PUH Theorem 364 — Redshifted Photon Energy Is Work Done on the Lattice: P dV Equals the Loss Exactly, and the Recipient's Tensor Is Under-Specified Rather Than Unknown

{"Photonic":[0],"Universe":[1],"Hypothesis":[2],"(PUH)":[3],"—":[4,47,174,269,365,369,447,509,582,630,637,730,793,832,899,934,940,1043,1097,1135],"Energy":[5],"Ledger.":[6],"THE":[7,38,160,196,283,352,419,422,459,463,516,520,645,652,697,720,767,771,828,892,957,1049,1108,1142],"QUESTION.":[8],"A":[9,230,513,579,593,597,726,740,963,1055],"photon":[10,152,356,496],"crossing":[11],"the":[12,23,66,99,107,110,120,145,177,181,193,205,219,226,233,239,249,256,273,279,303,311,315,391,398,405,412,426,430,434,438,443,478,527,573,577,589,616,628,638,655,660,665,678,683,687,691,717,785,788,803,810,815,848,862,878,902,925,945,969,976,992,995,1017,1063,1088,1098],"expanding":[13,54,77,111],"universe":[14,78],"arrives":[15],"with":[16,305,345,382,608,1015],"less":[17],"energy":[18,35,153,240,298,693,874,884,903,1012],"than":[19,29,321,937,952,968,1000,1022],"it":[20,48,175,191,270,535,762,813,900,1080,1162],"left":[21,307],"with;":[22],"microwave":[24],"background":[25],"has":[26,235,242,258,947,1069],"shed":[27,394],"more":[28,949],"99.9":[30],"per":[31,453,493,507],"cent":[32,454],"of":[33,293,455,498,530,1130],"its":[34,322,633,755,794,836,1123,1131],"since":[36,395],"recombination.":[37],"STANDARD":[39,598],"ANSWER":[40],"IS":[41,45,89,162,198,202,285,421,565,648,694,722,732,746,769,791,814,1054],"NOT":[42,90,166,170,199,229,603,723,825,895,919,961,1036,1057,1075,1105],"THAT":[43,563,670,1107],"ENERGY":[44,63,197,646,1053],"DESTROYED":[46],"is":[49,57,112,148,157,165,176,188,209,228,251,278,299,335,373,414,437,445,450,470,473,480,526,545,554,559,618,659,709,749,853,870,881,906,927,979,1033,1041,1095,1103,1125,1133],"that":[50,179,291,411,469,555,572,695,787,812,820,1038,1062,1092,1122,1128,1153,1161],"in":[51,302,588,876,886,1100],"a":[52,113,171,252,259,294,331,538,557,854,872,882,929,932,938,1004,1010,1066,1084],"general":[53,224],"spacetime":[55],"there":[56,1020],"NO":[58,266],"UNIQUE":[59],"GLOBALLY":[60],"CONSERVED":[61],"TOTAL":[62],"to":[64,213,244,318,400,552,801,950,1071,1086],"assign":[65],"difference":[67],"to,":[68],"because":[69,190,1079],"conservation":[70],"follows":[71,271],"from":[72,272,314,429,682,991],"time-translation":[73],"symmetry":[74],"and":[75,138,169,204,238,309,334,468,533,635,640,644,686,714,753,857,917,944,975,985,1127,1138,1145],"an":[76,167],"does":[79,96,1081,1148,1163],"not":[80,97,446,547,560,928,1034,1082,1151],"have":[81,799],"it.":[82,215,1149],"LOCAL":[83,1044],"COVARIANT":[84],"CONSERVATION":[85,1045],"HOLDS":[86,1046],"EXACTLY":[87,1047],"AND":[88,370,519,592,669,738,745,822,1048],"IN":[91],"QUESTION":[92,768],"HERE.":[93],"This":[94,164,817],"note":[95,818,909],"dispute":[98],"standard":[100,182,1039,1126],"account.":[101],"It":[102,187],"asks":[103],"what":[104,907],"changes":[105],"if":[106,924,983,1003,1025],"thing":[108],"doing":[109],"SUBSTANCE.":[114],"RESULT":[115,216,339,475,540],"364.1":[116],"(the":[117,542],"work":[118,146,234,257,497],"equals":[119],"loss,":[121],"exactly).":[122],"Radiation":[123],"carries":[124],"pressure":[125],"P":[126,134],"=":[127,131,135,142,384,610,620],"u/3.":[128],"With":[129],"u":[130,184],"4.2×10⁻¹⁴":[132],"J/m³,":[133],"1.400×10⁻¹⁴":[136],"Pa,":[137],"volume":[139],"growth":[140,362],"3VH":[141],"2.376×10⁶³":[143],"m³/s,":[144],"done":[147],"3.326×10⁴⁹":[149,158,499],"J/s.":[150,159],"The":[151,495,549,911],"loss":[154,357],"rate":[155,444],"H·E":[156],"RATIO":[161],"1.0000.":[163],"analogy":[168],"new":[172,487,1093],"claim":[173,786],"identity":[178],"produces":[180],"result":[183],"∝":[185],"a⁻⁴.":[186],"stated":[189],"locates":[192],"question":[194,208],"precisely:":[195],"MISSING,":[200],"IT":[201,731,780,833,1115],"WORK,":[203,1144],"only":[206,1121],"remaining":[207],"whether":[210],"anything":[211],"exists":[212],"receive":[214],"364.2":[217,553,942],"(where":[218],"two":[220,912],"frameworks":[221],"differ).":[222],"In":[223,246,482,627],"relativity":[225,953,1068],"expansion":[227,485],"SUBSTANCE,":[231],"so":[232,255,348,761],"no":[236,948],"recipient":[237,260,543,558,996],"simply":[241],"nowhere":[243],"be.":[245],"this":[247,264,377,483,531,908,1031,1154],"framework":[248,484,946,1064],"substrate":[250,274,926,1005],"PHYSICAL":[253],"MEDIUM,":[254],"BY":[261],"CONSTRUCTION.":[262],"And":[263,1150],"requires":[265,397],"NEW":[267],"ASSUMPTION":[268],"being":[275],"real,":[276],"which":[277,845,852,905],"framework's":[280,656],"founding":[281],"premise.":[282],"RESERVOIR":[284],"ALSO":[286],"ALREADY":[287],"FILED:":[288],"T316":[289],"holds":[290],"ALL":[292],"moving":[295],"body's":[296],"kinetic":[297,639],"motion":[300],"induced":[301],"medium":[304,939],"nothing":[306,1146],"over,":[308],"derives":[310],"relativistic":[312],"divergence":[313],"medium's":[316],"inability":[317],"reconfigure":[319],"faster":[320],"own":[323,795],"signal":[324],"speed.":[325],"That":[326,525],"paper":[327],"was":[328],"written":[329,989],"for":[330],"different":[332,890,915],"purpose":[333],"used":[336],"here":[337,1147],"unchanged.":[338],"364.3":[340],"(two":[341],"recipients":[342],"ruled":[343],"out,":[344],"arithmetic":[346,1099],"given":[347],"nobody":[349],"repeats":[350],"them).":[351],"COSMOLOGICAL":[353],"CONSTANT":[354],"FAILS:":[355,389],"3.33×10⁴⁹":[358],"J/s":[359,364,500],"against":[360],"Λ":[361,472],"1.43×10⁵⁴":[363],"short":[366],"by":[367,664,751,759],"4×10⁴":[368],"Λ's":[371],"density":[372,875,885,1013],"measured":[374],"constant":[375,658],"while":[376],"would":[378,536,1008],"raise":[379],"it,":[380],"conflicting":[381],"w":[383],"−1.":[385],"BULK":[386],"LATTICE":[387],"MOTION":[388],"storing":[390],"1.66×10⁷⁰":[392,448],"J":[393,449,506],"recombination":[396],"lattice":[399,413,488],"move":[401],"at":[402,632],"0.39c":[403],"throughout":[404],"observable":[406],"universe,":[407],"contradicting":[408],"T358's":[409],"finding":[410],"1":[415],"−":[416,614,624],"10⁻¹²³":[417],"crystallised.":[418],"RECIPIENT":[420],"EXPANSION":[423],"ITSELF,":[424],"where":[425],"thermodynamics":[427],"pointed":[428],"start.":[431],"WORTH":[432],"NOTING:":[433],"cumulative":[435],"figure":[436],"right":[439],"order":[440],"even":[441],"though":[442],"about":[451,510],"7":[452],"today's":[456],"dark":[457],"energy.":[458],"MAGNITUDE":[460],"NEARLY":[461],"WORKS;":[462],"TIME":[464],"DEPENDENCE":[465],"DOES":[466,602,824,894,960,1074],"NOT,":[467],"why":[471],"excluded.":[474],"364.4":[476,1158],"(and":[477],"entry":[479],"negligible).":[481],"means":[486],"cells":[489],"are":[490],"created:":[491],"5.628×10¹⁶⁷":[492],"second.":[494],"divided":[501],"among":[502],"them":[503],"gives":[504,901],"5.91×10⁻¹¹⁹":[505],"cell":[508],"3×10⁻¹²⁸":[511],"OF":[512,776,966,1051],"PLANCK":[514],"ENERGY.":[515],"LEDGER":[517],"CLOSES":[518],"ENTRY":[521],"ROUNDS":[522],"TO":[523,605,724,733],"NOTHING.":[524],"honest":[528],"size":[529],"result,":[532],"inflating":[534],"be":[537,764,859,988,1087],"mistake.":[539],"364.5":[541,973,1119],"tensor":[544,617,1007],"UNDER-SPECIFIED,":[546],"unknown).":[548],"obvious":[550],"objection":[551],"naming":[556],"having":[561],"one.":[562],"OBJECTION":[564],"ANSWERED":[566],"FURTHER":[567],"THAN":[568,703],"EXPECTED.":[569],"T340":[570,748],"establishes":[571,1120],"core-formation":[574],"constraint":[575],"makes":[576],"theory":[578],"SIGMA":[580,594,829],"MODEL":[581,595,830],"harmonic":[583],"maps":[584],"into":[585],"fixed-radius":[586],"spheres":[587],"248-dimensional":[590],"space.":[591],"HAS":[596,1112,1116],"STRESS-ENERGY":[599,1110],"TENSOR":[600,727,893,1111],"WHICH":[601],"HAVE":[604,1076],"BE":[606,920],"INVENTED:":[607],"L":[609],"½G_AB":[611],"∂_μφ^A":[612],"∂^μφ^B":[613],"V(φ),":[615],"T^μν":[619],"G_AB":[621,710,984,1137],"∂^μφ^A":[622],"∂^νφ^B":[623],"g^μν":[625],"L.":[626],"vacuum":[629,662,684,692],"field":[631,843],"minimum":[634],"static":[636],"gradient":[641],"terms":[642],"vanish":[643],"DENSITY":[647],"SIMPLY":[649],"V":[650,715,986,1139],"AT":[651],"MINIMUM.":[653],"So":[654],"cosmological":[657],"potential's":[661],"value,":[663],"ordinary":[666],"field-theoretic":[667],"identification.":[668],"LINKS":[671],"TWO":[672,698,736],"PREVIOUSLY":[673],"SEPARATE":[674],"STATEMENTS:":[675],"T358":[676],"derived":[677],"unsettled":[679],"fraction":[680],"1.295×10⁻¹²³":[681],"energy,":[685],"sigma":[688],"model":[689],"says":[690],"potential.":[696],"ARE":[699],"NOW":[700],"CONNECTED":[701],"RATHER":[702],"MERELY":[704,826],"COINCIDENT.":[705],"What":[706],"remains":[707,997],"unwritten":[708],"(from":[711,716],"E₈":[712],"geometry)":[713],"Casimir":[718,993],"constraint).":[719],"TASK":[721],"DERIVE":[725],"FROM":[728],"NOTHING":[729],"WRITE":[734],"THOSE":[735],"EXPLICITLY":[737],"SUBSTITUTE.":[739],"SUPERSESSION":[741],"CHECK":[742],"WAS":[743,774,781],"NECESSARY":[744],"RECORDED.":[747],"superseded":[750],"T342":[752,778,783,823,967],"had":[754],"winding":[756],"clause":[757],"withdrawn":[758],"T359,":[760],"cannot":[763,858,987],"cited":[765],"whole.":[766],"WHETHER":[770],"SIGMA-MODEL":[772,958],"IDENTIFICATION":[773,959],"PART":[775],"WHAT":[777],"REPLACED.":[779],"NOT.":[782,1117],"withdraws":[784],"Lagrange":[789],"multiplier":[790],"gravity":[792,869],"words:":[796],"\\"three":[797],"notes":[798],"tried":[800],"make":[802],"dimensionless":[804],"multiplier…":[805],"reproduce":[806],"Newtonian":[807],"gravity,":[808],"on":[809,840],"identification":[811,1032],"metric.":[816],"closes":[819],"attempt.\\"":[821],"LEAVE":[827],"STANDING":[831],"USES":[834],"IT:":[835],"central":[837],"argument":[838],"runs":[839],"\\"the":[841],"squared":[842],"gradient,":[844],"falls":[846],"as":[847],"inverse":[849],"fourth":[850],"power\\",":[851],"sigma-model":[855],"calculation":[856],"made":[860],"without":[861],"structure.":[863],"ONE":[864],"DISTINCTION":[865],"KEPT":[866],"SHARP:":[867],"T342's":[868,897],"σ,":[871],"SURFACE":[873],"J/m²;":[877],"tensor's":[879,977],"T⁰⁰":[880],"VOLUME":[883],"J/m³.":[887],"Different":[888],"objects,":[889],"units.":[891],"GIVE":[896],"GRAVITY":[898],"density,":[904],"needed.":[910],"results":[913],"answer":[914],"questions":[916],"SHOULD":[918],"MERGED.":[921],"KILL-CONDITIONS:":[922],"(i)":[923],"substance":[930,1085],"but":[931],"description":[933],"bookkeeping":[935],"rather":[936,999,1021],"Result":[941,972,1118,1157],"collapses":[943],"say":[951],"does;":[954],"(ii)":[955],"IF":[956],"SURVIVE":[962],"CLOSER":[964],"READING":[965],"one":[970,1129],"given,":[971],"fails":[974,1019],"form":[978],"unknown":[980],"again;":[981],"(iii)":[982,1002],"explicitly":[990,1140],"structure,":[994],"asserted":[998],"demonstrated;":[1001],"stress-energy":[1006],"produce":[1009],"gravitating":[1011],"inconsistent":[1014],"observation,":[1016],"approach":[1018],"here;":[1023],"(iv)":[1024],"another":[1026],"reservoir":[1027],"also":[1028],"matches":[1029],"P·dV,":[1030],"unique.":[1035],"CLAIMED:":[1037],"physics":[1040,1094],"wrong":[1042],"NON-UNIQUENESS":[1050],"GLOBAL":[1052],"THEOREM,":[1056],"AN":[1058],"OVERSIGHT.":[1059],"Not":[1060,1090],"claimed":[1061,1091,1152],"solves":[1065],"problem":[1067],"failed":[1070],"solve;":[1072],"RELATIVITY":[1073],"THIS":[1077],"PROBLEM,":[1078],"posit":[1083],"recipient.":[1089],"introduced":[1096],"Section":[1101],"2":[1102],"textbook.":[1104],"CLAIMED":[1106],"SUBSTRATE'S":[1109],"BEEN":[1113],"CONSTRUCTED.":[1114],"FORM":[1124],"values":[1132],"constrained":[1134],"writing":[1136],"REMAINS":[1141],"REAL":[1143],"matters":[1155],"quantitatively:":[1156],"states":[1159],"plainly":[1160],"not.":[1164]}