Can the study of reduction probabilities reveal ne

1Canthestudyofreductionprobabilitiesrevealnewsaboutthenatureofquantumstatereduction?GarreltQuandt-Wiese*Schlesierstr.16,64297Darmstadt,GermanyThequestion,whetherthevalidityoftheprojectionpostulateisuniversal,oriftheremightberegimesinwhichdeviationsfromitcouldbeobserved,isdiscussedwithhelpofaphenomenologicalmodel.Thecoreofthemodelrestsonlyupontheassumptionthatstatereductioniscausedbyaphysicalinteractionbetweenthesuperposedstates.Themodeliscalibratedforsuperpositionsoftwostatestotheprojectionpostulateanditsbehaviouristhenstudiedforquantumsuperpositionsofmorestates.Deviationsfromtheprojectionpostulatearepredicted,ifthecouplingsdescribingtheinteractionbetweenthestatesbecomesignificantlydifferent.TheapproachofthemodelisexplicitlyworkedoutfortheDiósi-Penrosehypothesisofgravity-inducedquantumstatereduction.Ananalysisofthemodeltakingintoaccountthespecificsofsolidstatescanexplainwhyinstandardquantummechanicalexperimentsonealwaysobservestheresultspredictedbytheprojectionpostulate.Fortheverificationanexperimentisproposed,inwhichasinglephotonissplitintofourbeamsandmeasuredateachbeambyaspecialdesigneddetectorbasedonavalanchephotodiodes.Animportantpropertyofthemodelisthatthepredictedreductionprobabilitiesarenotimpactedbydecoherence.Anoutlookisgiven,howthepredictionsofthemodelcanpossiblybeappliedtobiology.*E-Mailaddress:[e-mail]issueofquantumtheoryisthequestionaboutthereductionofthestate-vector,alsoknownasthecollapseofthewave-function.Thekeyproblemforestablishingatheoryforquantumstatereductionisthedifficultytogettheneededexperimentalfactsfordevelopingandverifyingatheoreticalapproach.Ourknowledgeaboutquantumstatereductionmightbesummarizedbythethreefollowingpoints:1.Themeasurementprocessforcesareductionofthestate-vectortowardsaneigenvectoroftheoperatordescribingthemeasurementprocess.2.ThereductionprobabilitiestowardstheseeigenvectorsfollowthevonNeumann’sprojectionpostulate[1].3.Alowerlimit“howmacroscopic”1quantumsuperpositionscanbe,beforetheydecaybystatereduction,canbeestimatedfromrecentexperimentsdemonstratinge.g.quantumsuperpositionsoffullerenes[2]orsuperconductingcurrents[3].Points1and2aretogethertheso-calledorthodoxinterpretation,withwhichtillnowmostoftheknownexperimentalresultscanbedescribedsufficiently.Thereallimithowmacroscopicquantumsuperpositionscanbe,beforethedecay,couldsofarnotbedetermined.Abigproblemaredecoherenceeffects(e.g.environmentaldecoherence)coveringtheactualreductionevents.Duetotherareexperimentalfactsaboutquantumstatereductionavarietyofdifferenttheoreticalapproachesweredevelopedinthelastdecades.Severalofthemtrytoexplainreductionbyphysicalmechanismslikee.g.uncertaintiesofthespace-time[4-6].Others,astheGRWapproach,introduceaspontaneouslocalizationprocess,withouthavingaconcretephysicalmechanisminmind[7,8].Paralleltothetheoreticalactivitiesalotofinterestingexperimentalproposalsweredevelopedbenefitingfromrecenttechnologicalprogress[9-20].Butwithnoneofthemitwassofarpossibletobringmorelightintothemysteryofquantumstatereduction.Inthisworkthequestionisdiscussedwhethertheinvestigationofreductionprobabilitiescanprovidemorefactsaboutquantumstatereduction,whichmighthelptotestexistingortostimulatenewtheoreticalapproaches.Herethisdiscussionisfocussedonthemoreconcretequestion,whetherthevalidityoftheprojectionpostulateisuniversal,oriftheremightberegionsinwhichdeviationsfromitcouldbeobserved.1I.e.whichmagnitudesoflengthsandmassescanbeinvolvedinthesuperposition.3Thisinvestigationisdonewithahelpofaphenomenologicalmodel,forwhichitisattemptedtomakeasfewaspossibleassumptions.Thecoreofthemodelrestsonlyupontheideathatstatereductioniscausedbyaphysicalinteractionbetweenthesuperposedstates.Thisapproachisdenotedhereas“reductionbyconcurrencyofstates”sincethestatescompetewitheachothertosurviveatthereductionevent.AlthoughthemodelisexplicitlyworkedoutfortheDiósi-Penroseapproachofgravity-inducedquantumstatereductionhere,otherapproachesforthephysicalinteractionbetweenthestatescanbepluggedintothemodelaswell.InChapter2thephenomenologicalmodelisintroducedandtheDiósi-Penroseapproachofgravity-inducedquantumstatereductionisrecapitulated.Thephenomenologicalmodeliscalibratedtotheprojectionpostulateforquantumsuperpositionsoftwostatesandthenitsbehaviourisstudiedforsuperpositionsofmorestates.Thisextrapolationshowsthatdeviationsfromtheprojectionpostulatecanoccur,ifthecouplingsdescribingtheinteractionbetweenthestatesaresignificantlydifferent.InChapter3thequestionisdiscussedwhetherthemodelcanexplainthereductionbehaviouroftypicalquantummechanicalexperiments,inwhichdeviationsfromtheprojectionpostulatearenotobservedsofar.Thisdiscussionisbasedonananalysisofthedecaybehaviourofsolidstatesinaquantumsuperposition.InChapter4thequestionisfollowedupwhetheritispossibletoverifythepredictionsofthemodelwithcurrentstateofthearttechnology.Thisisdonebyproposingandanalysingaconcretequantumopticalexperiment.InChapter5anoutlookisgivenwhereinnaturethepredictionsofthemodelcouldplayarole.Itisshownthatthepredictedreductionbehav