what quantum state really is

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1、Whatquantum“state”reallyis?AlexanderM.SOIGUINECopyright©2014Abstract:Togetoutoflogicaldeadlockininterpretinggedankenexperimentslike“Schrodingercat”,actualmeaningofa“wavefunction”,ora“state”,inthecaseofcomplextwo-dimensionalHilbertspace,isshowntorepresenttransformationsexecuti

2、ngbyelementsofevensubalgebraofgeometricalgebra[1],[2]overthree-dimensionalEuclidianspace.1Exodus23:21.IntroductionThegeometricalgebraG[1]formalismismoreprofoundcomparedtoformalquantummechanical3representationoftwo-stateobservablesby“complex”amplitudesascomponentsofelementsin

3、two-dimensionalHilbertspace.Ithasbeenusedintodescribetossedcoinexperimentthatwasprettysimilartotraditionalquantummechanicalformalism[3].MathematicalframewillhereistheevensubalgebraGofelements:3so,,SISofgeometricalgebraGoverEuclidianspaceE.Ghasthebasis3331,e,e,e,ee,e

4、e,ee,eee,123122331123whereeiareorthonormalbasisvectorsinE3,eiej-oriented,mutuallyorthogonalunitvalueareasspannedbyeiandejasedges,e1e2e3-unitvalueorientedvolumespannedbyorderededgese1,e2ande.31Youshallnotfollowthemajorityforevil,andyoushallnotrespondconcerningalawsuittofo

5、llowmanytopervert[justice].12SubalgebraGisspannedby1,ee,ee,ee.Variablesandinso,,Sare(real)scalars,3122331Iisaunitsizeorientedarea(lefthandedorrighthanded)inanarbitrarygivenplaneSE.S3Iexplainedindetail[4],[5]thatelementsso,,SIonlydifferfromwhatistraditionally

6、Scalled“complexnumbers”bythefactthatSEisanarbitrary,variableplaneandisnotthewhole3spaceofgame.Puttingitsimply,Iare“complexnumbers”dependingonEembeddedintoE.S23E2isthespacewhereSbelongs.Traditional“imaginaryunit”iisjustISwhenitisnotnecessarytospecifytheplane–everythingisgo

7、ingoninonefixedplane,notin3Dworld.Fullyformalwayofusingi2asa“number”,justwithadditionalalgebraicpropertyi1,maybeasourceofdeeplywronginterpretations,particularlyinquantummechanics.2.RotationsandelementsofG3IfgiselementofG,itsrotationin3Dcanbewrittenas[1],[2]:33g(I)g(

8、I),3S3S22whereIbeebeebeeisunitvalueelementofG,that’s