Geometric Origin of Planck's Constant The Reference Mode λ = c

{"This":[0,60],"preprint":[1],"proposes":[2],"a":[3,12,138,147,153,164,170,251,254,283,294,381,522,559,597,600,603,614,627],"geometric":[4,450,504,524,598],"interpretation":[5],"of":[6,49,54,93,115,121,126,129,229,250,266,273,434,458,462,499,536,605],"Planck's":[7,87,230,233],"constant":[8,88,306],"*h*":[9,111,213,426,520],"based":[10],"on":[11,677],"distinguished":[13],"electromagnetic":[14,123,376],"reference":[15,311,464,508],"mode:":[16],"the":[17,23,47,83,94,113,127,186,203,209,264,300,428,432,440,456,463,476,507,567,579,623,678,701],"plane":[18],"wave":[19,133,148,165,276],"whose":[20],"wavelength":[21],"equals":[22],"distance":[24],"light":[25],"travels":[26],"in":[27,140,155,172,431,439],"one":[28,50,116,286,459,609],"local":[29,453,487,496,569,586,670],"second,":[30,437],"λ₀":[31,644,653,673],"=":[32,36,41,97,102,145,160,177,316,318,328,330,340,342,351,353,363,365,385,387,400,414,482,511,514,517,519,556,645,649,654,658,665,669,674,682,688],"c·τ₀":[33],"with":[34,239,566,585],"τ₀":[35,648,681],"1":[37,42,135,141,512,515,572,650,659,683],"s,":[38],"giving":[39],"f₀":[40,657],"Hz.":[43,573],"We":[44],"show":[45],"that":[46,130,480,564],"energy":[48,67,74,92,114,144,159,176,180,199,205,259,298,441],"complete":[51,76,117,187,240,278,628],"phase":[52,77,119,242,629],"cycle":[53,78,120,139,154,171,188,204,210,256,296,424,461,611],"this":[55,309],"mode":[56,95,312],"is":[57,99,112,183,194,206,218,245,289,378,430,455,489,543,546,558,575,622,632,691,699,703],"exactly":[58,100],"*h*.":[59,191,417],"reframes":[61],"quantum":[62,231,664],"action":[63,220,361,625],"not":[64,162,197,224,438,577,693],"as":[65,72,447,527],"an":[66,73,122,195,198,219,448,491,619],"per":[68,75,181,200,436,442],"unit":[69],"time":[70],"but":[71,185,581],"(360°).":[79],"The":[80,91,179,445,452,486,503,541,553,685],"framework":[81,702],"develops":[82],"following":[84],"consequences:":[85],"1.":[86],"identified":[89,237],"geometrically.":[90],"λ":[96,395,409,471,555],"c":[98,510],"h":[101,193,621],"6.626":[103],"070":[104],"15":[105],"×":[106,322,334,346,357,369],"10⁻³⁴":[107,370],"J.":[108],"More":[109],"fundamentally,":[110],"360°":[118,241,302,423,460,518,610,666,689],"wave,":[124],"independent":[125],"duration":[128,211,457],"cycle.":[131,443],"A":[132,275],"at":[134,149,166,571],"Hz":[136,151,168,516,660],"completes":[137,152,169],"s":[142,157,174,513,651],"(cycle":[143,158,175],"*h*);":[146],"1/3":[150],"3":[156],"*h*,":[161],"*h*/3);":[163],"2":[167],"0.5":[173],"*h*).":[178],"second":[182,292,446,454,488,570,668],"*h*·*f*,":[184],"always":[189],"carries":[190,257,425],"2.":[192],"action,":[196],"second.":[201,287],"Because":[202],"invariant":[207,449,492,568],"while":[208],"varies,":[212],"has":[214],"dimension":[215],"J·s:":[216],"it":[217],"tied":[221],"to":[222,225,591],"phase,":[223,531],"time.":[226],"3.":[227],"Reformulation":[228],"hypothesis.":[232],"\\"packets\\"":[234],"(quanta)":[235],"are":[236],"geometrically":[238],"cycles.":[243],"Energy":[244],"released":[246],"only":[247],"upon":[248],"completion":[249],"full":[252,280],"turn;":[253],"fractional":[255,295],"its":[258,583],"forward.":[260],"Quantization":[261],"arises":[262],"from":[263,643],"geometry":[265],"phase.":[267,274],"4.":[268],"Fractional":[269],"cycles":[270,281,435],"and":[271,472,532,538,635],"continuity":[272],"may":[277],"N":[279,384],"plus":[282],"fraction":[284,604],"within":[285],"Phase":[288],"continuous":[290],"across":[291],"boundaries;":[293],"stores":[297],"until":[299],"next":[301],"completion.":[303],"5.":[304],"Unified":[305],"derivation.":[307],"From":[308],"single":[310,523],"emerge:":[313],"mass":[314],"*m*₀":[315],"*h*/*c*²":[317],"7.372":[319],"497":[320],"324":[321],"10⁻⁵¹":[323],"kg;":[324],"electric":[325],"potential":[326],"V₀":[327],"*h*/*e*":[329],"4.135":[331],"667":[332],"696":[333],"10⁻¹⁵":[335,347],"V;":[336],"magnetic":[337],"flux":[338],"Φ₀":[339],"*h*/2*e*":[341],"2.067":[343],"833":[344],"848":[345],"Wb;":[348],"momentum":[349],"*p*₀":[350],"*h*/*c*":[352],"2.210":[354],"219":[355],"094":[356],"10⁻⁴²":[358],"kg·m/s;":[359],"reduced":[360],"ħ":[362,642],"*h*/2π":[364],"1.054":[366],"571":[367],"817":[368],"J·s.":[371],"6.":[372],"Spectrum":[373],"classification.":[374],"All":[375],"radiation":[377],"classified":[379],"by":[380,475,578,582],"dimensionless":[382],"factor":[383],"c/λ":[386],"f/(1":[388],"Hz).":[389],"Contracted":[390],"modes":[391,405],"(N":[392,406],">":[393,402,410],"1,":[394,408],"<":[396,407,416],"c)":[397,411],"have":[398,412],"E":[399,413],"N·*h*":[401,415],"*h*;":[403],"dilated":[404],"In":[418,506],"both":[419],"regimes,":[420],"each":[421],"individual":[422],"—":[427,521],"change":[429],"number":[433],"7.":[444],"gauge.":[451,671],"mode.":[465],"Under":[466],"gravitational":[467,500],"dilation":[468],"or":[469,550],"contraction,":[470],"*t*":[473],"deform":[474],"same":[477],"factor,":[478],"so":[479],"λ/*t*":[481],"*c*":[483,557,655,675],"remains":[484],"invariant.":[485],"therefore":[490],"gauge":[493,539,560],"for":[494,562,626],"any":[495],"observer,":[497],"regardless":[498],"potential.":[501],"8.":[502],"identity.":[505],"configuration,":[509],"object,":[525],"viewed":[526],"length,":[528],"time,":[529],"frequency,":[530,615],"action.":[533],"9.":[534],"Continuity":[535],"space":[537],"choice.":[540],"vacuum":[542],"continuous;":[544],"there":[545],"no":[547],"absolute":[548],"grid":[549],"privileged":[551,576],"scale.":[552],"choice":[554,561,680],"measurement":[563,601],"coincides":[565],"It":[574],"vacuum,":[580],"alignment":[584],"Lorentz":[587],"invariance.":[588],"10.":[589],"Relation":[590],"uncertainty.":[592],"ΔE·Δ*t*":[593],"≥":[594],"ħ/2":[595],"acquires":[596],"reading:":[599],"isolating":[602],"space-time":[606],"smaller":[607],"than":[608],"cannot":[612,617],"define":[613,618],"hence":[616],"energy.":[620],"minimal":[624],"turn.":[630],"What":[631],"derived,":[633],"conventional,":[634],"interpretive.":[636],"Derived:":[637],"*m*₀,":[638],"V₀,":[639],"Φ₀,":[640],"*p*₀,":[641],"*c*.":[646],"Conventional:":[647],"⇒":[652,656],"(gauge":[661],"choice).":[662],"Interpretive:":[663],"cycle;":[667],"Limits.":[672],"depends":[676],"conventional":[679],"s.":[684],"identification":[686],"\\"quantum":[687],"cycle\\"":[690],"interpretive,":[692],"derived.":[694],"No":[695],"new":[696],"experimental":[697],"prediction":[698],"claimed;":[700],"reorganizational.":[704]}