, -0.0011907495791092515, -0.044516272842884064, 0.026381241157650948, -0.03198886662721634, 0.045496392995119095, -0.015569702722132206, 0.013937186449766159, 0.10242355614900589, 0.014701547101140022, 0.03182641416788101, 0.008685803040862083, 0.04068439453840256, -0.006259895861148834, 0.0028225439600646496, 0.0395406112074852, 0.008380190469324589, 0.00979338213801384, -0.017145153135061264, -0.03650496155023575, -0.00870526023209095, 0.05561554804444313, -0.014688807539641857, -0.03988434374332428, 0.03765864670276642, 0.01354791410267353, 0.04188061133027077, 0.02067711018025875, 0.01810034178197384, 0.02262129634618759, 0.01758393831551075, 0.027392372488975525, -0.003531154477968812, -0.01782168447971344, -0.011950838379561901, 0.04848317429423332, -0.022987570613622665, 0.023400919511914253, 0.04328281432390213, -0.014656821265816689, -0.014803202822804451, 0.038197822868824005, -0.020292257890105247, -0.0033102459274232388, 0.033718254417181015, 0.011631601490080357, 0.014873038977384567, 0.026979397982358932, -0.0026422529481351376, 0.009508534334599972, -0.03585087135434151, 0.05762752145528793, 0.01113947480916977, -0.04340391233563423, 0.06071373075246811, -0.05087645351886749, -0.008697710931301117, -0.025323109701275826, -0.057417094707489014, -0.07656967639923096, -0.02605382166802883, -0.004478349816054106, 0.061795033514499664, 0.0012021447764709592, -0.003421879606321454, -0.08416259288787842, -0.023872191086411476, -0.015008606016635895, 0.02110879309475422, 0.007811151444911957, 0.05956418067216873, 0.032543737441301346, 0.018268324434757233, 0.05745971202850342, 0.0100805489346385, -0.027647553011775017, 0.06935004144906998, -0.0519024133682251, 0.01758860982954502, -0.024092897772789, 0.015627248212695122, -0.05141731724143028, 0.007207863498479128, 0.014594781212508678, 0.043105266988277435, 0.03991718217730522, 0.018315013498067856, -0.013861562125384808, 0.04345552250742912, -0.014020038768649101, 0.04808283597230911, 0.018295278772711754, 0.029934614896774292, -0.06594239920377731, 0.00926191359758377, -0.013492750003933907, -0.030965760350227356, 0.015903523191809654, -0.02296765148639679, 0.07365472614765167, 0.036291830241680145, -0.07483876496553421, -0.010815584100782871, -0.02016151137650013, 0.010928147472441196, 0.026646573096513748, 0.040115632116794586, -0.06216241046786308, 0.037158042192459106, -0.002704259939491749, 0.008928371593356133, -0.006238785106688738, -0.04914532229304314, 0.013375543057918549, -0.08170463144779205, -0.012389774434268475, -0.00009762959962245077, -0.0009029616485349834, 0.047537509351968765, -0.010127645917236805, 0.006712954957038164, 0.03144507110118866, -0.0264554675668478, 0.014088152907788754, 0.01876017451286316, 0.024904703721404076, 0.013447506353259087, 0.017019739374518394, 0.025414999574422836, 0.06480873376131058, -0.03901267796754837, 0.010789457708597183, -0.013308404013514519, 0.05553548038005829, -0.05985703691840172, 0.047152984887361526, 0.016838477924466133, 0.04850626364350319, 0.048231810331344604, 0.04487120732665062, -0.0018998733721673489, -0.05731485038995743, 0.014241405762732029, -0.024547217413783073, -0.022299397736787796, -0.01166425459086895, -0.010087663307785988, -0.04674014449119568, -0.0362095981836319, -0.008741348050534725, -0.05064595863223076, 0.03274519369006157, 0.036763519048690796, -0.057984527200460434, 0.0010003246134147048, 0.00439679017290473, 0.026362339034676552, -0.013113564811646938, 0.0245476346462965, -0.04337881878018379, 0.03206095099449158, -0.014381534419953823, 0.08451327681541443, 0.0014741719933226705, 0.008952130563557148, -0.024763032793998718, -0.013347445987164974, -0.029240790754556656, -0.040933653712272644, -0.01121277641505003, 0.07109523564577103, -0.03900850564241409, -0.015562653541564941, 0.025213629007339478, -0.007345507387071848, -0.034297943115234375, 0.04368593171238899, -0.024644283577799797, -0.010567963123321533, -0.00591705646365881, 0.040761567652225494, 0.08534474670886993, 0.0013981048250570893, 0.023771654814481735, 0.02376767061650753, 0.027656426653265953, -0.017310503870248795, -0.014061294496059418, -0.00797490868717432, -0.015555419959127903, 0.005511751398444176, -0.045896291732788086, 0.05008561164140701, 0.09434238076210022, 0.03895179182291031, -0.053273994475603104, 0.00010038891923613846, -0.00657667126506567, 0.009284407831728458, 0.007197550032287836, 0.07635103166103363, 0.03504515439271927, 0.029555942863225937, -0.05387996882200241, 0.003563519800081849, 0.04948139190673828, 0.029461083933711052, 0.016755111515522003, 0.046435821801424026, -0.07613932341337204, -0.03977082669734955, 0.011467977426946163, -0.04158670827746391, 0.019805191084742546, 0.0362921841442585, -0.022765958681702614, -0.030033722519874573, 0.017807263880968094, -0.03168696537613869, -0.022679103538393974, 0.04319364205002785, -0.0124358544126153, -0.03872810676693916, 0.009919642470777035, -0.0017125231679528952, 0.015161219984292984, -0.008121877908706665, 0.016290931031107903, 0.05291559174656868, -0.00023131139460019767, -0.013982601463794708, -0.03903961554169655, -0.008424709551036358, -0.03860623762011528, 0.05608096346259117, 0.03538412228226662, -0.043163642287254333, -0.015278207138180733, -0.03689197078347206, 0.08251249045133591, -0.056525155901908875, 0.04612775892019272, -0.025156693533062935, 0.017553390935063362, 0.01931098848581314, -0.039196450263261795, 0.025327617302536964, -0.04095786064863205, 0.011123230680823326, -0.00012646810500882566, -0.038504891097545624, 0.01028513628989458, 0.02407391555607319, -0.0003241083468310535, -0.0055089774541556835, -0.08657169342041016, -0.024098962545394897, 0.005770990625023842, 0.02370484545826912, -0.04558667540550232, -0.01747898943722248, -0.025077568367123604, 0.017285626381635666, 0.022836364805698395, -0.0133503507822752, 0.07287923991680145, 0.03846893459558487, -0.07409180700778961, -0.03810490295290947, 0.03827952966094017, 0.007374566048383713, -0.03922921046614647, 0.04888021573424339, -0.014440387487411499, 0.05923851206898689, 0.00850797351449728, -0.012988160364329815, 0.0325632207095623, 0.011633536778390408, 0.02553817629814148, 0.02411361038684845, 0.04866461083292961, -0.006652734708040953, 0.052337825298309326, -0.06253765523433685, -0.019516097381711006, -0.06263786554336548, -0.000922259408980608, 0.03732391446828842, -0.04591947793960571, 0.04698161780834198, -0.0638410672545433, 0.00022154666658025235, 0.05680958554148674, 0.06193390116095543, 0.020082680508494377, 0.0011908792657777667, -0.026399560272693634, -0.03299782797694206, 0.01653449796140194, -0.014275562018156052, -0.020369770005345345, 0.028921132907271385, -0.0339631550014019, -0.030527587980031967, -0.08304654806852341, 0.02892068214714527, -0.027109550312161446, -0.009346363134682178, 0.012099034152925014, 0.019074954092502594, 0.017634304240345955, 0.0428575798869133, -0.005693291313946247, -0.01748170703649521, 0.027457579970359802, -0.007982742972671986, -0.030886733904480934, -0.019348667934536934, -0.006788952276110649, 0.016224661841988564, -0.02417435683310032, -0.006996223237365484, -0.04385564103722572, 0.05066320300102234, -0.01914127543568611, 0.0029048987198621035, 0.02688162960112095, 0.00894081685692072, 0.04694049060344696, 0.0422210767865181, 0.0005962795694358647, -0.035463739186525345, 0.009355545043945312, 0.07658301293849945, -0.009364777244627476, -0.023664256557822227, 0.0033813579939305782, -0.054098211228847504, 0.00845101848244667, -0.031085757538676262, -0.012398763559758663, -0.01569211855530739, -0.06297425925731659, 0.028967246413230896, 0.021492455154657364, 0.004404657520353794, -0.06758754700422287, 0.003546831663697958, -0.014684540219604969, 0.007074336521327496, 0.020116453990340233, -0.017014386132359505, -0.05500870943069458, -0.00969029776751995, -0.021518388763070107, -0.04787629470229149, -0.011443131603300571, -0.011957304552197456, -0.020296171307563782, -0.04891606420278549, -0.009247174486517906, 0.08146847784519196, -0.017432546243071556, -0.00036684187944047153, 0.02054729498922825, -0.01241193525493145, 0.09620887041091919, -0.07373949140310287, 0.014419999904930592, -0.0069304718635976315, 0.012292523868381977, -0.0277987252920866, 0.03480742871761322, -0.010625159367918968, -0.023906808346509933, 0.021740494295954704, 0.10181119292974472, 0.032375480979681015, -0.014593135565519333, -0.005792658310383558, -0.05843840911984444, -0.012486174702644348, -0.05467972904443741, 0.011991208419203758, -0.05446258932352066, -0.02050451934337616, -0.020009540021419525, 0.019338998943567276, -0.07744866609573364, -0.0034156462643295527, 0.0532844103872776, 0.012463738210499287, -0.03106061927974224, 0.044203005731105804, 0.031618811190128326, -0.0189081821590662, 0.01563473604619503, 0.05034669116139412, -0.07641256600618362, 0.0016975888283923268, 0.024869969114661217, 0.013472123071551323, -0.019573919475078583, 0.057843293994665146, 0.015406818129122257, -0.02643359638750553, -0.06787769496440887, 0.0022478888276964426, -0.0023914414923638105, -0.0675233006477356, 0.011776216328144073, 0.041400790214538574, 0.0012688083807006478, -0.016256188973784447, -0.03246041387319565, -0.028620095923542976, -0.004948735237121582, 0.10577905923128128, 0.017044488340616226, -0.042071178555488586, 0.02964208461344242, -0.009657364338636398, -0.00832214392721653, -0.06629949063062668, -0.015733225271105766, -0.039351169019937515, 0.025983665138483047, -0.031088920310139656, -0.02480616420507431, -0.0015018486883491278, 0.05811966583132744, 0.02198605053126812, -0.0375804528594017, 0.009738629683852196, -0.08442725986242294, -0.014395376667380333, 0.05040590465068817, -0.05987309291958809, -0.017886072397232056, 0.04639342799782753, -0.035764895379543304, -0.007928891107439995, -0.05040532350540161, 0.020800156518816948, 0.03379664942622185, -0.0003832234360743314, 0.09689690172672272, -0.03248708322644234, 0.02410462498664856, -0.03748127445578575, -0.008825440891087055, 0.0007009883411228657, -0.02034669928252697, -0.023264989256858826, -0.01303973700851202, -0.03012649342417717, 0.036652080714702606, -0.010276483371853828, -0.04544612020254135, -0.0005067089223302901, -0.020451558753848076, 0.0024580899626016617, 0.057655226439237595, -0.010645612142980099, -0.02646845020353794, -0.013078810647130013, -0.033252276480197906, -0.0444522388279438, 0.058707237243652344, 0.013072974979877472, 0.013140522874891758, -0.005870833061635494, 0.04292454943060875, 0.0023499440867453814, -0.013681500218808651, 0.014606871642172337, 0.05871468037366867, -0.04544097185134888, -0.06311299651861191, 0.005011402536183596, 0.038163989782333374, -0.007063416298478842, -0.014362353831529617, -0.0005514114163815975, -0.019035108387470245, 0.055118877440690994, -0.0071468655951321125, 0.053874365985393524, 0.011091978289186954, 0.004973229486495256, 0.03632187098264694, 0.025978785008192062, -0.01607183739542961, 0.00009192646393785253, -0.02029995620250702, 0.010235999710857868, 0.03909728303551674, 0.004836674779653549, -0.07792443782091141, 0.017144957557320595, 0.017508910968899727, 0.003487535286694765, -0.040394965559244156, 0.05310136079788208, 0.010866752825677395, -0.0313437357544899, 0.009383907541632652, -0.06434077024459839, 0.021728811785578728, -0.044852036982774734, 0.004923182539641857, 0.015809079632163048, -0.006648583337664604, -0.03600150719285011, -0.06359461694955826, 0.04442715272307396, 0.014085409231483936, 0.009572027251124382, -0.015887795016169548, -0.0017716310685500503, -0.0157674178481102, -0.015602394007146358, -0.02727944403886795, 0.06112222373485565, -0.02626006305217743, -0.009133643470704556, 0.0485723540186882, -0.016659321263432503, 0.03512422367930412, 0.06390562653541565, 0.03186355531215668, 0.055743344128131866, -0.004617814440280199, -0.0031260738614946604, 0.020872799679636955, -0.046900294721126556, -0.03754372522234917, 0.038589779287576675, -0.06183961033821106, -0.0009013439412228763, 0.0013673100620508194, 0.0176349226385355, -0.060581836849451065, -0.007575414143502712, -0.008637412451207638, 0.02416287735104561, -0.018887942656874657, 0.06150154396891594, 0.0031994576565921307, -0.019610200077295303, -0.03720680996775627, -0.046428121626377106, -0.04348747432231903, -0.0345272459089756, 0.03252224996685982, -0.0363229364156723, 0.03154762089252472, 0.0070024579763412476, 0.025758519768714905, -0.025606025010347366, -0.035890139639377594, 0.012224364094436169, 0.02030264586210251, -0.016431519761681557, -0.007177551742643118, -0.024937843903899193, 0.011715426109731197, 0.03959578648209572, 0.028467699885368347, 0.052491459995508194, 0.00928308442234993, 0.06293777376413345, -0.03623130917549133, 0.06961226463317871, 0.0003058146103285253, 0.040010854601860046, 0.013435413129627705, 0.007850248366594315, 0.0003691638703458011, 0.060952845960855484, 0.014340201392769814, 0.0005859843222424388, -0.024724477902054787, -0.06505190581083298, 0.02803344652056694, 0.016774339601397514, -0.056169431656599045, -0.07009974122047424, -0.02048316039144993, -0.0029124256689101458, -0.0029734494164586067, -0.0003637080662883818, -0.013738216832280159, 0.01318138837814331, -0.005411856342107058, 0.03275993466377258, -0.05552758276462555, 0.01281221117824316, 0.007876843214035034, 0.030143866315484047, 0.035685088485479355, -0.030872441828250885, -0.028462562710046768, 0.01090555265545845, 0.007297039497643709, 0.01007696334272623, 0.04647022858262062, 0.02036464959383011, -0.013831444084644318, -0.06714322417974472, -0.0012186914682388306, -0.015324681997299194, -0.040043655782938004, -0.020846348255872726, -0.07081778347492218, 0.0371166430413723, 0.055650170892477036, -0.009708295576274395, -0.0002702068886719644, -0.02328646183013916, 0.008860114961862564, 0.009898046031594276, -0.016524724662303925, -0.015468437224626541, 0.030002353712916374, 0.012368096970021725, -0.049805425107479095, 0.014794944785535336, -0.040248651057481766, -0.04765962436795235, 0.04998008534312248, -0.0008002983522601426, 0.003898696042597294, -0.017644280567765236, 0.0747319832444191, 0.05643337965011597, 0.017513500526547432, 0.0004370630776975304, 0.05568859353661537, -0.05057813972234726, -0.027095379307866096, 0.049647025763988495, 0.0014092219062149525, -0.0012301643146201968, -0.0947207435965538, -0.00205664848908782, -0.03605056554079056, -0.04563973471522331, -0.02489023469388485, 0.06455618888139725, 0.0019607923459261656, -0.017432378605008125, 0.011631797067821026, -0.049760423600673676, -0.010163892060518265, 0.07847385108470917 ]
<p>I understand that we can prove that for any process that occurs in an isolated and closed system it must hold that</p> <p>$$\Delta S\geq0$$</p> <p>via <a href="http://en.wikipedia.org/wiki/Clausius_theorem" rel="nofollow">Clausius' theorem</a>. My question is, how can I prove this in a mathematical way?</p>
g8374
[ 0.06080007925629616, 0.02893132157623768, -0.00817481242120266, 0.014038936235010624, 0.04488430544734001, -0.011065296828746796, -0.0034847494680434465, 0.01516447402536869, -0.050741396844387054, -0.08089450001716614, -0.044450026005506516, 0.09068158268928528, 0.04180590435862541, 0.05403317138552666, -0.06801850348711014, -0.05211130902171135, 0.02727900817990303, -0.02096831053495407, 0.012837158516049385, 0.07268059253692627, 0.007444177288562059, -0.004730076063424349, 0.035054437816143036, -0.02415534481406212, 0.05565240979194641, -0.029187384992837906, 0.016835590824484825, -0.011876799166202545, -0.022867023944854736, -0.030137300491333008, -0.023168791085481644, 0.007252088747918606, 0.06008999049663544, -0.017170758917927742, 0.03797821328043938, -0.031021973118185997, 0.01852659322321415, -0.00929311290383339, 0.01708165928721428, -0.03650572523474693, -0.009252304211258888, 0.016090702265501022, -0.004728212952613831, 0.008389389142394066, 0.016114505007863045, 0.026244288310408592, -0.0132142947986722, -0.004681689664721489, -0.03685428947210312, 0.02563360519707203, -0.014302395284175873, 0.06706683337688446, 0.014476695097982883, -0.07595019787549973, -0.0732971802353859, -0.0037754818331450224, 0.017331721261143684, -0.001519503304734826, -0.00033309555146843195, 0.00854737963527441, 0.017559103667736053, 0.006655526347458363, 0.033829886466264725, 0.027858586981892586, -0.01921137236058712, -0.007815809920430183, 0.02409846894443035, 0.02073284424841404, 0.010739421471953392, 0.03828711062669754, 0.02659636177122593, -0.04401811957359314, 0.0099415872246027, -0.0464872345328331, -0.00958853866904974, 0.017010318115353584, 0.012021488510072231, -0.000811006932053715, -0.013360441662371159, 0.04325328767299652, -0.04652563855051994, 0.032528121024370193, 0.04619717597961426, -0.0354536734521389, 0.003532538888975978, -0.01400839164853096, 0.018513944000005722, -0.0744221955537796, -0.012019241228699684, -0.006585202645510435, -0.00034220845554955304, -0.03515666350722313, 0.0038193464279174805, 0.014248773455619812, -0.03615890070796013, 0.056805286556482315, -0.012333479709923267, 0.011097578331828117, -0.018376866355538368, -0.0348086804151535, 0.032519157975912094, -0.029871050268411636, -0.0037858912255614996, -0.11875194311141968, 0.04638407751917839, -0.019750291481614113, 0.0060470812022686005, -0.0033311278093606234, -0.009905083104968071, -0.003157316241413355, -0.0068344553001224995, 0.03198997303843498, -0.1295109987258911, 0.00017459607624914497, 0.0533321313560009, 0.05762917548418045, -0.01463038194924593, 0.019192848354578018, 0.011207010596990585, 0.016762102022767067, -0.01693711429834366, 0.06014272943139076, -0.012859215959906578, 0.015011361800134182, -0.03246242180466652, 0.08069436252117157, 0.020810959860682487, -0.01943555288016796, 0.03533903509378433, 0.013813999481499195, 0.018345925956964493, 0.020222213119268417, 0.034263014793395996, 0.011345842853188515, 0.03194684535264969, 0.005594732239842415, 0.00770479254424572, -0.023791663348674774, -0.010462572798132896, -0.0017914518248289824, -0.006963267456740141, 0.013296322897076607, -0.023155800998210907, 0.011780795641243458, 0.04255539923906326, 0.00404351158067584, -0.017684806138277054, -0.01928899437189102, 0.002088297391310334, -0.043639276176691055, -0.031245319172739983, 0.11299574375152588, -0.03396035358309746, -0.01385138276964426, 0.03446236997842789, 0.015827301889657974, 0.006616201251745224, -0.003227023407816887, -0.005070048850029707, -0.045698486268520355, 0.06140141189098358, -0.008841720409691334, -0.01811620593070984, -0.043431613594293594, -0.04892648756504059, 0.004107062239199877, -0.03720058873295784, -0.028482988476753235, -0.05042267590761185, -0.05315955728292465, -0.1027500182390213, 0.023885561153292656, 0.01948990300297737, 0.04568115621805191, -0.029361912980675697, 0.03016863577067852, -0.04448642209172249, -0.022141093388199806, 0.06924183666706085, -0.0585332065820694, 0.010976539924740791, -0.020589500665664673, -0.03210734948515892, 0.005246911663562059, -0.023286880925297737, 0.047330379486083984, 0.022276144474744797, 0.02409246750175953, -0.06849220395088196, 0.00037938746390864253, 0.029510004445910454, 0.05434170365333557, 0.0029246252961456776, 0.04003423452377319, -0.004607725888490677, -0.016054760664701462, -0.013698223046958447, -0.062250666320323944, 0.04607715085148811, -0.01829236000776291, 0.029831677675247192, 0.04473162069916725, -0.007132044527679682, -0.04515759274363518, 0.01279426459223032, 0.006009235046803951, -0.022285932675004005, 0.02115078642964363, -0.015623638406395912, -0.01025491114705801, 0.01891106739640236, -0.04481778293848038, -0.003948725759983063, -0.04215794801712036, 0.009251099079847336, -0.023524578660726547, 0.03438517823815346, -0.012185812927782536, 0.031331658363342285, 0.021213697269558907, -0.04430045932531357, -0.011843474581837654, -0.05526724457740784, 0.03072970174252987, -0.009077442809939384, 0.06872015446424484, -0.04029696807265282, 0.014041544869542122, 0.013582499697804451, 0.06136580929160118, -0.036340296268463135, -0.0206894651055336, -0.02878151275217533, -0.01771698147058487, 0.004640853963792324, -0.010361189022660255, 0.00023144505394157022, 0.038792308419942856, 0.055769648402929306, 0.09427830576896667, -0.04131345450878143, -0.040806692093610764, -0.014743021689355373, -0.02400517836213112, 0.019381115213036537, -0.09747156500816345, 0.00402124272659421, -0.008383147418498993, 0.026546958833932877, -0.050535328686237335, -0.06041492149233818, -0.03333321213722229, 0.03617319092154503, 0.027511220425367355, 0.008995666168630123, -0.045720815658569336, 0.020375588908791542, 0.023161916062235832, 0.03262936696410179, -0.028444956988096237, -0.062333084642887115, -0.01997169479727745, 0.04697974771261215, -0.028290538117289543, 0.0047248126938939095, -0.022892290726304054, -0.05530889704823494, -0.05568108335137367, -0.01667603850364685, -0.018024981021881104, -0.027883771806955338, 0.06405090540647507, -0.020380301401019096, 0.0405261255800724, -0.03510284051299095, -0.043105777353048325, 0.03106933832168579, -0.022463157773017883, 0.014627190306782722, 0.03661502152681351, 0.018130790442228317, -0.06067362800240517, 0.010441006161272526, 0.029890164732933044, 0.015201801434159279, 0.014312142506241798, -0.021327616646885872, -0.004259162582457066, 0.018486004322767258, 0.030965758487582207, 0.012935337610542774, -0.011265916749835014, 0.026429837569594383, 0.01767435111105442, -0.05488405004143715, 0.03734171390533447, 0.00943032093346119, -0.0019718629773706198, 0.033386941999197006, 0.015811549499630928, 0.04112349823117256, -0.027940358966588974, 0.03710488602519035, -0.008621479384601116, 0.05262230336666107, 0.02796255238354206, -0.026516472920775414, 0.02282589115202427, -0.008869113400578499, 0.007849641144275665, 0.025163689628243446, -0.005511585623025894, 0.019920112565159798, -0.012471461668610573, -0.01765638403594494, 0.02688593603670597, -0.022907622158527374, 0.011716214008629322, 0.04431574046611786, -0.04269976168870926, -0.006390545517206192, -0.023860421031713486, 0.0416218526661396, -0.03218758851289749, 0.039175745099782944, -0.09133601188659668, -0.04019169509410858, 0.019042890518903732, -0.025185927748680115, 0.008430756628513336, 0.05816277116537094, 0.002069324254989624, 0.028475413098931313, -0.04332227259874344, -0.028877686709165573, 0.016618628054857254, 0.01802256517112255, -0.033819783478975296, 0.06975860148668289, 0.052651237696409225, 0.016553599387407303, -0.037103939801454544, -0.07347341626882553, 0.025793112814426422, 0.01652226224541664, 0.04227454587817192, 0.02932017110288143, 0.06310663372278214, 0.11141152679920197, 0.011617257259786129, -0.04253016412258148, -0.033069174736738205, -0.00030474725645035505, -0.021059952676296234, 0.03938717022538185, 0.027782035991549492, 0.007887929677963257, -0.003735356731340289, -0.011627918109297752, -0.006007264368236065, 0.03424639627337456, -0.015807107090950012, -0.013873574323952198, 0.03983365371823311, -0.001368478056974709, 0.04874138534069061, 0.0395023338496685, -0.008733303286135197, 0.03407161310315132, -0.038358837366104126, -0.039513953030109406, 0.010922674089670181, 0.046928420662879944, 0.020951641723513603, 0.07001915574073792, -0.04443017393350601, -0.021511904895305634, 0.050560954958200455, 0.004202615935355425, 0.05821090191602707, 0.0435909740626812, 0.009809881448745728, -0.020363222807645798, 0.03913160040974617, 0.03532753139734268, -0.028524475172162056, -0.013570697978138924, 0.07593642920255661, -0.006078217178583145, -0.026304952800273895, 0.05648436397314072, -0.01015593484044075, 0.008379540406167507, 0.02107260562479496, 0.005552056711167097, 0.02461436577141285, -0.006791832856833935, -0.015024861320853233, -0.04437662288546562, 0.003641244024038315, 0.019473547115921974, -0.03086705692112446, 0.046203672885894775, -0.00945819728076458, -0.008065779693424702, -0.01048706192523241, 0.01990586705505848, 0.048428814858198166, -0.019107334315776825, 0.019959868863224983, -0.004432391840964556, -0.013791806995868683, 0.013363963924348354, 0.022658100351691246, 0.030474787577986717, -0.02492436207830906, 0.04791475832462311, -0.014628647826611996, 0.028376741334795952, -0.0490930899977684, -0.006563040893524885, 0.029502805322408676, -0.02030905894935131, 0.02489791251718998, -0.009979136288166046, 0.11232975870370865, -0.02127927541732788, 0.009944228455424309, 0.01578468270599842, -0.03221853822469711, -0.03260130435228348, 0.0021673869341611862, 0.03843870386481285, 0.01670449785888195, -0.03306560218334198, -0.015915807336568832, -0.008940332569181919, 0.047967489808797836, -0.03891916200518608, 0.031353909522295, -0.013672291301190853, 0.019924795255064964, 0.03893032670021057, -0.03256170079112053, 0.016609935089945793, 0.08209692686796188, 0.013650616630911827, -0.07654927670955658, 0.046167340129613876, -0.07469424605369568, -0.021543040871620178, 0.07214407622814178, -0.0222687479108572, -0.006199990399181843, 0.02615438401699066, 0.006754775997251272, -0.037125252187252045, -0.029605571180582047, 0.020140884444117546, 0.016920056194067, -0.016732381656765938, -0.043362803757190704, -0.006352851167321205, 0.035264674574136734, 0.08814539760351181, -0.003003338584676385, -0.03781692683696747, -0.00032352854032069445, -0.01381163764744997, -0.04101109132170677, 0.027027154341340065, 0.01311688032001257, 0.02799997478723526, 0.022370852530002594, -0.05758056044578552, -0.06295530498027802, -0.026586348190903664, 0.015756750479340553, 0.05135326460003853, -0.013133459724485874, 0.026014748960733414, -0.03394985571503639, -0.033445071429014206, 0.001589265652000904, 0.023437319323420525, 0.01904759556055069, -0.024295900017023087, -0.09044117480516434, -0.030265549197793007, -0.018949326127767563, 0.017925862222909927, -0.0028630986344069242, 0.03922570124268532, 0.08116200566291809, 0.020049603655934334, -0.06653154641389847, -0.03901365026831627, -0.0826462134718895, -0.03542250394821167, -0.022746078670024872, -0.06316277384757996, -0.020003482699394226, -0.035346027463674545, 0.04147033393383026, 0.036301903426647186, 0.09728139638900757, -0.022097008302807808, -0.02735975757241249, -0.00438801571726799, 0.02396472729742527, 0.009344237856566906, 0.009397987276315689, 0.02155766636133194, 0.01980561949312687, 0.0021374723874032497, 0.0006806612364016473, -0.05622877925634384, -0.031497929245233536, -0.06459024548530579, -0.060161639004945755, 0.03179093822836876, 0.02064470387995243, 0.010070515796542168, -0.03668420389294624, -0.0082129817456007, -0.04674597084522247, -0.06467419117689133, 0.03366638347506523, 0.011179784312844276, 0.004473948385566473, 0.00960965733975172, -0.056267812848091125, -0.028130343183875084, -0.037441592663526535, -0.017519203945994377, -0.0723733901977539, 0.034926462918519974, 0.057940252125263214, -0.018328942358493805, 0.06899458914995193, -0.06387978792190552, -0.014058968052268028, -0.025212543085217476, 0.056897059082984924, -0.065609410405159, 0.026627670973539352, 0.001499247387982905, -0.015268856659531593, 0.031539496034383774, -0.07895462214946747, -0.06799635291099548, 0.03291374444961548, -0.011527485214173794, -0.03306775912642479, -0.0401441864669323, 0.05297723412513733, -0.015511744655668736, 0.002374859293922782, -0.007666403893381357, 0.02938620187342167, 0.05114475265145302, -0.005664152093231678, -0.013264083303511143, -0.001690670382231474, 0.007966230623424053, -0.10331172496080399, -0.02567363530397415, 0.05711469426751137, 0.007188644725829363, 0.037480633705854416, -0.006188790313899517, 0.004106616601347923, 0.013200594112277031, -0.024135293439030647, 0.031120700761675835, 0.02595311775803566, -0.028583325445652008, -0.02291620895266533, -0.007450042758136988, -0.015102798119187355, 0.003062276169657707, 0.007417453918606043, 0.02993907406926155, 0.008095556870102882, 0.03371785581111908, 0.06770073622465134, -0.032092805951833725, -0.02793101966381073, 0.03354961425065994, 0.07855794578790665, 0.03710993751883507, -0.014203144237399101, -0.06836521625518799, 0.023720484226942062, 0.0011700830655172467, -0.009088855236768723, 0.008050773292779922, 0.028903279453516006, -0.009257202036678791, -0.04892050847411156, -0.04686494916677475, -0.05575916916131973, 0.01048855297267437, -0.03481709957122803, -0.09130893647670746, 0.06500156223773956, 0.043199241161346436, -0.014790629968047142, -0.03173529729247093, -0.004018394276499748, -0.011226898059248924, 0.02658824808895588, 0.044360771775245667, -0.008024971932172775, 0.03835166245698929, -0.047770906239748, 0.007494006305932999, -0.031032489612698555, 0.044115714728832245, 0.04209762066602707, 0.005283678881824017, 0.0001875490415841341, -0.004634167067706585, -0.03533324971795082, 0.01020489539951086, 0.056140463799238205, -0.046061791479587555, -0.021909674629569054, 0.04046238213777542, 0.05612169951200485, -0.006769711617380381, 0.025282330811023712, -0.03459369018673897, 0.0075869509018957615, -0.053395915776491165, -0.0340522900223732, -0.018207216635346413, -0.008403021842241287, 0.08899747580289841, -0.031908031553030014, 0.011498594656586647, 0.05319490283727646, 0.03270890191197395, 0.00943872518837452, -0.05540146306157112, -0.026421675458550453, 0.002001721179112792, -0.05305808037519455, -0.03017638996243477, -0.016821319237351418, 0.03884534537792206, 0.03259201720356941, -0.02479313686490059, 0.020214233547449112, 0.036123864352703094, 0.026816442608833313, -0.0032541253603994846, -0.031052565202116966, -0.005693191196769476, -0.0638522356748581, -0.02505495212972164, -0.02731786109507084, 0.01774488389492035, 0.021217182278633118, 0.03224020078778267, 0.062157776206731796, -0.005137249827384949, -0.06530044972896576, -0.00658788438886404, 0.012681850232183933, -0.004760696552693844, 0.014091786928474903, 0.0015993287088349462, 0.03266468644142151, -0.02469950169324875, -0.010862987488508224, 0.0380028560757637, -0.009362762793898582, 0.05106275901198387, -0.006481627933681011, -0.021284248679876328, -0.025906480848789215, -0.025274336338043213, 0.026994118466973305, 0.014460748992860317, 0.03799565136432648, -0.009640585631132126, 0.02540281042456627, 0.032099999487400055, -0.022262172773480415, -0.022724060341715813, 0.016055859625339508, 0.017738578841090202, -0.010289501398801804, 0.029775550588965416, 0.005107790697365999, 0.024086249992251396, 0.013800399377942085, -0.016405856236815453, -0.004599923267960548, 0.023271918296813965, 0.03112914226949215, -0.03314609080553055, 0.05731134116649628, 0.054548509418964386, -0.017877528443932533, -0.029628299176692963, -0.02029557339847088, -0.04763271287083626, 0.03471967205405235, 0.04454238340258598, 0.011081975884735584, -0.049223143607378006, -0.014371482655405998, 0.09367043524980545, -0.024334192276000977, -0.037091512233018875, 0.029497016221284866, 0.035562556236982346, -0.009991653263568878, -0.015628457069396973, -0.03912866488099098, -0.028305262327194214, -0.021254397928714752, 0.004211698658764362, 0.011837221682071686, -0.04231838509440422, -0.03561306372284889, -0.00951862707734108, 0.0003745703143067658, -0.055778250098228455, -0.004204594995826483, -0.014192847535014153, 0.008375096134841442, -0.0362449549138546, 0.0043852245435118675, 0.013216707855463028, -0.09596411138772964, -0.027736777439713478, -0.04982053115963936, -0.018231194466352463, 0.015345156192779541, -0.015207656659185886, -0.03495591878890991, 0.06799152493476868, -0.06278089433908463, -0.029079798609018326, 0.028064033016562462, -0.028299465775489807, 0.01846718043088913, -0.018754063174128532, 0.05979546904563904, -0.06392046809196472, 0.003709541168063879, 0.034689899533987045, -0.033539678901433945, -0.01138872466981411, 0.017819110304117203, 0.011401071213185787, 0.00972277857363224, -0.014321423135697842, 0.05532974377274513, -0.02002877928316593, 0.050936322659254074, -0.039235811680555344, -0.05416499078273773, 0.017291536554694176, 0.01795913092792034 ]
<p>I am looking into the decay of a $\Phi$-meson decaying into $K^+$, $K^-$. My problem is, the $\Phi$-meson has a total angular momentum of 1 and the two Kaons have a total angular momentum of 0. On the first glance this seems to be a violation of the angular momentum conservation law.</p> <p>I tried to explain it to myself using the quark picture of the system. So the $\Phi (s \bar{s})$ goes under the production of a $u\bar{u}$ pair into $K^+(u \bar{s})$ and $K^- (\bar{u}s)$. Using Clebsch Gordon coefficients i noted down the possible combinations and that works out so far.</p> <p>My question is, how can the 'effective' total angular momentum be explained as it seems to me, that the conservation law is not conserved, which can not be. Do i miss something or have i got something wrong?</p>
g8375
[ -0.006281137466430664, -0.025542812421917915, 0.021731702610850334, -0.0069856238551437855, 0.06855779141187668, 0.02399621717631817, 0.012347990646958351, 0.05816838517785072, 0.04376578703522682, 0.0360969603061676, 0.007426396943628788, -0.016793938353657722, -0.02056637965142727, 0.011371049098670483, 0.060473520308732986, 0.019120411947369576, 0.03990330919623375, 0.0558425597846508, 0.04962243139743805, 0.04003778472542763, -0.09307685494422913, 0.024138513952493668, -0.07670214027166367, -0.06876173615455627, 0.04387073218822479, 0.007814494892954826, -0.059167973697185516, 0.008530033752322197, -0.11028331518173218, 0.052870869636535645, -0.01067846454679966, -0.030912600457668304, -0.013006779365241528, -0.026176437735557556, -0.016908273100852966, -0.022278770804405212, 0.1017243042588234, -0.018227485939860344, 0.030865518376231194, -0.057825420051813126, 0.00844840332865715, 0.0114219905808568, -0.04606509581208229, -0.0023205955512821674, -0.02039383538067341, 0.01393895410001278, -0.0004843102360609919, -0.01223484892398119, -0.017468469217419624, -0.011716935783624649, -0.02074398100376129, 0.046929337084293365, 0.060526762157678604, 0.010980209335684776, -0.04284466430544853, 0.02634165808558464, 0.018785029649734497, -0.06867365539073944, 0.003932472784072161, 0.026190847158432007, 0.008574473671615124, -0.011348392814397812, 0.013766109012067318, 0.018183477222919464, 0.06842164695262909, -0.03679553419351578, -0.024369560182094574, 0.04450828209519386, -0.002190738683566451, 0.021222101524472237, -0.007327947299927473, -0.01370961219072342, -0.0008167148334905505, -0.0388561449944973, 0.018378131091594696, 0.06391974538564682, 0.0013226752635091543, -0.06641712784767151, 0.0055452799424529076, -0.01112462766468525, -0.02507627010345459, -0.007830115035176277, 0.04594428464770317, 0.023976081982254982, 0.0263307373970747, -0.029852304607629776, -0.04185216873884201, -0.04293990135192871, -0.02682427130639553, -0.01583361253142357, 0.059174127876758575, -0.07286356389522552, -0.00019806632190011442, -0.005393936764448881, -0.003607559483498335, -0.01150907576084137, -0.022427760064601898, 0.07758170366287231, 0.017315950244665146, 0.016813009977340698, 0.01889074221253395, 0.021881988272070885, -0.028100809082388878, -0.004885516129434109, 0.023823654279112816, 0.03306548669934273, 0.04136348515748978, 0.04225362837314606, 0.015700671821832657, 0.05563366785645485, 0.0375097282230854, -0.006813664920628071, -0.021471552550792694, -0.029002124443650246, -0.021097702905535698, -0.02455279976129532, 0.05694169923663139, -0.01767011545598507, 0.018096039071679115, 0.020999792963266373, -0.009263159707188606, 0.04472115635871887, 0.01433433685451746, 0.06043195724487305, -0.02311922423541546, -0.026006923988461494, 0.018109705299139023, 0.005885525606572628, 0.0795825943350792, 0.04595189541578293, -0.029183795675635338, -0.06052655354142189, -0.006450952496379614, 0.05086880549788475, 0.06092985346913338, 0.00901140458881855, -0.02883458510041237, 0.040685418993234634, -0.012551511637866497, -0.052303019911050797, -0.0346163809299469, -0.008966178633272648, 0.02672300487756729, -0.05253424495458603, -0.009073031134903431, -0.018175723031163216, 0.012622078880667686, -0.018981821835041046, 0.025557221844792366, -0.002681639976799488, 0.028514817357063293, 0.03817259892821312, -0.007713626138865948, 0.005180716514587402, -0.0181680116802454, -0.06631168723106384, 0.028996195644140244, -0.01956198923289776, -0.028475824743509293, 0.032870110124349594, 0.07031745463609695, 0.009086131118237972, 0.035976480692625046, -0.041737355291843414, -0.09069568663835526, -0.021502338349819183, -0.006361200474202633, -0.05599408596754074, -0.04808562994003296, -0.02474323660135269, -0.05858181044459343, 0.0363309383392334, 0.075605109333992, 0.022458668798208237, -0.027208955958485603, 0.014438074082136154, 0.01638219691812992, -0.0420478917658329, 0.006215916946530342, 0.04765646532177925, -0.0038767210207879543, 0.015188966877758503, 0.038156650960445404, 0.03980632871389389, -0.012728296220302582, 0.07336471974849701, 0.04080389812588692, 0.07494885474443436, -0.04703359678387642, -0.025141168385744095, 0.040373630821704865, -0.028944596648216248, 0.004916240926831961, 0.024519724771380424, 0.021574944257736206, 0.03802122920751572, -0.022473648190498352, -0.07592104375362396, -0.05398920178413391, 0.03977571800351143, -0.02334067039191723, 0.004104133229702711, -0.006784993223845959, 0.011311308480799198, 0.015812037512660027, -0.03793974593281746, 0.022099539637565613, 0.0030353409238159657, 0.036438003182411194, -0.039435677230358124, 0.024958405643701553, -0.041124384850263596, -0.04712485894560814, 0.009923182427883148, -0.0015514121623709798, -0.05108809471130371, 0.031071892008185387, 0.048050928860902786, -0.06161849573254585, -0.011452199891209602, -0.08356805890798569, 0.015144364908337593, 0.028270753100514412, 0.01189009752124548, -0.06819156557321548, 0.02223588339984417, -0.002804531017318368, 0.05387178435921669, 0.00035267032217234373, 0.052386827766895294, -0.04686632379889488, 0.039771635085344315, -0.00639588525518775, 0.010657375678420067, 0.028940852731466293, 0.02523794397711754, 0.0044257459230721, 0.022284885868430138, -0.04983920231461525, 0.05572587996721268, 0.0045107644982635975, 0.027844060212373734, -0.03916923329234123, 0.01145537942647934, 0.07209987193346024, 0.03406660258769989, 0.00789350364357233, 0.010216708295047283, 0.003153291530907154, -0.0028421394526958466, 0.051067568361759186, -0.003882460296154022, -0.028194058686494827, -0.054061584174633026, 0.011606973595917225, -0.0146701755002141, -0.021152498200535774, 0.019935788586735725, -0.07648306339979172, 0.006296304054558277, -0.0007761258748359978, -0.014057913795113564, -0.009994376450777054, 0.03954485058784485, -0.01970798149704933, -0.02299138717353344, 0.012032357044517994, 0.08660372346639633, 0.04031213000416756, -0.01874043233692646, -0.06613408029079437, 0.0761028602719307, -0.06489759683609009, 0.05648324266076088, -0.016147466376423836, -0.05270012840628624, 0.008988026529550552, -0.030724897980690002, 0.005300889723002911, -0.021951131522655487, -0.0147326048463583, 0.08959739655256271, -0.03408213332295418, 0.030137868598103523, 0.04262493923306465, 0.008785460144281387, -0.025309961289167404, 0.03400876373052597, 0.041853152215480804, -0.0023747168015688658, -0.06133154779672623, 0.041926633566617966, 0.04395349323749542, -0.04916508123278618, 0.03094281069934368, 0.069890595972538, -0.03399037942290306, -0.04106496647000313, 0.04359807074069977, 0.023941688239574432, 0.024800032377243042, 0.0013163386611267924, -0.0004713687230832875, -0.0057039461098611355, 0.03750964626669884, 0.07638178765773773, -0.060135357081890106, 0.02996893785893917, -0.0011398781789466739, 0.038670677691698074, -0.07347605377435684, 0.059331078082323074, -0.02739359438419342, -0.01313520036637783, -0.019800180569291115, -0.015677258372306824, 0.007687462959438562, 0.016917971894145012, -0.0488293282687664, 0.030504630878567696, 0.02456437237560749, -0.027285391464829445, -0.00022965158859733492, 0.021286645904183388, 0.06308644264936447, 0.032891225069761276, -0.12715524435043335, 0.005212937947362661, 0.009750299155712128, -0.0493064783513546, -0.004012345336377621, 0.02246147394180298, 0.04073108360171318, -0.013673562556505203, -0.0484059639275074, 0.029481053352355957, 0.001955508254468441, -0.0054798489436507225, -0.01917923614382744, -0.027851777151226997, 0.0017646452179178596, 0.010161937214434147, -0.03588339313864708, -0.005752702243626118, 0.009638573974370956, 0.0026909385342150927, -0.008248968049883842, -0.005469312891364098, 0.019423138350248337, 0.0035613481886684895, 0.04529986530542374, 0.05138426646590233, -0.01233318168669939, 0.007237272337079048, -0.04915571212768555, 0.021106617525219917, 0.004619038198143244, 0.07012324780225754, -0.01592344418168068, -0.005075856111943722, 0.07553062587976456, 0.030011391267180443, 0.02026457153260708, -0.004670094233006239, -0.03547098860144615, -0.010305088013410568, -0.014845569618046284, -0.002597553189843893, 0.02541518583893776, 0.01681322418153286, 0.012094748206436634, -0.006205326411873102, 0.010109707713127136, -0.08811821788549423, -0.007219448685646057, -0.04403965175151825, 0.0076012518256902695, 0.01518754567950964, -0.02458280138671398, 0.047450609505176544, 0.01466095820069313, 0.047565024346113205, -0.013839895837008953, 0.05232272669672966, 0.023736536502838135, 0.057095881551504135, -0.01920175924897194, 0.009612242691218853, 0.010015875101089478, -0.02461051568388939, 0.021134309470653534, -0.029789581894874573, 0.015119592659175396, 0.001780327525921166, 0.03356005251407623, -0.0627453401684761, -0.007259987760335207, -0.0310421884059906, 0.016787320375442505, 0.03346654027700424, -0.03732147440314293, 0.044659584760665894, -0.007287358865141869, -0.0716036856174469, 0.0351223461329937, 0.04227745532989502, -0.01322027388960123, 0.031949762254953384, 0.009241539053618908, -0.02332198992371559, -0.005282166413962841, -0.0032020993530750275, -0.0050346339121460915, -0.02144075371325016, -0.009489089250564575, 0.03062104433774948, -0.07748004794120789, 0.008606652729213238, 0.0115874158218503, -0.03188898786902428, -0.009038914926350117, 0.020708290860056877, -0.04973343014717102, -0.00047657423419877887, 0.044379569590091705, 0.03795694187283516, -0.03714707866311073, 0.003930247388780117, 0.028217680752277374, -0.02841535024344921, 0.018160061910748482, 0.00502868602052331, 0.01254720613360405, 0.006547927390784025, -0.05190716311335564, 0.045376311987638474, -0.08284097164869308, 0.022936921566724777, -0.007141102571040392, 0.0742964819073677, 0.06899352371692657, -0.012250921688973904, -0.03109058178961277, -0.00378723768517375, 0.0214096549898386, -0.03455430641770363, 0.020023321732878685, -0.0333930104970932, 0.014512823894619942, 0.0011247294023633003, -0.0531231090426445, -0.026829244568943977, -0.04854700714349747, -0.023069534450769424, 0.01755700260400772, -0.0079655135050416, -0.06171049922704697, 0.015323716215789318, -0.042330190539360046, 0.013130661100149155, -0.07513628900051117, 0.0020744644571095705, 0.04898209124803543, -0.03291817381978035, 0.01481692399829626, -0.01343732513487339, -0.03162502869963646, -0.01627243123948574, -0.02940172143280506, -0.02804384008049965, 0.01828649267554283, -0.036259450018405914, 0.02379678003489971, 0.011101559735834599, 0.0551559180021286, 0.02616223506629467, 0.0009341515251435339, 0.04130641371011734, 0.024149110540747643, -0.04522646963596344, -0.007905217818915844, 0.0020406392868608236, -0.0005531281349249184, 0.03963182121515274, 0.050309740006923676, 0.007712045684456825, -0.021991362795233727, -0.02437046729028225, 0.007214959245175123, 0.05084593966603279, 0.038674771785736084, 0.11088364571332932, 0.013378864154219627, -0.037202320992946625, 0.08450711518526077, 0.06816709786653519, -0.02017398178577423, -0.011556700803339481, -0.0025663007982075214, -0.015423943288624287, -0.004504415672272444, -0.08810384571552277, -0.013221767731010914, 0.033066365867853165, -0.0006755088688805699, 0.02916514314711094, 0.013182834722101688, -0.00041950700688175857, -0.004619699437171221, 0.031002234667539597, -0.0218565184623003, -0.0528164878487587, 0.02779231406748295, -0.036315590143203735, -0.04703398048877716, 0.007695313077419996, -0.03562581539154053, 0.02134750597178936, -0.048592615872621536, -0.036519307643175125, 0.010912518016994, 0.0470220111310482, -0.040936194360256195, 0.001861365744844079, 0.006559057626873255, -0.011289959773421288, -0.051315296441316605, -0.035526126623153687, 0.06088363006711006, 0.027954785153269768, 0.04746337607502937, -0.0568813681602478, -0.037884898483753204, 0.020845597609877586, -0.005308154039084911, -0.05149076133966446, -0.0010024284711107612, -0.012779634445905685, -0.027003370225429535, -0.005665276199579239, -0.017141032963991165, 0.017346926033496857, 0.04542398080229759, 0.0170875396579504, -0.05125472694635391, -0.023945394903421402, -0.03813014179468155, -0.015330259688198566, 0.0588475838303566, -0.01840950734913349, -0.03733701631426811, 0.002626441651955247, 0.01272441353648901, -0.062174126505851746, 0.03611736372113228, 0.029070168733596802, 0.017088916152715683, -0.0005250811809673905, 0.02135612629354, -0.05732627958059311, -0.02805403620004654, 0.03355320543050766, 0.04308784008026123, 0.020565658807754517, 0.061418626457452774, -0.02102593332529068, -0.0034634761977940798, -0.04268704727292061, 0.015328018926084042, 0.03258683532476425, -0.04466331750154495, 0.033024661242961884, -0.06508239358663559, 0.034004710614681244, -0.018167560920119286, 0.03423340991139412, -0.05084284767508507, 0.031079841777682304, -0.054431721568107605, -0.0014419818762689829, 0.026517478749155998, -0.0178193561732769, -0.02027719095349312, -0.08305809646844864, -0.034500665962696075, -0.004327333997935057, -0.03670986741781235, -0.06018531322479248, 0.05038585886359215, 0.025726286694407463, -0.01499937940388918, 0.04584266617894173, -0.05230711027979851, 0.05532325059175491, 0.04695804789662361, 0.01951376162469387, 0.018458159640431404, -0.05577708035707474, -0.050889380276203156, -0.028371116146445274, 0.04558319225907326, -0.03373454138636589, 0.0232789795845747, -0.05237719789147377, -0.010110321454703808, -0.026768028736114502, -0.014406784437596798, 0.021668002009391785, -0.023645920678973198, -0.004600757732987404, -0.03029594197869301, 0.10073867440223694, -0.007503186352550983, -0.038634806871414185, 0.004441448487341404, -0.05787040665745735, 0.05634906515479088, 0.010651921853423119, -0.060324497520923615, -0.029186444357037544, 0.014711198396980762, 0.02208469994366169, -0.0018946730997413397, 0.020077457651495934, 0.004322623834013939, -0.0030602747574448586, 0.01319795660674572, 0.02440286986529827, 0.005633642431348562, 0.04905090481042862, -0.009792967699468136, 0.025733707472682, 0.03179842606186867, -0.031438738107681274, -0.02971554361283779, 0.04113427922129631, -0.02352849766612053, 0.030855508521199226, 0.00922519713640213, 0.03608043119311333, 0.03436119109392166, 0.011032813228666782, 0.02005619928240776, 0.004935883451253176, -0.04053691774606705, 0.013740605674684048, -0.012459875084459782, -0.045777760446071625, -0.08833282440900803, -0.03108302876353264, -0.013768482953310013, -0.014557864516973495, 0.016498824581503868, -0.042026374489068985, -0.031842947006225586, 0.0065598017536103725, 0.04512159153819084, 0.00639306241646409, -0.016296865418553352, -0.006743081379681826, 0.02219650335609913, -0.04935067892074585, 0.04840948060154915, -0.021660827100276947, -0.02593320980668068, -0.010207012295722961, -0.03138323128223419, -0.013729727827012539, 0.06944232434034348, -0.029559526592493057, 0.013348620384931564, 0.009894321672618389, -0.022163037210702896, 0.034407127648591995, -0.03324177861213684, 0.01788279600441456, 0.04662545770406723, -0.02050672098994255, -0.015272624790668488, -0.018067866563796997, -0.03196452930569649, 0.014169246889650822, -0.034907497465610504, -0.001135651022195816, 0.0029554027132689953, -0.006312398239970207, -0.025963883846998215, -0.00028310014749877155, 0.0012787164887413383, 0.036914121359586716, 0.012672319076955318, 0.035574980080127716, 0.03543393313884735, -0.02359672263264656, -0.007577179465442896, 0.02958839014172554, 0.040251508355140686, 0.01682090573012829, -0.02336120791733265, -0.0037401209119707346, 0.04873958230018616, 0.010472053661942482, 0.020014574751257896, 0.031709495931863785, 0.06248844787478447, 0.047973472625017166, 0.019601816311478615, -0.0577474907040596, -0.03994966670870781, 0.00049768784083426, 0.032169535756111145, -0.045338135212659836, 0.011268733069300652, -0.03455984592437744, 0.03627397119998932, -0.0052099027670919895, -0.02874058671295643, 0.00490183150395751, -0.002640991937369108, -0.045583341270685196, -0.0313115157186985, 0.006516850087791681, 0.007239657454192638, -0.10018350929021835, -0.02809811569750309, -0.05194970220327377, 0.025803547352552414, -0.003222708823159337, 0.0017949315952137113, 0.06062757596373558, -0.04371613636612892, 0.0061898548156023026, -0.08953537791967392, -0.01622241921722889, -0.008541282266378403, -0.05232646316289902, 0.002109375549480319, -0.04340630769729614, 0.017130611464381218, 0.012386927381157875, -0.013476980850100517, 0.002246282994747162, -0.0153679633513093, -0.014929617755115032, -0.028725488111376762, -0.04371832683682442, 0.028008298948407173, -0.0037733050994575024, 0.03461875393986702, -0.012860381044447422, 0.0346698984503746, 0.01329520158469677, -0.017242759466171265, 0.014125092886388302, -0.010149495676159859, -0.06934382021427155, 0.01178586483001709, 0.04065284505486488, -0.037393346428871155, 0.024502737447619438, -0.05406792461872101, 0.01258664857596159, -0.045245569199323654, -0.010381734929978848, 0.006025047041475773, -0.07901592552661896, -0.014668426476418972, -0.006298385560512543 ]
<p>If space itself is expanding, then why would it have any effect on matter (separates distant galaxies)? </p> <ul> <li><p>Space is "nothing", and if "nothing" becomes bigger "nothing" it's still a "nothing" that shouldn't interact with matter in any way (it doesn't have mass, energy, etc).</p></li> <li><p>Gravity doesn't have a cutoff distance afaik, so even the most distant galaxies should be attracted to each other. Gravity force would be very very tiny, but it would still dominate "nothing" from space expansion.</p></li> <li><p>Lets take inertia from Big Bang into account. Inertia would be the primary force that moves galaxies away comparing to their tiny gravity and even more tiny, if any, force of our "nothing" that is still expanding inbetween. Wouldn't expansion decelerate if driven mostly by inertia?</p></li> </ul>
g56
[ 0.054240547120571136, 0.045744284987449646, 0.02243674546480179, -0.0055503202602267265, -0.034858059138059616, 0.02721848525106907, -0.01108047366142273, 0.007878429256379604, -0.008722607046365738, -0.11746178567409515, 0.07234152406454086, -0.017963441088795662, -0.02534971386194229, 0.010151228867471218, 0.06706143170595169, 0.02977866493165493, 0.008218171074986458, -0.026802828535437584, 0.005874501075595617, 0.02624206803739071, 0.0113705825060606, -0.009479011408984661, 0.003020079107955098, -0.07032475620508194, -0.087457574903965, 0.014238778501749039, 0.06505272537469864, -0.0509464405477047, 0.012486769817769527, 0.02661820314824581, 0.020549437031149864, 0.02545042149722576, -0.026504481211304665, -0.04890231415629387, -0.021831082180142403, 0.004839317873120308, 0.029557056725025177, 0.017755886539816856, 0.014888554811477661, -0.04295318201184273, -0.03756538778543472, -0.023699885234236717, 0.007257659453898668, -0.004142881371080875, 0.0477619469165802, 0.02796599268913269, -0.022630631923675537, 0.03560318797826767, 0.04237544909119606, -0.08328801393508911, -0.07377897948026657, -0.02472756989300251, -0.03052888996899128, 0.06502068042755127, 0.028312714770436287, 0.016952507197856903, 0.04903034120798111, -0.02236897684633732, 0.06669525802135468, -0.018399419263005257, -0.05068567767739296, 0.0028963498771190643, 0.00584432203322649, 0.00011159016139572486, -0.01667264848947525, -0.03071296587586403, -0.04569869488477707, -0.05315232649445534, 0.04563456401228905, 0.01667756587266922, 0.030139310285449028, -0.03224308043718338, -0.03322792425751686, -0.05431945621967316, -0.04133961349725723, 0.06534237414598465, 0.018291577696800232, 0.0002504022850189358, -0.022684147581458092, -0.04960686340928078, -0.10412829369306564, -0.038369253277778625, 0.015058813616633415, 0.023852143436670303, 0.06831217557191849, 0.0006910334341228008, -0.026715261861681938, -0.01595468260347843, -0.012570937164127827, 0.028681373223662376, 0.0326809287071228, 0.07214542478322983, 0.05908016860485077, -0.029506182298064232, -0.008791026659309864, -0.034432947635650635, 0.006948063615709543, 0.03273267298936844, 0.0058955359272658825, -0.036647167056798935, -0.0612594410777092, 0.010650848969817162, 0.027689579874277115, -0.04381253570318222, 0.038788262754678726, -0.038682784885168076, 0.013186024501919746, 0.07791268080472946, 0.04343819618225098, -0.058403607457876205, -0.004635985475033522, -0.02933957800269127, 0.03939119353890419, -0.0335376039147377, 0.0047889407724142075, 0.01666215807199478, 0.03353026136755943, 0.03159768134355545, 0.06456686556339264, -0.001312441541813314, -0.020764503628015518, 0.02502300590276718, 0.031962018460035324, -0.010266191326081753, -0.003371617989614606, -0.08674769103527069, 0.05317095294594765, 0.022444454953074455, 0.027557039633393288, -0.03860841318964958, 0.0033571692183613777, 0.005058865062892437, -0.036600735038518906, 0.022698814049363136, 0.05279763415455818, -0.027674904093146324, -0.03416963294148445, -0.04296276345849037, -0.03474020957946777, 0.013246146962046623, -0.025157544761896133, 0.018553445115685463, 0.014680092222988605, 0.008304640650749207, -0.0536215603351593, 0.07111387699842453, -0.02766677550971508, 0.018478285521268845, -0.015357524156570435, 0.04008615389466286, 0.01912950538098812, 0.027074629440903664, -0.02484157122671604, -0.005377178080379963, -0.00992799922823906, 0.03317802771925926, 0.06359747052192688, -0.006580640561878681, -0.02131650224328041, -0.03599744290113449, 0.05152735859155655, -0.0025172545574605465, 0.04146169498562813, -0.024319903925061226, -0.04432353377342224, 0.05344834178686142, -0.026859460398554802, -0.017656924203038216, -0.01213361881673336, 0.022006604820489883, -0.046229954808950424, -0.0033091953955590725, -0.0022624479606747627, 0.07760576158761978, 0.033793091773986816, 0.020747054368257523, 0.013347046449780464, 0.02034202590584755, -0.024912424385547638, 0.003797182347625494, -0.019045786932110786, -0.04223313182592392, -0.009629624895751476, -0.0018519168952479959, -0.016784830018877983, -0.03671843186020851, 0.030271396040916443, -0.004166639409959316, -0.024542327970266342, -0.004010848235338926, 0.015859253704547882, -0.006472401786595583, 0.013607533648610115, -0.004155310802161694, -0.024605317041277885, 0.0033888746984302998, 0.055716414004564285, 0.026262303814291954, -0.030473558232188225, -0.0228282380849123, -0.02677796594798565, 0.031581223011016846, 0.01389134582132101, 0.007719495799392462, 0.016221294179558754, -0.02622402273118496, -0.04686971381306648, -0.01832614466547966, 0.03752400353550911, -0.038553446531295776, 0.014274952933192253, -0.030591238290071487, -0.0010981815867125988, 0.034608419984579086, -0.008750592358410358, 0.015555315650999546, -0.014371284283697605, 0.023827167227864265, -0.03407307341694832, 0.051289066672325134, -0.008803373202681541, -0.0022738350089639425, -0.0017254622653126717, -0.05977323651313782, 0.007849954068660736, -0.04724719002842903, -0.00026142902788706124, -0.015047607943415642, 0.01915491186082363, 0.06576040387153625, -0.046467117965221405, 0.026605192571878433, 0.00847670715302229, -0.018234366551041603, 0.025905722752213478, 0.03327449783682823, 0.008175567723810673, 0.029664169996976852, -0.0013400957686826587, 0.04286077246069908, 0.06706836074590683, -0.0480218306183815, -0.006049621384590864, -0.03781869634985924, 0.03079712763428688, -0.1183498352766037, 0.015884611755609512, -0.04303137585520744, -0.03296506404876709, -0.04829935356974602, 0.02404417097568512, 0.010628261603415012, -0.066019706428051, -0.04227418452501297, 0.009427042677998543, -0.011105171404778957, 0.00504968361929059, 0.08252982050180435, -0.10596784204244614, -0.04327097535133362, 0.007070090156048536, -0.051473259925842285, 0.055581867694854736, 0.009538786485791206, -0.0450248084962368, -0.0043460712768137455, -0.036408573389053345, 0.03764655441045761, -0.013279961422085762, -0.017635267227888107, 0.011285804212093353, 0.03775547817349434, -0.02486865222454071, 0.0429757684469223, 0.02842043526470661, 0.0650525614619255, 0.023191401734948158, 0.018292732536792755, 0.0669868215918541, -0.013583304360508919, -0.03338625282049179, 0.025248708203434944, -0.05959366261959076, 0.020078293979167938, 0.003549769287928939, -0.034037258476018906, -0.015633942559361458, -0.047128789126873016, -0.008854751475155354, -0.05831814557313919, 0.0647105798125267, 0.01722782291471958, 0.06879941374063492, 0.018275093287229538, 0.04472760856151581, 0.02568344585597515, -0.044487789273262024, 0.01168400701135397, -0.05969421565532684, -0.013262692838907242, -0.002737376606091857, -0.0362384058535099, 0.06442545354366302, -0.01857840083539486, -0.06885094940662384, 0.05139952898025513, -0.0006723458645865321, 0.02493477240204811, -0.03441726043820381, -0.034489214420318604, -0.0023189291823655367, 0.049427807331085205, 0.03836975619196892, 0.038512732833623886, -0.03583287447690964, 0.017943961545825005, 0.0061052110977470875, -0.03119400329887867, -0.012918107211589813, -0.03224446624517441, 0.05430149286985397, -0.06720573455095291, -0.019183285534381866, -0.04083993285894394, 0.027537213638424873, 0.03309360891580582, -0.04487815871834755, -0.06799500435590744, -0.02537458948791027, 0.04681982845067978, -0.003894948400557041, -0.036819592118263245, 0.021434564143419266, -0.004191558808088303, -0.10656769573688507, -0.018621331080794334, -0.009262707084417343, -0.004112746566534042, 0.03819488734006882, 0.04652795568108559, -0.00024949980434030294, 0.001194597571156919, -0.058508168905973434, 0.06982184201478958, -0.028553133830428123, 0.07968160510063171, 0.04564087092876434, -0.031139109283685684, -0.005656943190842867, -0.027061766013503075, 0.04359389841556549, -0.01941021718084812, 0.0395679846405983, -0.03328442946076393, 0.0019296837272122502, -0.012199186719954014, 0.03097301721572876, -0.03405771031975746, -0.008628277108073235, -0.009960668161511421, 0.007210728712379932, 0.012568212114274502, -0.008808137848973274, 0.0056988452561199665, -0.009011154994368553, 0.016454819589853287, 0.0037985770031809807, 0.010734368115663528, -0.03655993938446045, 0.03864109516143799, 0.05727485194802284, 0.004103103652596474, -0.06415395438671112, -0.019708817824721336, 0.10284297168254852, -0.02114839106798172, 0.06973128020763397, 0.02212906815111637, 0.04638335853815079, -0.018407760187983513, 0.03312414884567261, 0.01991346664726734, 0.0467076301574707, 0.03381245583295822, -0.017449267208576202, -0.02102484740316868, -0.05927375331521034, -0.0020841609220951796, -0.014689263887703419, -0.0038224435411393642, -0.006173891481012106, -0.0406721755862236, 0.02377045340836048, -0.017309317365288734, 0.00143103813752532, 0.007049783132970333, 0.005391902755945921, 0.005624743644148111, 0.06381581723690033, -0.030133085325360298, -0.011181455105543137, 0.04067433997988701, 0.011141045950353146, -0.005951784085482359, 0.037510041147470474, 0.009683476760983467, 0.032332584261894226, -0.006658551748842001, -0.06295831501483917, -0.04138373211026192, 0.023759251460433006, -0.01854720339179039, -0.028149764984846115, -0.038166385143995285, 0.026377016678452492, -0.03177604079246521, 0.03914618119597435, -0.03751081973314285, 0.023553313687443733, 0.03193686157464981, 0.017429687082767487, 0.02490265667438507, -0.03903038427233696, 0.016838032752275467, -0.0269174687564373, 0.057953670620918274, 0.006951044779270887, -0.0010653831996023655, -0.01804312877357006, 0.028677923604846, -0.024897661060094833, 0.05468905344605446, 0.03835573047399521, 0.02304171957075596, -0.053858209401369095, -0.011697245761752129, -0.033329810947179794, 0.12260120362043381, -0.006270952522754669, 0.01933770440518856, 0.07548489421606064, -0.01678278297185898, 0.04997304826974869, 0.047300003468990326, 0.029568884521722794, 0.06625515967607498, -0.05659795179963112, -0.02549157105386257, -0.032240819185972214, -0.0058167194947600365, -0.04114111140370369, -0.015119639225304127, -0.001973062986508012, -0.005959559231996536, -0.002336665755137801, -0.005772369913756847, -0.00490593072026968, -0.001323562697507441, 0.02390660159289837, 0.06936881691217422, -0.0377609059214592, 0.07409235835075378, 0.004159430507570505, 0.024460293352603912, -0.009114121086895466, 0.014809095300734043, -0.00964140985161066, -0.04380156099796295, 0.005052662454545498, 0.054216139018535614, -0.010557271540164948, 0.02841084450483322, 0.01011694222688675, -0.007136151194572449, 0.02063092216849327, 0.04793357476592064, 0.02842416986823082, -0.016961516812443733, 0.008575794287025928, -0.036184366792440414, -0.01909424550831318, -0.03565605729818344, 0.08041013032197952, -0.011701489798724651, 0.03781940042972565, 0.05813807249069214, -0.020095907151699066, 0.03215480223298073, -0.038778189569711685, -0.03082372061908245, 0.01336311548948288, -0.01778707467019558, -0.031773749738931656, -0.024780703708529472, -0.018416212871670723, 0.018554475158452988, 0.01578584872186184, 0.004824823699891567, -0.018761973828077316, -0.051490236073732376, 0.021038290113210678, 0.03588859364390373, -0.024981696158647537, -0.04367530718445778, -0.05334290862083435, -0.0004611073818523437, -0.02183193527162075, -0.017010705545544624, -0.018724989145994186, 0.01934126578271389, -0.06497734785079956, 0.0683736801147461, 0.015731673687696457, -0.005882165394723415, 0.01205091830343008, -0.03188676759600639, -0.02077295631170273, 0.004488850943744183, 0.059256453067064285, 0.0037064680363982916, 0.01810332015156746, -0.021918922662734985, 0.05219035968184471, -0.020218035206198692, 0.10150952637195587, 0.06175670772790909, 0.02445504441857338, -0.0024086523335427046, 0.03635507449507713, -0.006234308704733849, 0.01754804141819477, -0.008634434081614017, -0.012627188116312027, -0.046080801635980606, 0.015403741970658302, 0.009671058505773544, 0.001130343647673726, 0.01827266439795494, 0.0066849603317677975, -0.016436120495200157, 0.003270771587267518, 0.008373127318918705, -0.0366903617978096, 0.016740240156650543, -0.010892404243350029, 0.03813529014587402, -0.02215608023107052, -0.00273740547709167, 0.05208154395222664, -0.06256993860006332, -0.045979276299476624, 0.011037479154765606, 0.01752793975174427, 0.013726385310292244, -0.04286446422338486, 0.02675040438771248, 0.043128132820129395, 0.02035459131002426, -0.024684380739927292, -0.08256480097770691, 0.025986652821302414, 0.013766312040388584, -0.017920473590493202, -0.023572739213705063, 0.02070329710841179, -0.06673093885183334, 0.004907603841274977, -0.03815682232379913, 0.03304899111390114, -0.0019066875101998448, -0.07620976120233536, 0.04512295126914978, 0.00933176651597023, -0.013465022668242455, 0.004555150866508484, -0.0004482619115151465, -0.004978840705007315, 0.007798351813107729, -0.035321567207574844, 0.012273232452571392, 0.04593582823872566, -0.002079667989164591, 0.032359153032302856, -0.06738219410181046, -0.0574035607278347, 0.045159779489040375, -0.004951552487909794, 0.00020454259356483817, 0.10209501534700394, -0.034694604575634, 0.0018088133074343204, -0.024550940841436386, 0.024290254339575768, -0.003670318750664592, -0.023735573515295982, -0.000917299825232476, -0.014685656875371933, 0.012013374827802181, -0.015332842245697975, 0.022869834676384926, 0.0259611327201128, 0.05825822800397873, 0.043107978999614716, 0.027791066095232964, -0.004112488590180874, -0.032786186784505844, -0.036149658262729645, 0.03132583945989609, 0.06122172996401787, -0.0017554607475176454, -0.04232075437903404, 0.028248228132724762, 0.03876197710633278, 0.00818680226802826, 0.045155853033065796, -0.03759231045842171, 0.035736508667469025, -0.02666661888360977, 0.01579546555876732, 0.008215091191232204, -0.040445007383823395, -0.032324474304914474, -0.008349066600203514, -0.02524992637336254, 0.00780252693220973, 0.03925825655460358, -0.06134423613548279, 0.020880157127976418, 0.0016509813722223043, 0.0006105818902142346, -0.005526423919945955, 0.03557642176747322, 0.008178520947694778, 0.03854307532310486, -0.037372712045907974, 0.008288729935884476, -0.06395315378904343, -0.028092963621020317, 0.00802746880799532, -0.01637781225144863, 0.019501691684126854, -0.027319341897964478, 0.006209258455783129, 0.0054954723455011845, -0.028027581050992012, 0.01801348477602005, 0.01767631061375141, -0.012150953523814678, -0.02166580595076084, 0.010330919176340103, -0.024334372952580452, -0.03432874381542206, 0.006503998301923275, -0.053322985768318176, -0.06132832542061806, -0.010953972116112709, 0.01139745768159628, -0.05494711920619011, 0.010309669189155102, -0.038722019642591476, -0.046078938990831375, 0.0028201297391206026, -0.03494143486022949, 0.06403235346078873, 0.030121320858597755, 0.02874467708170414, 0.02990451455116272, 0.012801449745893478, 0.0006850009085610509, 0.0011213758261874318, -0.014073174446821213, -0.00763501925393939, -0.039968714118003845, 0.013928154483437538, -0.0009643076336942613, 0.011224477551877499, -0.015303747728466988, -0.06609763950109482, 0.09646669030189514, 0.02915242686867714, 0.025080839172005653, 0.04713372141122818, -0.0070505207404494286, 0.075445756316185, -0.05220445990562439, 0.03605596721172333, 0.039655715227127075, -0.0174593236297369, -0.061244551092386246, -0.012556451372802258, -0.009054533205926418, -0.025317620486021042, -0.04409397020936012, 0.0015327261062338948, -0.06921268254518509, 0.016527971252799034, 0.0458090677857399, 0.027703262865543365, -0.04241933673620224, -0.03680272400379181, -0.06581335514783859, -0.04910725727677345, -0.04247238114476204, -0.06108168885111809, 0.054272569715976715, 0.03422776982188225, 0.0153541574254632, 0.025860661640763283, -0.08151249587535858, -0.008878444321453571, 0.02247433364391327, 0.01719053089618683, 0.013983307406306267, -0.025552256032824516, -0.013610302470624447, -0.018374865874648094, 0.03524821251630783, 0.0012774261413142085, 0.020404353737831116, 0.004116883035749197, 0.009009561501443386, -0.014491288922727108, 0.04106241464614868, -0.01040599588304758, -0.03598988056182861, 0.0036287549883127213, 0.019697848707437515, -0.056664880365133286, 0.051879800856113434, -0.012845618650317192, -0.03786703199148178, -0.03284141421318054, 0.02167370170354843, -0.018810497596859932, -0.046357084065675735, 0.07035694271326065, 0.04739366099238396, -0.0195322148501873, -0.04260602965950966, 0.023354846984148026, 0.024563182145357132, -0.007564058993011713, -0.05215812847018242, -0.023490650579333305, 0.008873716928064823, -0.06206813454627991, 0.011664772406220436, 0.043313708156347275, 0.03170038387179375, 0.021517833694815636, 0.007302622310817242, -0.016582248732447624, -0.004999692551791668, 0.017369655892252922, 0.015519105829298496, -0.002866775495931506, -0.035330403596162796, 0.003976207226514816, -0.027819786220788956, -0.04883614182472229, -0.006626279093325138, 0.022554224357008934, -0.02789454720914364, 0.025634368881583214, -0.010447988286614418, -0.07317262142896652, -0.050391506403684616, 0.07047963887453079 ]
<p>If I'm correct a quark can change color by emitting a gluon. For example a blue up quark $u_b$ can change into a red up quark by emitting a gluon: $$u_b \longrightarrow u_r + g_{b\overline{r}}$$ (Here, the subscript indicates color and $\overline{r}$ means anti-red). This is needed to keep the color balance (left hand side: $b$, right hand side $r+b+\overline{r}=b$).</p> <p>My question is then, do color-neutral gluons exist? Eg a gluon that is blue-anti-blue? If it would, it could be created by any quark then: $$u_b \longrightarrow u_b + g_{b\overline{b}}$$</p> <p>I'm learning about the Standard Model in school, but the text isn't always that clear. </p>
g8376
[ 0.010748818516731262, 0.048590224236249924, 0.019795216619968414, -0.08008317649364471, 0.09538818895816803, 0.017337949946522713, -0.052313752472400665, -0.01096742507070303, -0.01192663237452507, -0.007292755413800478, 0.010076313279569149, 0.09843181073665619, 0.009340477176010609, 0.03682461753487587, -0.013005855493247509, 0.022674772888422012, 0.01913250982761383, -0.02536679245531559, 0.05169246718287468, 0.011619776487350464, -0.0356038436293602, 0.0002937018289230764, 0.05104865878820419, -0.02471940405666828, -0.03815868869423866, -0.04892028495669365, -0.03401721268892288, -0.053350843489170074, 0.0057196724228560925, -0.0369790643453598, -0.0075774709694087505, 0.0006248362478800118, 0.030724601820111275, -0.011575221084058285, 0.015616520307958126, -0.026953784748911858, 0.09353365004062653, 0.023636851459741592, 0.03130928799510002, 0.05472439154982567, 0.024995673447847366, 0.019945383071899414, 0.01345988642424345, -0.02347228303551674, -0.020822366699576378, 0.04129453003406525, 0.010743376798927784, 0.02530054934322834, -0.01915762946009636, -0.022351099178195, -0.013200019486248493, 0.0312182754278183, -0.0025806475896388292, -0.005194992758333683, -0.02708454430103302, -0.004772575572133064, 0.0061193606816232204, 0.030703354626893997, 0.034959759563207626, 0.09956163913011551, -0.04673406854271889, 0.01984954997897148, -0.0021766466088593006, 0.046714261174201965, 0.08048766851425171, -0.008699266240000725, 0.03695588931441307, -0.005091118160635233, -0.007376370020210743, 0.008280180394649506, 0.0009587755776010454, -0.01780778355896473, 0.0017842344241216779, 0.05826359614729881, 0.027217699214816093, 0.048303332179784775, 0.00020609104831237346, 0.008594496175646782, 0.0003714475897140801, 0.02344914712011814, -0.03471970930695534, 0.06206890195608139, 0.036160487681627274, 0.00042128609493374825, 0.060836438089609146, -0.010206948965787888, -0.013621977530419827, 0.02777257189154625, -0.025613758713006973, -0.000636136916000396, 0.007543831132352352, -0.024193214252591133, 0.025234850123524666, 0.03921997547149658, 0.002275774022564292, -0.05993233621120453, 0.006844301242381334, 0.061971891671419144, -0.07787756621837616, -0.06169205531477928, -0.01748955436050892, -0.01008302066475153, 0.0401465930044651, -0.02871481142938137, -0.06456740945577621, 0.0034107209648936987, 0.04761232063174248, -0.03394350782036781, 0.029170464724302292, -0.04672761261463165, -0.0033405693247914314, 0.00926797091960907, -0.06089986488223076, -0.0006466482882387936, -0.030099621042609215, 0.012213357724249363, 0.03169503062963486, -0.056106213480234146, 0.007443081587553024, 0.0707516148686409, -0.0006791248451918364, 0.0433768667280674, -0.04973310977220535, -0.03698788955807686, -0.050355661660432816, -0.048383209854364395, -0.03229131922125816, 0.026302501559257507, 0.006652476266026497, 0.036129191517829895, 0.017183303833007812, -0.02681293711066246, -0.03419282287359238, 0.0029912511818110943, 0.05914345383644104, -0.0014396803453564644, 0.0400884784758091, 0.06418297439813614, 0.02461477741599083, -0.012617544271051884, -0.015014369040727615, -0.02805468812584877, -0.03366326913237572, -0.039415791630744934, 0.01430563349276781, -0.002177321584895253, 0.01219854410737753, -0.008046602830290794, 0.01715747080743313, 0.038398876786231995, 0.017314646393060684, 0.03513267636299133, 0.020348191261291504, -0.042497556656599045, -0.04930156096816063, 0.011609815992414951, 0.04555919021368027, -0.026969987899065018, -0.020253455266356468, -0.04501043260097504, 0.03129662945866585, -0.03056923858821392, -0.010699253529310226, -0.008532327599823475, -0.06718280166387558, -0.06323888897895813, 0.024091485887765884, -0.02609640173614025, -0.04528691619634628, 0.014791254885494709, -0.031226681545376778, 0.0255595576018095, -0.032683711498975754, 0.04917160049080849, 0.0445215068757534, -0.009015463292598724, 0.012456857599318027, 0.008413538336753845, 0.01609732210636139, -0.02225230261683464, -0.09368196129798889, -0.03501556068658829, -0.00006272085738601163, -0.014633874408900738, 0.011253544129431248, -0.025319643318653107, -0.048416536301374435, 0.021919772028923035, 0.008512374944984913, 0.034914661198854446, -0.052177995443344116, 0.02737388387322426, 0.02212684042751789, 0.0038927446585148573, 0.016709253191947937, -0.09498794376850128, -0.05912710353732109, 0.01635749451816082, -0.03141656145453453, 0.10130352526903152, 0.002548636868596077, -0.015454687178134918, -0.03518727794289589, -0.030007390305399895, 0.06727572530508041, 0.006302147638052702, 0.0461072213947773, -0.011896638199687004, 0.06260265409946442, -0.04264053329825401, 0.03155243769288063, 0.057390887290239334, 0.00873425044119358, -0.01719551533460617, 0.0353969931602478, -0.01521720364689827, 0.0023952657356858253, 0.058690834790468216, -0.017526620998978615, -0.02066667005419731, -0.016947472468018532, -0.02194574475288391, 0.028856588527560234, -0.01267655286937952, 0.01235201209783554, 0.03655434027314186, -0.05499257147312164, -0.011223784647881985, 0.007877664640545845, -0.0429997555911541, -0.04696808010339737, -0.0030703928787261248, -0.025711873546242714, -0.055001795291900635, -0.03277921304106712, 0.04117583855986595, 0.0022315881215035915, 0.002996033290401101, 0.057032082229852676, -0.007410071324557066, 0.016443656757473946, -0.0158968735486269, -0.011075926944613457, 0.07291505485773087, -0.0332951657474041, -0.02015099488198757, 0.04131913557648659, 0.006080266088247299, -0.03469885513186455, 0.03243781253695488, 0.03735979273915291, 0.01716938614845276, -0.010652495548129082, -0.014722408726811409, -0.007852792739868164, -0.002842219080775976, -0.012088606134057045, -0.02011505328118801, -0.02163037098944187, -0.0339948944747448, 0.02594921924173832, -0.01782267726957798, -0.003308035433292389, 0.04052625596523285, -0.011284848675131798, 0.051874030381441116, 0.004418811295181513, -0.025953631848096848, -0.012520219199359417, 0.0738687664270401, -0.05241820588707924, -0.013342883437871933, 0.023487651720643044, -0.014955861493945122, -0.02398843877017498, -0.02115098387002945, -0.033275458961725235, -0.0186699740588665, 0.032645903527736664, 0.008962213061749935, 0.028695782646536827, -0.012244455516338348, -0.057823434472084045, -0.012034684419631958, 0.01349048875272274, 0.05110127106308937, 0.00012999623140785843, 0.005808223970234394, -0.008913974277675152, -0.0020587213803082705, -0.10213484615087509, -0.009292537346482277, 0.04438786581158638, 0.02049952931702137, -0.035097815096378326, -0.019249364733695984, -0.03896746411919594, -0.017888564616441727, -0.0017967771273106337, 0.05051741376519203, 0.01331662479788065, -0.01789807714521885, -0.029932646080851555, 0.039013974368572235, 0.0329042449593544, -0.01571759581565857, -0.04885710030794144, 0.0692702978849411, -0.008691391907632351, 0.024220682680606842, -0.03536384552717209, 0.10688631981611252, -0.03361217677593231, 0.06398722529411316, 0.03570828214287758, -0.003490547649562359, -0.011774202808737755, -0.012253371067345142, 0.011956010945141315, -0.08978305011987686, -0.04013797268271446, 0.004771005362272263, 0.004566121846437454, -0.013779666274785995, 0.03407992795109749, -0.047431059181690216, -0.06608887016773224, -0.015260654501616955, -0.08455798774957657, -0.020368201658129692, 0.05682031065225601, 0.026630567386746407, 0.009426061995327473, 0.0558292381465435, -0.04237671196460724, -0.0018633469007909298, 0.007102804258465767, -0.05380167067050934, 0.025016801431775093, 0.06804268807172775, 0.07975456863641739, -0.03596234321594238, 0.008521581999957561, 0.007761179935187101, -0.02487611584365368, -0.03370402753353119, 0.012862159870564938, -0.012567576952278614, 0.025694480165839195, 0.025591779500246048, 0.03985756263136864, 0.06424166262149811, 0.07150799036026001, -0.030524784699082375, -0.05378086864948273, -0.03563680499792099, 0.0415613017976284, 0.07623092830181122, 0.027449417859315872, -0.003681023372337222, 0.030445247888565063, -0.020846446976065636, 0.04830307140946388, -0.013127499260008335, 0.010119795799255371, -0.010285299271345139, -0.019900809973478317, -0.013015270233154297, 0.020632989704608917, 0.025668885558843613, 0.0583241730928421, 0.03180461749434471, 0.01075277104973793, 0.01134840864688158, -0.015497240237891674, -0.06797421723604202, 0.03570146858692169, 0.06847766041755676, -0.054218124598264694, 0.03477854281663895, 0.011670099571347237, 0.04842761158943176, 0.04048867151141167, -0.029096441343426704, 0.0056144376285374165, -0.007670936174690723, -0.02816060185432434, -0.0480310395359993, -0.03779284283518791, -0.014984194189310074, -0.028842855244874954, -0.039153918623924255, -0.031891852617263794, -0.004971275571733713, -0.0005025589489378035, 0.02906777523458004, 0.023372339084744453, -0.02863307297229767, -0.01222404558211565, 0.035441428422927856, -0.014859809540212154, 0.03359704837203026, 0.03378080576658249, -0.048031240701675415, -0.0266837477684021, -0.02056095562875271, 0.0009889634093269706, -0.025230195373296738, -0.019266001880168915, -0.017750298604369164, -0.011573165655136108, -0.0014237145660445094, 0.005591947119683027, -0.06972957402467728, 0.025446496903896332, 0.04405298829078674, -0.012222720310091972, 0.05603701248764992, -0.012459407560527325, 0.02023944817483425, 0.09290284663438797, 0.015955239534378052, 0.014321709051728249, -0.040298882871866226, 0.04147449880838394, 0.0549718402326107, 0.03517447039484978, 0.022331595420837402, 0.025310082361102104, 0.01946387067437172, 0.04818921536207199, -0.022128093987703323, -0.05108584463596344, -0.017412791028618813, 0.010300461202859879, 0.028939008712768555, -0.049830224364995956, -0.004774925764650106, -0.025379663333296776, -0.03298741206526756, 0.09080176800489426, -0.01968526653945446, 0.06117073819041252, -0.05113385245203972, -0.0019795363768935204, -0.010566762648522854, -0.02871680073440075, -0.040106263011693954, -0.06311473250389099, -0.01529968436807394, 0.006148268468677998, 0.06659600883722305, -0.02534463442862034, 0.02381782978773117, -0.014917251653969288, 0.013892000541090965, -0.0015943656908348203, -0.002193107269704342, 0.03061099164187908, 0.06342378258705139, -0.017415717244148254, -0.026716766878962517, 0.04727073013782501, -0.03431722894310951, 0.026392245665192604, 0.0065896823070943356, -0.06719422340393066, 0.026480432599782944, 0.01213009376078844, -0.01850765570998192, -0.0007331016240641475, 0.030871011316776276, 0.036347586661577225, -0.0036116670817136765, -0.00503078056499362, -0.045402128249406815, -0.036990899592638016, 0.0019122159574180841, 0.06713615357875824, -0.020947061479091644, -0.0047530741430819035, -0.014667576178908348, 0.02078484185039997, -0.009624590165913105, -0.020008623600006104, 0.026210198178887367, -0.0459522046148777, 0.028782377019524574, -0.0021956167183816433, -0.002036243211477995, -0.010892421007156372, -0.007025252562016249, 0.05412423238158226, 0.04666723683476448, 0.004191952757537365, 0.01753436215221882, -0.0021973587572574615, -0.00042417310760356486, -0.04481719806790352, -0.018335144966840744, -0.004416977986693382, 0.039452601224184036, 0.03673483058810234, 0.0011794749880209565, 0.004228194709867239, 0.031530290842056274, 0.028498610481619835, -0.009349784813821316, -0.013216245919466019, 0.023580390959978104, 0.0014829807914793491, -0.028013041242957115, 0.041550058871507645, 0.019324107095599174, -0.05055373162031174, 0.02104802615940571, -0.09048356115818024, -0.02585238218307495, -0.03959939256310463, -0.02960519678890705, -0.007185543887317181, -0.023577099665999413, -0.006622819229960442, -0.0030577650759369135, -0.031908415257930756, 0.05709037557244301, -0.04450114071369171, -0.01626632921397686, 0.053595010191202164, -0.03556721284985542, 0.03891368955373764, 0.013920052908360958, 0.01812702789902687, 0.02697840705513954, 0.006435803137719631, -0.010136284865438938, -0.04100527614355087, 0.060203395783901215, -0.017648804932832718, 0.05973764881491661, 0.02310672029852867, -0.008931968361139297, 0.035460058599710464, 0.03429979085922241, -0.021782970055937767, -0.013105923309922218, -0.06294332444667816, -0.011972938664257526, -0.010482694953680038, -0.04079442471265793, -0.032808516174554825, 0.02625555917620659, 0.06348618865013123, 0.03407822549343109, 0.03220336139202118, -0.014108175411820412, -0.017728259786963463, -0.032959140837192535, 0.013984574936330318, -0.02584225684404373, -0.029425136744976044, -0.005564405117183924, 0.008153711445629597, -0.020348379388451576, 0.0028818538412451744, -0.05004804953932762, -0.025762615725398064, -0.061913035809993744, 0.05579268932342529, 0.07295425981283188, 0.04855087772011757, 0.002243967493996024, -0.013182914815843105, -0.014861196279525757, 0.03242563083767891, -0.00759195676073432, -0.02939353510737419, -0.034209709614515305, -0.04159628599882126, 0.02479277178645134, 0.03065108321607113, 0.05344705283641815, -0.08618803322315216, -0.04628317430615425, -0.05419476702809334, 0.045508015900850296, 0.009174802340567112, 0.0080958167091012, 0.024685824289917946, 0.05260089039802551, -0.04531336575746536, -0.043881338089704514, -0.07471372932195663, 0.033885449171066284, 0.06117101013660431, -0.038623034954071045, -0.08086740225553513, -0.018356772139668465, -0.004197282250970602, -0.055261414498090744, 0.02505515329539776, -0.03132655471563339, -0.002190564526244998, -0.0011899563251063228, -0.0022869808599352837, 0.06202656403183937, -0.02831217087805271, 0.048084184527397156, 0.04263772442936897, -0.005892476532608271, 0.019318627193570137, -0.03274412825703621, -0.017163047567009926, -0.04879714921116829, 0.017012126743793488, -0.11086028069257736, 0.050097789615392685, -0.0034609357826411724, -0.02117854729294777, -0.028641022741794586, 0.02890520915389061, 0.017384814098477364, 0.016924697905778885, -0.018070770427584648, 0.02568395435810089, 0.0474841371178627, 0.009945857338607311, 0.06627510488033295, 0.05554361641407013, 0.005920635536313057, -0.011310347355902195, -0.05332668870687485, -0.021853134036064148, -0.04268888756632805, -0.008834965527057648, -0.0436558835208416, -0.06042459234595299, -0.01590074598789215, 0.0035801406484097242, 0.0469474159181118, -0.02774788625538349, 0.0007199391257017851, 0.061093177646398544, -0.004562039859592915, -0.008199144154787064, 0.09189560264348984, 0.02154780924320221, -0.008945852518081665, -0.002340049482882023, 0.014731007628142834, 0.014557779766619205, 0.022887500002980232, -0.03644641488790512, 0.0008969194605015218, -0.021523483097553253, -0.004992571193724871, 0.004745294339954853, 0.06841972470283508, 0.019782602787017822, -0.022937307134270668, 0.008005049079656601, -0.06956362724304199, -0.025965794920921326, 0.01455245167016983, 0.0678110346198082, 0.0068155312910676, 0.0059940386563539505, -0.03081325814127922, 0.023961272090673447, -0.002280977088958025, -0.059856630861759186, -0.025285206735134125, 0.036096032708883286, -0.02560587041079998, 0.00904350820928812, -0.049709562212228775, -0.04273022338747978, 0.10715116560459137, 0.040835022926330566, -0.020557263866066933, 0.04391957074403763, 0.040073178708553314, -0.004672226961702108, -0.004218231420964003, -0.04103441163897514, -0.0027630298864096403, 0.028715185821056366, -0.05051909387111664, -0.06944149732589722, -0.026197558268904686, -0.044038187712430954, 0.010777773335576057, -0.006182434037327766, -0.05164546146988869, 0.011360648088157177, -0.016701307147741318, -0.06920406967401505, -0.024794893339276314, 0.02348943240940571, 0.035321254283189774, 0.00973097700625658, -0.062342774122953415, -0.027248550206422806, -0.028648613020777702, 0.06952489912509918, -0.018141692504286766, 0.0011330562410876155, -0.0451386459171772, -0.06064696982502937, -0.029241759330034256, -0.035683657974004745, 0.044137999415397644, 0.03159330412745476, 0.04227646067738533, 0.02496451325714588, -0.00926491804420948, -0.02798965573310852, -0.010864515788853168, 0.006404138170182705, 0.037493783980607986, -0.02811519056558609, -0.012100651860237122, -0.0606081523001194, 0.022064030170440674, 0.008821752853691578, -0.004048082046210766, -0.00016826335922814906, -0.003761687083169818, -0.0018932619132101536, 0.07837674766778946, -0.05157477408647537, 0.016124965623021126, -0.015415237285196781, -0.004753324668854475, 0.017420070245862007, -0.022123824805021286, -0.02845616079866886, 0.0008688310626894236, -0.013069026172161102, 0.04100034013390541, -0.01661129854619503, -0.050536900758743286, -0.006840783637017012, 0.030521612614393234, -0.03182695806026459, -0.04243436083197594, -0.012182422913610935, -0.011253480799496174, -0.0032167453318834305, -0.04525519907474518, -0.007325966842472553, 0.04374684393405914, 0.02651006542146206, 0.02223222889006138, 0.0457877479493618, 0.0007589304586872458, 0.04331033304333687, 0.01592821069061756, -0.07449062913656235, -0.01500478945672512, -0.027576135471463203, 0.03867766633629799, -0.010553252883255482, -0.02142958715558052, -0.027017172425985336, -0.011352255940437317, 0.002690098248422146, -0.03209175914525986 ]
<p>The Higgs boson propagator can be written $$\frac{1}{p^2-m^2+\Sigma(p^2)}$$. If we take $p^2=m_P^2$ the physical mass, we get $m_P^2=m^2-\Sigma(m_P^2)$. Now, if $\Sigma\sim \Lambda^2$, we get $m^2\sim\Lambda^2+m_P^2$.</p> <p>It had assumed that the mass correction from fermion loops was positive, but from this it appears that the Higgs mass is renormalized to be smaller than the bare mass. Is this physical ?</p>
g8377
[ 0.03979520499706268, 0.0058999136090278625, 0.0082247881218791, -0.04759187623858452, 0.02109818533062935, 0.0272796880453825, -0.028022734448313713, 0.05207701027393341, -0.07546717673540115, 0.012223426252603531, -0.052300725132226944, 0.009415038861334324, 0.013042951934039593, 0.07335012406110764, 0.03781924024224281, 0.05620913952589035, 0.08340559154748917, 0.016510438174009323, 0.03893235698342323, -0.002981042955070734, -0.014426766894757748, -0.030878223478794098, -0.03697459027171135, -0.012770004570484161, -0.024020927026867867, 0.04335691034793854, 0.03271832689642906, -0.02002895437180996, 0.014703918248414993, 0.016973553225398064, 0.04985674098134041, -0.008177481591701508, 0.04122558608651161, -0.07387121766805649, -0.04441041499376297, -0.05270407348871231, 0.09333117306232452, 0.003345837350934744, 0.05323109030723572, 0.005340516101568937, 0.030311118811368942, -0.017239034175872803, 0.009517294354736805, 0.00732025783509016, -0.031633175909519196, -0.0005893236375413835, 0.0035598690155893564, 0.03475343436002731, -0.016500825062394142, 0.006277212407439947, -0.008656117133796215, 0.025819946080446243, 0.029849844053387642, 0.055634718388319016, 0.013696263544261456, 0.029743656516075134, 0.03998833894729614, -0.025144536048173904, 0.04304221644997597, 0.040711428970098495, 0.014964603818953037, 0.0019596461206674576, -0.0008234348497353494, 0.0008883137488737702, 0.04427417740225792, 0.00265039992518723, -0.06548026949167252, 0.0017326473025605083, 0.004244750831276178, 0.056064389646053314, -0.01626409776508808, -0.031240329146385193, -0.0036452419590204954, -0.020665936172008514, 0.04935836419463158, -0.023843256756663322, -0.055534716695547104, -0.03727713227272034, -0.03997286036610603, -0.06466776877641678, -0.02222198061645031, -0.08635023981332779, 0.012951916083693504, 0.011387623846530914, 0.0405871644616127, -0.06070652976632118, -0.044853027909994125, 0.004479588475078344, -0.0582379512488842, 0.015321198850870132, -0.038933511823415756, -0.027800673618912697, 0.025743680074810982, 0.025501804426312447, 0.021385733038187027, 0.003065762110054493, -0.010816402733325958, 0.004967401269823313, -0.023560531437397003, -0.015644241124391556, -0.023679286241531372, 0.026634661480784416, -0.000882305670529604, 0.02352440357208252, -0.025029098615050316, 0.018209729343652725, 0.054246239364147186, 0.009798645973205566, 0.031988102942705154, 0.017936551943421364, -0.014725316315889359, -0.09034573286771774, -0.03604263812303543, -0.052340067923069, -0.06901125609874725, 0.006698634475469589, 0.06527393311262131, -0.016066957265138626, 0.003235295182093978, 0.0755331814289093, 0.008044365793466568, -0.028231695294380188, 0.03682095929980278, 0.05223870649933815, -0.013873066753149033, -0.0665024071931839, -0.061337102204561234, 0.020966364070773125, 0.017982587218284607, -0.030876336619257927, 0.028570840135216713, -0.030704325065016747, 0.0028220631647855043, 0.005719554610550404, 0.012298624031245708, -0.040593016892671585, 0.04271739348769188, -0.01963188499212265, 0.02582712471485138, -0.042098209261894226, -0.006124743726104498, -0.016031598672270775, -0.015671662986278534, 0.004033864010125399, 0.0018087938660755754, 0.006193718872964382, 0.008371550589799881, 0.03277188912034035, 0.01561195682734251, 0.02938986010849476, 0.04863651096820831, 0.04260072484612465, -0.016310518607497215, 0.0324045866727829, -0.01011837087571621, 0.014963445253670216, 0.09067517518997192, 0.06560876220464706, -0.005393918603658676, 0.013294262811541557, 0.03531552106142044, -0.03928837180137634, 0.01296109240502119, -0.04936567693948746, -0.034487705677747726, 0.042829226702451706, 0.04975999519228935, -0.013176447711884975, -0.053466495126485825, -0.03162211924791336, -0.04796808212995529, 0.05056924372911453, -0.013280238956212997, 0.059375859797000885, 0.015173463150858879, 0.01812632940709591, 0.0036378875374794006, 0.04205137863755226, 0.00025869192904792726, 0.02790611982345581, 0.024133991450071335, -0.027338266372680664, -0.013127429410815239, 0.027511563152074814, -0.012610376812517643, 0.006352705415338278, -0.012847216799855232, 0.04482422024011612, 0.008008530363440514, -0.026140643283724785, -0.037227239459753036, 0.024806655943393707, -0.008514469489455223, 0.10363269597291946, 0.005304904188960791, -0.015714146196842194, 0.00642432039603591, -0.04915963485836983, -0.0020322108175605536, 0.009528964757919312, -0.011078017763793468, 0.019483326002955437, 0.06730198860168457, -0.054868414998054504, 0.04527167230844498, -0.0658021941781044, 0.024940941482782364, -0.02444574609398842, 0.006461378652602434, -0.010915745049715042, 0.010540672577917576, -0.026610873639583588, 0.019315574318170547, -0.02419557049870491, -0.058770935982465744, -0.0211942121386528, -0.02247714251279831, 0.03493038937449455, -0.0023425447288900614, -0.021673571318387985, -0.059830911457538605, -0.05016884580254555, 0.00854045432060957, 0.0023005548864603043, 0.012505980208516121, 0.01981978490948677, -0.0068110390566289425, -0.021343091502785683, -0.007491043768823147, 0.03874826431274414, -0.009062595665454865, -0.002013951539993286, 0.01385465543717146, 0.012734470888972282, -0.005869927816092968, 0.00977043155580759, -0.01667136885225773, 0.036878637969493866, 0.031658072024583817, 0.04245461896061897, 0.07230838388204575, -0.025997795164585114, -0.039563268423080444, 0.03168819844722748, 0.029960686340928078, -0.01458529382944107, 0.054005347192287445, 0.0627254843711853, -0.023386357352137566, 0.024421945214271545, 0.04582057148218155, 0.013762512244284153, 0.002883142326027155, 0.02703862637281418, 0.03621074557304382, -0.007429341319948435, -0.002424943959340453, -0.02202378585934639, -0.08091726154088974, -0.024437081068754196, 0.016017625108361244, -0.046960994601249695, 0.009113464504480362, 0.02633279748260975, -0.05360005423426628, 0.02732977643609047, -0.023373596370220184, -0.007741275243461132, 0.020374519750475883, 0.03664690628647804, 0.04184097424149513, 0.0062327198684215546, 0.017945660278201103, 0.040715720504522324, -0.0007547048735432327, -0.02522709220647812, 0.03234663978219032, 0.03192754089832306, 0.03223666921257973, -0.04997522383928299, -0.00047380212345160544, 0.0819832906126976, -0.06504681706428528, 0.04227621108293533, 0.03048921935260296, -0.06779702007770538, -0.030181879177689552, -0.0298503115773201, -0.0326865054666996, 0.05866701155900955, 0.0041794846765697, -0.0360645167529583, 0.05024851858615875, 0.0473901741206646, -0.024548465386033058, 0.04932368919253349, 0.03208141401410103, 0.001055645989254117, 0.006142427213490009, 0.032528940588235855, 0.028798498213291168, 0.028646137565374374, -0.049969617277383804, -0.02194754034280777, -0.007169023156166077, -0.004182151984423399, -0.053649380803108215, 0.054204560816287994, 0.02690310776233673, -0.0570642352104187, 0.018798602744936943, 0.07148189842700958, 0.01831483282148838, -0.032721906900405884, -0.02229592762887478, 0.017859777435660362, -0.00013040757039561868, 0.013270995579659939, -0.04290265217423439, -0.0023651239462196827, -0.06709858030080795, -0.04385249689221382, -0.006028895266354084, -0.005617301445454359, 0.03339888155460358, -0.028293397277593613, -0.013017924502491951, -0.01244295947253704, -0.04946066066622734, -0.02769472450017929, 0.0026794883888214827, 0.02677215449512005, -0.034471798688173294, 0.014473013579845428, -0.005056323483586311, -0.016645053401589394, -0.033714767545461655, 0.040643177926540375, 0.03129977360367775, -0.01918860897421837, -0.038616884499788284, 0.020238112658262253, -0.04943142086267471, 0.016594860702753067, 0.005518198013305664, 0.055470533668994904, -0.029232818633317947, -0.03298410028219223, 0.06320466846227646, -0.050637759268283844, 0.03437809646129608, 0.05707395821809769, 0.004131924360990524, 0.005852559581398964, -0.0317881740629673, 0.03793428838253021, -0.03257773816585541, 0.0533047616481781, 0.05693121254444122, -0.05944579839706421, 0.029800554737448692, -0.0014824162935838103, -0.04436836764216423, -0.0056886267848312855, -0.03648940846323967, -0.027466710656881332, -0.026299625635147095, -0.003939880058169365, -0.008921190164983273, -0.0235123410820961, -0.011585503816604614, -0.007908802479505539, 0.05416734889149666, 0.07855069637298584, -0.048945605754852295, -0.0047201914712786674, 0.05161597207188606, -0.00953018106520176, -0.02870333380997181, 0.025379562750458717, 0.012019742280244827, -0.01682438515126705, -0.016093093901872635, 0.008820968680083752, -0.005697455257177353, -0.010269276797771454, -0.036047179251909256, 0.02302004024386406, -0.01849987730383873, 0.013353445567190647, -0.05125930905342102, 0.015333432704210281, -0.016241855919361115, 0.009976765140891075, 0.043567586690187454, -0.03323330357670784, 0.047825396060943604, -0.015120302326977253, 0.013932205736637115, 0.004435088485479355, 0.009006518870592117, 0.03572402149438858, 0.01056580524891615, -0.012064950540661812, -0.0060741472989320755, 0.036144182085990906, 0.05422750487923622, 0.03138845041394234, 0.021994471549987793, -0.0037422089371830225, 0.0036562944296747446, 0.035701315850019455, 0.019693106412887573, -0.05575644224882126, 0.027881594374775887, -0.0153370825573802, 0.001263324054889381, -0.022589702159166336, 0.014849330298602581, -0.012155287899076939, 0.0041443658992648125, -0.015117076225578785, -0.0007278649718500674, 0.015690533444285393, -0.029092460870742798, 0.08697884529829025, 0.05723957717418671, 0.029467368498444557, -0.03968900069594383, -0.06924990564584732, 0.05978589132428169, 0.005700400564819574, -0.018020320683717728, 0.029810314998030663, -0.06903856992721558, 0.059494178742170334, -0.03206566348671913, 0.015296762809157372, -0.01697358675301075, 0.04799310490489006, 0.0395473875105381, -0.08071336150169373, -0.02815602719783783, -0.03028075583279133, 0.010463242419064045, 0.007671326398849487, -0.01971566118299961, -0.026333708316087723, -0.030200913548469543, 0.006395698059350252, -0.031402260065078735, 0.009060205891728401, 0.043791115283966064, -0.03669258952140808, 0.04759158939123154, 0.00495009683072567, -0.03421599790453911, 0.036413729190826416, 0.014955050311982632, -0.02281598001718521, -0.04113619774580002, -0.03311130404472351, 0.031096043065190315, 0.009091846644878387, 0.02351369522511959, -0.04095001146197319, -0.05545618385076523, -0.03919662535190582, 0.008267839439213276, 0.004217372741550207, -0.004702602047473192, -0.00971661601215601, 0.012735540978610516, -0.04721399396657944, 0.07737883925437927, -0.006702077575027943, -0.050852954387664795, -0.054787684231996536, -0.017199253663420677, -0.0594390369951725, 0.001025816542096436, 0.024244822561740875, -0.0004715799877885729, -0.027042841538786888, -0.013723250478506088, 0.009691537357866764, -0.08790183067321777, -0.005917920731008053, -0.002284239511936903, -0.014719870872795582, 0.008478456176817417, 0.0550670251250267, 0.031171578913927078, -0.0345332995057106, 0.05184095352888107, -0.009722110815346241, -0.023593375459313393, 0.01487730909138918, 0.04032672196626663, 0.03520594909787178, -0.042751751840114594, 0.010810475796461105, 0.04454917460680008, 0.046774160116910934, -0.021591605618596077, 0.08872544765472412, 0.03464356064796448, -0.026174847036600113, 0.06701351702213287, 0.019792186096310616, -0.012916699051856995, -0.008962396532297134, 0.006545595824718475, -0.0480659045279026, 0.003663521958515048, -0.008355830796062946, 0.02620893530547619, 0.03446349501609802, 0.02369742840528488, -0.017921460792422295, 0.03475319594144821, -0.022366492077708244, -0.022519715130329132, 0.001040457165800035, -0.03414955362677574, 0.00841089989989996, -0.04187026992440224, -0.07010728120803833, 0.056732237339019775, 0.005814835894852877, 0.04374772682785988, -0.04923196882009506, 0.04279472678899765, 0.025273695588111877, -0.0295519158244133, 0.023839138448238373, 0.01902000606060028, -0.0043198359198868275, 0.012511958368122578, -0.0035900981165468693, 0.005308721214532852, -0.016698110848665237, 0.031203074380755424, 0.03014785796403885, 0.03085019439458847, 0.02185397781431675, 0.0029596039094030857, -0.03276379778981209, 0.03281617537140846, -0.06730755418539047, -0.04409082978963852, 0.002505666809156537, 0.0072465804405510426, -0.03515966609120369, 0.02313537709414959, 0.011575605720281601, 0.03699154779314995, -0.006195252761244774, 0.04285870119929314, -0.004927688278257847, -0.034086983650922775, 0.034812960773706436, -0.0052711088210344315, 0.0017339822370558977, 0.038902491331100464, -0.04734901338815689, 0.018325725570321083, 0.00020437061903066933, 0.015388569794595242, -0.03325352445244789, -0.007171047851443291, 0.040383171290159225, -0.04480406269431114, 0.040923111140728, 0.018043626099824905, 0.03177192807197571, -0.029517829418182373, -0.010487785562872887, 0.011634093709290028, -0.013205332681536674, 0.01747007481753826, 0.008527679368853569, -0.027460355311632156, -0.0454174242913723, 0.03720376640558243, -0.030170490965247154, -0.07732507586479187, -0.004675505217164755, 0.009704123251140118, 0.05967633053660393, -0.018277844414114952, 0.04892036318778992, -0.08154740929603577, -0.024196062237024307, -0.023309778422117233, 0.014789634384214878, -0.0325094498693943, -0.0800284892320633, -0.021028142422437668, 0.00028529754490591586, 0.07302937656641006, 0.0007585557759739459, -0.03177559748291969, -0.05398034676909447, -0.005791833624243736, -0.0013565054396167397, -0.015117816627025604, 0.12227612733840942, -0.014984789304435253, 0.033077966421842575, 0.005823713727295399, 0.027407461777329445, -0.0007504445384256542, -0.05749201402068138, 0.02580025978386402, -0.05025797709822655, 0.014875393360853195, 0.057024091482162476, -0.05439629405736923, -0.03900657966732979, 0.04838107153773308, 0.022813057526946068, 0.007570273708552122, -0.06924610584974289, -0.02390517294406891, -0.0015111545799300075, 0.09707555174827576, -0.013255431316792965, 0.03351370617747307, -0.030236368998885155, -0.01406349241733551, 0.03732292354106903, 0.025687934830784798, 0.022885598242282867, -0.003668552963063121, 0.019796498119831085, -0.011044695042073727, 0.01090308278799057, -0.050364017486572266, 0.013227742165327072, 0.021692346781492233, -0.0351564958691597, -0.030107621103525162, 0.016947394236922264, -0.05512763559818268, -0.01207741443067789, 0.0384376160800457, 0.016862431541085243, -0.05450071394443512, -0.009316644631326199, -0.03819477558135986, 0.04256549850106239, 0.0036750894505530596, -0.005972282029688358, -0.09972454607486725, -0.03467869386076927, -0.05048392340540886, 0.07786042988300323, 0.06885149329900742, -0.04001856595277786, -0.05211065337061882, 0.017809590324759483, 0.05497926473617554, -0.0064268410205841064, 0.07340246438980103, 0.03871797025203705, -0.0133341234177351, -0.034393731504678726, 0.04439692571759224, -0.00843573734164238, 0.02934340201318264, -0.05505524203181267, -0.053806520998477936, 0.04669613763689995, 0.027477622032165527, -0.024422574788331985, -0.034636255353689194, -0.016675906255841255, -0.06776171177625656, 0.048910439014434814, -0.006233775522559881, 0.009491932578384876, -0.0376083105802536, 0.04135135933756828, 0.004137685522437096, -0.0021258334163576365, -0.0716388151049614, -0.010886144824326038, -0.009376049041748047, 0.051295023411512375, 0.052892912179231644, 0.008166223764419556, 0.05152963474392891, -0.025277890264987946, -0.03613821417093277, -0.00954542588442564, 0.02277386002242565, -0.006875279359519482, -0.005871859844774008, -0.04740743711590767, 0.005566065665334463, -0.03347782418131828, 0.008223472163081169, 0.01693200320005417, 0.08372326195240021, 0.01226858515292406, -0.0004285255854483694, -0.022127054631710052, -0.0519966222345829, -0.05790653079748154, 0.02041388861835003, 0.006640928331762552, -0.022207582369446754, 0.06446164846420288, 0.05458725616335869, -0.05437963455915451, -0.02400248870253563, -0.021550530567765236, -0.0035718746948987246, -0.029975641518831253, 0.013486446812748909, 0.017187362536787987, -0.07016893476247787, -0.052052441984415054, -0.05742181837558746, -0.013149254955351353, -0.010010153986513615, -0.0162859708070755, 0.002221581991761923, 0.09693446010351181, -0.027788976207375526, 0.022230828180909157, -0.05555933713912964, -0.034056406468153, -0.012631753459572792, -0.04515807330608368, 0.0005036674556322396, 0.023575754836201668, -0.0010112683521583676, -0.005635402165353298, -0.01861623488366604, -0.05368387699127197, -0.005207751411944628, 0.03137195482850075, 0.018485719338059425, -0.03287621960043907, -0.027703123167157173, -0.021587306633591652, 0.00988391786813736, -0.055721886456012726, 0.017798440530896187, -0.0013849122915416956, -0.08986777067184448, 0.038922760635614395, 0.005451274570077658, -0.059377945959568024, -0.000036914505471941084, -0.03208044171333313, -0.021934403106570244, -0.008235211484134197, 0.052483104169368744, -0.07274062186479568, 0.02859651856124401, -0.027634302154183388, -0.03906095772981644, -0.08196516335010529, 0.04844839870929718, -0.02359873615205288 ]
<p>Assuming it is possible in principle to entangle the degrees of freedom of the event horizons of two black holes, and that this is something that can be done, either after the black hole is formed, or only by careful preparation before collapse. </p> <blockquote> <p><strong>Question:</strong> Could exist a physically realisable entanglement configuration of the horizons that behaves as a traversable wormhole, in the sense that infalling information on one mouth becomes non-thermal Hawking radiation on the other mouth, that preserves some or all the original information?</p> </blockquote> <p>A while ago I made a relevant <a href="http://physics.stackexchange.com/q/48511/955">question regarding creating black holes with entangled light</a>. That method suggested there could provide two such entangled black holes</p>
g8378
[ 0.014932877384126186, -0.0015056614065542817, 0.025800585746765137, -0.019537542015314102, 0.018123408779501915, -0.030509229749441147, -0.01989584229886532, 0.04853840172290802, -0.014070967212319374, 0.021840408444404602, 0.022946277633309364, -0.014885112643241882, -0.009318799711763859, 0.012311761267483234, -0.04675072431564331, 0.043980322778224945, 0.04454353079199791, 0.0033810327295213938, 0.027093371376395226, -0.036769092082977295, -0.011371037922799587, 0.008964892476797104, 0.03240669146180153, 0.00886065885424614, -0.06511863321065903, -0.06210428848862648, 0.03805644065141678, -0.018133733421564102, -0.06492087244987488, -0.007963666692376137, 0.034277718514204025, -0.020366165786981583, 0.0017055810894817114, -0.018440719693899155, -0.02317727915942669, -0.00800238735973835, -0.023210886865854263, -0.023551836609840393, -0.044089943170547485, 0.020437942817807198, 0.024443162605166435, -0.010481443256139755, -0.051500678062438965, -0.02863289602100849, -0.00662276241928339, -0.01233656331896782, 0.0934353768825531, 0.03592035919427872, 0.09369073063135147, -0.07308459281921387, 0.03796384483575821, 0.028847970068454742, 0.05816351994872093, -0.00996299646794796, 0.05539250746369362, 0.09807448834180832, 0.02894597500562668, 0.025176649913191795, 0.03884952887892723, 0.018536081537604332, -0.009786268696188927, -0.05108768120408058, 0.03385251760482788, 0.000837557076010853, 0.04129474610090256, 0.008790719322860241, -0.08575519919395447, -0.019580338150262833, -0.04384947568178177, -0.03975435718894005, -0.01195007748901844, 0.0025407366920262575, 0.01538075227290392, -0.012072572484612465, 0.03315003588795662, 0.032829176634550095, 0.007859377190470695, -0.009737235493957996, -0.017676999792456627, 0.0003926088975276798, -0.044409677386283875, -0.010778417810797691, -0.010816080495715141, 0.007974264211952686, 0.12803345918655396, 0.012832209467887878, 0.007610714994370937, -0.040373969823122025, 0.012695054523646832, -0.005105501972138882, 0.02838863432407379, -0.0036014218349009752, 0.051378101110458374, 0.018671056255698204, -0.0007094241445884109, 0.020289234817028046, -0.0169456098228693, 0.06749244034290314, 0.005355315748602152, 0.05511915311217308, -0.03185609355568886, 0.01853671297430992, 0.054908350110054016, -0.0035753289703279734, -0.0207601860165596, -0.020054874941706657, -0.03488574177026749, 0.015222709625959396, 0.028937211260199547, 0.012584930285811424, -0.009605653584003448, -0.05729858577251434, 0.01908060722053051, 0.02684507519006729, -0.03493136167526245, -0.029163124039769173, 0.011659210547804832, -0.0022474604193121195, -0.016767259687185287, 0.10613081604242325, 0.0027053137309849262, -0.004701247904449701, 0.04069729521870613, 0.02519228123128414, 0.06179468333721161, 0.004123998805880547, 0.004018002189695835, -0.033228445798158646, 0.053787074983119965, -0.013349228538572788, 0.018651429563760757, 0.051388077437877655, 0.026732932776212692, 0.07447829842567444, -0.01995673030614853, 0.007199137005954981, 0.030789200216531754, 0.007647712714970112, 0.008397338911890984, -0.012931156903505325, -0.018038146197795868, -0.0552709735929966, 0.0057804398238658905, -0.0009293319890275598, 0.021879205480217934, 0.02149813249707222, 0.012189706787467003, -0.0029693301767110825, 0.02435978688299656, 0.02983824722468853, 0.023367827758193016, 0.07250324636697769, -0.04232630506157875, -0.042290523648262024, -0.007057346869260073, 0.05236542224884033, 0.08148113638162613, -0.056414324790239334, 0.0050012776628136635, 0.04457492753863335, 0.08343557268381119, -0.00013174225750844926, 0.02940065972507, 0.03511320427060127, 0.019134240224957466, 0.036297157406806946, 0.01974794827401638, -0.0755046159029007, 0.001229899120517075, -0.08092581480741501, -0.03749552369117737, -0.0031532731372863054, -0.009936177171766758, 0.08447986841201782, 0.025420166552066803, -0.017581073567271233, 0.02167154662311077, 0.007732297293841839, 0.060710035264492035, 0.006338919047266245, -0.042710740119218826, 0.025197135284543037, -0.07762456685304642, 0.03710388019680977, -0.001465749111957848, -0.043988097459077835, 0.02188614383339882, -0.03285130113363266, -0.01830746978521347, -0.010992748662829399, -0.030963227152824402, -0.024518705904483795, -0.0021635224111378193, 0.0069959345273673534, 0.01441474910825491, 0.008060899563133717, 0.10473208129405975, 0.00612452020868659, 0.02985895797610283, 0.05935639515519142, 0.014219111762940884, 0.07051713019609451, -0.06209000572562218, -0.010835202410817146, -0.040366753935813904, 0.034545984119176865, 0.006520324386656284, 0.02088042162358761, -0.010648233816027641, -0.018904130905866623, 0.034499261528253555, -0.027705295011401176, -0.011960424482822418, -0.057762403041124344, 0.0032179122790694237, 0.000012006440556433517, -0.024971676990389824, 0.0154265770688653, -0.03884526714682579, -0.04225480556488037, -0.04410682991147041, 0.002870181342586875, -0.022562319412827492, -0.0033158783335238695, -0.025168774649500847, 0.038488127291202545, -0.061220817267894745, -0.06625217944383621, -0.006256196182221174, 0.01306159794330597, -0.04916035756468773, 0.009095513261854649, 0.0029606821481138468, -0.046442028135061264, 0.030358338728547096, 0.073470838367939, 0.010293154045939445, 0.03288506343960762, 0.006602281704545021, -0.013161090202629566, 0.08132419735193253, -0.008725804276764393, -0.026223013177514076, -0.0048635876737535, 0.03787513077259064, 0.005101615563035011, -0.0064776185899972916, -0.024659685790538788, 0.030016010627150536, 0.0513862706720829, 0.03325976803898811, -0.07433044165372849, -0.0011558979749679565, -0.011096656322479248, -0.03628283739089966, 0.02256949432194233, 0.05444825813174248, 0.026788033545017242, -0.03903893753886223, -0.01680569164454937, -0.010573708452284336, 0.0009394730441272259, -0.019357750192284584, -0.002242518123239279, -0.07171865552663803, -0.0017357631586492062, -0.023579923436045647, -0.019016310572624207, -0.02116556651890278, 0.050021689385175705, -0.05085870623588562, -0.0272354818880558, -0.018290262669324875, 0.03923555091023445, -0.031079811975359917, 0.0028146731201559305, -0.047220028936862946, -0.006774139124900103, -0.035364922136068344, 0.02343391440808773, 0.010059273801743984, -0.001424718531779945, -0.06439730525016785, 0.026577267795801163, 0.03377982974052429, -0.11252205818891525, -0.04905390739440918, 0.04764479771256447, 0.02270917408168316, 0.02378794364631176, 0.015941426157951355, 0.015341543592512608, 0.055108167231082916, 0.06761814653873444, -0.04265959560871124, 0.016235942021012306, -0.02831280045211315, 0.006963139399886131, -0.0027324191760271788, 0.009444626048207283, 0.04969198256731033, -0.03910933434963226, 0.010102629661560059, 0.0667409747838974, 0.0028539381455630064, 0.013280230574309826, -0.046086084097623825, 0.030063571408391, 0.07060438394546509, -0.06014223396778107, -0.037964582443237305, 0.019895577803254128, 0.022360263392329216, -0.0007316912524402142, 0.01543821394443512, -0.0259675495326519, 0.007187449373304844, 0.022738024592399597, 0.017281457781791687, -0.025705859065055847, 0.03922855854034424, 0.07372802495956421, -0.00924322847276926, -0.00999247096478939, 0.09027538448572159, -0.01736372336745262, -0.0051948935724794865, -0.01683059148490429, -0.036785565316677094, -0.023027198389172554, -0.027450982481241226, -0.03621385991573334, 0.03820832818746567, 0.03564244508743286, 0.019673854112625122, -0.04518770053982735, -0.01381575409322977, -0.02253715880215168, 0.0338326059281826, 0.05966925248503685, 0.06083349138498306, -0.07561817020177841, 0.007580988574773073, 0.04167664423584938, 0.01054296549409628, 0.038011886179447174, -0.06005539745092392, -0.03927471116185188, 0.04435878247022629, -0.013802816160023212, 0.02217736467719078, -0.03311388939619064, 0.04339126870036125, -0.010863342322409153, 0.020608065649867058, -0.03653584420681, 0.0067674038000404835, -0.004784138407558203, 0.027952874079346657, -0.02910934016108513, -0.004497117828577757, -0.06822659820318222, 0.002812611171975732, -0.05772401764988899, -0.027620287612080574, -0.05908702313899994, 0.0267644040286541, -0.01529061608016491, 0.04691369831562042, 0.03321567922830582, 0.02092338353395462, 0.004380152095109224, -0.01098338607698679, -0.02814463898539543, -0.0028649787418544292, -0.07289929687976837, 0.030057435855269432, -0.013457751832902431, -0.015275130048394203, -0.0025455113500356674, 0.001900906558148563, 0.037327393889427185, 0.07838062942028046, 0.015949739143252373, 0.03602956235408783, 0.016646191477775574, 0.03265378251671791, -0.048094235360622406, 0.001703061512671411, -0.07460054755210876, 0.0018530742963775992, -0.05902008339762688, -0.024056874215602875, -0.09668850153684616, 0.0027791853062808514, 0.014738420955836773, -0.008448458276689053, -0.037347011268138885, -0.006442056968808174, -0.027973933145403862, 0.023371795192360878, 0.013165249489247799, 0.0059878709726035595, 0.011052722111344337, -0.023705312982201576, -0.05063765123486519, 0.018859466537833214, 0.000201168266357854, 0.0064085619524121284, -0.01030819583684206, 0.05345357954502106, 0.012037943117320538, -0.0013857504818588495, -0.009229768067598343, -0.02633095160126686, -0.056026022881269455, 0.022252744063735008, -0.022781267762184143, 0.02496173419058323, 0.00399430887773633, 0.01094161905348301, 0.054368309676647186, 0.057405173778533936, 0.04749947041273117, -0.036386292427778244, -0.009733566083014011, 0.008749507367610931, -0.02255631983280182, -0.008957725949585438, 0.012050336226820946, 0.042121101170778275, -0.04216685891151428, -0.028027895838022232, 0.01416107825934887, -0.09171202033758163, 0.014372174628078938, -0.041790757328271866, -0.005062812007963657, -0.01276257261633873, 0.029656950384378433, 0.013938927091658115, -0.0367647185921669, -0.0011590822832658887, -0.0628017708659172, 0.01798139698803425, 0.035801228135824203, -0.013786140829324722, -0.007756104692816734, -0.010684965178370476, -0.03198239952325821, -0.011921938508749008, -0.008381419815123081, 0.04282572865486145, -0.03696064651012421, -0.034315627068281174, 0.04705854505300522, -0.06183047592639923, 0.05773407220840454, -0.0055582704953849316, -0.03471319377422333, -0.00167785061057657, -0.0017957461532205343, 0.04128062352538109, 0.05462498962879181, 0.008335817605257034, -0.020710792392492294, -0.06564896553754807, -0.011539865285158157, -0.030321095138788223, 0.003797368612140417, -0.049867697060108185, -0.008987468667328358, -0.010906665585935116, 0.034622013568878174, -0.025956207886338234, 0.020697133615612984, -0.011562736704945564, -0.036922063678503036, -0.009936765767633915, -0.03284444659948349, -0.009140466339886189, 0.002035000128671527, 0.0021259142085909843, 0.03635202348232269, 0.048051998019218445, 0.04536416381597519, 0.00015786298899911344, 0.02411535568535328, 0.014365092851221561, 0.0002845521958079189, -0.04587263986468315, -0.07803192734718323, -0.006595937069505453, 0.05090830475091934, -0.030745672062039375, -0.05596398189663887, -0.018749067559838295, 0.0011048725573346019, -0.00040892866672948003, 0.01846984028816223, -0.005983027629554272, 0.010350148193538189, 0.048565082252025604, 0.009973498992621899, 0.012343869544565678, 0.03760906681418419, 0.009533840231597424, 0.03945152088999748, 0.009343447163701057, 0.043066009879112244, -0.02604840137064457, 0.010945886373519897, -0.0816553458571434, -0.000489814905449748, 0.07317259907722473, -0.056114546954631805, 0.006059601902961731, -0.025802744552493095, 0.0027738239150494337, -0.03282612934708595, 0.015415476635098457, 0.015725117176771164, 0.026304248720407486, 0.04712430760264397, -0.008987868204712868, 0.009211474098265171, -0.06792250275611877, 0.0064710285514593124, 0.034051213413476944, 0.05165687948465347, 0.06657788157463074, -0.0034776171669363976, 0.027815448120236397, -0.05215546488761902, 0.014965014532208443, -0.009880369529128075, 0.030458055436611176, 0.036719318479299545, 0.010452409274876118, -0.024482814595103264, 0.029387475922703743, -0.041340701282024384, 0.011296439915895462, 0.09654629230499268, 0.030095024034380913, -0.00795967597514391, -0.045346762984991074, 0.021758323535323143, -0.027942195534706116, 0.0021134205162525177, -0.05557499825954437, -0.003105390351265669, -0.03471968695521355, -0.003705187002196908, -0.03036665730178356, -0.01086298655718565, 0.027715206146240234, -0.03738763555884361, 0.01531263068318367, -0.04193035885691643, -0.012056761421263218, 0.003386255819350481, 0.010340232402086258, 0.010439503937959671, -0.05139336735010147, -0.02556624636054039, -0.014837410300970078, -0.032641030848026276, 0.07972025871276855, 0.053344592452049255, -0.05352556332945824, 0.03946246951818466, -0.026174310594797134, -0.01670566201210022, 0.04216224327683449, -0.03201516717672348, -0.02419016882777214, -0.005384246818721294, -0.0041419812478125095, -0.04046761989593506, -0.028074920177459717, -0.006959598045796156, 0.07436501234769821, -0.05501701310276985, 0.003198430174961686, -0.03549526259303093, -0.06568789482116699, 0.04743927717208862, -0.02329518459737301, 0.001540087047033012, 0.011197266168892384, 0.0394279770553112, -0.0439002625644207, -0.05414186418056488, -0.055084481835365295, 0.05539987236261368, -0.003980199806392193, -0.0026993146166205406, -0.049726780503988266, -0.025252193212509155, -0.026313740760087967, -0.03373841941356659, 0.04200305789709091, 0.04493888467550278, -0.03624442592263222, 0.01334415003657341, -0.08546064049005508, 0.04296331852674484, 0.07042956352233887, -0.017705600708723068, -0.012169093824923038, -0.01534858625382185, -0.04389716312289238, -0.018685968592762947, -0.04908222705125809, 0.06820158660411835, -0.046925514936447144, -0.04624742642045021, 0.020049944519996643, -0.010661114938557148, 0.008855757303535938, -0.03324249014258385, -0.024997606873512268, -0.06216677278280258, 0.0001049518832587637, 0.06284088641405106, -0.007774481549859047, -0.009576168842613697, 0.009999146685004234, 0.06616407632827759, 0.05308281630277634, -0.014133650809526443, 0.026589062064886093, -0.007479616906493902, 0.03299617022275925, 0.02394730970263481, -0.03920024633407593, 0.0254290122538805, 0.009824102744460106, -0.04062359780073166, 0.019087404012680054, -0.008946464397013187, 0.03396976366639137, 0.03412587195634842, -0.019684746861457825, 0.021264778450131416, 0.029902029782533646, 0.009137958288192749, -0.035696856677532196, 0.007041355594992638, 0.05187716707587242, -0.043355219066143036, -0.04491208493709564, 0.007806719280779362, -0.0018012231448665261, -0.04093826189637184, -0.047116752713918686, 0.020756658166646957, -0.04653778299689293, -0.02960469201207161, -0.000006468608717113966, -0.027471795678138733, 0.021912626922130585, -0.0357484333217144, -0.016717946156859398, 0.012068048119544983, 0.022314557805657387, -0.026988254860043526, -0.04394659399986267, -0.007752722129225731, 0.0010380682069808245, -0.04610789567232132, -0.05568303167819977, -0.032491207122802734, -0.08135934174060822, -0.090750552713871, 0.024420524016022682, 0.07138525694608688, -0.02095416747033596, -0.01985320821404457, 0.030536416918039322, 0.019390815868973732, -0.013523374684154987, 0.018125802278518677, 0.010016095824539661, 0.023629212751984596, 0.03904730826616287, 0.02661643736064434, 0.013365605846047401, -0.028451401740312576, -0.00378886959515512, 0.09115537256002426, -0.03474602475762367, -0.005299802403897047, -0.03384154289960861, 0.016277534887194633, 0.04396998882293701, 0.03009815886616707, -0.01744944229722023, -0.03581826016306877, 0.007603351026773453, 0.02121717669069767, -0.021699145436286926, 0.027464885264635086, 0.006989060435444117, 0.022769425064325333, 0.00027615748695097864, -0.0018239951459690928, -0.04763679578900337, 0.004727688618004322, 0.04324684664607048, 0.0051240320317447186, -0.037067946046590805, -0.007347750011831522, -0.03430052101612091, -0.08751809597015381, -0.008731997571885586, 0.003120743203908205, 0.0749642550945282, 0.010970883071422577, 0.0020751513075083494, -0.007871143519878387, -0.011416693218052387, 0.01601884327828884, 0.007335982751101255, -0.028815580531954765, -0.01788434013724327, -0.02080908976495266, -0.05647685378789902, 0.03821628540754318, 0.042401645332574844, -0.015433450229465961, -0.048184845596551895, 0.05517280474305153, 0.03557466343045235, -0.01764369197189808, 0.02326221577823162, 0.039387047290802, -0.001554058981128037, 0.007865002378821373, -0.02846931479871273, -0.027838530018925667, 0.009913242422044277, -0.09291646629571915, 0.015070398338139057, -0.014948476105928421, -0.016079766675829887, 0.04862171784043312, 0.045124977827072144, -0.01724211499094963, 0.00567708071321249, -0.0071202609688043594, -0.022345058619976044, -0.009111186489462852, 0.03136645630002022, -0.019072091206908226, -0.03183383494615555, -0.015854444354772568, 0.0037025725468993187, 0.048741452395915985, -0.019970232620835304, 0.04013896733522415, 0.00013869846588931978, -0.02757423371076584, -0.03660832345485687, 0.006313066463917494, 0.0729503408074379, -0.01136079616844654 ]
<p><a href="http://physics.stackexchange.com/questions/80773/the-example-of-relativity-of-simultaneity-given-by-einstein/80776#80776">This answer</a> to a recent question related to <a href="http://archive.org/details/relativitythespe00einsuoft#chapters.8.and.9" rel="nofollow">Einstein's thought-experimental definition of (how to determine) simultaneity</a> contained the following statement:</p> <blockquote>Suppose two people, $C$ and $D$, stand equal distances from you and are known to pitch balls at exactly the same speed. With everyone standing at rest, $C$ and $D$ each toss you a ball. You get the ball from $C$ *before* the one from $D$. This is not a logical inconsistency. It simply means $C$ threw a ball *before* $D$ <b>in your reference frame</b> [emphasis added].</blockquote> <p>I believe that I understand the described setup and the conclusion ("<i>It simply means $C$ threw a ball <em>before</em> $D$</i>") as such. But I question whether it is necessary to add the qualification "<i>in your reference frame</i>".</p> <p>Carefully applying Einstein's definition of (how to determine) simultaneity, as referenced above, which for the given setup involves a suitable observer "<i>at the midpoint between</i> $C$ and $D$", is there even any reference frame at all (necessarily other than "<i>your reference frame</i>") "in which" $C$ threw a ball &ast;simultaneous to&ast; $D$ throwing a ball ?</p> <p>Or is there even any reference frame at all (again necessarily other than "<i>your reference frame</i>") "in which" $C$ threw a ball &ast;after&ast; $D$ ?</p> <p>(If there are no such reference frames, then the qualification "<i>in your reference frame</i>" is apparently not necessary; and, indeed, it would seem inappropriate and misleading to add such a qualification as if it were necessary.) </p>
g8379
[ 0.04302186518907547, 0.025712396949529648, 0.02268039993941784, -0.034755025058984756, 0.03739086911082268, 0.006057047750800848, 0.086216501891613, 0.05506151169538498, -0.02995309606194496, -0.0025868993252515793, -0.04094306379556656, -0.02473132498562336, -0.002307346323505044, 0.008639613166451454, -0.011511136777698994, -0.07853464037179947, 0.0770750492811203, -0.04812481999397278, 0.0037000011652708054, 0.018533021211624146, 0.011325919069349766, 0.024634074419736862, 0.013198754750192165, 0.0006009983480907977, 0.002695053117349744, -0.03846890106797218, -0.006552401930093765, -0.05931027978658676, -0.05858409404754639, -0.013573948293924332, 0.018986281007528305, -0.003441897453740239, 0.02295336313545704, -0.00009638748451834545, 0.039536330848932266, -0.02825317531824112, 0.027392538264393806, 0.020427081733942032, -0.03258892521262169, -0.006682604551315308, 0.019246365875005722, 0.04209091514348984, 0.004418180789798498, -0.05815369263291359, -0.026575220748782158, 0.05794809013605118, 0.008360136300325394, 0.037707094103097916, -0.024553317576646805, -0.09016895294189453, 0.03137953579425812, 0.03793904930353165, 0.019548963755369186, 0.007406033109873533, -0.010016968473792076, 0.036660466343164444, -0.019409140571951866, 0.0028386933263391256, 0.030088288709521294, 0.01701735332608223, 0.009047496132552624, 0.0074472250416874886, -0.01827295869588852, -0.039447542279958725, 0.04340411350131035, 0.008629093877971172, -0.04813729599118233, 0.03103947639465332, -0.029248151928186417, -0.043180663138628006, 0.014591465704143047, -0.042918212711811066, 0.031001294031739235, 0.022565145045518875, -0.035746995359659195, 0.009658378548920155, -0.003327722894027829, -0.031068313866853714, 0.028589539229869843, 0.05488286539912224, 0.022938398644328117, -0.03942972049117088, 0.07452011853456497, 0.024655191227793694, 0.028644206002354622, 0.013698572292923927, 0.009542190469801426, -0.014905530028045177, -0.01005745679140091, 0.0121875936165452, 0.005801738239824772, -0.03288805112242699, 0.06213502958416939, 0.050946712493896484, -0.04762355238199234, -0.029047394171357155, -0.08164887875318527, 0.04812514781951904, 0.028294265270233154, 0.033087752759456635, -0.05007864907383919, 0.04987486079335213, -0.022678354755043983, 0.006294368300586939, -0.003515401156619191, 0.0054969945922493935, 0.05998237431049347, 0.03527888283133507, -0.024191005155444145, -0.07711376994848251, -0.04998316988348961, -0.030794406309723854, -0.021612467244267464, 0.014869698323309422, -0.09615343064069748, -0.05398043245077133, 0.04701540246605873, -0.027333291247487068, -0.022355565801262856, 0.050932273268699646, 0.0018744927365332842, 0.037467725574970245, 0.009430380538105965, 0.02628464438021183, -0.0483689047396183, 0.03332693502306938, -0.00044643835281021893, -0.0017584416782483459, 0.05256619676947594, -0.013644746504724026, 0.0007424126961268485, -0.005135978106409311, 0.04033307731151581, -0.0041591208428144455, -0.0700543001294136, 0.026547739282250404, 0.06375010311603546, -0.07215947657823563, -0.025125712156295776, 0.05340586230158806, -0.00210298178717494, 0.01898588240146637, -0.004627765156328678, -0.07726682722568512, -0.011928826570510864, 0.04063832759857178, -0.04608112573623657, 0.007722831796854734, 0.029362168163061142, 0.06039838120341301, 0.028754649683833122, 0.03747990354895592, -0.03423890098929405, -0.016372475773096085, 0.02354794181883335, -0.005224062129855156, -0.011775107122957706, 0.028343327343463898, -0.015156623907387257, -0.01036352850496769, 0.05451386049389839, -0.006173811852931976, -0.06101164594292641, -0.007547486107796431, 0.002972239628434181, 0.03131701424717903, -0.0366005040705204, -0.019434519112110138, -0.03561883419752121, -0.08326071500778198, -0.012343239039182663, -0.030181996524333954, 0.0700821653008461, -0.04118017479777336, 0.013767513446509838, 0.03384369611740112, 0.032508183270692825, -0.0496673658490181, -0.03523191809654236, 0.0012751793256029487, -0.01197402086108923, 0.01558711938560009, -0.0029095117934048176, -0.04112538695335388, -0.04860592260956764, -0.042152177542448044, 0.04132798686623573, 0.0001711894292384386, -0.03135765716433525, 0.01584358513355255, -0.038492120802402496, -0.0007739276043139398, -0.007879301905632019, 0.027531955391168594, -0.000968947249930352, 0.004957674536854029, 0.05012280121445656, 0.005620961077511311, -0.044947490096092224, 0.04447028413414955, -0.05349133536219597, 0.03253548964858055, -0.024622151628136635, 0.011448550038039684, -0.0525808110833168, 0.05470519885420799, 0.0174351055175066, 0.0027845066506415606, 0.014232255518436432, 0.017322149127721786, 0.023073706775903702, 0.0015453819651156664, 0.013862935826182365, -0.022333238273859024, -0.004437490366399288, 0.006791950669139624, 0.038655977696180344, -0.02277405560016632, -0.04754147306084633, 0.04670465365052223, -0.03128163889050484, 0.005701696500182152, 0.020623797550797462, -0.04025818407535553, -0.012792747467756271, -0.01707863248884678, -0.023194316774606705, 0.018257837742567062, -0.01699727773666382, 0.06000952422618866, -0.03075864352285862, -0.007322715595364571, -0.06373525410890579, -0.007522661704570055, 0.034078482538461685, 0.01999855600297451, 0.03296894580125809, 0.00017083142301999032, 0.016215508803725243, 0.06197775527834892, 0.004643291234970093, 0.017186205834150314, -0.04504663869738579, 0.02924375981092453, 0.011633563786745071, -0.043942227959632874, 0.08234298229217529, -0.04822886735200882, -0.015267636626958847, 0.0034586945548653603, -0.020869620144367218, -0.03399665281176567, -0.02088763751089573, -0.01955992914736271, -0.0015025435714051127, -0.04244603216648102, 0.006824676413089037, 0.04480290040373802, -0.07963453978300095, 0.03537820652127266, 0.03774339333176613, -0.09567759931087494, 0.019377637654542923, 0.019490351900458336, -0.009641481563448906, 0.031012972816824913, 0.0036695702001452446, 0.04378603771328926, -0.05296144261956215, -0.022637177258729935, -0.0234683807939291, 0.04284517094492912, 0.044621750712394714, 0.060150038450956345, -0.01829514093697071, -0.0023775489535182714, -0.015376714989542961, 0.02136603370308876, 0.06899315118789673, 0.009537731297314167, 0.01953291706740856, 0.04673617705702782, -0.07397273927927017, -0.019771946594119072, 0.04503200575709343, -0.022861503064632416, 0.021921047940850258, -0.020682012662291527, 0.0035627451725304127, -0.010982153005897999, -0.014839054085314274, 0.08834929019212723, 0.01716494746506214, 0.03532356768846512, 0.024932781234383583, 0.10674937814474106, -0.02624739706516266, -0.011390721425414085, -0.006911943666636944, 0.023787226527929306, 0.031472355127334595, 0.0008958537364378572, -0.018242180347442627, -0.02086479961872101, 0.050130341202020645, 0.002631488721817732, -0.032574113458395004, -0.0452590212225914, -0.006387163419276476, -0.01910071261227131, -0.03406606987118721, 0.03514667972922325, -0.008038880303502083, -0.01532378513365984, -0.013821322470903397, 0.05419618636369705, -0.025309551507234573, 0.0036414589267224073, -0.020738879218697548, -0.018290219828486443, 0.025326374918222427, 0.06460210680961609, -0.0147465905174613, -0.02189379371702671, 0.034289535135030746, 0.07900433987379074, 0.01620907336473465, -0.06865084171295166, -0.07246023416519165, -0.014564258977770805, -0.007111135870218277, -0.01358824409544468, 0.012964415363967419, -0.008936290629208088, 0.007459839340299368, -0.05470959469676018, -0.04135473817586899, -0.020059997215867043, 0.015173821710050106, 0.0399189367890358, 0.041198745369911194, 0.043619830161333084, -0.028464851900935173, 0.026195049285888672, 0.00045900538680143654, 0.03075459413230419, 0.01221557054668665, 0.03690401092171669, 0.017939263954758644, -0.02057177573442459, 0.03974540904164314, 0.023692509159445763, -0.04208318889141083, -0.010934834368526936, -0.022631440311670303, 0.049132704734802246, 0.018740925937891006, 0.021881453692913055, -0.05076703056693077, -0.012476763688027859, 0.02132132463157177, 0.03434152901172638, 0.03803066536784172, 0.041133999824523926, 0.08185971528291702, 0.0035837048199027777, -0.034452419728040695, 0.056412503123283386, 0.011285540647804737, -0.0017147482139989734, -0.03468041121959686, -0.028105273842811584, -0.024799225851893425, -0.015237369574606419, 0.030849043279886246, -0.048921745270490646, 0.08336339145898819, 0.03101944737136364, -0.04749298095703125, -0.013428254052996635, 0.0372718945145607, 0.02059430442750454, -0.01796039193868637, 0.0060514770448207855, 0.05530478432774544, -0.0009923401521518826, -0.0304418858140707, 0.002409188076853752, 0.02473345957696438, -0.011572422459721565, -0.02972433716058731, -0.03268028050661087, -0.05835060030221939, -0.03471468761563301, 0.05919407680630684, 0.04485051706433296, 0.02117205411195755, -0.05230361968278885, 0.004286196082830429, 0.08651678264141083, -0.02800665609538555, 0.01890536956489086, -0.0010292601073160768, -0.027535008266568184, -0.06670200079679489, -0.03652667999267578, 0.0017266684444621205, -0.041277386248111725, -0.0017855822807177901, 0.027667120099067688, 0.011163732968270779, -0.019586510956287384, -0.05403361842036247, -0.0677073523402214, 0.024803433567285538, -0.0001328557264059782, 0.01189991645514965, 0.03192268684506416, 0.03401873633265495, 0.04186205193400383, 0.019620945677161217, 0.02663261815905571, 0.07375597953796387, -0.058205496519804, 0.057408642023801804, 0.09837733209133148, -0.002755102701485157, -0.0047852653078734875, -0.035042669624090195, -0.030018113553524017, 0.0194320697337389, 0.0338839553296566, -0.018968433141708374, 0.017222275957465172, -0.015128062106668949, 0.027745457366108894, -0.015231345780193806, 0.04518257454037666, 0.03835613653063774, -0.011089780367910862, 0.0058499290607869625, -0.03797636181116104, 0.03288159519433975, -0.05871066823601723, -0.019016018137335777, 0.03148666024208069, -0.0807734876871109, -0.040780603885650635, -0.00912738312035799, -0.016245203092694283, -0.010972929187119007, 0.07796113938093185, 0.027651077136397362, -0.0044487593695521355, 0.00220314459875226, -0.008842349983751774, -0.028222784399986267, -0.008220055140554905, -0.020402714610099792, -0.05233168974518776, 0.0009654734749346972, -0.003623803611844778, 0.025921260938048363, -0.01501929946243763, 0.041917651891708374, 0.058747656643390656, -0.00817442312836647, -0.05562707781791687, -0.013131468556821346, -0.04300684109330177, -0.010099183768033981, -0.04876815900206566, -0.011991314589977264, -0.023852985352277756, 0.008390955626964569, 0.0557519793510437, 0.03255549073219299, -0.02967291884124279, -0.005140673369169235, -0.058828167617321014, -0.04931241646409035, -0.009288421832025051, 0.0005229834350757301, -0.006561717484146357, 0.053264155983924866, 0.00896163284778595, 0.03632654622197151, -0.006222973112016916, 0.027088956907391548, 0.019443130120635033, 0.029480651021003723, -0.014306214638054371, -0.016885166987776756, 0.02076973393559456, -0.07551640272140503, -0.021345574408769608, 0.027325395494699478, -0.009433766826987267, -0.03965359181165695, 0.020420188084244728, -0.0819278359413147, 0.08166626840829849, 0.04090569540858269, 0.014952014200389385, -0.0753096267580986, 0.008733323775231838, 0.010017648339271545, 0.02041870914399624, -0.001245728344656527, 0.03732678294181824, -0.005147719755768776, 0.04260668158531189, -0.05507012456655502, -0.007697539869695902, -0.009007571265101433, -0.02833392471075058, 0.0761592835187912, -0.08331720530986786, 0.0042212908156216145, -0.10544714331626892, -0.015701986849308014, 0.0007272898801602423, -0.01563888043165207, -0.02781672775745392, -0.05663566663861275, 0.004985715262591839, -0.0488787442445755, 0.022058896720409393, -0.015627413988113403, 0.026668082922697067, -0.021656183525919914, -0.015521258115768433, -0.0267309732735157, -0.015451938845217228, -0.0008171908557415009, 0.005980865564197302, -0.029397794976830482, -0.06156884878873825, 0.003999756183475256, -0.005214937496930361, -0.06701730936765671, 0.016495374962687492, 0.010942718014121056, 0.020959828048944473, 0.0029707076027989388, -0.049597278237342834, 0.028232820332050323, 0.01630502939224243, 0.08300945907831192, -0.06777284294366837, -0.01367467176169157, 0.0738288015127182, 0.031999845057725906, 0.06472941488027573, 0.032084040343761444, 0.05349447950720787, -0.013438316993415356, -0.017970776185393333, 0.01559500303119421, -0.02368817664682865, -0.07156622409820557, -0.03516273573040962, 0.01734788902103901, -0.012631195597350597, -0.010453092865645885, -0.019965654239058495, 0.013823885470628738, -0.004760901443660259, -0.005870805587619543, -0.00590638630092144, 0.006979396566748619, -0.06407365947961807, 0.021221105009317398, -0.011770106852054596, -0.00723247742280364, -0.009620449505746365, -0.021060870960354805, 0.028260914608836174, -0.05510465055704117, -0.0038557422813028097, -0.004277672152966261, -0.008108221925795078, 0.07114282995462418, 0.028929319232702255, -0.0021668104454874992, -0.0018811910413205624, -0.018589530140161514, 0.007343453820794821, -0.04187102988362312, -0.06706216186285019, -0.022937247529625893, -0.02403673529624939, -0.006204600911587477, -0.01885147951543331, -0.007757646031677723, 0.003813914256170392, 0.024914871901273727, 0.010659129358828068, -0.055779408663511276, 0.04632014408707619, -0.033789996057748795, -0.005434618331491947, 0.014378703199326992, -0.051444657146930695, -0.010090752504765987, 0.03401144966483116, -0.029948972165584564, -0.031223922967910767, -0.015521183609962463, 0.007587643805891275, -0.0014825958060100675, 0.02286248840391636, 0.04266903176903725, 0.06843790411949158, -0.052878689020872116, -0.021551407873630524, 0.0235765241086483, -0.02540215477347374, -0.018944723531603813, -0.057670727372169495, 0.06982250511646271, -0.018045587465167046, 0.03892053663730621, 0.00030404177960008383, 0.04667770862579346, 0.0021682444494217634, -0.02973625436425209, 0.0016961820656433702, 0.034287188202142715, -0.024718616157770157, 0.01612330600619316, -0.013606294058263302, -0.06137422099709511, 0.049214962869882584, -0.009883671067655087, 0.00010019329783972353, 0.05693690478801727, 0.03554657846689224, 0.012687738053500652, 0.02697131037712097, -0.004791744519025087, 0.037346579134464264, -0.002356557175517082, -0.004812433384358883, -0.013810541480779648, -0.014783215709030628, 0.07248505204916, -0.00350250955671072, -0.051977720111608505, -0.012792328372597694, 0.023646323010325432, -0.019158845767378807, -0.012344345450401306, 0.023665769025683403, -0.059276651591062546, -0.007180031388998032, 0.007458830252289772, 0.015777265653014183, 0.009117242880165577, -0.0925808846950531, -0.0157249104231596, -0.03422798961400986, -0.09839575737714767, -0.01347906794399023, -0.09456521272659302, 0.03889793902635574, 0.011326942592859268, -0.07890474051237106, 0.027684103697538376, 0.05423751100897789, 0.09052719920873642, -0.007882308214902878, -0.06439293175935745, 0.022144967690110207, -0.015514669939875603, -0.01553365308791399, -0.00012698560021817684, 0.02152096852660179, -0.012888768687844276, -0.034604575484991074, 0.014704792760312557, 0.055518604815006256, 0.0081951217725873, -0.04850774630904198, -0.06872081011533737, 0.01421058364212513, 0.05839414894580841, -0.04323134943842888, 0.024351174011826515, -0.004921414889395237, -0.01643468625843525, 0.015162592753767967, 0.05200166255235672, -0.04436152055859566, -0.03341928869485855, -0.041074518114328384, 0.06485532224178314, -0.017173996195197105, 0.00905646476894617, -0.005899292882531881, -0.01006676722317934, -0.010887335985898972, 0.01135092694312334, 0.01595870964229107, 0.0035263365134596825, 0.023886680603027344, -0.007222096435725689, 0.03522703796625137, -0.01010765042155981, 0.02559008076786995, 0.008492628112435341, 0.009438034147024155, 0.010048480704426765, -0.014467164874076843, -0.06639104336500168, -0.003760349005460739, -0.05764690041542053, 0.0030890884809195995, 0.0777418464422226, -0.029118649661540985, -0.012081686407327652, 0.008986742235720158, 0.03004090115427971, -0.02373674139380455, 0.004940434359014034, -0.011782804504036903, 0.03706921264529228, 0.0057450863532722, -0.019297990947961807, -0.014980441890656948, -0.017371974885463715, -0.03972631320357323, -0.01541114877909422, 0.07094038277864456, 0.021326839923858643, 0.05279511585831642, 0.005779769737273455, -0.01690700463950634, 0.001858663628809154, 0.01948673650622368, -0.003932894207537174, -0.01800563745200634, -0.030826931819319725, 0.004229732323437929, 0.033946022391319275, -0.05167883262038231, 0.028071029111742973, 0.04979056119918823, 0.03548048436641693, -0.019541073590517044, -0.060963794589042664, 0.016247546300292015, 0.006504606455564499, 0.021761704236268997, 0.05790760740637779, 0.007354662753641605, 0.0024684688542038202, -0.019811544567346573, 0.06310763210058212, 0.028529351577162743, -0.01607651822268963, 0.023032890632748604, 0.0470367930829525, 0.01560487411916256, -0.04560738056898117, -0.03013959713280201, 0.011581559665501118, 0.03147948533296585 ]
<p>This is quite embarrassing to ask, but I haven't done a fluid flow calculation in a very long time and when you don't use it, you lose it!</p> <p>I have a natural gas pipeline that I want to purge of air with natural gas. It's a 3" and 4" line totalling about 6,600 feet. I'll be injecting natural gas into the line through a 2" hose with a pressure of 15 psi and the outlet will be another 2" hose at the other end.</p> <p>My question is: How long will it take to push all of the air out of the pipe and fill it with natural gas (purge the line of air)?</p> <p>I've spent the last few hours Googling fluid flow questions and answers and just can't figure it out. Thanks in advance!</p>
g8380
[ 0.03937314450740814, 0.028086591511964798, -0.005419446155428886, 0.012732678093016148, -0.06311961263418198, -0.021245889365673065, 0.008934654295444489, 0.03581605851650238, -0.08821961283683777, -0.005014390219002962, -0.01229375135153532, 0.017004692927002907, -0.008583365008234978, -0.05539606884121895, 0.0520099475979805, 0.005955822300165892, 0.02384643442928791, -0.032263655215501785, 0.05853380635380745, -0.016605354845523834, -0.02624596655368805, 0.002787425182759762, 0.041703712195158005, -0.09197277575731277, -0.009935090318322182, -0.047842059284448624, 0.006804062519222498, 0.019454320892691612, -0.06279745697975159, 0.004881986416876316, -0.0022903415374457836, 0.08430565148591995, -0.019662775099277496, -0.021386217325925827, -0.07344484329223633, -0.011007522232830524, 0.02570151537656784, -0.021076297387480736, -0.02128353714942932, -0.11514601111412048, 0.008847014047205448, -0.001962601440027356, 0.0023104045540094376, 0.0167829729616642, 0.03027806058526039, -0.023151518777012825, -0.024764634668827057, 0.015790367498993874, -0.023050107061862946, -0.06394308060407639, -0.03228634223341942, 0.002776125445961952, -0.07497179508209229, -0.0294257290661335, -0.050397422164678574, 0.027886809781193733, 0.015565017238259315, -0.017249615862965584, -0.011185716837644577, -0.009424288757145405, -0.03835980221629143, -0.04240770265460014, -0.027780968695878983, -0.012650633230805397, -0.045435842126607895, 0.020937932655215263, -0.009249217808246613, -0.03772463649511337, 0.04380076006054878, 0.07442572712898254, -0.0022825265768915415, -0.029470205307006836, 0.09947898983955383, -0.07693196833133698, -0.01594473421573639, -0.005129398312419653, -0.0071649146266281605, -0.005769755691289902, 0.015140942297875881, -0.016332322731614113, 0.022805437445640564, 0.028124550357460976, -0.009547303430736065, 0.014048948884010315, 0.012599813751876354, -0.00847646128386259, 0.015051817521452904, -0.013344209641218185, 0.04536988586187363, -0.0026744550559669733, -0.0640791729092598, -0.004493263084441423, 0.009494946338236332, 0.0061898017302155495, 0.02132738195359707, -0.01751992478966713, -0.03246739134192467, -0.021675467491149902, -0.03944754973053932, -0.009996755048632622, -0.00047830695984885097, -0.009566018357872963, 0.00007346804341068491, -0.05179623141884804, -0.039129965007305145, -0.03830184042453766, 0.04627244547009468, 0.08501394838094711, -0.03444153442978859, -0.014828206971287727, 0.007411142345517874, 0.0003109983808826655, -0.052036769688129425, 0.029616616666316986, -0.02420775592327118, -0.010919805616140366, -0.005862186197191477, 0.006985495798289776, 0.015066542662680149, 0.030838090926408768, 0.08149607479572296, 0.04811345785856247, 0.015992989763617516, -0.05889935418963432, 0.0016331537626683712, -0.06949353963136673, 0.04037412256002426, 0.027341898530721664, 0.08334901183843613, 0.014146228320896626, -0.04009430855512619, -0.011906484141945839, -0.027635054662823677, 0.01052908319979906, 0.01147762592881918, -0.04256596788764, -0.002125486033037305, 0.035765040665864944, -0.00514858216047287, 0.030070023611187935, 0.06380466371774673, -0.031893786042928696, 0.019000636413693428, 0.009526471607387066, -0.014927998185157776, 0.015034676529467106, 0.013465670868754387, 0.0034935877192765474, -0.007715177722275257, -0.04176972806453705, 0.023836098611354828, 0.02478913776576519, -0.010889287106692791, -0.049174342304468155, 0.026010774075984955, 0.016443150117993355, 0.011686994694173336, -0.00187288923189044, 0.042943086475133896, -0.0063752681016922, -0.02524346485733986, -0.0007672356441617012, 0.03164868429303169, 0.0024417678359895945, -0.06609798967838287, 0.018374724313616753, -0.0286480113863945, -0.045662976801395416, 0.0692664384841919, -0.010059669613838196, -0.054085396230220795, 0.018727878108620644, -0.01410954724997282, 0.04431706666946411, -0.0010484181111678481, -0.019161144271492958, 0.06045273691415787, -0.0008369881543330848, -0.03475795313715935, 0.015928620472550392, 0.006138884462416172, -0.014720166102051735, -0.015096576884388924, -0.017024120315909386, -0.006787851918488741, 0.02334665320813656, -0.00264045805670321, 0.010403146967291832, -0.031138934195041656, -0.04279550164937973, 0.06637991964817047, 0.03998531028628349, -0.004438730422407389, 0.04696314036846161, -0.004048740025609732, 0.007732080761343241, 0.048095379024744034, -0.08466939628124237, -0.060984667390584946, -0.04680170491337776, 0.009364989586174488, -0.038395367562770844, 0.0601644292473793, 0.0027609283570200205, 0.03573297709226608, 0.015085569582879543, 0.015286529436707497, 0.00589111540466547, 0.006868402007967234, 0.055760566145181656, 0.013047938235104084, 0.024546118453145027, 0.08501116931438446, 0.06718684732913971, 0.017670970410108566, -0.011539673432707787, -0.009641153737902641, 0.028788963332772255, -0.042513757944107056, 0.03546619787812233, -0.017511287704110146, 0.010484806261956692, -0.007273009512573481, -0.03425874933600426, -0.03660796582698822, -0.003117647720500827, 0.04191106557846069, 0.009895644150674343, -0.037225086241960526, -0.08701828122138977, 0.00800510123372078, 0.0242677703499794, 0.020680304616689682, -0.015797937288880348, 0.029712380841374397, 0.0054600122384727, 0.014557958580553532, 0.018174780532717705, 0.006691919174045324, 0.00012365936709102243, -0.0019622112158685923, -0.0009113049018196762, -0.0193561390042305, 0.08624690026044846, 0.02233901061117649, -0.04753759875893593, 0.03447704389691353, -0.06282173097133636, -0.004769051447510719, 0.003152617486193776, -0.06143786385655403, 0.013061863370239735, 0.027126498520374298, 0.04226723313331604, -0.01625899225473404, 0.06294388324022293, 0.03872301056981087, 0.051777131855487823, -0.03075927309691906, -0.053817007690668106, -0.04275451600551605, 0.0071729314513504505, -0.031256746500730515, 0.019635312259197235, -0.07358567416667938, 0.0002457103691995144, -0.036929287016391754, 0.036031872034072876, 0.0514475554227829, 0.044977378100156784, 0.037279561161994934, -0.015251314267516136, -0.0035516570787876844, 0.017101168632507324, 0.0038931930903345346, -0.02343328297138214, -0.011704589240252972, -0.01895935647189617, 0.010171275585889816, 0.03128330409526825, -0.005373276770114899, -0.014035684056580067, -0.08057853579521179, 0.10814591497182846, 0.020364578813314438, -0.01945846527814865, 0.023489385843276978, 0.022799674421548843, 0.0065528699196875095, -0.0015229627024382353, 0.009667287580668926, 0.022702014073729515, -0.019908687099814415, 0.014217202551662922, 0.0264417827129364, 0.004396236035972834, 0.02443252131342888, 0.004004402551800013, 0.0088198222219944, -0.010865969583392143, -0.028571968898177147, -0.08920597285032272, -0.05949384346604347, -0.034913819283246994, -0.03219316527247429, -0.04467608779668808, -0.035916768014431, -0.039521150290966034, -0.018773328512907028, 0.0020443026442080736, 0.02016766555607319, -0.012610387988388538, 0.018656697124242783, -0.0005750973359681666, 0.010496147908270359, -0.029442043974995613, -0.01591375283896923, 0.014780045486986637, 0.006917005870491266, 0.07593923807144165, -0.008258748799562454, -0.07740384340286255, -0.027233663946390152, 0.034730467945337296, 0.013510992750525475, -0.053449057042598724, -0.015622607432305813, -0.03198573738336563, -0.037923507392406464, -0.03672897815704346, 0.00429827906191349, 0.06304148584604263, -0.06776143610477448, 0.010864063166081905, 0.010689478367567062, 0.03175361081957817, -0.021146336570382118, 0.03453490883111954, -0.008214093744754791, -0.010671012103557587, 0.008886588737368584, 0.004237880930304527, -0.029882147908210754, 0.0019055884331464767, 0.025377457961440086, -0.04270918667316437, 0.03509242832660675, 0.02835163101553917, -0.008101989515125751, 0.022577539086341858, 0.059522490948438644, -0.007489820942282677, 0.06106693670153618, -0.06032561883330345, -0.0488518588244915, -0.027889026328921318, 0.022214042022824287, 0.03551095351576805, -0.00560563150793314, -0.01776071824133396, 0.057229943573474884, -0.03463194891810417, 0.006705628242343664, 0.0829579085111618, -0.01683909259736538, -0.06459295004606247, 0.05163351446390152, 0.011054436676204205, -0.04216044396162033, -0.020237358286976814, -0.010908534750342369, -0.031237924471497536, -0.03127670660614967, 0.031679585576057434, -0.02835923247039318, -0.09801117330789566, 0.012012416496872902, 0.026288235560059547, 0.010013397783041, 0.06311070919036865, 0.009852004237473011, -0.002615477656945586, -0.0324537418782711, -0.016066739335656166, -0.04889750853180885, -0.02742568403482437, 0.008023863658308983, -0.00967208668589592, 0.08740267902612686, -0.052945900708436966, -0.068206287920475, -0.05727098882198334, -0.004836566746234894, -0.02246067486703396, 0.01107608899474144, -0.032221466302871704, -0.03115558624267578, 0.021227426826953888, -0.04872627183794975, 0.004465068690478802, -0.02894207462668419, -0.030509522184729576, 0.012294171378016472, 0.04728628322482109, 0.0027359139639884233, 0.030667176470160484, 0.05488389730453491, 0.012412948533892632, 0.05374704301357269, -0.02322673611342907, 0.009889923967421055, -0.005257639102637768, -0.030590739101171494, -0.018932709470391273, 0.0483870655298233, -0.049302175641059875, -0.03444446995854378, -0.020073726773262024, -0.019141895696520805, -0.00007582979742437601, 0.0333981066942215, -0.0006743344711139798, 0.023309901356697083, 0.008870531804859638, 0.009853812865912914, 0.02726645953953266, 0.006937963888049126, -0.017053762450814247, 0.04452246055006981, -0.03944401070475578, 0.029381366446614265, -0.0446658693253994, -0.005888673476874828, 0.010463499464094639, 0.02137703448534012, 0.04972971975803375, -0.014326163567602634, -0.0023099887184798717, 0.007045457139611244, 0.03381141275167465, 0.008540820330381393, -0.01308043859899044, 0.031384821981191635, 0.02765721082687378, 0.029553407803177834, -0.002046487759798765, 0.006062022875994444, -0.0034539750777184963, -0.046804625540971756, 0.01589556597173214, -0.023435069248080254, 0.00010629808821249753, 0.011794286780059338, -0.07414980232715607, -0.040097374469041824, 0.05360596626996994, -0.07248257845640182, 0.02248441055417061, -0.046324457973241806, -0.006061346270143986, -0.027272911742329597, 0.06118905544281006, 0.04572882130742073, -0.01384203415364027, 0.019334599375724792, -0.03907918184995651, 0.015906283631920815, 0.00011145370808662847, 0.03537566587328911, -0.05509781464934349, 0.010070464573800564, -0.057449474930763245, 0.08452600240707397, 0.025273604318499565, 0.009296806529164314, 0.03242616355419159, 0.015188775025308132, 0.07766513526439667, 0.07672729343175888, -0.03831659257411957, 0.010519673116505146, 0.0186977069824934, 0.0249747633934021, 0.08948972821235657, -0.01886172965168953, -0.0274122916162014, -0.014524322934448719, -0.019420558586716652, 0.03254319354891777, -0.002702893689274788, -0.06356112658977509, 0.048907823860645294, 0.006822978146374226, 0.017206599935889244, 0.010305550880730152, 0.02939714305102825, 0.06311099231243134, -0.04188842326402664, -0.0332755446434021, -0.02833230048418045, -0.031317196786403656, 0.021474920213222504, 0.011223988607525826, -0.044587548822164536, -0.05556100979447365, 0.06598897278308868, -0.01656968891620636, 0.005793342366814613, -0.038458481431007385, 0.034138210117816925, -0.007756328675895929, -0.01367142889648676, 0.021998990327119827, -0.0266115702688694, 0.030830126255750656, -0.0439857542514801, -0.0342651903629303, -0.056933190673589706, -0.02624400332570076, -0.012285325676202774, 0.051464807242155075, 0.025923360139131546, -0.006270017474889755, 0.04075034335255623, 0.0008255027350969613, 0.015384491533041, -0.05067990720272064, 0.05609868839383125, 0.033683083951473236, -0.027175532653927803, -0.0493808351457119, -0.02516833133995533, 0.005321217235177755, -0.007022546604275703, -0.008857857435941696, 0.04665243253111839, 0.04991273581981659, -0.009946527890861034, 0.04505156725645065, -0.037344176322221756, -0.01704534702003002, -0.0011727132368832827, -0.025332840159535408, 0.01346496120095253, -0.002672206610441208, 0.0308037418872118, 0.013190974481403828, -0.02234596200287342, 0.02340693213045597, 0.005832004826515913, -0.006766313686966896, -0.0003194321470800787, -0.014491165988147259, 0.0033778403885662556, 0.0008139904821291566, 0.003664847696200013, 0.05650319904088974, 0.0020791522692888975, 0.025072505697607994, -0.03773050382733345, -0.035205770283937454, -0.033851053565740585, -0.025597117841243744, 0.01476648636162281, -0.0070473733358085155, -0.004111913498491049, -0.020160933956503868, 0.03677656501531601, 0.017576230689883232, 0.04873448610305786, 0.03270545229315758, -0.03649148344993591, -0.035558395087718964, -0.021357228979468346, 0.03890138864517212, 0.01748356968164444, -0.022269539535045624, 0.016506509855389595, -0.010656883008778095, 0.010367936454713345, -0.0010466091334819794, -0.013741991482675076, 0.018056899309158325, -0.01361902616918087, 0.0112795764580369, 0.04639297351241112, -0.028219889849424362, 0.023487940430641174, -0.008029336109757423, 0.06624484062194824, 0.03038984350860119, -0.03672481328248978, -0.0019654342904686928, -0.03217916563153267, 0.028820056468248367, -0.08471497893333435, 0.02379520796239376, 0.0047013722360134125, 0.05657736584544182, 0.02475941739976406, -0.0015382262645289302, 0.04084332287311554, 0.006295729894191027, -0.07291538268327713, -0.008786482736468315, 0.0380459688603878, -0.040195267647504807, 0.012802333571016788, -0.027479227632284164, -0.02158067561686039, -0.012910164892673492, 0.009411021135747433, 0.04135943204164505, -0.0008016486535780132, 0.08892223238945007, 0.012801571749150753, 0.06236807256937027, -0.017737163230776787, 0.08264590054750443, 0.012805474922060966, 0.0037003105971962214, 0.047090932726860046, 0.0194071214646101, -0.0011289491085335612, 0.031797148287296295, 0.018539421260356903, 0.017730383202433586, -0.049554161727428436, 0.027233287692070007, 0.02492109127342701, 0.03933032229542732, -0.03832228481769562, -0.01714729145169258, -0.019156567752361298, 0.005620277486741543, -0.05446171015501022, -0.06166383996605873, -0.003961626905947924, 0.02875119261443615, 0.08518481254577637, 0.016207603737711906, -0.013681340031325817, -0.025272823870182037, 0.03915046155452728, 0.030253808945417404, 0.030862854793667793, 0.032656602561473846, 0.002469869563356042, -0.03048015385866165, 0.011015770956873894, -0.056581828743219376, 0.050385281443595886, -0.00281152012757957, 0.02580336295068264, -0.012864954769611359, 0.038238003849983215, -0.0833345577120781, -0.03539057821035385, -0.030520273372530937, -0.01402993407100439, 0.07802419364452362, 0.010867814533412457, -0.03694016486406326, 0.01306124683469534, 0.02241031639277935, 0.03658202290534973, 0.050405822694301605, -0.00802473071962595, 0.03945218399167061, -0.09188644587993622, -0.0037148490082472563, -0.024915523827075958, -0.028398647904396057, 0.08865249156951904, 0.006322530563920736, -0.014295290224254131, -0.040785983204841614, 0.0032475802581757307, 0.031422778964042664, -0.0016497706528753042, -0.05320761725306511, 0.05772974342107773, -0.014687062241137028, -0.029402900487184525, -0.0300031378865242, 0.00742269866168499, -0.020551256835460663, -0.0024594697169959545, -0.060290172696113586, -0.05016990751028061, 0.004600056912750006, -0.03699234127998352, 0.021919162943959236, -0.008580626919865608, -0.02959614247083664, 0.05289074033498764, 0.05235089361667633, -0.07916818559169769, 0.042497746646404266, -0.015156335197389126, 0.031497612595558167, 0.09868856519460678, -0.07648240029811859, -0.008786504156887531, -0.033475037664175034, -0.023078573867678642, 0.012415057979524136, 0.05436957627534866, -0.03522486984729767, 0.01025751605629921, -0.024103574454784393, -0.04959084093570709, 0.0010430593974888325, 0.04182124510407448, -0.027850620448589325, -0.008859398774802685, 0.014056574553251266, 0.021105732768774033, 0.025672772899270058, -0.025777574628591537, 0.020143484696745872, 0.03445952385663986, 0.04728143662214279, 0.0560963936150074, -0.0867789015173912, 0.05813279002904892, -0.009451758116483688, 0.062300194054841995, -0.04362967982888222, -0.03738421946763992, -0.017267761752009392, -0.03170375898480415, 0.05920969322323799, 0.01777736097574234, 0.03144906833767891, 0.00181266397703439, -0.021166548132896423, -0.016269290819764137, 0.017742782831192017, 0.0338042788207531, 0.034934159368276596, 0.044661492109298706, -0.006173008121550083, -0.018371786922216415, 0.042621321976184845, -0.04674207419157028, -0.028646357357501984, 0.012825152836740017, 0.005989264231175184, -0.005731067154556513, 0.09783650189638138, -0.0527815967798233, 0.058264199644327164, -0.022139009088277817, -0.027162056416273117, -0.026395460590720177, -0.054789695888757706, 0.03455664962530136, -0.05221797153353691, -0.027093173936009407, -0.013884704560041428, 0.02506205439567566, 0.035567332059144974, 0.015572345815598965, 0.026301570236682892, -0.018074672669172287, -0.020511489361524582, -0.03315240144729614 ]
<p>We have a long, cylindrical wire carrying a constant current I in an inertial frame. At a distance of R from the center of the wire, the magnitude of magnetic field is $μI/2πR$. What is the magnitude of magnetic field in another inertial frame moving at a certain speed opposite to the direction of electric current? </p> <p>Since the observed drift speed of the electrons is now greater, does this mean that the current as observed from this frame is greater? </p> <p>If so, what about the magnetic field due to this current? Does this change too? </p> <p>In general how do currents vary between different frames of reference?</p>
g8381
[ 0.034042518585920334, -0.010564961470663548, -0.006072027608752251, -0.03543628752231598, 0.08657262474298477, -0.0004985741688869894, 0.05477446690201759, 0.032799191772937775, -0.06837943941354752, 0.014704403467476368, -0.04370366781949997, 0.032595615833997726, -0.03329556807875633, -0.01889958418905735, 0.06656073033809662, -0.0070291548036038876, 0.05205368250608444, -0.029350189492106438, 0.06280074268579483, -0.007693888619542122, 0.06487319618463516, 0.0268135666847229, 0.0020245155319571495, -0.014280322939157486, 0.017712192609906197, -0.006136525887995958, 0.012647414579987526, -0.005320423748344183, 0.027293851599097252, -0.002142139244824648, -0.006124271545559168, -0.032332297414541245, 0.01808433048427105, -0.047079917043447495, 0.0023134141229093075, -0.05013253539800644, 0.014234399423003197, 0.038245294243097305, 0.07050980627536774, 0.005824771709740162, 0.03119884803891182, -0.0006552930572070181, 0.04803305119276047, 0.016834979876875877, 0.029957253485918045, -0.011735046282410622, -0.02371036261320114, 0.004122594371438026, -0.034250952303409576, -0.04269636794924736, -0.03507218137383461, 0.013872348703444004, 0.021908311173319817, 0.02594653330743313, -0.007936490699648857, -0.03652609512209892, 0.007765930611640215, -0.02914063259959221, 0.034766409546136856, 0.05417635291814804, 0.04579769819974899, -0.02015109546482563, -0.006437527481466532, -0.02756154164671898, 0.0048295301385223866, 0.0015206595417112112, -0.0552559420466423, 0.022840889170765877, -0.030503852292895317, 0.01352246105670929, -0.02563992328941822, -0.045333437621593475, -0.03855408355593681, -0.007862374186515808, -0.06308645755052567, 0.015126965008676052, 0.02901906706392765, -0.057919859886169434, 0.03201915696263313, 0.010456793941557407, -0.07845243811607361, 0.0017475178465247154, 0.008828092366456985, 0.04726703092455864, 0.07763311266899109, 0.010828777216374874, 0.029994653537869453, 0.0618656650185585, -0.0019418116426095366, -0.03228297457098961, 0.03118499554693699, -0.006877619307488203, 0.07187265902757645, -0.011145967058837414, -0.026975303888320923, -0.01004504133015871, -0.03900972008705139, 0.04964558407664299, -0.005511727184057236, 0.07604589313268661, -0.024892151355743408, -0.038847919553518295, 0.025840748101472855, 0.003004931379109621, -0.008537402376532555, 0.019708963111042976, 0.05895213782787323, 0.008268390782177448, -0.008947061374783516, -0.04764633625745773, 0.00041695465915836394, -0.11060400307178497, -0.03212212771177292, 0.028752917423844337, -0.09121676534414291, -0.04117866978049278, -0.00398989487439394, -0.01370775606483221, -0.009213543497025967, 0.017528673633933067, -0.009629985317587852, -0.01236305758357048, 0.016906535252928734, 0.044907692819833755, -0.005211730021983385, -0.026404771953821182, -0.01893102563917637, 0.022188564762473106, 0.015661632642149925, -0.03827878087759018, 0.017719363793730736, 0.028146063908934593, 0.001647920231334865, 0.01209231186658144, -0.018264438956975937, -0.02125963196158409, 0.019664641469717026, 0.015347790904343128, -0.019600022584199905, 0.015287818387150764, 0.022970909252762794, -0.09459640085697174, 0.07120320200920105, -0.05942164734005928, -0.028558410704135895, 0.020000850781798363, 0.005380022805184126, -0.012726681306958199, 0.10601265728473663, -0.01251253392547369, 0.008126857690513134, 0.055504895746707916, -0.0559404119849205, 0.003215863835066557, 0.02974340319633484, 0.004390329588204622, 0.034540433436632156, -0.02369922772049904, 0.011187930591404438, -0.017589116469025612, 0.04137582331895828, -0.014883916825056076, 0.03574548289179802, -0.0043228622525930405, -0.03800318390130997, -0.020186791196465492, 0.06243841350078583, 0.004551818128675222, 0.0635073184967041, -0.044651102274656296, -0.046159710735082626, 0.003965367563068867, 0.049194883555173874, 0.047831811010837555, -0.002416683826595545, 0.031391870230436325, 0.039845965802669525, -0.0187207143753767, -0.007553601637482643, 0.006776470225304365, -0.054643359035253525, -0.008866220712661743, 0.024252530187368393, -0.030697250738739967, -0.0258492361754179, 0.044821593910455704, -0.0662703886628151, 0.015726054087281227, -0.06611102819442749, -0.019471580162644386, -0.046436358243227005, -0.05913024768233299, -0.06004953011870384, 0.03837471455335617, -0.0502367801964283, -0.00530632259324193, -0.027286255732178688, -0.005097753833979368, -0.016524650156497955, -0.014984932728111744, -0.01955912820994854, 0.05028366670012474, 0.05166048929095268, 0.031168848276138306, -0.006022145971655846, -0.007973224855959415, -0.011806980706751347, -0.03446583449840546, 0.0813174918293953, -0.008843502961099148, 0.05254277214407921, 0.022833723574876785, -0.047329843044281006, 0.002590951044112444, 0.0010630645556375384, 0.008524845354259014, 0.043940961360931396, 0.028294427320361137, -0.02040492743253708, 0.01045920792967081, 0.021144207566976547, -0.05670905113220215, 0.058119501918554306, -0.060537587851285934, -0.03014904074370861, -0.03531757369637489, -0.03250908479094505, -0.001030115643516183, 0.042342305183410645, 0.024160651490092278, -0.02460986003279686, 0.0614486038684845, -0.030124107375741005, 0.05122917890548706, 0.013085535727441311, 0.02541043981909752, 0.00038181006675586104, 0.00949119497090578, 0.031110716983675957, -0.016634931787848473, -0.008593259379267693, 0.048815369606018066, -0.03133034706115723, 0.007985665462911129, -0.009980345144867897, -0.03225339576601982, 0.061089783906936646, 0.045449916273355484, -0.029805362224578857, 0.029315317049622536, 0.061630744487047195, -0.008271243423223495, -0.015253540128469467, 0.060557104647159576, 0.0106018902733922, 0.011064565740525723, -0.04580708593130112, 0.05552966147661209, -0.0781177431344986, -0.007475355640053749, 0.003924607764929533, -0.039424195885658264, -0.012442515231668949, 0.07041171938180923, 0.007960601709783077, -0.030438710004091263, 0.01100504957139492, 0.038080159574747086, -0.0033949350472539663, -0.0075440905056893826, -0.008279548026621342, 0.06829563528299332, -0.016443291679024696, 0.00243853940628469, 0.0007631299085915089, 0.010035143233835697, 0.017398564144968987, -0.05502279847860336, 0.0038431731518357992, -0.06424300372600555, -0.03680048882961273, 0.03740011900663376, -0.033617474138736725, 0.0017969467444345355, 0.03208669647574425, -0.03358127176761627, -0.029953347519040108, -0.035668931901454926, 0.0022727190516889095, 0.02871365286409855, -0.0821242704987526, 0.046698372811079025, 0.060247547924518585, -0.025543654337525368, 0.02476413920521736, 0.03977423906326294, 0.05969981476664543, -0.06562153249979019, -0.044353172183036804, -0.0195782370865345, 0.022420303896069527, -0.04771393910050392, -0.007620540447533131, 0.02417045459151268, 0.02489897422492504, 0.017698099836707115, -0.015607220120728016, -0.033595822751522064, -0.012830369174480438, 0.025264140218496323, -0.05989482253789902, -0.011216547340154648, 0.01948009617626667, -0.04314154013991356, -0.05571974441409111, -0.02532120607793331, -0.01995207741856575, 0.014448876492679119, 0.017783403396606445, 0.027134448289871216, 0.026308812201023102, 0.008470114320516586, -0.0551481693983078, -0.012762759812176228, 0.058238834142684937, 0.02491413801908493, 0.026738246902823448, 0.009252442046999931, -0.03973718360066414, -0.006690196227282286, -0.03317747265100479, 0.0020505834836512804, -0.009990677237510681, -0.03099757991731167, -0.02120712399482727, -0.014410522766411304, 0.005169649142771959, 0.015730172395706177, 0.0361483208835125, 0.004224384669214487, 0.026284102350473404, 0.012475745752453804, -0.07872061431407928, 0.014055254869163036, 0.018648896366357803, 0.04330200329422951, 0.034856874495744705, -0.017534760758280754, 0.03777032718062401, -0.0240174587816, 0.0338691845536232, -0.026854777708649635, 0.015271361917257309, -0.02928221970796585, 0.019028307870030403, -0.003916213754564524, -0.001943717012181878, -0.0022024447098374367, -0.05522340163588524, -0.0007839185418561101, -0.014317949302494526, -0.01729736477136612, 0.015166939236223698, 0.02561560831964016, -0.01121370680630207, 0.010052493773400784, 0.03284132480621338, 0.044769514352083206, 0.004164517391473055, -0.06400330364704132, -0.06220100447535515, -0.013178394176065922, -0.045233823359012604, 0.006731247063726187, -0.019228201359510422, -0.042827118188142776, 0.03436773270368576, 0.025526758283376694, -0.029173117130994797, -0.011997840367257595, -0.005251603201031685, -0.0022449600510299206, -0.06825994700193405, -0.02945786528289318, -0.0015950142405927181, -0.0376398041844368, 0.03874548524618149, 0.002098026918247342, -0.06296471506357193, -0.03979329764842987, -0.019338194280862808, -0.021624993532896042, -0.03575098514556885, -0.028832370415329933, 0.044366851449012756, 0.000621957762632519, 0.007968924008309841, 0.03956349939107895, 0.06875504553318024, -0.03715327009558678, 0.022267455235123634, 0.06188230216503143, -0.03175334259867668, 0.0049777221865952015, -0.0017655694391578436, 0.002174185123294592, 0.003955748863518238, -0.034887220710515976, 0.023611830547451973, -0.027914926409721375, -0.04055604711174965, 0.05546418949961662, -0.03889951854944229, -0.07206979393959045, 0.06091628968715668, 0.025775985792279243, 0.02856842242181301, 0.005541633348912001, 0.04882700741291046, -0.030995871871709824, 0.012402190826833248, 0.045140426605939865, 0.060487180948257446, -0.018794717267155647, -0.007771879434585571, 0.05586417019367218, 0.05719670653343201, -0.016648240387439728, 0.038763377815485, -0.027264457195997238, -0.01617785543203354, 0.05046221613883972, 0.010255063883960247, 0.022163214161992073, -0.052669063210487366, 0.06251119077205658, 0.014022432267665863, -0.0005094289663247764, 0.040993448346853256, 0.03457656502723694, 0.07810793817043304, 0.028938619419932365, 0.01839396357536316, -0.06392014771699905, -0.06311953812837601, 0.003592223860323429, -0.048157721757888794, 0.0080817099660635, 0.027573637664318085, -0.03568996489048004, 0.007809872273355722, 0.008595617488026619, -0.032079413533210754, 0.010033741593360901, 0.013245332054793835, -0.037549007683992386, -0.0232293251901865, -0.02676289714872837, -0.0070974030531942844, -0.0340888537466526, -0.06872955709695816, 0.03886459022760391, -0.00011082755372626707, 0.034463755786418915, 0.006850200705230236, 0.024051997810602188, -0.014586446806788445, -0.0552230104804039, -0.080724336206913, 0.05551101639866829, 0.008530180901288986, -0.013376370072364807, -0.027140844613313675, -0.02521388977766037, 0.04813297837972641, 0.02602258324623108, -0.0048224483616650105, -0.01643594168126583, -0.03324960917234421, -0.047748539596796036, -0.05873723700642586, -0.0056090145371854305, 0.037483058869838715, 0.016500035300850868, -0.012637555599212646, -0.022325577214360237, -0.00842304527759552, 0.029351873323321342, 0.039929769933223724, -0.08035658299922943, 0.011336195282638073, 0.05276838317513466, 0.0016149698058143258, 0.001273056142963469, -0.030841821804642677, 0.03777794539928436, 0.004819175228476524, -0.004317302722483873, -0.03168291971087456, -0.0025179563090205193, -0.04621756076812744, 0.029702873900532722, -0.007341681979596615, -0.003403355134651065, -0.022316116839647293, 0.11004528403282166, 0.02566550299525261, -0.001808262662962079, -0.04458066448569298, 0.039923496544361115, -0.025059321895241737, 0.06713156402111053, 0.004103424493223429, -0.013586422428488731, 0.011468012817203999, -0.03178734704852104, 0.011623892933130264, -0.016397271305322647, 0.030548924580216408, -0.016986001282930374, 0.012469831854104996, 0.018880954012274742, 0.005843182094395161, -0.007957560941576958, -0.06011873483657837, 0.04731878265738487, -0.024442452937364578, -0.026510905474424362, 0.027884945273399353, -0.02023443393409252, 0.02201782539486885, 0.020989831537008286, 0.01363812480121851, -0.019885234534740448, 0.027303878217935562, 0.016142994165420532, 0.036493998020887375, -0.05352366715669632, -0.018806489184498787, 0.025375578552484512, -0.002030693693086505, -0.014906657859683037, 0.055797453969717026, 0.05663318932056427, -0.035870954394340515, -0.02521619386970997, 0.02596930041909218, -0.01873902417719364, 0.0335395410656929, 0.002668522298336029, -0.07663759589195251, 0.044655103236436844, -0.0006546264630742371, 0.03401928022503853, 0.018422123044729233, 0.04576287418603897, 0.056489959359169006, -0.008106961846351624, -0.03800540417432785, -0.009571651928126812, 0.0375397615134716, -0.024063752964138985, 0.06596831977367401, -0.033860944211483, 0.010878548957407475, -0.026568790897727013, -0.007932702079415321, -0.025904685258865356, 0.1044699102640152, 0.01740182191133499, -0.010590876452624798, -0.06974846124649048, -0.057186175137758255, -0.02877378836274147, 0.002206411911174655, 0.028284410014748573, -0.09406648576259613, 0.01292947307229042, -0.07099241018295288, 0.010134897194802761, -0.0024945512413978577, 0.017667008563876152, 0.013659714721143246, -0.06419835239648819, -0.005371321924030781, 0.0469796359539032, 0.006293818820267916, 0.020096177235245705, 0.082150898873806, 0.010758358985185623, -0.026409929618239403, 0.024462906643748283, 0.0329592227935791, -0.05599512904882431, -0.02189883403480053, -0.016940053552389145, -0.052145227789878845, -0.012576460838317871, -0.021315347403287888, 0.08372868597507477, 0.0263028834015131, 0.005349095445126295, 0.017823822796344757, -0.04500469192862511, 0.040107350796461105, 0.03963581472635269, -0.009942921809852123, 0.00790516845881939, -0.019730979576706886, 0.03254413604736328, 0.10923121869564056, -0.04390961304306984, 0.01058268267661333, 0.03107490763068199, -0.02672208473086357, 0.0593152716755867, -0.009816566482186317, -0.018171794712543488, -0.01516116876155138, 0.026437003165483475, -0.023591138422489166, -0.055299047380685806, -0.04961435869336128, -0.0039903209544718266, 0.02844277210533619, 0.0531003475189209, -0.04623749107122421, -0.0065608243457973, -0.004123570863157511, -0.03258983790874481, -0.019687935709953308, 0.03057760000228882, -0.04832842946052551, 0.02918032556772232, 0.033264804631471634, -0.020665129646658897, 0.0803263857960701, -0.0025496489834040403, 0.02065623179078102, 0.021182626485824585, 0.060370657593011856, 0.005690320394933224, -0.043954696506261826, 0.003436678322032094, -0.02603853866457939, -0.07983715087175369, 0.0029984822031110525, 0.06718885898590088, -0.025486521422863007, 0.029210595414042473, -0.004418858792632818, 0.04280143976211548, 0.029824336990714073, 0.029334520921111107, 0.002821885282173753, -0.02371836267411709, 0.04949750751256943, 0.01242624782025814, 0.020911358296871185, -0.036691438406705856, -0.03953917697072029, -0.03493768349289894, -0.03125644102692604, -0.027965638786554337, 0.00867788027971983, -0.01241956278681755, -0.060786567628383636, -0.06759633123874664, -0.01083947904407978, 0.04862216114997864, 0.0000190053106052801, -0.031046045944094658, 0.0022307836916297674, 0.021113509312272072, 0.02705089934170246, 0.010741966776549816, -0.05906694009900093, -0.0339139886200428, -0.049399759620428085, -0.06396743655204773, -0.01425791997462511, 0.027698175981640816, 0.057239752262830734, -0.07090158015489578, -0.010974074713885784, 0.019426966086030006, 0.008882441557943821, -0.013585604727268219, -0.030254460871219635, -0.10334006696939468, 0.014740548096597195, 0.011610464192926884, 0.017787104472517967, -0.03009270876646042, -0.05962245166301727, 0.03837607428431511, 0.039057657122612, 0.007370924111455679, 0.021373769268393517, 0.0160779170691967, 0.017497926950454712, -0.027907179668545723, 0.02724381536245346, 0.06532556563615799, 0.04050415754318237, 0.004683052655309439, -0.014362155459821224, -0.010310443118214607, -0.06753532588481903, 0.060141243040561676, 0.03550155460834503, 0.041530758142471313, 0.016003265976905823, -0.017784293740987778, 0.032605309039354324, -0.028053510934114456, 0.00233547599054873, 0.0025502799544483423, 0.0160899069160223, -0.011937818489968777, 0.003944325260818005, 0.04685218632221222, -0.027561277151107788, -0.006454302463680506, -0.012040369212627411, -0.004003201145678759, -0.009859040379524231, 0.010505156591534615, -0.06863147765398026, -0.03438930958509445, -0.02125745266675949, -0.001861615921370685, -0.051275625824928284, -0.04952628165483475, -0.04075206443667412, -0.0018966876668855548, -0.006194581277668476, -0.026254890486598015, 0.032566338777542114, -0.02436872571706772, 0.03626031056046486, -0.04643350467085838, -0.03044298104941845, 0.015325800515711308, -0.025401674211025238, 0.05110704526305199, -0.00808231346309185, 0.02864839881658554, 0.014856934547424316, -0.007997805252671242, 0.00649240193888545, 0.03972099721431732, -0.026688050478696823, -0.014790832996368408, -0.0007257711258716881, 0.0197895560413599, -0.02848246321082115, 0.01741795986890793, -0.03829110413789749, 0.055202871561050415, -0.05925031751394272, -0.03444205969572067, 0.032345790416002274, 0.032685890793800354, -0.009939375333487988, -0.014431443996727467, -0.06852228194475174, 0.050462543964385986 ]
<p>I ran into a bit of physics yesterday, and couldn't understand the physics at work. I've been scouring the Internet, but haven't found the answer yet. I'm guessing there's a basic principle I'm misinterpreting or ignorant of.</p> <p>Basically, the sewer backed up into my house. Among other points of entry, water flowed up the shower drain, and up the toilet bowl.</p> <p>The shower filled to a bit under the lip of its basin. The toilet filled to a bit under the lip of the bowl, but neither overflowed.</p> <p>So basically I had a reservoir (the sewer), with one pipe (shower) extending to floor height + 4 inches, and another pipe (toilet) extending to floor height + 24 inches.</p> <p>Where I'm getting confused is that in my physics textbooks I recall seeing a diagram of a U-shaped vessel with differently sized "legs." I think that the water level in each leg of the U had to be the same, because otherwise there'd be a pressure differential at the base of the U preventing the system from stabilizing.</p> <p>Edit: Here's <a href="http://physics.stackexchange.com/questions/799/why-does-the-water-level-equalize-in-a-series-of-tubes">an example of what I'm talking about</a>.</p> <p>What would allow for this difference in water levels?</p>
g8382
[ 0.03178801387548447, 0.06357130408287048, -0.022687789052724838, -0.08498935401439667, 0.013533554971218109, 0.0806952714920044, 0.04745106026530266, -0.04131738841533661, -0.053787365555763245, -0.07124024629592896, -0.06918483972549438, 0.0245490912348032, 0.09222424030303955, 0.021592877805233, -0.014224464073777199, 0.001033355132676661, 0.02243809401988983, -0.04097704216837883, -0.002375244162976742, -0.0004289833887014538, -0.06598743796348572, -0.005946105346083641, -0.0024958099238574505, -0.05887395143508911, -0.021482784301042557, -0.03840005397796631, -0.017784269526600838, 0.020457925274968147, -0.007922775112092495, -0.015139847062528133, -0.038123536854982376, -0.015248769894242287, 0.01589135453104973, -0.064258873462677, -0.03300958871841431, -0.03512857109308243, 0.03123590536415577, -0.004373804200440645, -0.005606836173683405, -0.04720330238342285, 0.007770935073494911, -0.017052307724952698, -0.03050912544131279, 0.03992703557014465, -0.06456028670072556, -0.016600485891103745, -0.04231840744614601, 0.01206920575350523, 0.004997789394110441, -0.02547401748597622, 0.036082375794649124, 0.04114699363708496, -0.008347894996404648, 0.02724076807498932, 0.003297701943665743, 0.031212303787469864, -0.005130918696522713, -0.06022696942090988, 0.005664838943630457, 0.03713219240307808, -0.01796359196305275, 0.01241812389343977, 0.01750537008047104, 0.06888973712921143, 0.041621770709753036, 0.00805535539984703, 0.01069960743188858, -0.02306436374783516, -0.005045693833380938, 0.024214543402194977, -0.0066367085091769695, -0.05671330541372299, -0.03100527822971344, -0.06477852910757065, -0.01905042864382267, 0.04179632291197777, -0.015427520498633385, 0.01993672177195549, 0.017633676528930664, -0.03449919447302818, -0.02167058177292347, 0.07003574818372726, -0.018477287143468857, -0.00045850337482988834, 0.024746691808104515, 0.04318612813949585, -0.025023309513926506, -0.0230511873960495, -0.011572030372917652, 0.0010402454063296318, -0.05385975539684296, -0.04724645987153053, 0.05249616503715515, 0.04507005587220192, -0.0753789022564888, -0.04216129332780838, 0.011434073559939861, 0.05241833254694939, 0.008343452587723732, 0.0008288177778013051, -0.02489166520535946, -0.012666292488574982, 0.04700053110718727, 0.0008969949558377266, -0.039288971573114395, 0.034614212810993195, 0.052818190306425095, 0.040478773415088654, 0.02700961008667946, -0.021418437361717224, -0.053289465606212616, -0.044253185391426086, -0.01620875857770443, -0.023342689499258995, 0.031872838735580444, -0.03072758950293064, 0.060868266969919205, 0.05529645085334778, -0.014512349851429462, 0.022168144583702087, 0.03143398091197014, -0.0001226688182214275, -0.008251761086285114, 0.042293861508369446, 0.011193916201591492, 0.012440609745681286, 0.006908623967319727, 0.02476419508457184, 0.05146470665931702, 0.019878994673490524, 0.03526875376701355, -0.011569413356482983, -0.07460041344165802, 0.006899554282426834, 0.07022488117218018, 0.03404117748141289, -0.03726411238312721, -0.000691387802362442, -0.0006142248748801649, 0.00528298132121563, 0.005060970317572355, -0.008694197982549667, -0.0383625328540802, -0.0031804372556507587, -0.021470438688993454, 0.025762129575014114, -0.001765672815963626, 0.02050217241048813, -0.011897304095327854, 0.020182834938168526, -0.004191126208752394, 0.056814126670360565, -0.007838534191250801, 0.007473889738321304, -0.017320849001407623, -0.007474035024642944, -0.032502155750989914, 0.009823382832109928, 0.003784614149481058, 0.03151515871286392, -0.028308864682912827, 0.021956056356430054, -0.011456134729087353, 0.03565600886940956, -0.10673138499259949, 0.00400846591219306, -0.00749131478369236, -0.048422522842884064, -0.03350222110748291, -0.014923464506864548, -0.03458290547132492, 0.020330574363470078, -0.018842725083231926, 0.03635931387543678, -0.01174117624759674, 0.020766856148838997, 0.05284082517027855, -0.062141045928001404, 0.020850831642746925, 0.0016747483750805259, 0.0004991497262381017, -0.03580773249268532, 0.018331428989768028, 0.0305496733635664, -0.011748009361326694, -0.003713359357789159, 0.02680966816842556, -0.01579156145453453, -0.020125774666666985, -0.025320395827293396, -0.012200986966490746, -0.010023128241300583, 0.010292517021298409, -0.016526570543646812, -0.030392643064260483, -0.03975538909435272, 0.053251709789037704, -0.051508236676454544, -0.05147772654891014, 0.028231412172317505, 0.018607409670948982, 0.004556889180094004, 0.039298854768276215, -0.002436495153233409, -0.012637969106435776, 0.03822975605726242, -0.06364448368549347, -0.000385203689802438, 0.015753254294395447, 0.0010839953320100904, 0.002376795746386051, 0.03349866345524788, 0.045483727008104324, -0.0018027691403403878, -0.02049466222524643, -0.0065261670388281345, 0.013791638426482677, 0.026395168155431747, -0.025669394060969353, -0.01531516294926405, 0.0046007572673261166, -0.06860369443893433, -0.00963286217302084, 0.033654555678367615, -0.042952317744493484, 0.0018572278786450624, -0.004335200879722834, -0.014196619391441345, 0.0020240156445652246, -0.0006887243362143636, 0.002182391006499529, 0.002117194002494216, -0.027642052620649338, -0.06640941649675369, 0.035031456500291824, 0.06207618489861488, 0.022252317517995834, 0.0038775191642344, 0.027329575270414352, -0.002595264231786132, 0.008100319653749466, -0.004675723612308502, -0.048459723591804504, 0.02299591898918152, 0.010378326289355755, -0.021510405465960503, -0.019109010696411133, -0.06381815671920776, -0.012671868316829205, 0.02948610857129097, -0.053104642778635025, -0.010347824543714523, -0.0087492810562253, 0.024254707619547844, -0.022469384595751762, -0.019578436389565468, -0.00894947163760662, 0.0011600960278883576, -0.051054373383522034, -0.07522424310445786, -0.025587458163499832, 0.012249082326889038, 0.044672463089227676, 0.04604663699865341, -0.054354358464479446, 0.013270283117890358, -0.012304707430303097, -0.05899624899029732, 0.04967009276151657, 0.026419086381793022, 0.037430841475725174, 0.03897978365421295, -0.028308885172009468, 0.04628903046250343, 0.017518598586320877, 0.03595942631363869, 0.009061970748007298, 0.0005360742215998471, 0.010115467011928558, 0.04283244162797928, -0.01905825361609459, 0.026089200749993324, -0.053442809730768204, 0.01535962987691164, 0.0663166493177414, -0.033405520021915436, 0.041639696806669235, 0.004345924127846956, -0.020509015768766403, -0.005313888657838106, -0.0076885647140443325, -0.028689349070191383, 0.022393876686692238, 0.01832919381558895, 0.06617708504199982, 0.023978883400559425, -0.01968393474817276, -0.027187952771782875, -0.07628775388002396, -0.012858128175139427, -0.052463702857494354, -0.00043973056017421186, 0.04263204336166382, -0.02807745337486267, -0.07221348583698273, 0.05018211901187897, -0.0462544821202755, 0.007313464768230915, -0.007173662073910236, 0.015844564884901047, -0.03576470911502838, -0.006212661042809486, -0.03806788846850395, -0.03101225569844246, -0.0030769938603043556, 0.0017899228259921074, 0.003437180770561099, -0.018756644800305367, -0.021143417805433273, 0.03297973796725273, -0.03877318277955055, -0.017934003844857216, 0.0040098088793456554, 0.013505718670785427, -0.05910079926252365, -0.007001906633377075, -0.0036929473280906677, 0.04272117465734482, -0.08667933940887451, -0.018670683726668358, 0.013276017270982265, -0.016055533662438393, 0.029479319229722023, 0.03197244927287102, 0.009499741718173027, -0.00004947196794091724, 0.009892732836306095, 0.024990282952785492, 0.07813156396150589, 0.007398450281471014, 0.001596036134287715, -0.009533688426017761, 0.04661436006426811, -0.07478690892457962, -0.014869097620248795, 0.02524237334728241, 0.01894552819430828, 0.00841180607676506, -0.001603749580681324, 0.006642303895205259, 0.09427310526371002, 0.0785713866353035, -0.0022888362873345613, -0.03407973423600197, 0.021618155762553215, -0.05290968343615532, 0.061489690095186234, -0.009015236049890518, -0.02357136271893978, -0.03754684701561928, 0.013252509757876396, -0.04005056992173195, 0.018248779699206352, 0.004668195731937885, -0.04462406784296036, -0.011356187984347343, 0.01747739315032959, 0.02519523911178112, -0.04363347217440605, -0.01535648200660944, -0.019684161990880966, -0.006483178120106459, -0.08823691308498383, 0.018529333174228668, 0.011067510582506657, -0.04851444438099861, 0.10064894706010818, -0.0060841417871415615, -0.022584151476621628, 0.04252057150006294, 0.11945483833551407, -0.007629877887666225, 0.0030610859394073486, 0.02827940322458744, -0.046945277601480484, -0.03264075145125389, -0.02622109465301037, 0.017438288778066635, 0.028215564787387848, -0.04094911366701126, 0.029192231595516205, 0.030580604448914528, -0.03744790330529213, -0.06299453973770142, 0.03572891652584076, 0.06052732095122337, 0.014638764783740044, 0.02628893218934536, -0.07815354317426682, -0.002279010135680437, -0.014135986566543579, -0.0013538725906983018, -0.012199065648019314, -0.026986394077539444, -0.04091063141822815, -0.026126326993107796, 0.07284911721944809, -0.030898284167051315, -0.036946412175893784, -0.030010594055056572, 0.04952548071742058, -0.0054935794323682785, 0.009599785320460796, -0.06649024784564972, -0.0262286514043808, 0.053646620362997055, -0.02147180773317814, -0.019643478095531464, -0.007392481900751591, 0.008077925071120262, 0.0479394756257534, 0.006861328613013029, -0.02497626282274723, 0.021198363974690437, 0.00711506512016058, 0.030301934108138084, -0.0012577070156112313, 0.02794245071709156, -0.029536759480834007, -0.04234332591295242, 0.033826425671577454, 0.037309978157281876, -0.01048686821013689, 0.001219435129314661, 0.0012158176396042109, 0.05627825856208801, 0.0295146182179451, 0.008417924866080284, -0.11737065762281418, 0.020995890721678734, 0.04429517313838005, -0.026811033487319946, 0.01535909716039896, 0.015341130085289478, 0.013037536293268204, 0.020468009635806084, -0.028442105278372765, -0.04671555012464523, -0.016258075833320618, 0.014676962979137897, -0.04169885441660881, 0.045514803379774094, 0.0499047189950943, -0.051131993532180786, -0.008021154440939426, -0.02061479724943638, -0.0023218472488224506, 0.026682130992412567, -0.01560402661561966, 0.017674515023827553, -0.020405111834406853, -0.0052780089899897575, -0.0531555712223053, -0.013420208357274532, -0.0015376146184280515, -0.08144164830446243, 0.03651655465364456, -0.019978363066911697, -0.015371153131127357, -0.015309850685298443, 0.0773773118853569, 0.051641013473272324, 0.03549979627132416, 0.07089025527238846, 0.06578107178211212, 0.034061115235090256, -0.01317925937473774, 0.019475022330880165, 0.03373982384800911, -0.048452265560626984, -0.01012570783495903, 0.00023690461239311844, -0.020959245041012764, 0.07578664273023605, -0.014470266178250313, 0.009913749992847443, -0.047330986708402634, -0.008967331610620022, 0.02749691531062126, 0.022831711918115616, -0.011251946911215782, -0.0044106971472501755, 0.03210964798927307, 0.017103444784879684, -0.00400970596820116, -0.04338362440466881, 0.006724371574819088, -0.00249801529571414, 0.002470242092385888, 0.041739076375961304, -0.03632285073399544, 0.0302065871655941, -0.0059146215207874775, -0.023296097293496132, 0.07888693362474442, 0.009584506042301655, 0.0021006984170526266, 0.004302523098886013, -0.014440786093473434, -0.02801867201924324, 0.02574210800230503, 0.009570705704391003, 0.019401129335165024, -0.024427443742752075, 0.04619485139846802, -0.004892181139439344, -0.00033363793045282364, 0.0378572903573513, -0.016272762790322304, 0.0049201627261936665, 0.009923179633915424, 0.0060017285868525505, 0.0024077233392745256, 0.00046719127567484975, -0.06080812215805054, 0.031443122774362564, -0.05012619495391846, -0.017200738191604614, -0.018425479531288147, 0.018000993877649307, 0.019486237317323685, 0.0018774985801428556, -0.0021156882867217064, -0.008773437701165676, -0.06556295603513718, 0.002351728966459632, 0.01046532392501831, 0.003962371498346329, 0.07346001267433167, 0.007369171362370253, 0.038931988179683685, -0.01279990840703249, -0.0010054151061922312, 0.10717944800853729, 0.009913892485201359, -0.04405440762639046, -0.06533556431531906, -0.029609929770231247, 0.04027628153562546, 0.004491395782679319, -0.01104188896715641, 0.06945805996656418, -0.01838112063705921, 0.05551135167479515, 0.006695684511214495, -0.00754503021016717, 0.01547409500926733, -0.018277695402503014, -0.04294938966631889, -0.07189736515283585, 0.005917598959058523, -0.011690561659634113, 0.02311008796095848, 0.029323339462280273, -0.0012392348144203424, -0.01816699281334877, -0.058176204562187195, -0.017109757289290428, 0.03930685669183731, 0.05926382541656494, 0.014359564520418644, -0.028419431298971176, 0.0754682645201683, -0.029476935043931007, 0.004647627007216215, 0.05834980309009552, -0.05743425711989403, 0.004917777609080076, -0.015866270288825035, 0.04223556071519852, -0.02454279363155365, 0.027655689045786858, -0.03565259650349617, 0.03334175795316696, -0.040442872792482376, 0.051134027540683746, -0.04639069363474846, 0.0055159712210297585, 0.04063910245895386, 0.008545911870896816, -0.06933343410491943, -0.015667259693145752, -0.01773926429450512, 0.03913351520895958, 0.06143525242805481, -0.02603250741958618, 0.008790947496891022, 0.029230572283267975, 0.008002965711057186, 0.04744233936071396, 0.004879811313003302, 0.05913993716239929, 0.030632708221673965, -0.017306938767433167, -0.003600985510274768, 0.03927285596728325, 0.0016030108090490103, 0.019984453916549683, -0.028352176770567894, -0.0232718326151371, 0.03766100853681564, 0.06905454397201538, 0.045609816908836365, 0.02438516542315483, -0.005233276169747114, -0.08522064983844757, 0.011383436620235443, -0.025935113430023193, 0.01226778607815504, 0.05994309484958649, 0.06056426465511322, -0.027113953605294228, -0.003542048390954733, -0.060804612934589386, 0.051761694252491, -0.0220626313239336, -0.03817024454474449, -0.014409919269382954, 0.06034489721059799, -0.0008021355606615543, -0.012135742232203484, -0.023826196789741516, 0.012007802724838257, -0.009638601914048195, -0.02530810609459877, 0.04595478996634483, -0.004278326872736216, 0.03208545967936516, 0.09003370255231857, 0.09790827333927155, 0.02141696587204933, 0.002998343436047435, 0.0683756023645401, 0.06919518113136292, 0.008785182610154152, 0.014601979404687881, 0.035335153341293335, -0.03186657652258873, -0.04985922574996948, -0.011530539020895958, 0.014132561162114143, -0.013970185071229935, -0.061141643673181534, 0.03584051877260208, -0.033050186932086945, 0.04040370509028435, -0.027373181656003, 0.02753898873925209, 0.056204598397016525, -0.02439592219889164, 0.06918000429868698, 0.034618183970451355, 0.07411529123783112, 0.020166238769888878, 0.015586023218929768, 0.012143748812377453, -0.000647901208139956, -0.007117857225239277, -0.014855468645691872, 0.015845395624637604, 0.000574215897358954, 0.005323757883161306, -0.016406085342168808, 0.03286786377429962, 0.07966763526201248, 0.028337031602859497, 0.021977102383971214, 0.07880257815122604, -0.001581151271238923, 0.00446208193898201, -0.0325668640434742, 0.03079999051988125, -0.0011309959227219224, -0.032945264130830765, -0.08924280107021332, -0.006025657057762146, -0.038856275379657745, -0.006905738264322281, 0.03616165742278099, 0.01127621065825224, 0.0035629530902951956, 0.044643282890319824, -0.00009469034557696432, 0.02628793567419052, -0.014370729215443134, 0.0453970693051815, -0.008973153308033943, -0.046101391315460205, 0.03620221093297005, -0.05786176770925522, 0.026345521211624146, -0.036021485924720764, -0.04924234375357628, 0.04149485006928444, 0.04632261395454407, -0.04554608464241028, -0.054370053112506866, 0.07433156669139862, -0.03260400891304016, -0.06317540258169174, -0.028179237619042397, -0.0029848560225218534, 0.00016699708066880703, -0.005362347234040499, 0.010276827961206436, -0.027884138748049736, -0.034214042127132416, 0.0018353424966335297, -0.03478825092315674, -0.003947844263166189, -0.05622011050581932, -0.03599350154399872, 0.03553182631731033, -0.07247544080018997, -0.052879516035318375, -0.012281007133424282, 0.014822045341134071, -0.030139414593577385, -0.06258334219455719, 0.03272608295083046, -0.030776308849453926, -0.006714998744428158, -0.026606997475028038, -0.03211639076471329, -0.012979616411030293, 0.02603270299732685, -0.014471285045146942, 0.01641768589615822, -0.05435740575194359, -0.029508085921406746, 0.013663305900990963, -0.0020145101007074118, 0.018790751695632935, -0.04102161154150963, 0.008681293576955795, -0.06572187691926956, -0.02463987097144127, 0.03657681122422218, 0.031014693900942802, -0.059515330940485, 0.05555972829461098, 0.005069590639322996, 0.006232234183698893, 0.04813890531659126, 0.02847370132803917, -0.07577578723430634, -0.06156899034976959, 0.022367967292666435, -0.044995374977588654, -0.005000855308026075, 0.029497606679797173, 0.02071058377623558, 0.035575658082962036, -0.07671938836574554, 0.0031832277309149504, -0.011037619784474373, -0.06053020432591438, -0.02807532250881195 ]
<p>Suppose we have a disc with a hole, when computing moment of inertia of this about the disc's centre. Why do we subtract the moment of inertia of the removed part from the moment of inertia of complete disc? </p>
g8383
[ 0.0705837607383728, -0.04173538088798523, 0.008007869124412537, -0.030711833387613297, 0.046659257262945175, -0.02124411053955555, 0.089881032705307, 0.03409258648753166, -0.042167436331510544, 0.024708421900868416, -0.023248421028256416, -0.004833538085222244, -0.016133464872837067, -0.03940708190202713, 0.03330737352371216, -0.024453310295939445, -0.0577164888381958, 0.013508318923413754, -0.021844008937478065, 0.004981921520084143, 0.017116593196988106, -0.006077728234231472, 0.0012559602037072182, -0.03515378385782242, -0.0034937765449285507, -0.0263566505163908, 0.04361400380730629, 0.011064433492720127, -0.0030583124607801437, 0.04269619286060333, -0.014849252067506313, 0.01449926383793354, 0.02340570278465748, -0.03821173310279846, -0.024610860273241997, 0.011625205166637897, 0.09600092470645905, 0.0493696928024292, 0.023994239047169685, 0.016944075003266335, -0.04023674502968788, -0.08503115177154541, -0.006189161445945501, 0.03228900954127312, 0.0013169592712074518, -0.026672037318348885, -0.005022227298468351, 0.018890660256147385, -0.0016032734420150518, -0.025578103959560394, 0.006787414662539959, -0.033048611134290695, -0.0017713609850034118, -0.02166830189526081, -0.034637678414583206, 0.04159069061279297, 0.031206723302602768, -0.05614403262734413, 0.04412165656685829, 0.027352003380656242, -0.09585053473711014, -0.06440626829862595, 0.0031830158550292253, 0.08696142584085464, -0.01615910418331623, -0.047794755548238754, 0.009935731068253517, -0.009736829437315464, -0.04959563910961151, 0.015786362811923027, -0.007088726852089167, -0.009953811764717102, 0.045579809695482254, -0.032464854419231415, -0.08872830867767334, 0.06892458349466324, 0.009417618624866009, 0.04133686423301697, -0.03574036806821823, -0.001718454179354012, -0.03938060253858566, -0.008116057142615318, 0.04317038133740425, 0.02208893932402134, 0.032873183488845825, 0.022567298263311386, 0.011376693844795227, 0.018703022971749306, -0.0403631329536438, 0.023218190297484398, 0.03296349197626114, -0.06275161355733871, 0.052087269723415375, -0.00513786356896162, -0.0016562022501602769, -0.02515525370836258, -0.03804047778248787, 0.03166384622454643, 0.003752653021365404, 0.039213962852954865, 0.03925015404820442, -0.049491286277770996, 0.000943937455303967, -0.03966878727078438, 0.006894049234688282, 0.05569848790764809, -0.0032280064187943935, -0.006361206062138081, 0.0202055461704731, 0.011448749341070652, 0.025371788069605827, -0.03995879739522934, -0.007033663336187601, -0.03722348436713219, -0.016639264300465584, -0.014604918658733368, 0.07496379315853119, 0.001339575625024736, -0.03153596818447113, 0.02168586105108261, -0.07389964908361435, 0.00017118184769060463, 0.015254458412528038, 0.04626043885946274, 0.0000557201165065635, -0.03225361183285713, -0.006341715808957815, 0.0371953547000885, 0.07275155931711197, 0.051646023988723755, -0.028676224872469902, 0.03134369105100632, -0.03186699002981186, 0.041024841368198395, 0.04358495771884918, 0.003680160967633128, -0.007764835376292467, 0.00047271448420360684, -0.0033536944538354874, -0.001612211111932993, 0.019989121705293655, 0.023433256894350052, 0.0003809008339885622, 0.015433335676789284, 0.011063368059694767, 0.011732310056686401, -0.028636900708079338, 0.01532885804772377, -0.02058766409754753, -0.029644960537552834, 0.029856299981474876, 0.019400188699364662, 0.044505469501018524, 0.03298262506723404, 0.07362636923789978, 0.04963694140315056, 0.022516924887895584, -0.0004241221759002656, 0.009742967784404755, 0.05052727460861206, 0.013824551366269588, 0.018281472846865654, 0.00858592614531517, 0.04775712639093399, -0.0664459615945816, 0.0506107471883297, 0.020730193704366684, -0.05841881409287453, -0.01601947285234928, -0.08040910214185715, -0.03361653536558151, -0.007675020024180412, 0.016440274193882942, -0.0039056327659636736, 0.037860628217458725, 0.019087716937065125, 0.0166898425668478, -0.013661889359354973, -0.0015458982670679688, 0.00371307460591197, 0.01722991093993187, 0.04473580792546272, 0.043334197252988815, 0.0026097598019987345, 0.008288674056529999, -0.006494001019746065, 0.002443887060508132, 0.043201856315135956, -0.051371071487665176, -0.004237357992678881, 0.016269609332084656, -0.02843104675412178, 0.005532569717615843, 0.05673863738775253, -0.017382171005010605, 0.0056095849722623825, 0.03498069569468498, -0.017526518553495407, -0.03982819616794586, 0.07428579777479172, -0.050299014896154404, -0.021070631220936775, 0.022839797660708427, 0.008636417798697948, -0.00777843315154314, -0.0195451732724905, -0.014846110716462135, 0.0650789737701416, 0.01679042913019657, 0.011989169754087925, 0.02075759880244732, 0.01595490425825119, -0.01572568714618683, 0.04711967334151268, -0.06499738246202469, 0.004729753825813532, 0.02540670894086361, 0.03873840719461441, 0.006207354832440615, -0.04042259231209755, -0.014336635358631611, -0.04816903546452522, 0.009591752663254738, -0.02725132182240486, -0.019362403079867363, 0.059001095592975616, -0.005655273795127869, 0.03259938955307007, -0.02222995087504387, -0.02815883979201317, -0.04263785481452942, -0.049353960901498795, -0.049625564366579056, -0.0114744259044528, 0.03451785445213318, 0.016639841720461845, -0.010703341104090214, 0.011516648344695568, -0.013079813681542873, -0.004962925799190998, 0.03072494827210903, 0.020475156605243683, -0.04217521473765373, 0.03438565135002136, -0.025496771559119225, -0.012444772757589817, 0.032829463481903076, -0.05453953891992569, -0.08242102712392807, 0.022747250273823738, -0.009357227943837643, -0.02849869430065155, -0.056925658136606216, -0.007204793393611908, 0.06550651788711548, 0.04388782009482384, 0.011645144782960415, -0.014866308309137821, 0.01809779927134514, 0.0025398051366209984, -0.015273723751306534, 0.01014390867203474, 0.013078254647552967, 0.0008107976755127311, -0.05065291002392769, -0.025940295308828354, -0.054037515074014664, -0.009172889403998852, 0.0013259007828310132, 0.03610311821103096, -0.016969095915555954, 0.07419531047344208, 0.032772574573755264, 0.036321498453617096, 0.02577643096446991, -0.04245154932141304, 0.008806241676211357, -0.0024500552099198103, -0.02246950939297676, 0.005855921655893326, 0.028131095692515373, 0.05082966014742851, -0.05368832126259804, 0.05292927473783493, 0.0061401803977787495, -0.035376984626054764, -0.043177247047424316, 0.0018766190623864532, -0.028963778167963028, 0.006050691474229097, 0.028594911098480225, -0.021888570860028267, 0.005071117542684078, -0.006203912664204836, 0.09755770117044449, 0.07718881219625473, 0.07854118198156357, -0.07008359581232071, -0.04081287980079651, -0.0198662169277668, -0.00661076046526432, 0.02997634932398796, -0.020985452458262444, 0.008076348342001438, 0.03187331184744835, 0.06925410777330399, 0.07422325015068054, 0.033175934106111526, 0.007738170213997364, -0.0428914874792099, -0.0026596589013934135, 0.0391044095158577, 0.030196692794561386, -0.02557123266160488, -0.038536179810762405, 0.01373920775949955, -0.016680486500263214, -0.0598287507891655, 0.024097461253404617, 0.033827926963567734, -0.006972367409616709, 0.013169153593480587, -0.006899740546941757, 0.000601612962782383, 0.014065681956708431, 0.08313856273889542, -0.04873930662870407, 0.00768889207392931, 0.022117266431450844, -0.07052845507860184, -0.044308923184871674, 0.03814808279275894, 0.0016060505295172334, 0.014757340773940086, -0.04495912417769432, -0.01595900021493435, 0.005389371886849403, 0.06930635124444962, 0.0021765767596662045, -0.03441132232546806, 0.008074573241174221, 0.027249859645962715, -0.050009310245513916, -0.011787360534071922, 0.009186186827719212, -0.00859545823186636, 0.007135084364563227, 0.024725291877985, 0.004497460555285215, -0.011029739864170551, -0.014988877810537815, -0.0503973662853241, 0.00522964121773839, -0.053973954170942307, 0.0500020831823349, 0.10380064696073532, 0.01409228052943945, 0.02024935744702816, -0.04514623060822487, 0.03349867835640907, 0.06141839548945427, -0.031634896993637085, 0.004229356534779072, 0.00991741567850113, 0.04567938297986984, -0.02315502241253853, -0.018173612654209137, -0.01110896933823824, -0.06674998253583908, -0.03261939436197281, -0.020892750471830368, 0.0015130849787965417, -0.052393119782209396, -0.03979194536805153, -0.0021323359105736017, -0.0476534441113472, 0.023169543594121933, 0.030970636755228043, -0.011197283864021301, -0.039773255586624146, 0.030781056731939316, -0.028053799644112587, -0.01681457832455635, -0.060209836810827255, -0.026150261983275414, 0.039853889495134354, 0.011412088759243488, -0.019303131848573685, 0.02458973415195942, -0.07585717737674713, 0.07069175690412521, -0.0353844128549099, -0.02300138585269451, -0.05103764683008194, 0.03815567493438721, 0.03976510837674141, -0.012047028169035912, -0.049431923776865005, -0.02062416449189186, -0.031841833144426346, 0.02102676033973694, 0.04016712307929993, 0.025715019553899765, 0.02816452831029892, 0.07908231019973755, 0.024506814777851105, 0.004346128087490797, -0.05590048059821129, 0.028568590059876442, -0.022511132061481476, 0.00041788394446484745, -0.006735726725310087, -0.008652782067656517, 0.011739665642380714, 0.05532237887382507, -0.06525225937366486, 0.04005328565835953, 0.042945295572280884, 0.017741933465003967, 0.013979055918753147, 0.039538588374853134, 0.012331495992839336, 0.016843141987919807, 0.02863825298845768, -0.03860044106841087, 0.0023530249018222094, 0.025949331000447273, -0.023812294006347656, 0.013598998077213764, -0.056804802268743515, -0.03104703687131405, 0.023093879222869873, 0.003756116610020399, 0.010102270171046257, -0.025189967826008797, 0.008442677557468414, -0.01451868936419487, 0.024608612060546875, -0.030142951756715775, -0.021224336698651314, 0.029580432921648026, -0.0317048504948616, -0.035857707262039185, -0.030998459085822105, -0.012178834527730942, 0.022418269887566566, -0.01192784495651722, -0.03855986148118973, -0.062588170170784, -0.02306888811290264, -0.01883385144174099, 0.012863479554653168, -0.019899986684322357, -0.03445851802825928, 0.0357997789978981, -0.024688340723514557, -0.05860372260212898, -0.02012297324836254, -0.07409540563821793, 0.017870482057332993, -0.07410088181495667, 0.045752160251140594, -0.02843150682747364, -0.001716595608741045, 0.0454060360789299, 0.027199165895581245, -0.0017436821945011616, -0.049746740609407425, -0.03919148072600365, 0.003547845408320427, 0.07280906289815903, -0.0016870676772668958, -0.00771726667881012, -0.00849021878093481, 0.03089805692434311, 0.023982638493180275, -0.02867746353149414, -0.014806638471782207, 0.03281433507800102, -0.0713137686252594, -0.05084870383143425, -0.020983483642339706, 0.0005917683010920882, -0.045324910432100296, -0.03538689762353897, -0.003570518223568797, -0.04292043671011925, -0.0413314513862133, -0.035556018352508545, 0.03580209240317345, 0.012348734773695469, -0.007291743531823158, 0.04237694665789604, -0.0503968745470047, -0.029045334085822105, 0.0000959368990152143, 0.049763839691877365, 0.0006345228757709265, -0.029013564810156822, -0.023376546800136566, -0.08377017825841904, -0.0010564543772488832, -0.008472881279885769, 0.0378161258995533, -0.038540005683898926, 0.08328700810670853, 0.06781604886054993, -0.005150305572897196, -0.05536269769072533, -0.05166454240679741, 0.0855916440486908, 0.020137526094913483, 0.053336720913648605, 0.05915477126836777, -0.0028102854266762733, 0.022001653909683228, 0.04027746245265007, -0.03256388381123543, 0.024012964218854904, 0.03905206918716431, 0.05238303169608116, 0.03613876551389694, 0.0460810586810112, -0.01642530970275402, -0.015102135948836803, -0.0022571648005396128, -0.021917149424552917, -0.03325260803103447, -0.05250132456421852, -0.004427640698850155, 0.00825771875679493, -0.009890931658446789, 0.028234286233782768, -0.0406157523393631, -0.07986444979906082, -0.08129706978797913, -0.04805593192577362, -0.07009653002023697, 0.06289052218198776, -0.05467498302459717, -0.02430788055062294, -0.025927871465682983, -0.004898503422737122, 0.018173618242144585, -0.08036475628614426, -0.01848004199564457, -0.0351325161755085, -0.016440244391560555, 0.0004497070622164756, -0.05417381227016449, 0.04026784747838974, 0.06714297831058502, 0.03852340579032898, 0.026475273072719574, -0.023306366056203842, -0.010764602571725845, 0.04833194613456726, 0.05315522104501724, 0.010699344798922539, -0.0373457595705986, 0.007303675636649132, -0.04105790704488754, -0.010451785288751125, 0.018053658306598663, 0.002115980489179492, -0.0019907355308532715, 0.012349926866590977, -0.012748220935463905, 0.05815258249640465, -0.04463668167591095, 0.010442061349749565, -0.040410302579402924, -0.008452174253761768, -0.0033526248298585415, -0.004335130099207163, 0.034099385142326355, -0.009351314976811409, 0.04552591219544411, -0.012746281921863556, -0.020076299086213112, -0.026422997936606407, -0.04532488062977791, 0.09472104161977768, -0.026196174323558807, -0.008081895299255848, -0.013683981262147427, -0.05932135879993439, 0.004017227329313755, 0.028855592012405396, 0.017804168164730072, -0.015934765338897705, 0.03911406174302101, -0.008388444781303406, -0.05859116464853287, 0.06292126327753067, 0.020509952679276466, -0.03951401263475418, -0.0260958019644022, 0.0072763036005198956, -0.026576995849609375, 0.028959713876247406, -0.007578134071081877, 0.053130920976400375, -0.010320414789021015, 0.03873943164944649, 0.07862433791160583, 0.01146241370588541, -0.03750387579202652, 0.010101697407662868, -0.012659075669944286, 0.018001340329647064, -0.0020209511276334524, -0.021732307970523834, 0.04468528926372528, -0.013624943792819977, 0.0030122220050543547, -0.009942503646016121, -0.015351607464253902, 0.018399769440293312, -0.06147850304841995, -0.009148555807769299, -0.00511873560026288, -0.023329976946115494, -0.021436024457216263, 0.012897736392915249, 0.018299277871847153, -0.06610046327114105, -0.02105865068733692, 0.07635266333818436, 0.012130485847592354, 0.031497083604335785, 0.05455093830823898, 0.0038027241826057434, 0.06619612872600555, -0.04940451681613922, 0.08207639306783676, -0.040736179798841476, 0.04792946204543114, 0.016147391870617867, 0.0040360307320952415, 0.031197287142276764, 0.0605531744658947, 0.005184371490031481, 0.013362417928874493, -0.018979666754603386, 0.012864923104643822, 0.030829768627882004, 0.017713211476802826, 0.0037601685617119074, 0.015361173078417778, 0.0006500723538920283, 0.047100432217121124, -0.023722665384411812, 0.014464129693806171, -0.004959570709615946, -0.06076470762491226, -0.0685117170214653, 0.00012926403724122792, 0.011078824289143085, -0.004343122709542513, -0.0632052794098854, 0.035925306379795074, -0.02953358367085457, -0.04771533980965614, -0.028157629072666168, -0.059142787009477615, 0.028814079239964485, -0.04354187101125717, 0.01293534692376852, -0.027676789090037346, -0.03114842250943184, -0.030977224931120872, -0.0679561123251915, 0.015007288195192814, -0.002010498894378543, 0.07347431778907776, 0.010550674051046371, -0.061658091843128204, -0.07312320917844772, -0.034572333097457886, 0.0023455945774912834, 0.04097047075629234, 0.01738714799284935, -0.045120708644390106, -0.03207636624574661, 0.08686452358961105, 0.0034500218462198973, -0.03400234133005142, -0.000082493839727249, -0.016030030325055122, 0.03891653195023537, 0.034128040075302124, 0.04803387075662613, 0.024788009002804756, 0.0005675427964888513, -0.0043560778722167015, 0.03192993253469467, 0.0462505966424942, -0.0284937284886837, -0.038211848586797714, 0.014887785539031029, -0.03503160551190376, 0.05057653784751892, -0.0162961408495903, 0.02929389290511608, 0.03204059228301048, -0.014972273260354996, 0.05372326076030731, -0.03060799278318882, 0.0197005458176136, 0.0483882874250412, -0.0074723088182508945, -0.010870169848203659, -0.01721932925283909, -0.006902302149683237, -0.012617110274732113, -0.019269829615950584, -0.017020871862769127, -0.008216009475290775, 0.010425487533211708, 0.03848431631922722, -0.02657967619597912, -0.014236239716410637, -0.03153957426548004, -0.03210127726197243, -0.023367999121546745, 0.023008421063423157, -0.005333371926099062, 0.041898779571056366, -0.02880534715950489, 0.006791007239371538, -0.02084355615079403, -0.018846336752176285, 0.042093921452760696, 0.028038591146469116, -0.01994960568845272, -0.01581774465739727, -0.05879464000463486, -0.015286918729543686, -0.0017514147330075502, -0.0032782540656626225, -0.03719762712717056, 0.04252424091100693, -0.013999281451106071, -0.023564068600535393, -0.023867322131991386, -0.005882417783141136, 0.004740298725664616, 0.03829822689294815, 0.07446236163377762, -0.034769993275403976, -0.006132231093943119, -0.08238692581653595, -0.042021602392196655, 0.04575672745704651, 0.04045960679650307, -0.05448994040489197, -0.028361061587929726, -0.016305092722177505, -0.062272246927022934, -0.029398882761597633, 0.035884108394384384, 0.022845221683382988, 0.018085556104779243, 0.046936869621276855, 0.04317893460392952, 0.022843429818749428, 0.032193973660469055 ]
<p>$\vec F=m\vec a$ ,for moving object with 10 $km/s$ in a constant manner ,where acceleration is zero. ie No force on object ?</p> <p><a href="http://www.physicsforums.com/showthread.php?t=622711" rel="nofollow">http://www.physicsforums.com/showthread.php?t=622711</a></p>
g275
[ 0.07486787438392639, 0.03646393492817879, 0.0004461451026145369, -0.008251313120126724, 0.06824442744255066, -0.03339310735464096, 0.051254525780677795, 0.0558294951915741, -0.07593359053134918, -0.04080493003129959, -0.00038357885205186903, -0.015805033966898918, 0.00048112813965417445, 0.01532748807221651, -0.04563720151782036, 0.025374168530106544, -0.010326086543500423, -0.04695473611354828, -0.007583328988403082, -0.00885351188480854, 0.034414421766996384, -0.004375227261334658, -0.02883879654109478, -0.057612624019384384, 0.11409410834312439, 0.03590470924973488, 0.018601402640342712, -0.02972329966723919, -0.09185618162155151, -0.017354952171444893, 0.05639055743813515, -0.011844475753605366, 0.032257385551929474, -0.05338715761899948, -0.0010040603810921311, -0.002384509425610304, 0.028367960825562477, 0.040772393345832825, 0.009684679098427296, -0.029824823141098022, -0.011285180225968361, 0.0032458356581628323, 0.030319949612021446, 0.04174229875206947, 0.047442879527807236, 0.002136420691385865, -0.014358880929648876, -0.024439048022031784, -0.07478697597980499, 0.022447500377893448, -0.0031511797569692135, 0.03638956695795059, 0.005701542366296053, -0.03721031919121742, 0.00041511707240715623, 0.027689388021826744, 0.011317983269691467, -0.02197515405714512, -0.017505476251244545, -0.001820384874008596, -0.03929268568754196, -0.031900227069854736, 0.05525614693760872, -0.08175060153007507, 0.07568452507257462, 0.005877492483705282, -0.06566502153873444, 0.012101750820875168, -0.026333829388022423, 0.004870154894888401, -0.0000286664017039584, -0.010041516274213791, -0.04561576247215271, 0.008167656138539314, -0.06764597445726395, -0.0028913854621350765, -0.00039902509888634086, -0.03442218527197838, 0.02504093572497368, 0.0045641702599823475, -0.028966829180717468, 0.0031906391959637403, 0.020779158920049667, 0.017092496156692505, 0.007178317289799452, -0.06533965468406677, 0.013093962334096432, 0.020882150158286095, 0.02548757940530777, -0.016466403380036354, -0.012134027667343616, 0.026508208364248276, 0.04866059496998787, 0.042878903448581696, 0.039020195603370667, -0.06311369687318802, -0.01475266832858324, 0.09329140186309814, 0.002684395993128419, -0.030935687944293022, -0.03285141661763191, -0.004703240469098091, 0.009532371535897255, 0.027448203414678574, 0.0494784414768219, -0.08772915601730347, 0.010936036705970764, 0.018211977556347847, 0.017183203250169754, -0.052348002791404724, 0.037068646401166916, 0.0247647762298584, -0.04346318542957306, -0.08645963668823242, -0.05049049109220505, -0.0769006609916687, 0.0008724990766495466, 0.013948523439466953, -0.02460363879799843, -0.0006175055750645697, -0.030239706858992577, -0.009792680852115154, 0.012992314994335175, 0.08745317161083221, -0.03614160418510437, -0.03537731245160103, 0.019199049100279808, -0.03328773006796837, 0.005984754301607609, -0.05802788957953453, -0.013354741968214512, 0.0024485529866069555, 0.04784410819411278, -0.00028218465740792453, -0.07390226423740387, 0.03567742556333542, -0.06503869593143463, 0.015240056440234184, 0.001772328861989081, 0.036296311765909195, 0.0015905057080090046, -0.03624982386827469, 0.012061061337590218, -0.02940147928893566, -0.046245425939559937, -0.018641069531440735, -0.011515838094055653, 0.036770183593034744, 0.0913274958729744, 0.013568250462412834, 0.015630396082997322, 0.08316101133823395, -0.023387372493743896, 0.013136330991983414, 0.003029481042176485, -0.024985572323203087, 0.058528002351522446, 0.04923640936613083, -0.028603598475456238, -0.035425037145614624, 0.05319740250706673, 0.06556903570890427, 0.017685048282146454, -0.018089955672621727, -0.08730371296405792, 0.0009058564901351929, -0.02825193852186203, 0.03141644597053528, 0.015618122182786465, -0.0357016958296299, -0.0893639400601387, 0.024985358119010925, 0.05795044079422951, 0.046275295317173004, -0.0364639014005661, -0.0667126402258873, -0.00842469185590744, 0.011853407137095928, 0.006259015761315823, 0.036100998520851135, 0.02131364680826664, -0.04267914593219757, -0.0067648193798959255, 0.0008713703718967736, -0.015988510102033615, 0.02764233760535717, -0.039842892438173294, 0.06904244422912598, -0.07698412239551544, 0.010903147980570793, 0.001445131259970367, -0.018078146502375603, -0.026250483468174934, 0.053268734365701675, -0.03718678280711174, 0.045757491141557693, -0.02834533527493477, -0.0660591647028923, -0.009322239086031914, 0.02098805457353592, 0.05336623638868332, 0.08663519471883774, 0.025127645581960678, -0.007822807878255844, 0.010157408192753792, -0.06570995599031448, 0.02831845171749592, -0.029129547998309135, 0.033036597073078156, 0.0613543838262558, 0.048459336161613464, 0.017247669398784637, -0.039311327040195465, 0.04355822503566742, 0.02788206934928894, -0.028277210891246796, 0.02274409681558609, 0.012220840901136398, -0.026925014331936836, 0.03858606517314911, 0.004847028758376837, 0.018734458833932877, -0.016397511586546898, 0.012582791037857533, -0.06296167522668839, -0.06917216628789902, 0.024309324100613594, -0.05391428619623184, 0.02338598296046257, 0.04634345322847366, -0.0226130373775959, 0.005781791638582945, 0.0046086362563073635, 0.011003629304468632, 0.04122548922896385, 0.03646190091967583, -0.03270693123340607, 0.059743087738752365, -0.0177252609282732, 0.04273837432265282, 0.05089310184121132, -0.022750092670321465, -0.04029747098684311, -0.08113134652376175, 0.0356922522187233, -0.07877828180789948, 0.019982606172561646, 0.03098290227353573, 0.027781903743743896, -0.024395477026700974, -0.015054482966661453, -0.032761894166469574, 0.013253915123641491, 0.0393497534096241, 0.01609279401600361, 0.013659666292369366, -0.04085756838321686, 0.012117787264287472, -0.013821031898260117, 0.0003164290974382311, 0.006898792926222086, 0.013014407828450203, 0.015143772587180138, -0.013465745374560356, -0.031556546688079834, 0.05544253811240196, -0.06339932233095169, -0.0026551210321485996, 0.005300849676132202, -0.002502663293853402, -0.00821671262383461, 0.02717774361371994, 0.002685564337298274, 0.03032931126654148, -0.020489288493990898, 0.009096438065171242, 0.022795384749770164, 0.005551859736442566, -0.005642515141516924, -0.0035132314078509808, -0.0482480488717556, -0.009555395692586899, 0.03484387695789337, -0.022083669900894165, -0.03347565606236458, -0.020487697795033455, 0.013231992721557617, 0.033902209252119064, -0.035943470895290375, -0.03386850282549858, -0.03430105373263359, 0.03496869280934334, 0.054952267557382584, 0.01727926731109619, -0.01733505353331566, 0.05770092085003853, 0.038113437592983246, -0.00810285098850727, 0.010669727809727192, 0.05735914781689644, 0.045630477368831635, -0.03829333931207657, -0.003682128619402647, -0.03239800035953522, -0.007704238872975111, -0.05735575780272484, 0.014723972417414188, -0.07801728695631027, -0.03473319858312607, 0.05950593203306198, 0.008389387279748917, 0.07182980328798294, 0.009091684594750404, 0.013613251969218254, -0.04646267369389534, -0.005098650697618723, -0.0025879531167447567, -0.0186707004904747, 0.044334933161735535, 0.001081795897334814, 0.02124183624982834, -0.09870422631502151, 0.035879284143447876, -0.019415447488427162, 0.04449719190597534, 0.11290329694747925, 0.012575176544487476, 0.034508343786001205, 0.02559715323150158, 0.00989586766809225, -0.007740188390016556, 0.016295449808239937, 0.03968406096100807, -0.05374357849359512, 0.002567979507148266, -0.023206941783428192, -0.013520161621272564, 0.03742841258645058, -0.009849682450294495, 0.028090063482522964, -0.041721198707818985, -0.001571749453432858, -0.04694954305887222, 0.03648940101265907, 0.015696661546826363, 0.05521424114704132, 0.016036996617913246, 0.008968484587967396, 0.004847851116210222, -0.02699930965900421, 0.022434823215007782, -0.0413355752825737, 0.015766991302371025, -0.03674014285206795, -0.0036286860704421997, -0.02564358338713646, 0.017432037740945816, -0.02540542744100094, -0.027245381847023964, -0.03148723021149635, 0.000777006265707314, 0.004811474587768316, 0.01110025867819786, 0.061465341597795486, 0.0255472082644701, -0.015690956264734268, -0.055454403162002563, 0.0877675786614418, -0.03783898055553436, -0.026833612471818924, 0.009513387456536293, -0.03487218916416168, 0.0028615854680538177, -0.03157291188836098, 0.004211985971778631, -0.011687727645039558, 0.0017150137573480606, 0.018371321260929108, -0.037492528557777405, 0.04896046221256256, 0.07501853257417679, 0.05494185909628868, -0.055845096707344055, 0.012344330549240112, 0.001385507988743484, 0.006593362428247929, -0.04926889389753342, -0.03915533795952797, 0.022450225427746773, -0.035064175724983215, 0.051808591932058334, -0.020615411922335625, 0.0011781944194808602, 0.032441817224025726, 0.01179608702659607, -0.022572651505470276, 0.013739126734435558, -0.034864187240600586, -0.005073592532426119, 0.011186083778738976, 0.008488520048558712, 0.044131726026535034, 0.024842413142323494, -0.006004623137414455, 0.012699517421424389, 0.020402973517775536, 0.005355550907552242, 0.027145234867930412, 0.039600398391485214, -0.022398311644792557, -0.01117975078523159, -0.01073476579040289, -0.04814249277114868, -0.0524921752512455, -0.009225564077496529, 0.01317599881440401, 0.00045157319982536137, 0.03231300041079521, -0.008032760582864285, -0.05049151927232742, 0.005441434681415558, 0.05644482746720314, 0.02053218148648739, -0.02312820963561535, -0.01322946697473526, -0.007085381541401148, -0.044078927487134933, 0.022393129765987396, -0.0033383690752089024, 0.017538566142320633, -0.0216781347990036, 0.010229022242128849, 0.034878358244895935, 0.03258373960852623, -0.033205799758434296, 0.09589947015047073, 0.0029481975361704826, 0.042729154229164124, 0.05944904312491417, 0.018948020413517952, 0.005588345695286989, 0.045328546315431595, 0.01699579879641533, 0.035896703600883484, -0.01738656498491764, 0.05372605845332146, -0.0031917684245854616, -0.05175865441560745, 0.01267123594880104, -0.011213568970561028, -0.020856885239481926, 0.0010413267882540822, -0.027635471895337105, 0.004823943600058556, 0.007793653756380081, 0.022501524537801743, -0.02958822064101696, -0.007776367478072643, 0.03566443920135498, -0.01358072366565466, -0.07045497745275497, 0.03915075957775116, -0.02503742091357708, 0.00907842256128788, 0.029869526624679565, -0.003624245524406433, -0.040902696549892426, -0.023875193670392036, -0.0472591295838356, 0.01672310195863247, 0.02276919223368168, -0.01609552651643753, 0.0043736533261835575, 0.015359394252300262, 0.015910493209958076, 0.05918207764625549, 0.04033803194761276, 0.007887977175414562, 0.01679491437971592, 0.023376140743494034, -0.013441560789942741, -0.03368215635418892, 0.025004873052239418, -0.08212509006261826, 0.045705799013376236, 0.0043193865567445755, -0.021359845995903015, 0.019670723006129265, 0.03133948892354965, 0.01037670113146305, 0.060921791940927505, 0.04310865327715874, -0.04582199826836586, -0.05458827689290047, 0.02696838602423668, -0.030210120603442192, 0.01036587543785572, -0.021031199023127556, 0.012462960556149483, 0.02420911192893982, -0.08704186975955963, -0.04274227097630501, 0.00485185207799077, 0.015575350262224674, 0.01667044870555401, 0.06416196376085281, 0.06761597096920013, 0.020014386624097824, 0.01596365123987198, 0.047342654317617416, -0.010748517699539661, 0.05740197002887726, 0.10235041379928589, -0.030695267021656036, -0.04061400890350342, 0.006065593101084232, 0.015148901380598545, -0.027051517739892006, -0.03758848458528519, -0.03393712639808655, 0.047636426985263824, -0.03507860004901886, -0.010752545669674873, -0.0036475046072155237, 0.012694986537098885, 0.027885677292943, -0.0006426965701393783, -0.04126737266778946, -0.033043451607227325, 0.05579983443021774, 0.010936169885098934, -0.056267645210027695, 0.07435298711061478, -0.09197652339935303, -0.014454497024416924, -0.0067082783207297325, 0.06137217953801155, -0.027860570698976517, 0.014844625256955624, -0.02428186871111393, -0.04295974224805832, -0.04402593523263931, 0.007885328494012356, 0.06664968281984329, -0.06458316743373871, 0.0031304971780627966, -0.019777391105890274, 0.01374328974634409, 0.05952223390340805, -0.09591054171323776, -0.010227045975625515, 0.018464090302586555, 0.006132054608315229, 0.0034823953174054623, 0.04028031975030899, 0.04420100897550583, 0.004395660944283009, 0.021999314427375793, -0.02192983403801918, -0.07811776548624039, 0.058501578867435455, -0.00905586313456297, 0.05412441864609718, -0.023444857448339462, 0.013274145312607288, -0.06687605381011963, 0.04376917704939842, 0.0024211443960666656, 0.03013455495238304, 0.0012320933165028691, -0.03657517209649086, 0.043590642511844635, -0.06654965877532959, -0.022273287177085876, 0.02451467514038086, -0.016720620915293694, -0.024952836334705353, -0.005362506490200758, -0.06250224262475967, 0.033644478768110275, 0.013937737792730331, 0.0060488441959023476, 0.027238760143518448, -0.05165881663560867, -0.0012455624528229237, -0.023718468844890594, -0.004278936889022589, -0.04515988752245903, 0.051216695457696915, 0.007622354198247194, -0.042125485837459564, 0.0025367846246808767, -0.026752084493637085, -0.012100454419851303, -0.024905605241656303, -0.007063036784529686, -0.01580623909831047, -0.0036862038541585207, 0.009237841702997684, 0.045313768088817596, -0.0024683668743819, 0.06651291996240616, 0.007269661407917738, 0.034077517688274384, -0.02743379957973957, 0.014172590337693691, -0.026867184787988663, -0.01044617872685194, -0.017464803531765938, -0.0167408250272274, -0.042028333991765976, 0.041150424629449844, -0.012497455812990665, 0.022620534524321556, -0.011913211084902287, 0.019427575170993805, 0.008546704426407814, -0.02528334967792034, 0.009188083000481129, -0.028792940080165863, 0.0032799795735627413, -0.020740853622555733, -0.028421320021152496, 0.006439704913645983, -0.025978511199355125, 0.0053425501100718975, -0.04764855280518532, 0.014763666316866875, 0.06766338646411896, -0.04901067912578583, 0.0035769110545516014, 0.021398723125457764, -0.027774417772889137, -0.005093161016702652, -0.04313572123646736, 0.07903209328651428, -0.007515766657888889, 0.07156345993280411, 0.06624950468540192, 0.0011915237409994006, 0.004277324303984642, 0.015211069025099277, 0.010084157809615135, 0.0029592844657599926, -0.03658957779407501, -0.013112719170749187, 0.0037353564985096455, 0.04923245310783386, -0.010196389630436897, 0.01974710263311863, 0.016995199024677277, -0.017922066152095795, 0.021925561130046844, 0.02144494466483593, -0.05332275107502937, 0.012054894119501114, 0.026979781687259674, -0.01326113659888506, 0.021738629788160324, 0.006759180687367916, -0.0345781110227108, -0.03583383187651634, 0.03324291855096817, -0.03630177676677704, 0.007089944556355476, 0.009082783944904804, -0.06149887666106224, -0.026895225048065186, 0.0035592177882790565, 0.01728220283985138, 0.031153984367847443, 0.011122619733214378, -0.039456747472286224, -0.005160588305443525, -0.010458013974130154, 0.05452192947268486, -0.025492582470178604, 0.0449473075568676, 0.002658300334587693, -0.001868251129053533, 0.006650513503700495, 0.006647096481174231, -0.02488044463098049, -0.012292993254959583, 0.011757073923945427, -0.010309970937669277, -0.03073194809257984, 0.011123469099402428, 0.03546832874417305, -0.02709735371172428, 0.014956383965909481, 0.02751068025827408, 0.02468213438987732, -0.05345848575234413, 0.008512717671692371, 0.01383721549063921, -0.0579739511013031, -0.0026688603684306145, -0.010136219672858715, -0.006243589334189892, -0.04326795041561127, -0.0030864072032272816, -0.010709794238209724, 0.01772894337773323, -0.05556927248835564, 0.045752327889204025, -0.014705225825309753, -0.05695917829871178, -0.00970007386058569, 0.01585954986512661, -0.045079365372657776, 0.0035898045171052217, -0.006756721995770931, -0.027276767417788506, 0.030015630647540092, 0.021416032686829567, -0.008370114490389824, 0.05304170772433281, 0.005375829059630632, -0.037923816591501236, -0.019933901727199554, -0.05316801369190216, 0.029962027445435524, -0.042607810348272324, -0.00424782931804657, -0.004982904065400362, -0.06640342622995377, -0.0008406711276620626, 0.0032027428969740868, -0.032008472830057144, 0.005221676081418991, -0.04848536103963852, 0.0013223299756646156, 0.028546780347824097, -0.06464976817369461, -0.019987044855952263, 0.012258908711373806, -0.031186416745185852, -0.06256809830665588, 0.0531332790851593, -0.03674078732728958, -0.037897106260061264, -0.04599250108003616, 0.0734795331954956, 0.039328932762145996, -0.03593827411532402, -0.012885757721960545, 0.08798127621412277, 0.01843460649251938, 0.0014555825619027019, 0.038973335176706314, -0.026099754497408867, -0.0740559846162796, -0.02762535773217678, 0.03456157445907593, -0.010839794762432575, -0.017662230879068375, 0.02239825949072838, 0.027192113921046257, 0.0043435781262815, -0.014898519963026047, 0.006065950263291597, -0.03971494361758232, 0.02683308534324169, 0.031053297221660614, -0.06971948593854904, -0.025977090001106262, -0.0126468725502491 ]
<p>Water on earth has been theorized to have come through comets trapped inside crystals. But why wouldn't that water evaporate on impact, and wouldn't the atmosphere at that time allow the vapours to escape Earth?</p> <p>Also, what is the current scientific opinion of the validity of this theory ?</p>
g8384
[ 0.04214254766702652, 0.07624418288469315, 0.016893556341528893, -0.0016680426197126508, -0.06877966970205307, 0.09824243932962418, -0.003849866334348917, -0.0496491976082325, -0.02417951636016369, 0.012897202745079994, 0.008667401038110256, -0.0344037190079689, 0.0309183057397604, 0.004229143727570772, -0.04958502575755119, 0.049514804035425186, 0.014376071281731129, -0.08222062140703201, -0.050036847591400146, 0.05101854354143143, -0.006963365711271763, -0.08421146869659424, -0.027212947607040405, -0.022095616906881332, -0.023620551452040672, -0.005198335740715265, 0.027991008013486862, -0.05715935677289963, 0.049736227840185165, -0.012941593304276466, 0.03730735555291176, -0.005819329526275396, -0.009348249062895775, -0.07077576965093613, -0.03943122923374176, -0.013621590100228786, -0.03740868344902992, 0.011291188187897205, 0.06346733868122101, -0.08810895681381226, 0.013575035147368908, -0.026905639097094536, -0.0746234580874443, 0.073722243309021, -0.01701224036514759, -0.015922823920845985, 0.006456492934376001, -0.048466894775629044, 0.00794314593076706, -0.0580068975687027, -0.011902819387614727, 0.04402079060673714, 0.01440250314772129, 0.01022473443299532, -0.049111589789390564, 0.029526229947805405, 0.021040180698037148, -0.008809559978544712, 0.05284620821475983, -0.06322941184043884, -0.022908324375748634, 0.0328906811773777, 0.019686277955770493, 0.017810093238949776, 0.05724075064063072, -0.03334954008460045, -0.05815131217241287, 0.03393286466598511, 0.05254317820072174, -0.010859458707273006, 0.013788224197924137, -0.04778992012143135, -0.04005579650402069, 0.002793061314150691, 0.0051703848876059055, -0.007586358580738306, 0.013184920884668827, -0.001873504719696939, 0.08153652399778366, 0.013467540964484215, -0.0027752176392823458, 0.01834826171398163, -0.024596646428108215, 0.004967601969838142, 0.04598105698823929, 0.0009916210547089577, 0.006319490261375904, -0.03718976303935051, 0.007223216351121664, -0.08211550861597061, -0.06941050291061401, -0.07548471540212631, -0.006467513740062714, 0.03705568611621857, -0.0052002244628965855, 0.028099961578845978, 0.04351300746202469, 0.022984923794865608, -0.008960389532148838, 0.05555318295955658, 0.01956959441304207, -0.06577614694833755, 0.035618774592876434, 0.015636352822184563, 0.05720067024230957, 0.015933318063616753, 0.038982752710580826, -0.009861917234957218, 0.008532397449016571, -0.038044098764657974, 0.022757241502404213, 0.007447902578860521, -0.01161328423768282, -0.0026723442133516073, 0.005284127313643694, 0.01588587276637554, -0.03067292459309101, 0.014191025868058205, -0.008841450326144695, 0.01636243611574173, 0.03241095691919327, 0.07795573025941849, -0.014904100447893143, 0.008850457146763802, -0.02544909343123436, 0.011582729406654835, 0.02191614918410778, -0.05432332307100296, 0.025900237262248993, 0.006934552453458309, -0.011126228608191013, -0.0015389003092423081, -0.004438305739313364, 0.031110744923353195, 0.020246773958206177, -0.04454497620463371, 0.003766668727621436, 0.006171306129544973, -0.027419395744800568, -0.024837719276547432, 0.06693164259195328, 0.04299181327223778, -0.0037986431270837784, 0.06745278090238571, -0.029813189059495926, -0.010613632388412952, -0.04739297181367874, 0.08444143831729889, 0.019061997532844543, -0.020261891186237335, -0.0010856378357857466, 0.04641823470592499, 0.03020068258047104, 0.00521475076675415, -0.03038543090224266, -0.03369734063744545, 0.01700938493013382, 0.018899189308285713, -0.05578991770744324, 0.0016328144120052457, 0.03610663115978241, 0.051947157829999924, 0.015337921679019928, 0.02778879925608635, -0.041662681847810745, 0.027461770921945572, 0.02910451777279377, -0.026143888011574745, -0.008573394268751144, -0.007340083830058575, -0.06520631909370422, 0.013659100979566574, -0.009766430594027042, 0.016571907326579094, -0.0034400795120745897, 0.02593441680073738, 0.05136039853096008, -0.0033364708069711924, 0.02431889995932579, -0.0361805334687233, 0.020183704793453217, -0.03911220654845238, -0.024876641109585762, -0.013409432955086231, -0.02245713211596012, -0.015513586811721325, 0.032520897686481476, 0.009349413216114044, -0.005657600704580545, -0.015768736600875854, 0.011084010824561119, -0.08726954460144043, -0.010849939659237862, -0.033159516751766205, 0.03220793604850769, -0.056114982813596725, 0.0059222811833024025, 0.026226339861750603, -0.04285416007041931, -0.005037154536694288, -0.007767532020807266, 0.03490912541747093, -0.020609641447663307, -0.009650351479649544, 0.02622493915259838, 0.023520851507782936, -0.03955758363008499, 0.04538353532552719, 0.03548389673233032, -0.0035532687325030565, -0.030512096360325813, 0.011329863220453262, 0.019695308059453964, 0.023934803903102875, -0.046433430165052414, 0.014326340518891811, -0.014498008415102959, -0.015039917081594467, -0.009267893619835377, -0.00482372147962451, -0.051742397248744965, 0.03317662328481674, -0.05368465930223465, 0.028978265821933746, -0.034887928515672684, -0.00043683446710929275, -0.09067105501890182, 0.014363893307745457, 0.01865665800869465, -0.016218475997447968, -0.00933744665235281, 0.00006641558138653636, -0.04717499762773514, -0.02683108299970627, 0.006555345840752125, 0.0600179061293602, -0.001881286851130426, -0.03909889608621597, 0.0017056707292795181, 0.019284136593341827, 0.026719888672232628, -0.06595245748758316, -0.05465860664844513, -0.04554387554526329, 0.10093427449464798, -0.08015302568674088, 0.010703719221055508, -0.000112882764369715, -0.005847970023751259, 0.01057013962417841, -0.02204415760934353, 0.0005355098401196301, -0.04422437399625778, -0.0057174707762897015, -0.023578720167279243, 0.01215341966599226, -0.007555736694484949, 0.02066376991569996, -0.032119426876306534, -0.008294278755784035, 0.025076264515519142, -0.04392598569393158, 0.02475549653172493, 0.03438563644886017, -0.08011886477470398, 0.036736227571964264, -0.04279378056526184, 0.0797187089920044, 0.023088188841938972, -0.06257936358451843, 0.0014190471265465021, 0.03315246105194092, -0.05509825050830841, 0.04958220198750496, -0.049129802733659744, -0.028536900877952576, -0.028218835592269897, -0.009870325215160847, 0.03507070988416672, -0.036202725023031235, -0.008264165371656418, -0.01437399908900261, -0.040973152965307236, 0.007786869537085295, 0.039709385484457016, -0.013217429630458355, -0.01930452696979046, 0.06389997899532318, 0.03931941092014313, -0.04493415728211403, 0.07159677892923355, -0.0060348715633153915, -0.024754786863923073, 0.05133993923664093, -0.012815248221158981, 0.020448068156838417, 0.03702523186802864, -0.014117054641246796, -0.05999196693301201, 0.020604612305760384, -0.010516047477722168, -0.0018692633602768183, -0.017783842980861664, 0.021088944748044014, -0.030986176803708076, 0.06502766907215118, 0.01070848386734724, 0.031195836141705513, 0.035399485379457474, -0.09074931591749191, 0.013529922813177109, 0.08441643416881561, -0.04956863448023796, 0.017237588763237, -0.0007457847823388875, 0.03520163521170616, -0.036762259900569916, 0.03572613745927811, 0.09390616416931152, -0.022937383502721786, -0.0017652881797403097, -0.0028973391745239496, 0.03902022913098335, -0.0012212274596095085, -0.0366920530796051, 0.039677027612924576, -0.05491884425282478, -0.05302310362458229, -0.011937130242586136, -0.025116311386227608, -0.04532961547374725, 0.021868953481316566, 0.019178789108991623, 0.012716349214315414, -0.008088772185146809, -0.015660220757126808, 0.02426639385521412, 0.033532336354255676, 0.01569642312824726, 0.05228534713387489, -0.029774462804198265, 0.020918002352118492, -0.004146498627960682, 0.0044029951095581055, 0.02313123270869255, 0.02758515626192093, 0.02325364761054516, 0.015160557813942432, -0.03033970668911934, -0.008987951092422009, 0.07786142081022263, 0.006012187339365482, -0.016054680570960045, -0.02955613285303116, -0.046974048018455505, 0.04453917220234871, -0.045679252594709396, 0.007202459499239922, 0.02456577867269516, -0.005920981056988239, -0.008095459081232548, 0.03441271558403969, 0.03440328687429428, -0.024875402450561523, 0.016406701877713203, -0.049005381762981415, -0.032219890505075455, -0.007597988471388817, -0.03333006054162979, 0.019254673272371292, 0.03357933461666107, 0.014833063818514347, -0.00751775037497282, 0.06432898342609406, 0.07250917702913284, -0.06885743886232376, 0.05551805719733238, 0.03415968269109726, 0.021115742623806, 0.028162194415926933, 0.030840886756777763, -0.022446373477578163, 0.014407848007977009, 0.011661667376756668, -0.01459123007953167, 0.0007536513148806989, -0.04671696946024895, 0.04725295677781105, -0.034478988498449326, -0.029215427115559578, 0.0039027167949825525, -0.0214469525963068, 0.039529427886009216, -0.01732148788869381, -0.004523104056715965, 0.02977120876312256, -0.035579532384872437, 0.022919591516256332, -0.009262687526643276, -0.04009038954973221, 0.023757997900247574, 0.018974369391798973, -0.028325024992227554, -0.04099148511886597, 0.01762765273451805, 0.021028539165854454, -0.012351548299193382, -0.006638288497924805, 0.0011719365138560534, -0.02323831245303154, 0.03938426449894905, 0.010276516899466515, -0.08278252929449081, 0.01886863261461258, -0.013315210118889809, -0.03938454017043114, -0.021730700507760048, 0.027758628129959106, 0.049150921404361725, 0.04184466227889061, -0.010894452221691608, -0.001811382477171719, 0.0029320046305656433, -0.017917318269610405, 0.050342101603746414, 0.05260689929127693, 0.00916602835059166, -0.0005615658592432737, -0.022039717063307762, 0.012173620983958244, 0.0027945498004555702, 0.015313094481825829, -0.028145309537649155, 0.030213821679353714, 0.0437493659555912, 0.053042829036712646, 0.013235832564532757, 0.021249596029520035, -0.018267476931214333, 0.021894559264183044, 0.041706979274749756, 0.028888443484902382, 0.030028069391846657, 0.040422528982162476, -0.004842143505811691, 0.057063028216362, 0.09469279646873474, -0.006037051323801279, 0.04907825589179993, 0.014922570437192917, -0.07714762538671494, 0.0050052558071911335, -0.026906410232186317, 0.005083049181848764, -0.054654937237501144, 0.01261864136904478, -0.05529877543449402, 0.011348593980073929, -0.0032593095675110817, 0.09613313525915146, -0.08212762326002121, 0.020790189504623413, -0.01624504290521145, 0.05562742426991463, 0.031041542068123817, -0.04915769770741463, -0.046850401908159256, -0.059822358191013336, 0.02537444606423378, -0.03040394000709057, 0.005521824583411217, 0.025998683646321297, 0.05515456572175026, 0.07957890629768372, 0.0247889943420887, -0.02285698987543583, -0.031489938497543335, -0.027498606592416763, 0.053851883858442307, 0.0009725773124955595, 0.015830164775252342, 0.02070028707385063, 0.002102353610098362, 0.09707548469305038, -0.028039129450917244, -0.0006272118771448731, -0.06232092157006264, 0.01075787004083395, -0.032345302402973175, -0.029554884880781174, -0.007530197035521269, -0.021735046058893204, -0.016715243458747864, -0.047431789338588715, -0.020807355642318726, -0.020736010745167732, -0.05142919346690178, -0.058057524263858795, -0.0026725204661488533, 0.0035828708205372095, -0.06660686433315277, -0.02897697314620018, -0.006341959815472364, -0.017453240230679512, 0.026186667382717133, -0.021341457962989807, 0.023261135444045067, -0.025678278878331184, -0.008473552763462067, 0.024468911811709404, 0.00026800468913279474, -0.04261905327439308, -0.06816133111715317, 0.06875214725732803, 0.04148278757929802, 0.021352628245949745, -0.020933235064148903, -0.004835694562643766, 0.014306715689599514, -0.016200371086597443, -0.029040182009339333, -0.040944602340459824, -0.009988824836909771, 0.04510335996747017, 0.027776334434747696, -0.013816295191645622, 0.0014549237675964832, -0.043834932148456573, 0.014135420322418213, -0.020173216238617897, -0.012841782532632351, 0.009297388605773449, 0.03484739735722542, 0.004257580731064081, 0.03491935878992081, -0.04770778492093086, -0.06830288469791412, 0.024005742743611336, 0.026065021753311157, -0.040500443428754807, 0.026180051267147064, -0.029564814642071724, 0.024275116622447968, 0.06947920471429825, 0.02201480232179165, 0.05944116413593292, 0.035638127475976944, 0.019131721928715706, 0.032043419778347015, 0.0195468757301569, 0.004818309098482132, 0.03467896580696106, -0.06353949010372162, -0.004073936492204666, -0.016758384183049202, 0.0066468846052885056, 0.011838068254292011, -0.011165011674165726, -0.024790503084659576, -0.03367923945188522, -0.02408355474472046, 0.01868213154375553, -0.01324839610606432, 0.055559512227773666, -0.01222265139222145, 0.08733532577753067, 0.019983036443591118, 0.009038450196385384, -0.0015121621545404196, 0.002166098915040493, -0.015378845855593681, 0.03693656995892525, 0.006245715077966452, -0.026386702433228493, -0.0002998976851813495, 0.013179083354771137, 0.0091101648285985, 0.02203691191971302, 0.022663848474621773, -0.024676188826560974, 0.02864348515868187, -0.031211605295538902, 0.039608996361494064, -0.049952637404203415, -0.018012644723057747, -0.03258180245757103, -0.05478041246533394, -0.013871676288545132, 0.0328487791121006, -0.0058069308288395405, -0.006014742888510227, -0.010341993533074856, 0.0050348276272416115, -0.022784505039453506, -0.007628718391060829, -0.06830498576164246, 0.02660747990012169, 0.03276388347148895, -0.024986598640680313, -0.011471952311694622, 0.0003982889757025987, 0.03183579817414284, 0.044376175850629807, 0.04643438756465912, 0.004898848012089729, -0.00031286993180401623, 0.03541623800992966, -0.018797582015395164, 0.012493916787207127, 0.02967432327568531, -0.05625203996896744, 0.004376895725727081, 0.0406888872385025, -0.04626245051622391, 0.011466662399470806, -0.072420135140419, -0.002362303202971816, 0.02162398397922516, 0.004906749818474054, 0.022842101752758026, -0.014440739527344704, 0.004205058794468641, -0.028067169710993767, -0.05144800990819931, -0.0064629861153662205, -0.0033869820181280375, -0.03472812846302986, 0.006453230977058411, 0.08398639410734177, 0.034738995134830475, -0.026855995878577232, -0.02072419971227646, 0.0407031811773777, -0.0034109142143279314, -0.06869329512119293, 0.018049437552690506, 0.046707071363925934, -0.005238764453679323, -0.010472831316292286, -0.04545002803206444, -0.020861858502030373, -0.04066820070147514, -0.023553919047117233, 0.037680476903915405, -0.023037832230329514, 0.03582995757460594, -0.03150308504700661, -0.040282733738422394, -0.010189240798354149, -0.055888522416353226, 0.027005845680832863, -0.04229482635855675, 0.015331256203353405, -0.00611470453441143, 0.011333960108458996, 0.026507046073675156, -0.019209159538149834, 0.024118956178426743, -0.028950277715921402, -0.0006498623406514525, -0.03999941423535347, 0.0005267197848297656, 0.036906663328409195, -0.001214470132254064, 0.06953207403421402, -0.010453138500452042, 0.04144139215350151, -0.048145733773708344, 0.05658923462033272, -0.010296079330146313, 0.00793145876377821, 0.025032246485352516, -0.0408993698656559, -0.007228868547827005, -0.023745307698845863, 0.03588518500328064, 0.05085090920329094, 0.021436017006635666, -0.009315840899944305, 0.03588259965181351, 0.02526889741420746, -0.008517601527273655, 0.03880313038825989, 0.04379069060087204, -0.012776028364896774, 0.048253726214170456, -0.00043359771370887756, 0.019430523738265038, 0.05386993661522865, -0.06998030096292496, 0.018290948122739792, 0.04975273087620735, 0.05482936650514603, -0.012204734608530998, -0.025005316361784935, -0.002919895574450493, 0.02098730020225048, -0.036701593548059464, 0.015614950098097324, -0.04070732742547989, -0.003111850004643202, 0.031548094004392624, 0.05257469788193703, -0.026424333453178406, 0.05281262472271919, 0.014525647275149822, 0.031301338225603104, 0.10661957412958145, -0.04212421923875809, -0.03358125314116478, -0.052232880145311356, -0.018279919400811195, 0.05308514088392258, 0.0032628346234560013, 0.027126362547278404, -0.03854931518435478, -0.020044023171067238, 0.009906536899507046, 0.008874584920704365, -0.04356706887483597, -0.014507310464978218, -0.08655565232038498, -0.05533258244395256, -0.08699189126491547, 0.026940861716866493, 0.06297288835048676, 0.004362860694527626, -0.018012385815382004, 0.0050402358174324036, -0.06263027340173721, -0.016427217051386833, 0.04399767518043518, 0.009440068155527115, -0.011568660847842693, 0.012314011342823505, -0.01152352336794138, 0.020480843260884285, -0.08869299292564392, -0.03496707230806351, -0.00867247860878706, 0.011462047696113586, 0.014635058119893074, 0.03221643716096878, -0.05992111191153526, 0.05371206998825073, -0.0604441873729229, -0.0580822192132473, 0.004853277001529932, -0.05110691860318184, -0.009777582250535488, 0.04251497611403465, -0.0356503427028656, -0.03477960079908371, 0.017381491139531136, 0.03907015919685364, -0.06422264873981476, -0.027447909116744995, 0.0487884022295475, 0.06120539829134941, -0.006630908232182264, -0.02929043397307396, -0.01037332322448492, 0.060383494943380356, -0.03385293111205101, -0.005491906311362982, -0.02495870739221573, -0.016650745645165443, -0.02302953042089939 ]
<p>Why do we need to use the sign convention again in the mirror equation while solving numericals when we know we have already used a convention while deriving the mirror equation? The question is not about the importance of sign conventions but why do we need to use the sign conventions twice? Doesn't the equation already include a sign convention?</p> <p>1/u + 1/v = 1/ f</p> <p>Or say, in the magification formula: height of image/ height of object = - (v/u)</p> <p>Why do I need to bother about the signs ( -u or - v or +f) while using the above equations? </p>
g8385
[ -0.0487980879843235, 0.012372057884931564, 0.007492184638977051, -0.013135530054569244, 0.008001278154551983, -0.036155249923467636, 0.08827974647283554, 0.09160928428173065, -0.02048385702073574, -0.01565508358180523, -0.06025940552353859, 0.061723146587610245, 0.052736084908246994, 0.06044824421405792, -0.015067418105900288, 0.013597153127193451, 0.026341194286942482, 0.003322859527543187, -0.008631723001599312, 0.067936971783638, -0.12835460901260376, 0.0327661894261837, 0.048225436359643936, -0.05660422891378403, -0.08778516948223114, -0.013768930919468403, 0.012105662375688553, 0.00115452881436795, -0.007211894728243351, -0.0034017800353467464, 0.04688454791903496, 0.0021526606287807226, 0.10186313092708588, -0.05215184763073921, -0.016594653949141502, -0.03222111612558365, 0.052514832466840744, 0.025052158161997795, -0.016241131350398064, 0.013808725401759148, 0.02801511436700821, 0.016841797158122063, -0.0477815717458725, 0.055140070617198944, -0.03366834670305252, -0.017654795199632645, -0.015301881358027458, -0.06348459422588348, 0.042365849018096924, -0.043944478034973145, 0.02307095006108284, 0.002530510537326336, 0.019549429416656494, -0.01332251075655222, -0.00479144137352705, 0.06539864093065262, 0.013466703705489635, -0.02849738672375679, -0.0008738305186852813, 0.04333106055855751, 0.024413643404841423, -0.00614100182428956, -0.02342449687421322, 0.020215950906276703, 0.03507427126169205, 0.02404622733592987, -0.02428814209997654, 0.03778628632426262, -0.00903979130089283, 0.04749034345149994, -0.04967394843697548, -0.02056058496236801, 0.03020246885716915, -0.027986817061901093, 0.027877163141965866, -0.004696905147284269, 0.04168764129281044, -0.03789564594626427, 0.005571198649704456, 0.05548073351383209, 0.0036122931633144617, -0.008094248361885548, 0.09622395783662796, 0.05750146880745888, -0.018682226538658142, 0.03083725832402706, -0.0009244409739039838, 0.05264316499233246, -0.040055010467767715, 0.01749354600906372, 0.03840233385562897, 0.04510120302438736, 0.004952156450599432, 0.006393108516931534, -0.003103627124801278, -0.012151159346103668, 0.019473088905215263, -0.002524856710806489, -0.026976728811860085, 0.07161315530538559, -0.04059666022658348, -0.013125942088663578, -0.03825044259428978, 0.0017075001960620284, -0.04647392779588699, 0.020243624225258827, 0.0021321692038327456, 0.061203837394714355, -0.07441141456365585, -0.06538007408380508, -0.06731737405061722, -0.041303087025880814, -0.020253432914614677, -0.011243756860494614, -0.05616305023431778, -0.03924058377742767, 0.09603048115968704, -0.004876806866377592, -0.024833330884575844, 0.02328784018754959, -0.025119207799434662, -0.03654893860220909, 0.030378226190805435, 0.054879821836948395, -0.008513234555721283, -0.04687533900141716, 0.03864431008696556, 0.009432423859834671, 0.05317645147442818, -0.0059617916122078896, 0.0048719304613769054, -0.013912167400121689, -0.04117368906736374, 0.021791674196720123, 0.0026754795107990503, 0.02565191499888897, -0.030160967260599136, -0.03234817460179329, 0.014856407418847084, -0.03561513498425484, -0.002796450862661004, 0.024110540747642517, -0.008717022836208344, -0.07769297063350677, -0.06185675412416458, -0.05919869244098663, 0.007436360698193312, -0.039007216691970825, 0.04548183083534241, 0.018745211884379387, -0.024311065673828125, 0.03922341391444206, 0.018647994846105576, -0.018373651430010796, -0.03339307755231857, -0.010677818208932877, 0.04218146950006485, 0.0041928342543542385, 0.019545018672943115, -0.009339675307273865, 0.09019846469163895, -0.06143736094236374, -0.027114078402519226, 0.02837400510907173, -0.04491755738854408, 0.010903051123023033, -0.023955222219228745, -0.02821028232574463, -0.06176255643367767, -0.04144896939396858, -0.04449530690908432, 0.02523319609463215, 0.03610822930932045, -0.007796506397426128, 0.05377225577831268, 0.014352916739881039, 0.06145912781357765, -0.03647877275943756, -0.012593085877597332, 0.07785360515117645, -0.033185411244630814, 0.009732373058795929, -0.03146733343601227, -0.007614681962877512, 0.020448580384254456, 0.029032889753580093, -0.024058904498815536, 0.03235073387622833, -0.02175135724246502, 0.023406680673360825, 0.02288803644478321, 0.028280457481741905, -0.01892237737774849, 0.04744257777929306, -0.054232336580753326, 0.015383301302790642, -0.014295918866991997, -0.005348468665033579, -0.06339538097381592, 0.07253017276525497, -0.025767426937818527, 0.04610159993171692, 0.0528787337243557, 0.02480173110961914, -0.05075685679912567, 0.0384395569562912, -0.008702131919562817, 0.02868211455643177, 0.0034862018655985594, -0.0384463369846344, 0.020849622786045074, 0.029092509299516678, -0.02977031283080578, -0.01164199598133564, -0.04729260876774788, -0.020455561578273773, 0.032727669924497604, -0.0018044207245111465, -0.010158916004002094, 0.06711054593324661, -0.030341414734721184, -0.010545918717980385, 0.04414473846554756, -0.013649829663336277, -0.03052583709359169, 0.059532780200242996, 0.0028957128524780273, -0.016232497990131378, 0.02014421671628952, -0.029533404856920242, -0.002396444557234645, -0.04056256636977196, -0.017552629113197327, -0.008501811884343624, 0.02481330744922161, -0.003224364249035716, 0.004607595968991518, 0.04057614877820015, 0.07366102188825607, 0.0701506957411766, 0.021252527832984924, -0.004845134448260069, 0.011938927695155144, 0.01956234872341156, 0.03587069362401962, -0.025441192090511322, -0.014179875142872334, 0.010371475480496883, -0.03742186352610588, 0.04787468910217285, -0.0526430569589138, 0.021411316469311714, -0.003787995083257556, -0.05683661997318268, -0.009573511779308319, -0.0313553586602211, 0.030368467792868614, -0.0068572708405554295, 0.007911743596196175, 0.04760384559631348, 0.0459526889026165, -0.0029391665011644363, 0.009457428008317947, -0.0035181581042706966, -0.0453718937933445, -0.001081080292351544, -0.019589945673942566, 0.04815496876835823, 0.11620362102985382, 0.02136186696588993, -0.02279670536518097, 0.043601155281066895, 0.02019544690847397, -0.03068108670413494, -0.04140697047114372, -0.03431658819317818, 0.00928676687180996, -0.07313049584627151, 0.000020322311684140004, 0.07211568206548691, -0.017754677683115005, -0.03662431612610817, -0.07911098003387451, -0.025525754317641258, 0.02885439246892929, -0.017168549820780754, -0.0021904052700847387, 0.003897178452461958, -0.03969772532582283, 0.030555129051208496, -0.02317303605377674, -0.008747526444494724, -0.021910985931754112, -0.025190355256199837, -0.00022990527213551104, -0.02166290208697319, -0.031249288469552994, -0.053952302783727646, 0.044907525181770325, 0.009873449802398682, 0.00046778260730206966, 0.0010809801751747727, -0.027463944628834724, -0.04765518754720688, 0.0019979788921773434, 0.03664379566907883, 0.02114940620958805, -0.02967902272939682, 0.004951893351972103, -0.011051755398511887, -0.02453169971704483, 0.08011160045862198, -0.012506167404353619, 0.005850871559232473, -0.030960703268647194, 0.004305086098611355, -0.05833910033106804, -0.020502014085650444, -0.024820229038596153, -0.004230617545545101, -0.1006094291806221, -0.047839052975177765, 0.0608060397207737, 0.03005959838628769, 0.03426232561469078, 0.07003972679376602, 0.017513548955321312, 0.014910591766238213, 0.030765336006879807, -0.0027093440294265747, 0.04385386034846306, 0.00435103103518486, 0.051777489483356476, 0.0008106589666567743, -0.031119661405682564, -0.056732695549726486, 0.011051292531192303, -0.017811311408877373, -0.019256167113780975, -0.00073579594027251, 0.0006258386420086026, 0.005042894743382931, 0.02949213795363903, -0.050647418946027756, 0.05603187903761864, -0.03703826293349266, -0.014793870970606804, 0.06865500658750534, -0.02860887534916401, -0.030910547822713852, -0.028826860710978508, 0.057285986840724945, 0.005730113945901394, -0.010895187966525555, -0.0340304896235466, 0.05758059769868851, 0.04764999821782112, 0.06839260458946228, -0.0038839553017169237, -0.024858852848410606, 0.013551045209169388, 0.01734847202897072, -0.02740750089287758, 0.011570889502763748, 0.021008217707276344, 0.0005093542276881635, 0.006025020964443684, 0.053677983582019806, -0.022830653935670853, -0.006530702579766512, 0.020309418439865112, 0.03929220139980316, -0.0006942028412595391, -0.04358620196580887, -0.04290109500288963, 0.02935391664505005, 0.05417336896061897, 0.021059133112430573, 0.003077693982049823, -0.009232637472450733, 0.06086040660738945, -0.027578238397836685, 0.004014795180410147, -0.04024885222315788, -0.007689137477427721, -0.03930358588695526, -0.07420697808265686, -0.006082427222281694, 0.015565156005322933, 0.0019173341570422053, 0.06155441701412201, -0.014541258104145527, 0.013687358237802982, 0.031291890889406204, -0.00499295350164175, -0.005458812694996595, -0.009512290358543396, -0.023778967559337616, 0.020585106685757637, -0.053168702870607376, -0.08562446385622025, -0.0072469767183065414, 0.0343492366373539, 0.04441864416003227, -0.008874713443219662, -0.028651142492890358, 0.010914578102529049, -0.027813756838440895, 0.018965959548950195, -0.021094897761940956, -0.023363569751381874, 0.0336226150393486, 0.05296972766518593, -0.004781133960932493, 0.012949638068675995, 0.0037907951045781374, -0.0020631819497793913, -0.01720765046775341, 0.025664564222097397, -0.004558991175144911, 0.0017494386993348598, 0.07771043479442596, 0.012517389841377735, -0.0042241038754582405, 0.04200361296534538, -0.012861468829214573, 0.022591283544898033, 0.020100794732570648, 0.0036347159184515476, -0.04075508192181587, 0.0384245328605175, 0.040000785142183304, -0.014400343410670757, -0.05511181056499481, -0.06520376354455948, 0.0316041000187397, -0.015837186947464943, 0.039446182548999786, -0.04423997923731804, -0.0011542224092409015, 0.033164530992507935, 0.009002313949167728, 0.02667688950896263, 0.005485181696712971, -0.048517435789108276, -0.03148047626018524, -0.018085548654198647, -0.02662675455212593, -0.0169711671769619, 0.04312422499060631, -0.01294488925486803, 0.0697394385933876, 0.016831595450639725, -0.04165569320321083, 0.051176320761442184, 0.016513096168637276, -0.015995806083083153, -0.0018204820808023214, 0.04697344824671745, 0.014640836045145988, -0.009925208985805511, 0.053528714925050735, -0.07187271863222122, -0.00021628299145959318, 0.04253578558564186, -0.04401089996099472, -0.03140750527381897, -0.012905381619930267, 0.03392629325389862, 0.031272076070308685, -0.005212048999965191, -0.003910476807504892, 0.04698816314339638, 0.020440515130758286, 0.0020759745966643095, 0.03997671976685524, -0.0024132125545293093, -0.004729100037366152, -0.021533578634262085, -0.015514282509684563, -0.03973251208662987, 0.017556702718138695, 0.04069891199469566, -0.013721825554966927, -0.05298607796430588, -0.0263593178242445, -0.05795210227370262, -0.054655320942401886, 0.05463073030114174, -0.04790966585278511, 0.012203626334667206, -0.022672830149531364, -0.017935331910848618, 0.022437766194343567, -0.02414761856198311, 0.01516074687242508, 0.030758259817957878, 0.018228817731142044, 0.06096766144037247, -0.04235557094216347, 0.013076665811240673, 0.005971974227577448, -0.025946857407689095, -0.03822113201022148, 0.035340022295713425, 0.02202020213007927, 0.03407716751098633, -0.030554862692952156, 0.06779935210943222, 0.029947511851787567, 0.07613813877105713, -0.08626673370599747, 0.09281453490257263, -0.03357458859682083, -0.02340424619615078, -0.03315166011452675, 0.018489601090550423, 0.0016892123967409134, 0.006117112468928099, -0.07564614713191986, 0.023148322477936745, 0.020902050659060478, 0.0023247548379004, -0.041884858161211014, -0.015904806554317474, 0.00830123946070671, -0.013973596505820751, -0.07786613702774048, -0.020656678825616837, 0.00810770969837904, 0.048598408699035645, 0.026501193642616272, -0.015811828896403313, 0.05433257296681404, 0.03665939345955849, -0.04722152650356293, -0.047206051647663116, -0.009449693374335766, -0.004046922083944082, 0.0068262661807239056, -0.01082222256809473, -0.01851104199886322, 0.01902330480515957, 0.08745957165956497, -0.015674354508519173, -0.024442972615361214, 0.10918805748224258, 0.004229438956826925, -0.04787745326757431, -0.023375123739242554, 0.03709132596850395, -0.015153680928051472, -0.020116446539759636, -0.021947896108031273, -0.01602076180279255, 0.019484488293528557, -0.011302965693175793, 0.0035790156107395887, -0.03189088776707649, -0.01347316149622202, -0.015842562541365623, 0.0027864573057740927, -0.023441817611455917, 0.010302111506462097, -0.03356826305389404, -0.02151091769337654, 0.0289949681609869, 0.05086476728320122, 0.04949164390563965, 0.0037640435621142387, 0.046927087008953094, -0.01064953301101923, -0.031048981472849846, 0.01011217013001442, 0.03152068331837654, 0.05490982159972191, -0.023330971598625183, 0.0009974619606509805, -0.01686100848019123, 0.02757582813501358, -0.03641694411635399, 0.0011111495550721884, -0.026329945772886276, -0.04972191900014877, -0.050492145121097565, -0.03312166407704353, -0.04263488948345184, -0.020681116729974747, 0.015647735446691513, -0.06803467869758606, -0.02035519853234291, -0.008013377897441387, 0.034046471118927, 0.01644192263484001, 0.02948959358036518, -0.02840867079794407, 0.04346515238285065, 0.05967465043067932, -0.06230255216360092, -0.045961737632751465, -0.004520656540989876, 0.049408864229917526, 0.020209068432450294, 0.003987806383520365, 0.011480859480798244, 0.0011834860779345036, 0.042389772832393646, 0.02376111038029194, 0.008801196701824665, 0.0005027246079407632, 0.00599227100610733, 0.031700823456048965, -0.024865757673978806, 0.05842487886548042, -0.007764915470033884, -0.050779614597558975, 0.006736986804753542, 0.057146672159433365, -0.058069512248039246, -0.017389830201864243, 0.06447567045688629, -0.05964680388569832, 0.0056902258656919, -0.056566569954156876, 0.061931852251291275, 0.03020065650343895, -0.01750309020280838, 0.03398967534303665, 0.03369588032364845, -0.021361663937568665, -0.0077245766296982765, -0.011099616065621376, -0.07263735681772232, 0.0030565191991627216, -0.004359949380159378, -0.0032448640558868647, -0.015352355316281319, 0.025479279458522797, 0.019954901188611984, -0.018619224429130554, -0.004171127453446388, -0.027862083166837692, 0.044728320091962814, 0.028299666941165924, 0.002007643226534128, 0.02886478416621685, 0.030551472678780556, -0.024253148585557938, -0.09014412760734558, 0.04317186027765274, 0.03494704142212868, -0.018903421238064766, -0.040732141584157944, 0.02578156068921089, 0.010826049372553825, 0.0006403352017514408, -0.01900358311831951, 0.03526543080806732, -0.05738111212849617, 0.03947790712118149, 0.03337343409657478, -0.024879582226276398, -0.045177947729825974, -0.019481254741549492, -0.028034623712301254, -0.05679428204894066, 0.04708915576338768, -0.005741720553487539, 0.06228667125105858, 0.021698571741580963, -0.01500256359577179, -0.0343393050134182, -0.01157176773995161, -0.023634448647499084, 0.03327839449048042, 0.037445519119501114, 0.009279738180339336, -0.007146413438022137, -0.020294642075896263, 0.039300188422203064, 0.023175807669758797, -0.010828469879925251, -0.0048200637102127075, -0.08794312924146652, 0.0026729616802185774, -0.02391735091805458, 0.029917001724243164, 0.011420818977057934, 0.01009375974535942, -0.029659001156687737, 0.014658856205642223, 0.006755477748811245, 0.03355195373296738, -0.008233971893787384, -0.021832004189491272, -0.034344837069511414, 0.0023533240891993046, 0.020150840282440186, 0.00542106106877327, -0.002857757033780217, 0.06395582109689713, -0.024143051356077194, -0.019988076761364937, -0.026567185297608376, -0.015767116099596024, 0.007459885906428099, 0.021132251247763634, 0.03993002697825432, -0.018249712884426117, 0.007350807078182697, -0.011104291304945946, -0.0138111412525177, -0.015837103128433228, 0.06480661034584045, 0.008305619470775127, -0.026864344254136086, 0.013723441399633884, -0.040866121649742126, -0.02969677560031414, -0.022420715540647507, -0.028247728943824768, -0.03242964297533035, 0.0017969633918255568, -0.10136740654706955, -0.08516944944858551, 0.020290754735469818, 0.030573254451155663, -0.016060026362538338, -0.039396513253450394, 0.052589815109968185, -0.004293451085686684, 0.030781760811805725, -0.049332305788993835, 0.032954856753349304, -0.011348441243171692, 0.0011640802258625627, -0.011029062792658806, -0.06027872487902641, 0.0025154263712465763, -0.045328378677368164, -0.01058668177574873, -0.03360496833920479, 0.00046513706911355257, -0.01933627389371395, -0.0437917485833168, 0.012193664908409119, -0.047953687608242035, 0.029738934710621834, -0.022008050233125687, -0.05416661873459816, -0.026345646008849144, 0.004159585107117891, 0.022381868213415146, 0.004863154608756304, 0.056872326880693436, 0.0009713399922475219, -0.019987918436527252, 0.0047267163172364235, 0.019724193960428238, 0.0010429075919091702, -0.0018096533603966236, 0.004357496742159128, -0.035907622426748276, -0.01424519345164299, 0.00024103188479784876, -0.03796307370066643, -0.07962262630462646, 0.029163507744669914 ]
<p>We know that near a massive object, light's wavelength and frequency changes, but its speed remains same. I'd like to know how it is possible for frequency to change, unless we change the light source? </p>
g8386
[ -0.009876375086605549, -0.00659423740580678, 0.017958734184503555, -0.0005552353104576468, 0.022816818207502365, -0.017359422519803047, -0.004422273952513933, 0.005147848278284073, -0.03812086582183838, -0.018853722140192986, -0.001339467940852046, 0.066749706864357, 0.07111000269651413, 0.006830821745097637, -0.017768926918506622, 0.02230217307806015, 0.023190686479210854, -0.02327822707593441, 0.01391903031617403, 0.0238777007907629, -0.024302946403622627, -0.03690570592880249, 0.0114354332908988, -0.06197572872042656, -0.05680326744914055, 0.00233690207824111, 0.027577852830290794, -0.028856350108981133, 0.04429140314459801, 0.005178829189389944, 0.028079936280846596, -0.04093584045767784, 0.05723782256245613, -0.003158147679641843, 0.05212407931685448, -0.000059102134400745854, -0.02582017332315445, -0.001797890174202621, 0.01762477494776249, 0.04656526818871498, 0.03702118992805481, 0.014454296790063381, 0.006479491479694843, -0.044126033782958984, 0.021789144724607468, -0.035738322883844376, -0.0110328933224082, -0.019412856549024582, 0.003711113939061761, 0.003669604891911149, -0.03373166173696518, 0.06819061934947968, 0.004429052118211985, 0.0509500652551651, 0.01713087409734726, 0.017884476110339165, 0.0066329860128462315, 0.031244173645973206, 0.08583110570907593, 0.05805664137005806, -0.017339559271931648, -0.09580686688423157, 0.06045062839984894, 0.05334322154521942, -0.0018839894328266382, -0.0467648059129715, -0.04049736633896828, -0.05362871661782265, -0.007884902879595757, -0.006685641128569841, -0.025737732648849487, 0.004341353662312031, -0.05808514356613159, -0.022806042805314064, 0.005050205159932375, 0.010464178398251534, 0.044702835381031036, 0.005608753766864538, -0.03979231044650078, 0.0179377980530262, -0.0474536195397377, 0.009771580807864666, 0.03319540619850159, 0.03592928871512413, -0.007353250402957201, -0.034378066658973694, 0.020388953387737274, 0.0025945203378796577, 0.018629783764481544, 0.005872908513993025, 0.0417354479432106, 0.004506533499807119, 0.05672198161482811, -0.0034722869750112295, 0.044232022017240524, -0.04754665121436119, -0.02220473252236843, 0.09708482027053833, 0.0026058300863951445, -0.010450457222759724, -0.02098715677857399, -0.004771909210830927, 0.02381666749715805, 0.05591960251331329, -0.02648972161114216, 0.03139723837375641, -0.0019202238181605935, -0.010552391409873962, -0.0495506152510643, -0.001198710291646421, 0.020026786252856255, -0.1018599197268486, -0.029355445876717567, -0.02646949328482151, -0.0389493852853775, -0.0639331042766571, 0.020447300747036934, 0.03093346580862999, 0.016085684299468994, 0.07072705030441284, 0.03903784602880478, -0.0012841963907703757, -0.042399294674396515, 0.0008605056209489703, -0.0013888883404433727, -0.014749612659215927, 0.021177399903535843, 0.037256691604852676, 0.029524926096200943, -0.008074983023107052, -0.0010619398672133684, 0.042450495064258575, -0.01239605713635683, 0.06010511517524719, -0.0031734611839056015, 0.03325875848531723, 0.06996746361255646, 0.006602206267416477, 0.03272315114736557, -0.0004428223182912916, -0.011749393306672573, -0.013913165777921677, 0.03405577316880226, -0.02286921814084053, -0.01631772331893444, 0.049033746123313904, 0.01276004035025835, -0.018066709861159325, 0.03778347000479698, -0.030152224004268646, 0.08304153382778168, 0.08307304978370667, 0.03378786891698837, -0.05273691192269325, -0.014143150299787521, 0.0010990621522068977, -0.0026585946325212717, 0.019012155011296272, -0.02781371772289276, -0.004219764843583107, 0.0222589373588562, -0.06314502656459808, -0.019587621092796326, 0.014782088808715343, 0.0017917320365086198, 0.010975354351103306, -0.005404973402619362, -0.03542408347129822, -0.04223933815956116, -0.044267065823078156, -0.0712725818157196, 0.03145531192421913, 0.023963766172528267, 0.04756758362054825, 0.03597629815340042, 0.052263129502534866, -0.008363505825400352, 0.007290491368621588, -0.04669120907783508, 0.04951693117618561, -0.015472267754375935, -0.055294912308454514, -0.024169880896806717, -0.06962567567825317, 0.047788217663764954, 0.0004819274472538382, -0.01898818649351597, -0.012626647017896175, -0.06038915365934372, 0.04792868345975876, -0.07973197847604752, -0.06011509150266647, 0.0018427451141178608, 0.055302221328020096, 0.02903253212571144, -0.0005104003357701004, -0.03404712677001953, -0.03382774442434311, -0.014850451610982418, 0.03782534971833229, -0.015318447723984718, 0.04236664995551109, 0.021594492718577385, 0.023668136447668076, 0.014997628517448902, -0.00939969439059496, 0.015601111575961113, -0.017545005306601524, -0.011029756627976894, -0.030348820611834526, 0.06431709229946136, -0.027226630598306656, -0.005854492541402578, 0.01690067909657955, -0.027363408356904984, 0.0277085043489933, -0.0707523450255394, 0.01839325577020645, 0.016830677166581154, 0.02567187510430813, -0.003438161686062813, -0.008484512567520142, 0.032970916479825974, -0.006817083805799484, -0.005498060490936041, -0.019233979284763336, -0.020121892914175987, -0.00531874829903245, 0.06705582141876221, 0.05201968178153038, -0.006391605362296104, 0.033089764416217804, -0.017322219908237457, 0.019742947071790695, 0.03841959312558174, 0.030826173722743988, -0.04358499497175217, 0.03486822918057442, 0.0262950137257576, -0.020160706713795662, 0.027586432173848152, -0.030109044164419174, 0.001821307116188109, -0.0011167674092575908, -0.035312194377183914, -0.055426210165023804, 0.02328055538237095, -0.019523361697793007, 0.02323097549378872, 0.04540926218032837, 0.0581141822040081, -0.0366855189204216, -0.020849622786045074, 0.00503349956125021, -0.05288129672408104, -0.029611505568027496, -0.06306852400302887, 0.04088109731674194, -0.0847410261631012, -0.06378860771656036, -0.016285764053463936, 0.02150753326714039, 0.0695415660738945, 0.009871872141957283, -0.008353816345334053, -0.03476649522781372, 0.020587973296642303, 0.03932633996009827, -0.056244511157274246, 0.02124919556081295, -0.04531073570251465, 5.44572515082109e-7, 0.026720987632870674, 0.016461458057165146, -0.028571736067533493, 0.04495509713888168, -0.017426880076527596, -0.04300715774297714, 0.06571245193481445, 0.015102658420801163, -0.004887554794549942, 0.04475460946559906, -0.11303038150072098, -0.03765551745891571, 0.013498904183506966, -0.06557653844356537, 0.04157356545329094, 0.002106156898662448, -0.002254777355119586, -0.052139028906822205, -0.012323056347668171, 0.021096039563417435, 0.03737735375761986, 0.0031985610257834196, -0.009048353880643845, 0.024360787123441696, 0.015367604792118073, 0.021068131551146507, -0.04469352960586548, 0.009341929107904434, 0.05499187856912613, -0.033417295664548874, 0.0237816721200943, -0.005323677323758602, 0.049086786806583405, 0.03529126197099686, -0.06372286379337311, 0.00656831543892622, 0.044387828558683395, -0.002751486375927925, 0.0485122874379158, 0.04667127504944801, -0.03321979194879532, 0.004090598318725824, -0.036193087697029114, 0.03345920890569687, -0.027460284531116486, 0.006845367141067982, 0.008187013678252697, -0.037063587456941605, -0.05309177562594414, -0.026416171342134476, -0.04124734178185463, -0.03593229129910469, 0.006953328847885132, 0.020007912069559097, 0.013501659967005253, -0.028177432715892792, -0.050297074019908905, 0.017930233851075172, -0.0042891171760857105, 0.013441260904073715, -0.039064183831214905, -0.047865670174360275, -0.01404582429677248, 0.01459994912147522, 0.08721907436847687, 0.006066140253096819, 0.07541672885417938, 0.04661207273602486, 0.024990711361169815, -0.018705084919929504, -0.07569312304258347, 0.009527143090963364, -0.047827012836933136, 0.058862634003162384, -0.02663651667535305, -0.06713791191577911, 0.004555583465844393, 0.004464174620807171, 0.018968459218740463, -0.027214325964450836, -0.03023495338857174, 0.004693435505032539, 0.016709547489881516, 0.01779344119131565, 0.043888069689273834, 0.02291145548224449, -0.0020537511445581913, -0.06803590804338455, -0.006971259135752916, -0.07707689702510834, 0.07903756201267242, -0.01621677353978157, -0.014738142490386963, -0.0028556855395436287, -0.0032974528148770332, -0.010974472388625145, 0.0046463715843856335, 0.040865540504455566, -0.02043147385120392, -0.027083810418844223, -0.0289634857326746, 0.03267555311322212, -0.025391895323991776, 0.011153114028275013, 0.04079625383019447, 0.03246337175369263, -0.021464725956320763, 0.004744307603687048, 0.02087928168475628, -0.0066794827580451965, 0.011153110302984715, -0.09639176726341248, -0.006064099259674549, 0.015092933550477028, -0.046221405267715454, -0.014910660684108734, 0.011287439614534378, -0.006911079864948988, -0.044762153178453445, -0.055946577340364456, 0.02189844287931919, -0.0364433117210865, 0.017972324043512344, -0.0066016437485814095, -0.03497699275612831, -0.04711390286684036, -0.022536182776093483, 0.02434667758643627, 0.0038661579601466656, 0.06695358455181122, -0.04159253090620041, -0.05947191268205643, -0.01062402967363596, 0.02107163518667221, 0.027247538790106773, -0.050300393253564835, -0.0007644992438144982, 0.002989242784678936, -0.00985061377286911, -0.01747816614806652, -0.007341279648244381, -0.055651284754276276, -0.019349833950400352, 0.03233470022678375, 0.016217758879065514, -0.006349301431328058, 0.05432571843266487, 0.014364386908710003, -0.012714382261037827, 0.028384054079651833, 0.0007813891861587763, 0.02473522163927555, 0.01456094067543745, 0.018196577206254005, 0.01752920262515545, 0.0014478976372629404, 0.003004072466865182, 0.006468835286796093, 0.007408566772937775, 0.02002253197133541, 0.034121375530958176, 0.028417743742465973, -0.01294366829097271, 0.013588407076895237, -0.0124812051653862, -0.02926395833492279, 0.042424194514751434, 0.001211071154102683, 0.012126523070037365, 0.020186278969049454, -0.000980363111011684, -0.021136770024895668, -0.010168394073843956, 0.06256520003080368, -0.052781928330659866, 0.0013867698144167662, 0.0312814824283123, -0.007192636374384165, -0.03451455384492874, 0.01803714595735073, 0.008567205630242825, 0.005637669004499912, -0.00025333857047371566, 0.007182532921433449, -0.01564529724419117, 0.010073482058942318, 0.0595531091094017, -0.022461995482444763, -0.08761540800333023, -0.011570204980671406, -0.002488471567630768, 0.02233683504164219, -0.0003887336060870439, 0.02077486366033554, -0.039986349642276764, -0.02888445556163788, -0.05613188445568085, 0.03818251192569733, -0.03480837866663933, -0.053287409245967865, -0.005594332702457905, 0.03922594338655472, 0.06607046723365784, -0.0061128768138587475, -0.0012229805579409003, -0.06496132910251617, -0.009214437566697598, -0.07449248433113098, -0.00753795774653554, -0.019045116379857063, 0.04241881147027016, -0.02201450988650322, -0.003509380156174302, 0.03390450403094292, -0.07801315933465958, 0.059791382402181625, -0.011956237256526947, -0.07627886533737183, -0.013835128396749496, -0.003929109312593937, -0.004553908482193947, 0.035525429993867874, -0.009590739384293556, 0.02248450741171837, 0.021873340010643005, 0.0015794892096892, 0.01708371937274933, 0.003412998979911208, -0.020289918407797813, 0.010529069229960442, 0.015654243528842926, 0.007868786342442036, -0.007572944741696119, 0.06174831464886665, 0.04079640656709671, 0.001661747577600181, -0.02353135123848915, 0.08619487285614014, -0.018386460840702057, 0.040616944432258606, -0.0211399607360363, 0.052331432700157166, 0.048986755311489105, -0.05673457682132721, -0.005989765748381615, 0.02490237168967724, 0.01640169695019722, -0.01585300825536251, -0.09494335949420929, -0.028356101363897324, 0.03758217766880989, 0.03996555507183075, -0.006622171029448509, 0.058849919587373734, -0.0407317616045475, -0.01749383844435215, 0.007018773816525936, 0.0038065982516855, -0.05408995971083641, 0.018593329936265945, -0.05199503153562546, -0.0335298553109169, -0.06076105684041977, 0.04843979701399803, 0.03058377094566822, -0.04501168802380562, -0.02984214387834072, 0.01636466011404991, 0.03501705080270767, -0.044184550642967224, 0.03721737116575241, 0.009278824552893639, 0.01129694003611803, -0.02185659669339657, 0.005204064305871725, 0.033473532646894455, 0.017030788585543633, -0.01094779558479786, 0.005777285434305668, 0.06611955910921097, 0.0005055734654888511, 0.05257711559534073, -0.0015850224299356341, 0.008224474266171455, -0.0184487197548151, -0.026374470442533493, -0.03452354669570923, -0.0664348378777504, 0.04978279769420624, 0.025988398119807243, 0.0232072900980711, -0.05996185168623924, 0.06899821013212204, -0.08380105346441269, -0.004400303121656179, -0.007657534908503294, 0.09945700317621231, 0.019281182438135147, -0.07257966697216034, -0.04231972619891167, -0.07533613592386246, -0.06720300018787384, 0.0411609522998333, -0.03637157008051872, 0.0026945793069899082, -0.01997518539428711, -0.00922406930476427, -0.040287941694259644, -0.012375094927847385, -0.013085957616567612, -0.011480546556413174, -0.04246601089835167, -0.021913865581154823, -0.03408307582139969, 0.024214377626776695, 0.04947023093700409, 0.10144443064928055, 0.014246361330151558, -0.009210632182657719, -0.003218182362616062, -0.017246846109628677, -0.015048643574118614, -0.044945452362298965, -0.0719197615981102, -0.04055870324373245, 0.03808651864528656, -0.007572096772491932, 0.018201423808932304, -0.015969401225447655, -0.003313401946797967, 0.04393203556537628, 0.01984632946550846, 0.022440385073423386, 0.005047793500125408, 0.0003616748144850135, -0.027562599629163742, 0.0793791115283966, -0.01120702177286148, -0.0287778377532959, 0.022788887843489647, 0.007880251854658127, 0.018638795241713524, -0.04936271905899048, -0.04344550520181656, 0.07049766927957535, 0.027923204004764557, 0.03788578882813454, 0.0019747670739889145, 0.03014366142451763, -0.0731981098651886, 0.0040656449273228645, -0.04323221743106842, -0.026521146297454834, 0.006837727501988411, -0.020804917439818382, -0.008979197591543198, 0.06410127133131027, -0.009084440767765045, 0.04425037279725075, 0.040717046707868576, -0.011302918195724487, -0.007726495154201984, -0.0026682517491281033, 0.042752716690301895, -0.004747525788843632, 0.013638298027217388, 0.023128697648644447, 0.013516535982489586, 0.07147962599992752, -0.02113555185496807, 0.022105662152171135, 0.013014398515224457, -0.06750975549221039, 0.007903523743152618, 0.038650207221508026, -0.05720733478665352, 0.003643629839643836, 0.019728567451238632, -0.032293058931827545, -0.043628331273794174, -0.06842529028654099, 0.043144967406988144, 0.005925035569816828, 0.02890213578939438, -0.034350838512182236, 0.003392558777704835, -0.03634350374341011, -0.0810658186674118, -0.0725497454404831, -0.0010307511547580361, 0.0031353032682090998, 0.011386736296117306, -0.003529555629938841, 0.03739326447248459, 0.0502462275326252, -0.09573978185653687, -0.01674214005470276, 0.03201436251401901, 0.019514771178364754, -0.000777462322730571, 0.007968565449118614, -0.012994473800063133, 0.011720237322151661, 0.006733277812600136, -0.03565099835395813, 0.09668029844760895, 0.03073304332792759, 0.017282962799072266, 0.03929593041539192, 0.032486844807863235, 0.021101046353578568, 0.006293230224400759, 0.0372491292655468, 0.021289819851517677, -0.10817408561706543, 0.04569985345005989, -0.001690276782028377, -0.038621120154857635, -0.026351559907197952, 0.014340117573738098, -0.01184973493218422, 0.023442430421710014, -0.009032952599227428, -0.03624431788921356, -0.03391594439744949, -0.023716846480965614, 0.02110203169286251, 0.017720628529787064, -0.054664213210344315, -0.059186168015003204, -0.019857099279761314, -0.009380266070365906, -0.006124550476670265, -0.009066367521882057, -0.035201359540224075, 0.021079212427139282, 0.019557464867830276, 0.016295162960886955, 0.009121574461460114, 0.05579027161002159, 0.024820836260914803, 0.013117322698235512, 0.013876809738576412, -0.0024507413618266582, 0.021684329956769943, -0.020358342677354813, -0.03767889738082886, -0.03370719403028488, -0.04852651432156563, 0.018832627683877945, 0.014768588356673717, -0.01915401965379715, 0.032176289707422256, 0.029265372082591057, 0.07324578613042831, -0.011459680274128914, -0.03088006004691124, 0.010279898531734943, -0.02309570088982582, 0.04542496055364609, -0.0041546630673110485, -0.08364426344633102, 0.0013388204388320446, 0.024180183187127113, -0.014038663357496262, 0.042543694376945496, -0.01016792468726635, -0.02026533894240856, 0.023624137043952942, 0.030260637402534485, 0.003223688807338476, 0.034736648201942444, 0.0034327316097915173, 0.0012888045748695731, 0.011364145204424858, -0.005841053556650877, 0.03516640141606331, -0.06368371844291687, -0.016400370746850967, 0.04560265690088272, -0.06479877233505249, 0.05475490167737007, 0.04338959977030754, -0.03522828593850136, -0.0434747040271759, 0.01815912500023842, -0.029229076579213142, -0.05201281979680061, -0.003833088790997863, 0.042858000844717026, -0.011488785035908222, 0.0019730874337255955, 0.01634266972541809, -0.03686396777629852, -0.04934033751487732, 0.029388494789600372 ]
<p>I am not sure if I understand spin operators correctly. Given a two spin system in state $|++\rangle$ and an operator $S = S^{(1)} + S^{(2)}$</p> <p>Then I have</p> <p>$$ S_z |++\rangle = (S^{(1)}_z + S^{(2)}_z) (|\tfrac{1}{2}, \tfrac{1}{2}\rangle \otimes |\tfrac{1}{2}, \tfrac{1}{2}\rangle) = (S_z|\tfrac{1}{2}, \tfrac{1}{2}\rangle \otimes S_z|\tfrac{1}{2}, \tfrac{1}{2}\rangle) = (\tfrac{\hbar}{2} |\tfrac{1}{2}, \tfrac{1}{2}\rangle \otimes \tfrac{\hbar}{2} |\tfrac{1}{2}, \tfrac{1}{2}\rangle) = \tfrac{\hbar}{2} (|\tfrac{1}{2}, \tfrac{1}{2}\rangle \otimes |\tfrac{1}{2},\tfrac{1}{2}\rangle) = \tfrac{\hbar}{2} |++\rangle $$</p> <p>But everywhere I read, I see $$ S_z |++\rangle = \hbar |++\rangle $$</p> <p>What did I do wrong?</p>
g8387
[ -0.054091114550828934, -0.0037276886869221926, 0.0004898477345705032, 0.07426085323095322, 0.0494002103805542, -0.05443732440471649, 0.07202870398759842, 0.04590389505028725, 0.018777672201395035, 0.015077147632837296, -0.04016778618097305, 0.02500920370221138, 0.009930496104061604, 0.0016568893333896995, 0.008116607554256916, 0.017087100073695183, 0.07014692574739456, 0.044593337923288345, -0.020843010395765305, -0.06865771114826202, -0.06519447267055511, -0.04393889382481575, -0.01347668468952179, -0.04626539722084999, 0.01303641777485609, -0.017547806724905968, 0.0032114479690790176, -0.01099411491304636, -0.06840778142213821, -0.00522787356749177, -0.040629930794239044, 0.029588840901851654, -0.00557239493355155, -0.06398754566907883, 0.02757277712225914, -0.007695863954722881, 0.10804523527622223, 0.010592539794743061, -0.012676491402089596, -0.023640727624297142, -0.021165654063224792, 0.0015140448231250048, 0.015335493721067905, -0.04457758739590645, 0.04754868522286415, 0.004848786164075136, 0.04742765054106712, 0.02522144839167595, -0.04335181787610054, 0.02805362083017826, 0.010255022905766964, -0.012441827915608883, 0.013336523436009884, 0.047010134905576706, 0.02954886108636856, 0.02671501412987709, 0.0037496492732316256, -0.024893371388316154, 0.013231472112238407, 0.008283362723886967, -0.017706578597426414, -0.017481135204434395, -0.00360420742072165, 0.01467526238411665, -0.034064725041389465, 0.016606908291578293, 0.024543968960642815, -0.019500646740198135, -0.001016458380036056, 0.01411657128483057, 0.00405363691970706, -0.043496374040842056, 0.03260287269949913, -0.06638637185096741, -0.02456039935350418, -0.012025263160467148, 0.03808668628334999, -0.05385397747159004, -0.00909717008471489, 0.05710958316922188, -0.01772955060005188, -0.08553366363048553, -0.006468589883297682, 0.006606875918805599, -0.03279983624815941, 0.07472553849220276, -0.006890165153890848, -0.019632982090115547, 0.010148334316909313, 0.037679508328437805, 0.010679978877305984, -0.01831636391580105, 0.047763098031282425, 0.06499525159597397, 0.003838597796857357, -0.0029903885442763567, -0.026798298582434654, -0.04241330921649933, 0.03202016279101372, 0.048901550471782684, -0.03870631754398346, 0.014823157340288162, 0.0397171750664711, -0.04097209498286247, 0.044881753623485565, 0.00877697579562664, 0.03727252036333084, -0.009131483733654022, -0.02667301334440708, -0.03624017909169197, -0.0014781237114220858, 0.03960886225104332, 0.0021940860897302628, -0.015937916934490204, -0.0041008261032402515, -0.007967558689415455, 0.0378875732421875, -0.02426387369632721, -0.013862491585314274, 0.03062344901263714, 0.07097743451595306, 0.029130402952432632, 0.03345822915434837, 0.09166310727596283, 0.02719617448747158, -0.014467301778495312, 0.013181663118302822, -0.033937983214855194, 0.0924154594540596, -0.004918971564620733, -0.012510236352682114, -0.015500073321163654, 0.03004421293735504, 0.011459269560873508, -0.04434407502412796, 0.023623699322342873, 0.005884730257093906, -0.03362590819597244, 0.015924746170639992, -0.05220774933695793, -0.01912587881088257, -0.03570485860109329, -0.022238556295633316, -0.07544463127851486, 0.026674408465623856, -0.03501405939459801, 0.01701747439801693, -0.07645536214113235, -0.0075380573980510235, -0.01852375827729702, 0.04550311341881752, 0.05602831766009331, -0.03659158945083618, 0.052723441272974014, -0.020758697763085365, 0.00841446965932846, 0.050625674426555634, -0.004177996888756752, 0.030704250559210777, 0.01573132909834385, 0.018778614699840546, -0.020061952993273735, 0.012091047130525112, -0.03400195389986038, -0.06891517341136932, -0.003944951109588146, 0.01494072750210762, -0.05071810632944107, -0.02323359064757824, -0.044740621000528336, -0.0024740160442888737, 0.02863018587231636, 0.012378433719277382, 0.010066253133118153, 0.06196232885122299, 0.03646944463253021, -0.010800673626363277, 0.03953523561358452, 0.036870285868644714, 0.04755428805947304, -0.059321191161870956, 0.020069655030965805, 0.029708927497267723, 0.0025349303614348173, -0.0069563426077365875, 0.03568786755204201, -0.005163880996406078, 0.01696377620100975, -0.09059316664934158, -0.019275277853012085, -0.013498843647539616, 0.026426546275615692, 0.04470522329211235, 0.06433199346065521, -0.037073586136102676, 0.02867090329527855, 0.0013910882407799363, -0.08640801161527634, 0.025846490636467934, 0.03549810126423836, 0.014228062704205513, 0.012497254647314548, 0.023598482832312584, -0.01899540238082409, 0.004326888360083103, -0.07168588787317276, -0.021450256928801537, -0.005401134956628084, 0.03692963346838951, -0.0067105982452631, -0.0032199472188949585, -0.04360601678490639, -0.0028075447771698236, -0.0001770904491422698, -0.0430443212389946, -0.037920452654361725, 0.04096477851271629, 0.03172389790415764, -0.012718464247882366, -0.016181036829948425, -0.027624299749732018, -0.037281520664691925, 0.04766093194484711, 0.018876956775784492, -0.04665694013237953, -0.0002533787046559155, -0.022164370864629745, 0.0158587284386158, 0.0014382305089384317, 0.046742167323827744, 0.014898017980158329, -0.04494288191199303, 0.03536069765686989, -0.014182907529175282, 0.025917494669556618, -0.023943860083818436, 0.02687484212219715, 0.05383910611271858, -0.009124992415308952, -0.0240773968398571, 0.01927664503455162, 0.014958743005990982, 0.02398799918591976, 0.03714485466480255, 0.04126604646444321, 0.043164532631635666, 0.04970945790410042, 0.0006035835249349475, -0.011180351488292217, 0.03672807663679123, -0.011555040255188942, -0.04026300460100174, 0.022322839125990868, 0.023170147091150284, -0.02263040281832218, -0.00968179665505886, -0.015023996122181416, 0.027521703392267227, 0.00030324290855787694, -0.010258300229907036, 0.007804017048329115, 0.0517730712890625, -0.06525227427482605, 0.06481971591711044, -0.048469118773937225, -0.00919758528470993, -0.008147398009896278, -0.02655795030295849, 0.013704800978302956, -0.038475751876831055, 0.016238819807767868, 0.011449645273387432, -0.00025254065985791385, 0.01908750645816326, -0.02336607500910759, -0.08622341603040695, 0.002027255017310381, -0.012513652443885803, 0.014195622876286507, -0.022324511781334877, -0.029176492244005203, -0.037390708923339844, 0.025782806798815727, 0.0365925170481205, -0.005946876481175423, -0.04581398144364357, -0.019234005361795425, 0.040229905396699905, -0.008543313480913639, -0.006647258065640926, -0.04496061056852341, 0.05623239278793335, 0.024583812803030014, -0.05081888660788536, -0.013433871790766716, -0.010324904695153236, 0.0062358626164495945, -0.07076094299554825, -0.00004642602652893402, 0.11557836830615997, 0.03731705993413925, -0.019651785492897034, -0.005218150094151497, 0.009588995948433876, 0.017444735392928123, 0.0005101830465719104, -0.06246872991323471, -0.006557368207722902, -0.011078894138336182, 0.031242989003658295, -0.017652135342359543, 0.04212228208780289, -0.003601302159950137, -0.04641731455922127, 0.017539935186505318, 0.026872869580984116, -0.06573274731636047, -0.01002342440187931, 0.024532988667488098, -0.006273072678595781, -0.0697619616985321, -0.02768881991505623, 0.018667299300432205, 0.0002626416098792106, -0.00692101800814271, 0.005419128108769655, -0.06641041487455368, 0.02918185666203499, -0.01135068666189909, 0.007718907669186592, 0.029076531529426575, 0.02386999875307083, -0.015451020561158657, -0.04296693578362465, -0.0804734081029892, -0.017320509999990463, 0.02739056944847107, 0.0637206882238388, 0.015164654701948166, -0.017542533576488495, -0.02481231838464737, -0.01201685518026352, 0.013924221508204937, 0.02086651884019375, -0.031429681926965714, 0.018606992438435555, -0.016143793240189552, -0.017328454181551933, 0.015155086293816566, -0.035256728529930115, -0.03820757195353508, 0.052732814103364944, 0.024072391912341118, 0.02447003684937954, -0.07538720220327377, 0.011169090867042542, -0.029313569888472557, 0.036240991204977036, 0.02721564471721649, -0.03497913479804993, 0.06344441324472427, -0.021024813875555992, -0.024120816960930824, -0.0050003863871097565, -0.01100757997483015, 0.015243017114698887, 0.015371355228126049, 0.006217306945472956, -0.026465533301234245, -0.07121843844652176, 0.0010981211671605706, 0.022075455635786057, 0.030356712639331818, -0.011435795575380325, 0.022856522351503372, -0.06410805881023407, -0.06359705328941345, -0.02827349305152893, -0.06996291875839233, -0.0042288885451853275, -0.010564841330051422, 0.01255375612527132, 0.02697003446519375, 0.07365523278713226, 0.013929091393947601, 0.008711226284503937, 0.10138998925685883, 0.0017235492123290896, -0.008527375757694244, -0.02305750921368599, 0.0036691336426883936, -0.0007667870377190411, 0.012680073268711567, 0.05794477090239525, 0.06040035933256149, 0.014143362641334534, 0.008611331693828106, -0.07172276824712753, -0.04300141707062721, 0.06929904967546463, -0.058901671320199966, -0.03603522107005119, -0.004756394308060408, -0.05186033993959427, -0.004426382947713137, 0.012272495776414871, -0.00958424061536789, 0.012603005394339561, 0.021392585709691048, 0.013135287910699844, -0.06379248201847076, 0.06900579482316971, 0.05942799896001816, 0.0063523487187922, -0.003738151164725423, -0.008981678634881973, 0.013513804413378239, -0.039258576929569244, -0.05185329169034958, -0.026163116097450256, -0.04691160097718239, 0.0281894039362669, 0.04332917556166649, -0.04281424358487129, 0.0007011750130914152, 0.0010186120634898543, 0.01171188335865736, -0.04130847752094269, -0.01871834136545658, -0.025841429829597473, -0.023503271862864494, 0.049602605402469635, 0.03380594030022621, 0.07349002361297607, -0.10216858237981796, -0.013626608066260815, -0.008162655867636204, 0.0031789946369826794, -0.024328090250492096, 0.02517937682569027, -0.011360532604157925, -0.0422111414372921, -0.05507754907011986, 0.03048783726990223, 0.045659445226192474, -0.03555232658982277, 0.013703851960599422, -0.011578078381717205, -0.02107657864689827, -0.050503842532634735, -0.0654449611902237, 0.06137745827436447, 0.03142787143588066, -0.0119767552241683, 0.014641002751886845, 0.01898859441280365, -0.013207172974944115, 0.026398221030831337, -0.0021277922205626965, 0.014861431904137135, -0.029303915798664093, -0.013289567083120346, -0.03868011385202408, -0.04703434556722641, -0.00867572519928217, 0.015749091282486916, -0.04894745722413063, 0.02888667955994606, -0.031157946214079857, -0.02485225908458233, 0.023216761648654938, -0.04880806431174278, 0.044685471802949905, -0.07142039388418198, 0.020382188260555267, 0.05820465460419655, -0.02229476161301136, -0.009067815728485584, -0.02293403446674347, 0.05348118394613266, -0.03406010568141937, -0.012860090471804142, -0.033615417778491974, 0.009682677686214447, 0.018999869003891945, 0.030799981206655502, 0.043091338127851486, -0.013670261017978191, 0.011193357408046722, -0.004149836953729391, 0.03553566336631775, 0.023124460130929947, -0.005417118780314922, 0.025959506630897522, 0.018754208460450172, -0.04331883043050766, -0.015827003866434097, -0.02386438474059105, -0.021175283938646317, 0.03513769432902336, -0.04821808263659477, 0.009651835076510906, -0.053884487599134445, 0.07741658389568329, -0.014803861267864704, 0.040241990238428116, 0.03331490606069565, 0.01936972886323929, 0.0949876457452774, 0.03535812720656395, 0.015813017264008522, -0.026685195043683052, 0.07315254956483841, 0.009309777989983559, 0.007216732483357191, -0.02711544558405876, -0.02121901884675026, 0.07999664545059204, -0.023811930790543556, -0.031174296513199806, 0.007190205156803131, -0.020238211378455162, 0.024047425016760826, -0.03990507498383522, 0.03185127303004265, -0.0007737302803434432, -0.025448504835367203, 0.025825880467891693, -0.011819371953606606, 0.04563850909471512, 0.03075975738465786, -0.028305048123002052, 0.03185682371258736, -0.006357046775519848, 0.09999478608369827, -0.009614135138690472, 0.001669856603257358, -0.06235694885253906, -0.008651367388665676, 0.05354264751076698, 0.007710190489888191, -0.024723341688513756, -0.017864804714918137, 0.053986694663763046, -0.07163052260875702, 0.04269261658191681, -0.0035379643086344004, -0.08688484132289886, 0.0063072494231164455, 0.0017043277621269226, -0.0075134215876460075, -0.006725119426846504, -0.0381813682615757, -0.037973448634147644, 0.07706864178180695, 0.06119903177022934, 0.0001872505818028003, 0.0039090258069336414, -0.023137442767620087, 0.04126486927270889, 0.026278899982571602, -0.002065022010356188, -0.01923724077641964, 0.029225949198007584, -0.0024049996864050627, -0.06773652136325836, -0.013255409896373749, 0.023409029468894005, -0.014658406376838684, 0.027644122019410133, -0.08299553394317627, 0.0017812656005844474, -0.01083224918693304, 0.023021448403596878, 0.026377104222774506, 0.06885789334774017, -0.059952933341264725, -0.009951368905603886, 0.024831870570778847, -0.0044839996844530106, -0.00374840060248971, 0.01108508836477995, -0.05443761125206947, -0.01116666104644537, -0.003932442516088486, 0.009133576415479183, -0.07460445910692215, -0.04226352646946907, 0.031262341886758804, 0.008756201714277267, 0.0019787594210356474, 0.03417520970106125, -0.07401899993419647, -0.048433270305395126, -0.005870191380381584, -0.034222252666950226, 0.03934014216065407, -0.006068911869078875, -0.045612942427396774, -0.0424981452524662, 0.046912193298339844, -0.016649020835757256, 0.03099675104022026, -0.021094076335430145, -0.022183168679475784, 0.023432068526744843, -0.045920904725790024, -0.023448346182703972, -0.01748853549361229, 0.07431551814079285, -0.07932333648204803, -0.02111746557056904, -0.04732576757669449, 0.07261281460523605, 0.022749677300453186, -0.05023033544421196, 0.022067759186029434, 0.06767719238996506, -0.02541290782392025, -0.004050222225487232, 0.03572647273540497, 0.03195144981145859, 0.015443679876625538, -0.03820481896400452, 0.08665406703948975, 0.028536822646856308, 0.02842814289033413, 0.03739605471491814, -0.005570126697421074, -0.03746286779642105, 0.040350452065467834, 0.00737402681261301, -0.04963568598031998, 0.018993539735674858, 0.035714760422706604, -0.01645936444401741, 0.05239221453666687, 0.032069481909275055, 0.027527103200554848, 0.07939793914556503, -0.02243405394256115, 0.042675264179706573, 0.020097628235816956, 0.017533397302031517, -0.03504791483283043, -0.038111619651317596, 0.042135559022426605, -0.018592199310660362, -0.09813559800386429, 0.06726344674825668, -0.006616503931581974, -0.03436115011572838, -0.02632276341319084, -0.013365479186177254, 0.025273846462368965, -0.053708434104919434, 0.030000854283571243, 0.029637262225151062, 0.022540779784321785, -0.03268638253211975, -0.01072138175368309, -0.02821172960102558, -0.05394040793180466, 0.03176479414105415, -0.030338939279317856, 0.07070153951644897, -0.004447609186172485, 0.007935098372399807, 0.033105384558439255, -0.06132754310965538, -0.02719442918896675, -0.009103609248995781, -0.015381752513349056, 0.014267930760979652, 0.007358606439083815, 0.012123659253120422, 0.03727516531944275, -0.02308245375752449, 0.02910621464252472, -0.02422245219349861, 0.03196075186133385, -0.019347669556736946, -0.06689521670341492, 0.03914881497621536, 0.04129987210035324, 0.053706713020801544, -0.0033891245257109404, 0.014854525215923786, -0.012611388228833675, 0.014518139883875847, -0.0055960360914468765, -0.0012793467612937093, 0.053271375596523285, 0.04439181089401245, -0.02528422325849533, -0.02299409732222557, 0.012117769569158554, 0.07603324949741364, -0.017822647467255592, -0.008191334083676338, 0.014632145874202251, -0.008079099468886852, -0.023637805134058, 0.00574111845344305, -0.009431494399905205, 0.01646241918206215, 0.03741323575377464, -0.02472171187400818, 0.04489600658416748, 0.00020282878540456295, -0.03522566705942154, 0.030021950602531433, -0.025505440309643745, -0.024743201211094856, 0.023557526990771294, -0.014869892038404942, 0.006090870592743158, 0.003182783955708146, 0.011525994166731834, -0.05013662576675415, -0.03417317941784859, -0.04057745635509491, 0.01055708434432745, 0.004090480040758848, -0.031774070113897324, -0.02839753031730652, 0.030715614557266235, 0.038027722388505936, -0.01666884869337082, 0.03376609459519386, -0.011509470641613007, -0.033382598310709, -0.12600308656692505, -0.004292636178433895, -0.008309575729072094, 0.010336751118302345, 0.00389700080268085, 0.01769072748720646, -0.00466177286580205, -0.004418196622282267, -0.006553937215358019, -0.06496040523052216, 0.024398120120167732, 0.007378045003861189, -0.02132314257323742, -0.02358713373541832, 0.01383286714553833, -0.029987899586558342, 0.01658429205417633, -0.03635285794734955, -0.04193923994898796, 0.015112239867448807, -0.018691321834921837, 0.07113172113895416, 0.024320609867572784, -0.012442919425666332, 0.04207964241504669, 0.044104985892772675, 0.009799085557460785, 0.045698340982198715, -0.0019070374546572566, -0.042471952736377716, -0.039467960596084595, 0.0036000963300466537, -0.030786041170358658, -0.018275687471032143, -0.011369955725967884, 0.03121495433151722 ]
<p>Does a black body (imagine like a square of solid black-body-matter) thermally conduct well at room temperature?</p>
g8388
[ -0.009085005149245262, 0.009223035536706448, 0.04045760631561279, -0.02665071375668049, 0.0221331175416708, -0.022485695779323578, -0.026204822584986687, 0.030726177617907524, 0.03371760621666908, -0.0008571039652451873, -0.011787795461714268, 0.05812952667474747, 0.008640582673251629, 0.009731263853609562, -0.039969101548194885, -0.006471756845712662, 0.016282564029097557, -0.004589080344885588, 0.04930295795202255, -0.016159536316990852, -0.03715028241276741, -0.00859152339398861, 0.033485982567071915, -0.037560608237981796, -0.041721709072589874, 0.01894848421216011, 0.0021790910977870226, -0.013214473612606525, -0.08249670267105103, -0.04262285307049751, 0.007688502315431833, 0.007540056947618723, -0.005167811177670956, -0.04850759357213974, -0.066230408847332, 0.056644584983587265, -0.002749748295173049, 0.032075315713882446, -0.04164835065603256, -0.01779000274837017, 0.01006945502012968, -0.08748538047075272, 0.00010280061542289332, -0.0004675185482483357, 0.03348701447248459, 0.06014120951294899, 0.00921597145497799, -0.04578252136707306, -0.03490827977657318, 0.04491990804672241, 0.016395680606365204, 0.014896186999976635, 0.07769564539194107, 0.023765919730067253, -0.0008192788809537888, -0.05059834197163582, -0.015027607791125774, -0.014817462302744389, -0.00487359007820487, 0.0448622927069664, 0.0019746865145862103, 0.014121128246188164, -0.019198818132281303, -0.009109517559409142, 0.04834477975964546, 0.07301394641399384, -0.04136976599693298, 0.042582329362630844, -0.04885200411081314, 0.02214934304356575, 0.03228694200515747, -0.059376634657382965, -0.013233136385679245, 0.005917694419622421, -0.052986226975917816, 0.04624387249350548, -0.019506894052028656, 0.0044274828396737576, 0.010580452159047127, 0.015254422090947628, -0.043432530015707016, 0.04393761232495308, 0.009572046808898449, 0.06776594370603561, 0.06603961437940598, -0.031105296686291695, 0.01698983646929264, -0.05665871128439903, -0.015404975041747093, 0.056325506418943405, 0.0687221884727478, 0.045216355472803116, 0.01414430234581232, -0.031102312728762627, 0.08676127344369888, 0.048951901495456696, 0.00003958275920012966, 0.041194166988134384, -0.03971914201974869, 0.057453181594610214, -0.02664642222225666, 0.006220825016498566, 0.02267191745340824, 0.02093096449971199, -0.015732785686850548, 0.0011357397306710482, -0.01814713329076767, -0.017530221492052078, -0.0577562116086483, 0.06022626534104347, -0.023342160508036613, -0.05227506533265114, -0.0074851177632808685, -0.018912041559815407, -0.011136986315250397, 0.03622342273592949, 0.051354605704545975, -0.0803658589720726, -0.017207713797688484, 0.049957092851400375, -0.03289669007062912, 0.00125112384557724, 0.06354132294654846, 0.0016181243117898703, -0.044045340269804, -0.03359900042414665, -0.017826206982135773, 0.013704076409339905, -0.03422616049647331, 0.000664370774757117, -0.014152013696730137, 0.011616731993854046, -0.07384463399648666, 0.022132238373160362, 0.014736704528331757, 0.0680711418390274, 0.07999444752931595, -0.01071458961814642, -0.0020372080616652966, -0.010865803807973862, 0.013454658910632133, 0.010167540051043034, -0.057401251047849655, 0.004938884638249874, -0.0014014758635312319, 0.03765862435102463, -0.05641739442944527, -0.01469352375715971, 0.01706599071621895, 0.09092732518911362, -0.03402882441878319, 0.045702073723077774, 0.020564887672662735, -0.0025288944598287344, -0.02123413048684597, -0.051191769540309906, 0.03535335510969162, 0.0812077447772026, 0.05595703795552254, -0.04797643423080444, -0.008753061294555664, 0.025202373042702675, -0.004953286610543728, -0.003347816178575158, -0.004967625252902508, -0.06986662745475769, -0.12491704523563385, -0.02028457075357437, 0.05923640727996826, -0.03219765052199364, -0.008129122667014599, 0.049999091774225235, -0.05696634575724602, 0.08169883489608765, -0.005198752041906118, -0.028484532609581947, 0.011411494575440884, 0.019762864336371422, 0.03327353298664093, -0.09577570855617523, -0.028762467205524445, 0.03667920455336571, -0.004182477947324514, -0.07296622544527054, -0.033660292625427246, -0.008342997170984745, 0.04712797701358795, 0.04160572960972786, -0.01936444453895092, -0.008860656060278416, -0.0591810867190361, -0.07740907371044159, -0.039424724876880646, 0.018401339650154114, 0.05494336411356926, -0.03407556563615799, 0.029584351927042007, -0.017697229981422424, 0.01868385262787342, 0.014218696393072605, 0.018593573942780495, 0.04715843126177788, 0.017772166058421135, 0.0008713146089576185, 0.04920840263366699, 0.03311823680996895, -0.04700468108057976, -0.023128755390644073, -0.0059353928081691265, -0.022790027782320976, 0.01647615246474743, -0.016415288671851158, 0.03493129462003708, 0.030148018151521683, -0.03104911372065544, 0.015153896994888783, -0.06798645853996277, -0.01501390803605318, -0.014272577129304409, -0.008370115421712399, -0.021942876279354095, -0.0005321184289641678, -0.011462612077593803, -0.0026345478836447, 0.0073265875689685345, -0.010876464657485485, -0.08636429160833359, -0.04736503213644028, 0.021033138036727905, 0.0025062719359993935, -0.0803748071193695, -0.0026521815452724695, 0.0465511754155159, -0.007421608082950115, -0.00168233725707978, 0.06810873746871948, -0.0076624127104878426, -0.07091505080461502, -0.016307974234223366, -0.03642478585243225, 0.04316001385450363, -0.015094314701855183, -0.0656810849905014, -0.04097973555326462, 0.04492570087313652, 0.024243783205747604, -0.03433845564723015, -0.012312918901443481, 0.016563668847084045, -0.0003495421551633626, -0.026832958683371544, -0.012997960671782494, -0.011866935528814793, -0.017782557755708694, -0.010809779167175293, -0.020233603194355965, -0.0369233600795269, 0.0009333156631328166, -0.038380201905965805, -0.07299474626779556, 0.04507122561335564, -0.09060448408126831, -0.08708624541759491, 0.02555534429848194, -0.0917864590883255, -0.006020138971507549, -0.05192042514681816, -0.01107169408351183, 0.01428928505629301, 0.04804249480366707, -0.02258680760860443, 0.04362530633807182, 0.04241535812616348, 0.02724386751651764, 0.0028245255816727877, 0.030313652008771896, -0.02621426060795784, -0.01507740281522274, 0.06570994108915329, -0.03933382406830788, 0.007045296486467123, 0.02622702158987522, -0.05749934911727905, 0.042956314980983734, 0.006060635671019554, -0.02112988568842411, -0.02655610255897045, -0.005535795819014311, -0.02286086603999138, -0.04963580146431923, 0.013969146646559238, 0.03327010199427605, 0.013699784874916077, 0.042891040444374084, -0.002656271681189537, 0.03867132216691971, 0.05972740426659584, -0.023898402228951454, 0.041538361459970474, 0.04152734950184822, 0.022735757753252983, 0.018622461706399918, -0.013385525904595852, -0.011567850597202778, -0.08261125534772873, 0.031692054122686386, -0.04244167357683182, -0.06528760492801666, 0.04688682407140732, -0.009837718680500984, 0.0442974828183651, -0.0009378817048855126, -0.011141838505864143, 0.05872723087668419, 0.01729767955839634, -0.03783664479851723, -0.01667879894375801, 0.008140417747199535, 0.07226857542991638, -0.03927042707800865, 0.03778611123561859, 0.0011535764206200838, 0.06862116605043411, -0.03722638264298439, 0.03614549711346626, 0.06189925968647003, 0.02964296191930771, -0.03445002809166908, -0.03072064369916916, 0.0065656742081046104, -0.005092464853078127, -0.0077864923514425755, 0.003390523139387369, 0.049188148230314255, -0.017631011083722115, -0.0014936199877411127, 0.012192311696708202, -0.026624739170074463, 0.05477972701191902, 0.03365666791796684, -0.028281599283218384, -0.05759574845433235, -0.0019307516049593687, -0.03551040589809418, -0.024368103593587875, 0.003031577216461301, -0.032327938824892044, -0.0639873668551445, 0.012095402926206589, -0.004639092367142439, 0.027083713561296463, -0.05173700675368309, 0.014593832194805145, -0.0031545250676572323, -0.04381725192070007, -0.009114534594118595, 0.04066849127411842, 0.04563780874013901, -0.0214257650077343, 0.027457410469651222, -0.026646139100193977, -0.012966948561370373, 0.07815045863389969, 0.010639573447406292, 0.01911362260580063, 0.052052125334739685, 0.043081559240818024, 0.020755046978592873, 0.014676430262625217, 0.053756602108478546, -0.04292897507548332, -0.030799604952335358, -0.04704895243048668, 0.03415356203913689, 0.058579303324222565, 0.0483916811645031, -0.024500632658600807, -0.007150949444621801, -0.03313621133565903, 0.008478837087750435, 0.0036828997544944286, 0.016134949401021004, 0.00395782059058547, 0.0022614640183746815, -0.03814017400145531, 0.022034985944628716, 0.007814322598278522, -0.019429929554462433, -0.0017337608151137829, -0.02785089612007141, -0.04761412367224693, -0.021063214167952538, 0.0019849527161568403, -0.05751676484942436, 0.024466708302497864, -0.02453375607728958, 0.01968381553888321, 0.0005307263345457613, 0.028718212619423866, -0.042660608887672424, 0.04415478929877281, 0.06824624538421631, 0.020675288513302803, -0.04252156987786293, -0.008832288905978203, 0.002119475044310093, -0.04086114093661308, -0.05192077159881592, -0.04228682443499565, -0.008058766834437847, -0.0027656136080622673, 0.012249915860593319, -0.004193567205220461, -0.049387313425540924, 0.023449819535017014, 0.0247592031955719, -0.030570557340979576, -0.015258648432791233, -0.040590979158878326, -0.004191004205495119, 0.013981358148157597, -0.05074597895145416, -0.01451390702277422, 0.014234389178454876, 0.0148044154047966, -0.02831827849149704, 0.05137106031179428, 0.024850262328982353, -0.0033417597878724337, 0.012630535289645195, -0.017605111002922058, -0.007946773432195187, -0.009963631629943848, 0.0853343978524208, -0.026888588443398476, 0.005854127462953329, -0.05132388696074486, -0.018606549128890038, 0.01402943767607212, 0.05375749617815018, 0.03394282981753349, 0.007752565201371908, 0.02752419002354145, -0.07358749955892563, -0.008332556113600731, 0.03837032988667488, -0.04859764501452446, -0.015202932991087437, -0.013158154673874378, 0.010072908364236355, 0.032734811305999756, -0.005156841594725847, -0.05012825131416321, -0.036485910415649414, -0.03690514340996742, -0.011772220954298973, 0.027142565697431564, -0.014050779864192009, 0.027401143684983253, 0.075029157102108, -0.037484582513570786, -0.050530221313238144, -0.0002597914426587522, 0.03212130442261696, -0.09123075008392334, -0.03499959036707878, 0.0013508162228390574, 0.011388787999749184, 0.02322029508650303, 0.026687592267990112, -0.031083038076758385, 0.07406418770551682, 0.018144497647881508, 0.0528278611600399, 0.009338435716927052, -0.018817603588104248, -0.03080941177904606, -0.026786988601088524, -0.06425072997808456, 0.0022533712908625603, 0.00310438871383667, 0.06024591252207756, 0.06658121198415756, -0.01015178021043539, 0.012460963800549507, 0.03690164536237717, -0.05469054728746414, -0.004764852579683065, -0.004961807746440172, 0.0406954288482666, 0.007034138310700655, -0.02318098396062851, 0.008106529712677002, 0.029909389093518257, -0.021527886390686035, 0.039219677448272705, 0.0437617190182209, 0.00818752683699131, 0.01609579101204872, 0.07472318410873413, -0.022627780213952065, 0.03989027068018913, 0.031754784286022186, 0.0008869697339832783, 0.03799943998456001, 0.058093126863241196, -0.025562237948179245, -0.045343607664108276, -0.005751716438680887, -0.009852468967437744, -0.04302988201379776, 0.051800429821014404, -0.02299216203391552, 0.031033335253596306, 0.026047416031360626, -0.018360638990998268, -0.006483095232397318, -0.0267956480383873, 0.01568475551903248, -0.00897905696183443, 0.020602254197001457, -0.00024401090922765434, 0.0018281098455190659, 0.02142701856791973, -0.03203210234642029, 0.09045099467039108, -0.009396130219101906, -0.012733373790979385, -0.01559576578438282, 0.04533015936613083, 0.012254441156983376, 0.032994139939546585, -0.011345744132995605, -0.014135903678834438, -0.04782716557383537, 0.0005062308628112078, -0.041637104004621506, 0.028255680575966835, 0.026898754760622978, -0.015891775488853455, -0.008014616556465626, -0.013722652569413185, -0.0012055750703439116, 0.0008738425094634295, 0.043676868081092834, -0.009272769093513489, -0.034542206674814224, 0.007324790582060814, -0.01866019144654274, -0.018574275076389313, -0.004748003091663122, 0.007653063163161278, -0.0010569774312898517, 0.00693955784663558, 0.0054954467341303825, -0.019594542682170868, -0.012698023580014706, -0.027808893471956253, 0.03170495107769966, -0.0036975201219320297, 0.022264136001467705, 0.014160466380417347, 0.036150604486465454, -0.012440001592040062, 0.0033224630169570446, -0.05146235227584839, -0.0077475085854530334, -0.0164816752076149, 0.03815571218729019, 0.024963418021798134, -0.02002171240746975, -0.004647387657314539, 0.02862800471484661, -0.058967266231775284, -0.0509333498775959, 0.0014998860424384475, -0.04184756428003311, -0.013794228434562683, -0.018114469945430756, 0.028127582743763924, 0.020321909338235855, 0.025739379227161407, 0.033699147403240204, 0.05659959465265274, -0.01746623031795025, 0.06587812304496765, -0.0042317770421504974, 0.04380252957344055, 0.018773436546325684, 0.008625087328255177, 0.002146743470802903, -0.01413351483643055, 0.03781413286924362, -0.06485946476459503, -0.0648050382733345, 0.0006576240411959589, -0.02605363167822361, -0.005653578322380781, -0.05795315280556679, -0.010319533757865429, 0.006477699615061283, -0.031567588448524475, -0.011034618131816387, -0.052599553018808365, 0.018149780109524727, 0.008052261546254158, 0.011684284545481205, 0.0226235743612051, -0.023251255974173546, 0.04863319173455238, 0.002021302003413439, 0.007749125361442566, -0.015141833573579788, -0.008459068834781647, 0.004608910996466875, -0.033210769295692444, 0.06666387617588043, 0.02717592753469944, 0.0031949076801538467, 0.006161711644381285, -0.006095405202358961, -0.00820109061896801, -0.015664344653487206, -0.06386417895555496, 0.01983604021370411, 0.02870866097509861, -0.003937407396733761, 0.09808740764856339, 0.0365816168487072, 0.0017316819867119193, 0.045825328677892685, 0.011723495088517666, -0.00030830700416117907, 0.00512892659753561, 0.011061334982514381, 0.004873110447078943, -0.030712086707353592, -0.0045538912527263165, 0.01476842351257801, 0.011952191591262817, -0.028648730367422104, 0.009525271132588387, -0.012829895131289959, -0.0066726417280733585, -0.04562428221106529, 0.056336335837841034, 0.08408079296350479, 0.041470397263765335, -0.027577459812164307, -0.017048610374331474, 0.01964789628982544, -0.036308009177446365, -0.05702735111117363, -0.025056207552552223, -0.038581401109695435, -0.03372982516884804, -0.0035463599488139153, 0.005872684996575117, -0.017544647678732872, -0.053425777703523636, 0.0021579491440206766, -0.016136281192302704, -0.02801981009542942, 0.02742292918264866, 0.03723730891942978, 0.03753722831606865, 0.016597220674157143, -0.015470816753804684, 0.05742355436086655, -0.03298094496130943, 0.031037811189889908, -0.016864260658621788, -0.052704259753227234, 0.01950606144964695, -0.03965770825743675, -0.039863456040620804, 0.012580336071550846, 0.019233813509345055, 0.04897591844201088, 0.023748258128762245, 0.11385347694158554, -0.030489353463053703, 0.014852539636194706, 0.05944870784878731, -0.01495038066059351, 0.06841844320297241, -0.036825031042099, -0.01775296963751316, 0.06388640403747559, 0.02485378086566925, -0.007707840297371149, 0.0029360800981521606, -0.07412145286798477, -0.030635451897978783, 0.013316604308784008, -0.007493003737181425, -0.009491738863289356, 0.04476610943675041, 0.02628922648727894, -0.018846936523914337, -0.012167125009000301, 0.019634630531072617, 0.012851339764893055, -0.028346111997961998, 0.04047778248786926, -0.011178137734532356, 0.01679970882833004, -0.01760602369904518, -0.07121417671442032, -0.012019110843539238, 0.08865655213594437, 0.0816461369395256, 0.031236963346600533, 0.03169948235154152, -0.006608223542571068, 0.010270509868860245, -0.00779722398146987, -0.06389211863279343, 0.007050835993140936, -0.03856894001364708, 0.0013141778763383627, 0.058660898357629776, -0.04616737365722656, 0.019724421203136444, -0.000992311630398035, -0.058565303683280945, -0.030335405841469765, 0.01712910830974579, 0.046028610318899155, -0.03449351340532303, -0.03856869041919708, 0.006899547763168812, 0.02334517613053322, -0.05988449230790138, 0.011163835413753986, 0.03576507791876793, 0.0073157669976353645, 0.015448342077434063, 0.030283233150839806, 0.029985956847667694, -0.045068223029375076, -0.024706481024622917, -0.002405681647360325, -0.018663831055164337, -0.011019982397556305, 0.031150860711932182, -0.05509212240576744, 0.04297761991620064, 0.027731627225875854, 0.026270033791661263, -0.021738797426223755, 0.0003806878812611103, -0.06623820960521698, -0.001680778688751161, -0.014378164894878864, -0.04933406785130501, -0.016848428174853325, 0.006982973776757717, -0.015906915068626404, 0.03291504085063934, -0.0529886893928051, -0.01699107699096203, 0.0028277754317969084, 0.026916522532701492, -0.010263596661388874, -0.039914801716804504, 0.08112207800149918, -0.018526436761021614 ]
<p>There's a question on my homework about the process $e^{-} e^{+} \rightarrow \tau^{+} \tau^{-}$. Specifically, it is claimed that the minimum energy required of the colliding positron and electron beams is slightly less than twice the $\tau$ mass, and I am asked to explain this deviation and compute it. In the context of this course, we have only discussed the relativistic kinematics of such processes (which would predict a minimum energy of twice the $\tau$ mass), so I am not sure what might be responsible. I'm grasping at straws here, but might it have something to do with the Coulomb interaction between the opposite charges? Thanks in advance.</p>
g8389
[ 0.030975397676229477, -0.015812436118721962, 0.008733589202165604, -0.009783594869077206, 0.030561618506908417, 0.03615909814834595, 0.012577406130731106, 0.032725367695093155, -0.021176235750317574, 0.01776069775223732, 0.02573149837553501, -0.006999812554568052, 0.02371109277009964, 0.0002473296190146357, -0.008098681457340717, -0.03651713207364082, 0.0880725160241127, -0.017938675358891487, -0.018300974741578102, 0.03372754156589508, -0.04133819043636322, 0.010034454055130482, -0.013710753992199898, -0.04179762303829193, 0.07176464051008224, 0.005900850985199213, -0.015377405099570751, 0.03763270005583763, -0.03461575135588646, -0.020005764439702034, 0.039363548159599304, 0.009904724545776844, -0.0028928429819643497, -0.08573571592569351, -0.08179577440023422, -0.05420571193099022, 0.057579316198825836, 0.026412222534418106, -0.03539622575044632, 0.0023839420173317194, 0.02026725932955742, -0.050225045531988144, 0.01718338020145893, -0.009711886756122112, 0.06152499467134476, -0.033419594168663025, 0.028469974175095558, -0.021748937666416168, -0.04001978039741516, -0.0019545117393136024, -0.040909018367528915, 0.017121775075793266, -0.005504547152668238, -0.036506183445453644, -0.005785204935818911, -0.028175273910164833, 0.00863559264689684, -0.09432776272296906, 0.051526445895433426, 0.06691141426563263, 0.084628164768219, 0.00354714784771204, -0.0026323997881263494, -0.022430257871747017, 0.08260157704353333, -0.04729551449418068, -0.01893557235598564, -0.0022487964015454054, 0.008586375042796135, 0.0450112409889698, -0.025143938139081, -0.04624342545866966, -0.04149851202964783, -0.017589015886187553, 0.07075279951095581, -0.052226971834897995, 0.04002627357840538, 0.005541603546589613, 0.03614116832613945, -0.0264446921646595, -0.023285040631890297, -0.03740460053086281, 0.03677709028124809, 0.018047260120511055, 0.03811514377593994, 0.002918155863881111, -0.01753169670701027, 0.02230614237487316, -0.05620194971561432, -0.01401541568338871, 0.05187944695353508, -0.02418149635195732, 0.056063730269670486, -0.06679855287075043, -0.025859732180833817, 0.017579490318894386, -0.008950034156441689, 0.01869775354862213, 0.006783117540180683, -0.0028039568569511175, -0.011799114756286144, -0.03874830901622772, -0.03090372122824192, -0.009079459123313427, -0.01736331358551979, -0.03650315850973129, 0.01676277443766594, 0.006542859133332968, -0.0038213799707591534, 0.024336962029337883, -0.0766567811369896, -0.029475290328264236, -0.030434252694249153, -0.0646461546421051, -0.024391721934080124, -0.00599566288292408, 0.03002825565636158, -0.004651456605643034, -0.009258783422410488, 0.01740906946361065, -0.031167861074209213, -0.01227531861513853, -0.011989438906311989, 0.07966285198926926, -0.05049222335219383, -0.005276602227240801, -0.015079351142048836, -0.0012607363751158118, 0.030424578115344048, 0.003845537779852748, -0.022320322692394257, -0.019128791987895966, 0.04582955315709114, 0.0559934601187706, 0.005850862246006727, 0.05743884667754173, -0.01201912946999073, 0.031829360872507095, 0.04944165050983429, -0.05878494307398796, 0.05006347596645355, 0.018236953765153885, -0.017123468220233917, -0.04130274057388306, -0.009703350253403187, 0.0193464532494545, -0.03557364270091057, 0.0028760808054357767, 0.028615742921829224, 0.044024232774972916, -0.03970658406615257, 0.007907325401902199, -0.033883459866046906, -0.0027497741393744946, 0.0057794759050011635, 0.02489357814192772, 0.052755262702703476, -0.06265729665756226, 0.00321205728687346, 0.043000731617212296, 0.05765790492296219, 0.0016901185736060143, 0.05643045902252197, 0.016225270926952362, -0.018851634114980698, 0.05318177491426468, -0.01780053600668907, -0.02264000102877617, 0.0024474509991705418, -0.025127960368990898, -0.05260472744703293, -0.052696600556373596, 0.05160447955131531, 0.030885715037584305, -0.07009600847959518, 0.0942356139421463, -0.0035230531357228756, -0.01488118153065443, -0.012713168747723103, 0.008552736602723598, 0.00036569731310009956, -0.007902001962065697, 0.03363002464175224, 0.050449151545763016, 0.007778397761285305, -0.07876494526863098, -0.026794569566845894, 0.060428984463214874, -0.0063222721219062805, 0.023815970867872238, -0.006574045401066542, 0.0025232566986232996, -0.010609597899019718, 0.017342474311590195, -0.04992575943470001, 0.025329872965812683, 0.011431261897087097, -0.03718617185950279, -0.014911015518009663, -0.0016470392001792789, -0.02387164533138275, 0.029363054782152176, 0.002004347275942564, 0.025515152141451836, 0.024366604164242744, -0.05449792370200157, -0.02770661562681198, -0.048659246414899826, 0.055842652916908264, -0.03578510880470276, 0.014880466274917126, -0.017333677038550377, -0.03240261971950531, 0.050306808203458786, -0.011170359328389168, -0.016660461202263832, 0.019040599465370178, 0.013060490600764751, -0.018017057329416275, -0.01423253957182169, -0.08354565501213074, 0.002764205215498805, -0.01416700053960085, 0.007695819716900587, 0.012861980125308037, 0.04959161579608917, 0.015803983435034752, -0.040438756346702576, -0.0807611271739006, -0.0008476770017296076, -0.08543500304222107, 0.07246063649654388, -0.008931432850658894, -0.02770068123936653, 0.06261453777551651, -0.004076444543898106, -0.007725478615611792, 0.05081646889448166, 0.03861735016107559, -0.012304553762078285, 0.05234361067414284, -0.0023192332591861486, -0.06737139821052551, 0.015050988644361496, 0.026300378143787384, -0.055228106677532196, 0.07460982352495193, 0.01957729458808899, -0.044453926384449005, -0.015490371733903885, 0.038997069001197815, -0.01864432357251644, -0.002414638176560402, 0.0031955416779965162, 0.06132589653134346, -0.016989687457680702, -0.06333313882350922, 0.05100571736693382, -0.013970207422971725, 0.003999239299446344, -0.008626262657344341, 0.0066213542595505714, 0.01452510803937912, -0.017148757353425026, -0.032157160341739655, -0.0163776483386755, -0.019519265741109848, 0.013732434250414371, 0.03900766372680664, -0.05685437470674515, -0.009707118384540081, 0.08251258730888367, -0.041210077702999115, 0.008357560262084007, -0.007351281587034464, -0.037433139979839325, -0.004994033835828304, -0.04037584364414215, 0.023508822545409203, -0.04096659645438194, -0.07545515149831772, 0.024689557030797005, 0.02227727510035038, 0.06314609944820404, 0.03134747967123985, 0.0039922078140079975, -0.04520406201481819, 0.06584831327199936, 0.007135148625820875, 0.08204824477434158, -0.06292084604501724, -0.0408809557557106, 0.026655375957489014, -0.03301937133073807, 0.05386408418416977, 0.007767007686197758, 0.022577708587050438, -0.05034012347459793, -0.05054941400885582, 0.013455510139465332, -0.018789080902934074, -0.06225055456161499, -0.04286245256662369, -0.007908895611763, -0.05703837424516678, 0.00573584483936429, -0.05727490037679672, -0.025365574285387993, -0.05361228808760643, 0.04651668667793274, -0.07172702252864838, 0.03731489181518555, 0.07085231691598892, 0.02638726495206356, -0.029777133837342262, -0.05407288298010826, 0.011043290607631207, 0.010278030298650265, 0.004578514955937862, -0.016286659985780716, -0.008880242705345154, 0.008794714696705341, 0.048303961753845215, 0.012102688662707806, -0.02461669035255909, -0.00118498713709414, -0.010310583747923374, -0.010739599354565144, -0.009482347406446934, -0.007055667228996754, 0.04550446569919586, 0.001847828971222043, -0.016308359801769257, -0.025339527055621147, 0.025278175249695778, -0.014685055240988731, 0.05039309337735176, 0.08104768395423889, 0.04609077423810959, 0.04712248221039772, 0.01314526330679655, -0.027990736067295074, 0.009811252355575562, -0.009180588647723198, 0.009227694012224674, -0.030206725001335144, 0.006635928060859442, -0.021958017721772194, 0.05498760938644409, -0.012945352122187614, 0.06134164333343506, -0.011292966082692146, -0.05187147855758667, 0.0058101168833673, 0.04256536811590195, 0.009086327627301216, -0.008941085077822208, 0.010927966795861721, 0.045133382081985474, -0.0011328113032504916, 0.024631038308143616, -0.06015891954302788, -0.02688804641366005, -0.05196579545736313, -0.04566340893507004, -0.03377122804522514, -0.07122354209423065, 0.02450166828930378, 0.059798434376716614, -0.05370739847421646, -0.0027279069181531668, -0.05446956679224968, -0.03029581345617771, 0.001940873102284968, -0.021137947216629982, -0.046916086226701736, -0.01829363964498043, 0.04580376297235489, -0.011064891703426838, 0.018301736563444138, 0.02046138048171997, -0.023531707003712654, -0.0396488681435585, 0.03481977805495262, 0.004840950947254896, 0.05860545113682747, -0.02481805719435215, 0.019836531952023506, -0.015055372379720211, -0.051993731409311295, 0.015290397219359875, -0.01260938961058855, -0.04869331046938896, 0.005472610704600811, 0.02969544008374214, -0.0023326848167926073, 0.04726641625165939, -0.0334872230887413, -0.008380245417356491, 0.06429413706064224, 0.0042789592407643795, 0.02032901532948017, 0.014782640151679516, -0.052497729659080505, -0.04638410359621048, -0.005462349858134985, 0.007242686115205288, -0.013217498548328876, 0.013321385718882084, -0.03450358286499977, 0.02524629421532154, 0.008337419480085373, -0.048340462148189545, -0.02146693877875805, 0.029302997514605522, 0.01015213318169117, -0.050369374454021454, 0.06873346120119095, 0.01809650845825672, 0.0488719567656517, 0.04146610200405121, 0.010289330035448074, 0.013539512641727924, 0.0034631004091352224, -0.0009130654507316649, 0.06479490548372269, 0.05410163849592209, 0.05239051952958107, -0.008429346606135368, -0.005028122570365667, 0.031423572450876236, 0.03669719398021698, -0.04934972897171974, 0.03703729063272476, -0.057870540767908096, 0.036937814205884933, 0.021508468315005302, 0.0197959765791893, 0.018867695704102516, 0.01159557607024908, 0.049635302275419235, -0.004814973566681147, -0.0214155875146389, -0.02474561706185341, -0.014714299701154232, 0.06425464153289795, -0.005566657520830631, -0.08461657166481018, -0.0059613920748233795, -0.03358214721083641, 0.03000415489077568, -0.03501717001199722, 0.01685084030032158, 0.009831552393734455, 0.04942869767546654, -0.006033244077116251, -0.006459162570536137, 0.011304519139230251, 0.015468977391719818, 0.06699194759130478, -0.03189287334680557, -0.06503260135650635, 0.03459044173359871, 0.022760385647416115, 0.08385661989450455, -0.02833886630833149, -0.06676670163869858, 0.004302735906094313, -0.05357631295919418, 0.0247073732316494, -0.02921234257519245, 0.01540935318917036, 0.007303621154278517, 0.013765598647296429, -0.029860535636544228, 0.010937840677797794, -0.07354824990034103, -0.0021174238063395023, -0.011721081100404263, 0.0074564372189342976, 0.01654486171901226, -0.03927876800298691, -0.04225064441561699, -0.009122981689870358, -0.04456522315740585, 0.04012911766767502, -0.011534851044416428, 0.020614592358469963, 0.06791053712368011, -0.007707525044679642, 0.028765376657247543, 0.05485963448882103, 0.0021329952869564295, -0.015633288770914078, 0.0035576834343373775, 0.04522573947906494, 0.012686233036220074, -0.00969571340829134, 0.04343638941645622, 0.009919843636453152, -0.042125605046749115, 0.024833332747220993, -0.07648982107639313, 0.016873082146048546, 0.003273359267041087, 0.005175366066396236, 0.06990338116884232, -0.006074594799429178, -0.041931405663490295, 0.019502906128764153, -0.0430898480117321, 0.05143371596932411, 0.0902557373046875, -0.015159272588789463, -0.04969586059451103, -0.01093877013772726, -0.05430804193019867, 0.03094405308365822, -0.03242327645421028, -0.008824437856674194, 0.05802031606435776, 0.023935092613101006, -0.005951050668954849, -0.02347622439265251, 0.02193138189613819, -0.03571990132331848, -0.0028752393554896116, 0.005852100905030966, -0.01139634195715189, 0.03469247370958328, 0.050422728061676025, -0.005106352269649506, -0.026059407740831375, 0.029467467218637466, 0.032633014023303986, -0.04353322833776474, -0.008896398358047009, 0.004999792203307152, 0.027067074552178383, 0.011344012804329395, 0.024864867329597473, -0.03476906567811966, 0.04263528063893318, 0.08889564126729965, 0.012384546920657158, 0.011054708622395992, -0.03600503131747246, -0.011708492413163185, 0.009612523950636387, -0.04588959738612175, -0.019140295684337616, 0.01728157326579094, 0.047325778752565384, -0.03721536695957184, 0.003734427271410823, 0.047315530478954315, 0.03013426810503006, -0.0452386736869812, 0.011474390514194965, -0.01603871025145054, 0.028010999783873558, -0.08109261840581894, -0.0046656783670187, 0.07423801720142365, 0.05627576634287834, -0.06901904940605164, 0.0026854518800973892, -0.017288191244006157, 0.03695860877633095, 0.004917629528790712, 0.025082936510443687, -0.007663356140255928, -0.016476992517709732, -0.01920953206717968, 0.05281680077314377, 0.04217516630887985, -0.028089381754398346, 0.03230507671833038, -0.06704298406839371, -0.03675756976008415, 0.038375623524188995, -0.015483129769563675, -0.022624053061008453, -0.04652339220046997, 0.017102306708693504, 0.024244051426649094, -0.02595214731991291, -0.033365532755851746, 0.040188904851675034, 0.021338865160942078, -0.05888073146343231, -0.009979126043617725, -0.020645998418331146, 0.005309165455400944, -0.001093364553526044, -0.01037320401519537, -0.008428559638559818, -0.046788569539785385, -0.04001631215214729, 0.05167650803923607, 0.030000636354088783, 0.05633227899670601, 0.053968094289302826, 0.015058781951665878, 0.038326337933540344, 0.04079936817288399, 0.0023927122820168734, 0.09010475873947144, -0.05714382231235504, 0.05259096622467041, -0.026722129434347153, 0.008772497065365314, -0.059256598353385925, -0.042824070900678635, 0.0006063127075321972, -0.0032160768751055002, -0.06747546792030334, 0.01530519500374794, -0.027544952929019928, -0.038506437093019485, 0.07025119662284851, -0.03181898221373558, 0.004114231094717979, 0.016864778473973274, 0.01230540033429861, 0.008672294206917286, 0.028075316920876503, 0.016077103093266487, 0.047151125967502594, -0.01598541811108589, -0.010879090055823326, -0.03524501249194145, 0.0057668136432766914, 0.060522790998220444, -0.017104417085647583, 0.04223101586103439, -0.01347395684570074, 0.0494082048535347, -0.05818071961402893, -0.018840504810214043, 0.043185003101825714, 0.025205619633197784, -0.008307093754410744, 0.025959130376577377, -0.054884977638721466, 0.0023966003209352493, 0.039469365030527115, -0.01646186038851738, -0.03658682852983475, -0.030225398018956184, -0.02495364099740982, -0.006887701340019703, -0.019937928766012192, -0.010641520842909813, -0.03256795555353165, -0.049061764031648636, -0.005896075163036585, -0.025503259152173996, 0.06531844288110733, 0.013644994236528873, -0.034288957715034485, -0.027798602357506752, 0.017361847683787346, 0.026665177196264267, 0.05739770457148552, -0.003837479278445244, -0.032250236719846725, -0.02673528902232647, 0.004300645086914301, -0.05325203388929367, -0.025606883689761162, -0.04076533764600754, -0.06628184765577316, 0.0009524471242912114, 0.012883979827165604, -0.01724136993288994, -0.008014285005629063, 0.037063635885715485, -0.019474251195788383, -0.02649056725203991, -0.037020307034254074, 0.00022426403302233666, -0.05758285894989967, 0.029256490990519524, -0.010274571366608143, 0.05121437460184097, -0.02483760006725788, 0.025458944961428642, -0.017766736447811127, 0.00919435266405344, 0.011369244195520878, 0.011178174056112766, 0.03396852687001228, 0.061563506722450256, -0.016772005707025528, 0.035116441547870636, 0.03348986431956291, 0.005162845831364393, 0.013243339955806732, 0.028756802901625633, 0.01679948717355728, -0.044073436409235, 0.018490087240934372, 0.01618296653032303, -0.0011857958743348718, 0.054928142577409744, 0.006301148794591427, -0.06435450911521912, -0.014451190829277039, 0.02086099423468113, 0.038793981075286865, 0.06539668142795563, 0.017676709219813347, -0.022701840847730637, 0.06489944458007812, -0.014650609344244003, 0.012285125441849232, 0.026399148628115654, 0.01839655265212059, -0.009096916764974594, -0.03064984641969204, 0.025937672704458237, -0.07104744762182236, -0.047876909375190735, -0.011781753972172737, -0.06412694603204727, -0.02439676970243454, -0.020188571885228157, 0.04406874254345894, 0.013162066228687763, -0.018216785043478012, -0.011447315104305744, -0.033444713801145554, -0.05534617230296135, -0.024624710902571678, 0.0030394578352570534, -0.018660299479961395, -0.0067276619374752045, 0.01654772460460663, -0.016941623762249947, 0.02195184864103794, -0.052752092480659485, -0.0015820672269910574, -0.011397028341889381, -0.07544621080160141, -0.03174899145960808, 0.023517049849033356, 0.004749104846268892, 0.06194964423775673, 0.0199247058480978, -0.012186035513877869, 0.032970696687698364, -0.05632922798395157, 0.08065031468868256, 0.026318522170186043, -0.023562965914607048, 0.029344292357563972, 0.019991513341665268, 0.004581265617161989, 0.002031565411016345, -0.0063486904837191105, -0.010417276993393898, 0.000584577617701143, -0.005031995940953493, -0.004156916402280331, -0.04341578856110573, 0.021141095086932182, 0.012716108933091164 ]
<p>In the Schrödinger equation in the position representation $$ i\hbar\frac{\partial}{\partial t}\Psi(x,t) ~=~[\frac{-\hbar^2}{2m}\nabla^2+V(x,t)]\Psi(x,t), $$ is the potential $V(x,t)$ an operator acting on $\Psi$ or merely a scalar?</p>
g8390
[ 0.014179562218487263, 0.0022377129644155502, -0.030174925923347473, 0.0008520139963366091, 0.04528546333312988, -0.0059529319405555725, 0.05492331087589264, 0.026756197214126587, -0.023591257631778717, 0.014446026645600796, 0.008355436846613884, 0.02051795832812786, -0.04675105959177017, 0.0029316432774066925, 0.0005883729318156838, -0.023314813151955605, 0.0445106215775013, -0.004722447134554386, -0.01761580817401409, -0.01470707543194294, -0.09492998570203781, 0.008805917575955391, 0.0020367589313536882, 0.004659347236156464, 0.06443790346384048, -0.028379185125231743, 0.05759991705417633, -0.04796779900789261, -0.002479773247614503, -0.025797931477427483, -0.012806371785700321, 0.06976529210805893, 0.017614925280213356, -0.00612042099237442, -0.04979105293750763, -0.0250205360352993, 0.08798831701278687, 0.0067415083758533, -0.006192237604409456, -0.04459215700626373, -0.06750095635652542, -0.048149511218070984, 0.011712848208844662, -0.02677558921277523, -0.011675789020955563, -0.01626810058951378, 0.055802274495363235, 0.07101011276245117, -0.016809988766908646, 0.0076077659614384174, 0.048491187393665314, -0.01583753153681755, -0.000670572801027447, 0.0474388524889946, 0.055682409554719925, 0.021986648440361023, 0.020588120445609093, -0.012107938528060913, 0.020716272294521332, 0.056788355112075806, -0.04903364181518555, -0.0044020842760801315, 0.050192106515169144, 0.05158044025301933, 0.0189399104565382, -0.027645569294691086, -0.07116138935089111, -0.013194482773542404, -0.008468076586723328, -0.05303932726383209, 0.0165922399610281, -0.02361995354294777, -0.007598406169563532, 0.057153262197971344, -0.057589806616306305, 0.041393328458070755, -0.012207831256091595, -0.07248083502054214, 0.04640987515449524, 0.00717065017670393, -0.002775834873318672, -0.09443625807762146, 0.054028838872909546, 0.04509735852479935, 0.02801094390451908, -0.009205509908497334, -0.013804236426949501, 0.010341277346014977, -0.026974258944392204, 0.03108164481818676, 0.0001553719339426607, -0.007623711135238409, 0.005230394657701254, 0.039213474839925766, 0.011370396241545677, -0.044970277696847916, 0.007132107857614756, -0.0034267979208379984, 0.011013824492692947, 0.01646723970770836, -0.06511782854795456, 0.04376363754272461, 0.061350204050540924, 0.02286365255713463, 0.03532452881336212, -0.03687366098165512, -0.004482118878513575, -0.054717615246772766, 0.01803845912218094, -0.009534433484077454, 0.059221602976322174, 0.012324332259595394, -0.02255275845527649, -0.04502362385392189, -0.030167704448103905, -0.007345159072428942, 0.041671138256788254, -0.009690948761999607, -0.057189732789993286, 0.09138944000005722, 0.02187281660735607, 0.07590491324663162, 0.064323291182518, 0.01589464209973812, -0.0038871043361723423, 0.02787015400826931, -0.024341795593500137, 0.007698582485318184, -0.00459476700052619, -0.006530993152409792, 0.020435720682144165, -0.011600648052990437, 0.017015714198350906, 0.014835391193628311, 0.010887738317251205, 0.01893065683543682, -0.024431735277175903, -0.0473175086081028, 0.05273579806089401, 0.021658271551132202, -0.01615610532462597, -0.02402494288980961, -0.02782094106078148, 0.04012902081012726, -0.04743027314543724, 0.05069465935230255, -0.03057621791958809, -0.012837710790336132, 0.04078758507966995, -0.049816690385341644, 0.011252585798501968, 0.032973140478134155, -0.008767448365688324, 0.0031280461698770523, 0.0018367590382695198, -0.04655241221189499, 0.03114776685833931, 0.0823676586151123, 0.013175759464502335, -0.009405306540429592, 0.0364416241645813, 0.017177924513816833, 0.06345513463020325, -0.03465964272618294, -0.026028307154774666, -0.04203203320503235, -0.0477917306125164, -0.03483692929148674, 0.009405876509845257, -0.07088655978441238, 0.03789887949824333, 0.04853970557451248, -0.0007871331763453782, -0.018600694835186005, 0.002841712674126029, 0.062378477305173874, -0.06300892680883408, 0.017696907743811607, 0.013808043673634529, 0.1013520210981369, -0.051098067313432693, -0.04918020963668823, 0.01536594983190298, -0.07091281563043594, 0.015761375427246094, -0.023898985236883163, -0.005393947474658489, 0.03418822959065437, -0.024017708376049995, -0.015382112003862858, 0.007448899559676647, 0.05638798326253891, 0.08005998283624649, 0.03052089735865593, 0.020031576976180077, 0.024453826248645782, 0.022590359672904015, -0.07252668589353561, 0.024103855714201927, 0.027343010529875755, -0.02433111146092415, 0.05902423337101936, 0.04947146400809288, 0.003144104266539216, 0.008708210662007332, 0.029353568330407143, 0.022036371752619743, -0.049245916306972504, 0.023396329954266548, -0.04260972514748573, -0.0022158161737024784, -0.03610261157155037, -0.004263405222445726, -0.024977749213576317, -0.021142631769180298, -0.05501775071024895, -0.03929493948817253, 0.005770919844508171, -0.04426801577210426, 0.012837579473853111, -0.024743197485804558, 0.00265050632879138, -0.020373858511447906, 0.010758350603282452, -0.028758637607097626, 0.05275116488337517, -0.006155805196613073, -0.007009816821664572, -0.016202665865421295, 0.04174749553203583, -0.029994629323482513, 0.002494470216333866, 0.02237643674015999, -0.0013889854308217764, 0.025187445804476738, 0.019126128405332565, 0.032633181661367416, 0.034491222351789474, -0.017430029809474945, -0.0009363749413751066, 0.08368666470050812, -0.02162129618227482, -0.005339843221008778, 0.012896765023469925, 0.06606052070856094, 0.09933288395404816, 0.048053838312625885, -0.012935684993863106, 0.01535511203110218, 0.0026356540620326996, -0.039920881390571594, -0.05721708759665489, 0.014387612231075764, -0.014351770281791687, -0.016151390969753265, -0.014506017789244652, 0.015790337696671486, 0.009555870667099953, -0.011348661966621876, -0.025915317237377167, -0.04637535661458969, 0.058564383536577225, -0.008511636406183243, 0.03793070465326309, -0.0051804715767502785, 0.0341821126639843, -0.015839049592614174, 0.04485015943646431, -0.002634868724271655, -0.002319127321243286, 0.04431988671422005, 0.021260173991322517, -0.05270158499479294, 0.011857867240905762, -0.0361105352640152, -0.0620449036359787, 0.016062507405877113, -0.054122909903526306, 0.03044012375175953, -0.03174149990081787, -0.01898074708878994, -0.01648714207112789, 0.010843454860150814, 0.051020827144384384, 0.013634370639920235, -0.03235825151205063, 0.01137500535696745, 0.01238158717751503, 0.029952529817819595, 0.0022105334792286158, 0.009983072057366371, 0.009145449846982956, 0.02290240116417408, 0.04801015928387642, -0.02714407816529274, -0.014982243999838829, 0.031792350113391876, -0.0515294186770916, 0.00036493930383585393, 0.014227012172341347, -0.00614866241812706, 0.015944475308060646, -0.023089798167347908, -0.0006262497045099735, 0.030967233702540398, -0.0414198637008667, -0.049233514815568924, -0.040564730763435364, -0.004001636523753405, -0.0075884307734668255, -0.025032684206962585, 0.09059782326221466, -0.038842469453811646, 0.012144279666244984, -0.02115727961063385, 0.04175253584980965, -0.052635665982961655, -0.030058380216360092, -0.0547773651778698, 0.031986020505428314, 0.0069204336032271385, -0.04614310711622238, -0.02717931754887104, 0.008050897158682346, -0.003059370443224907, 0.014830691739916801, -0.008966950699687004, 0.02536509558558464, -0.03253567963838577, -0.043517012149095535, 0.023038726300001144, -0.0009981503244489431, 0.051723822951316833, -0.03368977829813957, -0.029932795092463493, -0.02159213274717331, -0.014772191643714905, -0.002286669332534075, 0.0224829763174057, -0.011554829776287079, 0.012927686795592308, -0.050256844609975815, -0.05781339481472969, 0.05846181884407997, 0.007547453977167606, -0.026786193251609802, -0.050190992653369904, 0.05181172862648964, 0.010197549127042294, -0.0281714778393507, -0.033959582448005676, -0.01296398788690567, 0.03377154842019081, -0.030362077057361603, 0.019376643002033234, -0.026766370981931686, 0.01829594373703003, 0.028157871216535568, -0.05820520967245102, 0.030725475400686264, -0.007439139299094677, -0.03365433216094971, 0.003705821465700865, 0.05362233892083168, 0.0007830136455595493, -0.035170942544937134, -0.03758864477276802, 0.02011767588555813, 0.02072281576693058, -0.0067739044316112995, 0.029742849990725517, 0.009211857803165913, 0.014882555231451988, 0.07559406012296677, 0.0078774718567729, -0.06831080466508865, -0.04900931939482689, -0.07657575607299805, 0.02566208690404892, 0.04170629009604454, -0.015692314133048058, 0.027013763785362244, -0.009260500781238079, 0.008709624409675598, 0.04906994849443436, -0.047674138098955154, 0.022398317232728004, 0.035304322838783264, 0.05231436714529991, -0.023993752896785736, -0.00393269956111908, -0.03569216653704643, -0.011249339208006859, 0.036093518137931824, -0.014123715460300446, 0.03495777025818825, 0.038212310522794724, -0.0010676993988454342, -0.020367911085486412, 0.022370843216776848, -0.025386778637766838, -0.018467357382178307, 0.03483191877603531, 0.0005511223571375012, 0.002258818130940199, 0.011863473802804947, 0.060951635241508484, -0.09589721262454987, -0.05407719314098358, -0.022737285122275352, -0.04265976697206497, -0.011938611976802349, -0.0344790443778038, -0.0056883892975747585, -0.039124105125665665, -0.00909695029258728, 0.01738286204636097, -0.01932736299932003, -0.015305537730455399, 0.0258229561150074, 0.04579641669988632, -0.015160273760557175, 0.047740913927555084, -0.01859520748257637, 0.043150998651981354, 0.011376014910638332, 0.016720853745937347, -0.0013440491165965796, -0.038376033306121826, -0.051659613847732544, -0.04299388453364372, 0.014538916759192944, 0.0404960997402668, 0.10606567561626434, -0.04858652129769325, 0.040125180035829544, -0.10001656413078308, -0.0828312560915947, 0.02169676311314106, 0.06368690729141235, 0.044646963477134705, 0.005451042205095291, 0.0005570422508753836, 0.013245591893792152, -0.020888732746243477, -0.002351768547669053, -0.022184263914823532, -0.08097516000270844, 0.004402196034789085, -0.025848496705293655, -0.0388847179710865, 0.04184218496084213, 0.005869756918400526, -0.043327782303094864, 0.07373165339231491, -0.011596370488405228, -0.009264515712857246, -0.03352218121290207, 0.0058276657946407795, -0.027877701446413994, 0.005311543587595224, -0.044846560806035995, -0.045442160218954086, -0.013517066836357117, 0.08032774180173874, -0.018583493307232857, -0.05895678699016571, 0.036123186349868774, -0.048394784331321716, -0.0856260359287262, 0.0592559389770031, -0.014568053185939789, 0.06217588484287262, -0.03301487863063812, 0.09832959622144699, -0.001181972213089466, 0.018722424283623695, -0.00036123517202213407, -0.040009524673223495, 0.008121347986161709, 0.003993958234786987, 0.032757971435785294, 0.01588170975446701, -0.023409083485603333, -0.012553885579109192, 0.028155991807579994, -0.03191225230693817, -0.021734140813350677, -0.02671625092625618, -0.016423741355538368, 0.031112736091017723, 0.0953448936343193, -0.03346935659646988, -0.0223053228110075, 0.00712713785469532, 0.01793554052710533, 0.02163853496313095, -0.003464137902483344, 0.02144664339721203, 0.03681043162941933, -0.017956895753741264, -0.013563019223511219, -0.02519953064620495, 0.006454208865761757, -0.05699280649423599, 0.03806905820965767, 0.06091267615556717, -0.016491973772644997, 0.018964217975735664, -0.00004425002043717541, 0.008907359093427658, -0.025433747097849846, -0.004731976427137852, 0.06160164251923561, 0.025980735197663307, -0.024099009111523628, -0.057954203337430954, 0.0008237854344770312, -0.04909077286720276, -0.05477943271398544, 0.05863342806696892, 0.053941916674375534, 0.032281436026096344, -0.04908455163240433, 0.03034437820315361, 0.023322828114032745, -0.024402430281043053, -0.04754287004470825, -0.02695249207317829, 0.0031053004786372185, 0.0017797840991988778, -0.01889672502875328, 0.0264191385358572, 0.0003069730300921947, 0.059675585478544235, -0.026321755722165108, -0.01591731235384941, 0.008830355480313301, 0.030158421024680138, 0.004540689289569855, -0.004661897663027048, -0.062114376574754715, -0.04284340888261795, 0.02861742302775383, -0.03536215424537659, 0.017640652135014534, -0.023897739127278328, 0.011566707864403725, 0.020181328058242798, 0.023585906252264977, -0.010526910424232483, 0.015305525623261929, -0.06099197268486023, 0.023217910900712013, 0.015837417915463448, -0.005956924986094236, 0.006692396476864815, -0.005596109200268984, -0.00687254685908556, -0.014122054912149906, 0.03715008869767189, 0.010884578339755535, 0.012319417670369148, 0.011746993288397789, 0.03471928462386131, -0.015362396836280823, -0.02332472614943981, -0.015419725328683853, 0.039026543498039246, 0.02152305655181408, -0.01253349520266056, 0.031131979078054428, -0.027974065393209457, 0.001353602041490376, 0.03403645381331444, -0.0026086776051670313, 0.013387514278292656, -0.026527710258960724, -0.01444112230092287, 0.04207584261894226, -0.057035114616155624, -0.007239552680402994, 0.014754170551896095, -0.042724791914224625, 0.0003467968781478703, 0.004325974732637405, -0.040618084371089935, -0.07305998355150223, 0.03788696974515915, 0.06612179428339005, -0.000977648887783289, 0.012821272015571594, -0.05560766160488129, 0.025731699541211128, 0.0016135622281581163, 0.004143009427934885, 0.004331784322857857, 0.011094833724200726, -0.037135399878025055, 0.030467592179775238, 0.0683322623372078, -0.020619263872504234, -0.024275904521346092, -0.022664399817585945, -0.01297708135098219, 0.008320133201777935, -0.08058623224496841, -0.008131290785968304, -0.02318793721497059, 0.02277890406548977, -0.06427869200706482, 0.02561977691948414, -0.03143000975251198, 0.00013317335105966777, 0.03702271729707718, -0.0538032166659832, 0.08377666026353836, 0.09525204449892044, 0.008647367358207703, -0.018884828314185143, 0.03957103565335274, 0.006106826011091471, 0.028708286583423615, -0.00591837614774704, 0.002842071233317256, -0.017098447307944298, 0.0008016228093765676, 0.027247732505202293, -0.005797383841127157, -0.009862088598310947, 0.08858394622802734, 0.004090744536370039, 0.0014091231860220432, 0.02931167557835579, -0.024942083284258842, 0.036183398216962814, -0.062369149178266525, 0.02971201390028, 0.003379038069397211, 0.012366541661322117, -0.0071122837252914906, -0.003014221088960767, 0.008933234959840775, -0.09425579756498337, -0.053701698780059814, 0.018943773582577705, 0.02496764063835144, 0.010635003447532654, -0.09764283150434494, 0.035814616829156876, 0.027669241651892662, -0.005584407597780228, -0.05949299409985542, 0.008170890621840954, -0.029798293486237526, -0.016547512263059616, -0.017565084621310234, 0.06219462677836418, -0.01944388821721077, -0.08185975253582001, -0.012277580797672272, 0.007187932729721069, -0.053626250475645065, -0.006527469027787447, -0.06066138669848442, 0.10191892832517624, 0.02378198690712452, -0.039012324064970016, 0.01438902597874403, -0.03408807888627052, -0.016492921859025955, -0.03265657648444176, -0.018783332780003548, 0.007486030925065279, -0.008699393831193447, -0.023534119129180908, 0.03627651184797287, 0.006365065462887287, -0.033595114946365356, 0.05824637785553932, 0.01725565828382969, 0.05693907290697098, -0.004552044905722141, -0.005549156107008457, -0.046071428805589676, -0.02472638711333275, 0.02043313719332218, -0.03008604235947132, -0.010651465505361557, 0.021020643413066864, 0.035850126296281815, 0.0035780847538262606, -0.017197364941239357, -0.03295128792524338, 0.010278566740453243, -0.019695766270160675, 0.010152842849493027, 0.07039424031972885, -0.030739597976207733, 0.04201748967170715, -0.004607910756021738, -0.07813403010368347, 0.026993120089173317, 0.0016665003495290875, 0.023635180667042732, -0.023855343461036682, -0.02920679561793804, 0.01470712199807167, -0.04571162536740303, -0.0494479201734066, 0.040623780339956284, 0.01643523760139942, 0.036585427820682526, 0.004457914736121893, 0.025127500295639038, 0.0015287670539692044, -0.019886210560798645, 0.03820257633924484, 0.032937631011009216, -0.055866390466690063, 0.04082350432872772, 0.015358401462435722, 0.01937778852880001, -0.06330769509077072, -0.0033701052889227867, -0.015088386833667755, -0.032323241233825684, -0.010386600159108639, 0.01610413007438183, 0.0012444219319149852, 0.00034010541276074946, 0.005033211782574654, -0.020168375223875046, 0.0027620436158031225, -0.01482895202934742, -0.03592472895979881, 0.0036113609094172716, 0.0006258416105993092, 0.03201992064714432, -0.0383961983025074, -0.006361784879118204, -0.09818446636199951, 0.030774705111980438, 0.022566474974155426, -0.005125010386109352, -0.01308898814022541, 0.0040627699345350266, -0.03199233487248421, 0.016180556267499924, 0.01200097519904375, 0.05316152423620224, 0.03350147232413292, -0.04041081666946411, 0.03211044892668724, -0.004596240818500519, -0.042411282658576965, -0.032942336052656174, 0.09800633043050766, 0.01384272426366806, 0.05757025629281998, 0.008465388789772987, -0.007452278397977352, 0.0010826538782566786, -0.04211455211043358, -0.046483978629112244, -0.049685485661029816, 0.014940626919269562, 0.00553868617862463 ]
<p>I found this solid-solid transformation in wikipedia. <a href="http://en.wikipedia.org/wiki/Phase_transition#Types_of_phase_transition" rel="nofollow">http://en.wikipedia.org/wiki/Phase_transition#Types_of_phase_transition</a> Please tell me what it is? It's present in types of phase transition in wiki.</p>
g8391
[ 0.0337039977312088, 0.04104858636856079, 0.00039544489118270576, -0.07498423010110855, 0.08630608022212982, -0.012541597709059715, 0.012346013449132442, -0.01569550670683384, -0.002019356470555067, -0.0029375480953603983, -0.07901117205619812, -0.01091692503541708, -0.02858497016131878, -0.016449136659502983, -0.01418216060847044, -0.023407932370901108, 0.0593465231359005, 0.011995043605566025, 0.0028493551071733236, 0.025555895641446114, -0.015344152227044106, -0.02898060344159603, -0.02431456185877323, -0.057069286704063416, -0.007912005297839642, 0.04639212414622307, -0.00514227757230401, -0.011777945794165134, -0.035741597414016724, -0.01604812778532505, 0.04622746258974075, -0.04696085676550865, 0.043720364570617676, 0.03951868414878845, 0.019463390111923218, -0.003801332088187337, 0.048719942569732666, -0.03230791166424751, 0.05625571683049202, 0.023052478209137917, -0.022939283400774002, 0.03486695885658264, 0.05759405717253685, -0.004622021224349737, -0.018782252445816994, 0.014411780051887035, -0.02376939170062542, -0.003880581585690379, -0.05541006103157997, 0.006190234329551458, 0.08222484588623047, 0.0656585618853569, 0.03577430546283722, -0.009705605916678905, 0.012935075908899307, -0.026995379477739334, 0.03721268102526665, -0.02422463893890381, 0.051618773490190506, -0.0037632121238857508, -0.0482434444129467, 0.002939175581559539, 0.026809196919202805, 0.006494326516985893, 0.041686490178108215, 0.00035813910653814673, 0.02808118425309658, 0.016074275597929955, -0.01393202506005764, -0.06376674771308899, -0.016483435407280922, 0.024053523316979408, 0.01713588647544384, 0.03471943736076355, 0.001509559922851622, -0.03614269196987152, 0.02832746133208275, -0.018376966938376427, 0.02088603563606739, -0.03179800882935524, -0.018650375306606293, -0.009814652614295483, -0.011229327879846096, 0.027334338054060936, 0.005062634125351906, 0.05688771232962608, 0.030254624783992767, -0.008187086321413517, -0.020218376070261, -0.05144190043210983, -0.008645317517220974, 0.030525779351592064, -0.03811981901526451, 0.017502840608358383, -0.011640173383057117, 0.02209426648914814, 0.00011981832358287647, 0.0524209588766098, 0.005237944424152374, -0.004021982662379742, -0.043546050786972046, -0.0937909185886383, -0.027328286319971085, -0.05808059498667717, 0.007082435302436352, -0.0014931109035387635, -0.069878950715065, -0.04045788571238518, -0.0312127023935318, 0.04172121733427048, -0.02857831120491028, -0.0053899590857326984, -0.03763775900006294, 0.007578431628644466, -0.003575625130906701, -0.005467289127409458, 0.014853715896606445, 0.03002639301121235, 0.03331868350505829, -0.009184030815958977, 0.06331203132867813, -0.06817931681871414, 0.05619801953434944, 0.08791978657245636, -0.030418068170547485, -0.059713639318943024, 0.019309401512145996, 0.007966194301843643, 0.03738117590546608, -0.019649725407361984, -0.0310120340436697, 0.022730786353349686, -0.001433796132914722, 0.015444988384842873, 0.0020586068276315928, 0.028833167627453804, 0.03537905216217041, -0.015555308200418949, -0.027958249673247337, 0.03672444447875023, 0.028303122147917747, -0.03414326533675194, -0.04693234711885452, -0.0019410735694691539, 0.07016728073358536, -0.01698237657546997, -0.012129816226661205, 0.07253331691026688, 0.005730291362851858, 0.06468159705400467, -0.06333138793706894, 0.029053932055830956, 0.06111956015229225, -0.05665425583720207, -0.007852314971387386, -0.0479242205619812, 0.01952824927866459, 0.03822730854153633, 0.015065982937812805, 0.02414996176958084, -0.0314217135310173, -0.05157535523176193, -0.06721577793359756, 0.014072315767407417, -0.02754644677042961, -0.020015638321638107, -0.03490407019853592, 0.014057422056794167, 0.021034112200140953, -0.005769446957856417, -0.0023030240554362535, 0.04978400096297264, -0.011438184417784214, 0.06096722558140755, 0.012272494845092297, 0.03166211023926735, 0.03337601572275162, 0.03697478398680687, 0.057893503457307816, 0.0012390463380143046, -0.03434811532497406, -0.0307602621614933, -0.01220298558473587, 0.009029709734022617, -0.020968690514564514, 0.012199613265693188, 0.053917210549116135, 0.05965534970164299, -0.055295802652835846, 0.025871137157082558, -0.07506433874368668, -0.08770885318517685, -0.01660633459687233, -0.02723059430718422, 0.03937527537345886, 0.0049781715497374535, -0.005560740362852812, -0.030197951942682266, -0.0030869566835463047, -0.08305027335882187, 0.03143167868256569, -0.015219920314848423, -0.014865517616271973, 0.009627350606024265, 0.002911963500082493, 0.000045040142140351236, -0.012960466556251049, 0.024297069758176804, -0.06350469589233398, 0.06565795093774796, 0.043308552354574203, -0.019450059160590172, 0.025508593767881393, -0.018578771501779556, -0.03710247203707695, 0.06702889502048492, -0.03057917021214962, -0.0373213067650795, 0.0070440382696688175, 0.03302096575498581, 0.05504175275564194, 0.02507561631500721, -0.0011315778829157352, 0.00588326808065176, 0.07011572271585464, -0.029676776379346848, 0.07312550395727158, -0.022646527737379074, 0.05327899381518364, -0.026220494881272316, -0.06316734105348587, -0.015047136694192886, -0.06498561054468155, -0.04835591837763786, 0.034708283841609955, 0.02292059175670147, -0.042244624346494675, 0.029523715376853943, -0.04753142222762108, 0.043916329741477966, -0.0005836101481691003, -0.02406785450875759, -0.02771320939064026, -0.031005773693323135, 0.012930858880281448, -0.03440847247838974, 0.006897666025906801, -0.01421600952744484, 0.0235186368227005, 0.016055375337600708, 0.04528434947133064, -0.05736592784523964, -0.038115374743938446, -0.02479265257716179, -0.030147776007652283, -0.023658161982893944, 0.021446513012051582, 0.0002711201668716967, -0.03930937498807907, 0.004176743794232607, 0.0065841032192111015, -0.03973597288131714, -0.001203074469231069, 0.0061552440747618675, -0.05713850259780884, -0.004842035006731749, -0.03301287814974785, 0.06869605928659439, -0.043192002922296524, 0.009535271674394608, -0.008766934275627136, -0.016014467924833298, -0.07310912013053894, 0.0014503425918519497, -0.0743749663233757, 0.030345281586050987, 0.034005094319581985, -0.028637545183300972, 0.03427766263484955, 0.024213852360844612, -0.017797796055674553, 0.003517690347507596, -0.000060519239923451096, 0.030212342739105225, -0.000954390736296773, 0.023172644898295403, -0.03252425044775009, 0.011693165637552738, -0.0813027024269104, 0.002162714721634984, 0.018707312643527985, -0.025727903470396996, 0.06996389478445053, 0.03900996968150139, 0.04139944911003113, -0.03632260113954544, 0.003828657791018486, -0.01723504811525345, 0.00981034617871046, 0.0397796630859375, -0.014429544098675251, -0.015541447326540947, 0.031976133584976196, 0.036378707736730576, 0.06255317479372025, -0.005749625153839588, 0.05477938428521156, -0.05624104291200638, -0.031880076974630356, -0.007641489617526531, -0.030727321282029152, 0.03999940678477287, 0.01691993698477745, 0.051018960773944855, -0.009722252376377583, 0.03150629997253418, 0.02438034676015377, 0.038880545645952225, 0.06421937793493271, -0.07996945083141327, -0.045092035084962845, -0.04438825696706772, 0.05648379772901535, 0.006042294669896364, -0.011585002765059471, 0.041945669800043106, 0.014769982546567917, 0.02922753617167473, 0.009682707488536835, -0.038798097521066666, -0.0018097821157425642, 0.002095073228701949, -0.010433699935674667, -0.06215425580739975, -0.07694599032402039, 0.004907800815999508, -0.07339111715555191, 0.0640125572681427, 0.00045410284656099975, -0.01315094530582428, 0.05850483849644661, 0.0329674556851387, 0.020149145275354385, 0.01475518848747015, 0.03341005742549896, -0.01920168288052082, -0.01764054410159588, -0.03622058033943176, 0.009582226164638996, -0.003017965704202652, 0.02508682571351528, 0.023205872625112534, 0.004581961315125227, -0.09752512723207474, -0.03945078328251839, 0.014591353014111519, 0.03305879980325699, -0.005776882171630859, -0.005938461981713772, 0.014255006797611713, 0.020090488716959953, -0.0649043396115303, 0.10698224604129791, -0.0030796779319643974, -0.007732904516160488, 0.04266178607940674, -0.027061190456151962, 0.005275180097669363, 0.01074963714927435, -0.014315908774733543, 0.01682516373693943, -0.08763162046670914, -0.005828659050166607, -0.031956497579813004, 0.024170033633708954, -0.017375467345118523, -0.043446216732263565, 0.03623882308602333, -0.032423581928014755, 0.033679328858852386, 0.022216033190488815, -0.006705559324473143, 0.038754068315029144, -0.03733363747596741, 0.01391062792390585, -0.036757756024599075, -0.023807751014828682, -0.0327436588704586, 0.008628870360553265, -0.04684726521372795, 0.06596697866916656, 0.04489773511886597, -0.012624853290617466, -0.025387538596987724, -0.01871475949883461, 0.04580691456794739, -0.02018524706363678, 0.030492087826132774, -0.016485992819070816, -0.011886701919138432, -0.009231065399944782, 0.031547825783491135, -0.02221088670194149, -0.013314920477569103, 0.056842654943466187, -0.03503327816724777, 0.011505399830639362, -0.04807291924953461, 0.004956168122589588, -0.09493713080883026, -0.015314231626689434, -0.012497752904891968, -0.03015439212322235, 0.005092042498290539, 0.004740238189697266, 0.01261974684894085, 0.0032078020740300417, -0.0416649654507637, 0.02765502780675888, 0.001260273507796228, -0.07295479625463486, 0.0061833541840314865, -0.030754869803786278, 0.00014143239241093397, 0.030368251726031303, 0.01009669341146946, 0.06453093886375427, 0.02252410352230072, -0.02154277078807354, -0.0025865393690764904, 0.02293306216597557, 0.02493372932076454, 0.0487942136824131, 0.014080403372645378, -0.011150266043841839, 0.01983773149549961, -0.02027820236980915, 0.04126359522342682, -0.02187465690076351, 0.022237392142415047, 0.0031012140680104494, 0.022847188636660576, 0.0115108173340559, 0.0036983108147978783, 0.024101682007312775, 0.02176465280354023, -0.029505208134651184, 0.0011062914272770286, -0.006914833560585976, -0.03160880133509636, -0.030205082148313522, 0.00720756221562624, -0.04858974367380142, 0.0012619176413863897, 0.023848455399274826, -0.02104985900223255, 0.01525997556746006, 0.04361690580844879, -0.018004171550273895, 0.06453146040439606, -0.032771170139312744, -0.039320025593042374, -0.02181783877313137, -0.006973873358219862, -0.021050482988357544, 0.020016195252537727, -0.02182490937411785, -0.02511262148618698, -0.015954546630382538, -0.024321556091308594, -0.004190706182271242, -0.03633460775017738, 0.017579982057213783, 0.06707317382097244, 0.035216324031353, 0.029731282964348793, 0.06512610614299774, -0.0276112612336874, 0.024875175207853317, 0.0062957038171589375, 0.007717483676970005, 0.050613563507795334, 0.069632887840271, -0.05631992965936661, 0.007376179099082947, 0.0656336173415184, -0.042947400361299515, 0.0170793067663908, -0.004383064806461334, 0.024615248665213585, 0.019859781488776207, -0.045646440237760544, 0.02357885055243969, -0.04795325919985771, -0.0000407827683375217, 0.022559097036719322, 0.05213749781250954, 0.022159475833177567, -0.011385081335902214, 0.048830579966306686, -0.03823922201991081, 0.004768941085785627, 0.062463242560625076, 0.042848531156778336, -0.007442243862897158, 0.06241864338517189, 0.07433409243822098, 0.035496924072504044, 0.0032702863682061434, -0.0924738347530365, 0.006716533098369837, -0.03801439329981804, -0.03490324318408966, 0.03921497240662575, 0.04824724793434143, -0.01434691995382309, -0.024777887389063835, -0.04022195562720299, -0.003828603308647871, -0.032454825937747955, -0.05812731757760048, 0.022130852565169334, 0.03917664662003517, -0.02208935283124447, -0.03392808511853218, 0.023692432790994644, -0.022633546963334084, -0.03232114017009735, 0.0020884156692773104, 0.015662597492337227, -0.05747392401099205, -0.03950104862451553, 0.053454723209142685, 0.003145120805129409, 0.015280443243682384, -0.01969761773943901, -0.04374530911445618, 0.030960993841290474, 0.03163724020123482, 0.05619874596595764, -0.03521980717778206, 0.023106370121240616, -0.00102433527354151, 0.04613840579986572, -0.014211230911314487, 0.020439336076378822, 0.014926903881132603, 0.042278140783309937, -0.015643125399947166, 0.025507673621177673, 0.07339125871658325, -0.0006825755117461085, 0.025460997596383095, -0.03382197022438049, -0.01919598877429962, -0.008148337714374065, -0.0001599636161699891, 0.038260094821453094, 0.017196154221892357, -0.08833977580070496, 0.018358418717980385, 0.035933393985033035, -0.04066034406423569, -0.0382654070854187, 0.06885657459497452, -0.05344589427113533, -0.058049917221069336, 0.020417645573616028, 0.013834422454237938, -0.003355514956638217, 0.02405218407511711, 0.034662336111068726, 0.0242001935839653, -0.04074588045477867, -0.003624995704740286, 0.0003236682678107172, -0.055635690689086914, -0.009749872609972954, -0.007811689283698797, 0.006005115807056427, -0.018813401460647583, -0.02057512104511261, 0.037347208708524704, 0.0364629328250885, -0.036467187106609344, -0.03310691937804222, -0.008282658644020557, -0.0045938752591609955, -0.10624688863754272, -0.006151220295578241, -0.05686522647738457, 0.04584336280822754, -0.0617920383810997, 0.013906190171837807, 0.028556613251566887, 0.02563628740608692, -0.048925913870334625, 0.06678764522075653, 0.02595231868326664, 0.053342025727033615, -0.04487897828221321, -0.032313860952854156, 0.04186972603201866, 0.018897386267781258, 0.005220236722379923, 0.06622425466775894, -0.019625181332230568, 0.040489837527275085, 0.010614301078021526, 0.009339990094304085, -0.014835070818662643, 0.027133682742714882, -0.036795780062675476, -0.02275008335709572, -0.017394207417964935, -0.041251275688409805, -0.0630360022187233, 0.0020744306966662407, -0.008235091343522072, -0.04275371506810188, -0.010497411713004112, -0.04814258962869644, 0.033846333622932434, 0.002668446861207485, 0.013592696748673916, 0.04046450927853584, -0.06313848495483398, -0.004474216140806675, 0.02091076970100403, 0.0010723836021497846, 0.010497329756617546, -0.044140685349702835, -0.02218015305697918, -0.009864440187811852, -0.005056590773165226, 0.0017779326299205422, -0.054569974541664124, -0.0029147008899599314, 0.10535991191864014, 0.03971057012677193, 0.02709352783858776, -0.034919317811727524, 0.03293624892830849, -0.013345868326723576, -0.03527894988656044, -0.0022505498491227627, -0.027220802381634712, -0.07370316237211227, -0.056129224598407745, 0.03867107257246971, 0.011695305816829205, 0.023482751101255417, -0.05405423790216446, -0.003764205612242222, -0.03245483338832855, 0.01583423838019371, 0.059006836265325546, -0.0002300166670465842, -0.011625431478023529, -0.02070898562669754, -0.07430166751146317, -0.016291629523038864, 0.0033622505143284798, -0.000054251577239483595, -0.03271615877747536, 0.05567105486989021, 0.015090027824044228, -0.021402038633823395, -0.010479319840669632, -0.018526867032051086, -0.07182864844799042, 0.05065607279539108, 0.006535753142088652, 0.01620158925652504, 0.030245831236243248, -0.02140001580119133, 0.04494475573301315, 0.049296922981739044, 0.030435610562562943, 0.001932189567014575, 0.04425935447216034, 0.06776149570941925, 0.01268779207020998, -0.06850861757993698, 0.005616440903395414, 0.02508660964667797, -0.01039129588752985, 0.06988414376974106, 0.01724831946194172, 0.02965964376926422, -0.0010499253403395414, 0.00577978091314435, -0.03972959890961647, 0.012702745385468006, 0.00729305949062109, -0.010545527562499046, 0.01927201636135578, -0.024528868496418, -0.045778848230838776, 0.011453845538198948, 0.020116858184337616, 0.014858615584671497, -0.043604493141174316, 0.05403014272451401, -0.040539659559726715, 0.015216748230159283, 0.014465444721281528, -0.028597336262464523, 0.007847866043448448, -0.04210618510842323, 0.01807442121207714, -0.0021000136621296406, 0.05979088693857193, -0.018438046798110008, 0.04755194112658501, 0.06022050231695175, 0.028192248195409775, -0.022567929700016975, -0.042858339846134186, 0.014240541495382786, 0.008640197105705738, -0.012221282348036766, -0.08186986297369003, -0.012775151059031487, -0.04739856719970703, -0.008013629354536533, 0.03186121582984924, 0.01940366066992283, 0.02876265160739422, -0.016204532235860825, -0.04606877267360687, -0.02276955358684063, 0.004691387061029673, 0.01502346433699131, 0.005416728090494871, -0.01694807969033718, 0.029049653559923172, -0.01062444131821394, 0.007705181837081909, -0.013758559711277485, 0.03178313001990318, 0.013375763781368732, 0.006614829879254103, -0.0066987802274525166, -0.00815560296177864, -0.05195768177509308, -0.020966820418834686, 0.10498128831386566, 0.015370849519968033, -0.10276229679584503, -0.034606367349624634, -0.0007856403826735914, 0.05364114046096802, -0.032448068261146545, -0.04493763670325279, 0.012102045118808746, -0.041663460433483124, 0.017743218690156937, 0.019294872879981995, -0.008283457718789577, 0.025652406737208366, -0.026513980701565742, 0.006424680817872286, 0.0414494052529335, -0.05075819790363312, -0.014112326316535473, -0.013217463158071041, 0.0289481058716774 ]
<p>Type I superstring theory is unoriented, and it seems that it needs to be so in order to exist. </p> <p>Now, we always have open-closed duality, that connects at least the ultraviolet sector of a theory with the infrared sector of another, so in principle we should have some oriented open strings coming from it, by duality with a closed oriented theory.</p> <p>And we have all the D-brane stuff, that surely produces another kinds of open string theories with the restriction of terminating there in the branes.</p> <p>¿Is some of these D-brane examples an oriented theory? ¿Is there some canonical, well known, example of a consistent oriented theory with open strings?</p>
g8392
[ 0.007377671077847481, -0.000580440741032362, 0.040594279766082764, -0.04066455736756325, 0.0013657406670972705, 0.045617442578077316, -0.0171249657869339, -0.02567606046795845, 0.00945403054356575, -0.04027436673641205, -0.01504314225167036, 0.007992350496351719, 0.024434875696897507, 0.027172977104783058, 0.008579264394938946, -0.013454696163535118, 0.008088583126664162, 0.007981098257005215, 0.0003085023781750351, 0.005756505765020847, 0.0332854762673378, -0.025694137439131737, 0.036246225237846375, -0.021016355603933334, -0.015726668760180473, 0.017895366996526718, 0.040691033005714417, -0.04738814756274223, -0.044676147401332855, -0.003547494998201728, 0.046173304319381714, -0.05169900134205818, 0.06865601241588593, -0.0022518327459692955, -0.012605753727257252, 0.01783144846558571, 0.03965744376182556, -0.0024972292594611645, 0.0695275217294693, 0.008343154564499855, -0.012559743598103523, -0.010123984888195992, 0.05370880290865898, -0.02893972210586071, -0.0028471825644373894, -0.038203638046979904, -0.041582293808460236, 0.06838469207286835, -0.022657591849565506, 0.00003737176302820444, 0.0677531287074089, 0.07246799021959305, 0.043233830481767654, -0.05011376366019249, 0.016314852982759476, -0.0023223129101097584, -0.05273586884140968, 0.00439858715981245, 0.000019034849174204282, 0.0012201379286125302, -0.025274790823459625, 0.04535726085305214, 0.06055053696036339, 0.010445874184370041, 0.040688637644052505, 0.0361226350069046, 0.036806147545576096, -0.04323321953415871, 0.050723426043987274, -0.0011871379101648927, 0.012615982443094254, -0.02725786156952381, -0.0051828776486217976, -0.02422269433736801, -0.05527825281023979, 0.0355040542781353, -0.010863078758120537, -0.09727799892425537, -0.04476485401391983, 0.02335486188530922, -0.044693805277347565, -0.04394610598683357, -0.04052496328949928, -0.044093817472457886, 0.055423106998205185, -0.062253184616565704, 0.008754946291446686, -0.007729644421488047, 0.034871239215135574, 0.029901742935180664, 0.02000923827290535, 0.007778185419738293, -0.02730580046772957, -0.018272029235959053, 0.0235251784324646, 0.04240228608250618, -0.012584964744746685, 0.07426635175943375, -0.06928873807191849, -0.06559821963310242, 0.042458049952983856, -0.014548822306096554, 0.07541248202323914, 0.03204105421900749, 0.0033174913842231035, -0.000706570572219789, 0.003719044616445899, -0.012059085071086884, -0.019995929673314095, 0.025234729051589966, -0.07956443727016449, 0.01348627358675003, -0.04924880340695381, 0.007044922560453415, -0.003876887960359454, 0.05172635242342949, -0.0005837559583596885, -0.03344385698437691, 0.003782621817663312, 0.035415831953287125, 0.0511135458946228, -0.012671987526118755, 0.05244196951389313, -0.0057109384797513485, 0.010113969445228577, -0.045299232006073, 0.024106666445732117, -0.02875448390841484, 0.008881405927240849, -0.028541704639792442, -0.002922981744632125, 0.0061745112761855125, 0.07078427821397781, 0.028697451576590538, 0.0024800302926450968, -0.028678102418780327, -0.011923612095415592, 0.003312132554128766, 0.030041160061955452, -0.07477589696645737, -0.010226549580693245, -0.044454459100961685, -0.02246825024485588, 0.038608476519584656, 0.0926084965467453, -0.036758385598659515, 0.0032022520899772644, -0.021330377086997032, -0.019381701946258545, 0.09250868856906891, 0.025534316897392273, 0.03658963367342949, -0.04720614105463028, -0.022356044501066208, -0.04456324130296707, 0.017842818051576614, 0.02652924321591854, -0.05052211508154869, 0.019604243338108063, -0.04873126745223999, 0.010916399769484997, -0.014197940938174725, -0.021170299500226974, -0.007392849773168564, -0.04685541242361069, -0.08290982991456985, -0.011514152400195599, 0.029279815033078194, -0.0008809876744635403, 0.00347900646738708, -0.08011797815561295, 0.07570730894804001, 0.041750483214855194, 0.08097364753484726, 0.015142261981964111, 0.05784548819065094, -0.013308740220963955, 0.05094960331916809, 0.03099614940583706, 0.03809518739581108, -0.057274363934993744, -0.02765496075153351, 0.02406172640621662, -0.015902988612651825, 0.018389467149972916, 0.019815804436802864, 0.0007231466588564217, 0.03588571771979332, -0.010171597823500633, 0.016630815342068672, 0.011458706110715866, 0.008420802652835846, -0.006174219772219658, 0.06973379105329514, -0.015286256559193134, -0.08892986923456192, -0.02291688695549965, -0.058642756193876266, 0.04990815371274948, 0.048210933804512024, 0.06566910445690155, 0.007997442036867142, 0.034772250801324844, -0.02574245072901249, 0.01209348626434803, -0.019368385896086693, -0.02697792835533619, 0.012623428367078304, 0.044513531029224396, 0.05462446063756943, -0.006419401150196791, -0.020296849310398102, -0.01450424175709486, 0.00014112284407019615, -0.03648032993078232, -0.03667239099740982, -0.02719751186668873, 0.006484571378678083, -0.033158618956804276, 0.014057888649404049, 0.04845971614122391, -0.03180893138051033, 0.06323305517435074, 0.05422953888773918, -0.03174380213022232, 0.02018764615058899, -0.023792149499058723, -0.01649220660328865, 0.001814689370803535, -0.0065503790974617004, -0.060994260013103485, -0.09135143458843231, 0.06339403241872787, -0.010796287097036839, 0.024043729528784752, -0.025417080149054527, 0.04644106701016426, -0.052020616829395294, 0.02062123827636242, -0.027826741337776184, 0.034474391490221024, -0.011267327703535557, 0.03251954913139343, 0.012743577361106873, 0.0185101218521595, -0.0011763189686462283, -0.006109282374382019, 0.027526594698429108, -0.026551712304353714, 0.05354676395654678, -0.035006094723939896, 0.029121965169906616, -0.02334412932395935, 0.008280309848487377, 0.003932034596800804, -0.02410700172185898, 0.014788521453738213, 0.004041809588670731, -0.0024257053155452013, -0.07528126984834671, 0.035421453416347504, -0.06555916368961334, 0.013726094737648964, -0.012313751503825188, -0.03562416508793831, 0.06216106936335564, 0.015957850962877274, -0.04444674029946327, -0.07306024432182312, 0.0049314056523144245, -0.02428445592522621, 0.003922342788428068, -0.0029955361969769, -0.04418836906552315, 0.023952607065439224, 0.039519667625427246, -0.0011235758429393172, 0.049157869070768356, -0.03455996885895729, 0.020413411781191826, 0.0013751337537541986, -0.0060502090491354465, 0.014372478239238262, -0.021726509556174278, 0.005310418549925089, -0.01630553975701332, -0.002035207813605666, -0.03879276290535927, -0.041763488203287125, -0.03398595750331879, 0.03036704659461975, 0.01623646542429924, 0.03932306915521622, 0.037925031036138535, -0.04579527676105499, 0.027754545211791992, 0.0010776873677968979, 0.06690695881843567, -0.009733930230140686, 0.03344040736556053, -0.08524689823389053, 0.00373451947234571, 0.03369590640068054, 0.013485100120306015, 0.03883389011025429, -0.04357144236564636, -0.08277207612991333, -0.05372775346040726, -0.0431339368224144, -0.028146803379058838, -0.03352101519703865, 0.045721396803855896, 0.024855049327015877, 0.002098474418744445, -0.00347341550514102, 0.014567721635103226, -0.010095829144120216, 0.0035680572036653757, 0.05996743217110634, -0.04296141490340233, -0.06620077043771744, 0.01652715913951397, 0.06556263566017151, 0.040224842727184296, -0.003659369656816125, -0.0028848431538790464, -0.04319259151816368, 0.01909736357629299, -0.02534106932580471, 0.043755415827035904, -0.02172142267227173, 0.043245553970336914, -0.039863232523202896, 0.05357162281870842, -0.05857686698436737, 0.0887782871723175, -0.004302299115806818, 0.01301095262169838, 0.06329210847616196, 0.051594968885183334, -0.008997444994747639, -0.020005524158477783, 0.018808262422680855, -0.01556276623159647, 0.021959932520985603, 0.051397159695625305, 0.04877004772424698, -0.02091197669506073, 0.013710935600101948, 0.034486740827560425, -0.030246946960687637, 0.03391885757446289, 0.03945644944906235, 0.012831958010792732, -0.02257777564227581, 0.09929307550191879, 0.026661409065127373, 0.07667926698923111, -0.01923249661922455, -0.05357489362359047, 0.000015466399418073706, 0.07292034476995468, -0.03160422667860985, -0.09085806459188461, 0.002622126368805766, -0.0338536873459816, 0.01675703562796116, -0.09107907116413116, -0.001798922661691904, 0.034844111651182175, 0.07472356408834457, -0.026984689757227898, 0.01816313900053501, -0.055743664503097534, 0.025178516283631325, -0.030498942360281944, -0.051063310354948044, 0.07836523652076721, -0.0014324858784675598, 0.039927683770656586, 0.024644507095217705, 0.0018953551771119237, 0.03841102868318558, -0.0017656359123066068, 0.0014325458323583007, -0.012735428288578987, -0.05447211116552353, -0.009877946227788925, -0.0593462772667408, 0.018431266769766808, 0.030083784833550453, 0.035211674869060516, 0.02066381834447384, -0.03801268711686134, -0.010292977094650269, 0.0012095645070075989, -0.0018030882347375154, -0.004977704957127571, 0.024577468633651733, -0.07015924155712128, 0.03926212340593338, -0.04027098789811134, 0.02359132096171379, -0.0604257807135582, -0.04964165389537811, 0.02934582158923149, -0.04047488421201706, 0.020817948505282402, -0.004414272494614124, -0.04630429670214653, 0.027525968849658966, -0.0011709269601851702, 0.032890431582927704, 0.008687863126397133, 0.014729856513440609, -0.04236695170402527, 0.015994206070899963, -0.05697932094335556, 0.06581246107816696, 0.011944090947508812, 0.029980426654219627, 0.04021139815449715, 0.018426213413476944, -0.06690622866153717, 0.05925415828824043, 0.0467434823513031, -0.0013713747030124068, -0.02722681500017643, 0.018559103831648827, -0.02216683141887188, 0.021218249574303627, -0.028515083715319633, 0.015666918829083443, -0.02195914275944233, -0.008582058362662792, 0.01640143245458603, -0.02100854553282261, 0.02681894227862358, 0.0023263979237526655, 0.022883517667651176, 0.015732992440462112, 0.013126993551850319, 0.0498419888317585, -0.01848173514008522, -0.020268874242901802, -0.007193634752184153, 0.004978943150490522, 0.01305299997329712, 0.02273809351027012, -0.04416336864233017, 0.0012092097895219922, 0.04785832390189171, -0.04061441868543625, 0.029502902179956436, -0.04405929148197174, -0.03754680976271629, -0.060275204479694366, 0.015202970243990421, 0.02904621884226799, 0.02953847125172615, -0.016154466196894646, -0.0677700936794281, 0.003965108655393124, -0.011706091463565826, 0.061079204082489014, -0.030301213264465332, -0.032225485891103745, -0.03175380453467369, -0.0386602021753788, -0.03714887052774429, 0.06259600073099136, 0.03181993588805199, 0.01667107827961445, -0.05848836898803711, -0.04146990925073624, -0.0032687250059098005, -0.0517146959900856, -0.03449093550443649, -0.04217926040291786, -0.00944756343960762, 0.019260667264461517, -0.03209659084677696, 0.02661164291203022, 0.017178580164909363, 0.00027232442516833544, -0.018034599721431732, 0.02117753028869629, 0.013923561200499535, -0.059831418097019196, -0.016678910702466965, -0.048757221549749374, 0.03894621133804321, 0.03792456164956093, 0.008278977125883102, -0.027188226580619812, 0.04435914382338524, -0.007013637572526932, -0.012096174992620945, -0.01142703928053379, -0.04614726081490517, -0.0508301816880703, -0.013897983357310295, 0.032833900302648544, 0.030126143246889114, -0.004359033890068531, 0.10635563731193542, 0.028483519330620766, 0.0041466825641691685, -0.05030937120318413, -0.06570644676685333, 0.020655518397688866, 0.04042290896177292, -0.08777181804180145, 0.07865381985902786, 0.04545949026942253, 0.02752264402806759, -0.06501590460538864, 0.018722811713814735, 0.014355394057929516, -0.0383516401052475, -0.0341905802488327, 0.050499264150857925, 0.004701754078269005, 0.02918187528848648, 0.01689857803285122, 0.02468998171389103, -0.02612723782658577, -0.0011734735453501344, 0.07089699059724808, -0.009154260158538818, -0.005684858653694391, -0.020981432870030403, 0.002792313927784562, 0.006785568315535784, 0.008376870304346085, -0.03259000554680824, 0.005753147881478071, 0.07231073081493378, -0.04110332578420639, 0.03996346518397331, -0.01628642901778221, 0.040555693209171295, -0.008633729070425034, -0.04204360768198967, -0.015174436382949352, 0.021553674712777138, -0.01106063649058342, 0.033758245408535004, 0.030708782374858856, -0.08444415032863617, -0.045391231775283813, -0.015471710823476315, -0.056650154292583466, 0.023392025381326675, -0.022296225652098656, 0.017190439626574516, -0.040867894887924194, -0.07551280409097672, -0.04053158685564995, 0.05139737203717232, 0.03588087484240532, -0.0013840222964063287, -0.026712261140346527, 0.02480386383831501, 0.0025845300406217575, -0.007176235318183899, -0.03959063068032265, -0.03181958571076393, 0.04681982100009918, 0.003338141832500696, -0.0632207915186882, -0.006447539199143648, 0.0035330685786902905, 0.06041261553764343, 0.07191567122936249, -0.029260406270623207, -0.016070814803242683, -0.047192033380270004, 0.04455363377928734, -0.010497182607650757, 0.04363814741373062, 0.012574988417327404, 0.03127951920032501, -0.014014393091201782, -0.027661096304655075, -0.006433872040361166, 0.014500914141535759, -0.044666584581136703, 0.03085188753902912, 0.02662365511059761, -0.008785024285316467, -0.011302133090794086, -0.04314073547720909, 0.01883486472070217, -0.02517607994377613, 0.02244550548493862, 0.017533335834741592, 0.0033879936672747135, -0.014438999816775322, -0.00479813851416111, -0.016895096749067307, -0.04630878567695618, 0.03486626595258713, 0.003256151918321848, -0.03867330774664879, 0.052130576223134995, -0.01494558621197939, 0.01716451533138752, 0.015408218838274479, 0.049153927713632584, 0.036231882870197296, 0.06455797702074051, -0.01613670215010643, -0.0017244587652385235, 0.02133140154182911, -0.06275295466184616, 0.00759146036580205, -0.034498389810323715, 0.04845640808343887, 0.005818161182105541, 0.047645311802625656, -0.013254248537123203, -0.01545148529112339, -0.031129511073231697, -0.048701222985982895, -0.0008914131321944296, -0.037375301122665405, -0.019563771784305573, 0.00011463726696092635, 0.027968203648924828, -0.0012377487728372216, -0.009601108729839325, 0.03295626863837242, 0.005847970023751259, -0.02761046588420868, 0.01838202029466629, -0.08898869156837463, 0.037174925208091736, -0.012769900262355804, -0.01283135823905468, -0.013379182666540146, 0.0047919112257659435, 0.02494683489203453, -0.034245505928993225, -0.006994117517024279, 0.01597597263753414, 0.07202698290348053, 0.012919671833515167, -0.08221559226512909, -0.0008656345307826996, 0.012699934653937817, -0.007148507982492447, -0.029825976118445396, -0.011951246298849583, -0.024480385705828667, -0.014003915712237358, -0.02875581383705139, -0.03432140126824379, -0.023743020370602608, -0.031481798738241196, 0.012687372043728828, 0.03559057042002678, -0.039048559963703156, -0.037248630076646805, -0.03609718754887581, 0.01479046605527401, 0.040741097182035446, -0.043645743280649185, -0.05555284768342972, 0.008215349167585373, -0.053382694721221924, 0.011269021779298782, 0.00825798325240612, 0.0032369287218898535, -0.01822526566684246, -0.023848623037338257, -0.04989421367645264, 0.0028480153996497393, -0.03731536120176315, -0.010218908078968525, -0.010764339938759804, 0.03226640075445175, 0.025441480800509453, 0.04073580354452133, -0.03646538034081459, 0.038854725658893585, 0.04780088737607002, 0.006189514882862568, -0.06405159085988998, 0.033917978405952454, 0.046010177582502365, -0.0066588083282113075, 0.039434242993593216, -0.030768297612667084, -0.0002784854150377214, -0.031263403594493866, -0.027637360617518425, 0.030060475692152977, 0.007586992811411619, 0.017087973654270172, 0.0027088746428489685, 0.011875015683472157, -0.01599937677383423, 0.002527755917981267, 0.03300090134143829, -0.0148953627794981, -0.0027175252325832844, -0.03655654564499855, -0.049261465668678284, -0.014955918304622173, -0.03319057449698448, -0.0174514539539814, 0.05573677271604538, 0.032073549926280975, 0.0642639547586441, -0.060737576335668564, 0.0005307532264851034, 0.036027129739522934, 0.013826300390064716, -0.024378763511776924, -0.0006183857331052423, -0.009597460739314556, 0.05114617943763733, 0.02597561851143837, -0.0073838247917592525, 0.029500426724553108, 0.029126660898327827, -0.021730704233050346, -0.007565689273178577, 0.0385165773332119, -0.031034355983138084, 0.01791883073747158, 0.051687389612197876, 0.007081283256411552, -0.06906381249427795, 0.00916210189461708, -0.005987437907606363, -0.0282275453209877, -0.0007220811676234007, -0.00011202091263839975, 0.006029130425304174, -0.04320754483342171, -0.025761360302567482, -0.0433841198682785, 0.006128434557467699, 0.01554024126380682, -0.0445755198597908, -0.020118258893489838, -0.029069840908050537, 0.017792213708162308, -0.021467195823788643, 0.027420850470662117, 0.026367079466581345, 0.018731655552983284, -0.00021051723160780966, 0.005025465507060289, -0.044459111988544464, 0.04728507623076439, 0.02727237157523632, 0.04724535346031189, 0.001830571098253131, -0.05764443799853325, 0.0325431264936924, -0.0020863923709839582, -0.02548143081367016, 0.007795827463269234, -0.014560171402990818, 0.012595596723258495 ]
<p>I have a gravity-related question. I am programming an orbit simulator. I have everything up and running, but I would like to render the smaller body's orbital path (the larger body is fixed). To do this, I need the parametric equations for the body's position for any given time (i.e. I need an $x(t)$ and $y(t)$ function). I have access to each body's position, velocity, and mass. I have no other accessible variables.</p> <p>P.S. <a href="http://www.colekito.com/projects/orbit" rel="nofollow">Here</a> is a link to what I have so far. The equations currently used to plot the orbit are $x(t)=x+v_xt$ and $y(t)=y+v_yt$.</p>
g8393
[ 0.000906916509848088, 0.07978444546461105, -0.013612679205834866, -0.04389877989888191, -0.05545100197196007, -0.01833490841090679, 0.014585812576115131, -0.06333404779434204, -0.040972672402858734, -0.010879982262849808, -0.0033239643089473248, -0.0027227408718317747, 0.021913329139351845, 0.0005457023507915437, -0.02614089846611023, 0.0017159152776002884, 0.09296246618032455, -0.015149962157011032, 0.0004545816918835044, -0.002154128858819604, 0.11541453003883362, -0.04501227289438248, 0.03621780872344971, 0.02060522697865963, 0.06398123502731323, -0.0062845563516020775, 0.0427129752933979, -0.016030028462409973, -0.07659120857715607, 0.021146945655345917, -0.00415328424423933, 0.012967403046786785, 0.040877364575862885, -0.04542181268334389, -0.004983676131814718, -0.0083544310182333, 0.01058023888617754, -0.023101015016436577, -0.00024003558792173862, -0.0033689572010189295, -0.003893852699548006, -0.037486329674720764, 0.012961719185113907, 0.04525510594248772, 0.0170770101249218, -0.05095408484339714, 0.017037931829690933, -0.0414021760225296, 0.0028970278799533844, -0.0307062529027462, -0.008955723606050014, 0.08511939644813538, -0.01943841576576233, -0.11854316294193268, -0.01203182153403759, 0.01583140157163143, 0.00823118258267641, -0.01848730258643627, -0.005254168529063463, 0.046867288649082184, 0.010120195336639881, 0.013791580684483051, 0.012277667410671711, -0.057940393686294556, 0.051864467561244965, -0.026575621217489243, -0.0684109777212143, -0.02641519531607628, -0.061317477375268936, 0.002540221903473139, -0.017822498455643654, 0.048622976988554, -0.029776694253087044, -0.05933060124516487, -0.05903381481766701, 0.0050247954204678535, -0.0005057891830801964, 0.0036614846903830767, -0.0593901202082634, 0.009582852013409138, -0.02848614752292633, 0.06262475252151489, 0.049667295068502426, 0.03282434865832329, 0.026231888681650162, -0.02109074965119362, 0.061110399663448334, 0.001269556931219995, -0.0001767246867530048, -0.009135203436017036, -0.004584027454257011, 0.02740815468132496, 0.018000375479459763, 0.034075748175382614, -0.004803352989256382, -0.02995247393846512, -0.05668127164244652, 0.09330306202173233, 0.004082989413291216, 0.02576897107064724, 0.00040214788168668747, 0.05685582756996155, -0.019251994788646698, -0.01825764589011669, 0.032403115183115005, -0.043489549309015274, 0.01690850593149662, 0.036725543439388275, 0.02413020469248295, 0.003917249850928783, -0.020459165796637535, -0.04745236039161682, -0.03642488270998001, 0.01598256081342697, -0.015760626643896103, -0.03864187002182007, 0.003410539822652936, -0.04966689273715019, -0.05431707575917244, 0.05284018814563751, -0.028696004301309586, 0.004314562771469355, 0.00495360279455781, 0.05283184349536896, -0.02706814743578434, 0.021611778065562248, -0.027239395305514336, 0.0353756919503212, 0.03090306930243969, 0.01102315541356802, 0.027399200946092606, -0.027693957090377808, 0.015153156593441963, 0.0814504325389862, -0.018619827926158905, 0.000054517720855074, -0.014630921185016632, -0.006802850402891636, -0.043139610439538956, 0.04240310564637184, 0.005030191969126463, -0.042958520352840424, -0.03943344205617905, -0.00028456051950342953, -0.07437843829393387, 0.017548320814967155, -0.049917012453079224, -0.000250109878834337, 0.004151859320700169, 0.005096889566630125, 0.02067556418478489, 0.07579528540372849, -0.02413693629205227, -0.0034008435904979706, -0.000113713089376688, -0.06551747769117355, 0.0008446199935860932, 0.021610097959637642, -0.0067293643951416016, -0.04328201338648796, 0.06717328727245331, 0.0596594363451004, 0.03127864748239517, -0.025553181767463684, -0.07930441945791245, 0.03549572452902794, -0.009401964955031872, -0.05636177584528923, -0.03514161705970764, -0.08641157299280167, -0.017622772604227066, -0.06431498378515244, -0.003615922760218382, 0.0531424842774868, -0.0638982355594635, 0.022137146443128586, -0.017216041684150696, -0.03156488016247749, 0.007830899208784103, 0.02055555023252964, 0.04755730926990509, 0.006863103713840246, 0.031598493456840515, -0.020948152989149094, -0.04500505328178406, -0.03289850428700447, -0.011570923030376434, -0.01604563184082508, -0.10634012520313263, 0.0013498126063495874, 0.01418023556470871, -0.0011033728951588273, 0.0011934880167245865, 0.011799082159996033, -0.005484120454639196, 0.0016789681976661086, 0.03653663396835327, -0.033486757427453995, -0.02355249971151352, 0.027150429785251617, 0.020116642117500305, 0.017543312162160873, 0.04079668968915939, 0.019855398684740067, -0.0027782584074884653, -0.02518605627119541, 0.021123355254530907, 0.01194651797413826, -0.015889272093772888, -0.026370812207460403, 0.0164163988083601, -0.017008807510137558, 0.06434744596481323, -0.0040183886885643005, -0.03982561081647873, -0.003209866816177964, -0.021595217287540436, -0.0370103195309639, -0.0002986468025483191, -0.006153292953968048, 0.030203884467482567, -0.03645758330821991, -0.025687983259558678, 0.008394161239266396, -0.01292772963643074, 0.006138508208096027, -0.018045790493488312, -0.021568676456809044, 0.022697625681757927, 0.04863320663571358, -0.0052878400310873985, -0.020287951454520226, 0.009648112580180168, 0.01716744527220726, 0.029032377526164055, -0.0335887186229229, 0.0008990997448563576, 0.01024410966783762, 0.024806421250104904, 0.040745023638010025, 0.031510110944509506, -0.01679728925228119, 0.01554429717361927, -0.01321237999945879, 0.09753423184156418, -0.02152378112077713, 0.0390356183052063, -0.002924563828855753, 0.04551216587424278, 0.0755983367562294, -0.0321391336619854, -0.0131096001714468, -0.08206538110971451, 0.005967613309621811, -0.0523751825094223, -0.007079556118696928, -0.016258645802736282, 0.015861814841628075, -0.06476402282714844, 0.0010891781421378255, -0.02758287824690342, 0.028092699125409126, -0.018548432737588882, 0.0006795483641326427, -0.034752704203128815, -0.01050489116460085, -0.010412138886749744, -0.06334555149078369, -0.010041543282568455, -0.00008568153862142935, -0.016827480867505074, 0.031041929498314857, 0.028798570856451988, 0.07261914014816284, -0.011473351158201694, -0.03625330701470375, 0.02323368936777115, -0.007244885433465242, -0.04006397724151611, 0.056619513779878616, 0.012454076670110226, -0.09534087777137756, -0.01684240810573101, 0.05569326505064964, 0.06250274181365967, 0.016103388741612434, 0.021675480529665947, 0.0150520084425807, 0.0070235575549304485, 0.0021530557423830032, 0.011615047231316566, 0.06724569201469421, -0.0035573611967265606, 0.03431031107902527, -0.08019769936800003, 0.016788437962532043, -0.007265529129654169, 0.02851918153464794, 0.014863107353448868, -0.027049824595451355, -0.040761418640613556, 0.06245599314570427, 0.06391745805740356, 0.04433276876807213, -0.015576624311506748, -0.02239822782576084, -0.05399817228317261, -0.0553060919046402, 0.035420261323451996, 0.013046017847955227, 0.04964571073651314, 0.023586291819810867, -0.04799909144639969, 0.0018451231298968196, 0.02800491265952587, 0.017781997099518776, -0.03322853520512581, -0.059768252074718475, 0.005120154470205307, -0.026043808087706566, -0.01044600922614336, -0.07314158231019974, -0.011840801686048508, -0.004849876742810011, -0.014319468289613724, 0.03059307113289833, 0.007296836469322443, -0.0014068320160731673, 0.011845400556921959, 0.014461756683886051, 0.021623220294713974, 0.012474789284169674, 0.04325415566563606, 0.04394364729523659, 0.047435808926820755, -0.005101310089230537, 0.03768594190478325, 0.00020089789177291095, 0.04598693922162056, -0.07655490934848785, -0.03371908888220787, -0.005077457521110773, -0.07237140089273453, -0.003838984062895179, -0.027486253529787064, -0.06657715141773224, 0.025928514078259468, 0.050993259996175766, 0.007578746415674686, -0.06190584972500801, -0.01210593432188034, 0.016686847433447838, 0.02821599878370762, -0.0635121762752533, 0.03839293122291565, 0.03752703592181206, 0.004908834584057331, -0.06080305576324463, 0.015437448397278786, 0.0177241750061512, -0.006112527102231979, -0.05503927916288376, -0.05906122922897339, 0.06546182930469513, 0.032790616154670715, -0.009626001119613647, 0.015538717620074749, 0.05522109195590019, -0.027884406968951225, -0.03199080005288124, -0.005489942617714405, 0.005769276060163975, 0.05061902478337288, -0.08210139721632004, 0.03117690421640873, -0.053675271570682526, -0.00541037879884243, -0.00950661301612854, -0.0061662569642066956, 0.007588723674416542, 0.00710394186899066, 0.010031879879534245, 0.03486436605453491, 0.04950098320841789, 0.044535450637340546, 0.026629535481333733, -0.03919287398457527, 0.016893800348043442, 0.05645569786429405, -0.01897064782679081, 0.012642687186598778, -0.06255781650543213, 0.0019230243051424623, 0.0219130776822567, 0.02570631355047226, -0.014174425043165684, 0.038418855518102646, -0.03965706750750542, -0.0029687448404729366, -0.00576430931687355, -0.04583160579204559, -0.02341499552130699, -0.02095009572803974, 0.013803311623632908, -0.03578655421733856, -0.031128836795687675, 0.023886345326900482, -0.007519056089222431, -0.028599344193935394, 0.015160879120230675, -0.01491033099591732, -0.0063550714403390884, 0.04222840815782547, -0.011967455968260765, 0.002227708464488387, 0.024086862802505493, 0.0039694057777523994, -0.028157416731119156, 0.02802373468875885, 0.03917853906750679, -0.051150452345609665, 0.09936444461345673, 0.03789282962679863, -0.07189825177192688, 0.012689728289842606, 0.028028642758727074, 0.0186048224568367, -0.04002666100859642, 0.0714174434542656, -0.0070359474048018456, -0.028454698622226715, 0.05084627866744995, 0.028262829408049583, 0.06619814038276672, -0.042701903730630875, 0.01206597313284874, -0.0012572136474773288, 0.014212897047400475, 0.04014090076088905, 0.01593303121626377, -0.007034131325781345, 0.0194703359156847, 0.0029528315644711256, -0.06667869538068771, -0.022114338353276253, 0.045845821499824524, 0.02705109305679798, -0.04596167057752609, -0.02810773253440857, -0.056896310299634933, 0.01174156740307808, 0.026171835139393806, -0.001807552413083613, -0.005217809230089188, -0.046026572585105896, -0.06937690079212189, -0.006566805765032768, -0.0022153372410684824, 0.0685419961810112, -0.014503172598779202, -0.005774700082838535, 0.008938674814999104, 0.03862977400422096, -0.024085212498903275, 0.01920446939766407, -0.05997317284345627, -0.09934352338314056, 0.04806046560406685, 0.008724856190383434, 0.011235159821808338, -0.011520348489284515, 0.027051664888858795, 0.03227870538830757, 0.027289241552352905, -0.047725360840559006, -0.022747542709112167, 0.028776930645108223, 0.00698492769151926, 0.03234127163887024, 0.018039166927337646, -0.04328097403049469, 0.05346299335360527, 0.017331881448626518, 0.06122530996799469, 0.015731466934084892, 0.026866761967539787, -0.022825326770544052, -0.05497764050960541, 0.02673056162893772, 0.03363250195980072, -0.012951965443789959, -0.03923938795924187, 0.07123352587223053, -0.008521456271409988, -0.031740453094244, -0.03529095649719238, 0.006923974957317114, -0.05291793867945671, 0.06052418053150177, 0.044050369411706924, -0.052978817373514175, 0.03439871966838837, 0.037588611245155334, -0.005254874937236309, -0.003970739431679249, 0.03991478309035301, 0.009912929497659206, -0.012401718646287918, -0.03189564496278763, 0.027813363820314407, 0.026154525578022003, 0.028831738978624344, 0.009421317838132381, -0.011309083551168442, -0.03594604507088661, -0.03889993578195572, 0.007113436236977577, 0.0015151887200772762, -0.028294913470745087, -0.03699836879968643, 0.10516798496246338, 0.016947999596595764, 0.05695672705769539, 0.029341725632548332, 0.0222819484770298, -0.02063019573688507, -0.007417329121381044, -0.006291464902460575, 0.009671886451542377, -0.009619385004043579, -0.04994116723537445, -0.024405330419540405, -0.01254827156662941, -0.019696226343512535, -0.042983733117580414, -0.0491197444498539, 0.007850244641304016, 0.009080784395337105, 0.044851258397102356, -0.048614900559186935, -0.04337280988693237, 0.016148004680871964, 0.012725899927318096, 0.04363561421632767, -0.055109113454818726, -0.013323009945452213, -0.026881732046604156, 0.06705257296562195, -0.009162171743810177, -0.03252135217189789, 0.0002230102982139215, 0.010718140751123428, 0.03478718176484108, 0.023749496787786484, 0.010312036611139774, 0.021009178832173347, -0.04571734368801117, -0.013641764409840107, -0.014412989839911461, -0.043266139924526215, 0.011244934052228928, -0.03530896082520485, 0.03741079568862915, 0.012978843413293362, 0.014686277136206627, -0.003325564553961158, -0.008902118541300297, 0.06028233841061592, -0.016389597207307816, 0.013534395024180412, -0.021951187402009964, -0.06613214313983917, -0.05003374442458153, 0.03527276962995529, 0.010638009756803513, 0.022511078044772148, -0.011114398017525673, -0.021898319944739342, -0.01517182681709528, 0.04458888620138168, -0.007164895534515381, -0.010469408705830574, -0.027182305231690407, 0.029625261202454567, 0.019776994362473488, 0.07077573984861374, -0.03982225060462952, -0.09038979560136795, 0.0009240273502655327, 0.018961280584335327, -0.006360189523547888, -0.011394748464226723, -0.03246516361832619, -0.01794692687690258, 0.009711317718029022, 0.003671194426715374, -0.04455370083451271, 0.01470353826880455, -0.02852400206029415, 0.01860162243247032, -0.06474345922470093, -0.022019270807504654, 0.06945428252220154, -0.042291220277547836, -0.023910893127322197, 0.015486557967960835, -0.034541863948106766, 0.020146569237113, 0.0784185379743576, -0.06607013195753098, 0.008956418372690678, 0.03954972326755524, 0.006706949323415756, 0.001994104590266943, -0.03522641956806183, -0.005814552307128906, 0.037848200649023056, 0.060731690376996994, -0.005289323162287474, -0.07063756138086319, -0.003659673035144806, -0.033555079251527786, 0.004666224122047424, 0.01918492466211319, -0.014447161927819252, 0.006457535549998283, -0.029160110279917717, -0.00289094727486372, -0.018190782517194748, -0.02799304574728012, 0.043745655566453934, -0.005100951995700598, -0.0307561494410038, -0.014185111969709396, -0.027142031118273735, 0.06617315113544464, -0.033168841153383255, 0.07843829691410065, -0.010457335039973259, 0.021315397694706917, 0.026522047817707062, 0.000009049714208231308, -0.01975454017519951, 0.01703379675745964, -0.02449651248753071, -0.019525699317455292, 0.03133999928832054, 0.007609163876622915, -0.05419908091425896, -0.022805241867899895, 0.022262606769800186, -0.005952352192252874, -0.0547189861536026, 0.03574012219905853, -0.00407969718798995, 0.06817980110645294, -0.04545209929347038, -0.0013308846391737461, 0.003180987900123, 0.00834340788424015, -0.03744131699204445, 0.005458098836243153, -0.01770734414458275, 0.004140024073421955, 0.05705416947603226, 0.024830762296915054, -0.00049453170504421, 0.013659917749464512, -0.012236339971423149, 0.040897492319345474, -0.0006500197341665626, 0.002532884245738387, -0.02609546110033989, 0.07891208678483963, 0.0031712581403553486, 0.03524811193346977, 0.01517843920737505, -0.000035481098166201264, -0.022526411339640617, -0.00530027411878109, 0.009245967492461205, 0.036588288843631744, -0.02533780410885811, 0.011103007011115551, 0.006668597459793091, -0.012447841465473175, -0.018107261508703232, -0.042315948754549026, -0.017953336238861084, -0.0018821806879714131, -0.015116635710000992, 0.09057281911373138, 0.03460962325334549, -0.045455578714609146, 0.014931398443877697, -0.03566402196884155, -0.017197052016854286, 0.06008719280362129, 0.06989390403032303, 0.004284335765987635, 0.06908964365720749, -0.036706533282995224, -0.010067691095173359, -0.018198076635599136, 0.025014150887727737, 0.011064414866268635, -0.012396812438964844, -0.027377253398299217, -0.045056771486997604, -0.01748764142394066, 0.02937053143978119, 0.06289827078580856, -0.02690586820244789, 0.01408377941697836, 0.02136787585914135, -0.024356083944439888, -0.05684446543455124, 0.03914976119995117, -0.0003063497133553028, -0.01876155659556389, 0.022678369656205177, -0.02027740143239498, 0.005383385345339775, -0.03789578378200531, 0.08398770540952682, -0.06826689094305038, -0.05306770280003548, -0.011632410809397697, 0.019699420779943466, -0.013006887398660183, -0.0030998506117612123, 0.028474539518356323, 0.003164447844028473, 0.04335659369826317, 0.017118290066719055, 0.0023739272728562355, -0.0649377629160881, -0.06461320072412491, 0.016584793105721474, 0.026064520701766014, -0.025624888017773628, -0.05565831437706947, -0.006341005675494671, 0.042320314794778824, 0.06370393931865692, 0.07930083572864532, -0.02384287118911743, -0.0012427391484379768, 0.050122275948524475, 0.016217008233070374, 0.05287577956914902, 0.034595903009176254, -0.08832769095897675, 0.0021093543618917465, -0.000713743269443512, -0.009545055218040943, 0.009803974069654942, 0.017158545553684235, -0.022495029494166374, 0.025704922154545784, -0.04848833382129669, 0.008785436861217022, 0.026912137866020203, 0.020039860159158707, -0.027408337220549583, -0.02019345760345459, 0.0094905449077487, 0.046180520206689835 ]
<p>Suppose you are doing an experiment to determine the work function of a metal.  You get $KE_1$, $\nu_1$ and $KE_2$, $\nu_2$.   We know that $KE = h\nu - W$ but when you solve the simultaneous equations, we have a $h$ slightly different from the textbook value.</p> <p>Question: In such a situation should you</p> <ol> <li><p>Use the textbook $h$ then average {$W_1,W_2$}; or</p></li> <li><p>Simply solve the simultaneous equations for $W$</p></li> </ol> <p>I believe that the values obtained will be different.</p> <p>Thank you.</p> <p>Added: Assume you don't get to do more repeats etc.</p>
g8394
[ -0.01789846457540989, -0.03238598257303238, 0.002116034971550107, -0.010081246495246887, 0.039671704173088074, -0.02382015623152256, 0.017836911603808403, 0.0009421015856787562, -0.040145162492990494, 0.030961083248257637, -0.0019841394387185574, 0.0362744964659214, 0.010193808004260063, 0.02285020612180233, -0.03198584169149399, -0.030838975682854652, 0.07748845219612122, -0.04170414060354233, -0.021250510588288307, 0.030852574855089188, -0.05943985655903816, 0.08704886585474014, -0.008096032775938511, -0.04228520393371582, 0.05064244195818901, -0.014538677409291267, -0.07355895638465881, 0.015728067606687546, -0.09556286782026291, 0.03750359266996384, -0.02042018249630928, -0.04295951873064041, 0.08097768574953079, -0.03679869323968887, -0.07248923927545547, 0.009714669547975063, 0.04514705017209053, 0.04111257568001747, -0.02114148624241352, 0.019587036222219467, 0.029336562380194664, -0.025184359401464462, 0.026230018585920334, -0.0069086928851902485, 0.011899026110768318, -0.022148603573441505, -0.040601301938295364, -0.0300200954079628, 0.044713202863931656, -0.0188345555216074, 0.001295214518904686, 0.06540579348802567, 0.05514797940850258, 0.020426521077752113, -0.007773770019412041, -0.0009262504172511399, 0.024799542501568794, -0.06699619442224503, 0.035216230899095535, 0.025531427934765816, -0.023645885288715363, 0.036765068769454956, -0.007408895529806614, -0.060142915695905685, 0.03007890097796917, 0.0063791899010539055, 0.042788032442331314, 0.03400349244475365, -0.0025214713532477617, 0.009013494476675987, -0.006807565689086914, 0.02185620740056038, 0.0443611815571785, -0.04318239167332649, -0.004716979339718819, -0.03245794028043747, 0.06066446378827095, -0.007765165064483881, 0.009144402109086514, 0.1009182408452034, -0.02392932027578354, -0.011480115354061127, 0.07025571167469025, 0.05719801411032677, -0.005381124094128609, -0.003589570289477706, 0.03871402516961098, -0.02281554788351059, -0.037949007004499435, 0.03111431375145912, 0.002592697972431779, 0.003925371449440718, 0.0783596858382225, 0.042203452438116074, -0.012884591706097126, -0.02045734040439129, -0.025126319378614426, 0.08033706247806549, 0.005645164288580418, 0.045263517647981644, -0.015017643570899963, 0.010532284155488014, 0.008487102575600147, 0.029936105012893677, -0.005628983024507761, -0.02422834001481533, 0.08136799931526184, 0.0040715825743973255, -0.07168170809745789, -0.03696943074464798, -0.047947920858860016, -0.018577422946691513, -0.03568727523088455, -0.02642962709069252, -0.035458043217659, 0.000844408932607621, -0.009031211026012897, -0.023967495188117027, -0.030459098517894745, -0.010465339757502079, -0.0412827730178833, -0.04466431215405464, 0.0151365976780653, -0.01177108846604824, 0.029014144092798233, -0.010780954733490944, 0.02196611277759075, 0.018296072259545326, 0.07113717496395111, -0.007888988591730595, 0.026169029995799065, 0.030978593975305557, -0.0920732319355011, 0.04019907861948013, -0.018316658213734627, 0.00326858414337039, -0.02776053175330162, 0.05922806262969971, -0.02374749816954136, -0.0239237230271101, -0.01757141202688217, -0.00294451299123466, -0.02217031829059124, -0.012221455574035645, -0.02435801737010479, 0.020547866821289062, -0.01441500335931778, -0.046090006828308105, -0.002296092454344034, 0.023256976157426834, -0.01185750961303711, 0.021879732608795166, 0.04614356905221939, 0.029355106875300407, -0.02780023403465748, -0.03732368350028992, 0.02369767799973488, -0.004321284592151642, 0.060496024787425995, -0.02415763959288597, 0.062327008694410324, -0.06534583121538162, 0.01782669499516487, 0.022701412439346313, -0.020108846947550774, 0.09650257229804993, -0.0031160954385995865, -0.0237837303429842, 0.023929158225655556, -0.027267148718237877, -0.004660897888243198, -0.06814645975828171, 0.014758044853806496, -0.03284434601664543, -0.017143553122878075, 0.015235565602779388, 0.08556576073169708, -0.05092061311006546, 0.005386362783610821, 0.08243846148252487, 0.002468063496053219, 0.013202998787164688, 0.04263291507959366, -0.07500810921192169, -0.005599698983132839, -0.007325227838009596, -0.06968698650598526, 0.04274902120232582, -0.08584856986999512, -0.007586804684251547, 0.00300196697935462, 0.0018734314944595098, 0.0009585130028426647, 0.0016717684920877218, -0.05390331521630287, 0.02358131855726242, 0.012444066815078259, 0.055857155472040176, -0.030095554888248444, -0.01136023923754692, -0.029130754992365837, 0.093134805560112, -0.013985354453325272, -0.008967242203652859, -0.052540794014930725, 0.016753455623984337, -0.02828199975192547, -0.009284546598792076, 0.04047286882996559, -0.04897979646921158, 0.02882237732410431, -0.0006383449072018266, 0.010564788244664669, 0.07091327756643295, -0.02679489552974701, -0.04389480873942375, 0.014963336288928986, 0.05308506265282631, -0.04543222486972809, 0.012344707734882832, 0.004883054178208113, -0.0008246569777838886, 0.018031565472483635, 0.021434109658002853, -0.014185058884322643, -0.03448592126369476, 0.004634100012481213, -0.002136501483619213, -0.011739347130060196, -0.003921582829207182, -0.04436611011624336, -0.01773703284561634, -0.013762060552835464, -0.03333888202905655, 0.0768403634428978, 0.03609171137213707, -0.0013711737701669335, -0.014852306805551052, 0.009050233289599419, 0.041380200535058975, 0.040986064821481705, 0.0168355330824852, 0.015482152812182903, 0.02756453864276409, -0.004416097886860371, -0.021837197244167328, 0.044869180768728256, -0.0068720243871212006, 0.008593612350523472, 0.04533236846327782, -0.05142233893275261, 0.015791449695825577, -0.039838533848524094, -0.027697568759322166, -0.012734821997582912, -0.029643375426530838, -0.02590864710509777, 0.007099132984876633, 0.004273358266800642, -0.012393186800181866, 0.03663698583841324, 0.026648499071598053, 0.023118257522583008, 0.05876960977911949, -0.015159998089075089, -0.020785648375749588, -0.02670164220035076, -0.006268793251365423, 0.0039034532383084297, -0.019497694447636604, -0.021656328812241554, -0.022377358749508858, -0.021045610308647156, 0.061609525233507156, 0.003378183813765645, -0.07959431409835815, 0.004825890529900789, -0.055762238800525665, 0.036356326192617416, -0.013257126323878765, -0.02722882106900215, -0.04771537333726883, -0.04639159515500069, 0.027983319014310837, 0.027376405894756317, -0.01631554588675499, 0.022048739716410637, -0.02409905381500721, -0.0065306853502988815, 0.027287188917398453, -0.06842312216758728, 0.06765531003475189, 0.03061971440911293, 0.013264935463666916, 0.021764593198895454, 0.012243501842021942, 0.0651375949382782, -0.0707593709230423, -0.024846574291586876, 0.01946250908076763, -0.01345384307205677, -0.063846156001091, -0.03161250799894333, 0.04032844677567482, 0.03496948629617691, -0.01566280610859394, -0.02195082977414131, -0.0014631752856075764, 0.01372949406504631, 0.026966998353600502, 0.02478932775557041, -0.025386536493897438, 0.010286777280271053, -0.018223777413368225, -0.0029975920915603638, 0.02843393385410309, 0.0070690009742975235, -0.03864210471510887, 0.00908425822854042, -0.04348393529653549, 0.006992989685386419, -0.050220128148794174, 0.04052436351776123, -0.022544430568814278, -0.05913795530796051, 0.05292057618498802, -0.00979647971689701, -0.012127263471484184, -0.0339081846177578, -0.008241911418735981, -0.015141831710934639, 0.0669352263212204, 0.00605560140684247, 0.000709168438334018, 0.02661477029323578, -0.03974592313170433, -0.0284762904047966, -0.03062703087925911, -0.002517957938835025, 0.012703600339591503, -0.027521835640072823, 0.0262973140925169, -0.021244943141937256, -0.0017831382574513555, -0.006438659969717264, -0.05403311178088188, -0.006136544048786163, 0.00995372049510479, -0.03947305306792259, -0.0004860815533902496, 0.029731443151831627, 0.018947899341583252, -0.02481597103178501, 0.005625106859952211, 0.011381191201508045, -0.04417029395699501, 0.0016295757377520204, 0.04002712666988373, 0.028024453669786453, 0.006191791035234928, 0.0126524418592453, -0.00646523293107748, -0.05232705548405647, 0.016876311972737312, -0.02715122513473034, 0.03016131930053234, 0.02668735943734646, 0.10131339728832245, 0.0037640584632754326, -0.033924832940101624, -0.036514535546302795, 0.04283860698342323, 0.047395944595336914, -0.05024674907326698, 0.03498087078332901, -0.013606134802103043, 0.03569607064127922, 0.013818326406180859, -0.007278569508343935, 0.05925517901778221, 0.0004955772310495377, -0.01910315454006195, -0.04297267645597458, -0.02768055349588394, -0.00271766004152596, -0.012729412876069546, -0.05564836785197258, -0.011144908145070076, 0.047490425407886505, -0.03941459581255913, 0.02315557561814785, -0.005812973715364933, -0.041928548365831375, 0.04622246325016022, -0.015906494110822678, -0.04725182056427002, -0.0009028493659570813, -0.02677968516945839, -0.00803285650908947, 0.06809082627296448, -0.039658501744270325, -0.040936537086963654, -0.025362612679600716, 0.015302181243896484, -0.044501323252916336, 0.019753973931074142, 0.04006234556436539, -0.03577679768204689, -0.023755691945552826, 0.04185080528259277, -0.06922291964292526, -0.041415173560380936, -0.019517511129379272, -0.020967237651348114, -0.012835993431508541, -0.04216712340712547, 0.042195070534944534, 0.0033924418967217207, -0.048772867769002914, 0.004499070346355438, -0.03155769407749176, 0.06757859140634537, -0.011988703161478043, -0.015957316383719444, 0.03664688393473625, -0.031075792387127876, 0.03542926162481308, 0.055909380316734314, 0.0048196748830378056, -0.06210091710090637, 0.03547084331512451, 0.008590181358158588, 0.0054832869209349155, -0.013034109957516193, -0.05721498280763626, -0.015461044386029243, -0.00435375701636076, 0.09291157871484756, -0.011806666851043701, 0.05214868485927582, -0.032020654529333115, 0.05367288365960121, -0.041160911321640015, 0.02675975300371647, -0.03539128229022026, 0.021931739524006844, -0.03043580800294876, -0.036320753395557404, -0.0000903099644347094, -0.04379737377166748, -0.036438364535570145, 0.021234268322587013, 0.002389352535828948, 0.004652380011975765, -0.012482407502830029, -0.035948242992162704, 0.02567489817738533, 0.0005032687331549823, 0.030420133844017982, 0.08395683020353317, 0.023130618035793304, -0.058229945600032806, 0.038453035056591034, 0.015068983659148216, 0.0011752924183383584, -0.016889290884137154, -0.02196153998374939, 0.039821259677410126, -0.043635088950395584, -0.025334354490041733, 0.008088178932666779, -0.0028945421800017357, 0.10701119154691696, 0.01098863035440445, 0.04143368452787399, -0.06076585128903389, -0.04503496736288071, 0.0015423092991113663, 0.017205454409122467, 0.005960340611636639, -0.03341438248753548, -0.06031343340873718, 0.07416041940450668, 0.01239921897649765, 0.0167124904692173, -0.006835226900875568, -0.04167908430099487, -0.027855927124619484, 0.06878811120986938, -0.03316784277558327, 0.04040637984871864, 0.0018108777003362775, 0.0609530471265316, -0.01893937587738037, -0.04447639361023903, -0.0011995849199593067, 0.016834832727909088, 0.02739749476313591, 0.04594441503286362, -0.017011981457471848, -0.044442318379879, 0.02552681416273117, -0.03841574490070343, -0.02588789537549019, 0.003334656124934554, 0.03910656273365021, -0.02366173453629017, 0.007157537154853344, 0.026872552931308746, -0.01279546320438385, 0.027085598558187485, -0.005554839503020048, 0.03027362748980522, 0.010284392163157463, -0.009257778525352478, -0.00782945565879345, -0.022178299725055695, 0.021879028528928757, -0.07026402652263641, -0.057753439992666245, 0.06872446089982986, 0.043402962386608124, 0.03767409548163414, -0.01970607601106167, -0.025084132328629494, -0.0568845197558403, 0.022834673523902893, -0.0026161051355302334, 0.0009622887591831386, 0.011072002351284027, 0.020246276631951332, 0.07401809096336365, -0.004088098648935556, 0.03175026923418045, 0.01907936856150627, -0.028529053553938866, -0.011153928004205227, 0.00539612490683794, -0.03434814512729645, 0.018118422478437424, -0.0007377611473202705, 0.0116032175719738, 0.11725100874900818, 0.004486272111535072, 0.003872454399242997, -0.006422517355531454, -0.004435080569237471, 0.008655630983412266, 0.036704156547784805, -0.029451759532094002, -0.03784286603331566, 0.04042980447411537, -0.020397603511810303, -0.0018810462206602097, 0.00890637468546629, 0.032296717166900635, 0.03511068597435951, -0.03178386390209198, 0.017020998522639275, -0.03165683522820473, 0.03752126917243004, -0.04438912868499756, 0.08074294775724411, 0.016522612422704697, 0.08303830772638321, -0.06818798184394836, -0.004102764651179314, -0.023589815944433212, -0.02064351737499237, 0.014795762486755848, -0.0418061688542366, -0.020622124895453453, 0.010140866972506046, -0.013778728432953358, 0.022516939789056778, 0.07096381485462189, 0.01420595496892929, -0.011632132343947887, 0.038307074457407, -0.0164912398904562, -0.012542755343019962, -0.0066706035286188126, -0.02559071220457554, -0.019209284335374832, -0.02205607108771801, 0.028960976749658585, 0.040436580777168274, 0.02610747516155243, 0.018523044884204865, -0.03411764279007912, -0.014372431673109531, -0.0013876142911612988, -0.01655515842139721, 0.025536170229315758, 0.04199700802564621, -0.01656288281083107, 0.008345432579517365, -0.017203286290168762, -0.05745245888829231, -0.011830531992018223, 0.026619765907526016, 0.017044171690940857, 0.08512851595878601, -0.03096744790673256, -0.0004307806375436485, -0.0063723428174853325, -0.053857650607824326, 0.020639343187212944, -0.012757981196045876, -0.019989119842648506, -0.00018393390928395092, 0.014943170361220837, 0.005291248206049204, 0.02297823689877987, -0.022197114303708076, -0.04288995638489723, 0.020686600357294083, 0.028559451922774315, 0.012074698694050312, 0.021389244124293327, 0.05407319590449333, -0.01176828145980835, 0.00027945791953243315, -0.03838801383972168, 0.019442426040768623, 0.057695209980010986, -0.0738869309425354, -0.014610463753342628, 0.03190668672323227, 0.013016248121857643, 0.0460948571562767, 0.0625956729054451, -0.003218278056010604, 0.0605495385825634, -0.07130551338195801, 0.004960177466273308, 0.004512412939220667, 0.03412223979830742, -0.0504140742123127, 0.05445336177945137, -0.009793379344046116, 0.04067252576351166, 0.0702129527926445, 0.06120062619447708, -0.009895139373838902, 0.004564487375319004, 0.04882725328207016, -0.020901544019579887, -0.07929231226444244, 0.0028549632988870144, 0.01909659057855606, -0.0375666469335556, -0.032127734273672104, -0.002972886897623539, 0.019615862518548965, 0.04594742879271507, 0.053184039890766144, 0.01661827601492405, 0.0024646215606480837, 0.05308021605014801, -0.06441832333803177, -0.028105473145842552, -0.04803185909986496, 0.00848856009542942, -0.030047181993722916, 0.024854378774762154, 0.02498384192585945, -0.039277881383895874, 0.008827118203043938, 0.0071346573531627655, -0.02482800930738449, -0.01622161455452442, 0.011533818207681179, 0.025142889469861984, 0.05305659398436546, 0.036815255880355835, -0.03848648816347122, -0.0026659888681024313, -0.04869438707828522, -0.011959905736148357, 0.012400935404002666, -0.02636031247675419, -0.007976902648806572, -0.04079405963420868, -0.02112816832959652, -0.04130128026008606, -0.0880417674779892, -0.037974294275045395, 0.03843222185969353, -0.039443422108888626, -0.006817508488893509, -0.004008757881820202, 0.03791585564613342, -0.005741243250668049, -0.031084585934877396, 0.03444058075547218, 0.008608140982687473, 0.0050063650123775005, 0.027682825922966003, 0.03732326626777649, 0.05138654634356499, -0.01864815130829811, -0.02443910762667656, -0.00951412320137024, -0.07529700547456741, 0.007574243936687708, -0.003587567014619708, -0.026440048590302467, -0.022016232833266258, -0.08657393604516983, -0.009212506003677845, 0.04711808264255524, 0.014061751775443554, -0.006452056113630533, 0.012964801862835884, -0.03514818102121353, -0.048642612993717194, -0.05627826228737831, 0.06090908125042915, -0.018628690391778946, 0.02924114093184471, 0.016822567209601402, -0.0027918952982872725, -0.004317937418818474, 0.031089596450328827, -0.10057961195707321, -0.045267872512340546, -0.0044533624313771725, -0.01915566623210907, 0.033101748675107956, 0.025097064673900604, -0.03191042318940163, -0.0492548942565918, 0.030799416825175285, 0.014413529075682163, -0.0030369723681360483, 0.05066639557480812, 0.023594733327627182, -0.020435094833374023, 0.0196818970143795, 0.006852747406810522, -0.006948136258870363, -0.018301257863640785, 0.03366273269057274, -0.028121892362833023, 0.008547211065888405, -0.04002154618501663, -0.016050118952989578, 0.04082581028342247, -0.06464514136314392, -0.099246084690094, -0.0008407180430367589, -0.03170520439743996, 0.07984762638807297, 0.04882923886179924, -0.03541586548089981, 0.01626734435558319, 0.00008350134157808498, -0.01624002493917942, 0.014809953980147839, -0.025088272988796234, -0.007426811847835779, -0.07074300199747086, 0.027775747701525688, 0.052128758281469345, -0.05724993720650673, -0.009286847896873951, 0.024166438728570938 ]
<p>I'm currently taking an introduction to Solid State Physics class, and is now on the subject of superconductivity (SC). Currently I'm reading about the BCS theory, and how this works on a microscopic scale. I then get presented with this picture (Electron-Phonon Interaction):</p> <p><img src="http://i.stack.imgur.com/ZJiFm.png" alt="Electron-Phonon interaction"></p> <p>Now, as far as I have understood, the electrons, when below $T_{C}$, attract the ions, but are too fast compared to the ions, which means that the ions contract after the electron is gone. This creates a higher potential in the area where they are "squeezed" together which the next electron is much more attracted to that usually. This again means that all electrons pretty much follow the same path, and somehow bond together in Cooper Pairs (Is this the way they get entangled?).</p> <p>Now, my main question is: Does this attraction of ions, after an electron has moved past them, not happen to a normal metal ? I mean, the electrons move in a normal metal, and also past ions. So don't they attract the ions as well, and make this attraction that another electron then can follow as well ?</p>
g8395
[ 0.01978226937353611, 0.038664091378450394, 0.00787556916475296, -0.0022138950880616903, 0.006900362204760313, 0.005893985740840435, -0.0009641930810175836, -0.021909642964601517, -0.016724711284041405, -0.0075102453120052814, -0.028042040765285492, 0.07069680094718933, -0.031107936054468155, -0.06060049682855606, 0.021202320232987404, -0.0016910930862650275, 0.03658769279718399, -0.023151129484176636, 0.04798164963722229, 0.03693777322769165, -0.019637586548924446, 0.05927707999944687, 0.00865783542394638, -0.030996324494481087, -0.04407601058483124, 0.008524837903678417, -0.01895957626402378, -0.006372114177793264, -0.010824243538081646, 0.011984922923147678, -0.006682756822556257, -0.011420938186347485, 0.06242717429995537, -0.05987536534667015, -0.04756169393658638, -0.046202752739191055, 0.04580838233232498, -0.01442467700690031, 0.0178665854036808, 0.025772465392947197, 0.025143351405858994, -0.02257121540606022, -0.0058599477633833885, -0.0753893330693245, 0.017669491469860077, -0.0165364108979702, 0.019465167075395584, -0.07062891125679016, 0.012972029857337475, 0.0038279984146356583, -0.006855433806777, 0.050930049270391464, -0.01916254684329033, 0.03973538428544998, -0.012400202453136444, 0.006752713583409786, 0.06787118315696716, 0.03160683810710907, 0.06501314043998718, 0.014979952946305275, 0.07167565822601318, 0.03564814105629921, 0.05481858551502228, -0.007637444883584976, 0.07849103212356567, 0.008731965906918049, -0.03702495992183685, 0.02968144603073597, -0.03535270690917969, -0.039374835789203644, -0.07187213003635406, -0.03989410027861595, -0.043116696178913116, 0.00026680712471716106, -0.04413594305515289, 0.04838928207755089, 0.016145864501595497, -0.07228711247444153, 0.051871415227651596, -0.02087549678981304, -0.09501200169324875, -0.055705197155475616, 0.01448736060410738, -0.02138567715883255, 0.03973075747489929, 0.018944012001156807, -0.06909235566854477, 0.04970956966280937, -0.05897218734025955, -0.02124330960214138, -0.022617099806666374, -0.0525101013481617, -0.020704615861177444, 0.016274401918053627, -0.06207610294222832, 0.0067530786618590355, -0.03943118453025818, 0.02807578444480896, 0.0028494768775999546, -0.021585362032055855, -0.052359942346811295, -0.04661152511835098, 0.009326107800006866, -0.011251986026763916, -0.08673392981290817, -0.028252046555280685, -0.014123395085334778, -0.01063105184584856, 0.06599146127700806, 0.02124689519405365, -0.026944167912006378, -0.07408753037452698, 0.0016102857189252973, 0.00981935765594244, -0.01725670136511326, 0.048953283578157425, -0.007089619990438223, -0.002361053368076682, 0.01573144644498825, 0.011874895542860031, -0.02537343092262745, 0.01944676600396633, 0.005969792138785124, 0.010978803038597107, 0.02324131317436695, -0.025386478751897812, 0.04435516893863678, 0.029344908893108368, 0.02300676330924034, -0.009720982983708382, 0.011629592627286911, 0.020416544750332832, -0.02373863197863102, 0.03588365390896797, 0.0008776569156907499, -0.0034349518828094006, 0.013772755861282349, 0.005564429797232151, 0.025960884988307953, -0.014616872183978558, -0.016179390251636505, 0.0021678837947547436, -0.0161655992269516, -0.04491255059838295, -0.030356917530298233, 0.0339653417468071, -0.05662553012371063, 0.024781277403235435, 0.00030093741952441633, 0.02570675127208233, -0.006210764870047569, 0.008489195257425308, 0.026937156915664673, 0.015258058905601501, -0.08425791561603546, -0.027164984494447708, 0.05574982985854149, -0.013623264618217945, -0.027988990768790245, 0.030208919197320938, 0.028161486610770226, -0.04152408987283707, -0.025337373837828636, 0.006451946683228016, 0.02675788663327694, -0.018795719370245934, 0.03436872363090515, -0.05224780738353729, 0.002993362955749035, 0.026869630441069603, -0.01414552703499794, 0.000027929105272050947, -0.010842976160347462, 0.05803089961409569, 0.05797204002737999, 0.02670295350253582, 0.010171478614211082, -0.01263341587036848, 0.04577895253896713, -0.020385198295116425, -0.020787129178643227, 0.028018305078148842, 0.06080259382724762, 0.027734218165278435, 0.011346448212862015, 0.0006803572177886963, -0.047971177846193314, 0.04443734511733055, 0.0029461239464581013, -0.005744262598454952, 0.003941820934414864, -0.02092571370303631, -0.014425016939640045, -0.02392297238111496, -0.0317583903670311, -0.03521862253546715, 0.019255420193076134, -0.029625892639160156, 0.012083594687283039, -0.06026509031653404, 0.019698044285178185, 0.05093296989798546, -0.03367369994521141, -0.033628784120082855, 0.043726760894060135, -0.0255290474742651, -0.04269447922706604, -0.015384363010525703, 0.018609926104545593, 0.002747495658695698, -0.009666279889643192, -0.002082760212942958, -0.06244831159710884, 0.037294305860996246, -0.0736243724822998, -0.05076219141483307, -0.02621188573539257, 0.00663320068269968, -0.008248764090240002, 0.03472321480512619, 0.0005312718567438424, -0.04451998323202133, 0.017981182783842087, -0.021372361108660698, 0.008205224759876728, -0.015090548433363438, 0.01789645478129387, 0.004411454778164625, 0.02601626329123974, 0.05612615495920181, -0.03507695719599724, 0.06622714549303055, 0.014281301759183407, -0.07151191681623459, 0.022847803309559822, 0.053535446524620056, 0.0026959420647472143, 0.01937895454466343, -0.03503232076764107, 0.01895264722406864, 0.019250229001045227, -0.0291137658059597, -0.028343258425593376, -0.02414116822183132, -0.007337263319641352, -0.017422378063201904, 0.033254195004701614, -0.02490711770951748, 0.005152802914381027, 0.02881251461803913, 0.07872080057859421, -0.04527440667152405, -0.031814295798540115, 0.020628461614251137, -0.006639512255787849, -0.033861879259347916, -0.011858969926834106, 0.024655409157276154, -0.07289761304855347, -0.07216747850179672, 0.005641784518957138, 0.015714703127741814, 0.006340190302580595, -0.038588330149650574, -0.05383182317018509, -0.038255877792835236, -0.006995758507400751, 0.00470974575728178, -0.02540508285164833, -0.04555666446685791, -0.032256923615932465, 0.08192731440067291, -0.0562794953584671, -0.0013111192965880036, -0.023746656253933907, -0.0041646952740848064, 0.013437079265713692, -0.008604193106293678, 0.01885373145341873, -0.04964176565408707, -0.07308387756347656, 0.0005944161675870419, -0.024420227855443954, -0.05529419705271721, -0.025489337742328644, -0.02740049734711647, -0.02394687384366989, -0.08240246772766113, 0.03453129157423973, 0.004904592409729958, -0.053869616240262985, -0.021476542577147484, 0.057262446731328964, 0.06694775819778442, 0.01031110156327486, -0.02153518609702587, 0.04809476435184479, -0.02348506636917591, -0.09505757689476013, 0.0647062286734581, -0.0172947496175766, -0.03790709003806114, 0.01289069838821888, 0.00966223981231451, 0.08234184235334396, 0.02324857749044895, -0.055208511650562286, -0.04491579532623291, -0.055502358824014664, -0.017553530633449554, 0.0198136605322361, 0.04860071465373039, 0.005555032752454281, -0.0010365847265347838, -0.012533199042081833, -0.019832978025078773, 0.04294024035334587, 0.036425452679395676, 0.013567929156124592, 0.0176621712744236, 0.017988350242376328, 0.003794435877352953, 0.00526799401268363, -0.03502771630883217, 0.03548065572977066, 0.01012947503477335, -0.05488814413547516, 0.0300371702760458, -0.05311388522386551, 0.010865866206586361, 0.028445692732930183, -0.027391858398914337, 0.03200767561793327, -0.00015343567065428942, -0.03727852925658226, -0.03784012049436569, 0.0025262548588216305, 0.05831996724009514, 0.025852691382169724, 0.06136089190840721, 0.05172870308160782, -0.004424643237143755, -0.0263188648968935, 0.02039376273751259, 0.028901495039463043, 0.013803137466311455, 0.04712069407105446, 0.02367103472352028, -0.017581747844815254, -0.019601881504058838, 0.009114757180213928, 0.02105710282921791, 0.010562163777649403, 0.0077455476857721806, -0.03101203590631485, 0.02769383043050766, 0.011706845834851265, -0.018966447561979294, -0.014981265179812908, 0.0040155746974051, -0.0010063698282465339, -0.0022076659370213747, 0.024883531033992767, 0.022780735045671463, -0.009194022975862026, -0.02634529024362564, -0.037570785731077194, 0.021861640736460686, 0.05285084620118141, -0.01914169080555439, -0.029742734506726265, 0.004876724444329739, 0.010105025954544544, 0.012642400339245796, 0.053272176533937454, -0.025726070627570152, 0.012977957725524902, 0.018565643578767776, -0.03266986086964607, 0.008058222010731697, -0.02255518175661564, 0.05517841503024101, 0.04317605867981911, 0.021142303943634033, 0.03174828737974167, -0.009970947168767452, -0.027735501527786255, 0.028696836903691292, -0.023967543616890907, -0.048193253576755524, -0.046612370759248734, -0.008005117066204548, 0.023380450904369354, -0.0020584806334227324, -0.010266674682497978, -0.02922976203262806, 0.06145995110273361, -0.025982018560171127, 0.06848601996898651, -0.051504701375961304, -0.07731012254953384, 0.0038483126554638147, -0.044691767543554306, -0.07385270297527313, 0.02773704193532467, 0.001027252059429884, 0.014849616214632988, 0.0028702241834253073, -0.035514071583747864, -0.08266735076904297, -0.02668791264295578, 0.018198808655142784, -0.013672448694705963, 0.03674442321062088, -0.02931884117424488, -0.006206006743013859, 0.010615219362080097, 0.05673376843333244, -0.01300798635929823, -0.026441175490617752, 0.026787446811795235, 0.05335872620344162, 0.028741881251335144, -0.0010418335441499949, -0.02107682265341282, 0.061929237097501755, 0.036964286118745804, -0.051414139568805695, -0.00593812670558691, -0.022178618237376213, -0.03347374126315117, 0.05115028843283653, 0.06278824061155319, 0.03394119814038277, -0.034102026373147964, 0.06541867554187775, -0.02924664504826069, 0.02030870132148266, -0.031165486201643944, 0.08297185599803925, 0.06108827143907547, 0.05360617861151695, 0.0003537620650604367, -0.0036646148655563593, 0.03636552393436432, -0.028206082060933113, -0.08776289969682693, -0.012514995411038399, -0.01661190204322338, -0.0644996240735054, -0.0009443113231100142, 0.027142498642206192, -0.0423198863863945, 0.02420530654489994, -0.01004974078387022, -0.06054802983999252, 0.041648395359516144, 0.02648644708096981, 0.015541205182671547, -0.00007958122296258807, -0.008256339468061924, 0.017071586102247238, -0.027370451018214226, 0.02907753363251686, -0.0057410551235079765, -0.044376224279403687, 0.03208331763744354, -0.06677450984716415, -0.05970005691051483, 0.005449037998914719, 0.060169562697410583, 0.04695746302604675, 0.042082447558641434, 0.01735140196979046, 0.018123744055628777, -0.03397519141435623, 0.016790859401226044, 0.07509156316518784, 0.05161646008491516, 0.0020518607925623655, -0.01834503747522831, 0.03384430706501007, 0.017078517004847527, 0.001217733952216804, -0.017993943765759468, -0.0717104971408844, 0.010842368006706238, 0.047069624066352844, 0.0035348788369446993, -0.024706749245524406, 0.042411815375089645, -0.03746851161122322, 0.003921418450772762, -0.007235648110508919, -0.018868757411837578, -0.012603038921952248, -0.030407188460230827, 0.030816802754998207, -0.005566231440752745, -0.004999249707907438, -0.05424490198493004, 0.03169794753193855, -0.0094881821423769, 0.0519016832113266, 0.010345611721277237, 0.031719572842121124, 0.04262024909257889, -0.006558428984135389, -0.037492673844099045, -0.038553450256586075, -0.01757131516933441, 0.02446831203997135, 0.012341387569904327, 0.052188724279403687, -0.0013143300311639905, -0.006252721417695284, -0.05003873631358147, -0.06288322806358337, -0.055429816246032715, 0.003454207442700863, 0.01300311740487814, 0.01567559689283371, -0.010856453329324722, -0.043978251516819, 0.01098785363137722, 0.005802445113658905, -0.05215267837047577, 0.049134910106658936, 0.059775203466415405, 0.06759419292211533, 0.03809664025902748, -0.03521490842103958, 0.11098919063806534, 0.06833004206418991, 0.03937487676739693, 0.01265669520944357, -0.028199752792716026, -0.007602945435792208, 0.014509117230772972, 0.04953698441386223, 0.057162631303071976, -0.05188365653157234, 0.01588023640215397, 0.10518883168697357, -0.004223523195832968, 0.021142369136214256, -0.011602133512496948, 0.01506834477186203, 0.050680745393037796, 0.003634145250543952, 0.007347587961703539, 0.04967864230275154, -0.043044313788414, 0.021501043811440468, -0.0243175458163023, 0.0236784927546978, -0.0007161736721172929, -0.024215001612901688, -0.010143033228814602, 0.016458744183182716, 0.015290838666260242, 0.025491930544376373, 0.0420401357114315, 0.045098233968019485, 0.04718651995062828, -0.03270215541124344, -0.04942331463098526, 0.06283391267061234, 0.06887227296829224, 0.035375796258449554, 0.012482292018830776, -0.03371504694223404, 0.027544477954506874, -0.009850314818322659, -0.029058394953608513, 0.04439924657344818, -0.042369913309812546, -0.015841487795114517, -0.021521251648664474, 0.004083248320966959, 0.030129415914416313, 0.01911935582756996, -0.06337343901395798, -0.020199300721287727, -0.02205856703221798, 0.03205081820487976, 0.004538953769952059, -0.013176885433495045, 0.06047951057553291, -0.051989391446113586, -0.030234957113862038, 0.013382460922002792, 0.006852216552942991, -0.015495922416448593, -0.03408699110150337, 0.03934571146965027, 0.03298017382621765, -0.03664099797606468, -0.02743164822459221, 0.12254343926906586, 0.047800298780202866, 0.032980840653181076, 0.03615645691752434, -0.00022569269640371203, 0.03142660856246948, 0.022881602868437767, 0.07393752783536911, 0.004469406325370073, -0.03234150633215904, 0.010460997000336647, -0.034145914018154144, -0.06089514121413231, 0.00532934395596385, 0.0003659441426862031, 0.03408059850335121, -0.030300049111247063, -0.042294081300497055, 0.00040657122735865414, 0.019809577614068985, -0.00033165368949994445, -0.04831530526280403, -0.05016329884529114, -0.03975364938378334, 0.03859015554189682, -0.0251811221241951, 0.012093630619347095, -0.024998877197504044, 0.03387836739420891, 0.04061984643340111, 0.0405295193195343, 0.008091887459158897, -0.007501508574932814, -0.04896547272801399, -0.024540407583117485, 0.004653096664696932, 0.023198364302515984, 0.03253619000315666, 0.018417242914438248, 0.015332065522670746, -0.008477714844048023, 0.016446128487586975, -0.042292382568120956, -0.018347149714827538, -0.0160637479275465, -0.009481356479227543, -0.020987113937735558, 0.019520467147231102, 0.028295187279582024, -0.0667886808514595, -0.016902128234505653, 0.02908087708055973, -0.031238557770848274, -0.0468040369451046, 0.05779871717095375, -0.03975182771682739, -0.01941368170082569, 0.01601102203130722, 0.05295345559716225, 0.010780259035527706, -0.07047683745622635, -0.04434336721897125, -0.05367182940244675, -0.013689654879271984, 0.039760176092386246, 0.014168922789394855, 0.06370019167661667, 0.011803698725998402, -0.029046587646007538, -0.04584096372127533, -0.05584511533379555, 0.0049788025207817554, -0.06470874696969986, 0.013021549209952354, 0.017181316390633583, 0.014494992792606354, 0.007379611022770405, 0.011639740318059921, 0.03150227293372154, 0.009967764839529991, -0.060324911028146744, 0.033960822969675064, -0.008476944640278816, 0.06821238994598389, -0.005574412643909454, -0.044932108372449875, 0.048644762486219406, -0.026582514867186546, -0.012918099761009216, -0.09819810092449188, 0.004376788157969713, 0.03797908499836922, -0.07041241973638535, -0.020267201587557793, -0.00038288155337795615, -0.0158398300409317, -0.0035319547168910503, 0.03136209398508072, 0.02530308999121189, 0.013559690676629543, 0.05223391577601433, -0.008501634933054447, 0.012031976133584976, 0.00714586116373539, 0.010100295767188072, 0.043126244097948074, 0.03828968480229378, 0.001898000598885119, -0.07951828092336655, -0.06429533660411835, 0.043700531125068665, 0.01694324240088463, 0.07379817217588425, 0.0378003753721714, -0.010103029198944569, 0.03449699655175209, -0.031623341143131256, 0.051331669092178345, -0.01937555894255638, -0.023891853168606758, 0.010519120842218399, -0.052835237234830856, 0.06101526319980621, 0.02977249212563038, -0.01113036833703518, -0.010124845430254936, -0.0076018813997507095, -0.03282242640852928, 0.04442208260297775, -0.06776579469442368, 0.018763886764645576, -0.009980232454836369, -0.005689793266355991, -0.017328914254903793, -0.05837375298142433, 0.020814670249819756, 0.013190452009439468, 0.039652466773986816, -0.01576928049325943, 0.0006086172652430832, 0.025485428050160408, 0.004426696337759495, -0.03488795459270477, 0.008215661160647869, -0.026310252025723457, 0.006330348085612059, -0.008178741671144962, -0.025531524792313576, -0.0073831877671182156, 0.024655763059854507, 0.00194998097140342, 0.009279563091695309, 0.011778341606259346, -0.07352301478385925, 0.049382440745830536, 0.004616167861968279, -0.008387823589146137, -0.041596412658691406, 0.03168134391307831, 0.015136271715164185, 0.007270982023328543, -0.038346920162439346, 0.0177618358284235, -0.038239650428295135, -0.020273927599191666, -0.02198699116706848, -0.013790564611554146, -0.06465613842010498, 0.036222122609615326 ]
<p>To external fields(H, - H) not equal to each other are acting on that material. <strong>Based on the hysteresis loop</strong> what would be the result? The hysteresis area of that materials is very narrow(i.e easy to magnetize &amp; demagnetize) H = 1000 A/m and, - H = 500 A/m. I know they are both vectors so it would be H - H = H(total). However, the material's coercively is 0.1 A/m.</p> <p>The thing is I can't imagine this condition properly, because both fields are opposing each other, and that ferromagnetic material is placed in-between them both. What would be the result? </p> <p>The material responds based on it's hysteresis... H points on the hysteresis loop. Why is it incorrect to state magnetization = 0?</p> <p>I'm relating this to an object that has to forces acting on it, they are both on opposite directions. F1 = 10N F2= 5N [x]= is the object. 10N ->[x]&lt;- 5N = 5N ->[x] Although it makes sense... The hysteresis loop changes everything. Magnetization depends on how the material reacts. The material could become magnetized and fully saturated at 100A/m, now we have both of those conditions... So M should = zero?!</p> <p>To picture what I mean, please take a look at this: <a href="http://uk.tdk-lambda.com/content/glossary/128522219667677500_Hysteresis%20Loop%20image.png" rel="nofollow">http://uk.tdk-lambda.com/content/glossary/128522219667677500_Hysteresis%20Loop%20image.png</a></p> <p>The two points on the loop on the H axis are 100 A/m(that is the force needed to magnetize the material), however, the field applied H = 1000 A/m and - H = 500 A/m</p> <p>Hope it helps!</p>
g8396
[ 0.03618409484624863, 0.0026031213346868753, -0.013188626617193222, -0.03160499408841133, 0.04953323304653168, 0.008451519533991814, 0.018060291185975075, 0.017987368628382683, -0.02548750676214695, -0.008758369833230972, -0.031127141788601875, 0.004297182895243168, 0.012039906345307827, -0.011128654703497887, 0.0046753231436014175, 0.014938228763639927, 0.00951931532472372, 0.011306301690638065, 0.01605864427983761, 0.011344305239617825, 0.007320920471101999, 0.049237802624702454, -0.0013625721912831068, -0.016326885670423508, -0.031749043613672256, -0.014726728200912476, 0.03340849280357361, -0.011415768414735794, -0.0578622929751873, -0.0052719274535775185, -0.01724979281425476, -0.008171246387064457, 0.03619520738720894, -0.07103823125362396, -0.05437518283724785, -0.02119838446378708, -0.025759553536772728, 0.0582854226231575, 0.013389138504862785, 0.011903767473995686, -0.0069196028634905815, 0.0014282901538535953, 0.06924166530370712, -0.04924171790480614, 0.0007988466531969607, -0.031400226056575775, -0.04370711371302605, 0.008622008375823498, 0.031090596690773964, -0.0070680854842066765, -0.06249048933386803, 0.042608391493558884, 0.0915222093462944, -0.08149372786283493, 0.07720495015382767, 0.01413667295128107, 0.03704957291483879, -0.024298356845974922, 0.06940659135580063, -0.007635632995516062, -0.0356072336435318, 0.020716702565550804, -0.030635004863142967, 0.009086187928915024, -0.007941901683807373, 0.05029432848095894, -0.053178224712610245, -0.021052921190857887, -0.027049090713262558, 0.016249099746346474, -0.020161274820566177, -0.031496811658144, -0.013413104228675365, -0.03781360760331154, -0.05658141151070595, 0.03324110433459282, 0.015436358749866486, -0.01234095636755228, 0.06890089809894562, -0.02331048622727394, -0.07301577180624008, -0.04926609992980957, 0.024964651092886925, 0.0359979048371315, 0.05443058907985687, 0.02200033701956272, 0.020599549636244774, -0.00039393987390212715, -0.01732666790485382, 0.04433060064911842, 0.013310771435499191, 0.019191686064004898, 0.04588516056537628, 0.037712451070547104, -0.03597032278776169, -0.0043306597508490086, 0.01819770410656929, 0.04744061082601547, -0.02379515767097473, -0.02652500756084919, -0.02744642272591591, -0.02532920427620411, -0.05553146451711655, -0.03820940852165222, -0.00822652131319046, 0.022929122671484947, 0.11910709738731384, 0.05299069732427597, -0.07389581203460693, -0.01726493239402771, 0.0017365732928737998, 0.018904510885477066, -0.10457772761583328, -0.04983257129788399, -0.04012436047196388, -0.03910055756568909, 0.03040553815662861, -0.03624577075242996, 0.002114158123731613, 0.01907840184867382, 0.059582676738500595, -0.025064971297979355, 0.0368267260491848, 0.10465490072965622, -0.02796374447643757, -0.03499552607536316, -0.027608495205640793, 0.03253984823822975, 0.028339669108390808, -0.0689435824751854, 0.012543357908725739, -0.0248417966067791, 0.07162727415561676, -0.014936696738004684, -0.03595010191202164, -0.029196985065937042, 0.007934803143143654, 0.0022626370191574097, -0.01368592120707035, -0.007281013764441013, -0.033688947558403015, -0.037097346037626266, -0.030257591977715492, -0.015239864587783813, -0.03092007339000702, 0.01886160299181938, 0.014910418540239334, -0.009712438099086285, 0.06382674723863602, -0.013670828193426132, -0.004655114375054836, 0.09414513409137726, -0.02286081202328205, 0.04130564257502556, 0.017108116298913956, -0.008068401366472244, 0.03449147194623947, 0.01006116159260273, 0.0141239482909441, -0.015937747433781624, 0.07957868278026581, 0.011597491800785065, 0.0329129584133625, 0.012819419614970684, -0.03006359562277794, 0.020503150299191475, 0.06304693967103958, 0.0006941086612641811, -0.010071768425405025, -0.0539325512945652, -0.0732492133975029, -0.009662535041570663, 0.006212062668055296, 0.005776551552116871, 0.04651531204581261, 0.04169127345085144, 0.04883694276213646, -0.046524375677108765, 0.008057588711380959, 0.04304398223757744, 0.016927622258663177, 0.05215662345290184, 0.025510312989354134, 0.029255907982587814, -0.008543490432202816, -0.023085642606019974, 0.01314160693436861, 0.07206903398036957, -0.07490154355764389, 0.0074015515856444836, -0.043945956975221634, -0.002297235419973731, -0.04206686094403267, 0.03896985575556755, -0.04009217768907547, -0.021051554009318352, 0.007849699817597866, -0.04019957780838013, 0.0007527374546043575, -0.05706118419766426, 0.001153576304204762, 0.00005372330633690581, 0.04795841500163078, 0.001290145330131054, -0.006975832860916853, -0.01799919269979, 0.026254821568727493, 0.01642426662147045, 0.04804180562496185, 0.0038611802738159895, 0.008808905258774757, 0.012241164222359657, -0.044130776077508926, 0.0506315678358078, -0.014333882369101048, -0.001708112540654838, 0.006075809244066477, 0.011418996378779411, -0.05609651654958725, -0.018232308328151703, 0.008896023966372013, 0.024809101596474648, 0.04785546660423279, 0.01924528367817402, -0.09307006001472473, -0.01888294517993927, 0.03628740832209587, 0.04141445457935333, -0.006083889864385128, -0.004481677431613207, 0.011393334716558456, 0.002531982958316803, -0.004234198480844498, -0.06651587784290314, 0.036944661289453506, -0.007899412885308266, -0.03325159102678299, 0.027957366779446602, -0.03791193291544914, -0.021516839042305946, 0.005427117925137281, 0.016860349103808403, -0.011740117333829403, -0.009821252897381783, 0.04091966524720192, -0.05070658400654793, 0.07212547957897186, 0.03267036750912666, -0.02340725250542164, 0.030004698783159256, 0.02537272870540619, -0.029376473277807236, 0.01097375899553299, 0.0038826900999993086, 0.04023713991045952, -0.021455563604831696, -0.036684248596429825, 0.01994587853550911, -0.04277920350432396, -0.04021867364645004, -0.006398768164217472, -0.0253774244338274, 0.059667300432920456, 0.04999662935733795, -0.07185091823339462, -0.024183016270399094, -0.02076861448585987, -0.05190102383494377, 0.016844529658555984, -0.041756801307201385, -0.02623073384165764, 0.025890983641147614, 0.03178080543875694, 0.07047926634550095, 0.011284262873232365, -0.012013410218060017, -0.01063550729304552, 0.0025246685836464167, 0.044410694390535355, 0.02972184494137764, -0.028096728026866913, 0.04082212969660759, 0.01985625922679901, 0.02451549470424652, 0.02953641675412655, -0.006152487825602293, -0.009782163426280022, 0.016181306913495064, -0.015827396884560585, 0.027091141790151596, -0.08499360829591751, 0.0483824759721756, 0.0450797863304615, -0.018699416890740395, 0.0003668429853860289, 0.04011755436658859, 0.013177110813558102, -0.04722614958882332, -0.0005217268480919302, 0.07732291519641876, 0.007635798770934343, -0.01608426123857498, 0.01763891614973545, -0.024502677842974663, 0.02236238867044449, -0.03457590565085411, -0.0386560782790184, -0.0968954935669899, -0.016851967200636864, 0.03198375925421715, -0.04746439680457115, -0.006107164081186056, -0.009990453720092773, -0.07209105044603348, 0.0178749468177557, 0.02891276404261589, 0.018042810261249542, -0.026916954666376114, 0.011837517842650414, -0.0405714251101017, 0.018989257514476776, -0.03314237296581268, 0.03264874964952469, 0.025807946920394897, -0.016490081325173378, 0.03315602242946625, -0.00009384778968524188, -0.0073282173834741116, -0.02423788607120514, -0.009806002490222454, 0.04202277958393097, 0.03678985312581062, -0.01074866484850645, -0.02802223339676857, -0.05346935987472534, -0.023444676771759987, -0.04634268209338188, 0.011001755483448505, 0.024616865441203117, 0.024370301514863968, -0.029038311913609505, -0.024584364145994186, -0.028298376128077507, 0.02498832903802395, 0.01649690419435501, 0.08606278896331787, 0.0005513166543096304, -0.006045675836503506, 0.036651402711868286, 0.013688241131603718, 0.02979065105319023, 0.0012433859519660473, 0.07170078158378601, 0.003488255199044943, 0.008657470345497131, -0.0038123575504869223, 0.05198029428720474, 0.00124380923807621, -0.01831338182091713, -0.004385818261653185, 0.016206543892621994, 0.00446918373927474, -0.030278027057647705, -0.021574046462774277, -0.012896545231342316, 0.06665131449699402, 0.03170304745435715, 0.030498038977384567, -0.029709618538618088, -0.039410922676324844, 0.03414393216371536, -0.05892631411552429, -0.03411994129419327, 0.0018653171136975288, 0.0016044131480157375, -0.07708906382322311, 0.02654135599732399, -0.023359954357147217, -0.005042791832238436, 0.025892632082104683, 0.03961051255464554, 0.08243276178836823, -0.02604721300303936, 0.061362575739622116, 0.01581992581486702, 0.0034385661128908396, -0.004907330963760614, 0.059006862342357635, -0.03782757744193077, -0.03146322816610336, -0.0142968175932765, -0.030732162296772003, 0.00472173560410738, 0.01115474570542574, 0.040291186422109604, -0.024519629776477814, 0.03504730761051178, 0.012781009078025818, 0.02473587915301323, -0.021797824651002884, 0.0289932694286108, 0.044476911425590515, -0.04122202843427658, -0.004657156299799681, -0.0017549500335007906, -0.026019303128123283, -0.021553773432970047, -0.03400302678346634, 0.012156263925135136, -0.018596911802887917, 0.020313216373324394, -0.0559823140501976, -0.012029627338051796, -0.07298809289932251, 0.04298309236764908, 0.005910302512347698, 0.013811195269227028, 0.0672101378440857, 0.016233325004577637, -0.06962700188159943, 0.01845034584403038, 0.05565064400434494, -0.00018632876162882894, -0.03475739806890488, -0.0019212969345971942, 0.04492161422967911, -0.014596866443753242, 0.027640325948596, 0.04043381288647652, -0.04651251807808876, -0.007113639730960131, 0.0652996301651001, -0.025751179084181786, -0.0017003484535962343, -0.06014689430594444, 0.05011169984936714, -0.05661166459321976, 0.046352751553058624, 0.021620769053697586, 0.024422649294137955, 0.011762844398617744, 0.009677164256572723, -0.0007437728345394135, 0.008972765877842903, -0.04237842932343483, 0.04002846032381058, -0.05540074035525322, -0.000704095175024122, -0.044556617736816406, -0.11008397489786148, -0.06603888422250748, -0.014414705336093903, 0.0024111659731715918, -0.011086390353739262, -0.028256557881832123, -0.009910407476127148, 0.048200055956840515, 0.042975567281246185, -0.030290931463241577, 0.028801284730434418, -0.010678865015506744, -0.041200075298547745, -0.07172268629074097, 0.004076245706528425, -0.0026093008928000927, 0.041943442076444626, 0.0002461001859046519, -0.028824031352996826, -0.008821162395179272, 0.037845976650714874, 0.04685778170824051, 0.0085006607696414, 0.042202215641736984, 0.024305611848831177, 0.07704571634531021, 0.04265109822154045, 0.005733122117817402, -0.03969897702336311, -0.002817489905282855, -0.0617673322558403, -0.055151697248220444, 0.0006770659238100052, 0.08105865865945816, 0.021677911281585693, -0.03193916752934456, -0.004128619097173214, -0.04819551855325699, 0.020213739946484566, 0.01886403001844883, 0.007155373692512512, 0.011560733430087566, 0.0033685367088764906, -0.03031828999519348, -0.038277577608823776, -0.0044618695974349976, -0.03366703540086746, -0.01807905174791813, 0.002426953287795186, -0.0617995411157608, -0.029175765812397003, -0.06541051715612411, -0.003293575020506978, -0.014701642096042633, 0.013496088795363903, -0.007471190299838781, 0.05999443307518959, 0.07418423891067505, -0.016144070774316788, 0.09084732085466385, -0.026366446167230606, -0.030194463208317757, 0.05193491280078888, 0.04560023173689842, -0.026156006380915642, -0.0032727434299886227, 0.021836595609784126, 0.004846727009862661, 0.0005707130767405033, 0.004831170663237572, -0.01196257583796978, 0.027131851762533188, 0.020212583243846893, -0.01265823096036911, -0.0785103291273117, 0.020284531638026237, 0.0003059040172956884, -0.026417234912514687, -0.04376785457134247, -0.009230528958141804, 0.06328810006380081, -0.004888783674687147, 0.04881378635764122, -0.010845225304365158, -0.01855856366455555, 0.024696817621588707, -0.05427113175392151, 0.09046400338411331, -0.03750262409448624, 0.03415687009692192, 0.051649902015924454, 0.007956817746162415, -0.021830862388014793, 0.03485211357474327, 0.047802191227674484, -0.047500722110271454, -0.018829500302672386, -0.03142000734806061, -0.07031101733446121, 0.009725461713969707, -0.022576287388801575, -0.08290063589811325, 0.015652330592274666, 0.03929227218031883, 0.0020784290973097086, 0.004483405500650406, 0.07183492928743362, 0.032993581146001816, -0.035514164716005325, -0.009719467721879482, -0.04257972165942192, 0.053062792867422104, -0.001038679969497025, 0.01755966804921627, 0.02546675316989422, 0.03805270418524742, -0.019397271797060966, -0.030874144285917282, 0.011959913186728954, 0.07196589559316635, -0.001737752347253263, -0.002179711824283004, -0.0026816013269126415, -0.014379668980836868, -0.02041313610970974, -0.00657686498016119, 0.02884119562804699, -0.031465642154216766, -0.036896273493766785, -0.04766537621617317, 0.030526526272296906, -0.023211769759655, -0.004296954721212387, 0.02690759487450123, 0.06148143485188484, 0.01610330492258072, 0.02682703360915184, -0.052299290895462036, -0.0677373930811882, 0.05965479835867882, -0.015256949700415134, -0.02631693333387375, 0.010523295029997826, -0.03562971204519272, -0.06344626843929291, 0.003049708902835846, 0.01611850969493389, -0.044465869665145874, 0.011378783732652664, -0.03980327025055885, 0.03484853729605675, 0.012126910500228405, -0.019026050344109535, 0.034610264003276825, -0.08642227202653885, 0.03227752074599266, 0.03570573031902313, -0.021718524396419525, 0.00996367633342743, 0.008311407640576363, -0.0235856082290411, -0.022219296544790268, -0.05429293215274811, -0.015764761716127396, 0.014521011151373386, 0.07937153428792953, 0.008631646633148193, 0.00858262274414301, 0.014614667743444443, -0.021977128461003304, -0.01994028501212597, -0.03774882107973099, -0.010436329059302807, 0.010524510405957699, -0.030178196728229523, 0.00588760431855917, 0.05855465307831764, -0.030335228890180588, 0.03140464052557945, 0.026074402034282684, 0.04167899489402771, -0.0062273540534079075, 0.0054966663010418415, -0.007379853632301092, 0.046412430703639984, 0.0037121311761438847, 0.053617123514413834, 0.006599397864192724, 0.031715333461761475, 0.03439567983150482, 0.04893045499920845, 0.003921192605048418, 0.032606884837150574, 0.0032371466513723135, 0.023410266265273094, 0.001829679822549224, -0.050613805651664734, -0.012262306176126003, 0.0015074413968250155, -0.0465875007212162, 0.054386988282203674, -0.019198546186089516, 0.036316003650426865, -0.06725454330444336, -0.01897503063082695, -0.04115189239382744, 0.05004344508051872, 0.04539000988006592, -0.0061366138979792595, 0.037508703768253326, 0.0019368288340047002, -0.07263178378343582, -0.04085813835263252, -0.04994906485080719, -0.008105170913040638, 0.05123872309923172, 0.030512822791934013, 0.016517044976353645, 0.009231706149876118, -0.013549654744565487, -0.008385272696614265, -0.02022239938378334, -0.03313463553786278, -0.005475721787661314, 0.020683137699961662, -0.0001244428422069177, -0.03987300023436546, -0.0018805109430104494, 0.011416940949857235, 0.013075594790279865, -0.001526578445918858, 0.022719772532582283, 0.015133659355342388, 0.005391874350607395, -0.003421114757657051, -0.04118658974766731, -0.0063001844100654125, -0.09077556431293488, 0.022855721414089203, 0.019801005721092224, 0.006737401243299246, 0.015544801019132137, 0.013316011056303978, 0.04454107955098152, 0.004066166467964649, -0.08699452131986618, 0.03908694162964821, -0.0007817743462510407, 0.04111478850245476, 0.005161532666534185, -0.0273502878844738, -0.001384529983624816, -0.0019717009272426367, -0.038099296391010284, 0.05811726674437523, 0.03311849385499954, 0.013733766973018646, -0.03519374504685402, 0.010388676077127457, -0.02943940833210945, -0.0015956248389557004, 0.003415124025195837, 0.047512684017419815, -0.003859632881358266, -0.040429357439279556, -0.004929146263748407, 0.03157935291528702, -0.0434800423681736, -0.04160558804869652, 0.008674845099449158, 0.014667210169136524, -0.08733778446912766, 0.012474755756556988, -0.006098086480051279, -0.016632048413157463, -0.012254316359758377, -0.027098199352622032, -0.009051908738911152, 0.019681552425026894, -0.00990607962012291, 0.025165576487779617, -0.01391020230948925, -0.03900451213121414, -0.011720077134668827, -0.02315739169716835, -0.031607821583747864, -0.00632397411391139, 0.011140606366097927, -0.06007814407348633, -0.04980495572090149, 0.0005206084460951388, -0.009845924563705921, -0.0884154886007309, -0.04033798724412918, -0.01458209939301014, 0.027201708406209946, 0.015146598219871521, -0.027430012822151184, 0.09145203232765198, 0.010968001559376717, -0.04107321798801422, -0.0066784825176000595, -0.03613197058439255, -0.053704142570495605, 0.024759873747825623, 0.03684820979833603, -0.01824573054909706, -0.04514315724372864, 0.018490860238671303, 0.07547060400247574, 0.02671423926949501, -0.016361845657229424, 0.01355873141437769, -0.05646318942308426, 0.044069334864616394, -0.009847299195826054, 0.014953149482607841, -0.0427265465259552, 0.03720710799098015 ]
<p>I am trying to determine the self-inductance of a toroidal coil of mean radius $R$ with $N$ loops of radius $a$ with a current $I$ flowing within them.</p> <p>I have calculated the magnetic field by noting that it must be in the circumferential direction (i.e. in the $\hat{\boldsymbol{\theta}}$ direction) and then using Ampéres Law to get:</p> <p>$$\oint_{\partial \Sigma} \mathbf{B}\cdot \mathrm{d}\boldsymbol{\ell}=\mu_{0}I_{\text{enc}} \implies \mathbf{B}=\frac{\mu_{0}NI}{2\pi r}\hat{\boldsymbol{\theta}}$$</p> <p>I know that we can get the self-inductance $L$ by using the relation:</p> <p>$$\Phi=LI$$</p> <p>And we know that:</p> <p>$$\Phi=N\iint_{\Sigma}\mathbf{B}\cdot\mathrm{d}\mathbf{A}$$</p> <p>Where $\Sigma$ is the area of a single loop. However, I am not sure how evaluate the surface integral, I'm not sure if perhaps I should be using the mean radius $R$ to give us:</p> <p>$$\Phi=\frac{\mu_{0}N^{2}}{2\pi R}\pi a^{2}I=\frac{\mu_{0}a^{2}N^{2}}{2R}I$$</p> <p>Or if I need to evalute the integral in a more complete way?</p>
g8397
[ 0.001717515755444765, 0.01839428022503853, -0.021561095491051674, -0.027735214680433273, 0.031167075037956238, -0.027555309236049652, 0.05515052005648613, -0.01810259185731411, -0.021149924024939537, 0.06322100013494492, -0.0451987199485302, 0.04123510420322418, -0.033470556139945984, 0.082522913813591, 0.05707734823226929, -0.019958127290010452, -0.009556551463901997, -0.004924165550619364, 0.08974611759185791, 0.006725022103637457, -0.021208299323916435, -0.03181830421090126, -0.0038533834740519524, 0.055699754506349564, 0.025200193747878075, -0.022338049486279488, 0.014271998777985573, 0.0044755470007658005, 0.020660512149333954, -0.028966033831238747, 0.002480720868334174, 0.05766259506344795, 0.0755142867565155, -0.08601414412260056, -0.05372598022222519, 0.010113643482327461, -0.01229055691510439, 0.03634684905409813, 0.04107510671019554, -0.03202185779809952, 0.03355257213115692, -0.03433939069509506, 0.057492487132549286, 0.013037517666816711, 0.047346632927656174, -0.01490026619285345, -0.0662812888622284, 0.07355897128582001, 0.009167971089482307, 0.00937948189675808, -0.013818611390888691, 0.03265882283449173, 0.06593456119298935, -0.016852153465151787, -0.04989394173026085, 0.004104487132281065, -0.0016016836743801832, -0.026337429881095886, 0.006549092475324869, 0.03291899338364601, 0.00034731265623122454, 0.019126970320940018, -0.05013088136911392, -0.01766972988843918, 0.024631092324852943, 0.058231234550476074, -0.0028738738037645817, 0.02137758582830429, -0.05513177439570427, 0.035645343363285065, 0.005108908284455538, -0.05715560540556908, 0.02858690917491913, -0.0739818885922432, -0.061253201216459274, 0.03987068310379982, 0.04419142007827759, 0.009482771158218384, 0.05976776406168938, -0.009771675802767277, -0.0641736313700676, -0.041713692247867584, -0.04198712483048439, 0.05379693582653999, 0.02244209498167038, -0.027296079322695732, 0.020186936482787132, 0.005262216553092003, 0.010195662267506123, -0.002220802241936326, -0.01006559282541275, 0.010444939136505127, 0.04562868922948837, -0.012554445303976536, 0.06037285178899765, -0.03239631652832031, 0.023445885628461838, 0.023559823632240295, -0.05584518983960152, 0.03063662350177765, -0.03339765965938568, 0.015032620169222355, -0.025152361020445824, 0.026266315951943398, -0.04636508226394653, 0.04513402283191681, -0.028524626046419144, 0.017626788467168808, 0.03900671377778053, -0.014104673638939857, -0.04121999070048332, -0.03989862650632858, 0.00652358029037714, 0.055085521191358566, 0.004760701674968004, 0.00032120925607159734, 0.047093465924263, -0.0017145801102742553, 0.021101031452417374, 0.08911088854074478, -0.023742934688925743, 0.007528382353484631, 0.038212139159440994, 0.07865376770496368, 0.013455991633236408, 0.01267855055630207, -0.059489499777555466, 0.03497060015797615, 0.07456804066896439, 0.01996428705751896, -0.01926424726843834, -0.0463525764644146, -0.01400285679847002, -0.003202645340934396, 0.021755680441856384, 0.01946623995900154, -0.08762750774621964, -0.007031164597719908, -0.043302010744810104, -0.005915496498346329, 0.014270227402448654, -0.024180911481380463, -0.005908144637942314, 0.013049004599452019, -0.05463381111621857, 0.0030023963190615177, 0.009143189527094364, -0.09584389626979828, 0.027277687564492226, -0.012002794072031975, 0.05371427908539772, 0.05302678421139717, -0.027557868510484695, -0.02164066955447197, 0.00005610282823909074, 0.010643980465829372, 0.012807938270270824, 0.016678061336278915, 0.07141987234354019, -0.00872060563415289, 0.023268042132258415, -0.015024645254015923, 0.026817062869668007, 0.006174186244606972, -0.06685739010572433, 0.025285160169005394, 0.0835208147764206, -0.007015630137175322, -0.033791761845350266, -0.03102981485426426, -0.008988218382000923, 0.022397328168153763, 0.034881509840488434, 0.004533212166279554, -0.0541779026389122, 0.010360334068536758, -0.0024476873222738504, -0.017008306458592415, 0.001994238467887044, 0.11114657670259476, 0.006459364201873541, -0.030275950208306313, 0.03787342831492424, -0.017299706116318703, 0.000687074032612145, -0.019904717803001404, -0.04672371223568916, -0.0008163616294041276, -0.028884340077638626, -0.040058404207229614, -0.03173379972577095, 0.03728847578167915, 0.013417425565421581, 0.011745626106858253, -0.011777246370911598, 0.038318779319524765, 0.019597714766860008, -0.0669422522187233, -0.02264579012989998, -0.08096704632043839, -0.010941680520772934, -0.016433093696832657, 0.08470898121595383, 0.052458301186561584, -0.05111048370599747, -0.037358928471803665, 0.0033345422707498074, 0.03908739611506462, 0.06131700053811073, 0.002057134173810482, -0.01567724160850048, -0.03992567956447601, -0.024066103622317314, -0.00743858003988862, -0.010088300332427025, 0.001035252120345831, 0.014389359392225742, 0.007513534277677536, -0.044408977031707764, -0.007049043197184801, 0.037230752408504486, -0.019537827000021935, 0.07830747961997986, -0.0006021871231496334, -0.046491727232933044, 0.01984955184161663, 0.009941212832927704, 0.017858510836958885, 0.00047805564827285707, -0.02013455331325531, -0.06398145854473114, -0.03834975138306618, -0.005859961733222008, -0.039282068610191345, -0.008318519219756126, 0.05850806459784508, 0.01167853269726038, -0.021852578967809677, -0.030786924064159393, -0.004944256506860256, 0.03710842877626419, -0.01178805623203516, 0.01295954454690218, -0.014569111168384552, -0.028719697147607803, 0.004310931079089642, 0.04516123980283737, 0.007536650635302067, -0.020577924326062202, -0.02687150612473488, 0.018750449642539024, -0.015982531011104584, -0.00066336989402771, 0.013636250980198383, -0.019165193662047386, 0.03978898376226425, 0.0201494749635458, 0.0047643911093473434, 0.01605076715350151, -0.005951298866420984, -0.03063996136188507, -0.0704154372215271, 0.022252343595027924, 0.048756975680589676, -0.05184033885598183, 0.002132409019395709, -0.05532102286815643, -0.0520583800971508, 0.05274995416402817, 0.008445733226835728, 0.013364102691411972, 0.06179025024175644, -0.008480070158839226, 0.01944103091955185, 0.07582855224609375, -0.02509058266878128, 0.0006213756860233843, 0.031855277717113495, 0.04092622175812721, 0.054110631346702576, -0.005717824213206768, -0.005136760883033276, 0.0067829713225364685, 0.06784877926111221, -0.014106004498898983, -0.052665676921606064, 0.06335588544607162, 0.05037355422973633, 0.01799781620502472, 0.017603088170289993, -0.0038893637247383595, -0.04141964763402939, 0.01576676033437252, -0.01633240096271038, 0.040913403034210205, 0.03750583902001381, -0.0022633220069110394, -0.06801769137382507, 0.08419893682003021, 0.040163248777389526, 0.02752053737640381, 0.0008829405414871871, -0.07272754609584808, -0.04223741218447685, -0.04988034442067146, -0.0022639455273747444, 0.018753619864583015, -0.039261605590581894, 0.011770203709602356, -0.007872805930674076, -0.027754319831728935, 0.03300958871841431, 0.05542534589767456, -0.10265220701694489, 0.006268463097512722, -0.048154521733522415, -0.00982210598886013, 0.0067907776683568954, -0.0007080528303049505, 0.013695137575268745, 0.0002697579620871693, -0.04604051634669304, 0.03172358497977257, 0.009628048166632652, -0.013608883135020733, -0.02548614703118801, -0.016061339527368546, -0.02338886819779873, -0.04684918001294136, -0.06433238089084625, -0.048396769911050797, 0.029402829706668854, 0.01638314314186573, -0.010248174890875816, -0.036543384194374084, -0.0426751933991909, -0.03275361284613609, 0.04066459462046623, -0.013543338514864445, 0.03791513293981552, -0.058179330080747604, -0.07064633071422577, -0.01812412217259407, -0.03288540616631508, -0.026325220242142677, 0.004079710226505995, -0.012314395979046822, 0.06268782913684845, 0.03355199098587036, -0.023038139566779137, 0.06496121734380722, 0.04206472262740135, 0.03896554931998253, -0.025481006130576134, -0.029476584866642952, 0.04504476860165596, 0.023351209238171577, 0.04227201268076897, -0.012596748769283295, -0.012148682028055191, -0.0013593279290944338, -0.06471970677375793, -0.023060325533151627, -0.019585520029067993, -0.023010030388832092, -0.05528923496603966, 0.0034769417252391577, 0.028932344168424606, -0.03133755549788475, -0.025191323831677437, -0.03083675168454647, -0.005763649009168148, 0.006770901381969452, 0.002370152622461319, -0.018413636833429337, -0.038332149386405945, -0.017020097002387047, 0.05940139293670654, -0.02027980051934719, 0.02126871980726719, 0.018623938784003258, 0.052637979388237, -0.04984629899263382, 0.03283187374472618, -0.03596613183617592, -0.014734593220055103, -0.014470775611698627, 0.02291053719818592, -0.01834890991449356, -0.058182813227176666, -0.011579416692256927, -0.007031246554106474, -0.042238011956214905, -0.0687507838010788, 0.010545928031206131, -0.0428369864821434, 0.0630204901099205, 0.005173373501747847, -0.011175152845680714, 0.005462790373712778, 0.01696646586060524, -0.04615536704659462, 0.04997732862830162, 0.01963857375085354, 0.008945072069764137, -0.018575333058834076, 0.0010409754468128085, 0.018612787127494812, 0.0456782802939415, -0.0019902223721146584, -0.04862116649746895, -0.0017825186951085925, 0.021085606887936592, -0.06953246146440506, 0.055213600397109985, 0.010325063951313496, -0.00837788637727499, -0.031898483633995056, -0.014437004923820496, -0.04536500200629234, -0.03793353959918022, -0.09097747504711151, -0.01055331900715828, -0.04465226083993912, -0.09920265525579453, -0.01326267421245575, 0.03203621506690979, 0.020737288519740105, 0.03163071721792221, -0.03611326962709427, -0.04129539430141449, 0.040943801403045654, -0.059980425983667374, -0.06007472053170204, -0.08029777556657791, 0.01337397564202547, -0.022867731750011444, 0.05141420662403107, 0.010028544813394547, 0.017828956246376038, -0.0025263680145144463, 0.013380232267081738, 0.03721698001027107, -0.009498346596956253, -0.014845263212919235, 0.02362613007426262, -0.0603036992251873, -0.010799866169691086, -0.020839979872107506, -0.02051379717886448, -0.0644860491156578, -0.0319133959710598, 0.00769197428599, -0.02003052830696106, -0.03713968023657799, 0.02100404165685177, 0.01975231245160103, 0.019916534423828125, -0.016870666295289993, -0.03229989856481552, -0.03681325912475586, -0.0072732907719910145, -0.02084338665008545, 0.02314521186053753, 0.0013891062699258327, -0.03291813284158707, 0.0010845493525266647, 0.0026795410085469484, 0.012598969973623753, 0.026969345286488533, 0.019220301881432533, 0.055282000452280045, 0.008891264908015728, -0.05111600458621979, 0.004583115689456463, 0.003230718430131674, 0.027853064239025116, 0.0022535056341439486, -0.050863247364759445, -0.015341521240770817, -0.024909518659114838, 0.007542819250375032, -0.011833562515676022, 0.041289377957582474, 0.0303848534822464, 0.05656890571117401, -0.026532288640737534, 0.010349171236157417, -0.02487083151936531, 0.021327774971723557, -0.009230378083884716, 0.06594817340373993, 0.06086919456720352, -0.017986970022320747, -0.03193926811218262, 0.0412626713514328, 0.029865914955735207, -0.013792820274829865, -0.02925366535782814, 0.0072953165508806705, -0.02029857039451599, 0.02666970156133175, -0.04906916245818138, 0.013968255370855331, -0.060555893927812576, 0.09238248318433762, -0.00038498040521517396, 0.00966444332152605, 0.05730695649981499, -0.02273518033325672, 0.042522091418504715, 0.047854870557785034, 0.03741002082824707, -0.05869879201054573, 0.032197240740060806, 0.04019995033740997, -0.03749528154730797, 0.0637136921286583, 0.026788396760821342, 0.017129098996520042, 0.07710713148117065, -0.01684609055519104, -0.003623428288847208, -0.05095336213707924, -0.004030798561871052, 0.015223211608827114, -0.04134964942932129, -0.06940394639968872, 0.09569533169269562, 0.03233062103390694, -0.004858807660639286, 0.04028170555830002, -0.05952337756752968, 0.029461108148097992, 0.022256378084421158, -0.05584950000047684, 0.041348282247781754, 0.01767095923423767, -0.0036270671989768744, 0.025428054854273796, -0.0007142885006032884, 0.005100724752992392, -0.03821851685643196, 0.022980617359280586, -0.04341379553079605, -0.005523987580090761, 0.0258901659399271, -0.04027588292956352, 0.06325217336416245, -0.017712505534291267, -0.05143104866147041, 0.005670398473739624, -0.013014240190386772, 0.016479134559631348, 0.009383386000990868, 0.0017064560670405626, 0.03178952634334564, 0.02430914342403412, -0.005289657972753048, 0.028113067150115967, 0.057905927300453186, -0.05434541404247284, -0.014465323649346828, -0.031939566135406494, 0.01278750505298376, -0.04924658685922623, -0.017726914957165718, -0.015774615108966827, -0.00360525562427938, -0.008870516903698444, 0.0036251882556825876, -0.02464219182729721, -0.0015169756952673197, -0.03809989243745804, 0.07382547110319138, 0.020380832254886627, 0.020437411963939667, 0.027400564402341843, 0.04357554391026497, 0.007207073271274567, -0.031636953353881836, 0.016226930543780327, 0.04480186849832535, -0.023966051638126373, 0.03199783340096474, 0.0007720139692537487, -0.015372052788734436, 0.03668341785669327, 0.05973529443144798, 0.003751950105652213, -0.0005587144405581057, 0.024228475987911224, 0.033828005194664, -0.037632912397384644, 0.014355339109897614, -0.010882272385060787, -0.03365549072623253, -0.004579294007271528, -0.027545204386115074, 0.039282575249671936, -0.006075270939618349, -0.033852722495794296, -0.018582390621304512, -0.026526739820837975, 0.05595526099205017, -0.03498353436589241, -0.0017043589614331722, 0.01270085945725441, -0.05195144936442375, -0.009484891779720783, 0.04631355404853821, 0.03277681767940521, -0.001968896482139826, 0.0013621674152091146, 0.029093004763126373, 0.02639399655163288, -0.03618272393941879, -0.02774815820157528, -0.02684059925377369, -0.006074862089008093, 0.03505583480000496, 0.02565465122461319, -0.011498253792524338, -0.00685194181278348, 0.05451070889830589, 0.02299465797841549, -0.04296048358082771, -0.01375494059175253, 0.04098321869969368, -0.00343644549138844, 0.024621933698654175, 0.03840763494372368, -0.0159640833735466, 0.031630538403987885, 0.10126832872629166, 0.0363059937953949, 0.019408633932471275, -0.05835852771997452, 0.023766299709677696, 0.10408010333776474, -0.04223235324025154, -0.004175151232630014, 0.0010018066968768835, -0.01062539592385292, -0.04003481566905975, -0.10578863322734833, 0.003033367218449712, 0.058553870767354965, -0.02487424574792385, 0.039138320833444595, 0.07660461962223053, 0.03229563683271408, -0.03159445896744728, -0.019880464300513268, -0.03754793107509613, -0.01875472627580166, -0.0012433234369382262, 0.03985223546624184, 0.032973531633615494, -0.029246946796774864, 0.018893757835030556, 0.0007033953443169594, -0.02435017190873623, -0.04256425425410271, 0.09247565269470215, 0.01203098613768816, -0.011101830750703812, 0.0016736248508095741, -0.0038816339801996946, -0.037635594606399536, -0.011754627339541912, -0.02979382872581482, -0.021690145134925842, 0.01143737230449915, -0.047574251890182495, -0.011160096153616905, -0.0002002866385737434, -0.001932485611177981, -0.02706732600927353, 0.015795838087797165, -0.06015511602163315, -0.04217169061303139, -0.0013150029117241502, 0.0030223538633435965, -0.06344478577375412, -0.0350988507270813, -0.03324444591999054, -0.06742056459188461, 0.009699901565909386, 0.0385306291282177, -0.01935584470629692, 0.04001648724079132, -0.0019469623221084476, -0.012481117621064186, 0.022121818736195564, 0.028577163815498352, 0.01147229503840208, 0.029543200507760048, 0.034164585173130035, -0.0015206873649731278, 0.05153932794928551, 0.026985272765159607, 0.01290824729949236, -0.04229537770152092, -0.012665550224483013, 0.039981234818696976, -0.04797084629535675, 0.04864809289574623, -0.04276134446263313, 0.010399896651506424, 0.0036931796930730343, 0.013148181140422821, -0.03301434591412544, -0.013901707716286182, 0.024569250643253326, 0.0039446852169930935, -0.06177568435668945, -0.030315011739730835, 0.029887521639466286, -0.03234989941120148, -0.017946425825357437, -0.000834017526358366, -0.01506358478218317, -0.006081526633352041, -0.02442662976682186, -0.04054838791489601, -0.02086498774588108, 0.0032455958425998688, 0.019359784200787544, -0.040706735104322433, 0.011268886737525463, -0.001335355220362544, -0.04391825571656227, -0.015690281987190247, -0.05095066502690315, 0.0294276624917984, 0.04054944962263107, -0.02471037581562996, 0.007243460509926081, 0.00015183110372163355, 0.04377434775233269, -0.05423268675804138, 0.049795303493738174, 0.003099919995293021, 0.005882106255739927, 0.019144965335726738, -0.03245909884572029, 0.023027395829558372, 0.0010182654950767756, -0.05472106859087944, 0.012061414308845997, 0.021952586248517036, -0.000505733594764024, -0.01225764025002718, 0.020354216918349266, -0.012675520963966846, -0.0060724783688783646, -0.04932091757655144, 0.04283841326832771, 0.06557473540306091, 0.022722380235791206, -0.019205955788493156, -0.022897351533174515, 0.04528861120343208, 0.03247768431901932, -0.05070890486240387, -0.03807014599442482, -0.019583210349082947 ]
<p>What does <a href="http://www.google.com/search?as_q=&amp;as_epq=smooth+dynamical+system" rel="nofollow">smooth dynamical system</a> mean? It is the title of a paper I am supposed to read in non linear systems.</p>
g8398
[ 0.04252385348081589, 0.040401335805654526, 0.008804256096482277, -0.01107015274465084, 0.02100325934588909, -0.04830879345536232, 0.0844680666923523, -0.05498817563056946, -0.024798966944217682, 0.0032766987569630146, 0.014365347102284431, 0.00945979729294777, 0.052916523069143295, 0.04225688800215721, -0.031540919095277786, 0.014332067221403122, 0.08266768604516983, 0.04336768388748169, 0.022609470412135124, -0.059106651693582535, 0.03554070368409157, 0.05619337037205696, 0.009097058326005936, -0.009236418642103672, 0.03738277405500412, 0.051669683307409286, -0.0397321954369545, -0.0237296000123024, -0.10512778908014297, -0.05380535498261452, 0.032710589468479156, -0.02141485922038555, 0.005494251847267151, -0.0054297903552651405, -0.03830045461654663, 0.0344046875834465, 0.04800749197602272, -0.024898964911699295, -0.03894437849521637, 0.041540637612342834, 0.03897123038768768, 0.05744808167219162, 0.00632669311016798, -0.006522477138787508, -0.0072412374429404736, 0.018999692052602768, -0.0402483306825161, -0.0513480007648468, -0.015738336369395256, -0.021053364500403404, 0.01595187745988369, 0.038498472422361374, 0.001380263944156468, -0.013810455799102783, 0.027763165533542633, 0.005543436389416456, 0.06296464055776596, 0.04624629393219948, 0.003421174827963114, -0.058921750634908676, -0.02466794103384018, -0.01870039477944374, 0.04826967418193817, -0.0034783382434397936, 0.0014085537986829877, -0.04132820665836334, 0.03303386643528938, -0.044737476855516434, -0.047264501452445984, -0.04064040631055832, -0.04699597880244255, 0.0036853845231235027, -0.013187581673264503, -0.044250741600990295, -0.05282708257436752, -0.01904231496155262, 0.016492586582899094, -0.0019863059278577566, 0.02535795047879219, 0.02328856848180294, -0.035732466727495193, 0.0356542132794857, -0.0008258056477643549, 0.02202988602221012, 0.07059086114168167, -0.011892372742295265, -0.00978146307170391, -0.06487960368394852, -0.01835535280406475, -0.0048388210125267506, 0.009335615672171116, 0.0018580053001642227, 0.05176617577672005, 0.046774931252002716, -0.0237176064401865, 0.011510596610605717, -0.06662057340145111, 0.031099922955036163, 0.02950919419527054, -0.0158550925552845, -0.10389645397663116, 0.013804659247398376, -0.0036076740361750126, -0.0482611209154129, 0.0017106282757595181, 0.0306993555277586, 0.038858190178871155, -0.0007239708793349564, -0.043793048709630966, -0.039700947701931, 0.04739225655794144, -0.009507550857961178, -0.032870881259441376, -0.019143814221024513, -0.020679131150245667, -0.019489401951432228, 0.04689783230423927, 0.0298156701028347, 0.024752521887421608, 0.04564907029271126, 0.0627848207950592, 0.00046966728405095637, -0.009319916367530823, 0.048743102699518204, -0.0005712730926461518, 0.053769636899232864, 0.0589316301047802, -0.003713801270350814, 0.054781924933195114, 0.017949076369404793, 0.03572661802172661, -0.01420739945024252, -0.006130870897322893, 0.026607681065797806, 0.012989937327802181, -0.004662751220166683, 0.014952100813388824, -0.032397471368312836, 0.02649296633899212, 0.017576145008206367, 0.016657978296279907, -0.045676469802856445, 0.0011968800099566579, 0.015454418957233429, -0.049816083163022995, -0.07793980091810226, 0.040688011795282364, 0.01283513754606247, 0.06533821672201157, -0.04578860104084015, -0.016927922144532204, 0.0538627952337265, 0.010790507309138775, -0.060601670295000076, -0.019032999873161316, 0.02718656323850155, -0.013510054908692837, 0.03924901410937309, -0.04215562716126442, -0.046808529645204544, 0.02636038325726986, 0.019604217261075974, 0.01895289309322834, -0.015608665533363819, -0.08841308206319809, 0.005583852529525757, 0.0005358372000046074, -0.057641688734292984, -0.04470529779791832, 0.0035042823292315006, -0.01239056047052145, 0.04089606553316116, 0.06036550551652908, 0.006843408104032278, 0.036875903606414795, 0.03356941416859627, 0.062400080263614655, -0.03042680025100708, 0.01659233309328556, -0.05412045121192932, -0.03299036622047424, -0.03709559142589569, 0.007752348203212023, -0.016224302351474762, 0.008601132780313492, 0.08685155212879181, -0.038044292479753494, 0.03467579185962677, -0.02975892275571823, 0.016374943777918816, 0.02286773920059204, -0.02898610383272171, -0.002202108968049288, 0.02144087664783001, -0.014806592836976051, 0.04674085974693298, 0.003963171038776636, -0.03773055970668793, -0.040123507380485535, -0.05933678150177002, 0.06169724464416504, 0.04196323826909065, -0.04056771844625473, -0.018251290544867516, -0.0026621760334819555, -0.008048309944570065, -0.020054185763001442, 0.02701881341636181, -0.01853794977068901, 0.031206393614411354, 0.025611383840441704, -0.029053280130028725, -0.030000919476151466, 0.04633427411317825, 0.019609950482845306, -0.04862552136182785, 0.042171332985162735, 0.00047757624997757375, 0.03565780073404312, 0.02833862043917179, -0.02794390171766281, 0.0016460121842101216, -0.03439275547862053, 0.006076680961996317, -0.04015989601612091, -0.02408389188349247, 0.012259958311915398, -0.03453060984611511, 0.015079766511917114, 0.045002393424510956, -0.024694303050637245, -0.05708663910627365, -0.03153960034251213, 0.011986585333943367, 0.04847579821944237, 0.07029760628938675, 0.040404729545116425, 0.01821051724255085, 0.002968148561194539, 0.037975478917360306, 0.004203722346574068, -0.03208177536725998, 0.03107653558254242, -0.007671426981687546, -0.010815114714205265, -0.0021465157624334097, 0.04337884485721588, -0.013696899637579918, -0.03164621442556381, 0.02172829583287239, 0.0176918413490057, -0.05585440248250961, 0.03839832916855812, 0.042498789727687836, -0.004640260711312294, -0.052677031606435776, -0.024028927087783813, 0.04118749126791954, -0.013891461305320263, 0.026732712984085083, 0.07677758485078812, -0.00991397351026535, -0.06694363057613373, -0.017414668574929237, -0.007586164865642786, -0.05083870887756348, 0.008044548332691193, -0.013269901275634766, 0.009667834267020226, 0.019544551149010658, 0.005543181207031012, -0.004391828086227179, 0.020129887387156487, 0.02600250393152237, 0.0007314120884984732, 0.029579998925328255, 0.012884560041129589, 0.015464776195585728, -0.044148389250040054, 0.0041579571552574635, 0.00066611438523978, -0.04468901455402374, 0.028760483488440514, -0.023982880637049675, -0.04053996503353119, -0.022167883813381195, 0.05060453712940216, 0.048477355390787125, -0.07264381647109985, 0.011041352525353432, -0.04255435988306999, -0.05772240087389946, -0.03875608369708061, 0.009293291717767715, -0.06855397671461105, 0.08724206686019897, 0.013932726345956326, -0.10359764844179153, 0.025948677211999893, 0.09125955402851105, 0.010936548002064228, -0.006054849363863468, 0.0046746088191866875, 0.022377915680408478, 0.008465196006000042, -0.0054608494974672794, -0.004214023239910603, -0.04582730308175087, -0.03380423039197922, 0.006177580915391445, 0.01653772033751011, -0.012944713234901428, 0.029304882511496544, 0.025473713874816895, -0.022165969014167786, 0.07920785993337631, -0.0030547066126018763, 0.015434041619300842, 0.02962733618915081, -0.034902893006801605, -0.053664304316043854, -0.09707846492528915, -0.02282581478357315, -0.010175173170864582, 0.002052182564511895, -0.0038368937093764544, 0.029719410464167595, 0.029373008757829666, -0.024774067103862762, -0.032695744186639786, 0.07524212449789047, -0.010609705001115799, -0.034989580512046814, -0.030458394438028336, 0.009300879202783108, -0.07007483392953873, -0.010693238116800785, 0.07282623648643494, 0.0245377067476511, 0.000714767025783658, -0.0066331312991678715, -0.04722009599208832, -0.034285176545381546, -0.03973999619483948, -0.05822351574897766, -0.010160351172089577, 0.009162289090454578, -0.025386277586221695, -0.02962358295917511, 0.018171004951000214, 0.04247872531414032, -0.019695285707712173, -0.029041476547718048, -0.06974554061889648, -0.01069331169128418, 0.012523419223725796, -0.003148215590044856, -0.04042874276638031, -0.009756887331604958, 0.028858885169029236, 0.004334194120019674, -0.05287874490022659, 0.019310645759105682, 0.045904990285634995, 0.0316917821764946, 0.035375867038965225, -0.01887284219264984, 0.10127032548189163, -0.06694541871547699, -0.016388533636927605, -0.003265740815550089, -0.014963928610086441, 0.011576461605727673, 0.059676576405763626, -0.005141346249729395, 0.011227993294596672, 0.012397130951285362, 0.02580304630100727, -0.0334496796131134, 0.027311811223626137, 0.08363674581050873, -0.04119390994310379, -0.01777288317680359, -0.03746073320508003, 0.08302067220211029, 0.03583187609910965, -0.05654177814722061, 0.005040247458964586, 0.014933831058442593, -0.01895492523908615, 0.06244133785367012, 0.027388151735067368, -0.006946688052266836, 0.06503687798976898, 0.016147775575518608, 0.013661028817296028, 0.025415493175387383, 0.019144341349601746, -0.023062344640493393, 0.03875787556171417, -0.016046583652496338, -0.01268983818590641, -0.02109530381858349, 0.06547904014587402, 0.007601690944284201, 0.02707080915570259, -0.019512537866830826, 0.0023258235305547714, -0.014015046879649162, 0.003714055521413684, -0.04095255583524704, -0.012894152663648129, 0.004006554838269949, -0.038985345512628555, 0.006085006054490805, 0.09276532381772995, 0.05169667676091194, -0.03770704194903374, -0.03512074425816536, -0.017752835527062416, -0.03190552815794945, -0.009074065834283829, -0.029038747772574425, -0.007252606563270092, -0.054476138204336166, -0.023079929873347282, 0.04496685415506363, 0.044175099581480026, 0.00521024689078331, -0.0023273511324077845, 0.03131270036101341, -0.019543755799531937, 0.01851160265505314, 0.020125769078731537, 0.00006112526170909405, 0.03146611899137497, -0.007053617853671312, 0.05932656303048134, 0.035768043249845505, 0.0307804923504591, -0.0445244237780571, -0.008685423992574215, 0.032930705696344376, -0.021962542086839676, -0.004334380384534597, 0.08921031653881073, 0.03186185657978058, -0.010452967137098312, -0.07359465211629868, -0.044484615325927734, -0.01269291341304779, 0.03874005377292633, -0.00196104240603745, 0.019738197326660156, 0.007804482243955135, -0.05275270342826843, -0.04760250076651573, -0.015777340158820152, -0.0013088507112115622, 0.04153404384851456, 0.024606911465525627, -0.011736788786947727, -0.0077843195758759975, -0.02197045460343361, -0.00948522612452507, 0.018061427399516106, -0.021420372650027275, 0.0024168628733605146, -0.00618633022531867, -0.04065366089344025, 0.013727152720093727, -0.05501529574394226, -0.059324949979782104, 0.05176756903529167, 0.0035382388159632683, -0.021594025194644928, 0.04340553283691406, -0.038411617279052734, 0.030087023973464966, 0.017741825431585312, -0.012774961069226265, -0.031013913452625275, 0.09027694165706635, -0.012839662842452526, 0.03582683205604553, 0.0002786446420941502, 0.014993316493928432, 0.025285392999649048, 0.000689724984113127, 0.04112771153450012, 0.0199445653706789, 0.040938600897789, -0.02123120427131653, -0.01032533310353756, -0.04121633991599083, -0.056424107402563095, 0.02174847573041916, -0.039617303758859634, -0.02511352114379406, -0.012444025836884975, -0.034463800489902496, -0.013697710819542408, 0.04890419915318489, 0.03314392268657684, -0.009385894052684307, 0.11606568098068237, 0.04762231931090355, -0.05012092366814613, 0.010935316793620586, 0.0330524817109108, 0.054211121052503586, 0.018929988145828247, 0.05097987875342369, 0.04702140390872955, -0.01465207152068615, -0.06612585484981537, -0.02409134805202484, -0.018750209361314774, -0.025536587461829185, 0.002844833768904209, 0.03346185013651848, -0.07143037766218185, 0.015590735711157322, -0.005671479273587465, -0.009031147696077824, -0.011174262501299381, 0.022065889090299606, -0.05075230076909065, 0.02369530126452446, 0.06968444585800171, -0.018595054745674133, 0.012766608037054539, 0.01756824553012848, 0.0012419938575476408, 0.05682799965143204, -0.03999865800142288, -0.0030116115231066942, -0.005459778010845184, 0.005749874748289585, -0.013991125859320164, -0.06622543185949326, -0.011611788533627987, 0.0009617150644771755, 0.03454868867993355, -0.005837264470756054, -0.013480632565915585, -0.01240058708935976, 0.012940013781189919, 0.05859409645199776, -0.06140187755227089, -0.017206301912665367, -0.044092584401369095, -0.010590661317110062, 0.035325005650520325, -0.010497776791453362, 0.040569741278886795, 0.003416787600144744, 0.041087184101343155, -0.018764467909932137, -0.05330565944314003, -0.007491983473300934, 0.02756623364984989, 0.04663481190800667, -0.048997487872838974, -0.01261468231678009, -0.04343631863594055, -0.04487123340368271, 0.03717264160513878, 0.060353223234415054, 0.006310900207608938, -0.013322684913873672, -0.004461047705262899, -0.03647524490952492, 0.07184688001871109, -0.006272679194808006, 0.000010571205166343134, -0.08224966377019882, -0.0056198881939053535, -0.08453131467103958, 0.003116982290521264, -0.04861348122358322, -0.04832617938518524, 0.07392823696136475, 0.02507544495165348, 0.006789146922528744, -0.05302055925130844, -0.044114697724580765, 0.024489255622029305, -0.02835659123957157, 0.05583495646715164, 0.0007906260434538126, 0.020806966349482536, -0.06303568184375763, -0.004330118652433157, -0.006297225132584572, 0.015545411966741085, -0.031377095729112625, 0.01460915245115757, -0.03781123086810112, 0.023105980828404427, -0.004008904565125704, 0.006458471994847059, 0.04732576385140419, -0.042590513825416565, -0.010169259272515774, 0.043082550168037415, 0.035404182970523834, 0.005953443702310324, -0.06281533092260361, 0.034167394042015076, -0.08599555492401123, 0.04508437588810921, 0.007962196134030819, 0.003826058004051447, 0.007928668521344662, -0.0123373344540596, -0.05051562935113907, -0.012135084718465805, -0.007770500145852566, -0.01714755780994892, -0.001809116918593645, -0.06857679784297943, 0.020973073318600655, 0.011177578940987587, 0.0019816067069768906, 0.06186733394861221, -0.06048312038183212, 0.004602614790201187, 0.02483486756682396, -0.008126389235258102, -0.02390241250395775, -0.009575048461556435, -0.03214200213551521, 0.014087759889662266, -0.018599005416035652, -0.04266843944787979, -0.07435771077871323, -0.0024519357830286026, 0.07336863875389099, -0.01740373484790325, -0.0021926353219896555, 0.06014876440167427, 0.04449223354458809, -0.016671638935804367, -0.001822924823500216, -0.06398104876279831, -0.025941899046301842, 0.019021419808268547, -0.016142498701810837, 0.02310718595981598, 0.036386795341968536, 0.005071825813502073, -0.0008160988800227642, -0.0023734651040285826, -0.004221667535603046, 0.0422707200050354, 0.05039820447564125, 0.043310392647981644, 0.04480332136154175, -0.012009265832602978, -0.03557271510362625, -0.019535871222615242, 0.025946397334337234, 0.037569742649793625, -0.022948553785681725, 0.03988276422023773, 0.009779486805200577, -0.04044049233198166, 0.0039377231150865555, 0.027508316561579704, -0.011303718201816082, -0.03658214583992958, 0.044495873153209686, 0.036127880215644836, -0.019563255831599236, 0.023791059851646423, -0.006001936737447977, -0.012689527124166489, 0.015107346698641777, 0.000005839914592797868, 0.0653313547372818, -0.03243047744035721, 0.018472012132406235, 0.007928714156150818, -0.04144047573208809, -0.003437380539253354, -0.06213478744029999, 0.006420019082725048, 0.006211123429238796, 0.026521110907197, -0.013929173350334167, 0.04146069660782814, -0.06839402765035629, -0.06769316643476486, -0.021900128573179245, -0.00810962449759245, -0.03144853189587593, 0.009889270178973675, -0.03016934171319008, -0.019621580839157104, 0.0019207099685445428, 0.03010559268295765, -0.018270201981067657, 0.06483153253793716, -0.015376647934317589, -0.06269554048776627, 0.04184660315513611, -0.04313196614384651, -0.0033611382823437452, 0.0033040328416973352, -0.035333532840013504, -0.009286188520491123, -0.0021365045104175806, 0.03676045313477516, 0.027323193848133087, -0.011055126786231995, -0.008536998182535172, 0.009210052900016308, -0.08125986158847809, -0.0073591964319348335, -0.008129378780722618, 0.018893886357545853, -0.030113529413938522, -0.021028969436883926, 0.0015655491733923554, 0.010527820326387882, 0.0008468630257993937, -0.03775783255696297, -0.0027534766122698784, -0.045381613075733185, -0.016019368544220924, -0.06712844222784042, -0.019255856052041054, 0.05415096879005432, -0.018910765647888184, 0.02066964842379093, 0.037967368960380554, 0.04597395658493042, -0.029849641025066376, 0.0024601321201771498, 0.015488791279494762, -0.053056228905916214, 0.01588083989918232, -0.01055307500064373, 0.05139898508787155, -0.03678881376981735, -0.002458603587001562, -0.012037222273647785, 0.057466231286525726, -0.013653375208377838, 0.018287302926182747, -0.013858978636562824, -0.028164323419332504, 0.006404360290616751, 0.08935388922691345, -0.016314715147018433, -0.022407468408346176, 0.01448840368539095, -0.019418537616729736, 0.005134181585162878, -0.017510799691081047, -0.02556343749165535, 0.02263396419584751, 0.027684064581990242, -0.015599941834807396, -0.0624677948653698, -0.009967951104044914, 0.03038065880537033 ]
<p>Ok, this is definitely a silly question and is partly inspired by the last 20 minutes or so of the film <em>The Avengers</em>, so look to that if you can't picture the situation.</p> <p>In the film a portal is opened up above new york, to somewhere in deep space. I.e. from an area where the gravitational field is effectively uniform and field lines would be parallel, to an area with negligible net gravitational acceleration.</p> <p>My question is, assuming this portal has literally linked the two bits of space, it makes sense that the gravity of the earth would be transmitted through the portal in some way, but in what form would the field take on the other side of the portal?</p> <p>Would it behave like a point source, or similarly to a diffraction slits? Would a mass slightly off to one side from the portal experience a force?</p> <p>Let's ignore all the practical factors like the air rushing out into the vacuum and the question of what happens on the "other side" of the portal (the bit you'd be looking at if you flew up from new york to above the portal) although there's plenty of scope for interesting things happening there as well.</p>
g8399
[ 0.03288112208247185, 0.051429279148578644, 0.002760891569778323, -0.015856260433793068, -0.03471404314041138, 0.04727144166827202, 0.0029479176737368107, 0.03450045362114906, -0.018925020471215248, -0.04211171343922615, 0.003731489647179842, 0.0412820503115654, 0.07022614032030106, -0.00884306151419878, 0.051783375442028046, -0.025318291038274765, 0.02704363688826561, -0.08406189829111099, 0.020250771194696426, -0.0039293840527534485, 0.03657104820013046, -0.03033437207341194, 0.020977143198251724, -0.008331957273185253, -0.08468770980834961, 0.001492486335337162, 0.009205679409205914, -0.045351289212703705, -0.06817331910133362, -0.007279768120497465, -0.016510672867298126, -0.017861785367131233, 0.029931090772151947, -0.057519879192113876, -0.056952495127916336, -0.01648629643023014, -0.06322627514600754, 0.08142951875925064, -0.018191523849964142, -0.038828566670417786, 0.02103663980960846, -0.05999782681465149, -0.048792820423841476, -0.012448851950466633, -0.003196297213435173, -0.0006452758680097759, -0.06489374488592148, -0.015161629766225815, 0.051920339465141296, -0.04578780755400658, -0.07588285207748413, 0.0179400984197855, -0.047179922461509705, 0.013914315029978752, 0.008569538593292236, 0.028527049347758293, 0.03255336731672287, 0.008456556126475334, 0.059254687279462814, 0.015259798616170883, -0.0006449474021792412, 0.03031526319682598, 0.03644910454750061, 0.008454215712845325, 0.04270418360829353, 0.056779757142066956, -0.07229949533939362, 0.04481175169348717, 0.03580985963344574, -0.0049563320353627205, 0.05346691980957985, -0.0067947073839604855, -0.04285746440291405, -0.019471045583486557, -0.036059290170669556, 0.033752940595149994, -0.0153716541826725, 0.06312470138072968, -0.002885284833610058, -0.021177496761083603, 0.008816947229206562, -0.0327688530087471, -0.010710903443396091, 0.005591378081589937, 0.0742003545165062, -0.008802739903330803, -0.0009744246490299702, 0.0005116749089211226, -0.009087443351745605, 0.06605387479066849, -0.0023424753453582525, 0.01958508975803852, 0.06569089740514755, -0.022305961698293686, -0.007331850007176399, 0.0037525712978094816, -0.0014099414693191648, 0.07264994829893112, -0.04757924750447273, -0.06463891267776489, 0.007702880539000034, -0.010961824096739292, 0.03745903819799423, 0.0088614821434021, 0.017501527443528175, 0.024415157735347748, 0.05200169235467911, 0.02070380374789238, 0.049260128289461136, -0.05662883445620537, -0.018582019954919815, -0.00021082082821521908, -0.0060502756386995316, -0.027200885117053986, -0.014348505064845085, -0.06772702932357788, 0.04587109014391899, 0.039973508566617966, 0.04466424137353897, 0.08878063410520554, -0.0067232646979391575, -0.002365713007748127, -0.04499305784702301, 0.04033422842621803, -0.028109567239880562, 0.00946328230202198, 0.0025424202904105186, 0.0019568437710404396, 0.004346923436969519, 0.003328055376186967, 0.007743435446172953, -0.013872559182345867, -0.014691743068397045, 0.044254958629608154, -0.00847192294895649, -0.015402089804410934, -0.005999395623803139, -0.01588919386267662, 0.012193591333925724, -0.019296696409583092, -0.024416549131274223, -0.06581278145313263, -0.05520354583859444, 0.0008420036174356937, -0.03184082359075546, -0.011303461156785488, 0.040750812739133835, 0.03333781287074089, 0.042721379548311234, 0.004856121726334095, -0.011604388244450092, 0.05538861081004143, 0.09350963681936264, -0.007085451390594244, 0.030384864658117294, 0.014523216523230076, 0.028767291456460953, -0.00657801516354084, 0.03030562959611416, -0.032290223985910416, 0.07411253452301025, -0.02139294147491455, 0.037568651139736176, -0.006147276144474745, -0.009122510440647602, -0.028868967667222023, 0.01927103102207184, -0.061208244413137436, 0.07320812344551086, -0.0021379899699240923, 0.008216283284127712, 0.024242760613560677, 0.015286214649677277, 0.05867740884423256, 0.013640853576362133, 0.03541342914104462, 0.04312903434038162, 0.013452723622322083, -0.02109931968152523, -0.005146138370037079, 0.028320901095867157, -0.03222726285457611, 0.009492645971477032, -0.044291600584983826, 0.061166174709796906, -0.08155415952205658, 0.005838231649249792, -0.008742576465010643, -0.05716728791594505, -0.004808227065950632, -0.004117906559258699, -0.03408869355916977, -0.006680593825876713, 0.06083245575428009, -0.07557836174964905, -0.0033416564110666513, 0.06460543721914291, -0.008533228188753128, 0.024709152057766914, 0.029921170324087143, -0.006102893501520157, 0.04557333514094353, 0.0355302058160305, 0.04735661298036575, -0.0004878672189079225, 0.015361232683062553, -0.013042108155786991, 0.07221049815416336, 0.015536956489086151, -0.03992917761206627, 0.02714650332927704, -0.005378523375838995, 0.036388881504535675, -0.017146602272987366, -0.060158923268318176, 0.049853358417749405, -0.02454720437526703, 0.005134848412126303, -0.05119499936699867, 0.017278386279940605, 0.013028556481003761, -0.02112429589033127, 0.04346538707613945, -0.0006178243784233928, 0.012357302010059357, -0.03289245441555977, -0.01002492569386959, -0.018056973814964294, 0.016809716820716858, 0.009321851655840874, -0.0657905712723732, 0.011092470958828926, 0.008602402172982693, -0.03521572798490524, 0.05327439308166504, 0.001981317298486829, -0.04102892801165581, 0.034678202122449875, -0.003458635648712516, -0.046958014369010925, 0.03441851958632469, -0.0404508039355278, -0.02197578176856041, -0.028278375044465065, 0.03266294300556183, -0.04133215546607971, 0.06028589978814125, 0.005839802790433168, -0.013224981725215912, 0.007928344421088696, -0.014640230685472488, -0.04991061985492706, -0.025102904066443443, 0.02172221429646015, 0.020124290138483047, -0.02745760791003704, -0.029187489300966263, 0.030188899487257004, -0.09413018077611923, -0.0649123564362526, -0.048354312777519226, -0.047674767673015594, 0.048274096101522446, 0.009292715229094028, -0.06204216182231903, 0.030874328687787056, 0.0158355962485075, 0.05335672199726105, -0.0033455295488238335, 0.006428214255720377, -0.006979575380682945, 0.0408732146024704, 0.00249262573197484, 0.055719226598739624, -0.012660006992518902, 0.03265678882598877, 0.032312504947185516, -0.05050346627831459, 0.025076206773519516, -0.006080899853259325, -0.014209873043000698, 0.028546011075377464, 0.027230149134993553, 0.015781104564666748, 0.0978424921631813, -0.01118056382983923, 0.01028071902692318, 0.0007228427566587925, -0.047636378556489944, -0.010800040327012539, -0.04190694913268089, -0.02358773536980152, 0.002515069441869855, 0.021444909274578094, -0.017509279772639275, 0.009607398882508278, 0.03970130905508995, 0.00821737665683031, -0.06683512777090073, -0.013952934183180332, -0.03241696208715439, -0.03262447938323021, 0.009429067373275757, 0.03130744397640228, -0.08084007352590561, -0.01265329122543335, -0.030665112659335136, -0.026044439524412155, -0.011378447525203228, -0.007064770441502333, -0.0026262907776981592, 0.055258557200431824, 0.04169103130698204, 0.024992896243929863, -0.012537561357021332, -0.050665441900491714, 0.0274567399173975, 0.01195176038891077, 0.012473098002374172, -0.01763489656150341, -0.01752663590013981, -0.011168574914336205, -0.03682814538478851, 0.0398193821310997, 0.025490550324320793, -0.0038852745201438665, -0.005406305659562349, 0.010114298202097416, -0.04038423299789429, -0.00408173305913806, -0.012060285545885563, 0.0014640254667028785, -0.05065053701400757, -0.0009217312908731401, -0.0339738205075264, 0.0583227314054966, -0.03878499194979668, 0.03793824091553688, 0.053917571902275085, 0.05059707164764404, 0.039847444742918015, -0.01699157990515232, -0.04009128361940384, -0.009438669309020042, 0.01138774398714304, 0.016074221581220627, 0.08162545412778854, 0.01727161929011345, 0.03906486928462982, 0.001741092768497765, 0.005167021416127682, -0.01646006479859352, -0.000165815552463755, 0.004103698302060366, -0.013459324836730957, -0.009275441989302635, 0.027111012488603592, 0.009555085562169552, 0.023240849375724792, 0.0020863250829279423, 0.003409258322790265, -0.03496353700757027, -0.028318297117948532, -0.037888746708631516, -0.04298298805952072, -0.002657635835930705, 0.008277881890535355, -0.024801334366202354, -0.03275229036808014, 0.000600874365773052, 0.06831259280443192, -0.052952222526073456, -0.041583526879549026, 0.003126312280073762, 0.024328025057911873, -0.039491768926382065, 0.03923743590712547, -0.06378522515296936, -0.031221313402056694, 0.019520636647939682, 0.009367380291223526, 0.04706890508532524, -0.028567414730787277, 0.027277233079075813, 0.0166142787784338, -0.04594898968935013, -0.036879416555166245, -0.003802327439188957, 0.03086886554956436, 0.0005853900220245123, 0.02032748982310295, -0.009045237675309181, -0.002645488129928708, 0.03131260350346565, 0.036934033036231995, 0.0283811092376709, -0.01215158961713314, -0.02543048746883869, -0.03411819413304329, -0.024741049855947495, 0.10917910188436508, 0.06891702860593796, -0.015837889164686203, 0.011957157403230667, -0.014685526490211487, -0.0191726665943861, 0.01194989588111639, -0.021177278831601143, -0.07783085107803345, 0.03447772562503815, 0.05373760312795639, -0.034911319613456726, -0.06200841814279556, -0.0417841412127018, 0.04400936886668205, 0.03341275081038475, 0.039580486714839935, 0.07048583030700684, -0.0003584743244573474, 0.007227391470223665, 0.005185908172279596, 0.040117453783750534, 0.06459002196788788, -0.0049296594224870205, -0.024352379143238068, 0.07269918918609619, 0.02129124104976654, -0.04551213979721069, -0.013064202852547169, 0.02358980104327202, -0.015445571392774582, 0.05750551074743271, 0.01585203781723976, 0.06149083375930786, -0.020913420245051384, 0.053409382700920105, -0.04826580360531807, -0.046132445335388184, 0.07430011034011841, 0.001444517751224339, 0.06340166181325912, 0.0013510388089343905, 0.032672323286533356, 0.010917192324995995, -0.0442044623196125, 0.07583071291446686, -0.047782834619283676, -0.009777250699698925, 0.003607199527323246, -0.03218313679099083, -0.08632992208003998, -0.0037580211646854877, -0.02435232326388359, -0.05111777037382126, -0.03228772059082985, -0.005199413746595383, -0.022870704531669617, -0.014345535077154636, -0.003307536942884326, 0.013178395107388496, -0.023631881922483444, 0.038971275091171265, -0.0412457175552845, 0.02284356765449047, -0.003179689170792699, -0.016468634828925133, -0.023862862959504128, -0.0547921322286129, -0.037405628710985184, -0.048071715980768204, -0.008443177677690983, 0.028157047927379608, -0.015253321267664433, 0.02255096659064293, 0.017663823440670967, 0.01697264425456524, -0.0010884269140660763, 0.008394830860197544, 0.0060950047336518764, -0.0673484057188034, -0.028872709721326828, 0.04537614807486534, 0.10237250477075577, -0.009645706973969936, -0.027602877467870712, -0.025657547637820244, -0.0411137230694294, 0.008139288984239101, -0.0046277535147964954, -0.05539567023515701, -0.03869234398007393, -0.06855128705501556, -0.04404792934656143, -0.027382701635360718, 0.007044540718197823, -0.032906465232372284, 0.0404849499464035, -0.044048260897397995, -0.006218382623046637, -0.007911884225904942, -0.02402372658252716, 0.014110020361840725, -0.01981079950928688, 0.029476134106516838, -0.04518111050128937, 0.042971283197402954, 0.0032017400953918695, 0.02388123981654644, 0.0028559428174048662, 0.07151700556278229, -0.08403320610523224, -0.005973089020699263, -0.06478112190961838, -0.010952414944767952, 0.041369419544935226, -0.01262656319886446, -0.00728973001241684, 0.008528066799044609, -0.02458530105650425, 0.014633099548518658, 0.05830113962292671, -0.022797562181949615, 0.07073257118463516, -0.006458197720348835, 0.055241283029317856, 0.04460858553647995, -0.020811304450035095, 0.042612701654434204, -0.022924495860934258, 0.004899734165519476, 0.013044256716966629, -0.0006995779694989324, -0.004709492903202772, 0.0005557214608415961, -0.023584116250276566, -0.04842958226799965, 0.0648094043135643, -0.020453261211514473, 0.07942932844161987, -0.01791541650891304, -0.040355656296014786, -0.03519188240170479, 0.008045791648328304, 0.03864564746618271, -0.0470222570002079, -0.010175024159252644, -0.015699587762355804, -0.00031092468998394907, 0.049411170184612274, -0.010659890249371529, -0.10086227208375931, 0.015629589557647705, 0.007605132181197405, 0.06516679376363754, 0.0330156534910202, -0.020611988380551338, -0.007856801152229309, 0.0373997762799263, -0.0058130561374127865, -0.05587700754404068, 0.0807778388261795, 0.03209415450692177, 0.006238366477191448, -0.0334136039018631, -0.02296372503042221, 0.029459841549396515, 0.0007184238638728857, -0.04807377606630325, 0.06594271212816238, -0.008561243303120136, -0.03815212473273277, -0.035978641360998154, -0.012517405673861504, -0.020608022809028625, 0.017951644957065582, 0.00749477744102478, 0.005038079805672169, 0.0013506279792636633, -0.0523187555372715, 0.021246548742055893, 0.023152170702815056, 0.001766019151546061, 0.0471213161945343, -0.0034730129409581423, -0.022916587069630623, 0.06152324751019478, -0.05893196538090706, 0.004385183099657297, 0.07756165415048599, -0.028229184448719025, -0.04678608104586601, -0.0719500482082367, 0.011856785975396633, -0.011829623952507973, -0.12048482149839401, -0.0021680688951164484, 0.005698159337043762, 0.011405473574995995, -0.028868714347481728, 0.05707384645938873, 0.043180860579013824, -0.006302006542682648, 0.012980586849153042, 0.01911053992807865, 0.01757381483912468, 0.00445753475651145, 0.02059774287045002, -0.03254469856619835, -0.02354172058403492, -0.013377076014876366, 0.036270007491111755, 0.026147812604904175, -0.02474139630794525, 0.02531448006629944, 0.004015798680484295, 0.04286562278866768, -0.0013210403267294168, -0.04294164851307869, 0.021167254075407982, 0.024022363126277924, -0.004708881955593824, -0.046215347945690155, 0.0016093346057459712, -0.008595820516347885, -0.03158101812005043, -0.016412168741226196, -0.051656365394592285, 0.041403546929359436, 0.020407384261488914, -0.0046678767539560795, 0.015614645555615425, 0.01919117011129856, 0.03693452477455139, -0.007779785431921482, 0.007623058278113604, 0.027880530804395676, -0.00842270813882351, 0.01842152327299118, 0.04266113415360451, -0.0005860882811248302, 0.03845961391925812, -0.0008938080281950533, -0.014819749630987644, 0.031346723437309265, -0.01730080507695675, -0.029295185580849648, -0.04919508472084999, 0.0185225997120142, -0.029010187834501266, -0.013120204210281372, -0.03513585031032562, -0.0712667778134346, -0.05876442417502403, 0.021289702504873276, -0.013925309292972088, 0.03271275758743286, -0.010018747299909592, 0.06004290282726288, 0.020992444828152657, -0.08101603388786316, 0.002563461195677519, 0.02527995966374874, -0.05257459729909897, 0.042296651750802994, -0.007260836660861969, 0.02119760401546955, 0.022044643759727478, -0.03853682056069374, -0.04287976026535034, 0.0239190012216568, 0.010523730888962746, -0.033212196081876755, 0.026449525728821754, 0.07913070172071457, 0.001408357173204422, -0.015734568238258362, -0.026963016018271446, -0.02289668470621109, 0.009088239632546902, 0.017127303406596184, -0.05392754077911377, 0.025515679270029068, 0.01426134817302227, 0.010748768225312233, -0.06342089176177979, 0.008331476710736752, -0.00604180758818984, -0.007982771843671799, -0.06705576181411743, -0.02399613708257675, 0.026269232854247093, 0.015040414407849312, 0.02906024642288685, -0.024720195680856705, -0.018128300085663795, 0.02404107339680195, 0.02714579366147518, 0.04644624888896942, -0.020644105970859528, -0.02548580802977085, -0.017370184883475304, 0.0596800372004509, -0.024072211235761642, -0.014070696197450161, 0.02027485892176628, -0.032718461006879807, 0.007638697046786547, 0.03925266116857529, -0.07951302081346512, 0.0008726843516342342, 0.06480114907026291, 0.043102655559778214, 0.05146846920251846, 0.04831067472696304, 0.000389413587981835, 0.012545065954327583, -0.0271653663367033, -0.026369528844952583, 0.04246542975306511, 0.011309499852359295, -0.03534969687461853, 0.00012428744230419397, -0.016327710822224617, -0.031664829701185226, -0.0008607959025539458, 0.014385798014700413, -0.049114637076854706, -0.050070300698280334, 0.019333669915795326, -0.05444338917732239, 0.06582999974489212, 0.008177797310054302, 0.02889755554497242, -0.02056746929883957, -0.016394754871726036, -0.025679340586066246, 0.007619739044457674, -0.04956844821572304, -0.005479880608618259, -0.03177608177065849, -0.0005773115553893149, -0.06757821887731552, -0.03224075958132744, -0.022211667150259018, -0.01230248436331749, 0.00821046344935894, 0.011599550023674965, 0.058265570551157, 0.025637850165367126, -0.02774599753320217, 0.015220925211906433, -0.027074791491031647, -0.04269659146666527, 0.030082054436206818, 0.03462136909365654, -0.05908649414777756, -0.010294966399669647, -0.007181051652878523, -0.03801549971103668, -0.016393300145864487, 0.04338347166776657, -0.0017125261947512627, 0.024232111871242523, -0.028047114610671997, -0.07776248455047607, 0.0005494625656865537, -0.030575694516301155, 0.05293630063533783 ]
<p>We know that Spin is described with $SU(2)$ and that $SU(2)$ is a double cover of the rotation group $SO(3)$. This suggests a simple thought experiment, to be described below. The question then is in three parts: </p> <ol> <li><p>Is this thought experiment theoretically sound? </p></li> <li><p>Can it be conducted experimentally? </p></li> <li><p>If so what has been the result?</p></li> </ol> <p>The experiment is to take a slab of material in which there are spin objects e.g. electrons all (or most) with spin $\uparrow$. Then rotate that object $360$ degrees (around an axis perpendicular to the spin direction), so that macroscopically we are back to where we started. Measure the electron spins. Do they point $\downarrow$?</p>
g8400
[ -0.03008335269987583, 0.0005722481873817742, -0.010787507519125938, -0.06533879786729813, 0.028798801824450493, -0.0053951796144247055, 0.006609093397855759, 0.004386676009744406, -0.007580209989100695, 0.0027879769913852215, -0.020609669387340546, 0.04530772939324379, 0.005644936114549637, -0.023787518963217735, -0.021846871823072433, -0.010050862096250057, 0.05462193116545677, -0.006388390436768532, 0.06880680471658707, 0.004447815008461475, 0.033590517938137054, -0.007456135470420122, -0.0196964293718338, -0.03942408040165901, 0.01534946821630001, 0.027419758960604668, -0.006170859094709158, 0.04960477724671364, -0.009800980798900127, 0.043121106922626495, -0.02633875235915184, -0.05306331440806389, -0.009301318787038326, -0.04306654632091522, -0.00654014153406024, -0.13020983338356018, 0.041780147701501846, 0.02335512824356556, -0.010181384161114693, 0.018064020201563835, 0.006186267826706171, -0.01031031459569931, -0.02142382599413395, -0.012483317404985428, 0.07423710823059082, 0.03102773427963257, 0.028418032452464104, 0.03132004663348198, 0.059556879103183746, -0.020537925884127617, -0.05893609672784805, 0.0035071878228336573, 0.0496244877576828, 0.03981921076774597, 0.008941611275076866, 0.0004167366132605821, -0.0030536765698343515, 0.0033645564690232277, 0.10731274634599686, -0.0099419467151165, -0.01467126701027155, 0.016072150319814682, -0.0335647314786911, -0.01878066174685955, 0.032972127199172974, -0.04444221034646034, -0.04519479721784592, 0.05112718418240547, -0.005676259286701679, 0.029556041583418846, 0.021235831081867218, -0.04275568202137947, 0.0407865084707737, -0.03516566380858421, -0.043181173503398895, 0.07768604159355164, 0.015361330471932888, 0.013191078789532185, 0.016944644972682, -0.01549802627414465, -0.05807419866323471, -0.0633380264043808, -0.031797271221876144, 0.0512116365134716, -0.0010597353102639318, -0.0012117235455662012, -0.037963416427373886, 0.002856293460354209, -0.03643128275871277, 0.048009857535362244, 0.040616847574710846, -0.03016488440334797, 0.01718362234532833, -0.0026590831112116575, -0.019826974719762802, 0.03120099939405918, -0.020481964573264122, 0.02085970900952816, -0.0544099286198616, 0.05886046588420868, -0.05699995532631874, -0.021207181736826897, -0.009698698297142982, 0.02168147824704647, -0.0026232735253870487, 0.033679503947496414, 0.017629064619541168, 0.027297038584947586, -0.029555510729551315, 0.019995570182800293, 0.01164310798048973, 0.0028130244463682175, -0.013513157144188881, 0.002479403978213668, -0.07008198648691177, 0.005844178609549999, 0.05485304817557335, -0.0074759419076144695, 0.0706120952963829, 0.054463453590869904, 0.018226392567157745, 0.06900958716869354, 0.015207154676318169, 0.10051693022251129, 0.03968852758407593, -0.01808265596628189, -0.02779640629887581, -0.03819978982210159, 0.08153543621301651, 0.015917068347334862, -0.05225885286927223, -0.018205612897872925, -0.030531011521816254, 0.02696603536605835, 0.015334071591496468, 0.03081269934773445, 0.0020049710292369127, -0.010447938926517963, -0.018190983682870865, -0.019109830260276794, 0.009643599390983582, -0.0015021378640085459, -0.005657802801579237, -0.008040346205234528, 0.05879611894488335, -0.052334975451231, 0.01544088777154684, -0.05135495588183403, -0.0144025394693017, 0.06037256494164467, -0.05154799297451973, 0.014316671527922153, 0.020890798419713974, -0.04053092747926712, 0.02378607913851738, -0.02189568430185318, 0.025922738015651703, 0.0029215484391897917, 0.1071043536067009, 0.04810959845781326, 0.022176695987582207, -0.016886228695511818, -0.06611809134483337, -0.018079325556755066, -0.02682279609143734, 0.032902851700782776, 0.011293974705040455, 0.05848897993564606, 0.045053135603666306, -0.0585455559194088, -0.0281077791005373, -0.021692020818591118, 0.01852443814277649, 0.03279039263725281, 0.01798555999994278, 0.028214620426297188, -0.008551948703825474, -0.0121316472068429, -0.0024472298100590706, 0.025718363001942635, -0.014925970695912838, 0.006316182669252157, 0.008786872960627079, -0.0067229922860860825, 0.042958490550518036, 0.019667671993374825, 0.016745634377002716, 0.06348112225532532, -0.013126281090080738, 0.01699802652001381, 0.02461180090904236, 0.0043878015130758286, -0.016201218590140343, -0.0020896578207612038, -0.03550548851490021, -0.0077713653445243835, 0.03984178602695465, 0.004897567443549633, -0.017198020592331886, 0.018727857619524002, 0.0100486995652318, 0.003264511004090309, 0.03598790988326073, -0.0007708810153417289, -0.027266722172498703, -0.022734511643648148, -0.012700929306447506, -0.028381217271089554, 0.03739984333515167, 0.01869722455739975, 0.04772784933447838, 0.10711973905563354, -0.018194640055298805, 0.04547993466258049, 0.0013059647753834724, -0.000004433487902133493, 0.004506861325353384, 0.029114214703440666, -0.02585827372968197, 0.016878768801689148, 0.013133463449776173, -0.004437830299139023, 0.04863905534148216, -0.003086236771196127, 0.026724012568593025, 0.003359989495947957, -0.029353167861700058, -0.025852836668491364, -0.05222100391983986, 0.00459629762917757, -0.04019291698932648, 0.00001888637234515045, 0.017112333327531815, -0.04612189903855324, 0.05171265825629234, -0.014862180687487125, -0.08395983278751373, 0.024922948330640793, -0.006822400260716677, -0.0009819690603762865, 0.03559587523341179, 0.0037284085992723703, -0.030923735350370407, -0.015511750243604183, 0.024395674467086792, -0.016770096495747566, 0.029006144031882286, 0.0125401197001338, 0.02077617309987545, 0.03544173389673233, -0.005347980186343193, 0.005946403834968805, -0.06468748301267624, 0.0003434339596424252, 0.0006235060864128172, -0.025997254997491837, -0.02629525028169155, 0.019430361688137054, -0.05723867192864418, -0.06418440490961075, -0.0034433449618518353, -0.019380314275622368, 0.07472717761993408, -0.020462555810809135, -0.03640974685549736, -0.008519253693521023, -0.052982889115810394, -0.05425611883401871, 0.025157291442155838, 0.0111110620200634, -0.05179692804813385, 0.013816650956869125, 0.012698217295110226, 0.01738710142672062, -0.060504645109176636, -0.053886763751506805, 0.010691742412745953, 0.009714887477457523, -0.029008086770772934, -0.037140537053346634, -0.006133925169706345, -0.025979019701480865, -0.053059838712215424, 0.04158833995461464, -0.018010983243584633, 0.04046323150396347, -0.07600034773349762, -0.022713402286171913, -0.03243548795580864, 0.021175889298319817, -0.022976718842983246, 0.020417192950844765, 0.12165610492229462, -0.012958258390426636, 0.02211030386388302, 0.014795850031077862, 0.04323195293545723, -0.02630680985748768, -0.04299348220229149, 0.06524773687124252, -0.003510227892547846, 0.017992114648222923, 0.00646039005368948, 0.019254151731729507, 0.04307960346341133, -0.009476075880229473, 0.003831445937976241, -0.07105837762355804, -0.0602705292403698, -0.0379197932779789, -0.08047924935817719, 0.040946539491415024, 0.007612079381942749, -0.024078644812107086, -0.051562897861003876, -0.028576089069247246, -0.022877346724271774, 0.019350942224264145, 0.04289094731211662, -0.03649319335818291, -0.015636079013347626, 0.010244719684123993, 0.03248659148812294, 0.03178144246339798, -0.0018284169491380453, 0.043005362153053284, -0.041648633778095245, -0.004870363511145115, -0.05844886973500252, -0.043855082243680954, 0.020541224628686905, 0.06737443059682846, -0.018480459228157997, -0.003248264780268073, -0.052702534943819046, 0.011497922241687775, -0.011869315057992935, 0.06365907937288284, 0.027240728959441185, 0.02969752997159958, -0.025412363931536674, -0.07446969300508499, -0.030428573489189148, -0.04755997657775879, 0.00985122099518776, 0.010001562535762787, -0.046579886227846146, -0.027865618467330933, 0.004427760373800993, 0.0406603142619133, 0.015245525166392326, 0.02862662263214588, -0.014543114230036736, -0.012981540523469448, 0.07296386361122131, 0.009087154641747475, 0.04500007629394531, 0.04635464400053024, 0.03788600489497185, 0.020486626774072647, 0.009069355204701424, -0.02841045893728733, 0.003882685210555792, -0.08165520429611206, 0.01804198883473873, 0.003783900523558259, -0.0603138767182827, 0.06352971494197845, 0.03476320952177048, 0.03457029536366463, -0.02708781138062477, -0.05673297867178917, -0.033359844237565994, 0.005145641043782234, 0.016356011852622032, -0.018420595675706863, -0.008269384503364563, 0.03695289045572281, -0.0005117006367072463, 0.000142752644023858, -0.009443080984055996, 0.03461571782827377, 0.04245223477482796, 0.036093611270189285, -0.059637539088726044, 0.03385176137089729, -0.014750936068594456, 0.019961325451731682, -0.02692411281168461, 0.01438502874225378, 0.00941298808902502, 0.025583313778042793, -0.027827896177768707, -0.014070870354771614, 0.010318026877939701, -0.05539197102189064, 0.0407869815826416, -0.10628092288970947, -0.03237881138920784, -0.024698009714484215, -0.005708746612071991, -0.021222352981567383, -0.026825476437807083, -0.040154412388801575, -0.03643183410167694, 0.018481429666280746, 0.061568714678287506, -0.02038491517305374, 0.010725623928010464, 0.002322831191122532, -0.006087561137974262, 0.03278007358312607, -0.026723608374595642, -0.023459143936634064, -0.0010066998656839132, 0.008383775129914284, -0.029995914548635483, 0.00853887852281332, -0.048032309859991074, 0.02581937611103058, -0.032560333609580994, 0.026115214452147484, -0.0008621753077022731, 0.018081195652484894, -0.03138433024287224, 0.014957038685679436, 0.009479778818786144, 0.0050733755342662334, 0.0049023134633898735, -0.014727883040904999, 0.0021673112642019987, -0.029132522642612457, 0.0012249683495610952, 0.0077381432056427, -0.042702410370111465, -0.039508454501628876, -0.017941433936357498, -0.012684046290814877, -0.08208254724740982, 0.020061315968632698, -0.012387321330606937, -0.026659559458494186, -0.007410984020680189, -0.006107127293944359, -0.017336111515760422, 0.032272979617118835, -0.01695183664560318, 0.001405666465871036, 0.029463566839694977, -0.04253605380654335, -0.05515247583389282, -0.007655980996787548, -0.05194471403956413, 0.03256721794605255, -0.04475905001163483, -0.001515390700660646, -0.0250292606651783, 0.022808287292718887, 0.02019658125936985, 0.019160965457558632, -0.021833809092640877, -0.05821659788489342, -0.017428208142518997, 0.009011502377688885, -0.01641410030424595, -0.045229583978652954, -0.04599447920918465, -0.016922909766435623, -0.06830860674381256, -0.03636672720313072, -0.043426863849163055, 0.005149798933416605, 0.04172549769282341, 0.013746965676546097, -0.002442055381834507, -0.002219480462372303, -0.028233440592885017, 0.006004005204886198, -0.0024023146834224463, -0.0077858432196080685, -0.0049916822463274, -0.03992338106036186, 0.06312792003154755, -0.07142019271850586, 0.016974641010165215, -0.04846589267253876, -0.07767967134714127, 0.03282713145017624, -0.012331691570580006, 0.0010281051509082317, 0.02978391945362091, -0.020635142922401428, -0.03140299394726753, -0.03138250112533569, -0.027696914970874786, 0.08016190677881241, -0.015446282923221588, -0.05263323336839676, -0.029798433184623718, -0.034102942794561386, 0.016373563557863235, 0.08703295886516571, 0.03712227940559387, 0.05230405181646347, -0.046919409185647964, 0.011995434761047363, 0.050478849560022354, -0.015538536943495274, -0.007571395020931959, 0.02155815064907074, -0.04099623113870621, -0.011420072056353092, -0.024496110156178474, 0.004540048073977232, 0.0289798304438591, -0.023983577266335487, 0.004035710357129574, -0.0026473808102309704, -0.0031041631009429693, -0.020465128123760223, -0.05514306575059891, 0.018542414531111717, -0.013279476203024387, -0.016345776617527008, 0.019040143117308617, -0.001896815956570208, -0.0333869606256485, 0.08428693562746048, 0.022102385759353638, 0.05157064273953438, 0.061570268124341965, -0.04829166829586029, 0.08127408474683762, -0.011903945356607437, 0.019820820540189743, -0.03972822055220604, -0.0022637336514890194, -0.00629270588979125, 0.030719371512532234, 0.002874787198379636, -0.011008832603693008, -0.04332495853304863, 0.07454325258731842, 0.05251943692564964, 0.005486789625138044, 0.0029729052912443876, 0.009188004769384861, 0.011744755320250988, 0.054149605333805084, -0.020025882869958878, 0.016763754189014435, 0.036740925163030624, -0.027493497356772423, -0.00085447944002226, 0.016229888424277306, -0.007648578844964504, -0.025438226759433746, -0.0623701810836792, 0.04349079355597496, 0.01067573856562376, 0.046051058918237686, -0.06336849927902222, 0.023274464532732964, 0.001071311766281724, 0.037913884967565536, 0.025936968624591827, 0.03213988244533539, -0.03430159017443657, 0.04247084632515907, 0.02718816138803959, -0.04756849631667137, -0.011185324750840664, -0.009847418405115604, 0.027002116665244102, -0.0120348846539855, 0.03938271850347519, -0.025055252015590668, 0.034069694578647614, -0.012030444107949734, -0.040513183921575546, 0.041861992329359055, 0.035298123955726624, 0.01801915653049946, -0.0026465384289622307, 0.01693703792989254, 0.07797235995531082, 0.0037166443653404713, 0.01604289747774601, 0.04665641859173775, -0.03524355962872505, -0.044593293219804764, 0.06106815114617348, -0.02789163775742054, -0.025765087455511093, 0.027941113337874413, -0.01651657000184059, 0.04416273161768913, -0.03936249390244484, -0.05187961831688881, -0.030632443726062775, 0.014468124136328697, 0.007901212200522423, 0.04893755540251732, 0.04888645559549332, 0.019185371696949005, 0.04122556373476982, -0.018953463062644005, 0.02437012642621994, 0.02023482322692871, -0.012815620750188828, -0.06831882148981094, -0.0031710700131952763, 0.02109539695084095, 0.06029525771737099, 0.002617154037579894, -0.01478086318820715, 0.052659329026937485, 0.01091413851827383, -0.008253158070147038, 0.03010718710720539, 0.05458078905940056, 0.011783062480390072, -0.01266304962337017, -0.10870199650526047, 0.0066670305095613, 0.032588157802820206, 0.012469078414142132, 0.00432489113882184, 0.08907701820135117, 0.05743999034166336, -0.018282536417245865, -0.011561695486307144, 0.01220414787530899, -0.00799011904746294, 0.03381066769361496, 0.013871104456484318, -0.015781795606017113, 0.008520971052348614, 0.03731314092874527, 0.031936902552843094, -0.005162807647138834, 0.0045155808329582214, -0.02212510257959366, 0.01084806676954031, -0.014420642517507076, 0.00763695640489459, 0.02772044576704502, -0.006230161525309086, 0.0015594703145325184, -0.03734461963176727, 0.060115229338407516, 0.0021304921247065067, -0.01622106321156025, -0.026540976017713547, -0.0312960110604763, -0.023880386725068092, 0.09168466180562973, 0.0040817828848958015, 0.014011832885444164, -0.07348866760730743, -0.09306486696004868, 0.007529827766120434, -0.07287951558828354, -0.06277596950531006, -0.11154242604970932, -0.03237200155854225, -0.04932279884815216, 0.012651514261960983, 0.00592791335657239, -0.07221034169197083, -0.04727098345756531, 0.03460061177611351, -0.013702339492738247, 0.00201366376131773, -0.04913346469402313, -0.04698054492473602, 0.04354684427380562, -0.03516679257154465, 0.009716750122606754, 0.006844005547463894, -0.04285375773906708, 0.052646003663539886, 0.039105374366045, 0.02386026456952095, -0.08020584285259247, -0.0025990966241806746, -0.024026883766055107, -0.005694249179214239, -0.029177362099289894, -0.014848161488771439, 0.03393246605992317, 0.010565219447016716, 0.014364839531481266, -0.00019168457947671413, -0.046823762357234955, 0.016987472772598267, -0.00039242178900167346, 0.007188254036009312, -0.02416587434709072, -0.015896189957857132, 0.010164176113903522, -0.009558376856148243, -0.03081315942108631, 0.01477159932255745, 0.033631086349487305, 0.02418350614607334, 0.04296065494418144, -0.01823871210217476, -0.055680226534605026, -0.0314055010676384, 0.016049424186348915, 0.05860580503940582, 0.017167221754789352, 0.02761518396437168, 0.04897359386086464, 0.020176632329821587, 0.008573907427489758, -0.023131797090172768, 0.0305556021630764, -0.012521511875092983, -0.015335393138229847, 0.05961017310619354, 0.0230479147285223, 0.02620997652411461, -0.022195963189005852, -0.011697779409587383, 0.0038529839366674423, 0.016992274671792984, 0.09904453903436661, 0.052132777869701385, 0.030193781480193138, 0.05936422571539879, -0.04594757407903671, 0.02984878234565258, 0.025887051597237587, 0.02757798694074154, 0.007847042754292488, -0.037772685289382935, 0.016248958185315132, 0.03152041509747505, 0.02728988416492939, 0.009749101474881172, 0.04394889250397682, -0.06325004994869232, -0.053940366953611374, 0.011553352698683739, -0.023731444031000137, -0.030357830226421356, 0.016254154965281487, -0.04723336175084114, 0.018033159896731377, 0.012834519147872925, -0.07538678497076035, 0.046275679022073746, 0.04652111604809761, -0.03539756312966347, -0.056959591805934906, -0.020831746980547905, 0.04132050275802612, 0.01036026980727911, -0.04188459366559982, 0.015952175483107567, -0.049663130193948746, 0.016726616770029068, 0.034463152289390564, -0.06849150359630585, -0.0007417619926854968, 0.0617123618721962 ]
<p>I am having some troubles trying to classify a modified photon gas into which phase transition it belongs (if it really is a phase transition).</p> <p>First of all, it is a photon gas that interacts with an external electric field, so the q-potential (from the grand canonical ensemble) depends on the external field and the temperature alone. The potential is continuous but not analytic only when the external field is varied (if the external field is maintained fixed it might be on one side or the other of the critical point, independently of the temperature). Because the density of energy is the derivative with respect to $\beta$, it has the same qualitative properties of the q-potential.</p> <p>Now, I've found two definitions for phase transitions, Ehrenfest's one and the "modern" one. Following Ehrenfest's classification I found that it's a first order transition since the discontinuity appears in the first derivative of the potential with respect to a thermodynamic variable, the electric field. But, following the "modern" definition, I found that it is a second order phase transition, or, in the modern classification, a continuous phase transition, because the entropy doesn't have a discontinuity and thus the system doesn't require a latent heat to perform the transition.</p> <p>My questions are, have I well understood the definitions? Is the system really having a phase transition? And, if it does, which one is it having or it is of a third kind I didn't mention?</p> <p>Thanks</p>
g8401
[ -0.005886537488549948, -0.04281163588166237, 0.010867871344089508, -0.012777334079146385, 0.018224669620394707, -0.02930430881679058, -0.037324920296669006, 0.04417009279131889, -0.0033740438520908356, 0.012107819318771362, -0.004057763144373894, 0.031234033405780792, 0.011208545416593552, -0.016826335340738297, -0.023267023265361786, -0.038834698498249054, 0.0668412372469902, 0.04447515681385994, 0.013642760924994946, -0.017330307513475418, -0.04489165171980858, -0.0011441177921369672, -0.0010413393611088395, -0.09770113974809647, 0.03137149661779404, -0.006312512326985598, 0.059845663607120514, -0.01484146248549223, 0.0035015386529266834, -0.07985875010490417, 0.006124406587332487, 0.05305192247033119, 0.028098013252019882, 0.017575714737176895, 0.029591646045446396, -0.015978731215000153, 0.08796426653862, 0.027137167751789093, 0.03436717763543129, -0.008867406286299229, 0.02765681780874729, 0.06385122239589691, 0.03632279112935066, -0.0033894723746925592, 0.03596126288175583, 0.03652764484286308, -0.02271874062716961, -0.019036201760172844, 0.017578406259417534, 0.06758958101272583, 0.07898831367492676, 0.05189366638660431, -0.0020295658614486456, -0.010180551558732986, 0.008253873325884342, 0.00019166822312399745, 0.013939977623522282, 0.05938422307372093, 0.022425279021263123, -0.027358338236808777, -0.050471317023038864, 0.026835504919290543, 0.027617931365966797, -0.012427091598510742, 0.03390999138355255, -0.03454536572098732, -0.04907752946019173, -0.014001067727804184, -0.0891910195350647, -0.03954211622476578, -0.03439946845173836, -0.034463368356227875, 0.011662681587040424, 0.061254583299160004, 0.039140425622463226, -0.019303208217024803, -0.04658730700612068, -0.056327033787965775, 0.007688069716095924, -0.03780008852481842, -0.0743720531463623, -0.02644498273730278, 0.009306530468165874, 0.022642437368631363, 0.03383312374353409, -0.03452334180474281, -0.021947648376226425, -0.03460049256682396, -0.0028972295112907887, -0.004032459110021591, 0.05921201780438423, 0.0074232337065041065, 0.05482514575123787, -0.016827063634991646, 0.037320949137210846, 0.001606605714187026, -0.02131282165646553, 0.03479467332363129, 0.0553169883787632, -0.017080355435609818, -0.04966611787676811, -0.016300823539495468, 0.011803305707871914, -0.0470009483397007, -0.06432360410690308, 0.017738528549671173, -0.0033724848181009293, -0.009840788319706917, -0.00271842023357749, 0.003785851178690791, -0.019992200657725334, 0.0039847190491855145, -0.03223128989338875, -0.017977891489863396, -0.015364056453108788, -0.009884966537356377, 0.05521607771515846, -0.07577699422836304, -0.005420204252004623, 0.03749783709645271, 0.04139705374836922, 0.01145949587225914, 0.07168732583522797, 0.056082598865032196, 0.0017092118505388498, -0.02520942874252796, -0.03918175399303436, 0.005155653692781925, 0.023275334388017654, -0.0374823659658432, -0.050278544425964355, 0.04082563892006874, -0.006419427692890167, 0.05145075172185898, 0.00715496763586998, -0.009186808951199055, 0.07350783050060272, 0.024682478979229927, -0.024056147783994675, -0.01130297128111124, 0.04862777888774872, -0.007846245542168617, 0.004828108008950949, 0.0012707073474302888, -0.031490858644247055, 0.003160034539178014, 0.004937952384352684, -0.005124643445014954, 0.006207290571182966, 0.032081540673971176, 0.0371817946434021, 0.046621911227703094, -0.02234465256333351, -0.05433095991611481, 0.007735061924904585, 0.01167867798358202, 0.018082017078995705, 0.02624097652733326, -0.02911755070090294, -0.014282145537436008, 0.04602707177400589, -0.0104836979880929, 0.024439362809062004, -0.009862804785370827, 0.028791749849915504, -0.07928044348955154, -0.001185808563604951, -0.031000247225165367, -0.01386282779276371, 0.00540944142267108, 0.05878729373216629, -0.0020842498634010553, -0.006668651942163706, 0.058706700801849365, 0.002430671127513051, 0.07168292999267578, 0.03850455954670906, -0.021353131160140038, 0.015349344350397587, -0.0031152048613876104, -0.05010949447751045, 0.002318704966455698, 0.022708697244524956, -0.014833169057965279, -0.0025105667300522327, 0.04063475877046585, -0.022512640804052353, 0.025788335129618645, -0.012070597149431705, -0.027035003527998924, -0.07665553689002991, 0.01384242344647646, 0.008341781795024872, -0.027672190219163895, 0.007346753031015396, 0.015594459138810635, -0.025757497176527977, -0.037908103317022324, -0.07335155457258224, -0.0795246884226799, -0.018373657017946243, 0.04980739206075668, 0.008010323159396648, 0.01251003798097372, 0.034476324915885925, 0.004671402741223574, 0.006148893386125565, -0.046821217983961105, -0.008988511748611927, 0.043360158801078796, 0.010035120882093906, -0.046229857951402664, 0.07314205914735794, 0.03088662587106228, -0.020695796236395836, 0.016544904559850693, -0.004782159812748432, 0.02656731568276882, 0.023269273340702057, 0.053263552486896515, -0.013974552974104881, 0.03480938449501991, 0.03849034756422043, -0.02970673330128193, 0.008091559633612633, -0.053435068577528, -0.004798206500709057, -0.0020233418326824903, -0.00003601586286094971, 0.05556058883666992, -0.01666058972477913, 0.003750181756913662, -0.0462176650762558, -0.06294608116149902, 0.027871329337358475, 0.020739195868372917, -0.08406179398298264, -0.004408149980008602, 0.059669144451618195, 0.04143098369240761, 0.026040643453598022, -0.06495273113250732, -0.05260905250906944, 0.04813866317272186, 0.013225676491856575, -0.05111759155988693, 0.03412431478500366, 0.02901567704975605, -0.005760790314525366, -0.043955013155937195, 0.03813425451517105, -0.022331060841679573, -0.017890265211462975, -0.027926724404096603, -0.026242898777127266, -0.0162507314234972, 0.008015031926333904, 0.045287322252988815, -0.029436547309160233, 0.003934063017368317, -0.022603875026106834, -0.006466270424425602, -0.015169612132012844, -0.0001533829781692475, 0.009811042807996273, -0.011496366001665592, -0.03965053707361221, 0.05884070694446564, -0.013948981650173664, -0.003616535570472479, 0.04659917950630188, 0.014677907340228558, 0.026745522394776344, -0.033506687730550766, 0.05160963907837868, 0.01874903216958046, -0.00940664578229189, -0.05001881346106529, 0.0990167185664177, -0.04167035594582558, -0.013028394430875778, -0.009188970550894737, -0.011774060316383839, -0.028468916192650795, 0.04601340368390083, -0.0544833205640316, 0.04069211706519127, 0.06896766275167465, -0.0024678281042724848, -0.015939917415380478, 0.0066016316413879395, 0.04188556969165802, -0.039766788482666016, 0.03413071110844612, -0.05428210645914078, -0.031476691365242004, -0.048457857221364975, -0.027405845001339912, -0.003586650127544999, 0.0063154189847409725, -0.029029907658696175, -0.06529897451400757, 0.007575159426778555, 0.016398366540670395, 0.07897356897592545, -0.017568126320838928, -0.056128185242414474, -0.053848713636398315, -0.009471048600971699, 0.0032143336720764637, -0.013926695100963116, 0.09101904928684235, 0.015235627070069313, -0.01567015051841736, -0.005509461276233196, 0.0033784247934818268, -0.0199965201318264, 0.03078141063451767, 0.03132859617471695, -0.00848199613392353, -0.014561583288013935, -0.00270104524679482, -0.027145113795995712, -0.03254891559481621, 0.062209974974393845, 0.05969651788473129, -0.0019105905666947365, -0.03013591468334198, 0.007034656126052141, 0.00420676963403821, -0.0012227753177285194, -0.013167530298233032, 0.007345018908381462, -0.06386064738035202, 0.00022438941232394427, 0.020528433844447136, -0.05192312225699425, 0.020821720361709595, -0.01410441193729639, 0.02424379251897335, 0.028644103556871414, -0.036249835044145584, -0.0008282054914161563, 0.060119885951280594, -0.05403140187263489, -0.08206260204315186, 0.02998672053217888, -0.012725120410323143, -0.06847580522298813, -0.022291358560323715, -0.0015829644398763776, -0.011384290643036366, 0.046136341989040375, 0.02421167865395546, -0.05015425756573677, 0.011603925377130508, -0.0024339391384273767, 0.004215584602206945, 0.016388362273573875, 0.010472593829035759, -0.02753089927136898, -0.061321429908275604, 0.03917999193072319, 0.006213672459125519, -0.00980949867516756, 0.015698792412877083, -0.007046957965940237, 0.0068479799665510654, -0.02410431206226349, -0.025616098195314407, 0.04377833381295204, 0.003936829511076212, -0.019790058955550194, -0.026658931747078896, 0.00044905501999892294, -0.006583437789231539, 0.005000773351639509, -0.028346892446279526, -0.025106918066740036, 0.02236528880894184, -0.034964077174663544, -0.043846458196640015, 0.05251944437623024, 0.012163737788796425, 0.07540351152420044, 0.0013283905573189259, 0.018548812717199326, -0.06955508142709732, -0.0001489172864239663, -0.057839926332235336, -0.012640631757676601, 0.024660589173436165, -0.02574540674686432, -0.05023478716611862, -0.01318699587136507, 0.036479249596595764, 0.03723011538386345, -0.021734027191996574, -0.03942934423685074, 0.007571341469883919, 0.06139591708779335, -0.03189213573932648, 0.050951872020959854, -0.04309949278831482, 0.01456076093018055, -0.020901430398225784, 0.018738193437457085, -0.06256262958049774, -0.034077852964401245, -0.07106403261423111, -0.011614546179771423, -0.0031756064854562283, -0.015967804938554764, -0.0444980263710022, 0.050599824637174606, -0.01636577397584915, 0.01331708300858736, -0.015416211448609829, -0.04134146124124527, -0.03282976150512695, -0.012660636566579342, -0.03647240251302719, -0.014401381835341454, -0.009346970357000828, 0.025839928537607193, 0.039280738681554794, 0.10667586326599121, 0.019030913710594177, -0.05573299527168274, -0.014526570215821266, 0.018320567905902863, 0.06446018069982529, 0.00914288591593504, 0.017811404541134834, -0.022931041195988655, 0.03601497411727905, -0.09084004908800125, -0.026426836848258972, 0.04998579993844032, 0.032958079129457474, 0.07264809310436249, -0.028521334752440453, 0.013108501210808754, -0.013032576069235802, 0.008702890016138554, 0.003852400230243802, -0.04394879192113876, -0.00603308854624629, 0.0004490606370382011, -0.011318211443722248, -0.025294817984104156, -0.003226688364520669, -0.018064869567751884, -0.008924813941121101, 0.017223890870809555, -0.022767137736082077, -0.038941651582717896, -0.02303195372223854, -0.04852212220430374, 0.022055964916944504, -0.021873699501156807, -0.019776973873376846, 0.023864129558205605, -0.004236813634634018, 0.057535700500011444, -0.0033069439232349396, -0.07400670647621155, 0.04269981011748314, -0.019741052761673927, -0.07754715532064438, 0.011945539154112339, -0.010786298662424088, -0.003415603656321764, 0.015772897750139236, 0.00705724349245429, 0.03274404630064964, 0.004965492058545351, 0.029197532683610916, 0.033515699207782745, -0.014184185303747654, 0.029059572145342827, 0.026362044736742973, 0.029589632526040077, 0.010392849333584309, -0.03342372924089432, -0.038203779608011246, -0.0009149567922577262, 0.010257408022880554, 0.04601111635565758, -0.01066767517477274, 0.013477465137839317, 0.020654819905757904, 0.023733768612146378, 0.006457822863012552, 0.03461148962378502, 0.022769426926970482, 0.0230863019824028, -0.00933112669736147, 0.018740715458989143, 0.016846081241965294, -0.10942760854959488, 0.045371949672698975, -0.018015392124652863, -0.005794500466436148, -0.015067853964865208, 0.044395916163921356, 0.01302780956029892, 0.0308917835354805, 0.019466422498226166, 0.038399312645196915, -0.03814058005809784, 0.009894752874970436, -0.03297432139515877, 0.02403104305267334, 0.02345377951860428, -0.013324860483407974, -0.046301644295454025, -0.0421430803835392, 0.0045145051553845406, -0.08166353404521942, 0.04292276129126549, 0.011011377908289433, 0.028984088450670242, -0.07769335061311722, 0.06759120523929596, -0.001975956605747342, -0.011325829662382603, -0.07071849703788757, 0.020793406292796135, 0.01264328695833683, 0.014706695452332497, 0.021775508299469948, 0.05358293280005455, -0.011529779992997646, -0.043383195996284485, -0.0584280751645565, -0.0230860635638237, 0.05811653286218643, 0.07005947828292847, 0.019383080303668976, -0.06758008152246475, -0.009804974310100079, -0.025444449856877327, -0.03495529294013977, 0.06745393574237823, -0.01495967898517847, 0.014479444362223148, 0.011770115233957767, -0.025423429906368256, -0.04702881723642349, 0.055922988802194595, -0.04178725928068161, 0.012230297550559044, -0.01963372528553009, -0.022226063534617424, 0.0234025027602911, 0.04270538315176964, 0.002598612802103162, 0.0014826621627435088, -0.0020002180244773626, 0.048223286867141724, -0.009051437489688396, -0.011230290867388248, -0.07257051765918732, 0.048318732529878616, -0.05758483707904816, 0.03830147534608841, -0.027400044724345207, 0.02476472221314907, 0.006772077176719904, 0.048597440123558044, 0.03110380843281746, 0.04283599555492401, 0.028478316962718964, -0.013958725146949291, -0.044190116226673126, -0.0225021131336689, 0.011402609758079052, -0.04130237177014351, 0.008815431036055088, -0.03245822712779045, 0.0015057718846946955, 0.06446019560098648, -0.054944682866334915, -0.0003299226227682084, 0.020301885902881622, -0.04021736979484558, 0.0015432988293468952, -0.012906873598694801, 0.02405603602528572, 0.00734242657199502, -0.02962474711239338, -0.07134328037500381, 0.0028497721068561077, 0.009755653329193592, 0.013662880286574364, -0.05405863747000694, -0.015618542209267616, 0.010207578539848328, 0.08743686228990555, -0.022146286442875862, -0.02096831239759922, -0.01094871573150158, -0.008146611973643303, 0.008724951185286045, 0.06625349074602127, 0.005368710029870272, 0.11290421336889267, 0.01380983553826809, 0.010166767053306103, 0.0036729113198816776, 0.03518896549940109, -0.05855930969119072, -0.023609677329659462, 0.008415808901190758, -0.01352920662611723, -0.046930111944675446, 0.057310063391923904, -0.02372336946427822, 0.01660015806555748, -0.0319276787340641, -0.02867279201745987, 0.05532253161072731, -0.0027377158403396606, 0.05198413133621216, 0.02560824528336525, -0.04816526547074318, 0.017810959368944168, 0.03203056380152702, 0.016300924122333527, 0.025028454139828682, -0.026907645165920258, -0.0074406955391168594, -0.004486721009016037, 0.016500374302268028, 0.008840528316795826, -0.1076173335313797, -0.0036178736481815577, 0.03283470496535301, 0.009111113846302032, 0.060934778302907944, 0.042966682463884354, 0.04795887693762779, -0.022494573146104813, -0.0012345195282250643, 0.015886608511209488, 0.0510416105389595, -0.006098549347370863, -0.03768610209226608, 0.050471510738134384, -0.011892552487552166, -0.022727621719241142, -0.007762925699353218, -0.01137359905987978, -0.01758858934044838, 0.11833134293556213, 0.005649670492857695, 0.055539365857839584, 0.0023147226311266422, -0.03712482005357742, -0.030929019674658775, 0.008859015069901943, -0.016996245831251144, 0.04957131668925285, -0.007906009443104267, 0.07250280678272247, 0.005688250530511141, -0.04446520283818245, -0.016841720789670944, -0.03957366943359375, -0.02071465738117695, -0.040192943066358566, -0.056322261691093445, 0.010033460333943367, 0.02327151782810688, -0.027947207912802696, 0.05626986175775528, 0.05313414707779884, 0.02113841101527214, -0.007147911936044693, 0.003549898276105523, 0.03998953849077225, -0.0011252638651058078, -0.09255054593086243, -0.05216299369931221, 0.05405322089791298, -0.04361627250909805, 0.02583242394030094, 0.03041130118072033, 0.023138483986258507, -0.008095896802842617, -0.017002731561660767, -0.05388728529214859, 0.016505930572748184, 0.029230983927845955, -0.00335756060667336, 0.013502221554517746, 0.012689365074038506, 0.0008263022755272686, 0.0019962689839303493, -0.023180635645985603, 0.011137989349663258, -0.05504106730222702, 0.001849871245212853, -0.022165747359395027, 0.000041219518607249483, 0.032323721796274185, -0.056575924158096313, 0.011726251803338528, 0.045041538774967194, -0.026062123477458954, 0.014581063762307167, 0.0027965714689344168, -0.0006812035571783781, -0.0024888464249670506, -0.0084768608212471, -0.0018354721833020449, 0.04555221647024155, 0.00041698734275996685, -0.00895095244050026, -0.020810503512620926, 0.009485763497650623, -0.03679009526968002, -0.02547215111553669, -0.0346996933221817, -0.005735341925173998, -0.03175283595919609, -0.041335053741931915, 0.00479621347039938, -0.05767954885959625, -0.05193714052438736, 0.019481105729937553, -0.013776436448097229, 0.0019520513014867902, -0.05900983884930611, 0.010320321656763554, 0.035101402550935745, 0.013779752887785435, 0.05865092575550079, -0.04691360890865326, -0.003998910542577505, -0.06639546900987625, 0.07339829206466675, 0.0022979520726948977, 0.07467807829380035, -0.06675537675619125, -0.019727567210793495, 0.04299125075340271, 0.05712657794356346, 0.03603873401880264, -0.06910528242588043, -0.042718373239040375, 0.021425701677799225, 0.033428728580474854, -0.02466472238302231, -0.029302937909960747, -0.004752596840262413, 0.049400776624679565, 0.035334933549165726, -0.03790882229804993, -0.008936842903494835, -0.0035449531860649586, 0.010591268539428711, 0.016785908490419388, -0.06565631181001663, -0.009027138352394104, 0.05872797593474388, 0.0007400294998660684 ]
<p>I'm thinking equivalence principle, possibilities of unbounded space-time curvature, quantum gravity ...</p>
g8402
[ -0.04679451510310173, 0.0706939622759819, -0.003743228502571583, -0.05484506115317345, 0.017849693074822426, 0.011579209938645363, 0.007127394899725914, -0.03516243398189545, -0.022516703233122826, 0.05093473941087723, 0.035402875393629074, -0.007321227807551622, 0.0008111093775369227, 0.06517823785543442, -0.029618827626109123, 0.06377621740102768, 0.030978692695498466, -0.005731114186346531, 0.04241395369172096, -0.03468214347958565, 0.03444996103644371, -0.010677107609808445, -0.006334672216325998, -0.003855740185827017, -0.005391228012740612, -0.009999576956033707, 0.03532656282186508, -0.039250556379556656, -0.03946959972381592, -0.03344489634037018, 0.00863044522702694, 0.019493162631988525, 0.0319136343896389, -0.0438888818025589, -0.011373757384717464, 0.0052431439980864525, 0.04276316985487938, 0.03260493278503418, 0.04106084257364273, -0.019214719533920288, 0.008700924925506115, -0.02217674069106579, -0.007798910140991211, 0.015388634987175465, 0.05272158980369568, 0.015207984484732151, 0.0204115379601717, 0.049577370285987854, 0.07096897810697556, -0.010210267268121243, 0.019642265513539314, 0.054696887731552124, 0.056488797068595886, -0.025113139301538467, 0.021403180435299873, -0.011340800672769547, -0.0005680500762537122, -0.027705535292625427, 0.054893068969249725, -0.00220471085049212, -0.018766820430755615, 0.0020675617270171642, 0.05587680637836456, 0.04013342410326004, 0.018473122268915176, 0.014307571575045586, -0.030293306335806847, 0.004690326750278473, -0.00812419131398201, 0.02087431773543358, 0.04742385074496269, -0.07763368636369705, -0.0008911337936297059, 0.051449745893478394, -0.011736871674656868, 0.06194328889250755, 0.005254226271063089, -0.0001772028481354937, -0.014361145906150341, -0.041349127888679504, -0.0679561048746109, -0.029967138543725014, 0.002456034766510129, -0.009906752966344357, 0.07540073245763779, -0.10670382529497147, -0.017488272860646248, 0.03303160518407822, -0.02530268207192421, 0.04869362711906433, 0.010186364874243736, -0.08671055734157562, 0.051146745681762695, 0.008363962173461914, 0.005101306363940239, -0.004278984852135181, 0.0414644218981266, 0.03790264204144478, -0.08302755653858185, -0.045676060020923615, -0.05633992329239845, -0.00016494317969772965, 0.055785562843084335, 0.03753460943698883, -0.03015301376581192, -0.022760506719350815, -0.010185887105762959, -0.0058051059022545815, 0.020829206332564354, -0.05883199721574783, 0.018119214102625847, 0.015468058176338673, -0.02295798249542713, -0.02715149149298668, -0.02471131831407547, -0.03110155649483204, 0.046624213457107544, -0.012636627070605755, -0.06073913723230362, 0.05609501153230667, 0.0004540751688182354, 0.038847457617521286, 0.017182055860757828, 0.04408736526966095, -0.015096142888069153, 0.05114196985960007, -0.02112438715994358, -0.010533173568546772, 0.03489653766155243, -0.007644742261618376, 0.0950353667140007, 0.006852917838841677, -0.008097794838249683, 0.013376650400459766, -0.024558324366807938, 0.022104831412434578, -0.03375367820262909, -0.011005986481904984, -0.032408032566308975, -0.042452652007341385, -0.0196792334318161, -0.06513587385416031, 0.007090329192578793, 0.015247661620378494, -0.018317824229598045, -0.033260028809309006, 0.0021117888391017914, -0.012176482938230038, -0.018367648124694824, 0.017703944817185402, 0.004097081255167723, 0.0887250080704689, -0.009844580665230751, -0.052889131009578705, 0.021702995523810387, 0.021864691749215126, -0.0418715663254261, 0.015470735728740692, 0.05008680373430252, -0.06525018811225891, -0.00819310825318098, 0.0013070052955299616, 0.03934389352798462, -0.0498269684612751, -0.008622914552688599, -0.001220071455463767, 0.01885068044066429, -0.01147179864346981, 0.04249124974012375, -0.04240472987294197, -0.041381094604730606, -0.013117715716362, -0.028282254934310913, 0.049552977085113525, -0.03705349192023277, 0.0495419017970562, -0.0788397341966629, -0.03436598554253578, -0.03795924037694931, 0.006914341356605291, 0.00812705047428608, -0.03646065667271614, 0.033776555210351944, 0.006944633089005947, -0.03345675393939018, 0.005807276349514723, 0.0035555551294237375, 0.0005135316750966012, -0.045948635786771774, 0.03261357918381691, -0.02520427294075489, -0.017750464379787445, 0.02720753289759159, 0.05415029078722, 0.01644822023808956, -0.003441873239353299, 0.03827676922082901, -0.02891417406499386, -0.030776700004935265, 0.02944078855216503, 0.03924347832798958, 0.09681117534637451, 0.04306173324584961, -0.008313363417983055, -0.0008206577622331679, 0.04826517775654793, -0.0005781931686215103, 0.009065893478691578, 0.029719838872551918, -0.03230808302760124, 0.13324417173862457, -0.07628195732831955, 0.061455391347408295, -0.0029180014971643686, -0.041195981204509735, 0.03777313232421875, 0.023295242339372635, 0.0049472348764538765, -0.0161553043872118, 0.030792297795414925, 0.04126101732254028, 0.009109364822506905, 0.08916734158992767, 0.0006195189198479056, 0.01564585603773594, -0.05920206010341644, -0.09083691239356995, -0.07186787575483322, -0.029217762872576714, -0.003926531877368689, -0.030577588826417923, -0.05333289876580238, 0.018443170934915543, -0.01713944599032402, 0.04106955602765083, 0.03401866927742958, 0.0295222457498312, 0.0012611143756657839, 0.022203095257282257, -0.011734971776604652, 0.03449917212128639, -0.010036968626081944, -0.007582670543342829, 0.04314291849732399, 0.04042431712150574, -0.02044539526104927, -0.0013281290885061026, -0.056193530559539795, 0.01664116233587265, 0.03836456686258316, -0.004534625913947821, -0.03309161961078644, -0.02491922862827778, -0.007482635788619518, -0.021183334290981293, 0.05581334978342056, 0.05414903163909912, -0.015275147743523121, -0.048555005341768265, -0.04565246403217316, 0.02129761502146721, 0.02646051160991192, -0.07152166962623596, 0.04761415347456932, -0.02778489701449871, -0.002873067045584321, -0.002394096925854683, 0.004311708267778158, -0.030197840183973312, 0.01911904849112034, -0.028253961354494095, 0.052605681121349335, -0.016368679702281952, 0.08131276816129684, -0.007235308177769184, 0.08014409244060516, -0.010908744297921658, -0.017131883651018143, -0.02868158370256424, -0.021869216114282608, 0.026395853608846664, -0.0017317392630502582, -0.029623836278915405, 0.02520870417356491, 0.0070623597130179405, -0.02412135899066925, -0.006205116864293814, 0.0455048531293869, 0.015883145853877068, 0.02407391183078289, 0.03410493955016136, 0.043973274528980255, -0.008612826466560364, 0.009172194637358189, -0.077632375061512, -0.0006276135100051761, -0.015806974843144417, -0.01619233377277851, 0.04380873590707779, -0.006654747296124697, -0.021285811439156532, -0.01652180776000023, 0.0587572380900383, -0.02971797063946724, -0.037715088576078415, -0.03186609968543053, -0.003899401519447565, -0.04770932346582413, -0.017814014106988907, -0.06558400392532349, -0.015477720648050308, 0.0097618093714118, -0.023752842098474503, -0.024329593405127525, 0.026328066363930702, -0.012341710738837719, 0.010986648499965668, -0.03486476466059685, 0.006392767187207937, -0.024410512298345566, -0.01332030538469553, -0.01923157088458538, -0.008245943114161491, -0.01586960069835186, 0.017804739996790886, 0.008044284768402576, -0.02809690497815609, 0.013877750374376774, -0.04243328049778938, 0.03708231449127197, 0.07291978597640991, 0.011750283651053905, 0.04842185229063034, 0.012084059417247772, -0.025126988068223, -0.02161017432808876, 0.025313720107078552, 0.03744794800877571, 0.08591014891862869, -0.025837920606136322, -0.07414041459560394, 0.03348572552204132, -0.03345659002661705, 0.03629712387919426, -0.016275737434625626, 0.0010506641119718552, 0.0324585996568203, 0.011232579126954079, 0.010297177359461784, 0.045069918036460876, -0.012181530706584454, -0.05704926699399948, 0.05233857408165932, 0.01826518215239048, 0.05783899873495102, 0.041126374155282974, 0.06559202820062637, 0.05938657000660896, 0.025561874732375145, -0.028011709451675415, -0.015363425947725773, 0.005327034275978804, 0.0475897490978241, 0.03833361715078354, 0.02998264878988266, -0.017043747007846832, -0.009551934897899628, 0.0014001462841406465, -0.01914672739803791, 0.01801401749253273, 0.04061337560415268, -0.01278515625745058, 0.016754360869526863, -0.021836567670106888, 0.03450741991400719, -0.06734708696603775, -0.00020235271949786693, -0.008040354587137699, 0.0017592478543519974, -0.023342693224549294, 0.069077268242836, 0.030244644731283188, 0.07322635501623154, -0.011868719942867756, 0.013726930133998394, 0.05846761167049408, -0.05296020954847336, -0.015004091896116734, -0.008882294408977032, 0.008942830376327038, -0.02454901486635208, -0.01320928055793047, -0.05015295743942261, -0.0031939875334501266, -0.02159152925014496, 0.0458284467458725, -0.02677861973643303, -0.04572472721338272, 0.005869665648788214, -0.02051289565861225, 0.04758051782846451, 0.01686936244368553, 0.014245118945837021, 0.019627375528216362, -0.04777601361274719, -0.045899759978055954, 0.0667230561375618, -0.03908989951014519, -0.054792620241642, 0.006138456519693136, 0.01619001291692257, -0.04689963534474373, 0.034705664962530136, -0.05471055582165718, 0.013756513595581055, 0.0017177668632939458, -0.013288674876093864, -0.10743995755910873, 0.021279796957969666, 0.02195459045469761, 0.001349004334770143, 0.020595349371433258, 0.04407712444663048, -0.02689669094979763, 0.014915195293724537, 0.06767404824495316, 0.02413995750248432, -0.03966343402862549, -0.04219497740268707, -0.09176269918680191, -0.031531739979982376, 0.003045934485271573, -0.03313789144158363, 0.007384757045656443, -0.03961435705423355, 0.02703060768544674, -0.01068418100476265, 0.036265626549720764, -0.040253616869449615, 0.008235331624746323, 0.07264145463705063, -0.004861797671765089, 0.02395368367433548, -0.024004345759749413, 0.03177938237786293, 0.04272447153925896, 0.013012164272367954, -0.05299666151404381, -0.007661620620638132, -0.025387277826666832, -0.03483176976442337, 0.011551649309694767, -0.04730125516653061, 0.01625901088118553, -0.03405289351940155, -0.043010909110307693, -0.048468995839357376, -0.005655068904161453, -0.01442953571677208, 0.04533393308520317, -0.03805898502469063, 0.03577132150530815, 0.0313618928194046, -0.000019976403564214706, -0.01584991067647934, -0.0134531045332551, -0.10510818660259247, 0.03873598203063011, -0.060734596103429794, -0.022330239415168762, -0.00715138204395771, 0.000010994291187671479, -0.0009843868901953101, 0.0009590145782567561, -0.021446464583277702, 0.024625401943922043, -0.015886329114437103, 0.0011895459610968828, -0.00026749991229735315, -0.031515516340732574, -0.055734191089868546, -0.038335420191287994, 0.0405564121901989, 0.005452687852084637, -0.005035559646785259, -0.042992569506168365, -0.019099503755569458, 0.023128677159547806, -0.050234004855155945, -0.04904523864388466, -0.0335213840007782, -0.01770200952887535, 0.024577248841524124, 0.0269507747143507, 0.04199350252747536, 0.03995789587497711, -0.004204912111163139, 0.025936448946595192, 0.01770724728703499, -0.03226502612233162, -0.027360549196600914, -0.009072239510715008, -0.013454018160700798, -0.005536149721592665, 0.03959619626402855, 0.05081348493695259, 0.05791549012064934, -0.002621042774990201, -0.07723353058099747, 0.054149944335222244, 0.0038422292564064264, 0.012953542172908783, -0.03418058156967163, 0.006524445489048958, 0.06946107745170593, 0.02819104865193367, -0.0517701730132103, -0.01481388695538044, -0.01515870075672865, -0.04429866001009941, 0.00934566743671894, 0.027777228504419327, 0.019596124067902565, 0.007093857508152723, 0.028756797313690186, 0.022795047610998154, 0.003993067424744368, -0.006968759931623936, 0.04691225290298462, -0.012710943818092346, 0.05973324552178383, -0.022851841524243355, -0.025209719315171242, -0.024602772668004036, -0.017076238989830017, -0.027868783101439476, 0.007041305769234896, 0.08649930357933044, 0.06310223042964935, -0.02139948308467865, -0.0552801787853241, -0.05519777163863182, -0.021168498322367668, -0.01290457509458065, -0.0332864411175251, 0.017062200233340263, -0.09497562050819397, 0.022874297574162483, 0.032149989157915115, -0.08716962486505508, -0.06488818675279617, -0.039974626153707504, -0.0036337508354336023, -0.022802289575338364, -0.012166081927716732, 0.017225658521056175, 0.00043629793799482286, -0.010653282515704632, -0.00287229404784739, 0.045403268188238144, 0.10232218354940414, 0.018822483718395233, 0.007650772109627724, -0.0014376388862729073, -0.052033476531505585, -0.047241877764463425, 0.0027907462790608406, -0.007768428418785334, 0.08034531772136688, -0.053147852420806885, -0.051148056983947754, 0.015269220806658268, 0.060443613678216934, -0.015057487413287163, 0.0011860947124660015, -0.05111338198184967, 0.039559219032526016, -0.06728094816207886, -0.03333818167448044, 0.0052213300950825214, -0.014659630134701729, 0.02091382071375847, 0.023535698652267456, -0.03606384992599487, -0.06643909215927124, 0.04906519129872322, -0.009825227782130241, -0.07136787474155426, 0.025398099794983864, 0.026152044534683228, -0.01089974120259285, -0.033468954265117645, 0.05692856013774872, -0.011721823364496231, 0.00866773258894682, 0.04148218780755997, 0.04495561867952347, -0.04169394448399544, -0.08488328754901886, -0.042562782764434814, -0.03439334034919739, 0.002955447183921933, 0.028789514675736427, -0.004304048605263233, 0.001974931452423334, 0.07903698086738586, -0.06402329355478287, -0.07759355008602142, -0.002290628384798765, -0.005738446488976479, 0.022022312507033348, -0.009890072047710419, -0.04241439327597618, 0.004795845597982407, 0.003089090110734105, -0.03748854994773865, -0.01417488232254982, -0.035988517105579376, 0.018479809165000916, -0.002902775537222624, 0.06494782119989395, 0.04554916173219681, 0.03471773862838745, -0.0007430688128806651, 0.022768378257751465, 0.007259111385792494, -0.011465868912637234, 0.006446071434766054, 0.04840688779950142, 0.033562496304512024, 0.02351151965558529, -0.02537173591554165, -0.0008272225968539715, -0.0039896294474601746, -0.02811671420931816, 0.030402077361941338, 0.014006382785737514, -0.005816016346216202, 0.00030573297408409417, 0.0022088505793362856, -0.032391298562288284, 0.027828799560666084, 0.009099649265408516, 0.013246171176433563, -0.031767185777425766, 0.034287407994270325, 0.002183871576562524, 0.005873206537216902, -0.009162195026874542, -0.017607487738132477, 0.065802663564682, 0.011673063039779663, -0.04692041501402855, -0.034835994243621826, -0.06597080081701279, -0.01843547821044922, -0.006565190386027098, -0.0037790618371218443, -0.028501030057668686, -0.06460357457399368, -0.018570151180028915, 0.007700938731431961, 0.0097674410790205, 0.02320708893239498, -0.010865731164813042, 0.055984415113925934, 0.01357827614992857, -0.007616356015205383, -0.05077401176095009, -0.009565351530909538, -0.00945085659623146, -0.057577602565288544, -0.03762253373861313, -0.03490438312292099, -0.004988283384591341, 0.020087655633687973, -0.035492513328790665, 0.059279464185237885, 0.017735067754983902, 0.05320284143090248, -0.0010416710283607244, 0.009830087423324585, 0.03995898738503456, 0.024402739480137825, 0.022269194945693016, 0.002198816742748022, 0.023070121183991432, 0.013724389486014843, -0.05219639465212822, 0.0041811177507042885, -0.004320771433413029, 0.0124955540522933, -0.010804029181599617, -0.07311176508665085, 0.0804227739572525, 0.029472628608345985, -0.006195355206727982, 0.015485933981835842, 0.007505913730710745, -0.03560446947813034, -0.02592286467552185, 0.005665931850671768, -0.010312446393072605, -0.026080816984176636, 0.013275926001369953, 0.028540974482893944, -0.02182447351515293, -0.009832278825342655, -0.0190486591309309, 0.023343419656157494, 0.03540385887026787, 0.014932073652744293, -0.01812106929719448, 0.04144451394677162, 0.016570135951042175, -0.004763435572385788, -0.07807816565036774, 0.00812078919261694, 0.02522280067205429, -0.051771070808172226, -0.002319145482033491, 0.04879322275519371, -0.012634189799427986, -0.04625912010669708, -0.01360983308404684, -0.040888238698244095, -0.054726604372262955, -0.0445999950170517, -0.05539670214056969, -0.054672062397003174, -0.0013027959503233433, -0.022217603400349617, -0.026383979246020317, 0.004644090309739113, -0.01353131141513586, 0.0338730588555336, -0.014022364281117916, 0.006685340311378241, -0.005626105237752199, -0.0018892090301960707, -0.0015545630594715476, -0.008850837126374245, 0.016413887962698936, -0.011659127660095692, -0.004349129740148783, 0.016678461804986, 0.004184297285974026, 0.002096266020089388, 0.03553266450762749, -0.0024619700852781534, 0.009053207002580166, 0.0456274189054966, 0.00021692240261472762, 0.04287943243980408, 0.06874773651361465, -0.065011166036129, 0.037552107125520706, 0.037537477910518646, 0.055312272161245346, 0.02476709708571434, -0.010264667682349682, 0.014154727570712566, -0.02954481542110443, 0.015248280949890614, -0.02239583060145378, 0.02837524004280567, -0.022599391639232635, 0.012813090346753597 ]
<p>Pre-face: My step-father and I were turning the heat down on the water heater. He demonstrated that touching the ground wire doesn't shock you.</p> <p>My understanding is that the ground wire doesn't have current unless the case of a short-circuit, or over-abundance of energy. The wire also has very little resistance.</p> <p>My question, if the water heater had a short-circuit or had an access flow of energy. Would he have been shocked? Please explain instead of yes or no.</p>
g8403
[ 0.058530230075120926, 0.0388033427298069, -0.018897496163845062, -0.02591765485703945, 0.0021300569642335176, 0.01641770265996456, 0.09847195446491241, 0.03881165012717247, -0.05481346324086189, -0.018341874703764915, -0.02165692113339901, 0.044581279158592224, -0.055919572710990906, 0.03677705302834511, 0.006979265715926886, -0.027847126126289368, 0.07258297502994537, -0.02967529371380806, 0.035797592252492905, 0.04413369670510292, -0.0165756493806839, -0.019939972087740898, -0.02198799140751362, -0.019700223580002785, -0.021354230120778084, -0.07566685229539871, -0.00041809416143223643, -0.02861626446247101, -0.01222123671323061, -0.017860539257526398, -0.007279415614902973, 0.026174373924732208, 0.03160509467124939, -0.08280108124017715, -0.12210846692323685, 0.014336206018924713, -0.010441412217915058, 0.025092527270317078, -0.03055635280907154, -0.04549306631088257, 0.027103586122393608, 0.0006988920504227281, -0.022410981357097626, -0.020236920565366745, 0.05411003157496452, 0.04506693035364151, -0.06012721732258797, -0.014121118001639843, -0.011607197113335133, -0.00431915232911706, -0.01372386422008276, 0.0003237476048525423, 0.029337918385863304, -0.009878816083073616, 0.00774213345721364, -0.06054408475756645, 0.05164971575140953, -0.028623024001717567, 0.057652220129966736, 0.04875238239765167, -0.039000049233436584, 0.04225791618227959, 0.026612579822540283, -0.026582011952996254, 0.005271719768643379, 0.0044461144134402275, -0.014544905163347721, -0.01813437044620514, 0.0453762449324131, 0.08961554616689682, -0.004121941048651934, -0.029071584343910217, -0.0030790967866778374, -0.0002196653076680377, 0.06331406533718109, 0.007075438741594553, -0.031525611877441406, 0.012397050857543945, 0.019745580852031708, -0.012321284040808678, 0.02791004441678524, -0.0168078001588583, 0.026049161329865456, 0.014500444754958153, -0.0000534345417690929, -0.005835247226059437, -0.02722509577870369, -0.0247962549328804, 0.014494984410703182, -0.04364631697535515, -0.005252290517091751, -0.014482596889138222, 0.04355795681476593, -0.00015057400742080063, -0.04251573607325554, -0.014820431359112263, -0.0009933090768754482, 0.02586241252720356, -0.002350329654291272, 0.01501719281077385, -0.03555198758840561, -0.08341267704963684, -0.03304961323738098, -0.024601493030786514, -0.03348438814282417, 0.053930532187223434, -0.02002384327352047, 0.0057120611891150475, -0.002989205066114664, -0.045636147260665894, -0.011312573216855526, -0.03379093483090401, -0.019206484779715538, 0.025516537949442863, -0.0046246787533164024, 0.016357026994228363, 0.0543234683573246, -0.005980696529150009, -0.039536748081445694, -0.005581509787589312, -0.024644726887345314, 0.027920065447688103, -0.01179785281419754, 0.06566069275140762, -0.0339738205075264, -0.004744533449411392, -0.022858543321490288, 0.036275509744882584, 0.034541938453912735, 0.01586570404469967, -0.048623569309711456, 0.0162483099848032, -0.047096263617277145, 0.011262418702244759, 0.07822607457637787, -0.02182505838572979, 0.0029360675252974033, 0.04212157428264618, -0.016134904697537422, 0.051248110830783844, 0.05732445791363716, 0.017243850976228714, -0.0024426435120403767, -0.053719233721494675, 0.008692871779203415, 0.08004262298345566, -0.043135467916727066, -0.006902194581925869, 0.038481149822473526, 0.0007562567479908466, 0.011264230124652386, 0.04481605812907219, 0.028757145628333092, -0.003272227942943573, 0.04557371139526367, 0.016881173476576805, 0.0056289490312337875, -0.007630782667547464, 0.045268699526786804, 0.023623108863830566, 0.009414559230208397, -0.03314080089330673, 0.05200594291090965, -0.024364659562706947, -0.03796276077628136, -0.021150508895516396, 0.013051623478531837, -0.03540860861539841, -0.007162942551076412, -0.032573044300079346, -0.015076175332069397, 0.037486083805561066, 0.028828341513872147, 0.00625498965382576, -0.05241286754608154, -0.01921931840479374, 0.03653905168175697, -0.05995897576212883, 0.0537438690662384, -0.05495884269475937, -0.07145790010690689, -0.0020291011314839125, 0.00048094757949002087, -0.031789422035217285, -0.01374125201255083, 0.021548477932810783, -0.018093038350343704, -0.016599344089627266, -0.026567667722702026, -0.021094772964715958, -0.07734908908605576, -0.02550460398197174, -0.0408710315823555, 0.055143363773822784, 0.004845783580094576, -0.08097521215677261, -0.011478100903332233, 0.043964751064777374, -0.036187782883644104, 0.013445606455206871, 0.04833587631583214, 0.06284332275390625, 0.025738416239619255, 0.011194715276360512, 0.010868147946894169, 0.06292517483234406, -0.04355398565530777, -0.013498135842382908, 0.04442639276385307, -0.06867079436779022, 0.07130388915538788, 0.027980713173747063, 0.05335765331983566, 0.00030334285111166537, -0.09602092951536179, -0.015056625008583069, -0.005194132216274738, -0.018087750300765038, -0.046902772039175034, -0.0722493976354599, 0.018126368522644043, 0.0023184872698038816, 0.031384292989969254, 0.0014285262441262603, -0.01945183426141739, 0.02293497510254383, -0.029597464948892593, -0.0635301023721695, -0.0584491491317749, 0.02949037402868271, -0.054757773876190186, -0.02945832349359989, -0.044151049107313156, -0.02944178879261017, -0.0007625303114764392, 0.07707986980676651, 0.04425862058997154, 0.0021494219545274973, -0.010175760835409164, -0.06806471943855286, -0.01237048115581274, -0.029809068888425827, 0.01287338137626648, 0.030490197241306305, 0.031397316604852676, 0.0007501982618123293, 0.04669128358364105, 0.01878698542714119, 0.03388683497905731, -0.013567032292485237, 0.050667308270931244, -0.0021947596687823534, -0.04053981974720955, 0.0353330634534359, -0.02787233144044876, -0.008374110795557499, -0.02927516959607601, 0.009658795781433582, -0.04204526171088219, -0.04382067918777466, 0.02522743120789528, 0.0012935659615322948, 0.02408739924430847, -0.010481664910912514, -0.0737239271402359, 0.008495882153511047, -0.049205437302589417, -0.00811214279383421, 0.0324375219643116, -0.020314449444413185, 0.016503935679793358, 0.04286570847034454, -0.03043796494603157, 0.057889990508556366, -0.04257180541753769, 0.017873596400022507, -0.026854971423745155, -0.02712976559996605, -0.015855124220252037, -0.009146338328719139, -0.011471441946923733, 0.02133939415216446, -0.024846531450748444, -0.0023038170766085386, 0.0543333999812603, 0.006057361140847206, -0.03842034190893173, -0.042933180928230286, -0.002033350756391883, -0.010431244038045406, -0.012792705558240414, -0.02303227223455906, 0.02910277247428894, -0.0025302227586507797, -0.00270264339633286, -0.02480730414390564, 0.004006639122962952, -0.042758844792842865, -0.010891365818679333, 0.06239282712340355, 0.01668265461921692, -0.04473235458135605, -0.09254474937915802, -0.0004613498458638787, -0.04507778212428093, -0.033971626311540604, 0.037870172411203384, -0.055082134902477264, 0.0019950484856963158, 0.015540343709290028, -0.0629190132021904, 0.00921162124723196, -0.009255108423531055, -0.004865438677370548, -0.04921397939324379, -0.014517317526042461, -0.039945200085639954, 0.010146446526050568, 0.02541019394993782, 0.010967121459543705, -0.04383965581655502, 0.041564587503671646, -0.011506122536957264, -0.017680574208498, -0.05133745074272156, 0.02576404996216297, -0.009764577262103558, 0.03550399839878082, -0.019260186702013016, -0.05854896456003189, 0.010524991899728775, -0.019377341493964195, -0.006511365063488483, -0.015682104974985123, 0.020666897296905518, -0.021296340972185135, -0.012630660086870193, 0.05790514126420021, 0.02815903164446354, 0.043476276099681854, -0.010870344005525112, 0.007394307758659124, -0.044360674917697906, -0.05364580452442169, -0.0005467393784783781, 0.01342067588120699, 0.006322416476905346, 0.01294567808508873, -0.04085729271173477, 0.027664972469210625, 0.08069507032632828, 0.0175995621830225, -0.057812806218862534, -0.033459506928920746, -0.00659083342179656, 0.03156281262636185, -0.028708722442388535, 0.07152418047189713, -0.035012055188417435, 0.004658874124288559, 0.013056645169854164, -0.0010618135565891862, 0.021264195442199707, -0.01725454442203045, 0.007224641274660826, 0.02785043604671955, -0.017443714663386345, 0.053670309484004974, -0.003201607847586274, -0.03915395215153694, -0.039983052760362625, 0.0010547812562435865, -0.011545823886990547, 0.054503995925188065, 0.05025022104382515, 0.0062289126217365265, 0.05273802578449249, 0.01841052435338497, -0.04835973680019379, 0.0719749704003334, 0.02786003239452839, -0.0035686069168150425, -0.002157677663490176, 0.06806596368551254, 0.057923946529626846, -0.05040767788887024, 0.003434515092521906, 0.013737723231315613, -0.00983535498380661, 0.05478822439908981, 0.03924521058797836, -0.011997834779322147, 0.007303291466087103, -0.0010962914675474167, 0.009569359011948109, 0.024928532540798187, 0.021127527579665184, -0.002582845278084278, -0.007636167574673891, 0.04424577206373215, 0.012861443683505058, 0.021305987611413002, 0.019121279940009117, -0.025042641907930374, 0.006339591462165117, 0.026915905997157097, 0.03299331292510033, -0.01619018241763115, -0.013690955936908722, -0.008793413639068604, 0.04847635328769684, -0.015531322918832302, -0.03474680706858635, -0.08948110044002533, -0.020354775711894035, -0.04159367084503174, 0.08123699575662613, -0.011044962331652641, -0.000806352763902396, -0.031265441328287125, 0.005635211244225502, -0.0355207622051239, -0.01104261539876461, 0.015387171879410744, -0.026832452043890953, 0.05638471245765686, 0.024807041510939598, -0.034455932676792145, 0.02657253108918667, 0.011647935025393963, 0.000619337020907551, 0.035030391067266464, -0.03966442495584488, -0.043237123638391495, 0.01803445629775524, 0.04549260810017586, 0.007950418628752232, -0.015200095251202583, -0.00358719564974308, 0.0763690173625946, 0.05688599869608879, 0.05656522139906883, 0.014332989230751991, 0.023283543065190315, 0.017404373735189438, 0.04082542657852173, -0.0074198585934937, -0.08105108886957169, -0.02676757611334324, 0.01174380723387003, -0.006315710488706827, 0.022381292656064034, -0.033753834664821625, -0.023733217269182205, 0.00967390090227127, 0.011597039178013802, -0.0270528644323349, -0.03195157274603844, -0.0838841050863266, 0.07059279084205627, -0.02892107330262661, 0.015767794102430344, -0.0173502080142498, 0.04308323189616203, 0.048338863998651505, -0.0529189370572567, 0.007731059566140175, -0.017169708386063576, -0.04601715877652168, 0.0076956176199018955, 0.027961190789937973, -0.005955913569778204, 0.037529993802309036, 0.04166538640856743, 0.0033439290709793568, 0.043421320617198944, 0.04219510033726692, -0.0021357357036322355, -0.02278410643339157, 0.038251589983701706, -0.012580235488712788, 0.076842300593853, -0.01548556424677372, 0.02649308554828167, -0.008523800410330296, 0.040091581642627716, -0.04264921694993973, 0.07381879538297653, -0.04115274176001549, 0.02656720019876957, 0.03010968118906021, 0.025576012209057808, -0.044560085982084274, -0.0020667605567723513, -0.024078309535980225, 0.010589072480797768, 0.02387434057891369, 0.04498978331685066, -0.01843933016061783, 0.044099584221839905, -0.026206867769360542, -0.019768038764595985, -0.0384540855884552, 0.01176766213029623, 0.03178075700998306, 0.07748480886220932, -0.03557300940155983, -0.051563944667577744, 0.022384990006685257, -0.014068958349525928, 0.00021872798970434815, 0.015686199069023132, 0.028036853298544884, 0.02721354551613331, 0.10909640789031982, 0.015620939433574677, -0.0615660697221756, -0.031994614750146866, -0.03173235431313515, 0.022754553705453873, 0.06312695890665054, -0.0433051772415638, 0.021690398454666138, 0.02179705910384655, -0.05795836076140404, -0.009168393909931183, -0.03710303083062172, 0.037987615913152695, -0.00007414586434606463, 0.09607037901878357, 0.042522769421339035, 0.03732847422361374, -0.030122827738523483, -0.006121526472270489, 0.019883600994944572, -0.028483010828495026, -0.01847928762435913, 0.047782860696315765, 0.048763953149318695, -0.040297068655490875, -0.015750929713249207, -0.004291350953280926, 0.06292618066072464, 0.003000580007210374, 0.02861395664513111, 0.0424322746694088, -0.031998906284570694, -0.04517275467514992, 0.004717149306088686, -0.04267087206244469, -0.013811299577355385, 0.04378539323806763, -0.04656524211168289, 0.039711903780698776, 0.038735128939151764, 0.048725858330726624, -0.001581437885761261, -0.029802244156599045, 0.025448905304074287, -0.044460784643888474, -0.0006063886103220284, 0.01421319879591465, -0.007092994637787342, 0.0076931556686758995, 0.10822292417287827, -0.049780525267124176, -0.05434393510222435, 0.005016178358346224, 0.020297428593039513, -0.003447876311838627, 0.008177923038601875, -0.05620935931801796, 0.04834076762199402, -0.053465284407138824, 0.02529844641685486, 0.016450922936201096, -0.07166478037834167, 0.03675356134772301, -0.032205432653427124, -0.006440422963351011, -0.024508364498615265, 0.032028522342443466, 0.035124488174915314, -0.03229617699980736, 0.025346670299768448, -0.04853042587637901, -0.03193505108356476, 0.05061737075448036, -0.029061488807201385, 0.00012435944518074393, -0.036023445427417755, 0.03419097885489464, 0.018193116411566734, -0.023065121844410896, 0.049240194261074066, 0.0022445691283792257, -0.019580382853746414, 0.0029643261805176735, -0.03347928449511528, 0.0665765330195427, -0.013939253985881805, -0.004004905465990305, 0.04070844128727913, -0.010573990643024445, -0.001323198201134801, 0.06251856684684753, 0.047606609761714935, 0.05101438984274864, -0.03010713681578636, 0.008960017934441566, -0.001455303281545639, -0.009164830669760704, -0.0014011842431500554, -0.0785704106092453, -0.0008283633505925536, -0.000628503505140543, -0.02852955274283886, -0.06854882836341858, 0.03026721067726612, 0.029876215383410454, 0.030709128826856613, 0.03426361829042435, 0.007656218018382788, -0.06037510931491852, 0.036136068403720856, 0.016051018610596657, -0.05454672873020172, 0.017116788774728775, 0.04840577021241188, -0.015639465302228928, -0.030224068090319633, -0.014694475568830967, -0.04308166354894638, 0.03382660076022148, 0.032015927135944366, 0.01714189723134041, 0.04599076882004738, -0.007601809687912464, -0.014378010295331478, 0.03748776763677597, 0.025956470519304276, 0.016235314309597015, -0.06850765645503998, 0.06615052372217178, -0.019112112000584602, -0.02988503873348236, 0.01931196264922619, 0.018931593745946884, -0.016937073320150375, -0.017356982454657555, -0.021681642159819603, 0.010320845060050488, -0.059845469892024994, 0.03225846216082573, -0.030732428655028343, 0.011923938989639282, -0.03411212936043739, 0.03255230560898781, -0.015119592659175396, -0.0057214475236833096, 0.04008062556385994, 0.007826528511941433, 0.03458649292588234, 0.01884380355477333, 0.017188191413879395, 0.05155929923057556, 0.04080002009868622, -0.034596998244524, 0.005729358177632093, 0.04978940263390541, 0.005247738678008318, -0.06800377368927002, 0.001952283433638513, -0.01089312881231308, -0.03348732367157936, -0.0008057404193095863, 0.030826082453131676, 0.027868280187249184, -0.012484011240303516, 0.0012011586222797632, -0.0029929226730018854, 0.02906043827533722, 0.013964246958494186, 0.0035656809341162443, -0.04722750559449196, -0.021437756717205048, -0.05992313474416733, -0.02350730448961258, -0.016541415825486183, 0.008284453302621841, -0.01044637430459261, 0.06260634958744049, 0.030299197882413864, -0.011819635517895222, 0.0019937048200517893, 0.019433176144957542, -0.019808147102594376, -0.010704326443374157, -0.019910451024770737, -0.020717818289995193, 0.03372484818100929, -0.003019997850060463, 0.04280661791563034, 0.01772601157426834, -0.024163460358977318, 0.02726106345653534, 0.05189262330532074, -0.03889967501163483, -0.06999652087688446, 0.010613751597702503, 0.0409611351788044, 0.10142284631729126, -0.003210267750546336, 0.03370613232254982, -0.008332343772053719, 0.03452619910240173, -0.03276494890451431, -0.034627772867679596, 0.024483082816004753, -0.084074005484581, -0.010479500517249107, -0.0012920248555019498, -0.04800134897232056, -0.0025831928942352533, 0.03333815932273865, 0.03928585350513458, -0.034486040472984314, -0.015816066414117813, -0.05281079187989235, -0.05049110949039459, -0.04926910251379013, -0.03432084619998932, 0.0018205461092293262, -0.02273252233862877, -0.094173863530159, 0.02001025713980198, 0.00928425695747137, -0.00956643931567669, 0.007133736275136471, 0.008619868196547031, 0.026587415486574173, 0.01747089810669422, -0.039289772510528564, 0.020852593705058098, 0.013407276012003422, -0.026750609278678894, 0.002803088864311576, 0.017722897231578827, -0.003507375717163086, -0.006314615253359079, 0.04039458930492401, -0.009559860453009605, 0.0016527113039046526, -0.07160774618387222, 0.0005467091104947031, 0.026446878910064697, -0.08920876681804657, 0.019797399640083313, -0.07639100402593613, 0.0347222238779068, -0.0504651702940464, 0.017016388475894928, 0.02819916605949402, -0.01083955354988575, -0.0043570068664848804, -0.02706516534090042, -0.011508874595165253, -0.09411357343196869 ]
<p>Although they have never been observed, theoretically gluons can exist outside of the nucleus of an atom in the form of a "glue ball". Since the predominant mechanism of Higgs creation at the LHC was observed to be a gluon-gluon interaction (with various virtual particles playing out in the conversion), what are the chances that a "glue ball" as predicted by QCD is the same animal from the particle zoo as a Higgs boson?</p>
g8404
[ 0.03408048301935196, 0.012796489521861076, 0.034951724112033844, -0.09557082504034042, 0.04425107687711716, 0.017849799245595932, -0.038338154554367065, 0.0018800232792273164, 0.009625408798456192, -0.05004867911338806, -0.020311009138822556, 0.006801040377467871, -0.010930042713880539, 0.020481592044234276, 0.023472696542739868, 0.0105587188154459, -0.005353861954063177, -0.049957748502492905, 0.015214621089398861, 0.030130919069051743, 0.040269315242767334, 0.0026436832267791033, 0.016736259683966637, 0.012332585640251637, -0.08479097485542297, -0.01626199670135975, 0.024136686697602272, 0.007253164425492287, -0.06255366653203964, -0.005299912765622139, 0.08095590770244598, -0.05084773525595665, 0.03392458334565163, -0.09042810648679733, 0.024353235960006714, -0.04611022397875786, 0.052959080785512924, -0.021467840299010277, 0.032573726028203964, 0.006308456417173147, -0.035498738288879395, 0.015373699367046356, 0.006354829762130976, 0.005830870009958744, -0.010938931256532669, 0.06121068075299263, 0.0821499228477478, 0.04854203015565872, 0.06807137280702591, -0.010319017805159092, 0.013662113808095455, 0.08201207220554352, -0.008326198905706406, -0.009346122853457928, -0.022896595299243927, 0.04772453382611275, 0.0984618291258812, 0.017606768757104874, 0.08004578202962875, 0.0732225701212883, 0.01167791336774826, 0.02763102948665619, -0.06818974018096924, -0.04315337911248207, 0.08649897575378418, -0.007747316733002663, -0.07627183943986893, 0.018486443907022476, -0.021771421656012535, -0.013376889750361443, 0.014983002096414566, -0.0633113831281662, 0.013105403631925583, 0.11081776022911072, 0.007454460021108389, 0.017301790416240692, -0.022952498868107796, -0.011769122444093227, 0.0031534561421722174, 0.004999454133212566, -0.027312852442264557, -0.04289679974317551, -0.05185722932219505, -0.0017676284769549966, 0.08960075676441193, -0.07868937402963638, -0.05169670283794403, -0.029370708391070366, -0.008525134064257145, 0.043890006840229034, 0.012815180234611034, 0.003630506806075573, 0.014608579687774181, -0.02216826193034649, -0.05413196608424187, -0.025025881826877594, -0.05353561416268349, 0.03926803544163704, -0.0005427045398391783, -0.04541746526956558, -0.019830308854579926, -0.031239181756973267, -0.0068492526188492775, -0.031109243631362915, -0.03560539335012436, -0.003756630700081587, 0.03387388214468956, -0.024604925885796547, 0.010554674081504345, 0.009023807942867279, -0.028164705261588097, 0.060615234076976776, 0.042286161333322525, 0.029816122725605965, 0.009751410223543644, -0.04958844557404518, 0.001982736401259899, 0.0012070761295035481, 0.017855819314718246, 0.029969602823257446, 0.07598927617073059, -0.016439413651823997, -0.016564564779400826, -0.042653102427721024, -0.049328990280628204, -0.015033754520118237, -0.01196670439094305, 0.021239642053842545, 0.02028151974081993, -0.01903064362704754, -0.023460624739527702, -0.02710856683552265, -0.0009381123818457127, 0.022689862176775932, 0.04235313832759857, 0.05376235395669937, 0.017930414527654648, -0.023111499845981598, 0.03160903602838516, -0.021027015522122383, -0.03239616006612778, 0.0018756360514089465, -0.009111766703426838, 0.020939890295267105, -0.02442551963031292, 0.07792834937572479, 0.01078353077173233, 0.028457213193178177, -0.04041381925344467, 0.07018567621707916, -0.03013567067682743, 0.02936960943043232, 0.03265688568353653, 0.00006415566895157099, -0.010772595182061195, 0.015750139951705933, 0.023808682337403297, 0.012786895036697388, -0.06537765264511108, -0.014288663864135742, 0.05629110336303711, -0.027179528027772903, 0.03756597265601158, -0.026917733252048492, 0.01265692338347435, 0.017176833003759384, 0.05509181693196297, 0.006385329645127058, -0.01359767746180296, 0.05625176057219505, -0.060937196016311646, 0.01841900497674942, -0.01899096928536892, 0.05570858344435692, 0.03368114307522774, -0.001096608117222786, -0.019341904670000076, -0.052819401025772095, 0.009819519706070423, -0.03351220861077309, 0.04859067499637604, -0.03151613846421242, -0.021940411999821663, -0.014435901306569576, 0.022619925439357758, 0.010464702732861042, -0.025787079706788063, -0.010672695003449917, 0.06919151544570923, 0.00691736675798893, -0.08756127208471298, -0.03006863221526146, -0.023755067959427834, 0.01564893126487732, 0.01034024078398943, 0.014310788363218307, -0.013546776957809925, -0.05686899274587631, -0.0007840408361516893, 0.04760565608739853, -0.00778393168002367, 0.017649639397859573, -0.03498336300253868, -0.03398917242884636, 0.017220119014382362, -0.09398914873600006, -0.02341315522789955, -0.007249405607581139, 0.03736194595694542, -0.020098019391298294, 0.02654344215989113, 0.00005572677400778048, -0.06290523707866669, -0.034610383212566376, 0.038976892828941345, -0.021956603974103928, -0.00706643657758832, 0.03242979198694229, -0.06612179428339005, -0.045488644391298294, 0.009901071898639202, 0.026117010042071342, 0.0016291918000206351, -0.06917373090982437, 0.0292695052921772, 0.0028588532004505396, -0.03312595933675766, -0.02550729364156723, -0.012208012863993645, -0.0010192871559411287, 0.006843797396868467, 0.02943711169064045, -0.008437320590019226, -0.03146757930517197, -0.03519550710916519, 0.059762146323919296, -0.0344986729323864, -0.0020669533405452967, 0.045375481247901917, -0.008438292890787125, 0.010167024098336697, -0.020756836980581284, -0.05238109827041626, -0.02888026461005211, 0.03871994838118553, -0.05918522924184799, 0.07008575648069382, 0.0021262040827423334, 0.013334430754184723, 0.02249087020754814, 0.04983857646584511, 0.025089094415307045, 0.00960049033164978, -0.01934407278895378, 0.01391705870628357, 0.049234915524721146, 0.08019641786813736, 0.01314504537731409, -0.042982615530490875, -0.09549647569656372, 0.031246937811374664, -0.06029920279979706, -0.010223589837551117, 0.014799032360315323, -0.01695983111858368, -0.058563847094774246, 0.00907716155052185, -0.020336100831627846, -0.025117933750152588, 0.05550462752580643, -0.055183324962854385, -0.030510080978274345, 0.007002199999988079, -0.03404790908098221, -0.00985281728208065, 0.05895672366023064, -0.048873722553253174, 0.021153181791305542, 0.018307412043213844, -0.07371455430984497, 0.028030462563037872, 0.05710242688655853, -0.04276641830801964, 0.005491938441991806, -0.00525754876434803, -0.011037047021090984, -0.050951216369867325, -0.02477576769888401, 0.021110553294420242, 0.02277098037302494, 0.00758914090692997, -0.013946562074124813, 0.042555514723062515, 0.03841652348637581, -0.0030049097258597612, 0.051021892577409744, 0.06775985658168793, 0.0919683501124382, -0.030785774812102318, 0.05716778337955475, -0.020343555137515068, -0.06186780706048012, -0.019346047192811966, 0.03197557106614113, 0.020037304610013962, 0.005722389090806246, -0.05389409139752388, 0.023604677990078926, 0.03801644966006279, -0.03752545267343521, 0.0015147057129070163, 0.05859660357236862, 0.014701438136398792, -0.006118715740740299, -0.017649222165346146, -0.007764534093439579, 0.02396693266928196, 0.06347977370023727, 0.010492268949747086, -0.026544786989688873, 0.024518584832549095, 0.0013783156173303723, 0.02015731669962406, -0.04268791526556015, 0.05048126354813576, 0.024057168513536453, 0.0037911590188741684, -0.03431563824415207, 0.026381179690361023, -0.06427585333585739, 0.02123713679611683, -0.01749413274228573, 0.030157312750816345, 0.006356041878461838, -0.07376275956630707, -0.032255999743938446, -0.05761623755097389, -0.030561361461877823, 0.03841795772314072, 0.04972372576594353, 0.00974678248167038, 0.01741420105099678, -0.004922227934002876, 0.03802816569805145, -0.03270692378282547, 0.04840996488928795, -0.016013365238904953, -0.040064144879579544, 0.013788832351565361, -0.03728428855538368, 0.023748278617858887, -0.0017645418411120772, 0.05051539093255997, 0.021314984187483788, 0.018345830962061882, -0.011245648376643658, 0.0004900039057247341, -0.0008518126560375094, 0.012375484220683575, -0.020111212506890297, 0.008435062132775784, -0.023514285683631897, 0.0706656351685524, -0.011139142327010632, -0.003221170511096716, -0.020014526322484016, -0.00022511881252285093, 0.01603700965642929, 0.012098977342247963, -0.0022975588217377663, -0.041899632662534714, 0.018190115690231323, 0.0707765594124794, 0.04355740174651146, 0.059001702815294266, -0.022129951044917107, 0.035473454743623734, 0.016076020896434784, -0.02704855054616928, -0.052217498421669006, -0.02516504004597664, 0.024603480473160744, 0.05126357078552246, -0.021386412903666496, 0.014819749630987644, -0.008286524564027786, -0.017266500741243362, -0.04253469407558441, -0.0349484458565712, 0.04063577950000763, -0.04418677091598511, 0.06574469804763794, 0.02465958520770073, 0.00922560878098011, -0.0005826319102197886, -0.04457459598779678, 0.04470428451895714, 0.023234572261571884, 0.03129486367106438, -0.03552692383527756, 0.002320042811334133, 0.02512480691075325, 0.015759047120809555, -0.0587691105902195, -0.016638189554214478, -0.008116481825709343, 0.011719492264091969, -0.018828880041837692, 0.00464856531471014, -0.07840719819068909, 0.04744071513414383, 0.026689819991588593, 0.015336034819483757, 0.01968381181359291, -0.027117082849144936, -0.009335154667496681, -0.01800128072500229, 0.05367990583181381, -0.03528619930148125, 0.014789823442697525, 0.0014267188962548971, -0.04847818613052368, 0.035665471106767654, 0.050129543989896774, -0.03753572329878807, 0.02188483253121376, -0.02273457869887352, 0.039983801543712616, -0.057101257145404816, -0.028047725558280945, 0.05707729980349541, -0.016208859160542488, 0.0031798204872757196, -0.05178448185324669, 0.008756844326853752, 0.02084079012274742, -0.030395466834306717, 0.02898457646369934, 0.061287771910429, 0.00492829829454422, 0.05402011424303055, -0.018486017361283302, 0.08362098783254623, -0.021023772656917572, 0.009667566977441311, 0.030354181304574013, -0.038043245673179626, -0.01241343468427658, -0.018185634166002274, -0.010465995408594608, 0.017522331327199936, 0.0005789942806586623, -0.03196615353226662, -0.00895049050450325, 0.03524475544691086, 0.002808802295476198, 0.004153783433139324, -0.008814224973320961, -0.06522871553897858, -0.012837774120271206, -0.05016130581498146, -0.02088797837495804, 0.015361686237156391, 0.03963746502995491, 0.047274138778448105, 0.022337473928928375, 0.0025822913739830256, -0.03168695792555809, 0.0070093427784740925, 0.0012221427168697119, -0.007923198863863945, 0.00248791859485209, 0.0016155573539435863, 0.003770815907046199, 0.061787985265254974, -0.03664610907435417, 0.023805910721421242, 0.018902648240327835, 0.030486738309264183, -0.05227317661046982, -0.0024422432761639357, 0.02034909278154373, -0.026198171079158783, -0.0720117837190628, -0.06191794201731682, 0.01798546500504017, -0.05355258658528328, 0.03060363605618477, -0.02600271999835968, 0.015599560923874378, 0.014069871045649052, -0.054094843566417694, 0.06308148056268692, -0.004458488896489143, 0.04619237408041954, -0.057074662297964096, -0.021154791116714478, -0.036004792898893356, -0.019246142357587814, 0.05841061472892761, -0.03303332254290581, 0.008823230862617493, 0.02427627705037594, -0.012831388041377068, 0.01123064011335373, 0.05919566750526428, -0.0076597039587795734, 0.03911310434341431, 0.0884220227599144, -0.010746626183390617, -0.03553081676363945, -0.006363022606819868, -0.07331279665231705, 0.015167019329965115, 0.006171718239784241, 0.02014707587659359, 0.002238933462649584, 0.0010423059575259686, -0.00484503572806716, 0.0022708869073539972, 0.016057131811976433, 0.0070054191164672375, -0.0005620165029540658, -0.02136397920548916, -0.03526853397488594, 0.08009154349565506, -0.01842908374965191, -0.035116881132125854, 0.017656441777944565, -0.019762476906180382, 0.026013333350419998, -0.007162229157984257, 0.04214989021420479, 0.04692217335104942, 0.015712710097432137, 0.00434232410043478, -0.05092015862464905, 0.008208822458982468, 0.009402912110090256, -0.011437932029366493, 0.04219505563378334, -0.023611143231391907, 0.06171285733580589, 0.00963999330997467, -0.031510308384895325, -0.011514922603964806, -0.1105484589934349, 0.012399156577885151, 0.0245058536529541, -0.03984101489186287, -0.06024644896388054, 0.031959936022758484, -0.0005560138379223645, 0.013036776334047318, -0.0019559860229492188, -0.02643989585340023, 0.011679469607770443, 0.012327132746577263, 0.0020271437242627144, 0.011437596753239632, 0.00529999565333128, 0.11104819178581238, -0.0014989349292591214, 0.04975380375981331, -0.009088692255318165, -0.0011080056428909302, -0.01891995221376419, -0.03762832656502724, -0.006693156901746988, -0.003083369694650173, -0.014032557606697083, -0.004655330907553434, -0.034335747361183167, 0.05013547092676163, 0.053339991718530655, -0.004932946991175413, 0.039663881063461304, 0.04940641671419144, 0.009795842692255974, 0.009406882338225842, 0.04971671476960182, -0.01570494845509529, -0.06209245324134827, -0.0018529159715399146, -0.020986124873161316, -0.002477766713127494, -0.021659109741449356, 0.007550293579697609, -0.023361630737781525, -0.009919689036905766, -0.0387665219604969, 0.026191700249910355, -0.04936046898365021, -0.022005310282111168, -0.016010301187634468, 0.00034384720493108034, -0.019185975193977356, -0.06423559039831161, -0.05251575633883476, 0.011085323989391327, 0.010557071305811405, -0.006745409220457077, -0.015403050929307938, 0.0092916339635849, -0.023399416357278824, 0.06746052950620651, -0.04706141725182533, 0.04360495135188103, -0.004216070752590895, 0.03474199399352074, -0.006575802806764841, 0.02306794747710228, 0.01944023184478283, -0.025504738092422485, 0.014757383614778519, -0.053528010845184326, 0.018346566706895828, -0.007532705087214708, -0.018764255568385124, -0.043758269399404526, -0.010329957120120525, 0.037946127355098724, -0.05735042691230774, -0.010272338055074215, -0.0017131182830780745, -0.00665984395891428, -0.02802671492099762, 0.06344962865114212, 0.03262433782219887, 0.04907548427581787, -0.030112549662590027, -0.02856464311480522, -0.007575775496661663, 0.023837821558117867, -0.037083301693201065, 0.0734337866306305, -0.009954681620001793, -0.00040929141687229276, 0.005107353441417217, -0.012012685649096966, -0.026288265362381935, -0.013614058494567871, 0.024035438895225525, 0.003809618530794978, -0.024137387052178383, 0.040768515318632126, 0.02387074939906597, 0.019560348242521286, -0.05898425728082657, 0.011534716933965683, -0.06152060627937317, -0.0342584066092968, -0.015102428384125233, -0.08184365183115005, -0.00040301878470927477, -0.014596105553209782, -0.009269902482628822, 0.007366791367530823, -0.011159548535943031, -0.024087661877274513, -0.014527793042361736, -0.05028589069843292, 0.07587303966283798, -0.0024006019812077284, -0.008860770612955093, -0.007310070097446442, 0.011349781416356564, -0.09779969602823257, -0.024018649011850357, -0.003522267797961831, 0.038311559706926346, -0.05818205699324608, -0.0235137976706028, 0.01819588430225849, 0.008467493578791618, -0.02412472479045391, -0.00816864799708128, 0.005829077214002609, 0.01208425872027874, 0.042864587157964706, -0.03134520351886749, 0.06301670521497726, -0.023643165826797485, 0.07494259625673294, -0.0381595678627491, -0.007021890487521887, 0.03797511011362076, -0.05049771070480347, -0.030204342678189278, 0.01035394612699747, -0.008235739544034004, 0.02824745513498783, 0.029703030362725258, -0.062092263251543045, 0.05093177780508995, -0.0005504913860931993, -0.008029213175177574, 0.021102093160152435, -0.012614862062036991, -0.027105065062642097, -0.012845994904637337, -0.009744171053171158, -0.006621807347983122, -0.03977655991911888, 0.04050573334097862, 0.007642327342182398, -0.002959326608106494, 0.02494456246495247, -0.00950575340539217, -0.0007158922380767763, -0.007526724133640528, 0.09182065725326538, 0.02421281300485134, 0.02178168296813965, 0.057381629943847656, -0.02999171055853367, -0.04959263280034065, -0.000017928043234860525, 0.04046004265546799, 0.015964701771736145, -0.033972594887018204, -0.003260600846260786, -0.05842384696006775, 0.003085272153839469, -0.00024803512496873736, 0.02083095721900463, 0.00018913389067165554, -0.007995729334652424, -0.04981842264533043, -0.00959272962063551, -0.011720860376954079, -0.014797721058130264, -0.0041203973814845085, -0.029379647225141525, -0.013595742173492908, -0.06752656400203705, 0.018244590610265732, 0.03888045996427536, -0.03215273842215538, 0.010712912306189537, -0.03392498195171356, -0.044782254844903946, 0.00942972581833601, -0.02659698948264122, -0.04612071439623833, -0.030739139765501022, -0.05282534286379814, 0.06237306073307991, 0.0034815978724509478, 0.057989709079265594, -0.024809176102280617, -0.022136209532618523, 0.027868157252669334, 0.03555990010499954, 0.07366228103637695, -0.02592906542122364, -0.046731993556022644, 0.06610796600580215, -0.07242478430271149, -0.013820668682456017, -0.00841916911303997, 0.009425871074199677, 0.051366861909627914, 0.020626025274395943, -0.022368174046278, -0.009123067371547222, 0.009786397218704224, 0.023288795724511147 ]
<p>I'm aware that electron pair-production from a single photon requires the presence of matter — say some large nucleus — able to absorb momentum, as in the process \begin{align} N \gamma \rightarrow N e^- e^+ \end{align} where $N$ represents the nucleus. My question is, how would one represent this process with a Feynman diagram? I'm having trouble constructing one with valid vertices that makes sense. Would the neutron interact with the photon? With the electron-positron pair? Both? Any help would be appreciated.</p>
g8405
[ -0.011627178639173508, 0.013894186355173588, -0.006070726551115513, -0.0421961210668087, 0.06861059367656708, 0.011118724942207336, -0.013498370535671711, 0.04137473180890083, 0.006551437079906464, 0.03382628411054611, 0.05651695653796196, 0.010663609951734543, 0.023309975862503052, 0.0075331395491957664, -0.03175212815403938, 0.03340309113264084, 0.0857856422662735, 0.030394867062568665, -0.03457416594028473, -0.013738146051764488, -0.04548659548163414, 0.004796580411493778, -0.010366684757173061, -0.015063231810927391, -0.016068773344159126, -0.0124382758513093, 0.024388756603002548, 0.0067479875870049, -0.008632891811430454, -0.023602286353707314, -0.00875955168157816, -0.02632952854037285, 0.027254045009613037, 0.0012710459996014833, -0.04151138290762901, -0.031069079414010048, 0.019297346472740173, 0.024325275793671608, 0.018691007047891617, 0.0170804001390934, 0.005645350553095341, -0.03879806026816368, -0.04145781323313713, 0.0006798480171710253, 0.00511604268103838, 0.03623323515057564, 0.021029509603977203, 0.020890694111585617, -0.0008733308059163392, 0.009753313846886158, -0.014415753073990345, 0.025012435391545296, -0.019898368045687675, 0.011429713107645512, 0.03508796915411949, 0.08869319409132004, 0.020080169662833214, 0.005046760197728872, 0.05175894871354103, 0.021408697590231895, -0.013514966703951359, 0.011189970187842846, 0.012611896730959415, 0.03706304728984833, 0.09686194360256195, 0.019090380519628525, -0.034484609961509705, -0.008696211501955986, 0.06813407689332962, 0.018210623413324356, -0.03797246143221855, -0.02443302795290947, 0.004477314185351133, 0.05164447799324989, 0.07658907026052475, 0.015537670813500881, -0.01244980376213789, -0.043280620127916336, 0.0242462195456028, -0.002945013577118516, -0.04545065388083458, 0.0071061961352825165, 0.06046053394675255, -0.05112516134977341, 0.03726022690534592, 0.007402139250189066, -0.04203462973237038, -0.04022124037146568, -0.06644155085086823, -0.007247835863381624, 0.06857138872146606, -0.015235270373523235, 0.004572325851768255, 0.0008158760610967875, -0.007063612807542086, -0.0688861757516861, -0.06417027115821838, 0.05516929179430008, -0.028816698119044304, 0.01050709467381239, -0.015316869132220745, 0.013278788886964321, -0.020934801548719406, -0.044518161565065384, -0.022937621921300888, -0.0024629186373203993, -0.01184031181037426, 0.005558973643928766, 0.06517748534679413, 0.031950850039720535, -0.10644382983446121, -0.039443276822566986, -0.007455746177583933, -0.02873075008392334, -0.0343104787170887, -0.04502840340137482, 0.012823826633393764, -0.0011961129494011402, -0.03952411562204361, 0.11404052376747131, 0.04918885603547096, 0.011251308023929596, 0.025970235466957092, 0.0342496857047081, 0.010598410852253437, -0.03995674476027489, -0.05710931867361069, 0.04003814980387688, -0.008326121605932713, 0.040635496377944946, 0.06887519359588623, -0.06912904232740402, 0.035258978605270386, 0.03877091035246849, 0.03352925553917885, 0.03300752490758896, 0.0062307449989020824, 0.046001240611076355, 0.04307233542203903, -0.02726644277572632, 0.01494885515421629, -0.01468826737254858, -0.05419085547327995, -0.06995387375354767, 0.0059754210524261, 0.02747756987810135, -0.027827667072415352, -0.015797343105077744, -0.05474471300840378, 0.02374526858329773, 0.014820770360529423, 0.020315522328019142, -0.015339159406721592, -0.007735118269920349, 0.035355862230062485, 0.003184535540640354, 0.10454653948545456, -0.04128626361489296, -0.029345357790589333, 0.013672209344804287, 0.078545942902565, -0.029030289500951767, 0.034968677908182144, -0.03509661927819252, -0.04059464856982231, -0.055098146200180054, 0.031602609902620316, -0.08259794861078262, -0.03204448148608208, -0.013905671425163746, -0.011714352294802666, -0.03285693749785423, -0.02502949722111225, 0.04930225759744644, -0.02501862682402134, 0.026654114946722984, -0.028804682195186615, -0.015190556645393372, -0.012097252532839775, 0.01961030438542366, 0.00532676512375474, 0.0007364234770648181, 0.06301027536392212, 0.06077737733721733, -0.020996861159801483, -0.0038123405538499355, 0.028401201590895653, 0.0546744205057621, -0.011035071685910225, 0.010536040179431438, 0.01385077927261591, 0.0042517283000051975, 0.009725561365485191, -0.001272981520742178, -0.014904478564858437, -0.011030795983970165, 0.02882855199277401, -0.09826643764972687, 0.032256416976451874, -0.020140454173088074, -0.07588455080986023, 0.014746266417205334, -0.023080499842762947, 0.03415286913514137, 0.04150365665555, -0.008973734453320503, -0.03568370267748833, -0.02957737445831299, 0.03749117627739906, 0.011748835444450378, -0.02557380497455597, -0.019692592322826385, -0.03236865997314453, -0.01153190154582262, -0.02428271435201168, -0.06354238837957382, -0.023470193147659302, -0.0074363816529512405, 0.005346821621060371, 0.004043098539113998, -0.01693323627114296, -0.058922674506902695, 0.004271789453923702, -0.05314447358250618, -0.005110389553010464, 0.016774939373135567, 0.023880599066615105, -0.02231166511774063, -0.05029323697090149, 0.07142148911952972, -0.08545556664466858, 0.1260301023721695, -0.03189655393362045, -0.06690779328346252, 0.01642526313662529, -0.0005542671424336731, -0.024955445900559425, 0.009888212196528912, -0.010407092049717903, 0.0003418354026507586, -0.00893047172576189, -0.03215940669178963, -0.06855932623147964, -0.052260298281908035, -0.007245744578540325, -0.026146158576011658, 0.075484499335289, 0.012949100695550442, -0.055416569113731384, 0.00974727887660265, 0.04828021302819252, -0.01908356510102749, -0.02193550392985344, -0.009954230859875679, 0.006595739629119635, -0.03956960514187813, -0.003447576193138957, 0.01762962155044079, -0.10117162019014359, -0.02487652748823166, -0.04072178155183792, -0.058680709451436996, -0.03919728472828865, 0.018849479034543037, -0.019370948895812035, -0.03733322396874428, -0.0007958146161399782, -0.013827965594828129, 0.028775176033377647, -0.01047415379434824, -0.027147339656949043, 0.01702921651303768, -0.008912185207009315, -0.02328678034245968, 0.018623273819684982, -0.055007454007864, 0.009591100737452507, 0.005787272937595844, 0.005157609470188618, -0.04825281351804733, -0.03918253630399704, 0.006257139146327972, -0.02042025700211525, -0.010247532278299332, 0.046479832381010056, -0.045380331575870514, 0.012677552178502083, 0.000381775782443583, 0.03999021276831627, 0.04229673743247986, -0.03714904934167862, -0.024006476625800133, 0.005464270245283842, -0.003339543240144849, -0.013790379278361797, -0.0026009944267570972, -0.0016555053880438209, 0.0243790615350008, -0.038879141211509705, 0.027279365807771683, -0.00713396305218339, -0.028915176168084145, -0.019239917397499084, 0.0004943620879203081, 0.034215640276670456, 0.03401227667927742, -0.10028000921010971, -0.008723254315555096, -0.019585251808166504, -0.026117371395230293, -0.04915502667427063, 0.027402294799685478, -0.014265351928770542, 0.006264643743634224, -0.011155654676258564, 0.017725737765431404, 0.04340116307139397, 0.02519207075238228, 0.04943149536848068, -0.03449583426117897, -0.024562038481235504, 0.0035271707456558943, 0.07449649274349213, -0.01896943710744381, 0.03749706223607063, 0.03388475626707077, -0.020143752917647362, -0.029486170038580894, -0.02253449708223343, 0.014264417812228203, 0.01259576715528965, -0.012082925997674465, 0.02449464611709118, 0.03977648541331291, -0.003138693980872631, -0.017832277342677116, -0.03269021958112717, -0.009664775803685188, 0.0262072142213583, -0.02438611350953579, -0.04209865629673004, -0.03762989863753319, -0.021587543189525604, -0.03903279826045036, 0.01053266879171133, -0.04472479596734047, -0.03578212112188339, -0.02799275703728199, 0.03926294669508934, -0.04068974778056145, -0.018023721873760223, -0.02376287244260311, -0.02225114405155182, 0.015345544554293156, 0.008402293547987938, -0.02294100821018219, 0.02272379770874977, 0.039063066244125366, 0.06473380327224731, -0.015196382999420166, 0.00869191437959671, 0.025418564677238464, 0.014974433928728104, -0.023691678419709206, -0.03674132749438286, -0.023386150598526, -0.07853048294782639, -0.003715354250743985, 0.05116651952266693, 0.0323776975274086, -0.03455892577767372, -0.03390711918473244, -0.04351002722978592, -0.01122311782091856, 0.027415962889790535, -0.0150771988555789, 0.012163291685283184, 0.04569400101900101, -0.052139803767204285, 0.07705079764127731, -0.07133332639932632, -0.009349267929792404, 0.00009056930139195174, 0.0441286601126194, 0.01283812802284956, 0.05414760857820511, 0.009789910167455673, 0.024558717384934425, -0.03780607879161835, 0.05195353552699089, 0.0423855222761631, -0.09897404164075851, -0.003937832545489073, 0.028303323313593864, -0.004551350139081478, 0.0020865232218056917, 0.0472169853746891, -0.0387209951877594, -0.03774863854050636, 0.01882912963628769, -0.013459906913340092, 0.0006933178519830108, 0.025114020332694054, -0.06486819684505463, 0.020091181620955467, -0.015161462128162384, -0.03179028257727623, -0.031072180718183517, 0.0047521707601845264, -0.019440649077296257, 0.02378208562731743, 0.03332607075572014, 0.0707782432436943, -0.0029589729383587837, -0.0030346086714416742, -0.0038553879130631685, -0.037900589406490326, 0.001818882767111063, -0.017664164304733276, 0.03387695550918579, -0.01221019122749567, 0.07446760684251785, 0.038882024586200714, 0.010188523679971695, -0.012653562240302563, 0.033303651958703995, 0.006877162493765354, 0.034615855664014816, 0.008861826732754707, -0.008732747286558151, 0.021227780729532242, 0.01617695577442646, 0.026909474283456802, 0.03598736226558685, -0.03526034951210022, 0.05252344533801079, -0.009454713203012943, -0.0036733828019350767, 0.03454045206308365, 0.057648200541734695, 0.07950522005558014, -0.03277548402547836, 0.03251080587506294, -0.053912144154310226, 0.023898454383015633, 0.039715539664030075, -0.04490991681814194, -0.04427066817879677, -0.051811378449201584, -0.004513241350650787, 0.015079082921147346, -0.010652225464582443, -0.0420183502137661, 0.0005486555164679885, 0.0073042637668550014, 0.0692884624004364, 0.0015764945419505239, 0.05071725696325302, 0.02743753418326378, 0.012894474901258945, -0.017588866874575615, 0.033694710582494736, 0.008874298073351383, 0.006337000988423824, 0.029397200793027878, -0.03177858516573906, -0.05061275139451027, 0.021649466827511787, -0.010232016444206238, -0.03214285895228386, 0.030962873250246048, -0.004611730109900236, 0.03908148407936096, 0.020263971760869026, 0.013744398951530457, -0.009339121170341969, -0.04843194782733917, -0.027084054425358772, 0.019518975168466568, -0.017912548035383224, 0.005922427400946617, 0.0485735647380352, 0.0111760925501585, -0.02568732760846615, 0.011557349003851414, 0.039946455508470535, 0.018061643466353416, 0.049307096749544144, 0.010525048710405827, 0.010221379809081554, 0.012097254395484924, -0.036359988152980804, 0.0139996986836195, 0.030090540647506714, 0.05707729980349541, 0.007494186516851187, -0.00516947777941823, 0.014071081764996052, 0.023345399647951126, 0.02878178097307682, 0.004948505666106939, -0.009236867539584637, -0.02991396002471447, -0.0338701456785202, 0.005820527207106352, 0.04976249113678932, 0.03023708425462246, -0.007415242027491331, 0.0002809709694702178, 0.004040589556097984, -0.03548567742109299, -0.021778225898742676, 0.06090298295021057, 0.024974824860692024, -0.012564978562295437, 0.024135872721672058, -0.0017996925162151456, -0.0272968839854002, -0.02396080642938614, -0.02517099678516388, 0.08070273697376251, 0.04860144108533859, 0.019764507189393044, -0.053746066987514496, 0.07823890447616577, -0.01364008616656065, -0.0722862184047699, 0.04784182459115982, 0.0747043788433075, 0.04171792045235634, 0.019904036074876785, -0.033876921981573105, -0.020191945135593414, 0.04478633776307106, 0.021782835945487022, -0.11728578805923462, 0.023448830470442772, -0.008657735772430897, 0.07489795237779617, -0.0156384464353323, -0.0009696901543065906, -0.019637422636151314, 0.020000074058771133, 0.1049022227525711, 0.017183654010295868, -0.01805412769317627, 0.007184938061982393, 0.03137901425361633, 0.03533761203289032, 0.054634418338537216, 0.0011653443798422813, -0.020890668034553528, -0.016605669632554054, -0.004492404870688915, -0.008910414762794971, 0.0281575545668602, 0.016414793208241463, -0.01640279032289982, -0.006055598612874746, -0.008265821263194084, 0.05711069330573082, 0.010088344104588032, 0.014582856558263302, 0.01814013533294201, -0.019311806187033653, -0.022916121408343315, 0.01008943747729063, -0.011568794958293438, -0.017159918323159218, 0.030943017452955246, 0.059800975024700165, -0.012761713936924934, -0.0014599758433178067, -0.015561887994408607, -0.004779626615345478, 0.036667823791503906, 0.027848565950989723, 0.03295828774571419, -0.04893772304058075, -0.02930360659956932, 0.03870980069041252, 0.05203051492571831, -0.031370218843221664, 0.014316445216536522, 0.025560816749930382, 0.015549122355878353, -0.0641482025384903, -0.03142993897199631, 0.028399193659424782, 0.06911524385213852, -0.05199209600687027, 0.01822754181921482, -0.009134499356150627, -0.0004593120829667896, 0.004801936913281679, 0.021265333518385887, 0.029359303414821625, -0.05630211532115936, -0.055667851120233536, 0.05368107929825783, 0.013592854142189026, 0.0080642094835639, 0.004569631535559893, 0.01569357141852379, -0.020718080922961235, 0.01846310868859291, -0.03346521034836769, -0.012258479371666908, -0.004725409671664238, -0.02093106135725975, 0.011105325073003769, 0.054816585034132004, -0.027241380885243416, 0.0127967968583107, -0.007683513220399618, -0.03764507919549942, 0.015264393761754036, 0.019252566620707512, -0.04869340360164642, -0.04221982881426811, -0.012377637438476086, -0.04926459118723869, 0.004103038925677538, -0.04701364412903786, 0.06697110831737518, 0.04040386900305748, -0.05485232174396515, 0.06113048642873764, 0.03431267291307449, 0.017719857394695282, -0.019638527184724808, 0.00485636293888092, 0.002414614660665393, -0.00516572454944253, 0.021164491772651672, 0.06520885229110718, -0.013380978256464005, -0.002690916648134589, -0.020054815337061882, -0.0021200086921453476, -0.01537926122546196, 0.021234596148133278, 0.059582553803920746, 0.04984350502490997, -0.043579742312431335, -0.004502048250287771, -0.007061985787004232, 0.015581746585667133, -0.04915087670087814, 0.016162879765033722, 0.015920063480734825, -0.03460878133773804, -0.04214964807033539, 0.031102072447538376, 0.001655836938880384, -0.009333970956504345, -0.04923873394727707, 0.029415829107165337, 0.024425867944955826, -0.03054603934288025, -0.0025491039268672466, -0.06498953700065613, -0.030534015968441963, -0.052950162440538406, 0.03560095652937889, -0.06538975238800049, -0.004573027137666941, -0.050706155598163605, -0.012737457640469074, -0.013464054092764854, -0.03792163357138634, -0.0652991235256195, -0.032877467572689056, 0.06144152209162712, -0.024726752191781998, -0.04550776258111, 0.014555761590600014, 0.0372457318007946, -0.06671608984470367, -0.029921794310212135, -0.06234099715948105, 0.02540411613881588, -0.033048730343580246, -0.022207144647836685, 0.008079353719949722, 0.04811369255185127, 0.01002905797213316, 0.040451373904943466, -0.032379455864429474, 0.055239468812942505, 0.019166627898812294, -0.024687444791197777, -0.036857571452856064, -0.015777703374624252, -0.005579640623182058, 0.04830101132392883, 0.009230298921465874, -0.006481700576841831, -0.0062067750841379166, 0.07415475696325302, 0.029205922037363052, -0.047535527497529984, 0.015218030661344528, -0.011124988086521626, 0.0339147113263607, -0.022871283814311028, -0.015709469094872475, -0.06291241198778152, 0.028443945571780205, -0.03801082447171211, 0.05021803081035614, 0.04751833900809288, -0.012973698787391186, 0.04970905929803848, 0.035657864063978195, -0.019076691940426826, -0.03556698188185692, 0.025587238371372223, 0.04637344554066658, 0.025230616331100464, -0.07902874052524567, 0.041735634207725525, -0.06494779139757156, -0.022818949073553085, 0.018368221819400787, -0.05072852596640587, 0.007132191676646471, 0.025972438976168633, 0.043690938502550125, -0.002329661278054118, 0.008489702828228474, -0.05347224697470665, -0.0593092143535614, 0.02473209984600544, 0.029175980016589165, -0.08080350607633591, -0.017272738739848137, -0.03873520717024803, 0.04282194748520851, 0.006670912262052298, 0.0020135631784796715, -0.1173844113945961, 0.023437367752194405, -0.04003750532865524, 0.046478334814310074, -0.07864078879356384, -0.008970356546342373, 0.021194959059357643, 0.051749441772699356, -0.0014222647296264768, 0.01154441386461258, 0.019095512107014656, 0.022429347038269043, 0.04799141362309456, 0.07150611281394958, -0.0017050799215212464, -0.017041249200701714, 0.012210195884108543, 0.005308762192726135, 0.0008248919039033353, -0.049784306436777115, 0.006072205025702715, -0.03297616168856621, 0.013669423758983612, -0.033153995871543884, -0.013836736790835857, -0.008764590136706829, 0.016674397513270378 ]
<p>I know that recent advances in technology are doing amazing things with very low amounts of electricity, with RFID being one of the most familiar examples, but I'm not very familiar with the principles involved. It makes me wonder: is it possible (with current technology, not "is it theoretically possible?") to use ambient sources (including body heat) to generate enough power to light up an LED, all in a device small enough for a person to hold in their hand? If so, how small could the whole assembly be made?</p> <p>I've actually got a very specific application in mind, but if it turns out we don't have the capability for it, that'll save a lot of time right there.</p>
g8406
[ 0.005807301960885525, 0.07123202830553055, -0.009286832995712757, 0.015467455610632896, -0.06257309019565582, -0.008009401150047779, -0.03597167879343033, 0.02630935050547123, -0.03672996163368225, -0.040317103266716, 0.019618891179561615, 0.018607810139656067, -0.009799615480005741, -0.04504942521452904, 0.0009319001110270619, 0.03137506917119026, -0.0018015516689047217, -0.020315196365118027, 0.033883195370435715, 0.06488990038633347, 0.013538369908928871, -0.043804701417684555, -0.006868002004921436, -0.021335242316126823, -0.039674609899520874, -0.008729490451514721, 0.008037928491830826, -0.015249330550432205, -0.0353267677128315, -0.07944653183221817, -0.06705845147371292, -0.018662014976143837, -0.015168757177889347, -0.01128439325839281, -0.03829903528094292, 0.014869200997054577, -0.0006478999857790768, -0.036876093596220016, -0.012574109248816967, 0.03520636260509491, -0.030841227620840073, 0.008191035129129887, 0.04112134873867035, -0.032549187541007996, 0.000451926258392632, 0.04349031299352646, 0.08889354765415192, 0.013806413859128952, -0.00161884690169245, -0.03503509238362312, -0.035150207579135895, -0.04716739431023598, 0.015190665610134602, 0.01762627251446247, 0.06980346143245697, -0.06784974038600922, 0.004774713423103094, -0.011256705038249493, 0.02891830913722515, 0.03454454988241196, -0.01870758831501007, -0.004567811731249094, -0.022649820894002914, -0.033934857696294785, 0.02333279326558113, 0.011507884599268436, -0.03992884233593941, -0.0540158636868, 0.05133732408285141, 0.018030812963843346, 0.027585744857788086, -0.0008834415348246694, 0.025105034932494164, -0.012876584194600582, 0.009425832889974117, 0.03524080663919449, -0.048195816576480865, 0.02538066729903221, 0.01418957207351923, 0.03997894749045372, -0.00630732998251915, -0.03938693180680275, 0.008323616348206997, -0.0010059599298983812, -0.01722392998635769, -0.050461236387491226, -0.018559683114290237, 0.01672522723674774, 0.04860283434391022, 0.04769127815961838, 0.07362362742424011, 0.06894132494926453, 0.05814671516418457, -0.020105550065636635, 0.019891731441020966, -0.0016135199693962932, 0.04165439307689667, -0.018529092893004417, -0.0025746505707502365, -0.02841990254819393, 0.01066724956035614, -0.05502598360180855, -0.0076993596740067005, 0.048659902065992355, -0.08122364431619644, 0.0036615042481571436, -0.0186491459608078, -0.013149297796189785, -0.012133779935538769, 0.032775573432445526, -0.002733740024268627, -0.01431700587272644, -0.02370661497116089, 0.006112989038228989, 0.019833458587527275, 0.00807035993784666, 0.05432375147938728, -0.006353892385959625, -0.020600616931915283, 0.07186467200517654, 0.03717173635959625, -0.023972095921635628, 0.008526794612407684, -0.0224910881370306, 0.028736453503370285, 0.019058646634221077, -0.015955613926053047, 0.008146354928612709, -0.004866782575845718, -0.01060428936034441, 0.02743394486606121, -0.0027571399696171284, -0.049857694655656815, -0.021896563470363617, 0.053603462874889374, 0.04650825262069702, -0.02740664780139923, -0.020393332466483116, 0.0265490785241127, -0.02003597281873226, 0.018286455422639847, -0.020570673048496246, -0.07923503965139389, -0.009558025747537613, 0.027161620557308197, 0.05583799630403519, -0.06840699911117554, 0.0318153090775013, -0.0014427101705223322, 0.08640877157449722, 0.005203810054808855, 0.0030431803315877914, 0.015149242244660854, -0.04279567301273346, 0.026404792442917824, 0.041992247104644775, 0.013614536263048649, -0.023458102717995644, -0.012106035836040974, -0.0944114401936531, 0.06457602977752686, 0.024822041392326355, 0.04611802101135254, -0.06952334940433502, -0.002250844147056341, -0.044154997915029526, 0.021307379007339478, -0.004896020051091909, -0.02678987756371498, 0.019037209451198578, -0.04179595038294792, -0.023169921711087227, -0.02884046733379364, 0.030171815305948257, 0.009081365540623665, 0.023774243891239166, 0.07151125371456146, -0.01861126907169819, 0.04191990941762924, -0.03638361021876335, 0.004276116844266653, -0.030903877690434456, -0.02986638806760311, -0.02879451960325241, -0.012784919701516628, -0.014952677302062511, 0.004677049349993467, 0.009752350859344006, 0.045273855328559875, 0.015795979648828506, -0.05224626883864403, 0.009084225632250309, -0.006537057925015688, 0.06178837642073631, -0.02359856851398945, 0.002205820055678487, -0.010289868339896202, -0.010284270159900188, 0.014348267577588558, -0.0175449401140213, 0.03521149605512619, 0.01734878681600094, 0.012980489991605282, 0.004029314033687115, 0.06493233144283295, 0.04104936867952347, 0.013874175027012825, -0.0594327375292778, 0.014261696487665176, -0.040136318653821945, 0.06942525506019592, 0.005630606319755316, 0.007744711358100176, -0.007250145077705383, -0.011136118322610855, -0.07013330608606339, -0.07271569967269897, -0.025887425988912582, 0.0043611363507807255, -0.03320502117276192, 0.017494628205895424, -0.002615945879369974, -0.006065727677196264, 0.018648400902748108, -0.002577332779765129, 0.02795559912919998, -0.060067068785429, -0.008710643276572227, -0.019560791552066803, -0.04019683972001076, -0.048394825309515, 0.04568025469779968, 0.01281253807246685, -0.05963582172989845, -0.02041836641728878, 0.03923822194337845, -0.04188540577888489, -0.014058558270335197, -0.035863883793354034, 0.003167499555274844, 0.0050299521535634995, -0.01998506486415863, 0.020447148010134697, 0.01973305270075798, -0.047033701092004776, -0.027389883995056152, -0.01833019033074379, 0.008457636460661888, -0.016060762107372284, 0.05002593621611595, -0.002813603961840272, 0.01597304455935955, -0.03544134646654129, -0.007648914586752653, -0.06325813382863998, -0.003868360538035631, 0.021953102201223373, 0.017656879499554634, 0.032875336706638336, -0.044536516070365906, -0.06725829094648361, -0.026020150631666183, 0.020786628127098083, 0.022560929879546165, 0.016236810013651848, -0.03564668819308281, -0.02810818888247013, -0.07977841794490814, 0.019645148888230324, 0.03842216357588768, 0.007474812678992748, 0.008045642636716366, -0.036395248025655746, 0.0005437842919491231, 0.0076880375854671, -0.0037679572124034166, -0.002675925847142935, 0.0010551760205999017, 0.1038174033164978, 0.028730014339089394, 0.06172005459666252, -0.04817063733935356, -0.05497235432267189, 0.015201720409095287, -0.011980547569692135, -0.0442829467356205, -0.03784101456403732, 0.026489682495594025, 0.032345760613679886, 0.03234630823135376, -0.010828295722603798, -0.05987929925322533, 0.006330176722258329, -0.05528578534722328, -0.038035836070775986, 0.025113504379987717, -0.002486014738678932, 0.012167560867965221, -0.003925985191017389, 0.022460011765360832, 0.0470302440226078, -0.07536858320236206, 0.013898568227887154, -0.02557482197880745, -0.05207314342260361, -0.021268408745527267, -0.0706285685300827, -0.06265713274478912, 0.0714496374130249, 0.023221001029014587, 0.010227367281913757, 0.011532249860465527, -0.04574667289853096, 0.06608876585960388, -0.031405769288539886, 0.008723283186554909, 0.003737448249012232, -0.014326604083180428, 0.0016073716105893254, -0.02751472219824791, 0.0540386326611042, -0.023171206936240196, -0.043531063944101334, 0.006015242077410221, 0.07528693974018097, -0.0011626232881098986, 0.03960070759057999, -0.015060396865010262, 0.03384840115904808, -0.017456205561757088, 0.03555712476372719, -0.016093626618385315, -0.06041011959314346, -0.005596024449914694, 0.002298678969964385, -0.04096890613436699, -0.00643527926877141, 0.0438971221446991, 0.05226365849375725, 0.022318342700600624, -0.04088979214429855, -0.013323475606739521, -0.0228266678750515, -0.03751274198293686, 0.048553138971328735, 0.05557582154870033, -0.04154650866985321, -0.020078817382454872, -0.008111296221613884, -0.02099062129855156, 0.06999307125806808, -0.023857183754444122, -0.03525969386100769, -0.03465067967772484, 0.0029462866950780153, 0.05969948694109917, 0.0034279287792742252, 0.06909478455781937, -0.004420531913638115, -0.045226871967315674, -0.04081030562520027, 0.03895517438650131, 0.10962507128715515, -0.09819068759679794, 0.046386994421482086, 0.025789743289351463, -0.011103692464530468, 0.04863264784216881, -0.03589480742812157, -0.01892753131687641, -0.012776891700923443, -0.031129132956266403, -0.0581117644906044, -0.00932097714394331, 0.01022043451666832, -0.012218714691698551, 0.06725244224071503, -0.0189984068274498, -0.034412872046232224, 0.029023386538028717, -0.054354868829250336, 0.03288211673498154, -0.0020603740122169256, -0.014169884845614433, -0.0003632310836110264, 0.017060263082385063, -0.05570334941148758, 0.018433962017297745, -0.019988246262073517, -0.05323294550180435, 0.008262183517217636, -0.03928639367222786, 0.020002560690045357, -0.039488282054662704, -0.014900792390108109, -0.0007244175649248064, -0.020039387047290802, -0.0962575152516365, 0.040299735963344574, 0.057844799011945724, 0.061998479068279266, 0.04947430267930031, 0.05663817748427391, 0.022136347368359566, -0.023219678550958633, 0.016397112980484962, 0.051892220973968506, -0.0026271375827491283, -0.002344283973798156, -0.06371889263391495, 0.04757925122976303, -0.011725419200956821, 0.021504737436771393, -0.022681813687086105, 0.04727507382631302, -0.006511146668344736, 0.012651609256863594, -0.04225706681609154, 0.06724154204130173, 0.06686829775571823, 0.011364721693098545, -0.011774691753089428, -0.01753898523747921, 0.010437383316457272, -0.058885540813207626, 0.07870453596115112, 0.022640714421868324, 0.019442470744252205, 0.027027763426303864, -0.04988233745098114, 0.04091009125113487, 0.025048505514860153, -0.017624596133828163, -0.02535535953938961, 0.04875478148460388, -0.014519958756864071, -0.008660580962896347, -0.009126710705459118, 0.05199245363473892, 0.03317488729953766, 0.025859123095870018, -0.036466289311647415, 0.05335519462823868, 0.02660752274096012, 0.027975978329777718, 0.02535294182598591, -0.03825762867927551, -0.033975519239902496, -0.023861946538090706, 0.003675400512292981, -0.01693880185484886, -0.02137603610754013, 0.01607360504567623, -0.04344895854592323, 0.03856857493519783, -0.019968736916780472, -0.049305934458971024, -0.02932901866734028, 0.08096460998058319, -0.010162067599594593, -0.0734921246767044, -0.006740707438439131, -0.011193249374628067, 0.01146748848259449, 0.022375961765646935, -0.027515055611729622, -0.07224641740322113, -0.00013339758152142167, -0.012948854826390743, -0.01504959911108017, 0.0044271573424339294, 0.04470163583755493, 0.003713339101523161, 0.04269353672862053, -0.06307163089513779, -0.015676002949476242, 0.020795557647943497, -0.0038319816812872887, -0.06364403665065765, -0.01390825491398573, 0.007838623598217964, 0.03905147686600685, -0.05493050813674927, 0.03601246327161789, 0.0038621267303824425, 0.016026288270950317, -0.06761334091424942, 0.01820085383951664, -0.006709492299705744, -0.0029635969549417496, 0.01769028604030609, 0.027011970058083534, 0.01144386176019907, -0.019785456359386444, -0.0511796660721302, 0.03645430877804756, 0.02521713636815548, -0.00031698503880761564, -0.05656074360013008, 0.03853674232959747, -0.005790789611637592, 0.01585497334599495, -0.015145289711654186, -0.034654974937438965, 0.04260632395744324, -0.027619345113635063, 0.007599958218634129, -0.04205126687884331, 0.060753535479307175, 0.07062391191720963, -0.08105835318565369, 0.025394955649971962, -0.0601784773170948, -0.04883192107081413, 0.003208750858902931, -0.046950869262218475, -0.03817219287157059, -0.0473591648042202, -0.012575985863804817, 0.04390513896942139, 0.03375772386789322, -0.038860514760017395, 0.044882722198963165, 0.05471730977296829, -0.05872576683759689, 0.06892058253288269, -0.03777609393000603, 0.04485021531581879, -0.024206098169088364, 0.05489659681916237, 0.04445497319102287, 0.026822511106729507, -0.010201305150985718, -0.054499302059412, -0.062458883970975876, -0.0040611401200294495, -0.004629494156688452, 0.05537758767604828, 0.0343138612806797, 0.04240894317626953, 0.03911923989653587, -0.03928292915225029, 0.02143639512360096, 0.04903566092252731, 0.021901540458202362, -0.040626633912324905, 0.034633539617061615, 0.058296892791986465, -0.023438312113285065, 0.01957465149462223, 0.05369185656309128, 0.07670760154724121, -0.029550010338425636, 0.05073758587241173, 0.01570269837975502, -0.025811394676566124, -0.006418121047317982, -0.031372424215078354, 0.057240843772888184, -0.04123888164758682, 0.11184556782245636, 0.02964635007083416, 0.008079605177044868, 0.008993543684482574, 0.0004415274888742715, -0.010335366241633892, 0.007646511308848858, -0.02297724410891533, -0.030999960377812386, 0.07261320948600769, 0.06143779680132866, -0.0333641916513443, 0.038754768669605255, -0.03354039043188095, 0.000922549283131957, -0.04912431165575981, 0.054029956459999084, 0.012425473891198635, 0.0021353394258767366, 0.015869611874222755, 0.00807282980531454, 0.033997792750597, -0.011564892716705799, 0.0025790645740926266, 0.020075956359505653, 0.020520338788628578, -0.03597389906644821, 0.020146772265434265, 0.0025720102712512016, -0.024504460394382477, -0.0035529336892068386, -0.01019844226539135, 0.005277308169752359, 0.011812410317361355, -0.09287656098604202, -0.0122909527271986, -0.011100832372903824, -0.04964534193277359, -0.025001399219036102, 0.02719327062368393, -0.03697792813181877, -0.002423943718895316, -0.0681205466389656, -0.02272629365324974, -0.007025186438113451, 0.019351864233613014, -0.03130948916077614, 0.034542594105005264, 0.06261526793241501, -0.031546611338853836, -0.03922049701213837, -0.02048976719379425, 0.01100202277302742, -0.024743609130382538, 0.02699751779437065, -0.006959393620491028, -0.0073407357558608055, -0.010285530239343643, 0.013051138259470463, 0.013109024614095688, 0.009464137256145477, -0.023324375972151756, -0.019128426909446716, -0.03290950506925583, -0.03742925077676773, 0.02078387886285782, -0.0014843635726720095, 0.06434868276119232, 0.025451110675930977, 0.037047963589429855, -0.017625592648983, 0.008277705870568752, 0.02246282994747162, 0.04437632113695145, 0.011839428916573524, 0.015403934754431248, 0.0006854321109130979, -0.05949392914772034, 0.0048529463820159435, -0.02252078242599964, -0.02863295003771782, -0.034039344638586044, 0.02358284406363964, 0.05551741644740105, -0.012113425880670547, 0.02103802002966404, 0.02997136488556862, 0.059103306382894516, 0.030887844040989876, -0.007438792381435633, 0.03019099123775959, -0.024358944967389107, -0.0412042997777462, -0.0053257085382938385, -0.03764308616518974, 0.04926053062081337, -0.05752131715416908, -0.007411465980112553, -0.07272764295339584, -0.03423408418893814, 0.024798307567834854, 0.03391170874238014, 0.03366289287805557, -0.01314673013985157, -0.009023038670420647, 0.019818391650915146, -0.001938189030624926, 0.030069157481193542, -0.022955140098929405, -0.03386179730296135, 0.040585752576589584, -0.0347721166908741, -0.05710941180586815, -0.04241696372628212, 0.0250089168548584, -0.021701231598854065, 0.003393238876014948, 0.055479224771261215, -0.030013268813490868, -0.04277113452553749, -0.01728365197777748, 0.0026500646490603685, -0.03739798441529274, -0.00008207443170249462, 0.006086192559450865, 0.021265558898448944, -0.020130833610892296, 0.012602136470377445, 0.06726929545402527, -0.03956589475274086, -0.0425066277384758, 0.0030704603996127844, -0.029930662363767624, 0.004794831853359938, -0.028317878022789955, 0.056581225246191025, 0.002604551613330841, -0.0066405851393938065, -0.0010389024391770363, 0.06869100779294968, 0.04495123773813248, -0.029730895534157753, 0.04255954176187515, -0.03204876556992531, -0.029654642567038536, 0.01616302877664566, 0.01247489545494318, 0.03191067650914192, -0.02016277238726616, 0.013473737984895706, 0.03239597752690315, 0.07178360223770142, 0.00003833595474134199, 0.027720950543880463, 0.028553342446684837, 0.017071768641471863, -0.051821596920490265, 0.04184127599000931, 0.022836659103631973, 0.037694524973630905, -0.029140692204236984, 0.06870295852422714, -0.00035161018604412675, 0.003115627681836486, 0.013141385279595852, 0.0338812917470932, 0.04393526911735535, 0.01598578505218029, 0.03564421087503433, -0.026101768016815186, -0.004271998535841703, -0.051803648471832275, -0.005390403792262077, -0.06072993576526642, 0.00938456505537033, -0.007415702100843191, -0.0200447216629982, -0.018093464896082878, -0.010543378069996834, -0.0014875681372359395, -0.01977504789829254, -0.0073075564578175545, -0.03858978673815727, 0.0033668961841613054, 0.04439554736018181, 0.02754921093583107, -0.08759589493274689, 0.01615455187857151, 0.03709433227777481, 0.028240565210580826, -0.07910754531621933, 0.01552414707839489, -0.05111834406852722, -0.004905523732304573, 0.08411251753568649, 0.014712820760905743, 0.014434890821576118, 0.009887571446597576, -0.014935010112822056, 0.0207660011947155, -0.00029702414758503437, 0.011135229840874672, -0.04762624204158783, 0.013085093349218369, -0.020520096644759178, 0.004443024285137653, 0.022258294746279716, 0.0010072331642732024 ]
<p>Is there a good way to directly measure a moment of inertia of the Earth, or say, other planet?</p>
g8407
[ 0.015303202904760838, 0.027243060991168022, -0.0045696706511080265, -0.05737551674246788, 0.06280095875263214, -0.01543812919408083, 0.002328109461814165, -0.03478578105568886, -0.026914404705166817, -0.004554131533950567, 0.0073298122733831406, -0.014980725012719631, 0.017438450828194618, 0.03655073791742325, 0.03960173949599266, -0.020089376717805862, 0.058901410549879074, -0.00836112629622221, 0.05175238475203514, 0.07399073243141174, 0.08355912566184998, -0.01802019029855728, -0.0027617826126515865, -0.012074567377567291, -0.00030209257965907454, 0.019519269466400146, -0.002075470518320799, 0.021075274795293808, 0.02535102143883705, 0.012872261926531792, -0.0397503525018692, -0.021771475672721863, -0.016401387751102448, -0.04152778536081314, -0.019679611548781395, -0.0021126868668943644, 0.008680297993123531, 0.05122218653559685, 0.011052783578634262, 0.008955476805567741, -0.030150718986988068, -0.07759209722280502, 0.018836786970496178, 0.03135440871119499, 0.09776315838098526, 0.0019213041523471475, -0.0035216689575463533, 0.011393463239073753, 0.04053818807005882, -0.06194153055548668, -0.035482846200466156, -0.006504226475954056, 0.04856281727552414, -0.024792039766907692, -0.025731829926371574, 0.040465377271175385, 0.023059917613863945, -0.031274065375328064, 0.06205587461590767, 0.01634465530514717, -0.06375687569379807, -0.08042719960212708, 0.007002063095569611, -0.02538907155394554, 0.00024656744790263474, 0.04217960312962532, -0.06274989992380142, 0.004831348080188036, -0.012698514387011528, -0.021230081096291542, 0.004669001325964928, 0.0011030351743102074, 0.015987925231456757, -0.04111181199550629, -0.09673513472080231, 0.04287807643413544, -0.04654233157634735, 0.012451172806322575, 0.02749202959239483, 0.023746628314256668, -0.0415162667632103, 0.03446171432733536, 0.03243168070912361, -0.019145051017403603, 0.0730084702372551, -0.036473602056503296, 0.04436621069908142, 0.03355249762535095, 0.018658200278878212, -0.03882431238889694, 0.02249911054968834, -0.034607525914907455, 0.020926974713802338, 0.017136216163635254, -0.02782554365694523, 0.002760239178314805, -0.03586803749203682, 0.05349211022257805, 0.026723936200141907, 0.06451084464788437, -0.01093387883156538, -0.013329222798347473, -0.047751519829034805, -0.03448259457945824, 0.05887783691287041, -0.044103655964136124, 0.009280255995690823, -0.03975005820393562, 0.02683020569384098, -0.09923776984214783, 0.00698502641171217, -0.050078343600034714, 0.03130840137600899, -0.01936831884086132, -0.01349103543907404, -0.007145961280912161, 0.07989329099655151, -0.039450470358133316, 0.0030870758928358555, 0.02491166815161705, -0.0027564247138798237, 0.00923246331512928, 0.027010047808289528, 0.06681612133979797, -0.04113275185227394, -0.013954882510006428, 0.006972975097596645, -0.009802497923374176, 0.024888377636671066, 0.021091027185320854, -0.03697919473052025, 0.003458122257143259, -0.04534579813480377, -0.029007907956838608, -0.0399760827422142, -0.0067116739228367805, -0.012286556884646416, -0.016571538522839546, -0.04358069226145744, 0.011279522441327572, -0.013481201604008675, -0.02837907150387764, 0.014653540216386318, 0.03659836947917938, 0.02614709734916687, 0.03932073339819908, -0.015619696117937565, 0.03108423575758934, 0.06009006127715111, -0.014637179672718048, -0.029879573732614517, 0.015354892238974571, 0.04323400557041168, 0.023783452808856964, 0.06643058359622955, 0.02247341349720955, 0.040614522993564606, 0.006489085499197245, -0.014977553859353065, 0.045080993324518204, 0.002329760231077671, 0.011156375519931316, 0.011056412011384964, -0.0059676216915249825, 0.006395887117832899, -0.0007790874224156141, -0.025636401027441025, -0.03560129180550575, 0.019998349249362946, -0.04066269099712372, -0.03342588245868683, -0.00811788346618414, 0.01756276749074459, -0.029430173337459564, -0.002581049920991063, 0.019310377538204193, -0.00166406761854887, -0.029787208884954453, 0.012163208797574043, -0.01471215020865202, 0.06402047723531723, -0.011376322247087955, 0.016685234382748604, -0.03768937662243843, -0.01726955734193325, -0.06049373745918274, 0.04044872894883156, -0.016579505056142807, -0.05546806380152702, 0.03123033419251442, -0.010948735289275646, -0.056919947266578674, -0.0056000277400016785, 0.0014184947358444333, -0.025406191125512123, 0.004991426132619381, 0.06498017907142639, 0.003011442720890045, -0.02468940056860447, 0.054685432463884354, -0.034214045852422714, 0.036858607083559036, 0.02919493056833744, 0.056050702929496765, -0.042075611650943756, -0.057823095470666885, 0.007676558569073677, 0.00785019714385271, -0.0020755664445459843, 0.012281837873160839, 0.07995913177728653, 0.02897452563047409, -0.04591311886906624, -0.010983497835695744, -0.03456548601388931, 0.03594934567809105, 0.000305772788124159, -0.04556477069854736, 0.006743965670466423, -0.01994015835225582, -0.027383485808968544, 0.022235898301005363, 0.0362955778837204, -0.005910499487072229, 0.03070857934653759, -0.03347630426287651, -0.03986361622810364, 0.056063491851091385, 0.0636601522564888, -0.004794117994606495, -0.04197429120540619, -0.002562924986705184, -0.04118064045906067, 0.0541265644133091, 0.037010613828897476, 0.08610720187425613, 0.0021207118406891823, -0.0335933081805706, -0.03919855132699013, 0.013219933956861496, 0.04003416746854782, -0.038155846297740936, -0.038654860109090805, 0.019679127261042595, -0.01398854237049818, -0.004150442313402891, 0.03800145536661148, 0.03320101648569107, -0.0037511105183511972, 0.003719217609614134, 0.009857113473117352, -0.021859925240278244, -0.01951146125793457, -0.06913552433252335, 0.015573211945593357, 0.03691163659095764, 0.03504383936524391, 0.016051605343818665, -0.03664558380842209, 0.012327232398092747, -0.0007834822172299027, -0.0395684614777565, 0.043664902448654175, 0.03987089544534683, -0.012853298336267471, -0.07873669266700745, -0.060747094452381134, 0.037732694298028946, -0.01224894542247057, 0.003403064562007785, -0.020343540236353874, 0.04933232441544533, 0.01303948275744915, 0.055586040019989014, -0.045200880616903305, -0.013093402609229088, 0.04305596277117729, -0.03750012814998627, 0.017201971262693405, -0.025557970628142357, -0.036941636353731155, 0.06056106463074684, -0.008227784186601639, 0.06804433465003967, 0.05539930611848831, 0.00943860411643982, -0.07716374844312668, -0.0015752005856484175, 0.00461351964622736, 0.002372914459556341, 0.027686472982168198, -0.01647486351430416, 0.028269095346331596, 0.04277705028653145, -0.018150676041841507, 0.026567135006189346, 0.04648745805025101, -0.07306399941444397, 0.04580637440085411, -0.001445611473172903, 0.04597383737564087, -0.048589423298835754, 0.023548388853669167, 0.0557711198925972, -0.00852607749402523, 0.0036434161011129618, 0.019605718553066254, -0.020799079909920692, 0.0509074442088604, -0.034912705421447754, -0.021425826475024223, 0.023083193227648735, -0.04941834509372711, 0.015539586544036865, -0.04328738525509834, 0.012411927804350853, -0.022767353802919388, 0.012149388901889324, 0.020910250023007393, 0.010444438084959984, 0.006220011506229639, -0.10731728374958038, -0.025102252140641212, 0.030720321461558342, -0.020746469497680664, 0.059879597276449203, -0.03367938473820686, -0.02527511492371559, -0.03565610945224762, -0.04094937816262245, -0.04168767109513283, 0.07429840415716171, -0.016111545264720917, 0.02955842763185501, -0.06128174439072609, -0.008708862587809563, -0.0070702382363379, 0.0009232821757905185, 0.05564359202980995, 0.09170739352703094, -0.059845082461833954, -0.004177528899163008, -0.05806043744087219, -0.006137065589427948, -0.007606973871588707, -0.014447103254497051, 0.0004274944949429482, -0.03269711136817932, -0.002017014194279909, -0.0293267909437418, 0.016634708270430565, -0.00612892908975482, -0.013472617603838444, -0.07476135343313217, 0.03959545120596886, 0.072963185608387, 0.049174416810274124, -0.023200999945402145, -0.052160702645778656, 0.03560792654752731, 0.04064330831170082, -0.007626495324075222, -0.02831915393471718, -0.014530711807310581, 0.019978871569037437, 0.003459473140537739, -0.01953345350921154, 0.022297294810414314, -0.012945888563990593, 0.004251097794622183, -0.027613526210188866, 0.06857281178236008, 0.017440369352698326, 0.028695382177829742, 0.037463217973709106, -0.07491504400968552, 0.04261193796992302, -0.0397363118827343, 0.014037146233022213, -0.00681353360414505, 0.00036499055568128824, -0.008864539675414562, -0.0013851599069312215, -0.0038298603612929583, 0.011390913277864456, -0.012087389826774597, 0.0020363638177514076, -0.038973137736320496, 0.025637643411755562, -0.0016754395328462124, 0.0570550374686718, -0.08072005212306976, -0.0701179951429367, -0.016646724194288254, 0.06272926926612854, -0.03401190787553787, 0.011821262538433075, 0.011939415708184242, -0.013700202107429504, 0.012722853571176529, 0.0015541819157078862, 0.02384594827890396, 0.026684638112783432, -0.016091901808977127, 0.0173571165651083, 0.028546130284667015, 0.020361104980111122, -0.003172025317326188, -0.05236005783081055, 0.013501184992492199, -0.0070461491122841835, 0.014843139797449112, -0.011710681021213531, -0.024630185216665268, 0.025105636566877365, 0.010031189769506454, 0.035322003066539764, -0.02278284542262554, 0.04078996554017067, 0.031550850719213486, 0.0016235160874202847, 0.0751822367310524, 0.007514146156609058, -0.04154146462678909, -0.05093936622142792, 0.0341259203851223, 0.05793447047472, 0.025129158049821854, -0.0322638563811779, 0.02297588437795639, -0.013926287181675434, -0.021052436903119087, 0.06432968378067017, 0.06264427304267883, 0.016652610152959824, 0.009030972607433796, -0.023049546405673027, 0.0013726376928389072, 0.009909706190228462, -0.025004440918564796, 0.018314369022846222, 0.03250325471162796, 0.021011706441640854, -0.012089391238987446, -0.08044988662004471, 0.11659116297960281, -0.013347587548196316, -0.026689905673265457, -0.025434795767068863, -0.02738594077527523, -0.015724247321486473, -0.012175221927464008, -0.019381165504455566, 0.03653040528297424, -0.0164564810693264, -0.042591728270053864, -0.014903039671480656, 0.030331766232848167, -0.07111933082342148, 0.02224680967628956, -0.0656343623995781, 0.012407968752086163, -0.0075547662563622, 0.009423279203474522, -0.013754455372691154, 0.0009202861692756414, -0.07483447343111038, -0.009348239749670029, -0.035477738827466965, -0.026018664240837097, 0.04225008934736252, -0.020292188972234726, 0.005240608472377062, 0.05820578336715698, 0.02695304900407791, 0.01952308788895607, -0.018612278625369072, 0.0036639333702623844, 0.013599105179309845, -0.020930469036102295, -0.045467473566532135, -0.0201177466660738, -0.0020053654443472624, -0.0283086858689785, 0.014198396354913712, 0.007063441909849644, -0.03765011206269264, -0.01526784896850586, 0.0461585596203804, -0.003598813433200121, 0.004119293298572302, 0.00013589460286311805, -0.0034152434673160315, -0.08329334855079651, -0.025653818622231483, 0.03835507109761238, 0.0047473302111029625, -0.07968692481517792, -0.02308027260005474, -0.0017833291785791516, -0.04771203175187111, 0.043877650052309036, -0.05437374487519264, 0.021451273933053017, 0.03855586051940918, 0.015112961642444134, 0.03448101878166199, 0.009266529232263565, -0.0378364659845829, 0.0020019172225147486, 0.04650762677192688, 0.07459964603185654, -0.0016844302881509066, 0.07876801490783691, 0.028643250465393066, -0.02484206110239029, 0.07538817077875137, 0.03508952260017395, -0.015610511414706707, -0.03403737023472786, 0.04343846067786217, -0.023280126973986626, 0.020579081028699875, 0.010900122113525867, 0.004521747585386038, 0.008458400145173073, -0.05060182884335518, -0.0025359184946864843, -0.034063179045915604, -0.016389671713113785, 0.006525279954075813, -0.06780287623405457, 0.012587528675794601, -0.07189016789197922, -0.02530180662870407, -0.06100175902247429, 0.012656054459512234, 0.025532042607665062, 0.05923914164304733, -0.057411130517721176, -0.030519023537635803, 0.006407484412193298, 0.02798696793615818, 0.005192556418478489, -0.03141932189464569, 0.027442630380392075, -0.009245689027011395, 0.04815543815493584, 0.04393387213349342, 0.007127563003450632, -0.03292791545391083, 0.010072892531752586, 0.031651463359594345, -0.06567675620317459, -0.06936033070087433, 0.012134629301726818, 0.03562181442975998, 0.02984577603638172, -0.04707198962569237, -0.003756023244932294, 0.04952739551663399, -0.009355276823043823, 0.02823074907064438, -0.015965601429343224, -0.04017883911728859, -0.03701023384928703, 0.025595324113965034, 0.005876972805708647, 0.04215675964951515, -0.05108821392059326, -0.005699850153177977, -0.008008536882698536, -0.023279540240764618, -0.0183666180819273, 0.007368253078311682, -0.010206125676631927, -0.03845776244997978, 0.026177598163485527, 0.03647773712873459, -0.021412957459688187, -0.040022049099206924, -0.001652501174248755, 0.07376226782798767, 0.01202683337032795, -0.008958009071648121, 0.00983533076941967, 0.0029630460776388645, -0.014011513441801071, -0.020646629855036736, -0.018601058050990105, 0.026656754314899445, 0.011676507070660591, -0.035045940428972244, -0.05429835990071297, -0.018877817317843437, 0.04138569533824921, -0.08637342602014542, -0.008962986059486866, 0.0010595136554911733, 0.08905650675296783, 0.031107941642403603, -0.058090802282094955, 0.06733977794647217, -0.08378438651561737, -0.024206260219216347, 0.021699106320738792, -0.02089470997452736, 0.012256690301001072, 0.03496285155415535, -0.007728505413979292, -0.017923109233379364, 0.00818990170955658, 0.03084460087120533, 0.06320483237504959, 0.01016318704932928, -0.01339204702526331, 0.03563844785094261, -0.03286965563893318, 0.01200102362781763, 0.0067863138392567635, 0.012954529374837875, -0.0698876827955246, 0.012986795045435429, -0.01603349857032299, -0.036875419318675995, 0.048979371786117554, -0.03994442895054817, 0.002571831224486232, 0.008688581176102161, -0.003374385880306363, 0.021198388189077377, 0.008953042328357697, -0.009868613444268703, 0.01593700796365738, 0.012939663603901863, 0.0825170949101448, -0.0006475167465396225, 0.0005069741164334118, 0.04557908698916435, 0.0390508808195591, -0.022348156198859215, 0.03201837092638016, -0.0200007576495409, 0.005510059650987387, -0.04766376316547394, 0.03167416527867317, 0.00005794101525680162, -0.0047220634296536446, 0.021549193188548088, -0.027697060257196426, 0.006249704398214817, -0.019837290048599243, 0.002982118632644415, 0.058654092252254486, -0.0140072675421834, 0.08036939799785614, 0.06715061515569687, -0.0014608127530664206, 0.05009359121322632, -0.04752948880195618, -0.006274529732763767, -0.03465432673692703, 0.016782661899924278, -0.05802417919039726, 0.004639831837266684, -0.008534991182386875, -0.03633907809853554, -0.030743183568120003, -0.02380281500518322, -0.02197917364537716, 0.040960893034935, -0.02560570277273655, -0.011692242696881294, 0.02824004925787449, -0.014624560251832008, 0.028924498707056046, -0.026495931670069695, -0.06560579687356949, -0.04166250675916672, -0.0551934540271759, -0.018697278574109077, 0.0483703538775444, -0.007034251932054758, 0.014962499029934406, -0.03798411041498184, 0.03941371664404869, 0.03187436982989311, 0.025366779416799545, 0.013183659873902798, -0.08107639849185944, 0.0007379470625892282, 0.09371894598007202, 0.0296526737511158, -0.05145590752363205, -0.03218184784054756, -0.00521325645968318, 0.06673537194728851, 0.02097366191446781, -0.023671532049775124, -0.0663764625787735, -0.043546222150325775, -0.0291804987937212, 0.04489092156291008, -0.01523694396018982, 0.03473244979977608, -0.03764075040817261, -0.03963388502597809, -0.027516257017850876, -0.005964243318885565, 0.04725964739918709, 0.021594468504190445, 0.06313282996416092, -0.021499507129192352, -0.008280184119939804, -0.017071986570954323, -0.05308220908045769, -0.027700606733560562, 0.0012735443888232112, 0.019123274832963943, 0.011750772595405579, 0.006339795887470245, -0.027724308893084526, 0.028266308829188347, -0.07446588575839996, -0.050235994160175323, -0.015427312813699245, 0.005882592406123877, -0.007492159027606249, 0.058016981929540634, -0.04438243806362152, 0.041128985583782196, 0.05292103439569473, 0.014067317359149456, 0.05002521350979805, -0.02299565263092518, 0.019679272547364235, -0.030055981129407883, -0.092958003282547, -0.03673393279314041, 0.03537529706954956, -0.02516382932662964, -0.04549713060259819, -0.0670868307352066, 0.005367535166442394, 0.027071166783571243, -0.004956689663231373, -0.011382678523659706, 0.054894860833883286, 0.005482363048940897, 0.021833034232258797, -0.009171416983008385, 0.06804805994033813, -0.008623531088232994, -0.0450894720852375, -0.045768994837999344, 0.03807425498962402, -0.03228180110454559, -0.03348718211054802, -0.008012614212930202, 0.0030687558464705944, 0.014156597666442394, 0.007754546590149403, 0.02358817681670189, -0.003741917898878455, -0.014026694931089878, -0.0193477775901556, -0.006352324038743973, -0.003981296438723803 ]
<p>What state is <a href="http://en.wikipedia.org/wiki/Fire" rel="nofollow">fire</a>? Solid, Liquid or Gas or Plasma? </p> <p>I was just roaming around when this question popped out of my mind. In what state is FIRE? </p>
g276
[ 0.046242281794548035, -0.005394102539867163, 0.01814102940261364, 0.00008706947846803814, 0.01437427569180727, 0.009744680486619473, -0.0018565695500001311, 0.03150877729058266, 0.018844006583094597, -0.09186342358589172, -0.02024519070982933, 0.002468433231115341, 0.0015167498495429754, 0.0019054566510021687, -0.04607681185007095, -0.027714740484952927, 0.07238317281007767, 0.03776184841990471, 0.05344606935977936, 0.016591936349868774, -0.036669522523880005, -0.019250595942139626, 0.02815382555127144, -0.03997408598661423, 0.0006998986937105656, -0.0034622852690517902, -0.042008429765701294, -0.024410778656601906, -0.027549412101507187, -0.040609948337078094, -0.021485092118382454, -0.013695502653717995, -0.013705328106880188, -0.02424287050962448, 0.00968162901699543, -0.04017218202352524, -0.012339556589722633, 0.006365340668708086, 0.05726078897714615, -0.005809217691421509, -0.039615530520677567, 0.06840594857931137, 0.004185672849416733, -0.0008751010755077004, -0.001768650719895959, 0.08503066748380661, 0.019789498299360275, -0.027166694402694702, -0.018694063648581505, -0.006026491988450289, -0.0026796383317559958, 0.0175018310546875, -0.04606667533516884, -0.04445553943514824, 0.029698142781853676, -0.011562425643205643, -0.027896689251065254, -0.0013403365155681968, 0.02913394384086132, -0.012968157418072224, -0.000641224323771894, -0.004599584732204676, 0.007868914864957333, -0.061471857130527496, 0.005904435645788908, 0.022921506315469742, -0.04194929823279381, 0.05528269708156586, 0.006322640459984541, -0.03760068118572235, 0.003902534954249859, -0.007763601839542389, -0.016408931463956833, -0.004317367449402809, -0.021275483071804047, -0.03583352267742157, -0.005432073026895523, -0.0013003770727664232, 0.03743734583258629, 0.03194873407483101, 0.03189382329583168, -0.014126689173281193, 0.01073785312473774, -0.006354914046823978, -0.015383992344141006, 0.02187499962747097, -0.03094489686191082, 0.019833752885460854, 0.026711484417319298, -0.038784656673669815, -0.028859997168183327, 0.05784010887145996, 0.09079178422689438, -0.0004295009421184659, -0.024492913857102394, -0.038101114332675934, -0.01665930449962616, 0.031198775395751, 0.04739876836538315, 0.016813447698950768, -0.0525260828435421, -0.07522490620613098, 0.020933058112859726, -0.010609143413603306, 0.1091306135058403, -0.016961047425866127, -0.025527656078338623, -0.05546615645289421, -0.04570578411221504, -0.01835222728550434, 0.003272341564297676, 0.02906978130340576, 0.0022704103030264378, -0.01824001967906952, -0.007537909783422947, 0.07914647459983826, -0.017868831753730774, -0.0056339409202337265, 0.006621602922677994, 0.012681662105023861, 0.0378805510699749, 0.009931951761245728, 0.05390000343322754, 0.05465604364871979, 0.007196905557066202, -0.013250058516860008, 0.03395598754286766, -0.04339652881026268, -0.030413324013352394, -0.0078094033524394035, -0.07389936596155167, -0.027113784104585648, -0.02627054788172245, -0.01934162527322769, -0.012054861523211002, -0.00781512912362814, -0.013309014029800892, -0.017673159018158913, -0.024323318153619766, 0.052549876272678375, 0.08463392406702042, 0.022001849487423897, 0.012103695422410965, -0.004833737388253212, 0.02956615760922432, -0.014856071211397648, -0.016240283846855164, -0.013763953931629658, 0.0567607656121254, 0.022623606026172638, 0.02413175255060196, 0.01333334669470787, 0.03336386755108833, -0.06307681649923325, 0.04313751682639122, -0.05079760029911995, 0.04188539460301399, 0.064390629529953, -0.030216647312045097, -0.03863680362701416, -0.028135182335972786, -0.008388345129787922, -0.0002830451703630388, -0.016930557787418365, -0.006251916754990816, -0.036273494362831116, -0.0408690944314003, -0.018385116010904312, 0.009190170094370842, -0.01888076215982437, -0.023643776774406433, 0.010522770695388317, -0.04881460964679718, 0.01921277493238449, 0.05873694643378258, -0.002536989049986005, 0.008401124738156796, 0.011032376438379288, 0.053025007247924805, -0.02728322707116604, 0.03628803417086601, -0.028343435376882553, -0.01135579776018858, 0.011192850768566132, 0.011750399135053158, 0.0304162185639143, -0.03920954838395119, -0.03494945168495178, -0.009630836546421051, 0.01720813661813736, -0.05414632335305214, -0.06267048418521881, -0.023883508518338203, -0.014270797371864319, 0.03357144072651863, -0.013169587589800358, 0.010636765509843826, -0.041155051440000534, -0.03624396026134491, -0.01712236925959587, -0.037819281220436096, 0.015650590881705284, -0.05046959966421127, 0.010066071525216103, -0.005409815348684788, 0.006044525187462568, 0.030160769820213318, -0.05106716603040695, -0.030942043289542198, 0.008944089524447918, -0.023482967168092728, -0.028261853381991386, -0.014787258580327034, 0.03012418933212757, -0.00008450352470390499, 0.05183931812644005, -0.011940467171370983, -0.04677543044090271, -0.0441133975982666, -0.04510876163840294, 0.01658414490520954, 0.015586446039378643, 0.03627317026257515, -0.03471117466688156, 0.05157988518476486, -0.000948529748711735, 0.033874474465847015, -0.0028224261477589607, 0.013642004691064358, 0.04106074199080467, -0.026578813791275024, 0.018037229776382446, 0.02802327647805214, -0.01616523042321205, 0.0219771396368742, 0.054066095501184464, -0.04412412270903587, 0.0011722216149792075, -0.06515565514564514, 0.03667765483260155, -0.01913227140903473, -0.04679901897907257, 0.03446560353040695, 0.0042101554572582245, 0.03848302364349365, -0.02731223590672016, -0.013969137333333492, 0.017747284844517708, 0.05210190266370773, 0.04723513498902321, -0.006153030786663294, -0.0499819740653038, -0.03486165776848793, 0.01744791306555271, 0.002126450650393963, -0.052365560084581375, -0.024562014266848564, 0.026955166831612587, -0.03675497695803642, 0.01570037752389908, -0.012211157940328121, -0.04788212850689888, -0.0527849979698658, -0.05894405394792557, -0.06532159447669983, 0.026544680818915367, -0.08522381633520126, -0.009957456961274147, -0.022665005177259445, -0.030351659283041954, 0.03161159157752991, -0.017269844189286232, -0.03565112501382828, -0.016966640949249268, -0.0012950667878612876, 0.028798099607229233, -0.00800730288028717, -0.01519839558750391, 0.040223654359579086, -0.009526515379548073, -0.026858970522880554, 0.048811063170433044, -0.004517614841461182, 0.09452178329229355, -0.02304448001086712, -0.005734517239034176, -0.0038191569037735462, 0.05596201866865158, -0.045926764607429504, -0.03241309896111488, 0.011270894668996334, 0.017658108845353127, -0.0012313928455114365, 0.005354444030672312, -0.054720230400562286, 0.010170281864702702, 0.034860365092754364, -0.04048694297671318, 0.03003486432135105, -0.001735400641337037, 0.016177557408809662, -0.04041832685470581, -0.016403483226895332, 0.019769299775362015, 0.016103509813547134, 0.016590910032391548, -0.007906570099294186, -0.022668661549687386, 0.057623423635959625, 0.040153902024030685, 0.004582064691931009, 0.06563364714384079, -0.02810050919651985, 0.035177718847990036, -0.007654977031052113, 0.03062564507126808, -0.025720274075865746, 0.05562865734100342, 0.04396447911858559, -0.01616397686302662, -0.027709415182471275, -0.02393239364027977, -0.008509211242198944, -0.08696040511131287, 0.0023350976407527924, 0.05113565921783447, 0.013324019499123096, 0.028306370601058006, -0.02820712886750698, -0.01256994716823101, -0.012010992504656315, -0.016022467985749245, -0.08106648921966553, -0.07045776396989822, -0.001650904188863933, -0.016692521050572395, -0.06343565881252289, 0.022213952615857124, 0.09097352623939514, 0.01606190949678421, 0.02225193940103054, -0.017876919358968735, 0.0006414595991373062, -0.041055161505937576, 0.01993457041680813, -0.0068668220192193985, -0.02213187702000141, -0.0012192471185699105, -0.02547813393175602, 0.028059981763362885, 0.014347787946462631, 0.009915179572999477, 0.004444700200110674, -0.05385928228497505, -0.029276708140969276, -0.017832767218351364, -0.005890257656574249, -0.05061022937297821, -0.013236509636044502, 0.04692979156970978, -0.0179291944950819, -0.03326956927776337, 0.0312720462679863, -0.032252002507448196, 0.00506017729640007, 0.000056714012316660956, -0.0031717217061668634, 0.009488713927567005, -0.004386732820421457, 0.0034173312596976757, -0.020978372544050217, -0.05297064036130905, 0.012604986317455769, 0.061058223247528076, 0.0658983364701271, 0.009823717176914215, -0.014268936589360237, 0.016774488613009453, -0.06431518495082855, -0.001399328582920134, 0.054111890494823456, 0.03890020772814751, 0.04423687979578972, 0.03380931541323662, -0.02817695029079914, 0.000910990172997117, 0.017520295456051826, 0.022530555725097656, 0.025714417919516563, -0.06595289707183838, 0.06626053154468536, -0.020464127883315086, -0.032011911273002625, -0.004595857113599777, 0.01679660752415657, 0.08759897947311401, 0.004871537908911705, 0.04337482154369354, -0.000704319856595248, 0.03429039567708969, 0.018236782401800156, 0.0049551622942090034, 0.009001500904560089, -0.031151657924056053, 0.012151088565587997, 0.05097383260726929, -0.014308947138488293, -0.06997675448656082, 0.0027782784309238195, -0.07153824716806412, 0.01654898375272751, 0.0699874684214592, -0.06339894235134125, -0.008735263720154762, 0.018662236630916595, -0.002148859668523073, 0.011052100919187069, 0.02704450860619545, -0.025838050991296768, -0.010347872041165829, -0.013618968427181244, 0.028718434274196625, 0.013080259785056114, 0.056448809802532196, -0.01632152684032917, -0.03412820026278496, 0.015232913196086884, -0.004628076683729887, 0.006345988251268864, 0.01794087514281273, 0.007794170640408993, -0.034920260310173035, 0.0299084410071373, 0.05299310386180878, -0.04191464185714722, -0.0017168711638078094, -0.06784383952617645, -0.01795729622244835, 0.03507149964570999, 0.08737672120332718, 0.0050494796596467495, 0.007977984845638275, 0.004850559867918491, 0.03662183880805969, 0.03791077062487602, 0.02106393128633499, 0.026588477194309235, 0.08491647988557816, -0.09009204059839249, -0.021684516221284866, -0.04515501484274864, -0.011692953296005726, -0.041985463351011276, -0.03967908397316933, -0.03103364259004593, 0.015135508030653, -0.01914576254785061, 0.013607457280158997, -0.018692441284656525, 0.047939401119947433, -0.04145803302526474, -0.008708472363650799, -0.005873155314475298, -0.005906930658966303, 0.023966357111930847, -0.0009541878825984895, 0.007647346705198288, -0.011750145815312862, -0.01010160706937313, 0.0058502512983977795, 0.02305150404572487, -0.04012412577867508, 0.03060631826519966, 0.04632306471467018, 0.05963120236992836, -0.02096342295408249, 0.07885138690471649, -0.0193284023553133, -0.004055545199662447, -0.02029540203511715, 0.009538127109408379, 0.0733468234539032, 0.048179395496845245, -0.02174226939678192, 0.07777637243270874, 0.08571922779083252, -0.023702017962932587, 0.017604278400540352, 0.004387583117932081, -0.011525285430252552, 0.03684840723872185, 0.032905347645282745, 0.0010529262945055962, 0.01737295463681221, -0.011837180703878403, -0.005163173191249371, -0.06044724956154823, -0.0613434873521328, 0.0015749989543110132, 0.014246993698179722, -0.026587601751089096, 0.03373289108276367, 0.07520011812448502, 0.06406969577074051, 0.008983776904642582, 0.03892995044589043, -0.028894269838929176, -0.04687044769525528, 0.04504992067813873, -0.03447681665420532, 0.02737751603126526, -0.02013501152396202, -0.08813992142677307, -0.024774394929409027, 0.01698014885187149, -0.0533037893474102, -0.02024867758154869, 0.0034406764898449183, 0.04023701697587967, -0.00006829481571912766, -0.030797937884926796, -0.026564229279756546, 0.010496226139366627, 0.03243677690625191, -0.08200407773256302, 0.006787883583456278, 0.005199267528951168, -0.03633296117186546, -0.04932805523276329, 0.03054630197584629, -0.011461716145277023, 0.01224763598293066, 0.046344708651304245, -0.017691822722554207, -0.022216511890292168, 0.01465190015733242, -0.02735947072505951, -0.015176269225776196, 0.08628671616315842, 0.03726360201835632, -0.05157943814992905, 0.013403463177382946, -0.05132412910461426, 0.06034381687641144, 0.004781053867191076, -0.015051765367388725, 0.018659336492419243, 0.029208607971668243, -0.029419614002108574, 0.0009716933127492666, 0.037409164011478424, 0.01800391636788845, 0.03538455069065094, -0.025374846532940865, 0.06092723459005356, -0.010664810426533222, -0.0021696765907108784, 0.04223756119608879, -0.02187936380505562, -0.073141910135746, -0.03486330434679985, 0.03275555372238159, 0.0033726051915436983, -0.017923744395375252, 0.08729055523872375, -0.027821414172649384, -0.02057054452598095, -0.019489632919430733, 0.008495750837028027, -0.014489698223769665, 0.010690947063267231, -0.04038301482796669, -0.06462737917900085, -0.05922304838895798, 0.010456698946654797, 0.008148141205310822, -0.06919586658477783, 0.021194957196712494, -0.008437779732048512, 0.06337244808673859, 0.03665819391608238, 0.024991152808070183, 0.0641690120100975, 0.044572170823812485, -0.0460582971572876, -0.0024166987277567387, 0.033327292650938034, 0.027257734909653664, -0.05292372778058052, 0.0012627304531633854, 0.013768721371889114, -0.006413821130990982, -0.005098681431263685, 0.04694897308945656, -0.06438533961772919, 0.008318775333464146, 0.03811715543270111, -0.028397087007761, -0.0038326233625411987, 0.034114543348550797, 0.004933462478220463, 0.04783443734049797, 0.019181355834007263, -0.007995640859007835, 0.004151490051299334, 0.044908877462148666, 0.02845938317477703, 0.04932977259159088, -0.011159059591591358, -0.03764669969677925, 0.002719865646213293, 0.01411527581512928, 0.004632930736988783, -0.04592680186033249, 0.009286711923778057, -0.0506378598511219, 0.0029691800009459257, -0.002640694845467806, -0.027317270636558533, 0.04712919145822525, -0.009091590531170368, -0.06847734749317169, 0.042786773294210434, 0.008807798847556114, 0.058165132999420166, 0.03227037563920021, -0.055389225482940674, 0.07180792093276978, 0.055297061800956726, -0.03788622468709946, 0.04586964473128319, -0.04918106272816658, 0.008968577720224857, 0.04414891451597214, 0.04320142790675163, -0.05587893724441528, -0.0013361673336476088, -0.012295741587877274, 0.08920229971408844, 0.0046209776774048805, 0.0018148208037018776, -0.03238869085907936, 0.10569784045219421, 0.0000647331980871968, -0.07737591117620468, 0.018208704888820648, -0.048477236181497574, -0.0585823729634285, -0.009032626636326313, -0.011526000685989857, -0.014949857257306576, 0.0014667114010080695, -0.04452762007713318, -0.024739140644669533, 0.008780840784311295, 0.027930131182074547, 0.035654328763484955, -0.004542969632893801, -0.03102690726518631, -0.016371233388781548, -0.07468810677528381, 0.011334036476910114, 0.024532722309231758, -0.0313970111310482, -0.00013577169738709927, 0.04844332113862038, 0.023896846920251846, -0.059137117117643356, -0.018346024677157402, -0.0296171847730875, -0.00922881904989481, -0.030960414558649063, 0.00472143804654479, -0.013022559694945812, -0.02447536028921604, 0.016419006511569023, 0.031095780432224274, 0.043646667152643204, 0.06769189983606339, -0.057601556181907654, 0.025517122820019722, 0.0559731088578701, -0.0023880223743617535, -0.017941858619451523, -0.05320528522133827, -0.06047017127275467, -0.0062445891089737415, 0.04359551891684532, 0.016924381256103516, -0.039614658802747726, 0.06840747594833374, 0.03773656487464905, -0.012302755378186703, 0.0015776584623381495, -0.028503060340881348, -0.030907047912478447, 0.05230795219540596, -0.043499648571014404, 0.02835872396826744, -0.06213275343179703, -0.025306396186351776, -0.020712601020932198, -0.0028660455718636513, -0.03872469440102577, -0.029136257246136665, -0.03453121706843376, 0.03695843741297722, 0.07175272703170776, -0.04934730380773544, -0.06177888438105583, -0.018769647926092148, -0.0010992811294272542, 0.07572558522224426, 0.0314955934882164, 0.05442187190055847, -0.02626042626798153, 0.028702864423394203, -0.023466380313038826, -0.011938302777707577, -0.0009497854043729603, 0.0003983446804340929, -0.01196819357573986, -0.013748426921665668, 0.006044886074960232, -0.013474280014634132, 0.042159002274274826, 0.04625307396054268, 0.03540799766778946, 0.025966543704271317, 0.0153877604752779, -0.022335438057780266, 0.005055947694927454, 0.034523677080869675, -0.0027439820114523172, -0.007576550357043743, -0.005213695578277111, 0.055177003145217896, -0.033768750727176666, 0.01608181558549404, 0.040631238371133804, 0.035375844687223434, 0.03433231636881828, -0.049856483936309814, 0.015231591649353504, 0.033773865550756454, -0.09035608917474747, -0.031199784949421883, 0.07058818638324738, 0.013319932855665684, -0.023212088271975517, 0.022518813610076904, -0.04094131290912628, -0.014062294736504555, -0.0633392408490181, 0.005145249888300896, 0.012575380504131317, 0.011497660540044308, 0.044569578021764755, 0.06540588289499283, 0.023809734731912613, -0.0392889603972435, -0.018175315111875534, 0.08255024999380112, 0.047380514442920685, -0.06817928701639175, -0.04799608886241913, 0.013042386621236801, -0.047917526215314865 ]
<p>Do magnets redshift light? </p> <p>Suppose we have an extremely powerful magnet (say the size of the Sun) and we have a smaller paramagnetic material above it (say. Titanium Brick which is indestructible) . Due to magnetic attraction it will fall toward the big magnet. </p> <p>Now suppose that when it hits the surface of the bigger magnet, the smaller paramagnetic material (Titanium Brick) is somehow converted into photons (light) equivalent to its mass using $E=mc^2$, plus its kinetic energy, $KE_1$. These photons are shot upwards via an perfect mirror perpendicular to the paramagnetic material above. When they reach the magnet's original position they are again converted into mass in the form of the titanium brick.</p> <p>If this is repeated many times it seems we will gain free energy, since the iron brick gains kinetic energy when it falls, but light is not effected by magnetic fields. (Or am I wrong?) But this will breach the energy conservation laws in specific "Energy cannot be created nor destroyed". </p> <p>Therefore I must conclude light is (or should be) redshifted (loses energy) as it travels through magnetic field. The problem arises when you take into consideration that light is not charged so it should not be effected by any magnetic fields but my intuition tells me light should still be affected so is my conclusion valid or not? Is light red shifted in presence of an magnetic field? </p> <p>If light is not red shifted then what is lost to ensure the system is not gaining energy but in this experiment it does not make sense since we are using photons which are not effected by magnetic fields and then recreating the para magnetic material (like Iron brick we used) so we should not loose energy as we are simply recreating the same object again. </p>
g8408
[ 0.03761867433786392, 0.03798298165202141, 0.00989855919033289, 0.03235787898302078, 0.0033390570897608995, 0.03322058543562889, 0.036898888647556305, 0.02784467302262783, -0.027423745021224022, -0.007924840785562992, -0.006964800879359245, 0.01942945085465908, -0.025430962443351746, -0.020073657855391502, -0.0608244389295578, 0.03383517637848854, 0.108812615275383, 0.019715391099452972, 0.0686332955956459, 0.02978617325425148, -0.04452326148748398, 0.03711521252989769, -0.008321897126734257, -0.0370551198720932, -0.058318160474300385, 0.03925164043903351, 0.013133177533745766, -0.019330963492393494, 0.0027413310017436743, -0.0590355284512043, 0.021469231694936752, -0.03314125910401344, 0.027415014803409576, -0.02251140959560871, -0.020355496555566788, -0.057734064757823944, 0.0606631301343441, 0.026754962280392647, -0.002086896914988756, -0.0030071528162807226, 0.024233143776655197, 0.04031207412481308, -0.0025342018343508244, 0.0012331570032984018, 0.0505029559135437, 0.023651836439967155, 0.018004193902015686, -0.014158039353787899, 0.007618334144353867, 0.0009792776545509696, -0.009166477248072624, -0.0059547084383666515, 0.04774453863501549, 0.05854630470275879, 0.016660558059811592, -0.05484185740351677, 0.035577550530433655, -0.050398074090480804, 0.051238611340522766, 0.035561397671699524, 0.029181398451328278, 0.005173865240067244, 0.00918546412140131, 0.0035382797941565514, -0.011410089209675789, 0.0062065888196229935, -0.039964769035577774, -0.022586936131119728, 0.01251577865332365, -0.03082725591957569, -0.00631672190502286, 0.0366329699754715, -0.03774884343147278, -0.01579422503709793, 0.019342530518770218, 0.006716354750096798, 0.027451923117041588, -0.030589906498789787, 0.0005489762406796217, 0.04477477818727493, -0.03808872029185295, -0.017449520528316498, 0.02644091099500656, 0.020879827439785004, 0.05184072628617287, 0.018306324258446693, -0.05738352984189987, 0.05051019787788391, -0.0026860004290938377, -0.0009190207347273827, 0.08672049641609192, -0.0028058942407369614, 0.11190158873796463, 0.030812932178378105, -0.013762983493506908, 0.024251095950603485, 0.010083753615617752, 0.0527360737323761, -0.029384862631559372, -0.0071164933033287525, -0.04944533854722977, -0.013731701299548149, -0.0021968919318169355, 0.00562969921156764, 0.035884276032447815, -0.033780258148908615, 0.043634332716464996, 0.006198424845933914, -0.0053673055954277515, 0.046145930886268616, -0.0019331860821694136, -0.08905772119760513, -0.08502606302499771, -0.04347634315490723, -0.05308680981397629, -0.01642475090920925, 0.09430260956287384, -0.026373235508799553, 0.02480585128068924, 0.07417910546064377, 0.0433419905602932, -0.002294851467013359, 0.02635451778769493, 0.08094898611307144, -0.006417832337319851, 0.029055321589112282, -0.016465866938233376, -0.0052504586055874825, 0.015549806877970695, -0.03382423520088196, -0.04031243920326233, -0.028406541794538498, 0.009767701849341393, 0.03551008924841881, -0.0038937092758715153, -0.002012923127040267, 0.04927792027592659, 0.023657990619540215, -0.0051308427937328815, -0.026515204459428787, 0.011789077892899513, -0.025250084698200226, 0.04007465019822121, -0.03446933999657631, -0.04132194072008133, 0.006962929852306843, 0.00015346039435826242, 0.00015761649410706013, 0.10697410255670547, 0.04632002115249634, 0.05055088922381401, 0.02545090578496456, -0.04251088947057724, -0.05965641140937805, 0.038912441581487656, -0.05140673741698265, 0.015874512493610382, -0.041922200471162796, -0.022641241550445557, -0.01935906521975994, 0.05354964733123779, -0.025286201387643814, 0.03804356977343559, -0.024347227066755295, 0.03561018407344818, -0.01904866471886635, 0.05400555580854416, -0.01225063856691122, -0.051400721073150635, -0.038516152650117874, -0.05484769493341446, -0.00422135042026639, 0.03226076066493988, 0.01794411987066269, -0.04174836724996567, 0.03419529274106026, 0.051589466631412506, -0.009563568979501724, -0.03709270805120468, 0.023744499310851097, -0.061678823083639145, -0.03803960978984833, 0.029962550848722458, -0.00843354407697916, 0.008094118908047676, 0.01985037326812744, -0.029220452532172203, 0.00711425393819809, -0.010119318030774593, -0.0004719605785794556, -0.0338454470038414, 0.023604143410921097, 0.03498905152082443, -0.00417286716401577, 0.01367475837469101, -0.03717517480254173, -0.02703038603067398, 0.041266992688179016, -0.031233670189976692, 0.002498143818229437, -0.00826704129576683, 0.07847701013088226, -0.021894054487347603, -0.014924377202987671, 0.021870294585824013, 0.004895130638033152, -0.0016898277681320906, 0.008285819552838802, -0.0003454277175478637, 0.011826762929558754, 0.04257811978459358, 0.04918977618217468, -0.02104230225086212, 0.010329348035156727, -0.003969534300267696, -0.011996599845588207, -0.023390786722302437, 0.025609508156776428, 0.0004654636140912771, 0.05052047595381737, -0.02044772356748581, 0.04051705822348595, 0.07926535606384277, -0.023076506331562996, -0.03870530426502228, -0.02775224857032299, -0.0707816556096077, -0.012881234288215637, 0.039940234273672104, 0.02572401985526085, -0.035929761826992035, -0.011361634358763695, 0.006511117331683636, -0.016132008284330368, 0.05911468714475632, 0.027178533375263214, -0.019226133823394775, -0.03355830907821655, 0.027072275057435036, 0.0011966562597081065, -0.01025896891951561, -0.024062253534793854, -0.025876948609948158, -0.06442180275917053, 0.001226029242388904, -0.06518757343292236, 0.03519883379340172, 0.005165546201169491, -0.01995679922401905, -0.0030568933580070734, 0.07688301801681519, -0.008933484554290771, -0.011556236073374748, -0.0292285718023777, -0.0385722741484642, -0.018808187916874886, -0.01808004267513752, 0.061861418187618256, -0.07641274482011795, -0.012409287504851818, 0.01353185623884201, -0.0756956934928894, -0.0009758419473655522, 0.031160518527030945, -0.0354253351688385, -0.018861491233110428, -0.023665891960263252, -0.010580307804048061, 0.03448782488703728, -0.0019999027717858553, -0.03136854246258736, 0.07357414811849594, 0.05973101407289505, 0.0530940480530262, 0.06321397423744202, 0.015042471699416637, -0.009691484272480011, -0.034910332411527634, 0.04290148243308067, -0.033767104148864746, 0.019322389736771584, -0.04111240431666374, -0.08017035573720932, -0.036067456007003784, 0.01780650019645691, -0.050334762781858444, -0.04186990112066269, -0.06033973768353462, -0.0085624223574996, -0.0007285483297891915, -0.08756958693265915, 0.03893823176622391, 0.06751791387796402, 0.020014967769384384, -0.05804689601063728, 0.04071855917572975, 0.028893904760479927, -0.04998456686735153, -0.05691339075565338, 0.04010903090238571, 0.013300085440278053, 0.018050972372293472, -0.06702584028244019, 0.026284759864211082, 0.0318412184715271, 0.05278797075152397, -0.08139707893133163, -0.06232810765504837, 0.018774086609482765, -0.012067768722772598, -0.035799846053123474, 0.0926450565457344, 0.035889752209186554, 0.04321741685271263, -0.07340312004089355, -0.007990124635398388, -0.015000578947365284, -0.03548550233244896, 0.07701386511325836, 0.04021785780787468, -0.006365177687257528, 0.0283068660646677, 0.01094480324536562, -0.038181859999895096, 0.061439719051122665, -0.02973921410739422, -0.01898244395852089, -0.03632434457540512, -0.03391497582197189, 0.017631253227591515, 0.02311285026371479, 0.05103364214301109, -0.02831793762743473, -0.020998558029532433, -0.02803226187825203, 0.046213142573833466, -0.019863978028297424, -0.02401331625878811, 0.02925725467503071, 0.0031422567553818226, -0.077705018222332, -0.03273103013634682, -0.03336876630783081, 0.007748332340270281, 0.05572403222322464, 0.040930334478616714, -0.03125830367207527, -0.013593299314379692, -0.003791018156334758, -0.020237255841493607, 0.07647667080163956, -0.004773336462676525, 0.038177572190761566, -0.0031479247845709324, -0.04292958974838257, 0.0709536150097847, -0.02150164172053337, 0.05488385632634163, 0.0020629882346838713, -0.011903450824320316, -0.016633272171020508, 0.019629918038845062, 0.007072256878018379, -0.026628220453858376, -0.02967802993953228, 0.08337020874023438, 0.003938452806323767, 0.016045810654759407, -0.0038125943392515182, -0.026378268375992775, 0.004690272267907858, -0.03648928552865982, -0.05927475914359093, 0.016187284141778946, -0.0027134760748595, -0.025294499471783638, 0.015601927414536476, -0.03932780399918556, -0.03319774195551872, -0.003208559239283204, 0.04887966811656952, 0.0061543663032352924, -0.008597282692790031, 0.0010600374080240726, 0.03929605707526207, 0.04790043085813522, 0.003609497332945466, 0.00829219724982977, -0.01052179653197527, 0.054033610969781876, -0.0592520497739315, -0.022359024733304977, 0.010480942204594612, -0.008641677908599377, -0.005781734827905893, 0.0028076700400561094, -0.04614627733826637, -0.06832840293645859, -0.00009798123937798664, -0.02192136086523533, 0.021990876644849777, 0.05092266947031021, -0.004610039293766022, 0.01826903410255909, 0.017049312591552734, -0.011826363392174244, 0.0686875581741333, -0.04396282508969307, -0.030145816504955292, 0.015988968312740326, 0.01645650900900364, -0.014709915965795517, -0.013956014066934586, -0.10251940041780472, 0.016402592882514, 0.005354803521186113, 0.014186033047735691, 0.02101871743798256, 0.016993630677461624, -0.032942961901426315, 0.03724514693021774, 0.05236929655075073, -0.004767100792378187, -0.054039761424064636, -0.031333453953266144, 0.030684731900691986, 0.01620694249868393, -0.05580464005470276, 0.007033581379801035, -0.0035883861128240824, -0.024002283811569214, 0.029627682641148567, 0.019604897126555443, 0.007077146787196398, -0.026491504162549973, 0.027374403551220894, -0.050576481968164444, 0.04796475172042847, 0.036254797130823135, 0.0077770850621163845, 0.06468597799539566, -0.0052366298623383045, 0.058964118361473083, -0.02296380139887333, 0.0027596259023994207, 0.04178711026906967, -0.05591880902647972, -0.006553183309733868, 0.030142705887556076, -0.05140569061040878, 0.009327206760644913, 0.02785254642367363, -0.007390429265797138, 0.014059998095035553, -0.017029382288455963, -0.04165462404489517, -0.030033094808459282, -0.04589157551527023, 0.058618832379579544, 0.08806489408016205, -0.022991210222244263, -0.013352716341614723, 0.026700813323259354, -0.00152192497625947, -0.022801775485277176, -0.011807087808847427, -0.01802939921617508, -0.04501305893063545, -0.03700973838567734, 0.02340567111968994, -0.002688642591238022, -0.006302055902779102, 0.0071022845804691315, 0.01341661624610424, 0.03876961022615433, -0.017013175413012505, -0.03787275031208992, -0.034087758511304855, 0.05566129833459854, -0.02624218910932541, -0.01378804724663496, -0.04141887649893761, 0.0372033417224884, -0.02320605330169201, -0.07332208752632141, 0.03391774743795395, -0.05525622516870499, 0.027981780469417572, 0.028912866488099098, -0.04482709988951683, -0.011964010074734688, -0.003643724601715803, -0.06467258185148239, -0.02837936021387577, 0.012498067691922188, 0.009933747351169586, -0.025309022516012192, 0.05674395710229874, -0.04922912269830704, -0.0427987165749073, -0.0443049855530262, 0.011463315226137638, 0.007425114046782255, -0.00918456818908453, -0.03156858682632446, -0.04274924099445343, 0.041288167238235474, -0.024267682805657387, -0.011024883948266506, 0.056953802704811096, -0.0914151594042778, -0.014883435331285, 0.025939885526895523, 0.02311811037361622, 0.03897185996174812, -0.039775069802999496, -0.009973431006073952, 0.044896453619003296, 0.03913823142647743, -0.024040458723902702, -0.02761871926486492, -0.012085226364433765, 0.013432548381388187, -0.08962516486644745, 0.06036316603422165, 0.01539611630141735, -0.017520751804113388, 0.021529752761125565, 0.0013225680449977517, 0.017301935702562332, 0.04768535867333412, 0.006272605620324612, 0.011658339761197567, -0.00021798968373332173, -0.014982410706579685, -0.019978070631623268, 0.07249567657709122, -0.013901912607252598, -0.00648498022928834, 0.009674537926912308, 0.01889093592762947, -0.016498101875185966, 0.0449855737388134, 0.014817553572356701, -0.003856385825201869, 0.017221277579665184, -0.03697953745722771, 0.020865323022007942, 0.009395446628332138, -0.051538918167352676, 0.0028790247160941362, 0.009462524205446243, 0.009974670596420765, 0.03835805132985115, 0.04984341189265251, -0.014196816831827164, -0.037973467260599136, -0.06254050880670547, 0.03133351355791092, -0.012954349629580975, 0.024610646069049835, -0.021207168698310852, 0.028902074322104454, -0.025547999888658524, 0.04494606703519821, -0.020953688770532608, 0.0110322255641222, -0.06976335495710373, -0.006589912809431553, 0.06539345532655716, 0.023904798552393913, 0.025035737082362175, 0.008507941849529743, 0.04289670288562775, 0.01918957382440567, -0.01015917956829071, -0.027045508846640587, -0.06763209402561188, -0.07317066937685013, -0.054822616279125214, 0.03066662885248661, 0.03266918286681175, -0.005231569521129131, -0.028969423845410347, 0.021274646744132042, 0.0057171364314854145, -0.05170157924294472, 0.021613383665680885, 0.05842561274766922, -0.016950078308582306, 0.018104905262589455, 0.005236053839325905, -0.034927282482385635, 0.0026552232448011637, -0.06558053940534592, -0.045197777450084686, -0.052447736263275146, 0.007750758435577154, -0.04782125726342201, 0.06954140961170197, -0.04741177335381508, -0.035173699259757996, -0.012109690345823765, -0.034741658717393875, 0.031529828906059265, 0.009832950308918953, -0.05418935418128967, 0.02571227215230465, 0.013066805899143219, 0.010367109440267086, -0.019419191405177116, -0.0017286184011027217, -0.01813695952296257, 0.02553778514266014, 0.015040543861687183, -0.03114985302090645, 0.05430760607123375, -0.016787713393568993, 0.015068775974214077, 0.031094126403331757, -0.01912778802216053, -0.08851170539855957, 0.009073369204998016, -0.061982203274965286, 0.04384825378656387, 0.05589742213487625, -0.0328260213136673, 0.018261676654219627, 0.012375211343169212, -0.0005820781225338578, -0.07299346476793289, 0.029177317395806313, -0.030457019805908203, 0.042725175619125366, 0.018136752769351006, 0.020221611484885216, 0.01016293279826641, 0.013545836322009563, -0.014458908699452877, -0.01568007841706276, 0.010060391388833523, -0.012174154631793499, -0.011269510723650455, 0.03358033299446106, -0.03196735680103302, 0.010595309548079967, -0.007948193699121475, -0.006955897901207209, -0.012038538232445717, 0.01155894622206688, -0.024649955332279205, 0.037393685430288315, -0.013081845827400684, -0.058743152767419815, -0.02481290139257908, 0.029546914622187614, -0.035902705043554306, 0.0686035230755806, 0.02919403277337551, -0.06866580247879028, -0.0320565402507782, -0.014601808972656727, -0.011038639582693577, -0.035424504429101944, 0.005158253945410252, 0.023583536967635155, 0.03996856138110161, -0.011291621252894402, 0.041715655475854874, 0.03555098921060562, -0.016577312722802162, -0.005828566383570433, 0.011746803298592567, -0.00010264346929034218, -0.018531791865825653, -0.005205404479056597, -0.024344496428966522, 0.04372188821434975, 0.02638259343802929, 0.0032769523095339537, -0.04922563582658768, -0.015036252327263355, 0.03285744786262512, 0.03504515811800957, 0.021072573959827423, 0.00630342960357666, -0.06580256670713425, 0.04934597760438919, 0.020702673122286797, -0.0011729258112609386, -0.032774150371551514, 0.00021993243717588484, 0.05790717154741287, 0.011042946949601173, -0.037218622863292694, -0.010602870024740696, 0.018755801022052765, -0.012919433414936066, 0.04334503784775734, 0.01006853487342596, -0.038638073951005936, 0.007420275826007128, 0.007911954075098038, 0.014631333760917187, 0.005783220753073692, 0.020394977182149887, -0.03916141763329506, 0.027119994163513184, -0.019041694700717926, 0.013283170759677887, 0.04865898936986923, 0.03449198231101036, 0.04652784392237663, 0.014247838407754898, 0.06146399676799774, 0.01737194135785103, 0.0032750656828284264, 0.011895190924406052, 0.028344295918941498, -0.036648716777563095, -0.03756635636091232, -0.009333169087767601, -0.05343891307711601, -0.09059589356184006, 0.027908241376280785, -0.03410946577787399, 0.03611747547984123, -0.03578673303127289, -0.02100442908704281, 0.00473437225446105, 0.004219413734972477, -0.010019796900451183, -0.044697683304548264, -0.042370762676000595, -0.017555618658661842, 0.002118667121976614, 0.04587959870696068, -0.04457617178559303, -0.01267311628907919, -0.054024141281843185, -0.0025863584596663713, -0.020400933921337128, -0.004154272843152285, 0.025717690587043762, 0.00520055927336216, 0.07696563005447388, -0.08995743840932846, 0.011465358547866344, 0.010902619920670986, -0.04635653644800186, 0.001999352825805545, 0.0458114929497242, -0.01963321678340435, 0.020726576447486877, 0.037641506642103195, -0.05589686334133148, 0.01631927490234375, 0.009314144030213356, 0.02305932156741619, -0.02382892556488514, 0.005643613636493683, -0.03848712146282196, -0.06441179662942886, -0.04590166360139847, 0.001296158879995346, -0.03536979854106903, -0.00011948536848649383, 0.04855266585946083 ]
<p>Suppose you know everything about Quantum Field Theory, but nothing about the very specific interactions and particles which exist in our real word.</p> <p>Which physical or mathematical principles could be used to reduce the infinite number of possibilities of QFT, to finish with some class of theories, in which the Standard Model, for instance, would belong.</p> <p>[If the question is too "extreme", one may soften it by considering having some partial information, to be detailed, about our real world]</p>
g8409
[ 0.052987270057201385, 0.04091065004467964, 0.01698477566242218, -0.03947269916534424, 0.03646842762827873, 0.0050435359589755535, -0.03512232005596161, 0.03620389848947525, 0.020832819864153862, -0.030490638688206673, -0.0012185798259451985, -0.03400680422782898, -0.021831410005688667, 0.009511170908808708, -0.031486429274082184, 0.03394641354680061, 0.024383805692195892, 0.015678301453590393, 0.013228454627096653, -0.017412008717656136, -0.010547712445259094, 0.01716792583465576, 0.04141063243150711, -0.01048518531024456, -0.11235766112804413, -0.007359790615737438, -0.04183468967676163, 0.03376871347427368, -0.00553146842867136, -0.011000039987266064, -0.05566515028476715, -0.024867810308933258, -0.008185920305550098, -0.0313674658536911, 0.010298656299710274, -0.026340704411268234, 0.07764460891485214, 0.022475987672805786, -0.004117592237889767, -0.012365222908556461, 0.00024987058714032173, -0.0014912700280547142, 0.02025695890188217, -0.029790882021188736, -0.037763770669698715, -0.0012937107821926475, 0.02783404290676117, 0.0021232441067695618, -0.006825413089245558, -0.021224308758974075, 0.0003877511771861464, 0.014594181440770626, 0.0688680112361908, 0.00848719384521246, 0.05152274668216705, 0.007737066131085157, 0.018922526389360428, -0.007406617049127817, 0.044961292296648026, -0.05839421600103378, 0.011688880622386932, -0.014476544223725796, 0.0004990678862668574, 0.06391078233718872, -0.005941517651081085, 0.00675412779673934, -0.06194664537906647, -0.006357384845614433, -0.004412119742482901, 0.013436730019748211, 0.034362345933914185, -0.011034783907234669, -0.019693605601787567, 0.031786058098077774, -0.03204253315925598, 0.058981284499168396, -0.024531686678528786, 0.0013505083043128252, 0.0514579601585865, -0.0021333382464945316, -0.04735096916556358, -0.05978729948401451, -0.0014655700651928782, -0.018271982669830322, -0.005229057744145393, 0.015396695584058762, -0.0018263786332681775, -0.017273463308811188, 0.026847688481211662, 0.022229380905628204, -0.03969797492027283, -0.003309492953121662, 0.06370001286268234, 0.031606752425432205, 0.02095198817551136, 0.0617351233959198, 0.05141841620206833, 0.02443760260939598, 0.019224490970373154, -0.02179260365664959, 0.010789328254759312, 0.01870761625468731, 0.052062541246414185, -0.0010136248311027884, -0.04631800204515457, -0.04171736165881157, -0.00013980036601424217, -0.005402043927460909, 0.08104758709669113, 0.06898462772369385, -0.054803211241960526, 0.019493214786052704, -0.03970488905906677, -0.02467193827033043, -0.001299400464631617, 0.0003760610707104206, 0.026664268225431442, -0.03071572445333004, -0.014433382079005241, 0.06847374141216278, 0.003845279337838292, -0.024089714512228966, 0.038213688880205154, 0.020844904705882072, -0.03900980204343796, -0.014568553306162357, -0.0026104117278009653, 0.05591835081577301, -0.026543185114860535, -0.06303156912326813, 0.054321907460689545, -0.012172636575996876, -0.03256954252719879, 0.023553038015961647, -0.05479368194937706, 0.048283208161592484, 0.00687129981815815, -0.02431127056479454, 0.07125718146562576, -0.008160530589520931, 0.009550867602229118, -0.03515205532312393, -0.032864462584257126, -0.0034434343688189983, 0.013916038908064365, -0.007514800410717726, 0.02947445958852768, 0.005523871164768934, -0.08410036563873291, 0.023094799369573593, 0.015115342102944851, 0.04503071680665016, 0.04377449303865433, 0.02852058783173561, 0.01673133671283722, -0.015236872248351574, 0.020411565899848938, -0.03222205862402916, -0.03551821783185005, -0.04231146350502968, 0.03221757337450981, 0.038537997752428055, -0.03467776998877525, -0.019126050174236298, -0.02880716696381569, 0.023294705897569656, -0.04143605753779411, -0.03590884804725647, 0.028077194467186928, 0.005510629620403051, -0.062145624309778214, -0.015354138799011707, 0.026722509413957596, 0.0814642682671547, -0.01742822863161564, 0.03413870185613632, 0.026473864912986755, -0.01596708595752716, -0.026272643357515335, -0.00781059917062521, -0.03723111003637314, -0.004835327155888081, 0.031120914965867996, 0.048643678426742554, -0.024774014949798584, 0.07397495210170746, -0.01673186756670475, 0.06787082552909851, -0.04990250989794731, 0.04416549950838089, -0.056815970689058304, -0.01077535841614008, 0.05276254191994667, -0.006909538991749287, -0.007322190795093775, 0.005444894079118967, 0.033105190843343735, 0.02124667540192604, -0.06265720725059509, -0.06115396320819855, -0.007693901192396879, 0.07552468776702881, -0.012139490805566311, 0.028320325538516045, 0.03422544151544571, -0.024784507229924202, -0.00830757711082697, -0.009529604576528072, 0.004918958526104689, -0.024220816791057587, 0.02745763026177883, -0.040701307356357574, 0.015612421557307243, 0.07588905096054077, -0.04695115238428116, -0.031168585643172264, -0.00744028901681304, -0.022955546155571938, -0.032262302935123444, 0.06262291222810745, 0.02389645017683506, 0.00342979421839118, 0.07179214060306549, 0.049046359956264496, -0.008876299485564232, -0.033959951251745224, -0.02280827797949314, 0.004650774411857128, -0.018483009189367294, 0.01959848776459694, -0.07265029102563858, -0.021158870309591293, 0.013257271610200405, -0.012618472799658775, -0.0011544073931872845, -0.00852880533784628, -0.019013451412320137, -0.026656080037355423, 0.023595638573169708, 0.09961097687482834, 0.0290997251868248, 0.0220988430082798, 0.006279719527810812, -0.034499261528253555, -0.042305540293455124, -0.05343925207853317, -0.03227062523365021, 0.0030178786255419254, 0.015178726986050606, 0.05139509215950966, 0.00233906926587224, 0.04849923774600029, -0.005642253439873457, 0.008932475931942463, 0.026975490152835846, 0.029150934889912605, -0.014675168320536613, 0.04757445305585861, 0.013943439349532127, -0.06735656410455704, 0.019343074411153793, 0.01969800516963005, -0.008860880509018898, 0.033192772418260574, -0.02426842786371708, 0.02217988669872284, -0.08308957517147064, 0.05359945818781853, -0.058009400963783264, 0.01198165025562048, 0.010906475596129894, 0.04802093282341957, -0.00420429976657033, 0.03382107615470886, 0.014924377202987671, 0.03043942153453827, 0.010710762813687325, -0.02003154717385769, 0.03120756894350052, -0.00775103410705924, 0.002132185036316514, -0.02700101211667061, -0.03765339404344559, 0.039882317185401917, 0.016111640259623528, -0.04280883073806763, 0.03451899439096451, -0.06675633043050766, 0.0011611367808654904, -0.017007136717438698, -0.0012318259105086327, 0.0009156404994428158, 0.034142300486564636, 0.05618257075548172, -0.03856676444411278, -0.008528260514140129, 0.007556367665529251, -0.06309626251459122, -0.002213220577687025, 0.043656911700963974, -0.028613897040486336, 0.004297324456274509, 0.016519658267498016, 0.0728883221745491, 0.000299467530567199, 0.026297349482774734, -0.01913360133767128, 0.0013154726475477219, 0.012481475248932838, -0.034813910722732544, -0.033815983682870865, 0.05804647505283356, 0.023919302970170975, -0.0001439806801499799, -0.0540522076189518, 0.01802760362625122, 0.059112876653671265, 0.030333654955029488, 0.02143212966620922, -0.04828375205397606, 0.011573496274650097, -0.03513932228088379, 0.07027196139097214, -0.061516329646110535, 0.06921982020139694, 0.12206912785768509, -0.07204429805278778, -0.011576522141695023, -0.05540855601429939, -0.005611002445220947, 0.021090172231197357, -0.0112984087318182, -0.016931626945734024, -0.04155980795621872, -0.09266578406095505, 0.0021651210263371468, -0.01589583046734333, -0.03269021585583687, 0.07573183625936508, -0.01754859648644924, 0.020157847553491592, 0.014162706211209297, -0.04176937788724899, -0.030024509876966476, -0.005566423758864403, 0.01068984717130661, 0.010586920194327831, -0.027061907574534416, 0.039628513157367706, -0.012974084354937077, -0.01932622864842415, 0.00948977842926979, -0.018721528351306915, 0.005430672317743301, 0.01564352959394455, 0.04232938215136528, 0.0701051875948906, 0.1065768152475357, 0.0435371920466423, -0.02954239211976528, -0.04547577723860741, -0.025740157812833786, 0.02635635994374752, 0.022798996418714523, 0.0042113796807825565, 0.03163953870534897, -0.04308618977665901, -0.03012031316757202, -0.03702104836702347, -0.004657616373151541, 0.00823865458369255, 0.01703452505171299, -0.0061472682282328606, 0.04536818712949753, -0.01811884716153145, 0.009708407334983349, 0.02887125127017498, -0.03090185485780239, -0.06531348824501038, -0.007044976111501455, 0.05945097655057907, 0.0635528489947319, 0.0021592769771814346, -0.015496315434575081, 0.05396163836121559, 0.014834136702120304, -0.0876125618815422, -0.006174883339554071, -0.026271695271134377, 0.07135103642940521, -0.033694569021463394, -0.04352761059999466, 0.0007029201951809227, -0.019874321296811104, -0.03322259336709976, -0.031783681362867355, -0.012903669849038124, -0.049484316259622574, 0.029104728251695633, 0.005879632662981749, 0.031713709235191345, -0.02396976388990879, -0.0030288437847048044, 0.008151661604642868, 0.008835655637085438, -0.03161085397005081, -0.021761339157819748, -0.021034177392721176, 0.03197233006358147, -0.04288281872868538, 0.0004038468177895993, -0.0281780157238245, 0.002383529208600521, -0.02343139611184597, 0.019194895401597023, -0.004537250380963087, -0.007844005711376667, -0.08192003518342972, 0.02502628043293953, -0.023416627198457718, 0.011413928121328354, 0.01692969724535942, -0.024040108546614647, 0.026867348700761795, -0.006678554695099592, 0.023579971864819527, -0.007667173631489277, -0.02092784270644188, -0.0608338862657547, -0.020005233585834503, 0.06826761364936829, 0.008144901134073734, -0.04595544561743736, -0.006243111565709114, -0.04614957794547081, -0.02808770164847374, -0.04972267523407936, 0.045894041657447815, -0.020909994840621948, 0.04522097855806351, 0.021733134984970093, 0.012555978260934353, 0.004574120044708252, -0.031246008351445198, -0.020194802433252335, 0.06571901589632034, -0.026115791872143745, -0.04023098200559616, -0.04134159907698631, -0.00683508301153779, 0.00764896534383297, -0.012410490773618221, -0.04581281915307045, 0.012976794503629208, -0.017806073650717735, -0.04971115663647652, -0.06336414813995361, 0.03653167933225632, 0.025677509605884552, 0.01772777922451496, -0.07096220552921295, -0.004194916225969791, -0.016810404136776924, 0.03825801610946655, -0.008315196260809898, -0.0026778648607432842, -0.06720175594091415, -0.004103802144527435, -0.08962781727313995, -0.04688695818185806, -0.025175385177135468, 0.01970849558711052, 0.06379938125610352, 0.015744168311357498, -0.07191731780767441, -0.01550437230616808, -0.05018490180373192, -0.05191527307033539, -0.021630283445119858, -0.05613240227103233, 0.040803227573633194, -0.023218318819999695, 0.02712511643767357, 0.035418130457401276, -0.009328908286988735, -0.016510022804141045, -0.0015985840000212193, 0.011024612933397293, -0.031198877841234207, -0.050422970205545425, -0.008901887573301792, 0.017574744299054146, 0.03229883313179016, 0.009464348666369915, -0.06432849168777466, -0.007743882481008768, 0.04728396236896515, 0.029101647436618805, 0.0008088831673376262, 0.0017484888667240739, -0.01225940603762865, -0.01436630729585886, -0.03450048342347145, -0.048325322568416595, -0.018906716257333755, 0.012981491163372993, 0.057129714637994766, -0.03954921290278435, -0.026671968400478363, 0.008048605173826218, 0.010364925488829613, -0.0007062783697620034, -0.002103595994412899, 0.0014258540468290448, 0.0410546138882637, 0.05490387976169586, -0.06088925525546074, -0.030094202607870102, 0.003802691353484988, -0.07696380466222763, 0.0017803877126425505, -0.05204526335000992, -0.020700577646493912, -0.0275867972522974, -0.01771761290729046, 0.004852230194956064, -0.049406833946704865, -0.017225267365574837, -0.010678828693926334, 0.023344244807958603, 0.037227973341941833, 0.00529726967215538, -0.01954406499862671, 0.028132310137152672, -0.013561108149588108, 0.050135187804698944, 0.02867247723042965, -0.01435809675604105, 0.017458101734519005, 0.06590262800455093, -0.030320290476083755, 0.044773418456315994, 0.016628172248601913, 0.03706100210547447, 0.004860505927354097, -0.01182526908814907, -0.03136270493268967, 0.023287897929549217, 0.06109660491347313, -0.05860818177461624, -0.039173394441604614, -0.016675760969519615, 0.00916832871735096, -0.004557452164590359, -0.003823419800028205, 0.000851561373565346, 0.0018781207036226988, 0.018303029239177704, -0.03724740445613861, 0.034906767308712006, -0.0072553278878331184, -0.03972391411662102, -0.00836760364472866, -0.02952837385237217, -0.00772329093888402, -0.006780683994293213, -0.016503727063536644, -0.03843588009476662, 0.06702426075935364, -0.004763386677950621, -0.012782580219209194, 0.03565075621008873, 0.058051593601703644, -0.01672629453241825, 0.026108339428901672, -0.03834905847907066, 0.054165929555892944, -0.002623331733047962, -0.04486258700489998, -0.06450503319501877, -0.0349908210337162, 0.07507491856813431, -0.012409624643623829, -0.09553338587284088, 0.024298151955008507, 0.08146867901086807, -0.05161657929420471, -0.023142699152231216, 0.004961117636412382, 0.022004129365086555, 0.04573152959346771, 0.0029228064231574535, -0.014219996519386768, -0.0018382422858849168, 0.008255371823906898, -0.0002929195179603994, 0.07835198938846588, -0.028146754950284958, -0.02987012267112732, 0.010911921039223671, 0.002812793944031, -0.01903218775987625, 0.012049510143697262, 0.04411866143345833, 0.08537027984857559, 0.0840512365102768, -0.03184473142027855, 0.003548283129930496, 0.00039408504380844533, -0.028594138100743294, 0.006811747793108225, -0.023906471207737923, 0.00736186932772398, -0.01725715957581997, 0.00974332820624113, -0.044879209250211716, 0.0017219382571056485, -0.022036919370293617, -0.04938027262687683, 0.020644409582018852, 0.025011137127876282, -0.007563990540802479, 0.008853308856487274, -0.005346060264855623, -0.007598753087222576, 0.010952279902994633, 0.0009113645646721125, 0.0042611705139279366, 0.07655059546232224, -0.05794789269566536, 0.009084600023925304, 0.028632130473852158, 0.0701322928071022, 0.015005111694335938, -0.052566345781087875, 0.0589342936873436, -0.009929012507200241, -0.001619761809706688, -0.036854613572359085, 0.0016822823090478778, -0.01456602942198515, 0.03241577371954918, 0.060679081827402115, 0.03731152042746544, -0.01724330708384514, -0.02829430252313614, 0.0377834215760231, -0.016646573320031166, -0.06473302096128464, -0.005990267265588045, 0.0711107924580574, -0.006540579255670309, -0.07660423964262009, -0.019018663093447685, -0.024135014042258263, 0.022595040500164032, 0.02238096483051777, -0.009214905090630054, 0.029829472303390503, -0.01773092709481716, 0.006453441921621561, -0.029945753514766693, 0.005845689680427313, -0.012010707519948483, 0.015565523877739906, 0.03484903648495674, 0.01462632231414318, -0.05098608136177063, -0.014798233285546303, -0.008594153448939323, -0.012800591066479683, -0.059419866651296616, -0.0385315828025341, -0.030485481023788452, 0.024865632876753807, -0.06233804672956467, 0.008918504230678082, 0.07601897418498993, -0.017738966271281242, -0.006451474502682686, 0.010215586982667446, 0.08238270878791809, 0.002095887903124094, -0.03813478350639343, -0.007322551682591438, -0.02927546203136444, 0.048327766358852386, 0.0451655313372612, -0.02639317326247692, 0.024650009348988533, 0.010966319590806961, -0.05501052364706993, -0.025569047778844833, -0.053398605436086655, 0.034331388771533966, 0.05910341814160347, -0.018964944407343864, 0.010744486935436726, 0.05261426046490669, 0.023822326213121414, 0.036798641085624695, -0.024601148441433907, 0.021368570625782013, -0.03555888310074806, 0.041642386466264725, -0.017758376896381378, 0.004380593542009592, -0.03520118445158005, -0.012383939698338509, 0.027830788865685463, 0.0027098723221570253, 0.06259697675704956, 0.08444233238697052, 0.038900040090084076, 0.03362172469496727, 0.009761805646121502, -0.003223671577870846, 0.00862063281238079, 0.08925801515579224, -0.008984362706542015, -0.02705417014658451, 0.03565074875950813, -0.050106827169656754, 0.009841634891927242, -0.015496565029025078, 0.015460588969290257, -0.020009057596325874, -0.052863262593746185, 0.02332277223467827, -0.01659591868519783, -0.02127663791179657, -0.03328424692153931, -0.022777553647756577, 0.03434617072343826, -0.07408361881971359, 0.03555436059832573, -0.0710461214184761, 0.005195171106606722, -0.0583907887339592, 0.013471982441842556, 0.012677762657403946, 0.015539617277681828, 0.017776446416974068, 0.0017352541908621788, -0.026135478168725967, -0.05706686154007912, -0.03691812977194786, -0.023686233907938004, 0.05794571712613106, 0.034302983433008194, -0.06545140594244003, 0.0029941811226308346, -0.022274576127529144, 0.057435136288404465, 0.023633258417248726, -0.02270333655178547, -0.03246093541383743, 0.04256053268909454, 0.04021685570478439, 0.010466044768691063, 0.03270982205867767, -0.013924744911491871, 0.05843722075223923, 0.08415955305099487, -0.02523425966501236, 0.011872543953359127, -0.0031484332866966724, -0.030898721888661385 ]
<p>I can understand that animals need some battaries to run. But, we learn that plants serve like batteries for animals because they accumulate the sun energy in the first place! You can eat them or burn to extract the accumulated energy. This means that they consist of structures that they want to blow-up and disintegrate to fall apart at the lower energy level. But why? </p> <p>This is strange to me since the <a href="http://en.wikipedia.org/wiki/Principle_of_minimum_energy" rel="nofollow">most fundamental law of nature</a> says that battaries spontaneously leak and discharge themselves. This means that the hydrocarbon structures that all life organisms are made of on the Earth are not stable. The photosinthesis, $\mathrm{H_2 O + CO_2 + \text{photo} \mapsto O_2 + CH_2O}$, is costly. It not only needs (photo) energy but uses it to produces the hydrocarbons, the $\mathrm{CH_2O}$-like spontaneously degrading structures! Why do you want to consist of something unstable that has tendency to blow up as soon as possible (why not immediatly, BTW?) if your purpose is survival, as any life organism on the Earth?</p> <p>I watched the <a href="http://www.youtube.com/watch?v=DPjMPeU5OeM&amp;feature=youtu.be" rel="nofollow">Gibbs Free Energy</a> but could not understand anything. Is it because of the min. energy law we have everything at the min energy already on the Earth and if you want to produce some structures (fortunately, there is a Sun), you have no other choice but to make them unstable?</p>
g8410
[ 0.019785236567258835, 0.03025120683014393, -0.014123519882559776, 0.05952471122145653, 0.03257514163851738, -0.0001627417659619823, -0.013200138695538044, 0.0046684653498232365, -0.05307783931493759, -0.028050381690263748, 0.031876783818006516, 0.02006998099386692, -0.008109627291560173, 0.019340328872203827, -0.02248304896056652, -0.010973181575536728, 0.047814443707466125, -0.02556641958653927, 0.11173230409622192, 0.03763517364859581, -0.05068982020020485, -0.048814594745635986, 0.012486940249800682, 0.008039684034883976, -0.04428092762827873, 0.026079047471284866, -0.004282117821276188, -0.04941409453749657, -0.02551162801682949, 0.008027131669223309, 0.05493245646357536, -0.012692616321146488, 0.0393969789147377, -0.05490845441818237, -0.008788788691163063, -0.03541621193289757, 0.031119266524910927, -0.02057766541838646, -0.003841290483251214, -0.011610211804509163, -0.0317845456302166, 0.014446848072111607, 0.04258182644844055, 0.0166754350066185, -0.0294323842972517, -0.0070756953209638596, 0.024635085836052895, -0.027240488678216934, -0.0027583343908190727, -0.07931280136108398, 0.029310429468750954, -0.021526999771595, 0.011142302304506302, -0.02485565096139908, 0.06614450365304947, 0.012216680683195591, 0.000012774588867614511, -0.06463025510311127, 0.05142710357904434, -0.00695597380399704, -0.011654139496386051, 0.04718912020325661, 0.0024811618495732546, 0.06674174964427948, 0.009646912105381489, -0.03547977656126022, -0.007597807329148054, -0.014511401765048504, 0.08207783848047256, 0.036249615252017975, 0.014734194613993168, -0.03190348297357559, 0.005095146596431732, -0.011344598606228828, 0.07193438708782196, -0.0026534367352724075, 0.004872112534940243, 0.0145619111135602, -0.026770804077386856, -0.0012027608463540673, 0.054485708475112915, 0.021484799683094025, 0.03270812705159187, 0.02244464121758938, 0.03684667870402336, -0.04227127134799957, 0.015967000275850296, -0.02686910144984722, -0.002266061957925558, 0.0405762642621994, 0.02072897180914879, -0.012429602444171906, 0.11257239431142807, 0.006632882636040449, -0.08552782237529755, 0.004531017038971186, -0.03620937466621399, 0.014697437174618244, 0.00745573453605175, -0.0013538930797949433, -0.034793172031641006, -0.044000279158353806, 0.0006651062285527587, 0.03312590718269348, -0.0012288176221773028, 0.013856573030352592, 0.003810928203165531, -0.032025862485170364, -0.011978745460510254, -0.020101260393857956, -0.008957885205745697, 0.06337920576334, -0.018835145980119705, -0.02013310045003891, 0.0047648013569414616, 0.0010378975421190262, 0.08665966242551804, 0.02285437285900116, 0.07450785487890244, 0.036461129784584045, 0.039642561227083206, 0.011013554409146309, 0.03988250717520714, -0.01008608564734459, 0.0008797021582722664, -0.002800525864586234, 0.019930167123675346, -0.023742491379380226, 0.04200736805796623, 0.015373730100691319, -0.014872372150421143, 0.04067448899149895, -0.0489872582256794, -0.03186235949397087, 0.08002044260501862, 0.03434833884239197, -0.0636558011174202, -0.0172123946249485, 0.02765977755188942, -0.016825444996356964, 0.00017000437946990132, 0.0158032588660717, 0.035495173186063766, -0.006884117145091295, -0.02897142805159092, 0.023805106058716774, 0.048283036798238754, 0.037111662328243256, 0.044304847717285156, 0.06252103298902512, -0.04208860546350479, 0.0382707305252552, -0.0001687048643361777, -0.06640970706939697, 0.08542279154062271, 0.017690211534500122, 0.06259278208017349, -0.010213936679065228, -0.04337198659777641, 0.005476458929479122, 0.05233359709382057, 0.030904224142432213, -0.03399546071887016, -0.022325733676552773, -0.09103778004646301, 0.0012298409128561616, 0.037147924304008484, -0.054070841521024704, 0.0053068408742547035, 0.07507991045713425, -0.02310071885585785, -0.03154416382312775, -0.028350014239549637, 0.07185547053813934, 0.008460908196866512, -0.005887269973754883, 0.05671210587024689, -0.008357767015695572, -0.02473594807088375, -0.06015414744615555, 0.0013020493788644671, -0.006452064495533705, -0.002006592694669962, -0.0214323028922081, -0.013038797304034233, 0.04355267435312271, -0.009981638751924038, -0.002241465263068676, -0.05060742422938347, -0.018538326025009155, 0.007854694500565529, 0.027227701619267464, -0.0009970865212380886, -0.014723052270710468, -0.0051057105883955956, 0.024558190256357193, -0.027556205168366432, -0.011925788596272469, -0.035000573843717575, -0.01782103069126606, 0.042079973965883255, -0.001459835679270327, -0.025891510769724846, 0.003896861569955945, -0.06250414997339249, -0.004178046248853207, -0.07604759931564331, -0.00605367636308074, 0.026276390999555588, -0.06582561880350113, 0.0648922249674797, -0.0633910670876503, -0.010479489341378212, 0.00885197427123785, -0.030869152396917343, -0.11239004135131836, -0.03107425943017006, -0.04741677641868591, -0.010149127803742886, -0.04753955453634262, 0.018806859850883484, -0.000013232099263404962, 0.05631346255540848, 0.02200607769191265, 0.017163479700684547, 0.04541667923331261, -0.009312635287642479, -0.06101354584097862, 0.014858895912766457, -0.024851853027939796, -0.0582495853304863, 0.0037254225462675095, 0.033097751438617706, -0.0015889923088252544, -0.028206104412674904, 0.06751220673322678, 0.009029604494571686, -0.02956598810851574, 0.011092758737504482, 0.024906214326620102, 0.013796049170196056, -0.05269099399447441, -0.04026015102863312, -0.012980666942894459, 0.035602740943431854, -0.035184137523174286, 0.043522778898477554, 0.007083085831254721, -0.030372491106390953, 0.009854895062744617, 0.08256138116121292, -0.04198499768972397, 0.008262716233730316, 0.018195101991295815, -0.03536270186305046, -0.022512134164571762, -0.045397281646728516, -0.00017352345457766205, -0.03411388397216797, -0.007996931672096252, 0.04511413723230362, -0.00094465387519449, -0.025448685511946678, -0.043965794146060944, -0.07310488075017929, 0.011714803986251354, -0.01384328119456768, -0.0370466448366642, -0.02649070881307125, -0.03915849328041077, -0.02580650895833969, 0.013559390790760517, -0.014041182585060596, 0.005821431055665016, -0.04635290056467056, 0.010380595922470093, -0.03938625007867813, -0.009902500547468662, 0.041692104190588, -0.031629327684640884, 0.0029712836258113384, -0.04125778377056122, -0.06725649535655975, 0.016311941668391228, 0.009372944012284279, -0.022362183779478073, -0.02049669250845909, 0.03425823524594307, 0.011234837584197521, -0.014108379371464252, -0.014900333248078823, 0.007894258014857769, 0.013533646240830421, 0.048857398331165314, -0.0046981764025986195, -0.07214752584695816, 0.00560398306697607, 0.023596961051225662, -0.04795275256037712, 0.053417034447193146, 0.006673567462712526, 0.016501136124134064, -0.004114375449717045, -0.011635848321020603, -0.06294897198677063, 0.046524107456207275, -0.031254176050424576, -0.07492553442716599, -0.030046844854950905, 0.023814167827367783, 0.03867129236459732, -0.036868616938591, -0.017145846039056778, 0.04273928329348564, -0.038103990256786346, 0.04563775658607483, -0.054152268916368484, -0.018590623512864113, 0.061393629759550095, -0.0444219708442688, -0.021626891568303108, 0.006123300641775131, -0.01309891976416111, -0.03817719593644142, 0.021894842386245728, 0.007564172614365816, -0.030369607731699944, -0.059231948107481, -0.031586047261953354, -0.05360757187008858, 0.04457678645849228, 0.040870316326618195, -0.0049615963362157345, -0.011473419144749641, -0.05672619864344597, -0.07757870107889175, -0.03526223450899124, 0.013849792070686817, -0.01571735180914402, -0.021603437140583992, -0.047885216772556305, 0.022734036669135094, -0.029209677129983902, -0.0007764000911265612, -0.00211902242153883, 0.006622830871492624, 0.012158437632024288, -0.028107259422540665, -0.04104774072766304, -0.0212082602083683, 0.04153925180435181, -0.02995668351650238, -0.003505106084048748, 0.010422520339488983, -0.0665457472205162, -0.0019503746880218387, -0.010773810558021069, -0.022726314142346382, 0.00563752232119441, 0.011912748217582703, 0.00902228057384491, -0.004609942901879549, 0.05065011605620384, 0.03491545468568802, -0.021422723308205605, 0.0496671237051487, -0.043570466339588165, 0.05055812746286392, -0.013710392639040947, -0.03264309838414192, 0.017490968108177185, -0.026009881868958473, -0.04639948904514313, -0.023430896922945976, 0.0020972364582121372, -0.04241323471069336, 0.04188699647784233, -0.025961941108107567, -0.056226909160614014, 0.011996140703558922, 0.05212066322565079, -0.06814394891262054, 0.032117560505867004, 0.014562271535396576, 0.023915600031614304, 0.06296712905168533, -0.036334697157144547, -0.0341937355697155, -0.029665803536772728, 0.05360681936144829, -0.035407841205596924, -0.014453076757490635, -0.012738681398332119, -0.032087862491607666, 0.01689392887055874, -0.03358623385429382, 0.01613694429397583, -0.010972016490995884, 0.004222269169986248, 0.09133943170309067, 0.012004384770989418, -0.014654389582574368, -0.036797359585762024, -0.01254751905798912, 0.029317578300833702, 0.0854533389210701, 0.04299463331699371, -0.05366230756044388, -0.007697245571762323, -0.039215851575136185, 0.07113634049892426, 0.039353687316179276, 0.02497386746108532, -0.03948293626308441, 0.051350049674510956, -0.04389112815260887, -0.040232088416814804, -0.028971774503588676, 0.07231312245130539, 0.03299105912446976, 0.004582391586154699, 0.025465713813900948, 0.017090752720832825, -0.06835564225912094, -0.013781203888356686, 0.07589279860258102, 0.03254062682390213, -0.016600433737039566, 0.010969234630465508, -0.04066481441259384, 0.017490029335021973, -0.022115951403975487, -0.04532623291015625, -0.03947627544403076, -0.03948856145143509, 0.01920231617987156, -0.03100903518497944, 0.03625299036502838, 0.03790445625782013, 0.0598621740937233, 0.08175330609083176, -0.0031889593228697777, 0.027117984369397163, -0.012872716411948204, 0.030958300456404686, 0.04292342811822891, -0.027530822902917862, -0.01588093303143978, 0.0006094987620599568, -0.041295427829027176, 0.005342735908925533, 0.04401188716292381, 0.07057090848684311, -0.018171831965446472, 0.0263895895332098, -0.001931036007590592, -0.07866073399782181, 0.007099071051925421, 0.06120714545249939, 0.0459538958966732, -0.08226436376571655, -0.051857300102710724, 0.02943097986280918, 0.032815542072057724, 0.0552908331155777, 0.044324398040771484, -0.023731527850031853, -0.005723982118070126, 0.006569591350853443, 0.045445315539836884, -0.012178434059023857, -0.012967023998498917, -0.004072259180247784, -0.004157321527600288, 0.029794897884130478, -0.06290087103843689, -0.020848270505666733, -0.03794068470597267, 0.009151031263172626, -0.027302121743559837, -0.004298707004636526, 0.04770525544881821, -0.013431552797555923, 0.018388401716947556, 0.005504460074007511, -0.008944614790380001, -0.025411779060959816, -0.04070890694856644, 0.030558202415704727, 0.0016885068034753203, -0.02860756777226925, 0.021501164883375168, 0.029231376945972443, 0.019963080063462257, 0.008310363627970219, 0.015946218743920326, 0.0713680163025856, -0.05122528597712517, -0.012783916667103767, 0.015902290120720863, -0.049603018909692764, -0.006303067319095135, -0.05074916407465935, 0.03846607729792595, 0.04840667173266411, -0.000014464229934674222, 0.10056892037391663, -0.0071757035329937935, 0.03482920676469803, 0.02786264754831791, 0.018262237310409546, 0.015561453066766262, -0.035152923315763474, 0.05487567186355591, -0.0005114939995110035, -0.06212341785430908, 0.0016071655554696918, -0.017098862677812576, -0.05184599384665489, -0.06356947124004364, 0.06792193651199341, -0.038212113082408905, 0.038701869547367096, -0.00007521314546465874, 0.059149082750082016, 0.06225454434752464, -0.0663866475224495, -0.019947189837694168, 0.016376180574297905, 0.01026590634137392, -0.011901510879397392, -0.005818367935717106, -0.008120658807456493, -0.02874111942946911, -0.0771040990948677, 0.01487764436751604, 0.01802227832376957, 0.04404718801379204, 0.07622440904378891, -0.023959089070558548, 0.007040963973850012, 0.001674762344919145, 0.025573059916496277, 0.027532201260328293, 0.037953317165374756, -0.01852840557694435, -0.027182525023818016, 0.029068181291222572, -0.0006526861689053476, -0.010086324997246265, 0.01598825305700302, 0.06317270547151566, 0.041964806616306305, 0.004442630801349878, 0.022596465423703194, -0.0010140826925635338, -0.03508559986948967, 0.009947923943400383, -0.003488479182124138, -0.021075386554002762, 0.018349431455135345, 0.08917304128408432, 0.012172912247478962, 0.03472316637635231, 0.05108098313212395, -0.020376216620206833, 0.015787161886692047, -0.0076397559605538845, -0.022563785314559937, 0.09001515805721283, 0.03614218905568123, 0.04611877351999283, 0.036570195108652115, -0.003579514566808939, -0.002552129328250885, -0.026041701436042786, -0.010093322023749352, -0.027026867493987083, -0.04093411564826965, -0.028583675622940063, 0.06021229550242424, -0.04988880828022957, 0.001723622321151197, -0.0453459732234478, 0.038763634860515594, -0.00017593731172382832, 0.025647306814789772, -0.00017247888899873942, 0.027625342831015587, -0.06593017280101776, 0.023630233481526375, 0.023274941369891167, -0.013013488613069057, 0.02507631666958332, -0.0007683802978135645, -0.017568496987223625, -0.017397619783878326, -0.029536988586187363, 0.02220541052520275, -0.0977528989315033, -0.05370311439037323, 0.01629050262272358, 0.021149246022105217, -0.06100628897547722, 0.025034399703145027, 0.030917437747120857, 0.004878297448158264, 0.034905921667814255, -0.02678561583161354, 0.024440106004476547, -0.05648702010512352, 0.03544126823544502, -0.004922537598758936, -0.02779725007712841, -0.010720615275204182, 0.016810167580842972, -0.0656571164727211, 0.004964920692145824, 0.0030562481842935085, 0.027477549389004707, 0.002214994980022311, -0.012253017164766788, 0.05774684250354767, -0.01785697042942047, 0.020693697035312653, -0.0114827835932374, -0.010913264937698841, 0.04733370244503021, 0.0508662648499012, -0.024551503360271454, -0.0029812436550855637, 0.024579163640737534, -0.04290751740336418, 0.03321598842740059, 0.028644975274801254, 0.0011657720897346735, -0.05740556865930557, 0.022837895900011063, 0.0019278539111837745, -0.034728921949863434, 0.0018070300575345755, 0.009724185802042484, 0.07022859156131744, 0.043545905500650406, -0.009885653853416443, 0.05893385037779808, 0.011984214186668396, -0.04972662776708603, 0.013638494536280632, -0.0257561057806015, 0.03121034801006317, -0.04972163215279579, -0.031034298241138458, -0.07418158650398254, 0.01178612932562828, 0.05214298516511917, -0.06041005626320839, -0.051452409476041794, 0.0281300637871027, -0.08376964181661606, -0.004725584760308266, 0.01870134472846985, 0.07581858336925507, -0.0171511210501194, 0.03583226352930069, 0.05115031823515892, 0.03699106350541115, -0.024163734167814255, -0.020842431113123894, 0.04024869576096535, 0.004606315866112709, -0.02535894699394703, 0.00528440997004509, -0.016172995790839195, 0.016585901379585266, 0.000962439167778939, -0.004593988880515099, 0.014322269707918167, 0.04425843805074692, -0.035538528114557266, 0.056888263672590256, -0.013209217227995396, 0.018498379737138748, -0.03993654623627663, -0.006622845772653818, 0.018998604267835617, 0.029503680765628815, 0.006948431488126516, 0.005000871140509844, -0.0452878512442112, -0.024188313633203506, 0.018167411908507347, 0.0473705418407917, -0.01028451044112444, 0.030869876965880394, -0.032290149480104446, 0.03407716751098633, -0.037946026772260666, 0.02290271408855915, -0.03841720148921013, -0.006617093924432993, -0.08289720118045807, -0.003047166857868433, 0.009131274186074734, 0.04653501138091087, 0.01706913486123085, 0.021396270021796227, 0.03846811130642891, -0.03723132982850075, -0.013580775819718838, -0.019066017121076584, -0.018848184496164322, -0.0037687495350837708, 0.022741686552762985, 0.04436938837170601, -0.03626197203993797, 0.012402287684381008, 0.05289774015545845, 0.004213419742882252, 0.027870750054717064, -0.040927741676568985, -0.0756339505314827, 0.022407134994864464, -0.0036693864967674017, -0.018080592155456543, 0.0012195872841402888, 0.0067922454327344894, -0.023362915962934494, -0.01849050261080265, -0.010256972163915634, -0.055572498589754105, -0.032706212252378464, 0.00785908568650484, 0.01023205928504467, -0.016637826338410378, 0.0028676881920546293, 0.004710893612354994, -0.0121205048635602, -0.027330994606018066, -0.00005064353899797425, 0.021501431241631508, 0.026932748034596443, -0.020630452781915665, -0.03886183723807335, -0.019520221278071404, -0.040719110518693924, -0.07124452292919159, 0.030175555497407913, 0.05729913339018822, -0.030252838507294655, 0.0013795039849355817, -0.019721491262316704, 0.029882315546274185, 0.0008034604834392667, 0.016287030652165413, -0.024549726396799088, 0.009633100591599941, 0.02341069094836712, 0.01474276464432478, -0.004525771830230951, -0.018651515245437622, 0.017021043226122856, 0.029983961954712868, -0.010844048112630844, 0.007148315664380789, -0.044024016708135605, 0.010602711699903011, -0.038304369896650314 ]
<p>Space isn't a perfect vacuum and I wonder how an image of a galaxy can travel billions of years without becoming diffused by photon collisions with space matter?</p>
g8411
[ 0.009212185628712177, 0.04717915505170822, -0.010084310546517372, 0.02659756876528263, 0.02052314765751362, 0.06985817849636078, -0.019128160551190376, 0.027756379917263985, 0.024846121668815613, -0.03736499324440956, 0.050597384572029114, 0.026112470775842667, 0.039132457226514816, 0.015519620850682259, -0.0077876076102256775, 0.008270765654742718, 0.04196598753333092, -0.034854188561439514, 0.028253111988306046, 0.007069808896631002, -0.021900786086916924, -0.04523671418428421, 0.010065094567835331, -0.037900298833847046, -0.025845970958471298, -0.030046921223402023, 0.027821147814393044, -0.021024055778980255, -0.033529192209243774, -0.035385116934776306, 0.07786403596401215, -0.029410678893327713, -0.07505563646554947, -0.0613546147942543, -0.00945825781673193, -0.024477098137140274, -0.03150445967912674, 0.010527875274419785, 0.07078873366117477, -0.001377115841023624, -0.027053875848650932, -0.031944554299116135, 0.022485537454485893, 0.00160829012747854, 0.023557985201478004, 0.01752898283302784, -0.026727408170700073, -0.03832127898931503, 0.029643138870596886, -0.018942445516586304, -0.06610124558210373, 0.028834722936153412, -0.007526939269155264, 0.029004815965890884, 0.0017337079625576735, -0.03777544945478439, 0.01931956596672535, -0.04646622762084007, 0.07414009422063828, -0.04252052307128906, -0.07052743434906006, -0.04100147634744644, 0.04879740998148918, 0.05721350759267807, 0.04018385335803032, -0.0019563317764550447, -0.07185494899749756, -0.019888361915946007, 0.04987998306751251, -0.035180605947971344, 0.06823793053627014, -0.009924140758812428, -0.04973018169403076, -0.011585038155317307, -0.01738288626074791, 0.03546999767422676, 0.013996846973896027, 0.023775644600391388, -0.0008232471882365644, 0.048345111310482025, -0.029113076627254486, -0.012819475494325161, -0.03147825971245766, -0.0510646291077137, 0.07142779976129532, -0.011351194232702255, -0.03418658301234245, -0.05544724315404892, 0.015958812087774277, -0.00010312929953215644, 0.021237613633275032, 0.037234317511320114, 0.05893225967884064, -0.009586858563125134, 0.06618940085172653, 0.020010504871606827, -0.009847277775406837, 0.10778102278709412, -0.031810346990823746, -0.023120054975152016, -0.042269863188266754, 0.01298696082085371, 0.061546243727207184, 0.03292146697640419, -0.0014793386217206717, 0.002706031082198024, -0.004730749875307083, -0.010811363346874714, 0.044578708708286285, -0.010558457113802433, -0.04805649444460869, -0.01090903952717781, -0.015571659430861473, -0.01596936769783497, 0.0010670905467122793, 0.029284946620464325, 0.01836789958178997, 0.025800734758377075, 0.03952983021736145, 0.027591656893491745, 0.04558452218770981, 0.01076202467083931, -0.04725418984889984, -0.04210173338651657, -0.033402249217033386, -0.02436591312289238, 0.024289552122354507, -0.04846915975213051, 0.005175619851797819, 0.011625711806118488, -0.04348677024245262, 0.07965536415576935, -0.014298798516392708, 0.05184633284807205, 0.022954082116484642, -0.011768750846385956, 0.0017507236916571856, 0.009234783239662647, -0.02112729661166668, 0.01609763130545616, 0.019636625424027443, 0.011789766140282154, 0.003454608377069235, -0.02016574889421463, -0.015341577120125294, -0.0485704205930233, -0.016141897067427635, 0.05400088056921959, -0.0035387661773711443, -0.035249095410108566, 0.03260857239365578, 0.058997392654418945, 0.019499311223626137, -0.010659584775567055, 0.010044405236840248, -0.030200572684407234, 0.05057656764984131, 0.03427594527602196, 0.013392731547355652, -0.04419264569878578, 0.03384954109787941, -0.02561601623892784, -0.017419591546058655, -0.053695518523454666, -0.061620552092790604, -0.03222589194774628, -0.015390871092677116, -0.07007110118865967, 0.02559402957558632, -0.019634919241070747, -0.010613047517836094, 0.015882596373558044, 0.037220995873212814, 0.03461729735136032, -0.006366885732859373, -0.012657921761274338, -0.033629558980464935, -0.02603590115904808, -0.03210524469614029, -0.013520379550755024, 0.00430310470983386, -0.06307702511548996, -0.008195462636649609, -0.015154045075178146, 0.03741850703954697, -0.0025372065138071775, -0.026843838393688202, -0.019086088985204697, -0.007743443828076124, -0.003494798205792904, 0.022974302992224693, 0.008299107663333416, -0.0005068029859103262, 0.028554456308484077, -0.01157787162810564, 0.0018998919986188412, 0.038620028644800186, -0.0396389365196228, -0.09151256084442139, 0.05607974901795387, -0.01919517107307911, 0.06342586129903793, -0.0027054916135966778, 0.06055467203259468, 0.028134869411587715, -0.016954822465777397, -0.03810330107808113, -0.00970284454524517, 0.030237706378102303, -0.04181120544672012, 0.029394999146461487, -0.000380685378331691, -0.004802235402166843, -0.00022143771639093757, -0.039264194667339325, -0.01569940522313118, -0.04645797610282898, 0.006521286442875862, 0.0040035550482571125, 0.018973451107740402, -0.022217078134417534, 0.012201929464936256, 0.029857292771339417, -0.05338127166032791, 0.02323320135474205, -0.052794378250837326, -0.027387095615267754, -0.03854886814951897, -0.01102521363645792, 0.06753388047218323, -0.044782865792512894, -0.010351331904530525, 0.014173002913594246, 0.030355148017406464, 0.07425999641418457, 0.048749323934316635, -0.03403867036104202, 0.0012791460612788796, -0.034813135862350464, 0.018477967008948326, 0.045621681958436966, 0.01850169152021408, -0.05641040578484535, -0.014575673267245293, 0.039761681109666824, -0.061550818383693695, -0.02396214008331299, -0.04157210886478424, -0.015257601626217365, 0.0007823252817615867, 0.02370096743106842, 0.009694221429526806, 0.009048450738191605, -0.05588095635175705, -0.042522698640823364, -0.04245604947209358, 0.0074817282147705555, 0.0722789391875267, -0.03150461986660957, 0.012916874140501022, 0.022669419646263123, -0.01415135059505701, -0.045780885964632034, -0.03840530291199684, -0.013699190691113472, -0.04501565918326378, 0.004590771626681089, 0.03955975919961929, 0.00018604975775815547, 0.025708675384521484, 0.04665134847164154, 0.029439397156238556, 0.032060619443655014, 0.009122120216488838, -0.006746387109160423, 0.08517798781394958, 0.022052593529224396, 0.005427150055766106, 0.021301379427313805, -0.0231914184987545, -0.010713264346122742, 0.034199438989162445, -0.049696799367666245, -0.009926465339958668, 0.020930001512169838, -0.0777682363986969, 0.0017431983724236488, 0.06491608917713165, 0.0408586785197258, 0.0020594645757228136, 0.006754883099347353, 0.010674508288502693, 0.010251026600599289, 0.017789414152503014, 0.016649911180138588, 0.06219760701060295, 0.030658194795250893, 0.040708091109991074, -0.03124106489121914, -0.030428964644670486, 0.019126078113913536, -0.017216918990015984, 0.048816464841365814, 0.014281095005571842, -0.009278230369091034, -0.030611006543040276, -0.03247920423746109, -0.022301113232970238, -0.0063254451379179955, -0.020205877721309662, 0.07606767863035202, 0.036613788455724716, -0.01510871946811676, 0.0794917643070221, 0.0038300654850900173, -0.055158160626888275, -0.011005266569554806, -0.003147449577227235, -0.001983530120924115, 0.05974461883306503, 0.026790468022227287, -0.01163883600383997, -0.026057422161102295, -0.07024819403886795, 0.0535384900867939, -0.00460536265745759, -0.06296702474355698, -0.011004772037267685, -0.030129145830869675, 0.05937928706407547, -0.0099370451644063, -0.01031220331788063, -0.05940460413694382, -0.00173999706748873, -0.05666444078087807, 0.011020894162356853, -0.04152615740895271, 0.0286384429782629, 0.04501303285360336, 0.021693691611289978, -0.05304348096251488, -0.03265969827771187, -0.054947711527347565, 0.02819851040840149, 0.037128906697034836, 0.041306886821985245, 0.01026192493736744, -0.046748045831918716, 0.012100673280656338, -0.04253225401043892, 0.06265665590763092, -0.017839714884757996, 0.03337976709008217, -0.04575497284531593, -0.04214595630764961, 0.037187397480010986, -0.02715795859694481, -0.005279569886624813, 0.05794161185622215, -0.08776257932186127, 0.018097786232829094, 0.027200601994991302, -0.02554129809141159, -0.02404596097767353, 0.0329112783074379, 0.0038709493819624186, 0.025785764679312706, 0.02867123857140541, 0.03947720676660538, 0.04756180942058563, 0.001687096431851387, -0.021070009097456932, -0.03446357324719429, 0.07034192979335785, 0.03830985352396965, -0.04329578951001167, 0.02229338325560093, 0.0017611891962587833, -0.017690127715468407, 0.02670363336801529, -0.007019662763923407, 0.01229891087859869, 0.009364056400954723, -0.03785413131117821, -0.008284764364361763, 0.033325884491205215, -0.012258282862603664, -0.03278660401701927, -0.014847255311906338, 0.010301067493855953, 0.053692761808633804, 0.010239502415060997, 0.025981327518820763, -0.013777130283415318, 0.01043649297207594, -0.06984762102365494, 0.015366541221737862, -0.0017411588924005628, 0.016445111483335495, -0.07747603952884674, 0.029408028349280357, 0.08507480472326279, 0.00654138857498765, -0.010019298642873764, -0.04151925444602966, -0.014773206785321236, 0.009657311253249645, -0.025829223915934563, 0.028374478220939636, -0.01971699297428131, -0.005758143030107021, 0.020372677594423294, -0.029082968831062317, -0.060731757432222366, 0.0501273050904274, -0.028067562729120255, 0.00849727913737297, 0.005468367133289576, -0.003011021763086319, 0.013432670384645462, -0.005933388136327267, 0.07241464406251907, -0.0007033536676317453, 0.036902375519275665, 0.01421403232961893, 0.06156553700566292, 0.0021647813264280558, 0.028669485822319984, 0.0438649021089077, 0.021179331466555595, 0.025748416781425476, 0.016298850998282433, -0.01787741109728813, 0.09049460291862488, -0.0548492856323719, 0.022589029744267464, -0.03328952565789223, 0.02092030830681324, 0.0327206552028656, 0.03535466268658638, 0.11842872202396393, -0.05627739429473877, 0.09054911136627197, 0.0223526693880558, 0.024443764239549637, 0.10108445584774017, 0.011578178033232689, -0.040424201637506485, 0.017490580677986145, 0.021921278908848763, -0.0119293462485075, -0.01612195372581482, -0.05198872834444046, 0.022586584091186523, -0.014227007515728474, -0.004562773276120424, -0.0654570460319519, 0.04486524313688278, 0.03710181266069412, 0.021610502153635025, -0.05887202173471451, 0.09773416072130203, 0.01884479634463787, 0.021529046818614006, -0.012367023155093193, 0.03131755068898201, 0.0025963967200368643, -0.021666990593075752, -0.016678830608725548, 0.047681912779808044, -0.011358589865267277, 0.004302011337131262, -0.013471079058945179, 0.03326508030295372, -0.03514241799712181, 0.035316210240125656, -0.0390477292239666, 0.013859851285815239, -0.030700495466589928, 0.00034797601983882487, 0.028914613649249077, -0.04386286437511444, 0.03378909081220627, -0.009166608564555645, -0.022705217823386192, 0.07975517958402634, -0.06693345308303833, 0.004126320593059063, -0.028292842209339142, -0.029018035158514977, -0.012997222132980824, -0.005678194109350443, -0.03108488768339157, 0.017776018008589745, -0.02572917379438877, 0.015668213367462158, -0.012307269498705864, -0.055826399475336075, 0.01884150132536888, 0.022065231576561928, -0.0013429162790998816, -0.009573754854500294, -0.013713699765503407, -0.03451832756400108, -0.02188633196055889, 0.0197670366615057, 0.006014736834913492, -0.03609348088502884, -0.04187249392271042, 0.06205425783991814, -0.03841428458690643, 0.0005279949982650578, 0.0023126020096242428, 0.07126650214195251, 0.05639059841632843, -0.0452965646982193, -0.02580975741147995, 0.013386232778429985, 0.06687290966510773, -0.04850272834300995, -0.04149860888719559, -0.01660550758242607, 0.05174550414085388, 0.05852054804563522, 0.05170147493481636, 0.03266502544283867, 0.009230722673237324, -0.014868482016026974, 0.049903880804777145, -0.007740940432995558, 0.011984512209892273, -0.02182573825120926, 0.027330221608281136, -0.030271016061306, -0.025281470268964767, -0.01585971564054489, 0.06343365460634232, 0.03915967792272568, 0.03559737652540207, -0.006235549692064524, -0.011231792159378529, -0.04079783335328102, -0.03563498705625534, 0.06222084164619446, 0.05305128172039986, 0.025186851620674133, -0.006375239230692387, 0.02012098766863346, 0.02649722248315811, -0.09753347188234329, -0.0015632105059921741, -0.005305932369083166, -0.033467769622802734, 0.01731160283088684, -0.0025872625410556793, 0.010793422348797321, 0.054615408182144165, -0.07636666297912598, -0.02010216750204563, 0.002764409640803933, 0.0031523334328085184, 0.0012943176552653313, 0.011983166448771954, -0.02011563815176487, 0.005914431530982256, -0.06597135215997696, 0.008978860452771187, -0.02441571094095707, 0.07001917064189911, 0.01864231377840042, -0.058419618755578995, 0.06162814050912857, -0.027907604351639748, -0.00872011948376894, 0.0018241943325847387, -0.07756657153367996, -0.01868058554828167, -0.018512200564146042, -0.08227510005235672, -0.015853866934776306, 0.028753548860549927, -0.004059241618961096, 0.06851793080568314, -0.03616992011666298, -0.004097719211131334, -0.010777097195386887, -0.006947435438632965, 0.006638800725340843, 0.08349001407623291, 0.02504037506878376, 0.0003882954188156873, -0.052293505519628525, 0.046811457723379135, -0.041637446731328964, -0.017734332010149956, -0.04397251084446907, 0.02149171568453312, -0.04620055854320526, -0.059872522950172424, 0.02566002868115902, 0.005024041514843702, 0.03642844408750534, -0.02312234416604042, 0.03733774274587631, -0.011241735890507698, 0.012356461957097054, -0.04989670217037201, 0.04153301939368248, 0.08087582141160965, 0.037878360599279404, -0.010179607197642326, 0.008210496976971626, -0.009633814916014671, -0.0014474905328825116, -0.012805452570319176, -0.01511748880147934, -0.002568385098129511, -0.024458205327391624, -0.009032788686454296, 0.017632337287068367, -0.03549439460039139, -0.014944733120501041, -0.03211358189582825, -0.005273066461086273, -0.04264730215072632, 0.007019005250185728, -0.0011937846429646015, 0.04287933185696602, 0.0174704696983099, 0.009282484650611877, -0.021899759769439697, -0.013529390096664429, 0.012555384077131748, 0.029214873909950256, -0.030349180102348328, 0.010500391945242882, -0.08737717568874359, 0.014881637878715992, -0.003078931476920843, -0.01977490819990635, 0.018802432343363762, -0.028576873242855072, 0.02981588803231716, -0.0010604271665215492, 0.0010248988401144743, 0.06759542971849442, -0.005794703960418701, -0.013563418760895729, 0.011724208481609821, -0.04124925285577774, 0.026017384603619576, -0.003997986204922199, -0.0009778778767213225, -0.02145509049296379, -0.05639876425266266, 0.04508869722485542, -0.0027265932876616716, -0.04205356910824776, -0.007829575799405575, -0.05376658961176872, 0.004331314004957676, -0.07467927038669586, -0.02455987222492695, 0.04266688600182533, 0.0245945043861866, 0.01361931674182415, 0.005932355299592018, -0.050620682537555695, 0.04167477786540985, -0.02894749492406845, 0.0289316363632679, -0.0022894765716046095, -0.0633513554930687, -0.0055625862441957, -0.01920032501220703, -0.05122961476445198, -0.03716101124882698, 0.027056872844696045, 0.03951379656791687, 0.030528796836733818, 0.027776533737778664, 0.05482570081949234, -0.01632622815668583, 0.034968383610248566, -0.005088099744170904, -0.016694193705916405, -0.029969781637191772, -0.0134612200781703, -0.024355832487344742, -0.020820463076233864, -0.0006794601213186979, -0.06235416978597641, 0.004437058232724667, 0.01548764854669571, -0.011502653360366821, 0.0008715832373127341, 0.01894955523312092, 0.0007663354044780135, -0.02776706963777542, -0.050713516771793365, -0.062281616032123566, 0.017419004812836647, -0.0021914334502071142, -0.07102693617343903, 0.001263655605725944, -0.01395593024790287, 0.0034190367441624403, 0.03927328810095787, 0.011464360170066357, 0.020215563476085663, 0.04448700323700905, 0.06378860771656036, -0.09357847273349762, -0.006300317123532295, -0.005043337121605873, -0.03736433759331703, -0.007128295488655567, 0.01555973757058382, 0.02658899687230587, 0.022357724606990814, 0.024778973311185837, 0.03277100995182991, 0.015110905282199383, -0.05863121896982193, 0.03992182016372681, -0.004423134494572878, 0.06708002090454102, -0.0667005404829979, 0.016196222975850105, -0.028447531163692474, -0.050962209701538086, 0.018778890371322632, -0.04594793543219566, -0.06425653398036957, -0.009262161329388618, 0.015871986746788025, 0.01625974103808403, -0.0753411203622818, -0.005586970131844282, -0.007148349657654762, -0.012883002869784832, -0.016867555677890778, -0.0331115797162056, -0.05031759291887283, 0.018240712583065033, -0.00415367865934968, -0.040196239948272705, -0.06090627610683441, 0.010683882981538773, -0.007003158796578646, 0.03409428894519806, 0.062480803579092026, 0.020991358906030655, -0.0017749267863109708, 0.04935097321867943, -0.009618228301405907, 0.04359583929181099, 0.007122400216758251, -0.02927430532872677, -0.0026277315337210894, 0.0022283843718469143, -0.053010862320661545, 0.026403464376926422, 0.0349765382707119, -0.012300046160817146, -0.06503821164369583, 0.03990219533443451, -0.004325682297348976 ]
<p>I am unable to visualize any case where angular momentum and angular velocity of an object are not parallel.</p>
g8412
[ 0.03848448023200035, 0.0726483091711998, -0.020144304260611534, -0.051291290670633316, 0.051142510026693344, -0.022846972569823265, 0.04466049000620842, 0.010161911137402058, 0.042976610362529755, -0.01847429946064949, 0.02352694235742092, -0.00627751462161541, 0.003547840053215623, 0.025049325078725815, 0.011659601703286171, 0.00827359315007925, 0.009801059029996395, -0.019133832305669785, 0.021537235006690025, -0.0001696671242825687, 0.0007515507750213146, 0.047381144016981125, 0.018216228112578392, 0.006748791318386793, -0.00842199381440878, 0.012947186827659607, -0.08913278579711914, -0.016263850033283234, -0.0659933090209961, 0.06338793784379959, 0.03673090413212776, -0.012213006615638733, -0.016840018332004547, -0.034451957792043686, -0.005025054328143597, -0.02984759211540222, -0.008091959170997143, 0.005346571560949087, -0.0017898355145007372, 0.01911543309688568, 0.019766725599765778, 0.0213967002928257, 0.00037273982889018953, 0.004156503360718489, 0.008506371639668941, 0.03776576370000839, 0.04012022167444229, 0.028169361874461174, 0.007623995654284954, -0.0027590058743953705, -0.00910684559494257, 0.045552853494882584, 0.042056359350681305, -0.060364287346601486, 0.019634855911135674, 0.030189204961061478, -0.007744221948087215, 0.010758508928120136, 0.052032213658094406, 0.005975150037556887, 0.0051171132363379, 0.022148897871375084, 0.018522098660469055, -0.004183676093816757, 0.05727872997522354, -0.003252530936151743, -0.10981979966163635, -0.025225503370165825, -0.023850664496421814, -0.023133104667067528, 0.020456558093428612, 0.029420383274555206, 0.008714438416063786, -0.002465690253302455, -0.08804181963205338, 0.012641726061701775, 0.021321138367056847, -0.0171856377273798, -0.03311644122004509, 0.022343074902892113, 0.03308677673339844, 0.02013804018497467, -0.032520294189453125, 0.029730675742030144, 0.07729995995759964, -0.05023215711116791, 0.0020304901991039515, 0.0054735662415623665, -0.05661296099424362, -0.032061632722616196, 0.02322745881974697, -0.017860691994428635, 0.001709832577034831, 0.051471661776304245, 0.00032521950197406113, -0.062289122492074966, -0.09783997386693954, 0.11018560081720352, 0.0275217667222023, 0.038004450500011444, -0.05745074898004532, 0.04664988070726395, -0.036613237112760544, 0.007366915233433247, 0.04051199182868004, -0.04580053314566612, 0.01190239004790783, 0.0010882194619625807, 0.00929868221282959, -0.0363888293504715, -0.019332146272063255, -0.055053599178791046, -0.04194342717528343, -0.004909006413072348, -0.013663813471794128, -0.09852664172649384, 0.0789375752210617, -0.02861586958169937, -0.017831027507781982, 0.05245760828256607, -0.002473348518833518, -0.01750461384654045, 0.03133386746048927, 0.0500212125480175, -0.02004745602607727, -0.04567631334066391, -0.020801473408937454, -0.016650989651679993, 0.08199479430913925, -0.06073547899723053, 0.01675751805305481, -0.044284891337156296, 0.017956392839550972, 0.06757907569408417, -0.04272187501192093, 0.0028729871846735477, -0.023641522973775864, -0.016455814242362976, -0.05030228570103645, 0.00877346470952034, -0.0011475890642032027, -0.05827384814620018, 0.024169590324163437, 0.0007438331958837807, 0.011183424852788448, -0.08938702940940857, 0.028697621077299118, -0.018955817446112633, 0.03383880853652954, -0.002626430708914995, 0.006193394772708416, 0.0834251269698143, 0.003577528288587928, 0.03213483467698097, 0.005042599979788065, -0.045851364731788635, 0.06879616528749466, 0.00988866202533245, 0.06349864602088928, 0.037816137075424194, 0.021055476740002632, 0.08019871264696121, -0.033434439450502396, -0.009069113992154598, -0.04377162829041481, -0.05881594866514206, -0.023992137983441353, 0.01622278243303299, 0.026169901713728905, -0.06798612326383591, -0.09043554216623306, -0.004657595884054899, 0.04333808273077011, 0.012458494864404202, 0.05139949917793274, 0.023842940106987953, -0.04501297324895859, -0.03855211287736893, -0.046474989503622055, 0.06374722719192505, -0.009219401516020298, -0.007957866415381432, 0.018882839009165764, -0.0259390901774168, 0.020047158002853394, 0.01178068295121193, -0.006948783062398434, 0.09245622903108597, -0.056507889181375504, 0.014638792723417282, 0.06628774106502533, -0.041074611246585846, -0.02459835261106491, -0.01656276546418667, 0.018622029572725296, -0.0590856671333313, 0.029436489567160606, -0.010340050794184208, -0.04181761294603348, 0.019085777923464775, 0.005431693978607655, 0.038595911115407944, 0.040848761796951294, 0.07816001027822495, -0.02945645898580551, -0.06813888996839523, 0.004592106211930513, -0.021760260686278343, 0.021634412929415703, 0.019358407706022263, 0.001658164313994348, 0.020347440615296364, -0.013811317272484303, 0.004577481187880039, 0.006303812842816114, 0.04391040280461311, 0.01706846058368683, -0.0069359904155135155, -0.06376195698976517, 0.027092307806015015, -0.02467188984155655, -0.052496202290058136, 0.0036905172746628523, -0.042975667864084244, -0.0038237671833485365, -0.03249109536409378, -0.017553184181451797, 0.010060410015285015, 0.022112203761935234, -0.010235901921987534, -0.022601956501603127, -0.002623830921947956, 0.0695001408457756, 0.030734887346625328, 0.02121369168162346, 0.010035005398094654, -0.008184264414012432, 0.0162083450704813, -0.0005626000929623842, -0.002654018811881542, -0.022066082805395126, -0.0002509587211534381, 0.0022612952161580324, -0.019675828516483307, 0.08109328150749207, 0.015145252458751202, 0.08109685033559799, 0.008585914969444275, 0.060796525329351425, 0.06669891625642776, 0.011215507052838802, -0.004768872633576393, -0.019596358761191368, 0.013720626011490822, -0.014527328312397003, 0.044350992888212204, -0.01440306194126606, -0.02269362099468708, -0.06769925355911255, -0.005614603869616985, -0.05553765594959259, -0.026058128103613853, 0.010055525228381157, 0.02942110225558281, -0.05113577842712402, 0.004844398703426123, 0.0261400006711483, 0.011304016225039959, 0.05092301964759827, 0.02127760276198387, -0.06568652391433716, 0.037272460758686066, -0.014481699094176292, 0.004985405597835779, -0.019076449796557426, -0.0028188396245241165, 0.024249568581581116, -0.001176249934360385, -0.06803322583436966, 0.03930183872580528, -0.022185370326042175, 0.029412919655442238, 0.007220801431685686, -0.004585610702633858, 0.02474125102162361, -0.03385140374302864, 0.011864329688251019, 0.03543625771999359, 0.004232051316648722, 0.06542710214853287, -0.08657679706811905, 0.0565798245370388, -0.0023135333321988583, -0.0019134754547849298, -0.02040189877152443, 0.027460260316729546, 0.01158836018294096, 0.02511557936668396, 0.011157551780343056, 0.01924980990588665, -0.017235470935702324, 0.02550680562853813, 0.049438782036304474, 0.061385225504636765, 0.031039027497172356, -0.028169414028525352, 0.023177610710263252, -0.023418854922056198, -0.02342030219733715, 0.04336328059434891, -0.061078306287527084, -0.04112711548805237, -0.03092809207737446, 0.018417825922369957, 0.01089966669678688, 0.0440860353410244, -0.027806196361780167, 0.042184893041849136, -0.06011328846216202, 0.028145017102360725, -0.025430357083678246, 0.0008732445421628654, 0.020667223259806633, 0.006938661448657513, 0.0022334204986691475, 0.053611837327480316, 0.008611117489635944, -0.015399501658976078, 0.045525483787059784, 0.017246700823307037, -0.008295634761452675, -0.014786253683269024, 0.04036032035946846, 0.006501454859972, 0.007782788947224617, 0.02245856076478958, -0.011261031962931156, -0.006818041671067476, 0.032874226570129395, -0.016446558758616447, 0.05730670318007469, -0.022847097367048264, -0.05869787186384201, -0.054210301488637924, -0.046373363584280014, -0.0033091639634221792, -0.020580239593982697, -0.02840709500014782, 0.06821808964014053, -0.039917852729558945, 0.01837630197405815, 0.03244056552648544, 0.03894302248954773, -0.052288200706243515, 0.0045060510747134686, 0.022012906149029732, 0.038859132677316666, 0.015056162141263485, -0.05069508031010628, 0.0027382592670619488, -0.04241260513663292, -0.01798993907868862, -0.005993804428726435, 0.0049916403368115425, -0.005676188040524721, 0.011646164581179619, -0.03363008052110672, 0.02677762508392334, 0.004448438994586468, -0.006603317800909281, 0.020767178386449814, -0.031411852687597275, 0.04338117316365242, -0.003419585293158889, 0.0021303496323525906, -0.02075786329805851, 0.030824141576886177, 0.013309932313859463, -0.017711419612169266, 0.0036818028893321753, 0.08440955728292465, -0.009428410790860653, -0.04240450635552406, 0.05997658148407936, -0.02863193117082119, 0.036243245005607605, -0.003055165521800518, 0.024897657334804535, -0.005011707544326782, 0.012214631773531437, 0.04262056574225426, -0.02829894609749317, -0.02570468559861183, -0.011955519206821918, -0.004222197458148003, -0.07972312718629837, 0.0014683378394693136, -0.02809319645166397, -0.016966277733445168, -0.004342090338468552, -0.08100341260433197, 0.008064965717494488, -0.03378765657544136, -0.055247608572244644, -0.033716678619384766, 0.02332492358982563, 0.011569242924451828, 0.03494811803102493, -0.018498919904232025, -0.018393950536847115, -0.009036310017108917, 0.025242997333407402, 0.032990675419569016, -0.012280388735234737, -0.0031694988720119, -0.011057211086153984, -0.010551119223237038, -0.029969552531838417, -0.008448001928627491, 0.016520733013749123, 0.008746622130274773, 0.12972404062747955, -0.04238874092698097, -0.07300975173711777, 0.05132525414228439, 0.043204981833696365, 0.014523514546453953, -0.011343225836753845, -0.029084812849760056, 0.051375191658735275, -0.04053112119436264, -0.010700414888560772, 0.0030798206571489573, -0.0025793532840907574, -0.022259779274463654, 0.03784776106476784, 0.010630236007273197, 0.04791005700826645, 0.02317109890282154, 0.035599756985902786, -0.014976238831877708, 0.04063936695456505, -0.026508666574954987, -0.03561592474579811, -0.06717374920845032, 0.08021184802055359, 0.05547351390123367, 0.010758591815829277, -0.0671200081706047, -0.03366100788116455, -0.02200349234044552, -0.025381196290254593, -0.0682070404291153, -0.0010037043830379844, -0.015127467922866344, -0.028037406504154205, -0.0703633651137352, 0.04299617558717728, -0.04321857541799545, 0.034332524985075, -0.0496976412832737, 0.06512303650379181, -0.025871364399790764, -0.023778215050697327, -0.00947481207549572, -0.020428327843546867, -0.02256886288523674, -0.03550199046730995, 0.010480362921953201, -0.04103575274348259, -0.005014220718294382, -0.014335266314446926, -0.011342422105371952, -0.005066975485533476, -0.01562674716114998, 0.021933171898126602, 0.019715914502739906, 0.047997720539569855, 0.027471492066979408, 0.0005233999108895659, -0.01725642755627632, 0.010388541966676712, 0.047378651797771454, -0.007346059661358595, -0.008381285704672337, -0.018888283520936966, -0.02156754396855831, 0.05963345989584923, 0.030114267021417618, 0.0010169856250286102, 0.007583962753415108, 0.03969227522611618, -0.05201949551701546, 0.04209147021174431, 0.00324654602445662, 0.009882919490337372, 0.01636139117181301, 0.05512155219912529, 0.010078123770654202, 0.01957203634083271, -0.05082889646291733, -0.062426552176475525, -0.0006456073606386781, 0.026110228151082993, 0.02877441793680191, 0.020882509648799896, 0.04358536750078201, -0.012425482273101807, -0.007099850103259087, 0.050277870148420334, 0.05268544703722, -0.014926513656973839, 0.0038747997023165226, -0.033209700137376785, -0.018243014812469482, -0.01273210160434246, 0.02983281761407852, -0.032944206148386, -0.03247414901852608, -0.02414890192449093, 0.025873495265841484, -0.018562370911240578, -0.01920299418270588, -0.031377922743558884, -0.0026173319201916456, -0.009949097409844398, -0.004220824223011732, -0.0008306617382913828, 0.03806615620851517, 0.10329987853765488, 0.018848391249775887, -0.03816886618733406, 0.02185792848467827, -0.055874940007925034, -0.02665027044713497, -0.05901072919368744, 0.03700410574674606, 0.0024063107557594776, 0.01954762078821659, 0.02081228420138359, -0.006718833930790424, -0.03384441137313843, -0.020390450954437256, 0.018998173996806145, -0.05586718022823334, 0.03665515035390854, 0.018130049109458923, 0.012154677882790565, 0.08964043855667114, -0.05840688571333885, 0.008173080161213875, 0.051072899252176285, -0.014085762202739716, -0.034882985055446625, 0.0007524146349169314, -0.01944577693939209, 0.012335230596363544, -0.021604664623737335, -0.032850757241249084, -0.0453149788081646, 0.030779050663113594, -0.002225717296823859, 0.07724127918481827, 0.027981434017419815, -0.009930646046996117, -0.01921493373811245, 0.010713526979088783, 0.009001794271171093, 0.02144230715930462, -0.01610514707863331, -0.05231378600001335, 0.012046203948557377, -0.030429953709244728, -0.005061918403953314, 0.10248302668333054, 0.01952519826591015, 0.018582595512270927, 0.0315127968788147, -0.02369489148259163, -0.01869693212211132, 0.0014071083860471845, 0.027361564338207245, 0.017658943310379982, 0.040127046406269073, -0.0230349600315094, -0.03394869714975357, -0.03358563780784607, -0.009250324219465256, -0.04143422842025757, -0.03658677637577057, -0.09937450289726257, 0.009042451158165932, -0.07089900970458984, -0.05370991677045822, 0.008136531338095665, -0.009419756941497326, -0.0330200269818306, 0.033993616700172424, -0.07034536451101303, 0.025136958807706833, 0.019359158352017403, -0.0793314129114151, -0.016823694109916687, 0.0062024034559726715, -0.005232060793787241, 0.027760427445173264, -0.05188653990626335, -0.03564738854765892, -0.020925180986523628, 0.011957477778196335, -0.03477887064218521, 0.08598712086677551, 0.023792997002601624, 0.038959801197052, -0.05186350271105766, 0.020246431231498718, -0.004443813115358353, -0.03277508541941643, -0.033894360065460205, -0.04463692009449005, 0.07350215315818787, 0.01748853363096714, 0.010882388800382614, 0.04133265092968941, 0.004096816293895245, -0.0007001736667007208, -0.04702059179544449, 0.05956511199474335, 0.05639209970831871, -0.001207726658321917, 0.04049188643693924, -0.0002802190720103681, -0.05155558884143829, -0.017480019479990005, 0.035156648606061935, 0.01643599383533001, -0.024014202877879143, 0.03951900079846382, 0.06684458255767822, 0.005517958663403988, 0.04220042750239372, 0.04932917654514313, -0.0200808048248291, -0.010761444456875324, -0.018176333978772163, -0.042167142033576965, 0.021239539608359337, -0.008833562955260277, -0.03497026115655899, -0.03826398402452469, 0.006840244401246309, -0.009486353024840355, 0.018340852111577988, -0.0003903571341652423, -0.06731569766998291, 0.003899150062352419, 0.054923806339502335, -0.017455026507377625, -0.023423880338668823, -0.011030314490199089, -0.06836189329624176, 0.04870092496275902, -0.04260551184415817, -0.051219891756772995, -0.03172820806503296, -0.019877774640917778, -0.028882820159196854, -0.0036489570047706366, 0.023669777438044548, 0.0038007479161024094, -0.018778031691908836, 0.0327986516058445, -0.024026144295930862, 0.017843954265117645, -0.01532873883843422, 0.01472237054258585, -0.01505354419350624, -0.0019767724443227053, -0.016554445028305054, -0.01307153981178999, -0.02651088312268257, 0.06903333216905594, 0.013811695389449596, 0.05693339556455612, -0.005667233373969793, -0.012832537293434143, -0.023484287783503532, -0.013832950964570045, -0.02781791053712368, 0.006158775649964809, -0.01085162814706564, 0.0727761834859848, 0.016114769503474236, -0.0751536414027214, 0.020731152966618538, 0.0027779319789260626, 0.0075841546058654785, 0.0021607272792607546, 0.04373471066355705, -0.04201633110642433, -0.021901141852140427, 0.018566058948636055, 0.025328243151307106, 0.035952500998973846, -0.021720904856920242, 0.004411814268678427, -0.0019622831605374813, -0.02362104505300522, 0.011535906232893467, -0.016632040962576866, -0.009439264424145222, 0.0720406100153923, 0.017135851085186005, -0.04469487443566322, -0.01226900890469551, -0.03171894699335098, -0.022062458097934723, -0.004893908277153969, -0.013334517367184162, 0.028939858078956604, -0.04335454851388931, -0.014733738265931606, 0.021692859008908272, -0.03898411989212036, 0.010631455108523369, -0.08962243050336838, 0.017306651920080185, 0.020680131390690804, 0.016755197197198868, -0.013317137956619263, 0.019763214513659477, 0.06843547523021698, -0.02891630493104458, 0.03791644796729088, -0.0898006334900856, 0.05016288161277771, -0.05124511569738388, -0.043653812259435654, 0.0269601009786129, 0.0176183320581913, -0.0351220965385437, -0.02497517317533493, -0.007867404259741306, -0.002177163492888212, 0.009526554495096207, -0.020236631855368614, 0.04213946312665939, -0.01309575792402029, 0.0386212058365345, 0.04050755873322487, 0.008897474966943264, 0.0440349318087101, -0.0016749793430790305, -0.021120931953191757, 0.019970903173089027, 0.006278445944190025, -0.005807569250464439, 0.03790591284632683, 0.022539451718330383, -0.0266156904399395, -0.04255969822406769, -0.022919056937098503, -0.01303428690880537, -0.02900017984211445, -0.012557875365018845, -0.06970459967851639, -0.08056185394525528, 0.00951591320335865 ]
<p>Say there is $\hat{J} = \exp[-i \hat{p} l/ \hbar]$ and $\hat{U}= \exp[-i\hat{H}t/ \hbar]$, where $\hat{H}$ is time-independent. </p> <p>Can we say anything about $[\hat{J},\hat{U}]$? Is it zero? How do we show this? </p> <p>For example if $\hat{H} = \hat{p}^2 /2m + m\omega^2 \hat{x}^2/2$.</p>
g8413
[ -0.004075171891599894, 0.05561966449022293, -0.044960010796785355, -0.019410356879234314, 0.03136200085282326, -0.047078121453523636, 0.016414958983659744, -0.014005125500261784, -0.016513610258698463, 0.05093235895037651, -0.06351559609174728, 0.0673011988401413, 0.029685916379094124, 0.03523546829819679, 0.013744457624852657, -0.02139674313366413, 0.04614211246371269, -0.027138760313391685, 0.00888810120522976, 0.03437259420752525, -0.040056291967630386, -0.03642279654741287, 0.03777033090591431, -0.008285505697131157, 0.14654479920864105, -0.030819961801171303, 0.013315975666046143, -0.0885561853647232, -0.040080975741147995, -0.0010593929328024387, 0.029602831229567528, -0.02193477749824524, 0.07260684669017792, 0.006996737793087959, 0.014273129403591156, -0.005888975225389004, 0.07636556029319763, 0.010923544876277447, 0.058049969375133514, -0.001698303734883666, -0.01665862277150154, 0.05815640464425087, 0.017021436244249344, 0.01885058917105198, -0.019247369840741158, 0.016903582960367203, -0.012968548573553562, 0.09141863137483597, -0.04561560973525047, 0.014261366799473763, 0.017076276242733, 0.02507927268743515, 0.10204385221004486, -0.051239192485809326, -0.060859888792037964, -0.011383009143173695, 0.010569133795797825, -0.03402072563767433, 0.030267678201198578, 0.08114654570817947, 0.03286014869809151, -0.04548171907663345, 0.030925368890166283, 0.04654937610030174, 0.07644099742174149, -0.0011461267713457346, -0.0048315986059606075, 0.00823007058352232, -0.012045394629240036, 0.052571848034858704, -0.03011123277246952, 0.011846900917589664, 0.024887235835194588, -0.006880076602101326, -0.05026484653353691, 0.02537490800023079, 0.051065124571323395, 0.02170301042497158, 0.02709546498954296, 0.026361439377069473, -0.0017389414133504033, -0.008345860056579113, 0.03161872178316116, -0.057048436254262924, -0.03525526449084282, -0.028375310823321342, 0.046420224010944366, -0.017110133543610573, -0.027545712888240814, 0.059569671750068665, 0.025892505422234535, -0.05645274743437767, 0.030477991327643394, 0.07854202389717102, 0.006374393589794636, -0.04449372738599777, 0.026307346299290657, 0.03766622766852379, 0.011532808654010296, -0.04042365774512291, 0.008054711855947971, 0.03293386101722717, -0.0028927887324243784, -0.026890726760029793, 0.011713040061295033, -0.0020615863613784313, 0.06573150306940079, -0.011559962294995785, -0.05856236070394516, -0.05087592452764511, -0.010518213734030724, 0.05240138992667198, -0.07751154899597168, 0.014060690067708492, -0.03494160994887352, -0.0262689720839262, -0.005298893433064222, -0.05788872390985489, -0.0470760203897953, 0.025343991816043854, 0.01782621070742607, -0.027397919446229935, 0.019077645614743233, 0.10337968170642853, -0.010800824500620365, 0.02346721850335598, -0.010082296095788479, 0.0008040746324695647, -0.002916906727477908, 0.00029697330319322646, -0.02143862284719944, 0.016697006300091743, 0.02810712158679962, 0.010233798064291477, -0.04032886028289795, 0.04624957963824272, 0.009317344054579735, -0.015483427792787552, 0.004943940322846174, -0.006366897374391556, -0.03859288990497589, -0.03428995981812477, 0.0078353900462389, -0.03961529955267906, -0.00032220277353189886, -0.011203964240849018, 0.02223747968673706, -0.058821357786655426, 0.0026835512835532427, 0.016585689038038254, -0.0023838176857680082, 0.09043174237012863, -0.015564538538455963, 0.018155133351683617, 0.006901517044752836, 0.01001742109656334, 0.006045682355761528, -0.05193750187754631, 0.015770046040415764, 0.007729177363216877, 0.03401944413781166, 0.03487937152385712, 0.019834889099001884, -0.019976582378149033, -0.040682028979063034, -0.016375040635466576, 0.017035678029060364, 0.002383412327617407, -0.01684052124619484, -0.01877269707620144, -0.019491471350193024, 0.06179998815059662, 0.026217559352517128, -0.0019536518957465887, 0.003204843495041132, -0.022436736151576042, -0.010761496610939503, -0.00831808801740408, -0.01598254032433033, -0.00013892991410102695, -0.018570559099316597, -0.042440980672836304, -0.0029759127646684647, -0.0060880910605192184, 0.015958426520228386, 0.006293728481978178, 0.0007680526468902826, 0.015548248775303364, -0.04849977791309357, -0.009079575538635254, -0.01823144033551216, 0.04431938752532005, 0.042138274759054184, 0.008608401753008366, 0.013372601009905338, -0.022153763100504875, -0.023946745321154594, -0.017713652923703194, -0.0005417524371296167, -0.003411897923797369, -0.007830651476979256, 0.0650661289691925, 0.030466563999652863, 0.015745127573609352, -0.05556206405162811, -0.025690393522381783, 0.030014336109161377, -0.017693424597382545, 0.013491775840520859, 0.007323062513023615, 0.07084351032972336, 0.005483747459948063, -0.04243149608373642, -0.013151949271559715, -0.027437003329396248, -0.037629105150699615, -0.011836431920528412, -0.002146507380530238, 0.013164246454834938, -0.03835263475775719, 0.012148603796958923, 0.024219125509262085, 0.05297056585550308, 0.008020785637199879, -0.011349041014909744, -0.01910574361681938, -0.019742202013731003, 0.009244593791663647, -0.01928725652396679, 0.015123517252504826, 0.012070823460817337, -0.037344157695770264, 0.014039761386811733, -0.027189739048480988, 0.02590816281735897, -0.030248774215579033, 0.036282796412706375, 0.017415041103959084, 0.03013928420841694, 0.09788285195827484, 0.03675829619169235, -0.039792221039533615, -0.04422210901975632, 0.05307837948203087, -0.006852197460830212, -0.009120647795498371, 0.014154286123812199, 0.020648842677474022, -0.03757992386817932, 0.03473939374089241, -0.04832370579242706, 0.008028787560760975, -0.0216948464512825, 0.01734234020113945, -0.0015107921790331602, -0.03123360686004162, 0.02886149287223816, -0.05192403122782707, -0.10912635922431946, 0.017954068258404732, 0.012177753262221813, 0.012838068418204784, 0.03602565452456474, 0.01620115339756012, -0.04907497391104698, -0.04461243003606796, -0.017875274643301964, -0.037243880331516266, 0.028636474162340164, -0.038129836320877075, -0.0026530965697020292, 0.06955057382583618, 0.0238050427287817, 0.06298943608999252, -0.019480964168906212, -0.0023187410552054644, -0.032368335872888565, -0.018626157194375992, -0.022689975798130035, -0.007955524139106274, 0.0011065953876823187, -0.024730810895562172, -0.03409816697239876, 0.0528319850564003, -0.0030814148485660553, -0.008765949867665768, 0.02393687330186367, 0.051364049315452576, 0.02652423456311226, 0.001692394376732409, -0.015204880386590958, 0.005352819804102182, 0.029325535520911217, 0.016965189948678017, -0.023928014561533928, -0.0024101415183395147, 0.02146271988749504, -0.0353349931538105, 0.03284125030040741, -0.008032565005123615, -0.025288911536335945, 0.011218956671655178, -0.0037666563875973225, -0.017550325021147728, 0.0609230175614357, 0.008094004355370998, -0.0026381313800811768, -0.0834670141339302, -0.005373530555516481, -0.030930178239941597, -0.016394078731536865, 0.05966179445385933, -0.014905462972819805, -0.019130712375044823, -0.022030005231499672, 0.006818810477852821, 0.003015657654032111, -0.02587319165468216, 0.03194645047187805, 0.009993702173233032, -0.05994587391614914, -0.06958391517400742, 0.03443186730146408, 0.0028799576684832573, -0.018195008859038353, -0.02156912535429001, -0.03686859458684921, -0.05673335865139961, -0.054734814912080765, 0.010091475211083889, 0.0008220140589401126, 0.02783445455133915, 0.04846109077334404, 0.01988978125154972, -0.017497289925813675, -0.010477118194103241, 0.050631679594516754, -0.000889482325874269, 0.013505571521818638, 0.021287979558110237, 0.0004922313964925706, -0.01836216449737549, -0.02699136920273304, 0.02465808019042015, -0.03763401508331299, -0.026224955916404724, 0.018149305135011673, 0.024804582819342613, 0.01584748923778534, -0.030699316412210464, 0.034489572048187256, 0.014953754842281342, 0.012493903748691082, -0.04699842259287834, 0.05870404839515686, 0.059692319482564926, 0.030907319858670235, 0.02803765796124935, 0.0152098024263978, -0.03788420185446739, 0.011117180809378624, -0.030529771000146866, 0.019851475954055786, 0.019636834040284157, 0.010996347293257713, -0.04011325165629387, 0.0142015116289258, 0.026793286204338074, 0.014054873958230019, -0.01177985593676567, 0.04429410770535469, 0.029624491930007935, 0.040045689791440964, 0.006288972217589617, -0.02068241313099861, -0.08358413726091385, 0.011207284405827522, 0.0034167764242738485, 0.016668567433953285, 0.06833843141794205, 0.02528475411236286, -0.027004340663552284, -0.03619833290576935, 0.033547841012477875, 0.0379493422806263, 0.019792165607213974, -0.03994648903608322, -0.030039522796869278, 0.028113285079598427, 0.021491870284080505, 0.0328531339764595, -0.0012502417666837573, 0.043017834424972534, 0.010101905092597008, -0.00885841716080904, -0.02780831605195999, 0.03217124938964844, -0.057443469762802124, -0.05758659914135933, 0.004444889724254608, -0.03892518952488899, -0.027307061478495598, -0.0018592247506603599, -0.04347541928291321, -0.008688532747328281, 0.046709224581718445, 0.023307831957936287, -0.02314152382314205, 0.02397576905786991, -0.02288513258099556, -0.025269465520977974, -0.08205245435237885, 0.02386389672756195, -0.044451091438531876, -0.000622077495791018, -0.05300652235746384, 0.03269986808300018, -0.05672888457775116, 0.014034033752977848, -0.04064680635929108, 0.007458277978003025, 0.0010565574048087, -0.001695715938694775, -0.007086501456797123, 0.00868300348520279, 0.06007945165038109, 0.040367551147937775, 0.01200337428599596, -0.013178051449358463, -0.030658092349767685, 0.019037527963519096, 0.0026833051815629005, 0.015523700043559074, 0.023190977051854134, -0.046984005719423294, 0.028616994619369507, -0.04553506150841713, 0.06501790136098862, -0.03645911440253258, -0.006116143893450499, 0.024144746363162994, -0.0019093540031462908, 0.009680583141744137, -0.00889528077095747, -0.0056111011654138565, 0.016940386965870857, 0.006834802217781544, -0.05241395905613899, 0.005710959434509277, -0.03152535855770111, -0.08559108525514603, 0.03996497020125389, -0.024472076445817947, -0.05187401548027992, -0.008220960386097431, -0.04485040158033371, -0.026267511770129204, 0.0010449764085933566, 0.039465196430683136, 0.037425778806209564, -0.05738884210586548, -0.058213356882333755, 0.007636403664946556, 0.046587470918893814, -0.005854178685694933, -0.03398707136511803, -0.08086993545293808, 0.04187565669417381, 0.030249381437897682, 0.05601684749126434, 0.016733095049858093, 0.04615514725446701, 0.07214479893445969, 0.010646556504070759, -0.038705866783857346, -0.00768524594604969, -0.0415356382727623, -0.040329981595277786, 0.016961604356765747, 0.0175769180059433, -0.01647358015179634, -0.0315987765789032, -0.02884269319474697, 0.003455851227045059, -0.0033573685213923454, 0.01089636143296957, -0.024987652897834778, -0.07756529003381729, -0.02262778766453266, -0.05783817917108536, 0.023149754852056503, -0.025311505421996117, 0.015855370089411736, 0.03341502696275711, -0.04768848419189453, -0.0886835902929306, -0.02213732711970806, -0.05081882327795029, 0.023431437090039253, -0.011151022277772427, -0.04692384973168373, 0.020197506994009018, -0.00828912016004324, 0.026938114315271378, 0.0582522377371788, 0.01231895200908184, 0.044030021876096725, -0.00925962720066309, -0.026609262451529503, -0.0026781130582094193, 0.04986172914505005, 0.032334960997104645, -0.03571018949151039, 0.06442150473594666, -0.005576288793236017, -0.002311041811481118, -0.0317617766559124, 0.010774186812341213, -0.0650937631726265, -0.03845931962132454, 0.048140011727809906, -0.04112100973725319, 0.05263272300362587, -0.00434894859790802, 0.04433969408273697, -0.019271759316325188, -0.041155144572257996, -0.07800642400979996, 0.005569260101765394, 0.03284354507923126, 0.03504013270139694, -0.0245194248855114, -0.053061794489622116, -0.06867359578609467, 0.034365177154541016, -0.04769538715481758, -0.012927128933370113, -0.0014856007182970643, -0.0304681695997715, 0.00829536747187376, -0.039776962250471115, -0.05078403279185295, 0.025828726589679718, 0.03910490870475769, -0.019081179052591324, -0.026630006730556488, -0.010104535147547722, -0.0029258420690894127, 0.05900498852133751, 0.004169371444731951, -0.05381038784980774, 0.03207722678780556, 0.0019388124346733093, -0.03059144876897335, 0.0195766594260931, 0.05170143023133278, 0.028005193918943405, -0.018079562112689018, -0.022048022598028183, 0.006790515035390854, 0.07009327411651611, 0.001762544154189527, 0.021935787051916122, 0.008753307163715363, -0.06263035535812378, -0.02924809232354164, 0.06662596762180328, -0.018946070224046707, -0.013947972096502781, 0.03842669352889061, -0.0021948199719190598, 0.03779304400086403, 0.04176470264792442, -0.028534816578030586, 0.03682582080364227, 0.052914995700120926, 0.009595975279808044, 0.010557149536907673, 0.00006267322169151157, -0.030950723215937614, -0.031720247119665146, 0.04974621161818504, -0.005672389175742865, -0.050124987959861755, -0.007124908734112978, 0.04414350911974907, -0.012096665799617767, -0.04641714692115784, 0.047270163893699646, 0.05445346608757973, -0.06409983336925507, -0.02923007681965828, -0.04469333216547966, -0.03849273920059204, 0.003334763925522566, 0.09280645847320557, -0.004273596685379744, 0.050608038902282715, -0.00788101926445961, -0.0708388164639473, 0.019214771687984467, 0.0011489872122183442, 0.06497139483690262, -0.051806192845106125, -0.04463551566004753, 0.055511973798274994, -0.04771212488412857, 0.012859699316322803, 0.013212439604103565, -0.02189711295068264, -0.02802872657775879, 0.014059999026358128, 0.024544572457671165, 0.016678104177117348, -0.02833016775548458, -0.06417582929134369, 0.015817219391465187, -0.045020733028650284, -0.06810374557971954, 0.017121080309152603, 0.0868903324007988, -0.02152373269200325, -0.03385818377137184, 0.027247311547398567, 0.058081962168216705, 0.030871212482452393, 0.018665697425603867, 0.013261768966913223, -0.05272842198610306, -0.026888806372880936, 0.028789425268769264, 0.0725259780883789, -0.05345583334565163, 0.0031393656972795725, -0.05414509028196335, 0.07256221771240234, -0.03808816522359848, 0.05163891986012459, -0.004004871007055044, 0.04716643691062927, 0.03834565728902817, 0.10095611214637756, 0.012522948905825615, -0.014932275749742985, -0.015610035508871078, 0.01092172134667635, 0.052554864436388016, 0.00343535328283906, -0.0820864886045456, 0.021053839474916458, 0.007788711693137884, 0.04003829509019852, 0.005783863831311464, 0.01620154082775116, -0.0021516999695450068, -0.018259137868881226, -0.038517627865076065, 0.010116614401340485, -0.0038395270239561796, -0.005145374219864607, 0.005502517335116863, -0.007934950292110443, -0.02026611752808094, -0.03342195227742195, 0.0354231633245945, 0.049986034631729126, 0.026152092963457108, 0.007530373986810446, 0.020140448585152626, -0.02655036747455597, 0.029878193512558937, -0.042563989758491516, -0.06625670194625854, -0.004149140790104866, 0.010220946744084358, 0.03435307741165161, -0.014765337109565735, 0.06808550655841827, -0.051144979894161224, 0.012527033686637878, 0.044081784784793854, 0.027882011607289314, -0.014514652080833912, 0.005201797001063824, -0.012859131209552288, 0.02191721275448799, 0.020703544840216637, -0.03191828727722168, 0.028738608583807945, 0.024776563048362732, -0.027967818081378937, 0.029961228370666504, 0.0662652924656868, -0.01798323355615139, 0.023211833089590073, -0.00838278979063034, 0.022913647815585136, -0.010370412841439247, -0.020860878750681877, 0.009261487983167171, 0.038564637303352356, -0.002239797729998827, 0.0083429841324687, -0.015188848599791527, 0.05907903239130974, 0.04350455850362778, -0.0259771179407835, -0.04191913828253746, -0.02249315194785595, -0.046260036528110504, -0.009270911104977131, 0.05327833816409111, -0.038905080407857895, -0.07665590941905975, 0.024433674290776253, -0.02156630903482437, -0.11885238438844681, 0.0052428292110562325, 0.02887261100113392, -0.0001483589585404843, -0.05189811810851097, -0.07694076746702194, 0.004484562203288078, -0.07388752698898315, -0.0235081035643816, -0.004360052291303873, -0.005976771004498005, 0.005579702090471983, 0.0052161505445837975, 0.027009647339582443, 0.010604700073599815, -0.030267229303717613, -0.029917648062109947, 0.07656349986791611, -0.014358068816363811, -0.05511660873889923, 0.0007179146050475538, 0.03436323627829552, -0.0079544922336936, 0.029711399227380753, -0.027087651193141937, -0.049310773611068726, 0.004503054544329643, 0.032901205122470856, -0.022120043635368347, -0.01655612885951996, 0.04779641330242157, -0.011482177302241325, 0.040791310369968414, 0.0154423201456666, -0.017559150233864784, 0.06650849431753159, -0.06915444880723953, 0.012426846660673618, 0.04591067507863045, -0.04793473705649376, -0.02322622761130333, 0.004304601810872555, 0.028806833550333977, 0.001441232510842383, -0.0255599282681942, -0.04161909967660904, -0.04610457271337509, -0.013229481875896454, 0.024886827915906906, -0.029634302482008934, 0.009214681573212147, -0.0484577976167202 ]
<p>I want to know the properties and the behavior of the gapless excitation for the traditional <a href="http://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_condensate" rel="nofollow">BEC</a>s. Could you give me some idea or references about this? </p>
g8414
[ -0.0449574813246727, 0.004613487049937248, -0.006503612268716097, 0.014150832779705524, 0.031762391328811646, -0.0006425281753763556, 0.023253658786416054, 0.05550945922732353, 0.020817726850509644, -0.07010102272033691, 0.02758091501891613, 0.049934688955545425, 0.02117219939827919, 0.014487821608781815, 0.006316492799669504, 0.03465412184596062, 0.026937760412693024, -0.02400103025138378, 0.039269763976335526, -0.049545664340257645, -0.03417341038584709, -0.033776357769966125, -0.06971016526222229, -0.024332858622074127, 0.022375693544745445, 0.03280235826969147, 0.017927078530192375, 0.024499787017703056, -0.022710856050252914, -0.06947451829910278, 0.0034919518511742353, -0.01652972213923931, 0.04620055854320526, 0.01103923749178648, -0.0011606744956225157, 0.05801977962255478, 0.019617954269051552, 0.04020517319440842, 0.024312419816851616, 0.03432270884513855, 0.016253281384706497, 0.0022860390599817038, -0.008467280305922031, 0.017516138032078743, -0.007240740582346916, -0.04348617419600487, 0.0014177473494783044, -0.0025559973437339067, -0.06492717564105988, -0.06972812116146088, -0.013412395492196083, 0.06612172722816467, 0.025008969008922577, 0.029072754085063934, -0.016907276585698128, 0.019520578905940056, -0.06388445943593979, 0.008866578340530396, 0.04205125570297241, 0.016008926555514336, -0.08838746696710587, 0.049111053347587585, 0.0568062961101532, 0.04108915850520134, 0.024124931544065475, -0.05402979627251625, -0.05984945967793465, -0.003183576511219144, -0.02672543376684189, -0.037639766931533813, -0.03911907598376274, -0.06871901452541351, -0.03446418419480324, 0.051784977316856384, -0.025373315438628197, 0.030098458752036095, -0.03396714851260185, 0.00513454107567668, 0.005797959864139557, 0.03640270233154297, -0.049503009766340256, -0.05647880584001541, 0.04174342006444931, -0.053996797651052475, 0.06579680740833282, -0.04085216298699379, -0.008485953323543072, 0.021344855427742004, -0.01766708306968212, 0.008261353708803654, -0.011584050953388214, 0.00640292139723897, 0.03550878167152405, -0.005987720564007759, 0.050729330629110336, 0.04709131270647049, 0.02186756022274494, -0.034607548266649246, -0.022457493469119072, 0.03469577431678772, -0.022069528698921204, -0.013751420192420483, 0.03953321650624275, -0.006258330307900906, -0.01763022504746914, -0.039805684238672256, 0.014277254231274128, -0.05568791925907135, 0.018969470635056496, 0.01528377179056406, -0.0030024030711501837, 0.004525596741586924, 0.035272885113954544, -0.010805957950651646, -0.06301500648260117, 0.023011302575469017, -0.01739443652331829, -0.006935288198292255, 0.001034997752867639, -0.005711646284908056, 0.02461951971054077, 0.057992808520793915, -0.021895186975598335, 0.007241459563374519, -0.05102098360657692, -0.011738134548068047, 0.05497976019978523, 0.004959616344422102, -0.021791959181427956, 0.00628551235422492, 0.04028093069791794, -0.0367017537355423, 0.0025330341886729, 0.0010589755838736892, 0.053940415382385254, -0.05575323849916458, 0.020584356039762497, -0.04302379488945007, 0.009652338922023773, -0.024513911455869675, -0.030261024832725525, -0.022208258509635925, 0.002476840279996395, -0.03335334733128548, -0.00196516839787364, -0.032293252646923065, 0.008877187967300415, 0.0015299769584089518, 0.006981301587074995, 0.0018159887986257672, -0.01161614153534174, 0.011393500491976738, 0.05785039812326431, -0.01095527783036232, -0.01864899881184101, 0.0031628452707082033, 0.03245222568511963, 0.007398401387035847, -0.05551828816533089, -0.013143246993422508, -0.026078302413225174, 0.011246142908930779, 0.006794182118028402, -0.011946768499910831, -0.0579134039580822, -0.03123849257826805, 0.018070146441459656, -0.013966222293674946, 0.061177194118499756, -0.02451665885746479, -0.031775519251823425, 0.04910370334982872, 0.0010421538027003407, 0.054630622267723083, 0.036565691232681274, 0.021603107452392578, -0.019609829410910606, -0.0544121116399765, 0.10076186060905457, 0.02076444961130619, -0.04514235630631447, 0.039564162492752075, 0.008576339110732079, -0.01071995310485363, -0.03267518803477287, 0.06563428044319153, 0.038141511380672455, -0.04317862540483475, -0.028340818360447884, 0.028976531699299812, -0.021241698414087296, -0.04348341375589371, 0.013296700082719326, 0.011337519623339176, -0.019004860892891884, 0.009136981330811977, -0.024599479511380196, -0.002091913716867566, 0.02728855423629284, -0.00767192617058754, -0.03246259689331055, 0.026517778635025024, 0.040139369666576385, 0.02994575910270214, 0.0073908595368266106, -0.008448431268334389, 0.057976845651865005, -0.03432760015130043, 0.01476463582366705, 0.011057437397539616, -0.008489126339554787, -0.013013653457164764, -0.011758099310100079, -0.038715947419404984, 0.015457309782505035, -0.000294889003271237, -0.01607183739542961, -0.07661844789981842, -0.00010799065785249695, 0.08826763927936554, -0.0530683770775795, 0.010348559357225895, -0.04168177768588066, 0.0053064050152897835, -0.037153083831071854, -0.05463274195790291, 0.006530399899929762, -0.0021970714442431927, 0.026147712022066116, 0.05600494518876076, -0.07081843912601471, -0.007621792145073414, 0.04296198859810829, -0.00432213768362999, -0.034553349018096924, 0.033768586814403534, -0.023892143741250038, -0.04408581182360649, 0.027452656999230385, 0.015909966081380844, -0.002505266573280096, -0.023243112489581108, -0.05126003548502922, 0.05066852271556854, 0.028803667053580284, -0.0378422886133194, -0.0063810502178967, -0.035338472574949265, 0.043698593974113464, -0.05246606469154358, 0.0018693753518164158, 0.0005973906954750419, 0.009734266437590122, 0.058486465364694595, -0.033791434019804, -0.01707584783434868, 0.020382944494485855, 0.028245477005839348, 0.014284777455031872, -0.06582186371088028, 0.0058637880720198154, -0.06534324586391449, -0.0017514348728582263, 0.02963286079466343, 0.029063284397125244, 0.032271940261125565, -0.005440988577902317, 0.03356911987066269, -0.017727544531226158, -0.014959749765694141, 0.021158305928111076, 0.037302132695913315, -0.006147250533103943, 0.01213090866804123, -0.04441964626312256, 0.021518899127840996, 0.00005830346708535217, 0.027903126552700996, 0.005655396264046431, -0.04411877691745758, 0.0015243804082274437, 0.03614424169063568, 0.03498676419258118, 0.013466027565300465, 0.030793411657214165, -0.01896766573190689, -0.0032998467795550823, 0.07825532555580139, 0.038387954235076904, -0.018920492380857468, -0.08618272840976715, 0.0006950958631932735, -0.012159963138401508, 0.028977112844586372, -0.0020182784646749496, -0.020074501633644104, -0.013333240523934364, -0.014863604679703712, -0.0581020824611187, 0.09725484251976013, -0.012062390334904194, -0.05762414634227753, -0.047735173255205154, -0.02779485285282135, -0.039129529148340225, -0.014797593466937542, -0.02034669555723667, 0.004877328407019377, -0.08271857351064682, 0.11413953453302383, -0.04158097133040428, -0.022135775536298752, 0.027305547147989273, -0.025284960865974426, 0.00620721559971571, 0.0280563086271286, 0.036232709884643555, 0.018623419106006622, 0.03999246284365654, 0.02529982477426529, -0.013132280670106411, -0.018399398773908615, 0.05579604208469391, -0.028821729123592377, 0.034560225903987885, 0.0445215106010437, 0.03290935233235359, -0.025886571034789085, -0.026706121861934662, -0.014188187196850777, -0.01662522740662098, -0.048475075513124466, 0.002905028872191906, -0.01265813410282135, -0.06039292365312576, -0.04815701022744179, 0.03018701821565628, 0.07477908581495285, 0.00463826721534133, 0.016229679808020592, 0.03787265717983246, -0.068327896296978, -0.018695520237088203, 0.010018549859523773, -0.09632612019777298, -0.021110307425260544, 0.006059450097382069, 0.010018288157880306, -0.020087819546461105, -0.015638481825590134, 0.06010297313332558, -0.05376976728439331, -0.012558944523334503, -0.00756538100540638, -0.03413981944322586, 0.01476755179464817, 0.059642620384693146, -0.004904208239167929, 0.03932762145996094, 0.014673523604869843, 0.010671285912394524, -0.05157089978456497, 0.10353275388479233, -0.006140570621937513, -0.06759465485811234, -0.0855473130941391, -0.07191529124975204, -0.001283307676203549, 0.027221690863370895, -0.022339532151818275, 0.015462487004697323, -0.03995481878519058, 0.006501571275293827, -0.034161362797021866, 0.03897885978221893, -0.030009301379323006, -0.0166772548109293, 0.015066087245941162, -0.021728595718741417, 0.028076227754354477, -0.016537941992282867, 0.033216800540685654, 0.0590338334441185, -0.020946187898516655, 0.02837561070919037, -0.029163502156734467, -0.017972463741898537, 0.049968820065259933, -0.06895217299461365, -0.039472952485084534, -0.0026575843803584576, -0.025756601244211197, -0.016238562762737274, 0.024973107501864433, -0.06006602197885513, -0.0016474160365760326, -0.026421982795000076, 0.013871273025870323, -0.02967657707631588, 0.03293118253350258, -0.030062859877943993, 0.01618204638361931, 0.003010211745277047, -0.024896981194615364, 0.031118284910917282, 0.01926993764936924, 0.027890555560588837, -0.030534351244568825, 0.0005187882925383747, -0.0201552864164114, 0.005534702446311712, 0.049020569771528244, 0.011914876289665699, -0.046809107065200806, 0.07681851089000702, -0.02970872074365616, 0.05216966196894646, -0.034831102937459946, -0.008467822335660458, -0.021173954010009766, -0.030727623030543327, 0.00024005262821447104, -0.03220890834927559, 0.010544068180024624, -0.020666662603616714, 0.0022053816355764866, 0.01895146816968918, -0.009591740556061268, 0.0206750575453043, 0.016155075281858444, -0.002946959575638175, -0.032451000064611435, -0.017327111214399338, 0.04977129399776459, -0.051314134150743484, 0.034118130803108215, -0.07952968776226044, -0.0007052027503959835, -0.0345768928527832, 0.027605557814240456, 0.012325464747846127, 0.029569679871201515, 0.012407609261572361, 0.022334260866045952, 0.029666878283023834, 0.05225476622581482, -0.04297265037894249, -0.008281935006380081, 0.015766898170113564, -0.07179463654756546, 0.07386485487222672, 0.011161183938384056, -0.028180748224258423, -0.06790278851985931, 0.02196228690445423, 0.027898641303181648, 0.017243044450879097, 0.035215262323617935, 0.03751726448535919, 0.03629232197999954, -0.06400924175977707, -0.02953479252755642, -0.03368231654167175, -0.044778674840927124, 0.002914471784606576, -0.022747134789824486, -0.030797826126217842, -0.053097739815711975, -0.003109324024990201, -0.028285009786486626, -0.003713068086653948, -0.04772206023335457, 0.08292809873819351, 0.06266215443611145, 0.005451726261526346, 0.007868243381381035, 0.01787104457616806, -0.0003980407491326332, -0.024256059899926186, 0.02798984758555889, -0.03266912326216698, -0.0024432006757706404, 0.0036221726331859827, 0.003891914850100875, 0.026596659794449806, 0.011021406389772892, 0.013983264565467834, 0.021063946187496185, -0.04764994978904724, -0.039245154708623886, 0.0029064437840133905, 0.00756059680134058, 0.005167069844901562, -0.02318064495921135, 0.054773636162281036, -0.027083631604909897, -0.001054471475072205, -0.00011193517275387421, -0.023644698783755302, 0.02557273395359516, -0.05463818833231926, 0.016497377306222916, 0.025690479204058647, 0.02803921140730381, 0.013823572546243668, 0.0480886735022068, 0.05681909620761871, 0.01572263613343239, 0.055800799280405045, 0.03272971138358116, -0.015067812986671925, 0.0062300716526806355, 0.03017815388739109, 0.11977585405111313, -0.008513597771525383, 0.027853960171341896, -0.023048263043165207, -0.004263894632458687, -0.039998989552259445, -0.01940051279962063, -0.03579671308398247, -0.045665062963962555, -0.00028875310090370476, 0.025906087830662727, 0.02111927419900894, 0.0347570963203907, 0.03784502297639847, -0.01912957988679409, 0.06443414092063904, -0.02031637169420719, -0.028303999453783035, -0.04159347712993622, 0.023244258016347885, -0.058158744126558304, 0.10933990776538849, -0.008780166506767273, -0.0030306074768304825, 0.0307523924857378, -0.015519057400524616, -0.0328834131360054, -0.03517494350671768, -0.005623602773994207, -0.011088735423982143, 0.005187541712075472, 0.0005683471681550145, -0.011299222707748413, -0.04345222935080528, 0.03856609761714935, 0.033989083021879196, -0.01467022392898798, -0.059276774525642395, -0.02795301377773285, -0.006132989190518856, 0.01580606959760189, 0.05841667950153351, 0.028018437325954437, -0.038069214671850204, 0.007436415180563927, 0.04434162378311157, 0.023534070700407028, -0.009650042280554771, 0.03839200362563133, 0.010746858082711697, 0.032124944031238556, -0.004107301123440266, 0.030881252139806747, 0.03336397185921669, 0.01741086132824421, 0.032313331961631775, -0.0758281946182251, -0.01558986771851778, 0.0031919789034873247, 0.020624106749892235, -0.02298085205256939, 0.03630334511399269, -0.015662122517824173, 0.0348644033074379, 0.011745885945856571, -0.020846504718065262, 0.012739836238324642, -0.02815341018140316, 0.024887293577194214, 0.03324020281434059, 0.006798415910452604, 0.029972972348332405, 0.020000137388706207, 0.015452807769179344, 0.02490103617310524, -0.0034297045785933733, 0.014931377954781055, -0.021932478994131088, 0.011132996529340744, 0.0033596523571759462, -0.0015386787708848715, 0.004603866022080183, 0.028850233182311058, -0.04015550762414932, 0.019848914816975594, 0.03113842010498047, -0.055739592760801315, -0.007229028269648552, 0.0304721612483263, -0.006192604545503855, 0.032829102128744125, -0.03096892312169075, 0.0730123296380043, -0.010991008952260017, -0.006612604949623346, -0.02448844723403454, 0.06326860934495926, -0.03872387483716011, -0.022734414786100388, -0.02181956358253956, -0.08986560255289078, -0.01757894828915596, -0.059362493455410004, 0.01284838654100895, -0.01800711080431938, 0.05195435881614685, 0.04024573042988777, 0.027605131268501282, -0.023984426632523537, -0.009842104278504848, 0.007641970179975033, 0.03127124905586243, 0.03982764482498169, -0.012207656167447567, 0.005774799268692732, -0.014338940382003784, -0.011305024847388268, 0.02518445812165737, 0.019687358289957047, 0.02813672460615635, 0.0377337783575058, -0.07725744694471359, 0.06793003529310226, -0.040271539241075516, 0.03237925097346306, 0.029811345040798187, 0.006489874329417944, -0.007574659772217274, 0.05595966801047325, 0.055775076150894165, 0.02726847678422928, -0.06225399300456047, 0.041627008467912674, 0.016981977969408035, 0.03237196430563927, -0.01943814381957054, 0.007974149659276009, 0.023186275735497475, -0.045016735792160034, 0.01062818057835102, 0.0662447139620781, -0.07094890624284744, -0.057497117668390274, 0.016559548676013947, -0.024463539943099022, 0.06191729009151459, 0.028972670435905457, -0.011415828950703144, -0.023418134078383446, 0.00684994924813509, 0.009476330131292343, 0.05550006777048111, 0.010101329535245895, 0.028199031949043274, -0.06015918776392937, 0.07202351838350296, 0.004498643334954977, 0.0020861178636550903, -0.04758935049176216, -0.01716383546590805, -0.08299588412046432, -0.04148684814572334, 0.04858243465423584, 0.004464198835194111, 0.02053849957883358, 0.015127720311284065, -0.05013447627425194, -0.03143302723765373, 0.012448680587112904, -0.03724316135048866, -0.008688511326909065, -0.03183893859386444, 0.056190457195043564, -0.06591102480888367, 0.07181784510612488, 0.05020756274461746, 0.02202678471803665, 0.017456747591495514, 0.027349097654223442, -0.003956074360758066, -0.056499380618333817, -0.004814485553652048, -0.017947537824511528, -0.05173761397600174, 0.0010339870350435376, 0.01363861933350563, -0.0034565043170005083, 0.06348622590303421, 0.004627659451216459, -0.023447511717677116, -0.026156505569815636, -0.003698015119880438, -0.014267226681113243, -0.013220816850662231, -0.047314226627349854, -0.014412649907171726, -0.0071603404358029366, 0.03414464741945267, 0.06309090554714203, -0.010983994230628014, -0.01516844891011715, 0.07479715347290039, -0.01259741559624672, -0.05881282314658165, 0.010117934085428715, -0.0015162040945142508, -0.015877438709139824, -0.055964820086956024, -0.03034648299217224, -0.05660175904631615, 0.06829763203859329, -0.01624474860727787, -0.030537180602550507, -0.06541306525468826, 0.0630558505654335, 0.03603949397802353, 0.04726441949605942, -0.0772351548075676, -0.03725152462720871, 0.04858636483550072, 0.0034081507474184036, -0.051610369235277176, 0.007246734108775854, 0.08347196877002716, -0.02798604592680931, 0.0049071782268583775, 0.025876684114336967, 0.011776888743042946, -0.006146250292658806, 0.03261918947100639, -0.053850334137678146, -0.0028697915840893984, -0.019414428621530533, -0.052458755671978, -0.010104948654770851, 0.0888601616024971, -0.025442233309149742, -0.022243686020374298, 0.010230029933154583, 0.013951065950095654, 0.0375775508582592, 0.04702943190932274, -0.06664804369211197, 0.021002095192670822, 0.05465210974216461, 0.06391983479261398, 0.0015489165671169758, -0.013433026149868965, -0.007393812760710716, -0.05492208153009415, 0.04151168093085289, -0.016293466091156006, -0.024994852021336555, -0.0244444590061903, 0.014078906737267971 ]
<p>For rigid body we need to know position of three points and their velocities to determine everything. So that would make 12 DOF. Why do text books say it has six DOFs?</p>
g8415
[ 0.04915890097618103, 0.07478872686624527, -0.0048349942080676556, 0.005070952698588371, 0.08518490195274353, -0.018808552995324135, 0.046153727918863297, 0.0342181958258152, -0.051180675625801086, -0.06983104348182678, -0.041975237429142, -0.0668526291847229, 0.04198271781206131, -0.03876950591802597, -0.023357806727290154, -0.042934600263834, 0.07101359218358994, -0.006288259755820036, 0.03789013996720314, 0.062250398099422455, 0.08000042289495468, 0.06583593785762787, 0.0009010105859488249, -0.01141498051583767, -0.01560394186526537, 0.048564743250608444, -0.06985695660114288, -0.04952678829431534, -0.039947573095560074, 0.050190623849630356, 0.05129755288362503, 0.004117107950150967, -0.0034735144581645727, -0.03418019041419029, -0.008622895926237106, -0.046001531183719635, 0.01759520173072815, 0.05558670312166214, -0.021265510469675064, 0.009982137009501457, -0.03853978216648102, -0.048585351556539536, -0.043610721826553345, -0.01235212478786707, -0.017513031139969826, 0.0009404344600625336, -0.016473643481731415, -0.06328699737787247, -0.033046357333660126, -0.0018447033362463117, -0.009742964059114456, 0.010974141769111156, 0.018115416169166565, -0.01601116918027401, 0.00952465832233429, 0.04015191271901131, -0.029064437374472618, -0.05486486479640007, -0.00861307606101036, -0.01906232163310051, -0.015376634895801544, -0.018268227577209473, -0.029295209795236588, 0.022914545610547066, 0.024758605286478996, 0.021125761792063713, -0.06361503154039383, 0.025044817477464676, -0.03518778458237648, -0.02729894034564495, 0.018679417669773102, -0.06037217006087303, 0.04469513148069382, -0.026815783232450485, -0.07977313548326492, 0.01033910270780325, -0.020671861246228218, -0.019879907369613647, 0.021992428228259087, 0.013177289627492428, 0.01591705158352852, -0.01602865941822529, 0.013568995520472527, 0.013010692782700062, 0.12691591680049896, 0.019181517884135246, 0.0637524202466011, 0.07507528364658356, 0.019933439791202545, -0.02770400233566761, 0.0020926576107740402, 0.013277865946292877, 0.06818093359470367, 0.007412684615701437, 0.0394202396273613, 0.008642422966659069, -0.040378373116254807, 0.06976846605539322, 0.005366186145693064, -0.00470247445628047, -0.028250105679035187, 0.02783459983766079, -0.013910581357777119, -0.015330052934587002, -0.01451739203184843, -0.0883256271481514, 0.07013233751058578, 0.022274678573012352, 0.045649830251932144, -0.08186421543359756, -0.053566381335258484, -0.005249767564237118, -0.034722741693258286, 0.049503225833177567, -0.022124601528048515, 0.002350391587242484, 0.06207693740725517, 0.006889121141284704, 0.02320706471800804, 0.015971379354596138, 0.002305453410372138, -0.05258094519376755, 0.007473652251064777, 0.09065311402082443, -0.036296188831329346, -0.04708224907517433, -0.010744660161435604, -0.006988914217799902, 0.03461284562945366, -0.020769434049725533, -0.022764021530747414, 0.042627956718206406, -0.06436068564653397, -0.013147969730198383, -0.014669264666736126, 0.06549020856618881, -0.02044730633497238, -0.0326092503964901, -0.032402023673057556, 0.025647368282079697, 0.003320027142763138, 0.028173761442303658, 0.010249814949929714, -0.035353321582078934, 0.01746971532702446, -0.021304186433553696, -0.043997764587402344, -0.016002057120203972, 0.05321672931313515, 0.009579464793205261, 0.019266245886683464, 0.028519077226519585, 0.003805853659287095, 0.036946289241313934, 0.014119121246039867, -0.07042641937732697, 0.046064477413892746, -0.0029315652791410685, -0.0007325062179006636, 0.015904556959867477, 0.06781405955553055, 0.00044477329356595874, -0.019839931279420853, 0.01875811256468296, -0.03946946933865547, 0.029485058039426804, -0.07511617988348007, 0.008759649470448494, 0.0231484342366457, -0.025060374289751053, -0.026221074163913727, -0.010007230564951897, 0.04098236560821533, 0.010687245987355709, -0.019838662818074226, -0.011540519073605537, -0.03986173868179321, -0.03422538563609123, 0.04728357121348381, 0.06632163375616074, 0.029209278523921967, -0.00939934141933918, 0.06519156694412231, 0.006535539869219065, -0.06755436211824417, 0.05780363082885742, -0.008493871428072453, -0.016263402998447418, -0.0644872710108757, 0.050279583781957626, 0.0005975372041575611, 0.0073966397903859615, -0.031332727521657944, -0.008000243455171585, 0.043059222400188446, 0.00009996387962019071, 0.01607448048889637, -0.03737230971455574, -0.0476062148809433, 0.03629631921648979, -0.022764455527067184, 0.01748982071876526, -0.0030357330106198788, 0.0008086838060989976, -0.04698885604739189, -0.020311178639531136, 0.005297270603477955, 0.044480808079242706, 0.012238558381795883, 0.049879781901836395, 0.021866057068109512, -0.028559831902384758, -0.020488837733864784, 0.06715143471956253, -0.012848042882978916, -0.03067217394709587, -0.008363681845366955, -0.03270544484257698, 0.010521357879042625, -0.01035993080586195, 0.008585340343415737, 0.010974019765853882, -0.029523173347115517, 0.022259948775172234, -0.03847029060125351, -0.04071899875998497, -0.020727496594190598, -0.05617312341928482, 0.0426446907222271, 0.011914331465959549, -0.0617755763232708, -0.007862064056098461, 0.021622376516461372, -0.013819697313010693, 0.03319771587848663, -0.029153432697057724, 0.03136320784687996, -0.01176562998443842, -0.01772642694413662, 0.0918230414390564, 0.04001917690038681, -0.0451519675552845, 0.008900664746761322, -0.023074684664607048, 0.008542210794985294, 0.015688952058553696, 0.01721217855811119, -0.00813629012554884, -0.00722368061542511, 0.08281649649143219, -0.007683383766561747, -0.008450527675449848, -0.030503809452056885, 0.007225333247333765, 0.01017606258392334, 0.07272059470415115, -0.07063307613134384, -0.003996469080448151, -0.08974301069974899, 0.0014101515989750624, -0.0006362340645864606, -0.03207544609904289, 0.005576670169830322, -0.0076520987786352634, -0.05715717747807503, -0.023789113387465477, -0.01627865806221962, -0.04365224391222, -0.04287409782409668, -0.03708433359861374, -0.0031769515480846167, -0.016058437526226044, 0.06357601284980774, 0.015362832695245743, -0.0572098083794117, -0.013801107183098793, 0.00009667342237662524, -0.036942899227142334, -0.04852943494915962, 0.052102379500865936, -0.05453004688024521, -0.001543555990792811, -0.041574474424123764, 0.03319944441318512, -0.02110195904970169, 0.014910739846527576, 0.019580988213419914, 0.005365690682083368, -0.047060053795576096, -0.033130086958408356, -0.02835116721689701, 0.027968786656856537, 0.010736983269453049, -0.03984491154551506, 0.08087658137083054, 0.06706245243549347, -0.001008001621812582, -0.020517608150839806, -0.0022205079440027475, 0.02990691177546978, 0.0019588880240917206, 0.013389644213020802, 0.037568043917417526, 0.03643203154206276, -0.01745881326496601, -0.026475142687559128, 0.04157451167702675, -0.025858821347355843, 0.035992175340652466, -0.02495337650179863, 0.039200473576784134, 0.025123300030827522, -0.0019375788979232311, -0.018448011949658394, -0.0881986990571022, 0.003285418264567852, 0.04341968521475792, 0.07445292919874191, 0.009105827659368515, 0.0286509171128273, 0.0047207968309521675, -0.021346449851989746, -0.008525017648935318, -0.02936837449669838, 0.04596136510372162, 0.09216998517513275, -0.009411952458322048, 0.01796538382768631, -0.04019607976078987, 0.0020740998443216085, -0.0014665477210655808, 0.03682323172688484, -0.026568736881017685, 0.00041806904482655227, -0.015156610868871212, 0.01842959225177765, -0.013267390429973602, 0.03601729869842529, 0.05258842185139656, -0.030433256179094315, -0.005948162637650967, 0.008578616194427013, -0.06344380229711533, -0.023457007482647896, 0.009507748298346996, 0.010337011888623238, 0.03380996733903885, -0.027306195348501205, -0.028912801295518875, 0.007742095272988081, -0.000596388999838382, -0.04885516315698624, -0.03687039017677307, -0.03620076924562454, 0.022500135004520416, 0.08143503218889236, 0.02415269799530506, -0.005710917990654707, -0.06074438616633415, 0.026992078870534897, -0.0018567959778010845, 0.032538291066884995, -0.000492205610498786, 0.010345405898988247, 0.04840750992298126, 0.03490251675248146, -0.025015071034431458, 0.08500412106513977, 0.0025419245939701796, -0.014077185653150082, -0.00987755786627531, -0.12586265802383423, -0.02043421007692814, -0.05792626366019249, 0.03794289752840996, -0.0056121270172297955, 0.027295343577861786, -0.0023685940541327, -0.021731391549110413, 0.029662447050213814, 0.0452219657599926, 0.006055846810340881, -0.001996601466089487, 0.005133728962391615, -0.02572430483996868, 0.010653444565832615, -0.05876747891306877, 0.0010834286222234368, 0.0005116800311952829, -0.013029313646256924, 0.00390223297290504, -0.05361867696046829, -0.04997541010379791, -0.04165472090244293, 0.04316912591457367, -0.02723110467195511, 0.04524405673146248, 0.0568302683532238, -0.020557254552841187, 0.052346862852573395, 0.005709170829504728, -0.022528160363435745, -0.0065169259905815125, -0.01577571965754032, -0.07657290250062943, 0.07418934255838394, 0.005331959575414658, -0.021736323833465576, 0.028277020901441574, -0.014420848339796066, -0.013893515802919865, -0.017747079953551292, 0.015690375119447708, -0.01663607731461525, -0.0040826816111803055, 0.02529144287109375, 0.018269050866365433, -0.024448027834296227, 0.022116655483841896, -0.003693045349791646, 0.06231512501835823, 0.029335137456655502, -0.014202211052179337, -0.020897941663861275, -0.026096472516655922, 0.016768384724855423, 0.026771079748868942, 0.0007478499901480973, -0.02149667963385582, -0.03734501823782921, -0.0007254185620695353, -0.0009734784252941608, 0.026928048580884933, 0.043223313987255096, -0.038246430456638336, 0.02533859945833683, -0.013832435011863708, 0.06713612377643585, -0.027656370773911476, 0.0619446225464344, -0.0653584823012352, 0.0052181691862642765, -0.010479169897735119, -0.05181974917650223, -0.0681648775935173, 0.001778468955308199, -0.07914811372756958, -0.021100059151649475, -0.05029730871319771, 0.00995273794978857, 0.04322464019060135, -0.006572387181222439, -0.04510430619120598, 0.07535577565431595, -0.003259234130382538, 0.03496021404862404, 0.030413322150707245, -0.06438591331243515, -0.03374519199132919, 0.05920664221048355, -0.06764711439609528, -0.03704482689499855, 0.010972029529511929, 0.00524901831522584, -0.019220052286982536, 0.038477908819913864, 0.022099141031503677, -0.0192270427942276, -0.04954369738698006, 0.04221782088279724, -0.015960438176989555, 0.0329919196665287, -0.00006245700205909088, 0.017671942710876465, -0.012501783668994904, -0.015285822562873363, 0.022647647187113762, -0.007121141534298658, 0.002251374302431941, -0.018893543630838394, -0.006446904968470335, 0.020523864775896072, 0.018416382372379303, -0.0010454009752720594, -0.00542116304859519, -0.010900544002652168, -0.0035595044028013945, -0.041672393679618835, -0.039507415145635605, -0.03224160522222519, 0.004013847094029188, -0.011703348718583584, 0.008402626030147076, -0.012603763490915298, -0.03549501672387123, 0.09598428010940552, 0.019303064793348312, 0.008454801514744759, -0.013955557718873024, -0.017492111772298813, -0.08458869904279709, 0.0448630191385746, 0.01956328935921192, -0.015803392976522446, 0.01039582397788763, 0.07608064264059067, 0.100143201649189, -0.005361398681998253, -0.00205968227237463, -0.014305058866739273, 0.0474100299179554, 0.025261471047997475, -0.012554307468235493, -0.035885728895664215, 0.028524793684482574, -0.04293401539325714, 0.022969115525484085, 0.031751878559589386, 0.012034950777888298, 0.0020701049361377954, 0.09128870069980621, 0.03168380632996559, 0.05376503989100456, -0.01779744029045105, -0.007870292291045189, -0.014934267848730087, -0.03617749363183975, -0.03173791989684105, 0.028999608010053635, 0.052457574754953384, 0.003711545839905739, -0.002862978493794799, 0.007464963011443615, 0.029704367741942406, -0.03720688074827194, 0.006850359495729208, 0.04725490137934685, 0.012156227603554726, 0.09089235216379166, -0.02751903049647808, -0.06508816033601761, 0.01394883543252945, -0.028591345995664597, 0.046808090060949326, -0.03360595926642418, -0.024196196347475052, 0.036455199122428894, -0.013997424393892288, -0.007983925752341747, -0.05890234187245369, -0.008510502055287361, 0.0407320037484169, 0.0073198010213673115, -0.04736744239926338, -0.030764741823077202, 0.01175198145210743, -0.005012607201933861, -0.004711344372481108, 0.025300078094005585, -0.021260065957903862, -0.040456004440784454, -0.012444674968719482, -0.005022459663450718, -0.018315881490707397, 0.031691282987594604, -0.023188836872577667, 0.003323986195027828, 0.06894271820783615, 0.055447787046432495, -0.019261179491877556, 0.013239648193120956, -0.014743827283382416, -0.00359662645496428, 0.05297768861055374, 0.05560515820980072, 0.00973998662084341, 0.004555343650281429, 0.013194490224123001, -0.04223425313830376, 0.012160771526396275, -0.005519004072993994, 0.026430785655975342, 0.025393204763531685, -0.021523889154195786, -0.011750634759664536, 0.059521038085222244, 0.012702462263405323, 0.02005508542060852, -0.05946385860443115, 0.01888399012386799, 0.03726032003760338, 0.029099712148308754, -0.009518682956695557, -0.04365697130560875, -0.034642305225133896, 0.02029312215745449, 0.025499654933810234, 0.06051144748926163, -0.010228332132101059, 0.004310700111091137, 0.0453934408724308, 0.04900207743048668, 0.09165608882904053, -0.04138747975230217, 0.02807985059916973, 0.03465597704052925, -0.022145891562104225, 0.016692927107214928, -0.024877291172742844, -0.03958569094538689, -0.016313448548316956, 0.0542617067694664, -0.017961397767066956, 0.022809991613030434, 0.008497980423271656, 0.007372214924544096, 0.05495040491223335, 0.012216905131936073, 0.005928898695856333, -0.019320795312523842, 0.0756707414984703, -0.044963762164115906, 0.0050343903712928295, 0.004663913045078516, 0.0040519931353628635, 0.008684665895998478, -0.07523100823163986, 0.03274168074131012, 0.018398050218820572, -0.04991963133215904, -0.004553706850856543, -0.011378753930330276, -0.004083465784788132, -0.006251547485589981, 0.00019007646187674254, 0.004153046756982803, -0.07237289845943451, -0.00211806851439178, 0.06634881347417831, -0.010361112654209137, 0.02308008261024952, -0.014106325805187225, 0.026427315548062325, -0.011541815474629402, -0.03233558312058449, -0.03799476474523544, 0.0796375572681427, 0.02927754819393158, -0.03394974395632744, -0.04384488984942436, -0.017603743821382523, -0.02070743218064308, -0.017817988991737366, 0.023076847195625305, -0.03469144180417061, 0.004551673773676157, 0.005994506645947695, -0.03745728358626366, -0.0227537639439106, -0.0015557761071249843, 0.012629608623683453, 0.0445413663983345, 0.007180704735219479, 0.0032496654894202948, -0.06008363515138626, 0.0072372606955468655, 0.02271105907857418, -0.03894966095685959, -0.008787398226559162, 0.02794978953897953, -0.01661074347794056, -0.015235846862196922, -0.04744410887360573, 0.04936053976416588, 0.010001891292631626, 0.040969450026750565, 0.005834367126226425, -0.03590914234519005, 0.007335504051297903, 0.005680895410478115, 0.006369761191308498, 0.06851755827665329, 0.005574987735599279, -0.04735420271754265, -0.07168864458799362, 0.007160104811191559, -0.004981279373168945, -0.0398697629570961, 0.00712260976433754, -0.001124175381846726, 0.035406485199928284, 0.04273185878992081, 0.038284074515104294, -0.08919738978147507, -0.04231065884232521, -0.024365335702896118, 0.04509483277797699, 0.003050064668059349, -0.007752071134746075, -0.004865626804530621, 0.008033565245568752, -0.016592051833868027, -0.012446901760995388, 0.03397750481963158, 0.01390387024730444, 0.03306116536259651, -0.010175531730055809, -0.007522954605519772, -0.005909499246627092, 0.0045197936706244946, 0.02574133314192295, -0.05015268921852112, 0.04076886922121048, -0.019372547045350075, -0.004544148221611977, 0.042050544172525406, -0.021061033010482788, -0.008323081769049168, -0.018329720944166183, -0.03450680524110794, 0.04193588346242905, -0.04066845774650574, -0.04917691648006439, -0.04266965761780739, 0.015051511116325855, -0.040769483894109726, -0.010060368105769157, -0.0500352680683136, 0.0528150275349617, -0.05151288956403732, -0.029698148369789124, -0.03162074089050293, 0.011480608023703098, 0.011066177859902382, -0.02033832296729088, -0.03931647911667824, 0.01375411357730627, -0.04714487865567207, -0.014398534782230854, 0.05798281356692314, 0.03258834406733513, 0.003979885019361973, -0.0007509203278459609, -0.0033767339773476124, 0.004454946145415306, -0.04982448369264603, -0.028189806267619133, 0.02250290848314762, 0.08733835071325302, 0.03284013643860817, 0.021931027993559837, -0.03920162841677666, 0.0006113721174187958, -0.03187603875994682, -0.005595411639660597, -0.02887597493827343, 0.02817261777818203, -0.02700633741915226, 0.01571066677570343, 0.009544494561851025, -0.03991131857037544, 0.003568463958799839, 0.05073485150933266, 0.014310630038380623, 0.001987393479794264, -0.045656781643629074, -0.041825536638498306, -0.01335481833666563 ]
<p>If my understanding of wormholes is correct, anything that moves into a wormhole can be transported from one region of space-time to another. Consider a situation where an object of mass $m$ in space at $(x_1,y_1,z_1)$ and time $t_1$ travels through a wormhole and appears at $(x_2,y_2,z_2)$ in a distant future time $t_2$. In between time $t_1$ and $t_2$, it seems this object of mass $m$ doesn't exist. Hence during this span of time, the total mass-energy of the universe should be less than before. Doesn't this violate law of conservation of mass-energy?</p>
g8416
[ 0.015198295004665852, 0.03788198530673981, 0.008539276197552681, -0.003490157425403595, -0.01322123408317566, 0.00964736845344305, 0.03716181218624115, 0.03498389944434166, -0.10642196983098984, 0.034052737057209015, 0.039381250739097595, -0.02605726383626461, -0.006618541199713945, 0.014302840456366539, -0.059129953384399414, -0.010978623293340206, 0.08058295398950577, -0.026834508404135704, 0.010883890092372894, 0.06445381045341492, -0.0038797948509454727, -0.010529043152928352, -0.009319515898823738, 0.0014307324308902025, -0.04093300178647041, -0.006290987133979797, 0.05239126458764076, 0.013750310987234116, -0.07369034737348557, -0.0016361703164875507, 0.10016860067844391, -0.01296259742230177, 0.017752671614289284, -0.06232934445142746, -0.005725869443267584, -0.008164608851075172, -0.012875556014478207, -0.029050786048173904, 0.0838259905576706, 0.017779001966118813, 0.004855538252741098, 0.007310160435736179, -0.03958175703883171, -0.029990211129188538, 0.048378586769104004, -0.007366372738033533, -0.027417035773396492, -0.012687196023762226, 0.01939396746456623, 0.006323215551674366, -0.026181312277913094, 0.05271616205573082, -0.005893731024116278, -0.020066970959305763, 0.0012953068362548947, -0.0734543427824974, 0.030402835458517075, -0.021549372002482414, 0.033985961228609085, 0.04443252459168434, 0.024499358609318733, 0.02377668395638466, 0.03930177539587021, 0.051943954080343246, 0.0826047956943512, 0.013766600750386715, -0.0922379195690155, 0.004446135368198156, 0.011749175377190113, -0.0048635900020599365, 0.03104044497013092, 0.024139009416103363, -0.051746297627687454, -0.04144419729709625, 0.015445196069777012, 0.027778614312410355, 0.042894698679447174, 0.039084505289793015, -0.04361376911401749, -0.013076364062726498, -0.07301811873912811, 0.033173494040966034, -0.0021131555549800396, 0.0457775741815567, 0.0734800472855568, 0.004007670562714338, -0.0482574887573719, 0.0010498333722352982, -0.039904166013002396, 0.03360705450177193, 0.001908496138639748, -0.0008948464528657496, 0.11611387878656387, 0.013916551135480404, -0.008707519620656967, 0.00665076170116663, -0.024692287668585777, 0.07653895765542984, -0.04386093467473984, -0.020632503554224968, 0.016541719436645508, 0.015659881755709648, 0.008006833493709564, -0.032728008925914764, -0.010111087933182716, -0.00897237192839384, -0.011525257490575314, 0.048136573284864426, 0.016462428495287895, -0.01623876765370369, 0.03934337571263313, -0.044750556349754333, -0.007299321237951517, 0.0190486591309309, -0.021839385852217674, -0.025283001363277435, 0.017701031640172005, -0.02307945489883423, 0.025307193398475647, 0.03188690170645714, -0.017524326220154762, 0.03030204400420189, -0.023823358118534088, 0.052663251757621765, -0.012946431525051594, -0.028570011258125305, -0.014716805890202522, -0.027099883183836937, 0.045989178121089935, 0.009521348401904106, -0.023200679570436478, 0.03069971688091755, 0.018367545679211617, 0.023187533020973206, -0.02732016146183014, -0.012817907147109509, -0.01722554862499237, -0.024287017062306404, -0.027706414461135864, 0.024799978360533714, 0.008331298828125, -0.019639624282717705, 0.07977379858493805, -0.02159195765852928, -0.03263296186923981, 0.03753947839140892, -0.06289514154195786, -0.001740492065437138, -0.010685008019208908, -0.014721754938364029, 0.0031174144241958857, 0.12274851649999619, -0.00025125217507593334, 0.003414884675294161, 0.03968909755349159, -0.012248468585312366, 0.010848252102732658, -0.02058742754161358, -0.017901143059134483, 0.006235477514564991, 0.04579798877239227, 0.02036217972636223, 0.1060759425163269, 0.019654296338558197, -0.041220325976610184, -0.009817516431212425, -0.011247849091887474, -0.0573221817612648, -0.02186264656484127, -0.02043670043349266, -0.04403112828731537, -0.01321096159517765, 0.02480614371597767, 0.05589859187602997, 0.011965902522206306, -0.005022988189011812, -0.011090955697000027, -0.031903889030218124, -0.021063005551695824, -0.037323370575904846, -0.01066379901021719, -0.06501217931509018, -0.0052865613251924515, 0.02597547322511673, 0.022065820172429085, -0.01375188585370779, 0.002955156145617366, 0.001139990403316915, -0.06432730704545975, 0.018052496016025543, 0.01269210409373045, -0.024456076323986053, -0.011324114166200161, 0.0005943221040070057, -0.0014188488712534308, -0.00040094603900797665, 0.03197586536407471, -0.030421951785683632, -0.033029548823833466, 0.02229302003979683, 0.01595075987279415, 0.024391591548919678, 0.040102411061525345, -0.03641308844089508, 0.0020822614897042513, 0.02950880117714405, -0.0585089735686779, 0.0352947860956192, 0.012538823299109936, -0.06777241080999374, 0.05487491190433502, -0.013611149042844772, -0.009716127067804337, 0.0031648967415094376, -0.03838735446333885, -0.025672821328043938, -0.032612692564725876, 0.03284304589033127, 0.010576700791716576, -0.03649091348052025, -0.06160946562886238, 0.013005404733121395, 0.07941968739032745, -0.061506014317274094, 0.023541344329714775, 0.0021811681799590588, -0.05279301479458809, -0.0429050512611866, -0.03617701679468155, 0.0290045365691185, -0.023709123954176903, 0.056390680372714996, -0.03199204429984093, -0.027592655271291733, 0.05576916038990021, -0.01310293935239315, 0.011789267882704735, 0.026053594425320625, -0.00029193429509177804, -0.020955726504325867, 0.017070084810256958, 0.030373483896255493, -0.033102355897426605, -0.011584874242544174, 0.09124395251274109, -0.06717831641435623, -0.00561873521655798, -0.023084798827767372, 0.0478542260825634, 0.00522979348897934, 0.04843854904174805, -0.04918632656335831, 0.010825085453689098, 0.06299217790365219, -0.02483571320772171, -0.04118458181619644, 0.00543853547424078, 0.025057975202798843, -0.06496760994195938, -0.04369916021823883, 0.022606661543250084, 0.017429884523153305, 0.04137807339429855, -0.017320038750767708, -0.037661127746105194, -0.03179560974240303, 0.01738438755273819, 0.038435280323028564, -0.010229264385998249, -0.0338345430791378, -0.06705349683761597, 0.003303392091766, -0.011108624748885632, 0.0681675523519516, 0.021702267229557037, -0.01920465938746929, -0.005841943901032209, -0.019304996356368065, 0.00489427987486124, 0.03189586102962494, -0.033878128975629807, -0.04013175517320633, -0.04767940193414688, -0.006427197251468897, -0.006108433473855257, -0.08373349159955978, -0.04248928651213646, 0.004466567188501358, 0.001557813724502921, -0.006285602692514658, 0.0017657856224104762, 0.04200201481580734, 0.034031305462121964, -0.00324891391210258, 0.06739687919616699, 0.05805746838450432, -0.005736633203923702, 0.0146236727014184, -0.031552452594041824, -0.016138480976223946, 0.00822656974196434, -0.022407440468668938, 0.0482647530734539, -0.003171933116391301, 0.006854044273495674, 0.0026633997913450003, -0.02855776622891426, -2.1824197915520926e-7, 0.011115998029708862, -0.009563995525240898, -0.02884182706475258, 0.04580862820148468, 0.020054612308740616, 0.005602745804935694, -0.006379909347742796, 0.011082075536251068, -0.02462943270802498, 0.005305877421051264, -0.030169544741511345, 0.01448260247707367, -0.012608793564140797, 0.09577106684446335, 0.002933504758402705, -0.0016441444167867303, 0.0071259899996221066, 0.044533275067806244, -0.061312273144721985, -0.023294921964406967, -0.07062721997499466, 0.03766182065010071, -0.01757974363863468, -0.03231869637966156, 0.01093272678554058, 0.007395781576633453, -0.016173630952835083, 0.01830081269145012, 0.02760043926537037, -0.01840481162071228, 0.025048362091183662, 0.04856913536787033, -0.02539706788957119, -0.004981792997568846, 0.04131079837679863, 0.018739942461252213, 0.0401494987308979, 0.06940774619579315, -0.04140773043036461, 0.07714268565177917, 0.015760082751512527, -0.007895402610301971, 0.041822485625743866, -0.013217520900070667, 0.05196359008550644, 0.025894109159708023, -0.04453124478459358, 0.024724572896957397, -0.05085405334830284, -0.004075591452419758, 0.05332861468195915, -0.00772747490555048, 0.03057904914021492, 0.007159649860113859, -0.006576670799404383, -0.03347495198249817, -0.017292359843850136, 0.0019477417226880789, 0.01308825146406889, 0.015002322383224964, 0.09405680000782013, 0.013289863243699074, 0.043017223477363586, 0.004719048272818327, 0.019193777814507484, 0.014901082962751389, 0.04011497274041176, -0.08403648436069489, 0.06986331939697266, -0.011037955991923809, -0.03080035001039505, 0.014728475362062454, 0.06805276870727539, -0.003399175126105547, -0.015630198642611504, 0.027490070089697838, 0.024705665186047554, 0.03650246560573578, -0.060131482779979706, -0.013654946349561214, 0.030134029686450958, -0.024233639240264893, 0.014119678176939487, -0.0429111048579216, 0.05727731063961983, -0.027464963495731354, 0.0352853462100029, 0.03669677674770355, -0.00960252434015274, -0.042830608785152435, 0.027228370308876038, -0.014255350455641747, 0.027017461135983467, 0.07322612404823303, -0.030639193952083588, -0.002467636251822114, 0.010304967872798443, 0.006020738277584314, 0.048405539244413376, -0.025762010365724564, 0.0006667810375802219, -0.017439162358641624, 0.00534247700124979, -0.02568018063902855, -0.05631643906235695, -0.025496874004602432, -0.0683036744594574, -0.03201335668563843, 0.018390754237771034, -0.06832407414913177, -0.002069647889584303, 0.03699112311005592, -0.017872914671897888, 0.03869754076004028, -0.06858597695827484, -0.04021814838051796, -0.05252401530742645, 0.06942036747932434, -0.019577573984861374, -0.03239312767982483, -0.05355659872293472, 0.04162878170609474, -0.025388335809111595, 0.04322320967912674, -0.05840779468417168, 0.017407039180397987, -0.06266798079013824, 0.031156161800026894, 0.013522036373615265, -0.00792979821562767, 0.014570560306310654, 0.03803471103310585, 0.10742543637752533, -0.018529552966356277, -0.01646295003592968, 0.02816864475607872, -0.02787168323993683, 0.056081373244524, -0.019477326422929764, -0.07511570304632187, 0.0029488971922546625, -0.02650008536875248, -0.04785122722387314, 0.04083038866519928, 0.04926439747214317, -0.030426546931266785, -0.016912125051021576, 0.010799686424434185, -0.05421716719865799, 0.026614340022206306, -0.008435511961579323, 0.022037813439965248, -0.10436712205410004, 0.05840786546468735, 0.007583586499094963, 0.018814509734511375, 0.038132451474666595, -0.026328017935156822, -0.00417825672775507, -0.013161913491785526, -0.042054008692502975, 0.026214666664600372, -0.0010548352729529142, 0.01792926713824272, -0.007690565660595894, 0.015530641190707684, -0.014092116616666317, 0.021694544702768326, -0.020655013620853424, -0.0304680485278368, -0.01172046922147274, -0.022538291290402412, -0.05919070169329643, 0.011286618188023567, 0.04436759650707245, 0.0681108608841896, -0.005002919118851423, 0.056499093770980835, -0.033971939235925674, 0.03521357476711273, 0.04257037863135338, 0.0392351970076561, -0.02573925070464611, 0.0012505706399679184, 0.025487763807177544, 0.018036341294646263, 0.04132360965013504, 0.024415750056505203, 0.05151602625846863, -0.013202019967138767, -0.07710632681846619, 0.005787818226963282, -0.05066458508372307, -0.0033978833816945553, 0.005603373982012272, -0.03773844242095947, 0.02582048624753952, 0.023845607414841652, -0.0022349583450704813, 0.026218729093670845, -0.05789755657315254, 0.023023253306746483, -0.020764963701367378, 0.015284078195691109, -0.040335219353437424, 0.024082740768790245, 0.052650533616542816, -0.07293674349784851, 0.03468646481633186, -0.02080005593597889, 0.023971866816282272, -0.017074190080165863, -0.010300264693796635, 0.02250237949192524, 0.04005615785717964, 0.05084887146949768, -0.012552482075989246, 0.06390565633773804, -0.01912648417055607, -0.03142761439085007, -0.014825661666691303, 0.02258267067372799, 0.05820497125387192, -0.0329371802508831, 0.02584386244416237, 0.009419132955372334, -0.0039968895725905895, -0.024802105501294136, -0.021045343950390816, 0.03315703943371773, 0.042990293353796005, -0.0182044617831707, -0.01931747794151306, -0.10111414641141891, 0.04377162829041481, 0.05447818338871002, 0.0247003473341465, 0.021612554788589478, -0.0358273945748806, -0.015257374383509159, -0.005613821092993021, -0.098636694252491, -0.0016234171343967319, 0.02689141035079956, -0.04516861215233803, 0.007053658366203308, -0.004757316317409277, 0.051341112703084946, 0.0173775814473629, 0.004268297925591469, -0.03582419827580452, -0.033660415560007095, -0.01892714388668537, 0.055236782878637314, -0.015666073188185692, -0.014573891647160053, 0.04975200816988945, -0.058835919946432114, -0.026332896202802658, -0.04628802835941315, 0.05788359045982361, -0.005799650214612484, -0.010138161480426788, 0.03795172646641731, -0.009339122101664543, -0.0015679512871429324, 0.002992113819345832, 0.0035094472113996744, -0.03844162076711655, -0.04699457809329033, -0.04897703602910042, -0.02333926223218441, 0.03035023622214794, -0.012596630491316319, 0.06720611453056335, -0.04155264422297478, -0.04103812202811241, 0.011605621315538883, -0.01725875958800316, -0.05219165235757828, 0.07050822675228119, -0.05049901083111763, -0.0018669333076104522, 0.02365364134311676, 0.013559723272919655, -0.013757575303316116, -0.010116007179021835, 0.008027033880352974, 0.012606850825250149, -0.027099013328552246, -0.04304763302206993, -0.004179490264505148, -0.02974858321249485, -0.06061653420329094, 0.08754067867994308, -0.008854224346578121, -0.02865746058523655, -0.003167499089613557, -0.10811858624219894, 0.037187255918979645, -0.0009452466038055718, -0.013269749470055103, 0.0444309301674366, 0.033545996993780136, -0.031720470637083054, 0.0032137951347976923, -0.013606606982648373, 0.006385702174156904, -0.05346387252211571, 0.007687343750149012, -0.023762226104736328, -0.00863598007708788, -0.006452043075114489, 0.020128555595874786, -0.01034991629421711, -0.032743219286203384, 0.04113512858748436, 0.03338922932744026, -0.04675965756177902, 0.0451231375336647, 0.032901179045438766, 0.02800443023443222, -0.034157220274209976, -0.007810256909579039, -0.02763320319354534, 0.0015279700746759772, 0.03197671100497246, 0.015574718825519085, -0.02743365429341793, 0.008765876293182373, -0.027374889701604843, -0.00039940918213687837, 0.038108255714178085, -0.038194332271814346, 0.039829883724451065, 0.025474531576037407, -0.025181708857417107, 0.019287358969449997, 0.07043889164924622, 0.06718506664037704, -0.05104375630617142, -0.07047462463378906, 0.04714203253388405, -0.03547156974673271, -0.036408647894859314, -0.02423574961721897, -0.0031358024571090937, -0.055777356028556824, -0.06970365345478058, 0.0025896169245243073, 0.020767413079738617, -0.07577673345804214, -0.004501421004533768, -0.018547752872109413, 0.016489271074533463, 0.04309524595737457, 0.028772303834557533, 0.10127774626016617, 0.02426932193338871, -0.052824102342128754, 0.010006816126406193, -0.0320778414607048, -0.022374525666236877, 0.0335177443921566, -0.042002227157354355, -0.03856399655342102, -0.031742483377456665, -0.031135788187384605, 0.034755975008010864, 0.018602699041366577, 0.01729811169207096, 0.011114011518657207, 0.005543828941881657, 0.006534154526889324, -0.03595656529068947, 0.02855619601905346, -0.014727290719747543, 0.03365330770611763, -0.01469454076141119, -0.01680816523730755, -0.031749412417411804, -0.009403872303664684, 0.008650591596961021, -0.008117587305605412, 0.03869083523750305, -0.022518878802657127, 0.006025665905326605, -0.01302019041031599, 0.056702304631471634, 0.03976743295788765, -0.002593145938590169, -0.05377578362822533, 0.006298528052866459, 0.009010186418890953, 0.0007770558004267514, 0.012255881913006306, 0.004127697553485632, 0.052938029170036316, -0.007369445636868477, -0.03261016309261322, -0.02543698623776436, 0.026832157745957375, 0.05474678426980972, 0.01882910169661045, 0.009793444536626339, -0.010619585402309895, 0.025224953889846802, -0.019105562940239906, -0.03346778079867363, -0.01788811758160591, -0.025393057614564896, -0.042100463062524796, 0.0075779748149216175, -0.005349962972104549, -0.01329098641872406, -0.057725176215171814, -0.012588538229465485, 0.00928738247603178, -0.023138996213674545, -0.018391704186797142, -0.025892527773976326, -0.03314104303717613, -0.019138973206281662, 0.000017496007785666734, -0.06435508280992508, 0.03181106224656105, -0.00068963214289397, 0.03267822414636612, 0.022390788421034813, 0.009494121186435223, 0.011398297734558582, -0.005003765691071749, 0.008931283839046955, -0.07292996346950531, -0.03120894357562065, 0.00800824724137783, -0.0035269856452941895, -0.01148669607937336, -0.021391088142991066, -0.007503088563680649, 0.04871116951107979, -0.001291662803851068, 0.015932034701108932, 0.01936858892440796, -0.018759459257125854, 0.007313916459679604, 0.04074086621403694, -0.034057099372148514, 0.04706190899014473, -0.05365753918886185, -0.07934092730283737, 0.023371407762169838, -0.047109995037317276, 0.02935769595205784, -0.012122128158807755, -0.04331544041633606, -0.030552048236131668, -0.03251901641488075, 0.03601270914077759, -0.010798762552440166 ]
<p>I know I should have listened to my teacher in physics class but I didn't. I need help on a thing I am trying to do for a game.</p> <p>I want to be able to calculate Gravity pushing down on a object over a certain amount of time. (I want the object to slow down to a stop and then go back down due to gravity).</p> <p>I've been looking on the internet and I guess I'm not using the right search terms. So I am hoping that this fine community can help me.</p> <p>*The object(Player) is only moving upward. The Player is not moving forward or anything. Just Up</p> <p>Given the initial velocity, how do I compute the motion (position, velocity) of the object as a function of time?</p>
g8417
[ 0.0582297183573246, 0.04727325960993767, -0.0029123187996447086, -0.022291259840130806, -0.001329635619185865, 0.006568502634763718, 0.06669522076845169, 0.004211668390780687, -0.08522240817546844, 0.018108047544956207, -0.005626413505524397, 0.007434871047735214, -0.007350493688136339, -0.01727980189025402, -0.0019407019717618823, -0.0045213839039206505, 0.058673374354839325, 0.015439524315297604, 0.026828305795788765, 0.014928111806511879, 0.09246517717838287, -0.00017959058459382504, 0.015353641472756863, -0.011019385419785976, -0.02066788263618946, -0.01920057088136673, 0.02287238836288452, 0.008584760129451752, -0.052463315427303314, 0.03796485811471939, -0.016076069325208664, 0.04664018377661705, -0.00456317700445652, -0.03485686704516411, -0.013548917137086391, 0.002089973771944642, 0.027214746922254562, -0.032634079456329346, 0.023529600352048874, -0.007985034957528114, -0.04288668558001518, -0.006434457376599312, 0.031682778149843216, 0.024793770164251328, 0.03002728335559368, -0.0126554686576128, 0.0021565137431025505, -0.009836792945861816, -0.04586472362279892, -0.03771095350384712, -0.03475456312298775, 0.020687656477093697, -0.03741960600018501, -0.04697134345769882, -0.06422646343708038, -0.0026444813702255487, -0.011194286867976189, -0.038125697523355484, 0.04172666743397713, 0.033449042588472366, 0.0027136732824146748, 0.00021638655744027346, 0.014182738959789276, -0.0420641154050827, 0.03947313874959946, 0.005672804545611143, -0.04706328362226486, -0.06557278335094452, -0.03206591308116913, -0.031131545081734657, 0.031759269535541534, -0.002412158763036132, 0.005498285870999098, -0.02162410318851471, -0.025299623608589172, 0.0192436333745718, -0.008274022489786148, -0.0012417720863595605, 0.038655634969472885, -0.018031971529126167, -0.0029848027043044567, 0.0037285732105374336, 0.028137950226664543, -0.01636495254933834, 0.05170920491218567, -0.039542607963085175, -0.011862588115036488, 0.0624273382127285, -0.019218308851122856, -0.0329446904361248, 0.03060765564441681, -0.01327505148947239, 0.03996523842215538, 0.027916336432099342, 0.02167401649057865, -0.023478973656892776, -0.0733695775270462, 0.053337324410676956, 0.0392451174557209, 0.015549542382359505, -0.030923983082175255, -0.004320735111832619, 0.02777571603655815, -0.02475297637283802, 0.05337504670023918, -0.0454232357442379, 0.004304828122258186, 0.00986190140247345, -0.029062580317258835, -0.045574087649583817, 0.02635008841753006, -0.033117420971393585, -0.023046918213367462, -0.0742436945438385, -0.04638732969760895, -0.051313988864421844, 0.028591610491275787, 0.056606367230415344, -0.02145320363342762, 0.015098944306373596, -0.013627687469124794, 0.03567476570606232, 0.012556181289255619, 0.06019255146384239, -0.0031243537086993456, -0.0038242212031036615, -0.030896076932549477, -0.028087632730603218, 0.020439498126506805, 0.021064141765236855, 0.023784806951880455, 0.022339172661304474, 0.03587229177355766, 0.032074060291051865, -0.03633830323815346, 0.030022811144590378, -0.01858397014439106, 0.021580863744020462, -0.005484140943735838, 0.06021042913198471, 0.03474804759025574, -0.05119289085268974, 0.017352227121591568, -0.028112296015024185, -0.036462243646383286, 0.02983981743454933, 0.0186245609074831, -0.023121491074562073, 0.017938271164894104, -0.02140066772699356, 0.05542510747909546, 0.08470465242862701, -0.0008677143487147987, -0.03061247617006302, 0.0910697653889656, -0.03501077741384506, 0.03262055292725563, 0.06340881437063217, 0.021238746121525764, -0.009549134410917759, 0.06366347521543503, 0.019059166312217712, 0.03442955017089844, -0.0015109962550923228, -0.07499095797538757, 0.04884048178792, -0.015458404086530209, -0.024200493469834328, -0.027088765054941177, -0.055133283138275146, -0.028637036681175232, -0.041392840445041656, 0.0019828437361866236, 0.03054986335337162, -0.01827993243932724, 0.025000112131237984, 0.03479330614209175, 0.01731538586318493, -0.05538720265030861, 0.020648671314120293, 0.01788451336324215, -0.045937955379486084, 0.05161096155643463, 0.015047844499349594, -0.007912147790193558, -0.0024364148266613483, 0.03302568569779396, 0.022159753367304802, -0.0663469061255455, 0.00967563595622778, -0.03875797241926193, -0.020238414406776428, 0.06472448259592056, -0.0285556148737669, -0.014485122635960579, -0.03378193452954292, 0.07340236008167267, -0.01250497717410326, -0.05415632203221321, 0.03482693061232567, 0.0025282606948167086, 0.01718921959400177, 0.07551635801792145, 0.002822368871420622, 0.02958105504512787, 0.004529705736786127, -0.012179254554212093, 0.023347677662968636, -0.030115419998764992, -0.011403579264879227, 0.09057404100894928, -0.016936756670475006, 0.05847594514489174, -0.027603693306446075, -0.010176791809499264, 0.0014580127317458391, -0.013324127532541752, -0.030879052355885506, -0.027553733438253403, 0.02541228011250496, -0.019553381949663162, -0.0258565004914999, 0.03393140062689781, 0.008641493506729603, -0.045405030250549316, -0.008535676635801792, 0.0011704848147928715, -0.002633381634950638, 0.0005746104870922863, -0.029228292405605316, -0.015514547005295753, 0.05594053119421005, -0.03696414828300476, -0.0506148487329483, 0.10899714380502701, 0.02234005741775036, -0.028455650433897972, 0.05014899745583534, 0.05111375451087952, 0.0011746968375518918, -0.041874323040246964, 0.00009431947546545416, 0.056092724204063416, -0.08985728770494461, 0.05458315089344978, -0.087481789290905, 0.048592083156108856, -0.007072668522596359, -0.00967294629663229, -0.02927207015454769, -0.024118036031723022, -0.07907763123512268, -0.045362282544374466, 0.042454399168491364, -0.005096780601888895, 0.010494827292859554, -0.0329318605363369, 0.04953715577721596, -0.039190664887428284, -0.06101314350962639, 0.05311060696840286, 0.024504831060767174, -0.013130046427249908, -0.009915146976709366, -0.035037145018577576, -0.01703854836523533, -0.06527193635702133, 0.0038023998495191336, 0.042203277349472046, 0.033978357911109924, -0.0002435883943689987, -0.010428755544126034, -0.0010418896563351154, 0.03194848820567131, -0.007605487946420908, -0.06251752376556396, 0.04702259227633476, 0.03080889768898487, 0.04393911734223366, 0.001371982740238309, 0.0008819674840196967, -0.03774181753396988, -0.034265387803316116, 0.02234570123255253, 0.01130402646958828, -0.05840831995010376, 0.03600171580910683, 0.041773196309804916, -0.030730385333299637, -0.02922351285815239, 0.036365631967782974, 0.08465608954429626, 0.0038181638810783625, 0.04406832158565521, -0.008149865083396435, 0.04971038177609444, -0.005217021331191063, -0.012602679431438446, -0.002567284507676959, 0.017594769597053528, -0.021196747198700905, -0.059910502284765244, 0.014729448594152927, -0.0013535631587728858, 0.027724379673600197, -0.01940963789820671, 0.030227266252040863, -0.012946982868015766, -0.027218496426939964, -0.01482513640075922, 0.013267437927424908, 0.08782914280891418, -0.04450053721666336, -0.011689264327287674, -0.029541723430156708, -0.040740225464105606, 0.0011352041037753224, -0.00014424463734030724, -0.021050991490483284, -0.007761114276945591, -0.04242417961359024, -0.08653372526168823, -0.010279658250510693, 0.01619042083621025, 0.018488094210624695, 0.03515803441405296, -0.016785167157649994, 0.02928989939391613, -0.023849014192819595, -0.031104525551199913, 0.04383058473467827, 0.007944273762404919, 0.016098015010356903, 0.006342181470245123, -0.014918391592800617, -0.008856852538883686, 0.023702887818217278, -0.020105142146348953, 0.004736024420708418, -0.01318802498281002, -0.005389314144849777, -0.0034918987657874823, -0.02264108508825302, 0.014844633638858795, 0.027112459763884544, 0.02504965104162693, -0.02841906063258648, 0.08685832470655441, -0.048730868846178055, 0.003683107439428568, 0.027827877551317215, 0.0108706746250391, 0.026698710396885872, -0.037706293165683746, 0.005405333824455738, 0.05788354203104973, 0.05464399605989456, -0.005016176961362362, -0.05200307443737984, 0.02001509815454483, -0.018278833478689194, -0.0012224199017509818, -0.018555080518126488, 0.0945163294672966, 0.024844171479344368, -0.00999140739440918, 0.005710748489946127, 0.049123041331768036, -0.010331608355045319, 0.014788608066737652, 0.03622042387723923, -0.004080993589013815, 0.008871176280081272, -0.03694940358400345, -0.001894195331260562, -0.08474384993314743, 0.048858966678380966, -0.02807471714913845, 0.002005703281611204, -0.011276119388639927, 0.10029654204845428, 0.053444623947143555, 0.07109326869249344, -0.005874332040548325, 0.0409039705991745, 0.06300770491361618, -0.04843489080667496, 0.006647244095802307, 0.09664022922515869, -0.031669627875089645, 0.028209444135427475, -0.06383825838565826, -0.03471625968813896, 0.012584291398525238, 0.0406615175306797, 0.012683650478720665, 0.00635779183357954, -0.008372098207473755, -0.0253949835896492, -0.06461390852928162, -0.029848666861653328, 0.03269125893712044, -0.009777520783245564, 0.009939945302903652, -0.028151456266641617, 0.01076249685138464, 0.11162253469228745, -0.020134424790740013, -0.020396843552589417, 0.014022084884345531, -0.02656000666320324, -0.024190053343772888, -0.022008828818798065, -0.045829400420188904, -0.06378762423992157, 0.020097393542528152, 0.04271697998046875, 0.025851663202047348, -0.0046212379820644855, 0.021454066038131714, 0.03538968414068222, 0.052437543869018555, 0.032066088169813156, -0.06088831275701523, -0.09085710346698761, 0.06056021526455879, 0.006210654508322477, 0.012986003421247005, 0.007603585720062256, -0.00988316722214222, 0.008014273829758167, 0.037696994841098785, 0.03330356627702713, 0.01603046804666519, -0.02066117152571678, 0.05316733568906784, 0.10377892106771469, 0.012398977763950825, 0.03667711466550827, 0.008932392112910748, -0.00768762594088912, 0.026444554328918457, -0.005119767971336842, -0.007591718807816505, -0.028052041307091713, 0.07147379964590073, -0.04772701859474182, -0.06711149960756302, -0.0014853884931653738, -0.019512232393026352, -0.0009449978824704885, 0.062384288758039474, -0.043513406068086624, -0.0013522369554266334, -0.03145482391119003, 0.061426300555467606, -0.005375685170292854, -0.033241383731365204, -0.016044333577156067, -0.01358763687312603, 0.013323139399290085, -0.01879381760954857, -0.026186363771557808, -0.031182995066046715, -0.03591535612940788, -0.0175598356872797, 0.02629629708826542, 0.009461711160838604, 0.011966132558882236, 0.013614436611533165, 0.0029190510977059603, -0.028957899659872055, -0.003870529355481267, 0.05305371806025505, 0.0016405928181484342, 0.052324697375297546, -0.02529618702828884, 0.016742784529924393, 0.08431490510702133, -0.021340731531381607, -0.041148025542497635, 0.004123490769416094, 0.011824154295027256, -0.027436845004558563, -0.05486559495329857, -0.046239156275987625, -0.021321620792150497, 0.010213317349553108, 0.01800108142197132, -0.010021034628152847, 0.005717867985367775, -0.03390892595052719, 0.04480138048529625, -0.007755928672850132, -0.08587469905614853, -0.02911575324833393, -0.0018846712773665786, -0.004810789134353399, -0.019410476088523865, -0.03670038655400276, -0.0726202130317688, -0.045380666851997375, -0.015957403928041458, 0.0016844162018969655, -0.01243376825004816, 0.02620258368551731, 0.015955913811922073, 0.010755052790045738, -0.056546762585639954, 0.0732681155204773, 0.04193713143467903, 0.06185149773955345, 0.013515426777303219, 0.0006167080136947334, -0.03150789067149162, -0.036005910485982895, 0.04021088033914566, -0.01236398983746767, -0.04343627765774727, 0.0037549904081970453, 0.03421661630272865, -0.00475977873429656, 0.03393993154168129, -0.00680713402107358, 0.042151566594839096, 0.003927018493413925, -0.05051145702600479, -0.01743541844189167, 0.0170473400503397, 0.02435174770653248, 0.011215345934033394, -0.046375177800655365, -0.04232873022556305, -0.0407441146671772, -0.08776646852493286, 0.023761484771966934, 0.03719359263777733, -0.04821821674704552, 0.040225379168987274, -0.019132565706968307, -0.04928671941161156, -0.019807802513241768, -0.01387694664299488, 0.00012115768186049536, -0.08116346597671509, 0.022138945758342743, -0.05684225633740425, 0.012086817063391209, 0.021602444350719452, -0.044749386608600616, -0.04955942928791046, 0.04069521650671959, -0.008991977199912071, -0.02720068022608757, -0.009727741591632366, 0.01382118184119463, -0.003070646896958351, -0.01543076429516077, 0.015074826776981354, -0.024349531158804893, 0.022726861760020256, -0.009486823342740536, 0.014513270929455757, 0.005865504499524832, 0.0436411090195179, -0.01839793287217617, 0.007342566270381212, -0.022747617214918137, 0.033342644572257996, -0.01766011491417885, -0.0538211390376091, 0.01885768212378025, -0.05266180261969566, 0.004822073504328728, 0.002598101506009698, 0.0570705309510231, 0.009989134036004543, -0.03288897126913071, -0.048771414905786514, 0.0073333000764250755, 0.006646248046308756, 0.04985843226313591, 0.003182456362992525, -0.03310693800449371, -0.031328875571489334, 0.019741181284189224, -0.04987752065062523, -0.024265028536319733, 0.001120293396525085, -0.022745788097381592, -0.00023006068659015, 0.007261567749083042, -0.05565241724252701, -0.05006789416074753, -0.023511124774813652, -0.040004078298807144, -0.009900184348225594, -0.08618628978729248, 0.00209756288677454, 0.03323705866932869, -0.02015496790409088, -0.010874118655920029, -0.0018861816497519612, -0.07982881367206573, -0.0009770875331014395, 0.05944666266441345, -0.026586856693029404, -0.0015458008274435997, 0.05700867250561714, -0.08289220929145813, -0.027155311778187752, 0.02413707599043846, 0.003923033829778433, 0.055212464183568954, 0.008037587627768517, -0.010419841855764389, 0.04307407885789871, -0.006722071673721075, 0.018505843356251717, -0.060857292264699936, 0.04881672188639641, 0.0059066168032586575, 0.01587008312344551, -0.04703940451145172, 0.04407000541687012, -0.0291589368134737, -0.03370833396911621, -0.018652185797691345, 0.031186455860733986, -0.02361813560128212, 0.023192912340164185, -0.02552959881722927, -0.014521623030304909, -0.0002435806964058429, 0.018999233841896057, 0.05427725985646248, -0.0022745304740965366, 0.08964501321315765, -0.01828049123287201, 0.07841403037309647, 0.04831153526902199, -0.023529207333922386, -0.047824278473854065, 0.058737389743328094, -0.0476083941757679, -0.006852069403976202, 0.025337614119052887, -0.026475979015231133, -0.06507603079080582, -0.03844023495912552, -0.010699017904698849, -0.016702106222510338, 0.022341953590512276, 0.04804990068078041, -0.06398730725049973, -0.0033455942757427692, 0.07031267881393433, -0.012478531338274479, 0.028110003098845482, -0.02459488809108734, -0.005201647058129311, -0.05773851275444031, -0.055683840066194534, 0.02125733532011509, -0.012494930066168308, 0.07545892894268036, -0.031186603009700775, 0.002729806350544095, 0.01896141842007637, -0.06509704887866974, -0.03103110007941723, -0.019747672602534294, -0.05157987400889397, 0.05412622168660164, 0.0040741367265582085, 0.034279707819223404, -0.01638478972017765, 0.012506832368671894, -0.05139341205358505, -0.02117547020316124, -0.024205772206187248, 0.04684992879629135, -0.04151570424437523, -0.01669793576002121, 0.01606951653957367, 0.043141257017850876, 0.0037814744282513857, 0.005526977125555277, -0.013527198694646358, -0.00323879043571651, -0.018803562968969345, 0.08270658552646637, -0.005518803372979164, -0.056532565504312515, 0.026467451825737953, -0.017536696046590805, -0.02249249629676342, 0.006841770373284817, 0.03649519383907318, -0.00005067874371889047, 0.019297512248158455, -0.020877746865153313, 0.010849674232304096, 0.006150994449853897, -0.050644032657146454, 0.01165833044797182, -0.0482378825545311, -0.026548229157924652, -0.012317411601543427, -0.0011374133173376322, 0.019080407917499542, 0.01835368201136589, -0.00834533292800188, -0.006635917350649834, 0.008670548908412457, 0.05653604492545128, -0.02040938287973404, 0.002953398274257779, -0.015592946670949459, -0.010528447106480598, 0.008309489116072655, 0.00768907368183136, 0.0317462719976902, -0.060931798070669174, -0.01835922710597515, -0.0007905236561782658, -0.01877654902637005, 0.003091489663347602, 0.0049530393444001675, -0.03284476697444916, 0.009121086448431015, -0.049783140420913696, -0.00013132960884831846, 0.034878384321928024, 0.010572455823421478, 0.045969799160957336, -0.0489237904548645, -0.03623572736978531, 0.02716836892068386, 0.04110823571681976, -0.003973937593400478, -0.03251456841826439, -0.018337612971663475, 0.021823255345225334, 0.0455133430659771, -0.02426968328654766, 0.009924396872520447, 0.05021733418107033, 0.057754725217819214, 0.006552824284881353, 0.07852230221033096, 0.07117927074432373, 0.006212691776454449, -0.006841396447271109, -0.011420562863349915, 0.000794531311839819, -0.0421573668718338, 0.022476401180028915, -0.04469592869281769, -0.07277936488389969, -0.01788732223212719, 0.01449637208133936, 0.01901361346244812, -0.007549629546701908, 0.021100718528032303, -0.02339019440114498, 0.004128601402044296, 0.030651280656456947 ]
<p>I was drawing a diagram and trying to resolve all the forces. It seems to me that because of gravity, centrifugal force will produce a sort of "dragging" motion along the surface of the earth. The centrifugal force is quite small (I got around 2.5 N at the equator). This force is easily neutralized by friction. Is this right?</p> <p>EDIT: I did not consider any complexities that may arise due to revolution, I just considered rotation.</p>
g18
[ 0.05145763233304024, 0.09159182012081146, -0.012370619922876358, 0.04010444134473801, 0.04403946176171303, 0.07497846335172653, 0.077316515147686, 0.007725154515355825, -0.02282218635082245, -0.07011735439300537, -0.005785495042800903, -0.03265652805566788, 0.01939377188682556, 0.009511839598417282, 0.03512909635901451, -0.0015579380560666323, 0.026947876438498497, -0.022301143035292625, 0.03601294755935669, 0.08622952550649643, 0.040619682520627975, 0.009318004362285137, 0.02131541445851326, -0.0548710897564888, -0.011722339317202568, 0.009045956656336784, -0.0199087243527174, -0.016422133892774582, -0.03342809900641441, -0.004246811848133802, 0.002103156875818968, 0.02654419280588627, 0.001165701076388359, -0.076392762362957, -0.06848249584436417, -0.040383197367191315, -0.016536546871066093, -0.03598302975296974, 0.05869966372847557, -0.03897160291671753, 0.04170537367463112, 0.01806720905005932, 0.0026646696496754885, 0.0022833251859992743, 0.005187437869608402, -0.03597118332982063, 0.00165688362903893, 0.0013316227123141289, 0.0008094304939731956, 0.005680522415786982, -0.0732477679848671, -0.007846247404813766, 0.015559053048491478, -0.008895409293472767, -0.039281848818063736, 0.03800376504659653, 0.06045743450522423, -0.02451956830918789, -0.024039650335907936, 0.011449102312326431, -0.019295960664749146, -0.011567190289497375, -0.00941387377679348, -0.020229537039995193, 0.023100905120372772, -0.019348179921507835, -0.009125865995883942, -0.013881000690162182, 0.055522557348012924, 0.024875011295080185, -0.019164038822054863, -0.008626382797956467, 0.01783318631350994, -0.035742126405239105, -0.06080060824751854, 0.08566559106111526, 0.01680867001414299, 0.008475121110677719, 0.019034728407859802, -0.03494153544306755, -0.03997008875012398, 0.030190644785761833, -0.02557588554918766, -0.0051088109612464905, 0.10956791043281555, -0.041225530207157135, -0.0176194217056036, -0.0072990357875823975, 0.013462201692163944, 0.045549798756837845, 0.01732432283461094, -0.005217640660703182, 0.062190212309360504, 0.009341582655906677, -0.037719305604696274, -0.054126497358083725, 0.00009223630331689492, 0.09200141578912735, -0.012354657985270023, 0.00672928849235177, -0.05397782847285271, -0.018227187916636467, 0.010648826137185097, -0.06880065053701401, 0.06981590390205383, -0.02574378065764904, 0.027543898671865463, 0.011229418218135834, 0.004565819166600704, -0.05357709527015686, 0.005927331745624542, -0.027618274092674255, -0.04802878573536873, 0.01563889905810356, 0.08455310016870499, -0.07392087578773499, 0.007224730681627989, 0.009011262096464634, 0.021967332810163498, 0.07075437903404236, -0.0023803345393389463, 0.046565115451812744, 0.009287772700190544, 0.0453869104385376, -0.03452131152153015, -0.021068761125206947, 0.0676928386092186, -0.007093554362654686, 0.02313939481973648, 0.011418323963880539, -0.00029091836768202484, 0.040709011256694794, -0.02326422557234764, -0.0017988241743296385, 0.04700978845357895, -0.015025072731077671, -0.10052815824747086, -0.0007005230872891843, -0.026751888915896416, 0.004860769957304001, 0.044927000999450684, -0.03601839020848274, 0.011726087890565395, -0.010789444670081139, -0.005249647423624992, 0.03604593873023987, -0.01489985641092062, 0.025923293083906174, 0.05828044191002846, -0.025870325043797493, -0.012942290864884853, 0.03678780049085617, 0.021834446117281914, -0.05977366119623184, 0.06061287596821785, 0.009486793540418148, 0.04459838196635246, 0.015570957213640213, -0.04380473122000694, -0.03681741654872894, 0.058840468525886536, -0.04048643261194229, 0.037130601704120636, 0.008201242424547672, 0.0005502253770828247, 0.015573001466691494, -0.061241209506988525, -0.06437293440103531, -0.0025956337340176105, 0.02364632673561573, -0.0608505979180336, 0.01081632636487484, 0.034692805260419846, 0.07858382165431976, 0.0016085943207144737, -0.0054604965262115, 0.0205644853413105, 0.01512916199862957, -0.008067190647125244, -0.00834606308490038, 0.010793701745569706, -0.002359928097575903, -0.015513340942561626, 0.02621152065694332, 0.011678214184939861, -0.05333394929766655, 0.023296507075428963, -0.003159594489261508, -0.02490128017961979, -0.002308616414666176, 0.017937013879418373, -0.01035972498357296, -0.01993163302540779, -0.012783963233232498, 0.002011180156841874, 0.018580107018351555, -0.04322361573576927, -0.04794638976454735, -0.03223627433180809, 0.013547949492931366, -0.004103123210370541, 0.022329183295369148, 0.028972191736102104, -0.029355552047491074, -0.03522082418203354, -0.01152757741510868, 0.019506137818098068, 0.0013940924545750022, 0.03419876471161842, -0.007455010898411274, 0.03564226254820824, 0.019399968907237053, 0.023936109617352486, -0.004934917204082012, -0.09658057242631912, 0.009107005782425404, 0.04174725338816643, 0.020913152024149895, -0.005132521037012339, 0.022270673885941505, 0.016914350911974907, -0.022230708971619606, -0.020773056894540787, 0.032883044332265854, -0.01628144271671772, 0.016337022185325623, -0.0430801697075367, -0.020225193351507187, -0.023428238928318024, 0.027149168774485588, -0.0008903418201953173, -0.034430574625730515, 0.044934678822755814, 0.00882406160235405, 0.03845754265785217, 0.037683431059122086, 0.012061175890266895, -0.025750961154699326, -0.039365388453006744, -0.008198420517146587, -0.0028010020032525063, -0.05026775225996971, 0.021074645221233368, -0.06167171150445938, 0.06208642199635506, -0.05775616690516472, 0.05299181118607521, 0.036353699862957, 0.04027291759848595, -0.0013174692867323756, 0.09328493475914001, -0.05510653555393219, -0.03186718374490738, 0.06549704819917679, 0.018600381910800934, -0.01858408749103546, -0.05063527077436447, 0.08117341995239258, -0.01332109421491623, -0.004681816790252924, -0.019080407917499542, -0.010474622249603271, 0.012811883352696896, 0.09251876920461655, -0.04005345702171326, -0.0421178825199604, -0.0672534853219986, -0.001968438271433115, 0.003143235109746456, 0.04867396503686905, -0.04503948986530304, -0.015766220167279243, -0.019023893401026726, 0.09060300141572952, -0.026132769882678986, -0.025158431380987167, 0.022477513179183006, -0.009833434596657753, -0.02982090413570404, 0.017336405813694, 0.03324372321367264, 0.026369737461209297, 0.014856069348752499, 0.012667766772210598, 0.04564746469259262, 0.012480193749070168, -0.03486034274101257, 0.012041476555168629, -0.0386432409286499, 0.015778332948684692, -0.02140284702181816, 0.00007332846143981442, 0.09359848499298096, 0.008564084768295288, -0.004407974425703287, 0.034242305904626846, 0.04121587797999382, -0.05283554270863533, -0.050468627363443375, -0.002942169550806284, 0.027595851570367813, -0.05710580199956894, 0.03989114984869957, 0.06958946585655212, -0.07119204103946686, 0.03689280152320862, 0.03080715984106064, -0.08992677181959152, -0.03565949201583862, -0.0009231796720996499, -0.07760994136333466, 0.07072346657514572, -0.020086055621504784, -0.02753419615328312, -0.07610759884119034, -0.02358964830636978, 0.009303472936153412, -0.027858655899763107, 0.040467388927936554, 0.05791538953781128, -0.0539584644138813, -0.08383117616176605, -0.017936989665031433, -0.03290777653455734, 0.011749482713639736, 0.054682835936546326, -0.08588960766792297, -0.013112097978591919, -0.013049200177192688, -0.04237386956810951, 0.05972237512469292, 0.03482593595981598, -0.0749565064907074, 0.03703295812010765, -0.04307439550757408, 0.014426929876208305, 0.02843819372355938, -0.009738985449075699, -0.0064666857942938805, 0.048392750322818756, -0.016334688290953636, -0.05247390270233154, -0.040417563170194626, -0.04978072643280029, -0.011983899399638176, 0.059430088847875595, -0.02034059539437294, -0.010118772275745869, -0.015024025924503803, 0.005438277497887611, 0.06040867045521736, -0.06137307360768318, 0.03448748216032982, -0.032204676419496536, 0.0501263327896595, 0.040541548281908035, 0.001996117876842618, -0.014599191024899483, -0.061483874917030334, 0.016673685982823372, -0.031718458980321884, -0.010367423295974731, -0.03643340617418289, 0.044885940849781036, 0.024110961705446243, -0.0023212102241814137, -0.009377547539770603, 0.03592391684651375, -0.05841943621635437, -0.03924908861517906, 0.006374565418809652, 0.006962439976632595, -0.02130148746073246, 0.039888180792331696, 0.04274248704314232, -0.0564139187335968, 0.056574515998363495, 0.0012069947551935911, 0.015534752979874611, 0.0026848025154322386, 0.047945789992809296, -0.0090967221185565, -0.038580525666475296, 0.01619088277220726, 0.007139770779758692, 0.03604615107178688, -0.052967313677072525, 0.025203073397278786, 0.011709636077284813, -0.020707042887806892, -0.013354722410440445, -0.04877937585115433, 0.043442897498607635, -0.03113730624318123, 0.047269951552152634, 0.004784312564879656, -0.0029458669014275074, 0.03253965824842453, 0.030360911041498184, -0.04337787628173828, 0.007420867215842009, 0.02190280146896839, -0.016205081716179848, 0.05575839430093765, 0.01303714606910944, 0.0231940820813179, -0.014910471625626087, -0.022570379078388214, -0.014336854219436646, 0.0007620624965056777, 0.06054119020700455, 0.04452404007315636, -0.0018001727294176817, -0.03257044032216072, 0.006991545204073191, 0.00877820048481226, -0.03233679383993149, 0.027144500985741615, 0.03867224603891373, -0.017570458352565765, 0.035690102726221085, 0.09561604261398315, 0.03574104234576225, -0.005511205643415451, -0.09651464968919754, 0.042864665389060974, 0.0689828023314476, -0.006579585373401642, -0.03151663765311241, -0.027998562902212143, -0.013125317171216011, -0.0010604308918118477, -0.023450439795851707, 0.01517575979232788, -0.07419698685407639, 0.022106923162937164, -0.039291366934776306, 0.025216883048415184, 0.04993616044521332, 0.033084478229284286, 0.021594231948256493, 0.048385005444288254, 0.0690680518746376, -0.0050858245231211185, -0.03243909776210785, 0.09759911894798279, 0.03553009033203125, -0.04815804213285446, 0.005273880437016487, -0.04622168838977814, -0.026919947937130928, -0.02986222878098488, -0.01430385559797287, 0.003521905979141593, -0.04366951435804367, 0.05391881614923477, -0.031117359176278114, 0.024355214089155197, -0.034546975046396255, -0.007102916482836008, -0.013483949936926365, -0.018177689984440804, -0.024385105818510056, -0.0023648361675441265, 0.02088524028658867, -0.04940935969352722, -0.0211580041795969, -0.0021312348544597626, -0.01929584890604019, -0.022821413353085518, 0.026327384635806084, -0.009336174465715885, 0.029490286484360695, 0.02351415529847145, -0.06815548986196518, 0.026110993698239326, 0.03226810321211815, 0.009762683883309364, 0.017712362110614777, -0.037636980414390564, 0.0180894136428833, 0.0024661868810653687, 0.008349564857780933, 0.02755017578601837, 0.006227433681488037, -0.01582673005759716, -0.034626252949237823, -0.011504504829645157, -0.051812686026096344, 0.007645568810403347, -0.008846183307468891, -0.019844887778162956, -0.045565664768218994, -0.04400579258799553, -0.028665179386734962, -0.04246268421411514, 0.009253371506929398, 0.005139798857271671, 0.008719397708773613, 0.020438088104128838, 0.020274693146348, 0.013990960083901882, -0.007287134882062674, 0.021635470911860466, 0.009279120713472366, -0.00825852807611227, 0.0001984177652047947, -0.009592229500412941, 0.011239228770136833, 0.07281386852264404, -0.09808210283517838, -0.00950155034661293, -0.02194892428815365, -0.02021685056388378, 0.007904274389147758, -0.01460085716098547, -0.016647279262542725, 0.008314806036651134, 0.055103156715631485, 0.03783135861158371, 0.03981069475412369, -0.009016182273626328, 0.00781816616654396, -0.055913351476192474, 0.016654957085847855, -0.011011735536158085, -0.037501148879528046, 0.0375654473900795, 0.024493960663676262, 0.037144679576158524, 0.007354096509516239, 0.0003815433010458946, 0.04310193285346031, 0.01260977890342474, 0.044606372714042664, -0.04159368947148323, 0.0843496099114418, -0.02877124957740307, 0.09036394953727722, -0.0024621114134788513, -0.04098575934767723, -0.010204371064901352, 0.004408156033605337, 0.02012319676578045, 0.0005299271433614194, 0.05704377591609955, 0.03185351565480232, -0.0046590352430939674, 0.028682608157396317, -0.026656057685613632, -0.04302539303898811, 0.03328525274991989, -0.015403321012854576, 0.04433417320251465, -0.10777393728494644, 0.04596497118473053, -0.0033912041690200567, -0.0323467031121254, -0.02707533910870552, -0.0214073583483696, 0.03978194668889046, 0.016652911901474, 0.02641415409743786, 0.010809832252562046, -0.03702087327837944, -0.0038575087673962116, 0.0032651820220053196, 0.0014406924601644278, 0.032916124910116196, 0.02203773334622383, 0.02218456007540226, -0.01101410761475563, -0.016060633584856987, 0.04682803526520729, 0.02869107574224472, 0.007999212481081486, -0.041113000363111496, 0.008428744040429592, -0.085087850689888, 0.047376491129398346, 0.015644164755940437, -0.0436820313334465, -0.0038766616489738226, -0.044890739023685455, -0.04581413045525551, 0.028649283573031425, -0.03269809111952782, 0.0008487019222229719, 0.03732369840145111, -0.05968692526221275, -0.011776723898947239, 0.041144274175167084, -0.018171897158026695, 0.01841268129646778, 0.0419563390314579, -0.043961912393569946, -0.009339705109596252, -0.020373273640871048, 0.014171839691698551, -0.015568037517368793, 0.0020691221579909325, 0.029317183420062065, 0.028523869812488556, -0.015700800344347954, 0.04989505186676979, -0.049930915236473083, -0.014916270971298218, -0.036959804594516754, 0.02898198738694191, -0.020815791562199593, -0.022583451122045517, -0.018519552424550056, -0.012975959107279778, -0.004687089007347822, 0.010266190394759178, -0.04314866662025452, 0.017001984640955925, 0.024669677019119263, 0.01063766423612833, 0.018553854897618294, -0.017900707200169563, 0.018567891791462898, 0.0000916067510843277, -0.02884434349834919, 0.003332040272653103, 0.024260250851511955, -0.04452970251441002, 0.05149594694375992, 0.0535239577293396, -0.00775129022076726, 0.012848478741943836, 0.06746741384267807, 0.025066625326871872, 0.01835807040333748, 0.023202519863843918, 0.04279015213251114, -0.07178452610969543, 0.03131188452243805, 0.04026176780462265, 0.025187905877828598, -0.03387096896767616, -0.01366875134408474, 0.017314443364739418, 0.001004018122330308, -0.04094928503036499, 0.0071899560280144215, -0.008097805082798004, -0.016166234388947487, -0.0025746093597263098, -0.03333307057619095, -0.017127657309174538, -0.04386954382061958, -0.03154143691062927, 0.0011916432995349169, -0.014070968143641949, 0.005992544814944267, -0.044326458126306534, -0.017353130504488945, 0.040218740701675415, -0.03837278485298157, -0.01563052088022232, -0.0395287349820137, -0.02966809645295143, -0.005755370948463678, -0.0289378110319376, 0.028907332569360733, -0.03661656752228737, 0.040911976248025894, 0.011966866441071033, 0.03187448903918266, 0.004504222422838211, -0.05901327356696129, 0.03457479923963547, 0.01958305947482586, -0.021954869851469994, 0.009863005019724369, -0.021156445145606995, -0.11532559245824814, 0.039754558354616165, 0.03041318617761135, -0.01760844513773918, -0.016240639612078667, 0.016420302912592888, 0.030607955530285835, -0.0057634394615888596, -0.042246993631124496, 0.04109684005379677, 0.018366897478699684, -0.08208205550909042, -0.01713632233440876, 0.06585834920406342, 0.043563567101955414, -0.0685853436589241, 0.015002227388322353, 0.01774924248456955, 0.010064666159451008, -0.0018365982687100768, -0.009539864026010036, 0.012025566771626472, -0.02155996300280094, 0.02282547578215599, -0.0336395688354969, -0.03907420486211777, -0.025937724858522415, 0.04100383073091507, 0.015951311215758324, -0.015253080055117607, 0.011897758580744267, -0.05058849975466728, 0.007829271256923676, 0.061782170087099075, -0.01762731745839119, 0.03364119678735733, -0.04726220294833183, 0.0019163723336532712, 0.04844726249575615, -0.01740380749106407, -0.005420659203082323, -0.010565555654466152, -0.03013300709426403, -0.015293835662305355, 0.0525992214679718, 0.0016487512039020658, -0.07104597240686417, -0.04167487472295761, 0.03423717990517616, -0.014821494929492474, -0.0440092496573925, 0.006683767307549715, 0.015667762607336044, -0.03421953693032265, -0.020574776455760002, -0.0054149930365383625, -0.012784039601683617, -0.017584912478923798, 0.01089917216449976, -0.02477453462779522, -0.045059096068143845, -0.0433855876326561, -0.02565048262476921, 0.009445481933653355, -0.0216793455183506, 0.0023422345984727144, -0.017079006880521774, 0.018982701003551483, 0.025095684453845024, -0.013257870450615883, 0.04134860634803772, 0.002601727144792676, 0.03199495002627373, 0.01989836059510708, 0.020909611135721207, 0.0023016787599772215, -0.07148458063602448, -0.002451988635584712, -0.02601456455886364, -0.08124543726444244, -0.009064183570444584, 0.019284430891275406, -0.029590316116809845, -0.02481965906918049, -0.03630392998456955, 0.02795071341097355, -0.000572505290620029, 0.0071350280195474625, -0.01035064272582531, -0.02673349343240261, 0.030508369207382202 ]
<p>Long ago, I realized this: (super)string theory can NOT give a well-defined/unique prediction of why the electron (muon, tau) or the neutrino (any flavor) masses have the masses we measure. String theory can NOT give a concrete prediction of any SM particle mass (even resonances like the Higgs and other particles). The question is: Is this lack of predictive ability of the mass of the SM "elementary particles" a hint that string theory in its current status is not complete or wrong? Or perhaps even better:</p> <p><strong>Even when string theory provides a framework in which you can accomodate every Standard Model field, and hence, a priori you can have the SM spectrum, we have not a string theory explanation of the values of the masses and charges. Should a explicit derivation of particle properties like (rest) masses and (bare) charges (like the electron charge value) be "predicted" and "derived" in a more fundamental version of the theory?</strong></p>
g8418
[ 0.034711889922618866, -0.02042297087609768, 0.03501635417342186, -0.01739702746272087, 0.0363801009953022, 0.01571183279156685, -0.024894798174500465, 0.04060845077037811, 0.008072555996477604, -0.039635591208934784, -0.004194627515971661, -0.043955858796834946, 0.02981662005186081, 0.024515485391020775, -0.03354305773973465, 0.011704906821250916, 0.07846818119287491, -0.03228220343589783, 0.026339683681726456, 0.000889472255948931, 0.06608706712722778, 0.012690574862062931, 0.008477989584207535, -0.024204686284065247, -0.058132611215114594, 0.031479157507419586, 0.049237869679927826, 0.023474182933568954, 0.06911835074424744, -0.01866311952471733, 0.013122251257300377, -0.022768260911107063, 0.047033291310071945, -0.012424148619174957, 0.016815247014164925, -0.03177332133054733, 0.056951262056827545, 0.02277807891368866, -0.02758018486201763, 0.013960872776806355, 0.02241503819823265, -0.008596910163760185, -0.008645489811897278, 0.017726493999361992, -0.01613437943160534, 0.024771394208073616, -0.03359421715140343, -0.004266239237040281, -0.008263131603598595, -0.022092953324317932, 0.036069877445697784, -0.03846859931945801, 0.05821569263935089, 0.009571596048772335, 0.03580084070563316, 0.03028906136751175, 0.010595845989882946, 0.019386308267712593, 0.03159834071993828, 0.008289609104394913, 0.034883104264736176, 0.04822826758027077, -0.02747732773423195, -0.00940187368541956, 0.05559462681412697, 0.02333197556436062, -0.07583272457122803, -0.033845964819192886, 0.017903827130794525, 0.00817060749977827, 0.03104904107749462, -0.0021358863450586796, 0.005135927349328995, -0.02153879776597023, -0.04423755407333374, -0.005414111539721489, -0.08448872715234756, -0.00056488998234272, -0.019896769896149635, -0.010274664498865604, 0.043818216770887375, -0.025283332914114, 0.013987415470182896, 0.02057819254696369, 0.05467633530497551, -0.1221638098359108, -0.04099767655134201, 0.018123822286725044, 0.053337063640356064, 0.0406976193189621, -0.005093436688184738, 0.0326506569981575, 0.009190176613628864, -0.009228023700416088, 0.027483057230710983, -0.05901998654007912, 0.007326647639274597, 0.020800098776817322, -0.015519113279879093, -0.03162584453821182, 0.010761610232293606, 0.03981229290366173, -0.0037261571269482374, 0.03880131617188454, 0.007522477302700281, 0.009790435433387756, -0.018483424559235573, 0.026712100952863693, 0.01725718379020691, 0.013912617228925228, -0.01569908857345581, 0.02049987018108368, -0.011630930006504059, 0.06132626160979271, -0.11687955260276794, -0.0653061792254448, 0.043125614523887634, -0.02935810759663582, -0.05825381726026535, 0.059029269963502884, -0.024333525449037552, -0.013984447345137596, 0.0658901184797287, 0.027595600113272667, -0.028001489117741585, -0.038289837539196014, -0.008002766408026218, 0.0481317937374115, -0.012285297736525536, -0.0463462695479393, -0.0872461199760437, 0.004083689767867327, -0.022005364298820496, 0.005987393669784069, 0.046598758548498154, 0.008963360451161861, 0.010345324873924255, 0.013252644799649715, 0.004056083038449287, -0.04255053028464317, 0.02365504577755928, 0.04310358315706253, 0.028507526963949203, 0.0016912745777517557, -0.023251036182045937, -0.02468465082347393, -0.03189198672771454, 0.05391785502433777, -0.04176267609000206, 0.10138848423957825, 0.016637859866023064, 0.04113676771521568, -0.011203547939658165, 0.06203196942806244, -0.013151745311915874, 0.014205560088157654, 0.023442121222615242, -0.02252224087715149, -0.040720343589782715, -0.003564698388800025, 0.044726621359586716, -0.020030412822961807, -0.0009037364507094026, -0.06107579171657562, 0.01044983509927988, -0.04057602211833, 0.002274050610139966, -0.029863430187106133, -0.06186053156852722, -0.05068689584732056, -0.07510390132665634, 0.042944006621837616, 0.029958751052618027, 0.07298897206783295, -0.06371167302131653, -0.006362625863403082, 0.05615364387631416, -0.016988351941108704, 0.029280906543135643, 0.002452004700899124, -0.039032697677612305, 0.010826937854290009, 0.06502267718315125, -0.01982506737112999, -0.04934070631861687, 0.010294514708220959, -0.037928156554698944, 0.01990622654557228, 0.0444638766348362, 0.019002515822649002, -0.044208064675331116, 0.02636931836605072, 0.00023359784972853959, 0.08380735665559769, 0.03376093506813049, -0.0016149778384715319, 0.017275340855121613, -0.00533210439607501, 0.010266869328916073, -0.019134435802698135, -0.00828290730714798, 0.06678837537765503, -0.02181761898100376, -0.005460705608129501, 0.054980769753456116, -0.017746537923812866, -0.005368733312934637, 0.027401698753237724, 0.027012290433049202, 0.014437311328947544, 0.010015202686190605, -0.027331678196787834, -0.053220123052597046, -0.009701412171125412, -0.04430161044001579, -0.07169435918331146, -0.04020915925502777, 0.03688907250761986, 0.04739886149764061, 0.010207976214587688, -0.027572287246584892, -0.06575984507799149, -0.007075989153236151, 0.04067116230726242, -0.044612180441617966, 0.05734881013631821, -0.01563084125518799, -0.00280345743522048, 0.009598457254469395, -0.0037788290064781904, -0.050547562539577484, -0.05476824566721916, 0.02097029983997345, -0.001093920785933733, 0.019931966438889503, 0.02314075082540512, -0.020490296185016632, -0.06757160276174545, 0.042990125715732574, 0.02905881591141224, 0.04439355805516243, -0.017741715535521507, 0.028769342228770256, -0.006534116342663765, 0.03358915075659752, -0.03822031244635582, 0.026661483570933342, -0.022855477407574654, -0.042744483798742294, 0.047773800790309906, -0.03690195083618164, 0.0484929196536541, -0.00347452936694026, -0.01812884770333767, 0.037041496485471725, 0.007160419598221779, 0.037181198596954346, 0.019511835649609566, -0.05877101793885231, -0.029569096863269806, 0.0031579965725541115, -0.016849283128976822, -0.011103580705821514, 0.04506932944059372, -0.04986812174320221, -0.0478210374712944, 0.015705954283475876, -0.004422609694302082, -0.03978324308991432, -0.0600518174469471, -0.03459908068180084, 0.01610523834824562, 0.028609173372387886, -0.031275223940610886, -0.002451864769682288, 0.0038964534178376198, -0.012230521067976952, 0.08846243470907211, 0.07689397782087326, 0.008960100822150707, 0.007977362722158432, 0.059455160051584244, -0.023104935884475708, -0.016024714335799217, 0.00846070796251297, -0.059069979935884476, -0.043713558465242386, -0.10487528890371323, 0.03644835203886032, 0.03702913969755173, 0.028957566246390343, -0.03476564586162567, 0.06088324636220932, -0.01731395348906517, -0.011566400527954102, 0.057034075260162354, 0.006495022680610418, 0.011465160176157951, -0.0016970683354884386, -0.024760928004980087, 0.032643307000398636, 0.03198693320155144, -0.03745371848344803, 0.003893759334459901, 0.020590363070368767, 0.02781076729297638, -0.01659788377583027, -0.010864761658012867, 0.01720273122191429, -0.06643781810998917, 0.010122356005012989, 0.06647185236215591, 0.07959823310375214, -0.017717944458127022, -0.0389881506562233, 0.036871131509542465, -0.03628680855035782, 0.023797204717993736, -0.004385922569781542, -0.047802962362766266, -0.017709873616695404, -0.03528283163905144, 0.033325862139463425, -0.01332180667668581, -0.018687564879655838, 0.0159679614007473, -0.0408049151301384, 0.019853554666042328, -0.09165102988481522, -0.02405056543648243, -0.015674229711294174, 0.025970157235860825, -0.04405714571475983, 0.06634330749511719, -0.010693104937672615, 0.006838155910372734, 0.020276064053177834, -0.00505092041566968, 0.04946093261241913, -0.035144511610269547, -0.020009588450193405, -0.011748136952519417, -0.0044059548527002335, 0.01305294968187809, -0.05903789401054382, 0.025304293259978294, -0.04228213056921959, -0.11346562206745148, 0.04337397962808609, -0.006849347613751888, 0.019903147593140602, 0.07823509722948074, -0.009836963377892971, 0.10601915419101715, -0.011975892819464207, 0.03944261744618416, 0.06545073539018631, 0.052188802510499954, 0.036023546010255814, -0.02619755268096924, 0.018890174105763435, 0.004201922100037336, 0.010292436927556992, -0.02865862287580967, 0.024347353726625443, 0.02220769412815571, -0.009045962244272232, -0.01391187310218811, 0.019232217222452164, -0.033027514815330505, 0.008172793313860893, -0.03473560884594917, -0.013199525885283947, -0.020029548555612564, 0.019773559644818306, -0.0305137000977993, 0.050383061170578, 0.02470501698553562, -0.06099914014339447, -0.005405331961810589, 0.07102847844362259, 0.0033945036120712757, -0.03500256687402725, 0.0015036168042570353, -0.029119644314050674, -0.01347578689455986, -0.060831304639577866, 0.049063969403505325, -0.07004725933074951, -0.022584596648812294, -0.022614052519202232, -0.04419665411114693, -0.0005752266151830554, 0.012781503610312939, 0.0019089061534032226, -0.06513597071170807, 0.06234908476471901, -0.05850519239902496, 0.051592838019132614, -0.020456815138459206, -0.03992239013314247, 0.03798312693834305, -0.0036172084510326385, -0.06833154708147049, 0.017143240198493004, 0.0323733314871788, -0.009111850522458553, -0.034098416566848755, 0.004679507575929165, -0.048328716307878494, 0.03734556958079338, 0.020830657333135605, 0.01822194829583168, -0.014086630195379257, -0.013848590664565563, 0.010774445720016956, -0.029160935431718826, -0.0650641992688179, 0.04004606604576111, 0.005932719446718693, 0.01924803853034973, 0.04376126080751419, 0.005403760354965925, -0.03502151370048523, -0.03770007938146591, 0.028589298948645592, -0.00412081740796566, -0.00035406832466833293, -0.014916210435330868, -0.0024571791291236877, 0.040525492280721664, 0.0015588647220283747, 0.006029363255947828, -0.015598402358591557, -0.07088851928710938, 0.035981085151433945, 0.003726294031366706, -0.01636189967393875, 0.0034674450289458036, 0.0343719944357872, 0.03404400870203972, -0.008198520168662071, 0.023605626076459885, -0.018853764981031418, -0.025004277005791664, 0.003996906336396933, -0.0651596188545227, 0.012325295247137547, -0.023586779832839966, 0.0037501549813896418, -0.03421169891953468, 0.0190503541380167, -0.043756987899541855, 0.024965571239590645, -0.030442161485552788, -0.00808041077107191, 0.005632904823869467, 0.0475841723382473, -0.0032268078066408634, 0.004009973257780075, -0.06644543260335922, -0.010252713225781918, 0.03550829365849495, 0.05222263187170029, 0.029777850955724716, 0.0022907122038304806, -0.009125842712819576, -0.008971137925982475, 0.0056163240224123, -0.010109982453286648, -0.029701799154281616, -0.01609034836292267, 0.040170781314373016, -0.044440120458602905, -0.007993513718247414, -0.04705043509602547, -0.025153234601020813, -0.053841471672058105, -0.006934944540262222, 0.03725583478808403, -0.026919275522232056, -0.006869146600365639, 0.004672556649893522, -0.010230140760540962, -0.001503379549831152, 0.04831439256668091, -0.030001308768987656, 0.012551949359476566, -0.05418287590146065, -0.0089285122230649, -0.027156880125403404, 0.015719624236226082, 0.019115962088108063, -0.036874473094940186, -0.011329025961458683, 0.019838614389300346, 0.020115502178668976, -0.027426034212112427, -0.05305219441652298, -0.0009356284281238914, -0.05063878372311592, 0.02424621768295765, 0.012149820104241371, 0.03576339781284332, 0.019211022183299065, 0.027420440688729286, 0.01622980460524559, -0.048888497054576874, -0.0117174182087183, -0.058519069105386734, 0.03315252065658569, 0.06633947044610977, 0.03005482628941536, -0.011811215430498123, 0.006841923575848341, 0.02100030519068241, 0.005073733162134886, 0.01293741725385189, 0.023488016799092293, 0.011964288540184498, 0.004383951425552368, 0.04580024257302284, 0.051249176263809204, -0.03214973956346512, 0.01751808449625969, -0.011541945859789848, -0.024789733812212944, -0.006307669449597597, 0.045356813818216324, 0.050875499844551086, 0.04001406952738762, -0.04407127574086189, 0.018842389807105064, 0.0017566831083968282, 0.05025852471590042, -0.04200083389878273, -0.03448396921157837, 0.008866558782756329, -0.03323916718363762, 0.003557157702744007, 0.012868803925812244, 0.040783077478408813, 0.021308407187461853, 0.048064593225717545, 0.047572653740644455, 0.021693993359804153, 0.028630459681153297, -0.008002229034900665, 0.05767589807510376, -0.04861630126833916, -0.0397472120821476, 0.07205481827259064, -0.059202227741479874, -0.026812199503183365, -0.027232810854911804, 0.07734978944063187, 0.024920428171753883, -0.010703308507800102, -0.041570995002985, 0.03401857241988182, -0.021323900669813156, 0.005591884255409241, -0.005514024291187525, 0.06589038670063019, 0.00032318165176548064, -0.0006091924151405692, -0.004075570497661829, -0.04109518602490425, 0.06529299169778824, 0.04399022459983826, -0.058388449251651764, 0.049073778092861176, 0.04736835137009621, 0.014743512496352196, -0.0436900295317173, -0.03409826382994652, -0.013239361345767975, 0.008733194321393967, 0.013931582681834698, -0.05411504581570625, 0.06092606484889984, 0.012510035187005997, 0.08340533822774887, -0.04998280107975006, -0.015975654125213623, -0.017403069883584976, -0.007494849618524313, -0.005958499386906624, 0.007005670107901096, 0.05089924857020378, -0.006017195526510477, 0.023913010954856873, -0.010673100128769875, -0.012308570556342602, -0.07137805223464966, 0.037206247448921204, -0.007042694371193647, -0.030936522409319878, -0.009685084223747253, 0.029733654111623764, 0.06256161630153656, 0.034509528428316116, 0.012095484882593155, -0.020052725449204445, 0.07197210192680359, 0.0004509969148784876, 0.019233744591474533, 0.0349370501935482, -0.021258963271975517, -0.03653496131300926, -0.016286475583910942, 0.006365273613482714, -0.003550410270690918, 0.0013460001209750772, 0.02825806848704815, -0.06515294313430786, -0.00676766037940979, 0.07795920222997665, -0.05620681867003441, -0.019005177542567253, 0.03638488054275513, 0.03354525938630104, 0.022753944620490074, -0.02886456437408924, 0.03785931318998337, -0.022046782076358795, -0.004549718927592039, 0.0378272719681263, 0.05379677191376686, -0.02462139166891575, -0.001260307733900845, 0.007453355006873608, 0.07544504851102829, 0.01996094547212124, -0.035277362912893295, 0.03670777752995491, 0.026542887091636658, 0.03138463944196701, -0.04228265583515167, -0.016780400648713112, -0.057799410074949265, -0.011656133458018303, 0.013247676193714142, -0.01463018823415041, -0.10400886833667755, -0.041571956127882004, 0.08322945982217789, 0.02994331158697605, -0.014233039692044258, -0.037348423153162, -0.01586736924946308, -0.03719229996204376, 0.029157942160964012, -0.022860601544380188, 0.026950741186738014, -0.03720707446336746, 0.028373073786497116, -0.03683355450630188, 0.08816830068826675, -0.023804886266589165, -0.04140327870845795, -0.0228999275714159, 0.021181587129831314, -0.05096053704619408, -0.00037160111241973937, -0.002821757923811674, 0.002737125614657998, -0.09710889309644699, 0.015729257836937904, -0.01094325352460146, 0.029124293476343155, -0.08361084014177322, -0.008961175568401814, -0.03607012331485748, -0.01769893988966942, -0.034487005323171616, -0.029916251078248024, 0.011338326148688793, -0.05153796449303627, -0.006437542848289013, -0.008168823085725307, 0.011471248231828213, 0.014181450009346008, 0.06388788670301437, -0.013580630533397198, 0.013494877144694328, -0.07233171910047531, 0.02224060893058777, -0.01836244948208332, 0.007995831780135632, 0.016825763508677483, -0.0078026000410318375, 0.01877032034099102, -0.0720769390463829, -0.032905567437410355, -0.006503623444586992, -0.045942842960357666, 0.04921238124370575, 0.0639844685792923, 0.02060370147228241, -0.02362966723740101, -0.015846308320760727, 0.0009919076692312956, 0.0024082213640213013, 0.043732836842536926, 0.03345663473010063, 0.004000136628746986, -0.049105528742074966, -0.05639272555708885, 0.03634411096572876, -0.011877667158842087, 0.03257978707551956, -0.022388534620404243, 0.06828635185956955, 0.029826784506440163, -0.0020142081193625927, -0.002469802275300026, -0.06317593157291412, 0.008344880305230618, -0.04106556624174118, -0.036327511072158813, -0.022574681788682938, 0.01204554084688425, -0.0378250889480114, -0.03340829163789749, -0.029062602669000626, 0.03619634732604027, -0.003251016605645418, 0.0043285260908305645, -0.0044258669950068, -0.009565897285938263, 0.058671776205301285, -0.006672786548733711, -0.023357080295681953, -0.022691141813993454, 0.03366278484463692, 0.013536600396037102, 0.033039629459381104, -0.052251316606998444, -0.022887373343110085, 0.008566468022763729, -0.010356808081269264, 0.00930742546916008, -0.00587757071480155, -0.03192904219031334, 0.022572331130504608, -0.029520640149712563, 0.018272027373313904, -0.05287724733352661, -0.020103231072425842, -0.012821346521377563, -0.007789550349116325, -0.022025467827916145, 0.03127747401595116, 0.032314520329236984, -0.04012146592140198, 0.024285733699798584, -0.020688427612185478, 0.016844002529978752, -0.024257509037852287, -0.015020388178527355, -0.011517345905303955, 0.044377170503139496, -0.020393412560224533, -0.014007488265633583, -0.033878251910209656, 0.03986275941133499, -0.022582463920116425 ]
<p>There are the eddy currents in thin circular copper plate thickness h and radius a, in a harmonic magnetic field which is perpendicular to plate and the effect of auto-induction is negligible. Now we must get average heat generated on it.</p> <p>As I said, I have final equation, but how do you get to this eqution. Does anyone know solution from first step to this? $$ \overline P=\frac{1}{16}\pi\gamma ha^4B_0^2\omega $$</p>
g8419
[ 0.06749165058135986, 0.008466113358736038, -0.018471237272024155, -0.03208330646157265, 0.06390460580587387, -0.0007917513721622527, 0.03822420537471771, 0.0386233851313591, -0.08084622025489807, -0.003909012768417597, -0.05206845700740814, 0.0893864780664444, -0.050339195877313614, -0.01800963282585144, 0.051279302686452866, -0.003332310589030385, 0.02323221229016781, -0.04294236749410629, 0.03836577385663986, 0.0459294468164444, -0.014147876761853695, -0.00864147488027811, 0.03404809907078743, -0.02255217544734478, 0.03800690546631813, -0.02552349679172039, -0.027050063014030457, 0.007867330685257912, 0.028248509392142296, -0.04102256894111633, -0.046142321079969406, -0.00010841777111636475, 0.07030879706144333, -0.0026482136454433203, -0.060447581112384796, 0.025522394105792046, 0.045909710228443146, 0.0698239877820015, 0.0014004029799252748, -0.02564402110874653, -0.008965089917182922, 0.02106345258653164, 0.0181589275598526, 0.04764620214700699, 0.014161367900669575, -0.0027090338990092278, -0.04429763928055763, 0.06408318877220154, -0.04526277631521225, 0.03976909816265106, -0.008886792697012424, 0.020639706403017044, 0.1213788390159607, -0.06672283262014389, -0.07166710495948792, 0.04302901029586792, 0.017191145569086075, -0.02825971320271492, 0.03310281038284302, 0.021981224417686462, -0.014477156102657318, 0.0038819080218672752, -0.027575533837080002, 0.005202477797865868, 0.01603958010673523, -0.0016934199957177043, -0.0003974144347012043, -0.013739138841629028, -0.021771812811493874, -0.005668138153851032, -0.07708726823329926, -0.0725582167506218, -0.003593845758587122, -0.07866104692220688, -0.047280024737119675, 0.012834024615585804, 0.04047955572605133, -0.025679290294647217, 0.047377340495586395, -0.022591659799218178, -0.05508987978100777, 0.017645172774791718, 0.012449916452169418, 0.028672024607658386, -0.011763744987547398, -0.03033139556646347, 0.055321913212537766, 0.00760662741959095, -0.04421486705541611, -0.04453374445438385, 0.022442931309342384, 0.008907527662813663, -0.0009358527022413909, -0.01686377450823784, 0.08452250808477402, 0.038144294172525406, -0.014917619526386261, -0.0007065694080665708, -0.035287510603666306, -0.014980675652623177, -0.020176129415631294, -0.015839893370866776, -0.0197038184851408, -0.04584852606058121, -0.033120278269052505, -0.007797747850418091, -0.009071461856365204, 0.03764323517680168, -0.012003997340798378, 0.01728872023522854, -0.0406281054019928, -0.04167938232421875, -0.05401553958654404, -0.029151154682040215, -0.04306093230843544, -0.026690566912293434, 0.008482731878757477, -0.009945087134838104, 0.04077621549367905, 0.07973182946443558, -0.002109672874212265, -0.0401046946644783, 0.0018452738877385855, 0.11621136218309402, 0.05017905309796333, 0.029428180307149887, -0.008957520127296448, 0.03805798292160034, 0.06904896348714828, -0.01649397239089012, 0.03348652645945549, -0.008149663917720318, 0.01974347047507763, -0.007837492041289806, 0.023295808583498, 0.07376231253147125, -0.016971049830317497, 0.0386628657579422, -0.020589394494891167, 0.002281605964526534, -0.03780404105782509, -0.0812574028968811, 0.050728991627693176, -0.06130450591444969, -0.045334212481975555, 0.0810403898358345, 0.026109442114830017, -0.13413770496845245, 0.08391997963190079, 0.027588361874222755, 0.04639127478003502, 0.06263827532529831, -0.01935601979494095, -0.02055121399462223, -0.021132908761501312, 0.04205615445971489, 0.029495535418391228, -0.04615435004234314, 0.026850415393710136, -0.02335287071764469, 0.007856805808842182, -0.005467926152050495, -0.005587415769696236, -0.019447926431894302, -0.02343406155705452, 0.03061283379793167, -0.018307840451598167, 0.008541432209312916, -0.0027135128621011972, -0.007695742882788181, -0.009980953298509121, -0.016621099784970284, 0.0015538535080850124, 0.02916964516043663, 0.01817282661795616, 0.07316011190414429, 0.001518144505098462, -0.03128388524055481, 0.07529528439044952, 0.012646662071347237, 0.02040451392531395, 0.007667990867048502, 0.09124873578548431, -0.03534981608390808, 0.010627293959259987, 0.009784417226910591, -0.005765208974480629, 0.02970908395946026, -0.021988190710544586, 0.0027532395906746387, -0.029188036918640137, 0.010714201256632805, 0.013568682596087456, 0.006865191273391247, 0.0134254926815629, 0.06254781782627106, 0.04491584748029709, -0.00788045022636652, -0.0384402833878994, -0.018562067300081253, 0.052037350833415985, 0.03797800466418266, 0.12276729196310043, -0.013150716200470924, -0.002589218318462372, 0.012697682715952396, 0.0001661026617512107, -0.02478092722594738, 0.027986813336610794, -0.00825065840035677, -0.00780898705124855, -0.003189241513609886, -0.02152705192565918, 0.038655802607536316, -0.03596093878149986, -0.030346693471074104, -0.037830810993909836, -0.02817593887448311, -0.03608568012714386, -0.0035001884680241346, 0.01702236570417881, -0.013376951217651367, 0.00670574139803648, 0.022418616339564323, -0.03446556255221367, -0.00662713497877121, -0.017483843490481377, -0.01598646119236946, 0.010258616879582405, -0.017634402960538864, -0.020623866468667984, -0.03895881026983261, 0.004377054050564766, -0.034047484397888184, -0.004804055206477642, -0.03653331473469734, -0.040027834475040436, -0.003725231159478426, -0.07859210669994354, 0.011219783686101437, -0.021864617243409157, 0.013389966450631618, 0.013148115016520023, -0.04106764867901802, 0.007315346039831638, 0.02048434130847454, 0.058353979140520096, 0.001959193032234907, -0.003512760391458869, 0.029800178483128548, 0.04327283054590225, -0.01917349174618721, 0.004730221815407276, 0.00045391853200271726, -0.025894949212670326, -0.031266950070858, -0.06442258507013321, 0.09688711166381836, 0.005643060896545649, -0.06621170789003372, -0.02684139460325241, -0.060344427824020386, 0.03380635753273964, 0.0330132432281971, -0.10558557510375977, -0.006044543348252773, -0.06121910735964775, -0.03665241226553917, -0.002880444983020425, 0.02640642784535885, -0.011274337768554688, 0.03356029465794563, -0.006338902283459902, 0.08065540343523026, 0.01623222976922989, -0.05130353942513466, 0.04097955301403999, 0.028978990390896797, 0.05890193581581116, -0.0008677611476741731, -0.0050376709550619125, -0.0646144226193428, 0.013138148933649063, -0.009767691604793072, -0.016714120283722878, -0.06259511411190033, -0.02904183231294155, 0.021029265597462654, 0.03920911252498627, 0.00331239216029644, -0.007354788016527891, -0.06400321424007416, -0.002374656731262803, 0.008432632312178612, 0.02244843728840351, 0.006280109286308289, 0.0754457414150238, -0.045782435685396194, -0.0344848670065403, -0.030067382380366325, 0.034618016332387924, -0.0009480280568823218, -0.01580617018043995, -0.04610181599855423, 0.00483234878629446, 0.0069681634195148945, 0.05016763508319855, -0.09053483605384827, 0.010083111934363842, 0.014996014535427094, 0.037019409239292145, -0.011555478908121586, 0.049733489751815796, -0.010252945125102997, -0.05468009039759636, 0.05028195679187775, -0.04951221123337746, -0.045309606939554214, 0.008856059052050114, -0.005321837496012449, -0.015800688415765762, -0.05968338996171951, 0.011532350443303585, -0.02840546704828739, -0.025189794600009918, -0.0489928275346756, 0.003787267953157425, -0.03444552794098854, -0.047753021121025085, -0.01804153434932232, -0.010930296033620834, 0.007333120796829462, -0.011036165989935398, -0.004472378641366959, 0.008276022970676422, -0.016931621357798576, -0.002362672472372651, 0.05190492048859596, 0.0077240485697984695, 0.05095500126481056, -0.020679470151662827, -0.04614260047674179, -0.031380925327539444, -0.0033968889620155096, -0.01566869392991066, 0.013645078986883163, 0.02487127296626568, 0.026301639154553413, -0.005632291082292795, 0.04608416557312012, 0.014194312505424023, 0.037276022136211395, 0.009408035315573215, 0.0151312705129385, -0.013852499425411224, 0.021145924925804138, 0.03330829367041588, 0.01793905720114708, 0.02253834158182144, 0.0014676515711471438, 0.019585352391004562, -0.0421898327767849, 0.0420084148645401, -0.012173526920378208, 0.04837413504719734, 0.028472239151597023, -0.009124485775828362, 0.045772235840559006, -0.005307549610733986, -0.014903029426932335, -0.004565377254039049, -0.05252373218536377, 0.019547728821635246, -0.02077721245586872, 0.009474734775722027, -0.054780133068561554, -0.00446769455447793, 0.023058073595166206, 0.00507017457857728, 0.05728226155042648, -0.0840853899717331, -0.014763439074158669, 0.004895304329693317, 0.008645647205412388, -0.012907822616398335, 0.048656485974788666, -0.026527782902121544, 0.04001425951719284, -0.05792144685983658, -0.038136400282382965, 0.014974456280469894, -0.004827881697565317, 0.03766697645187378, -0.0010197123046964407, -0.08730056881904602, -0.030164388939738274, 0.004188854247331619, -0.01136783231049776, -0.0731414258480072, -0.02486119419336319, 0.045048538595438004, -0.006564425304532051, 0.03791618347167969, 0.03698444738984108, -0.03330110386013985, -0.015294722281396389, 0.03345431014895439, -0.05456237494945526, 0.05527694895863533, -0.04170192778110504, -0.03417455032467842, -0.01399437990039587, -0.025979777798056602, -0.023862911388278008, 0.04765406623482704, -0.05503556504845619, 0.03948676213622093, -0.0023608049377799034, 0.02617708593606949, -0.05916961282491684, -0.05042729154229164, -0.014687692746520042, 0.017871670424938202, 0.019154593348503113, -0.0058371578343212605, 0.018670685589313507, 0.016045579686760902, 0.011112688109278679, -0.019982967525720596, -0.005027403123676777, -0.03220275416970253, -0.00623364420607686, -0.031378187239170074, 0.0025109609123319387, -0.06391823291778564, 0.011403707787394524, -0.02615208737552166, 0.06604984402656555, -0.025767751038074493, 0.012134675867855549, -0.011534580960869789, 0.0017502192640677094, 0.056174878031015396, -0.0000956879957811907, -0.02102673612535, 0.0431741364300251, -0.0016203271225094795, -0.053226884454488754, 0.026654357090592384, -0.042405661195516586, 0.04098309576511383, -0.014375593513250351, -0.006153357680886984, 0.02707495167851448, 0.020085694268345833, -0.02226342260837555, -0.05068609490990639, 0.04570673406124115, 0.051954660564661026, 0.01433238573372364, -0.00921205710619688, -0.010250416584312916, -0.05941556766629219, 0.017850400879979134, 0.01885671727359295, -0.03724966570734978, 0.025511132553219795, -0.022005459293723106, 0.015420377254486084, 0.009035455994307995, 0.032756950706243515, 0.021502839401364326, 0.012590496800839901, 0.0076489076018333435, -0.0047362856566905975, 0.018583690747618675, 0.03196007013320923, -0.014725260436534882, -0.06145782396197319, -0.011094729416072369, -0.013254341669380665, -0.0033315573818981647, 0.054177913814783096, 0.05918041244149208, -0.0063102408312261105, 0.010486469604074955, -0.05440482869744301, 0.026581838726997375, 0.03696657344698906, -0.032315824180841446, -0.033342909067869186, 0.08952131122350693, -0.010825593955814838, -0.0242189709097147, -0.028529170900583267, -0.01521780714392662, -0.023780595511198044, -0.0010586996795609593, -0.0020975423976778984, 0.014981032349169254, -0.013239762745797634, 0.03869887813925743, -0.045723456889390945, 0.016782257705926895, 0.0058473930694162846, 0.023484397679567337, 0.04512752220034599, 0.02202107384800911, 0.03739552199840546, 0.0007722275913693011, 0.018247537314891815, 0.0030855017248541117, 0.061148785054683685, -0.04903136193752289, -0.005880281329154968, -0.003175890538841486, -0.04347437620162964, 0.003810315392911434, -0.0026614179369062185, -0.023155927658081055, 0.08061131089925766, 0.022982150316238403, 0.004977553151547909, -0.03291451930999756, 0.06156810745596886, -0.0010084450477734208, -0.08998164534568787, -0.015432923100888729, 0.0866994708776474, -0.028469160199165344, -0.003959831781685352, -0.013007129542529583, -0.012051425874233246, 0.005094145890325308, 0.029915766790509224, 0.04056597128510475, 0.059681978076696396, -0.025507112964987755, -0.03144500404596329, 0.009522520005702972, 0.014965715818107128, -0.044672854244709015, 0.025593170896172523, 0.019056282937526703, -0.034880924969911575, 0.016833515837788582, 0.0386849120259285, 0.0026264693588018417, 0.043003249913454056, 0.010814603418111801, 0.006806732155382633, -0.023201696574687958, 0.10938449949026108, 0.010461929254233837, -0.0009300531237386167, 0.015674058347940445, 0.03667587414383888, -0.04099578782916069, -0.02316088229417801, -0.012162069790065289, 0.01799909956753254, -0.04624534770846367, 0.017044758424162865, 0.00868965033441782, 0.037132441997528076, -0.0014969388721510768, -0.02805200219154358, -0.06613244861364365, 0.07304137200117111, 0.017641691491007805, -0.020517269149422646, -0.003272624686360359, -0.000248558382736519, 0.021305158734321594, 0.06445161253213882, 0.031654566526412964, 0.022048579528927803, 0.01864524930715561, -0.004291105084121227, 0.01971331425011158, -0.048484742641448975, 0.06236790120601654, 0.02458435483276844, 0.0012899970170110464, -0.0010689512128010392, 0.06872191280126572, -0.06530123949050903, -0.006008489988744259, 0.010215798392891884, -0.011106434278190136, 0.016249291598796844, -0.010688243433833122, 0.027627145871520042, 0.03784853219985962, 0.03345614671707153, -0.006276268977671862, -0.0006478842697106302, -0.021571071818470955, 0.002350181806832552, 0.05078757181763649, -0.020424196496605873, -0.026838770136237144, -0.0238652266561985, 0.019576208665966988, 0.03368021175265312, -0.02932136319577694, 0.019774923101067543, -0.023054365068674088, -0.06846784055233002, -0.005614728666841984, 0.006194885820150375, -0.023110711947083473, 0.013451260514557362, -0.048876333981752396, -0.00353654264472425, -0.010371810756623745, 0.02444942109286785, 0.010898066684603691, 0.009615778923034668, 0.03380764275789261, 0.043033476918935776, -0.03687943518161774, -0.02085224539041519, -0.016624070703983307, 0.050953350961208344, 0.015166985802352428, -0.03821009770035744, 0.013802642934024334, 0.033262237906455994, -0.001501276041381061, 0.027079790830612183, 0.01853404939174652, -0.059886634349823, 0.06281672418117523, 0.02542082779109478, 0.009435690939426422, 0.04131489619612694, -0.02439066208899021, 0.05248279124498367, 0.06927401572465897, -0.023601306602358818, 0.04878411814570427, 0.046598222106695175, -0.017391080036759377, -0.06307116150856018, -0.05857269465923309, -0.0027726953849196434, 0.011183864437043667, -0.06328973919153214, 0.03514302894473076, 0.01814280077815056, 0.00939846783876419, -0.05758184939622879, 0.03429243713617325, 0.011044674552977085, -0.022238167002797127, 0.011562444269657135, 0.025019291788339615, 0.02761310711503029, 0.029535744339227676, -0.005363831762224436, -0.02226482890546322, -0.010295168496668339, -0.00006298187508946285, 0.01835876889526844, 0.03174356371164322, 0.005248109810054302, 0.020544420927762985, 0.011378688737750053, -0.07202059030532837, -0.055926304310560226, -0.04395664483308792, -0.023436304181814194, -0.02537570707499981, -0.016311125829815865, -0.0022532944567501545, 0.0355224683880806, 0.010222992859780788, 0.003937301691621542, -0.054296884685754776, -0.09953077137470245, 0.015367762185633183, -0.006914191413670778, -0.033008500933647156, 0.022701341658830643, -0.036648280918598175, -0.04824398085474968, -0.016005758196115494, 0.03320515155792236, 0.04515690356492996, -0.055984530597925186, 0.04258505254983902, 0.013797677122056484, -0.017104333266615868, -0.020649408921599388, 0.007932175882160664, -0.013174150139093399, 0.03438199684023857, 0.05413680523633957, 0.012143773026764393, -0.0006933839176781476, 0.03171396255493164, -0.02448318526148796, 0.000999925658106804, -0.028649890795350075, 0.01007708441466093, -0.023079900071024895, -0.009783850982785225, -0.04371867701411247, 0.010753227397799492, 0.06885473430156708, 0.028738869354128838, -0.03853590041399002, 0.017046183347702026, 0.008565796539187431, 0.012185709550976753, -0.03444711118936539, -0.012115671299397945, 0.008482098579406738, -0.0195066649466753, -0.03254125267267227, 0.04279224947094917, -0.030039047822356224, -0.035718753933906555, 0.023579346016049385, 0.004117446020245552, -0.02434932254254818, -0.017383519560098648, 0.00312641984783113, -0.07269878685474396, 0.014725888147950172, 0.005564182065427303, -0.053988922387361526, -0.08859667927026749, -0.02764025889337063, -0.017448091879487038, -0.01951281912624836, 0.001036155503243208, 0.04314010217785835, -0.018654586747288704, 0.009153989143669605, -0.05296965688467026, -0.011262879706919193, -0.03606794402003288, -0.004836247302591801, 0.04971059784293175, -0.0859982967376709, 0.023053565993905067, 0.024942057207226753, -0.03805060684680939, 0.039121802896261215, 0.0366731621325016, -0.0512719564139843, -0.03412923589348793, 0.013927816413342953, -0.0823817253112793, 0.022612102329730988, -0.0009389168117195368, 0.062723308801651, 0.013525172136723995, -0.021092085167765617, -0.02456793189048767, -0.01711571030318737, 0.03856015205383301, 0.022645914927124977, 0.008392409421503544, -0.005262972321361303, -0.009116945788264275 ]
<p>In an ideal situation, we can use a simple formula to determine the velocity at which a body revolves around a massive body at a particular distance. I was wondering if there is an intuitive way to understand the motion of a body influenced by two other massive bodies (say the moon being influenced by the earth and the Sun). Is there any analogy to the motion of a wheel that can be considered as a combination as translational and rotational motion (and both these motions can be mathematically treated separately)? Or do we need a simulator to visualize the actual path?</p>
g8420
[ 0.03776831924915314, 0.08691936731338501, 0.008222883567214012, 0.031128190457820892, 0.029431838542222977, -0.04097688943147659, 0.0361979641020298, 0.013311718590557575, 0.005166724789887667, -0.010815905407071114, 0.011112657375633717, -0.021167505532503128, 0.10890427231788635, 0.008718350902199745, 0.0101928124204278, -0.020587895065546036, 0.005499967839568853, -0.011603763327002525, 0.014029008336365223, 0.029357925057411194, 0.02870253287255764, 0.06298079341650009, 0.016863936558365822, 0.02678716741502285, -0.032342009246349335, -0.015285877510905266, -0.024993816390633583, -0.03979973495006561, 0.006870300974696875, 0.02533525787293911, 0.00026195537066087127, -0.04191115126013756, 0.040883868932724, -0.026438798755407333, -0.024135399609804153, 0.0116178710013628, -0.0014182244194671512, -0.028153330087661743, -0.044094573706388474, -0.013413817621767521, 0.03924211859703064, -0.004357707686722279, 0.03515687212347984, 0.046800702810287476, 0.04241484776139259, -0.056778568774461746, 0.025980262085795403, -0.02994299679994583, 0.024536365643143654, 0.027561265975236893, -0.025253817439079285, 0.022866539657115936, 0.004091070964932442, -0.011719664558768272, -0.02653556875884533, 0.024984270334243774, 0.03525408357381821, -0.06453396379947662, 0.020708519965410233, 0.05750580132007599, 0.016637474298477173, -0.057892970740795135, -0.02812965400516987, -0.01890628971159458, 0.07029889523983002, -0.02341347001492977, -0.06548008322715759, 0.014869969338178635, 0.023003436625003815, -0.03317158669233322, 0.04417711868882179, 0.015458543784916401, 0.004811989609152079, -0.037141844630241394, -0.03770297020673752, 0.0032020732760429382, 0.03688538074493408, -0.017344847321510315, 0.05544418469071388, 0.03405975550413132, -0.014345481991767883, 0.02662692219018936, 0.048000629991292953, 0.05649786442518234, 0.010996047407388687, -0.04992520064115524, 0.01127711683511734, 0.039110664278268814, -0.020141907036304474, 0.010737486183643341, 0.07643862813711166, -0.056578364223241806, -0.004885848145931959, 0.026283573359251022, -0.018875084817409515, -0.01575125940144062, -0.06293051689863205, 0.09509766846895218, 0.04177839308977127, 0.047985322773456573, -0.020434213802218437, 0.06773899495601654, -0.027339976280927658, 0.02713038958609104, 0.06117350235581398, -0.004432756919413805, 0.02279319055378437, 0.040069613605737686, 0.03236570209264755, -0.007240814156830311, -0.05190429836511612, -0.11726058274507523, 0.009998148307204247, 0.0010656991507858038, -0.025409754365682602, -0.06619377434253693, 0.04704001918435097, 0.0073649086989462376, 0.01725943200290203, 0.07188049703836441, 0.014026373624801636, 0.0221853069961071, -0.05696643516421318, 0.08838273584842682, 0.027101123705506325, -0.014320455491542816, -0.011541228741407394, 0.02004861645400524, 0.03141516074538231, -0.006583180278539658, 0.048095911741256714, -0.004835320170968771, 0.034306883811950684, 0.01668708585202694, 0.017349189147353172, 0.03830625116825104, -0.017393721267580986, 0.01770639233291149, -0.04259597882628441, 0.029771512374281883, -0.0018441398860886693, -0.053623538464307785, -0.05313052237033844, -0.008823146112263203, -0.07803916931152344, 0.04870859161019325, -0.010250518098473549, -0.009522940032184124, 0.013818111270666122, 0.0006035171099938452, 0.03439846634864807, 0.07057052850723267, -0.0007885729428380728, -0.036249034106731415, 0.0646914392709732, 0.008995496667921543, 0.0026121996343135834, 0.007911819033324718, -0.02793380618095398, -0.021772438660264015, 0.030689459294080734, 0.0068534319289028645, 0.0013154776534065604, 0.008922928012907505, -0.010396873578429222, -0.01316293329000473, -0.048314325511455536, -0.04936137795448303, -0.03625008091330528, -0.02902328036725521, -0.08421345055103302, -0.043219488114118576, -0.003045744728296995, 0.09394730627536774, 0.026810375973582268, 0.03520164638757706, -0.006925077177584171, -0.021710921078920364, -0.04507521912455559, 0.041083239018917084, -0.029378853738307953, -0.010004589334130287, -0.03150065988302231, 0.027748925611376762, -0.001908387173898518, 0.003089179750531912, 0.01982223428785801, 0.026720769703388214, -0.08187990635633469, 0.04664967581629753, -0.007470758631825447, 0.0004483822558540851, 0.008891290985047817, -0.012055445462465286, -0.003491109935566783, 0.012393409386277199, 0.007748935371637344, 0.002980234567075968, -0.019929366186261177, 0.043024394661188126, 0.004297649022191763, 0.015690719708800316, 0.048216283321380615, -0.01123022474348545, -0.016771771013736725, 0.015938328579068184, 0.005330776795744896, 0.0046606119722127914, -0.007821439765393734, -0.004452943801879883, 0.035733457654714584, 0.041630566120147705, 0.014682476408779621, 0.0009668467100709677, -0.09315148741006851, -0.007194981910288334, -0.04451179504394531, -0.017331061884760857, 0.022872988134622574, -0.013741414994001389, 0.021241426467895508, -0.020912492647767067, 0.02219950407743454, -0.018322573974728584, -0.018706487491726875, -0.01579863205552101, -0.08444597572088242, 0.016031509265303612, 0.05041397362947464, 0.024552565068006516, -0.03362871706485748, -0.0038827606476843357, 0.05829261988401413, 0.014618722721934319, -0.000457657384686172, 0.005871199071407318, -0.031357258558273315, -0.012515256181359291, 0.001174330711364746, 0.06464675813913345, 0.06449011713266373, -0.04889751970767975, -0.03719373047351837, -0.05280619114637375, 0.039192430675029755, -0.02209804207086563, 0.07828264683485031, 0.03770171478390694, 0.010730658657848835, 0.03542718291282654, -0.03551347181200981, -0.009976563043892384, -0.058104053139686584, -0.032625485211610794, 0.008602207526564598, 0.005556514021009207, -0.07397887855768204, 0.0019696250092238188, -0.033289585262537, 0.022012637928128242, 0.014268447645008564, -0.03858812898397446, 0.03173451125621796, 0.030237514525651932, -0.03661348670721054, -0.054459597915410995, -0.0038128788582980633, -0.00911798793822527, 0.023126211017370224, -0.029051559045910835, -0.045244500041007996, 0.004612368997186422, 0.034006986767053604, 0.007090038154274225, -0.052223168313503265, -0.01285438984632492, -0.0034406522754579782, -0.0379326269030571, 0.012068319134414196, 0.04760058596730232, -0.000542798254173249, -0.010826470330357552, -0.028561538085341454, 0.01705765724182129, 0.06582014262676239, -0.00459865340963006, -0.0008672004914842546, 0.024019848555326462, 0.013262652792036533, 0.002257617423310876, -0.017878562211990356, 0.008486706763505936, 0.05963870882987976, 0.03571143001317978, -0.013786002062261105, 0.07251472771167755, 0.03505362570285797, 0.022984886541962624, -0.010390445590019226, 0.028422528877854347, 0.0009208605624735355, -0.04394112154841423, 0.039049047976732254, 0.06902091950178146, 0.013621208257973194, 0.001336956862360239, -0.04748003929853439, -0.05776291713118553, 0.06019464135169983, 0.008397159166634083, -0.041846927255392075, 0.011099700815975666, -0.06029028818011284, -0.0011317151365801692, -0.0549929253757, 0.03264667093753815, -0.05267021432518959, 0.023602092638611794, 0.04825674369931221, 0.019146693870425224, -0.030742470175027847, -0.06050390750169754, 0.009762861765921116, 0.003475363366305828, 0.00286861602216959, 0.058943796902894974, -0.03245740756392479, -0.05056954175233841, -0.014447608031332493, -0.0830192044377327, -0.028088193386793137, -0.014400151558220387, -0.0330517552793026, -0.0012217427138239145, -0.0457276813685894, -0.00016060154302977026, 0.05067170411348343, -0.03873829543590546, 0.0686446875333786, -0.023187875747680664, 0.003727739444002509, -0.049265872687101364, -0.0046862829476594925, -0.0476209819316864, 0.009501135908067226, 0.0030509037896990776, -0.009866461157798767, -0.028821580111980438, -0.008582825772464275, -0.08941097557544708, -0.0025042230263352394, 0.01190404873341322, -0.02137714810669422, -0.06960872560739517, -0.005656292662024498, 0.0006019299617037177, 0.05637738108634949, 0.0044301883317530155, -0.048542965203523636, -0.02257644198834896, -0.03460388630628586, 0.01491229422390461, -0.09294120967388153, 0.0409671925008297, 0.055832408368587494, -0.0036545037291944027, -0.029803277924656868, -0.02331089787185192, -0.03358275070786476, 0.006900670938193798, -0.002376375487074256, -0.020295722410082817, -0.007685445714741945, -0.006180784199386835, 0.06354305893182755, -0.0087112532928586, 0.04950939863920212, 0.010130846872925758, -0.03939715772867203, 0.010236040689051151, 0.05938192084431648, 0.03635789453983307, 0.01392081007361412, 0.012689915485680103, 0.017329663038253784, -0.021065518260002136, -0.03169628232717514, -0.013153587467968464, 0.03260474652051926, 0.003973995801061392, 0.028317799791693687, -0.08816410601139069, 0.0037409677170217037, -0.04033858701586723, 0.07664206624031067, -0.030614737421274185, -0.026935435831546783, -0.028870515525341034, 0.007085262332111597, -0.01153395976871252, -0.030280951410531998, 0.0322330966591835, -0.04009459540247917, -0.029554294422268867, -0.03987259417772293, -0.017664562910795212, 0.061411309987306595, -0.05087047442793846, 0.03985339030623436, 0.004524502903223038, 0.00863777007907629, 0.021919462829828262, 0.04980861768126488, -0.018757719546556473, 0.003319894429296255, 0.03435293957591057, -0.02976170741021633, -0.002272044774144888, 0.005319490097463131, 0.06533597409725189, -0.04458959028124809, 0.0796760842204094, 0.006604358088225126, -0.02082081511616707, -0.03127678856253624, 0.040011607110500336, 0.04676423221826553, -0.052921000868082047, -0.010552681051194668, 0.013322646729648113, -0.007614666596055031, 0.04350593313574791, 0.011319811455905437, 0.02111133560538292, -0.018118789419531822, 0.02442414127290249, 0.009260754100978374, 0.057466257363557816, 0.03880812227725983, 0.008810910396277905, -0.011289139278233051, 0.029242027550935745, 0.008473829366266727, -0.06177351996302605, -0.020434357225894928, 0.04833894968032837, -0.016641946509480476, -0.037596479058265686, -0.027903376147150993, -0.07551758736371994, -0.037484947592020035, -0.005268842913210392, -0.03728347644209862, 0.04530748724937439, -0.031241122633218765, 0.014314345084130764, 0.012074194848537445, 0.00030080348369665444, -0.013576490804553032, -0.04304392635822296, -0.0348985455930233, 0.002850810531526804, -0.025177977979183197, 0.002950047142803669, -0.056645121425390244, -0.05108004808425903, -0.0411217026412487, 0.05728527158498764, -0.002316781086847186, 0.03959943726658821, -0.05498957633972168, 0.014528291299939156, -0.024050472304224968, 0.03176330029964447, -0.019225196912884712, -0.02668157033622265, -0.02223030850291252, -0.029175082221627235, 0.027178306132555008, -0.052186980843544006, -0.01717396266758442, -0.018305273726582527, 0.05011295899748802, -0.04096325859427452, -0.004404174629598856, -0.033157188445329666, -0.016343019902706146, 0.006648510694503784, 0.03010725788772106, 0.05329083278775215, 0.008080468513071537, -0.0380680151283741, -0.021458877250552177, 0.01055933441966772, -0.04858759045600891, 0.0005063575808890164, -0.0033671727869659662, -0.005117484368383884, 0.015374948270618916, -0.00046043115435168147, 0.012799992226064205, 0.039832282811403275, 0.025176823139190674, 0.0447901152074337, 0.02748958207666874, 0.05526842921972275, 0.06631335616111755, -0.019170386716723442, -0.028614750131964684, 0.0736394077539444, -0.007550007198005915, 0.04308261722326279, -0.04719274491071701, 0.056092534214258194, -0.032394394278526306, -0.018496591597795486, 0.0391659252345562, -0.021163059398531914, 0.028353620320558548, -0.02850661799311638, 0.03827337548136711, -0.009460997767746449, 0.0157763734459877, 0.010949266143143177, 0.010683894157409668, -0.038943350315093994, -0.00017639818543102592, 0.019337857142090797, -0.0015632093418389559, 0.0068203178234398365, 0.003145456314086914, -0.07429653406143188, -0.013516716659069061, 0.03740692511200905, -0.037558265030384064, -0.07040975242853165, 0.04150315746665001, -0.03178625926375389, 0.06505616754293442, -0.044541358947753906, -0.0026311525143682957, 0.01344635896384716, 0.03586588054895401, 0.05945153161883354, -0.055123671889305115, 0.006037647370249033, 0.0011591875227168202, 0.05459817498922348, 0.052627768367528915, 0.02749652974307537, -0.05003425106406212, 0.03938120976090431, 0.005565714556723833, -0.0263445433229208, -0.018651839345693588, 0.04372624680399895, -0.03161836788058281, -0.0752318874001503, 0.03910931199789047, -0.032476264983415604, -0.013299405574798584, -0.010412350296974182, 0.05992620438337326, -0.02724270150065422, 0.003123464062809944, -0.020535269752144814, 0.009048528037965298, 0.0019931725692003965, 0.059178490191698074, 0.024832895025610924, -0.019058892503380775, -0.05975079536437988, -0.01919855922460556, 0.0018296249909326434, 0.04122383892536163, 0.0024707154370844364, 0.011359363794326782, 0.01079379953444004, -0.029000969603657722, 0.04260466992855072, 0.0297178253531456, -0.030038630589842796, 0.03922376036643982, 0.0043107992969453335, -0.02592639811336994, -0.014523928053677082, -0.06324747204780579, -0.0027424462605267763, 0.010560927912592888, -0.0030200837645679712, -0.017919469624757767, -0.0013949422864243388, -0.07215436547994614, -0.02836083620786667, -0.020579392090439796, -0.028291866183280945, -0.013503557071089745, -0.005243169609457254, -0.018772685900330544, 0.018496859818696976, 0.016092799603939056, -0.02708257921040058, 0.06095821410417557, -0.029270518571138382, -0.003629384795203805, 0.014323043636977673, -0.044354211539030075, -0.048847928643226624, 0.05224156007170677, -0.0176521148532629, 0.03375283256173134, 0.03071407973766327, 0.014346110634505749, 0.04854990541934967, -0.040567751973867416, 0.01114684622734785, 0.009708398953080177, -0.01797400787472725, -0.026941662654280663, -0.0462518148124218, -0.004609670024365187, -0.03446865826845169, 0.0116649828851223, -0.04416726529598236, 0.01200677640736103, -0.023085469380021095, -0.08700861036777496, 0.03272724896669388, 0.030782325193285942, -0.01297781802713871, 0.06915736198425293, 0.009592406451702118, 0.011007585562765598, 0.034161895513534546, 0.055215585976839066, 0.034294988960027695, -0.0393502376973629, 0.06083421781659126, 0.0032087238505482674, 0.06168106943368912, -0.004168481100350618, 0.022547651082277298, -0.037888042628765106, 0.06038564443588257, -0.06645816564559937, -0.05057418718934059, 0.03245702013373375, 0.0012834618100896478, -0.02616795152425766, 0.006689767818897963, -0.01917990855872631, -0.038407064974308014, -0.01082490012049675, 0.05870838463306427, -0.02081252634525299, 0.03168562799692154, -0.033253204077482224, -0.0047340658493340015, -0.005930999293923378, -0.03364628925919533, -0.04173359274864197, 0.009984968230128288, -0.03398823365569115, -0.03614294156432152, -0.015373433008790016, -0.003578010480850935, -0.018458902835845947, -0.003917860798537731, -0.029551807790994644, 0.028562016785144806, 0.026997460052371025, -0.00599327776581049, -0.04773079603910446, 0.09381961822509766, -0.03083175979554653, -0.02242746576666832, 0.0003762451815418899, -0.02874891087412834, -0.034201961010694504, -0.02036138065159321, 0.024355128407478333, 0.016230741515755653, 0.04539822041988373, 0.02708943746984005, 0.025553705170750618, 0.036272432655096054, 0.0011887958971783519, 0.020522018894553185, -0.08014393597841263, -0.04598130285739899, -0.025056878104805946, 0.05735211446881294, -0.04434650391340256, 0.006914261728525162, -0.02824513427913189, 0.023393606767058372, 0.0025203602854162455, 0.05458272248506546, 0.01988053321838379, 0.03347322344779968, -0.016138233244419098, 0.015093902125954628, 0.021986810490489006, -0.0008441683603450656, 0.0434526652097702, -0.0011995666427537799, -0.00742206210270524, 0.011305851861834526, 0.003187777940183878, -0.007422153372317553, 0.02702707052230835, 0.050907328724861145, 0.015861349180340767, 0.05179404467344284, -0.025630934163928032, 0.014574573375284672, 0.03175736218690872, 0.07673178613185883, -0.021736562252044678, 0.03757406398653984, -0.009518299251794815, -0.007077795919030905, 0.022097863256931305, -0.09311887621879578, -0.007198986131697893, -0.05412646010518074, 0.014865938574075699, -0.029673771932721138, 0.019923683255910873, -0.011652391403913498, 0.01285953912883997, 0.04541129246354103, -0.02095998078584671, 0.011273765936493874, -0.09706812351942062, 0.017499569803476334, -0.09711910784244537, -0.06281685084104538, -0.04790719971060753, 0.013838574290275574, -0.013895360752940178, -0.023637840524315834, 0.016226062551140785, -0.00476653128862381, -0.01859055645763874, 0.04317793250083923, 0.023649616166949272, 0.0068178847432136536, 0.024430152028799057, 0.010179516859352589, 0.05090917646884918, 0.04630845785140991, -0.0425356887280941, -0.030117092654109, 0.03500760346651077, -0.0005176811246201396, -0.09901605546474457, 0.00666886568069458, -0.05233737453818321, -0.021210746839642525, -0.03506968542933464, -0.0011246458161622286, -0.002230204176157713, -0.054215218871831894, -0.013610596768558025, -0.018234213814139366, -0.051223527640104294, 0.05101988464593887 ]
<p>There seems to have some (deep) relation between <a href="http://ncatlab.org/nlab/show/Seiberg-Witten+theory" rel="nofollow">Seiberg-Witten theory</a> and <a href="http://en.wikipedia.org/wiki/Superconductivity" rel="nofollow">superconductivity</a>. e.g. <a href="http://www.ams.org/journals/bull/2007-44-03/S0273-0979-07-01167-6/S0273-0979-07-01167-6.pdf" rel="nofollow">this Witten paper</a>.</p> <blockquote> <p>Q: Could someone introduce the relations between the twos both <strong>physically in terms of intuition</strong>? and <strong>mathematically in terms of formalism</strong>? How exactly is the relation?</p> </blockquote>
g8421
[ 0.02155349589884281, 0.04222128540277481, -0.0014172373339533806, 0.020805979147553444, 0.010903400368988514, 0.0007009284454397857, -0.0029701401945203543, 0.015766438096761703, -0.048737045377492905, 0.016220560297369957, -0.0861121118068695, -0.03650395944714546, 0.01986568048596382, 0.028155002743005753, -0.006741043645888567, -0.03269663453102112, 0.04337264597415924, 0.029243173077702522, 0.08723439276218414, -0.05645090341567993, 0.05579563230276108, 0.03915997967123985, -0.023880841210484505, -0.06379479169845581, -0.03598184883594513, -0.018090538680553436, 0.007750851567834616, -0.013996630907058716, 0.009142219088971615, -0.004765622317790985, 0.025137009099125862, -0.008452429436147213, 0.06093890219926834, 0.016909494996070862, -0.018875623121857643, 0.0006567042437382042, 0.0458388552069664, 0.03275949880480766, -0.018650980666279793, 0.02275191992521286, 0.00733904866501689, 0.08164118230342865, 0.018292447552084923, -0.05305508151650429, -0.043973714113235474, 0.014387155883014202, -0.052118439227342606, 0.01806618832051754, 0.017508160322904587, -0.0166217889636755, -0.016046661883592606, 0.02747316099703312, 0.04356751590967178, 0.011151564307510853, 0.010317342355847359, -0.013627615757286549, 0.1101190522313118, 0.04901481047272682, 0.025038238614797592, 0.017324084416031837, -0.006998230237513781, 0.0631512776017189, 0.03390307351946831, 0.03403463214635849, 0.0913199856877327, 0.017280859872698784, -0.001564229722134769, -0.028548387810587883, -0.0024690604768693447, 0.0058464971370995045, -0.05168604850769043, -0.08784034848213196, -0.0155746815726161, -0.024125821888446808, -0.012973594479262829, 0.05593032389879227, 0.06966850906610489, -0.016241448000073433, 0.04691338911652565, 0.007865933701395988, -0.014448815956711769, -0.01977429911494255, 0.04274503514170647, 0.025104453787207603, -0.021889759227633476, -0.029329583048820496, -0.033246126025915146, 0.010265999473631382, 0.013419275172054768, 0.01868481934070587, 0.007597284857183695, -0.02192661724984646, -0.0013823406770825386, -0.002445767866447568, 0.025372056290507317, -0.0003096105356235057, 0.03364543989300728, 0.022703707218170166, -0.03241298720240593, -0.04714444652199745, -0.01611340045928955, 0.01324580516666174, -0.020987728610634804, 0.01614021323621273, -0.025146804749965668, -0.027172543108463287, 0.024722114205360413, 0.022464614361524582, -0.01073244959115982, 0.02320641092956066, -0.09215085953474045, -0.0014030395541340113, -0.043974872678518295, 0.04632354900240898, 0.0028690414037555456, -0.017587311565876007, -0.02892433851957321, -0.03198729828000069, -0.02382681518793106, 0.0519094243645668, 0.005537050776183605, 0.0613178089261055, 0.024290306493639946, 0.07668986171483994, -0.01906549744307995, 0.013131605461239815, 0.035547468811273575, 0.03496098145842552, 0.006416009739041328, -0.0019027813104912639, 0.05702333524823189, -0.021581541746854782, 0.0313110388815403, 0.04277198016643524, 0.03497948497533798, 0.030230870470404625, -0.015574110671877861, -0.007575885858386755, -0.013514962047338486, -0.08335365355014801, -0.02739112824201584, 0.03272039443254471, -0.009099604561924934, -0.03857029229402542, -0.06735962629318237, -0.006034445948898792, -0.05140668898820877, -0.006382860708981752, -0.008096530102193356, -0.037007760256528854, 0.005521101877093315, 0.008128593675792217, -0.007026273291558027, -0.04627709463238716, -0.0045556011609733105, -0.01707339845597744, 0.0002807032142300159, -0.08183267712593079, -0.014628681354224682, -0.0178743414580822, -0.027684761211276054, -0.06578284502029419, 0.00004871760029345751, -0.06113538518548012, -0.03228584676980972, -0.031653061509132385, 0.046107217669487, 0.0023765035439282656, -0.047728944569826126, -0.0026592828799039125, -0.015953607857227325, 0.05030658468604088, -0.024404684081673622, 0.11889661848545074, 0.03618095442652702, 0.010473490692675114, 0.015641391277313232, -0.016864614561200142, -0.041147381067276, -0.014625763520598412, -0.031144147738814354, 0.02584466151893139, 0.00974352564662695, -0.0004556716594379395, -0.018173187971115112, 0.04343774542212486, 0.02615799382328987, 0.03652607649564743, -0.034888677299022675, -0.009990613907575607, -0.04997905343770981, -0.05159056559205055, -0.0004189237079117447, 0.038527414202690125, -0.0364980474114418, 0.021084362640976906, -0.026769060641527176, 0.03483441099524498, 0.0060758208855986595, -0.05883637070655823, -0.012297243811190128, 0.03066803328692913, 0.04124322906136513, -0.020365407690405846, -0.034676242619752884, 0.05914650857448578, -0.039469532668590546, -0.00842005293816328, 0.036027953028678894, -0.02520965412259102, -0.027912084013223648, -0.02406030334532261, 0.030272644013166428, -0.009687731973826885, -0.047366466373205185, -0.014894422143697739, 0.009360802359879017, -0.011509752832353115, -0.05901853367686272, 0.03684016689658165, 0.039636097848415375, -0.03323676064610481, 0.020777488127350807, 0.019095882773399353, -0.07961296290159225, -0.015622606500983238, 0.02199416048824787, -0.011396131478250027, 0.00032092948094941676, -0.02250717766582966, -0.062246546149253845, -0.033379148691892624, -0.008410216309130192, 0.01334945298731327, 0.014706899411976337, 0.09466297179460526, 0.014577837660908699, -0.022973965853452682, 0.017087707296013832, 0.03495430946350098, 0.041670896112918854, -0.012380494736135006, 0.002579015912488103, 0.0309734046459198, 0.014792351983487606, -0.06323742866516113, 0.035946790128946304, -0.014467249624431133, -0.021543610841035843, -0.009358513168990612, -0.02477087453007698, -0.02068125642836094, -0.020977191627025604, 0.002995529444888234, 0.05258503556251526, 0.01840849779546261, -0.007549999747425318, 0.05858762562274933, -0.04157600551843643, -0.059982165694236755, -0.0003828244807664305, -0.05118999257683754, 0.000045679655158892274, 0.050947342067956924, -0.05786003917455673, -0.017966507002711296, -0.03338021785020828, -0.0002573977399151772, -0.018095320090651512, -0.060049958527088165, -0.025886917486786842, 0.042755283415317535, -0.015112406574189663, -0.04639299213886261, -0.0476885549724102, -0.01665847934782505, 0.0033232811838388443, -0.013277039863169193, 0.0015043284511193633, -0.03360224887728691, 0.0007691415376029909, -0.01083623617887497, 0.015436257235705853, 0.014128726907074451, -0.03090166114270687, -0.03495137393474579, -0.022620366886258125, 0.030565356835722923, -0.004393207374960184, 0.005272690672427416, -0.03287506103515625, -0.002949574962258339, 0.04361187294125557, 0.029983123764395714, -0.02871597185730934, 0.04096062481403351, 0.05509144067764282, 0.007659240625798702, -0.017345178872346878, 0.016946787014603615, -0.05627995356917381, 0.026332387700676918, -0.018234331160783768, 0.010564598254859447, 0.032866597175598145, 0.04594392329454422, -0.01004717219620943, -0.051576465368270874, -0.01879947818815708, -0.004641273524612188, 0.003025521757081151, 0.08489154279232025, 0.014910397119820118, -0.02423097938299179, -0.0028080802876502275, 0.020063349977135658, -0.00881180539727211, 0.08260000497102737, 0.03219480812549591, -0.04707648232579231, -0.06497880071401596, -0.013685328885912895, 0.007806313224136829, 0.02790042571723461, 0.04740774258971214, -0.002701819408684969, -0.06850963085889816, 0.013248651288449764, -0.04876451939344406, -0.04472272843122482, 0.022299865260720253, 0.0027899930719286203, 0.008535124361515045, -0.006737331859767437, -0.10879596322774887, 0.0036417951341718435, -0.03054329939186573, 0.025776971131563187, 0.006992907263338566, 0.020139198750257492, 0.016260407865047455, -0.05696277692914009, -0.06391843408346176, 0.04895462095737457, -0.030111979693174362, 0.07596325874328613, -0.00048269645776599646, 0.006819126196205616, 0.00649908697232604, 0.0013471483252942562, -0.010583695024251938, 0.004652311559766531, 0.017882632091641426, 0.07195565849542618, -0.03663511574268341, 0.0015099033480510116, 0.03264778479933739, 0.019619926810264587, -0.029548024758696556, -0.013179199770092964, 0.02136996015906334, 0.042846281081438065, 0.024073490872979164, -0.04056055471301079, -0.0552983321249485, -0.018901607021689415, 0.017832987010478973, 0.015551633201539516, -0.032605644315481186, -0.016771426424384117, -0.020031604915857315, -0.059195950627326965, 0.0015281082596629858, 0.03558826819062233, 0.07442368566989899, -0.04771976172924042, 0.001314504654146731, 0.022691044956445694, -0.04161765053868294, 0.06305350363254547, 0.0633317083120346, 0.04752461612224579, 0.06068522855639458, 0.014080175198614597, 0.04029669985175133, -0.05761076509952545, -0.012842348776757717, 0.060531068593263626, 0.0013265202287584543, -0.04450880363583565, -0.021182484924793243, 0.06196670979261398, -0.03769543766975403, 0.0049387565813958645, 0.03683396428823471, 0.017956441268324852, 0.003918307833373547, -0.004947748500853777, -0.038750775158405304, -0.005936235189437866, -0.0012923675822094083, 0.016064448282122612, 0.03804607689380646, -0.02977081574499607, -0.01430797390639782, -0.024409499019384384, -0.02345794253051281, -0.04768577590584755, -0.007652642671018839, -0.04284544661641121, 0.022890660911798477, -0.062118496745824814, 0.010937179438769817, -0.06691159307956696, 0.017550328746438026, -0.003077087691053748, -0.027864469215273857, -0.08864395320415497, 0.05735093355178833, -0.01401885412633419, 0.022852882742881775, -0.02897052839398384, 0.05339481681585312, -0.027312781661748886, 0.0028858152218163013, 0.052140869200229645, -0.01309568714350462, -0.006709257606416941, 0.020010940730571747, -0.015364845283329487, 0.012304181233048439, 0.04025132209062576, -0.0056669702753424644, 0.016102563589811325, -0.07995391637086868, -0.006420898251235485, -0.03531184047460556, 0.13369198143482208, -0.058764152228832245, -0.0012974654091522098, 0.03321906551718712, 0.04129176214337349, 0.010316803120076656, -0.04438471794128418, 0.03911587968468666, 0.053295113146305084, -0.011942424811422825, 0.0196737851947546, -0.019148455932736397, -0.07572606205940247, -0.030038807541131973, 0.021017638966441154, 0.004187629092484713, -0.01161728985607624, -0.04563345015048981, -0.008979648351669312, 0.039383914321660995, 0.0073544797487556934, 0.018343839794397354, -0.03334331884980202, 0.00502242473885417, 0.029653066769242287, 0.03195099160075188, 0.004374267067760229, -0.013932541944086552, -0.002532715443521738, -0.041582491248846054, -0.04492891579866409, -0.01603548228740692, -0.019049758091568947, 0.017721185460686684, -0.008663929998874664, 0.016538288444280624, 0.01814850978553295, 0.02289571985602379, -0.006751095876097679, 0.012250175699591637, -0.0022497931495308876, -0.05056140199303627, -0.034802600741386414, -0.052480198442935944, -0.003428842406719923, 0.026145240291953087, -0.03291234374046326, 0.04260185360908508, 0.04505673795938492, -0.0006605663802474737, 0.02059468813240528, -0.04953258857131004, -0.024583622813224792, 0.0015825252048671246, -0.02991042472422123, 0.041049160063266754, 0.035210806876420975, -0.02158115990459919, -0.07075333595275879, 0.035530757158994675, -0.0018469559727236629, -0.019364364445209503, 0.010968772694468498, -0.020749777555465698, 0.0020797071047127247, 0.050283487886190414, 0.08411519229412079, 0.012214700691401958, 0.0784815326333046, 0.0689689889550209, -0.01259428821504116, -0.005463631823658943, -0.0083974190056324, 0.014532960020005703, 0.04484562948346138, -0.07570256292819977, 0.05490803346037865, 0.024857962504029274, 0.09368330985307693, -0.021976230666041374, -0.007362279109656811, -0.018818428739905357, -0.0035383645445108414, 0.05798579379916191, 0.03440628573298454, 0.019649647176265717, -0.059161119163036346, 0.0032780556939542294, -0.016850546002388, -0.0666290745139122, -0.009376883506774902, 0.10285859555006027, 0.03866112232208252, 0.006030983757227659, 0.0006743567646481097, 0.05520453304052353, -0.020794205367565155, 0.04856729879975319, -0.006439599208533764, 0.03474583849310875, 0.017544511705636978, -0.018892185762524605, 0.02324547991156578, 0.004532849881798029, 0.053071461617946625, -0.021833984181284904, 0.08559580892324448, 0.03796681389212608, -0.03777886927127838, -0.004826512187719345, -0.006462408229708672, 0.03925034776329994, -0.018344130367040634, -0.023488201200962067, 0.008472631685435772, -0.05173881724476814, 0.023710226640105247, 0.058186620473861694, 0.04637444391846657, -0.022936208173632622, -0.026395190507173538, -0.028769681230187416, 0.00900830514729023, 0.028056716546416283, 0.07853418588638306, -0.003830099245533347, 0.03945292532444, -0.025337204337120056, -0.020495403558015823, -0.028271380811929703, -0.0267641544342041, 0.06980357319116592, 0.056343693286180496, 0.03862302750349045, -0.004949469584971666, -0.007926003076136112, -0.04680172726511955, -0.028860483318567276, 0.03987317159771919, -0.0037325790617614985, -0.0303872749209404, 0.025772148743271828, -0.010083192959427834, 0.03332466632127762, 0.02928723208606243, 0.011630524881184101, 0.012493123300373554, -0.02616214193403721, 0.04783519729971886, -0.07277676463127136, 0.036196377128362656, 0.05441109091043472, 0.012392994947731495, -0.030938301235437393, -0.017229799181222916, -0.0295252725481987, -0.04623265191912651, 0.0021704286336898804, 0.056996915489435196, 0.035346414893865585, -0.026017801836133003, -0.026110954582691193, 0.01736554317176342, 0.00935633946210146, 0.04076676443219185, 0.03350101038813591, 0.05644448846578598, 0.022398585453629494, 0.0802561342716217, 0.044748108834028244, -0.002076334087178111, -0.05199696123600006, -0.024315103888511658, 0.013172668404877186, 0.06821791082620621, 0.006859391462057829, -0.0022402761969715357, 0.05451211705803871, -0.010020229034125805, -0.03573764115571976, -0.029586460441350937, -0.009357327595353127, 0.025486988946795464, -0.0006292611942626536, -0.034090470522642136, -0.011391377076506615, -0.019853636622428894, -0.026317749172449112, 0.015758845955133438, 0.012530404143035412, 0.0379144586622715, 0.015653666108846664, -0.004484019707888365, 0.014130549505352974, -0.07374867051839828, 0.05711657926440239, 0.00013156357454136014, 0.030804678797721863, -0.019899023696780205, -0.019379664212465286, 0.014031495898962021, 0.011107103899121284, 0.00666422164067626, -0.034611087292432785, -0.027637293562293053, 0.0159465242177248, -0.005622729659080505, -0.06649093329906464, -0.08741801232099533, 0.0276322141289711, 0.00006284702976699919, -0.07068286836147308, 0.015252984128892422, 0.06826292723417282, -0.03094075620174408, -0.07935255765914917, 0.012567698955535889, -0.05355105921626091, -0.00864753220230341, -0.05049882084131241, -0.03374405577778816, 0.015734370797872543, -0.02763868123292923, -0.03980245441198349, 0.009286988526582718, -0.03267335146665573, -0.03774218633770943, -0.0026743344496935606, 0.025488045066595078, 0.013079865835607052, -0.03408815711736679, 0.005567015148699284, -0.025011558085680008, -0.025050492957234383, -0.01633410155773163, 0.02058093436062336, -0.06114121899008751, -0.013379335403442383, -0.014620009809732437, 0.014158159494400024, -0.03370236977934837, -0.01388748548924923, -0.05515230819582939, -0.006695809308439493, -0.003985581453889608, -0.037434376776218414, 0.0018657559994608164, -0.03712749853730202, 0.057849712669849396, -0.02631228417158127, -0.006566736847162247, -0.06135014444589615, 0.028033552691340446, 0.017603324726223946, -0.005803159903734922, -0.0440686009824276, -0.0075090667232871056, 0.019517121836543083, 0.036666929721832275, -0.023203939199447632, 0.007148405071347952, 0.009724194183945656, 0.059163641184568405, 0.004238239023834467, -0.005775165744125843, -0.0008676087018102407, -0.03521433845162392, 0.008804857730865479, -0.006601272150874138, 0.013851488940417767, -0.009487029165029526, -0.08229635655879974, 0.011130285449326038, -0.020632607862353325, 0.03244161233305931, 0.05592164397239685, 0.02707996405661106, 0.04409785941243172, 0.01958957128226757, 0.004065405577421188, -0.030043067410588264, 0.02647981606423855, 0.00540151447057724, -0.030043337494134903, 0.0069534131325781345, 0.024517467245459557, -0.034899771213531494, -0.09057966619729996, 0.05078500509262085, -0.004382658749818802, -0.017737822607159615, -0.01359982043504715, 0.02866252139210701, -0.034586772322654724, 0.011299040168523788, 0.005872981622815132, 0.05824195593595505, -0.019476445391774178, 0.025910135358572006, 0.054546646773815155, 0.027073029428720474, -0.014602217823266983, -0.01877252757549286, 0.029040958732366562, -0.022974174469709396, -0.009543266147375107, -0.03714766353368759, -0.03921357914805412, -0.015584195032715797, -0.05506317317485809, 0.036517880856990814, -0.024140996858477592, -0.020302779972553253, 0.014436202123761177, 0.029431188479065895, -0.03976425528526306, 0.057129841297864914, 0.0061745294369757175, -0.009747311472892761, -0.04632232338190079, -0.045063260942697525, 0.068580761551857, 0.05799994617700577, 0.0039098551496863365, 0.0009056053240783513, -0.00017398738418705761, 0.02132830210030079, -0.02776666171848774, 0.007226826157420874, -0.04991386830806732, 0.025407886132597923 ]
<blockquote> <p>A chip has a thermal resistance of 0.007 K/J s and thermal capacitance of 1.6 J/K. You give it an impulse of heat equal to 100 J. How long does it take for the chip to cool to within 10% of the ambient temperature?</p> </blockquote> <p>I understand that I have to implement Newton's Law of Cooling, but I can't seem to grasp how I can find the ambient temperature nor the initial temperature.</p> <p>Any and all help is greatly appreciated.</p>
g8422
[ 0.06787055730819702, -0.006768381223082542, -0.005234279669821262, -0.013187623582780361, -0.01183491013944149, -0.06355087459087372, 0.036347419023513794, 0.05260929837822914, -0.047154493629932404, 0.013034434989094734, -0.05804555118083954, 0.07398909330368042, -0.00945302378386259, 0.021663421764969826, 0.019725877791643143, 0.02728399634361267, 0.06148380786180496, -0.020553555339574814, 0.08567388355731964, 0.056223127990961075, -0.05006597191095352, -0.06386316567659378, -0.04792372137308121, -0.043989673256874084, -0.04009324684739113, -0.021831192076206207, 0.026174018159508705, -0.010398832149803638, -0.10294962674379349, 0.03520725667476654, -0.04423394054174423, -0.013946736231446266, -0.014159726910293102, -0.04314212501049042, 0.01738041639328003, 0.020346423611044884, 0.040493398904800415, -0.020228343084454536, -0.026765964925289154, -0.02096293866634369, 0.013840682804584503, -0.030709413811564445, 0.03614269942045212, 0.035098735243082047, 0.03275437280535698, 0.04211502522230148, -0.02904587611556053, -0.037707261741161346, -0.07317313551902771, -0.036569345742464066, -0.029042184352874756, 0.027865929529070854, 0.01125625055283308, -0.03889617323875427, -0.06442472338676453, -0.02203337661921978, -0.02465808391571045, 0.042742177844047546, 0.02312043495476246, 0.01204736065119505, 0.024312617257237434, -0.032061491161584854, -0.019346065819263458, -0.04980754107236862, 0.030350476503372192, 0.010493193753063679, 0.007689440622925758, 0.00015466664626728743, -0.0038097475189715624, 0.044122543185949326, 0.025384224951267242, -0.05609625577926636, -0.022417468950152397, -0.013144131749868393, -0.023059844970703125, -0.058138906955718994, -0.0036652374546974897, 0.0065980879589915276, 0.01606879197061062, 0.03489769622683525, -0.0042509278282523155, -0.004152148496359587, 0.005800601560622454, -0.03951429948210716, -0.0209712665528059, -0.013257318176329136, -0.025477025657892227, -0.020126082003116608, -0.04975350201129913, 0.05510440096259117, -0.012293887324631214, 0.08741290867328644, 0.040724292397499084, 0.036771152168512344, 0.04889277368783951, 0.0075464448891580105, -0.03705146536231041, 0.037992678582668304, 0.0039458973333239555, 0.0347251296043396, 0.034953176975250244, -0.01934676058590412, 0.032914336770772934, -0.04909487068653107, -0.03964356705546379, 0.05488404259085655, -0.007367146201431751, 0.016666946932673454, -0.03917612507939339, 0.013466421514749527, -0.0018189647234976292, -0.030578942969441414, -0.0034647686406970024, -0.030512304976582527, -0.04133324697613716, -0.0009219745988957584, -0.006809446960687637, -0.020444609224796295, 0.012017765082418919, 0.06159380078315735, -0.025162214413285255, 0.041884832084178925, -0.03278721123933792, 0.014729858376085758, 0.038143090903759, -0.016695315018296242, 0.040006473660469055, -0.02412549778819084, -0.014309641905128956, 0.026429107412695885, 0.01492035761475563, 0.07802373915910721, -0.02664373628795147, -0.012111938558518887, 0.0051093995571136475, 0.017815198749303818, 0.02201027423143387, 0.023128949105739594, -0.04606730490922928, 0.02790812775492668, -0.012438607402145863, -0.004767735954374075, 0.01521483063697815, 0.017296457663178444, -0.06885542720556259, 0.022932428866624832, -0.036187250167131424, -0.014620468951761723, 0.02119271457195282, -0.013493853621184826, -0.008947600610554218, 0.08498834818601608, 0.028727039694786072, -0.0322914719581604, 0.008444362320005894, 0.011410362087190151, 0.05942279472947121, 0.011016123928129673, 0.032206982374191284, -0.002449305960908532, 0.0036087476182729006, 0.030884627252817154, 0.014699487946927547, 0.049964070320129395, -0.058285556733608246, -0.001932239974848926, -0.05331728607416153, 0.023475920781493187, 0.02888290211558342, -0.05118560791015625, -0.04391254484653473, -0.006645987741649151, -0.026882490143179893, 0.05048155039548874, -0.026125002652406693, 0.02092268317937851, 0.046911753714084625, 0.07821565866470337, 0.0395711213350296, -0.033641595393419266, 0.012891072779893875, -0.03184319660067558, 0.0020745291840285063, -0.03217451274394989, -0.004999520257115364, 0.03089040331542492, 0.037473760545253754, -0.012752631679177284, -0.01216468121856451, 0.020403988659381866, -0.024413911625742912, -0.034613318741321564, -0.0299661997705698, 0.06416750699281693, 0.00024692874285392463, -0.017055176198482513, 0.02370072901248932, -0.07261870056390762, -0.05069515481591225, 0.014814392663538456, 0.06368066370487213, 0.019388284534215927, -0.02410869486629963, 0.013499605469405651, 0.00958976149559021, 0.019721655175089836, 0.013028254732489586, 0.020286090672016144, -0.015340723097324371, 0.01269624475389719, 0.009436932392418385, 0.009963374584913254, 0.008888288401067257, 0.055716585367918015, 0.03679651394486427, 0.06300480663776398, 0.058592114597558975, 0.02425924874842167, -0.0426020622253418, 0.016042063012719154, 0.012507408857345581, 0.04928719624876976, 0.0034609001595526934, -0.05622245371341705, -0.04815524071455002, -0.03532601520419121, -0.06285493820905685, 0.023352617397904396, -0.02203463390469551, 0.03738424926996231, -0.08431451767683029, 0.010357472114264965, -0.03479533642530441, -0.017843768000602722, 0.030101101845502853, 0.06674835830926895, 0.003933506086468697, -0.0030173626728355885, 0.007172019686549902, 0.039575256407260895, -0.02164561115205288, 0.004559905268251896, -0.025679688900709152, 0.08878450095653534, -0.06152229383587837, -0.03784383460879326, -0.009496447630226612, -0.029661765322089195, -0.037157606333494186, -0.011061322875320911, -0.017617926001548767, 0.015619682148098946, -0.06276258081197739, -0.007893398404121399, -0.03821636363863945, -0.024092791602015495, 0.00033731406438164413, -0.0046900357119739056, -0.006995311006903648, -0.018891707062721252, 0.0056347958743572235, -0.04134276509284973, -0.022899020463228226, -0.015704642981290817, -0.05022726207971573, -0.003549403278157115, -0.03079424612224102, 0.01613951474428177, 0.0004374238196760416, 0.02553386241197586, -0.040526676923036575, 0.07263694703578949, 0.020666806027293205, 0.008403750136494637, -0.004887130111455917, -0.03625688701868057, 0.023636650294065475, -0.03545976057648659, 0.0027211359702050686, 0.0009882031008601189, -0.015578635968267918, -0.010576950386166573, -0.06132560968399048, 0.02151632495224476, 0.014512971043586731, -0.0663192868232727, -0.00047992024337872863, 0.05393002927303314, 0.022768601775169373, -0.07107862830162048, -0.013815134763717651, 0.00628153420984745, -0.029759762808680534, 0.009805172681808472, 0.034270692616701126, 0.042123544961214066, 0.04006647318601608, 0.011097212322056293, 0.03851684555411339, 0.054405055940151215, 0.04592542350292206, -0.013903006911277771, -0.008732610382139683, -0.02203039638698101, 0.007406070362776518, 0.029501231387257576, -0.028386976569890976, -0.047651201486587524, 0.02174891158938408, 0.01553258579224348, 0.03962939977645874, 0.006372897885739803, 0.07317963987588882, -0.05192480981349945, -0.038299866020679474, 0.0013830286916345358, -0.030500194057822227, 0.01954447478055954, 0.040497198700904846, -0.0038633099757134914, -0.03816308081150055, -0.058087076991796494, 0.013001801446080208, 0.0592581145465374, 0.032508160918951035, 0.03294210880994797, -0.016848605126142502, -0.030216550454497337, 0.052721645683050156, -0.020129363983869553, -0.019780157133936882, 0.012447976507246494, -0.052194368094205856, -0.009685409255325794, -0.050313983112573624, -0.055785004049539566, 0.01929844170808792, 0.01993495598435402, -0.0002422021934762597, 0.015524646267294884, -0.009817598387598991, -0.028208112344145775, -0.010212566703557968, 0.0121491439640522, -0.0021241868380457163, -0.04652484133839607, -0.027957115322351456, 0.0388670340180397, -0.02273259125649929, 0.018649151548743248, 0.0562574677169323, -0.04817358776926994, 0.006149833556264639, -0.007835502736270428, -0.03602219000458717, 0.06619089096784592, 0.007226868532598019, 0.04847606271505356, -0.027431149035692215, 0.03155926987528801, 0.03964397311210632, -0.0019920316990464926, 0.08524511009454727, -0.008182115852832794, -0.007413071114569902, 0.0140355434268713, 0.030448028817772865, 0.047192126512527466, 0.006965586915612221, 0.004866407252848148, -0.005835595075041056, -0.0011509283212944865, -0.002780514070764184, 0.024789955466985703, 0.04660078138113022, -0.0015482783783227205, 0.009426133707165718, 0.014008652418851852, 0.026493949815630913, 0.019835909828543663, -0.02912033535540104, -0.0006804831209592521, -0.03168880566954613, -0.01811256818473339, 0.06361838430166245, 0.03616218641400337, 0.020121660083532333, -0.016966920346021652, 0.017765911296010017, -0.045106757432222366, 0.030921421945095062, -0.020121395587921143, -0.008142883889377117, 0.01760849915444851, -0.005646311677992344, -0.022413179278373718, -0.0016226532170549035, 0.05641433224081993, -0.022665729746222496, -0.026259807869791985, 0.024081582203507423, 0.020739693194627762, 0.049897827208042145, -0.002234352519735694, 0.014109103940427303, 0.013632094487547874, 0.02954494021832943, -0.019218236207962036, 0.03612261638045311, 0.004823919851332903, -0.033775705844163895, 0.006646302528679371, 0.028014034032821655, -0.057268787175416946, 0.030374009162187576, -0.044979169964790344, 0.047451045364141464, -0.01562744565308094, 0.023489590734243393, -0.00098925712518394, -0.08244818449020386, -0.02609742432832718, -0.04562941566109657, -0.0016167382709681988, 0.011191992089152336, 0.028589844703674316, 0.017949378117918968, -0.041166145354509354, 0.05166158825159073, 0.009961356408894062, 0.006607641000300646, -0.009253296069800854, -0.0749116763472557, 0.05802594870328903, -0.06430476158857346, 0.04723823815584183, 0.013721215538680553, 0.038373976945877075, -0.022732045501470566, 0.05018462985754013, -0.010247045196592808, -0.022755339741706848, -0.054955173283815384, 0.03405158221721649, 0.022551825270056725, 0.11650988459587097, -0.014864599332213402, -0.0406811349093914, -0.03343462198972702, -0.02578011341392994, 0.026320690289139748, 0.04306349530816078, -0.12337975949048996, 0.028952347114682198, -0.028048677369952202, 0.021037867292761803, 0.009857788681983948, 0.01992572657763958, 0.033673640340566635, 0.05202198028564453, -0.08217385411262512, 0.010143903084099293, -0.025490906089544296, -0.027698323130607605, -0.05852847173810005, -0.01021043211221695, 0.04324378818273544, -0.005092805717140436, -0.03144341707229614, 0.04560361057519913, 0.035590630024671555, 0.02112356759607792, -0.012441376224160194, 0.06056883931159973, -0.0052393763326108456, 0.06266691535711288, 0.014878423884510994, 0.000023204265744425356, 0.0015860202256590128, 0.035128168761730194, -0.03577962890267372, 0.027659278362989426, -0.017020348459482193, 0.04483182728290558, -0.038698773831129074, -0.05212289094924927, -0.0534256286919117, 0.0026219328865408897, 0.030742378905415535, -0.0001445965317543596, 0.01176510564982891, 0.038783565163612366, 0.0008289244724437594, 0.054764650762081146, -0.009713257662951946, -0.021272098645567894, 0.01005434151738882, -0.034412432461977005, 0.01503436453640461, 0.0488557368516922, -0.023424839600920677, -0.01862536370754242, 0.015203476883471012, 0.04689705744385719, -0.026856321841478348, 0.0414261594414711, 0.00888085924088955, 0.008346150629222393, -0.011566785164177418, -0.0035933954641222954, 0.003932153806090355, 0.06270650774240494, 0.028815269470214844, -0.034001465886831284, 0.028292560949921608, -0.014024849981069565, 0.007353230379521847, -0.050270840525627136, -0.01908309943974018, 0.011119034141302109, 0.07763305306434631, -0.08302866667509079, -0.008730788715183735, 0.034178007394075394, -0.05537129193544388, 0.0652519091963768, -0.10665249079465866, -0.028429588302969933, -0.020461779087781906, 0.017951281741261482, -0.014299031347036362, -0.0035008362028747797, 0.00666127959266305, -0.037651389837265015, 0.013268768787384033, 0.024068569764494896, -0.024888312444090843, -0.02782045677304268, 0.010248316451907158, 0.0013786179479211569, -0.0033591915853321552, -0.009025457315146923, 0.0434032678604126, -0.030145935714244843, 0.017009729519486427, 0.0010756434639915824, -0.00929187424480915, 0.005153579171746969, 0.042253173887729645, -0.03889322280883789, 0.031141256913542747, 0.0026080282405018806, 0.02655183896422386, -0.06984134763479233, 0.060813210904598236, 0.011609749868512154, 0.01992587372660637, -0.03786858543753624, -0.005429847165942192, 0.022034786641597748, 0.03690515086054802, -0.009122231975197792, -0.015297375619411469, 0.005949460435658693, 0.017645062878727913, -0.03595597669482231, -0.030237263068556786, 0.009230270981788635, 0.062064748257398605, -0.0016652201302349567, 0.041710805147886276, -0.03178718686103821, -0.00986489187926054, -0.06274064630270004, 0.02477732114493847, 0.02486085332930088, -0.05323566123843193, 0.026525603607296944, 0.00933479331433773, 0.031757958233356476, -0.060727350413799286, 0.037126414477825165, 0.009184359572827816, -0.01163671724498272, -0.0019862663466483355, 0.02222440578043461, 0.014122790656983852, 0.00999485608190298, 0.034165069460868835, 0.019661858677864075, -0.013773486949503422, -0.03602629899978638, -0.020444698631763458, -0.0250809658318758, -0.04213191941380501, -0.028302647173404694, 0.003842899575829506, -0.03724295645952225, 0.0490582138299942, -0.028028234839439392, -0.003994487226009369, -0.06410445272922516, -0.0023951914627104998, -0.05966149643063545, -0.002593884477391839, 0.011515277437865734, -0.008377880789339542, 0.013034066185355186, 0.013713842257857323, 0.06705030053853989, -0.0008585582836531103, -0.013025273568928242, 0.06896793842315674, -0.020419469103217125, -0.002880557905882597, 0.04437655583024025, 0.06791094690561295, 0.02469046786427498, -0.04585433378815651, -0.03884686157107353, 0.06824085116386414, 0.09037794917821884, -0.012484950013458729, -0.01698467880487442, 0.011838664300739765, 0.020094241946935654, 0.02888653613626957, 0.04751600697636604, 0.026056984439492226, -0.010931087657809258, 0.007411647122353315, -0.03427920863032341, -0.03740672767162323, 0.031094975769519806, 0.014931087382137775, 0.04729369282722473, -0.024078303948044777, 0.04799525812268257, -0.0010320129804313183, 0.05437057465314865, 0.01762242428958416, -0.04764305800199509, -0.0263688787817955, 0.04117410629987717, -0.018746139481663704, -0.03795186057686806, 0.03981003537774086, 0.041753098368644714, -0.05008464679121971, 0.017712732776999474, 0.03518252447247505, 0.014543400146067142, -0.004486945923417807, 0.025912098586559296, -0.0062222592532634735, 0.010802952572703362, 0.03436155244708061, -0.053556300699710846, 0.0008667655056342483, 0.0008360203937627375, -0.04415290802717209, -0.07437058538198471, -0.017413554713129997, -0.000336676137521863, 0.03563520312309265, 0.042436156421899796, 0.013936938717961311, 0.01924731396138668, 0.03662240132689476, -0.12669891119003296, -0.03088885359466076, -0.06087159737944603, -0.04460764676332474, 0.02397402748465538, -0.021876055747270584, 0.00999277364462614, -0.014002090319991112, 0.011911090463399887, -0.043660689145326614, -0.044273603707551956, 0.00875681173056364, 0.007174788974225521, -0.05401903763413429, -0.03501715138554573, 0.011959412135183811, 0.07639576494693756, -0.00892212800681591, -0.015589593909680843, 0.04837191104888916, 0.003241503844037652, -0.05736705660820007, -0.01324833557009697, -0.035498280078172684, -0.07636461406946182, -0.006714235991239548, 0.07256090641021729, -0.0014125026063993573, 0.002185384277254343, -0.0027053665835410357, 0.015463392250239849, 0.0342087522149086, -0.04296658933162689, 0.05148829147219658, 0.02274206653237343, -0.07331828027963638, 0.020468810573220253, -0.011663004755973816, -0.04456523060798645, -0.06887297332286835, 0.030561646446585655, -0.004728478845208883, 0.004716333467513323, 0.0038133261259645224, -0.04431819170713425, 0.017211979255080223, 0.010658591985702515, -0.06068970635533333, -0.044016025960445404, -0.0010268939658999443, -0.0133420554921031, -0.024444257840514183, -0.0037332596257328987, 0.017433669418096542, -0.004972964059561491, 0.0020548617467284203, -0.04857610911130905, -0.05402896925806999, 0.0448007732629776, 0.01842268742620945, -0.04939476400613785, 0.00421711802482605, -0.01619751751422882, 0.004835924133658409, -0.03151089325547218, -0.03434119373559952, 0.04688630998134613, 0.011939248070120811, -0.020296236500144005, 0.029964474961161613, 0.07695495337247849, -0.004060763865709305, -0.02763134241104126, -0.04682309553027153, -0.02500341832637787, 0.003203455125913024, -0.029956571757793427, -0.0296548493206501, 0.06650266796350479, 0.05621776357293129, -0.04219137877225876, 0.06626980751752853, -0.029058106243610382, -0.0833841860294342, -0.022084122523665428, 0.007250186521559954, -0.03769117593765259, -0.038653209805488586, 0.02929145283997059, -0.007116761989891529, -0.028043432161211967, -0.07727304846048355, -0.026869429275393486, 0.003693261882290244, 0.0657288134098053, 0.06895583868026733, 0.010770702734589577, 0.010751631110906601, -0.09495475888252258 ]
<p>I've been struggling with this question all morning, yet I get the feeling the answer is frightfully simple. </p> <p>If Orion appears upside down in the Southern Hemisphere and the right way up in the Northern Hemisphere, what does it look like in equatorial countries such as Kenya, Colombia, and Ecuador, bearing in mind that Orion itself is in the equatorial region of the celestial sphere?</p> <p>I initially thought it could just be a matter of perspective: If you're on the equator and facing North you'll see it the right way up,but see it upside down if you're facing South. But then surely that approach would apply even if you were in the Northern or Southern Hemisphere. </p> <p>I reckon the times Orion is visible in various parts of the world will also have to be factored in. For example, it is visible at night late spring to summer in the Southern Hemisphere.</p> <p>Could anyone offer me some advice? I fear I may be over-thinking this.</p> <p>Thanks in advance.</p>
g8423
[ 0.011766926385462284, 0.02049332857131958, 0.006702949292957783, -0.03307800740003586, 0.020565930753946304, 0.04331859573721886, 0.020625239238142967, 0.005104304291307926, 0.004585959482938051, 0.023680726066231728, 0.03276139870285988, 0.005062569864094257, 0.026257913559675217, 0.006039115600287914, 0.06032146140933037, -0.0024614003486931324, -0.01876954175531864, -0.01915774866938591, 0.036336749792099, 0.03984872251749039, 0.006249043624848127, -0.014433012343943119, 0.003594842040911317, 0.00900852307677269, -0.07137438654899597, 0.02818141132593155, -0.012133260257542133, -0.01486383005976677, -0.003951048944145441, -0.013259991072118282, 0.05437520518898964, 0.023364951834082603, 0.03996116295456886, -0.03921389952301979, -0.05367693305015564, 0.05695910379290581, 0.006531077437102795, 0.04147116467356682, 0.002255552913993597, 0.0005393250030465424, 0.009848779998719692, -0.020991696044802666, -0.025113478302955627, 0.04008497670292854, 0.004874962382018566, -0.0032116917427629232, 0.014433218166232109, -0.00039885647129267454, 0.023448942229151726, -0.01788264699280262, -0.012247195467352867, 0.021699346601963043, 0.02276967279613018, 0.011148305609822273, 0.027765164151787758, 0.013124880380928516, 0.05656522884964943, 0.0052790334448218346, 0.0494224987924099, 0.022701671347022057, 0.003747776849195361, -0.004083595704287291, -0.008702840656042099, -0.03018377162516117, 0.015323899686336517, 0.04254493862390518, 0.010808738879859447, 0.01613427884876728, 0.011224840767681599, -0.025233924388885498, 0.030308052897453308, -0.048507507890462875, -0.03178047016263008, -0.0579039491713047, -0.09900899976491928, 0.053280413150787354, 0.008285067044198513, -0.017056627199053764, 0.012970663607120514, 0.04422727972269058, 0.0030767633579671383, 0.017514148727059364, -0.03352676331996918, 0.04597830772399902, -0.0005828910507261753, 0.04081730544567108, 0.037998899817466736, -0.06630787998437881, -0.029396554455161095, 0.007174962665885687, 0.031004441902041435, 0.0522441640496254, 0.013054762966930866, -0.018186915665864944, 0.023887190967798233, -0.04733102396130562, -0.02351403795182705, 0.06492529064416885, -0.022999625653028488, 0.04004199802875519, -0.01597857102751732, -0.0210481658577919, -0.006623045541346073, 0.0072032250463962555, -0.005796840880066156, 0.01201440580189228, 0.052036263048648834, -0.059195395559072495, -0.022874465212225914, -0.06390118598937988, -0.09170970320701599, 0.017310472205281258, 0.03542376309633255, 0.04230322316288948, -0.0795804113149643, -0.0035276992712169886, 0.030867604538798332, -0.01595785841345787, 0.06985856592655182, 0.09380357712507248, 0.03129719942808151, 0.04694901779294014, 0.008558408357203007, 0.01993643119931221, 0.020041830837726593, -0.011261483654379845, -0.035837411880493164, -0.031250596046447754, -0.00699700228869915, -0.01291415374726057, 0.050415702164173126, 0.051023248583078384, -0.04666624218225479, 0.014724616892635822, 0.0014811964938417077, -0.04508784040808678, -0.002478026319295168, -0.007336670532822609, 0.002255665138363838, -0.012882435694336891, 0.0748496800661087, -0.016582880169153214, 0.041796743869781494, -0.0023998888209462166, 0.013230030424892902, -0.034630656242370605, -0.006481312680989504, -0.010918905958533287, 0.0368490144610405, -0.042697735130786896, -0.011016503907740116, 0.010499279014766216, 0.02554304711520672, -0.02731124870479107, -0.018377108499407768, -0.016064077615737915, 0.0004092053568456322, 0.012418856844305992, 0.02415609546005726, 0.014464297331869602, 0.029139474034309387, -0.026644501835107803, 0.05461770296096802, -0.010680178180336952, -0.027564888820052147, 0.015595936216413975, -0.053938128054142, -0.05523419752717018, 0.013059784658253193, -0.035241588950157166, 0.0015660474309697747, -0.010970034636557102, 0.015185321681201458, -0.008636988699436188, 0.027943575754761696, -0.008822347968816757, 0.0777868777513504, 0.01851479895412922, -0.03860990330576897, 0.001314941793680191, -0.03519217297434807, 0.020217686891555786, -0.023599212989211082, 0.0015445303870365024, -0.02004452981054783, -0.1043493002653122, -0.015373718924820423, 0.005380857735872269, 0.009718727320432663, 0.004168269690126181, 0.0856994241476059, -0.04574836418032646, -0.039053816348314285, 0.03351987525820732, 0.013452465645968914, -0.013164373114705086, -0.019594138488173485, -0.00959688425064087, -0.035238999873399734, 0.03966376557946205, 0.010382385924458504, -0.03676323965191841, 0.008827664889395237, 0.05707917734980583, -0.02064439281821251, 0.011809646151959896, 0.029616042971611023, 0.049892544746398926, 0.0440305657684803, -0.05338126793503761, -0.03039293922483921, -0.03871788829565048, 0.022074488922953606, -0.009758739732205868, -0.01711747981607914, 0.07235933095216751, -0.030316082760691643, 0.019324183464050293, -0.0328512042760849, 0.013706505298614502, 0.014826914295554161, -0.08339330554008484, -0.016988076269626617, -0.01817571558058262, 0.025129804387688637, -0.005601300857961178, -0.12180444598197937, -0.008781804703176022, 0.03198054060339928, 0.01861329935491085, -0.03555784374475479, -0.02805284410715103, 0.03349396958947182, -0.012537514790892601, 0.021208712831139565, -0.018609941005706787, 0.007912098430097103, -0.051002562046051025, 0.02145175263285637, -0.06327302008867264, -0.06572021543979645, -0.025259487330913544, 0.002941628685221076, -0.01255487184971571, 0.02587396651506424, -0.026021363213658333, 0.056753434240818024, 0.015570580959320068, -0.05313349515199661, 0.03736843168735504, 0.07061532884836197, -0.006504518911242485, -0.0638808161020279, 0.01839435286819935, 0.002181689953431487, 0.06641345471143723, -0.0617850236594677, 0.08230194449424744, -0.014595638029277325, -0.0008577097905799747, -0.04598658159375191, -0.07238844037055969, -0.020676277577877045, 0.00792772602289915, -0.03768879547715187, -0.00037793771480210125, -0.05953822284936905, -0.010498099960386753, 0.00044384662760421634, 0.0007481623906642199, -0.036590974777936935, 0.04878322035074234, 0.00669220881536603, 0.045741140842437744, -0.05710447579622269, -0.031474120914936066, -0.031048286706209183, -0.013612406328320503, -0.0024121247697621584, 0.006788121536374092, 0.030933436006307602, -0.04614083468914032, 0.01044901181012392, 0.05654992163181305, 0.061740580946207047, 0.01961652562022209, -0.048926129937171936, 0.045435477048158646, -0.04729728400707245, -0.0004950236179865897, -0.012019953690469265, 0.03519104793667793, 0.014708053320646286, -0.012788143940269947, 0.03586195409297943, 0.0052736434154212475, 0.02751525118947029, -0.025224141776561737, -0.016673371195793152, -0.047839194536209106, -0.008855244144797325, -0.015510188415646553, 0.014429965987801552, 0.015827374532818794, 0.06578678637742996, 0.0012032455997541547, 0.013292078860104084, -0.013561191968619823, -0.002293888246640563, -0.00531978253275156, -0.025293702259659767, 0.06655886024236679, -0.006127181928604841, -0.012952062301337719, 0.014157854951918125, 0.023653460666537285, -0.03900418430566788, -0.0473327711224556, 0.02926475927233696, -0.008239843882620335, -0.033691078424453735, -0.05699285492300987, -0.022015662863850594, 0.048646241426467896, 0.03915488347411156, -0.02389826811850071, 0.00894765555858612, -0.015450898557901382, -0.10575186461210251, 0.007156915031373501, -0.04671558365225792, 0.001120864530093968, -0.019026782363653183, 0.03588998317718506, -0.012106804177165031, 0.06763889640569687, -0.00961774680763483, -0.015141143463551998, 0.008099178783595562, 0.0514284148812294, 0.05373534932732582, -0.01828566938638687, -0.02837333083152771, -0.02515501342713833, 0.002827131189405918, -0.01396264135837555, -0.04919925332069397, -0.017696795985102654, -0.029366714879870415, 0.023869141936302185, -0.01188166718930006, -0.03940423205494881, 0.06153209134936333, -0.04398732632398605, 0.023099888116121292, 0.00932189542800188, 0.03023463301360607, 0.023945225402712822, 0.021161744371056557, -0.007990527898073196, 0.003144504502415657, -0.0033472473733127117, 0.0072789378464221954, -0.004394852090626955, -0.019208265468478203, -0.01825123280286789, 0.028953468427062035, 0.01465133298188448, -0.025764474645256996, -0.01773632876574993, 0.04680429399013519, 0.04262372851371765, -0.035233139991760254, 0.004429603461176157, -0.0390903502702713, -0.020988551899790764, -0.024031708016991615, 0.03005894087255001, 0.04560905694961548, 0.01692797988653183, -0.06069231405854225, -0.024071721360087395, 0.017448635771870613, -0.01923278160393238, 0.0642298012971878, 0.059961143881082535, 0.025867190212011337, -0.022739045321941376, -0.008875234052538872, -0.01958457939326763, 0.011641433462500572, -0.05193467438220978, 0.0004242270370014012, 0.039558060467243195, 0.012293140403926373, 0.0074910675175487995, 0.023879675194621086, 0.0051915207877755165, 0.013590718619525433, -0.01067215297371149, 0.0009050325024873018, -0.015393855981528759, 0.06004290282726288, -0.011602314189076424, -0.02572258561849594, -0.008678457699716091, -0.009082270786166191, -0.0017142315628007054, -0.031238039955496788, -0.0153532475233078, 0.06123567000031471, 0.039718978106975555, 0.024277612566947937, -0.02582983486354351, 0.038508422672748566, 0.0744696855545044, 0.02287113666534424, 0.02779005467891693, 0.05483565106987953, 0.02527656964957714, 0.042330071330070496, 0.043908581137657166, 0.0017982774879783392, -0.04105052724480629, -0.06357698142528534, 0.09849673509597778, 0.021638374775648117, 0.02701740711927414, -0.030591612681746483, 0.009897366166114807, 0.04040423408150673, -0.028232036158442497, 0.0439194031059742, 0.004906076937913895, -0.0843864381313324, -0.002756495727226138, 0.03637975826859474, 0.01932818628847599, 0.05320504307746887, -0.05392250791192055, -0.0009638965711928904, 0.04726472124457359, 0.013269892893731594, -0.021051956340670586, -0.04025183618068695, 0.06446535885334015, -0.011601783335208893, -0.01382411364465952, 0.029221365228295326, -0.08349071443080902, -0.03036627173423767, -0.0028140966314822435, 0.000514013459905982, -0.01360121089965105, -0.03659166395664215, -0.023836521431803703, 0.002343539847061038, 0.05978363752365112, 0.012338929809629917, -0.036786049604415894, -0.008932662196457386, -0.06077883020043373, 0.0010529994033277035, -0.026594875380396843, 0.024996289983391762, -0.005164025351405144, -0.040020186454057693, -0.012523983605206013, -0.016158968210220337, 0.01840098574757576, -0.04410591349005699, 0.032348014414310455, 0.016557015478610992, -0.041946474462747574, -0.04337076097726822, 0.016985928639769554, 0.009529905393719673, -0.015416890382766724, 0.0008518346585333347, -0.012514404021203518, -0.02289622090756893, -0.018436089158058167, 0.05736761912703514, 0.03653612732887268, -0.07059533149003983, 0.0024545073974877596, 0.0453592948615551, -0.05477246642112732, 0.016017090529203415, -0.017385708168148994, 0.011348352767527103, -0.03644690662622452, -0.017528723925352097, 0.006595607381314039, -0.03512820601463318, 0.0155662652105093, -0.032951150089502335, -0.03163895383477211, 0.02627052739262581, -0.0223186407238245, -0.054154470562934875, 0.05439818650484085, -0.003376382403075695, 0.03964921087026596, 0.02037002146244049, 0.06506293267011642, 0.03468840941786766, -0.02739572897553444, 0.07399391382932663, 0.03778832405805588, -0.07175645977258682, -0.05951187014579773, -0.07735118269920349, 0.052248265594244, -0.0067005460150539875, -0.07858333736658096, -0.07254990935325623, 0.04897179827094078, 0.03780892491340637, -0.023858055472373962, -0.030338162556290627, -0.01450328715145588, -0.020757224410772324, -0.008330654352903366, 0.026179911568760872, -0.01978166401386261, 0.0023342734202742577, 0.048520348966121674, 0.015534985810518265, -0.0714615061879158, -0.004665064625442028, 0.026139281690120697, 0.022131631150841713, 0.011085673235356808, 0.04574374482035637, -0.017282266169786453, 0.0416901670396328, 0.03923220559954643, 0.11351180821657181, 0.003203850705176592, 0.012303970754146576, -0.04980191960930824, 0.05194295570254326, 0.013668513856828213, -0.07188869267702103, 0.014123735949397087, 0.0273868590593338, 0.024181552231311798, -0.00865266378968954, 0.03402581438422203, -0.03484274074435234, 0.012217782437801361, -0.01515608374029398, 0.06357406079769135, -0.03250475227832794, -0.01285336259752512, 0.023832542821764946, 0.002620360814034939, 0.00016805343329906464, -0.033044591546058655, 0.0781426951289177, -0.044603150337934494, 0.030336551368236542, 0.01002101507037878, -0.0037029788363724947, -0.028764987364411354, -0.029708337038755417, 0.04513714835047722, 0.07178812474012375, 0.025735074654221535, 0.03874605521559715, -0.03255929425358772, 0.0368480421602726, 0.01069258525967598, 0.05455809459090233, 0.006436873227357864, -0.026373669505119324, 0.004576729144901037, 0.005033116787672043, 0.02899443544447422, 0.04278642684221268, -0.028477787971496582, 0.008765135891735554, 0.033122215420007706, 0.005840491969138384, 0.015168844722211361, -0.01305739488452673, 0.0480659082531929, 0.018793292343616486, -0.0276158656924963, 0.014086603187024593, -0.025532495230436325, 0.01595868542790413, -0.0016764706233516335, 0.023031098768115044, -0.025227701291441917, -0.06991244852542877, 0.011790008284151554, -0.050318751484155655, -0.011172286234796047, -0.004392705392092466, -0.04984569549560547, 0.05701678618788719, 0.0011459836969152093, 0.05423108488321304, -0.00462453905493021, -0.006970252376049757, 0.061161842197179794, 0.12157004326581955, 0.016644198447465897, 0.03310820087790489, -0.019907856360077858, -0.0032821346540004015, -0.022186866030097008, 0.0029525349382311106, -0.06430602073669434, 0.0018112012185156345, -0.024718832224607468, -0.044409412890672684, 0.06077873334288597, -0.0015079256845638156, 0.04214158281683922, -0.019802479073405266, -0.01088374387472868, -0.033815477043390274, -0.012130477465689182, -0.07014498114585876, 0.008617551997303963, 0.00017668982036411762, -0.02751404233276844, -0.020633341744542122, 0.03299810364842415, -0.005874781869351864, 0.023305805400013924, 0.019365444779396057, -0.054089415818452835, -0.05394277721643448, 0.003231261856853962, 0.01317705400288105, -0.02042824774980545, -0.0028750819619745016, -0.024067489430308342, 0.0036652772687375546, -0.04765147715806961, -0.04530732333660126, 0.00888917874544859, -0.004343063570559025, -0.008727401494979858, 0.0005588363274000585, 0.04464283213019371, 0.0020476533100008965, -0.04358737915754318, -0.0007185165886767209, -0.015500599518418312, 0.01881282590329647, 0.048556700348854065, 0.027206895872950554, 0.021078824996948242, 0.02175816148519516, -0.03334696590900421, -0.033928435295820236, -0.0514475554227829, -0.11365560442209244, 0.03516533970832825, -0.016548875719308853, -0.038405854254961014, 0.04773693531751633, -0.0656963586807251, -0.03414178639650345, 0.002922052750363946, -0.029033267870545387, 0.028667723760008812, 0.01051341649144888, -0.029772384092211723, -0.028247971087694168, -0.045416317880153656, -0.010542952455580235, -0.013483391143381596, -0.041031066328287125, -0.04312070459127426, -0.025187304243445396, 0.026661714538931847, -0.006473830435425043, 0.003291635075584054, -0.03700651228427887, -0.05639997497200966, 0.0050257290713489056, -0.025551334023475647, -0.05835198983550072, -0.06967499107122421, 0.020824577659368515, 0.042160846292972565, -0.04376476630568504, -0.048978451639413834, -0.021751174703240395, 0.021500417962670326, 0.047844525426626205, 0.01696881279349327, -0.0398508720099926, -0.030155161395668983, 0.022476067766547203, -0.01683533564209938, 0.020582377910614014, -0.02090422250330448, 0.015972699970006943, -0.027149179950356483, 0.019921042025089264, 0.04276575148105621, -0.028967656195163727, 0.011277111247181892, 0.0675637274980545, 0.030816951766610146, 0.08478652685880661, 0.042008038610219955, 0.03166429325938225, -0.027250276878476143, -0.02119152620434761, -0.03238378092646599, -0.03581837937235832, 0.024138474836945534, -0.05740593746304512, -0.021003708243370056, 0.03722824528813362, 0.013078462332487106, 0.032298848032951355, 0.03244289010763168, -0.013028666377067566, 0.01805439591407776, 0.02461753413081169, -0.06689649075269699, 0.016932619735598564, 0.11104989051818848, -0.03605092689394951, 0.06719370186328888, 0.0029527507722377777, 0.04107588157057762, -0.06389118731021881, -0.09503909945487976, 0.005657332483679056, -0.06944005936384201, -0.0038333919364959, -0.05581117421388626, -0.001885577687062323, -0.04775170609354973, -0.04953933507204056, -0.0036212033592164516, 0.02839541807770729, 0.05319187417626381, -0.0014674519188702106, -0.007784551475197077, -0.023044897243380547, 0.013227677904069424, 0.024629153311252594, 0.0008525128941982985, 0.023348119109869003, 0.04259827733039856, -0.035818275064229965, -0.05030268803238869, -0.02975447103381157, 0.043183743953704834, 0.018199389800429344, -0.021854570135474205, -0.009157983586192131, -0.013464441522955894, 0.003908291459083557, -0.005084121599793434, -0.06652852892875671, 0.035639625042676926 ]
<p>Ancient Greek astronomer Aristarchos who lived around 300 BC found a method to compute the Eart-Sun distance by applying geometry. </p> <p><a href="http://www.youtube.com/watch?v=7ne0GArfeMs" rel="nofollow">In this video about the cosmic distance ladder</a>, at 26:30, Terence Tao explains that Aristarchos was basically limited by nonexisting clock technology. So he was not able to accurately measure the time difference between the time of (1/2 (new moon - fullmoon)) and time at which sun-moon distance was exactly at 90 degrees to the intersection of earthorbit - moonorbit. See screenshots.</p> <p><img src="http://i.stack.imgur.com/YnS0l.jpg" alt="Aristarchos 1"></p> <p><img src="http://i.stack.imgur.com/bGR9e.jpg" alt="Aristachos 2"></p> <p>Why was his method never refined in more modern times? Someone could have independently discovered the computation by a similar way of reasoning, but with better clocks.</p> <p>Or <em>did</em> some European Astronomer else do this after mechanical clocks were invented, and it was just not accurate enough so they went for the transit-of-venus-method? </p>
g8424
[ 0.042171891778707504, 0.016875674948096275, -0.0001024589073495008, -0.020563693717122078, -0.027488522231578827, 0.013156043365597725, 0.0369768887758255, -0.04300747439265251, -0.0061697643250226974, -0.010197663679718971, 0.03442220389842987, -0.0013778699794784188, 0.10691120475530624, 0.009474322199821472, 0.016815850511193275, -0.003147820010781288, 0.057250671088695526, -0.04970146343111992, 0.025961540639400482, 0.042632490396499634, 0.03338901698589325, 0.007270329631865025, 0.0006647921982221305, -0.02763056568801403, -0.032823678106069565, -0.00914949830621481, 0.045189306139945984, 0.009871196001768112, -0.016251567751169205, -0.035632241517305374, -0.003930910490453243, -0.036963533610105515, 0.022122973576188087, 0.010358442552387714, 0.007863400503993034, 0.03142761439085007, -0.03965581953525543, -0.02486800029873848, 0.018063366413116455, -0.012416025623679161, -0.018045227974653244, -0.03176857531070709, -0.011456795036792755, 0.02855207584798336, 0.026011236011981964, -0.026582011952996254, -0.08589835464954376, 0.040169477462768555, 0.015443573705852032, -0.014135449193418026, 0.01293001789599657, 0.04581768810749054, -0.0018238852499052882, -0.031215282157063484, -0.027250168845057487, -0.004556630272418261, 0.06080658733844757, -0.012511310167610645, 0.07622363418340683, 0.021558592095971107, 0.009110620245337486, -0.006926798727363348, 0.04871455207467079, 0.010093186981976032, 0.03478007763624191, 0.017956746742129326, 0.04107666015625, 0.01032888051122427, 0.03195475414395332, 0.010561088100075722, 0.01907411403954029, -0.033894866704940796, 0.0018627436365932226, -0.03205743059515953, -0.05180409178137779, 0.027080941945314407, 0.03827865421772003, 0.012279865331947803, 0.011006913147866726, 0.01234213076531887, -0.043524470180273056, -0.008793068118393421, -0.00027302579837851226, 0.022181130945682526, 0.05363768711686134, -0.033012937754392624, 0.012240094132721424, 0.020574942231178284, 0.041395045816898346, 0.07417026162147522, -0.06779398024082184, -0.053145114332437515, 0.038877785205841064, -0.01618863455951214, -0.0408543199300766, 0.008172640576958656, -0.013450456783175468, 0.04575235769152641, 0.010701088234782219, 0.03304826095700264, -0.040343109518289566, -0.023717649281024933, 0.032269131392240524, 0.01764489896595478, 0.007649640552699566, -0.004830142483115196, 0.036448340862989426, -0.011834745295345783, -0.02842249721288681, 0.029531020671129227, 0.02158445306122303, -0.05516931042075157, 0.0031923912465572357, -0.04605899006128311, 0.03512474521994591, -0.010282589122653008, 0.0645274743437767, 0.024447118863463402, 0.01825234293937683, -0.018436945974826813, -0.029028395190835, -0.007631007116287947, 0.02555081620812416, 0.036352477967739105, -0.05518127232789993, 0.0029276260174810886, -0.010329200886189938, -0.047442857176065445, -0.004882158245891333, -0.014612670987844467, -0.03454066812992096, 0.0530313178896904, 0.0005829018191434443, 0.018305620178580284, 0.009541268460452557, -0.009412750601768494, 0.03631078824400902, -0.0380462110042572, -0.03573339432477951, 0.04130116105079651, 0.026518072932958603, -0.05246441438794136, 0.018592024222016335, -0.05892709270119667, -0.028710292652249336, 0.04757088050246239, -0.030198097229003906, -0.041202444583177567, -0.014168675057590008, 0.012238404713571072, -0.015028197318315506, 0.049422673881053925, 0.004111432936042547, 0.06980343908071518, -0.021417753770947456, -0.005966991186141968, 0.011212474666535854, -0.00044664699817076325, -0.0060234228149056435, 0.03423529863357544, 0.044213056564331055, -0.0028592755552381277, -0.019556526094675064, -0.047136999666690826, -0.00925025250762701, 0.05687262490391731, -0.024738289415836334, -0.046982910484075546, -0.0331258587539196, -0.05509401112794876, -0.13211829960346222, 0.009774954989552498, 0.013803957961499691, -0.00417513819411397, -0.03697028383612633, 0.05155554413795471, 0.06620042771100998, 0.01136157475411892, -0.013468640856444836, -0.005607529543340206, -0.021208524703979492, 0.0022791132796555758, -0.04374770075082779, 0.02850564941763878, -0.025922132655978203, 0.010157948359847069, -0.0004786037316080183, -0.08314964175224304, -0.028236206620931625, -0.05034588277339935, 0.04417234659194946, 0.011666812002658844, -0.05482684448361397, 0.04160774499177933, -0.05607447773218155, 0.0007773171528242528, -0.0023666233755648136, 0.033711038529872894, -0.043227024376392365, 0.025227315723896027, -0.06179938465356827, 0.02186432108283043, 0.04961727187037468, 0.010510657913982868, -0.006984273437410593, 0.009260314516723156, -0.0018192309653386474, -0.04886568710207939, 0.007517950143665075, -0.002943155588582158, -0.0029221465811133385, 0.08799058198928833, 0.009369350969791412, 0.009892161004245281, -0.077736996114254, -0.00014631192607339472, -0.00740051968023181, -0.006122049875557423, 0.013987484388053417, 0.011374259367585182, 0.007934276014566422, -0.0015879410784691572, 0.03483534976840019, -0.028054069727659225, 0.0026583578437566757, -0.013642298988997936, -0.02391415648162365, 0.012127639725804329, -0.02820398658514023, 0.007263512816280127, 0.003210603492334485, 0.013475715182721615, -0.020968539640307426, 0.049499087035655975, 0.04987432062625885, 0.0450056828558445, 0.05650622397661209, -0.0005329660489223897, 0.02551198936998844, 0.0674007311463356, 0.06488422304391861, -0.03755757957696915, -0.04114772751927376, -0.009483386762440205, 0.011873078532516956, -0.04550474137067795, 0.011215574108064175, -0.028626805171370506, -0.08224445581436157, 0.02664392814040184, 0.004668802954256535, 0.03815682232379913, -0.04115423932671547, -0.011210313066840172, -0.033022910356521606, -0.0019475080771371722, 0.021072158589959145, 0.012431060895323753, -0.03651900589466095, 0.03972389176487923, -0.005703986156731844, 0.019084379076957703, 0.06303608417510986, -0.06308994442224503, 0.0404922217130661, 0.011373423039913177, -0.10979985445737839, 0.06659164279699326, -0.06368376314640045, -0.02881515398621559, 0.033311884850263596, 0.03429630398750305, 0.056690752506256104, 0.024086300283670425, -0.06406307965517044, 0.005463370122015476, -0.01573793776333332, -0.009274258278310299, 0.04589248076081276, 0.052487149834632874, -0.006220343988388777, -0.013353132642805576, -0.055075809359550476, 0.0006442322046495974, 0.005968387238681316, -0.02715458534657955, 0.00867351982742548, 0.039026569575071335, 0.020182667300105095, -0.02071702852845192, 0.015018582344055176, -0.018228696659207344, -0.012472124770283699, -0.024725615978240967, -0.023031068965792656, 0.03690895438194275, -0.018911780789494514, -0.0014260561438277364, -0.0060854097828269005, -0.059410419315099716, 0.019290806725621223, 0.016583384945988655, -0.021318331360816956, 0.023928817361593246, 0.056719522923231125, -0.003476348239928484, 0.006859468296170235, -0.02771182730793953, -0.02972581423819065, -0.03193213790655136, 0.09675665199756622, -0.008627194911241531, 0.014138697646558285, -0.0128944618627429, -0.015400566160678864, -0.00437698932364583, -0.00322848092764616, 0.028742816299200058, -0.016762636601924896, 0.04880746454000473, 0.008908598683774471, 0.010557168163359165, -0.0270441472530365, -0.07285458594560623, 0.004799348767846823, 0.005695161875337362, -0.0009078493458218873, -0.0024119364097714424, -0.02713785506784916, -0.019344236701726913, -0.030078133568167686, 0.0030334137845784426, -0.04224271699786186, -0.020569855347275734, -0.042892467230558395, -0.009688102640211582, 0.03438694402575493, 0.028716715052723885, -0.0023307364899665117, -0.010500411503016949, -0.11750941723585129, 0.03639642149209976, -0.04998823255300522, -0.016873694956302643, 0.0711042657494545, 0.0048674833960831165, 0.026795757934451103, 0.008138756267726421, -0.036264337599277496, -0.025380436331033707, 0.05323854088783264, 0.015513958409428596, -0.04227003455162048, -0.004931694362312555, 0.008665649220347404, 0.05912148952484131, -0.020245680585503578, 0.0635807141661644, 0.03085252270102501, -0.0022371774539351463, 0.031289394944906235, 0.06290140002965927, -0.040402479469776154, -0.00919076707214117, 0.020320555195212364, 0.02049468643963337, 0.022653678432106972, 0.06414401531219482, 0.02668520249426365, -0.007676627021282911, -0.008046193048357964, 0.01101637165993452, 0.027208693325519562, -0.015927482396364212, 0.06034248322248459, -0.0036123974714428186, 0.026023512706160545, 0.02732556313276291, 0.02327755093574524, 0.04252784326672554, 0.02770758979022503, -0.002435785485431552, -0.00134723458904773, -0.03657156974077225, 0.03931121528148651, -0.019289908930659294, -0.030480770394206047, -0.0549236424267292, -0.038141217082738876, -0.05627097189426422, -0.02652534656226635, -0.0733255073428154, 0.03261325880885124, -0.05234868824481964, 0.008163937367498875, -0.034121353179216385, 0.010722363367676735, -0.02899741381406784, -0.01656942255795002, -0.015323099680244923, 0.0010378520237281919, 0.026250353083014488, -0.01588723622262478, 0.04364178702235222, -0.03451697900891304, 0.039126910269260406, 0.02102360688149929, -0.007370274048298597, 0.05758044123649597, 0.02269119769334793, -0.019017871469259262, 0.050883449614048004, 0.005387965124100447, -0.07409734278917313, 0.02082272805273533, 0.028111744672060013, -0.030979176983237267, -0.012361819855868816, -0.008130746893584728, 0.02756693959236145, -0.014414958655834198, 0.07882843166589737, 0.0341387540102005, -0.0013430031249299645, 0.03817347437143326, 0.05306752771139145, 0.0026748960372060537, -0.03163106366991997, -0.023151574656367302, -0.010747539810836315, 0.035755351185798645, 0.017764609307050705, -0.0125057278200984, -0.022109676152467728, -0.015324204228818417, 0.009569131769239902, 0.07441353797912598, 0.04660555347800255, 0.026266086846590042, -0.028550026938319206, 0.03219696506857872, 0.024968678131699562, 0.030178040266036987, 0.000432108121458441, 0.03180377930402756, -0.006530744954943657, -0.05144356191158295, -0.060730136930942535, 0.01531012263149023, 0.03947285935282707, -0.003935997374355793, -0.03247898444533348, -0.0019177328795194626, 0.036449071019887924, -0.017699018120765686, -0.023302115499973297, -0.06720834970474243, 0.01202287059277296, 0.0009172429563477635, 0.015894951298832893, -0.04115001857280731, -0.03270271047949791, -0.02365211211144924, 0.05057274550199509, 0.026658009737730026, -0.001178680220618844, -0.043906670063734055, 0.00739833852276206, -0.06164676323533058, 0.05125408247113228, -0.041380416601896286, 0.05834241211414337, -0.02338951639831066, 0.0433107428252697, -0.02586677111685276, -0.02884160913527012, -0.024399835616350174, 0.0008585688192397356, -0.029417859390378, 0.013665540143847466, 0.025500260293483734, -0.007250690367072821, 0.016153715550899506, 0.033603303134441376, -0.030948009341955185, 0.10537225753068924, -0.07817528396844864, -0.04561512544751167, 0.03854213282465935, 0.008550272323191166, 0.04023512080311775, -0.04798877239227295, 0.027609122917056084, -0.08751749247312546, 0.0029804024379700422, -0.02081204764544964, 0.01256079412996769, 0.013289758935570717, 0.02584296651184559, -0.010453674010932446, -0.04742051661014557, 0.05195530876517296, -0.026479244232177734, -0.07369236648082733, 0.06938326358795166, -0.017896685749292374, -0.015531311742961407, -0.0033799789380282164, 0.0028678199741989374, 0.014980267733335495, -0.00041753752157092094, 0.017588157206773758, -0.005467014387249947, 0.05423661693930626, 0.03684317693114281, -0.012036439962685108, 0.029146457090973854, -0.041016146540641785, -0.021941134706139565, -0.10424529016017914, 0.0038407654501497746, 0.030754078179597855, 0.005930737592279911, 0.010257367044687271, 0.01960865408182144, -0.002537189284339547, -0.0005763552035205066, -0.04637013375759125, -0.03984636068344116, -0.01820511370897293, -0.006751608103513718, -0.028885019943118095, -0.05794910341501236, 0.020307667553424835, -0.031726595014333725, -0.010658292099833488, -0.0029097553342580795, 0.0525764599442482, 0.02645963616669178, -0.06488706171512604, -0.033201638609170914, 0.009149448946118355, 0.06677611172199249, 0.050935324281454086, -0.006362835876643658, -0.02513776905834675, -0.032386887818574905, 0.01980154775083065, 0.016147926449775696, -0.018831027671694756, -0.03474186360836029, 0.043572958558797836, -0.022508136928081512, -0.017651444301009178, -0.05072205513715744, 0.04818263649940491, -0.044136036187410355, -0.012135261669754982, -0.0694538801908493, 0.004323306027799845, 0.03159867972135544, -0.006511211395263672, -0.01225935947149992, 0.06416493654251099, -0.005602921824902296, -0.03890639543533325, -0.0005903138080611825, 0.021481407806277275, 0.05214827135205269, 0.027942145243287086, 0.018011106178164482, -0.06173892319202423, -0.002256400417536497, 0.012255271896719933, 0.00446583516895771, -0.003916867543011904, -0.028333080932497978, -0.05505940690636635, -0.05883964151144028, -0.07039070129394531, 0.03289055451750755, -0.010069066658616066, -0.005981958471238613, -0.00022319027630146593, 0.027740418910980225, -0.04147053509950638, -0.014404808171093464, -0.01619207300245762, 0.043763354420661926, -0.051676616072654724, 0.006667017005383968, 0.014315584674477577, -0.01885182037949562, -0.05759122967720032, -0.051974717527627945, -0.030689233914017677, -0.003435049206018448, 0.04137276113033295, -0.07336189597845078, 0.05732456222176552, -0.023834196850657463, -0.0336838960647583, 0.07078438997268677, -0.009578481316566467, 0.018137501552700996, 0.057240355759859085, 0.0005523969884961843, 0.0367826446890831, 0.05377398058772087, -0.026796940714120865, 0.026640724390745163, 0.02918202616274357, -0.006411897949874401, 0.022982614114880562, -0.0694698616862297, -0.016624918207526207, -0.008791371248662472, -0.05451977998018265, -0.07170365750789642, 0.00004974497278453782, 0.07153389602899551, 0.01617431826889515, 0.007750437129288912, 0.015932543203234673, 0.036526717245578766, -0.0006542374030686915, -0.0366022102534771, 0.019630366936326027, 0.012021590955555439, -0.01640634983778, 0.02310081385076046, -0.06389831006526947, -0.035122793167829514, 0.0460968092083931, 0.010020461864769459, 0.007481103762984276, -0.007638823240995407, 0.03927436098456383, 0.010412574745714664, 0.03269084170460701, -0.01822850853204727, -0.006049749441444874, 0.007830093614757061, 0.011138229630887508, 0.004869862925261259, -0.03670978918671608, -0.019761402159929276, 0.052389100193977356, -0.05107833072543144, 0.0200896468013525, 0.009372551925480366, -0.006998744327574968, 0.006723928265273571, 0.02622946910560131, 0.04330635815858841, -0.017420854419469833, -0.0368121974170208, 0.02458345890045166, -0.005786350928246975, -0.08300960063934326, 0.03206261619925499, -0.00016278323892038316, 0.009158656001091003, 0.053858958184719086, -0.010207285173237324, -0.0034531138371676207, -0.05514140427112579, -0.05478750541806221, 0.0064529841765761375, -0.0748627632856369, 0.002833080943673849, 0.0411495603621006, -0.033959221094846725, -0.02846566215157509, 0.008385523222386837, -0.00045799562940374017, 0.05577554926276207, -0.029329601675271988, -0.09808100014925003, -0.009935050271451473, -0.03006742335855961, 0.04242652282118797, -0.03160887584090233, -0.02467474527657032, -0.0023855636827647686, 0.01925281062722206, -0.0038664950989186764, 0.007866020314395428, 0.037343572825193405, -0.06070178747177124, -0.018133411183953285, 0.04767432063817978, -0.02745656482875347, -0.008032397367060184, 0.0204918272793293, 0.017967557534575462, 0.07068198919296265, 0.014599964022636414, 0.005222470965236425, -0.03066105954349041, 0.08386271446943283, -0.06251876056194305, 0.031148279085755348, 0.04997400939464569, 0.07601700723171234, 0.037865038961172104, 0.004140738397836685, 0.05948905274271965, -0.0440530851483345, 0.05006500333547592, 0.033932607620954514, 0.06753742694854736, -0.02299981750547886, 0.007213178090751171, 0.0046203103847801685, 0.011917011812329292, 0.03606516495347023, 0.01901562698185444, -0.028204385191202164, 0.010180818848311901, -0.02917787991464138, -0.086051806807518, 0.04651263356208801, -0.10469267517328262, -0.0252285934984684, 0.05733596161007881, 0.035399533808231354, -0.012626812793314457, -0.002544065471738577, -0.0813102200627327, 0.07550594210624695, 0.026407480239868164, -0.02253677509725094, 0.009158803150057793, -0.05876336246728897, 0.0034445554483681917, -0.03911958634853363, -0.0328083299100399, -0.035882171243429184, -0.008561433292925358, -0.06721197813749313, 0.058997854590415955, 0.0046371957287192345, 0.0036049943882972, -0.005015432368963957, -0.03138643130660057, -0.020339157432317734, 0.05707818269729614, 0.0010087982518598437, -0.06418704986572266, -0.028933651745319366, 0.04164503514766693, -0.020308595150709152, -0.022686831653118134, 0.001425299677066505, 0.04581325873732567, 0.004086235538125038, -0.05802878364920616, 0.04900367930531502, -0.007153838872909546, -0.00003548703170963563, -0.020610669627785683, 0.023876337334513664, 0.017992092296481133, -0.006662905681878328, 0.01461837999522686, 0.02508162334561348, 0.00997165497392416 ]
<p>Let us pretend for a moment that there are two identical planets that are exactly opposite their star from each other and are the same distance from said star. (This would make them, at all times, double the distance from their star apart from each other.)</p> <p>Would they, under the definition of a planet, be considered planets? One could argue they have not cleared their neighborhood by virtue of one not having cleared the other. But, it would seem strange to assume a planet would be capable of clearing something that always has its sun in the way.</p>
g8425
[ -0.024104880169034004, 0.02077355980873108, 0.03934110701084137, 0.005512721370905638, 0.023251336067914963, 0.03272295743227005, -0.03430011123418808, -0.0021113373804837465, 0.03251032903790474, 0.011574478819966316, 0.03458033502101898, 0.04022901505231857, 0.0061202272772789, -0.03207302838563919, 0.007442759815603495, -0.004711604211479425, 0.003037968883290887, -0.08068855851888657, 0.044133685529232025, 0.03961167857050896, 0.020153935998678207, 0.029178358614444733, 0.002484247088432312, -0.011615663766860962, -0.060468949377536774, -0.043445322662591934, 0.008089074864983559, -0.04039834439754486, 0.01644207164645195, 0.011811156757175922, 0.022773688659071922, 0.012537053786218166, 0.03180573135614395, -0.0204685740172863, -0.049471888691186905, 0.0040245093405246735, 0.01890789531171322, -0.04416663944721222, 0.01116869319230318, -0.03416977450251579, 0.06535904854536057, -0.0028984129894524813, 0.012008163146674633, 0.007795048411935568, 0.08525154739618301, -0.0228066798299551, 0.007449761498719454, 0.0004200422263238579, 0.055066779255867004, -0.04098561033606529, 0.01489643007516861, -0.011690373532474041, -0.009097421541810036, -0.011825303547084332, -0.010959724895656109, 0.02708428166806698, 0.0778840109705925, -0.018008090555667877, 0.0607050359249115, 0.003939102869480848, -0.006184253375977278, 0.040421292185783386, 0.03025486133992672, 0.049878522753715515, 0.01912631466984749, -0.003304417012259364, 0.007132713217288256, 0.05235091596841812, -0.009156323038041592, -0.07689561694860458, 0.039547454565763474, 0.018634723499417305, -0.0196489579975605, -0.021247711032629013, -0.028534667566418648, 0.060033299028873444, 0.014918221160769463, 0.005453083198517561, 0.013343053869903088, 0.06794507801532745, 0.012067731469869614, -0.03890875726938248, -0.010237771086394787, 0.04396585375070572, 0.07219767570495605, -0.010671641677618027, -0.0442059300839901, -0.038068629801273346, -0.06144343316555023, 0.04371755197644234, -0.01962386444211006, -0.0007348745712079108, 0.04227450489997864, 0.0063008833676576614, -0.03262138366699219, -0.004994930233806372, -0.02857368253171444, -0.0032542026601731777, -0.06930428743362427, 0.01854471117258072, -0.0057822163216769695, 0.02681356854736805, 0.10353519767522812, -0.05600890889763832, 0.04905728995800018, -0.012634233571588993, 0.1202772706747055, 0.018837787210941315, -0.027398666366934776, -0.04015788435935974, -0.011371761560440063, -0.07543084770441055, 0.05024932324886322, -0.013745436444878578, -0.03051336482167244, -0.01200900413095951, 0.08196751028299332, -0.02580564096570015, 0.055906325578689575, 0.03948817402124405, 0.04110640287399292, 0.04897060990333557, -0.022199872881174088, 0.03493065759539604, -0.0372028574347496, -0.015132507309317589, 0.017859263345599174, -0.018097257241606712, 0.06876451522111893, -0.019630007445812225, 0.04615925997495651, 0.01906576380133629, -0.0013453259598463774, 0.04243771359324455, -0.05664204806089401, -0.02257252298295498, 0.05215706676244736, -0.018418947234749794, 0.00944795086979866, -0.0442756824195385, 0.06126383692026138, 0.001716971630230546, 0.02539055235683918, 0.036916669458150864, -0.028355184942483902, -0.01950150355696678, -0.0339658260345459, -0.013487771153450012, 0.01267321314662695, 0.061608828604221344, -0.0031108648981899023, 0.05060644447803497, 0.005534911993891001, 0.008396617136895657, -0.011073381640017033, 0.01112089678645134, 0.003070223145186901, 0.04108011722564697, 0.004617462400346994, 0.04108856990933418, 0.05427803844213486, -0.024644766002893448, -0.008750883862376213, -0.05004504695534706, -0.04569635167717934, 0.04727912321686745, -0.008077962324023247, -0.03569081425666809, -0.0509670153260231, 0.02083459682762623, -0.02434711344540119, -0.012258514761924744, 0.006353072822093964, 0.022711902856826782, 0.01812930218875408, 0.002096372889354825, -0.03214658051729202, -0.013123498298227787, -0.026505861431360245, 0.04300856217741966, -0.0020342792849987745, 0.03745492920279503, 0.025692222639918327, 0.05744776502251625, -0.0167829729616642, -0.04226066544651985, -0.011551771312952042, -0.02397957257926464, -0.015010411851108074, 0.01897260919213295, -0.020413393154740334, -0.014222225174307823, -0.0012179602636024356, 0.024012401700019836, 0.029127201065421104, -0.019330764189362526, -0.023605812340974808, 0.02959279716014862, 0.012912818230688572, 0.006312240846455097, -0.03603716567158699, 0.0465242899954319, 0.0479532927274704, 0.0025145818945020437, -0.033263612538576126, 0.0365060418844223, 0.03157005459070206, -0.03710900992155075, 0.059728965163230896, -0.04093818739056587, 0.000948795466683805, -0.06708157062530518, 0.010155625641345978, 0.03919604420661926, -0.048657868057489395, -0.06568264961242676, -0.08923963457345963, -0.014084268361330032, -0.04570797458291054, -0.05387246608734131, -0.003828958375379443, 0.019079340621829033, 0.0874132439494133, -0.06060117483139038, -0.02836746536195278, 0.08425569534301758, -0.08892443776130676, 0.04820531979203224, -0.029101412743330002, 0.0370643176138401, 0.03558644652366638, -0.054558999836444855, 0.029904592782258987, -0.013499230146408081, 0.0072696455754339695, -0.013936080038547516, -0.003506514010950923, 0.03623497486114502, -0.027880927547812462, 0.027399931102991104, 0.00505719892680645, -0.0338897630572319, -0.029335226863622665, 0.023455079644918442, 0.07075485587120056, -0.02269301749765873, 0.005914444103837013, 0.015638360753655434, -0.015323303639888763, 0.04732222855091095, -0.0022097660694271326, 0.019393935799598694, -0.05734258517622948, 0.03640841692686081, 0.02974977344274521, -0.02423008903861046, 0.047497186809778214, -0.006747150328010321, -0.030635325238108635, -0.030732953920960426, 0.03884052857756615, -0.07012320309877396, 0.0366935171186924, 0.023283153772354126, 0.016328921541571617, -0.01556265726685524, 0.0022772501688450575, 0.02959504723548889, 0.02405405044555664, 0.007930824533104897, 0.049152251332998276, 0.02954293228685856, 0.06992434710264206, 0.017301753163337708, -0.06773311644792557, 0.07795410603284836, 0.00283985142596066, -0.030615733936429024, 0.012749697081744671, 0.056706272065639496, -0.011412080377340317, 0.06409234553575516, -0.060700979083776474, 0.009494402445852757, 0.08118078112602234, -0.02241578698158264, 0.04073183238506317, 0.014161166734993458, 0.022400839254260063, 0.010026750154793262, -0.020435070618987083, 0.030706726014614105, 0.03765476867556572, 0.017869099974632263, -0.009563003666698933, 0.07564426213502884, 0.006541327573359013, 0.0005360073409974575, -0.022540170699357986, -0.009639833122491837, -0.01383409183472395, -0.001856597955338657, 0.012204190716147423, 0.009249694645404816, 0.05486735329031944, 0.009763296693563461, -0.04937971383333206, -0.008376380428671837, -0.06200806051492691, -0.08720637112855911, 0.013344468548893929, 0.0755186602473259, -0.03671204298734665, 0.06977709382772446, 0.02103935182094574, -0.020744584500789642, -0.00875090155750513, -0.06757735460996628, -0.02669288031756878, 0.048747193068265915, 0.0006363765569403768, 0.038806796073913574, -0.043416209518909454, 0.07671213895082474, 0.011941145174205303, 0.02317873202264309, -0.03293297812342644, 0.022553464397788048, -0.025977952405810356, 0.026065070182085037, -0.03708109259605408, 0.034237176179885864, -0.055264491587877274, 0.00854277703911066, -0.04559842497110367, 0.011821199208498001, 0.009046493098139763, 0.024698080494999886, 0.03417736664414406, 0.031639572232961655, -0.009533757343888283, 0.05148744583129883, -0.0010436810553073883, -0.0385621152818203, -0.026626305654644966, 0.10541782528162003, 0.01466414425522089, -0.02927696891129017, 0.0071316673420369625, -0.024409916251897812, 0.020779000595211983, -0.01527368277311325, 0.06545675545930862, -0.04374915733933449, 0.02957175485789776, 0.02194494567811489, 0.0034339381381869316, 0.03713195025920868, 0.01193980686366558, 0.0023087034933269024, 0.026233715936541557, 0.024154169484972954, -0.0001796644792193547, 0.00814927089959383, 0.02906980738043785, -0.034881435334682465, 0.008729075081646442, -0.002875936683267355, 0.04827890917658806, -0.009334464557468891, 0.04493704438209534, -0.008290055207908154, -0.04584342986345291, -0.018152771517634392, 0.03814622759819031, -0.02067369781434536, 0.04422762989997864, -0.0035163334105163813, -0.04735342040657997, 0.016067521646618843, 0.051812391728162766, -0.007338362745940685, -0.003659070935100317, 0.034425802528858185, 0.04508982598781586, 0.010787134058773518, -0.02545248158276081, -0.005339202005416155, 0.023285038769245148, -0.008470086380839348, -0.01862025447189808, -0.033529702574014664, 0.004695828538388014, -0.05213793367147446, -0.007193238474428654, 0.014731265604496002, -0.01513694692403078, -0.046984102576971054, -0.0011279707541689277, -0.00436978368088603, 0.007547696586698294, -0.01577923074364662, 0.023251185193657875, -0.041345685720443726, -0.02946440875530243, -0.040451690554618835, 0.0029665243346244097, 0.011553998105227947, -0.0345056876540184, 0.018260018900036812, -0.011502440087497234, 0.062120601534843445, -0.02682206593453884, -0.053980931639671326, 0.004179251380264759, 0.08772366493940353, 0.016301413998007774, 0.00006042564200470224, 0.013031141832470894, 0.02387944422662258, -0.06415363401174545, 0.01725468412041664, 0.045988284051418304, -0.0015986945945769548, 0.06914633512496948, 0.0997839868068695, 0.011177251115441322, -0.019415440037846565, -0.07405403256416321, -0.05266189947724342, 0.022654149681329727, 0.015348530374467373, 0.032343700528144836, -0.017869478091597557, -0.031893085688352585, 0.012679058127105236, -0.07707084715366364, 0.055735863745212555, 0.023703165352344513, 0.049218300729990005, -0.01501339953392744, 0.0044763037003576756, -0.01321653462946415, 0.0036558432038873434, -0.002889368450269103, 0.026967331767082214, 0.04674609377980232, -0.05288442224264145, -0.021315764635801315, -0.015189637430012226, -0.04924110323190689, -0.003373856656253338, -0.02363259717822075, -0.0064161960035562515, -0.10008278489112854, -0.04757249355316162, -0.07358098030090332, -0.035516317933797836, -0.024357538670301437, -0.006865179166197777, -0.004021306522190571, -0.008118009194731712, 0.058549538254737854, 0.03759343549609184, 0.03296862542629242, -0.03170246630907059, -0.03513927757740021, 0.027499767020344734, -0.06107277423143387, 0.01150478608906269, -0.009530557319521904, 0.035531435161828995, -0.0010899241315200925, 0.0672033354640007, -0.020979389548301697, -0.04856744408607483, -0.006059517152607441, 0.024744713678956032, -0.0021194713190197945, -0.045893386006355286, -0.035747479647397995, -0.01537010446190834, 0.032967738807201385, 0.007189017720520496, -0.06388570368289948, 0.032298292964696884, -0.05364990234375, 0.013895566575229168, 0.016665546223521233, 0.012965792790055275, -0.04843272268772125, 0.015738943591713905, 0.03160354122519493, -0.01416944619268179, 0.013661080971360207, -0.038693252950906754, -0.03200538083910942, -0.034691222012043, -0.0017780717462301254, 0.016776015982031822, -0.04202355444431305, 0.04836020618677139, 0.0379345528781414, -0.006743511185050011, 0.030789021402597427, 0.049083102494478226, -0.040063876658678055, -0.04604293406009674, -0.005196339916437864, -0.028548896312713623, -0.01075049676001072, 0.03360723704099655, 0.004013961646705866, 0.10639545321464539, 0.0034828055649995804, -0.03252606466412544, -0.01296475064009428, -0.05008986219763756, -0.005753142759203911, -0.017866695299744606, 0.02962653897702694, -0.01781945861876011, -0.015836862847208977, -0.012085693888366222, 0.052120596170425415, 0.026891766116023064, -0.005060936324298382, -0.004520849324762821, -0.0656270682811737, 0.056811366230249405, -0.020833931863307953, -0.03043977916240692, -0.009846468456089497, -0.028188271448016167, -0.0557575523853302, -0.0599476620554924, 0.024882737547159195, 0.010919849388301373, 0.05722048133611679, -0.01866801828145981, -0.032070476561784744, -0.019765786826610565, 0.014876045286655426, 0.0162960197776556, -0.02339465171098709, -0.02986558899283409, -0.005042846780270338, -0.009011158719658852, 0.032638851553201675, -0.024345638230443, -0.006887553725391626, -0.03806623816490173, -0.009717922657728195, -0.04127763956785202, 0.048274360597133636, 0.04816458001732826, -0.036996107548475266, 0.03176981210708618, 0.022918544709682465, -0.06686706840991974, -0.021029043942689896, -0.0010874078143388033, 0.005642687436193228, 0.010759791359305382, -0.012341727502644062, 0.029247276484966278, 0.019926046952605247, 0.0012922283494845033, 0.07019337266683578, -0.021353567019104958, 0.021871687844395638, -0.039957355707883835, 0.05413410812616348, 0.0023074450436979532, 0.02106892503798008, -0.01021536998450756, -0.0511818490922451, 0.010247418656945229, -0.0023532367777079344, -0.06981924921274185, 0.017561471089720726, -0.0355025939643383, -0.019130807369947433, -0.05340748280286789, -0.04245975241065025, 0.03264354541897774, 0.013160054571926594, -0.030467670410871506, 0.025441035628318787, -0.08199238032102585, -0.04371744021773338, -0.06703496724367142, -0.03900040313601494, -0.042817045003175735, -0.0041364701464772224, -0.004984339699149132, -0.0266105979681015, 0.02473429962992668, -0.04053186997771263, -0.010621972382068634, 0.002219089772552252, -0.00965761300176382, 0.09646493941545486, -0.008980847895145416, 0.006666062865406275, 0.09578581899404526, -0.06578997522592545, 0.06565040349960327, -0.013509467244148254, -0.03887076675891876, 0.014969504438340664, 0.007330301683396101, 0.002762505551800132, 0.015065622515976429, -0.05539172887802124, -0.03273108974099159, -0.027118591591715813, -0.03399284929037094, -0.018391085788607597, 0.023473495617508888, 0.030327169224619865, 0.004882902838289738, -0.03255987912416458, -0.044565603137016296, -0.02153618633747101, 0.051519811153411865, 0.03376661613583565, 0.010521472431719303, 0.06035367399454117, 0.023733507841825485, -0.03759007155895233, -0.00025848005316220224, 0.03801504522562027, -0.013383850455284119, -0.008070861920714378, -0.0016003737691789865, -0.03867167979478836, 0.016354074701666832, -0.048454880714416504, -0.02141028270125389, 0.005742649547755718, -0.018758470192551613, -0.03289211168885231, 0.052980937063694, 0.0344105139374733, 0.003808755660429597, -0.005081727169454098, -0.03952055796980858, 0.001857310882769525, 0.00898581650108099, -0.0067229620181024075, -0.02102210931479931, -0.012795600108802319, 0.01248101145029068, -0.014694932848215103, -0.013474556617438793, -0.03986499831080437, 0.01878431811928749, -0.023998074233531952, -0.0040719518437981606, -0.0103508485481143, -0.024046508595347404, -0.08147403597831726, -0.025039399042725563, 0.01123734749853611, -0.0005896793445572257, 0.04381338879466057, -0.011100338771939278, -0.08985096961259842, -0.01720665581524372, 0.005831950809806585, -0.03325764089822769, -0.022111309692263603, 0.011370275169610977, -0.012034661136567593, 0.009005446918308735, 0.018422594293951988, -0.05111747235059738, -0.029803475365042686, -0.05783424526453018, 0.030202515423297882, -0.016569241881370544, -0.019152086228132248, -0.005372769199311733, 0.017784355208277702, 0.029195886105298996, 0.011566339991986752, 0.0046633160673081875, -0.00590389734134078, -0.07370150834321976, 0.03077717497944832, 0.047861021012067795, 0.023752396926283836, -0.03838954120874405, 0.018787018954753876, -0.0011881879763677716, 0.036597397178411484, 0.005960753653198481, 0.024527153000235558, -0.09984853118658066, -0.02439085766673088, -0.00001967649586731568, 0.014640267007052898, -0.049419403076171875, -0.01501085888594389, -0.010892334394156933, -0.031464267522096634, 0.08123308420181274, -0.04064086079597473, -0.013156188651919365, 0.06442377716302872, 0.002934540156275034, 0.02510402724146843, 0.006683350540697575, -0.010413628071546555, -0.04226651415228844, -0.02531871385872364, -0.026043906807899475, 0.02323252335190773, 0.009250312112271786, 0.0053790416568517685, -0.02085910551249981, 0.054053567349910736, -0.07200770825147629, 0.0003374051593709737, 0.010081482119858265, -0.01135109830647707, -0.00292477710172534, 0.025768402963876724, -0.027094779536128044, 0.04339532181620598, 0.03689196705818176, 0.020435981452465057, 0.012056592851877213, -0.06369467824697495, -0.02895028330385685, -0.009648078121244907, -0.028677301481366158, -0.058248888701200485, -0.021728938445448875, -0.0519067645072937, -0.009676945395767689, 0.07013919204473495, -0.02866240218281746, -0.04438873007893562, -0.031894341111183167, 0.0038097614888101816, -0.01655452325940132, -0.018936816602945328, 0.020065834745764732, -0.003911610227078199, 0.042323168367147446, -0.017313601449131966, 0.0315108485519886, 0.007668206002563238, 0.014883768744766712, -0.047078877687454224, -0.02850997820496559, -0.042415548115968704, 0.015592161566019058, -0.056160420179367065, -0.026134857907891273, 0.019500968977808952, -0.019736498594284058, 0.0009260510560125113, 0.01349671557545662, -0.02732706256210804, 0.0036624555941671133 ]
<p>I'd like to understand the physics of dynamic light scattering experiment. In particular I want to understand the basic relation between relaxation time $\tau_q$ and the diffusion coefficient $D$:</p> <p>$\tau_q=(q^2 D)^{-1}.$</p> <p>I suppose that more or less the following steps are necessary:</p> <p>1) Calculate the scattered wave from Maxwell equations. 2) Find a relation between the scattered intensity autocorrelation function and the brownian motion of the particles.</p> <p>I found this book by Berne and Pecora, but at least for point 1 I got lost because there seem to a strange version (or an approximation) of maxwell equations that I don't understand (it is citing Landau but looking at this book was not such an help).</p> <p>Is there any book were I can find what I need or at least point 1 written with some detail?</p> <p>thank you</p>
g8426
[ -0.00743173249065876, 0.03528246283531189, -0.026221824809908867, 0.01930609904229641, 0.04340054839849472, 0.006914518773555756, 0.06458484381437302, -0.0029577831737697124, -0.011880215257406235, -0.014355089515447617, -0.008633648045361042, 0.058985982090234756, 0.06472685188055038, -0.0014301349874585867, -0.028125323355197906, -0.02783006615936756, 0.05533840134739876, 0.030062686651945114, -0.0026454271283000708, -0.00038926233537495136, 0.03043804131448269, 0.056834422051906586, -0.01736927032470703, -0.08798863738775253, -0.009763550013303757, 0.028202196583151817, -0.049570150673389435, 0.023385416716337204, -0.020283155143260956, -0.05921592935919762, 0.05624137073755264, -0.055434450507164, 0.017776677384972572, -0.029607726261019707, 0.007505382411181927, 0.00547174783423543, 0.0379050187766552, -0.01368983369320631, -0.036988623440265656, 0.05878158658742905, 0.028089189901947975, -0.017542991787195206, 0.014396777376532555, -0.016475124284625053, 0.0795716941356659, 0.032882798463106155, -0.08414197713136673, -0.03424537554383278, -0.053461071103811264, -0.0014036338543519378, -0.0034510716795921326, 0.0744994729757309, 0.06292864680290222, -0.010578479617834091, -0.011633474379777908, 0.046773411333560944, 0.0032771320547908545, -0.029997171834111214, 0.05740364268422127, 0.0182830598205328, 0.0013921232894062996, -0.01577044650912285, -0.00699575012549758, -0.07314056903123856, 0.033061958849430084, -0.046476613730192184, 0.020040273666381836, -0.048251260071992874, -0.004924648907035589, -0.024331606924533844, -0.025800498202443123, -0.03142814710736275, -0.06040038540959358, -0.04181573912501335, 0.06814369559288025, -0.02598734013736248, 0.023054160177707672, -0.011937880888581276, 0.01895683817565441, -0.002656403463333845, -0.06507682800292969, -0.029975099489092827, 0.0012518047587946057, 0.012764700688421726, 0.040432076901197433, -0.030240193009376526, -0.0011274713324382901, 0.011813410557806492, 0.04871528968214989, -0.03554932400584221, -0.009497973136603832, -0.03549103066325188, 0.09455128014087677, -0.010325624607503414, 0.03270433098077774, 0.034426406025886536, -0.05129673704504967, 0.05768723040819168, -0.03257380425930023, 0.0032078861258924007, -0.05061951279640198, 0.0006437235861085355, -0.0377940870821476, 0.037718500941991806, -0.03266965225338936, -0.028390677645802498, 0.0005334469606168568, 0.030715089291334152, -0.04795118793845177, 0.07039642333984375, -0.04333529993891716, -0.023198163136839867, -0.0351790115237236, -0.011918037198483944, -0.009269817732274532, -0.054882023483514786, 0.022090578451752663, -0.025477508082985878, 0.017992958426475525, -0.012159101665019989, 0.003482677973806858, 0.02234574966132641, 0.05651511624455452, 0.021436277776956558, 0.036222029477357864, 0.005621904972940683, 0.023727526888251305, 0.024386340752243996, 0.019321750849485397, 0.05525415763258934, 0.010452201589941978, -0.006429878994822502, -0.04143521562218666, 0.03640381246805191, -0.013329285196959972, -0.007018860429525375, 0.014811943285167217, 0.016951922327280045, -0.012232968583703041, 0.025409091264009476, 0.06607531011104584, -0.002038344042375684, 0.019727028906345367, -0.004013539757579565, -0.06402353197336197, 0.0620078481733799, 0.007711001206189394, -0.047963280230760574, -0.006954592652618885, 0.006956812925636768, 0.04102388024330139, -0.011473791673779488, -0.011758245527744293, -0.059203751385211945, 0.004291732795536518, -0.0368502251803875, 0.011725220829248428, -0.033600885421037674, -0.0015039171557873487, 0.029598675668239594, 0.013436551205813885, -0.027461009100079536, -0.01644372008740902, 0.020368264988064766, 0.004219638183712959, 0.007676007226109505, 0.04123422130942345, -0.051708199083805084, -0.019964497536420822, -0.07134700566530228, -0.04594181105494499, -0.016357125714421272, 0.04926697909832001, 0.04957474023103714, -0.06228550896048546, 0.08444062620401382, -0.016177771613001823, -0.03552618995308876, -0.01665610447525978, 0.022720476612448692, -0.020748013630509377, -0.048419538885354996, 0.016690734773874283, -0.07335194945335388, -0.005036075133830309, 0.03178073465824127, -0.015347744338214397, -0.02154954895377159, -0.039851050823926926, -0.02575336955487728, 0.030598318204283714, -0.08186885714530945, -0.02151639759540558, -0.0010365379275754094, -0.0086011728271842, 0.020418938249349594, 0.05182856321334839, -0.036455340683460236, -0.020870529115200043, 0.0006600655033253133, -0.0002165494952350855, 0.024409756064414978, 0.05050498992204666, 0.026208974421024323, 0.04128306731581688, 0.005039380397647619, -0.019337479025125504, 0.015722110867500305, -0.014198603108525276, 0.026714002713561058, 0.02193213813006878, -0.003964022267609835, 0.01701223850250244, 0.03591917082667351, -0.04861290007829666, -0.05631086975336075, -0.020552275702357292, 0.02581830509006977, 0.04858643561601639, 0.044635921716690063, -0.047194257378578186, 0.002121887169778347, -0.06449645757675171, -0.028705762699246407, -0.0377473384141922, 0.017362739890813828, -0.00507094943895936, 0.007064029108732939, -0.002916344441473484, 0.06266597658395767, -0.06493454426527023, 0.04858008399605751, -0.06963939219713211, 0.029714705422520638, 0.04608592018485069, 0.0692019835114479, -0.04224538803100586, -0.034019168466329575, 0.0292315986007452, 0.02404390089213848, -0.06930794566869736, 0.024239346385002136, -0.028024975210428238, 0.01721881702542305, -0.002929059322923422, -0.013456830754876137, 0.020159009844064713, 0.021426817402243614, 0.004288851749151945, -0.02735845558345318, 0.029460662975907326, 0.010325858369469643, 0.04164021834731102, -0.04239590838551521, -0.022457197308540344, -0.03760264068841934, -0.023110486567020416, -0.0006155479932203889, -0.04969099164009094, -0.031775884330272675, 0.00377185782417655, 0.012485041283071041, 0.03745213896036148, -0.0035850387066602707, -0.003146566217765212, -0.010966464877128601, -0.003017896320670843, 0.015205081552267075, 0.0014392004813998938, -0.00003237350028939545, -0.01214570365846157, 0.020566733554005623, 0.06537175923585892, -0.014630213379859924, -0.012631772086024284, -0.051797833293676376, -0.003447504248470068, -0.029248660430312157, 0.009379156865179539, -0.028547832742333412, 0.047373101115226746, -0.05846748873591423, -0.031306661665439606, -0.004128540866076946, 0.023317448794841766, -0.05493488535284996, 0.033977895975112915, 0.04969578608870506, -0.04161018133163452, 0.010198067873716354, 0.004713401198387146, 0.03293302282691002, -0.0523277185857296, 0.05631893873214722, -0.01600395329296589, 0.0991496667265892, 0.04203759878873825, -0.029946282505989075, -0.00899031013250351, 0.04170437902212143, -0.034151557832956314, 0.011067030020058155, -0.01541020255535841, 0.0074048638343811035, 0.0392918698489666, 0.0180492140352726, -0.049742478877305984, -0.03615596517920494, -0.0035200128331780434, 0.06684943288564682, -0.003266725456342101, 0.044507186859846115, -0.003465718822553754, 0.0141673032194376, -0.010905744507908821, -0.017959265038371086, 0.06030754745006561, 0.023434365168213844, 0.004062628839164972, -0.013295313343405724, 0.07407724112272263, -0.03664030879735947, 0.023740168660879135, -0.04915133863687515, 0.05386653169989586, -0.05836610123515129, -0.03509196266531944, 0.01594599150121212, -0.0733071118593216, -0.03552717715501785, 0.04550126940011978, 0.03304147720336914, -0.007731317076832056, -0.03525010496377945, -0.04901673644781113, -0.06304270774126053, 0.005005509126931429, 0.03446429222822189, 0.019941207021474838, 0.03679315373301506, 0.014605111442506313, -0.011349350214004517, -0.11472149938344955, 0.03718036413192749, -0.0024537649005651474, -0.03751566261053085, 0.029568782076239586, -0.003237925935536623, -0.012577615678310394, -0.01071389764547348, 0.058992624282836914, 0.040480464696884155, -0.009431608952581882, -0.027286002412438393, -0.10684921592473984, 0.060603175312280655, 0.04902825504541397, -0.017077937722206116, 0.08495064824819565, -0.029729820787906647, -0.004944168496876955, -0.05486666411161423, 0.010838004760444164, -0.01325907651335001, 0.004721938632428646, 0.02314329892396927, -0.016771454364061356, 0.0642879381775856, 0.019020795822143555, -0.01595958322286606, -0.04824255034327507, 0.0018519157310947776, 0.02660413831472397, 0.0036796603817492723, -0.033650439232587814, -0.02500879019498825, -0.009044775739312172, 0.0405217707157135, -0.04107191413640976, 0.05226661637425423, 0.0029722941108047962, 0.02500341460108757, 0.014914887957274914, -0.004274645354598761, 0.051446978002786636, 0.0023920233361423016, -0.05238625034689903, -0.03442191705107689, 0.005224249325692654, -0.08019474148750305, 0.04416414350271225, -0.037393588572740555, -0.06299573928117752, 0.0033859878312796354, 0.020951366052031517, -0.026528140529990196, 0.013930580578744411, 0.028973624110221863, -0.019378965720534325, -0.02140597254037857, -0.045720431953668594, 0.006672486197203398, -0.018099436536431313, 0.0117286192253232, -0.03746889531612396, 0.022186366841197014, 0.018191948533058167, -0.03355482593178749, 0.014679143205285072, -0.0008105066372081637, -0.04050377383828163, -0.016288787126541138, -0.04730593413114548, -0.04104432091116905, -0.014876791276037693, -0.04247044026851654, 0.038356706500053406, -0.0578308030962944, -0.05230535939335823, 0.04001520201563835, 0.039219386875629425, -0.025934936478734016, 0.04299986734986305, -0.013578426092863083, -0.05146671459078789, -0.00032373625435866416, -0.019777832552790642, 0.029575834050774574, 0.009614120237529278, -0.03863077610731125, -0.022193316370248795, 0.00009497606515651569, -0.045323725789785385, 0.050014179199934006, -0.03551376238465309, 0.05205691605806351, 0.030992211773991585, 0.02733607031404972, 0.010417712852358818, 0.028862368315458298, 0.042755015194416046, -0.00783165730535984, 0.07109091430902481, -0.019724298268556595, 0.03195580840110779, 0.08950816094875336, -0.035145893692970276, -0.05639930069446564, 0.007079069968312979, -0.03213744983077049, -0.026008205488324165, 0.031147217378020287, -0.01262656506150961, -0.054530560970306396, 0.008377115242183208, -0.012372241355478764, -0.025266611948609352, 0.06736070662736893, 0.0426337793469429, 0.04082508385181427, -0.02234862744808197, -0.01635853387415409, 0.014335487969219685, -0.035117633640766144, 0.04423835128545761, -0.06059983745217323, 0.04189601168036461, 0.01641591638326645, -0.08849481493234634, 0.0061712730675935745, 0.01288711279630661, -0.0011266103247180581, 0.026227116584777832, -0.005234575364738703, 0.013702244497835636, -0.010456046089529991, -0.07157911360263824, 0.04754728823900223, -0.005095744971185923, -0.04042236506938934, 0.029973037540912628, 0.0268125981092453, 0.021259404718875885, -0.030881362035870552, 0.003912772983312607, -0.005354013293981552, -0.0546816848218441, 0.037024348974227905, -0.02528127282857895, -0.044387172907590866, -0.009829113259911537, -0.05722684785723686, 0.02466939017176628, -0.029582761228084564, -0.007509761024266481, -0.05843701213598251, 0.04912156984210014, -0.03272717818617821, 0.026797115802764893, 0.014323754236102104, 0.015687519684433937, -0.018406452611088753, 0.010985847562551498, -0.0006100554019212723, -0.06574824452400208, 0.03372921049594879, 0.06757908314466476, 0.0020548622123897076, -0.03817985951900482, 0.02800256758928299, 0.039108313620090485, 0.07089023292064667, 0.036900170147418976, 0.02418845146894455, -0.0010742307640612125, -0.02021106891334057, -0.03112773410975933, 0.05060015991330147, -0.016118446364998817, -0.044896118342876434, 0.011398183181881905, 0.008561231195926666, -0.001496984506957233, 0.006839305628091097, -0.011648758314549923, -0.002726910635828972, -0.03048187680542469, 0.038688674569129944, 0.06422014534473419, -0.0029908716678619385, -0.002854050835594535, 0.031185170635581017, 0.04558125138282776, 0.0010634245118126273, -0.011200882494449615, -0.05929330363869667, 0.03665518760681152, 0.008229567669332027, -0.07052864134311676, -0.008698784746229649, -0.05007295310497284, 0.01793430931866169, 0.04929524287581444, 0.010233241133391857, 0.061254166066646576, 0.007729819975793362, 0.014721340499818325, -0.020035218447446823, 0.06532599031925201, -0.04911954328417778, -0.00539793074131012, -0.031821295619010925, 0.012576434761285782, 0.004321423824876547, 0.011168464086949825, -0.005619619507342577, 0.001312204054556787, -0.03576592355966568, -0.050257328897714615, 0.03141891956329346, 0.0394265279173851, 0.007342904806137085, -0.02270376682281494, -0.029431520029902458, 0.008212185464799404, -0.08302497863769531, 0.010797574184834957, 0.040626201778650284, 0.037117522209882736, -0.022606614977121353, 0.0676421970129013, 0.034417878836393356, 0.006874543149024248, 0.024608904495835304, -0.015098599717020988, 0.053245458751916885, 0.015105533413589, -0.0817505270242691, -0.08324772864580154, -0.033673595637083054, 0.005801917985081673, 0.020835816860198975, 0.0447678379714489, -0.022905005142092705, 0.007727506570518017, 0.01889638975262642, 0.02595147117972374, -0.01475998293608427, 0.01892009563744068, -0.04700731858611107, -0.024586442857980728, 0.006076432764530182, -0.03796863555908203, -0.06896831095218658, 0.010944483801722527, -0.019280964508652687, 0.03859824687242508, -0.06030672416090965, 0.01710350438952446, 0.016368189826607704, -0.03446617349982262, 0.021683765575289726, -0.01079927571117878, -0.009523115120828152, 0.004425346851348877, 0.012794673442840576, -0.014633851125836372, -0.0046198186464607716, 0.033264756202697754, 0.07642628252506256, -0.03995167464017868, 0.0014018778456375003, 0.01969279907643795, 0.024773551151156425, -0.002551923505961895, -0.03559400513768196, -0.03693879395723343, 0.05969323590397835, 0.0016326212789863348, 0.01902284286916256, -0.019226638600230217, -0.009977754205465317, 0.0156802237033844, -0.019932910799980164, -0.0036590546369552612, 0.04665038362145424, -0.042668767273426056, -0.04060522839426994, 0.03330616280436516, -0.032068490982055664, 0.05270642787218094, -0.0320722758769989, 0.03626207262277603, 0.03795823082327843, 0.031876519322395325, 0.023676080629229546, -0.05178045481443405, 0.05297413468360901, 0.012630175799131393, 0.07065234333276749, 0.006474640220403671, 0.02968253567814827, 0.05410148203372955, -0.05595420300960541, -0.005679822061210871, -0.03110630065202713, 0.03673802688717842, -0.046839144080877304, -0.034354068338871, -0.010551818646490574, 0.05316786840558052, -0.0004973075701855123, 0.007755903527140617, 0.02759239636361599, 0.022870399057865143, 0.022736363112926483, 0.02412973716855049, 0.035473838448524475, 0.0015163779025897384, -0.01704183593392372, -0.019981086254119873, -0.038065578788518906, -0.009114525280892849, 0.01463968027383089, 0.014186264015734196, 0.0647379457950592, 0.013439523056149483, -0.03113197349011898, 0.04102027416229248, -0.01752661168575287, -0.008133961819112301, -0.039956096559762955, -0.027011068537831306, -0.0050165955908596516, -0.02076539769768715, 0.037493687123060226, 0.018573325127363205, 0.03553038462996483, -0.040249355137348175, -0.011616257950663567, 0.02227153815329075, -0.021089201793074608, -0.0014171719085425138, -0.00038837274769321084, -0.04019870236515999, 0.09973400086164474, -0.07405983656644821, -0.0171947218477726, 0.059476111084222794, 0.029769927263259888, -0.05675775185227394, -0.015889592468738556, -0.0033573408145457506, -0.03873126581311226, 0.003595039714127779, -0.005958769470453262, 0.07181215286254883, -0.009371169842779636, 0.03577312082052231, -0.030768737196922302, -0.017717275768518448, -0.024885257706046104, 0.011337386444211006, -0.01900719664990902, -0.014234395697712898, 0.0022523910738527775, -0.03955353423953056, -0.07171078026294708, -0.025203950703144073, -0.04426118731498718, 0.04655032604932785, 0.015575774013996124, -0.011204184964299202, -0.009227960370481014, -0.01495420467108488, 0.030879080295562744, -0.014158932492136955, 0.040631260722875595, -0.021388579159975052, 0.009207005612552166, 0.04706151783466339, -0.011103496886789799, 0.018939701840281487, -0.025278262794017792, 0.040783558040857315, -0.04271029680967331, -0.03755739703774452, -0.03698227182030678, 0.024286527186632156, 0.013196522369980812, 0.0022793435491621494, 0.005919452756643295, -0.04850355535745621, -0.057289429008960724, 0.05111559107899666, 0.03253789246082306, 0.04123206436634064, -0.0012638530461117625, 0.041036006063222885, 0.0260874405503273, -0.0006450704531744123, -0.030926557257771492, -0.0019132441375404596, -0.018708281219005585, 0.017407573759555817, -0.05898342281579971, -0.027376549318432808, -0.007950293831527233, 0.09121987968683243, -0.008158732205629349, -0.028969060629606247, 0.030747145414352417, -0.014947857707738876, 0.053460411727428436, 0.05863068252801895, -0.07427682727575302, 0.03316153585910797, 0.0275428369641304, 0.04452350363135338, -0.022811150178313255, -0.0234084390103817, -0.0439283661544323, 0.003988866228610277, 0.03586459532380104, 0.0009687031270004809, -0.021748563274741173, -0.0006189713021740317, -0.012228106148540974 ]
<p>Using a <a href="http://www.fluke.com/fluke/usen/electrical-test-tools/thermometers/fluke-62.htm?PID=56096" rel="nofollow">Fluke 62 Mini Infrared Thermometer</a> today on a stainless steel pipe with coolant I noticed that it gives incorrect temperature readings. There is a temperature sensor inside the coolant saying about 90° Celsius. I spray painted a spot on the pipe and the IR thermometer instantly gave more correct readings on the painted spot.</p> <p>So why? Why is it the coolant fluid is about 90° Celsius (both the painted spot and the temperature sensor suggest that), while the unpainted clear stainless steel says about 50° Celcius? I.e. apx 55%</p>
g8427
[ 0.09107493609189987, -0.10710518807172775, 0.016209525987505913, -0.04537712410092354, 0.030940525233745575, -0.0012122816406190395, 0.040800437331199646, 0.018170736730098724, -0.03603726252913475, -0.019845565780997276, 0.005020480137318373, 0.06547006219625473, -0.01065109483897686, -0.0015477566048502922, 0.015356163494288921, -0.0408310666680336, 0.046075936406850815, -0.03213853761553764, 0.009966481477022171, 0.10826817154884338, -0.01665443181991577, -0.03929761424660683, 0.011117449030280113, -0.0381593331694603, 0.04216277226805687, -0.009732118807733059, 0.0025688812602311373, -0.004775752779096365, 0.022687911987304688, 0.018076419830322266, -0.01928296871483326, 0.06581592559814453, -0.05321444943547249, 0.02881741337478161, 0.04633356258273125, -0.02298787422478199, 0.05865232273936272, 0.01913139596581459, 0.03436349704861641, -0.010111849755048752, 0.005597046576440334, 0.015382065437734127, 0.058848440647125244, 0.02593398652970791, -0.024446146562695503, 0.020006192848086357, -0.026054346933960915, 0.01736898347735405, -0.01268088910728693, 0.028610195964574814, -0.026990270242094994, -0.07005125284194946, -0.008279425092041492, -0.03200323134660721, 0.02115023508667946, 0.04441121593117714, -0.018102752044796944, 0.02843768708407879, -0.02541731297969818, 0.01954391784965992, 0.029744302853941917, 0.05124140903353691, 0.01562565565109253, 0.033169910311698914, -0.05977703630924225, 0.020357489585876465, -0.003743179840967059, -0.040662091225385666, -0.021540530025959015, 0.05411934852600098, -0.040833376348018646, -0.014335989020764828, 0.05114943906664848, -0.016857387498021126, -0.061592720448970795, -0.003840020392090082, -0.027217116206884384, 0.005692025646567345, 0.019611906260252, -0.00010675548401195556, 0.013398006558418274, -0.0321391262114048, -0.08117128908634186, 0.006403660401701927, -0.01667153462767601, 0.044453687965869904, -0.055708277970552444, 0.006565227638930082, -0.02869238704442978, -0.027157830074429512, -0.03570697829127312, -0.011203770525753498, 0.04199296981096268, 0.015643488615751266, 0.0330117866396904, 0.008652791380882263, 0.0016711789648979902, 0.015394176356494427, 0.0014798748306930065, 0.04909475892782211, 0.019077906385064125, -0.015029472298920155, 0.03365219011902809, -0.009956751950085163, 0.014204330742359161, -0.004205122124403715, 0.03759991005063057, -0.007016654592007399, -0.085071861743927, -0.016487406566739082, -0.05399726703763008, -0.02241586335003376, -0.06884937733411789, -0.027862736955285072, 0.06756384670734406, 0.01749453879892826, 0.03962400555610657, -0.004498481284826994, 0.016120795160531998, 0.006359631661325693, 0.027716245502233505, 0.01636313647031784, 0.02280062437057495, 0.03615574911236763, -0.045776594430208206, -0.020759642124176025, 0.03622746095061302, -0.010438905097544193, 0.017566580325365067, -0.07069220393896103, -0.029580727219581604, 0.02711249329149723, 0.007330188527703285, 0.010540340095758438, 0.007265155669301748, -0.05789332464337349, 0.015501121059060097, -0.028644293546676636, 0.050333231687545776, -0.005221682135015726, 0.004569202661514282, -0.0006603136425837874, 0.01677827723324299, -0.00702913012355566, 0.004486032295972109, -0.0025816853158175945, -0.08371802419424057, -0.006231823470443487, 0.046028267592191696, -0.04375011846423149, 0.00622994638979435, -0.024410083889961243, 0.04240315407514572, -0.01040744874626398, -0.019927753135561943, -0.03762570396065712, -0.014325657859444618, -0.04991784319281578, 0.025712836533784866, 0.031759295612573624, 0.021847670897841454, -0.0007225905428640544, 0.0524580217897892, 0.01711391843855381, -0.03614341467618942, 0.07584547996520996, -0.020413335412740707, -0.01959598995745182, -0.04099104180932045, -0.03724154829978943, -0.05010836198925972, 0.03734266757965088, -0.05319365859031677, -0.02983677014708519, 0.07348385453224182, 0.029142092913389206, 0.046052951365709305, 0.033846378326416016, 0.039295438677072525, -0.04580440744757652, -0.001054725842550397, -0.019841313362121582, 0.022393878549337387, -0.046812932938337326, -0.027065033093094826, -0.044968582689762115, 0.020621323958039284, -0.015958651900291443, -0.009129674173891544, -0.0008916708757169545, -0.00743915094062686, -0.08304715901613235, -0.008763832040131092, 0.0018784758867695928, 0.026889823377132416, 0.006066763773560524, -0.040764179080724716, -0.00280206766910851, 0.0031882214825600386, 0.07959920912981033, -0.0038527795113623142, -0.04671323299407959, -0.044427305459976196, -0.016218965873122215, -0.019805489107966423, 0.004958972334861755, -0.006325440015643835, -0.027366209775209427, -0.013183866627514362, -0.03320956602692604, -0.011880957521498203, 0.01672476716339588, -0.009787360206246376, -0.003935534507036209, -0.00110262306407094, 0.00664651021361351, 0.0494174063205719, 0.018082160502672195, -0.07889291644096375, 0.05621014162898064, 0.032494816929101944, 0.017168749123811722, 0.0548478402197361, 0.013994522392749786, -0.04407190904021263, 0.06995243579149246, -0.08193499594926834, -0.004117197822779417, -0.024181243032217026, 0.047057121992111206, -0.0016420825850218534, -0.048113152384757996, 0.013952343724668026, 0.060740530490875244, 0.03632696717977524, -0.04682202637195587, 0.009773424826562405, -0.046272050589323044, 0.05123458057641983, 0.03965087980031967, -0.006399370264261961, -0.0035360786132514477, -0.05395527929067612, 0.056888580322265625, -0.017901470884680748, 0.07197116315364838, -0.019585371017456055, -0.05351269990205765, 0.013407638296484947, -0.004762841388583183, -0.029367361217737198, 0.0637747272849083, -0.019811339676380157, 0.06763452291488647, -0.032405730336904526, -0.008321230299770832, -0.03099467046558857, 0.014759021811187267, -0.010194264352321625, -0.01506639551371336, -0.03708118945360184, -0.014895908534526825, 0.015115465968847275, 0.04539557918906212, -0.018559027463197708, 0.004708425607532263, -0.04032787308096886, 0.028060177341103554, -0.013980085030198097, -0.004694100469350815, 0.009357568807899952, 0.000307526090182364, -0.0020313074346631765, 0.03006010316312313, 0.011968626640737057, 0.013485862873494625, 0.0007320053409785032, -0.04846751317381859, 0.047293104231357574, -0.05557063966989517, -0.03142497316002846, 0.0031445419881492853, -0.043430816382169724, -0.018812669441103935, 0.002557159401476383, -0.044831566512584686, -0.03651959449052811, 0.007512305397540331, 0.03904913738369942, -0.013927483931183815, 0.026122143492102623, 0.0202732402831316, -0.06483019888401031, -0.013101930730044842, 0.019664563238620758, 0.0027167731896042824, 0.024132562801241875, -0.007829258218407631, 0.02667010948061943, -0.013745720498263836, 0.04012487083673477, 0.02882036380469799, -0.08064546436071396, -0.006002155598253012, 0.0518600232899189, -0.02421480230987072, -0.034896887838840485, -0.0009570490219630301, 0.055035874247550964, 0.009078278206288815, 0.01779945194721222, -0.03385649994015694, -0.011797221377491951, -0.021944327279925346, 0.021334433928132057, 0.02333458885550499, -0.09943050891160965, -0.0044036018662154675, 0.029359908774495125, 0.029590807855129242, -0.008490948006510735, 0.030186183750629425, -0.012951775453984737, 0.0453917570412159, 0.05479021742939949, -0.01499803178012371, 0.020199285820126534, 0.02473817765712738, -0.007772685959935188, 0.008385343477129936, 0.05699143931269646, 0.0077781048603355885, -0.011782463639974594, -0.02092650905251503, 0.014512668363749981, -0.06511470675468445, -0.08173399418592453, 0.09942351281642914, -0.01916305162012577, 0.01563348062336445, -0.053714752197265625, -0.021858828142285347, 0.03264913707971573, -0.013572737574577332, 0.024451809003949165, 0.03780870884656906, -0.01187190879136324, 0.02665325254201889, -0.015230607241392136, 0.04559643566608429, 0.041278399527072906, 0.060349028557538986, -0.010047934018075466, -0.040739934891462326, -0.04896583780646324, -0.018383821472525597, -0.00046270358143374324, 0.06795745342969894, -0.023986324667930603, 0.04306088015437126, 0.03184780478477478, -0.038889430463314056, -0.0021187164820730686, -0.06245337426662445, -0.015314177609980106, 0.04163411632180214, 0.04122292995452881, -0.005858008284121752, 0.02640969678759575, 0.01136635523289442, -0.04268307611346245, 0.025775182992219925, 0.011912038549780846, 0.045499756932258606, 0.03415112569928169, -0.03547842800617218, 0.023130405694246292, -0.0072393110021948814, -0.03806651756167412, 0.016530897468328476, 0.04605555534362793, -0.015074706636369228, -0.020369073376059532, -0.026539118960499763, -0.011192026548087597, -0.03351539000868797, -0.03804023563861847, 0.035859718918800354, 0.006634864024817944, -0.09691188484430313, 0.044764406979084015, -0.012220825999975204, 0.04351087659597397, 0.05126657336950302, 0.009941469877958298, 0.00959322601556778, 0.08742660284042358, -0.009241755120456219, -0.005074506159871817, -0.007831361144781113, -0.09413127601146698, 0.001690362929366529, 0.06802182644605637, -0.01623513177037239, -0.003862785641103983, -0.01799975335597992, 0.004892273340374231, -0.008106769993901253, 0.028464799746870995, 0.0119237769395113, -0.011993777006864548, 0.006356385536491871, -0.006960593163967133, -0.015139663591980934, -0.030791927129030228, -0.012061435729265213, 0.03632476553320885, 0.021730802953243256, 0.0026450513396412134, 0.008206646889448166, 0.011899501085281372, -0.0065702819265425205, 0.003738055471330881, -0.0029921827372163534, 0.07536403834819794, -0.007209368050098419, 0.01166362315416336, 0.051805999130010605, 0.017154036089777946, -0.05795665830373764, 0.0708782747387886, -0.09386558085680008, -0.10808215290307999, 0.026463186368346214, 0.031413763761520386, 0.027951650321483612, -0.032903093844652176, 0.01605212315917015, -0.04381636157631874, 0.06148961931467056, -0.03472466394305229, 0.016188615933060646, -0.048016320914030075, -0.017671411857008934, 0.010165615007281303, 0.0640086978673935, -0.025154612958431244, 0.012408914044499397, -0.032229211181402206, 0.003528244560584426, -0.04157865419983864, 0.01709665358066559, -0.007443864829838276, 0.017233729362487793, -0.007845529355108738, -0.03276047855615616, -0.006962622981518507, -0.010907754302024841, -0.010732654482126236, -0.001099284621886909, 0.021051714196801186, 0.005154226440936327, 0.007775580044835806, -0.013207887299358845, -0.000019009554307558574, 0.01165169756859541, 0.07201314717531204, -0.00981347169727087, -0.018674004822969437, -0.013437051326036453, -0.028383662924170494, 0.07974069565534592, 0.020631324499845505, 0.06236213818192482, 0.012539475224912167, 0.07224558293819427, 0.0760413184762001, -0.014384563080966473, 0.024344535544514656, 0.01601623184978962, -0.038673628121614456, -0.011224018409848213, 0.03616510331630707, 0.08382284641265869, -0.026497650891542435, -0.02999555505812168, -0.04538631811738014, 0.024126093834638596, 0.04126239940524101, -0.0771019384264946, 0.03754275292158127, 0.008298295550048351, 0.08368762582540512, 0.023486480116844177, -0.03151974454522133, 0.030367128551006317, 0.013984966091811657, 0.005415006540715694, 0.008083511143922806, -0.02521088905632496, -0.056519992649555206, -0.0013728486374020576, -0.024390341714024544, 0.003486612578853965, 0.01119622029364109, 0.008330246433615685, -0.001350093400105834, -0.01101619005203247, 0.06568070501089096, 0.0430663526058197, 0.04609343782067299, 0.031470149755477905, 0.02058604173362255, -0.013250852935016155, 0.048296477645635605, -0.043222859501838684, 0.0014988478505983949, -0.029748132452368736, 0.02109857089817524, -0.021383041515946388, 0.001259244978427887, -0.037406135350465775, 0.011413182131946087, 0.0010285490425303578, -0.03208578750491142, 0.019853906705975533, 0.0013406594516709447, -0.038042470812797546, 0.05515091121196747, 0.0019093280425295234, 0.025412334129214287, 0.041397977620363235, 0.0898742601275444, 0.012800311669707298, -0.008405829779803753, 0.011134899221360683, -0.017464015632867813, -0.027936700731515884, 0.028924783691763878, 0.09968526661396027, 0.07165894657373428, 0.0107605941593647, 0.03087957575917244, 0.015976199880242348, -0.023165855556726456, -0.008801616728305817, -0.006077585741877556, 0.015807323157787323, 0.03213248774409294, -0.047058433294296265, 0.056851282715797424, 0.04667236655950546, -0.05310015380382538, -0.005409039091318846, 0.06035007908940315, -0.009736897423863411, 0.03167855367064476, 0.011958480812609196, -0.026112990453839302, -0.03745313361287117, -0.035493914037942886, -0.06515669822692871, 0.04397115856409073, 0.044457174837589264, 0.02339818701148033, -0.00043183215893805027, -0.08464541286230087, -0.012844276614487171, -0.027863645926117897, -0.002756767440587282, 0.01438530720770359, -0.0006470807711593807, -0.04707075282931328, -0.09044331312179565, -0.025676503777503967, 0.04765164107084274, -0.05200652405619621, 0.002102459082379937, 0.009963140822947025, -0.02257593907415867, -0.001851232722401619, 0.013287071138620377, -0.060509536415338516, 0.004867785610258579, 0.019095899537205696, -0.030442601069808006, -0.05072382092475891, 0.0347977876663208, 0.016926174983382225, 0.048067763447761536, -0.047419071197509766, -0.00035768741508945823, -0.02510695904493332, 0.01698586344718933, 0.004021409433335066, -0.04556248337030411, -0.05578954890370369, 0.018630648031830788, -0.031034167855978012, -0.03282376006245613, -0.05033151060342789, -0.037350405007600784, 0.07713401317596436, -0.01498139463365078, -0.056710585951805115, -0.03500978648662567, 0.03680034354329109, 0.028011437505483627, -0.024051634594798088, -0.00916591938585043, -0.02023322880268097, 0.05423635244369507, -0.00884171947836876, 0.007548069581389427, 0.009936073794960976, 0.012202267535030842, 0.0101817287504673, 0.02764769084751606, -0.06848590821027756, -0.027438664808869362, 0.030981482937932014, 0.03568590432405472, -0.022494014352560043, -0.03690715506672859, -0.013978698290884495, -0.006816137582063675, -0.009686551056802273, 0.040373750030994415, -0.006822008173912764, -0.055444151163101196, 0.01122630387544632, 0.001753510208800435, -0.020297853276133537, -0.0015565631911158562, -0.020561151206493378, 0.001212665461935103, 0.01672767475247383, 0.024920707568526268, 0.07337065041065216, 0.04573052003979683, -0.023975344374775887, -0.03341306746006012, 0.005608227103948593, -0.02008010633289814, -0.019864965230226517, 0.008089536800980568, -0.0026610468048602343, 0.038080696016550064, -0.07922351360321045, -0.0008963103755377233, 0.00626893388107419, -0.0656275525689125, -0.055561363697052, -0.006701579317450523, 0.026408782228827477, 0.019489014521241188, -0.03198814392089844, 0.053934916853904724, 0.026912253350019455, -0.04695546627044678, 0.009913048706948757, -0.050500303506851196, -0.012845037505030632, 0.034915726631879807, 0.010455220937728882, -0.013912474736571312, 0.031217418611049652, -0.04549795016646385, 0.001176632707938552, -0.04641187936067581, -0.017547357827425003, 0.024146681651473045, 0.04636925086379051, -0.05932197719812393, 0.022834714502096176, 0.03388650342822075, -0.02868502214550972, 0.021931296214461327, 0.03488392010331154, 0.05880539491772652, -0.020969409495592117, -0.031153148040175438, 0.028082240372896194, -0.038116712123155594, -0.08809652924537659, 0.0010115975746884942, -0.04400239139795303, -0.026405924931168556, 0.06107977405190468, -0.07461219280958176, 0.0231863334774971, 0.016701243817806244, 0.031476330012083054, -0.03408457711338997, 0.016490604728460312, -0.009902493096888065, -0.015529470518231392, -0.012949596159160137, 0.038966841995716095, -0.006458076648414135, 0.006829626392573118, -0.0005779500352218747, 0.008428984321653843, 0.0062233638018369675, -0.023705702275037766, 0.03595590218901634, -0.00039527242188341916, 0.015206580050289631, -0.043886423110961914, -0.01790246181190014, -0.010190525092184544, 0.016273492947220802, 0.08766165375709534, -0.004335564095526934, -0.05322660505771637, -0.035809192806482315, -0.050799477845430374, -0.0234108604490757, -0.015812251716852188, -0.04779217019677162, -0.023430734872817993, 0.004928749520331621, -0.020136253908276558, -0.007233382668346167, 0.022007668390870094, 0.025703666731715202, 0.006153288763016462, 0.020992077887058258, -0.05285440385341644, 0.03816445916891098, 0.007725434377789497, 0.06777975708246231, -0.060445427894592285, 0.026953695341944695, -0.03476382791996002, 0.012735982425510883, 0.08829931914806366, -0.004648360889405012, 0.03077787719666958, 0.02879554219543934, 0.04747277498245239, 0.05072232335805893, 0.01273150835186243, -0.048061080276966095, -0.022582273930311203, -0.06844501942396164, -0.03250311315059662, 0.020247822627425194, -0.02744937315583229, -0.03767095506191254, -0.043354954570531845, 0.0031628720462322235, -0.0121526550501585, -0.0042460886761546135, -0.029387742280960083, -0.0005348158883862197, -0.04132434353232384, 0.047475870698690414, 0.011758178472518921, -0.03945668041706085, -0.023531613871455193, -0.014485154300928116, -0.03982184827327728, 0.023013534024357796, -0.010628079995512962, 0.00687915226444602, -0.042688339948654175, -0.02777128852903843 ]
<p>It's a physics club for undergraduates (first three years of university); I'm looking for projects idea that aren't too obvious like a small rocket or an electromagnet (school projects) but also not too advanced. Since most members know Newtonian mechanics, electrostatics &amp; magnetostatics and some simple notions of thermodynamics, waves, special relativity &amp; geometric optics, I came up with the project "<em>The Solar System</em>" with the following objectives:<br/></p> <ul> <li>Study the motion of the earth in the gravitational field of the fixed sun (analytical solution) and compare the results to the available data.</li> <li>Study the earth as a 2-body system (analytical solution)</li> <li>Study the sun-earth-moon system numerically (3-body problem)</li> <li>Study the sun-earth-moon-other planets as a 10-body problem</li> <li>Treat the bodies as point particles and then as rotating solid bodies</li> <li>Calculate the value of the year</li> </ul> <p>Any refinements to this projects are welcomed. Any other project?</p>
g8428
[ -0.012734399177134037, 0.029223915189504623, -0.007042465265840292, -0.002348217647522688, 0.025476722046732903, -0.015364842489361763, -0.04052980616688728, -0.013787462376058102, 0.004708658438175917, -0.003796336939558387, 0.0977478101849556, 0.047250162810087204, 0.05984020233154297, 0.008814429864287376, -0.007616632618010044, 0.038749340921640396, 0.05248206481337547, -0.008682435378432274, 0.014980846084654331, 0.0504286102950573, 0.085084930062294, 0.033988602459430695, 0.06401611864566803, -0.006076392717659473, 0.017871379852294922, 0.06171930581331253, 0.013836083933711052, -0.03309797868132591, -0.06873975694179535, -0.002926136367022991, -0.04848342388868332, -0.021630730479955673, 0.03761487081646919, -0.0575999841094017, -0.046777334064245224, -0.029998552054166794, 0.05437513068318367, 0.019693173468112946, -0.022909605875611305, -0.03581739589571953, -0.039471741765737534, -0.04917405918240547, -0.0016568112187087536, 0.07786019146442413, 0.03896564245223999, -0.050794877111911774, 0.03264840692281723, -0.06233598664402962, 0.041844628751277924, 0.030021680518984795, 0.03896157816052437, 0.052953168749809265, 0.06537114083766937, -0.0066463155671954155, 0.01094441581517458, -0.0371992252767086, -0.02298523485660553, -0.06656042486429214, 0.04508798196911812, 0.013455397449433804, 0.04816114902496338, 0.020944351330399513, -0.023632949218153954, -0.029071131721138954, -0.05166388303041458, -0.039299510419368744, -0.013573880307376385, 0.005930752027779818, -0.015687957406044006, 0.017825931310653687, 0.05306551605463028, -0.012101205997169018, 0.03729301691055298, -0.012242418713867664, -0.011564692482352257, 0.01333503145724535, 0.00496166804805398, 0.019564924761652946, 0.039707001298666, 0.0034726588055491447, -0.026264721527695656, -0.01438204851001501, -0.009580029174685478, -0.04919377714395523, 0.07788959890604019, -0.0761399194598198, -0.04145551472902298, 0.032367806881666183, -0.04317391663789749, -0.032557908445596695, -0.008061638101935387, 0.006121630780398846, 0.02178901992738247, -0.02191006764769554, -0.027089674025774002, 0.015841403976082802, 0.0006033691461198032, 0.03258996084332466, 0.039217591285705566, 0.07656240463256836, -0.05845053493976593, -0.02468515746295452, -0.044589463621377945, 0.07075938582420349, 0.01367945596575737, -0.009159514680504799, 0.019382817670702934, 0.013156170956790447, 0.013430417515337467, -0.004322691820561886, -0.04493660107254982, -0.03544969484210014, -0.04123944416642189, -0.0038182029966264963, -0.012616029009222984, -0.0338071808218956, 0.008474496193230152, -0.07117444276809692, 0.06965409964323044, 0.06104476749897003, 0.022277161478996277, 0.026835551485419273, 0.0103762187063694, 0.01360989734530449, -0.0066710240207612514, -0.02291974425315857, 0.007059923838824034, -0.01914866268634796, 0.022691017016768456, -0.05739431828260422, 0.0011425712145864964, -0.018466772511601448, -0.08242063969373703, -0.013270544819533825, 0.0028600094374269247, 0.06201648712158203, -0.002379262587055564, 0.0037485144566744566, 0.008457469753921032, 0.027811484411358833, 0.03406572341918945, -0.015036708675324917, -0.02995731122791767, -0.0033821649849414825, -0.04603124409914017, 0.011380217969417572, -0.04993676766753197, -0.04639861360192299, 0.008391372859477997, 0.044850386679172516, -0.0031436984427273273, 0.05235134810209274, 0.0261768139898777, -0.06707587838172913, -0.012495910748839378, 0.0015909740468487144, -0.021621452644467354, -0.016528956592082977, -0.047913018614053726, 0.00023060664534568787, 0.011985722929239273, 0.016618985682725906, -0.050433699041604996, 0.053893622010946274, -0.02387208491563797, 0.06196901202201843, -0.05057138204574585, -0.054841794073581696, 0.0093612689524889, 0.026932086795568466, -0.06309881806373596, -0.059785131365060806, 0.00546783534809947, 0.08737466484308243, -0.0465884655714035, 0.015784405171871185, 0.03928657993674278, -0.058883968740701675, 0.02249395102262497, 0.020688412711024284, 0.015969811007380486, -0.060271210968494415, 0.011788137257099152, 0.01349582802504301, -0.058095093816518784, 0.03089044615626335, 0.0015107516665011644, 0.05805126205086708, -0.06298241764307022, 0.01788581907749176, 0.00042487564496695995, -0.001156176091171801, -0.003761882660910487, -0.031771816313266754, 0.006681112106889486, -0.03613952919840813, -0.0008246602956205606, 0.010858073830604553, -0.047050707042217255, 0.03548870235681534, -0.018062010407447815, 0.054893311113119125, 0.038811374455690384, 0.020684458315372467, 0.04288511350750923, -0.009509500116109848, -0.010373041033744812, -0.010745616629719734, -0.02480657398700714, 0.03847256675362587, 0.05187403783202171, -0.059450775384902954, -0.0059486920945346355, -0.005465349182486534, -0.003060425166040659, -0.014659776352345943, -0.06071532517671585, 0.019906431436538696, 0.01057559996843338, 0.012934635393321514, -0.030172431841492653, 0.006573702674359083, 0.02963227778673172, 0.024616174399852753, 0.036554109305143356, 0.006669113412499428, -0.06735925376415253, 0.016009125858545303, 0.02790975198149681, 0.018301578238606453, -0.009928395040333271, 0.046424973756074905, 0.036637160927057266, -0.007462230045348406, 0.014606724493205547, -0.01193790789693594, -0.017756382003426552, -0.049090929329395294, 0.03799469396471977, 0.008794160559773445, -0.006298650521785021, -0.0011974042281508446, -0.003578981850296259, -0.028178535401821136, 0.06533446907997131, -0.032057762145996094, 0.06654022634029388, 0.08845347166061401, -0.04165279120206833, 0.012838761322200298, 0.03536675497889519, 0.007620717398822308, -0.09452977031469345, 0.01454996783286333, 0.004692419432103634, -0.004401312675327063, -0.01783926412463188, 0.04973205551505089, -0.027167806401848793, -0.04219326004385948, 0.04221231862902641, -0.042061857879161835, 0.020578915253281593, 0.026634445413947105, -0.00037349757621996105, -0.03361844643950462, -0.05683078616857529, -0.07313219457864761, -0.0035233721137046814, -0.01291902456432581, 0.02732117846608162, 0.01297671440988779, 0.057045191526412964, 0.024030474945902824, -0.04261217266321182, 0.010902422480285168, -0.0007819923921488225, -0.016950348392128944, 0.011025494895875454, -0.025011617690324783, 0.008921799249947071, 0.003827892243862152, -0.011217569932341576, 0.04145534336566925, -0.0321071520447731, -0.010312704369425774, -0.027800852432847023, 0.03439580649137497, 0.0153456786647439, -0.0061994451098144054, -0.019891656935214996, -0.0187373049557209, 0.07131534814834595, -0.02467176876962185, -0.003344639902934432, 0.01645970530807972, -0.007578772492706776, -0.022215086966753006, -0.06031229719519615, -0.0011373930610716343, -0.010940099135041237, 0.060976918786764145, -0.016317233443260193, 0.010379469022154808, -0.025849875062704086, -0.03495534136891365, -0.017093682661652565, -0.0333690382540226, 0.027068737894296646, 0.0028537544421851635, 0.03637424483895302, 0.034258414059877396, 0.032173577696084976, 0.046505626291036606, -0.04294910654425621, 0.055110298097133636, -0.024148959666490555, -0.01873253844678402, 0.06651715189218521, -0.04997147619724274, 0.014145857654511929, -0.024439936503767967, 0.07298224419355392, -0.04364001005887985, 0.033922113478183746, 0.11158008873462677, -0.022773172706365585, -0.09148858487606049, -0.03095870465040207, -0.020726168528199196, -0.034603286534547806, 0.05878611281514168, -0.018831918016076088, 0.015889491885900497, -0.049416061490774155, -0.040807656943798065, 0.023465413600206375, -0.004328713286668062, 0.06098729372024536, -0.04686722531914711, -0.027230894193053246, 0.0015961515018716455, 0.0043099443428218365, -0.06908517330884933, 0.016271479427814484, -0.01384723000228405, 0.010881410911679268, -0.05498679727315903, -0.0025055010337382555, 0.015403419733047485, 0.056798480451107025, 0.031163876876235008, -0.01830005832016468, -0.026221442967653275, -0.00013541227963287383, -0.0023669388610869646, 0.04569583013653755, 0.016576936468482018, -0.019833805039525032, -0.020332586020231247, -0.03532745689153671, 0.021808627992868423, -0.0437619686126709, 0.048529766499996185, 0.019007762894034386, 0.04046326130628586, 0.0343838632106781, 0.001187003101222217, 0.006848287768661976, -0.017704658210277557, 0.02563602477312088, 0.04918893799185753, 0.006180610973387957, -0.05943100526928902, -0.030525539070367813, -0.06442992389202118, -0.008744115009903908, -0.037526004016399384, -0.04178982973098755, 0.019209284335374832, 0.03591249883174896, 0.026129769161343575, 0.02954581007361412, 0.031246639788150787, -0.01693722978234291, 0.06133294478058815, 0.015659138560295105, 0.04623069986701012, -0.040407661348581314, -0.006249756086617708, 0.05006935074925423, -0.0844612866640091, -0.0007322704186663032, 0.01108343806117773, 0.04495183750987053, -0.07374735176563263, 0.026470612734556198, -0.08307501673698425, 0.0334077849984169, 0.017159586772322655, -0.008782554417848587, -0.011893626302480698, 0.04578728601336479, -0.013305377215147018, -0.026285547763109207, 0.015497901476919651, 0.039363499730825424, -0.02234538644552231, -0.02919284626841545, 0.0563279464840889, 0.05171188339591026, -0.03348727524280548, 0.0948781967163086, -0.05045231059193611, 0.0002615402627270669, -0.01709260605275631, -0.03220231458544731, 0.007020880468189716, 0.03221803158521652, 0.04351905733346939, -0.062417879700660706, 0.08872291445732117, 0.02359652891755104, -0.013194655999541283, 0.006931222043931484, -0.005286736413836479, 0.06568700075149536, -0.01567559875547886, 0.012239335104823112, 0.013665248639881611, -0.008140617050230503, 0.0022888993844389915, -0.0034837438724935055, -0.0011595169780775905, -0.015057223848998547, 0.017422350123524666, 0.002283406211063266, -0.03255448862910271, -0.051566001027822495, -0.00623654667288065, 0.03197501599788666, -0.016665330156683922, 0.012798801995813847, -0.003537504468113184, -0.02441825345158577, 0.08841145783662796, -0.04551661014556885, -0.06887079030275345, -0.0322481207549572, 0.052279308438301086, 0.02098456583917141, -0.0052367690950632095, -0.024996502324938774, 0.06409658491611481, -0.06636452674865723, 0.021054044365882874, -0.026185031980276108, 0.020414946600794792, 0.03898259624838829, 0.06434004008769989, -0.03190140053629875, -0.017045367509126663, -0.029672984033823013, 0.013704953715205193, 0.019182706251740456, -0.05942568928003311, -0.025626178830862045, -0.02454356476664543, -0.015899689868092537, -0.06226757913827896, -0.003868632484227419, 0.03542333468794823, 0.06011078879237175, -0.02957223355770111, 0.002756848931312561, -0.025665756314992905, -0.030428413301706314, -0.03710828348994255, -0.006039795931428671, -0.00467083090916276, 0.005026917904615402, 0.05613856762647629, 0.01353274006396532, 0.008979030884802341, -0.04455465078353882, -0.003988100215792656, -0.032299675047397614, 0.014194347895681858, -0.021811706945300102, 0.04118102416396141, 0.011917821131646633, -0.045362599194049835, 0.029414094984531403, -0.032886892557144165, -0.002270081778988242, 0.010089460760354996, -0.007900875061750412, 0.03116263821721077, 0.020101353526115417, -0.015883097425103188, 0.014926079660654068, 0.04589112848043442, -0.05367852374911308, 0.026779811829328537, 0.03625224903225899, 0.00010354362893849611, 0.012047970667481422, 0.023038236424326897, -0.00494039012119174, 0.0074334656819701195, -0.008110163733363152, -0.015877047553658485, 0.05836276710033417, -0.018765633925795555, -0.03766633942723274, 0.03567591682076454, 0.010051076300442219, 0.011250907555222511, 0.002444019541144371, 0.006157444324344397, 0.03519320860505104, -0.013335579074919224, 0.04156676307320595, 0.007345353718847036, 0.06340789049863815, 0.010766064748167992, -0.06332052499055862, -0.013756511732935905, -0.02179163135588169, 0.028354179114103317, -0.03355930373072624, -0.047175198793411255, 0.03405572846531868, -0.03901757672429085, -0.015468016266822815, -0.014028511941432953, -0.03238284960389137, 0.016176626086235046, 0.048633135855197906, -0.04314554110169411, -0.0043939813040196896, -0.01673075370490551, 0.0727267861366272, -0.04043923318386078, -0.059316281229257584, 0.028371134772896767, 0.000005698394488717895, 0.029748283326625824, 0.1180189922451973, -0.08262269198894501, -0.04376404732465744, -0.016128551214933395, 0.01780962571501732, -0.08132892102003098, -0.06525032222270966, 0.021587824448943138, -0.020319268107414246, -0.01318106148391962, 0.03991394862532616, 0.04143594577908516, 0.03555009141564369, -0.09687210619449615, 0.02834363654255867, -0.0014162095030769706, -0.043274521827697754, 0.0029320279136300087, -0.017064185813069344, -0.04427884891629219, 0.04414535313844681, 0.007852175273001194, -0.043195903301239014, 0.004883353598415852, -0.008939276449382305, -0.04224046692252159, 0.02610127627849579, -0.037716422230005264, 0.0027723575476557016, -0.007598468568176031, -0.038338277488946915, -0.016311580315232277, -0.0009707559947855771, 0.08242970705032349, 0.04983329400420189, 0.02287682704627514, -0.013358185067772865, 0.019160227850079536, -0.024140970781445503, -0.05998413264751434, 0.010602970607578754, -0.08782974630594254, -0.0338294617831707, 0.01472474541515112, -0.017161749303340912, 0.001836022362112999, -0.04165066406130791, 0.019666358828544617, 0.04600672423839569, -0.0016411375254392624, -0.01895741932094097, 0.05808419734239578, -0.013886134140193462, 0.005543222185224295, 0.005883609876036644, -0.00352735654450953, 0.030324751511216164, 0.004408123437315226, -0.008902298286557198, -0.006845212075859308, -0.031045988202095032, -0.037875548005104065, -0.026324445381760597, 0.02715248055756092, -0.06429040431976318, 0.06564812362194061, -0.019284069538116455, -0.016151683405041695, 0.08782869577407837, 0.017518293112516403, 0.033264607191085815, -0.02524842508137226, 0.004537085071206093, -0.04186682030558586, 0.009952908381819725, -0.013591784983873367, -0.017954716458916664, -0.010275057516992092, -0.04188482090830803, -0.025054654106497765, 0.04357796907424927, 0.004459389019757509, 0.02585544064640999, -0.019471509382128716, 0.03743114694952965, 0.05189206823706627, -0.0024046842008829117, 0.03510010614991188, 0.017825748771429062, 0.008495476096868515, 0.008895528502762318, 0.0022279475815594196, -0.03318442404270172, 0.001273157773539424, 0.013924642466008663, 0.005438735708594322, 0.009186490438878536, -0.053089894354343414, -0.019012069329619408, -0.0062683578580617905, -0.02877683751285076, -0.005998333916068077, -0.01934460923075676, -0.0558168962597847, -0.007900695316493511, -0.0075294445268809795, -0.006317435298115015, 0.034983884543180466, -0.01620972529053688, 0.029700404033064842, 0.05210050567984581, -0.03183260187506676, -0.030719278380274773, -0.005302185192704201, -0.0015046782791614532, -0.020776165649294853, -0.00599517161026597, 0.05568261072039604, -0.013744058087468147, 0.00521228089928627, -0.018822547048330307, 0.004006239585578442, 0.013046552427113056, 0.005615582689642906, -0.08119504153728485, 0.041255876421928406, -0.005760843865573406, 0.0015188205288723111, 0.009213012643158436, -0.06550881266593933, -0.002415127819404006, -0.026426050812005997, -0.006291448138654232, -0.00489342026412487, -0.030513785779476166, 0.003524947678670287, 0.0017923081759363413, 0.017785480245947838, -0.008192124776542187, -0.0015653365990146995, 0.03633984178304672, 0.019292045384645462, 0.059334930032491684, 0.07142191380262375, -0.020588181912899017, -0.007069041021168232, 0.014702261425554752, -0.007594855967909098, 0.01704331673681736, 0.003685879521071911, 0.07511298358440399, -0.014266879297792912, -0.025650201365351677, -0.014063667505979538, 0.029913397505879402, -0.040150102227926254, -0.012891407124698162, 0.02248833328485489, -0.018494324758648872, -0.015056165866553783, -0.007192782126367092, 0.017182279378175735, 0.018309708684682846, 0.06067131832242012, 0.013619990088045597, 0.00023939124366734177, -0.03510319069027901, 0.05882313475012779, -0.012146171182394028, 0.04826543107628822, -0.017320435494184494, -0.011609535664319992, -0.031530290842056274, -0.01921534352004528, 0.012777243740856647, -0.0430392287671566, -0.01299940887838602, -0.021010080352425575, -0.01920570433139801, -0.037351883947849274, 0.06457226723432541, -0.042045947164297104, 0.007546074688434601, 0.03357360139489174, -0.029053939506411552, -0.013844192959368229, -0.04893503338098526, -0.019657770171761513, -0.03861348703503609, -0.06885440647602081, -0.020662670955061913, 0.028476055711507797, -0.04601394757628441, -0.060270171612501144, 0.0038917663041502237, -0.03517797589302063, 0.023717978969216347, 0.019624456763267517, -0.076120525598526, 0.057027075439691544, 0.09337726980447769, -0.015120568685233593, 0.007296707481145859, 0.09100055694580078, -0.022985203191637993, 0.03614456206560135, 0.015319768339395523, 0.0039173332042992115, 0.029829349368810654, -0.0077587757259607315, -0.019600696861743927, -0.03593883663415909, 0.002858236199244857, 0.004640655126422644, 0.004057631827890873, -0.015981236472725868, 0.0355953611433506, 0.01375362928956747, 0.014941882342100143, 0.038889653980731964 ]
<p>Once day, I talked to my Prof. about Computational Physics and he showed me his work. I'm quite surprised that why Prof. use C++ for computation because C++ quite complicated. I heard he talked about memory talk about pointer. Why didn't he use Python or Java that more easier? no need to manage memory no need to busy with pointer.</p>
g8429
[ 0.0362699031829834, 0.04241206869482994, 0.01612204872071743, -0.04377143085002899, 0.003878167364746332, -0.033076949417591095, 0.06204655393958092, -0.002063178224489093, -0.048031438142061234, -0.038638465106487274, 0.005770272109657526, -0.0005221875617280602, 0.020159222185611725, 0.02627132646739483, -0.01887059211730957, -0.017625020816922188, 0.03257826343178749, -0.02955278567969799, -0.042015571147203445, 0.015569915063679218, -0.0034020079765468836, -0.007451220415532589, 0.040810320526361465, -0.032373253256082535, -0.05356373265385628, 0.043929342180490494, -0.06985896080732346, -0.015660876408219337, -0.027413981035351753, 0.0431179404258728, 0.06430594623088837, -0.008694789372384548, -0.0621628500521183, -0.04111963137984276, -0.03354790434241295, -0.036520279943943024, 0.00547963147982955, 0.008487116545438766, 0.043297428637742996, -0.02993771620094776, -0.023873362690210342, -0.031297869980335236, 0.03782420605421066, -0.007343210279941559, 0.030690887942910194, 0.0005502331187017262, 0.026518873870372772, -0.034467339515686035, -0.045953571796417236, 0.0036667266394943, -0.009377538226544857, -0.011793122626841068, -0.01260741800069809, -0.018329869955778122, 0.0025793733075261116, 0.018397755920886993, 0.0064737387001514435, 0.03038455918431282, 0.04935247451066971, -0.02552999183535576, 0.07710286974906921, -0.01714353822171688, -0.022886307910084724, -0.0222135279327631, -0.016448698937892914, 0.00537700392305851, 0.014572964049875736, -0.0053536719642579556, -0.06109333410859108, 0.04717430844902992, 0.012049941346049309, -0.03534417226910591, 0.045837994664907455, -0.010687818750739098, -0.009600711986422539, 0.041662365198135376, 0.019474660977721214, -0.04713258892297745, 0.02250027470290661, 0.044133711606264114, -0.05423029512166977, -0.0492888018488884, -0.03096410445868969, -0.022918403148651123, 0.05528063327074051, -0.01849735900759697, -0.02535034343600273, 0.06938894838094711, 0.02329098992049694, 0.0016547454288229346, -0.07426309585571289, -0.011819559149444103, 0.05357242375612259, -0.008774039335548878, 0.017467012628912926, -0.0042660050094127655, 0.01284997072070837, 0.008485765196383, 0.042608194053173065, -0.029668066650629044, -0.0065942127257585526, -0.008107810281217098, 0.05100085958838463, 0.0417838953435421, 0.0027410448528826237, -0.006964473519474268, 0.01567862555384636, 0.012427144683897495, -0.007720964960753918, -0.04506748542189598, 0.0026152192149311304, 0.019406281411647797, -0.050705693662166595, 0.01548125222325325, -0.07409895211458206, 0.030681151896715164, 0.040690816938877106, -0.07283876091241837, 0.04860413447022438, 0.04367903247475624, -0.045366160571575165, -0.053680650889873505, 0.06943067163228989, 0.0520949624478817, 0.057326506823301315, -0.03546830639243126, 0.04444626718759537, -0.006166006438434124, 0.04197008162736893, -0.005588200408965349, -0.009462442249059677, -0.016257168725132942, -0.07934686541557312, 0.032810017466545105, -0.0559457428753376, 0.03411925584077835, -0.04596799239516258, 0.02352781780064106, 0.039617471396923065, -0.03561751917004585, 0.0012147050583735108, -0.018245331943035126, -0.050381481647491455, -0.019945375621318817, 0.02689632959663868, 0.0029658221174031496, -0.07845328748226166, 0.0013624221319332719, -0.012007851153612137, 0.010796425864100456, 0.0396600179374218, 0.03691181540489197, -0.03171129152178764, -0.015003635548055172, 0.025563983246684074, 0.04352854937314987, 0.009365769103169441, 0.011138333939015865, 0.050994910299777985, 0.01342962309718132, 0.033421266824007034, 0.006985230837017298, -0.045981407165527344, 0.04507077857851982, 0.06759190559387207, -0.02772962860763073, 0.02995932847261429, -0.0365743450820446, -0.02181987836956978, -0.0012506414204835892, -0.02633754350244999, -0.0011494079371914268, 0.027720382437109947, -0.025092478841543198, 0.008822278119623661, 0.01176411472260952, -0.06069831922650337, 0.03280935063958168, 0.04570229724049568, 0.01881987228989601, -0.015225479379296303, 0.016632024198770523, -0.030805669724941254, 0.000765601231250912, -0.029969068244099617, 0.04722123593091965, -0.027636300772428513, 0.04770001024007797, -0.048283278942108154, -0.037984807044267654, -0.09257935732603073, -0.031104277819395065, -0.003583658719435334, 0.0566205196082592, -0.04524074122309685, 0.007040285971015692, -0.0072236256673932076, 0.01691991277039051, -0.01293131522834301, 0.04260844364762306, 0.006128630135208368, -0.015294656157493591, 0.043534185737371445, 0.04726285859942436, -0.022028092294931412, -0.019266881048679352, 0.02595987170934677, -0.019080178812146187, 0.015776298940181732, 0.027794530615210533, 0.0860242247581482, 0.05642077699303627, 0.012953835539519787, 0.05710715427994728, -0.030913999304175377, -0.03739386424422264, -0.05801030993461609, -0.07456074655056, -0.0054827528074383736, 0.02196202240884304, 0.006580785382539034, -0.09551630169153214, 0.013894171454012394, 0.03456169739365578, -0.008262744173407555, 0.031857315450906754, 0.0469030998647213, 0.05054932460188866, -0.016656864434480667, -0.04093027859926224, -0.057773392647504807, 0.023247122764587402, 0.006368505302816629, 0.02911975421011448, 0.11233765631914139, 0.002929119858890772, -0.00833543948829174, 0.01487553957849741, 0.022826170548796654, 0.029849937185645103, 0.038738176226615906, -0.015132484957575798, 0.026547377929091454, -0.013678007759153843, -0.016792841255664825, -0.0009557908633723855, 0.05851438641548157, 0.024292143061757088, 0.004242260940372944, -0.01597702130675316, -0.004281626548618078, -0.0436263382434845, -0.03167787939310074, 0.02477225475013256, 0.017141401767730713, 0.012980608269572258, 0.0346924290060997, -0.02888864278793335, -0.01260356418788433, 0.006630075629800558, 0.05449023097753525, -0.04899556562304497, -0.07312384992837906, -0.01733042113482952, 0.0006725894054397941, -0.0010052730794996023, -0.021612295880913734, -0.00769751938059926, 0.03866713494062424, -0.007076723035424948, 0.005851884372532368, -0.006335541605949402, -0.004039690364152193, -0.02101912349462509, -0.03295173496007919, -0.019135884940624237, 0.030619030818343163, -0.008192860521376133, 0.03343089669942856, -0.0441260039806366, -0.03570001944899559, -0.03367998078465462, -0.07247629761695862, 0.00705768633633852, 0.05293959379196167, 0.023809382691979408, -0.021605292335152626, 0.04481206834316254, 0.003513503819704056, -0.007255695294588804, 0.03867443650960922, 0.011945078149437904, 0.038748908787965775, -0.014949065633118153, 0.03781035915017128, 0.032308775931596756, 0.016722921282052994, 0.021432098001241684, -0.026059355586767197, 0.031840547919273376, 0.020396530628204346, 0.0009665418765507638, 0.004257374443113804, -0.009967746213078499, -0.019534608349204063, -0.010826820507645607, -0.0097440704703331, 0.018037283793091774, -0.02853141352534294, 0.006189252249896526, 0.040477532893419266, 0.013094866648316383, 0.028875086456537247, 0.012766783125698566, -0.026697451248764992, -0.04000740498304367, -0.01786612719297409, 0.042693912982940674, 0.061304137110710144, -0.026036549359560013, -0.0215142909437418, -0.019711999222636223, 0.07638753205537796, -0.062157273292541504, -0.006389550399035215, 0.050919100642204285, 0.027758903801441193, 0.028672708198428154, 0.020833363756537437, 0.025527549907565117, -0.015231196768581867, -0.014164621010422707, -0.01357614528387785, 0.024910740554332733, -0.06850924342870712, -0.05995162948966026, 0.015738340094685555, 0.013455942273139954, 0.009614448994398117, -0.05294151231646538, -0.05810801684856415, -0.032781559973955154, -0.04262842983007431, -0.017063410952687263, 0.03888929635286331, 0.04399225488305092, 0.0958404615521431, 0.019295237958431244, 0.06650519371032715, -0.030707743018865585, 0.014499501325190067, 0.04747362807393074, -0.0017910494934767485, -0.03228909522294998, -0.010926872491836548, -0.02488466538488865, -0.007051214575767517, 0.04830068722367287, -0.03741899132728577, -0.016532300040125847, 0.0008708569803275168, 0.008589593693614006, 0.0014701425097882748, -0.02836817130446434, -0.0801081582903862, -0.016268927603960037, 0.03501332551240921, 0.042141806334257126, -0.036913320422172546, -0.03417098894715309, -0.026154225692152977, -0.04703855141997337, 0.03903713449835777, 0.006440779194235802, 0.039074353873729706, -0.0695810467004776, 0.000493923609610647, 0.008453886955976486, -0.008938035927712917, 0.00932979304343462, -0.002659160178154707, -0.04055456072092056, 0.011422817595303059, -0.03984856978058815, -0.02507021464407444, -0.05189584568142891, -0.0014110092306509614, 0.01807318814098835, -0.004607041832059622, 0.006323537323623896, 0.00876091979444027, -0.04837517440319061, -0.053287483751773834, -0.019400643184781075, 0.020983178168535233, -0.012660028412938118, -0.018594786524772644, 0.01227251160889864, 0.013018143363296986, -0.011137462221086025, -0.05232743173837662, -0.0001650619087740779, 0.016573341563344002, -0.017400700598955154, -0.0046382201835513115, -0.011511523276567459, 0.0034668848384171724, -0.011679079383611679, -0.0535760261118412, -0.014700647443532944, -0.03658219426870346, -0.008358976803719997, -0.005495166406035423, -0.011789408512413502, -0.02339569665491581, -0.09563033282756805, -0.021519212052226067, 0.057372234761714935, 0.0020073081832379103, -0.03344254195690155, -0.027215002104640007, 0.026966137811541557, -0.0018804911524057388, 0.003991974517703056, 0.0364028699696064, 0.026345986872911453, -0.02474358305335045, 0.03850747272372246, 0.0013404577039182186, 0.005603190045803785, 0.014593719504773617, 0.03279344365000725, 0.012934204190969467, 0.018064578995108604, 0.031867366284132004, 0.02036060020327568, 0.053457535803318024, 0.041666727513074875, -0.01180761307477951, 0.005525524728000164, 0.014721101149916649, 0.05197734385728836, -0.0036943622399121523, 0.020646296441555023, -0.0347147062420845, -0.010011479258537292, 0.009140881709754467, -0.0012590150581672788, -0.0908190980553627, 0.02413429692387581, 0.014669273979961872, 0.03764018416404724, -0.0215561855584383, 0.02202562801539898, -0.011441838927567005, 0.006829232443124056, -0.041534971445798874, 0.015721989795565605, 0.04842352494597435, 0.10848674923181534, -0.050050001591444016, 0.009219987317919731, -0.033853109925985336, 0.007242308463901281, 0.026504719629883766, 0.026921965181827545, -0.04376216605305672, -0.05951396003365517, -0.02007196471095085, -0.023123204708099365, 0.0012454669922590256, 0.00295423436909914, 0.02052401565015316, -0.02248237654566765, 0.037110861390829086, -0.0006449815118685365, 0.005367279518395662, 0.014417434111237526, 0.03367844223976135, 0.039291057735681534, -0.000040874594560591504, 0.041569702327251434, 0.015506342053413391, 0.0007657249225303531, -0.010234258137643337, 0.030721619725227356, -0.03593653067946434, 0.012955949641764164, -0.009771504439413548, -0.06860391050577164, 0.046770937740802765, -0.001302690478041768, 0.07506933063268661, 0.019852004945278168, -0.0671825110912323, -0.051814887672662735, -0.05252332612872124, 0.03779207915067673, 0.06179935485124588, -0.025512225925922394, -0.058371275663375854, 0.0005145215545780957, -0.04921744763851166, -0.04431268945336342, -0.019861841574311256, 0.004468350671231747, 0.01817958988249302, 0.034644246101379395, -0.013681983575224876, 0.01938384212553501, 0.03149116039276123, 0.0227873083204031, -0.02872954122722149, 0.0315096415579319, 0.026256123557686806, -0.005406781565397978, -0.004084412008523941, -0.09364288300275803, -0.029662154614925385, -0.041430626064538956, 0.04258623719215393, -0.012081447057425976, 0.02914757840335369, 0.07870835065841675, 0.052202001214027405, -0.010596651583909988, -0.04586130753159523, -0.03525577858090401, -0.04300929605960846, 0.06128114461898804, 0.019825074821710587, -0.044425953179597855, -0.03179388865828514, -0.0019001684850081801, -0.010238307528197765, -0.029938507825136185, -0.028675667941570282, 0.057493869215250015, 0.037553101778030396, 0.020447857677936554, 0.033205870538949966, 0.02510054223239422, -0.038547027856111526, 0.08985628187656403, -0.011892104521393776, -0.02947205863893032, 0.05645404011011124, -0.009444127790629864, 0.06705256551504135, -0.10464239120483398, -0.016120929270982742, 0.012820490635931492, 0.056343238800764084, -0.050759460777044296, 0.04160121828317642, 0.03022313117980957, 0.010823288932442665, -0.060669854283332825, -0.015488021075725555, 0.02999250590801239, -0.07291250675916672, 0.01765514723956585, 0.027541909366846085, -0.02586359903216362, 0.04923800006508827, -0.04064841568470001, 0.006438880693167448, -0.048282526433467865, 0.023646308109164238, -0.007304301951080561, -0.02972145937383175, -0.051386523991823196, -0.06104898452758789, 0.006937832105904818, 0.07759422808885574, 0.08136356621980667, -0.039326537400484085, 0.025333372876048088, -0.006276573054492474, -0.09139887988567352, 0.0777253732085228, 0.004308757837861776, 0.014949150383472443, -0.05247270688414574, -0.022936012595891953, -0.009915883652865887, 0.02595912478864193, 0.005922255106270313, 0.011465787887573242, 0.005765626672655344, -0.03446544334292412, 0.021665794774889946, 0.02619757503271103, 0.004365698434412479, 0.007772284094244242, 0.005521797575056553, 0.017457621172070503, -0.03933199495077133, -0.04554997757077217, -0.026975121349096298, -0.003250190056860447, 0.039588745683431625, 0.0023668729700148106, 0.03732087463140488, -0.015767844393849373, 0.06363396346569061, -0.025863472372293472, -0.007244003005325794, -0.031040651723742485, -0.005734757520258427, -0.0665145143866539, 0.07144250720739365, 0.019699078053236008, 0.05567220598459244, -0.026873063296079636, -0.01758759282529354, -0.05024166405200958, 0.03194484859704971, 0.0046748211607337, -0.07434525340795517, 0.04717545211315155, -0.01859109103679657, 0.006310601718723774, -0.032827865332365036, 0.004644233267754316, 0.029403837397694588, -0.015143320895731449, 0.06501395255327225, 0.062440358102321625, -0.026330066844820976, 0.04621671512722969, 0.015516611747443676, 0.013537547551095486, 0.055613789707422256, 0.012675651349127293, -0.044043026864528656, -0.014453507959842682, -0.005332323722541332, 0.02183392271399498, 0.03451678156852722, 0.02062678337097168, -0.043430402874946594, 0.0029901990201324224, -0.022942567244172096, -0.015441914089024067, -0.0762505754828453, 0.03237628936767578, 0.021847395226359367, -0.05815985053777695, 0.0194858368486166, 0.00250904425047338, 0.020841578021645546, -0.0280610341578722, -0.006930165458470583, -0.011988193728029728, -0.027774207293987274, 0.03210685774683952, 0.007398106623440981, 0.03742638975381851, -0.00864427536725998, -0.06333791464567184, -0.02043572999536991, -0.01945476233959198, -0.003741589607670903, 0.06262475997209549, 0.035369016230106354, 0.0025040204636752605, 0.0523039773106575, -0.03991582617163658, -0.00006645630492130294, -0.028022166341543198, 0.0008793644956313074, -0.04729311540722847, 0.04832512512803078, 0.054322127252817154, 0.007522067055106163, -0.033670373260974884, -0.06698182225227356, -0.05423225834965706, -0.039549462497234344, -0.006275231018662453, 0.05167768895626068, -0.034162409603595734, 0.037932731211185455, 0.0220185574144125, 0.006664132233709097, -0.02069866843521595, 0.018242092803120613, -0.024764953181147575, -0.054289646446704865, 0.0026112438645213842, -0.023553824052214622, 0.02807537280023098, -0.03955322131514549, 0.05321789160370827, -0.0013388532679527998, 0.05683987960219383, -0.0488068088889122, 0.11271904408931732, 0.08646966516971588, -0.08067873120307922, -0.03360578790307045, 0.0006980394828133285, 0.0386517234146595, -0.04404089227318764, 0.03612580522894859, -0.027293195948004723, 0.03508239611983299, -0.008284205570816994, 0.007117200177162886, -0.07327328622341156, 0.014530494809150696, 0.02529960311949253, 0.010984890162944794, 0.007626866921782494, -0.011004181578755379, 0.00607462041079998, 0.013094661757349968, -0.005525187123566866, 0.032539382576942444, -0.0029646416660398245, -0.054884858429431915, -0.04193537309765816, 0.03764226287603378, 0.0486542209982872, -0.007118481211364269, 0.005038991570472717, -0.029026364907622337, -0.036223024129867554, 0.039446160197257996, -0.005097061861306429, -0.07170331478118896, -0.038465581834316254, -0.01447642594575882, -0.02051279880106449, 0.009616168215870857, 0.013091403990983963, 0.04684704542160034, -0.03295334428548813, 0.04575001075863838, -0.01897578313946724, 0.0032245845068246126, -0.030008871108293533, 0.0025285109877586365, -0.00901841651648283, -0.06735456734895706, -0.031592290848493576, -0.015009800903499126, 0.03335730731487274, -0.04218004271388054, -0.03677322715520859, 0.021571366116404533, -0.07181286066770554, 0.03132319822907448, -0.0020602960139513016, 0.01701636053621769, 0.07099134474992752, 0.03379048779606819, 0.013554340228438377, 0.01625603251159191, 0.009517688304185867, 0.013464436866343021, -0.0036842902190983295, 0.028059815987944603, 0.0009089074446819723, 0.007120025809854269, 0.02993953973054886, -0.03044656105339527 ]
<p>Well the following question I really struggle to find an answer</p> <blockquote> <p>A thin lens creates an image of an object with magnification -3. A second identical lens is positioned very close to the first lens such that the distance between the two lenses can be neglected. What is the magnification with this two lens system assuming that the object distance has not changed?</p> </blockquote> <p>At first the solution seemed very simple, name the distances between some virtual objects $d_0$, $d_1$ &amp; $d_2$. </p> <p>Then the total magnifying factor can be found using: $$M_t = -\frac{d_2}{d_0}$$ $$M = -3 = -\frac{d_1}{d_0}$$ $$M = -3 = -\frac{d_2}{-d_1}$$</p> <p>(last equation has an extra minus sign as the image is a virtual location, the image $d_1$ is behind the lens, the distance of this virtual image to the lens is $d_1$ given that the lenses are "positioned very close".</p> <p>Now the problem is: I can't solve this, 4 unknowns and only 3 equations. Also going by hand and stating simply "well the magnification factor is the combination of both lenses so $M_t = M * M = 9$ results in a "wrong answer".</p>
g8430
[ 0.04754660278558731, -0.018244557082653046, 0.018454913049936295, 0.010965578258037567, 0.045212142169475555, -0.025463668629527092, -0.010495377704501152, -0.0073465704917907715, -0.021868327632546425, -0.007660095579922199, -0.04824254661798477, 0.04207029938697815, 0.052495282143354416, -0.0234841275960207, 0.011493520811200142, 0.05768654868006706, 0.08640166372060776, -0.038396093994379044, -0.02627626433968544, 0.024765659123659134, -0.012691717594861984, 0.04793013259768486, -0.014298536814749241, -0.05303671583533287, -0.057313453406095505, -0.019793087616562843, 0.01751650683581829, 0.04347804933786392, -0.09052390605211258, 0.027864933013916016, -0.016762947663664818, 0.0016455725999549031, 0.06315982341766357, -0.004915625788271427, 0.024352997541427612, 0.015668263658881187, 0.07454179227352142, 0.0296487994492054, -0.016107844188809395, -0.004115747287869453, 0.03895819932222366, 0.0010443439241498709, -0.007540691178292036, -0.02450253814458847, -0.0029574930667877197, -0.026212291792035103, -0.033396847546100616, 0.01311684213578701, 0.01072932593524456, -0.008374534547328949, 0.0013040350750088692, 0.06753656268119812, 0.020768819376826286, 0.02556549198925495, -0.023345528170466423, 0.030531803146004677, 0.02501058019697666, -0.04119565337896347, 0.00930692721158266, 0.037607282400131226, -0.020479200407862663, -0.07245820760726929, 0.016488049179315567, 0.004706366918981075, 0.06035826355218887, 0.008017735555768013, -0.05624403432011604, 0.020401587709784508, 0.02631494216620922, 0.0001827238011173904, -0.022385887801647186, -0.028273075819015503, 0.0513373501598835, 0.013041501864790916, -0.0334242582321167, -0.04068702831864357, 0.035342179238796234, -0.02073041722178459, -0.020865263417363167, 0.03524396941065788, -0.022804340347647667, 0.010759790427982807, 0.029949719086289406, 0.0009535024873912334, 0.011697637848556042, 0.04247888922691345, 0.02915983460843563, 0.009451288729906082, -0.028826918452978134, 0.006518312729895115, -0.02894124947488308, 0.005541156977415085, 0.020740222185850143, 0.019245406612753868, 0.028343800455331802, 0.010948264971375465, 0.018707197159528732, 0.024945000186562538, -0.013006659224629402, 0.009324784390628338, 0.018198668956756592, 0.03594447299838066, 0.02655445970594883, -0.002276353072375059, -0.013782253488898277, -0.011088489554822445, 0.04988427460193634, 0.012761835940182209, -0.02124815620481968, -0.02145940624177456, -0.052361395210027695, -0.12875603139400482, -0.022369664162397385, -0.07449306547641754, -0.0366368405520916, -0.06397230923175812, 0.02561451494693756, 0.03926282003521919, -0.022704321891069412, -0.006731840316206217, -0.03718554601073265, 0.03264116495847702, -0.014150087721645832, 0.01538002211600542, 0.01270375121384859, -0.08771128952503204, 0.01587270386517048, 0.024205880239605904, 0.06562560051679611, -0.014974823221564293, 0.02054285630583763, -0.030619004741311073, 0.07381636649370193, -0.02406901679933071, -0.011067504063248634, 0.027796398848295212, -0.0006366960587911308, -0.0005029327585361898, -0.012171836569905281, 0.030019868165254593, -0.06312099099159241, -0.011983532458543777, 0.0016071817371994257, -0.039059288799762726, -0.005188051611185074, -0.05556190758943558, 0.011936101131141186, -0.026159025728702545, 0.06650043278932571, -0.05864957347512245, -0.01047567930072546, 0.05312928929924965, -0.018050404265522957, 0.007535252254456282, 0.02166888117790222, -0.0274643674492836, 0.01809236779808998, 0.00995782669633627, 0.0036530112847685814, -0.06086291745305061, 0.003421528497710824, -0.032690614461898804, 0.03261180222034454, 0.013815801590681076, -0.06755728274583817, 0.03324071690440178, -0.011365027166903019, -0.044415488839149475, 0.01773209311068058, -0.084212526679039, -0.024500004947185516, -0.0022746066097170115, 0.07740966975688934, -0.00036498979898169637, 0.012241692282259464, 0.016919367015361786, 0.06501711905002594, 0.0026441048830747604, -0.05386843532323837, 0.05816246196627617, -0.05431300029158592, 0.014979243278503418, -0.021049177274107933, 0.021141713485121727, 0.015490473248064518, 0.021812498569488525, 0.043495938181877136, 0.04202357307076454, -0.05182119458913803, 0.02087736874818802, -0.03739156201481819, 0.02091130241751671, 0.05014963820576668, 0.05343722552061081, -0.02993144653737545, 0.025294387713074684, 0.056573573499917984, -0.05927354842424393, -0.0016892566345632076, 0.002399799646809697, -0.07533802092075348, -0.021531829610466957, 0.013233957812190056, 0.056873008608818054, -0.0015651194844394922, 0.012675181031227112, 0.0021783041302114725, 0.00826469250023365, -0.00027740589575842023, -0.04313362017273903, -0.0561407133936882, -0.04352296516299248, -0.08007180690765381, -0.0198118407279253, -0.03161418437957764, -0.02637319639325142, 0.05488155037164688, 0.02757795713841915, -0.07627353817224503, -0.011045553721487522, 0.009493660181760788, 0.02622801810503006, 0.03829308971762657, -0.016970515251159668, -0.011096719652414322, -0.07185006886720657, 0.0065347738564014435, -0.00464898906648159, -0.022372035309672356, 0.04449692741036415, -0.044940318912267685, -0.013257384300231934, -0.008506634272634983, -0.004312805365771055, 0.04761729761958122, 0.007947052828967571, -0.03636545687913895, 0.058280836790800095, 0.03055841661989689, 0.08673001080751419, 0.05436458811163902, 0.01711707003414631, -0.021183067932724953, 0.015326924622058868, 0.03398337960243225, -0.02834579162299633, 0.03757849335670471, 0.029853571206331253, 0.02792149968445301, 0.05585538595914841, -0.042010825127363205, 0.017396679148077965, -0.0264500193297863, -0.07983890175819397, 0.001271447166800499, 0.011675922200083733, -0.022488556802272797, 0.04394464194774628, -0.011966414749622345, 0.02545049414038658, -0.04217221215367317, -0.03369700163602829, 0.03382263705134392, 0.0014271191321313381, -0.03101196140050888, 0.0050174095667898655, -0.07371562719345093, 0.024393344298005104, 0.05761779844760895, 0.026332639157772064, -0.0005520701524801552, 0.014964981004595757, 0.015286006033420563, -0.0020162768196314573, 0.0007713869563303888, -0.009849769063293934, 0.009125742129981518, -0.0103872986510396, 0.014545848593115807, 0.060441773384809494, 0.0017892707837745547, 0.059197984635829926, -0.05678125470876694, 0.012610692530870438, 0.024219375103712082, -0.01797354593873024, 0.02731565199792385, 0.046252403408288956, 0.03428279235959053, -0.047986775636672974, -0.08360768854618073, 0.048522233963012695, 0.04761253297328949, -0.026876909658312798, 0.005063691176474094, 0.05174793303012848, 0.01755470596253872, -0.016653835773468018, 0.031233049929142, -0.012736975215375423, 0.01708207093179226, -0.028948837891221046, 0.023562530055642128, -0.0023882247041910887, 0.07706629484891891, -0.05312100797891617, -0.0226487647742033, -0.014178235083818436, -0.014090053737163544, 0.028425607830286026, 0.02008397877216339, -0.010775139555335045, 0.011502026580274105, -0.05026875436306, 0.01428668200969696, 0.025779152289032936, -0.005489216186106205, -0.040114399045705795, -0.022313738241791725, 0.0006629345589317381, -0.038789164274930954, 0.01383989118039608, 0.0025607303250581026, -0.01705019548535347, 0.047451507300138474, 0.04632767289876938, -0.05621219053864479, 0.03200807794928551, 0.024978486821055412, 0.021632632240653038, -0.022387193515896797, 0.002453636145219207, -0.05733862146735191, -0.06472817808389664, 0.0017839743522927165, 0.0046141985803842545, 0.015602544881403446, 0.05086266249418259, 0.07630939781665802, -0.006419674959033728, 0.04061594605445862, 0.019775476306676865, -0.0002105414605466649, 0.0230544600635767, 0.05436189845204353, 0.010104358196258545, -0.05526911839842796, 0.028691574931144714, 0.031428396701812744, -0.043817538768053055, 0.0073195090517401695, 0.025776654481887817, 0.02727862074971199, 0.01704229973256588, -0.015347841195762157, 0.054316889494657516, -0.018336042761802673, 0.012173895724117756, 0.005885920021682978, -0.10840695351362228, 0.05444031581282616, -0.014110308140516281, 0.015787538141012192, -0.05211615189909935, 0.009202728979289532, -0.028687292709946632, -0.032089076936244965, -0.052717503160238266, -0.0534132644534111, -0.023321451619267464, 0.00868235807865858, -0.04814985394477844, -0.06272396445274353, 0.00502637168392539, 0.008553159423172474, -0.011111992411315441, 0.0047978926450014114, -0.028231769800186157, -0.09494239091873169, 0.0040154485031962395, -0.016276124864816666, 0.012201227247714996, 0.018140751868486404, 0.007826789282262325, 0.0049606310203671455, -0.009620667435228825, -0.02866075374186039, -0.06142708659172058, 0.09346842020750046, -0.024668250232934952, -0.015227247029542923, 0.030743231996893883, -0.03864869475364685, 0.045284174382686615, -0.00917387381196022, 0.0014931837795302272, 0.01900571770966053, -0.028732258826494217, -0.007905280217528343, 0.010853013955056667, 0.007567817810922861, 0.004227231256663799, 0.029565615579485893, -0.006761070340871811, -0.060429446399211884, -0.0757502093911171, 0.03770234435796738, 0.03718468174338341, 0.026476813480257988, 0.0415954664349556, -0.05110956355929375, -0.008567750453948975, 0.06523684412240982, -0.06879065930843353, 0.03681598976254463, 0.006171088200062513, 0.04016438499093056, 0.0187259279191494, -0.006235015578567982, 0.02918531745672226, -0.02081495150923729, 0.0838509127497673, -0.08384791761636734, -0.028091639280319214, -0.024475380778312683, 0.034459780901670456, 0.020012032240629196, -0.01604291796684265, 0.002392596798017621, 0.0036964186001569033, 0.029291566461324692, 0.03088035061955452, -0.013487089425325394, 0.05785386264324188, -0.009425217285752296, -0.0036995764821767807, -0.026936108246445656, 0.020049475133419037, -0.0018454025266692042, 0.03348592668771744, -0.032089125365018845, -0.013140713796019554, -0.0009893426904454827, 0.007579828146845102, 0.006049995310604572, 0.007666838821023703, -0.051603686064481735, 0.003944947849959135, 0.02006550505757332, -0.00047841123887337744, 0.0011287947418168187, 0.02170807309448719, 0.002598803024739027, -0.02891479805111885, -0.006174321286380291, -0.006232351530343294, -0.02357909269630909, -0.01243919413536787, 0.011347804218530655, -0.026156814768910408, 0.00607908284291625, 0.05860063433647156, 0.007601063698530197, 0.04659130796790123, 0.021650735288858414, -0.0013009464601054788, -0.03950459137558937, -0.03083585388958454, -0.048264939337968826, 0.021608425304293633, 0.0005931282066740096, 0.01234806701540947, 0.010030952282249928, 0.040365301072597504, -0.015586864203214645, -0.016689138486981392, -0.02948484569787979, 0.013944961130619049, 0.06001657620072365, 0.0005737107712775469, -0.041222069412469864, -0.0014202423626556993, 0.058028142899274826, -0.01586092822253704, 0.0296566691249609, 0.012363553047180176, -0.0032223714515566826, 0.043143775314092636, 0.034540146589279175, -0.023708192631602287, 0.027779877185821533, -0.0034383810125291348, -0.003694734303280711, -0.0026060091331601143, -0.017772531136870384, -0.00864406768232584, -0.009130760096013546, 0.07834926247596741, 0.0004708089982159436, 0.056789580732584, 0.007418974302709103, -0.008386263623833656, -0.013715657405555248, -0.0006549280951730907, 0.01211349107325077, -0.006123113911598921, -0.0010799249866977334, -0.027268854901194572, 0.08584675192832947, 0.050881512463092804, -0.017176277935504913, -0.021599678322672844, 0.02952267974615097, -0.01175500825047493, 0.0024726230185478926, -0.0636221393942833, -0.010136359371244907, 0.0447111614048481, -0.0477788969874382, -0.018114930018782616, 0.036644015461206436, -0.038669612258672714, -0.03498222678899765, 0.030590476468205452, 0.004302321467548609, 0.01608629710972309, -0.06195070594549179, -0.006870945915579796, 0.022715210914611816, 0.01084071770310402, -0.016175728291273117, -0.026413993909955025, -0.020153947174549103, -0.00547447195276618, -0.007602033670991659, 0.012275208719074726, -0.010038118809461594, -0.02717219851911068, -0.0075929840095341206, -0.007035456597805023, 0.02662341482937336, -0.015021972358226776, 0.03061072528362274, 0.12959051132202148, -0.008177598938345909, -0.03054811805486679, -0.013659732416272163, -0.021969741210341454, 0.0476047657430172, 0.029272159561514854, -0.004037053789943457, -0.012676841579377651, 0.006366229150444269, 0.03211429342627525, 0.03492744266986847, 0.0126766636967659, 0.022751618176698685, -0.0006522446637973189, 0.03396511450409889, -0.07531077414751053, 0.019726194441318512, -0.0013952219160273671, -0.05264861136674881, 0.07341364026069641, -0.012753190472722054, -0.04145834222435951, -0.00843062624335289, 0.06374740600585938, 0.017813565209507942, -0.004273404832929373, -0.07242219150066376, -0.0281203705817461, -0.004057230427861214, -0.020902104675769806, 0.09812015295028687, 0.03998908773064613, 0.006784262601286173, 0.021615471690893173, -0.021349960938096046, 0.014115454629063606, -0.017970338463783264, -0.004752111621201038, 0.008936171419918537, -0.03865343704819679, -0.012179523706436157, 0.05492208153009415, -0.003087936667725444, -0.03844266012310982, 0.05652498081326485, -0.019489198923110962, -0.009261876344680786, 0.0012304707197472453, -0.07615218311548233, -0.03447571024298668, 0.03632235527038574, 0.022161860018968582, -0.005983763374388218, 0.03831220418214798, -0.09019741415977478, 0.06539840251207352, 0.020430775359272957, 0.03573445603251457, 0.07761316001415253, -0.014353815466165543, 0.0012881364673376083, 0.04628382995724678, -0.07102569937705994, 0.031750548630952835, 0.06185762584209442, -0.016482912003993988, -0.003943117335438728, 0.05513234809041023, 0.016241300851106644, 0.06972537934780121, 0.011526023037731647, -0.009397218935191631, 0.010591819882392883, -0.007000913843512535, -0.09460229426622391, -0.040873147547245026, 0.0006864646566100419, -0.07066930085420609, -0.032592348754405975, -0.02198759838938713, -0.010628841817378998, 0.02655976451933384, -0.0142448078840971, -0.05017777904868126, 0.053271885961294174, 0.035389866679906845, 0.0503808967769146, -0.08370493352413177, 0.00001755937591951806, -0.0012929681688547134, 0.0026454951148480177, -0.002853642450645566, -0.03304006904363632, 0.036243241280317307, 0.017767878249287605, 0.019503429532051086, 0.02251734584569931, -0.03747398406267166, 0.034742146730422974, -0.0007026308448985219, 0.022478964179754257, -0.05511648952960968, 0.031203558668494225, -0.02526019513607025, -0.05360526219010353, 0.017213134095072746, 0.018723376095294952, 0.043277040123939514, 0.014033248648047447, 0.009480043314397335, 0.006303928326815367, 0.02756061963737011, 0.008703847415745258, -0.041521381586790085, -0.06299979984760284, 0.018203331157565117, -0.07132215797901154, -0.05355730280280113, -0.06066984683275223, -0.017484907060861588, -0.06295554339885712, 0.024000559002161026, -0.032706089317798615, -0.037475358694791794, -0.0056470297276973724, -0.001232112175785005, 0.033875275403261185, -0.010537588968873024, -0.04796833544969559, 0.03716634586453438, -0.01683746464550495, 0.024544572457671165, 0.016051258891820908, 0.0538717582821846, -0.008482612669467926, -0.03787090629339218, 0.06225423514842987, 0.049151711165905, -0.009598166681826115, -0.07541284710168839, -0.018948102369904518, -0.03075322136282921, -0.0017964026192203164, 0.008292934857308865, -0.006869726814329624, -0.05090546980500221, 0.027716340497136116, -0.03339399769902229, 0.03675304725766182, 0.0014847726561129093, -0.03452618047595024, 0.02049780823290348, 0.05430298671126366, 0.013054335489869118, 0.021716412156820297, -0.004830796271562576, -0.046191420406103134, -0.025320881977677345, -0.03158415108919144, 0.028928831219673157, -0.025137653574347496, 0.013713325373828411, -0.0032927601132541895, 0.08174468576908112, -0.013654323294758797, -0.024465925991535187, 0.024813873693346977, 0.0012880034046247602, 0.005168380681425333, -0.02964385598897934, -0.02380836196243763, -0.07686648517847061, -0.03658115118741989, -0.004455847665667534, -0.020740794017910957, -0.03298558294773102, -0.009132136590778828, -0.03261781856417656, -0.01052581425756216, -0.13237521052360535, -0.06713616102933884, -0.04514596238732338, 0.06003382056951523, -0.056392062455415726, 0.02046365663409233, -0.012384963221848011, -0.044858913868665695, -0.013709485530853271, -0.044823504984378815, 0.020934054628014565, 0.026899434626102448, 0.04176587983965874, 0.01278542447835207, -0.06602378934621811, -0.00799006037414074, 0.03888837620615959, -0.010544901713728905, -0.0339110791683197, -0.006796693429350853, -0.0048582060262560844, 0.025230534374713898, -0.0046028755605220795, 0.017893753945827484, 0.006496937945485115, 0.0379147082567215, -0.03211955726146698, -0.015181735157966614, 0.024471059441566467, 0.00986401829868555, 0.004356875084340572, 0.07609683275222778, -0.019320478662848473, -0.001460963161662221, -0.03961007669568062, -0.006957515142858028, -0.02160961739718914, -0.024655381217598915, -0.008105520159006119, -0.045531801879405975, 0.03474321588873863, 0.03617563843727112, -0.05049334466457367, -0.011381823569536209, 0.03769877180457115 ]
<p>My book starts section 2.2 like this:</p> <p><img src="http://i.stack.imgur.com/obS89.png" alt="enter image description here"></p> <p>Equation 1.1 is this: $$q_x=-k\frac {\partial T}{\partial x}$$</p> <p>As you can see in the picture I posted, my book says that one can go from equation 1.1 to equation 2.1 by integration. I don't see how this is done by integration at all.</p> <p>Thank you</p>
g8431
[ 0.035182543098926544, 0.00210962793789804, -0.016459254547953606, 0.02375713363289833, 0.02648920938372612, 0.00015104265185073018, 0.037489041686058044, 0.029647288843989372, -0.07847923040390015, 0.01027641911059618, -0.04799306392669678, 0.007844103500247002, 0.0523027665913105, 0.007750331424176693, -0.009892712347209454, -0.022626644000411034, 0.04761187732219696, 0.020436085760593414, 0.00580441951751709, 0.022951819002628326, -0.017731882631778717, 0.038544975221157074, 0.021510019898414612, -0.043962474912405014, -0.017450882121920586, -0.053110428154468536, -0.032019346952438354, 0.003941768780350685, -0.108057901263237, -0.0015714042820036411, -0.04687874764204025, -0.004945792723447084, 0.030299022793769836, 0.033889494836330414, -0.04710466414690018, 0.0018290160223841667, 0.0658097043633461, -0.021633578464388847, 0.013818963430821896, -0.021626900881528854, 0.002865414135158062, -0.03172512724995613, -0.049735523760318756, -0.0072345673106610775, -0.02149970643222332, -0.032070763409137726, 0.01965065859258175, 0.008129139430820942, -0.01741235889494419, -0.00022278749383985996, -0.025282490998506546, 0.052751488983631134, -0.018281936645507812, -0.010315600782632828, -0.08600424975156784, 0.09420140832662582, 0.035082828253507614, -0.055188585072755814, 0.09586777538061142, 0.009622780606150627, -0.045568764209747314, -0.06865159422159195, 0.06825106590986252, 0.019144685938954353, 0.05416599661111832, 0.008063417859375477, 0.008889200165867805, -0.01797696389257908, -0.05741451680660248, -0.022081393748521805, -0.006482210010290146, 0.04825885221362114, 0.07326504588127136, 0.04837232083082199, 0.018770910799503326, -0.00485586142167449, 0.08024515956640244, -0.013795269653201103, 0.01357905101031065, 0.003964399918913841, 0.030423099175095558, 0.04811176657676697, 0.019227713346481323, -0.0032796142622828484, 0.004997056443244219, -0.012109237723052502, 0.011760417371988297, -0.02584855630993843, -0.047090619802474976, 0.00504098366945982, -0.057250428944826126, 0.02190615050494671, 0.04237121716141701, 0.0385713055729866, 0.06434942781925201, -0.045592427253723145, -0.04805433377623558, 0.006664003245532513, -0.0033906216267496347, -0.03161374107003212, -0.04219481721520424, -0.0071351476944983006, 0.009386847727000713, 0.01341924350708723, -0.0622209832072258, 0.01785755157470703, -0.027654942125082016, 0.015172263607382774, -0.010593208484351635, -0.014748812653124332, 0.005634179804474115, -0.01851673796772957, -0.012814839370548725, -0.026464739814400673, 0.013581608422100544, 0.06413097679615021, 0.05005127564072609, -0.005759250372648239, -0.010484426282346249, 0.010122956708073616, 0.02898392267525196, 0.008799516595900059, 0.0473339781165123, 0.02252371795475483, -0.005965577904134989, -0.03571562096476555, -0.010723939165472984, -0.013950655236840248, 0.06160832569003105, 0.007808034308254719, 0.026593893766403198, 0.011396164074540138, 0.03339603915810585, -0.011288770474493504, 0.00878150761127472, 0.06848044693470001, 0.014069221913814545, 0.013688399456441402, -0.036823760718107224, -0.005197298247367144, -0.02640233002603054, -0.030743170529603958, -0.017743593081831932, 0.012174773029983044, 0.01868193969130516, -0.006078159436583519, -0.04232756793498993, -0.028641166165471077, -0.010412459261715412, -0.0272661242634058, 0.0562797412276268, 0.007627278566360474, 0.05055597424507141, -0.0094413161277771, 0.020199770107865334, -0.004112929571419954, 0.07753540575504303, -0.028333786875009537, 0.07527187466621399, -0.04490617662668228, 0.03575090318918228, 0.03174956887960434, 0.020953569561243057, -0.017273789271712303, -0.04381958022713661, 0.04393472522497177, -0.045111894607543945, -0.06893432885408401, 0.002454251516610384, -0.03840070590376854, 0.027743250131607056, 0.01170912105590105, -0.014070774428546429, 0.013110917061567307, 0.0066175926476716995, 0.04661804437637329, 0.038155704736709595, 0.04634767398238182, -0.00821002759039402, 0.03397252783179283, -0.002136398572474718, 0.026355747133493423, 0.01898076757788658, -0.059700414538383484, -0.021771246567368507, 0.0012772142654284835, 0.00471730250865221, 0.07668343931436539, -0.04924964904785156, -0.014356072060763836, 0.00028965246747247875, 0.027605406939983368, 0.0007157152285799384, 0.029667073860764503, -0.013156024739146233, 0.03381740674376488, 0.009775104932487011, -0.07113845646381378, -0.03331762179732323, 0.010715874843299389, 0.07596901059150696, 0.055616170167922974, 0.06041761115193367, 0.012887081131339073, 0.0913274735212326, -0.0021132351830601692, 0.009444664232432842, -0.037019357085227966, -0.0460934191942215, -0.020968835800886154, -0.07574420422315598, -0.006728855427354574, -0.011590950191020966, 0.06130902096629143, 0.017151160165667534, -0.041578516364097595, 0.021982820704579353, -0.02061464823782444, -0.030763231217861176, -0.021241048350930214, -0.06521765142679214, 0.03117050975561142, 0.011459249071776867, -0.014900601468980312, -0.031123915687203407, 0.029666302725672722, 0.0423847958445549, -0.008877476677298546, -0.06347716599702835, -0.011503373272716999, -0.07832396030426025, 0.007723354268819094, -0.06003904715180397, -0.009751055389642715, 0.07784650474786758, 0.06829897314310074, -0.028059091418981552, 0.03732369840145111, -0.009227579459547997, 0.05477478727698326, 0.0003763598797377199, -0.04417771100997925, 0.029364194720983505, 0.011383169330656528, 0.00785932969301939, 0.011271717958152294, 0.01837901771068573, 0.025556150823831558, -0.03509598970413208, -0.021149974316358566, 0.041392069309949875, -0.07510922849178314, 0.02470499649643898, -0.04116351157426834, -0.05400460585951805, -0.027842767536640167, -0.03228970989584923, 0.024602510035037994, 0.026183603331446648, 0.005359266884624958, -0.0032441280782222748, -0.03889116644859314, 0.02861945703625679, -0.0029767954256385565, -0.10443176329135895, 0.019024062901735306, 0.0037109816912561655, -0.008247235789895058, 0.04487081617116928, 0.004626268986612558, -0.012846249155700207, 0.056877266615629196, 0.00273704226128757, 0.04461830481886864, -0.04218963906168938, -0.06270194053649902, 0.03627500310540199, -0.0013992859749123454, 0.02708037756383419, -0.002033594762906432, 0.029575321823358536, -0.038330283015966415, -0.005984824150800705, 0.048699457198381424, 0.007695930078625679, -0.059039946645498276, 0.05670033395290375, 0.02541159652173519, 0.016435544937849045, 0.0014470095047727227, -0.03230573236942291, -0.039683591574430466, -0.036700714379549026, 0.0151158282533288, 0.03622426092624664, -0.026125295087695122, 0.011831584386527538, -0.058065515011548996, 0.026028571650385857, -0.006375053897500038, -0.005878642201423645, 0.004507903009653091, 0.007892381399869919, -0.0013985313707962632, -0.01028579194098711, -0.020452111959457397, 0.03312380984425545, -0.04097338393330574, 0.0060688708908855915, -0.00545399310067296, 0.006977362092584372, 0.011037921532988548, -0.0075683267787098885, 0.030661558732390404, 0.021136809140443802, -0.020775500684976578, 0.03226547688245773, 0.008649885654449463, 0.03169640898704529, 0.018686285242438316, -0.06484659761190414, -0.06726764887571335, 0.012051735073328018, 0.039943378418684006, -0.013954222202301025, -0.06943013519048691, -0.012298683635890484, 0.00802624225616455, -0.023785490542650223, -0.03342273831367493, 0.013059304095804691, 0.013953029178082943, 0.021843010559678078, -0.05010167881846428, 0.016943583264946938, -0.030433140695095062, -0.014409043826162815, 0.016046898439526558, -0.006514987908303738, 0.007356571964919567, -0.06474022567272186, -0.03290865570306778, -0.025178853422403336, 0.0015256794868037105, -0.05123043432831764, -0.09192154556512833, -0.04566339775919914, 0.06984000653028488, 0.023379873484373093, -0.035338614135980606, 0.03617316111922264, 0.042217470705509186, -0.03187781199812889, -0.03429626673460007, -0.045299042016267776, 0.025232946500182152, 0.05781479552388191, 0.07332279533147812, -0.025467121973633766, 0.023776547983288765, 0.0734134241938591, -0.08218101412057877, 0.07573828846216202, 0.022304201498627663, -0.0012761370744556189, -0.03063272312283516, 0.030284913256764412, 0.04164721444249153, -0.08991818875074387, 0.05744864419102669, -0.04162735864520073, -0.029821852222085, 0.02653323858976364, -0.0005719420150853693, -0.019918784499168396, -0.04782859608530998, -0.03630581870675087, 0.0389246791601181, 0.049198608845472336, 0.05553489550948143, 0.007819396443665028, -0.003598445327952504, 0.008304538205265999, -0.008709847927093506, 0.05006137117743492, 0.045482832938432693, 0.001377495820634067, -0.01120499987155199, 0.04527605324983597, 0.018126007169485092, 0.059436164796352386, 0.005308269057422876, -0.03981715813279152, 0.0231016855686903, -0.02039514295756817, -0.03216106444597244, -0.024264922365546227, -0.027417344972491264, -0.057201530784368515, 0.029256749898195267, -0.026104217395186424, -0.008008605800569057, 0.015305262990295887, 0.01853152923285961, 0.00006980427860980853, 0.02298590913414955, 0.002300446853041649, -0.006490959785878658, 0.03857690840959549, -0.016062235459685326, -0.008841249160468578, -0.05808109790086746, -0.013695641420781612, -0.0157758891582489, 0.03616049885749817, -0.01916593499481678, 0.013445683754980564, -0.0023258179426193237, 0.0033194415736943483, -0.04960617050528526, -0.005395619198679924, -0.007456568535417318, -0.05094952508807182, 0.017048940062522888, 0.004773393739014864, 0.05741342529654503, 0.026080571115016937, -0.01278777327388525, -0.010507695376873016, -0.006815617438405752, -0.06447388976812363, -0.00044173834612593055, 0.07151563465595245, -0.015009215101599693, -0.03943555802106857, 0.03490909934043884, -0.00967743992805481, 0.02593063749372959, -0.035478897392749786, 0.02360747754573822, 0.022816892713308334, 0.026102112606167793, -0.03332347422838211, 0.011467605829238892, 0.08800367265939713, 0.03008388727903366, 0.008106320165097713, -0.040457017719745636, 0.020208897069096565, -0.04327528178691864, 0.005814426578581333, 0.03687502071261406, 0.009919588454067707, -0.028345530852675438, -0.002472097519785166, 0.014519882388412952, 0.004465859849005938, 0.010971047915518284, 0.004298689775168896, 0.008989665657281876, -0.026741519570350647, 0.046706996858119965, 0.029415743425488472, -0.026829475536942482, 0.039474714547395706, -0.05913536250591278, -0.029361911118030548, 0.06131663918495178, -0.06371460855007172, -0.025377843528985977, 0.02186037227511406, -0.006884293630719185, -0.024907443672418594, 0.01572726108133793, 0.08559422940015793, -0.0065513779409229755, -0.010737360455095768, 0.009286056272685528, 0.041856952011585236, -0.023771578446030617, 0.031636301428079605, 0.029414940625429153, 0.020957984030246735, -0.00591367669403553, 0.0014549063052982092, 0.014241727069020271, 0.03989070653915405, 0.052420273423194885, 0.017091305926442146, 0.021456772461533546, 0.028123395517468452, 0.04595508053898811, 0.012696007266640663, -0.026075121015310287, -0.011155265383422375, 0.03511881083250046, 0.05974172428250313, -0.03905428946018219, 0.06068650260567665, 0.01774907484650612, -0.01954813115298748, -0.024478310719132423, -0.03855259343981743, -0.003045486519113183, 0.030092330649495125, 0.033557526767253876, 0.043106839060783386, -0.006580774672329426, -0.043441418558359146, 0.03921489790081978, 0.08515334874391556, -0.06317509710788727, -0.015391873195767403, 0.017647571861743927, 0.013344794511795044, -0.02256087213754654, -0.016586925834417343, 0.02608630247414112, -0.040694985538721085, -0.04608525335788727, 0.05384861305356026, -0.03821874409914017, -0.018627677112817764, -0.02902134507894516, -0.016142796725034714, 0.014964638277888298, -0.07773887366056442, -0.08357164263725281, 0.029268505051732063, -0.013838046230375767, -0.11174847930669785, -0.005090185906738043, -0.003783315420150757, 0.050875768065452576, -0.021501144394278526, -0.012920687906444073, -0.03277382254600525, -0.013778608292341232, 0.04082848131656647, 0.04495188593864441, -0.0067303115501999855, 0.011731535196304321, -0.028275731950998306, 0.05664386972784996, -0.02976103313267231, -0.006372768897563219, 0.008654473349452019, 0.07633207738399506, 0.033435508608818054, -0.00659942114725709, 0.0056108348071575165, 0.003314884379506111, -0.0074189952574670315, 0.018383167684078217, 0.030373264104127884, -0.002955984091386199, -0.004705979488790035, -0.012739063240587711, -0.03109518624842167, -0.01842890866100788, 0.007946692407131195, -0.04357234016060829, 0.0013098662020638585, -0.049324896186590195, 0.023314176127314568, -0.05420077592134476, 0.006946494337171316, 0.021561451256275177, 0.00018421723507344723, 0.011330518871545792, 0.022509057074785233, -0.031999971717596054, -0.039102744311094284, -0.021783843636512756, 0.02012552134692669, 0.03362572193145752, -0.024925732985138893, -0.02941546030342579, 0.027970436960458755, -0.010768287815153599, -0.07958600670099258, 0.06164441257715225, -0.01038979459553957, -0.030224375426769257, -0.008192772977054119, -0.012888787314295769, -0.044582001864910126, -0.007459117565304041, 0.030356386676430702, 0.028542812913656235, -0.04242096096277237, 0.05115153267979622, -0.05457364022731781, -0.008206125348806381, 0.04541704058647156, -0.025323526933789253, 0.04446156695485115, 0.07323477417230606, 0.002269311808049679, -0.008958057500422001, -0.02547461912035942, -0.008879311382770538, 0.01353986281901598, -0.0013509608106687665, 0.011289254762232304, -0.013280291110277176, -0.0010109510039910674, -0.016053607687354088, 0.020751073956489563, 0.01788436621427536, -0.03039284609258175, 0.026419200003147125, 0.0006599074113182724, -0.04441974312067032, 0.037185728549957275, -0.049952518194913864, -0.020334238186478615, 0.014962014742195606, 0.057131554931402206, -0.01177553553134203, 0.02224111743271351, -0.04130787029862404, 0.017496755346655846, -0.01610676757991314, -0.00548182800412178, 0.010721546597778797, 0.012597220949828625, 0.06300146132707596, 0.01733151078224182, -0.03576473519206047, 0.033537618815898895, -0.024749400094151497, -0.05645820125937462, -0.027382362633943558, -0.002024218440055847, 0.03972512483596802, -0.01500741858035326, 0.005484485533088446, -0.003501634579151869, 0.04434163495898247, -0.024976372718811035, 0.04004938155412674, 0.03210730105638504, 0.004886876791715622, -0.05318322405219078, -0.0056388587690889835, -0.0065062278881669044, -0.05481076240539551, -0.135390043258667, 0.020471207797527313, 0.0871981754899025, 0.032172445207834244, -0.07310063391923904, 0.010023945942521095, -0.015940997749567032, 0.008849211037158966, 0.0033128561917692423, -0.01494451705366373, -0.0036545477341860533, 0.011905170977115631, -0.027727525681257248, -0.04156016185879707, -0.02355816960334778, 0.0234507005661726, 0.013986844569444656, 0.039161864668130875, 0.047678392380476, 0.004488189239054918, 0.030194858089089394, -0.04829913750290871, -0.02514524571597576, -0.00529948016628623, 0.011918687261641026, 0.023074990138411522, -0.015259668231010437, -0.0009441880392841995, 0.04471481218934059, 0.05892656743526459, 0.01094089262187481, 0.03509663790464401, 0.017420673742890358, 0.03340118005871773, 0.008762354031205177, -0.05703519284725189, -0.04506382346153259, -0.02247929759323597, -0.036084871739149094, -0.038721177726984024, -0.01631711609661579, 0.021113736554980278, -0.04746158421039581, -0.02586841583251953, 0.048063311725854874, 0.05122235044836998, 0.02491498552262783, -0.00877431035041809, -0.015256853774189949, 0.006456117611378431, -0.022390849888324738, -0.013609849847853184, 0.052035823464393616, -0.008923127315938473, -0.005331491585820913, -0.05080480873584747, -0.0653935968875885, -0.04667792096734047, 0.012500090524554253, -0.05169294774532318, 0.00426315376535058, -0.03620561212301254, 0.0015475080581381917, 0.02335495315492153, 0.013959874399006367, -0.006189160048961639, 0.004269062541425228, -0.034077711403369904, -0.004354950971901417, 0.035001274198293686, -0.03707800433039665, -0.06617867946624756, -0.03162745386362076, -0.0009803047869354486, -0.027504190802574158, -0.07128015905618668, 0.02614312246441841, 0.005361124873161316, -0.010351268574595451, -0.028613733127713203, -0.06767810136079788, 0.008136408403515816, -0.0577528178691864, 0.0058334581553936005, -0.018590128049254417, 0.05338648334145546, 0.0482572503387928, 0.004942900035530329, -0.0077543118968605995, -0.06527309864759445, 0.02898598648607731, 0.07311487942934036, 0.0073312558233737946, -0.05318446829915047, -0.039629098027944565, 0.033395905047655106, 0.022814380005002022, -0.045265547931194305, -0.030393406748771667, 0.0667596086859703, 0.054601795971393585, -0.03743215650320053, 0.04275168105959892, 0.010842777788639069, -0.019694460555911064, -0.02284395694732666, 0.033290062099695206, -0.07845509052276611, -0.036897338926792145, 0.060967154800891876, 0.002252426464110613, 0.0408857986330986, 0.010955638252198696, 0.02019544318318367, -0.04255030304193497, 0.007860344834625721, 0.014187796972692013, -0.054405923932790756, -0.016188981011509895, -0.020664330571889877 ]
<p>I've always been not so bad in mathematics, but I'm terribly bad at physics. For me, abstract concept are totally understandable, but when it come to reality, I'm lost !</p> <p>So, for my job, I need to understand something.</p> <p>I have an object, travelling during $t_o$ on a distance $d_o$.</p> <p>It has an inital speed $v_1$, and a final speed $v_2$.</p> <p>I need to find an exponential curve which fits the condition, and I'm lost in my equation, I don't know where to begin.</p> <p>I try to start from the equation of the acceleration. I wan't it to be exponential, so </p> <p>$$ a = e^{kt} $$</p> <p>The speed curve is then the integration of the acceleration</p> <p>$$ v = \frac{e^{kt}}{k}$$</p> <p>I can substitute condition for finding k, </p> <p>$$ v_1 = \frac{e^{k\cdot0}}{k} \implies k = \frac{1}{v_1}$$ $$ v_2 = \frac{e^{k\cdot t_0}}k \implies v_2 = v_1\cdot e^{{t_0}\cdot{v_1^{-1}}}$$</p> <p>Which makes no sense. Where did I go wrong ?</p> <p>My final idea is to have something like $$ t = f(d) $$ so I can find the time with the distance, and vice verse.</p>
g8432
[ 0.06924890726804733, 0.021219981834292412, -0.013287053443491459, -0.014945773407816887, 0.022708015516400337, 0.004027626011520624, 0.03415117785334587, 0.02615530416369438, -0.05219985544681549, -0.0023954904172569513, 0.002667129971086979, 0.011024226434528828, 0.05393977090716362, -0.005154523998498917, -0.011905311606824398, -0.007844872772693634, 0.047751061618328094, -0.025977984070777893, 0.0015140558825805783, 0.001011002343147993, 0.04228367656469345, -0.009639383293688297, 0.004692398943006992, -0.04947951063513756, 0.017370184883475304, -0.03880499303340912, -0.014431689865887165, -0.0176182109862566, -0.04000619053840637, -0.004615651443600655, -0.008741537109017372, 0.024465449154376984, 0.051629383116960526, -0.02031232789158821, -0.014585980214178562, -0.04059409722685814, 0.0007759960717521608, 0.02551010623574257, 0.08348257839679718, -0.0034497070591896772, -0.00967385619878769, -0.046041637659072876, -0.011688091792166233, 0.04609612748026848, 0.07573435455560684, -0.04566001519560814, -0.03763045743107796, 0.04019424319267273, -0.010091268457472324, -0.04041574150323868, -0.041695404797792435, 0.06094374135136604, -0.0006256288033910096, -0.04489172250032425, -0.08319561928510666, 0.04685176536440849, -0.019163144752383232, -0.008347386494278908, -0.01153118908405304, 0.026311693713068962, 0.003671858459711075, -0.06702332943677902, -0.008917668834328651, -0.04644973203539848, 0.11136500537395477, -0.019959934055805206, 0.014779860153794289, -0.033202145248651505, 0.0207951869815588, -0.045275039970874786, 0.03568653389811516, -0.028742697089910507, 0.015944965183734894, 0.0011137631954625249, -0.056732334196567535, -0.03785117343068123, 0.042292773723602295, -0.0029880525544285774, 0.008368453942239285, 0.036521051079034805, -0.021722475066781044, 0.053745679557323456, 0.04346226900815964, -0.005050013307482004, 0.010983346030116081, -0.0036014332436025143, 0.006550848018378019, 0.011105912737548351, -0.02892938256263733, -0.07283426076173782, -0.03334052115678787, -0.025549979880452156, -0.0007546835113316774, -0.009716806933283806, -0.0028061969205737114, -0.05326366797089577, -0.05643187835812569, 0.06125934422016144, -0.011825738474726677, -0.018907053396105766, -0.007948252372443676, -0.052452754229307175, 0.014495416544377804, 0.020861444994807243, 0.0314059816300869, -0.026471789926290512, 0.0005346285179257393, -0.01187124103307724, 0.0303378626704216, -0.04298517107963562, 0.013285957276821136, -0.02619009278714657, -0.03946944698691368, -0.1127239316701889, -0.00003514609852572903, -0.028180649504065514, -0.022949056699872017, 0.02028418891131878, -0.0155390165746212, 0.017745710909366608, 0.005696028005331755, 0.00046250797458924353, 0.003960723523050547, 0.06263513118028641, 0.033054452389478683, 0.003954165615141392, -0.023267267271876335, -0.05547909438610077, -0.02622496522963047, -0.01804005540907383, 0.006156419403851032, 0.05601571872830391, 0.05506333336234093, 0.031438276171684265, -0.016972806304693222, 0.07053927332162857, -0.024852603673934937, 0.03275113180279732, -0.030439380556344986, 0.06928198784589767, -0.008199878968298435, -0.052294064313173294, -0.005491392686963081, 0.011120297946035862, -0.0912386104464531, 0.04235667362809181, -0.06575486809015274, -0.025203896686434746, 0.012393808923661709, -0.04655054956674576, 0.02199382148683071, 0.04279228672385216, -0.04627622291445732, 0.027365095913410187, 0.04509994015097618, -0.01615273207426071, 0.04487885907292366, 0.03270593658089638, 0.07017771154642105, -0.059232715517282486, 0.06140283867716789, 0.023266877979040146, -0.03221870958805084, 0.02056371420621872, -0.02582363970577717, 0.03680720925331116, 0.014839095063507557, -0.0026685588527470827, 0.0059372964315116405, -0.045532189309597015, -0.0742914155125618, 0.009203225374221802, 0.085276298224926, 0.043710436671972275, -0.018415508791804314, 0.011876416392624378, 0.03372093662619591, -0.005449378862977028, -0.05605923384428024, -0.016661660745739937, 0.03216654434800148, -0.05048012733459473, 0.05055231228470802, -0.011016224510967731, -0.024666255339980125, -0.04617825895547867, -0.03589901700615883, 0.014004900120198727, -0.07692639529705048, 0.022429663687944412, 0.036447566002607346, -0.022503498941659927, 0.007951172068715096, 0.04860430583357811, -0.055610284209251404, 0.005115588195621967, 0.03906211629509926, -0.09349305182695389, -0.018123118206858635, 0.00021769755403511226, 0.06319768726825714, 0.047704461961984634, 0.07908479124307632, -0.009489734657108784, 0.04999827966094017, -0.030363433063030243, -0.0014404056128114462, -0.029950657859444618, 0.0197517778724432, 0.023530639708042145, 0.024298910051584244, -0.02076217718422413, -0.0021723108366131783, 0.016415344551205635, 0.012215583585202694, -0.025747600942850113, 0.051906853914260864, 0.008257591165602207, -0.03733951970934868, 0.02040371485054493, 0.029641905799508095, -0.018925942480564117, 0.015187786892056465, -0.022773655131459236, -0.014264026656746864, -0.01846693456172943, -0.02107435278594494, -0.0458737351000309, -0.01538859587162733, 0.027850866317749023, -0.030628496780991554, 0.022849615663290024, -0.04653237387537956, -0.02886423096060753, 0.08334694802761078, -0.0021158666349947453, -0.004185765981674194, -0.0005293527501635253, 0.010084402747452259, 0.03470541909337044, 0.002564524533227086, 0.00048424399574287236, -0.030300823971629143, -0.06455868482589722, 0.02372942492365837, -0.03232179954648018, 0.019225360825657845, 0.021196728572249413, -0.023225298151373863, 0.010082220658659935, -0.005498667247593403, -0.0091978395357728, -0.00688219117000699, -0.0027909527998417616, 0.027180952951312065, -0.04250757768750191, -0.041591573506593704, 0.026501579210162163, 0.0048902821727097034, -0.02099343203008175, -0.0494907945394516, 0.0038123030681163073, 0.008192305453121662, 0.02113199420273304, -0.08560989052057266, -0.0073688155971467495, -0.0777420923113823, -0.03883923590183258, 0.006050631403923035, -0.0041679805144667625, -0.04117847606539726, 0.00479799322783947, -0.033145781606435776, -0.010025989264249802, 0.03491242602467537, -0.0804251953959465, 0.02053499035537243, -0.007144690956920385, 0.058004964143037796, -0.028066296130418777, 0.04092882573604584, -0.01861422508955002, -0.0400681272149086, 0.05569150671362877, 0.0030576977878808975, -0.07693798094987869, 0.0665992945432663, 0.0836736336350441, -0.004290442913770676, -0.038721032440662384, 0.012787539511919022, -0.005505085922777653, 0.02531207725405693, -0.001986792776733637, 0.040585990995168686, 0.029114888980984688, 0.0005962654249742627, 0.002015249105170369, 0.029826916754245758, -0.03268861398100853, 0.00259402790106833, -0.016531789675354958, -0.0004575266211759299, -0.08179586380720139, 0.025448035448789597, -0.018622443079948425, -0.017903968691825867, -0.08399488031864166, 0.0059989443980157375, 0.00443358113989234, 0.019717928022146225, 0.042452652007341385, 0.01090399082750082, -0.025988126173615456, -0.023504478856921196, -0.0025616660714149475, 0.04084227234125137, -0.007485781330615282, 0.07894505560398102, 0.017424816265702248, -0.0059799933806061745, -0.07237572222948074, -0.021831778809428215, 0.009929066523909569, -0.0016112931771203876, 0.00788230448961258, 0.01890384964644909, -0.027928167954087257, -0.01674177683889866, -0.0057148016057908535, 0.028246546164155006, -0.005441082641482353, 0.030894547700881958, -0.03460855036973953, 0.0035761697217822075, -0.055486321449279785, -0.0054681492038071156, 0.04966765642166138, 0.021796144545078278, -0.011408979073166847, -0.0561177097260952, -0.013298281468451023, 0.01794886216521263, 0.0314902737736702, -0.004198494367301464, -0.022328244522213936, -0.024256056174635887, 0.0709947720170021, 0.04575669765472412, -0.02119603380560875, -0.0050818766467273235, -0.05289322882890701, -0.027789760380983353, -0.023250645026564598, -0.03449932113289833, 0.006401487160474062, 0.0653962641954422, 0.005043353419750929, 0.014921179041266441, -0.04950752854347229, -0.012536512687802315, -0.006986155640333891, -0.004466130863875151, 0.053141821175813675, -0.029621737077832222, -0.0175390113145113, -0.0006396858370862901, 0.09220530837774277, -0.0009312742040492594, 0.020991386845707893, 0.0362347811460495, 0.011785434558987617, 0.05742686986923218, 0.0036359832156449556, -0.005580638535320759, -0.04467850178480148, -0.014697221107780933, 0.06583376228809357, -0.05379607528448105, 0.04158609360456467, 0.04013529047369957, 0.05239517241716385, 0.011751800775527954, -0.006662786938250065, 0.05349811539053917, -0.0008343618828803301, 0.021539513021707535, -0.016407636925578117, 0.011554384604096413, -0.014138749800622463, 0.03510662540793419, -0.06054062768816948, -0.021544266492128372, 0.025357402861118317, 0.03227280452847481, -0.032481033354997635, 0.011583193205296993, 0.020937763154506683, -0.04992295056581497, -0.0014604799216613173, -0.04078461602330208, -0.008219948038458824, 0.0374908484518528, -0.008012402802705765, -0.06470490992069244, -0.01843765191733837, 0.01972871460020542, -0.036001838743686676, 0.02843269146978855, -0.010220469906926155, -0.028384428471326828, -0.010309088043868542, -0.02787153236567974, -0.04765983670949936, -0.04844355210661888, 0.007424652110785246, 0.04515053331851959, -0.03224055841565132, 0.02620667591691017, -0.0002049353497568518, 0.026747839525341988, -0.0009729365119710565, 0.049783382564783096, -0.059974636882543564, -0.02543032169342041, 0.08501040190458298, 0.040339529514312744, 0.03496344015002251, -0.01199793815612793, 0.04395399987697601, -0.03883716091513634, 0.01773230731487274, -0.009170399978756905, 0.03140240162611008, -0.013390067033469677, 0.03213926777243614, 0.03733297437429428, 0.053103506565093994, -0.011271313764154911, -0.00025156463379971683, -0.00434414716437459, -0.025702333077788353, -0.016673356294631958, -0.03261100873351097, 0.013718989677727222, 0.08720318973064423, -0.03599497675895691, -0.053946059197187424, 0.0018681399524211884, 0.028281647711992264, 0.00709060113877058, 0.04093476012349129, 0.006550787482410669, 0.016279399394989014, -0.005808049347251654, 0.014354457147419453, 0.009847080335021019, -0.008023141883313656, 0.038094595074653625, 0.014036867767572403, -0.06927286088466644, 0.023427775129675865, 0.02221882902085781, -0.032765891402959824, 0.03681216016411781, -0.04031219705939293, -0.02733653597533703, 0.005146143026649952, -0.034709472209215164, -0.00876721739768982, -0.03372351825237274, -0.002440674463286996, -0.0006071904790587723, 0.01615549623966217, 0.04201122745871544, 0.03318703919649124, -0.016525285318493843, 0.03740055486559868, -0.038825783878564835, -0.00338315824046731, 0.0027917353436350822, -0.01712929829955101, 0.00512834032997489, 0.01043923944234848, -0.00959879532456398, -0.002138355281203985, -0.06226428225636482, 0.03807690367102623, 0.0193531084805727, -0.004142634570598602, 0.03596897050738335, 0.015689020976424217, 0.022498343139886856, -0.01161431334912777, -0.022317247465252876, -0.01225524116307497, 0.014641178771853447, 0.009818390011787415, 0.054858312010765076, 0.014320212416350842, -0.07185453921556473, -0.025591783225536346, -0.030124273151159286, -0.01236584410071373, 0.008426477201282978, 0.0651954784989357, 0.07018911093473434, 0.022493451833724976, -0.015009874477982521, 0.06295052915811539, 0.03257421404123306, 0.030209284275770187, 0.02707546576857567, -0.013466455042362213, -0.04074771702289581, 0.00986239779740572, -0.044295914471149445, 0.01573505997657776, 0.002774136373773217, -0.06040759012103081, 0.06074320897459984, 0.01998233236372471, -0.014617588371038437, -0.03910442069172859, 0.023624852299690247, -0.003066047327592969, -0.08728799223899841, -0.032359663397073746, 0.059668686240911484, -0.007684397045522928, -0.017929628491401672, -0.051139697432518005, -0.032202862203121185, -0.0769161805510521, -0.047010622918605804, 0.0030856006778776646, -0.009392987005412579, -0.042442262172698975, 0.01845693401992321, -0.030800560489296913, -0.07190342247486115, -0.037683650851249695, -0.00023849538411013782, 0.02091953344643116, -0.02291262336075306, 0.03163423761725426, -0.0033142808824777603, 0.007194954436272383, 0.05798496678471565, -0.055722687393426895, 0.00143482256680727, -0.007539358455687761, -0.005226785782724619, -0.05643770098686218, -0.04116234928369522, -0.004048606380820274, 0.03790564462542534, 0.03993664309382439, 0.0006490653031505644, -0.005619145464152098, 0.009833024814724922, 0.02326872944831848, -0.01229016948491335, 0.023122470825910568, -0.017172085121273994, -0.0046876706182956696, 0.062353093177080154, 0.046938132494688034, 0.06171582266688347, 0.0038845844101160765, -0.0004256913671270013, 0.013281861320137978, -0.008303822949528694, 0.026227250695228577, 0.02120276913046837, -0.003020198317244649, 0.006540055852383375, -0.044868942350149155, -0.019100358709692955, -0.022636307403445244, -0.014554900117218494, 0.02521371655166149, 0.03152313828468323, -0.03648313507437706, -0.02658882923424244, -0.028574546799063683, -0.013435830362141132, -0.04991510882973671, 0.05563921853899956, -0.07495886832475662, -0.013533806428313255, 0.03030424937605858, 0.017514707520604134, -0.06201082095503807, -0.06524641066789627, 0.007058547344058752, 0.01604108139872551, -0.04437733814120293, -0.021630074828863144, 0.0889662355184555, -0.021755769848823547, -0.035026878118515015, -0.007963640615344048, 0.026340508833527565, 0.03183560073375702, 0.004527001641690731, 0.00734216021373868, 0.004701041150838137, 0.029656128957867622, -0.07488574832677841, 0.00032370095141232014, 0.052260611206293106, -0.015091442503035069, 0.04640265181660652, -0.053514186292886734, 0.02115473337471485, 0.015111442655324936, 0.027553165331482887, 0.012752850539982319, -0.025756891816854477, 0.057928234338760376, 0.024372268468141556, -0.008970689959824085, 0.017035173252224922, 0.027408743277192116, 0.006490212865173817, -0.011418157257139683, 0.04393242299556732, 0.06301948428153992, -0.08976086229085922, 0.02782818302512169, -0.039525050669908524, -0.036458078771829605, 0.010410023853182793, 0.03177506849169731, 0.09001369029283524, 0.02387084811925888, 0.0943065658211708, 0.0038680890575051308, 0.06430287659168243, 0.042333535850048065, -0.0025352833326905966, -0.05297687649726868, 0.04708152264356613, -0.057229381054639816, -0.031208017840981483, 0.03418342396616936, 0.005034374538809061, -0.04526554420590401, -0.02711465209722519, 0.03549142926931381, 0.016369018703699112, -0.02871064841747284, 0.02591589279472828, -0.0039206757210195065, -0.011788970790803432, 0.003831746056675911, 0.04816451668739319, -0.01492970809340477, 0.010173963382840157, -0.02881200984120369, -0.018264086917042732, -0.020810771733522415, 0.006055314093828201, -0.00455936323851347, 0.02300223521888256, -0.024974700063467026, -0.06940796226263046, -0.03926635906100273, -0.05265641212463379, -0.011638837866485119, 0.014109513722360134, -0.012437683530151844, 0.03210866078734398, 0.013712993822991848, 0.07082673907279968, 0.006939053535461426, 0.06539800763130188, -0.03782253339886665, -0.03990746662020683, -0.010784346610307693, 0.05265936627984047, 0.008392298594117165, -0.03381284698843956, 0.018885860219597816, 0.04697798192501068, -0.052789054811000824, -0.02091260626912117, 0.0060941013507544994, 0.03575313091278076, -0.05255107581615448, 0.02946900948882103, 0.06359021365642548, -0.02117343060672283, 0.008974660187959671, -0.021379346027970314, -0.054219041019678116, 0.011783288791775703, -0.0074578239582479, -0.02108670212328434, 0.015347291715443134, -0.038837555795907974, 0.0669497549533844, 0.01695369742810726, -0.06602548062801361, -0.003201772691681981, -0.05679775029420853, -0.014480800367891788, -0.0037118089385330677, 0.048084475100040436, -0.009519793093204498, -0.0005110534257255495, 0.032739751040935516, -0.019209878519177437, 0.03378145396709442, 0.004317453131079674, -0.025032849982380867, 0.018883513286709785, 0.0363469161093235, -0.025924358516931534, -0.024957790970802307, -0.007978691719472408, 0.06321076303720474, -0.05173832178115845, 0.030906690284609795, -0.018932538107037544, -0.0390806645154953, 0.002067779190838337, -0.03841845691204071, -0.008175857365131378, -0.013500040397047997, 0.024179864674806595, -0.0014411405427381396, 0.08281288295984268, -0.0486542247235775, -0.017302826046943665, -0.00042999113793484867, -0.021811796352267265, -0.029063282534480095, 0.07448878139257431, 0.012825279496610165, -0.04629921168088913, -0.06710883975028992, 0.025813762098550797, 0.0539059191942215, -0.05674223229289055, 0.028405580669641495, 0.024631837382912636, 0.08147156983613968, -0.02520502731204033, 0.018708016723394394, -0.008571788668632507, -0.05201779305934906, -0.0007758000865578651, 0.025104358792304993, -0.027483688667416573, 0.04430641606450081, 0.04595395550131798, 0.02244788408279419, 0.0395679846405983, -0.026769699528813362, 0.013309882022440434, -0.029846858233213425, 0.07781163603067398, 0.005781405605375767, -0.011632311157882214, -0.00530178751796484, 0.04327976331114769 ]
<p>I am studying quantum statistical mechanics from the mathematician's perspective. I don't quite understand what the duality formula for entropy is <em>really</em> saying (or why there is a "duality"). </p> <p>If $A$ is an $n\times n$ Hermitian (self-adjoint, diagonalizable) matrix, then $$S(A)=\sup\bigl[{\operatorname{Tr}(AH) - \ln\bigl(\operatorname{Tr}[E^H]\bigr) : H \in H_n}\bigr]$$ where $H_n$ is the set of Hermitean matrices. </p> <p>What does this even mean? </p>
g8433
[ -0.026333192363381386, 0.0015935678966343403, -0.020374128594994545, -0.03467373177409172, 0.02548336237668991, -0.028774287551641464, 0.0355444997549057, 0.052002016454935074, -0.0163457989692688, 0.009249788708984852, -0.034889500588178635, 0.02051909826695919, 0.05364849045872688, -0.040845803916454315, -0.015275662764906883, -0.006304799113422632, 0.03690608590841293, 0.013951079919934273, 0.0010730487992987037, 0.0025859654415398836, -0.06947016716003418, -0.00794562790542841, 0.01563851162791252, -0.04923234507441521, 0.06827174872159958, -0.04874427244067192, -0.006445583421736956, -0.02059159055352211, -0.004511700943112373, -0.012140513397753239, 0.019645867869257927, -0.017019210383296013, 0.03282194584608078, -0.05220409855246544, -0.07943837344646454, 0.013232520781457424, 0.029482092708349228, -0.003305960912257433, 0.07479005306959152, -0.07039671391248703, 0.008167911320924759, -0.03854789584875107, 0.02029304951429367, -0.08628842979669571, 0.008045987226068974, 0.014948815107345581, -0.0024779438972473145, 0.0376756452023983, 0.009699664078652859, -0.006843795068562031, -0.0027424057479947805, 0.019928988069295883, 0.06417626142501831, 0.021856684237718582, 0.007358335889875889, 0.003679797984659672, 0.03952157869935036, 0.06088006868958473, 0.039035748690366745, 0.0612342432141304, 0.03306112438440323, -0.018536897376179695, 0.004237744957208633, 0.06755457818508148, 0.009770729579031467, 0.000781023409217596, 0.05048021674156189, -0.04011368751525879, 0.007550138980150223, 0.007853992283344269, -0.023228920996189117, -0.03766665607690811, 0.030975060537457466, -0.027099967002868652, 0.030957357957959175, 0.03369498997926712, 0.055925268679857254, 0.007096979767084122, 0.008989335969090462, 0.0213742945343256, -0.021480297669768333, -0.07113587111234665, 0.010924466885626316, 0.0027780260425060987, 0.0004222590068820864, 0.013236764818429947, 0.025386950001120567, -0.04749995842576027, -0.016378119587898254, 0.032096654176712036, 0.022685198113322258, 0.0064811622723937035, 0.05986643582582474, 0.07427932322025299, -0.0020812880247831345, -0.007984992116689682, -0.03414337709546089, 0.034093331545591354, -0.021368136629462242, -0.006454803049564362, -0.010825265198946, -0.025450821965932846, 0.06317956745624542, -0.01760023646056652, 0.0382005013525486, 0.021496035158634186, -0.04409617930650711, -0.03451026231050491, -0.01948256604373455, -0.025113729760050774, -0.025159668177366257, 0.027795862406492233, -0.0026077355723828077, -0.03472612425684929, -0.02818889170885086, 0.018598228693008423, 0.002581550506874919, -0.10090962797403336, 0.006454993970692158, -0.0019236005609855056, 0.01018377672880888, 0.03206811472773552, 0.009869450703263283, 0.014791610650718212, -0.03666486218571663, 0.06422275304794312, -0.016143716871738434, 0.05922481417655945, 0.05917752906680107, -0.08595986664295197, 0.08709807693958282, 0.007392451632767916, 0.002892333548516035, 0.01862139254808426, 0.030211085453629494, 0.03414204716682434, -0.10586486011743546, 0.02888156846165657, 0.016222774982452393, -0.023736286908388138, -0.03615327551960945, -0.004721848759800196, -0.0009309620363637805, -0.006429219618439674, -0.027771171182394028, -0.04871610552072525, -0.030003834515810013, -0.029429445043206215, 0.017461232841014862, 0.013551951386034489, 0.055571138858795166, 0.020883139222860336, -0.000026162828362430446, -0.0380752868950367, -0.026275165379047394, 0.02771906740963459, 0.03624999150633812, -0.03195640444755554, -0.03220567852258682, -0.007155686616897583, -0.023820700123906136, 0.025889111682772636, 0.026561126112937927, 0.012845910154283047, -0.024641675874590874, -0.012123075313866138, 0.0037293615750968456, -0.0684020072221756, -0.002512535313144326, -0.033858366310596466, 0.028871839866042137, 0.05356793478131294, -0.0024835432413965464, -0.023486383259296417, 0.005405704025179148, 0.04262285307049751, -0.0626986101269722, -0.003523381892591715, 0.03380792215466499, 0.0475374236702919, -0.009642301127314568, 0.03739481791853905, 0.04297160729765892, -0.07229046523571014, 0.03414306417107582, -0.0041526430286467075, 0.0722740888595581, -0.005353973712772131, -0.04987696558237076, -0.013479191809892654, 0.04407855123281479, -0.019952207803726196, -0.02783912606537342, 0.012101558968424797, 0.0603211335837841, -0.05138837918639183, -0.004424763843417168, -0.012623019516468048, 0.02354395017027855, -0.0033672801218926907, 0.0538642592728138, 0.010108767077326775, -0.007280671503394842, -0.010368348099291325, 0.012463194318115711, 0.06185384839773178, 0.020088210701942444, -0.0013431194238364697, 0.041739653795957565, -0.028879862278699875, 0.014121423475444317, -0.05269753187894821, -0.003357531037181616, -0.021278444677591324, 0.03405074030160904, -0.07252302020788193, 0.040000032633543015, 0.019348155707120895, -0.008823812007904053, 0.03792330622673035, 0.021567637100815773, 0.016682123765349388, 0.033454764634370804, 0.04175959900021553, -0.04320307821035385, 0.03318227827548981, -0.0978344976902008, -0.07786120474338531, -0.02084951475262642, 0.022346310317516327, -0.03722694516181946, -0.005900149699300528, -0.02094086818397045, -0.00413176417350769, -0.03876160457730293, 0.09109211713075638, 0.05400054156780243, -0.0046110027469694614, 0.037529587745666504, -0.005037680733948946, -0.03582076355814934, -0.03655755892395973, -0.0075732870027422905, 0.03409643843770027, 0.03909217193722725, 0.0005497452802956104, 0.03974336385726929, -0.006744288839399815, -0.03235248476266861, 0.05001210421323776, -0.03353433310985565, 0.0070155588909983635, -0.06246103346347809, -0.027647437527775764, -0.01709343120455742, -0.03220608830451965, -0.03826197236776352, -0.011595307849347591, -0.0068514090962708, -0.014717684127390385, 0.041510362178087234, 0.03829670697450638, -0.0405644029378891, 0.018045198172330856, -0.031123165041208267, -0.023815477266907692, -0.030001211911439896, 0.010275873355567455, 0.07330358773469925, -0.02871101349592209, 0.053647615015506744, 0.105079285800457, 0.06454073637723923, -0.028326960280537605, 0.01541970856487751, -0.01752561703324318, -0.05480336397886276, 0.02618861198425293, 0.059397660195827484, -0.10587611049413681, -0.04715937003493309, -0.012033145874738693, -0.018355324864387512, 0.01945517584681511, 0.055764276534318924, -0.051433153450489044, 0.0361718088388443, 0.056666869670152664, 0.03386352211236954, 0.03352857008576393, -0.009551312774419785, 0.035993725061416626, 0.029061591252684593, -0.02027142234146595, -0.06950593739748001, -0.009603812359273434, -0.0174079779535532, -0.04800130054354668, -0.010117442347109318, 0.05610664561390877, -0.050270192325115204, 0.0029511291068047285, 0.0253727026283741, 0.0017961363773792982, 0.03824402764439583, 0.036224085837602615, -0.0923088937997818, -0.05429945886135101, -0.043278004974126816, 0.034368451684713364, -0.03441473841667175, 0.009355912916362286, -0.06546477228403091, -0.059075452387332916, -0.02472984790802002, 0.03399544209241867, -0.05437511205673218, -0.04070764407515526, 0.028181517496705055, -0.03651374205946922, 0.001615253509953618, -0.05634552240371704, 0.014672636985778809, 0.014080123044550419, 0.01307882834225893, -0.03979350998997688, -0.054224610328674316, 0.06962212920188904, -0.019527042284607887, -0.03509863466024399, 0.0001707383489701897, -0.045219436287879944, 0.02842145785689354, 0.006819786969572306, -0.06470481306314468, 0.0050620283000171185, -0.042410291731357574, -0.018973637372255325, 0.019404511898756027, -0.01368305180221796, -0.024523552507162094, 0.032820478081703186, 0.009444315917789936, 0.00962517037987709, -0.01435727346688509, 0.016281992197036743, -0.012821081094443798, 0.011803269386291504, 0.01719530299305916, 0.0033558562863618135, 0.0032878248021006584, -0.03167125955224037, 0.04139148071408272, -0.002338229678571224, -0.03768814355134964, -0.013568300753831863, 0.013495637103915215, 0.02019890584051609, 0.05758381262421608, -0.016357053071260452, -0.05588364973664284, -0.005283084698021412, 0.010933375917375088, 0.016920262947678566, -0.004734374582767487, -0.02148701809346676, 0.03447357192635536, 0.014433435164391994, 0.004160628188401461, -0.003339005634188652, 0.0013921244535595179, 0.012721136212348938, -0.008233364671468735, 0.02893945202231407, -0.011128096841275692, -0.0324537418782711, -0.025012806057929993, -0.021591268479824066, -0.016623640432953835, 0.035600822418928146, -0.006993292830884457, -0.004713575355708599, -0.03273151442408562, 0.03976142033934593, 0.055870503187179565, 0.01727987825870514, -0.005252942908555269, 0.03996017575263977, 0.023662826046347618, -0.04037584736943245, -0.020646439865231514, -0.029017413035035133, -0.03368464484810829, -0.003481899620965123, 0.041714247316122055, 0.031159887090325356, 0.085093654692173, 0.040778160095214844, 0.018594341352581978, 0.004705256316810846, -0.012637807056307793, 0.031571485102176666, 0.03042466565966606, -0.04260025918483734, 0.029961470514535904, -0.03113490529358387, 0.015121201053261757, 0.0035793581046164036, -0.011714472435414791, -0.07025391608476639, -0.003524448024109006, 0.0037967076059430838, 0.028908459469676018, 0.0010234862565994263, 0.006763892713934183, 0.04701041430234909, -0.01958008110523224, -0.07426832616329193, -0.03336959332227707, -0.019544092938303947, -0.01024495717138052, 0.01665041409432888, 0.05493439361453056, 0.012897046282887459, -0.007416718639433384, -0.00860659684985876, 0.07458066940307617, -0.034492284059524536, -0.04866410046815872, -0.036226995289325714, -0.05083959177136421, 0.005653214640915394, -0.030678335577249527, 0.06665492802858353, 0.0019212646875530481, 0.008410949259996414, -0.00871376320719719, -0.011683324351906776, -0.020398927852511406, -0.014118116348981857, 0.02660428360104561, -0.016207227483391762, 0.030221251770853996, 0.020755253732204437, -0.009524130262434483, -0.02885528653860092, 0.0013965398538857698, -0.021948983892798424, -0.011735727079212666, 0.0037948244716972113, -0.015241206623613834, 0.002211353974416852, 0.022473622113466263, -0.029722610488533974, -0.022573374211788177, -0.0024568357039242983, 0.002658258192241192, 0.07993470877408981, -0.030365146696567535, -0.03277983143925667, -0.05171104520559311, -0.04508533701300621, 0.0029293824918568134, 0.016198905184864998, 0.013808163814246655, -0.03161334618926048, -0.07180596888065338, 0.04469427838921547, -0.01726604625582695, -0.07075251638889313, 0.03823000565171242, -0.032238416373729706, -0.046221133321523666, 0.005627830978482962, -0.030233845114707947, -0.009533739648759365, 0.0010814368724822998, -0.0025875435676425695, -0.0037394461687654257, 0.003587451996281743, -0.017057357355952263, 0.006106175482273102, 0.010665333829820156, 0.0967411994934082, 0.017549527809023857, -0.019594401121139526, 0.01963595673441887, -0.03767237812280655, -0.01185845397412777, 0.03498448431491852, -0.06430134922266006, 0.06687053292989731, 0.05801922082901001, 0.012547560967504978, -0.03933291137218475, -0.006833044346421957, 0.019022570922970772, -0.025078359991312027, -0.04122646525502205, -0.011388552375137806, -0.040490489453077316, 0.013119610026478767, -0.020509496331214905, 0.023518159985542297, 0.01038962323218584, -0.010879739187657833, 0.04275984689593315, 0.009516436606645584, 0.03829250857234001, 0.022898241877555847, 0.07142283022403717, -0.013642176985740662, 0.013722690753638744, -0.0001974794577108696, 0.019382763653993607, -0.04312349855899811, 0.02684524469077587, -0.03702133521437645, 0.014324668794870377, -0.023059947416186333, 0.032096438109874725, -0.02709237113595009, 0.054075464606285095, -0.08686092495918274, -0.02151690050959587, 0.01595480740070343, -0.06468676030635834, -0.031704485416412354, 0.054735537618398666, 0.08177448064088821, -0.004450972657650709, 0.03797322139143944, -0.009786487556993961, -0.04068862274289131, -0.015252734534442425, -0.004182201810181141, -0.012404234148561954, -0.003366272896528244, 0.04383320361375809, -0.002793645253404975, 0.02654963731765747, -0.05602268502116203, -0.03543633967638016, 0.04566347971558571, 0.025704149156808853, -0.010105328634381294, -0.022513549774885178, -0.07441472262144089, 0.00683272909373045, 0.04459020867943764, -0.023875396698713303, 0.013428637757897377, -0.08057062327861786, -0.030473580583930016, 0.024021098390221596, 0.014570937491953373, 0.05540163069963455, -0.014700380153954029, 0.004556374158710241, 0.049806974828243256, 0.06318354606628418, 0.04871766269207001, 0.04585839435458183, 0.00716131879016757, 0.050230707973241806, -0.013638872653245926, 0.02842879667878151, 0.006101993843913078, -0.021921468898653984, 0.04172443971037865, 0.0025547149125486612, 0.05870974436402321, 0.049511536955833435, 0.0212935209274292, 0.04443575069308281, 0.06250321120023727, -0.020005429163575172, -0.06981872767210007, -0.04279613494873047, -0.036767181009054184, -0.03133993223309517, -0.05201316252350807, 0.04974681884050369, -0.015195994637906551, -0.03190631419420242, 0.009924361482262611, -0.028666386380791664, -0.024159612134099007, 0.06427595764398575, 0.0503377690911293, -0.04561065137386322, -0.006744109559804201, -0.02495657466351986, -0.016037296503782272, -0.00256403349339962, 0.00832071341574192, -0.00953829474747181, -0.01900026574730873, -0.0267450213432312, -0.031630102545022964, -0.05676520988345146, 0.012347051873803139, 0.027108022943139076, -0.03614138066768646, -0.02066286839544773, 0.11511103808879852, -0.0029047681018710136, 0.007378790993243456, -0.01654047705233097, 0.043229006230831146, 0.0014606593176722527, -0.037054404616355896, -0.005244782194495201, 0.03852489963173866, -0.034115951508283615, -0.023099668323993683, -0.03733823075890541, 0.045633070170879364, -0.015219638124108315, 0.029460586607456207, 0.02419722080230713, 0.016276199370622635, -0.039436694234609604, 0.02325129136443138, 0.0343925878405571, 0.09394251555204391, -0.010594680905342102, 0.0012426136527210474, -0.01490791980177164, -0.01835571974515915, -0.012836827896535397, -0.000767475226894021, 0.03126482293009758, 0.03831629827618599, -0.012593135237693787, -0.05535048991441727, -0.07322502881288528, -0.0017576842801645398, 0.017348643392324448, 0.054244812577962875, -0.038958027958869934, 0.07324716448783875, 0.02128301002085209, -0.012912509962916374, 0.002491509076207876, 0.06799401342868805, -0.02054755575954914, 0.01791856251657009, -0.10457170009613037, -0.024265620857477188, 0.027472976595163345, 0.021472763270139694, -0.03436248004436493, 0.04595990478992462, -0.04518022760748863, 0.004317939281463623, 0.012758721597492695, 0.028768571093678474, 0.010376435704529285, -0.0210336335003376, 0.00419977679848671, -0.0005844657425768673, -0.01034889742732048, 0.007928877137601376, 0.041249025613069534, 0.020661944523453712, 0.021578138694167137, -0.03892773389816284, -0.01959230564534664, -0.05551118776202202, 0.00015654279559385031, -0.007158314809203148, -0.03462040796875954, -0.018066441640257835, -0.03881986811757088, -0.00021214211301412433, 0.039665523916482925, 0.01548717450350523, -0.054164811968803406, -0.01586529240012169, 0.029573751613497734, 0.003951616585254669, 0.014248424209654331, -0.0011029974557459354, -0.006591188721358776, 0.004170471802353859, -0.011908154934644699, -0.012135406956076622, 0.003033490153029561, 0.01636468805372715, -0.010884201154112816, -0.024693792685866356, -0.037480056285858154, 0.03310178220272064, -0.024819493293762207, 0.016282884404063225, 0.05148617923259735, 0.052240174263715744, -0.02569490112364292, 0.01801498979330063, -0.04156780242919922, -0.012307665310800076, 1.682192873886379e-7, 0.007009529508650303, 0.060536231845617294, 0.050520285964012146, 0.03389759361743927, 0.0008416802738793194, 0.009929944761097431, -0.026164110749959946, -0.06607091426849365, -0.04431707412004471, -0.017301812767982483, -0.003058284753933549, 0.02050008438527584, -0.03922287002205849, -0.018555277958512306, 0.01985435001552105, 0.047181934118270874, -0.1041208878159523, 0.04497252777218819, 0.03635737672448158, -0.03520924970507622, -0.018586648628115654, -0.023384878411889076, -0.0388987734913826, -0.022855248302221298, 0.023703668266534805, 0.021551886573433876, 0.014807034283876419, -0.0277398694306612, 0.012273382395505905, 0.012822586111724377, -0.018235033378005028, -0.06244213879108429, 0.04328000545501709, 0.04117187485098839, -0.0023325695656239986, 0.08796942234039307, 0.0483182892203331, 0.001727234572172165, -0.024862000718712807, 0.06912753731012344, -0.03265731409192085, -0.034916575998067856, -0.0746573805809021, -0.06759438663721085, -0.013070030137896538, 0.023350046947598457, -0.014839896000921726, -0.04717874899506569, -0.0224868543446064, 0.011955360881984234, 0.041623521596193314, 0.04085279628634453, -0.03457091376185417, 0.028742477297782898, 0.055080119520425797, 0.03960886225104332, 0.030354689806699753, 0.03399873524904251, -0.0027581064496189356, -0.008375960402190685, 0.034078449010849, 0.0014967391034588218, -0.050246112048625946, -0.02571156807243824, -0.01648465171456337 ]