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OntheMethodofTheoreticalPhysicsAuthor(s):AlbertEinsteinSource:PhilosophyofScience,Vol.1,No.2,(Apr.,1934),pp.163-169Publishedby:TheUniversityofChicagoPressonbehalfofthePhilosophyofScienceAssociationStableURL:http://www.jstor.org/stable/184387Accessed:08/05/200812:51YouruseoftheJSTORarchiveindicatesyouracceptanceofJSTOR'sTermsandConditionsofUse,availableathttp://www.jstor.org/page/info/about/policies/terms.jsp.JSTOR'sTermsandConditionsofUseprovides,inpart,thatunlessyouhaveobtainedpriorpermission,youmaynotdownloadanentireissueofajournalormultiplecopiesofarticles,andyoumayusecontentintheJSTORarchiveonlyforyourpersonal,non-commercialuse.Pleasecontactthepublisherregardinganyfurtheruseofthiswork.Publishercontactinformationmaybeobtainedathttp://www.jstor.org/action/showPublisher?publisherCode=ucpress.EachcopyofanypartofaJSTORtransmissionmustcontainthesamecopyrightnoticethatappearsonthescreenorprintedpageofsuchtransmission.JSTORisanot-for-profitorganizationfoundedin1995tobuildtrusteddigitalarchivesforscholarship.Weenablethescholarlycommunitytopreservetheirworkandthematerialstheyrelyupon,andtobuildacommonresearchplatformthatpromotesthediscoveryanduseoftheseresources.FormoreinformationaboutJSTOR,pleasecontactsupport@jstor.org.http://www.jstor.org OntheMethodofTheoreticalPhysics*BYALBERTEINSTEIN'FYOUwishtolearnfromthetheoreticalphysi-cistanythingaboutthemethodswhichheuses,wouldgiveyouthefollowingpieceofadvice:~5'KIDon'tlistentohiswords,examinehisachieve-ments.Fortothediscovererinthatfield,theconstructionsofhisimaginationappearsonecessaryandsonaturalthatheisapttotreatthemnotasthecreationsofhisthoughtsbutasgivenrealities.Thisstatementmayseemtobedesignedtodrivemyaudienceawaywithoutmoreado.Foryouwillsaytoyourselves,'Thelecturerishimselfaconstructivephysicist;onhisownshowingthereforeheshouldleavetheconsiderationofthestructureoftheoreticalsciencetotheepistemologist'.SofarasIpersonallyamconcerned,Icandefendmyselfagainstanobjectionofthissortbyassuringyouthatitwasnosuggestionofminebutthegenerousinvitationofotherswhichhasplacedmeonthisdais,whichcommemoratesamanwhospenthislifeinstrivingfortheunificationofknowledge.Butevenapartfromthat,Ihavethisjustificationformypains,thatitmaypossiblyinterestyoutoknowhowamanthinksabouthisscienceafterhavingdevotedsomuchtimeandenergytotheclarificationandreformofitsprinciples.*TheHerbertSpencerLecture,deliveredatOxford,JuneIo,I933.ReprintedbypermissionoftheOxfordUniversityPress,NewYork,Inc.163 164TheoreticalPhysicsOfcoursehisviewofthepastandpresenthistoryofhissubjectislikelytobeundulyinfluencedbywhatheexpectsfromthefutureandwhatheistryingtorealizeto-day.Butthisisthecommonfateofallwhohaveadoptedaworldofideasastheirdwelling-place.Heisinjustthesameplightasthehistorian,whoalso,eventhoughunconsciously,disposeseventsofthepastaroundidealsthathehasformedabouthumansociety.Iwantnowtoglanceforamomentatthedevelopmentofthetheoreticalmethod,andwhiledoingsoespeciallytoobservetherelationofpuretheorytothetotalityofthedataofexperience.Hereistheeternalantithesisofthetwoinseparableconstituentsofhumanknowledge,ExperienceandReason,withinthesphereofphysics.WehonourancientGreeceasthecradleofwesternscience.Sheforthefirsttimecreatedtheintellectualmiracleofalogicalsystem,theassertionsofwhichfollowedonefromanotherwithsuchrigorthatnotoneofthedemonstratedpropositionsadmittedoftheslightestdoubt-Euclid'sgeometry.Thismar-vellousaccomplishmentofreasongavetothehumanspirittheconfidenceitneededforitsfutureachievements.Themanwhowasnotenthralledinyouthbythisworkwasnotborntobeascientifictheorist.Butyetthetimewasnotripeforasciencethatcouldcomprehendreality,wasnotripeuntilasecondele-mentarytruthhadbeenrealized,whichonlybecamethecommonpropertyofphilosophersafterKeplerandGalileo.Purelogicalthinkingcangiveusnoknowledgewhatsoeveroftheworldofexperience;allknowledgeaboutrealitybeginswithexperienceandterminatesinit.Conclusionsobtainedbypurelyrationalprocessesare,sofarasRealityisconcerned,entirelyempty.Itwasbecauseherecognizedthis,andespeciallybecauseheimpressedituponthescientificworldthatGalileobecamethefatherofmodernphysicsandinfactofthewholeofmodernnaturalscience.Butifexperienceisthebeginningandendofallourknowledgeaboutreality,whatroleisthereleftforreasoninscience?Acompletesystemoftheoreticalphysicsconsistsofconceptsandbasiclawstointerrelatethoseconceptsandofconsequencesto AlbertEinsteinI65bederivedbylogicaldeduction.Itistheseconsequencestowhichourparticularexperiencesaretocorrespond,anditisthelogicalderivationofthemwhichinapurelytheoreticalworkoccupiesbyfarthegreaterpartofthebook.ThisisreallyexactlyanalogoustoEuclideangeometry,exceptthatinthelatterthebasiclawsarecalled'axioms';and,further,thatinthisfieldthereisnoquestionoftheconsequenceshavingtocorrespondwithanyexperiences.ButifweconceiveEuclideangeometryasthescienceofthepossibilitiesoftherelativeplacingofactualrigidbodiesandaccordinglyinterpretitasaphysicalscience,anddonotabstractfromitsoriginalempiricalcontent,thelogicalparallelismofgeometryandtheoreticalphysicsiscomplete.Wehavenowassignedtoreasonandexperiencetheirplacewithinthesystemoftheoreticalphysics.Reasongivesthestructuretothesystem;thedataofexperienceandtheirmutualrelationsaretocorrespondexactlytoconsequencesinthetheory.Onthepossibilityaloneofsuchacorrespondencereststhevalueandthejustificationofthewholesystem,andespeciallyofitsfundamentalconceptsandbasiclaws.Butforthis,theselatterwouldsimplybefreeinventionsofthehumanmindwhichad-mitofnoapriorijustificationeitherthroughthenatureofthehumanmindorinanyotherwayatall.Thebasicconceptsandlawswhicharenotlogicallyfurtherreducibleconstitutetheindispensableandnotrationallydeduciblepartofthetheory.Itcanscarcelybedeniedthatthesupremegoalofalltheoryistomaketheirreduciblebasicelementsassimpleandasfewaspossiblewithouthavingtosurrendertheadequaterepresentationofasingledatumofexperience.Theconceptionhereoutlinedofthepurelyfictitiouscharacterofthebasicprinciplesoftheorywasintheeighteenthandnine-teenthcenturiesstillfarfrombeingtheprevailingone.Butitcontinuestogainmoreandmoregroundbecauseoftheever-wideninglogicalgapbetweenthebasicconceptsandlawsontheonesideandtheconsequencestobecorrelatedwithourexperi-encesontheother-agapwhichwidensprogressivelywiththedevelopingunificationofthelogicalstructure,thatiswiththereductioninthenumberofthelogicallyindependentconceptualelementsrequiredforthebasisofthewholesystem. 166TheoreticalPhysicsNewton,thefirstcreatorofacomprehensiveandworkablesystemoftheoreticalphysics,stillbelievedthatthebasicconceptsandlawsofhissystemcouldbederivedfromexperience;hisphrase'hypothesesnonfingo'canonlybeinterpretedinthissense.Infactatthattimeitseemedthattherewasnoproblem-aticalelementintheconcepts,SpaceandTime.Theconceptsofmass,acceleration,andforceandthelawsconnectingthem,appearedtobedirectlyborrowedfromexperience.Butifthisbasisisassumed,theexpressionfortheforceofgravityseemstobederivablefromexperience;andthesamederivabilitywastobeanticipatedfortheotherforces.OnecanseefromthewayheformulatedhisviewsthatNewtonfeltbynomeanscomfortableabouttheconceptofabsolutespace,whichembodiedthatofabsoluterest;forhewasalivetothefactthatnothinginexperienceseemedtocorrespondtothislatterconcept.Healsofeltuneasyabouttheintroductionofactionatadistance.Buttheenormouspracticalsuccessofhistheorymaywellhavepreventedhimandthephysicistsoftheeighteenthandnineteenthcenturiesfromrecognizingthefictitiouscharacteroftheprinciplesofhissystem.Onthecontrarythescientistsofthosetimeswereforthemostpartconvincedthatthebasicconceptsandlawsofphysicswerenotinalogicalsensefreeinventionsofthehumanmind,butratherthattheywerederivablebyabstraction,i.e.byalogicalprocess,fromexperiments.ItwasthegeneralTheoryofRela-tivitywhichshowedinaconvincingmannertheincorrectnessofthisview.Forthistheoryrevealedthatitwaspossibleforus,usingbasicprinciplesveryfarremovedfromthoseofNewton,todojusticetotheentirerangeofthedataofexperienceinamannerevenmorecompleteandsatisfactorythanwaspossiblewithNewton'sprinciples.Butquiteapartfromthequestionofcomparativemerits,thefictitiouscharacteroftheprinciplesismadequiteobviousbythefactthatitispossibletoexhibittwoessentiallydifferentbases,eachofwhichinitsconsequencesleadstoalargemeasureofagreementwithexperience.Thisindicatesthatanyattemptlogicallytoderivethebasicconceptsandlawsofmechanicsfromtheultimatedataofexperienceisdoomedtofailure. AlbertEinstein167Ifthenitisthecasethattheaxiomaticbasisoftheoreticalphysicscannotbeaninferencefromexperience,butmustbefreeinvention,haveweanyrighttohopethatweshallfindthecorrectway?Stillmore-doesthiscorrectapproachexistatall,saveinourimagination?Haveweanyrighttohopethatex-periencewillguideusaright,whentherearetheories(likeclassicalmechanics)whichagreewithexperiencetoaverygreatextent,evenwithoutcomprehendingthesubjectinitsdepths?TothisIanswerwithcompleteassurance,thatinmyopinionthereisthecorrectpathand,moreover,thatitisinourpowertofindit.OurexperienceuptodatejustifiesusinfeelingsurethatinNatureisactualizedtheidealofmathematicalsimplicity.ItismyconvictionthatpuremathematicalconstructionenablesustodiscovertheconceptsandthelawsconnectingthemwhichgiveusthekeytotheunderstandingofthephenomenaofNature.Experiencecanofcourseguideusinourchoiceofserviceablemathematicalconcepts;itcannotpossiblybethesourcefromwhichtheyarederived;experienceofcourseremainsthesolecriterionoftheserviceabilityofamathematicalconstructionforphysics,butthetrulycreativeprincipleresidesinmathematics.Inacertainsense,therefore,Iholdittobetruethatpurethoughtiscompetenttocomprehendthereal,astheancientsdreamed.Tojustifythisconfidenceofmine,Imustnecessarilyavailmyselfofmathematicalconcepts.Thephysicalworldisrepre-sentedasafour-dimensionalcontinuum.IfinthisIadoptaRiemannianmetric,andlookforthesimplestlawswhichsuchametriccansatisfy,Iarriveattherelativisticgravitation-theoryofemptyspace.IfIadoptinthisspaceavector-field,orinotherwords,theantisymmetricaltensor-fieldderivedfromit,andifIlookforthesimplestlawswhichsuchafieldcansatisfy,IarriveattheMaxwellequationsforfreespace.Havingreachedthispointwehavestilltoseekatheoryforthosepartsofspaceinwhichtheelectricaldensitydoesnotvan-ish.DeBrogliesurmisedtheexistenceofawave-field,whichcouldbeusedtoexplaincertainquantumpropertiesofmatter.Diracfoundinthe'spinor-field'quantitiesofanewkind,whosesimplestequationsmakeitpossibletodeduceagreatmanyofthepropertiesoftheelectron,includingitsquantumproperties.I i68TheoreticalPhysicsandmycolleaguediscoveredthatthese'spinors'constituteaspecialcaseofafieldofanewsortwhichismathematicallycon-nectedwiththemetricalcontinuumoffourdimensions,anditseemsthattheyarenaturallyfittedtodescribeimportantprop-ertiesoftheelectricalelementaryparticles.Itisessentialforourpointofviewthatwecanarriveattheseconstructionsandthelawsrelatingthemonewithanotherbyadheringtotheprincipleofsearchingforthemathematicallysimplestconceptsandtheirconnections.Inthepaucityofthemathematicallyexistentsimplefield-typesandoftherelationsbetweenthem,liesthejustificationforthetheorist'shopethathemaycomprehendrealityinitsdepths.Themostdifficultpointforsuchafield-theoryatpresentishowtoincludetheatomicstructureofmatterandenergy.Forthetheoryinitsbasicprinciplesisnotanatomiconeinsofarasitoperatesexclusivelywithcontinuousfunctionsofspace,incontrasttoclassicalmechanicswhosemostimportantfeature,thematerialpoint,squareswiththeatomisticstructureofmatter.Themodernquantumtheory,asassociatedwiththenamesofdeBroglie,Schr6dinger,andDirac,whichofcourseoperateswithcontinuousfunctions,hasovercomethisdifficultybymeansofadaringinterpretation,firstgiveninaclearformbyMaxBorn:-thespacefunctionswhichappearintheequationsmakenoclaimtobeamathematicalmodelofatomicobjects.Thesefunctionsareonlysupposedtodetermineinamathematicalwaytheprobabilitiesofencounteringthoseobjectsinaparticularplaceorinaparticularstateofmotion,ifwemakeameasure-ment.Thisconceptionislogicallyunexceptionable,andhasledtoimportantsuccesses.Butunfortunatelyitforcesustoemployacontinuumofwhichthenumberofdimensionsisnotthatofpreviousphysics,namely4,butwhichhasdimensionsincreasingwithoutlimitasthenumberoftheparticlesconsti-tutingthesystemunderexaminationincreases.IcannothelpconfessingthatImyselfaccordtothisinterpretationnomorethanatransitorysignificance.Istillbelieveinthepossibilityofgivingamodelofreality,atheory,thatistosay,whichshallrepresenteventsthemselvesandnotmerelytheprobabilityof AlbertEinstein169theiroccurrence.Ontheotherhand,itseemstomecertainthatwehavetogiveupthenotionofanabsolutelocalizationoftheparticlesinatheoreticalmodel.ThisseemstometobethecorrecttheoreticalinterpretationofHeisenberg'sindeterminacyrelation.Andyetatheorymayperfectlywellexist,whichisinagenuinesenseanatomisticone(andnotmerelyonthebasisofaparticularinterpretation),inwhichthereisnolocalizingoftheparticlesinamathematicalmodel.Forexample,inordertoincludetheatomisticcharacterofelectricity,thefieldequationsonlyneedtoinvolvethatathree-dimensionalvolumeofspaceonwhoseboundarytheelectricaldensityvanisheseverywhere,containsatotalelectricalchargeofanintegralamount.Thusinacontinuumtheory,theatomisticcharactercouldbesatisfac-torilyexpressedbyintegralpropositionswithoutlocalizingtheparticleswhichconstitutetheatomisticsystem.OnlyifthissortofrepresentationoftheatomisticstructurebeobtainedcouldIregardthequantumproblemwithintheframe-workofacontinuumtheoryassolved.
