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1、PHYSICALREVIEWA85,062116(2012)CollapseofthestatevectorStevenWeinberg*TheoryGroup,DepartmentofPhysics,UniversityofTexasatAustin,Texas78712,USA(Received6May2012;published20June2012)Modificationsofquantummechanicsareconsidered,inwhichthestatevectorofanysystem,large
2、orsmall,undergoesastochasticevolution.Thegeneralclassoftheoriesisdescribed,inwhichtheprobabilitydistributionofthestatevectorcollapsestoasumofδfunctions,oneforeachpossiblefinalstate,withcoefficientsgivenbytheBornrule.DOI:10.1103/PhysRevA.85.062116PACSnumber(s):03.
3、65.−wI.INTRODUCTIONquantumjumps.TheoriesoftheevolutionofthedensitymatrixareexaminedasanimportantspecialcaseofthemoregeneralThereisnowinmyopinionnoentirelysatisfactoryformalism.interpretationofquantummechanics[1].TheCopenhageninterpretation[2]assumesamysteriousd
4、ivisionbetweenthemicroscopicworldgovernedbyquantummechanicsandaII.EVOLUTIONOFTHESTATEVECTOR’SmacroscopicworldofapparatusandobserversthatobeysPROBABILITYDENSITYclassicalphysics.Duringmeasurementthestatevectorofthemicroscopicsystemcollapsesinaprobabilisticwaytoon
5、eWeconsiderageneralisolatedsystem,whichmayorofanumberofclassicalstates,inawaythatisunexplained,maynotincludeamacroscopicmeasuringapparatusand/orandcannotbedescribedbythetime-dependentSchrodinger¨anobserver.Weassumeasinordinaryquantummechan-equation.Themany-worl
6、dsinterpretation[3]assumesthaticsthatthestateofthesystemisentirelydescribedbythestatevectorofthewholeofanyisolatedsystemdoesavectorinHilbertspace.Thestatevectorhereistakennotcollapse,butevolvesdeterministicallyaccordingtotheinasortofHeisenbergpicture,inwhichope
7、ratorsA(t)time-dependentSchrodingerequation.Insuchadeterministic¨haveatimedependencedictatedbytheHamiltonianHastheoryitishardtoseehowprobabilitiescanarise.Also,exp(iHt)A(0)exp(−iHt).Butthestatevectorinthissortthebranchingoftheworldintovastnumbersofhistoriesisof
8、theoryisnottimeindependent;itundergoesastochasticdisturbing,tosaytheleast.Thedecoherenthistoriesapproachevolution,slowformicroscopicsystemsbutrapidforlarger[4]liketheCopenha
