KarlSvozil∗
Institutf¨urTheoretischePhysik,UniversityofTechnologyVienna,
WiednerHauptstraße8-10/136,A-1040Vienna,Austria
Abstract
Quantummechanicsismorethanthederivationofstraightforwardtheoremsaboutvectorspaces,Hilbertspacesandfunctionalanalysis.Inordertobeapplicabletoexperimentandtechnology,thosetheoremsneedinterpretationandmeaning.Interpretationistotheformalismwhatascaffoldinginarchitectureandbuildingconstructionistothecompletedbuilding.
PACSnumbers:01.70.+w,03.65.Ta
Keywords:philosophyofquantummechanics
Notlongago,weweresittingintheuniversitycafeteriawithagiftedmathstudent.Thestudentlistenedtothequantummechanicalproblemssomecondensedmatterphysicistswereworkingon.Afterawhilehejumpedupandshouted,“butthisismerelylinearvectorspacetheory!”Heseemeddisappointed.Atleastfromaformalpointofview,thisexclamationappearsnottobetotallyunreasonable.Ioftenhavethechancetoobservetheastonishmentofmathematicians,forinstancegrouptheorists,whenIwatchthembrowsingthroughvenerablephysicsjournals.Theypointtonumberedequations,lemmas,theoremsandconjectures.Whileshakingtheirheadsdisparagingly,theytellmethattheseresultshavebeenknownforalong,longtime,So,whyaremathematiciansworkinginfunctionalanalysisnotthe“better”quantumphysicists?
RecentlyChristopherFuchsandAsherPeresseemtoargueinarelateddirection,performinganiceexercisein“interpretation-bashing”[1],asIwouldcallit.IfIinterpretthemcorrectly,theyassurethatquantumtheoryisanoperationallytestableformalismconcernedwithpredictionsandfrequencycountswhichareultimatelybasedonclicksindetectors,nothingmore.Indeed,itisalmosttautologicthattheonlyrelevantpartofanapplicableformalismistheformalismitself.(Justasanyphysicalsystemobviouslyisaperfectcopyofitself.)Anyemanationofaphysicalsystemcanbecodifiedintodiscretedetectableclicks.Thestatisticalaccumulationofsuchdetectorclicksservesasaninterfacetothequantumprobabilitieswhichcanbecomputedaccordingtoalgorithmic(“cookbook-like”)rules,nomorebutnoless.Thisisultimatetestability,andintermsofpredictions,quantumtheoryhasbeenstandingoutwonderfullyforalmostacenturynow,withnotthefaintestindicationoffailureevenintheremotestareaofphenemenology.
Anyvariationofthiscriticismagainstinterpretationcouldbeheardaroundtheworld,yearroundandfrommanyprominentphysicists.Ithasbecomealmostfashionabletodiscreditinter-pretation.AlreadySommerfeldwarnedhisstudentsnottogetintotheseissues,and,asmentionedbyJohnClauser[2],notlongagoscientistsworkinginthatfieldhadtobeverycarefulnottobecomediscreditedas“quacks.”RichardFeynman[3,p.129]oncementionedthe“perpetualtormentthatresultsfrom[[thequestion]],‘Buthowcanitbelikethat?’whichisareflectionofuncontrolledbututterlyvaindesiretosee[[quantummechanics]]intermsofananalogywithsomethingfamiliar”andadvisedhisaudience,“Donotkeepsayingtoyourself,ifyoucanpossiblyavoidit,‘Buthowcanitbelikethat?’becauseyouwillget‘downthedrain’,intoablindalleyfromwhichnobodyhasyetescaped.”Onlyrecently,someofthatthinkingandexperimenting,asaspin-off,turnedintothehighlyrespectedandveryactiveresearchareasofquantumcryptographyandcomputing.
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Indeed,almostnoresearchfieldhasbeenplaguedwithmorefruitless“meta”papersand“voodoo”thoughtsthanquantummechanics,manysuchtreatiseswrittenbyuninformedlaymenwithmerelysuperficialworkingpracticeofquantummechanics.Surely,whenreadingthesetrea-tises,oneisoftenremindedofthepressingquestionofscholasticismhowmanyangelsfitonthetopofaneedle.Manyofthese“explanations”simplymisinformthepublic,therebydiscreditingscience.Nottomentionthemoreradical“quacks,”whohoweverseemtofavorrelativitytheoryoverquantummechanicsfortheirvainattemptstounfoldwhatappearstothemtheoccultmys-teriesofphysics.Thesepeopleeithercannotunderstandordonotaccepttherationalscientificpracticesandmathematics.
Letusgetbacktointerpretation-bashing.Ofcourse,thereexistsa“quickanddirty”rebuttaltothe“No-Interpretation”interpretationofquantummechanics:thatitisalsoaninterpretation,afterall!JustasatheismisalsoasystemofbeliefwhosecentralelementisthenonexistenceofGod.Nevertheless,thematteristooserioustoleaveitthere.Because,iftakenearnestly,thesuggestionto“notinterpretquantummechanics”couldseverelyhamperresearchinthisfield.
Abandoninginterpretationissuesfromquantumphysicsproperamountstothrowingthebabyoutwiththebathwater,andtocensorshipatworst.Why?Becausewewouldbeatalossinex-tendingthepresentknowledgebaseofphysicaltheorytonewphenomenologicaldomains!Statedpointedly,abandonmentofinterpretationamountstoimposingrestrictionstowhatisconsidered“legal”science.Thosestopsignsforspeculativethinkingcouldbedetrimental,cripplingthemindofthegeniuseswhosepreciousweirdideasaretherootforscientificrevolutionsandprogress.Soofteninhistorythecontemporarypeershavecommittedthemselvestowhatappearedtothemtheconsolidatedcanonofknowledge,andtoooftensuchattemptshaveturnedouttobevainatbestandscientificimpedimentsatworst.Indeed,Ibelievethatthedangerofsuchimpedimentsbyrestrictingphysicsproperishigherthantheannoyanceanddistractioncausedbyuselessinterpre-tations.
Interpretationistotheformalismwhatascaffoldinginarchitectureandbuildingconstructionistothecompletedbuilding.Veryoftenthescaffoldinghastobeerectedbecauseitisanindis-pensablepartofthebuildingprocess.Oncethecompletedbuildingisinplace,thescaffoldingistorndownandtheopusstandsinitsownfullglory.Noneedforauxiliaryscaffoldanymore.Butbewareofthosetechnicianswhoclaimtobeabletoerectsomeofthose“internationalstyleskyscrapers”withoutanypolesandplanks!
Iclaimthat“soft”interpretationissuesveryoftenserveasaguidelineorintuition,whichisab-3
solutelynecessaryforthequantummechanicalresearchprogram.Almostbydefinition,a“good”interpretationfostersresearch,whilea“bad”onecripplesit.Thereby,Iwoulddefinitelynotliketolinkinterpretationto“reality”or“truth,”butwouldkeepaverypragmaticattitude:aslongasaninterpretation,asweirdasitmaysound,fostersresearch,itisa“good”one,otherwiseitmayjustbeawasteoftime.However,aspointedoutbyLakatos[4]sooften,thecontemporarypeersmaynotbeabletoacknowledgewhatsoonerorlaterwillbecomeaprogressiveresearchprogram,andoneisleftwiththerequestfortoleranceandanopennessfornewideas.
Letmegivesomeexamples.OftenonehearsthatmanyresearchersinthequantumcomputationcommunityprofitfromtheintuitionobtainedfromtheEverettinterpretation.Otherresearchersinquantumtheoryseemtofavortheinformationaspectsoftheprocessesinvolved,inparticularthereversibility(one-to-oneness)oftheunitarytimeevolution.Byandlarge,myexperienceisthatthereexistsasmanyinterpretationsofquantummechanicsastherearephysicists(theauthor’sownfancycanbereadin[5]).EventhoseclaimingtoclingtotheCopenhageninterpretationhavetheirownveryoriginalthoughtsaboutandadditionstoit(e.g.,considerAntonZeilinger’sfoundationalprincipleforquantummechanics[6]).Otherexamplesarethepictorialrepresentationoftheformalism,suchasFeynmandiagramsinthetheoryofquantizedfields,orinterferometricschemesinquantumoptics[7].
Iwouldliketosuggestamoretolerantattitudetowardsinterpretationalsoinotherareasofphysicalresearch,inparticularinrelativitytheory.Theetherinterpretation,forexample,nowadaysappearstobehighlyexotic,althoughithasbeentakenquiteseriouslybyscientistssuchasPaulDirac[8],JohnBell[9]andevenAlbertEinstein[10],tonamebutafew.
Withoutinterpretationandintuition,theapplicationoftheformalismwouldberestrictedtoautomaticproofing,toan“athousandmonkeystyping-awayscenario”.Asimilarhopewasex-pressedaround1900bythemathematicalformalists,mostnotablybyDavidHilbert,whoexpectedtobeabletofindafinal,finitesystemofaxiomsfromwhichalltruemathematicaltheoremscouldbededucedbysimilarmethodsasrecipesinacookbook.Todaywewouldcallsuchmethods“algorithmic.”Itmightbeatedioustask,buteventuallyeverymathematicaltheoremwouldbeun-coveredautomatically;evenAndrewWiles’proofofFermat’slasttheorem,andalsothetheoremsbyGleason,BellandKochen&Specker,tonamebutafew.Eventually,G¨odel,Tarski,Turing,Chaitinandothershaveputanendtotheformalist’shopeforanultimate,all-encompassingthe-oryofeverythinginmathematics.Theirfindingshavegivenwaytomorerealisticpossibilitiesofconstructiveproofing.
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Supposeyoucouldprogramacomputertohandlecomplicatedquantumcomputationsbyaverygeneralknowledgebaseofquantumtheory.Wouldyoureallybelievethatanysuchcom-puterwouldbecomeagoodquantumtheorist?Mysuspicionisthatthismachinewouldchurnoutzillionsoftautologiesandcorrectbutunusableexpressions.Bythetimeitwouldstartproduc-ingimportantrevelations(ifever),themachinewouldhavedevelopeditsintrinsic“meaning”or“understanding,”its“interpretation”ofquantummechanics.Thismightbeconsideredasathird,independenttypeoftestforintelligence,besidesthefamousTuringtestorDanielGreenberger’stestofintelligence([11];inshort:disobedienceofsuperrules,justasintheGenesis).
Ofcourse,bymerebruteforce,eventually,everyautomatic,algorithmicmethodwouldresultinallpossibletheoreticalexpressions.Butthen,whocouldfilteroutthescarcesingularimportanttreasuresfromthemyriadsofformulae,thepromisingtechnologicalandexperimentalapplicationsfromthewastefulrepetitionsofuselessby-products?Atleastuntilnow,thequantumformalismdoesnotcontainanysuchmeta-formalisms.Presently,thisworkisdonebyhumanswithintuitionandinterpretationsintheirminds.Icannotseeanypresentlyexisting(meta-)theoryormachinewhichwouldbecapableoftakingawaythatselectionchallengeandburdenfromthescientist.ThereissomuchcreativityrequiredinapplyingscientificresultsintopracticalusethatIhavenohighhopesforanyfastautomatedsolution.
Letmeconcludewithapartialanswertothequestionofthetitle,“Whatcouldbemorepracticalthanagoodinterpretation?”Iwouldarguethatproposalsofanewtheorywhichcanbedistin-guishedfromquantummechanicsandextendsitexperimentallywouldbemoreexcitingthananynewinterpretation.Likewise,anyunexplainedphenomenonwhichgivesahinttothinkaboutnewdirectionswouldbemostwelcomed.Atthemoment,Iamatalossofseeinganyoneofthesepos-sibilities(butmaybeitisjustmyignorancewhichpreventsmefromdoingthis).Inthemeantime,letusbetoleranttoallthoseweirdinterpretationsofquantummechanicsoutthere,sincetheyaretheguaranteeforavividandabundantscientificresearch.Indoingthis,oneshouldnotacceptclaimsofabsolutetruthofanyparticularinterpretationfortworeasons:nointerpretationcanbedistinguishedfromotherinterpretationsbyoperationalizablemeans,anditmaybejustascaffold-ing,afterall!Ireadilyacknowledgethatanytrickeryquantumtalkmaydegeneratetofruitlessspeculations.Yet,inviewofthemindboggling[7],incomprehensiveness[3,p.129]ofquantummechanics,anyoutrightnegationofinterpretationmayamounttoamistakementionedalreadyinDemocritusofAbdera’sfragments(translatedbyCyrilBailey[12]citedbyErwinSchr¨odinger[13,p.87]),inwhichthesenses,whenattackedbyreason,say,“···fromusyouaretakingthe
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evidencebywhichyouwouldoverthrowus?Yourvictoryisyourfall.”
[1]C.A.FuchsandA.Peres,PhysiccsToday53,70(2000),furtherdiscussionsofand
reactionstothearticlecanbefoundintheSeptemberissueofPhysiccsToday,53,11-14(2000),URLhttp://www.aip.org/web2/aiphome/pt/vol-53/iss-9/p11.htmlandhttp://www.aip.org/web2/aiphome/pt/vol-53/iss-9/p14.html.[2]J.Clauser(2000),talkat‘Quantum[Un]Speakables,ConferenceinthecommemmorationofJohnS.
Bell,Nov.10th,10.00-10.40,URLhttp://www.quantum.at/programs/Bell.htm.[3]R.P.Feynman,TheCharacterofPhysicalLaw(MITPress,Cambridge,MA,1965).
[4]I.Lakatos,PhilosophicalPapers.1.TheMethodologyofScientificResearchProgrammes(Cambridge
UniversityPress,Cambridge,1978).
[5]K.Svozil,FoundationsofPhysics32,479(2002),e-printarXiv:quant-ph/0110054.[6]A.Zeilinger,FoundationsofPhysics29,631(1999).
[7]D.M.Greenberger,M.A.Horne,andA.Zeilinger,PhysicsToday46,22(1993).[8]P.A.M.Dirac,Nature168,906(1951).
[9]J.S.Bell,PhysicsWorld5,31(1992),abridgedversionbyDenisWeaire.
¨[10]A.Einstein,AtherundRelativit¨atstheorie.Redegehaltenam5.Mai1920anderReichs-Universit¨at
Leiden(Springer,Berlin,1920).
[11]D.M.Greenberger,inMillenniumIII,editedbyC.CaludeandK.Svozil(BlackSeaUniversityFoun-dationincolaborationwiththeRomanianAcademyofSciences,Bucharest,Romania,2002),pp.141–145.
[12]C.Bailey,TheGreekAtomistsandEpicurus(OxfordUniversityPress,Oxford,1928).[13]E.Schr¨odinger,NatureandtheGreeks(CambridgeUniversityPress,Cambridge,1954).
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