Holism, Physical Theories and Quantum Mechanics

arXiv:quant-ph/0402047v34Feb2005Holism,PhysicalTheoriesandQuantumMechanics⋆M.P.SeevinckaaInstituteforHistoryandFoundationsofNaturalScience,P.O.Box80.000,UniversityofUtrecht,3508TAUtrecht,TheNetherlandsAbstractMotivatedbythequestionwhatitisthatmakesquantummechanicsaholisticthe-ory(ifso),Itrytodefineforgeneralphysicaltheorieswhatwemeanby‘holism’.ForthispurposeIproposeanepistemologicalcriteriontodecidewhetherornotaphysicaltheoryisholistic,namely:aphysicaltheoryisholisticifandonlyifitisimpossibleinprincipletoinfertheglobalproperties,asassignedinthetheory,bylocalresourcesavailabletoanagent.Iproposethattheseresourcesincludeatleastalllocaloperationsandclassicalcommunication.Thisapproachiscontrastedwiththewell-knownapproachestoholismintermsofsupervenience.Thecriterionforholismproposedhereinvolvesashiftinemphasisfromontologytoepistemology.IapplythisepistemologicalcriteriontoclassicalphysicsandBohmianmechanicsasrepresentedonaphaseandconfigurationspacerespectively,andforquantummechanics(intheorthodoxinterpretation)usingtheformalismofgeneralquan-tumoperationsascompletelypositivetracenon-increasingmaps.Furthermore,Iprovideaninterestingexamplefromwhichonecanconcludethatquantumme-chanicsisholisticintheabovementionedsense,although,perhapssurprisingly,noentanglementisneeded.Keywords:holism,supervenience,classicalphysics,quantummechanics,entanglementPACS:03.65.-w,01.70.+w⋆Thispaperisbasedontalksgivenatthe‘InternationalWorkshoponHolisminthePhilosophyofPhysics’heldatBonnon4-5July2003andatthe‘12thUKConferenceontheFoundationsofPhysics’heldatLeedson2-5September2003.Emailaddress:[e-mail](M.P.Seevinck).PreprintsubmittedtoElsevierScienceAugust20041IntroductionHolismisoftentakentobetheideathatthewholeismorethanthesumoftheparts.Becauseofbeingtoovague,thisideahasonlyservedasaguidelineorintuitiontovarioussharperformulationsofholism.HereIshallbeconcernedwiththeonerelevanttophysics,i.e.,thedoctrineofmetaphysicalholism,whichistheideathatpropertiesorrelationsofawholearenotdeterminedorcannotbedeterminedbyintrinsicpropertiesorrelationsoftheparts1.Thisistakentobeopposedtoaclaimofsupervenience(Healey,1991),toreduction-ism(Maudlin,1998),tolocalphysicalism(Teller,1986),andtoparticularism(Teller,1989).Inallthesecasesacommonapproachisusedtodefinewhatmetaphysicalholismis:viathenotionofsupervenience2.Accordingtothiscommonapproachmetaphysicalholismisthedoctrinethatsomefacts,prop-erties,orrelationsofthewholedonotsuperveneonintrinsicpropertiesandrelationsoftheparts,thelattertogethermakingupthesuperveniencebasis.Asappliedtophysicaltheories,quantummechanicsisthentakentobetheparadigmaticexampleofaholistictheory,sincecertaincompositestates(i.e.,entangledstates)donotsuperveneonsubsystemstates,afeaturenotfoundinclassicalphysicaltheories.However,inthispaperIwanttocriticallyreviewthesupervenienceapproachtoholismandproposeanewcriterionfordecidingwhetherornotaphys-icaltheoryisholistic.Thecriterionforwhetherornotatheoryisholisticproposedhereisanepistemologicalone.Itincorporatestheideathateachphysicaltheory(possiblysupplementedwithapropertyassignmentruleviaaninterpretation)hasthecrucialfeaturethatittellsushowtoactuallyinfer1Thismetaphysicalholism(alsocalledpropertyholism)istobecontrastedwithexplanatoryandmeaningholism(Healey,1991).Thefirstistheideathatexplana-tionofacertainbehaviorofanobjectcannotbegivenbyanalyzingthecomponentpartsofthatobject.Thinkofconsciousnessofwhichsomeclaimthatitcannotbefullyexplainedintermsofphysicalandchemicallawsobeyedbythemoleculesofthebrain.Thesecondistheideathatthemeaningofatermcannotbegivenwithoutregardingitwithinthefullcontextofitspossiblefunctioningandusageinalanguage.2Thenotionofsupervenience,asusedhere,ismeanttodescribeaparticularre-lationshipbetweenpropertiesofawholeandpropertiesofthepartsofthatwhole.Themainintuitionbehindwhatparticularkindofrelationshipismeant,iscap-turedbythefollowingimpossibilityclaim.Itisnotpossiblethattwothingsshouldbeidenticalwithrespecttotheirsubvenientorsubjacentproperties(i.e.,thelower-levelproperties),withoutalsobeingidenticalwithrespecttotheirsuperveningorupper-levelproperties.Thefirstarethepropertiesoftheparts,thesecondarethoseofthewhole.Theideaisthattherecanbenorelevantdifferenceinthewholewith-outadifferenceintheparts.(Cleland(1984)usesadifferentdefinitionintermsofmodallogic.)2propertiesofsystemsandsubsystems.Theguidingideaoftheapproachheresuggested,isthatsomepropertyofawholewouldbeholisticif,accordingtothetheoryinquestion,thereisnowaywecanfindoutaboutitusingonlylocalmeans,i.e.,byusingonlyallpossiblenon-holisticresourcesavailabletoanagent.Inthiscase,thepartswouldnotallowforinferringthepropertiesofthewhole,notevenviaallpossiblesubsys-tempropertydeterminationsthatcanbeperformed,andconsequentiallywewouldhavesomeinstantiationofholism,calledepistemologicalholism.Thesetofnon-holisticresourcesiscalledtheresourcebasis.Iproposethatthisbasisincludesatleastalllocaloperationsandclassicalcommunicationofthekindthetheoryinquestionallowsfor.Theapproachsuggestedherethusfocusesonpropertymeasurementinsteadofonthesu