ALSOBYLEESMOLIN

TheSingularUniverseandtheRealityofTime(withRobertoMangabeiraUnger)

TimeReborn

TheTroublewithPhysics

ThreeRoadstoQuantumGravity

TheLifeoftheCosmos

PENGUINPRESSAnimprintofPenguinRandomHouseLLC

penguinrandomhouse.com

Copyright©2019byLeeSmolinIllustrationscopyright©2019byKaćaBradonjić

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LibraryofCongressCataloging-in-PublicationData

Names:Smolin,Lee,1955-author.|Bradonjic,Kaca,illustrator.Title:Einstein’sunfinishedrevolution:thesearchforwhatliesbeyondthequantum/LeeSmolin;illustrationsbyKaca

Bradonjic.Description:NewYork:PenguinPress,2019.|Includesbibliographicalreferencesandindex.

Identifiers:LCCN2018045679(print)|LCCN2018060769(ebook)|ISBN9780698169135(ebook)|ISBN9781594206191(hardcover)

Subjects:LCSH:Quantumtheory.|Physics--Research.Classification:LCCQC174.13(ebook)|LCCQC174.13.S65452019(print)|DDC530.12--dc23

LCrecordavailableathttps://lccn.loc.gov/2018045679

Version_2

ForDinaandKai

Allamusiciancandoistogetclosertothesourcesofnature,andsofeelthatheisincommunionwiththenaturallaws.

—JOHNCOLTRANE

Icansafelysaythatnobodyunderstandsquantummechanics.

—RICHARDFEYNMAN

Contents

AlsobyLeeSmolinTitlePageCopyrightDedicationEpigraphPreface

PART1.ANORTHODOXYOFTHEUNREALONENatureLovestoHideTWOQuantaTHREEHowQuantaChangeFOURHowQuantaShareFIVEWhatQuantumMechanicsDoesn’tExplainSIXTheTriumphofAnti-Realism

PART2.REALISMREBORNSEVENTheChallengeofRealism:deBroglieandEinsteinEIGHTBohm:RealismTriesAgainNINEPhysicalCollapseoftheQuantumStateTENMagicalRealismELEVENCriticalRealism

PART3.BEYONDTHEQUANTUMTWELVEAlternativestoRevolution

THIRTEENLessonsFOURTEENFirst,PrinciplesFIFTEENACausalTheoryofViewsEpilogue/Revolutions:NotetoSelf

AcknowledgmentsNotesGlossaryFurtherReadingIndexAbouttheAuthor

WPreface

ehumanbeingshavealwayshadaproblemwiththeboundarybetweenrealityandfantasy.Toexplaintheworldtoourselveswemakeupstoriesandthen,becausewearegoodstorytellers,

wegetinfatuatedbythemandconfuseourrepresentationsoftheworldwiththeworlditself.Thisconfusionafflictsscientistsasmuchaslaypeople;indeed,itaffectsusmore,becausewehavesuchpowerfulstoriesinourtoolkits.

Aswegodeeperintoourunderstandingofthenaturalworld,movingtosmallerandmoreelementaryphenomena,oursuccessesimposebarrierstofurtherprogress.Toavoidgettingstuck,wemustbalanceourwell-justifiedconfidenceinthepowerofestablishedknowledgewithanacuteconsciousnessofjusthowhypotheticalevenourmostsuccessfulhypothesesare.Ahardlessontolearnisthatoursensationsarepartlycausedbyreality,butarefullyconstructedbyourbrainstopresenttheworldtousinjusttheformweneedtomakeourwayinnature.Beyondthosesensations,naturehovers,fundamentallymysteriousandjustattheedgeofwhatwecanknow.

Themostimportantfeaturesofnature,asweunderstandthemnow,werenotperceived.Thesimplestgeneralfactsweknowabouttheworld—thatmatterismadeofatoms,forexample,orthattheEarthisasphericalshellofrocksurroundingamoltencoreandenvelopedwithinathinatmosphere,whichmoves,suspendedinanearvacuum,asitorbitsanaturalthermonuclearreactor—theseplainfactswelearnjustoutofourcribsaretheresultofcenturiesofintenseeffortbyscholarsandscientists.Eachofthesefactsaroseasanalmostcrazyideainconflictwithamuchmoreobviousandreasonable—butwrong—hypothesis.

Tohaveascientificmindistorespecttheconsensusfacts,whicharetheresolutionofgenerationsofdispute,whilemaintaininganopenmind

aboutthestillunknown.Ithelpstohaveahumblesenseoftheessentialmysteryoftheworld,fortheaspectsthatareknownbecomeevenmoremysteriouswhenweexaminethemfurther.Themoreweknow,themorecuriousitallis.Thereisnotathinginnaturesoordinarythatitscontemplationcannotbearoutetoawordlesssenseofwonderandgratitudejusttobeapartofitall.

Thisspringmorningtheaircomingthroughtheopenwindowcarriesfreshsmellsfromthegarden—butbywhatmiracledoesthathappen?Howaremoleculeswaftedbyabreezeturnedbyanoseintothathappyscent?Weseevividcolors,andwerecallthatthereisastoryabouthowdifferentwavelengthsoflightexcitedifferentneurons.Buthowcouldthesensationsofrednessorbluenesspossiblybecausedbydifferentneuronsbeingexcited?Whatkindsofthingsarethesensations,thequalia,asthephilosopherscallthem,ofthedifferentcolors,orthedifferentscents?Inwhatwayarescentsdifferentfromcolors,andwhydotheydiffer,ifitisallelectricalimpulsesinneurons?WhoistheIthatwakesandwhatistheuniversethatsurroundsmewhenIopenmyeyes?Thesimplestfactsaboutourexistenceandourrelationshiptotheworldaremysteries.

Letustiptoepastthehardquestionofconsciousnesstosimplerquestions.Asascientist,Ibelievethatisthebestwaytogetsomewhere.Let’sstartwithoneverybasicquestion:Whatismatter?Mysonhasleftarockonthetable.Ipickitup;itsweightandshapefitcomfortablyinmyhand—surelyanancientfeeling.

Butwhatisarock?Weknowwhattherocklookslike,whatitfeelslike.Buttheseareat

leastasmuchaboutusastheyareabouttherock.Littleinarock’sfeelorappearancegivesahintastowhat,essentially,constitutestheexistence—therockness—ofarock.Weknowmostoftherockisemptyspaceinwhichatomsarearranged.Thesolidityandhardnessoftherockisaconstructionofourminds,whichintegrateperceptionsonscalesverycoarsecomparedtothesizesoftheatoms.

Mattercomesinmanyforms,someofwhich,liketherock,liketheorganicmaterialwovenintoourblankets,sheets,andclothes,weknowmustbecomplex.Solet’sconsiderfirstasimplerformofmatter:thewaterinourglass.Whatisit?

Tooureyesandtoourtouch,waterappearstobesmooth,continuous.Untilrelativelyrecently,abitmorethanacenturyago,physiciststhought

thatmatterwasentirelycontinuous.Earlyinthetwentiethcentury,AlbertEinsteinshowedthatwaswrongandthatwaterismadeofmyriadatoms.Inwater,theseareorganizedintotriplets,boundtogetherintomolecules,eachconsistingoftwohydrogenandanoxygen.

Yes,butwhatisanatom?IttooklessthanadecadeafterEinsteinforittobeunderstoodthateachatomislikeatinysolarsystem,withanucleusinthecenterinplaceoftheSunandtheplanetsrepresentedbyelectrons.

Sofarsogood,butthenwhatisanelectron?Weknowthatelectronscomeindiscreteunits,eachonecarryingacertainquantityofmassandcharge.Anelectroncanhavealocationinspace.Itcanmove:whenwefirstlookitishere;whenwelookagainitisthere.

Beyondthoseattributesitisnoteasytogiveapictureofwhatanelectronis.Itwilltakemuchofthisbook.

Thebestunderstandingofwhatrocksare,whatwateris,whatmoleculesandatomsandelectronsare,isexpressedbythebranchofsciencecalledquantumphysics.But,asitseemseveryoneknowsbynow,thatisarealmfullofparadoxandmystery.Quantumphysicsdescribesaworldinwhichnothinghasastableexistence:anatomoranelectronmaybeawaveoraparticle,dependingonhowyoulookatit;catsarebothaliveanddead.Thisisgreatforpopularculture,whichhasmade“quantum”abuzzwordforcool,geekmystification.Butit’sterribleforthoseofuswhowanttounderstandtheworldwelivein,forthereseemstobenoeasyanswertothesimplequestion,“Whatisarock?”

Inthefirstquarterofthetwentiethcenturyatheorycalledquantummechanicswasdevelopedtoexplainquantumphysics.Thistheoryhasbeen,eversinceitsinception,thegoldenchildofscience.Itisthebasisofourunderstandingofatoms,radiation,andsomuchelse,fromtheelementaryparticlesandbasicforcestothebehaviorofmaterials.Italsohasbeen,forjustaslong,atroubledchild.Fromthebeginning,itsinventorsweredeeplysplitoverwhattomakeofit.Someexpressedshockandmisgivings,evenoutrage.Othersdeclareditarevolutionarynewkindofscience,whichshatteredthemetaphysicalassumptionsaboutnatureandourrelationshiptoitthatpreviousgenerationshadthoughtessentialforthesuccessofscience.

InthesechaptersIhopetoconvinceyouthattheconceptualproblemsandragingdisagreementsthathavebedeviledquantummechanicssince

itsinceptionareunsolvedandunsolvable,forthesimplereasonthatthetheoryiswrong.Itishighlysuccessful,butincomplete.Ourtask—ifwearetohavesimpleanswerstooursimplequestionsaboutwhatrocksare—mustbetogobeyondquantummechanicstoadescriptionoftheworldonanatomicscalethatmakessense.

Thistaskmightseemoverwhelminglydifficult,wereitnotforonealmostforgottenandlong-ignoredaspectofthehistoryofquantummechanics.Sincetheverybeginningofthequantumera,inthe1920s,therehasbeenanalternativeversionofquantumphysicsthatdoesmakecompletesense.Thisshadowtheoryresolvestheapparentparadoxesandmysteriesofthequantumdomain.Thescandal—andIbelievethattermiswarranted—isthatthisalternativeformofquantumtheoryisrarelytaught.Itisseldommentioned,eitherintextbooksforbuddingphysicistsorinpopularizationsforlaypeople.

Thereareseveralalternativeformulationsofquantumphysicsthatmakeconsistentsense.Thechallengenowistobuildonthesetofindtherightwaytounderstandquantumphysics—theonethatnatureuses.Ibelievethiswillhavewiderepercussions,becausethenewformofquantumphysicswillbethebasisofthesolutionstomanyoftheoutstandingproblemsinphysics.Problemssuchasquantumgravityandtheunificationoftheforces,onwhichwehavemadelittledefinitiveprogress,are,Ibelieve,founderingbecauseatthefoundationsofourtheorizingisanincorrecttheory.

Physicistsagreeabouthowthequantumworldbehaves.Weagreethatatomsandradiationbehavedifferentlythanrocksandcats,andweagreethatquantummechanicsworkstopredictsomeaspectsofthatbehavior.Butwedon’tagreeaboutwhatitmeansthatourworldisaquantumworld.Itisclearthatsomeradicalchangeinourunderstandingofnatureisrequired,butwedisagreeastowhatthatchangeneedstobe.Somearguethatwemustgiveupholdinganypictureofrealityandsettleforatheorywhichdescribesonlytheknowledgewecanhaveoftheworld.Othersclaimthatournotionofrealitymustbevastlyextendedtoembraceaninfinitudeofparallelrealities.

Infact,neitherisnecessary.Thealternativewaysofunderstandingthequantumworlddonotrequireustogiveuptheideathatphysicsdescribesarealityindependentofourknowledgeofit.Nordotheyrequirethatweexpandthatrealitybeyondthecommonsensenotionthat

thereisoneworldanditiswhatweseewhenwelookaroundus.AsI’llexplaininthesepages,commonsenserealism,accordingtowhichsciencecanaspiretogiveacompletepictureofthenaturalworldasitis,orwouldbeinourabsence,isnotactuallythreatenedbyanythingweknowaboutquantumphysics.

Itisthusbothunfortunateandunnecessarythatthequantumrealmhasbeenpresentedasmysteriousandcounterintuitive.Oneoftheaimsofthisbookistopresentthealternativequantumtheoriestolaypeopleand,bydoingso,toliftthemysteryandpresentthequantumworldinawaythatisintuitiveandaccessibletopeoplewhoarenotspecialistsinphysics.

Iimaginemyreaderassomeonewithastrongcuriosityaboutnature,whomayfollowsciencethroughnews,blogs,andpopularbooks,butwhoseeducationhasnotincludedthemathematicsusuallyassumedasthelanguageofphysics.InsteadIusewordsandpicturestoconveythebasicphenomenawefindinthequantumworldaswellastheprinciplestheirstudyhasinspired.Afteranintroduction,thebookstartswiththreeshortchapterswhichdescribethebare-bonesbasicsofquantumphysics.Thesewillequipustoexplorethediverseconceptualuniverseswhicharisefromthedifferentformsofquantumtheorythathavebeenproposed.

—WHATISATSTAKEintheargumentoverquantummechanics?Whydoesitmatterifourfundamentaltheoryofthenaturalworldismysteriousandparadoxical?

Behindthecentury-longargumentoverquantummechanicsisafundamentaldisagreementaboutthenatureofreality—adisagreementwhich,unresolved,escalatesintoanargumentaboutthenatureofscience.

Twoquestionsunderlietheschism.Firstoff,doesthenaturalworldexistindependentlyofourminds?

Moreprecisely,doesmatterhaveastablesetofpropertiesinandofitself,withoutregardtoourperceptionsandknowledge?

Second,canthosepropertiesbecomprehendedanddescribedbyus?Canweunderstandenoughaboutthelawsofnaturetoexplainthehistoryofouruniverseandpredictitsfuture?

Theanswerswegivetothesetwoquestionshaveimplicationsforlargerquestionsaboutthenatureandaimofscience,andtheroleofscienceinthelargerhumanproject.Theseare,indeed,questionsabouttheboundarybetweenrealityandfantasy.

Peoplewhoansweryestothesetwoquestionsarecalledrealists.Einsteinwasarealist.Iamalsoarealist.Werealistsbelievethatthereisarealworldoutthere,whosepropertiesinnowaydependonourknowledgeorperceptionofit.Thisisnature—asitwouldbe,andmostlyis,inourabsence.Wealsobelievethattheworldmaybeunderstoodanddescribedpreciselyenoughtoexplainhowanysysteminthenaturalworldbehaves.

Ifyouarearealist,youbelievethatscienceisthesystematicsearchforthatexplanation.Thisisbasedonanaivenotionoftruth.Assertionsaboutobjectsorsystemsinnaturearetruetotheextentthattheycorrespondtogenuinepropertiesofnature.

Ifyouanswernotooneorbothofthesequestions,youareananti-realist.

Mostscientistsarerealistsabouteverydayobjectsonthehumanscale.Thingswecansee,pickup,andthrowaroundhavesimpleandeasilycomprehendedproperties.Theyexistateachmomentsomewhereinspace.Whentheymove,theyfollowatrajectory,andthattrajectoryhas,relativetosomeonedescribingthem,adefinitespeed.Theyhavemassandweight.

Whenwetellourpartnerthattherednotebooktheyarelookingforisonthetable,weexpectthatthisissimplytrueorfalse,absolutelyindependentofourknowledgeorperception.

Thedescriptionofmatteratthislevel,fromthesmallestscaleswecanseewithoureyesuptostarsandplanets,iscalledclassicalphysics.ItwasinventedbyGalileo,Kepler,andNewton.Einstein’stheoriesofrelativityareitscrowningachievements.

Butitisnoteasy,orobvious,forustoberealistsaboutmatteronthescaleofindividualatoms.Thisisbecauseofquantummechanics.

Quantummechanicsispresentlyourbesttheoryofnatureattheatomicscale.Thattheoryhas,asIhavealludedto,certainverypuzzlingfeatures.Itiswidelybelievedthatthosefeaturesprecluderealism.Thatis,quantummechanicsrequiresthatwesaynotooneorbothofthetwo

questionsIaskedabove.Totheextentthatquantummechanicsisthecorrectdescriptionofnature,weareforcedtogiveuprealism.

Mostphysicistsarenotrealistsaboutatoms,radiation,andelementaryparticles.Theirbelief,forthemostpart,doesnotstemfromadesiretorejectrealismonthebasisofradicalphilosophicalpositions.Instead,itisbecausetheyareconvincedquantummechanicsiscorrectandtheybelieve,astheyhavebeentaught,thatquantummechanicsprecludesrealism.

Ifitistruethatquantummechanicsrequiresthatwegiveuprealism,then,ifyouarearealist,youmustbelievethatquantummechanicsisfalse.Itmaybetemporarilysuccessful,butitcannotbethefullycorrectdescriptionofnatureatanatomicscale.ThisledEinsteintorejectquantummechanicsasanythingmorethanatemporaryexpedient.

Einsteinandotherrealistsbelievethatquantummechanicsgivesusanincompletedescriptionofnature,whichismissingfeaturesnecessaryforafullunderstandingoftheworld.Einsteinsometimesimaginedthattherewere“hiddenvariables”whichwouldcompletethedescriptionoftheworldgivenbyquantumtheory.Hebelievedthatthefulldescription,includingthosemissingfeatures,wouldbeconsistentwithrealism.

Thus,ifyouarearealistandaphysicist,thereisoneoverridingimperative,whichistogobeyondquantummechanicstodiscoverthosemissingfeaturesandusethatknowledgetoconstructatruetheoryoftheatoms.ThiswasEinstein’sunfinishedmission,anditismine.

—THEREAREDIFFERENTKINDSofanti-realists,whichleadstodifferentviewsonquantummechanics.

Someanti-realistsbelievethatthepropertiesweascribetoatomsandelementaryparticlesarenotinherentinthoseobjects,butarecreatedonlybyourinteractionswiththem,andexistonlyatthetimewhenwemeasurethem.Wecancalltheseradicalanti-realists.ThemostinfluentialofthesewasNielsBohr.Hewasthefirsttoapplyquantumtheorytotheatom,afterwhichhebecametheleaderandmentortothenextgenerationofquantumrevolutionaries.Hisradicalanti-realismcoloredmuchofhowquantumtheorycametobeunderstood.

Anothergroupofanti-realistsbelievesthatscience,asawhole,doesnotdealinortalkaboutwhatisrealinnature,butratheronlyevertalks

aboutourknowledgeoftheworld.Intheirview,thepropertiesphysicsascribestoanatomarenotaboutthatatom;theyareinsteadonlyabouttheknowledgewehaveoftheatom.Thesescientistscanbecalledquantumepistemologists.

Andthentherearetheoperationalists,agroupofanti-realistswhoareagnosticaboutwhetherthereisafundamentalrealityindependentofusornot.Quantummechanics,theyargue,isnotinanycaseaboutreality;itisratherasetofproceduresforinterrogatingatoms.Itisnotabouttheatomsthemselves;itisaboutwhathappenswhenatomscomeintocontactwiththebigdevicesweusetomeasurethem.Heisenberg,thebestofBohr’sprotégés,whoinventedtheequationsofquantummechanics,was,atleastpartly,anoperationalist.

Incontrasttothedisputesbetweenradicalanti-realists,quantumepistemologists,andoperationalists,allrealistsshareasimilarperspective—weagreeabouttheanswertobothquestionsIposedabove.Butwedifferonhowweanswerathirdquestion:Doesthenaturalworldconsistmainlyofthekindsofobjectsthatweseewhenwelookaroundourselves,andthethingsthatconstitutethem?Inotherwords,iswhatweseewhenwelookaroundtypicaloftheuniverseasawhole?

Thoseofuswhosayyestothisquestioncancallourselvessimpleornaiverealists.IshouldalertthereaderthatIusetheadjective“naive”tomeanstrong,fresh,uncomplicated.Forme,aviewisnaiveifitisnotinneedofsophisticatedargumentsorconvolutedjustifications.Iwouldarguethatanaiverealismis,wheneverpossible,tobepreferred.

Therearerealistswhoarenotnaiveinthissense.Theybelievethatrealityisvastlydifferentfromtheworldweperceiveandmeasure.

AnexampleofsuchaviewistheManyWorldsInterpretation,whichteachesthattheworldweperceiveisonlyoneofavastandever-growingnumberofparallelworlds.Itsproponentscallthemselvesrealists,andtheyhavesomeclaimtothatdesignationbyvirtueoftheiransweringyestothefirsttwoquestions.But,inmyopinion,theyarerealistsonlyinthemosttechnical,academicsense.Theymayperhapsbecalledmagicalrealists,fortheybelievethatwhatisrealisfarbeyondtheworldweperceive.Magicalrealisminthissenseisalmostaformofmysticism,foritimpliesthatthetrueworldishiddenfromourperception.

Isitpossibletoformulateatheoryofatomsthatisrealistinthemostgeneralandnaivesense,andsoanswersyestoallthreequestions?Itis,

andthatisthestoryIwanttotellinthisbook.Butthattheoryisnotquantummechanics,andifitisright,thenquantummechanicsiswrong,inthesensethatquantummechanicsmustthengiveaveryincompletedescriptionofnature.

PartofthestoryIwanttotellhereishowthisnaivelyrealistictheoryofnaturewaspushedaside,whileatheorythatrequiredustoembraceeitheranti-realismormysticismthrived.ButIwillendonahopefulnote,bysketchingawaywemayprogresstoarealistviewofnaturethatencompassesthequantum.

—THISALLMATTERSbecausescienceisunderattackintheearlytwenty-firstcentury.Scienceisunderattack,andwithitthebeliefinarealworldinwhichfactsareeithertrueorfalse.Quiteliterally,partsofoursocietyappeartobelosingtheirgripontheboundarybetweenrealityandfantasy.

Scienceisunderattackfromthosewhofinditsconclusionsinconvenientfortheirpoliticalandbusinessobjectives.Climatechangeshouldnotbeapoliticalissue;itisnotamatterofideology,butanissueofnationalsecurity,andshouldbetreatedassuch.Itisarealproblem,whichwillrequireevidence-basedsolutions.ScienceisalsounderattackfromreligiousfundamentalistswhoinsistancienttextsaretheteachingsofunchangingtruthsbyGod.

Inmyview,thereislittlereasonforconflictbetweenmostreligionsandscience.Manyreligionsaccept—andevencelebrate—scienceasthewaytoknowledgeaboutthenaturalworld.Beyondthat,thereismysteryenoughintheexistenceandmeaningoftheworld,whichbothscienceandreligioncaninspireustodiscuss,butneithercanresolve.

Allthatisrequiredisthatreligionsnotattackorseektounderminethosescientificdiscoverieswhichareconsideredtobeestablishedknowledgebecausetheyaresupportedbyoverwhelmingevidence,asjudgedbythoseeducatedsufficientlytoevaluatetheirvalidity.Thisisindeedtheviewofmanyreligiousleadersfromallfaiths.Inreturn,scientistsshouldviewtheseenlightenedleadersasalliesintheworkforabetterworld.

Inaddition,scienceisunderattackfromafashionamongsomehumanistacademics—whoshouldknowbetter—whoholdthatscienceis

nomorethanasocialconstructionthatyieldsonlyoneofanarrayofequallyvalidperspectives.

Forsciencetorespondclearlyandstronglytothesechallenges,itmustitselfbeuncorruptedbyitsownpractitioners’mysticalyearningsandmetaphysicalagendas.Individualscientistsmaybe—and,let’sfaceit,sometimesare—motivatedbymysticalfeelingsandmetaphysicalpreconceptions.Thisdoesn’thurtscienceaslongasthenarrowcriteriathatdistinguishhypothesisandhunchfromestablishedtruthareuniversallyunderstoodandadheredto.

Butwhenfundamentalphysicsitselfgetshijackedbyananti-realistphilosophy,weareindanger.Weriskgivinguponthecenturies-oldprojectofrealism,whichisnothinglessthanthecontinualadjustment,bitbybitasknowledgeprogresses,oftheboundarybetweenourknowledgeofrealityandtherealmoffantasy.

Onedangerofanti-realismistothepracticeofphysicsitself.Anti-realismlowersourambitionforatotallyclearunderstandingofnature,andhenceweakensourstandardsastowhatconstitutesanunderstandingofaphysicalsystem.

Inthewakeofthetriumphofanti-realismabouttheatomicworld,wehavehadtocontendwithanti-realistspeculationsaboutnatureonthelargestpossiblescale.Avocalminorityofcosmologistsproclaimsthattheuniverseweseearoundusisonlyabubbleinavastoceancalledthemultiversethatcontainsaninfinityofotherbubbles.And,whereasitissafetohypothesizethatthegalaxieswecanseearetypicaloftherestofouruniverse,onemustregardtheotherinvisiblebubblesasgovernedbydiverseandrandomlyassignedlaws,soouruniverseisfarfromtypicalofthewhole.This,togetherwiththefactthatall,oralmostall,oftheotherbubblesareforeveroutofrangeofourobservations,meansthemultiversehypothesiscanneverbetestedorfalsified.Thisputsthisfantasyoutsidetheboundsofscience.Nonetheless,thisideaischampionedbynotafewhighlyregardedphysicistsandmathematicians.

ItwouldbeamistaketoconfusethismultiversefantasyfortheManyWorldsInterpretationofquantummechanics.Theyaredistinctideas.Nonetheless,theyshareamagical-realistsubversionoftheaimofsciencetoexplaintheworldweseearoundusintermsofonlyitself.Iwouldsuggestthattheharmdonetoclarityabouttheaimandpurposeofsciencebytheenthusiasticproponentsofthemultiversewouldnothave

beenpossiblehadnotthemajorityofphysicistsuncriticallyadoptedanti-realistversionsofquantumphysics.

Certainly,quantummechanicsexplainsmanyaspectsofnature,anditdoessowithsupremeelegance.Physicistshavedevelopedaverypowerfultoolkitforexplainingdiversephenomenaintermsofquantummechanics,sowhenyoumasterquantummechanicsyoucontrolalotaboutnature.Atthesametime,physicistsarealwaysdancingaroundthegapingholesthatquantummechanicsleavesinourunderstandingofnature.Thetheoryfailstoprovideapictureofwhatisgoingoninindividualprocesses,anditoftenfailstoexplainwhyanexperimentturnsoutonewayratherthananother.

Thesegapsandfailuresmatterbecausetheyunderliethefactthatwehavegottenonlypartwaytowardsolvingthecentralproblemsinsciencebeforeseemingtorunoutofsteam.Ibelievethatwehavenotyetsucceededinunifyingquantumtheorywithgravityandspacetime(whichiswhatwemeanbyquantizinggravity),orinunifyingtheinteractions,becausewehavebeenworkingwithanincompleteandincorrectquantumtheory.

ButIsuspectthattheimplicationsofbuildingscienceonincorrectfoundationsgofurtheranddeeper.Thetrustinscienceasamethodtoresolvedisagreementsandlocatetruthisunderminedwhenaradicalstrandofanti-realismflourishesatthefoundationsofscience.Whenthosewhosetthestandardforwhatconstitutesexplanationareseducedbyavirulentmysticism,theresultingconfusionisfeltthroughouttheculture.

—IWASPRIVILEGEDtomeetafewofthesecondgenerationofthefoundersoftwentieth-centuryphysics.OneofthemostcontradictorywasJohnArchibaldWheeler.Anucleartheoristandamystic,hetransmittedthelegaciesofAlbertEinsteinandNielsBohrtomygenerationthroughthestorieshetoldusofhisfriendshipswiththem.Wheelerwasacommittedcoldwarriorwhoworkedonthehydrogenbombevenashepioneeredthestudyofquantumuniversesandblackholes.HewasalsoagreatmentorwhocountedamonghisstudentsRichardFeynman,HughEverett,andseveralofthepioneersofquantumgravity.Andhemighthavebeenmymentor,hadIhadbetterjudgment.

AtruestudentofBohr,Wheelerspokeinriddlesandparadoxes.HisblackboardwasunlikeanyI’deverencountered.Ithadnoequations,andonlyafewelegantlywrittenaphorisms,eachsetoutinabox,distillingalifetimeofseekingthereasonwhyourworldisaquantumuniverse.Atypicalexamplewas“Itfrombit.”(Yes,readitagain—slowly!Wheelerwasanearlyadopterofthecurrentfashiontoregardtheworldasconstitutedofinformation,sothatinformationismorefundamentalthanwhatitdescribes.Thisisaformofanti-realismwewilldiscusslater.)Hereisanother:“Nophenomenonisarealphenomenonuntilitisanobservedphenomenon.”HereisthekindofconversationonehadwithWheeler:Heaskedme,“SupposewhenyoudieandgoupbeforeSaintPeterforyourfinal,finalexam,heasksyoujustonequestion:‘Whythequantum?’”(I.e.,whydoweliveinaworlddescribedbyquantummechanics?)“Whatwillyousaytohim?”

Muchofmylifehasbeenspentsearchingforasatisfyinganswertothatquestion.AsIwritethesepages,Ifindmyselfvividlyrecallingmyfirstencounterswithquantumphysics.WhenIwasaseventeen-year-oldhighschooldropout,IusedtobrowsetheshelvesattheUniversityofCincinnatiPhysicsLibrary.ThereIcameuponabookwithachapterbyLouisdeBroglie(wewillmeethiminchapter7),whowasthefirsttoproposethatelectronsarewavesaswellasparticles.Thatchapterintroducedhispilotwavetheory,whichwasthefirstrealistformulationofquantummechanics.ItwasinFrench,alanguageIreadfitfullyaftertwoyearsofhighschoolstudy,butIrecallwellmyexcitementasIunderstoodthebasics.Istillcanclosemyeyesandseeapageofthebook,displayingtheequationthatrelateswavelengthtomomentum.

MyfirstactualcourseinquantummechanicswasthenextspringatHampshireCollege.Thatcourse,taughtbyHerbertBernstein,endedwithapresentationofthefundamentaltheoremofJohnBell,1which,inbrief,demonstratesthatthequantumworldfitsuneasilyintospace.IvividlyrecallthatwhenIunderstoodtheproofofthetheorem,Iwentoutsideinthewarmafternoonandsatonthestepsofthecollegelibrary,stunned.IpulledoutanotebookandimmediatelywroteapoemtoagirlIhadacrushon,inwhichItoldherthateachtimewetouchedtherewereelectronsinourhandswhichfromthenonwouldbeentangledwitheachother.Inolongerrecallwhoshewasorwhatshemadeofmypoem,orifIevenshowedittoher.Butmyobsessionwithpenetratingthemysteryof

nonlocalentanglement,whichbeganthatday,hasneverleftme;norhasmyurgencytomakebettersenseofthequantumdiminishedoverthedecadessince.Inmycareer,thepuzzlesofquantumphysicshavebeenthecentralmysterytowhichI’vereturnedagainandagain.Ihopeinthesepagestoinspireinyouasimilarfascination.

ThestoryItellinthisbookisshapedlikeaplayinthreeacts.Part1teachesthebasicconceptsofquantummechanicswewillneedwhiletracingthestoryofitsinvention.Themainthemehereisthetriumphoftheanti-realists,ledbyBohrandHeisenberg,overtherealists,whosechampionwasEinstein.PleasenotethatthestoryItellhereisjustasketch;therealhistoryisfarmorecomplex.Part2tracestherevivalofrealistapproachestoquantummechanics,beginninginthe1950s,andexplainstheirstrongandweakpoints.TheheroeshereareanAmericanphysicistnamedDavidBohmandanIrishtheorist,JohnBell.

Theconclusionofpart2willbethatrealistapproachesarepossible,andworkwellenoughtounderminetheclaimsthatquantumphysicsrequiresusalltobecomeanti-realists.Still,forme,noneoftheseapproacheshavetheringoftruth.Ibelievewecandobetter;indeed,forreasonsIwillexplain,Iwouldventurethatthecorrectcompletionofquantummechanicswillalsosolvetheproblemofquantumgravity,aswellasgiveusagoodcosmologicaltheory.Part3introducescontemporaryeffortstoconstructthisrealisttheoryofeverything,somemine,somebyothers.

—WELCOMETOTHEQUANTUMWORLD.Feelathome,foritisourworld,anditisourgoodfortunethatitsmysteriesremainforustosolve.

PART1

ANORTHODOXYOFTHEUNREAL

Q

ONE

NatureLovestoHideRealityisthebusinessofphysics.

—ALBERTEINSTEIN

uantummechanicshasbeenthecoreofourunderstandingofnatureforninedecades.Itisubiquitous,butitisalsodeeplymysterious.Littleofmodernsciencewouldmakesensewithoutit.

Butexpertshaveahardtimeagreeingwhatitassertsaboutnature.Quantummechanicsexplainswhythereareatoms,andwhythose

atomsarestableandhavedistinctchemicalproperties.Quantummechanicsalsoexplainshowatomscombineintodiversemolecules.Asaresult,itisthebasisforhowweunderstandtheshapesandinteractionsofthosemolecules.Lifewouldbeincomprehensiblewithoutthequantum.FromthebehaviorofwatertotheshapesofproteinstothefidelityandtransmittalofinformationbyDNAandRNA,everythinginbiologydependsonthequantum.

Quantummechanicsexplainsthepropertiesofmaterials,suchaswhatmakesametalaconductorofelectricity,whileanotherisaninsulator.Itexplainslightandradioactivity,andisthebasisofnuclearphysics.Withoutitwewouldn’tunderstandhowthestarsshine.Norcouldwehaveinventedthechipsorthelasersonwhichsomuchofourtechnologyisbased.Quantummechanicsisthelanguagethatweusetowritethestandardmodelofparticlephysics,whichcontainsallweknowabouttheelementaryparticlesandthefundamentalforcesbywhichtheyinteract.

Accordingtoourbesttheoryoftheearlyuniverse,allmatter,alongwiththepatternsthateventuallycoalescedintothegalaxies,wasyanked

intoexistencefromthequantumrandomnessofthevacuumofemptyspacebytherapidexpansionoftheuniverse.Idon’texpectthereadertounderstandpreciselywhatthismeans,butperhapsthewordsevokeanimage.Inanycase,ifthisisright,thenwithoutquantumphysicstherewouldliterallybenothingexceptemptyspacetime.

Yetforallitssuccess,thereisastubbornpuzzleattheheartofquantummechanics.Thequantumworldbehavesinwaysthatchallengeourintuition.Itisoftensaidthatinquantumphysicsanatomcanbeintwoplacesatonce,butthatisonlythestart;thefullstoryisfarweirderthanthat.Ifanatomcanbehereorthere,wemustspeakofstatesinwhichitis,somehow,simultaneouslybothhereandthere.Thisiscalledasuperposition.

Ifyouarenewtothequantumworld,youareundoubtedlywonderingwhatitmeansforanatomtobesomehowbothhereandthere.Don’tbediscouragedifyoufindthisconfusing.Youareabsolutelyrighttowonderwhatitmeans.Thisisoneofthecentralmysteriesofquantummechanics.Itisenough,fornow,ifyoujustacceptthisasamystery,towhichweattachtheterm“superposition.”Laterwewillbeabletodemystifyit.

Hereisafirststep.Whenwesaythataquantumparticleisina“superpositionofbeinghereandthere,”thisisrelatedtothewavelikenatureofmatter,forawaveisadisturbancethatisspreadout,andsoitcanbebothhereandthere.

Wespeakofelementaryparticles,buteverythingquantum,includingatomsandmolecules,isbothaparticleandawave.Hereisatasteofwhatthatmeans.Ifwedoanexperimentthataskswhereanatomis,theresultwillbethatitissomewheredefinite.Butbetweenmeasurements,whenwearenotlookingforit,itturnsouttobeimpossibletoprojectwhereitmightbe.Itisasifthelikelihoodorpropensityoffindingtheparticlespreadsasawavewhenwearenotlooking.Butassoonaswelookagain,itisalwayssomewhere.

Imagineplayingagameofhide-and-seekwithanatom.Weopenoureyes,orturnonadetector,andweseeitsomewhere.Butwhenwecloseoureyesitdissolvesintoawaveofpotentiality.Openoureyesagainanditisalwayssomewhere.

Anotherfeatureuniquetothequantumworldiscalledentanglement.Iftwoparticlesinteract,andthenmoveapart,theyremainintertwinedin

thesensethattheyseemtosharepropertieswhichcannotbebrokendowntopropertieseachenjoysindividually.

Wecanstretchourimaginationtoapplythesenewconceptstoatomsandmoleculeswhicharetoosmalltoseedirectly.Wemuststudythemindirectly,andtodothatweemploylargeandcomplexmeasurementdevices.

Thosemeasurementdevicesarepartoftheeveryday,familiarworldoflargeobjects.Onethingwecanbesureofisthatbigeverydaythingsdisplaynoneofthebizarrebehaviorquantummechanicsdescribes.Achairishereoritisthere,neverinacombinationofsuchstates.Whenwewakeupinthemiddleofthenightinastrangehotelroom,wemaybeunsurewherethechairis,butwecanbesureitissomewhere.Andafterwecollidewithitinthedark,ourfuturedoesnotbecomeentangledwithitsfuture.

Intheworldasweexperienceit,catsareeitheraliveordead,eveniftheyarelockedinabox.Whenweopenthebox,thecatdoesnotsuddenlyresolvefromacombinationofdeadandalivetodead.Ifwefinditdeaditwilllikelyhavebeensoforsometime,aswewillinstantlysmell.

Ordinaryobjectsappeartosharenoneofthequantumweirdnessesoftheatomsofwhichtheyaremade.Thisseemsobvious,butitraisesamystery.Quantummechanicsisthecoretheoryofnature.Assuchitmustbeuniversal.Ifitappliestoanatomitmustapplytotwoatoms,ortenorninety.Andwehaveexcellentexperimentalevidencethatitdoes.Delicateexperiments,inwhichlargemoleculesareputinquantumsuperpositions,showusthattheyarejustasquantumweirdaselectrons.Foronething,theydiffractandinterfereaswaves.

Butthenquantummechanicsmustapplytothevastcollectionsofatomsthatmakeupyouormeorourcatorthechaironwhichsheisperched.Butitdoesn’tseemto.Nordoesquantummechanicsappeartoapplytoanyoftheinstrumentsandmachinesweemploytoimagetheatomsandrevealtheirquantumweirdnesses.

Howcanthisbe?Inparticular,whenwemeasureapropertyofanatom,weemploybig

devices.Theatomsmaybeinsuperpositionsofstatesandsobeseveralplacesatonce,butthemeasuringinstrumentalwaysindicatesjustoneoutofthepossibleanswerstothequestionswepose.Whyisthat?Why

doesquantummechanicsnotapplytotheverydevicesweusetomeasurequantumsystems?

Thisiscalledthemeasurementproblem.Ithasbeencontroversialandunresolvedsincethe1920s.Thefactthat,afterallthistime,wehavefoundnoagreementamongexpertsmeansthereissomethingbasicaboutnaturewehaveyettounderstand.

Sothereissomewhereatransitionbetweenthequantumworld,inwhichanatomcanbeseveralplacesatonce,andtheordinaryworld,inwhicheverythingisalwayssomewhere.Ifamoleculemadefromtenorninetyatomscanbedescribedbyquantummechanics,butacatcannot,thensomewherebetweenthetwothereisalinedelineatingwherethequantumworldstops.Ananswertothemeasurementproblemwouldtelluswherethatlineisandexplainthetransition.

Therearepeoplewhoaresuretheyknowtheanswertothemeasurementproblem.Wewillmeetsomeofthemandtheirideaslateron.Wewillwanttolookoutforwhatpricewehavetopaytoexpungethisquantuminsanityfromourunderstandingoftheworld.

—BROADLYSPEAKING,thepeoplewhoaimtoaddressthemysteriesofquantummechanicsfallintotwoclasses.

Thefirstgroupassumesthatthetheoryasitwasformulatedinthe1920sisessentiallycorrect.Theybelievetheproblemisnotwithquantumtheory;itisinsteadwithhowweunderstanditorspeakaboutit.Thisstrategytomitigatethestrangenessofquantummechanicsgoesbacktosomeofthefounders,beginningwithNielsBohr.

NielsBohrwasaDanishphysicistwho,whilestillinhistwenties,wasthefirsttoapplyquantumtheorytoatoms.Ashegrewolderhebecamethedefactoleaderofthequantumrevolution,partlyduetotheattractivenessofhisideasandpartlybecauseheeducatedandmentoredmanyoftheyoungquantumrevolutionaries.

Thesecondgrouphasconcludedthatthetheoryisincomplete.Itcan’tbemadesenseofbecauseitisnotthewholestory.Theyseekacompletionofthetheorythatwilltellustherestofthestoryand,bydoingso,resolvethemysteriesofquantummechanics.ThisstrategygoesbacktoAlbertEinstein.

Morethananyoneelse,Einsteinwasresponsibleforinitiatingthequantumrevolution.Hewasthefirsttoarticulatethedualnatureoflightasaparticleandawave.Heisbynowbetterknownforhistheoryofrelativity,buthisNobelPrizewasforhisworkonquantumtheory,andhehimselfadmittedthathespentmuchmoretimeonquantumtheorythanonrelativity.Yet,evenifheinitiatedthequantumrevolution,Einsteindidnotbecomeoneofitsleaders,becausehisrealismrequiredthatherejectthetheoryasitwasdevelopedinthelate1920s.

Inthelanguageintroducedinthepreface,thoseinthefirstgrouparemostlyanti-realistsormagicalrealists.Realistsfindthemselvesinthesecondgroup.

Thosewhoarguefortheincompletenessofquantummechanicspointtothefactthatinmostcasesitcanonlymakestatisticalpredictionsfortheresultsofexperiments.Ratherthansayingwhatwillhappen,itgivesprobabilitiesforwhatmighthappen.InalettertohisfriendMaxBornin1926,Einsteinwrote:

Quantummechanicsiscertainlyimposing.Butaninnervoicetellsmethatitisnotyettherealthing.Thetheorysaysalot,butdoesnotreallybringusanyclosertothesecretofthe‘oldone’.I,atanyrate,amconvincedthatHeisnotplayingatdice.1

EinsteinwasalsofriendswithNielsBohr,andtheirdivergentresponsestoquantummechanicsfueledapassionatedebatebetweenthemthatlastedmorethanfortyyears,tillEinstein’sdeath.Itcontinuesbetweentheirintellectualdescendantstothisday.Einsteinwasthefirstpersontoclearlyarticulatetheneedforarevolutionarynewtheoryofatomsandradiation,buthewasunabletoacceptthatquantummechanicswasthattheory.Hisfirstresponsetoquantummechanicswastoarguethatitwasinconsistent.Whenthatfailed,hearguedinsteadthatquantummechanicsgivesanincompletedescriptionofnature,whichleavesoutanessentialpartofthepicture.

IbelievethatEinsteinwasunabletoacceptquantummechanicsasadefinitivetheorybecausehehadexceedinglyhighaspirationsforscience.Hewasdrivenbythehopeoftranscendingsubjectiveopinionanddiscoveringatruemirrorofnaturethatexhibitstheessenceofrealityina

fewtimelessmathematicallaws.Forhim,scienceaimedtocapturethetrueessenceoftheworld,andthatessenceisindependentofusandcanhavenothingtodowithwhatwebelieveorknowaboutit.

Einstein,ofallpeople,musthavefelthehadtherighttodemandthisbecausehehadachieveditinhisdiscoveriesofspecialandgeneralrelativity.Havinglaidthegroundworkforquantumphysics,hesoughttocapturetheessenceoftheatomicworldinacompletedescriptionofatoms,electrons,andlight.

Bohrrepliedthatatomicphysicsrequiredarevolutionaryrevisioninhowweunderstandwhatscienceis,aswellasinourconceptionoftherelationshipbetweenrealityandourknowledgeofit.Thisstemmedfromthefactthatweareapartoftheworld,sowemustinteractwiththeatomsweseektodescribe.

Bohrassertedthatonceweabsorbedthisrevolutionarychangeinourthinking,thecompletenessofquantummechanicswouldbeunavoidable,becauseitwasbuiltintoourbeingparticipantsintheworldweseektodescribe.FromBohr’sperspective,quantumtheoryiscompleteinthesensethatthereisnomore-completedescriptionoftheworldtobehad.

Ifwerefusethesephilosophicalrevolutionsandinsistonmaintaininganold-fashioned,commonsenseviewofrealityanditsrelationtoourobservationsandknowledge,wehavetopayadifferentkindofprice.Wehavetocontemplatethatwearewrongaboutsomeaspectofnature.Wehavetofindoutwhichcommonassumptioniswrongandreplaceitwitharadicallynewphysicalhypothesisthatopensthewaytoanewtheorythatwillcompletequantummechanics.

Thankstoacombinationoftheoryandexperiment,startingwithapaperbyEinsteinandtwocollaboratorsin1935,weknowoneaspectofthiscompletion.Thenewtheorymustviolatethecommonplaceassumptionthatthingsinteractonlywithotherthingsthatareneartheminspace.

Thisassumptioniscalledlocality.AbigpartofthestoryIwillbetellinginlaterchaptersishowthiscommonsenseideamustbetranscendedinthetheorywhichwillreplacequantummechanics.

—THISBOOKHASTHREEPURPOSES.First,Iwanttoexplaintolaypeoplejustwhatthepuzzlesattheheartofquantummechanicsare.Aftermorethan

acenturyofstudyingquantumphysics,itisremarkablethattherecontinuestothisdaytobenoagreementonthesolutionofthesepuzzles.

Buthavingexplainedthereasonsforthedebateinawaythatisfairtobothsides,Iwillnotstayimpartial.Inthegreatdebateaboutwhetherquantummechanicsisthelastwordornot,IsidewithEinstein.IbelievethatthereisalayerofrealitydeeperthanthatdescribedbyBohr,whichcanbeunderstoodwithoutcompromisingold-fashionednotionsofrealityandourabilitytocomprehendanddescribeit.

Thus,mysecondpurposeistoadvocateapointofviewaboutthepuzzlesofquantummechanics.Thisisthattheproblemscanberesolvedonlybyprogressinsciencewhichwilluncoveraworldbeyondquantummechanics.Wherequantummechanicsismysteriousandconfusing,thisdeepertheorywillbeentirelycomprehensible.

Icanmakethisclaimbecausewehaveknownsincetheinventionofquantummechanicshowtopresentthetheoryinawaythatdissolvesthemysteriesandresolvesthepuzzles.Inthisapproach,thereisnochallengetoourusualbeliefsinanobjectivereality,arealityunaffectedbywhatweknowordoaboutit,andaboutwhichitispossibletohavecompleteknowledge.Inthisreality,thereisjustoneuniverse,andwhenweobservesomethingaboutit,itisbecauseitistrue.Thiscanjustlybecalledarealistapproachtothequantumworld.

Ananti-realistapproachascribesthemysteriesofquantummechanicstosubtletieshavingtodowithhowwegainknowledgeaboutnature.Suchapproacheshaveradicalproposalstomakeaboutepistemology,whichisthebranchofphilosophyconcernedwithhowweknowthings.Realistapproachesassumeweareabletoarrivesoonerorlateratatruerepresentationoftheworldandsoaredeliberatelynaiveaboutepistemology.Instead,realistsareinterestedinontology,whichisthestudyofwhatexists.Bycontrast,anti-realistsbelievewecannotknowwhatreallyexists,apartfromourrepresentationoftheknowledgewehaveoftheworld,whichisgainedonlythroughinteractingwithit.

SoIwillendeavortoreassurereadersthatquantummechanicscanbeunderstoodcompletelywithinarealistperspectiveinwhichtheexternalworldcanbecompletelycomprehendedasindependentfromus.Thereisnomysteriouseffectoftheobserverontheobserved.Realityisoutthere,recalcitranttoourwillandthechoiceswemake.Thatrealityisfullycomprehensible.Andthatrealityconsistsofasingleworld.

Theexistenceoftheserealistapproachestoquantummechanicsdoesnotbyitselfmeanthatthephilosophicallymoreextravagantproposalsarewrong.Butitdoesmeanthatthereisnostrongscientificreasontobelieveinthem,becauserealismisalwaystobepreferredinscience,whenitcanbeachieved.

Why,then,issomuchofthetalkaboutquantumtheoryinspiredbytheweirderideasinwhichrealitydependsonourknowledgeofitortherearemultiplerealities?Thisisaproblemforhistoriansofideas.Onesuchhistorian,PaulForman,hastiedthedominanceofBohrandHeisenberg’santi-realistphilosophywithinthescientificcommunityinthe1920sand1930stotheembraceofchaosandirrationalityadvocatedbySpenglerandothersinthewakeoftheFirstWorldWar.

Thathistoryisfascinating,butitisforscholarstodojusticetoit.Iamnotascholar,Iamascientist,andthisbringsmetomythirdpurposeinwritingthisbook.

IhavebeenonEinstein’ssideinthesearchforadeeperbutsimplerrealitybehindquantummechanicssincefirstreadinghimonthesubjectasahighschooldropout.MyjourneyinphysicsbeganwithreadingEinstein’sautobiographicalnotes,where,inthelastfewyearsofhislife,inthe1950s,hereflectedonthetwomaintaskshefeltwereleftincompleteinphysics.Theseweretomakesenseofquantumphysicsand,afterthat,tounifythenewunderstandingofthequantumwithgravity,bywhichhemeanthisgeneraltheoryofrelativity.IrecallthinkingthatmaybeIcouldtrytohelp.Iwasunlikelytosucceed,butperhapsherewassomethingworthstrivingfor.

After,asitwere,gettingmymissionfromreadingEinstein’sautobiographicalnotes,IfoundthatbookbydeBroglie,talkedmywayintoagoodcollege,foundgreatteachers,andgotluckyseveraltimesinmyapplicationsforgraduateschoolandbeyond.I’mhavingawonderfullife,andasascientistonthefrontier,I’vehadmanychancestotakeashotongoal,aimedatsolvingEinstein’stwobigquestions.

Ihaven’tsucceeded,atleastsofar.Veryunfortunately,neitherhasanyoneelse.Atthesametime,overthepastseveraldecadestherehasatleastbeenprogresstowardunderstandingtheproblem.Thatisnotnearlyasgoodasitwouldbetosolvetheproblem,butneitherisitnothing.WeknowmuchbetterthanEinsteindidtheobstaclesthatatheorythattranscendsthelimitsofquantummechanicsmustovercome.And

becauseofthat,someveryinterestingproposalsandhypotheseshavebeenputforward,whichmayframethedeepertheoryforwhichwesearch.*

Ihavebeenthinkingaboutthequestionofhowtogobeyondquantummechanicssincethemid-1970s,andI’veneverbeenmoreexcitedandoptimisticabouttheprospectsforsuccess.Sothisismythirdreasonforwritingthisbook,whichistobringtoawideraudienceareportfromthefrontinoursearchfortheworldbeyondthequantum.

I

TWO

Quanta

fwebreakquantummechanicsdowntoitsmostessentialprinciple,itisthis:

Wecanonlyknowhalfofwhatwewouldneedtoknowifwewantedtocompletelycontrol,orpreciselypredict,thefuture.

Thisdisruptsthebasicambitionofphysics,whichistobeabletopredictthefuture.Itwashopedthatthispowerwouldfollowifonlywecouldgivethephysicalworldacompletedescription.Bydescribingfullythemotionofeveryparticleandtheactionofeveryforce,wewouldbeabletoworkoutexactlywhatwouldhappeninthefuture.Beforequantummechanicswasformulatedinthe1920s,wephysicistswereconfidentthatifwecouldlearnthelawsthatgovernthefundamentalparticles,wewouldbeabletopredictandexplaineverythingthathappenedintheworld.

Thehypothesisthatthefutureiscompletelydeterminedbythelawsofphysicsactingonthepresentconfigurationoftheworldiscalleddeterminism.Thisisanextraordinarilypowerfulidea,whoseinfluencecanbeseenindiversefields.Ifyouappreciatetheextenttowhichdeterminismdominatedthoughtinthenineteenthcentury,youcanbegintounderstandtherevolutionaryimpactofquantummechanicsacrossallfields,becausequantummechanicsprecludesdeterminism.

Toemphasizethispoint,IliketoquotefromTomStoppard’splayArcadia,inwhichhisprecociousheroine,Thomasina,explainstohertutor:

Ifyoucouldstopeveryatominitspositionanddirection,andifyourmindcouldcomprehendalltheactionsthussuspended,thenifyouwerereally,reallygoodatalgebrayoucouldwritetheformulaforallthefuture;andalthoughnobodycanbesocleverastodoit,theformulamustexistjustasifonecould.1

Acompletedescriptionofnature,atagiventime,iscalledastate.Forexample,ifwethinkoftheworldascomposedofparticleswhizzingaround,thestatetellsuswhereeachofthemis,andhowfastandinwhatdirectioneachismoving,atthatmoment.

Thepowerofphysicscomesfromitslaws,whichdictatehownaturechangesintime.Theydothisbytransformingthestateoftheworldasitisnowtothestateatanyfuturetime.Alawofphysicsfunctionsinsomewayslikeacomputerprogram:itreadsininputandputsoutoutput.Theinputisthestateatagiventime;theoutputisthestateatsomefuturetime.*

Alongwiththecomputationcomesanexplanationofhowtheworldchangesintime.Thelawactingonthepresentstatecausesthefuturestates.Asuccessfulpredictionofthefuturestateistakenasavalidationofthatexplanation.Thepredictionisdeterministic,inthatapreciseinputleadstoapreciseoutput.Thisconfirmsabeliefthattheinformationthatwentintodescribingthestateisinfactacompletedescriptionoftheworldatonemomentoftime.

Thisconceptofalawisbasictoarealistconceptionofnatureand,assuch,transcendsanyonetheory.NewtonianmechanicsandEinstein’stwotheoriesofrelativityallworkthesameway.Oneappliesthelawtothestateataninitialtime,andittransformsthatstatetothestateatsomefuturetime.ThisschemaforexplainingnaturewasinventedbyNewton,sowecallittheNewtonianparadigm.

Itisalsoworthmentioningthatinalmostallcasessofarknown,thelawsarereversible.Onecaninputthestateatsomefuturetimeandrunthelawbackwardtooutputthestateatanearliertime.(Theissueofthereversibilityoftimeandofthefundamentallawsisacentralconcernofchapters14and15.)

Itisoftenthecasethattheinformationneededtocompletelydescribethestateofaphysicalsystemcomesinpairs.Positionandmomentum.*

Volumeandpressure.Electricfieldandmagneticfield.Weneedbothtopredictthefuture.Quantummechanicssayswecanknowonlyone.

Thismeanswecan’tpreciselypredictthefuture.Thatisjustthefirstoftheblowstoourcomfortableintuitionsthatwewillhavetoabsorbfromquantumtheory.

Whichmemberofeachpairistheonethatcanbeknown?Quantummechanicssaysyouchoose!Thisisthebasisofitschallengetorealism.

Thereismoretosayabouttheimpossibilityofpredictingthefuture.Togetthere,let’stakeadvantageofthegreatgeneralityquantummechanicsclaims,andspeakabitabstractly.Wewanttodescribesomephysicalsystemintermsofapairofvariables—wewillcallthemAandB.Quantumphysicsassertsatwo-partprinciple.

1. IfweknewbothAandBatagiventime,wecouldpreciselypredictthefutureofthesystem.

2. WecanchoosetomeasureAorwecanchoosetomeasureB;andineachcasewewillsucceed.Butwecan’tdobetter.WecannotchoosetosimultaneouslymeasurebothAandB.

AsIhavestatedit,thisisaprohibitionofwhatwecanmeasure;but,ifweprefer,wecanexpressitasaprohibitionofwhatwecanknowaboutthesystem.

Butwait,whycan’tyoumeasureAandthen,atalatertime,measureB?Youcan.ButyourmeasurementofBwillrenderirrelevant(forthepurposeofpredictingthefuture)yourpastknowledgeofA.OnewaythiscanhappenisthatafterthemeasurementofB,thevalueofAisrandomized.WecannotmeasureBwithoutdisruptingthevalueofA,andviceversa.Thus,ifwemeasureA,thenB,thenAagain,thevalueofAwegetthesecondtimewillberandom,andhenceunrelatedtothevaluewegotthefirsttimewemeasuredA.

1.and2.togetherarecalledtheprincipleofnon-commutativity.Twoactionsaresaidtocommuteifitdoesn’tmatterinwhatorderwedothem.Iftheactionthatisdonefirstmatters,wesaytheyarenon-commutative.Itdoesn’tmatter(excepttoafewfanatics)inwhatorderyouputmilkandsugarintocoffee;theycommute.Gettingdressedinvolvesnon-commutativeoperations;theorderinwhichyouputon

yourunderwearandpantsmatters.Butitdoesn’tmatterwhichsockyouputonfirst,orwhetheryouputyoursocksonfirst,partwaythroughtheprocess,orlast.Soputtingonsockscommuteswitheverythingexceptputtingonshoes.(Themathematicallymindedwillunderstandthisasanapplicationofalgebratotopology.)

WhatifweallowtheretobesomespecifiedamountofuncertaintyinthemeasurementofA?ThenwecanmeasureB,butonlyuptosomeaccuracy.Theseuncertaintiesarereciprocal—thebetterweknowA,theworsewecanknowB,andviceversa.

Forexample,let’ssupposethatAisthepositionofaparticle.ThenBisitsmomentum.Supposewedoameasurementthattellsitslocationtowithinameter.Thenwecanmeasurethemomentumtoacorrespondinguncertainty.IfweincreasetheuncertaintyinA,thenwecanmakethemeasurementofBmorepreciseandviceversa.Thisgivesusaprinciplecalled,notsurprisingly,theuncertaintyprinciple.*

(UncertaintyinA)×(UncertaintyinB)>aconstant

Appliedtopositionandmomentum,itreads

(Uncertaintyinposition)×(Uncertaintyinmomentum)>aconstant

Physicsislikeacollegecampuswhereeverybuildingisnamedaftersomeone.TheconstantisnamedafterMaxPlanck,andtheuncertaintyprincipleisnamedafterWernerHeisenberg.

Theuncertaintyprincipleisquitepowerful,asisshownbythisimportantconsequence.Let’sgobacktothescenarioinwhichyoumeasureA,thenyoumeasureB,thenyoumeasureAagain.AsIsaidabove,onceyouknowtheresultofmeasuringB,thesecondmeasurementofAisrandomized;itisnolongerequaltotheoriginalvalueofA.Butsupposethat,justbeforeyouremeasureA,youdosomethingtoforgetwhatthevalueofBwas.Thenthesystemremembers—yes,thatwordistheoneweusetodescribethissituation—theoriginalvalueofA.

Thisiscalledinterference.ItisallowedbytheuncertaintyprinciplebecauseonceyouforgetthemeasurementofB,B’suncertaintyisvery

large,soA’suncertaintycanbesmall.Buthowcanweundoameasurement?Letmegiveafancifulexample.

TherearemanysimplecasesinwhichAandBeachhavetwopossiblevalues.Letthesystemswestudybepeople,andletAbepoliticalidentity,whichwewillsimplifytobeabinarychoice:eitherleft-wingorright.IwillletBbepetpreference,catloversversusdoglovers.Wenowplayagameinwhichapersoncan’thavebothadefinitepetpreferenceandapoliticalidentity.Wegotoapartywhereeveryonehasleft-wingviewsandaskeachwhethertheyareacatpersonoradogperson.Weputthecatloversinthelivingroomandthedogloversinthekitchen.Ifwegointoeitherroomandinquireabouttheirpoliticalviews,thenhalfwillnowberight-wingers.Thatiswhatmusthappenifpoliticalidentityandpetpreferencedon’tcommute.

Butlet’safterwardcalleveryonetogetherintothediningroom.Weletthemmingleforawhile,thenwegoinandpickarandomperson.Theycouldhavecomefromeitherthelivingroomorthekitchen,wedon’tknowwhich,sowe’velosttrackoftheirpetpreference.Then,whenweaskthemaboutpolitics,wefindtheyareallleft-wingersagain.

Theseprinciplesareentirelygeneral.AandBareoftentheanswerstoyes/noquestions.Butintheoriginalcase,Awasthepositionofanelementaryparticle,sayanelectron,andBwasthemomentumoftheparticle.

Momentumisoneofthosewordsthatfunctionsasabarriertocomprehension,solet’stakeamomenttodefineit.

Inphysicsweoftenhavetorefertothespeedandthedirectionofmotionofaparticle.Wecombinetheseintoonequantitywhichwecallthevelocity.Youcanthinkofaparticle’svelocityasanarrowthatpointsinthedirectionofitsmotion.Thefasterthespeed,thelongerthearrow.

Tosurviveacollisionyouwanttoexperienceaslittleforceaspossible.Theforceatruckwillimpartonacarisproportionaltothetruck’schangeofspeed.Butit’salsoproportionaltothemassofthetruck.You’drathercollidewithaPing-Pongballthanatruck,eveniftheyaretravelingtowardyouatthesamespeed.Toexpressthis,physicistsdefinemomentumastheproductofthemasstimesthevelocity.Thisisalsoanarrowpointinginthedirectionofmotion,onlynowthelengthisproportionaltoboththespeedandthemass.

Momentumisacentralconceptinphysicsbecauseitisconserved.Thatmeansthatinanyprocessesatall,wecanaddupthemomentaofthevariousparticlesinvolvedatthebeginning,and,nomatterwhathappens,theresultingtotalmomentumwon’tchangeintime.Before,during,andafteracollision,thetotalmomentumwillbethesame.Whathappensinacollisionisthatmomentumisexchangedfromonebodytoanother.Thischangeofmomentumisexperiencedasaforce.

Energyisanotherconservedquantity.Thetotalenergyofasystemofparticlesneverchangesintime.Whenparticlesinteract,onemaygainenergywhiletherestloseenergy.Butthetotalenergyremainsthesame;noneiscreatedordestroyed.

FIGURE1.AtruckcarriesmuchmoremomentumthanaPing-Pongballgoingthesamevelocity,becauseitsmassissomuchgreater,andthemomentumistheproductofthemassandthevelocity.

Energyandmomentumarerelated.Wewon’tneedtheexactrelation,butweneedtoknowthataparticlethatismovingfreely,andhasanexactvalueofmomentum,alsohasanexactenergy.

Theuncertaintyprinciplethensaysthatwecan’tknowboththepositionandmomentumofabodyatthesametime.Thismeanswecan’tmakeaprecisepredictionofitsfuture,becausetodosowewouldneedto

knowbothwheresomethingisandhowfastandinwhatdirectionitismoving,withcompleteaccuracy.

Ifwewanttodevelopanintuitionabouthowquantumparticlesbehave,wewillneedtobeabletovisualizeaparticlewithadefiniteposition,but,becauseoftheuncertaintyprinciple,nodefinitemomentumorvelocity.Thisisnothard:visualizetheparticlebeingsomewheremomentarily.Inthenextmomentitwillalsobesomewheredefinite,justsomewhereelse.Becauseitsmomentumisindefinite,itjumpsaroundrandomly.

Buthowdowevisualizeaparticlewithadefinitemomentum,butacompletelyindefiniteposition?Thisseemsmorechallenging.Ifyoulookforit,youhaveanequalchanceoffindingitanywhere.Soitiscompletelyspreadout.Buthowdowevisualizeitsdefinitemomentum?

Theansweristhataparticlewithadefinitemomentum,butacompletelyindefiniteposition,canbevisualizedasawave.Andnotjustanywave,butapurewave,onewhichvibratesatasinglefrequency.

Awavecanbecharacterizedbytwonumbers.Oneisitsfrequency;thisisthenumberoftimespersecondthatitoscillates.Theotheristhedistancebetweenthepeaks,whichisknownasthewavelength.Thesearerelatedinthefollowingway:ifyoumultiplythesetwonumberstogether,yougetthespeedatwhichthewaveistraveling.Thusawavewhichoscillateswithasinglefrequencywillalsohaveadefinitewavelength.

Quantummechanicsassertsthatthemomentumoftheparticleandthewavelengthofthewavethatrepresentsitarerelatedinasimpleway,whichisthattheyareinverselyproportional.Thatis,

wavelength=h/momentum

histhesamePlanck’sconstantthatcameintotheuncertaintyrelations.

Letusassumeforamomentthatnoforceactsonourparticle,perhapsbecauseitisveryfarfromeverythingelse.Intheabsenceofforces,aparticlewithadefinitemomentumalsohasadefiniteenergy.Thatenergyisinturnrelatedtothefrequencyofthewave,inthattheyvaryproportionately.

Energy=h×frequency

Theserelationsandcorrespondencesareuniversal.Everythinginthequantumworldcanbeviewedasbothawaveandaparticle.Thisisadirectconsequenceofthebasicprinciplethatwecanmeasuretheparticle’spositionormeasureitsmomentum,butwecannotmeasurebothatthesametime.

Whenwewishtomeasureitsposition,wevisualizeitasaparticle,localized,butjustmomentarily,atapointinspace.Themomentumiscompletelyuncertain,sothenextmoment,ifwelookagain,wewillfindithasrandomlyjumpedsomewhereelse.Itcan’tremaininoneplacebecause,ifitdid,itwouldhaveadefinitevalueofmomentum,namelyzero.

If,ontheotherhand,wechoosetomeasuretheparticle’smomentum,wewilldiscoverithassomedefinitevalue.Itisnowhereinparticular,sowevisualizeitasawave,butonewithadefinitewavelengthandfrequency,accordingtotherelationsjustmentioned.

Whatissocrazilyfabulousaboutthisisthatwavesandparticlesarequitedifferent.Aparticlealwayshasadefiniteposition,localizedsomewhereinspace.Itsmotiontracesoutapaththroughspace,whatwecallitstrajectory.Moreover,accordingtoNewtonianphysics,ateachmomentaparticlealsohasadefinitevelocityand,consequently,adefinitemomentum.Awaveisalmosttheopposite.Itisdelocalized;itspreadsoutasittravels,occupyingallthespaceavailabletoit.

Butnowwearelearningthatwavesandparticlesaredifferentsidesofaduality,thatis,differentwaysofvisualizingonereality.Asinglerealitywithadualnature:adualityofwavesandparticles.

Aquantumparticlecanhaveaposition.Weaskwhereitis,andwewillfinditsomewhere.Butaquantumparticleneverhasatrajectory,because,ifweknowwhereitis,whereitwillbenextiscompletelyuncertain.Wemustgetusedtothinkingofparticlesatdefinitepositionswhicharenotpointsontrajectories.Similarly,ifwemeasureamomentumwewillalwaysfindavalue.Butthenit’sawave,spreadouteverywhere.Wherewewillfindtheparticle,ifwenextmeasureitsposition,iscompletelyuncertain.

Thisscheme,itmustbeadmitted,hasanincredibleelegance.Butwhatismostcompellingisitsuniversality.Itappliestolight,itappliesto

electrons,anditappliestoalltheotherelementaryparticlesknown.Itappliestocombinationsofthoseparticles,suchasatomsandmolecules.Ithasworkedsuccessfullytodescribethemotionsoflargemolecules,suchasbuckyballsandproteins.Thereisnocaseofanexperimentthatwassensitiveenoughtorevealthequantumnatureofanobject,butfailedtodoso.Atleastsofar,sizeandcomplexityprovidenolimit.Wedonotyetknowifthewave-particledualityappliestopeopleorcatsorplanetsorstars,butthereisnoreasonknownwhyitdefinitelycan’t.

Inallthesecasestheeffectisthesame:wecanonlyknowhalfofwhatwewouldneedtoknowtopreciselypredictthefuture.

I

THREE

HowQuantaChange

nthefirstlectureofhiscourseonquantummechanics,myteacherHerbertBernsteinassertedthatphysicsisthescienceofeverything.Ourgoalinphysicsistofindthemostgenerallawsofnature,from

whichthemultitudeofphenomenaexhibitedbynaturemayallbeexplained.

Quantummechanicsexplainsthewidestvarietyofphenomenaofanytheorysofar.Atthesametime,itgreatlyrestrictsthequestionsthatcanbeaskedofanyparticularphenomenon.Wehavealreadyencounteredonekindoflimitation:thatwecanknowonlyhalfwhatwewouldneedtoknowaboutasystemtomakeprecisepredictionsforitsfuture.Asaresult,wemustgiveupdescribingexactlywhatgoesoninindividualatomsinfavorofstatisticalpredictions,whichapplyonlytoaveragestakenovermanycases.Hence,tobelieveinquantumtheorywemustgiveuptheambitiontopreciselypredictthefuture.

Mostphysicistshavegivenupthoseambitionsinthefaceofthesuccessofquantummechanics.ButIbelievethatthisisshortsightedandthereisadeeperlevelofrealitytobediscovered,themasteryofwhichwillrestoreourambitionsforacompleteunderstandingofnature.

Anotherrestrictionlimitstherangeofquantumtheory.WecanexpressthisinaprincipleIcallthesubsystemprinciple:

Anysystemquantummechanicsappliestomustbeasubsystemofalargersystem.

Onereasonforthisisthatquantummechanicsrefersonlytophysicalquantitieswhicharemeasuredbymeasuringinstruments,andthese

mustbeoutsidethesystembeingstudied.Further,theresultsofthesemeasurementsareperceivedandrecordedbyobservers,whoarealsonotpartofthesystembeingstudied.

Mostofusapproachsciencewiththenaiveexpectationthatitwilltelluswhatisreal.WecanfollowJohnBellandcallarealpropertyofasystemabeable:itispartofwhatis.Bellcoinedthewordasacontrasttothetermobservables,whichiswhatanti-realistswantoutofatheory.

“Observables”and“beables”areloadedterms,whoseusecansignifyallegiancetoasideofthedebatebetweenrealismandanti-realism.Anobservableisaquantityproducedbyanexperimentoranobservation.Thereisnocommitmenttobelieveitcorrespondedtosomethingthatexistsapartfromthemeasurementorhadavaluebeforethemeasurement.Anti-realistsusethistermtoemphasizethatthequantitiesquantumphysicistsmeasureneedhavenoexistenceapartfrom,orpriorto,ourobservationofthem.RealistsuseJohnBell’sterm“beable”torefertotherealitythattheybelieveexistswhetherwemeasuresomethingornot.

Mostscientificexplanations,whetheroftheflightsofcannonballsorofbirdsandbees,speakintermsofbeables.

Butnotquantummechanics!AsHeisenbergandBohrinsisted,quantummechanicsspeaksnotintermsofwhatis,butonlyofwhathasbeenobserved.Thereis,accordingtothem,nousefultalkaboutbeablesintheatomicdomain;instead,quantummechanicsdealsonlyinobservables.

Tomeasureanatom’sobservables,weimposeonitalarge,macroscopicinstrument.Bydefinition,thatdeviceisnotpartofthesystemwhoseobservableswearestudying.Noristheobserver.

Therefore,tobedescribedinthelanguageofquantummechanics,asystemmustbepartofalargersystemthatincludestheobserverandhermeasuringinstruments.Henceoursubsystemprinciple.

Mostapplicationsofquantumtheoryaretoatomsandmoleculesorothertinysystems;inthesecasestherestrictionisirrelevant.Butsomeofushavetheambitiontodescribethewholeuniverse.Wefeelthatistheultimategoalofscience.However,theuniverseasawholeisnot,bydefinition,partofalargersystem.Thesubsystemprinciplefrustratesourhopetohaveatheoryofthewholeuniverse.

Thereisasubtlebutkeydifferencebetweentheideathatquantummechanicsisthetheoryofeverything,andthehopeofextendingquantumtheorytoincludethewholeuniverse.WhatProfessorBernsteinmeantbyhisclaimisthatphysicsistherootofthecorrectdescriptionofeverything—eachconsideredasasubsystemofthewhole.Itisverydifferenttoimagineapplyingquantumtheorytotheentireuniverse,whichwouldmeanincludingusobserversinsidethesystembeingstudied,andourmeasuringinstruments.

Overthelastcenturyseveralattemptsweremadetoextendquantummechanicstoatheoryofthewholeuniverse.Wewillmeetoneoftheselateron;apartofouroverallargumentisthattheseattemptsfail.

Foronething,makingtheobserverapartofthesystembeingdescribedraisestrickyquestionsofself-reference.Itisnotevenclearthatanobservercangiveacompleteself-description,becausetheactofobservingordescribingyourselfchangesyou.

Buttherearedeeperreasonswhyquantummechanicscannotbeextendedtoatheoryofthewholeuniverse.

Inseveralofmybooks(namelyTheLifeoftheCosmos,TimeReborn,andTheSingularUniverseandtheRealityofTime,writtenwithRobertoMangabeiraUnger),Iinvestigatethequestionofhowphysicsmaybeextendedtogiveatheoryofthewholeuniverse.Iconcludethatatheoryofthewholeuniversemustdifferinseveralcrucialaspectsfromanyofthephysicaltheoriessofardeveloped,includingquantummechanics.Allthesetheoriesonlymakesensewheninterpretedasdescriptionsofaportionoftheuniverse.

Indeed,thefactthatquantummechanicsonlymakessensewhenreadasatheoryofapartoftheuniverseis,byitself,asufficientreasonforregardingquantummechanicsasincomplete.Onethingwemayaskofatheorythatcompletesquantumtheoryisthatitmakessensewhenextendedtoadescriptionoftheuniverseasawhole.

However,thisisnottheonlylineofthoughtthatleadstotheconclusionthatquantummechanicsisincomplete.Otherconcernsanddifficultieshadfarmoreinfluenceonhowthesubjecthasevolvedhistorically.Forthetimebeing,Iwillignorethecosmologicalissuesandfocusonmoreimmediatechallenges.

—

THEPROCESSOFAPPLYINGgenerallawstoaspecificphysicalsystemhasthreesteps.

First,wespecifythephysicalsystemwewanttostudy.Thesecondstepistodescribethatsystematamomentoftimein

termsofalistofproperties.Ifthesystemismadeofparticles,thepropertieswillincludethepositionsandmomentaofthoseparticles.Ifitismadeofwaves,thenwegivetheirwavelengthsandfrequencies.Andsoon.Theselistedpropertiesmakeupthestateofthesystem.

Thethirdstepistopostulatealawtodescribehowthesystemchangesintime.

Beforequantumphysics,physicistshadasimplebutpowerfulambitionforscience.Atthesecondstepwewouldbeabletodescribeasystemintermsthatwerecomplete,intwosenses.Completemeans,firstofall,thatamoredetaileddescriptionisneitherneedednorpossible.Anyotherpropertythesystemmighthavewouldbeaconsequenceofthosealreadyincluded.Additionally,thelistofpropertiesshouldbeexactlywhatisneededtogiveprecisepredictionsofthefuture.Thisisdoneusingthelaws.Thefuturecanbedeterminedprecisely,givenourcompleteknowledgeofthepresent.Thisisthesecondmeaningofthedescriptionbeingcomplete.

BetweenNewton,inthelateseventeenthcentury,andtheinventionofquantummechanicsinthe1920s,itwasbelievedthatthepropertiesmakingupthatcompletedescriptionwerethepositionsofalltheparticlesandtheirmomenta.

Itmight,ofcourse,happenthatwedon’tknowtheprecisepositionsandmomentaofalltheparticlesmakingupasystem.Theairinthisroomconsistsofaround1028atomsandmolecules,soacompletelistingoftheirpositionsisimpossible.Wehavetouseaveryapproximatedescriptionintermsofdensity,pressure,andtemperature.Theserefertoaveragesoftheatoms’positionsandmotions.Ourbulkdescriptionwillhavetoemployprobabilities,andthepredictionsitmakeswillthenbetosomedegreeuncertain.

Buttheuseofprobabilitiesisjustforourconvenience,andtheresultinguncertaintiesjustexpressourignorance.Behindourbulkdescriptionofagasintermsofdensityandtemperature,wecontinuetobelievethereisaprecisedescription,whichincludeslistingwhereeverylastatomisandhowitismoving.Weshareafaiththatifwehadaccessto

thatdescriptionwecouldusethelawstopredictthefutureprecisely.Thatfaithisbasedonthebeliefinrealism—thatthereisanobjectivereality,whichitispossibleforustoknow.

Quantummechanicsblocksthiscomplacentambition,becauseitsfirstprincipleassertswecanknow,atmost,onlyhalftheinformationthatwouldbeneededtorealizeit.

—THECOMPLETEINFORMATIONNEEDEDtopreciselypredictthefutureiscalledaclassicalstate.“Classical”ishowwerefertophysicsasitwasbetweenNewtonandthediscoveryofthequantum.Itisthennaturaltocallaspecificationofhalfofthatinformationaquantumstate.Thehalfisarbitrary;itcanbechosentobeonlythemomentum,oronlytheposition,orsomemixtureofthese,aslongashalftheinformationneededtopreciselypredictthefutureispresent,andhalfismissing.

Thequantumstateisacentralnotioninquantumtheory.Arealistwillwanttoask:Isitreal?Doesaparticle’squantumstatecorrespondpreciselytothephysicalrealityofthatparticle?Orisitjustaconvenienttooltomakepredictions?Perhapsthequantumstateisadescription,notoftheparticle,butonlyoftheinformationwehaveabouttheparticle?

Wearenotgoingtoresolvethesequestionshere.Expertsdisagreeaboutthem.Wewillsoonenoughhavethechancetofocusontheseandotherquestionsaboutthemeaningandcorrectnessofquantummechanics.Fornowwetakeapragmaticviewpointandregardthequantumstateasatoolformakingpredictionsaboutthefuture.

Aquantumstateisausefultoolbecauseitcandojustthat.Thisisournextprinciple:

Giventhequantumstateofanisolatedsystematonetime,thereisalawthatwillpredicttheprecisequantumstateofthatsystematanyothertime.

ThislawiscalledRule1.ItisalsosometimescalledtheSchrödingerequation.Theprinciplethatthereissuchalawiscalledunitarity.

Thus,whiletherelationbetweenthequantumstateandthebehaviorofanindividualparticlecanbestatistical,thetheoryisdeterministic

whenitcomestohowthequantumstatechangesintime.Aswesaid,quantumstateswithdefinitevaluesofenergyand

momentumarerepresentedbypurewaveswithexactfrequencyandwavelength.Butthesequantumstatesareveryspecial.Whataboutotherquantumstates,whosemomentaareuncertain,sothattheydonotvibrateatasinglefrequencyandwithasinglewavelength?Moregeneralquantumstatesarerepresentedbywaveswitharbitraryprofiles.Thesearesharpinneitherpositionnormomentum,soifeitherofthesequantitiesismeasured,therewillbeuncertainties.*

Therearealsostatesofdefinitepositionandcompletelyindefinitemomentum;ifwegraphthem,theylooklikespikes,whicharezeroeverywhereexceptthesinglepointwheretheparticleis.Otherstatesarepeakedoveraregionofspaceandcorrespondtoparticleswhicharelocalizedimprecisely,soweknowonlyapproximatelywheretheyare.

Onewaytomakeageneralquantumstateisbyaddingtogetherpurewaves,eachwithadifferentfrequencyandwavelength.

FIGURE2.Threewavefunctionsareillustratedshowinghowdifferentkindsofstatesarerepresented.(A)showsapurewaveofasinglewavelength,whichcorrespondstoadefinitemomentum.Thepositioniscompletelyuncertain,asisrequiredbytheuncertaintyprinciple.The

spikein(B)showsastatewithadefiniteposition,butthewavelengthiscompletelyindefiniteanduncertain.Theintermediatecase(C)isbuiltbycombiningseveralwavelengths,sothemomentumandpositionarebothsomewhatuncertain.

Ifwemeasuretheenergyofsuchacombination,wegetarangeofvaluescorrespondingtothedifferentfrequenciesthatmakeupthewave.

Ifthisweremusic,thewaveswouldbesoundwaves.Apurewavewithasinglefrequencysoundsasinglenote.Playingseveralnotessimultaneouslyproducesachord.Thereisnolimittohowmanynotesyoucanplayatonce,nortohowmanyquantumstatescanbeaddedtogether.

Combiningtwostatesbyaddingthewavesthatrepresentthemiscalledsuperposingthestates.Itcorrespondstocombiningtwowaystheparticlemayhavetraveledtoarriveatthedetector.Earlier,whenwedividedcatanddogpeopleintothelivingroomandthekitchen,eachroomrepresentedaquantumstate,definedbyadefinitepetpreference.Whenwebroughteveryonetogetherinthediningroomwesuperposedthosetwostates.

Thisisanexampleofageneralprinciplecalledthesuperpositionprinciple.

Anytwoquantumstatesmaybesuperposedtogethertodefineathirdquantumstate.Thisisdonebyaddingtogetherthewavesthatcorrespondtothetwostates.Thiscorrespondstoaphysicalprocessthatforgetsthepropertythatdistinguishedthetwo.

Logically,asuperpositionoftwostatesCandDcommunicatesCorD.Thepersoncouldbeadogloverorshecouldbeacatlover.Theconnector“or”meanssomethinghasbeenforgotten.SomeonemighthavebeenaCortheymighthavebeenaD,butwhenwe’veforgottenwhich,wecanonlysaytheyareaCoraD.

AsIhaveemphasized,quantumstatesareimportantbecausetheyevolveintimeaccordingtoadefiniterule.Therelationbetweenthequantumstateandanobservationisprobabilistic,buttherelationshipbetweenthatstatenowandthequantumstateatadifferenttimeisdefinite.Butthereisanimportantcaveat,whichisthatthedefinite

evolutionruleappliesonlytosystemsthatareisolatedfromtherestoftheuniverse.Onlyincaseswherethesystemisfreefromdisturbancesorinfluencesfromoutsidesourcesistheevolutionruledeterministic.

Whenwemakeameasurementonasystem,wedisturbit,typicallybyforcingittointeractwithameasuringinstrument.SoRule1doesnotapplytomeasurements.Thisistruenotonlyofmeasurements,butofanyinteractionbetweenthesystemandoutsideforces.Soisthereanythingspecialaboutmeasurements?

Measurementsarespecialbecausetheyarewhereprobabilitiesenterquantumtheory.

Quantummechanicsassertsthattherelationshipbetweenthequantumstateandtheoutcomeofameasurementisprobabilistic.Generally,thereisarangeofpossibleoutcomesofagivenmeasurement.Thesewilleachoccurwithsomeprobability,andtheseprobabilitiesdependonthequantumstate.Inthecasewherewemeasurethepositionofaparticle,thisdependenceisparticularlysimple:

Theprobabilityoffindingtheparticleataparticularlocationinspaceisproportionaltothesquareoftheheightofthecorrespondingwaveatthatpoint.

ThisiscalledtheBornrule,afterMaxBorn,whoproposedit.Whythesquare?Probabilityisalwayspositive,butwavesgenerally

oscillatebetweenpositiveandnegativevalues.Butthesquareofanumberisalwayspositive,anditisthesquarethatisrelatedtoprobability.Theimportantthingtorememberisthatthelargerthemagnitude,orheight,ofawave,themorelikelythatyouwillfindthecorrespondingparticlethere.

Theselastfewpointsarekeytohowquantummechanicsworks,soletmesummarizethem:Thewaverepresentsthequantumstate.Whenweleavethesystemalone,itchangesintimedeterministically,accordingtoRule1.Butthequantumstateisonlyindirectlyrelatedtowhatweobservewhenwemakeameasurement,andthatrelationisnot

deterministic.Therelationbetweenthequantumstateandwhatweobserveisprobabilistic.Randomnessentersinafundamentalway.

But,evenifthequantumstategivesusonlyprobabilitiesforwhatweobserve,oncewegetaresult,thereissomethingthatisdefinite,becauseafterwardyouknowexactlywhatthestateis.Itisthestatecorrespondingtotheresultobtainedbythemeasurement.Supposewemeasureanelectron’smomentum,andgettheresultthattheelectronismovingnorthwithmomentum17(insomeunits).Then,justafterthemeasurementweknowthatthequantumstateisNORTHWARD,MOMENTUM=17.

Thisisenshrinedinasecondrule,*whichwecallRule2:

Theoutcomeofameasurementcanonlybepredictedprobabilistically.Butafterward,themeasurementchangesthequantumstateofthesystembeingmeasured,byputtingitinthestatecorrespondingtotheresultofthemeasurement.Thisiscalledcollapseofthewavefunction.

Forexample,inourstoryaboutpoliticalandpetpreferences,assoonasapersonanswersaquestionabouteitherone,theygointothequantumstatedefinedbyhavingthatdefinitepreference.

Sincetheoutcomeofthemeasurementisprobabilistic,soisthechangeinthequantumstatedictatedbyRule2.

Oncethemeasurementisover,thesystemcanbeconsideredtobeisolatedagainandRule1takesover,untilthenextmeasurement.

Rule2raisesawholebunchofquestions.

Doesthewavefunctioncollapseabruptlyordoesittakesometime?

Doesthecollapsetakeplaceassoonasthesysteminteractswiththedetector?Oronlylater,whenarecordismade?Orperhapslaterstill,whenitisperceivedbyaconsciousmind?

Isthecollapseaphysicalchange,whichmeansthatthequantumstateisreal?Orisitjustachangeinourknowledgeofthe

system,whichmeansthequantumstateisonlyarepresentationofthatknowledge?

Howdoesasystemknowaparticularinteractionhastakenplacewithadetector,sothatitshouldthen,andonlythen,obeyRule2?

Whathappensifwecombinetheoriginalsystemandthedetectorintoalargersystem?DoesRule1thenapplytothewholesystem?

Thesequestionsarealldifferentaspectsofthemeasurementproblem.Diverseanswershavebeengiven,whichhavebeenasourceof

controversyfornearlyacentury.Wewillhavealottosayaboutallthis,oncewehavethefullpicture.

T

FOUR

HowQuantaShareUsefulasitisundereverydaycircumstancestosaythattheworldexists“outthere”independentofus,thatview

cannolongerbeupheld.—JOHNARCHIBALDWHEELER

hesuperpositionofquantumsystemsposesagravechallengetorealism.Butanevenmoreinsidioussetofobstaclestorealismcomesfromhowquantummechanicsdescribessystemswhichare

builtbycombiningsimplersystems.Superpositionisaboutcombiningdifferentpossiblestatesofasingle

system.AsIsaid,itcorrespondsto“or.”Quantummechanicsalsohasinterestingthingstosayaboutcombiningtwodifferentsystemstomakeacompositesystem.Supposewehaveanelectronandaproton.Eachhastobeginwithitsownquantumstate.Wecancombinethemtomakeahydrogenatom.Thewholeatomhasitsownquantumstate,whichismadebycombiningthestatesofitsconstituents.Thiscorrespondsto“and.”Eachquantumstaterepresentshalfthepossibleinformationneededforacompletedescriptionofitscomponents.Thejointquantumstatealsorepresentshalfthepossibleinformationabouttheatom.Thisleadstoveryinterestingnewphenomena.

Letusconsideragainpeoplewithtwoincompatibleproperties,politicalviewsandpetpreference.Let’ssupposeAnnaandBethshareanapartment.Theytalkaboutgettingapet.Individually,AnnaisacatloverandsoisBeth.Thestateoftheircoupleisjustthecombinationofthese.Eachhasadefinitepetpreference,soeachhasindefinitepoliticalviews.Ifaskedforherpoliticalpreference,eachwillhavea50percentchanceof

answeringleftanda50percentchanceofansweringright.So,ifaskedaboutpolitics,halfthetimetheywilldiscovertheyagreeandhalfthetimetheywilldiscovertheydisagree.Inthestateinquestion,inwhichtheyeachseparatelyhaveadefinitepetpreference,theirpoliticalviewsarerandomanduncorrelated.AnnastatingherpoliticalviewshasnoeffectonBeth’sviews.

Quantumphysicsalsoallowsustodefinestatesforthecoupleinwhichalltheirindividualviewsareindefinite,butwecanhavedefiniteknowledgeofhowtheirviewsrelate.Animportantexampleofsuchastateisoneinwhichtheonlythingthatiscertainisthat,ifweaskAnnaandBeththesamequestion,theywilldisagree.ThisstateiscalledCONTRARY.Inthisstateyoucanaskthembothanyquestion,andwhateveroneasserts,theotherwillasserttheopposite.Yetitisimpossibletopredicttheirindividualanswers.

CONTRARYisanexampleofasurprisingphenomenon,whichisthatquantumstatesexistfortwoparticlesinwhichweknowsomethingabouthowtheparticlesarerelatedtoeachother,butnothingabouteachparticleindividually.Wecallsuchstatesentangled.Thephenomenonofentanglementissomethingnew,whichcomesintophysicswiththequantumandhasnoclassicalanalogue.

Theinformationthattheywilldisagree,whateverquestiontheyareasked,addsuptoexactlyhalftheinformationthatwouldbeneededtopredicttheiractualanswers.Theotherhalfisabouttheirindividualresponses.SointheCONTRARYstate,weknownothingabouttheirindividualviews,andeverythingabouthowtheirviewscorrelate.Hence,whenintheCONTRARYstate,AnnaandBethshareapropertywhichisnotjustthesumofpropertiestheyhaveindividually.

ThecouplespendtheeveningtogetherandwakeupintheCONTRARYstate.Theyeachgoofftowork.OverlunchAnna’scolleagueswillaskherabouteitherpoliticsorpets.Theydecideonlyatthelastminutewhichquestiontoask.AfterwardtheyrecordwhichquestionwasaskedofAnnaandwhatshesaid.Beth’scolleaguesdothesame.Thisisrepeatedeverydayforayear,afterwhichthetwosetsofcolleaguesmeetataconferenceandcomparenotes.Whatdotheydiscover?

Halfthetime,AnnaandBethwillhavebeenaskeddifferentquestions.Let’signorethesecasesandlookonlyatthedayswhentheywereaskedthesamequestion.In100percentofthesecases,their

answersdisagreedwitheachother.Thisisinspiteofthefactthat,lookedatindividually,eachoftheiranswersappearstohavebeencompletelyrandom.

AsI’vedescribedthis,itwouldnotbehardtoexplain.Allthatisneededisthateachmorningoverbreakfastthecoupletossacointodecidewhowillgivewhichanswers,ifasked.Butthereareanalogousstoriesinwhichwestudypairsofphotons,ratherthanpairsofpeople.WecanputpairsofphotonsintheCONTRARYstateandmeasurevariouspropertiesofthem.Wheneverweaskeachthesamequestion,theydisagree.Butwecanshowthatthiscannotbeexplainedbyanyagreementestablishedinadvanceofourasking.Thiswasprovedinanimportantpaper,writtenbytheIrishphysicistJohnBell,in1964.

Inthecaseofphotons,weasknotaboutpoliticalorpetpreferences,butaboutpolarization.Anelectromagneticwaveconsistsofoscillatingelectricandmagneticfields.Theoscillationsareperpendiculartothedirectioninwhichthewaveistraveling.Theseoscillationsdefineaplane,whichjumpsaroundasthefieldsoscillate.Wesaythatlightispolarizedwhentheelectricfieldoscillatessteadilyinaparticularplane.Individualphotonsthatpassthroughapolarizedlens,suchasarecommoninsunglasses,haveawell-definedpolarization.

FIGURE3.Thisfigureshowswhatwemeanbysayingthatelectromagneticradiationcanbepolarized.Herearetracesoftwowavesmovingthroughtheelectricfield,intheabsenceofexternalcurrentsandcharges.Notethattheelectricfieldpointsperpendiculartothedirectionofmotionofthewave.Theoscillationsofthefield,togetherwiththedirectionofmotion,defineaplaneinthree-dimensionalspace.Thisiscalledtheplaneofpolarization.Weshowtwoplanesofpolarization,perpendiculartooneanother.

WecanproducepairsofphotonsthattogetherhavepolarizationsintheCONTRARYstate.Toshowthisweletthemtravelinoppositedirectionstilltheyarefarfromeachother,thenweputintheirpaths

polarizedglass,whichtheyeitherpassthroughornot.InthestateCONTRARY,iftheglasseshavethesameplaneofpolarization,oneofthetwophotonswillpassthroughtheglass,buttheotherwon’t.Whichonepasses,however,israndombecauseinthestateCONTRARYtheirindividualpropertiesarecompletelyuncertain.

Wecanalsoswiveloneglass,whichrotatestheplaneofpolarizationtooneside.Thetwopolarizersarenowatdifferentangles.Nowsomeofthetimebothphotonspass.Howfrequentlybothpassdependsontheanglebetweenthepolarizers.Whentheanglebetweenthetwopolarizersiszero,weareaskingthesamequestiononeachsideanditneverhappensthatbothpass.Letusthenrotateonepolarizerabit,sothattheyareaskingslightlydifferentquestions.Nowinafewinstancesphotonspassonbothsides.Weaskabouthowtheproportionofcasesinwhichtheybothpassincreasesaswevarytheanglebetweenthetwoplanesofpolarization.

Bellintroducedanassumptionwhichexpressedtheideathatphysicsislocal,inthatinformationcannottravelfasterthanlight.Thisrequiresthatwhenthetwophotonsareveryfarapart,thequestionsIchoosetoaskonephotoncannotaffecttheanswerstheotherwillgive.

Fromthisassumption,Bellderivedarestrictionontheproportionofcasesinwhichbothphotonspasstheirpolarizers.Thisrestrictiondependsontheanglebetweenthetwoplanesofpolarization.

Bellaskedfirstwhethertherestrictionisviolatedbythepredictionsofquantummechanics.Hefoundthatforcertainanglesitisviolated.ThismeansthatquantummechanicsviolatesBell’sprincipleoflocality.Wecaneasilyseethatthisisthecaseinthestoryofourcouple.WhenAnnaandBetheachgoofftowork,theyshareasinglequantumstate,thestateCONTRARY.Thisisnotapropertyofeitheroftheirsasindividuals.Itisasharedproperty;itmakessenseonlywhenitisascribedtothecouple.Thissituationisalreadyintensionwiththephilosophythatphysicalpropertiesarelocal.

Butitgetsworse.WhenBeth’scoworkersaskheraboutherpetpreferenceshesaysshelovescats.Thisimmediatelychangesherquantumstate,asprescribedbyRule2.Itwasoriginallyindefinite,butnowsheispurelyacatperson.Ifaskedagainaboutpetpreferencesheiscertaintosay“cat,”sothestateCATdefinesher.

Butbythesamelogic,becausetheystartedthedayintheCONTRARYstate,Annabecameatthatmomentapersonwithadefinitepreferencefordogs.Ifaskedbyhercolleagueswhichpetssheprefers,Annaisnow100percentcertaintosay“dogs.”

ThusthemeasurementofBeth’spreferenceappearstoinstantlyaffectAnna’sstate.InspiteofthefactthatitwasBethwhowasmeasured,andAnnahastalkedtonoone,Rule2appliestoAnnaaswell.Thisisanexampleofthephenomenonknownasquantumnonlocality.

ThestorywouldbeexactlythesameifBethwereaskedherpoliticalleanings.Whicheverwaysheanswered,Annawouldinstantlybecometheother.

OnceBethisaskedaboutoneofherpreferences,sheandAnnanolongershareastate.Bethnowhasadefinitestateofherown,andyoucansaythiswastheresultofherbeingmeasured.Whatisweirdisthat,becausetheywereoriginallytogetherintheentangledstateCONTRARY,whenBethisqueriedthisimmediatelychangesAnna’sstateaswell.ByvirtueoftheanswerthatBethgives,Annaisimmediatelydefinedasbeinginaquantumstateofherown,towit,theoppositeofwhateveranswerBethgives.

ThishappenseventhoughnoonehasyetaskedAnnaanything.Bethandhercolleaguesmaybelight-yearsaway,sonoinformationaboutwhatBethwasaskedandwhatsheansweredcouldreachAnnaforyears,assumingtheusualrestrictiononthetransmissionofinformation.ThisistosaythatAnnaherselfcannotknowyetthatherquantumstatehaschanged.Butithas,ifquantumtheoryiscorrect.

Ofcourse,thestorywouldbethesameifitwereAnnawhohadbeenaskedfirst.Theconsequencesofsharinganentangledstateareentirelysymmetric.

—THESTRANGEBEHAVIORofthequantumstateCONTRARYwasdiscoveredbyEinstein,anditwasthecenterpieceofapaperhewrotein1935withtwoyoungercolleagues,BorisPodolskyandNathanRosen.1Thethreeauthors(sometimesabbreviatedasEPR)usedanexperimentlikeI’vedescribedtoarguethatquantummechanicsmustbeincomplete.Toarriveatthatconclusiontheygaveacriterionforwhenapropertyofaphysicalsystemmustbeconsideredreal.Hereistheircriterion:

If,withoutinanywaydisturbingasystem,youcandetermineapropertyofitwith100percentcertainty,theremustbeanelementofphysicalrealityassociatedtothatproperty.

Einsteinandhiscollaboratorsalsoassumedthatyoucouldonlydisturbasystembydoingsomethingphysicallytoit.Mostimportantly,theyalsoassumedthatanyphysicaldisturbanceislocal,andishencerestrictedtotravelingatthespeedoflightorless.Thisimpliesinparticularthat

AnnacannotbephysicallyaffectedbythechoiceofquestionsBethisaskeduntilenoughtimehaspassedforalightsignaltohavecarriedtheinformationaboutwhichquestionBethwasaskedfromBethtoAnna.

WehavejustseenthatonceBeth’scolleaguesqueryBethaboutherpetpreference,theyalsoknowAnna’spetpreference.However,Einsteinandhisfriendsbelievedstronglyintheprincipleoflocality,whichimpliesthat,becausetheyarefarapart,AnnacannothavebeendisturbedbyquestionsaskedofherfarawayfriendBeth.Hence,thecriterionforrealityjustenunciatedissatisfiedandwecanconcludethatAnna’spetpreferenceisanelementofreality.

Moreover,whatisrealconcerningAnnacan’tbeaffectedbyanythingthathappensordoesn’thappentoBeth.SoAnna’spetpreferencemustberealwhetherornotBeth’spetpreferencewasqueried.

Now,noticethatBeth’scolleaguesmightinsteadhaveaskedaboutherpolitics.ThesameargumentworksandwemustconcludethatAnna’spoliticalpreferenceisalsoanelementofreality.Andagain,thisistruewhetherornotBeth’spoliticswasqueried.

SowemustconcludethatbothAnna’spetpreferenceandherpoliticsareelementsofreality!

Butquantumstatescannotsimultaneouslydescribebothsomeone’spoliticsandtheirpetpreference.Hence,Anna’squantumstateincompletelydescribesher.

Andso,concludedEinstein,Podolsky,andRosen,thedescriptionoftheworldintermsofquantumstatesisincomplete.

I’vebeenthinkingaboutthisargumentsincemyfirstyearofcollege.SofarasIcantellit’slogicallycorrect.Butnoticethatitdependsontheassumptionthatphysicsislocal.EinsteinandhisyoungfriendsassumedlocalitywhentheypositedthatAnnacannotbephysicallyaffectedbythechoiceofquestionsBethisaskedwhentheyarefarapart.

Bellmadeexactlythesameassumption,regardingphotonsratherthanpeople,inderivinghisrestriction.

Whenthetwophotonsareveryfarapart,thequestionsIchoosetoaskonephotoncannotaffecttheanswerstheotherwillgive.

Thisis,indeed,theonlynon-trivialassumptioninBell’sargument.Sosince,asIsaid,Bell’srestrictiondisagreeswithquantummechanics,itmustbethatquantummechanicsitselfdisagreeswithlocality.

Butwecangofurtherandtestdirectlywhetherlocality,asassumedbyEPRandBell,isviolatedbynature.

TheimportanceofBell’srestrictionisthatitappliesnotonlytoquantummechanics.TherestrictionhederivedconstrainsanytheorythatsatisfiesBell’sandEPR’sprincipleoflocality.Thisincludestheoriesthatareintendedtoreplacequantummechanics.Itwillapplyequallytoanytheorywhichmightbeinventedinthefuture.Thismeansthatwecansetupexperimentsthatdirectlytestthelocalityprinciple.

Fortunately,Bell’srestrictioncouldbetestedbyarelativelyinexpensivedevice,hand-builtinasingleroom.Afewbravesoulsbegantheworkofbuildingexperimentstotestthetheorem.Afterseveralattemptsgotpartialandcontradictoryresults,thedefinitiveexperimentswerecarriedoutinOrsay,nearParis,intheearly1980sbyAlainAspectandhiscollaborators,JeanDalibard,PhilippeGrangier,andGérardRoger.2

InAspect’sexperimentstheentangledparticlesarephotonsandthequestionsaskedareabouttheirplanesofpolarization.Theseexperimentsbeginwithanatomraisedfromitsgroundstateintoanexcitedstate,byaphotonfromalaser.Thesearechosensothatwhentheexcitedatomdecaysbacktothegroundstate,itdoessoinawaythatproducesapairofentangledphotons,inthestateCONTRARY.Thephotonsflyoffinoppositedirectionsandafterafewfeetencounterpolarizers,whichmeasuretheirpolarizationsrelativetoaplane.Theplaneofeachpolarizercanbesetfreely,inwhateverpositiontheexperimenterchooses,sothecorrelationsofthepolarizationsofthetwophotonscanbe

measured.TheresultscleanlyviolatedBell’srestrictionwhileagreeingpreciselywiththepredictionsofquantumtheory.

TheexperimentstellusthattheassumptionofBelllocalityhighlightedaboveisfalse!Thequantumworlddoesnotobeytheprincipleoflocality.

Ifthisisnotthemostshockingnewsyouhaveheardfromtheworldofscience,youhaveperhapsnotunderstoodit.Naturedoesnotsatisfytheideaoflocality.Twoparticles,indeedtwoobjectsintheworld,situatedfarfromeachother,cansharepropertiesthatcannotbeattributedtopropertiesseparatelyenjoyedbyeither.

Atthispointitisnaturaltowonderiftheprinciplethatinformationcannotbetransmittedfasterthanlightcouldbeviolated,bytakingadvantageofthecircumstancethatBethandAnnashareanentangledstate.CouldthefactthatAnna’sstateischangedabruptly,basedonwhichquestionBethisasked,beusedbyBeth’scolleaguestosendamessageinstantaneouslytoAnna’scolleagues?

Theansweristhatinformationcannotbesentfasterthanlight,becausetherelationbetweenAnna’sstateandtheanswersshegivesisrandom.NomatterwhatquestionAnnaisasked,heranswersare50percenteitherway.ThisistruebeforeBethisqueried,whenshesharesthestateCONTRARYwithAnna,anditremainstrueafterward.Itisonlywhenthelistsofanswerseachgavetoaseriesofquestionsarebroughttogetherandcomparedthatevidenceofmysteriouscorrelationsappears.Andthelistsareordinaryclassicalobjectsthatcannotbetransmittedfasterthanlight.

Thereisanother,relatedpossibility,whichAspectandhiscolleaguescouldalsotest.Perhaps,atsomedeeperlevelthanthatdescribedbyquantumtheory,thetwoatomsareincommunication,sothatthefirstphotontobemeasuredtransmitsinformationtotheotherphotonaboutwhatquestionitwasasked.Thentheprincipleoflocalitycouldstillbesatisfied.Butnowwehavetoreckonwithspecialrelativity,whichmaintainsthatnoinformationcantravelfasterthanlight.Totestforthispossibility,theexperimentwasredonewitharandomswitchononeside,whichcouldveryrapidlychoosewhichquestionwouldbeaskedofitsphoton.Thisswitchwasfastenoughthatthechoicewasmadewhilethephotonswereinflight.Thustheswitchinghappenedfasterthancouldbecommunicatedtotheotherphotonbyanysignaltravelingatlightspeed

orless.Theresultwasunchanged.Ifthetwophotonsareincommunication,theirmessagesarebeingtransmittedmuchfasterthanlight,andrelativitytheoryisviolated.

WhatarewethentomakeoftheargumentofEinstein,Podolsky,andRosen?Ascleverasitwas,theargumentmustbeconsidered,inlightoftheexperimentalfindings,tobewrong,becauseitreliesonanincorrectassumption,whichistheassumptionoflocality.TheexperimentaltestsofBell’sinequalityshowusthat,onceAnnaandBethareentangledinthestateCONTRARY,AnnainfactisphysicallyaffectedbythechoiceofquestionsBethisasked.Thisremainstrueevenwhentheyarefarapart.Thisistrueinquantummechanics,and,theexperimentsimply,itmustbetrueinanydeepertheorythatcompletesquantummechanics.

Nevertheless,EPR’spaperwasenormouslyimportant,becauseitexposedanunexpectedaspectofquantumphysics,whichwasentanglement.Thistookdecadestoappreciate;indeed,theEPRpaperwaswayaheadofitstime.Apartfromthediscoveryofentanglement,thepaperwasthestartingpointforBellandhencefortheshockingexperimentaldiscoverythatphysicsviolatestheprincipleoflocality.

Bohr,thegreatanti-realist,repliedrightawaytotheEPRpaper,withanespeciallyobscureexampleofhisstyleofreasoning.3HetookissuewithEPR’scriteriaforrealitybypointingoutthatameasurementofoneoftheparticlesdisturbstheotherparticleindirectly,bydisturbingthecontextwithinwhichthepropertiesoftheotherparticlemakesense.

ForthenextfifteenyearsthereisjustonepaperwrittenwhichcitestheEPRpaper.ThenextseveralcitationsarebyBohmandEverettinthe1950s.JohnBellwasjustthesixthauthortociteEPR,whichhedidinhisgreatpaperof1964,almostthirtyyearslater.Yetthepaperwascitedmorethansixtytimesin2015,andagainin2016.Wenow,finally,liveintheeraofentanglement.

Inrecentyears,thesharingofpropertiesamongentangledpairshasbeenconfirmedinexperimentsinwhichthepairsareseparatedbyhundredsofkilometers.Entanglementisfastevolvingfromalaboratorycuriosityintoatechnology.Itisnowconsideredaresource,whichisattheheartofanewkindofcomputer—aquantumcomputer.Inthenearfutureentanglementmayallowustobreakcodeslongthoughtsecureasitalsomakespossiblenewkindsofcodesthataretrulyunbreakable.

Therearealreadyinorbitquantumcommunicationssatellites,whichemployentangledpairstoencryptmessagestheytransmit.

Einstein’sfirstrevolutionarypapersappearedin1905,whenhewastwenty-six.Thirtyyearslater,theEPRpaperwasthelastpaperbyEinsteintoshakephysicstothecore.Itisgiventoveryfewtoleadscienceoverthreedecades.Einsteinneverceasedtryingtofindthedeepertheorybeyondquantummechanics,andtwodecadesfurtheron,hewasstillworkinginhisnotebookinthehospitalthenighthedied.Buthefailed,andthesimplereasonwasthatheneverunderstoodthatthecentralassumptionbehindmanyofhisgreatpapers—theprinciplethatphysicsislocal—waswrong.

ThereisnoreasonBell’s1964papercouldnothavebeenwritteninthelate1930s,shortlyafterEPR.Andtheexperimentaldisproofoflocalitycouldhavehappenedshortlyafter.OnecanonlywonderwhatEinsteinwouldhavethoughthadhelearnedofBellandAspectinthe1940s.

—TOGETHERTHESTORIESIhavetoldsofarillustratethestrangenessofthequantumworld.Theyhavetaughtusaboutthewave-particleduality,superposition,andtheuncertaintyprinciple.

Strangerstillwashowquantumpropertiescanbeentangledandsharedamongsystemsthatarewidelyseparatedinspace.ThiswastheultimatelessonofthestorytoldbyEinstein,Podolsky,andRosen.ButitwasonlyinJohnBell’sretellingthatthetruemoralofthestorywasrevealedtobetheradicalnatureofquantumnonlocality.

Aswesaw,superpositioncanbeunderstoodasaquantumversionof“or,”whichIwillindicateasor.Whenwecombinetwosystems,weuseaquantumversionof“and.”Iwillwritethisasand.Eachbehavesdifferentlyfromtheordinaryusageof“or”and“and”thatweareusedtofromeverydaylife.Butitiswhentheyacttogetherthattrulystrangethingshappen.WeseethisinafamousexperimentcalledSchrödinger’scat.

Letusstartwithaverysimplemodelofanatom,whichcanexistintwostates:anexcited,unstablestate,whichwecallEXCITED,andastablegroundstatewithlowerenergy,calledGROUND.EXCITED,beingunstable,willdecayintoGROUNDbyemittingaphoton,whichcarries

awaytheenergy.Thesedecaystakeplaceataratemeasuredbythehalf-lifeoftheexcitedstate.

LetusputanatominthestateEXCITEDinaboxandwaitatimecomparabletothehalf-life.Ifwedon’tlookinthebox,wecandeduceonlythattheprobabilityisabouthalfthatifweopentheboxwewillseethattheatomhasdecayedtothestateGROUND.Butwhatisthestatebeforewelookinsidethebox?Accordingtoquantummechanics,itisneitherEXCITEDnorGROUND,butasuperpositionofthem.Wecanwritethisas

ATOM=EXCITEDorGROUND

AccordingtoRule2,thissuperpositionhasthepotentialofbecoming,whenwelook,eitherofthetwostates:EXCITEDorGROUND.Ifwehavealargecollectionofsuchstates,thenwecandetermineprobabilitiesforeachoftheseoutcomes.Theseprobabilitieschangeintime.Justaftermakingtheatom,theprobabilitythatithasdecayedisverysmall.Manytimesthehalf-lifelater,ithasalmostcertainlydecayed.

Asuperpositionisnotthesameashavingoneortheotherstatewithvaryingprobabilities.Onereasonisthatwhenwemaketheenergyuncertainbysuperposingtwostatesofdifferentenergies,anotherobservablewillbemadecertain.Thisislikethewaywemadeourvisitorshavedefinitepoliticalviewsbysuperposingtheirstateswithdifferentpetpreferences.SowecanalwaysfindaquestioncomplementarytotheenergythattheanswertowillbeYESwithcertainty.ThatwouldnotbethecaseifwewerejustdealingwiththeprobabilitiesofbeingEXCITEDorGROUND.

WenextputaGeigercounterinthebox,andsetituptosendoutapulseofelectricitywheneveritseesaphoton.

Fromthepointofviewofquantummechanics,theGeigercountercanalsoexistintwodifferentstates.ThereisthestateNO,inwhichithasn’tseenaphoton,andthestateYES,whenithas.Itcanalsoexistinsuperpositionofthesetwostates.

WeputtheatomintheboxwiththeGeigercounter.WemustbecarefultosetthemupsothatinitiallytheatomisinthestateEXCITEDandtheGeigercounterisinthestateNO.

INITIAL=EXCITEDandNO

Byandweunderstandthatthesestates,beingstatesoftwodifferentsystems,arebeingcombined,notsuperposed.

Muchlater,ifeverythingisworkingwell,weexpecttoseetheatominthestateGROUNDandtheGeigercounterinthestateYES.ThiscorrespondstotheGeigercounterhavingdetectedthephotonemittedwhentheatomdecayed.

FINAL=GROUNDandYES

Inbetween,thesystemisinasuperpositionofthesetwostates.

INBETWEEN=(GROUNDandYES)or(EXCITEDandNO)

ThetotalsystemisasuperpositionofastatewheretheatomisintheundecayedstateEXCITEDandtheGeigercounterisinthestateNOwiththeotherpossibility,whichisthestateinwhichtheatomhasdecayedtoGROUNDandtheGeigercounterisinthestateYES,inwhichithasseenthephoton.

ThisstateINBETWEENisanexampleofacorrelatedstate.Wecallitthatbecausethepropertiesofthetwosystemsarecorrelated.Thestateoftheatomisuncertain,butifweknowwhatstatetheatomisin,wecandeducewhichstatetheGeigercounterwillbein.

Butifwethenopentheboxandlookinside,weneverseeasuperposition.LookinginsideisameasurementwhichisgovernedbyRule2.WeseeeitherthattheGeigercounterhasclicked,sotheatomhasdecayed,orthattheatomisstillexcitedandthecounterhasyettoclick.

Thisseemsdownrightweird.Herearesomeofthequestionsitraises.Whyaretheretworulesforhowquantumsystemschangeintime,

ratherthanone?Whydowetreatmeasurementsandobservationsdifferentlyfrom

otherprocesses?Certainlyameasurementdeviceisjustamachinemadeoutofatoms.Shouldn’ttherejustbeoneruleforhowthingschangeintime,whichappliesinallcases?

Andjustwhatisitaboutmeasuringdevicesthatmakesthemdifferent?Isitjustthesizeorcomplexityofthedevice?Isitthevastnumberofatomsmakingitup?Orisitthefactthatitcanbeusedtogaininformation?

Whendoesthecollapsetoadefinitestatehappen?Isitwhentheatommeetsthedetector?Orwhenthesignalisamplified?Orisitnotuntilwebecomeconsciousoftheinformation?

Thesequestionsareallaspectsofthemeasurementproblem.Thesimplestansweristhat,onewayoranother,itmustbethisway.

Weneverobservelargethingstobeindefinite:inourworldtherearenoGeigercountersthatbothhaveandhavenotclicked.Everyquestionweaskhasadefiniteanswer.Butweneedsuperpositionstoexplainatomsandradiation.

Toemphasizehowstrangethisallis,SchrödingerputacatintheboxalongwiththeatomandtheGeigercounter.HewiredupthesignalfromtheGeigercountertoatransformer,whoseoutputwasclippedtothecat’sears.WhentheGeigercountersignaleditsdetectionofthephoton,thecatgotafatalpulseofelectricity.

(OfcourseSchrödingerdidn’tactuallydothis.Thisisathoughtexperimentintendedtoshockus,notthecat.)

Wewaitahalf-lifeandthenopenthebox.DoweapplyRule1orRule2?Let’sdiscusswhateachofthetworuleswouldpredict.

AssumefirstthatRule1appliestothewholesysteminsidethebox,includingthecat.Thatsystemconsistsoftheatom,theGeigercounter,andthecat.Thereareagaintwostateswitheasyinterpretations.Oneoftheseistheinitialstate

INITIAL=EXCITEDandNOandALIVE

Thisisthestateinwhichtheatomisexcited,theGeigercounterhasdetectednothing,andthecatisalive.Afteralongtimewecanbesuretheatomhasdecayedandthecathasdied.

FINAL=GROUNDandYESandDEAD

Thisstateistheresultofthedecayandfeaturesastableatominthegroundstate,adetectorthatclicked,andadeadcat.

Inbetween,thestateisasuperpositionofthesetwopossibilities.

INBETWEEN=(EXCITEDandNOandALIVE)or(GROUNDandYESandDEAD)

Butacatisamammal,withabrainandperhapsaconsciousmind.Itisnearlyascomplexasweare.Sowhydoesitmakesenseforthecattobeinasuperpositionofaliveanddead?Ifitdoesn’tmakesenseforustoexistinasuperposition,itsurelydoesn’tforthecateither.IfweapplyRule2toourobservation,weshouldalsoapplyittothecat,whoinessenceobservesthesignalfromthedetector.

Sowe’dbetterapplyRule2.Whenweopenthebox,thesystemmakesachoiceandjumpsintoadefinitestate.Wefindeitheralivecatoradeadcat.

SoRule1alonedoesnotapplytohumansorcats.ButdoesitapplytoGeigercounters?Andwhereistheline?Whydoesitapplytoatomsandnottobigcollectionsofatomslikedetectors,cats,andhumans?

FIGURE4.TheSchrödinger’scatthoughtexperiment.Adetectorisconstructedtorespondwithanelectricalpulsetoaphotonthatwouldbeemittedbyanatomdecayingandjumpingdownfromanexcitedstateintothegroundstate.Thecatisconnectedtothecircuit,sowhenthepulsecomesitwillelectrocutehim.Afterashorttime,theatomisinasuperpositionofitsexcitedanddecayedstates.Rule1appliedtothiscasepredictsthatthecatinsidetheclosedboxistheninasuperpositionoftwostates,aliveanddead.

ThisconversationiscalledthepuzzleofSchrödinger’scat.Ameasureofthefecundityofthehumanimaginationisthenumberofresponsesthathavebeenofferedtothispuzzle.

—AFEWYEARSAFTERBellpublishedhisrestriction,anevenmorepowerfulresultwaspublishedwhichfurtherlimitstheoptionsforrealistquantumtheories.TodescribeitwegobacktoBell.

OnewaytoputwhatissurprisingaboutBell’sresultisthattheanswersthatAnnagivestothequestionssheisposedhavetodependonthequestionsthatBethisasked.ThisisshockingbecauseAnnaandBethareseparated,solocalitywouldprecludesuchadependence.Butnoticethattheydon’tneedtobeseparatedfortheconclusiontoapply.Thenthe

resultthatAnna’sanswersdependonthequestionsBethisaskedissurprisingforanotherreason.

Earlierwetalkedaboutpairsofmeasurementswhicharemutuallyincompatible,likeaparticle’spositionandmomentum.Inthesecasesitseemsthattheactofmeasuringonequantityinterfereswithordisturbsthevalueoftheother.Wedescribedthisbysayingthattheorderinwhichthetwomeasurementsaremadematters.

ButnoticethatthecaseofAnnaandBethisnotlikethis.QuestionsaskedofBetharecompletelycompatiblewithquestionsaskedofAnna.Theorderinwhichtheyarequestioneddoesn’tmatter.Thiswastruewhenthetwofriendswerefarapartwhentheywerequestioned,butitwouldremaintrueiftheywerestandingnexttoeachother.

Still,eveniftheorderinwhichwequestionthetwofriendsisirrelevant,sothatquestionstoonearecompatiblewithquestionstotheother,itremainsthecasethattheanswersAnnagivesdependonthechoiceofwhichquestionsBethisasked.

Thisdependenceiscalledcontextuality,becausetheanswersAnnagivesturnouttodependontheoverallcontext,eventothepointthattheydependonchoicesmadeaboutwhichotherquestionswillbeasked.Itturnsouttobewidelytrueofquantummechanicalsystems.Contextualityoccursinsituationsinwhichoursystemisdescribedbyatleastthreeproperties,whichwecancallA,B,andC.AiscompatiblewithbothBandC,soAmaybemeasuredsimultaneouslywitheitherBorC.ButBandCarenotcompatiblewitheachother,sowecanmeasureonlyoneatatime.

SowecanmeasureAandBorwecanmeasureAandC.Wemakeaseriesofexperimentsinwhichwemakebothchoices,andwerecordalltheanswers.Whenwedowewillfind—assumingthatquantummechanicsiscorrect—thattheanswerstoAdependonwhetherwechosetomeasureBorCalongwithA.Theconclusionisthatnatureiscontextual.Thisisthecasewithquantummechanics,andexperimentshavebeendonewhichconfirmthispredictionofthetheory.Soitmustbetrueinanydeepertheorywhichwillreplacequantummechanics.

ThisresultwasfirstprovedbyJohnBellintheearly1960s,beforehepublishedhisresultonnonlocality.Hesubmittedittoajournalbutthepaperwasapparentlylostfortwoyears,“ontheeditor’sdesk,”soitwasn’tpublishedtill1966.Bythentheresulthadbeenprovedagainby

twomathematicians,SimonKochenandErnstSpecker,sotheresultthatquantummechanicsiscontextualisoftenattributedtothem,butitoughtproperlytobecalledtheBell-Kochen-Speckertheorem.4

Quantummechanicswasinventedinordertoexplaincertainpuzzlingexperimentalresultsconcerninglight,radiation,andatoms.Thethreenewphenomenawediscussedinthischapter—entanglement,nonlocality,andcontextuality—areafardistancemorepuzzling.Eachissoweirdthattheywereforatimeusedtoarguethatquantummechanicsmustbewrong,tillexperimentsconfirmedthattheyareindeedallaspectsofthenaturalworld.Thiswascertainlynotanticipated.Entanglement,nonlocality,andcontextualityeachemergedfromthestudyofquantumsystems,anditisveryfairtosaythattheywereeachpredictionsofthequantumtheorywhich,verysurprisingly,turnedouttobetrue.

Thesethreeaspectsofquantumphysicspresentseverechallengestorealism.Indeed,theyruleoutlargeclassesofrealisttheories.Inparticular,nonlocalentanglementisincompatiblewithalltheorieswhosebeablesinfluenceeachotheronlythroughlocalforces,whoseactionspropagateatthespeedoflightorslower.Anyrealisttheorywhichcanmimicquantummechanicsmustthendescribeaworldwhichviolatesthisconditionandsoopenlyembracesnonlocality.ThisiswhyEinsteintalkedof“spookyactionatadistance.”Thechoicewefaceissimple:wemaygiveuprealismandacceptquantummechanicsasthefinalword,orwecanmoveaheadandseektounderstandhownatureviolateslocalitywhilestillmanagingtomakesenseatall.

Q

FIVE

WhatQuantumMechanicsDoesn’tExplain

uantummechanicsdoesn’tanswereveryquestionwecanaskabouttheatomicworld,butitgetsalotright.Thisisagoodtimetosumupwhatwe’velearnedaboutwhatquantummechanics

doesanddoesnotexplain.Roughlyspeaking,quantummechanicspredictsandexplainstwo

kindsofproperties:propertiesofindividualsystems,andaveragestakenovermanyindividualsystems.Theseareverydifferent.

Whenwecanattributeadefinitevaluetoaquantity—aswecanwhenwemakeameasurement—thisisapropertyoftheindividualsystemthathasbeenmeasured.Butoftentheuncertaintyprincipleforbidsusfromdiscussinganythingotherthanaverages.

Towhatdotheseaveragesrefer?Becauseoftheuncertaintyprincipleitcanhappenthattwoatoms,preparedidenticallyinthesameinitialstate,givedifferentvalueswhenmeasuredlater.Forexample,atomspreparedinthesamestartingpositionwilltendtospreadout,andbefoundindifferentplaceslater.Whenthefinalanswersvarywecanstillmeasuretheiraveragevalue.Quantummechanicstellsustheseaveragesaretakenovermanyrunsofanexperiment.Anexperimentrequiresustopreparemanycopiesofasystem,waitandthenmeasureeachcopy,andthentaketheaverageoftheresults.

Acollectionofatomswhicharesimilarinsomewaybutdifferentinothersiscalledanensemble.Quantummechanicsdealswithensembles.Thesemaybedefinedbyfixingonequantity,suchasenergy,tohavesomedefinitevalue,whileotherparametersvaryoverarangeofvalues,asrequiredbytheuncertaintyprinciple.Whenwespeakofaveragesor

probabilityinquantummechanics,weareusuallyreferringtosomethingthatcanbemeasuredbytakinganaverageoverthemembersofanensembleconsistingofmanycopiesoftheatominquestion.

Thatisofteneasytodobecausemanyexperimentsdealwithacollectionofatoms,suchasagas.Thesearerealensembles,becausetheatomsinthecollectionarereal.Sometimes,though,theensembleexistsonlyinthetheorist’simagination.

Itisnormaltoexplaintheresultsofaveragingovermanycopiesofanindividualsystemintermsofthepropertiesofthoseindividualsystems.However,inquantummechanicsitisoftentheotherwayaround,andapropertyofanindividualatomwillbeexplainedintermsofaveragesovermanyatoms.Buthowcanthecollectivedeterminetheindividual?Thesekindsofcasesareattheheartofwhatismostmysteriousaboutthequantumworld.

Oneoftheindividualpropertiesthatquantummechanicscandiscussistheenergyofanatomormolecule.Itturnsoutthatinquantummechanicstheenergiesofmanysystemscomeincertaindiscretevalues,calledthespectrum.Thespectrumisapropertyofindividualatoms,asitcanbeobservedinexperimentsinvolvingjustoneatom.Atoms,molecules,andvariousmaterialsallhavespectra,andinallthesecasestheyarecorrectlypredictedbyquantummechanics.Morethanthat,quantummechanicsexplainswhythesesystemscanhaveonlytheseenergies.Itaccomplishesthisbymakinguseofthewave-particleduality.Thisisoneplacewhereaveragesovermanysystemsareusedtoexplainwhathappensinanindividualsystem.

Theexplanationinvolvestwosteps.Thefirstistousetherelationbetweenenergyandfrequency,whichisthefoundationofthewave-particleduality.Aspectrumofdiscretevaluesofenergycorrespondstoaspectrumofdiscretefrequencies.Thesecondstepexploitsthepictureofaquantumstateasawave.Awaveringingatadefinitefrequencyislikeabelloraguitarstringproducingsound.Thestringresonateswhenplucked,asdoesthebellwhenstruck,ringingatadefinitefrequency.

Wethenusetheequationforquantumstateschangingintimetopredicttheresonantfrequenciesofthesystem.Theequationtakesasinputthemassesoftheparticlesinvolvedinthesystemandtheforcesbetweenthem,andgivesasoutputthespectrumofresonantfrequencies.Thesearethentranslatedintoresonantenergies.

Thisworkswell.Forexample,ifweinputthatthesystemismadeofanelectronandaproton,boundtogetherbytheirelectricalattraction,theequationoutputsthespectrumofthehydrogenatom.

Inmostcases,thereisastateoflowestenergy,whichiscalledthegroundstate.Statesofhigherenergyarecalledexcitedstates.Youexcitethegroundstatebyaddingtheenergyneededtobringituptothelevelofoneoftheseexcitedstates.Thiscausesthestatetotransitionfromthegroundstatetotheexcitedstate.Theaddedenergyisoftendeliveredbyphotons.Excitedstatestendtobeunstable,becausetheycandropbackdowntothegroundstatebyradiatingawaytheexcessenergyintheformofaphoton.Thegroundstatehasnostatebelowittodecayto,andsoitisstable.Mostsystemsspendmostofthetimeintheirgroundstates.

Thismethodhasbeentestedonagreatmanysystems,includingatoms,molecules,nuclei,andsolids.Inallcasesthepredictedspectraareobserved.Inadditiontogettingthespectrumofpossibleenergiesright,quantummechanicsmakespredictionsforaveragedquantities,suchasaveragevaluesofthepositionsoftheparticlesmakingupthesystem.

Foreachresonantfrequency,theequationthatdefinesquantummechanicscanbesolvedtoyieldthecorrespondingwave.WethenuseBorn’srule(thatthesquareofthewaveisproportionaltotheprobabilityoffindingtheparticle)topredictprobabilitiesfortheparticletobefounddifferentplaces.

Thestatesofdefiniteenergyhaveindefinitepositions.Supposeweprepareamilliondifferenthydrogenatoms,allinthegroundstate.Ineachofthese,wemeasurethepositionoftheelectron(relativetotheproton,whichisheldfixedinthecenteroftheatom).Eachindividualmeasurementresultsinadifferentposition.Measuringamilliondifferentatomsgivesusamilliondifferentpositions.Somewillbefarfromtheproton,butmostwillbeclusteredaroundtheprotoninthecenter.Thearrayofpossiblepositionsmakesupastatisticaldistributionanditisthisdistribution,ratherthanadefiniteposition,thatquantummechanicspredicts.

Accordingtotheuncertaintyprinciple,thepositionofanyoneoftheelectronscannotbepredicted.Butthestatisticaldistributionofpositions,whichresultsfrommeasuringagreatmanycases,canbefound.Thesestatisticaldistributionsarecomputedbysquaringthewave.

Tosummarize,quantummechanicsmakestwokindsofpredictions.Itmakespredictionsforthediscretespectraofenergies,orotherquantities,asystemcanhave.Anditalsomakespredictionsforstatisticaldistributionsofquantitiessuchaspositionsofparticles.

IneverycaseIknowof,thesetwokindsofpredictionshavebeenconfirmedbyexperiment.Thisisexceedinglyimpressive.

Butdoesquantummechanicsexplainhowindividualatomswork?Isasuccessfulpredictionalwaysthesameasanexplanation?

—ITISEQUALLYIMPRESSIVEwhatquantummechanicsdoesnotdo.Itdoesnotdescribeorpredictwhereaparticularindividualelectronwillbefound.Becauseitdealsinaverages,quantummechanicshaslittletotellusaboutwhatgoesoninindividualsystems.

Therearelotsofcaseswherewedealwithaverages.WehavenoproblemmeasuringtheaverageheightofCanadians.ThisisbecauseeachCanadianissomedefinitenumberofcentimeterstall.Weaddallthosecentimetersup,dividebythenumberofCanadianswemeasured,andwegettheaverage.

Incaseslikethis,theaverageismadeupofindividualheights,whicharepropertiesofindividuals.Wecouldchoosetoworkwiththewholelistofheights,butformanypurposes,suchasdesigningfurnitureorcars,theaveragedvalueisallweneed.Ifweneedanythingelse,itislikelytobethestandarddeviation,whichtellsusthetypicalrangeofvariationsofheight.Usingtheaverageandstandarddeviation,anairlinecould(ifitwantedto)buildairplaneseatsinwhich95percentofCanadianswouldbecomfortable.

Inthesecases,theinformationwhichweignorewhenweuseaveragesisreallypresentintheworld,butwechoosetosuppressitinfavoroftheaverages.Theuncertaintieswhicharisefromouruseofprobabilitiesarepurelyduetoourignorance.

Butsupposethateachtimewemeasuredsomeone’sheight,wegotadifferentresult.Thereisthenanelementofgenuinerandomness,becausethereisnowayforustoknowhowtallsomeonemightbethenexttimetheyaremeasured.Thatisclosertothecasewedealwithinquantumtheory.Whatdoestheaveragesignify,andwhatdoesitexplain,whenthereisnostoryaboutindividualcases?

Quantummechanicsmakescorrectpredictionsforaverages,inspiteofhavingnothingdefinitetosayaboutindividualcases.Weseemtolackthekindofexplanationweusuallyexpectincaseslikeheight,wherethebasisofanaverageisfoundinthefactthattheaverageiscomposedofindividualcases.

—ONEOFTHEMOSTUNEXPECTEDASPECTSofquantummechanicsisthatasystemcanchangeovertimeintwoways.Idescribedtheseinchapter3.MostofthetimethequantumstateevolvesdeterministicallyunderRule1.ButwhenwemakeameasurementofthesystemitevolvesinaverydifferentwayunderRule2.Themeasurementwillproduceonenumberoutofarangeofpossiblevalues.Justafterthemeasurement,thequantumstatejumpsintoastatecorrespondingtothedefinitevaluewhichwasmeasuredintheexperiment.

Rule1iscontinuousanddeterministic;Rule2bycontrastisabruptandprobabilistic.Thestatejumpsabruptlyjustafterthemeasurement,butquantummechanicspredictsonlyprobabilitiesforthedifferentoutcomes,andhenceforwhichstatethesystemjumpsto.

Mostpeopleareperplexedwhentheylearnaboutthesetworules.Aswediscussedbefore,thesituationisgenuinelypuzzling.Thefirstthingthatpuzzlesthemisthemeasurementproblem:What’ssospecialaboutameasurement?Aren’tmeasuringdevicesandthepeoplewhousethemmadeofatoms,towhichRule1applies?

Rule1,bydictatinghowaquantumsystemchangesintime,playsthesameessentialroleinthetheorythatNewton’slawsofmotionplayedinpre-quantumphysics.LikeNewton’slaws,Rule1isdeterministic.Ittakesaninputstateandevolvesittoadefiniteoutputstateatalatertime.Thismeansittakesinputstateswhichareconstructedassuperpositionstooutputstateswhicharesimilarlyconstructedfromsuperpositions.Probabilityplaysnorole.

Butmeasurements,asdescribedbyRule2,donotevolvesuperpositionstoothersuperpositions.Whenyoumeasuresomequantity,likepetpreferenceorposition,yougetadefinitevalue.Andafterwardthestateistheonecorrespondingtothatdefinitevalue.Soeveniftheinputstateisasuperpositionofstateswithdefinitevaluesof

someobservablequantity,theoutputstateisnot,asitcorrespondstojustonevalue.

Rule2doesnottellyouwhatthedefinitevalueis;itonlypredictsprobabilitiesforthedifferentpossibleoutcomestooccur.Buttheseprobabilitiesarenotspurious;theyarepartofwhatquantummechanicspredicts.Rule2isessential,becausethatishowprobabilitiesenterquantummechanics.Andprobabilitiesareessentialinmanycases;theyarewhatexperimentalistsmeasure.

However,quantummechanicsrequiresthatRule1andRule2neverbeappliedtothesameprocess,becausethetworulescontradicteachother.Thismeanswemustalwaysdistinguishmeasurementsfromotherprocessesinnature.

Yetifwearerealists,thenmeasurementsarejustphysicalprocesses,andthereisnothingspecialthatshoulddistinguishthemfundamentallyfromanythingelsethathappensinnature.Thus,itisveryhardtojustifygivingaspecialroletomeasurementswithinrealism.Hence,itishardtosquarequantummechanicswithrealism.

—ATTHEENDOFTHEDAY,thequestionwillbethis:Canwelivewiththesecontradictionsandpuzzles,ordowewantandexpectmorefromscience?

T

SIX

TheTriumphofAnti-RealismQuantumtheorydoesnotdescribephysicalreality.Whatitdoesisprovideanalgorithmforcomputingprobabilitiesforthemacroscopicevents(“detectorclicks”)thataretheconsequencesofourexperimentalinterventions.This

strictdefinitionofthescopeofquantumtheoryistheonlyinterpretationeverneeded,whetherbyexperimentersor

theorists.—CHRISFUCHSANDASHERPERES

hepersonwhofirstunderstoodthatquantumphysicswouldrequirearadicallynewtheorybasedonadualityofwavesandparticleswasAlbertEinstein.Einsteinwasarealisttothecore.Yet

thequantumrevolutionhesparkedculminatedtwentyyearslaterinatheorythatrequiresthatmeasurementsbesingledoutandtreateddifferentlythanallotherprocesses—adistinctionthat,asIdiscussedinthelastchapter,isforeigntorealism.Theresolution,accordingtomostofthepioneersofthequantumworld,wastogiveuprealism.Howdidthisabandonmentofrealismcometohappen?

TheideaofadualityofwaveandparticlefirstappearedinEinstein’sstudiesofthenatureoflightintheearlyyearsofthetwentiethcentury.Bythattimephysicistshadconsideredtheoriesinwhichlightisaparticleandtheoriesinwhichlightisawave,butalwaysoneortheother.Newtonconsideredthewavetheoryandrejecteditinfavorofatheoryinwhichlightisconveyedbyastreamofparticlestravelingfromobjectstotheeye.(Someancientthinkershadthemgoingtheotherway,whichledtotroubleexplainingwhywedon’tseeinthedark.)Newton’sreasonforthis

choicewasinteresting:hethoughtthatparticlesdidabetterjobofexplainingwhylighttravelsinstraightlines.Waves,heknew,couldbendastheydiffractaroundobstacles,andhedidn’tthinklightcoulddothat.Newton’sparticletheoryoflightreigneduntilanEnglishscientistnamedThomasYoungshowedintheearlyyearsofthenineteenthcenturythatlightdidindeedbendanddiffractattheedgesofobstaclesandasitpassedthroughslits.YoungwasamedicaldoctorwhocontributedtoseveralareasofscienceandmedicineaswellasEgyptology.Hewasanexpertinabroadrangeoffields,somethingthattherapidexpansionofthescienceswasshortlytomakeimpossible.Hewassometimescalled“thelastpersontoknoweverything,”buthisgreatestaccomplishmentwashiswavetheoryoflight,which,togetherwiththeexperimentalevidenceheprovidedfordiffraction,ledtotheoverthrowofNewton’sparticletheory.

OneoftheexamplesYoungconsideredwasthedoubleslitexperiment,whichisillustratedinfigure5.Waterwavesoriginatingfromtheleftpassabreakwallbrokenbytwoslits,onthewaytoabeachontheright.Thewavesfromthetwoslitsinterferewitheachother:theheightofthewaterateachpointtotherightofthewallisacombinationofwavespropagatingfromthetwoslits.Whenthepeaksofthetwowavescoincide,youseereinforcement—thecombinedwaveisatitshighest;butwhenthepeakofonewavearrivesincoincidencewiththetroughoftheother,theycanceleachotherout.Theresultisthepatterngraphedattheright,whichiscalledaninterferencepattern.Thekeythingtounderstandandrememberisthattheinterferencepatternistheresultofwavesarrivingfromthetwoslits.

ThomasYoungwasabletoconstructtheanalogueofadoubleslitapparatusforlight,andhesawaninterferencepattern.Thismadeastrongcaseforlightbeingawave.

FIGURE5.Thedoubleslitexperiment,whichshowsthatlightbehavesasawave.

FurthersupportfortheideathatlightisawavecamefromtheScottishphysicistJamesClerkMaxwell,whoshowedaround1860thatlightisawaveshimmyingthroughtheelectricandmagneticfieldsthatfillspaceastheyconveyforcesbetweenchargesandmagnets.

EinsteinacceptedMaxwell’shypothesisbutaddedoneofhisown,whichwasthattheenergycarriedbylightwavescomesindiscretepackets,whichhecalledphotons.Thuswasborntheideathatlighthasadualnature—ittravelslikeawavebutconveysenergyindiscreteunitslikeaparticle.Einsteintiedtogetherthewavesandparticlesbyasimplehypothesis,accordingtowhichtheenergyaphotoncarriesisproportionaltothefrequencyofthelightwave.

Visiblelightspansarangeoffrequencies,withinwhichredlighthasthelowestfrequency.Bluelightisalmostthehighestfrequencywecansee,vibratingroughlytwiceasfastasred.Thus,abluephotoncarriesroughlytwicetheenergyofaredphoton.

WhatledEinsteintomakesucharadicalproposal?Heknewofexperimentswhichcoulddistinguishtheeffectofincreasingtheintensityofabeamoflightfromtheeffectsofchangingitscolororfrequency.Thiswasdonebyshininglightonmetal,whichcausedsomeoftheelectronsin

themetaltojumpout,makinganelectriccurrentthatcouldbedetectedbyasimpleinstrumentanelectricianmightuse.

Theexperimentsmeasuredhowmuchenergythejumpingelectronsacquiredfromthelightshiningonthemetal.Theresultsshowedthatifyouwanttoincreasetheenergyeachelectrongets,youhavetoturnupthelight’sfrequency.Dialinguptheintensityhaslittleornoeffect;thismerelyraisesthenumberofphotonsfallingonthemetal,withoutchangingtheenergytheelectronacquiresfromindividualphotons.ThisaccordswithEinstein’shypothesisthattheelectronstakeenergyfromlightbyabsorbingphotons,whoseenergyiseachproportionaltothelight’sfrequency.

Electronsarenormallyimprisonedinametal.Theenergyaphotongivestoanelectronislikeatomicbail:itliberatestheelectron,allowingittotravelfreeofthemetal.Butthatbailissetatacertainamount.Photonswhichcarrytoolittleenergyhavenoeffect.Iftheelectronistoescape,ithastogetitsenergyfromasinglephoton;itcannotcollectupalotofsmallincrements.Hence,redlightdoesn’tsufficetogetacurrentstarted,butevenafewphotonsofbluelightwillliberatesomeelectrons,becauseeachphotoncarriesenoughtobailoutanelectron.

Thefactthatnoamountofredlight,nomatterhowintense,willsufficetoliberateanelectron,whileevenatinyamountofbluelightsucceeds,wastoEinsteinabighintthattheenergyoflightiscarriedindiscretepackets,eachunitproportionaltothefrequency.Anevenmoredirecthintcamefrommeasurementscarriedoutin1902thatshowedthat,oncethethresholdforbailwasmet,theliberatedelectronflewawaywithanenergyproportionaltohowfarthefrequencywasoverthethreshold.Thiswascalledthephotoelectriceffect,andEinsteinwastheonlyonewhocorrectlyinterpreteditassignalingarevolutioninscience.Thiswasoneoffourpapershewroteinhismiracleyearof1905,whenhewastwenty-sixandworkinginapatentoffice.

AtthattimethereigningtheoryoflightwasMaxwell’s,namelythatlightisawavemovingthroughtheelectricandmagneticfields.EinsteinknewMaxwell’stheoryintimately,havingcarriedMaxwell’sbookinhispackforayearhespenthikingthemountainsasateenagedropout.NooneunderstoodbetterthanEinsteinthat,greatasitwas,Maxwell’swavetheoryoflightcouldnotexplainthephotoelectriceffect.ForifMaxwell

wereright,theenergyawaveconveystoanelectronwouldincreasewithintensity,whichisexactlywhattheexperimentswerenotseeing.

Thephotoelectriceffectwasnottheonlyclue.ThegenerationofEinstein’steachershaddevelopedthestudyoflightgivenoffbyhotbodies,suchastheglowofred-hotcharcoal.Therewerebeautifulexperimentalresults,whichthetheoristshopedtoexplain,whichshowedthatthecolorsoftheemittedlightchangeasthecharcoalisheatedup.In1900,theoreticalphysicistMaxPlanckexplainedtheresultthroughaderivationthatfeaturedoneofthemostcreativemisunderstandingsinthehistoryofscience.Togetaglimpseintothiscomedy,youneedtoknowthatevenattheturnofthetwentiethcentury,thescientificconsensusamongphysicists,whichPlanckshared,wasthattherearenoatoms—rather,matteriscompletelycontinuous.Therewereafewprominenttheoristswhobelievedinatoms,amongthemLudwigBoltzmannofVienna.Boltzmanndevelopedamethodforderivingthepropertiesofgasesbytreatingthemascollectionsofatoms.

Planck,eventhoughhewasaskepticoftheatomichypothesis,borrowedthemethodsBoltzmannusedtostudygasesandappliedthemtothepropertiesoflight.*Withoutmeaningtodoso,heeffectivelydescribedlightasagasmadeupofphotons,ratherthanatoms.Navigatingindeepwatersunfamiliartohim,hefoundhecouldgetananswerthatagreedwithexperimentsifhetooktheenergyofeachphotontobeproportionaltothefrequencyofthelight.

Planckdidn’tbelieveinatomsoflightanymorethanhebelievedinatomsofmatter.Sohedidn’tunderstandthathehadmadetherevolutionarydiscoverythatlightismadeofparticles.ButEinsteinbelievedinboth,and,almostsingle-handedly,heunderstoodthatthesuccessofPlanck’stheoryrestedontreatinglightasagasofphotons.Whenhelearnedaboutthephotoelectriceffect,heimmediatelythoughtofapplyingtoittheproportionalitybetweentheenergyofaphotonandthefrequencyoflightthathadappearedinPlanck’swork.Soitwashe,andnotPlanck,whowasgiventhegoodfortuneofmakingoneofthegreatdiscoveriesinthehistoryofscience:thatlighthasadualnature,partparticleandpartwave.

AtfirstEinstein’sproposalwasgreetedwithahighdegreeofskepticism.Afterall,therewasstillthedoubleslitexperimenttocontendwith,whichclearlyshowedlighttraveledthroughbothslits,likeawave.

Somehow,lightisbothwavelikeandparticle-like.Einsteinwastowrestlewiththisapparentcontradictionfortherestofhislife.Butby1921somedetailedpredictionshe’dmadeinhis1905paperhadbeenconfirmed,andEinsteinwasawardedtheNobelPrizeforthephotoelectriceffect.

Asafootnotetothisstory,wecanmentionthatanotherofthefourpapersEinsteinwrotethatyeargavethefinal,convincingproofthatmatterismadeofatoms.Atomsweretoosmalltoseeevenwiththebestmicroscopesatthattime.SoEinsteinfocusedhisattentiononobjectsjustbigenoughtoseethroughamicroscope:pollengrains.Thesewereknowntodanceunceasinglywhensuspendedinwater,whichwasatthetimeagreatmystery.Einsteinexplainedthatthedancewasduetothegrainscollidingwiththewatermolecules,whicharethemselvesconstantlymoving.*

TheothertwopapersEinsteinwroteinthatmomentousyearpresentedhistheoryofrelativityandtheiconicrelationbetweenmassandenergy:E=mc2.

IfwewanttofindananalogueofwhatEinsteinachievedinthatsingleyear,wecanonlylookatNewton.Einsteinlaunchedtworevolutions—relativityandthequantum.Ofthelatterhehadwrestedfromnaturetwopreciousinsights:thedualnatureoflight,andtherelationbetweentheenergyoftheparticleandthefrequencyofthewave,whichtiestogetherthetwosidesoftheduality.

FIGURE6.BROWNIANMOTIONBrownianmotionistherandommotionofmoleculesandothersmallparticlesfoundinnature.Einsteinexplainedthatthemotionresultsfromthefrequentcollisionsofmoleculesmakinguptheairorwater,andwasabletopredicthowthemagnitudeoftheeffectsdependsonthedensityoftheatoms.

Einstein’sfourthpaper,whichprovedtheexistenceofatoms,saidnothingaboutthequantumnatureoflight.Butitcontainedtwomysteries,whichitwouldtakethequantumtheorytoresolve.Howcouldatomsbestable?Andwhydoatomsofthesamechemicalelementbehaveidentically?

Whilethetheoristshadbeensquabblingoverwhetheratomsexisted,experimentalistshadbeenbusyseparatingtheirconstituents.Firsttobeidentifiedwastheelectron,whichwasrevealedtocarryanegativechargeandtohaveatinymass,aboutonetwo-thousandthofthatofahydrogenatom.Thechemicalelementswereunderstoodtobeclassifiedbyhowmanyelectronstheycontained.Carbonhas6electrons,uranium92,forexample.Atomsareelectricallyneutral,soifanatomcontains,say,6electrons,thatmeansifyouremovethoseelectronsyougetastructurewith6positivecharges.Sinceelectronsaresolight,thisstructure,whichwecancallthenucleus,hasmostofthemass.

In1911ErnestRutherforddeterminedthatthenucleusofanatomistiny,comparedtothewholeatom.Iftheatomisasmallcity,thenucleusisamarble.Shrunkintothattinyvolumeareallthepositivechargesandalmostallthemassofanatom.Theelectronsorbitthenucleusinthevastemptyspacethatismostoftheatom.

Theanalogytothesolarsystemisinevitable.Theelectronsandthenucleusareoppositelycharged,andoppositechargesattractthroughtheelectricalforce.Thisholdstheelectronsinorbitaroundthenucleus.Thismuchissimilartoplanetsbeingheldinorbitaroundastarduetotheirmutualgravitationalattraction.ButtheanalogyismisleadingbecauseithidesthetwopuzzlesImentioned.EachprovidesareasonwhyNewtonianphysics,whichexplainsthesolarsystem,cannotexplainatoms.

Electronsarechargedparticles,andMaxwell’sgreattheoryofelectromagnetismtellsusthatachargedparticlemovinginacircleshouldgiveofflightcontinuously.AccordingtoMaxwell’stheory,whichistosaypriortoquantumphysics,thelightgivenoffshouldhavehadthefrequencyoftheorbit.Butlightcarriesenergyaway,sotheelectronshoulddropclosertothenucleusasitsenergydecreases.Theresultshouldbeaquickspiralintothenucleus,accompaniedbyaflashoflight.IfMaxwell’stheoryisright,therecanbenopictureofelectronscirclingingentle,stableorbitsaroundthenucleus.Thiscanbecalledthecrisisofthestabilityofelectronorbits.

Youmightaskwhythesameproblemdoesn’tafflictplanetaryorbits.Planetsareelectricallyneutral,sotheydon’tgiveofflightinthesameway.But,accordingtogeneralrelativity,planetsinorbitdoradiateenergyingravitationalwavesandspiralintothesun.Itisjustthatgravityisextremelyweak,sothisprocessisextraordinarilyslow.Theeffecthasbeenobservedinsystemsconsistingofpairsofneutronstarsincloseorbits.And,verydramatically,gravitationalwaveantennashavedetectedtheradiationgivenoffbypairsofmassiveblackholesspiralingintoeachotherandmerging.

Thesecondproblemiswhyallatomswithacertainnumberofelectronsappeartohaveidenticalproperties.Twosolarsystemswithsixplanetseachare,beyondthat,notgenerallyverysimilar.Theplanetswillhavedifferentorbitsandmassesandsoon.Butchemistryworksbecauseanytwocarbonatomsinteractwithotheratomsinexactlythesameway.

Thisdiffersfromhowoxygenatomsinteract,anytwoofwhicharealsoidenticaltoeachother.Thisisthepuzzleofthestabilityofchemicalproperties.TheanalogytothesolarsystemfailsbecauseNewtonianphysics,whichworksjustfinetoexplainthesolarsystem,cannotexplainwhyallatomswithsixelectronshavethesamechemicalproperties.

TheanswertoboththesequestionsaboutatomsrequiredapplyingtoatomstheradicalnewideasEinsteinwasdevelopingaboutthenatureoflight.ThiswasaboldstepofthekindthatEinsteinwascapableof,butevenhemissedit.ThephysicistwhohadtheinsightwastheyoungDaneNielsBohr.ThisinsightmeantitwasBohr,notEinstein,whowouldassumetheleadershipoftherevolutionarieswhoinventedquantummechanics.Throughouthislife,Bohrwasaradicalanti-realist,anditwashe,morethananyoneelse,whowasresponsibleformakingthequantumrevolutionatriumphofanti-realism.Overhiscareer,Bohrfashionedaseriesofargumentsthatthebehaviorofatomsandlightcouldnotbeunderstoodfromarealistperspective.

Bohrgrewupinanacademicfamily,thesonofaprofessorofphysiology,thebrotherofamathematician.Hewasthatfortunatesortwhogottolivehiswholelifeinthecityofhisbirth,inmoreorlessthesamesettingashisparents.Butinhiscase,asimpleandconservativelifewasanincubatorofradicalthought.

Inthiscomfortable,intellectualmilieu,heandhiswifebroughtupsixsons,severalofwhomalsobecameprofessors.OneevenfollowedhisfathertoaNobelPrizeinphysics.Anotherson,theoldest,drownedwhilesailingwithhisfather.StillanothersonrepresentedDenmarkattheOlympics,asdidanuncle.

Denmarkisasmallcountrythatvaluesscience,andBohr’sleadershipofthequantumrevolutionwasfacilitatedbythecreationofanewinstitutetosupporthisactivities,sponsoredbytheDanishgovernmentandtheCarlsbergbeercompany.ThisgaveBohrtheperfectsettinginwhichtoextendhisinfluence,bysurroundinghimselfwiththebestyoungtheoristsfromaroundtheworld.TheywerestimulatedbyasteadystreamofvisitorswhocametocollaboratewithBohrortoarguewithhimaboutquantumtheory.Theinstituteprovidedhimwithacomfortablehouse,whereBohrandhisfamilyhostedmanyofthevisitors.

NielsBohr’ssonshadtosharehimwithmanyoftheseyoungquantumrevolutionaries,wholookeduptohimasamentor.Hiswife

lookedafterthemandplayedmatchmaker,introducingseveralofthemtothewomenwhowouldbecometheirwives.(TherewerefewwomenwhowerescientistsinBohr’scircle.)

Bohrclearlyfascinatedthosewhoworkedwithhim.Hesawscienceasadialoguewithnatureandhismethodofworkingwasalsobasedondialogue—althoughofakindthatoftenlapsedintomonologue.Heusedcollaboratorsasscribes,whohadthejoboftakingdownBohr’sthoughts,utteredinwhisperedriddles,correctedandcorrectedagain,asBohrpacedincirclesaroundtheroom.

BohrbegantoworkonquantumphysicsshortlyafterreceivinghisPhD.Hewentrighttotheheartoftheproblembyproposingasimplebutradicalquantummodeloftheatom.HebuiltonEinstein’snascentquantumtheory,particularlytheideathatenergyiscarriedbyphotons.Toaddresstheproblemofthestabilityoftheelectronorbits,BohrsimplypostulatedthatMaxwell’stheoryiswrongontheatomicscale.Hehypothesized,instead,thatthereareasmallnumberoforbitsoftheelectron,whicharestable.Todistinguishthesegoodorbits,hemadeuseofPlanck’sconstant,whichistheconversionfactorbetweenfrequencyandenergy.Thisconversionfactorhasunitsofaquantitycalledangularmomentum.Thisworksjustlikemomentum,butforcircularmotion.Aspinningbodyhasaninertiatocontinuerotating.Thisisbecausespinningororbitingbodiescarryangularmomentum,which,likeenergyandregularmomentum,cannotbecreatedordestroyed.Itisthisconservationofangularmomentumthatkeepsabicyclewheelspinning;itisalsowhatcausesafigureskatertospinmorerapidlywhenshepullsherarmsin.

Let’sthinkaboutahydrogenatom,whichhasonlyasingleelectron.Bohrpostulatedthatthegoodorbitsarethoseinwhichtheelectronhascertainspecialvaluesofangularmomentum.Thesespecialvaluesareintegermultiplesoftheunitofangularmomentum,givenbyPlanck’sconstant.Bohrcalledthesestationarystates.Thereisanorbitwithzeroangularmomentumwhichalsohasthelowestpossiblevalueofenergyforanelectroninorbitaroundthenucleus.Thisstateisstable;itisthegroundstate.Athigherenergiesabovethegroundstateareadiscreteseriesofenergieswhicharetheexcitedstates.

Atomscanabsorblight,gainingenergy,andtheycanalsoradiateenergyawaybygivingofflight.Bohrnextpostulatedthattheseprocesses

happenwhentheelectronjumpsbetweenthestationarystates.Todescribethesejumps,BohrmadeuseofEinstein’sphotonhypothesis.Whenanelectronjumpsdownfromanexcitedstatetothegroundstate,itgivesoffaphoton.Thatphotonhasanenergyequaltothedifferenceinenergiesofthetwostates,sothatthetotalenergyisunchanged.Ithasaspecificfrequency,givenbyPlanckandEinstein’srelationbetweenfrequencyandenergy.

Ifyoureversethisprocessyoucancauseanelectrontojumpfromthegroundstateuptoanexcitedstate,bygivingitaphotonwithanenergyequaltothedifferenceofthetwostates.

Agivenatomcanthengiveuporabsorblightonlyatthespecialfrequenciesthatcorrespondtotheseenergydifferencesbetweenstatesofitselectrons.Thesespecialfrequenciesarecalledthespectrumoftheatom.

BythetimeBohrworkedthisallout,in1912,chemistshadmeasuredthespectrumofhydrogen.UsingtheideasI’vejustdescribed,Bohrwasabletocalculatethespectrum,andhissimpletheoryreproducedwhattheexperimentalistshadseen.

Thiswasahugestep,butitwasonlyafirststeptowardanunderstandingofthequantum.Thereremainedmanyopenquestionsandproblems.Whatisanelectronsuchthatitcantravelfreelyoutsidetheatom,butcanexistonlyinoneofthestationarystateswheninanatom?And,mosturgently,canthetheorybeappliedtoatomsbesideshydrogen?

ThenextdecadewastakenupbynumerouscleverattemptstoapplyBohr’stheorytodifferentatomsandothersystems.Wecangenerouslysaytheresultsweremixed,evenasweadmiretheingenuityoftheattempts.ThiswasthesituationbythetimeayoungFrencharistocratnamedLouisdeBrogliestartedgraduateschoolinParisaround1920.

LouisVictorPierreRaymond,ducdeBroglie,wasbornofanoblefamilyinthelastyearsofthenineteenthcenturyandstudiedhistorybeforeswitchingtophysics.HeservedinthearmyduringtheFirstWorldWarinthewirelesstelegraphysection;hewasstationedattheEiffelTower.

Thesmallworldoftheoreticalphysicswasthen,asitisnow,intenselysocial.Duringthecrucialperiodwhenquantummechanicswasbeingdeveloped,theproponentswerecontinuallyintouchbyletterand

postcard,andtheymadefrequenttraintripstovisitandconsult.ThearistocratdeBrogliewasanoutsidertothisworldbydintofhispersonalityandposition,andbecausePariswasatthetimeabackwaterintheoreticalphysics.LouisdeBrogliespokeregularlyabouthisworkwithonlyoneperson,hisbrother,MauricedeBroglie,anexperimentalphysicistwhoworkedonX-rays.

Isolationisusuallyanobstacleforscientists,butsometimesitcanleadtosomeonestumblingonaninsightthateveryoneinthecrowdhasmissed.DeBrogliewasstilladoctoralstudentwhenheshookphysicstothecorebyputtingforthanaudacioushypothesis:thatthewave-particledualityisnotjustafeatureoflight—itisuniversal.Inparticular,electrons,likelight,arewavesaswellasparticles.

Asheremarked,“Whenin1920Iresumedmystudies...whatattractedme...totheoreticalphysicswas...themysteryinwhichthestructureofmatterandofradiationwasbecomingmoreandmoreenvelopedasthestrangeconceptofthequantum,introducedbyPlanckin1900inhisresearchesintoblack-bodyradiation,dailypenetratedfurtherintothewholeofphysics.”1

Thepowerofafreshmindtakingafreshlookataproblemisoneofthewondersoftheworld.TheyoungdeBrogliehadtheobviousidea,whichhadsomehoweludedevenEinsteinandBohr.Theysoughttoavoidtheembarrassmentofthewave-particleduality.DeBrogliedoubleddownonit.Iflightwasbothawaveandaparticle,whycouldn’tthesamebetrueofelectrons?Whynothypothesizethatthewave-particledualityappliesuniversallytoallmatterandradiation?

AsdeBroglielaterrecountedit,“AsinmyconversationswithmybrotherwealwaysarrivedattheconclusionthatinthecaseofX-raysonehadbothwavesandcorpuscles,thussuddenly...Igottheideathatonehadtoextendthisdualitytomaterialparticles,especiallytoelectrons.”2

WhatmotivateddeBroglietocomeupwithanideawhichmanymoreexperiencedphysicistshadmissed?DeBrogliewasengagedinanambitiousprojecttoreinventphysicsfromthegrounduptoincorporatethewave-particleduality.Hestartedwithlight,wheretherewasalreadygoodevidenceforadualityofwavesandparticles,andaskedasimplequestionfewhadaskedbefore:Howdothelightquantamove?

RecallthatNewtonhadfavoredaparticletheoryoflightbecausehebelievedthatparticlestravelinstraightlines.Thesameassumptionhad

ledThomasYoungtoabandontheparticlepictureandembracetheideathatlightisawavewhenheunderstoodthatlightcouldbendwhendiffractedbyanobstacleorrefractedbypassingbetweentwomedia.Itmakessensethatiflightdoesn’ttravelinstraightlines,itisnotmadeofparticles.Whatthenofphotons?Didn’ttheyhavetotravelinstraightlines?DeBroglie’sideawasthattheydon’tbecausetheyareguidedbythewaves,whichdodiffractandrefract.

Thisisstunninglyrevolutionary.Theideathatparticlestravelinstraightlinesisaconsequenceofthemostbasicprincipleinallofphysics,whichisNewton’sfirstlawofmotion.Alsocalledtheprincipleofinertia,itstatesthataparticlewithnoforcesonitmovesataconstantspeedinastraightline.Oneconsequenceisthatmomentumisconserved.Itisalsocloselyrelatedtotheprincipleofrelativity,foranotherconsequenceisthatvelocityisapurelyrelativequantity.

DeBroglieunderstoodthatlightquantaweregoingtohavetobendaroundobstacles,violatingallthesefundamentalprinciples.Thegoalofhisthesiswastoformulatearevolutionarynewtheoryofmotion,whichwouldapplytotheparticlescontemplatedbythewave-particleduality.Inthiscontext,itwasasmallandnecessarysteptoextendthewave-particledualityfromlighttoallformsofmatterandenergy.

In1924hewrotethisupashisPhDthesis.Thethesiswasshortanduncompromising.Thelegendistoldthathadhenotbeenfromthearistocracy,itispossibledeBrogliewouldsimplyhavebeenfailed.Notknowingwhatelsetodo,hiscommitteesentthethesistoEinsteintoevaluate.EinsteinsawdeBroglie’spointandrecommendedapproval.Atthesametime,hesentdeBroglie’sthesistoafewpeopleheknewwouldbeveryinterestedinit.

OneofthesewashisfriendMaxBorn,thenayoungprofessorinGermany.Anexperimentalistcolleagueofhis,WalterElsasser,heardofitandsuggestedthatdeBroglie’spredictionthatelectronscouldbediffractedmightbetestedbyscatteringabeamofelectronsoffacrystal.MaxBornpassedthesuggestiontoexperimentalistsinEngland.Nonesucceeded,butmeanwhiletwoAmericanexperimentalistsworkingatBellLabs,ClintonDavissonandLesterGermer,were,forotherreasons,studyinghowelectronsscatteroffthesurfacesofmetals.Theyaccidentallydiscoveredthediffractionofelectronswhen,in1925,theytriedanewprocedurewhichhadtheunintendedconsequenceof

developingalayerofatomsorganizedintheregulararraysofacrystalonthesurfaceoftheirsample.Whentheymeasuredwheretheelectronswentthatscatteredoffthemetalwiththecrystalsurface,theysawinterferencepatterns.DavissonwasunawareofthesignificanceofthisuntilheattendedaconferenceinOxfordinthesummerof1926,andhappenedtolistentoatalkbyMaxBorn,whoshowedafigurefromoneofDavisson’sownpapersasevidencefordeBroglie’srevolutionaryhypothesisofmatterwaves.WhenDavissonreturned,heandGermerwentbacktothelabandwereabletodefinitivelyconfirmthatelectronsdiffract,justasdeBrogliehadpredicted.

—ERWINSCHRÖDINGERWASAbrilliantmathematicalphysicist,originallyfromVienna,whohadbecomeaprofessorattheUniversityofZurich.SchrödingerwasclosinginonfortyanddidnotbelongtotheyounggenerationofdeBroglieandtheotherphysicistswhowererevolutionizingtheirfield.OnNovember23,1925,heattendedacolloquiumbyPeterDebye,whogaveanenthusiasticpresentationofdeBroglie’smatterwavehypothesis.DebyeendedbysayingtherewasonethingmissingfromdeBroglie’sbeautifulpicture:anequationtodescribehowtheelectronwavestravelinspace.LeavinghiswifebehindinZurich,SchrödingertookdeBroglie’spaperswithhimtoaChristmasholidayinthemountainswithhisgirlfriend.(HiswifewasspendingtheChristmasholidayswithherlover,thegreatmathematicianHermannWeyl,whowasalsoSchrödinger’sbestfriend.)Thefirstday,heexcusedhimselffromskiing,stayedintheirchaletroom,andreaddeBroglie’spapers.HechallengedhimselftoinventtheequationthatwouldgoverndeBroglie’selectronwave.Hesucceededthenextday,andbythetimehereturnedfromthemountains,hehadcapturedtheequationthatbearshisname,thefundamentalequationofquantumtheory.

Notonlythat,but,shortlyafterreturning,withthehelpofWeyl,Schrödingersolvedhisequationforthecaseofasingleelectroninorbitaroundanucleus,andreproducedBohr’stheoryofstationarystatesandhispredictionofthespectrumofhydrogen.Thekeyideaisthattheelectronwaveshavetofitaroundanorbit,asweseeinfigure7.Thethoughtsofthegirlfriend—and,indeed,hername—arelosttohistory.But

legendtellsusthatwhenSchrödingerwenttoStockholmtoreceivehisNobelPrizeheshowedupwithhiswifeandtheirgirlfriend.

FIGURE7.Electronwavesintheatom.Thewaveontheleftfitsaroundthenucleusinthreesteps,sothewavelengthisthediameteroftheatomdividedbythree.Therightfigurehashalfthewavelengthandsofitsaroundinsixsteps.

Thusquantummechanicswasborn.ThequestioneveryonethenfacedwashowtothinkoftheelectronwavethatdeBrogliehadinventedandSchrödingerhadtamed.Schrödingeratfirstthoughtthattheelectronsimplyisawave.Thisdidn’tholdupbecauseitwaseasytoshowthatthewavetendedtospreadoutinspaceasittraveled,whereasonecouldalwaysfindalocalizedparticle.MaxBornthenproposedhisrulethatthewaveisrelatedtotheprobabilityoffindingtheparticle.

ForEinstein,thewave-particleduality,whileaprofoundchallenge,hadbeenlimitedtospeculationabouttheconstitutionoflight.Confinedtothatdomain,itdidlimiteddamage,perhapsbecauseparticleandwavetheoriesoflighteachhadlonghistoriesandrecognizedvirtues.Buttheideaofmatterwavescameasacompleteshock.DeBroglieandSchrödingertransformedphysicsbybringingthewave-particledualityintothecoreofphysics,whereitsatenshrinedasthecentralmysteryoftherevolutionarynewquantumphysics.

Thequestionwasnolonger“Howcanlightbebothaparticleandawave?”butrather,“Howcaneverythingbebothaparticleandawave?”

Einstein,whohadbeenthefirsttoformulatethewave-particleduality,wasstumped.Despite,byhisownadmission,spendingfarmoretimeonquantumphysicsthanheeverdidonrelativity,hewasunableto

makeaconvincingmove.Hispeerlessintuitionfailedhim,anditisworthwonderingwhy.Perhapshisrealism,hisdemandforcompleteconceptualclarity,heldhimback.

Schrödingeralsowas,foratime,ataloss.Asweremostothers.Ofthegreatpioneers,onlyBohrknewwhattodo.Itwashismoment

andheseizedit,announcingthebirthnotjustofanewphysicsbutofanewphilosophy.Themomentforradicalanti-realismhadcome,andBohrwasreadyforit.

Bohrcalledthenewphilosophycomplementarity.Hereishowhetalkedaboutit:Neitherparticlesnorwavesareattributesofnature.Theyarenomorethanideasinourminds,whichweimposeonthenaturalworld.Theyareusefulasintuitivepicturesthatweconstructfromobservinglarge-scaleobjectssuchasmarblesandwaterwaves.Electronsareneither.Electronsaremicroscopicentitiesthatwecannotobservedirectly,andsowehavenointuitionaboutthem.Tostudyelectronswemustconstructbigexperimentaldevicestointeractwiththem.Whatweobserveisnevertheelectronitself;itisonlytheresponsesofourbigexperimentaldevicestothetiny,invisibleelectrons.

Todescribehowtheexperimentaldevicesrespondtoelectrons,wemayfinditusefultoemployintuitivepicturessuchasthewavepictureortheparticlepicture.Butwecannottakethesepicturestooseriouslybecausedifferentexperimentsrequiredifferentpictures.Thedifferentpictureswouldcontradicteachotherifweforgotthecontextandappliedthemtotheelectronsthemselves.Butthereisnoactualcontradictionsolongasweremembertwothings.Thepicturesareusefulonlyasadescriptionofanelectroninaspecificcontext,whichisinaparticularexperimentaldevice.Andthereisnoexperimentaldevicethatforcesustoapplybothcontradictorypicturessimultaneously.

Bohr’spositionisanti-realistintheextreme,inthathedeniesitisevenpossibletotalkaboutordescribeanelectronasitisinitself,outsidethecontextofanexperimentweconstruct.Scienceaccordingtothispictureisnotaboutelectrons;itisabouthowwetalkaboutourinteractionswiththem.

ForNielsBohr,complementaritywasmorethanaprinciple;itwasaproposalforawholephilosophyofscience.Andwhataradicalproposalitwas.Bohrchampionedthephilosophyofcomplementaritythroughout

hislife,asdidotherfoundersofquantummechanics,including,tosomeextent,Heisenberg.

ForBohr,scienceisnotaboutnature.Itdoesnotandcannotgiveusanobjectivepictureofwhatnatureislike.Thatwouldbeimpossible,becauseweneverinteractwithnaturedirectly.Wegainknowledgeaboutthenaturalworldonlythroughintermediaries,whichareexperimentaldevicesweinventandconstruct.

Thus,wemustgiveuptheideathatsciencegivesusanobjectivedescriptionofnature,orhasanythingatalltosayaboutwhatnatureislike,absentourexistenceandourinterventions.Scienceisratheranextensionofacommonlanguageweusetodescribetoeachothertheresultsofourinterventionsintonature.

Inessaysandbooks,NielsBohrarguedthathisphilosophyofcomplementarityhadwideapplicability.IthasbeenclaimedhegottheideaofcomplementarityfromtheKabbalah,theJewishmysticalwritings,whichspeakofthecomplementaritybetweenGod’sloveandGod’sjustice.Bohrtalkedaboutthecomplementaritybetweenlifeandphysics,betweenenergyandcausation,and,indeed,betweenknowledgeandwisdom.ForBohrthelessonofquantummechanicswasarevolutionthatextendedbeyondphysics,beyondscience.

—ONEREASONQUANTUMMECHANICScapturedtheinterestoftheyoungergenerationofphysicistswasthatitcouldbeapproachedfromseveralpointsofview.Ihavesofartoldthestoryofonewaythequantumtheorywasinvented,centeringonthewave-particleduality,buttherewasanotherroute,whichhadbeendiscoveredshortlybeforeSchrödingertookhisChristmasholiday.ThiswaspioneeredbyWernerHeisenberg,ayoungandveryconfidentGermantheorist,whocompletedhiseducationinMaxBorn’sgroupinGöttingenandthenin1925wentonaresearchfellowshiptoworkinCopenhagenwithBohr.HespentthenextseveralyearsbouncingbetweenGöttingenandCopenhagen,whichistosayhewasinclosetouchwiththetwomostdynamicscientificpersonalitiesofthatmoment,BornandBohr.MaxBornandseveralofhisstudentsandassistantsalsoplayedimportantrolesinthestory;indeed,thefullstoryofhowquantummechanicswasinventedinvolvesatleasthalfadozentheorists,infrequentcommunication.

Heisenbergworkedfromaparticularideaaboutphysics,anideathatwasanti-realisttobeginwith.Heassertedthatphysicsdoesnotgiveadescriptionofwhatexists,asrealistssuppose,butisonlyawaytokeeptrackofwhatisobservable.Forlarge-scaleobjects,wehavegottenusedtoconfusingthetwo.Butifwewanttomakesenseofatomicphysics,wemustadherestrictlytothedictumthatsciencecanonlyrefertowhatcanbeobserved.

Hence,Heisenbergassertsthatitismeaninglesstotalkabouthowtheelectronmovesintheatom,unlessthatmotionhasconsequenceswhichcanaffectlarge-scalemeasuringdevices.AccordingtoBohr’smodel,anatomicelectronspendsmostofitstimeinstationarystates,duringwhichithasnointeractionwithanythingoutsidetheatom.Itisthenmeaninglesstoaskhowtheelectronmoveswhileitisinastationarystate.Itisonlywhenitjumpsbetweenstationarystatesthattheatomcaninteractwiththeworldoutside,becausethejumpisaccompaniedbytheabsorptionorcreationofaphoton,andthatphoton’senergycanbemeasuredbyaspectrograph.

Heisenberg’sadmonitionnottotrytomodelthetrajectoriesofelectronsinstationarystatesmusthavecomeasabreathoffreshairtoothersofhisgenerationwhowerespendingmuchoftheirtimeinfrustratingandultimatelyfruitlessattemptstodojustthat.

Heisenbergwasinspiredbythisthinkingtoinventanewwayofrepresentingtheenergyoftheelectron.Notbyasinglenumber,becausetodosowouldbetoclaimthattheenergyisapropertyoftheatomalone.Whatisrelevantforphysicsisonlywhataspectofenergyaffectsameasuringdevice.Thesearetheenergiescarriedbythephotonsthattheatomsabsorboremitwhentheelectronsjumpbetweenenergylevels.Thesearethedifferencesbetweentheenergiesinthedifferentstationarystates.

Heisenbergarrangedtheseenergydifferencesasatableofnumbers.Hethenimaginedthatsuchtablescouldrepresentobservableaspectsofotherquantities,suchastheelectron’spositionandmomentum.Tomakeatheoryhehadtodomore,whichwastofindawaytowriteequationsinvolvingthesetablesofnumbers.Intheequationsofphysicsweoftenfindourselvesaddingormultiplyingnumbers.Heneededtodothesamewithtablesofnumbers.Sohehadtoinventrulesforhowtodothis.

AsamemberofbothBohr’sinstituteandMaxBorn’sresearchgroup,Heisenbergwasundertheinfluenceoftwomasterswithverydifferentstylesofwork,andthecontrastbetweenthemundoubtedlystimulatedhisthinking.Buttorealizehisideasindetail,heneededisolation,nolessthanEinstein,deBroglie,andSchrödingerhad.LikeSchrödinger,hetookoffonaholiday,inhiscasetoasmallislandcalledHelgoland.

Oncethere,ittookhimonlyafewdaystotakehimselfonthejourneyI’vejustsketched,andtoinventwaystowriteandsolveequationswithhistablesofobservablequantities.

Hetestedhisideasonasimpletoymodelofanatom,inwhichtheelectronisboundbyaconstantlyincreasingforce,asifonaspring.Thiswasnotmeanttoberealistic,butitwasasimpletest,becausetheanswerwasknown,andhismethodpassed.Therewasonlyonehitch:hediscoveredthattheorderinwhichhemultipliedtwotablestogethermatters.InthelanguageIproposedearlier,Heisenberg’stablesofnumbersdon’tcommute.Thisisofcoursenotthecaseforordinarynumbers,andatfirstthisdiscoverydismayedHeisenberg.

Nonetheless,hewroteuphisfindingsinapaperpublishedattheendof1925.Itwasintheintroductiontothatpaperthatheannouncedhisprogramofconstructinglawsofphysicsthatdispensedwithmechanicalmodelsdescribingthetrajectoriesoftheelectronsandinvolvedonlyrelationshipsbetweenobservablequantities,namelythespectraoflighttheatomsemitandabsorb.

Thiswasabigstep,butitwasnotyetthecompletetheory.HethenreturnedtoGöttingenandworkedwithMaxBornandabrilliantstudentofhis,PascualJordan.BornandJordanwerealreadypartwaytoanewtheory,andexplainedtoHeisenbergthathistablesofnumberswereknowntomathematiciansasmatrices;andtheywereabletoreassurehimthatthefailuretocommutewasafeatureandnotabug.Heisenbergthenunderstoodthatsincethetables/matricesrepresentaprocessofmeasurement,theorderdoesmatter—becauseitmattersinwhichorderwemakemeasurements.Togetherthethreetheoriststhenworkedouttherestofthenewtheory,whichtheynamedquantummechanics.Ajointpaperbythethreeofthemwasthefirstcompletestatementofthenewtheory.

AustrianwunderkindWolfgangPauliquicklyfollowedupandappliedthenewtheorytofindthespectrumofthehydrogenatom,anditcame

outexactlyright.Thuswasquantummechanicsbornbyasecondroute,andinawaythatwasdirectlyinspiredbytheanti-realistprinciplesHeisenberghadexpressedinhis1925paper.ThenewtheoryofBorn,Heisenberg,andJordanisexpressedintermsofquantitiesthatdescribehowanatomrespondstobeingprobedbyanexternalmeasurementdevice;therearenoquantitiesthatdescribetheexacttrajectoriesoftheelectrons,independentofourinteractionswiththem.

Onequantumtheoryoftheatomisgreat,buttwoareaproblem,especiallysincetheybothreproducedtherightspectrumofhydrogen.Thetwotheoriescouldnothavedifferedmore,asreflectsthephilosophiesoftheirdiscoverers.Einstein,deBroglie,andSchrödingerwererealists.Evenifthereweremysteries,theybelievedanelectronwasrealandsomehowexistedasbothwaveandparticle.BohrandHeisenbergwereenthusiasticanti-realistswhobelievedwehavenoaccesstoreality,onlytotablesofnumberswhichrepresenttheinteractionswiththeatom,butnottheatomdirectly.

Thetensionlastedafewmonths,andthenhadanunexpectedresolutionwhenSchrödingershowedthatthetwoformsofquantummechanicsarecompletelyequivalent.Liketwolanguages,youcouldspeakintermsofwavesortalkthelanguageofmatrices,butthemathproblemsyouhadtosolveturnedouttobejustdifferentexpressionsofthesamelogic.

HeisenbergandBohr,togetherinCopenhagen,sharedananti-realistperspective.Theysoughtawaytospeakconsistentlyaboutpropertiesthatcouldnotberealizedsimultaneously,suchaswavesversusparticlesorpositionversusmomentum.Bohr’sresolutionoftheapparentparadoxeswashisprincipleofcomplementarity.Heisenberg’swashisgreatuncertaintyprinciple,whichwetalkedaboutinchapter2.

Theuncertaintyprincipleisaverygeneralprinciple,asitsaysthatwecannotknowexactlybothwhereaparticleisandwithwhatmomentumitismoving.Ithas,asHeisenbergandhismentorBohrrealizedimmediately,stunningconsequences.OneisthatthedeterminismofNewtonianphysicscannotsurviveinthequantumworld,becausetopredictthefuturemotionofaparticleyoumustknowbothitspresentpositionandhowfastandinwhatdirectionitismoving,andhenceitsmomentum.Ifyoucannotknowbothprecisely,youcannotpredictwhere

theparticlewillbeatlatertimes.Asaresult,thebestthatquantumtheorycandoistomakeprobabilisticpredictionsaboutthefuture.

Theconsistencyofcomplementaritydependsonthereneverbeingacasewhereweareforcedtouseboththeparticlepictureandthewavepictureinthedescriptionofasingleexperiment.TheimpossibilityofdoingsoissafeguardedbyHeisenberg’suncertaintyprinciple,whichheproposedin1927,afterhehadmovedbacktoCopenhagenandwasinclosecontactwithBohr.

Historianstellusthatluckplaysabigroleinscience.Heisenbergwasdoublyfortunatefor,astheprotégéofbothMaxBornandNielsBohr,hewasnotjustintherightplaceattherighttime,butdoublyso!FromhismentorBohrhewasinspiredtoabandonrealismandmodeltheatomonlyintermsoftheenergiesitexchangeswithourmeasuringdevices,andfromhismentorBornhegotthemathematicaltoolsneededtogivetheseideasapreciseexpression.

Ofcourse,Heisenbergknewhisgoodfortuneandwastheonewhopushedtoframethenewtheoryprecisely.TherewereperhapshalfadozenyoungtheoristswhowerealsointheorbitsofBohrandBorn,whocontributedpieces,likePauli,orgotpartwaythere,likeJordan,orwereafewmonthslateandsogottoelegantlyframethenewtheory,liketheEnglishtheoristPaulDirac.ThefullstoryoftheinventionofthematrixformofquantummechanicsisfarmorecomplexthanIcantellhere,asitrevealsaverydynamic,collectiveeffortofadiversecommunityoftheorists,incloseinteraction.

Still,diverseastheywere,thematrixmechanicianswereby1927allframingthenewtheoryintermsoftheradicallyanti-realistphilosophythatBohrpreached.Theonlyholdoutswerethosewhohadcometoquantummechanicsthroughthewave-particleduality,Einstein,deBroglie,andSchrödinger,whostubbornlyremainedrealists.ButonceitwasprovedthatSchrödinger’swavemechanicswasequivalenttoHeisenberg’smatrixmechanics,therealistscouldbedismissedasstubbornlygraspingontooldmetaphysicalfantasies,andignored.

TheessenceofBohr’sphilosophyisthenecessityofbasingscienceonincompatiblepicturesandlanguages.HeisenbergpreachedaviewwhichdifferedinemphasisfromBohr’swhilebeinglooselycompatiblewithit.Heisenbergemphasizedthatscienceconcernsonlymeasurablequantitiesandcan’tgiveanintuitivepictureofwhatishappeningatatomicscales.

Theobservablequantitiesrelevantforinteractingwithanatomincludetheenergiesandlifetimesofthestationarystates,butdonotincludethepositionsormotionsofelectronsintheirorbitsaroundthenucleus.Soquantumphysicsonlyhastoyieldananswertoaquestionofwhereanelectronisifyouforceitintoacontextwherethatpositionismeasured.AccordingtoHeisenberg,observablequantitiesarebroughtintoexistenceonlybytheactofmeasuringthem.Whenanatomisfreeofameasuringapparatus,noquantitydescribesit.

Thismaybecalledanoperationalistperspective.Itiscertainlyanti-realist,inthatHeisenbergstressedthatthisviewismandatory.Therewas,accordingtohim,nopossibilityofseeingdeeperintotheatomtoperceivehowtheelectronsmoveintheirorbits.Hisuncertaintyprincipleprecludedit.

Heisenbergexplainedthatuncertaintyandcomplementaritywerecloselyconnected.

Wecannolongerspeakofthebehavioroftheparticleindependentlyoftheprocessofobservation.Asafinalconsequence,thenaturallawsformulatedmathematicallyinquantumtheorynolongerdealwiththeelementaryparticlesthemselvesbutwithourknowledgeofthem.Norisitanylongerpossibletoaskwhetherornottheseparticlesexistinspaceandtimeobjectively....

Whenwespeakofthepictureofnatureintheexactscienceofourage,wedonotmeanapictureofnaturesomuchasapictureofourrelationshipswithnature....Sciencenolongerconfrontsnatureasanobjectiveobserver,butseesitselfasanactorinthisinterplaybetweenmanandnature.Thescientificmethodofanalyzing,explainingandclassifyinghasbecomeconsciousofitslimitations,whichariseoutofthefactthatbyitsinterventionsciencealtersandrefashionstheobjectofinvestigation.Inotherwords,methodandobjectcannolongerbeseparated....

[T]hedifferentintuitivepictureswhichweusetodescribeatomicsystems,althoughfullyadequateforgivenexperiments,areneverthelessmutuallyexclusive.Thus,forinstance,theBohratomcanbedescribedasasmall-scaleplanetarysystem,havingacentralatomicnucleusaboutwhichtheexternalelectronsrevolve.

Forotherexperiments,however,itmightbemoreconvenienttoimaginethattheatomicnucleusissurroundedbyasystemofstationarywaveswhosefrequencyischaracteristicoftheradiationemanatingfromtheatom.Finally,wecanconsidertheatomchemically....Eachpictureislegitimatewhenusedintherightplace,butthedifferentpicturesarecontradictoryandthereforewecallthemmutuallycomplementary.3

Bohr’spointwasevenmoreradical.Forhim,

Anindependentrealityintheordinaryphysicalsensecan...neitherbeascribedtothephenomenanortotheagenciesofobservation....

Acompleteelucidationofoneandthesameobjectmayrequirediversepointsofviewwhichdefyauniquedescription.Indeed,strictlyspeaking,theconsciousanalysisofanyconceptstandsinarelationofexclusiontoitsimmediateapplication.4

Otherquantumluminaries,suchasWolfgangPauli,awunderkindwhopublishedatextbookongeneralrelativitywhenhewastwenty-one,andJohnvonNeumann,aHungarianmathematicianwhoisfamousforhisinventionsinabroadrangeoffields,fromthearchitectureofcomputerstothemathematicsofquantumtheory,taughtvariantsoftheseanti-realistphilosophies.Theirviewsdifferedinemphasis,butanythingwrittenbythemwasclassifiedaspartofthe“Copenhageninterpretation”ofquantummechanics.ThisnamerecognizedBohr’sdominanceastheoldestofthegroupandmentortomost,aswellastheoriginatorofnothinglessthananewwayoftalkingaboutscience.ThenamealsorecognizedBohr’sinstituteasthecentralnodeinthenetworkofquantumphysicists,wheretheyallstudied,worked,orvisited.

Oneofthehardestlessonstolearninacademiclife—andformeoneofthemostdisconcerting—isthespeedwithwhicharadicalinsurgencycanbecomeorthodoxy.Injustafewyearsagenerationofstudentschampioningadangerousnewideaareelevatedbyaninitialsuccessintoprofessorships.Fromthesepositionsofinfluencetheyformapowerfulnetworkofacademicpowerbrokers,whichtheyusetoensurethe

continuationoftherevolution.Suchwasthecasewiththegenerationofquantumrevolutionaries.In1920Heisenbergwasastudent,aswereDirac,Pauli,andJordan;1925foundthemyoungresearchersfullyengagedintheinventionofquantumtheory;by1930theywereseniorprofessors,andtherevolutionwasover.Thefactthatthereremainedahandfulofdefectors—EinsteinandSchrödingerfromtheoldergeneration,anddeBroglieamongtheircontemporaries—didnothingtodiminishtheirtriumph,forstudentsknewwhichwaythewindblewandfollowedtheascendantorthodoxy.Forthenexthalfcentury,theanti-realismoftheCopenhagenistswouldbetheonlyversionofquantumtheorytaught.

PART2

REALISMREBORN

T

SEVEN

TheChallengeofRealism:deBroglieandEinstein

herewasneverasingleCopenhageninterpretation.Bohr,Heisenberg,andvonNeumanneachtoldasomewhatdifferentstory.Buttheyallagreedthatsciencehadcrossedathreshold.

Therecouldbenoretreatbacktoarealistversionofphysics.Theygavediverseargumentsagainstthepossibility,allleadingtotheconclusionthatquantumphysicsisinconsistentwithrealism.Noversionofatomicphysicscouldexistifitincludedelectronswithdefinitepositionsandtrajectories.

Onewayalltheseargumentsmighthavebeendefeated—onewouldthink—wasforsomeonetocomeupwithanalternativequantumtheorybasedonrealistideas.

Whatisreallybizarre,lookingback,isthatfrom1927on,therehadexistedarealistversionofquantummechanics.Thisisbasedonastunninglysimpleidea.Perhapsyouhavealreadythoughtofit.Itissimplytopositthattherearebothwavesandparticles.Whatgetscreatedanddetected,whatgetscounted,isaparticle.Meanwhile,awaveflowsthroughtheexperiment.Thewaveguidestheparticle.Theresultofthisguidanceisthattheparticlegoestowherethewaveishigh.

Facedwithachoiceofwhichwaytogoaroundanobstacle,suchasinthedoubleslitexperiment,thewavegoesbothways.Theparticlegoesthroughonlyoneslitaroundonlyoneside,butwhereitgoesonceitgetsthroughisguidedbythewave,andshowstheinfluenceofbothpaths.

Thisobvioussolutiontothechallengeofthewave-particledualitywasthoughtupbyLouisdeBroglie.Heworkeditoutindetailandcalleditthepilotwavetheory.DeBrogliepresentedhistheoryatafamous

conferenceheldinBrusselsin1927.NamedtheFifthSolvayConferenceafteritssponsor,theconferencefeaturedtalksbymostoftherevolutionariesofthenewquantumphysics.

ThecoreofpilotwavetheorywasdeBroglie’sideathattheelectronisactuallytwoentities,oneparticle-likeandonewavelike.Theparticleisalwayslocatedsomeparticularplaceandalwaysfollowssomeparticularpath.Meanwhile,thewaveflowsthroughspace,takingsimultaneouslyallthepossiblepathsorroutesthroughtheexperiment.Thewavethendirectstheparticlewheretogo,andthatpilotingwillbebasedonconditionsalongallthepaths.Eventhoughtheparticlemusttakeonerouteoranother,whichrouteittakesisinfluencedbythewave,whichflowsthroughallroutes.

Thisinfluenceofawaveonaparticleisthenewthingwhichisresponsibleformuchofwhatisstrangeinthequantumworld.Therearetwolaws,oneforthewaveandonefortheparticle.Thewavelawisrelativelyfamiliar;itisnotsodifferentfromthelawsthatphysicistsusetodescribesoundwavesorlightwaves.Thewavesspreadout,andastheytraveltheydiffractandinterfere.Likewaterandsound,thesequantumwaveswillflowdowneverychannelopentothem.Andwhenwavescomingdowndifferentchannelsmeet,theywillinterfere.

Thewaveinquestioniscalledthewavefunction.ItpropagatesaccordingtothesimpleequationthatSchrödingerinventedduringhisromanticskiweekend.ThisisRule1,anditisthekeyequationineveryapproachtoquantumphysics.

ThereisnoRule2inthisframework.Butthereisanewlawthatdirectstheparticletofollowthewave,whichiscalledtheguidanceequation.Thesystemdefinedbythewavefunctiontogetherwiththeparticleevolvesdeterministically,whichsuggestsitiscomplete.

Inotherapproachestoquantummechanics,itissimplypositedthattheparticlewillbefoundwherethewaveislarge.Moreprecisely,theprobabilityoffindingtheparticleatsomeparticularplaceisproportionaltothesquareofthewavefunctionthere.ThisiswhatweearliercalledtheBornrule.

Inpilotwavetheoryitisalsothecasethattheparticleismorelikelytobefoundwherethewaveishigh.Butthisisnotposited.Rather,itturnsouttobeaconsequenceofthelawthatdrivestheparticletofollowthewave.

Placeaballonahillsideandwatchitrolldownfromthere.Youmayobservethattheballtendstofollowthesteepestpathdownward.Thisiscalledthelawofsteepestdescent.Roughlyspeaking,deBroglie’sguidanceequationdoestheopposite,guidingtheparticleonthesteepestpathtoclimbthewavefunction.*Wecancallitthelawofsteepestascent.Amountainclimberfollowingthislawwouldateachmomentofherclimbchoosetogointhedirectionofthesteepestslopeofthemountain.

DeBrogliewasabletodemonstratethattheprobabilitylawpositedbyMaxBornisaconsequenceoftheparticlefollowingthesteepestascent.Toillustratethisimportantpoint,imaginethatyouthrowabunchofparticlesdownonahillsiderepresentingthewavefunction.Whereveryouthrowthem,theparticleswillquicklyarrangethemselvessothattheyaremorelikelytobefoundwherethesquareofthewavefunctionislargest,whichreproducesBorn’slaw.

FIGURE8.SQUARINGTHEWAVEFUNCTIONThedashedlinedenotesawavetravelingalongthehorizontallinetotheright.Notethatitspendsasmuchtimewithnegativevaluesasitdoeswithpositive.Thesolidlineisthesquareofthewave,whichisalwaysabovezero.

Thepilotwavetheorypredictseverythingquantummechanicsdoes,butexplainsagooddealmore.Themysteriouswayinwhichtheensembleseemstoinfluencetheindividualisclearedupandexplainedstraightforwardlyastheinfluenceofthewaveontheparticle.Botharereal,andbothexistforeveryindividualatom.Everythingthatwaspuzzlingandmysteriousaboutquantummechanicsisrevealedtobeaconsequenceofthattheoryleavingouthalfofeverystory.

DespitewhatBohrandHeisenbergsay,theelectronalwayshasapositionanditfollowsadefinitetrajectory,whichisperfectlypredictableifyouknowtherightlaw.Noneedforoperationalism,andnosensewastingtimetryingtomakesenseofBohr’sobscurepronouncementsoncomplementarity.Wavesandparticlesdon’tcontradicteachother;instead,botharealwayspresentandtheyworktogethertoexplainatomicphysics.Whatis,simplyis.

Thereisanalternativehistoryinwhichallthebright,ambitiousstudentsflockedtoParisinthe1930stofollowdeBroglie,andwrotetextbooksonpilotwavetheory,whileBohrbecameafootnote,disparagedfortheobscurityofhisunnecessaryphilosophy.Itwas,alas,nottobe.Butwhytheconvolutedphilosophyofcomplementaritytriumphed,whileitwasdeBroglie’spilotwavetheorywhichbecametheforgottenfootnote,isaquestiontobepondered.

Thepilotwavetheoryoverlapswithquantummechanics,butitalsodiffersonseveralpoints.Rule1iscommontoquantummechanicsandpilotwavetheory.ButpilotwavetheorydiffersfromquantummechanicsinhavingnoRule2.Insteadthereisalawtoguidetheparticle.Thelawsofpilotwavetheoryaredeterministic.

WithnoRule2,thequantumstateinpilotwavetheorynevercollapses.Thishassomestrangeconsequenceswhichtookitsadherentssometimetoappreciate,andtowhichwewillreturninthenextchapter.

—ATTHESOLVAYCONFERENCEthetalkswerefollowedbydiscussions,andtheseweretranscribedandpublishedinabookwiththetalks.ThereisnotmuchevidencethatdeBroglie’spresentationchangedminds,althoughitwasdiscussed.OnepersonwhodidgetitanddidcommentwasEinstein.

Althoughhedoesn’tsaysointhetranscribeddiscussion,Einsteinhadhimselfthoughtoftheideaofpilotwavetheory.InMay1927EinsteingaveatalktothePrussianAcademyofSciencesinwhichhepresentedarathercomplicatedversionofthepilotwaveidea.HediscussedtheideaincorrespondencewithHeisenbergandothersandsubmittedapaperbasedonthetalkforpublication.Butjustbeforeitwastoappear,Einsteinwithdrewhispaper.*Hehadapparentlyrealizedhisversionofpilotwavetheoryhadseveralproblems,someofwhichpreventedthe

theoryfromreproducingallthepredictionsofquantummechanics.Sofarasisknown,henevermentioneditagain.

EinsteinhadbeenscheduledtogiveatalkattheSolvayconference,probablyaboutthatpaper.Hebackedoutofthattalkatthelastminute,writingtotheconferenceorganizer,“IkepthopingtobeabletocontributesomethingofvalueinBrussels;Ihavenowgivenupthathope....Ididnottakethislightlybuttriedwithallmystrength.”1

Einsteinnonethelessdidattend,and,ofcourse,hecontributedtothediscussionsthattookplaceaboutthenewquantumtheory.AmongthemwerethefirstdiscussionsbetweenhimandBohrinwhichEinsteintriedtofindinconsistenciesinthenewquantummechanics.Theseintensediscussionswereinformalandunfortunatelywerenottranscribed.Butmuchlater,Bohrpublishedhisreminiscencesofthosediscussions,inapaperthatisbothoneofthemostcompellingreadsinthehistoryofphysicsandamasterpieceinscholarlypropaganda.

Duringthemealsandbreaksoftheconference,EinsteinpresentedBohrwithseveralargumentsthatquantummechanicsisinconsistent.Hepositedthattogiveacompletedescriptionwouldrequireadditionalvariables,whicharehiddeninthequantummechanicaldescription.Bohrdoesn’tmentionthatthisiswhatdeBrogliehadachievedwithhispilotwavetheory.Onthecontrary,inBohr’stellinghewasable,afterasleeplessnight,torefuteEinstein’sobjection,leavinginplacehisviewastotheconsistencyandeventheinevitabilityofcomplementarity.

EinsteinrespondedpositivelyduringthediscussionofdeBroglie’stalk.AfterdescribinganobjectiontotheCopenhagenversion,hesaid,“Inmyopinion,onecanremovethisobjectiononlyinthefollowingway,thatonedoesnotdescribethisprocesssolelybytheSchrödingerwave,butthatatthesametimeonelocalizestheparticleduringthepropagation.IthinkthatMr.deBroglieisrighttosearchinthisdirection.”2

—FEWQUANTUMPHYSICISTSMENTIONEDdeBroglie’stheoryintheyearsafteritspresentationin1927.InspiteofdeBrogliebeingjustlyadmiredforhisinsightofextendingthewave-particledualitytomatter,andinspiteofhishavingpresentedthepilotwavetheoryatthemostimportantconferenceonquantumphysics,withanaudienceofvirtuallyeveryonewhomatteredinatomicphysics,itwasasifdeBrogliehadnever

publishedorpresentedhistheory.SofarasIknow,notextbooksmentioneditfordecadesafter.ItisnotthattherewereCopenhagentextbooksandpilotwavetextbooks.TherewereonlyCopenhagentextbooks.TheseeitherignoredthefoundationalissueswiththetheoryorpresentedaconfidentassertionthatallquestionsthatweremeaningfulhadalreadybeenansweredbyBohrandHeisenberg.

Oneimportantreasonanti-realismtriumphedwasthatthemathematicianJohnvonNeumannpublishedaproofheclaimedshowedtherecouldnotbeaconsistentalternativetoquantummechanics.ThiswaspublishedafewyearsaftertheSolvayconferenceinabookonthemathematicalstructureofquantummechanics.Thisclaimhadtobewrong,asitimplieddeBroglie’spilotwavetheoryhadtobeinconsistent,whichitwasn’t.Youmighthavethoughtthatsomeonewouldhavementionedthis.

VonNeumann’sincorrectproofseemstohavebeenoneofthosecasesthathappensfartooofteninthehistoryofscience,wherearesultisasinfluentialasitiswrong.VonNeumannhadaformidablereputation,andinthefaceofhistheorem,oppositiontotheviewthatquantummechanicswasthemostcompletetheorypossiblecaved.Inparticular,deBrogliehimselfcapitulatedtothecombinedcriticismsofvonNeumannandothertheorists,includingWolfgangPauli.

ItisnotquitetruethatnobodynoticedthatvonNeumann’stheoremcontainedamistake.AyoungmathematiciancalledGreteHermanntookaninterestinquantummechanicsandwasnaturallydrawntostudyvonNeumann’sbook.Agoodmathematicianinherownright,HermannwasaPhDstudentofEmmyNoether,*andamongheraccomplishmentsareseveralresultswhichanticipatedthemodernstudyofalgorithmsincomputerscience.Shealsohadakeeninterestinphilosophyandwasconcernedwiththeimplicationsofquantummechanicsfortheneo-KantianphilosophythenpopularintheGerman-speakingacademy.

GreteHermannquicklynoticedamistakeintheproofofthetheoremontheimpossibilityofhiddenvariablesinvonNeumann’sbook.Oneoftheassumptionsofthetheoremwasalreadyequivalenttothebasicstructureofquantummechanics.Soallthetheoremprovedwasthatanytheoryequivalenttoquantummechanicswouldturnouttobeequivalenttoquantummechanics.

Veryunfortunately,thepapershewroteexposingthefaultinvonNeumann’sproofhadnoimpact.3Partofthereasonmayhavebeenthatshepublisheditinanobscurejournal,butitishardtoavoidthethoughtthatshewasn’ttakenasseriouslyasshemighthavebeenduetohergender,aswellastothefactthatherpaperpuncturedoneofthemainargumentsusedtoestablishtheinevitabilityofquantummechanics.

IttooktwolongdecadesforsomeoneelsetonoticethatvonNeumann’sproofhadtobewrong,becauseitdisagreedwiththemanifestexistenceofpilotwavetheory.ThiswasDavidBohm,whowillbetheprotagonistofthenextchapter.Tenyearsafterthat,JohnBellisolatedtheerrorasanerroneousassumption.Hereishowheputit:

[T]hevonNeumannproof,ifyouactuallycometogripswithit,fallsapartinyourhands!Thereisnothingtoit.It’snotjustflawed,it’ssilly....Whenyoutranslate[hisassumptions]intotermsofphysicaldisposition,they’renonsense.Youmayquotemeonthat:TheproofofvonNeumannisnotmerelyfalsebutfoolish!4

DavidMermin,inalucidreviewofvariousimpossibilitytheorems,regrettedthe“manygenerationsofgraduatestudentswhomighthavebeentemptedtotrytoconstructhiddenvariablestheories[who]werebeatenintosubmissionbytheclaimthatvonNeumann...hadprovedthatitcouldnotbedone.”Mermin“wonder[ed]whethertheproofwaseverstudiedbyeitherthestudentsorthosewhoappealedtoittorescuethemfromspeculativeadventures.”5

Itishardnow,lookingbackfromourpresentvantagepoint,inwhichseveralcompetingviewsabouthowtounderstandquantumtheoryflourish,toappreciatethestateofmindofthefirstseveralgenerationsofquantumphysicists.InspiteofthepersistentandpowerfuldissentsofEinstein,deBroglie,andSchrödinger,foratleastthefirsthalfcenturyfollowingtheinventionofquantummechanicsin1925,theanti-realistphilosophyinitiatedbyBohrdominatedalldiscussionsofquantumtheory.

Throughallthoseyears,ifsomeoneraisedthepossibilityofarealistversionofquantummechanics,theresponse,Iwastold,wasagooddose

ofCopenhagen-speakwhich,ifonepersisted,wascappedoffwith“VonNeumannprovedthereisnoalternative.”OnecanimagineitwouldhavechangedthingsatleastalittleifGreteHermann’spapershowingthatno,vonNeumannhadn’tprovedanything,hadbeenknown.Butitsimplywasn’t.

B

EIGHT

Bohm:RealismTriesAgainIn1952,DavidBohmsolvedthebiggestofallproblemsinquantummechanics,whichistoprovideanexplanationofquantummechanics....Unfortunately,itiswidelyunder-appreciated.Itachievessomethingthatwasoften(beforeandevenafter1952)claimedimpossible:Toexplaintherulesofquantummechanicsthroughacoherentpictureof

microscopicreality.—RODERICHTUMULKA

y1930deBrogliehadgivenup.Fromthenon,theanti-realistCopenhageninterpretationdominatedtheteachingandapplicationofquantummechanics,aswellasmostdiscussionof

thenewtheory’simplications.TheonlysignificantexceptionswereEinsteinandSchrödinger,whocontinuedtochallengetheCopenhagenschoolandinsistontheneedforarealistformulationofquantumtheory.Buttheirdissenthadlittleimpact.

Thatwasthesituationintheearly1950swhentheyoungAmericantheoristDavidBohmsetouttowriteatextbookonquantummechanics.Bohmwasaninterestingcharacterdestinedtohaveaninterestinglife.AtthatpointhewasanassistantprofessorofphysicsatPrincetonUniversity,specializinginplasmaphysics.HehadcometoPrincetonfromBerkeley,wherehehadbeenastudentofJ.RobertOppenheimer.LikemanypeoplearoundOppenheimer,hehadbeenacommunistsympathizerandbrieflyaCommunistPartymemberbeforethewar.Asaresult,theU.S.ArmyhadrefusedOppenheimer’srequesttobringBohmalongtoworkontheatomicbombatLosAlamos.

ThereisnoevidencethatBohmwaseveraspyoraSovietagent,but,likeotherswithintegrity,whencalledin1950totestifybeforetheHouseUn-AmericanActivitiesCommittee,heassertedhisFifthAmendmentrightsandsoavoidedinformingonothers.HewasarrestedandchargedwithcontemptofCongress,butacquitted.Princeton,toitsshame,suspended,andthendeclinedtorenew,hisfacultyappointment.

EinsteinproposedappointinghimattheInstituteforAdvancedStudy,butwasunabletoovercomeoppositionfromitsadministration.Atthatverymoment,whenBohmfoundhimselfunemployedand,intheUnitedStates,likelyunemployable,histextbookwaspublishedtohighpraise.

Therehasbeennoshortageoftextbookspublishedonquantummechanicssincethefirst,byPaulDirac,oneoftheinventorsofthetheory,whichappearedin1930.Bohm’sisoneofthebest.Anddespitepersistentdoubtsovermanyyears,whenhediscussedinterpretationalissueshekeptclosetotheCopenhagenorthodoxy.Onesectionofhisbookwastitled“Proofthatquantumtheoryisinconsistentwithhiddenvariables.”Anotherwasaboutthe“Unlikelihoodofcompletelydeterministiclawsonadeeperlevel.”

Einsteinsummonedhim.HeexpressedhisadmirationforthelucidityofBohm’sdefenseoftheCopenhagenview,butaskedforachancetoexplainhispointofviewandperhapschangeBohm’smind.

ItappearsEinsteinsucceeded.AftertalkingwithEinstein,Bohmbegantothinkaboutwhethertheremightbeadeepertheory,whichwasrealistanddeterministic.PerhapsitwastheappealofrealismtoaMarxistmaterialist;perhapsitwastheclarityofEinstein’sthinking.Butitdidn’ttakelongforBohmtoinventarealistcompletionofquantummechanics.Whathedidwas,basically,toreinventdeBroglie’sforgottenpilotwavetheory.

Thereis,itshouldbementioned,adifferencebetweendeBroglie’sandBohm’stheories,inthatBohmchoseadifferentlawfortheguidanceequationbywhichthewaveguidestheparticle.AsIexplainedabove,deBroglie’sguidanceequationhastheparticletakingthepathofsteepestascentupthewavefunction.Thisdeterminesthespeedanddirectionofmotionoftheparticle.

InBohm’stheory,thelawthatguidestheparticleisaversionofNewton’slawofmotion:itdescribeshowaparticleacceleratesin

responsetoaforce.Whatisnewisthatthereisaforcewhichguidestheparticletomovetowherethewavefunctionislargest.Inaddition,Bohmhastoassumeonemorecondition,whichisthatattheinitialmoment,thevelocitiesoftheparticlesarethosegivenbydeBroglie’sguidanceequation.

Apartfromthisdifference,deBroglie’sandBohm’stheoriesaredifferentversionsofthesameidea,whichisthatboththewavefunctionandtheparticlesarereal,withthewavesguidingtheparticles.Aspresentedoriginally,theyareequivalentinthattheypredictthesametrajectoriesfortheparticles.Asaresult,boththeoriespredictthatifanensembleofparticlesstartsoffdistributedaccordingtoBorn’srule,thatrulewillcontinuetobesatisfiedasthewavefunctionchangesandtheparticlesmovearound.

Itdidn’ttakelongforBohmtowritetwopaperspresentinghisnewtheory.1Hesubmittedthemtothemostprestigiousjournalatthattime,PhysicalReview.Healsosentdraftstoseveralpeople,includingdeBroglie,whoquicklypublishedashortarticleexplainingwhyBohm’stheory,likehisownpreviousproposal,waswrong.

Bohmaddedaveryinterestingsentencetohismanuscript:“Afterthisarticlewascompleted,theauthor’sattentionwascalledtosimilarproposalsforanalternativeinterpretationofthequantumtheorymadebydeBrogliein1926,butlatergivenupbyhim.”

Thissentencecertainlyclaimsthathedidn’tknowofdeBroglie’spilotwavetheorywhenheinventedhisownversion.Thisinitselfisalittleshocking,giventhatdeBrogliewasaworld-famousNobelPrizewinner,universallyrecognizedforhavingproposedthatelectronsandotherparticleshavewaves.Butthereitis.

BohmalsodevotedasectionofhissecondpapertoexplainingwhyvonNeumann’stheoremdoesn’tapplytothetheoryheisproposing.

Bohm’sfirstpaperonthepilotwavetheoryappearedinJanuary1952.BythenhehadtakenaprofessorshipinSãoPaulo,Brazil.Fromthatfarremove,lonelyandsickfromtheunfamiliarfood,hewaitedastheresponsestohisrevolutionarypapersdriftedinbyletter.

OnepersonBohmmighthavehopedforsupportfromwasEinstein.Thegreatsavanthad,afterall,praisedpilotwavetheorywhenitwasfirstpresentedbydeBroglie.But,apparently,bythetimeBohmpublishedhispapers,twenty-fiveyearslater,Einsteinhadchangedhismind.

EinsteindescribedhisreactioninalettertoMaxBorn:“HaveyounoticedthatBohmbelieves(asdeBrogliedid,twenty-fiveyearsago)thatheisabletointerpretthequantumtheoryindeterministicterms?Thatwayseemstoocheaptome.”2

Hewenton,“Thispathseemstometooeasy.”Itisa“physicalfairy-taleforchildren,whichhasrathermisledBohmanddeBroglie.”3

EinsteinelaboratedinapaperinhonorofBorn,posinganobjection.Bohm’stheorypredictsthemotionoftheparticle,andoneconsequenceisthatinastationarystateofanatom,theelectronispredictedtobesimplystandingstill.AsEinsteinexplained,“Thevanishingofthevelocitycontradictsthewell-foundedrequirement,thatinthecaseofamacro-systemthemotionshouldagreeapproximatelywiththemotionfollowingfromclassicalmechanics.”4Butitdoesn’tbecause,accordingtoclassicalmechanics,theelectronshouldbeorbitingthenucleus,andnotjuststandingstill.

ItshouldhavebeenimmediatelyapparentthatEinstein’sobjectioniswrong,becauseatomsarenot“macro-systems.”Butnonetheless,Einstein’sobjectionpointstohowdifferenttheparticlesofpilotwavetheoryarefromthoseofNewtonianphysics.AsIstressedearlier,deBrogliehadunderstoodfromthebeginningthathisparticleswouldmoveinwaysthatviolatebasicprinciplesofNewtonianphysics,suchastheprincipleofinertiaandtheconservationofmomenta.Thiswasnecessaryiflightquantacouldbendtheirtrajectoriestodiffractaroundobstacles.DeBroglie’sandBohm’sguidanceequationsresultedintrajectoriesthatdiffractedandrefracted,buttherewasapricetopay,whichwasapparentviolationsofbasicprinciples.Particlesthatjuststoodstillinanatom,anddidnotneedtoorbittokeepfromfallingintothenucleus,alsocontradictedtheseprinciples.ForEinstein,itseemed,thepricewastoohigh.

Einstein’sdislikeofpilotwavetheorydidn’tpreventhimfromwritingsympatheticallywhenheheardthroughamutualfriendaboutBohm’s“feelingofdistressforbeingclosedoutandclosedinatthesametime.Whatimpressedmemostwastheinstabilityofyourbelly,amatterwhereIhavemyselfextendedexperience.”5

Indeed,theotherresponsesBohmreceivedorheardaboutwerenotlikelytohavehelpedhisdigestion.

Heisenbergrepliedthatfromhisoperationalpointofview,theparticletrajectoriesinBohm’stheoryconstitutedanextraneous“ideologicalsuperstructure.”Thereweretwopossiblefatesforanyproposedalternativetoquantummechanics.Eitherthenewtheorygavepredictionsthatdisagreedwiththoseofquantummechanics,inwhichcaseitismostlikelywrong,oritpredictsthesamephenomena,inwhichcaseithasnothingnewtoofferphysics.Hewrotethat“Bohm’sinterpretationcannotberefutedbyexperiment....Fromthefundamentally‘positivistic’(itwouldperhapsbebettertosay‘purelyphysical’)standpoint,wearethusconcernednotwithcounter-proposalstotheCopenhageninterpretation,butwithitsexactrepetitioninadifferentlanguage.”6

Pauliissuedasimilarcriticism,butafterfurtherstudy,conceded:“Idonotseeanylongerthepossibilityofanylogicalcontradictionaslongasyourresultsagreewiththoseoftheusualwavemechanicsandaslongasnomeansisgiventomeasurethevaluesofyourhiddenparameters.”7

Infact,therearecircumstancesinwhichthepredictionsofpilotwavetheorydisagreewiththoseofquantummechanics,butittooksometimeforthattobecomeclear.Wewillreturntothispointshortly.

Noteveryonewassokind.BackinPrinceton,RobertOppenheimerdeclinedtoreadBohm’spapers,callingthemawasteoftime.ButthisdidnotpreventhimfrompronouncingthatBohm’sworkwas“juveniledeviationism.”8Doesn’tthatsoundexactlylikelanguageoneMarxistwouldusetocondemnanother?Oppenheimer’slastwordonthesubjectwas“IfwecannotdisproveBohm,thenwemustagreetoignorehim.”9

ThemathematicianJohnNash,nowfamousforhistheoremonequilibriumineconomics,wrotetoOppenheimertocomplainaboutthedogmaticattitudeshefoundamongthePrincetonphysicists,whotreatedanyonewho“expressesanysortofquestioningattitudeorabeliefin‘hiddenparameters’...asastupidoratbestquiteignorantperson.”Nonetheless,hewaswiththeotherlosers,becauseheconfessed,“Iwanttofindadifferentandmoresatisfyingunder-pictureofanon-observablereality.”10

ThecompleterejectionofhisbreakthroughworkbyOppenheimer,whohadbeenbothamentorandafatherfiguretoBohm,musthavehurtdeeply.BohmwasdoublyexiledfromPrinceton,thenthecenterofAmericanphysics,forhisrebellionagainsttheCopenhagenphilosophy

andhissimultaneousrefusaltocapitulatetotheMcCarthyistwitchhunt.Onemustadmirethecouragethattook,whilerememberingthecost.BohmwasisolatedatwhatmusthavefelttohimliketheendoftheEarth.

Bohm’sfriendsandhisbiographerintimatethatOppenheimerhadmotivestodistancehimselffromasuspected“red,”ashewashimselfindanger,abouttobecaughtupinthesamewitchhunt.Butevenputtingthataside,itwouldbenaivetobelievethatintheabsenceofhispoliticalcatastropheandexile,aBohmwhohadstayedinPrincetonwouldhavesucceededanybetteringaininginterestinhissubversionoftheCopenhagenideology.

Inanycase,theresponsefromCopenhagenappearedequallydismissive.Thereisareport,bythephilosopherPaulFeyerabend,whovisitedCopenhagenthen,thatBohrwasatleastmomentarily“stunned”byBohm’spapers.Butifhewasstunneditwasnotenoughtoevermentioninhisownwritings,letalonepickupapenandrespondtoBohmdirectly.Instead,BohmreceivedaletterfromaprotégéofBohrnamedLéonRosenfeld.

HereisasampleofCopenhagen-speak,takenfromthatletter:

Icertainlyshallnotenterintoanycontroversywithyouoranybodyelseonthesubjectofcomplementarity,forthesimplereasonthatthereisnottheslightestcontroversialpointaboutit....[T]hereisnotruthinyoursuspicionthatwemaybetalkingourselvesintocomplementaritybyakindofmagicalincantation.IaminclinedtoretortthatitisjustamongyourParisianadmirersthatInoticesomedisquietingsignsofprimitivementality.

Thedifficultyofaccesstocomplementaritywhichyoumentionistheresultoftheessentiallymetaphysicalattitudewhichisinculcatedtomostpeoplefromtheirverychildhoodbythedominatinginfluenceofreligionoridealisticphilosophyoneducation.Theremedyforthissituationissurelynottoavoidtheissuebuttoshedoffthismetaphysicsandlearntolookatthingsdialectically.11

ReadingthisaloneinhisSãoPauloapartment,DavidBohmmusthavefeltalongwayfromKansas,or,inhiscase,Pennsylvania.

Despitehisdisappointments,BohmwasproductiveduringhistimeinBrazil.Hecontinuedtomakecontributionstoplasmaphysicswhilehefocusedonhisnewquantumtheory,andhebeganacollaborationwithJean-PierreVigier,astudentandcolleagueofdeBroglie.ButhewasnothappyinBrazilandin1955movedtotheTechnioninIsrael,thenafewyearslatertoEngland.AfterastayinBristolheendedhisodysseyatBirkbeckCollege,UniversityofLondon,wherehewastostayfortherestofhislife.

InLondon,Bohmmoderatedhiscommunistsympathies;likemanywhohadgiventheSovietUnionthebenefitofthedoubt,hewasshockedasthethawingofSovietpowerunderNikitaKhrushchevledtotheconfirmationthattheStalinistgulaghadindeedbeeneverybitasmurderousashadbeenreported.Bohm’sdesireforaroadtotheperfectibilityofhumanbeingsthenturnedtomysticism,andafterashortimmersionintheteachingsofthemysticGurdjieff,hefellundertheinfluenceoftheIndianguruKrishnamurti.

Bohmmeanwhilecontinuedhisrelentlesssearchforadeeperviewpointonnaturethatwouldtakehimbeyondthequantumtheory.Thisledhimtodevelopahighlyoriginallineofthought,franklyspeculativeandphilosophical,bothrelatedtoandtranscendinghisphysics.Hewroteseveralbooks,throughwhichhereachedanewaudienceofartists,philosophers,andseekers,whilehisdialogueswithKrishnamurtibecameverypopularinthewiderworld.

—ALTHOUGHHISLATERWORKisofnorelevanceforjudgingtheimportanceofhisworkonpilotwavetheory,Idofeelitwouldbeirresponsibleandcowardlytonotattemptasummingupofthelife’sworkofthiscomplexandcontradictorysage.IfeelagenuinesympathyforDavidBohminhissearchfortranscendence,firstthroughtheMarxistvisionofanewhumanpsychologyarisingfromthedreamofajustandequalsociety,andthen,whenthatfantasywasexposedasacruelillusion,throughhisworkwithmystics.*FromOppenheimertoKrishnamurti,someweaknessinBohmmadehimsusceptibletothatkindofdominating,supremelyconfidentfigure.

ButasmuchasonecancriticizeBohmforwhatinretrospectlookslikethenaiveandignorantsuspensionofhisbetterjudgment,hisyearsof

hard,determinedeffortinsearchofthesciencebeyondthequantumrescueshislife’sworkandrestorestoitintegrity,seriousness,andpromise.Hewasonaquestforanewtranscendentformofscience,informedsimultaneouslybythedeepeststrandsofwhatisbestcalledreligiousthoughtandtheknottiestpuzzlesoftheoreticalphysics.Itisadomainfewgoodphysicistshaveexplored;perhapsonlyDavidFinkelsteincanbementionedhere.ItiseasytosaythatBohmfailed,andthathisgreatestachievementsbyfarwerehisearlycontributionstoquantumphysics.Atthesametime,heexploredaroadthatfewofushavehadthecourageorthevisiontoeventakeonesteptoward,inspiteoftheobviousfactthatthegreatestdangerswefaceasaspeciescanbetiedtotheutterincoherenceofhumanculture,abreakthathasitsrootsintheincommensurabilityofscientificandspiritualunderstandingsoftheworld.

—INTHEWAKEOFwhatwe’velearnedfromBohm,let’ssumup.Thepilotwavetheoryexplainseverythingthatordinaryquantummechanicsdoes,withouttheawkwardnessofRule2.ThewavefunctionevolvesalwaysaccordingtoRule1,soitneverjumpsorcollapses.Whatisnewisthatthereisaparticlethatmovesaccordingtoitsownlaw,guidedbythewavefunction.Togetherthetwolawsgiveanentirelyrealistdescriptionofquantumphenomena.

Inaddition,pilotwavetheoryexplainswhatquantumtheorydoesnot.Itgivesacompletedescriptionofwhatgoesonineveryindividualprocess.Itexplainshowandwhyelectronsmove.Itexplainswheretheuncertaintiesandprobabilitiescomefrom,whichisourignoranceaboutthestartingpositionsoftheparticles.Anditsolvesthemeasurementproblembecausethereisnoneedtodistinguishexperimentsfromotherprocesses.

InthesecondpaperBohmwrotein1952onthenewtheory,hestudiedthemeasurementprocessindetailandshowedthat,inthecaseofanatominteractingwithadetectorsetuptomeasuresomepropertyofit,thedetectorendsupcorrelatedwiththeatom,intermsofwheretheparticlesareaswellasintermsofthewavefunctions.Thus,measurementsworkcorrectlyonbothsidesofthedoubleontology.

Fromarealistpointofview,pilotwavetheoryisvastlysuperiortotheCopenhageninterpretation.ByitsveryexistenceitgivesthelietoBohrandHeisenberg’sargumentthatitisimpossibletohavearealistdescriptionofquantumphysics.Onemighthavethoughtthatthecommunityofphysicistswouldhavejumpedtoembracepilotwavetheory,eitherwhendeBrogliefirstproposedittotheSolvayconferencein1927orin1952whenBohmproposeditagain.ThisisclearlywhatBohmexpected,andhisdisappointment,ashewaitedinSãoPaulo,maybeoursaswell.

Somehistorianshavesuggestedthattheembraceofanti-realismbytheEuropeanphysicscommunityinthe1920swaspartofalargerculturalmovementwhichembracedirrationalityasaresponsetotheslaughterinthetrenchesthattheirgenerationhadrecentlyexperienced.Butthisdoesnotexplainthesimilarrejectionofpilotwavetheorybythephysicscommunityofthe1950s,whichhadrecentlycometobedominatedbythetriumphant,optimistic,andpragmaticAmericanspirit.

Somemightexplainitbythepowerofresearchschoolsledbycharismaticleaders,particularlyNielsBohr,whoinspiredandmentoredmanyofthequantumrevolutionarieswhocamefromacrossEuropeandAmericatoworkwithhim.DeBroglie,bycontrast,hadjustafewstudentsthroughouthislonglife,andtheywere,tomyknowledge,allFrench.HissmallgroupofacolyteswasisolatedevenwithinthecommunityofFrenchphysicists.

BohminspiredthedevelopmentofacommunityoftheoristsinBrazil,forwhichheisunappreciatedbeyondthatcountry.AfterBrazil,inIsraelandLondon,hehadafewgoodstudents,oneofwhom,YakirAharonov,becamealeadingtheoristwithhisownideasandprogram,quitedifferentfromBohm’s.AhandfulofBohm’sstudentsbecamespecialistsinquantumfoundations,buttheypursueddiverseideasanddidnotformintoacoherentBohmianschoolofthought.Itdidn’thelpthat,bythetimeBohmhadrelocatedtoLondonandwasbackinaplacewherehecouldassertinfluence,muchofhisattentionwascapturedbymysticism.

Nonetheless,interestinpilotwavetheorygrewslowlybutsteadilyovertheyears,asitwastakenupanddevelopedbyasmallnumberofgoodscientistsaroundtheworld.Bythe1990s,whatwassometimescalled“Bohmianmechanics”constitutedasmallbutdistinctandvisiblesubcultureofthecommunityofscientists,mathematicians,and

philosopherswhodevotedthemselvestothepuzzlesofquantumfoundations.

—DUETOTHEWORKofthese“Bohmians,”somesubtlequestionsaboutpilotwavetheoryhavebeenraisedandanswered.Oneofthetrickiestquestionshastodowithhowprobabilitiesariseinpilotwavetheory.Thetheoryisdeterministic.Givenawavefunctionatonetime,wecanuseRule1todeterminethewavefunctionatanyfuturetime.Theequationthatdescribeshowthewavefunctionguidestheparticleisalsodeterministic,andifwespecifywheretheparticleisataninitialtime,itwilltellusexactlyhowtheparticlemovesfromthenon.Eachparticlehasadefinitetrajectory.

Sowheredoprobabilitiescomefrom?ProbabilitiesenterforthesamereasontheycanenterNewtonianphysics:becauseofourignoranceabouttheexactpositionsoftheparticles.Aswecannotknowwheretheparticlestartsout,weareuncertainaboutwhereitwillbeinthefuture.Probabilitiesinpilotwavetheoryexpressourignoranceofwheretheparticleswereinitially.

Tomakesenseofprobabilitiesinpilotwavetheory,wehavetopictureacollectionofsystemswiththesamewavefunction,butwithdifferentstartingpositionsoftheparticles.Theparticlesaredistributedinitiallyaccordingtoaprobabilitydistributionfunction,whichtellsushowcommonthedifferentinitialpositionsareinthecollection.

Wearefreetochoosetheinitialpositionsoftheparticles,tomaketheprobabilitydistributionfunctionbeanythingwelike.Weevolvethesystemforwardintime,usingRule1toevolvethewavefunctionandtheguidancelawtomovetheparticlesaround.Whenwedothis,theprobabilitydistributionfunctionchangesintimeaswell,reflectingtheparticlesmovingaround.

Inquantummechanics,asIdescribedearlier,theprobabilitiesoffindingtheparticlesindifferentplacesaregivenbyBorn’sruletobethesquareofthewavefunction.ThatissimplypositedinquantummechanicsaspartofRule2.Inpilotwavetheorytheparticleshavetheirownreality,andwearefreetochoosetheinitialprobabilitydistributionfunction.Onechoicewecanmakeisthatitisgiven,justasinquantummechanics,byBorn’srule.Todothis,wedistributetheparticlessothat

thelargerthesquareofthewavefunctionis,themoreparticlesinthecollectionareplacedthere.

Whenwemakethischoice,itismaintainedintime.Theparticlesmovearoundandthewavefunctionchangesintime,butitremainstruethatthesquareofthewavefunctiongivestheprobabilityoffindingaparticle.

ButindeBroglie’sformulation,thereismore.Supposeonestartsthecollectionoffwithadifferentprobabilitydistributionfortheparticles,onenotgivenbythesquareofthewavefunction.Thenthesystemwillevolveinawaythatbringstheactualprobabilitydistributionintoagreementwiththatgivenbythesquareofthewavefunction.ThiswasshowninanimportantresultofAntonyValentini’s.12Ithasbeenconfirmedbynumericalsimulationssince.13

Thisisanalogoustohowthermodynamicsworks.Whenasystemofmanyparticlesisinequilibriumwithitssurroundings,theentropyismaximal.Thisisbecauseentropyisameasureofdisorder,whichtypicallyincreasesovertime.Ifonestartsthesystemoffinadifferentconfiguration,onemoreorderedthanequilibrium,itismostprobablethatthedisorderwillincreaseuntilthesystemisinequilibrium.

ThecaseofdeBroglie’spilotwavetheoryisverysimilar.Wecansaythataquantumsystemisoutofquantumequilibriumiftheprobabilitydistributionforwhereaparticlemightbefoundisdifferentfromthatgivenbythesquareofitswavefunction.Whentheyagree,thesystemisinquantumequilibrium.Valentini’stheoremtellsusthataquantumsystemoutofquantumequilibriumismostlikelytoevolveuntilitreachesthestateofquantumequilibrium.

Onceasystemisinequilibrium,thepredictionsofpilotwavetheoryagreewiththoseofconventionalquantummechanics.Thus,onehastosomehowdriveasystemoutofquantumequilibriumtosetupasituationinwhichanexperimentcoulddistinguishpilotwavetheoryfromquantummechanics.

Physicsoutofquantumequilibriumcontainsseveralsurprises.Oneisthatitbecomespossibletosendinformationfasterthanlight.ThisisaconsequenceofanotherresultofValentini’s,whichtellsusthatwhilethesystemisoutofquantumequilibrium,informationandenergycanbesentinstantaneously,contradictingspecialrelativity.14Needlesstosay,ifthisweretobeconfirmedexperimentallyitwouldbeofthefirst

importanceforourunderstandingofnatureandpossiblyevenfortechnologiesthatsciencefictionwritersdreamof.Thisisonewayanexperimentcouldverydramaticallydistinguishpilotwavetheoryfromconventionalquantummechanics.Therehavebeenafewattemptstodrivequantumsystemsoutofquantumequilibriumandtestthesepredictions,but,sofar,theyhaven’tsucceededineitherdiscoveringquantumnon-equilibriumorrulingoutpilotwavetheory.

Oneplacetolookforout-of-quantum-equilibriumphysicsisintheveryearlyuniverse.Valentiniandcollaboratorshavehypothesizedthattheuniversebeganinthebigbangoutofequilibrium,andequilibratedasitexpanded.Thismighthavelefttracesinthecosmicmicrowavebackground,orCMB,whicharebeingsearchedfor,butthereisnoclearevidenceyet.15

—LET’SCOMEBACKTOtheSchrödinger’scatexperimentandseehowpilotwavetheoryresolvesit.

Pilotwavetheoryassertsthatquantummechanicsappliesuniversally.ThereisonlyRule1,anditappliestoallcases.Thismeansthatmeasurementsarenodifferentfromotherprocesses.

Everything—atoms,photons,Geigercounters,cats,andpeople—hasadualexistence,asawaveandaparticle.BothsidesofthisdoubleexistencearecomplexforlargecomplicatedobjectssuchasGeigercountersorcats,whicharemadeofmanyparticlesworkingtogether.Weneedawordtotalkaboutallthewaysthattheparticlesmakingupacatmaybearrangedinspace,andwehaveone:theconfigurationoftheatoms.Ifyouspeakofwherealltheatomsmakingupthecatarelocatedwithrespecttoeachother,youaredescribingtheconfigurationofthecat.Becausetherearemanyatoms,ittakesagreatdealofinformationtodescribethecat’sconfiguration.

Allthisinformationmustbecodedintoalistofnumbers.Howmanynumbersdoesittaketodescribeacat?Forjustoneatomittakesthreenumbers.Theselocatetheatominthree-dimensionalspace.Fortwoatomsittakessixnumbers,threeforeachatom.Sotolocatetheatomsinacattakesthreenumbersperatom.Thereareveryroughly1025atomsinacat,soittakes1025multipliedbythreetodescribethecat’sconfiguration.

Theimportantthingaboutpilotwavetheoryisthattheatomsareallreal,andtheyareeachlocatedsomewheredefiniteinspace.Eachatomhasalocation,whichisapointinspace.Eachcathasaconfiguration,whichamountstosayingthateachofitsatomsislocatedsomewheredefiniteinspace.

Anatomalsohasawave,whichislocatedinthree-dimensionalspace.Eachcatalsohasawaveassociatedwithit.Thestrangethingiswherethatwaveislocated.Itisn’tawaveinthree-dimensionalspace.Instead,it’sawaveinaveryhigh-dimensionalspace,calledtheconfigurationspace(seefigure9).Eachpointofthisspacecorrespondstoaconfigurationofthecat.

Itisdifficult,ifnotimpossible,tovisualizeaspacewithmanydimensions.IoncewatchedinaweasRogerPenrosedidacalculationontheblackboardwhichrequiredhimtoslideatwo-dimensionalsurfacearoundasix-dimensionalobstacleinaneight-dimensionalspace,andIdidhavethethrillingexperienceoffollowingstepbystep,butthat’sthelimitofmyexperience.Mostmathematiciansarenotasvisuallygifted,butwecanreasonourwayaroundinahigh-dimensionalspace.WhenIdrawathree-dimensionalobject,Iamreallydrawingatwo-dimensionalprojectionofit.Likewise,whatIseeinmymindwhenIimagineaconfigurationspacelikethatofacat,withperhaps3×1025dimensions,isathree-dimensionalprojection,togetherwithasilentadmonishmenttobecarefulandnotdrawfalseconclusionsfromthistotallyinadequatevisualization.

FIGURE9.CONFIGURATIONSPACETwoatomsliveonaline,inonedimension.Theirconfigurationismeasuredbytwonumbers,sotheircombinedconfigurationspaceisapointonaplane,intwodimensions.Wetreatthetwoatomsasidentical,soatom2isalwaystherightmostatom.

Awaveontheconfigurationspacecarriesavastamountofinformation.Recall,forexample,thestateCONTRARY,whichdescribescorrelationsbetweentheanswerstoquestionsaskedsimultaneouslyoftwoparticles,whiletellingnothingatallabouteachparticleseparately.Tocodequantumstateslikethis,intotalgenerality,weneedmorethanathree-dimensionalwaveforeachatominthecat.Weneedawaveflowingonthespaceofallpossibleconfigurationsofthecat.

Onceoneacceptstheexistenceofawaveonthespaceofalltheconfigurationsofacat,theresolutionsofthequantumpuzzlesfollowdirectly.

Thereisonlyonecat,whichallthetimeisinsomeconfiguration.Theconfigurationofthecatmaybeoneinwhichthecatisalive,oritmaybeoneinwhichthecatisdead.Itmustbeoneortheother,butitcannotbeboth.Sothecatisateverymomenteitheraliveordead.

Thewavefunctionofthecatcanbethesumoftwowaves,becauseyoucanalwaysaddwaves.Thatiswhattheydo:wavessuperpose,whichmeanstheyadd.Thewaveguidestheconfiguration,justasitdoesforasingleelectron.Thewavefunctionmayflowsimultaneouslythrough

configurationsofalivecatandconfigurationsofadeadone.Justasarivercanbranch,andtakebothbranches,awavefunctionmaybranchandtakeboththebranchoverlivingconfigurationsandthebranchoverdeadconfigurations.

Thewavefunctionendsuprelatedtotheprobabilityoffindingdifferentconfigurations.Whenthewavefunctionislargeoversomeconfiguration,soistheprobability.Sotheprobabilityoffindingthecatinaliveconfigurationoradeadconfigurationmaybeeachroughlyonehalf.Butthereisonlyonecat,andjustasanelectroncanbeinonlyoneplaceatatime,theonecatiseitherdeadoralive.

Isitweirdthatthewavefunctionwillspawnbranchesthatflowtowheretheparticlesortheirconfigurationsarenot?Abit,butthismustbe,becausetheparticlecanfollowonlyonebranch.Butanemptybranchmayhaveconsequencesinthefuture.Thedifferentbranchesmayflowbacktogetherinthefuture,makinginterferencepatternsthatinfluencewheretheparticlesgo.

—EIGHTEENYEARSAGOIhadadifficultdecisiontomake.Twofuturesbeckonedtome,eachofwhichseemed,fromalltheinformationIcouldgather,attractive.Ofcourseoneneverhasenoughinformationtomakeadecisionlikethis,foreverythingaboutmyfuturewasatstake.Thequestionwas,WhichcountryandwhichcitywouldIcallhome?WhomImightmarry,whomychildrenwouldbe,whatlanguagestheymightspeak,andhowlongImightlivewouldallbeinfluencedbythisdecision.

Unabletodecide,Iconsultedfriendswithaquantumlabandletaradioactiveatomdecideforme.Iftheatomdecayedwithinitshalf-life,Iwouldtakethenewopportunityinanewcityandcountry;ifitdidn’t,Iwouldstaywiththefamiliar.Well,itdecayed,andhereIaminToronto,withmyfamily,friends,andneighbors,noneofwhomIwouldeverhavemethadthatatomheldoffdecayingabitlonger.

Thereisnothingspecialaboutme.Allofusaremadeofparticlesthathavebeenguidedtothepresentbyawavefunctiononourvastspaceofpossibleconfigurations.

ThewavefunctionsurroundswhereIamnow,butitalsohasotherbrancheswhereImightbe,butamnot.SomeofthembranchfromthatexperimentanddeveloptheemptyhistorythatIdidnottake,butwould

havehadtheatomnotdecayed.Theemptywavefunctionoftheparticleflowsonfromthere,tothisday.ThisemptybranchofmywavefunctioncontinuestoinhabitLondon.

Havewenotallfeltabitwistfulcontemplatingliveswemighthavehad,hadadecisionturnedoutjustabitdifferently?Ifthepilotwavetheoryisright,thentheselivesnottakenaretracedbyanemptywavefunction,readytoguidemyatoms,which,however,areelsewhere.

Afewyearsbeforethat,mywavefunctionfacedanotherfork,fromwhichtwoverydifferentbranchesflowed.Itookonebranch,buthadItakenanother,Iwouldhavefacedaverydifferentfate.

IwasbookedonaSwissairflightfromNewYorktoaconferenceinVienna.Thenightbeforemytrip,Iheardfromtheorganizersthatmytalkwasn’tscheduledtilltheendofthemeeting,andso,onatotalwhim,forareasonInolongerremember,Icalledthetravelagentandrebookedforadaylater.BeforegoingtosleepthenexteveningIturnedontheradioandheardthattheflightIwouldhavebeenonhadcrashedoffHalifax.So,ifpilotwavetheoryiscorrect,itisreallytruethatabranchofthewavefunctionoftheatomsthatthenconstitutedmeistothisdaybunchedupatthebottomofSt.MargaretsBay,offthevillageofPeggy’sCove,NovaScotia.

Thatbranchisempty,asaremyriadothers.Butifpilotwavetheoryisright,theyarereal.Theonlydifferencebetweenthemandtheonebranchthatguidesmenowisthatonlyonebranchcoincideswith,andguides,theatomsthatmakemeup.Themyriadotherbranchesflowon,empty.

DoIcareabouttheseotherbranches?ShouldI?Thereisalwaysthechancethatatsometimeinthefutureanemptybranchrecombineswithmybranch,causinginterference,whichchangesmylifeabruptly.

Thechancesforthistohappenareextraordinarilysmall.Theyareinacategoryofpossibleeventsthatwouldbepermissibleunderthelawsofphysicsbutwhichessentiallyneverhappen.AlltheatomsintheairintheroomwhereI’mtypingthismightbychancelineuptogetherandflyoutthewindow,asphyxiatingme.Butthiswouldbeextraordinarilyunlikely,giventhattheatomsspendtheirdaybouncingaroundrandomly.

Sothereisbasicallynochancethattheemptybranchesrepresentingtheliveswedidn’tliveandthechoiceswedidn’tmakewillhaveanyeffectonourfutures.Butwerewemereatoms,interferencebetweenfullandemptybranchesofthewavefunctionwouldbehappeningallthetime.

Soforallpracticalandmoralpurposes,ifpilotwavetheoryisright,wecanignoretheemptybranches.Wearerealonlyonce,andliveoutthatlifeonthatoneoccupiedbranch.Weneedcareabout,andberesponsiblefor,onlywhattheonerealversionofeachofusdoes.

E

NINE

PhysicalCollapseoftheQuantumState

xperimentandcommonsensesuggestthattherearenosuperpositionsofmacroscopicobjects,becauseeverylargebodyisalwayssomewhereparticular.Rule2wasinventedto

accommodatethis,atleastasregardsthebehaviorofmeasurementinstrumentsandthesystemsthatcomeintocontactwiththem.Toavoidsuperpositionsofthestatesofameasuringinstrument,Rule2dictatesthatjustafterameasurementofaparticle’sposition,itswavefunctionimmediatelycollapsestoastatecorrespondingtothepositionthatwasmeasured.

Justbeforethemeasurement,acertainatom’swavefunctionmighthavebeenspreadallaroundtheEarth,givingitanequalprobabilityofbeingfoundanywhereontheglobe.Butwhenameasurementisdoneofitsposition,andifthatmeasurementreportstheatom’slocationtobesomewhereinNewYorkCity,then,atthemomentthatreportismade,theatom’swavefunctioncollapsesdowntotheextentofthefiveboroughs.

Instandardquantummechanicsthiscollapseofthewavefunctionhappensonlyastheresultofameasurement.Thisraisesaproblemforrealism,becauseitisonlyouruseandinterpretationoftheresultthatdetermineswhetheraninteractionwithalargebodyisameasurementornot.

Accordingtoarealistperspective,ameasuringinstrumentisaphysicalsystem,whichhappenstobelarge,andwhichhasaspecialcapacitytoamplifytinydifferencesinanatom’sbehaviortomakearecordofwhatwasnthatcanbeetchedinamacroscopicchange.But

becauseitisaphysicalsystemitshouldobeythesamelawsastheatomswhichcomposeit.Iftheatomscanbeinsuperpositions,thesameshouldbetrueofthevastcollectionsofatomsthatmakeupthemeasuringinstrument.Inthelastchapter,wesawthatinpilotwavetheory,partofthepricewepayforrealismisaworldfullofemptybranchesofwavefunctions,whichhavelongsincedisconnectedfromtheobjectstheymightguide.

Butwhatifthecollapsewerearealphysicalprocessthatoccurswheneveralargebodyisinvolvedinaninteraction?Thecollapsewouldbetriggeredbythesizeoftheobject,measuredinmassorinthenumberofatomsthatmakeitup,irrespectiveofitsuseasameasuringinstrument.Thewavefunctionsofalllargebodieswouldcollapse,wipingouttheirsuperpositions.Themeasurementsystems,madeofmyriadatoms,wouldcollapsetoo.Thissuggestsastrategyforarealistversionofquantumphysics.

TheideawouldbetomodifyquantummechanicsbycombiningRule1andRule2intoasinglerule,whichspecifieshowwavefunctionsevolveintime.Whenthesystemitisappliedtoismicroscopic,theoldRule1isagoodapproximation.Collapsesofthewavefunctionsofatomsmayhappen,butonlyrarely.Butwhenthesystemislarge,collapsehappensfrequently,sothatitappearsthatthebodyisalwayssomewheredefinite.

Theoriesofthiskindhavebeenconstructedsincethe1960s;theyarecalledphysicalcollapsemodels.

Thefirstphysicalcollapsemodelwasinventedin1966byJeffreyBub,astudentofDavidBohm,anddevelopedbythetwoofthem.1Inthesameyear,F.Károlyházypublishedapaperarguingthatnoisyfluctuationsinthegeometryofspacetimecouldcausethewavefunctiontocollapse.AswithpilotwavetheoryandBell’sworkofthesameperiod,theresponsetothesepioneeringpaperswasslow.ThefirstpersontodevelopacompletelypreciseversionofatheoryofthiskindwasPhilipPearle,anAmericantheoristwhohasdoneveryimportantworkinspiteofspendinghiscareeratasmallundergraduatecollege.Hestruggledforalmostadecadetoinventaconsistenttheoryforphysicalwave-functioncollapse,andhisfirsttheoryincorporatingaphysicalcollapseofthewavefunctionwaspublishedin1976.2

Pearle’sversionofacollapsemodeladdsarandomelement,sothatthereissomethingakintoarollofthedicethatdecideswhenandwhere

awavefunctioncollapses.Therollsareinfrequentforwavefunctionsofatoms,andsosmallsystemsconsistingofafewatomscollapseinfrequently.Butcollapseoccursoftenformacroscopicsystemscontainingmanyatoms.Pearlecalledhistheorycontinuousspontaneouslocalization,orCSL.

ForseveralyearsPearlewasnearlytheonlyoneworkingonthisapproachtorealism.Thenin1986threeItaliansworkinginTriesteproposedaratherelegantversionoftheidea,whichhasbeenknownsinceastheGRWtheoryaftertheirnames,Ghirardi,Rimini,andWeber.3

Otherpeoplejoinedintodevelopthesedynamicalcollapsemodels,includingLajosDiósi,LaneHughston,andNicolasGisin.

Thesetheoriesdifferfromeachotheratthelevelofdetails,buttheysharethekeyfeaturethatthebehaviorofanyquantumsystemisamixtureofRule1andRule2.Mostofthetimethewavefunctionofanatomicsystemchangesslowlyandsmoothly,followingRule1.Butfromtimetotimeitjumpsabruptlyintoadefinitestate,followingaformofRule2.

Onedefectofthesespontaneouscollapsemodelsisthattherateofthespontaneouscollapseshastobecarefullyspecifiedsothatthecollapsesarerareenoughnottocorruptinterferencepatternsbuiltbydelicatesuperpositionsinatomicsystems.Thisguaranteesthesuccessesofquantummechanicsbypreservingthecoherenceofsuperpositionsofmicroscopicsystems,whereitisneeded.Butthewavefunctionofalargebodywillgethitwithacollapsefarmoreoften,becauseitconsistsofmanyatoms.Eventsthatarerareforoneatomwillhappenfrequentlytosomeatomoranotherinalargecollectionofthem.Butwhenoneatomcollapses,somusttheothersmakingupthesamebody.Asaresult,themodelcanbetunedsothatthewavefunctionsdescribingmacroscopicsystemscollapsefarmorefrequently,explainingwhylarge-scaleobjectsarealwayssomewhere.Thissolvesthemeasurementproblem.

Thesetheorieshavenoneedofparticles,inthesenseofpilotwavetheory.Thereareonlywaves,buttheresultofaspontaneouscollapsewillbeawavehighlyconcentratedaroundonelocation.Suchaconcentratedwaveishardtodistinguishfromaparticle.

Becausetherearenoparticles,themysteriesofthewave-particledualityevaporate.Onejusthastounderstandwhywavesevolveundertwoverydifferentprocesses.

Thesecollapsetheoriesareentirelyrealist.Thewavefunctionisthesystem,andtherearenomysteriesastohowtointerpretit.Bycollapsingthewavefunctiondowntoonlywhatisphysicallyrelevant,collapsetheoryavoidstheextravagantproliferationofbranchesthatburdenthepilotwavetheory.Thereisnomeasurementproblembecausebigobjects,includingmeasuringdevices,arealwaysincollapsedstates.Thereisnospecialroleforconsciousness,information,ormeasurement.Whatyouseeiswhatyouget.

Todefineoneofthesetheoriesyouhavetodecidewhichoftheincompatiblequestionsthecollapsedwavefunctionistoanswer.Theusualanswerispositioninspace.Thecollapsedwavefunctionsarepeakedsomewhereinspace,whichmakesthemlikeparticles.

Oneconsequenceisthatenergyisnolongerpreciselyconserved.Ametalblockshouldslowlyheatupasaresultofallthecollapsesthewavefunctionsofitsatomsundergo.This,forme,istheleastattractivefeatureofspontaneouscollapsemodels.Ontheplusside,thereareexperimentsplannedtolookforthisheating.

Asisoftenthecasewithnewtheories,thereisalotoffreedom.Oneisfreetoadjusthowoftenthecollapsestakeplace.Onecanmakethisratedependonthemassortheenergyoftheatoms.Ifthehypothesisofspontaneouscollapseistobeviable,theremustbeawaytosettheratessothatwavefunctionsofatomsandelementaryparticlesrarelycollapse,whilebigthingscollapseoftenenoughthattheyarealwaysinsomedefiniteplace.Andonehastomakesureallunintendedconsequences,suchasheatingupofmatter,areundetectable.Remarkably,theseconditionscanallbemet,sothesetheoriesareviable.

Insomeofthesemodelsthespontaneouscollapsesarerandomprocesses.Thetheoryspecifiesonlyaprobabilityforcollapsetohappen.Thisleadstouncertaintiesandprobabilities,whicharebuiltinfromthebeginning.Theprobabilitiesarecodedintothefundamentallaws,ratherthanbeingaconsequenceofignoranceorbelief.Theintrinsicrandomnessofthecollapseprocessthenexplainstheuncertaintiesinquantumphysics,anditdoessoinawaythatdoesnotsingleoutmeasurements.Thus,theprobabilitiesareexplainedinawaythatisperfectlycompatiblewithrealism.Thatisagreatadvantage.(Ofcourse,ifonewantsadeterministictheory,thisisadisadvantage.)Relatedtothisisthefactthatthefundamentallawsareirreversible,sothatthearrowor

directionoftimeiscodedinatthebottomlevel.Somemayseetheseasdefects,butmyviewisthattheyareverypositivefeaturesofthecollapsemodels.

Oneworryingaspectofspontaneouscollapsemodelsisthatthecollapseofthewavefunctiontakesplaceallinonemomentoftime.Asthewavefunctionmaybespreadoutoverspace,itscollapsedefinesamomentofsimultaneityoverawholeregion.Thisappearstocontradictrelativitytheory,whichassertsthatthereisnophysicallymeaningfulnotionofsimultaneityoverregionsofspace.Whilethisdoesseemtobeaproblemfortheoriginaldynamicalcollapsemodels,therehavebeenproposalsformakingcollapsemodelsthatareconsistentwithspecialrelativity.4

Butthemostattractivefeatureofallthecollapsemodelsisthattheypredictnewphenomena,whicharesubjecttoexperimentaltesting.Therandomcollapsesintroducenoiseintoasystem.Forsomevaluesoftheparameters,theeffectwouldbelargeenoughtobeseen.Noneedforsuchanoisesourcehasbeenseeninseveralrecentexperiments,whichrulesoutcertainvaluesoftheparameters,ifnotthetheoryitself.Thisisrealscience,andtheexperimentscontinue.Nothingwouldbemorewonderfulthanthediscoveryofaneffectwhichcontradictsquantummechanicsandconfirmsapredictionofoneofitsrealistalternatives.

Oneweaknessofsomeofthesecollapsemodelsisthattheymakenoreferenceto,oruseof,otherkeyquestionsofphysics.Itwouldbemorecompellingifthemodificationswemaketoquantummechanicsaremotivatedbyaproblembesidesthemeasurementproblem,suchastheproblemofquantumgravity.ThisbringsustotheworkofRogerPenrose.

—IFTHEREISONElivingtheoristwhoseachievementanddepthofinsightandinfluencematchthoseofthesagesoftheearlytwentiethcentury,itisRogerPenrose.Simplyput,heistherealthing.

Penrosefollowshisowncompassandhehas,asaresult,novelandsurprisingthingstosayaboutmostissuesinfundamentalphysics,includingquantumgravityandquantumfoundations.Becauseeverythingheenvisionsistiedtogetherbyanoften-hiddenconsistency,thebestwaytoapproachhisproposalforquantumtheoryisbytracinghisworkbacktohistimeasayoungmathematicianintheearly1960s,whenhewas

fascinatedbythefoundationsofourunderstandingofspace,time,andthequantum.

Itiseasy,butinadequate,todescribePenroseasthemostimportantcontributortogeneralrelativitysinceEinstein.Intheearly1960sheinventedrevolutionarynewmathematicaltoolstodescribethegeometryofspacetime,basedoncausality.Ratherthantalkingabouthowfarawaytwoeventsare,orhowmuchtimeelapsesonaclock,hedescribedspacetimeintermsofwhicheventswerethecausesofwhichevents.Thisledhimtopositandprovetheoremsthatshowedthat,ifgeneralrelativityisright,thegravitationalfieldbecomesinfinitelystrongwithinthecoreofblackholes.5Oncethathappens,thetheorybreaksdown,becauseitsequationsstopworkingtopredictthefuture.Suchplaces,wheretimemaystartorstop,arecalledsingularities.Afterward,workingwithStephenHawking,heextendedhismethodtotheexpandinguniverseandprovedthatgeneralrelativitypredictsthattimebeganafinitetimeintoourpast,whenthewholeuniversebeganitsexpansioninastateofinfinitedensity.6

Buthisinventionsexceedeventhesetransformativecontributionstogeneralrelativity.LikeEinstein,Penrosecaresmoredeeplythanmostforthecoherenceofourunderstandingoftheworld.And,justasitdidinthecasesofDavidBohmandDavidFinkelstein,thispassionhasdrivenPenrosetodevelopauniquevisionoffundamentalphysics,whichisunmistakablyhis.Moreover,Penrose’svisionhas,overthemanyyearsofhiscreativecareer,ledhimtoinventmathematicalstructuresthatotherslaterutilized.

Aftertransformingthepracticeofgeneralrelativity,Penroseturnedhisattentiontofundamentalphysics.HewasstruckbyasympathybetweenquantumentanglementandMach’sprinciple—theidea,whichhadinspiredEinstein’sinventionofgeneralrelativity,thatwhatisrealingeneralrelativityisrelationships.Bothideashintataglobalharmonywhichtiestheworldtogether.

Penrosewasthefirsttoaskwhethertherelationswhichdefinespaceandtimecouldemergefromquantumentanglement.Seekinginsightintothisquestion,hewasinspiredtoinventasimplegamebasedondrawingdiagrams,therulesofwhichrepresentedsimultaneouslyquantumentanglementandaspectsofphysicalgeometry.Thisgame,hisfirst

visionofafiniteanddiscretequantumgeometry,Penrosecalledspinnetworks.

Mosttheoreticalphysicistsworkouttheirideasbydoingcalculationsinexistingtheories.Penroseworkssometimesinsteadbyinventinggames.Theirsimplicitycapturesprofoundquestions,whichoneinvestigatesbyplayingthegame.ItistypicalofPenrosethathismainpaperonspinnetworkswasnotonlyunpublished—itwasnevereventypedup.Mimeographs(nowtheywouldbecalledphotocopies)ofhishandwrittennotescirculatedamonghisstudentsandfromfriendtofriend.Thesenoteswereanexhilaratingread,eventhoughtheyendedinthemiddleofthemainproof.*

Fordecadesspinnetworksremainedakindofphilosophicalparlortrick,passedonbysketchesonnapkinsduringdessertatconferencedinners.Buttheyturnedout,yearslater,tobethecentralstructureinanapproachtoquantumgravitycalledloopquantumgravity.Inthatcontext,spinnetworksembodyonewaythattheprinciplesofquantumtheoryandgeneralrelativitycancoexist.

Extendingspinnetworks,Penrosediscoveredtwistortheory,whichisanextraordinarilyelegantformulationofthegeometryunderlyingthepropagationofelectrons,photons,andneutrinos.Intrinsictotwistorsisabeautifulasymmetryofneutrinophysics,whichiscalledparity.Wesaythatasystemisparitysymmetricifitsmirrorimageexistsinnature.Wehavetwohands,whichareeachmirrorimagesoftheother,soourhandsareparitysymmetric.Butoverallhumansarenotparitysymmetric,becauseourheartsandotherinternalorgansarearrangedasymmetrically,andweeachtendtofavoronehand.Neutrinosexistinstateswhosemirrorimagesdon’texist,andhenceareparityasymmetric.Penrose’stwistortheoryexpressesthisfeatureofneutrinos,becauseitusesmathematicalstructureswhicharenotthesamewhenlookedatinamirror.

FormanyyearsPenroseandafewstudentsdevelopedtwistortheory,workinginisolationinOxford.Inthelate1970sthiscaughttheattentionofEdwardWitten,whomanyyearslatermadetwistorsthekeystoneofapowerfulreformulationofquantumfieldtheoryheinventedwithsomeyoungertheorists,whichisstillinprogress.

WhatIfindsoremarkableaboutPenroseisthathehasaninnernarrativethatconnectseverythinghedoesintoacoherentstory.Soit’s

nosurprisethathisexpansivevisionofanewphysicsledhimtoareinventionofquantummechanics.Thiswaspartofalargerstrategytocombinequantumtheorywithgeneralrelativity,tomakeaquantumtheoryofgravity.

Typically,Penrosestartedoffhisattackonquantumgravitybyignoringtheobviouspathtakenbynearlyeveryoneelse.Thestandardpathistoconstructaquantumdescriptionofasystem,aprocesscalledquantization.ThisstartswithadescriptionofthesystemgiveninthelanguageofNewtonianphysics.We“quantize”thisbyapplyingacertainalgorithm.Thedetailsofthisdon’tconcernushere,butsufficeittosaytheoutputisaquantumtheorywhichisabsolutelyconventionalandstandard.

Thistechniqueworksinmanycasestogiveussuccessfulquantumtheoriesofatoms,elementaryparticles,andradiation.Itcanbeappliedtogravity;indeed,loopquantumgravitywasmadeby“quantizing”generalrelativity.

Penrosetookadifferentroad.Quantumtheoryandgeneralrelativityclashonafewkeypoints.Themostcrucialisthattheyhavedeeplydifferentdescriptionsoftime.Quantummechanicshasasingleuniversaltime.Generalrelativityhasmanytimes—ifbytimewemeandurationasmeasuredbyclocks.ThebeginningofEinstein’stheoriesofrelativityisadiscussionofsynchronizingtwoclocks.Youstartoffbysynchronizingthem,buttheydonotgenerallystaysynchronized.Theyslipoutofsynchronicityataratethatdependsontheirrelativemotionsandrelativepositionsinthegravitationalfield.

Anotherpointonwhichthetwotheoriesclashisthesuperpositionprinciple.Aswediscussed,giventwostatesofaquantumsystem,wecanmakenewstatesbyaddingthemtogether.Somethingwehaven’tneededtomentionsofaristhatwecanmakealotofdifferentstatesfromsuperposingthesametwostates.Wedothisbyvaryingthecontributionofeachstatetothesuperposition.ThuswecansuperposeCATandDOG(fromourearlierexample)equally,asin

STATE=CAT+DOG

orwecanchooseinstead

STATE=3CAT+DOG

or

STATE=CAT+3DOG

Thenumberwemultiplyeachstatebyiscalledanamplitude.Itssquareisrelatedtotheprobability.HenceinthestateCAT+DOGyouareequallylikelytofindacatloveroradoglover,whilesomeoneinthestate3CAT+DOGisninetimesmorelikelytolovecatsthandogs.

Generalrelativitydoesnothaveasuperpositionprinciple.Youcannotaddtwosolutionstotheequationsofthetheoryandgetanewsolution.Math-speakforthisistosaythatquantummechanicsislinear,whilegeneralrelativityisnonlinear.

Thesetwodifferencesarerelated.Thesuperpositionprincipleispossibleinquantummechanicsbecausethereisasingleuniversaltimethatwecanusetoclockhowitsstatesevolveintime.Ontheotherhand,becausedistantclocksgooutofsync,thereisnosimplewaytoaddorcombinetwospacetimestomakeanewspacetime.

Penroseembracesthemulti-fingerednatureoftimeingeneralrelativityandtheabsenceofsuperpositionsashometruths.Hesuspectsthatthesuperpositionprinciplemustbeviolatedoncequantumphenomenaaredescribedinthelanguageofgeneralrelativity.Thesimplicityandlinearityofthesuperpositionprinciple,hesuspects,areonlyapproximatelytrue,andholdonlytotheextenttowhichtheroleofgravitycanbeignored.

Thus,Penroseobjectstoquantizinggravity.Insteadhesuggestsweshouldtryto“relativizethequantum.”Bythishemeanstointroducethemulti-fingerednotionoftimeintoquantumtheorybyviolatingthesuperpositionprincipleandmakingquantumstatesnonlinear.

Penroseisarealist,buthemakesanunusualmoveforarealistonquantumtheory.Ratherthanascribingrealitytobothwavesandparticles,orinventingnew“hiddenvariables,”Penrosetakesrealitytoconsistofthewavefunctionalone.ThisleadshimtotakeupthesuggestionbyPearleandothersthatthecollapseofthewavefunctionduringameasurementisarealphysicalprocess.Thesuddenchangeof

thewavefunctionisnot,assomehold,duetoanupdateinourknowledgeofwheretheparticleis;itisagenuinephysicalprocess.

Penrose,followingtheearlierworkofPearleandofGRW,proposedthatcollapseofthewavefunctionisaphysicalprocessthatoccursfromtimetotime,7interruptingthesmoothchangesmandatedbyRule1.AndhetookupasuggestionmadebyDiósiandKárolyházy:thatthecollapseprocesshassomethingtodowithgravity.8Whenawavefunctioncollapses,superpositionsarewipedout.Therateatwhichasystem’swavefunctioncollapsesdependsonthesizeandmassofthesystem.Aswediscussedearlier,thisratecanbespecifiedsothatatomicsystemsalmostnevercollapse,whilemacroscopicsystemscollapseoften,sothatsuperpositionsoflargeobjectsareimpossible.

WhatisreallyexcitingabouttheworkofDiósi,Károlyházy,andPenroseisthattheyproposedacriterionforwhencollapseswouldtakeplacethatmakesthecollapseaneffectofgravity.Roughlyspeaking,asuperpositionofanatombeinghereorthereiscollapsedtoonelocationwhenthelocationoftheatomwouldbecomemeasurablebytheeffectofitsgravitationalattraction.

Thisrelatestothemany-fingeredtimeofgeneralrelativity.Imaginethatthewavefunctionisasuperpositionofanatombeinginthelivingroomwiththeatombeinginthekitchen.Wherevertheparticleis,itsmasshasagravitationalfieldwhichaffectsclocks.Oneofthemoststrikingpredictionsofgeneralrelativityisthatclocksdeeperinagravitationalfieldappeartoslowdown.Thisiswelltested.AtomsonthesurfaceofthesunhavebeenobservedtovibratemoreslowlythanthesameatomsdoonEarth.Theeffectisevenseenbycomparingtheratesatwhichatomicclocksinthebasementofabuildingtickcomparedtoclocksontheroof.

Theresultisthatclocksintheroomwheretheparticleisrunslowerthanclocksintheotherroom.Butwhatofastatewhichisasuperpositionoftheatombeinginthelivingroomandinthekitchen?Thisseemstoimplythatthegravitationalfieldmustbeinasuperpositionofstatessuchthateachclockrunsslow.

Butthereisnosuchstate,becauseonecannotaddspacetimegeometriestogetnewspacetimegeometries.Hencethewavefunctionmustcollapse.

Penrosegivesapredictionforwhenthewavefunctionwillcollapse,andworkisunderwaytobuildanexperimenttotestPenrose’sprediction.Veryrecentlytwoexperimentalteams9haveproposedthattheymaybeabletoconstructsuperpositionsofdifferentgravitationalfields,contrarytoPenrose’shypothesis.Thisisfabulous,butwhatisworryingisthatPenrosehasnotputforwardadetailedtheoryunifyinggravityandquantumtheoryfromwhichhisheuristicmodelcanbederived.

Penrosehasatleastproposedamodelforhowthismightallwork,whichcombinestheusualevolutionofthequantumstate,givenbyRule1,withcollapseofthewavefunction,givenbyRule2.Theygotogetherintoasingleevolutionrule.

Penrose’stheoryisnotquantummechanics;itisanewtheory,whichcontainsquantummechanicswithinarealisticframework,basedonanewevolutionlaw,calledtheSchrödinger-Newtonlaw.ThisunifiesRule1andRule2intoasingledynamicallaw.

Ifwefocusonthebehaviorofatomsandradiation,thissingleevolutionlawmimicsstandardquantummechanics.Thesuperpositionprincipleissatisfiedtoagoodapproximation.Thewavefunctionbehaveslikeawave,andRule1issatisfied.Schrödinger’sequationforthewavefunctionisthenrecoveredforatomicsystems.

Butifwepullbacktodescribethemacroscopicworld,Penrose’smodeldescribesawavefunctionwhichiscollapsedandconcentratedonsingleconfigurations.Theseconcentratedwavefunctionsbehavelikeparticles.Soonthemacroscopiclevel,Newton’slawsforthemotionofparticlesarerecovered.

Thus,inthemicroscopicregime,thistheoryreproducesquantummechanics,whileintheoppositesituation,itpredictsthatmacroscopicobjectsbehavelikeparticlesandobeyNewton’slaws.

Physicalcollapsemodelscontinuetobedeveloped.RecentlyPearlehasmadeprogressconstructingacollapsemodelconsistentwithspecialrelativity.10Theideathatgravityisresponsibleforcausingthequantumstatetolosecoherence,andhencecollapse,hasalsobeendevelopedbyRodolfoGambiniandJorgePullin,whocalltheirproposaltheMontevideointerpretationofquantummechanics.11AndSteveAdlerhasfoundaroleforspontaneouscollapseinahiddenvariablesmodelhehasbeendeveloping.12

—PILOTWAVETHEORYandthecollapsemodelshavegivenusoptionsforquantumphysicistswhowanttoberealists.Thedifferencesarestriking,butsoarethesimilarities.

Oneoptionistobelievetherearebothwavesandparticles;thisleadstopilotwavetheory.Thiseasilyresolvesthemeasurementproblem,butatacost.Thepilotwavetheoryisdoublyextravagant.Ithasadoubledontology,butanasymmetricdynamicbywhichthewavefunctionguidestheparticleswithouttherebeinganyreciprocalactionbywhichtheparticlesinfluencethewave.Andwehavetolivewithavastworldinwhichthewavefunctionhasmanyempty,ghostlikebranches.

Thecollapsemodelsavoidalltheseobjections.Thereareonlywaves,sothereisnodoubledontologyandnoissuewithreciprocation,andtherearenoemptybranchesbecausetheyareeliminatedbythecollapses.Thisalsosolvesthemeasurementproblem,buthere,too,thereisaprice,whichisthatthetheorycomeswithnewadjustableparametersthatmustbetunedtokeepthetheoryoutofharm’sway.

Bothapproachesagreeontwokeylessons:thewavefunctionisanaspectofreality,andthereisatensionwithrelativitytheory.Thesearevitalcluesforthefutureofphysics.

W

TEN

MagicalRealismEveryquantumtransitiontakingplaceoneverystar,ineverygalaxy,ineveryremotecorneroftheuniverseis

splittingourlocalworldonearthintomyriadsofcopiesofitself.

—BRYCEDEWITT

esawinthelastfewchaptersthatthereareoptionsforrealists,butnoticethattheyallrequirechangingthetheory.Thespontaneouscollapsemodelsmakethesuddencollapseofthe

wavefunctionpartofthedynamicsofthetheory.Thecollapseoccurswhetherornotmeasurementstakeplace,andwithoutregardtowhatweknow.Theresultingtheoriesdisagreewithquantummechanicsgenerally,butpreserveadomainofagreementsufficientforthemnottocontradicttheresultsofexperimentsdonesofar.

Pilotwavetheoryisanotheroptionforrealists.Rule2issuspended,sothewavefunctionevolvesalwaysaccordingtoRule1.Butanewelementisadded:particles,whosetravelisguidedbythewavefunction.Sothistheoryisalsodifferentfromquantummechanics.Whentheparticlesareinquantumequilibrium,thepredictionsofthetwotheoriesoverlap,butoutofquantumequilibrium,thepredictionsofpilotwavetheorydifferfromthoseofquantummechanics.

Itwouldbewonderfulifsomedayexperimentsconfirmthatnaturefavorsoneoftheserealisttheoriesoverquantummechanics.Butsupposeitturnsoutthataftermanyyears,orindeedcenturies,wehavenoexperimentalresultswhichrequireamodificationorcompletionofquantummechanics.Inparticular,whatifnolimitisfoundtohowlarge

orcomplexasystemcanbeandstillbeputinasuperposition?Suppose,inotherwords,thatquantummechanicsinitsoriginalformappearstobecompletelycorrect.Wouldtherebeanyoptionsforrealists?

ThereasonitishardtobearealistandbelieveinquantummechanicsisRule2,whichgivesaspecialroletomeasurement.ThesuddennessofthecollapseofthewavefunctiononmeasurementdictatedbyRule2meansquantumstateschangeintimeinawaythatpaysnoheedtolocalityorenergyandinsteadseemstodependonwhatweknoworbelieve.Sinceitmakesthequantumstatedependonourknowledge,thiscannotbepartofarealisttheory.

SuchatheorycouldnothaveRule2amongitspostulates,becausethatwouldcontradictrealism.SowewouldhavetobuildourtheoryonRule1alone.Thisisalsoamodificationofthetheory,butitisoneitshareswithpilotwavetheory,soperhapsit’sachangeworthexploring.Suchatheoryhasnoobviousreferencetoexperiment,alsonoapparentnotionofuncertaintyorprobability,becauseRule1isdeterministicandmakesnoreferencetoprobability.Canwepossiblymakesuchatheoryworkandstayconsistentwithrealism?

OnewaytoaccomplishthiswouldbetoderiveRule2fromatheorythatdoesn’tpostulateit.Thecollapseofthewavefunctionwouldhappenonlyincertainspecialcircumstances,suchaswhenanatominteractswithalarge,human-sizemeasuringinstrument.Todothiswehavetofindrolesforuncertaintyandprobabilityarisinginaworlddescribedbyatheorythathasnone.

TheprojecttomakesenseofquantummechanicsbasedsolelyonRule1,andinawaythatisconsistentwithrealism,hasalonghistory.Itwasinitiatedin1957byaPhDstudentofJohnWheeler’snamedHughEverettIII,andsocanbecalledEverettianquantummechanics.ButitismostoftenreferredtoastheManyWorldsInterpretationofquantummechanics,becausesomehaveargued,notwithoutcontroversy,thatitimpliesthattheworldweexperienceisjustoneofavastnumberofparalleluniverses.

Everett’sproposalwaspresentedinhisPhDthesisof1957,andwaspublishedthesameyear.1ItwasunusuallyshortforaPhDthesis,yetitwastohave,afterawhile,abigimpact.

Everett,asmanyhave,leftacademicsciencejustafterhisPhDtobeginacareerinthedefenseindustry,sohisthesiswashisonly

contributiontophysics.Andittookmanyyearsbeforeitwaswidelyread.But,apartfromdeBroglie’sthesis,IcanthinkofnootherPhDthesiswhichwastohave,overthelongterm,suchadisruptiveorrevolutionary(youchoose)effectonthefoundationsofphysics.

—ONEOFEVERETT’SIDEASiscertainlycorrectanduseful.IfthereisnoRule2,wavefunctionsdon’tcollapse,sowehavetodescribewhathappensinameasurementusingonlyRule1.AswesawinourdiscussionofSchrödinger’scatattheendofchapter4,interactions,includingmeasurements,leadtocorrelatedstates.Theexamplewediscussedwas

INBETWEEN=(EXCITEDANDNOANDALIVE)OR(GROUNDANDYESANDDEAD)

TheORsignifiesasuperpositionofdifferentpossiblesituations,ineachoneofwhichtheatom,Geigercounter,andcatareallcorrelated.Giventhattheyareinasuperpositionofstates,observablessuchasthealivenessofthecathavenodefinitevalue.ButEverettnoticedthat,nonetheless,wecanreadthissuperposedstateasgivingustwocontingentstatementsaboutthestateofthecombinedsystemafterthemeasurement.Thesecontingentstatementsare

Iftheatomisintheexcitedstate,thenthecounterwillreadNOandthecatwillbealive.

and

Iftheatomisinthegroundstate,thenthecounterwillreadYESandthecatwillbedead.

Thesetellusthattheatom,thecounter,andthecathavebecomecorrelatedbythephoton’spossiblepassagethroughthedetector.*

Thesuperposedstatedoesn’ttelluswhichoutcomewillbeobserved,butittellsusthattheoutcomeexpressesacorrelationbetweenthestate

oftheatomandthestatesofthecounterandcat.ThismuchofEverett’sthesisisunimpeachable.Itisgenerallytrue

thatinteractionsbetweentwoquantumsystemssetupcorrelationbetweenthestatesofthetwosystems,andthesecorrelationscanbereadassetsofcontingentstatements.ThisisaconsequenceofRule1,appliedtointeractions.

Butnoticewhatthisdoesn’tdo.Itdoesn’ttelluswhichoutcomewillbeobserved.Contingentstatementsmaybeusefulastheygiveusdefiniteinformationaboutthesystem.Buttheydonotgiveuscompleteinformation.Atheorythatgaveusonlycontingentstatementscouldnotbeenoughforarealist.

SoEverettwentfurther.TomakethetheorywithonlyRule1realist,heproposedtochangeourconceptionofreality.Everettsuggestedthatastatewhichconsistsofasuperpositionofstatesofdetectorsdescribesarealityinwhichbothoutcomeshappen.Inthisenlargedreality,bothcontingentstatementswillbetrue.Thatis,Everettassertedthatafulldescriptionofrealityisthesuperpositionofthetwostates.Part(butonlypart)ofwhatthatimpliesisthatthefollowingstatementistrue:

Theatomisintheexcitedstate,thecounterreadsNO,andthecatisalive,andtheatomisinthegroundstate,thecounterreadsYES,andthecatisdead.

Thiswouldseemtobeblatantlyfalse.Intheworldwelivein,thecatexperiencesonlyoneoutcome.Thisiswhyinchapter3wedescribedthesuperpositionascharacterizingan“or.”Eithersheexperiencesthatsheisalive,orsheisdeadandexperiencesnothing.Inourworld,itisoneortheother.

Everettproposedthattheworldweexperienceisonlyapartofthefullreality.Intheenlargedworldwhich,heproposed,makesupthatfullreality,versionsofourselvesexistthatexperienceeverypossibleoutcomeofeveryquantumexperiment.

Inotherwords,the“or”ofordinaryexperiencebecomes,inquantummechanics,an“and.”Wesay“thecatisaliveorthecatisdead”becausethetwostatesaremutuallyexclusive.Butinthisformulation,itcannonethelessbetruethat“thecatisaliveandthecatisdead.”

Theideaisthateachtimeanexperimentisperformedwhichcouldhavedifferentoutcomes,theuniversesplitsintodifferent,parallelworlds,oneforeachofthepossibleoutcomes.Wesplitaswell,alongwiththeworld.Theexperimentcreatesanadditionalversionofourselvesforeachofthepossibleoutcomes.Eachversionofourselveslivesfromthenoninaworlddescribedconsistentlybyoneofthecontingentstatementswecanreadoffthecombinedstate.

Incontrastwithpilotwavetheory,Everettianquantummechanicshasnoparticles,sonothingdistinguishesthedifferentbranchesfromeachother.*Wethenareinvitedtoregardallbranchesasequallyreal,andworkouttheconsequences.SoifEverettisright,IamatthismomentinToronto,andIaminLondon,andindeedsimultaneouslyinmyriadplacesmylifemighthavetakenme,includingtheoceanflooroffPeggy’sCove.

Thesebranchesaresometimescalledworlds.YoucanseewhyEverett’sproposalhascometobecalledtheManyWorldsInterpretationofquantummechanics.

Forthistowork,eachversionofanobservermusthavenowaytocommunicatewiththeothers;thebranchesmustbeautonomous.

—WHATIHAVEDESCRIBEDsofarwasEverett’sinitialversionoftheManyWorldsInterpretation.Onexamination,itturnedouttobeabitnaive,asitranintoseveralbigproblems.

ThefirstproblemwithEverett’sformulationisthathesuggestedthatthebranchinghappenswhenameasurementismade.Butthismakesmeasurementsappeartobespecial,whereasitisabasictenetofrealismthatmeasurementsareordinaryinteractionstobetreatedlikeanyothers.

Indeed,Rule1makesnodistinctionforexperiments.So,ifyouarearealist,*youmustinsistthatwhathappensforameasurementmusthappenmoregenerally.Thekeythingthatcausesasplittingisaninteraction,whichproducescorrelationsbetweenthesystemsthatinteracted.Thesecorrelationscan,aswesaw,beexpressedascontingentstatementsdescribingdifferentpossibleoutcomesofthatinteraction.

Toavoidmakingexperimentsspecial,theuniversemustspliteachandeverytimethereisaninteractionwhichhasmorethanonepossibleoutcome.Butthisishappeningliterallyallthetime—allthatisrequiredis

fortwoatomstocollidewitheachother,andthatishappeningmyriadtimesasecondjustintheairinthisroom.

Moreover,theinteractionthatcausesthesplittingcanhappenanywhereintheuniverse.Sowhileyouarereadingthissentenceyouaresplittingavastnumberoftimes,intoavastnumberofversionsofyourself.*

Thisisalottoasksomeonetobelieve,allinthenameofrealism.NowonderittooksometimeforEverett’sideastocatchon.

AsecondproblemisthatifthebranchingistoreplaceRule2,thenitmustbeirreversible,toreproducethebasicfactthatweobserversexperienceeveryexperimenttohaveadefiniteoutcome.Indeed,theactionofRule2,whichthebranchingissupposedtoreplace,isirreversible.ButthebranchingissupposedbyEveretttobeaconsequenceonlyofRule1,whichisreversible.

AthirdbigproblemwithgivingupRule2hastodowithprobabilities—orrather,theirabsence.

Experimentsmeasureprobabilitiesfordifferentoutcomestooccur,andcomparingthesetothepredictionsofthetheoryisanimportantpartoftestingquantummechanics.Butnoticesomethingimportant:Rule1doesn’tspeakofprobabilities.AllreferencetoprobabilitiesinquantummechanicscomesfromRule2,whichgaveusaformulaforhowprobableeachpossibleoutcomeis.Thatformula,aswenotedbefore,iscalledBorn’srule,anditrelatesprobabilitiestothesquareofthewavefunction.Thisistheonlypartofquantumtheorythatreferstoprobabilities,anditispartofRule2.IfweeliminateRule2fromquantumtheory,wehavenothingleftinthetheorythatspeaksofprobabilities.

Asaresult,Everett’sversionofquantummechanicstellsusonlythateverypossibleoutcomeoccurs.Notwithsomeprobability,butwithcertainty.

Thatis,foreverypossibleoutcomeofanexperiment,theManyWorldsInterpretationassertsthereisabranchinwhichitoccurs.Thereisnosenseinwhichsomebranchesaremoreprobablethanotherbranches.AllRule1canassertisthatwithcertainty,allbrancheswillexist.Soweseemtohavelostanimportantpartofquantummechanics—thatpartwhichpredictstheprobabilitiesthatdifferentoutcomesoccur.

Everettwasnotdumb;hewasawareofthisissue,andheattemptedtoaddressit.Inhisthesis,heofferedawaytopredictprobabilitiesusing

onlyRule1.Toaccomplishthis,hesuggestedawaytoderivetherelationbetweenprobabilitiesandsquaresofthewavefunction—arelationwhichRule2postulates—directlyfromRule1alone.

Atfirstmanywereimpressedbythisresult.IknowIcertainlywaswhenIfirstreadEverett’spaper.Butitturnsoutsomethingwasconcealedinhisderivation.Likemanyerroneousproofs,theargumentassumedwhatwastobeproved.Therelationbetweenthesquareofthewavefunctionandprobabilitywassnuckintoaseeminglyinnocuousstep,whichassumedthatbrancheswithsmallwavefunctions*havesmallprobabilities.*Butthatwastantamounttoassumingarelationbetweenthesizeofthewavefunctionsandprobabilities,andsotheproofprovedlessthanwasfirstclaimedforit.

Everett’sproofdidestablishoneimportantthing:thatifonewantedtointroducequantitiescalledprobabilities,itwouldbeconsistenttoassumetheyfollowBorn’srule.Butitdidnotprovethatitwasnecessarytointroduceprobabilities,nordiditprovethatthoseprobabilitiesmustberelatedtothesizeofthewavefunction.

YetanotherproblemwithEverett’soriginalformulationoftheManyWorldsInterpretationwasthatsplittingthequantumstateintobranchesisambiguous.AsIexplained,eachbranchisdefinedbysomequantityhavingadefinitevalue.Thereisonebranchinwhichtheatomisexcitedandthecatisaliveandanotherbranchinwhichtheatomisinthegroundstateandthecatisdead.Butwhytheseandnotsomeotherquantities?Groundandexcitedarestatesofdifferentenergy.Butthereareotherincompatiblequantitiesthatwemightuseinsteadtodefineasplit.Therewillbesomesuperpositionofgroundandexcitedstatesthatcorrespondstotheelectronbeingontheleftsideoftheatomandadifferentsuperpositionthatcorrespondstotheelectronbeingontherightside.

Let’scallthesestatesleftandright.Whynotsplitwithrespecttothese?Thesewouldleadtostatesofthecatwhichweresuperpositionsofaliveanddead.Shenolongerwouldexperienceaworldwheretherearedefiniteoutcomestoexperiments.ButRule1doesn’tcarewhethersheexperiencesdefiniteoutcomesordoesnot.Wecallthisthepreferredsplittingproblem.

Atfirstthereseemstobeanobviousanswertothepreferredsplittingproblem:wemustsplitthewavefunctionsothatthedifferentbranches

describesituationsinwhichmacroscopicobserverslikethecatseedefiniteoutcomes.

ButthisistantamounttoreintroducingRule2,becauseitgiveswhatmacroscopicobserversseeaspecialrole.Youhavenotsolvedthemysteryofwhymacroscopicobserversseedefiniteoutcomes.Andbygivingobserversaspecialrole,yougiveuponachievingarealistinterpretation,whichmustbebasedonhypothesesaboutwhatisrealintheabsenceofobservers.

T

ELEVEN

CriticalRealism

hereisanearconsensusamongthepeoplewhohaveexaminedtheoriginalversionoftheManyWorldsInterpretation,theversionputforwardbyEverettandchampionedbyWheelerandDeWitt,thatit

failsasarealistapproachtoquantumtheory.Eitheryoumakemeasurementspecialandgiveuponrealism,oryoufacethebigissuesIraised.Themostimportantofthesearethepreferredsplittingproblemandthequestionofwherethetheorycontainstheprobabilities,andtherelateduncertainties,thatexperimentalistsmeasure.

So,cantheprojectofgivingarealistversionofquantumtheory,basedonlyonthewavefunctionevolvingstrictlyaccordingtoRule1,besaved?

Inrecentyearssomeratherradicalsolutionshavebeenofferedtothetwobigpuzzles—thepreferredsplittingproblemandthequestionofwheretheprobabilitiescomefrom.Thepreferredsplittingproblemiswidelythoughttohavebeensolvedbyanideacalleddecoherence,whichIwillexplainshortly.IdeasabouttheoriginofprobabilitiesmostlyoriginatedfromagroupofdeepthinkersatOxford,centeredinitsphilosophydepartment.ThenewapproachtoprobabilitieswasformulatedbyDavidDeutsch,andithasbeenextensivelystudiedanddevelopedbyhisOxfordcolleagues.1

Oxfordhashadaverysmartgroupofphilosophersofphysics,andseveralofthemhavefocusedonmakingsenseofEverett’sideas.TheyhaveincludedHilaryGreaves,WayneMyrvold,SimonSaunders,andDavidWallace.*TogetherwithDeutschandafewothers,theyhaveputforwardwhathassometimesbeencalledtheOxfordinterpretationofquantummechanics.2Theseproposalsandtheargumentsofferedintheirsupportarebothingeniousandsubtle,butsoaretheobjectionsmadebyseveralphysicistsandphilosophers.Giventheveryhighlevelofcareful

thoughtthathasgoneintothesedevelopments,Ithinkitisfittingtocallthisanepisodeofcriticalrealism.

Aftermanyspiritedandelaboratearguments,theprojectofmakingsenseofarealistquantumtheorybasedonlyonRule1isstillinprogress.Theissuesaresurprisinglyintricateandelusive,andthereisasyetnogeneralagreementamongexpertsastowhathasbeenachieved.Tomakeitevenmorecomplicated,theproponentsdisagreeamongthemselves,sothatamongthefiveorsixmaininitiatorsofthisview,severaldifferentversionsaredefended,whichdifferinsubtlebutimportantwaysfromeachother.Consequently,Icanpresentonlyaroughintroductiontothekeyideasandissuesbehindthisnew“Oxfordinterpretation.”

—THEIDEAOFDECOHERENCEstartswiththeobservationthatamacroscopicsystem,suchasadetectororanobserver,isneverisolated.Instead,itlivesinconstantinteractionwithitsenvironment.Theenvironmentismadeupofavastnumberofatomsallmovingaboutunpredictablyhitherandthither,andthisintroducesabigdoseofrandomnessintothesystem.Thisrandomelementaffectsthemotionsoftheatomswhichmakeupthedetector.This,roughlyspeaking,leadsthedetectortoloseitsdelicatequantumpropertiesandbehaveasifitweredescribedbythelawsofclassicalphysics.

Considerwhatanobservercanlearnbylookingatadetector.Theobserverisalsoabigobjectmadeofvastnumbersofatoms,allincontactwitharandomenvironment.Ifwelookatthedetailedsmall-scalebehavioroftheatomsmakingupthedetectorandtheobservers,wewillseechaos,asthepicturewillbedominatedbytherandommotionsoftheindividualatoms,bothouratomsandthoseinthedetector.Toseeanykindofcoherentbehaviorwehavetolookatbulk,large-scalemotionsofrelativelylargepiecesofthedetector.Theserequireaveragingoverthemotionsofmyriadatoms.Whatemergesarebulkquantitieswhichmeasuremacroscopicquantitiessuchasthecolorofapixelorthepositionofadial.Onlythesebehavereliablyandpredictably.

Indeed,thesebulkquantitiesbehaveasifthelawsofNewtonianphysicsaretrue.Itisonlywhenwefocusonthesebulk,large-scalequantitiesthatwecanperceivesomethingirreversibletohavehappened,suchastherecordingofanimage,inwhicheachpixelcomprisesavast

numberofatoms.Andaccordingtothispicture,itisonlywhensomethingirreversiblehashappenedthatwecansaythatameasurementhastakenplace.

Decoherenceisthenamewegivetotheprocessbymeansofwhichirreversiblechangesemergebyaveragingouttherandomchaosoftheatomicreal.Decoherenceisaveryimportantfeatureofquantumtheory,foritiswhythebulkpropertiesoflarge-scaleobjects,suchastheroughmotionsofsoccerballs,swingbridges,rocketships,planets,andsoforth,appeartohavewell-definedvalues,whichobeythelawsofNewtonianphysics.

Theword“decoherence”referstothefactthatsuchbulkobjectsappeartohavelosttheirwaveproperties,andsotheybehaveasiftheyaresimplymadeofparticles.Accordingtoquantummechanics,everything,includingcats,soccerballs,andplanets,haswaveaswellasparticleproperties.Butforthesebulkobjects,thewavepropertieshavebeensorandomizedbytheirinteractionswiththeirchaoticenvironmentthattheycannotbeaccessedinanyexperiment,sothewavehalfofthewave-particledualityhasbeenrenderedmute,andtheobjectsbehavelikeordinaryparticles.

Butsometimesthereismorethanonewaythesystemcoulddecohere.AperfectexampleofthisisSchrödinger’scat.Thecatcoulddecohereasalivecatoritcoulddecohereasadeadcat.Whatmakesthedifferenceisaquantumvariable:iftheatomwasdecayedthecatwoulddecohereasdead;iftheatomwasexcitedthecatwoulddecohereasliving.Soadetectorisakindofamplifier,withafilterthatonlyallowsittoregisterstateswheretheatomisdefinitelyeitherexcitedordecayed.

Thepuzzle,youmayrecall,was:Whathappenedtothecatwhiletheatomexistedinasuperpositionofexcitedanddecayed?Theanswerisstillthesame—ifyoulookatthequantumstatemicroscopically:itisacorrelatedsuperpositionofanexcitedatomwithalivecatsuperposedwithadecayedatomandadeadcat.

Butifyoulookonlyatbulkpropertiessothatdecoherencecandoitswork,therandomnessturnsthesuperpositionintoanalmostirreversiblechange.Nowtherearetwooutcomes—thelivecatandthedeadcat—andbothemerge!This,accordingtothedecoherencestory,ishowtheworldsplitsintwo.

TheOxfordthinkersthenclaimthatthebranchingsandthesplittingsofthewavefunctionaredefinedbydecoherence.*Thesplitismadesothatitseparatesdifferentoutcomeswhichhavedifferentvaluesofmacroscopicproperties,suchasthepositionofadial.

Themainclaimthenisthatonlythosesubsystemswhichdecoherecanbecountedontohaveobserversassociatedwiththem.Asweareinterestedinwhatobserverssee,weshouldfocusontheseandthrowtherestaway.Thisopensuparoutetoderivingprobabilitiesinwhichyoucompareonlythelikelihoodsofwhatwouldbeobservedonbranchesthatdecohered.

Thisintroducesanotionofobserversintothetheory,whichmightbethoughttoweakenitsclaimtorealism.However,thisisawayofdiscoveringaroleforobserversthatarisesfromthedynamicsofthetheory,whichissurelybetterthanjustpostulatingaspecialroleforobserversatthebeginning.Onemightarguethatprobabilitiesarenotintrinsictotheworld,butareonlyaspectsofobservers’beliefsabouttheworld.Thensuchadescriptioncouldbeconsistentwithrealismbecausethereisanobjectivecharacterizationofapropertythatdistinguishesobserversfromothersubsystems.Observersaresubsystemsthatdecohere.

Decoherencesolvesthepreferredsplittingproblembecausedecoherencetakesplaceonlywithrespecttocertainobservables.Oftenthesearepositionsoflarge-scaleobjects.

Beforewegofurther,Ishouldmentionthatthereis,unfortunately,aproblemwithmakingdecoherenceanecessarypartoftheinterpretationofthetheory,whichwaspointedoutalongtimeagobymyteacherAbnerShimony.Thisproblemcanbeputverysimply.Rule1isreversibleintime,soeverychangeastateundergoesunderRule1canbeundone,andindeedwillbeundoneifwewaitlongenough.ButRule2isirreversible,andthewayitintroducesprobabilitiesfortheoutcomesofmeasurementsmakessenseonlyifmeasurementsareirreversibleandcannotbeundone.Thus,Shimonyargued,itisimpossiblethatRule2couldbederivedfromRule1alone.

AsIdescribeditabove,decoherenceisanirreversibleprocessinwhichcoherenceofstates,neededtodefinesuperpositions,islosttorandomprocessesintheenvironmentofthemeasuringinstrument.But

howcandecoherenceariseinatheorybasedonRule1alone,asallchangesdictatedbyRule1arereversibleintime?

Theansweristhatdecoherenceisalwaysanapproximatenotion.Completedecoherenceisimpossible.Indeed,ifwewaitaverylongtime,decoherencewillalwaysbereversed,astheinformationneededtodefinesuperpositionsseepsbackintothesystemfromtheenvironment.

Thisisduetoageneraltheorem,calledthequantumPoincarérecurrencetheorem.3Undercertainconditions,whichcanbeexpectedtoholdforsystemscontaininganatomicsystemplusadetector,thereisatimewithinwhichthequantumstateofthesystemwillreturnarbitrarilyclosetoitsinitialstate.Thistime,calledthePoincarérecurrencetime,canbeverylarge,butitisalwaysfinite.Theconditionsincludethatthespectrumofenergiesbediscrete,whichiscertainlyreasonable.*

Decoherenceisastatisticalprocess,similartotherandommotionofatomsthatleadstoincreasesofentropy,bringingsystemstoequilibrium.Theseprocessesappeartobeirreversible.Buttheyareactuallyreversible,becauseeveryprocessgovernedbyRule1isreversible.ThisistrueinbothNewtonianandquantumphysics;bothhavearecurrencetime.Ineithercasethesecondlawofthermodynamics,accordingtowhichentropyprobablyincreases,canholdonlyfortimesmuchshorterthanthePoincarérecurrencetime.Ifwewaitlongenough,wewillseeentropygodownasoftenasitgoesup.

Similarly,onemighttrytoarguethatovershortertimes,thereisalowprobabilityfordecoherencetoreverse,givingwaytorecoherence.

Now,aslongasweareinterestedonlyinwhathappensovermuchshortertimesthanittakestorecohere,andwewantonlyanapproximatedescriptionofwhatgoesonwhenatomicsystemsinteractwithlargebodies,suitableforpracticalpurposes,decoherenceprovidesausefulapproximatedescriptionofwhathappensduringameasurement.Indeed,decoherenceisaveryusefulconceptwhenanalyzingrealquantumsystems;forexample,muchofthedesignofaquantumcomputergoesintocounteractingdecoherence.Butasamatterofprinciple,thatdescriptionisincomplete,asitleavesouttheprocessesthatwillrecoherethestateifwewaitlongenough.

However,whenthestaterecoheres,measurementsbasedondecoherenceareundone.Therefore,measurementsasdescribedbyRule

2cannotbetheresultofdecoherence,atleastasdecoherenceisdescribedinatheorybasedonlyonRule1.

SoitseemsthatdecoherencecannotalonebethekeytohowprobabilitiesappearintheEverettquantumtheory,becauseitisbasedsolelyonRule1.

—THISDISCUSSIONMAKESitclearthatthequestionofwhereprobabilitiescomefromiscentraltomakingsenseoftheManyWorldsInterpretation.ThekeytounderstandingtheOxfordapproachliesinunderstandingwhataprobabilityis.Thisquestionisfarmoredifficultthanitappears.Weallhaveanintuitiveideaofwhatitmeanstosaytheprobabilityofaflippedcoinlandingonheadsis50percent.Peopleknowthedifferencebetweenwhattoexpectwhentheforecastsaysthechanceofraintomorrowis10percentandtheforecastsaysthechanceofrainis90percent.Butwhenwelookintowhatweactuallymeanwhenwetalkofprobabilities,wefindthenotiongetssurprisinglyslippery.

Partofthereasonprobabilityisconfusingisthatthereareatleastthreedifferentkinds,ormeanings,ofprobability.

Thesimplestnotionisthatprobabilityisameasureofourcredenceorbeliefthatsomethingwillhappen.Whenwesaythereisa50percentchanceofheadsonthenextcointoss,thatisnotastatementaboutthecoin;itisadescriptionofourbeliefabouttheresultoftossingthecoin.ThesearecalledBayesianprobabilities.

WhenwesaytheBayesianprobabilityforraintomorrowis0percent,thatisjustawayofsayingwebelieveitwillnotrain,andwhenwesaythatprobabilityis100percent,thatsayswearesureitwill.Probabilitiesbetweenthem,suchas20percent,50percent,or70percent,refertothestrengthofourbeliefthatitwillrain.Inparticular,whenwesaysomethinghasa50percentprobabilityofhappening,wearereallyconfessingwehavenoideawhetheritwillhappen.

Bayesianprobabilitiesareclearlysubjective.Theyarebestevaluatedintermsofourbehavior.Thehighertheprobabilityforrain,themorelikelyitwillbethatwewouldbetonrain,oratleastcarryanumbrella.

Manyprobabilitieswedealwithinordinarylifearebestunderstoodinthisway,asbettingodds.Certainly,probabilisticpredictionsaboutthestockmarketorthehousingmarketareofthiskind.Indeed,mostofthe

timewhenwerefertotheprobabilityofsomefutureevent,wearemakingasubjectivestatementofbelief,usingBayesianprobabilities.

Asecondkindofprobabilitycomesintoplaywhenwekeeprecordsoftherelevantevents.Ifwetossalargenumberofcoinsandkeeprecordsofhowoftentheycomeupheads,wecandefinetheproportionofheadsinthatsequenceoftossestobeaprobability.Thesearecalledfrequencyprobabilities.

Battingaveragesandothersportsstatisticsarefrequencyprobabilities.Theygivetheproportionofthetimesthatabattergotonbaseafterhewasatbat.

Sometimesweatherforecastsareofthiskind.WhentheNationalWeatherServicewebsitetellsusinthemorningthatthereisa70percentprobabilitythatitwillrainthisafternoon,whattheymightbesayingisthatwithintheirvastrecords,roughly70outof100dayswithconditionslikethoseofthismorninghadrainintheafternoon.

Ofcourse,theseprobabilitiesareimprecise.Theproblemwiththeseisthatsolongasthenumberofdaysobservedisfinite,thefrequencieswillvary.Butthemoredaysofwhichtheweatherservicehasrecords,themorereliabletheforecastwillbe.

Ifoneflipsacoin100times,thenonecanaskhowoftenonegetsheads.Theproportioniscalledtherelativefrequencyofgettingheads.Thiswilltendtobearound50;wearenotsurprisedifitturnsoutoftentobe48or53.

Foranyfinitenumberoftrials,then,thenumberofheadswillrarelybeexactlyhalf.Thekeyideaisthat,wereweabletodoaninfinitenumberoftrials,theproportionofdifferentoutcomeswouldtendtosomefixedvalues.Thisdefinestherelativefrequencynotionofprobability.

Theproblemwiththisisthatintherealworld,weonlygetafinitenumberoftries.Aslongasthenumberoftrialsisfinite,thereisagoodchancethatthenumberofheadswillbedifferentfromexactlyhalfthetrials.Asurprisinglyhardquestiontoansweriswhatittakestoshowthataprobabilisticpredictioniswrong,giventhatwecanonlydoafinitenumberoftests.Indeed,oftenallwecansayisthatourpredictionisimprobable.Butforthistobemeaningfulwehavetodefinewhatwemeanbyimprobable.Wecannotassumeweknowwhatimprobablemeansasweareintheprocessofdefiningit.

Supposewetossacoinamilliontimesandcomeupwith900,000heads.Itispossiblethatthisisarareflukeandourcoinisnormal.Butwecanconcludethatit’sveryprobable—althoughnotcertain—thatthecoinisweighted.

Bydefinition,wechooseoursubjectiveprobabilities.ButwecanaskthattherebearelationbetweenthesubjectiveBayesianprobabilitieswechooseandobjectivefrequenciestakenfrompastrecords.Solongaswehavenomoreinformation,thebestbetwecanmakeistheonethatfollowstheoddsthatarebasedonhistoricalrecords.Whatwemeanhereby“bestbet”isthechoicethat,mostofthetime,willserveourinterests.Ineconomic-speakwecouldsaythatthisisthe“mostrationalchoice.”

Wemightputthisasfollows:

Itismostrational,inasituationwhereyouhavelimitedknowledge,tochoosetoalignyoursubjectivebettingoddswiththefrequenciesobservedinthehistoricalrecord.

Thisisaversionofthe“principalprinciple”ofthephilosopherDavidLewis.Thisprinciplehasatitsrootanassumptionthat,everythingelsebeingequal,thefuturewillresemblethepast.Oratleastthat,givenincompleteinformation,itisrationaltobetonthefutureresemblingthepast.Thisbetmaysometimesputyouonthewrongsideofhistory,butitisstillthesafestbetyoucanmake.*

Now,supposeweaskadifferentquestion,whichistoexplainthefrequenciesobservedintherecordsofaparticularexperiment.Supposethefrequencyobservedwascloseto50percent.Itwouldbenaturaltotrytoexplainthatresultbyanapplicationofthelawsofphysicstotheparticularexperiment.

Suchanexplanationmightgivereasonswhyheadswouldbeaslikelyanoutcomeastails.Thiswouldincludethehypothesisthatthecoinwasfair,aswellashypothesesaboutthetosses,howthecoinbehaveswhenithitsasurface,andsoon.Ourexplanationmightalsorefertoresultsfromotherexperiments,whichsupportourbeliefinthetheory.

Oncewehavesuchanexplanation,wewoulduseittopredictthatasingletosshasanequalchancetoendupheadsortails.Thispredictionisabelief,andhenceasubjectiveBayesianprobability.Butitreferstothe

singletoss.Thistossneednotbepartofalargenumberoftrials;hencenorelativefrequencyisinvolved.Itthenmakessensetosaythattheparticularcoinhas,initscontext,aphysicalpropensityforasinglethrowtoendupheads50percentofthetime.

Thepropensityisanintrinsicpropertythecoinhasasaconsequenceofthelawsofphysics.Itcanbeexpressedasaprobability,butitisnotabelief.Rather,itjustifiesabelief.Itissomethingintheworldthatwemayhaveabeliefabout.Nor,aswesaid,isapropensityafrequency,foritisapropertyofthecoin,whichappliestoeachindividualtoss.Propensitywouldthenseemtobeathirdkindofprobability,differentfromeitherbeliefsorfrequencies.

Notethatunliketheothertwokindsofprobabilities,propensitiesareconsequencesoftheoriesandhypothesesaboutnature.Buttheyhavedistinctrelationstothetwootherkindsofprobabilities.Wecanhavebeliefsaboutpropensities.Propensitiesinturncanexplainrelativefrequenciesandcanjustifybeliefs.

Inordinaryquantummechanics,probabilitiesarisefromRule2,inparticulartheBornrule,whichconnectstheprobabilityofseeingaparticleatsomepositiontothesquareoftheamplitudeofthewaveatthatposition.Thatprobabilityispositedtobeanintrinsicpropertyofthequantumstate;henceitisapropensityprobability.Quantummechanicsassertsthatthereisnodeeperexplanationforthatprobabilityandtheresultinguncertainty;itisanintrinsicpropertyofthequantumstate.

WhenEverettdroppedRule2,theresultwasatheorywithoutanynotionofprobability,intrinsicorotherwise.AsIdescribed,hetriedandfailedtoreplacethiswithafrequencynotionofprobability.

ThedilemmaproponentsoftheEverettformulationofquantummechanicsfacedwasthattherearebranchesinwhichobserversseethatBorn’sruleconnectingmagnitudeswithfrequenciesholds,andthereareotherbrancheswhoseobserversseethatBorn’sruleisviolated.Let’scallthesebenevolentbranchesandmalevolentbranches.Thelattermayhavesmallerwavefunctionsthantheformer,butonecannotusethistoarguethatthelatterareanylessprobable,becausetodosowouldbetoimposeonthetheorytherelationbetweensizeormagnitudeofthewavefunctionandprobability.ButthatisexactlywhatproponentsofEverett’sformulationaretryingtoderivefromRule1;toassumeitwouldbetosneakinRule2bythebackdoor.

—THEEVERETTTHEORYisahypothesisaboutthenatureofreality.Itpositsthatallthatexistsisawavefunctionevolvingdeterministically.Fromtheimaginaryperspectiveofagodlikeobserveroutsidetheuniverse,therearenoprobabilities,becausethetheoryisdeterministic.Allbranchesofthewavefunctionexist;allareequallyreal.

TheEveretttheoryassertsthateachofusleadsmanyparallellives,eachdefinedbyabranchthathasdecohered.Thetheoryalsotellsusthateachofthesebranchesexists,withcertainty.Soifthistheoryisright,sincethereisnoRule2,therearenoobjectiveprobabilitiesatall.LetuscallthisEverett’shypothesis.

Butwearenotgodlike;weareobserverslivinginsidetheuniverse,and,accordingtothehypothesis,wearepartoftheworldthatthewavefunctiondescribes.Sothatexternaldescriptionhasnorelevanceforusorfortheobservationswemake.

Wearethenfacedwithapuzzle.Whereinthisworlddowefindtheprobabilitiesthatordinaryquantummechanicsclaimstopredict,whicharetobecomparedwithfrequenciescountedbyexperimentalists?WithnoRule2,theseprobabilitiesarenotpartoftheworldasitwouldbeinourabsence.Frequenciesarecountsofdefiniteoutcomes,butsuchthingsarenotuniqueorexclusivefactsinEverettianquantumtheory,becausegivenanypossiblecountingofoutcomesofarepeatedexperiment,therearebrancheswhichhavethatcount.Therearebranchesinwhichthosecountsagreewiththepredictionsofquantummechanics(withRule2)andbranchesinwhichtheydon’t.Wecannotsaytheformeraremoreprobablethanthelatter,becauseinEverettianquantumtheorytherearenoobjectiveprobabilities.Wecannotevensaythattheformeraremorenumerousthanthelatterbecauseinrealisticcasestherewillbeinfinitenumbersofeach.

Youreadthisright:Everettianquantummechanicspredictsthataninfinitenumberofobserverswillobserveexperimentalresultsthatdisagreewiththepredictionsofquantummechanics!Thatisthefateoftheinfinitenumberofobserverswhoseillfortunetakesthemalongmalevolentbranches.Itisalsothecasethataninfinitenumberofobserversonbenevolentbranchesseeexperimentalresultsconsistent

withquantumtheory’spredictions.Butthatissmallconsolation,becauseabenevolentbranchcanturnmalevolentatanymoment.

Whatitseemswecannotsay,inEverettianquantummechanics,isthatquantumtheorypredictsobjectiveprobabilities,whichareinherentfeaturesofnaturethatexistinourabsence.And,unlesswefindanotherwaytointroduceprobabilities,wecannotsaythatthetheorycanbetestedbydoingtheexperimentandcountingthedifferentoutcomes,becausethefailureofanysuchtestcanbedismissedbysupposingthatwearejustonamalevolentbranch—andthosearenotanylessprobableoranylessnumerousthanthebenevolentbrancheswhichconfirmtheprobabilisticpredictionsofquantummechanics.

Toaddressthissituation,DavidDeutschmadeaninterestingproposal,whichwastoasknotwhethertheEveretttheoryistrueorfalse,buthowwe,asobserversinsidetheuniverse,shouldbet,werewetoassumethatitistrue.Inparticular,themajorthingwehavetobeton,assumingtheEverettstoryistrue,iswhetherthebranchweliveonisbenevolentormalevolent.Everyotherbetwemightmakedependsonthatsinglebet.Ifweareonabenevolentbranch,thenbetsweplacebasedonBorn’srulewillpayout.Ifwearen’tsofortunate,thenallbetsareoff,becauseliterally,anythingcouldhappen.

Thisisnotabetabouttheuniverse,becauseitiscertainthattheuniversecontainsobserverswholiveonbothkindsofbranches.Itisinsteadabetonwhereweareintheuniverse.Thereisnorightanswertothisquestion,because,ifEverettisright,therearebothkindsofobservers,andsomeofuswillbeonekind,sometheother.

Nonetheless,Deutschproposesthatitismorerationaltobetweareonabenevolentbranch.Theargumentistechnicalandemploysabranchofprobabilitytheorycalleddecisiontheory.Deutsch’sresultthenassumescertainaxiomsofdecisiontheory,whichspecifywhatitmeanstomakearationaldecision.

Someexpertshavecriticizedthisapproach;somedefendanddevelopit,whilestillotherexpertsofferalternativeargumentstothesameconclusion.GiventhatIamnotaspecialistinthisarea,Iamnotgoingtospeculateonwhichexpertsareright.

Butnoticewhatthiskindofargumentdoesn’t—indeedcannot—do.ItcannotofferusevidencethattheEveretthypothesisistrue,becauseDeutschandhiscolleaguesbeginbyassumingthatthehypothesisis

correct.Theirargumentsalsoassumetheaxiomsofdecisiontheory.Ifyoudon’tacceptthemyoudonotprovethattheprobabilitiesarerelatedtothemagnitudes.Alltheargumentcouldshowisthat,assumingtheaxiomsofdecisiontheory,itisconsistentwiththeEveretthypothesistoplacebets,andmakeotherkindsofdecisions,asifBorn’sruleweretrue.

Noticethat,evengiventheassumptionthatEverettistrue,theobserversmodeledaspartofanEverettworlddonotknowthattheyliveinanEverettworld.Thereisnoreasontheyshould,andiftheynonethelessdid,theywouldnotbemodelsofus,asobserversinauniversewhosefullsetofprinciplesremaintobediscovered.Forthemasforus,theEveretthypothesismustbeoneofseveralcompetinghypothesesastothenatureofthebeablesofthequantumuniverse.

LetusthenconsiderthesituationofobserversinsideanEverettianuniverse.Therearetwocases,dependingonwhichkindofbranchweliveon.Supposewearefortunateandliveonabenevolentbranch,sothatourbetsbasedonBorn’srulepayout.Wellthen,bydefinition,wedonobetter,andnoworse,thanpeoplewhobelieveinotherformulationsandinterpretationsofquantummechanicsandsoalsoplacebetsbasedonBorn’srule.Whattheotherapproacheslackisajustificationbasedondecisiontheory.Ontheotherhand,pilotwavetheoryandcollapsemodelshavenoneedofsuchjustification,becausetheyrelyoncompletelyobjectivenotionsofprobabilityarisingfromourignoranceofthedetailsoftheindividualexperiment.

Thus,onitsownterms,inwhichitcannotaddresswhatistrue,butcanonlyofferadviceabouthowbesttoplacebets,Deutsch’sargumentimpliesthatitisnomorerationalforobserversinsideanEverettianworldtobelieveinEverettthanitisforthemtobelieveinBohrordeBroglie,Bohmoranyotherinterpretation.So,inthebestcase,evenassumingthatEverettisright,observersinanEverettianworldcannotmusteranyevidencetobelieveEverett’shypothesesoverthealternativehypotheses.

Whatabouttheversionsofourselvesthatliveonmalevolentbranches?TheirbetsbasedonBorn’sruledon’tpayoffbecausethefrequenciestheymeasuredisagreewiththosepredictedbyBorn’srule.Sohowdoesitlookfromthepointofviewoftheseunluckyobservers?Rememberthatforthem,theusualformulationofquantummechanics

(say,aspresentedinvonNeumann’sbook)mustbeahypothesis,andEverett’shypothesisisadifferent,competing,hypothesis.

ObserversonamalevolentbranchconcludethatthefirsthypothesisissimplyfalsebecauseBorn’sruledoesnotpredicttheresultstheyobserve.Thesecondhypothesis,Everett’s,isnotfalsified,becausethatpredictsthatsomeobserverswillseeBorn’srulefail.Butit’sworsethanthat.Givenanyresultsofrepeatedmeasurements,Everett’sstorypredictsthatsomeobservers,livingonamalevolentbranch,willseeexactlythoseresults.SoEverett’shypothesiscannotbefalsifiedbytestinganyprobabilisticpredictionbasedonBorn’srule,asthereisnooutcomeofarepeatedmeasurementthatisinconsistentwithanEverettianuniverse.

Soitseemsthatthebulkofexperimentalpredictionsthatcouldfalsifyordinaryquantummechanics—thosethatcomparetheoreticalprobabilitiestoexperimentallyobservedfrequencies—wouldnotcountasfalsifyingEverettianquantummechanics.Whilenotcompletelyunfalsifiable—becausethetheorymakesotherkindsofpredictions,whichdonotinvolveprobabilities—Everettianquantummechanicsseemstobefarlessvulnerabletofalsificationthanordinaryquantummechanics.

That,initself,isagoodreasontopreferanalternativeapproach.Atheorythatislessfalsifiableisbydefinitionlessexplanatory.

Ontheotherhand,ifweaccepttheassumptionsofDeutschandtheotherOxfordians,thenwemustdisregardthepointofviewofthemalevolentbranches,becausethosebranchesareveryimprobable.Inthiscasethereisworkthatshowsthatonceoneneglectsthemalevolentbranches,thetheoryistestable.

—THEOXFORDIANSEMPHASIZEthatifyouassumetheaxiomsofdecisiontheoryarecorrect,thenyouareallowedtodeducethatitisrationaltoreasonasifthemagnitudesarerelatedtotheprobabilities.Itfollowsthatitisrationaltoreasonasifwehaveaverysmallprobabilityofendinguponamalevolentbranch,sothatpossibilitycanbeignored.

Theymightfurtherclaimthatsomethinglikethisisalwaysthecasewhenwereasonprobabilistically.Wecouldalwaysbeunluckyandhaveacointossresultinheadsathousandtimesinarow.Butthereisadifference.Inafinitelife,inasinglefiniteworld,wecanrestassuredthatsuchthingsalmostneverhappen.Butinstrongcontrast,Everettian

quantummechanicsassertsthatcorrespondinglymalevolentbranchesnotonlyexist—theyareasnumerousasbenevolentbranches.WhileDeutsch’sargumenttellsusaboutsubjectivebettingprobabilitiestakenbyobserversinsidetheEverettworld,itremainsthecasethattheoveralltheoryisdeterministicandthateachofthebranchesdefinitelyexists.

Itseems,atleastasbestI’vebeenabletounderstand,thattheattemptsbyDeutschandothers*torescuetheprojectofmakingsenseoftheEveretthypothesisbymeansonlyofsubjectiveprobabilitiesforobserversinanEverettuniverse,introducedviadecisiontheory,donotconvincinglysucceed.Argumentsbasedonsubjectivenotionsofprobabilityalonefailtoexplainwhywecanneglectthemalevolentbranches—for,ifEverettisright,theyareobjectivelyreal.

—SOMETHINGNEWISNEEDED.Tosavetheday,SimonSaundershasproposedtocuttheGordianknotbypositingthatthemagnitudesofthebranchesgiveobjectiveprobabilities(ratherthanbettingprobabilities)ofanobserverfindingthemselvesonadecoheredbranch,inagreementwithBorn’srule.Hisargumentforthisisthatthemagnitudesofthebranchesdoindeedturnouttohavemanyofthepropertieswewouldwantobjectiveprobabilitiestoenjoy.Indeed,hisclaimisthattheyhavethesepropertiesasaconsequenceofRule1—hencethisisadiscoveryofaconsequenceofthelawsbywhichquantumstatesevolve.Itisnotanadditionalpostulate,asRule2is.Ifhisproposalsucceeds,itwouldbeagenuinederivationofRule2andtheBornrulefromthetheorybasedpurelyonRule1.

Thisgetsusoutoftheproblemsraisedbythemalevolentbranches,because,assumingSaundersisright,itisnotveryprobabletofindourselvesononeofthem.ButSaundersclaimsitwouldaccomplishmorethanthat:itwouldbeagenuinederivationofhowobjectiveprobabilitiesariseinnature,anditwouldexplainwhywemustalignoursubjectivebettingoddswiththeobjectiveprobabilities.

MyunderstandingisthattheexpertsinOxfordareatpresentdividedastowhetherSaunders’sproposalsucceeds.Oneissueisthatthebranchmagnitudeshavesomebutnotallpropertiesofobjectiveprobabilities.Sowemustleavethisdiscussionhere;aftermorethansixtyyearsofstudy,itisstillunresolvedwhethersensecanbemadeofEverett’sstartlingidea.

—RECOGNIZINGTHATTHEPROJECTofmakingsenseofEverett’shypothesisremainsaworkinprogress,Icanofferaseriesofremarks.

MyoverallunderstandingisthattheEveretthypothesis,ifsuccessful,wouldexplainvastlytoomuch,andalsomuchtoolittle.Toomuch,becausewehavetobelievethatthewholeworldweusedtothinkofasrealisjustonebranchwithinavastlylargerreality.Andtoolittle,becauseagreatdealisleftoutofthispictureofreality.Whatismostcharacteristicaboutexperiencedrealityisthateveryprocessweobservehasadefiniteoutcome.Whatisalsomostimpressiveaboutquantumtheoryisitsability,usingRule2,tomakeprecisepredictionsoftheobservedfrequenciesofthosedefiniteoutcomes.WhatIwantfromrealismisadetailedexplanationforhowthoseprobabilitiesariseasrelativefrequencies,byaveragingoverasetofrepeatedrunsoftheexperiment.

Therealitythatwerealistsseekistheworldasitis,orwouldbe,inourabsence.Subjectiveprobabilitiesthatguidedecisionmakerstoplacebetsarenotpartofthatworld,sincetheywouldnotexistifwedidnot.Thequestionisnotwhetherdecisionmakersarereal,forwearecertainlyreal.Noristhequestionwhetherwecould,ifwewereinterested,seekascientificaccountofwhatconstitutesrationaldecisionmaking.Thequestionisinsteadwhetherwecanrealizetheambitionofphysicstodescribelightandatomsinawaythatiscompletelyindependentofwhetherweexistornot.

LetmeemphasizethatthejuryisstilloutastowhethertheOxfordapproachsucceeds,onitsownterms,inmakingsenseoftheManyWorldsInterpretation.TheEveretthypothesismayyetbeshowntobeinconsistentorincoherent.Oritmayturnouttobetheonlyrealistapproachtoquantummechanics,inwhichRule1alonesufficestoframethetheory.Forme,eitheroutcomewouldjuststrengthentheargumentthatweneedanewtheory.

—WHENEMPIRICALTESTSoftheoriesfail,westillhavetomakedecisionsaboutwhichtheorytoworkon.Asanumberofphilosophersandhistorianshavestressed,beforedefinitiveevidenceisin,thereisno

avoidingbringinginfactorsthatmayseemnonscientificwhenevaluatingwhichresearchprogramandtheoryisdeservingofourtimeandattention.Thisisespeciallythecasebecausetheseareinpartindividualdecisions,andwhenempiricalcriteriahaveyettobedecisive,itisintheinterestsofthescientificcommunityasawholetoencouragethewidestdiversityofapproachesconsistentwiththeevidenceinhandatthemoment.AsPaulFeyerabendexplainsinhisbookAgainstMethod,itiscompetitionamongdiverseviewpointsandresearchprogramsthatdrivestheprogressofscience,especiallythroughcriticalperiodswhentheevidenceisnotsufficienttodecidewhichapproachwillultimatelyyieldthebestexplanations.

Evaluatingaresearchprogrambasedonnon-empiricalfactorsispartlyamatterofindividualtasteandjudgment.*Afteralotofefforttounderstandthethinkingofitsproponents,hereishowthecasefortheEverettprogramseemstome.Iexpect,indeedIknow,thatotherswhohavethoughtitthroughdonotagree.IamnotafraidtoconfessthatnoissueinquantumfoundationshasbeenmorechallengingandmorepainfultomepersonallythantheissueofEverett,whereIfindmyselfindisagreementwithfriendsandcolleaguesforwhomovertheyearsIhavegrowntohavegreatrespect.

WeknowthattheoriginalformoftheManyWorldsInterpretationfailsasarealistapproachbecauseitrunsintotwobigproblems,whicharethepreferredsplittingproblemandtheproblemthatthetheoryisdeterministicandhasnoprobabilities.Afteragreatdealofefforttodevelopamoresophisticatedversionbasedondecoherenceandsubjectiveprobabilities,expertscontinuetodisagreeovertechnicalissues.Buteveniftheydosucceed,whatwouldbeestablishedisthattheaxiomsofdecisiontheoryrequirethatobserverslivinginanEverettworldbetasifBorn’sruleweretrue.Thatdoesnot,however,giveusareasontobelievethatweliveinanEverettianuniverse.NoramIawareofanyempiricallybasedargumentthatwouldrequireustopreferEverettoverotherapproaches.Despitesomeprovocativeclaimstothecontrary,thereisnoexperimentaloutcomethatcannotbeexplainedatleastaswellbytheotherrealistapproaches.ThereareclaimsthatEverettalonecanexplainphenomenasuchasthespeed-upofquantumcomputing,butthesearecontradictedbythefactthatthealternativerealistprograms,

suchaspilotwavetheory,provideaccountsoftheseexperimentswhichareatleastequallyexplanatory.

OneargumentforEverettbeginswiththeassertionthatthereareonlythreerealisticformulationsofquantumtheory,andthattheothertwo,pilotwavetheoryandcollapsetheory,havetensionswithrelativityandhencehavetroubleincorporatingquantumfieldtheory.Thisargumentthenimpliesthat,assumingitcanbemadesenseof,Everettmustbecorrect.Idisagree,andtakethisasstrongmotivationtoseektoinventotherrealistapproaches,asIdescribeintheclosingchaptersofthisbook.

Thatiswherethescientificcaseleavesoff;let’sthenturntonon-empiricalfactors.ThephilosopherImreLakatosrecommendedinvestinginresearchprogramsthatareprogressive,bywhichhemeantthattheyarerapidlydevelopingandhavethepotentialtoleadtoabreakthrough.Aprogressiveresearchprogramisalsoonethatisopentofuturedevelopmentsandsurprises,incontrasttoprogramswhichassumethebasicprinciplesandphenomenaareunderstood.Progressivecriteriafavorrealisticapproachestoquantumfoundationsovertheanti-realistapproachesbecausethelatterconfineustodevelopingnewwaysoftalkingaboutquantumphenomenawhichareassumedtobealreadyknown,whiletheformerunderstandthatquantummechanicsisincompleteandhenceaimtodiscovernewphenomenaandnewprinciplesinwhichtosituatethem.

Withintherealistapproaches,IbelievethereisacasetobemadethatEverett’shypothesisistheleastprogressive—althoughthereareargumentsonbothsides.AnenormousefforthasgoneintodevelopingEverettquantummechanics,muchofittechnicalandextremelyclever,butmostofthatworkhasgonetoaddressingproblemsthatariseonlyintheManyWorldsInterpretation,butdonottroubletheotherapproaches.ImightsuggestthattheEverettprogramis,oftherealistapproaches,theleastopentothepossibilitythatfuturediscoverieswillleadustomodifytheprinciplesandthemathematicalformalismofquantummechanics.

Ontheotherside,itshouldbepointedoutthattheEveretttheorystimulatedmuchworkondecoherence,whichwasimportantgenerallyforourunderstandingofquantumphysics.Italsoinspired,andcontinuestoprovoke,muchprogressinquantumcomputing.TheManyWorldsInterpretationplayedaroleinthepioneeringworkofDavidDeutsch.Yetwemustalsocreditpilotwavetheoryandcollapsemodelsforthe

experimentalproposalstheyhavestimulatedregarding,forexample,out-of-equilibriumphysicsintheearlyuniverse.Soitseemsthatanargumentaboutwhichrealistapproachismoreprogressivecomesoutabouteven.

TheoddthingabouttheOxfordapproachisthat,whileittellsusnothingabouttheworldweexperiencethatwedidn’talreadyknow,orcouldn’thavededucedwithinotherversionsofquantumtheory,ithasalottosayaboutalltheworldswedon’tandcan’texperience,andespeciallyaboutthenearcopiesofourselveswhichpopulatethem.Giventhattheyarepresumablyjustasaliveandjustasconsciousasweare,Ifindmyselfwonderingifwe—orthoseofuswhobelieveinEverettenoughtocontemplateitasaseriouspossibility—shouldcareaboutourcopies,andwhetherwehaveanyresponsibilitiestowardthem.

Iadmitthattoinquireintothequalityoflivesofourcopiesonotherbranchesmayseemabitacademic.Butonethingweacademicsaretrainedtodoistoworkoutthelogicalconsequencesofhypothesesandassumptions.Andthemostprovocativeand,tome,distastefulconsequenceofEverettisthatwemustbelievethateachofushasaninfinitenumberofcopies,eacheverybitasaliveandconsciousasweare.Thissoundsmorelikesciencefictionthanscience,butitdoesseemastraightforwardconsequenceofEverett’shypothesis.Sincethisisscienceandnotfaith,wedon’thavetheoptionoftakinga“liberal”interpretationofEverettinwhichwechoosetobelievecertainaspects,suchastheexistenceofawavefunctionoftheuniverse,whileignoringothers.

ItthenseemstomethatEverettraisestwokindsofethicalquandaries.First,itcondemnsavastnumberoflivingandconsciousbeingstosufferingwhichcannotbemitigatedbyeffortswemake.Beyondthat,Iwouldworrythatthefactthatmanyofourmosttalentedandaccomplishedscientistsbelieveweliveinthatunhappyuniverseisinimicalforthelong-termpublicgood,because,byerasingthedistinctionbetweenpossibilityandactuality,itdiminishesthemotivationtoworktoimproveourworld.

Couldn’twesaythesameabouttheincreaseinentropymandatedbythesecondlawofthermodynamics,whichisultimatelythecauseofthedeathofmostlivingcreatures?Thedifferenceisthatweknowthesecondlawistrue.Wehavenochoicewhethertobelieveit,whereastherearealternativeformulationsofquantumtheorywhichdonotimposeonustheexistenceofcopies.Itisalsoverylegitimatetocriticizethescientists

andphilosopherswhodrewunnecessarilypessimisticconclusionsbasedonanincompletepicturethatneglectedthepositiveeffectsofself-organizationinfar-from-equilibriumsystems.

Thewholenotionofanobserver“living”onamalevolentbranchcanbeobjectedtoonthegroundsthatnoneofthebiochemistrythatlifedependsonwouldfunctionwellinaworldinwhichBorn’sruleregularlyfailed.Tobemoreprecise,wemightratemalevolentbranchesbytheproportionofeventsinwhichBorn’srulefailedtohold.Wecouldthencataloguebranchesbytheseverityofsuchfailures.Livinginamildlymalevolentbranchwouldbelikebeingsubjecttoalowdoseofionizingradiation,withsimilarconsequencesofdecreasedhealth.

Evenamongthebenevolentbranchestherewouldbedisparitiesinhealth.TomorrowagammaraywillstrikeastrandofmyDNA,andtheconsequenceswillincludethesplittingofusandourworldintoabunchofdecoheringworlds.Someofmycopieswilldevelopcancerasaresult;somewon’t.Thereareversionsofmeinbothsets;henceIcareaboutboth.Theextremeversionofthisargumentsuggeststhat,farintothefuture,someveryfortunatecopiesofme,whohadthelucktododgeeverybulletandsurviveeverycancer,willbestillalive.

ItseemstomethattheManyWorldsInterpretationoffersaprofoundchallengetoourmoralthinkingbecauseiterasesthedistinctionbetweenthepossibleandtheactual.Forme,thereasontostrivetomakeabetterworldisthatwecanhopetomaketheactualfuturebetterthanthepossiblefuturesweweredealttobeginwith.Ifeveryeventualityweworkedtoeliminate,whetherstarvation,disease,ortyranny,wasactualsomewhereelseinthewavefunction,thenoureffortswouldnotresultinanoverallimprovement.IssuessuchasnuclearwarandclimatechangearelessurgentiftherearemultipleversionsofEarthandthehumanracehasmorethanonechancetogetthingsright.

Theexistenceofallthesecopiesofourselveswouldthenseemtometopresentamoralandethicalquandary.IfnomatterwhatchoicesImakeinlife,therewillbeaversionofmethatwilltaketheoppositechoice,thenwhydoesitmatterwhatIchoose?TherewillbeabranchinthemultiverseforeveryoptionImighthavechosen.TherearebranchesinwhichIbecomeasevilasStalinandHitlerandtherearebrancheswhereIamlovedasasuccessortoGandhi.Imightaswellbeselfishandmakethechoicesthatbenefitme.IrrespectiveofwhatIchoose,thekind

andgenerouschoicewillbemadebyaninfinitenumberofcopieslivinginaninfinitenumberofotherbranches.

Thisseemstometobeanethicalproblembecausesimplybelievingintheexistenceofallthesecopieslessensmyownsenseofmoralresponsibility.

AdearfriendwhoworksonEverettianquantumtheorywouldinsistthat,nonetheless,thisisawaytheworldmightbe.Ourjobistofigureouthowtheworldis,anditisnotuptoustoimposeourpersonallikesanddislikes.Myreplyisthat,solongasthereisnodecisiveargumenttopreferEverettoverotherapproaches,Iamfreetobetonanotherapproach.Theyarefreetodootherwise,butIchoosetoinvestmytimeindevelopingcosmologiesthatinspireustolookfornewparticles,newphenomena,newphysics,overthescholasticcontemplationofthelivesofcopiesofourselves.

And,Imightadd,giventhatIdon’tbelieveitislikelythatEverettoranythinglikeitisgoingtoturnouttobetrue,thereislittledangerofharmifafewbrilliantphilosopherschoosetospendtheireffortsworkingouttheconsequencesofatrulystartlingandsubtlehypothesis.(Weretheideatocometoinfluencethezeitgeist,thatwouldbesomethingelsetoworryabout.)Evenifitisawrongidea,itisanideathatprobablyhadtocomeupsoonerorlater,andtheyhavetherightkindofanalyticallyableminds,rigorouslytrained,thataresuitedtothequestion,whichmineisclearlynot.LetusthenhopetheywillfinallyresolvethequestionofwhetherornotarealisttheorybasedonRule1alonecanmakesense.

—THEDISTINGUISHEDPARTICLETHEORISTStevenWeinbergrecentlyweighedinonthefailureofeffortstodeduceprobabilitiesfromquantummechanics.

Thereisanotherthingthatisunsatisfactoryaboutthe[ManyWorlds]realistapproach,beyondourparochialpreferences[e.g.,“notliking”theideaofhavingcopies].Inthisapproach,thewavefunctionofthemultiverseevolvesdeterministically.Wecanstilltalkofprobabilitiesasthefractionsofthetimethatvariouspossibleresultsarefoundwhenmeasurementsareperformedmanytimesinanyonehistory;buttherulesthatgovernwhatprobabilitiesareobservedwouldhavetofollowfromthe

deterministicevolutionofthewholemultiverse....Severalattemptsfollowingtherealistapproachhavecomeclosetodeducingruleslikethe[probability]Bornrulethatweknowworkwellexperimentally,butIthinkwithoutfinalsuccess.4

—THEREISALASTMORALtodrawfromthestoryofEverettianquantummechanics.SomeofitsproponentsclaimthatEverettianquantummechanicsisquantummechanics,andthatallelseisamodificationofit.Butthatissimplynotthecase.Ordinarytextbookquantummechanics—bywhichImeanthetheorythatistaughtinthestandardtextbooks(Dirac,Bohm,Baym,Shankar,Schiff,etc.),andthereforethetheoryincommonusebyrealphysicists—isbasedonRule1andRule2.Thattheorysimplydoesnothavearealistinterpretation.

Sorealism,inanyversion,hasaprice.Thequestionisonlywhatpricewehavetopaytogetanewtheorythatmakescompletesenseanddescribesnaturecorrectlyandcompletely.

PART3

BEYONDTHEQUANTUM

I

TWELVE

AlternativestoRevolutionIntheendwearedriventosearchforwhatwehopewillturnouttobethecorrectontologyoftheworld.Afterall,itisthedesiretounderstandwhatrealityislikethatburns

deepestinthesoulofanytruephysicist.—LUCIENHARDY

nthelastfewyearsthefieldofquantumfoundationshasundergonealivelyascension.Aftereightdecadesintheshadows,itisfinallypossibletomakeagoodcareerasaspecialistinquantumfoundations.

Thatisforthegood;however,mostoftheprogress(andmostoftheyoungpeople)hasbeenontheanti-realistsideofthefield.Theaimofmostofthenewworkhasnotbeentomodifyorcompletequantumtheory,butonlytogiveusanewwayofspeakingaboutit.Toexplainwhy,Ineedtoreviewabitofthehistoryofthefieldofquantumfoundations.

Quantummechanicsdidnotspringupovernight.Itwastheresultofalonggestation,whichbeganin1900withPlanck’sdiscoverythatenergycarriedbylightcameindiscretepackets,andculminatedinthefinalformofquantummechanicsbeingestablishedin1927.Therefollowedaperiodofdebateamongthefounders,duringwhichmanyofthequantumphysicistswereconcernedwiththefoundationsofthenewtheory.However,thisperiodoffreedebatesooncametoanend,and,despitetheobjectionsofEinstein,Schrödinger,anddeBroglie,itculminatedwiththetriumphoftheCopenhagenview.

Fromtheearly1930sthroughthemid-1990s,mostphysicistsregardedthequestionofthemeaningofquantummechanicsassettled.

ThislongdarkagewaspunctuatedbytheimportantworksofBohm,Bell,Everett,andafewothers,butmostofthecommunityofphysicistspaidlittleattentiontotheseworksortofoundationalquestionsingeneral.Onecanseethisfromthefactthatthecrucialpapersbythoseauthorshadveryfewcitationsintothemid-1970s,whentheexperimentaltestsofBell’srestrictionbegantobedone.Evennow,itisnotuncommontofindveryaccomplishedphysicistswhobelieve,incorrectly,thatBellprovedallhiddenvariabletheoriesmustbewrong.*Untilveryrecently,therewerevirtuallynoacademicpositionsinphysicsdepartmentsforphysicistsfocusedonquantumfoundations.Thetinycommunityofspecialistsinquantumfoundationseitherearnedtheirtenureforotherwork,asBelldid,or,likeBohm,foundplacesinout-of-the-waycornersoftheacademicworld.Afewmadecareersinphilosophyormathematics,othersbyteachinginsmallundergraduatecolleges.

Itwasthepromiseofquantumcomputingthatbegan,justbeforetheturnofthiscentury,toopendoorstopeoplewhowantedtoworkonquantumfoundations.TheideathatquantummechanicscouldbeusedtoconstructanewkindofcomputerwasbroachedbyRichardFeynmaninalecture1in1981.Thattalk,andotherearlyanticipationsoftheidea,seemedtomakelittleimpressionuntilDavidDeutsch,originallyaspecialistinquantumgravitywhoheldapositionatOxford,proposedin1989anapproachtoquantumcomputationinthecontextofapaperonthefoundationsofmathematicsandlogic.2Inhispaper,Deutschintroducedtheideaofauniversalquantumcomputer,analogoustoaTuringmachine.AfewyearslaterPeterShore,acomputerscientistworkingforanIBMresearchlaboratory,provedthataquantumcomputercouldfactorlargenumbersmuchfasterthanaregularcomputer.Atthatpointpeoplebegantotakenotice,becauseoneapplicationofbeingabletofactorlargenumbersisthatmanyofthecodesnowincommonusecouldbebroken.

Researchgroupsbegantospringuparoundtheworld,andtheyquicklyfilledwithbrilliantyoungresearchers,manyofwhomhadadualresearchstrategyinwhichtheywouldattacktheproblemsinquantumfoundationswhilecontributingtothedevelopmentofquantumcomputing.Asaresult,anewlanguageforquantumphysicswasinventedthatwasbasedoninformationtheory,whichisabasictoolofcomputerscience.Thisnewlanguage,calledquantuminformationtheory,isa

hybridofcomputerscienceandquantumphysicsandiswelladaptedtothechallengesofbuildingquantumcomputers.Thishasledtoapowerfulsetoftoolsandconceptsthathaveprovedinvaluableatsharpeningourunderstandingofquantumphysics.Nonetheless,quantuminformationtheoryisapurelyoperationalapproachthatismostcomfortabledescribingnatureinthecontextofexperiments,inwhichsystemsarepreparedandthenmeasured.Natureoutsidethelaboratoryhardlymakesanappearance,andwhenitdoes,itisoften,notsurprisingly,analogizedtoaquantumcomputer.

Thecurrentrenaissanceofthefieldofquantumfoundations/quantuminformationisalmostallforthegood,notleastbecausemuchofthetheoreticalworkisanchoredinrealexperiments.Thedrivetowardquantumcomputationhasledtomanyspin-offswhichilluminatethefoundationalquestions,suchasquantumteleportation.Thisisatechnologybymeansofwhichthequantumstateofanatomcanbetransferredtoadistantatomwithoutbeingmeasured.Ifnotquiteuptosciencefiction’stransporters,thistechnologyisherenowandisalreadyplayingarole.Forexample,itisusedtomakeanewkindofcode,whichisunbreakable.

Thesedevelopmentshavealsodeepenedourappreciationforhowquantumtheoryisstructured.Forexample,anewtypeofapproach,initiatedbyLucienHardy,seekstheshortestandmostelegantsetofaxiomsfromwhichthemathematicalformalismofquantummechanicsmaybederived.Oftheseaxioms,thereareseveralthatareunremarkableandtellusthingsthataretrueforeverytheory;thenthereisoneintowhichallthestrangenessofthequantumworldispacked.

Atthesametime,thereislittleroom,inaclimatedominatedbyoperationalapproaches,forold-fashionedrealistsinsearchofacompletionofquantumtheorythatwillexplainwhathappensinindividualevents.Someofthoserealistsaremany-worlders,buttherepersistsasmallcommunityofBohmians.Ahandfuldeveloptheoriesofwave-functioncollapse.Thosewhotrytopushthesearchforrealitybeyondtheseestablishedapproachesareevenfewer.Mostofusinthisclasswereoriginallyspecialistsinotherfields,someatthehighestlevelofaccomplishment,suchasStephenAdlerandGerard’tHooft.Wefitimperfectlyintothelivelyfieldquantumfoundationshasbecome,especiallyasourconcernsandambitions—andthetheorieswedevelopto

realizethem—cannotbeexpressedintheoperationallanguagewhosemasteryisthesignofaprofessionalquantuminformationist.Still,wepersistinoursearchforarealistandcompletepictureofthequantumworld.

Ibelievethat,asexpressedbyLucienHardyinthequotethatopensthischapter,manyphysicistswouldpreferrealismtooperationalism,andwouldtakeaninterestinthediscoveryofarealistapproachtoquantumtheorythatovercametheweaknessesoftheexistingapproaches.If,duringthepresentperiod,operationalapproachesdominate,thisispartlyduetothelackofarealistalternativewhichhastheringoftruth.

Therestofthisbookisaboutthefutureofrealistapproachestoquantumphysics.Butbeforewedismissthenon-realistapproaches,let’sseeifthereisanythingtobelearnedfromtherecentfocusonthem.

OnelessonI’velearnedisthattherearemanydifferentwaystoexpresshowthequantumworlddiffersfromtheclassicalworldofNewtonianphysics.Ifyouarehappytakingananti-realistpointofview,therearearangeofoptions.YoucanadoptBohr’sradicaldenialthatscienceisanythingotherthananextensionofcommonlanguageweusetotelleachotherabouttheresultsofexperimentswedo.YoucanembraceanapproachcalledquantumBayesianism,accordingtowhichthewavefunctionisnomorethanasymbolicrepresentationofourbeliefs,andpredictionisafancywordforbetting.Anotheroptionistoembraceapurelyoperationalperspective,whichallowsonetospeakonlyofprocessesdelineatedbyandsandwichedbetweenpreparationsandmeasurements.

Inallthesethemeasurementproblemissidestepped,orrather,definedoutofexistence,becauseyoucannotevenposethepossibilitythatthequantumstatedescribestheobserversandtheirmeasuringinstruments.

Severalofthenewproposalshaveattheircoretheconceptthattheworldismadeofinformation.ThiscanbesummarizedinJohnWheeler’sslogan“itfrombit,”modernizedas“itfromqubit,”whereaqubitisaminimalunitofquantuminformation,i.e.,aquantumbinarychoice,asinourstoryaboutpetpreference.Inpracticalterms,thisprogramimaginesthatallphysicalquantitiesarereducibletoafinitenumberofquantumyes/noquestions,andalsothatevolutionintimeunderRule1canbeunderstoodasprocessingthisquantuminformationasaquantum

computerwould.Thismeansthatthechangeintimecanbeexpressedastheactionofasequenceoflogicaloperationsappliedtooneortwoqubitsatatime.

JohnWheelerputitlikethis:

Itfrombitsymbolizestheideathateveryitemofthephysicalworldhasatbottom—ataverydeepbottom,inmostinstances—animmaterialsourceandexplanation;thatwhatwecallrealityarisesinthelastanalysisfromtheposingofyes-noquestionsandtheregisteringofequipment-evokedresponses;inshort,thatallthingsphysicalareinformation-theoreticinoriginandthisisaparticipatoryuniverse.3

Thefirsttimeyouhearthiskindofviewexpressed,youmaynotbesurethespeakermeansit.Buthedoes.Hereisanother,brieferquote:“Physicsgivesrisetoobserver-participancy;observer-participancygivesrisetoinformation;informationgivesrisetophysics.”4

WhenWheelerspeaksofaparticipatoryuniverse,hemeansthattheuniverseisbroughtintoexistencebyourobservingorperceivingit.Yes,youmightreply,butbeforewecanperceiveorobserveanythingwehavetobebroughtintoexistencewithinandbytheuniverse.Yes,saysJohn.Both.Isthereaproblem?

Doesthisyieldanyinsight?Somesystemswithafinitenumberofpossibleoutcomescanberepresentedthisway,anddoingsodoesilluminatethephysics:forexample,theimportanceofentanglementinquantumphysicscanbebroughtintotheforeground.Butothersystemswhichhaveaninfinitenumberofphysicalvariables,suchastheelectromagneticfield,donotfitaseasilywithinthisprogram.Nonetheless,thisquantuminformationapproachtoquantumfoundationshashadagoodinfluenceondiversefieldsofphysics,fromhard-coresolid-statephysicstospeculationsonstringtheoryandquantumblackholes.

However,weshouldbecarefultodistinguishseveraldifferentideasabouttherelationshipbetweenphysicsandinformation,someofwhichareusefulbutalsotriviallytrue;othersofwhichareradicalandwouldneed,inmyview,morejustificationthanthey’vebeengiven.

Let’sstartbydefininginformation.OneusefuldefinitionwasgivenbyClaudeShannon,whomaybeconsideredthefounderofinformationtheory.Hisdefinitionwassetintheframeworkofcommunication,andcontemplatesachannelwhichcarriesamessagefromasendertoareceiver.These,itisassumed,sharealanguage,bymeansofwhichtheygivemeaningtoasequenceofsymbols.Theamountofinformationinthemessageisdefinedtobethenumberofanswerstoasetofyes/noquestionsthatthereceiverlearnsfromthesenderbyunderstandingwhatthemessagesays.

Putthisway,fewphysicalsystemsare,orcanbeconstruedas,channelsofinformationbetweensendersandreceiverswhosharealanguage.Theuniverseasawholeisnotsuchachannelofinformation.WhatispowerfulaboutShannon’sideaisthatameasureofhowmuchinformationistransmittedcanbeseparatedfromthesemanticcontent,i.e.,fromwhatthemessagemeans.Thesenderandreceivershareasemanticsthatgivesmeaningtothemessage,butyoudon’thavetosharethatknowledgetomeasurethequantityofinformationcarried.Still,withoutthesharedsemanticsthemessagewouldnotcarryinformation.Onewaytoseethisisthattomeasurehowmuchinformationamessagecarries,youneedsomeinformationaboutthelanguage,suchastherelativefrequencieswithwhichdifferentletters,words,orphrasesoccurinthelinguisticcommunityofthosewhospeakthatlanguage.Thisinformationaboutcontextisnotgoingtobecodedintoeverymessage.Ifyoudon’tspecifythelanguage,theShannoninformationisnotdefined.Thismeans,inparticular,thatthemessagehastobeinalanguagethatthesenderandreceivershare.Apatternofirregularsymbolscarriesnoinformation.So,totheextentthatShannon’smeasureofinformationdependsonthelanguageandotheraspectsofthecontextwhicharesharedbythesenderandreceiverandnotcodedintothemessage,itisnotpurelyaphysicalquantity.

Oneofthestubbornproblemsinthephilosophyoflanguageistounderstandhowspeakershaveintentionsandconveymeaning.Thatthisisahardproblemdoesnotmeanthatintentionsandmeaningsarenotpartoftheworld.Buttheyareaspectsoftheworldthataredependentfortheirexistenceontheexistenceofminds.Shannoninformationisameasureofwhatgoesoninthisworldofmeaningsandintentions.Itiswelldefinedevenifwedon’thaveagoodunderstandingofhowmeaning

andintentionfitintothenaturalworld,butitisnonethelessapartofthatworld.

Letmegiveanexampletomakethisdistinctionclear.Iheardropsofwaterfallingintermittentlyfromaleakydrainpipeafterasummerrain.Thepatternofthedripsseemsirregular,butitcarriesnomessageformeoranyoneelse.Thereisnosender,andIamnoreceiver;hencenoinformation,inShannon’ssense,iscontainedinthedrips.Ontheotherhand,someonecoulduseMorsecodetosendmeamessageviaasequenceofshortandlongpausesbetweendrips.Thepatternsbetweenthetwocaseswoulddifferinawaythatreflectsthepresenceorabsenceofanintentiontoconveymeaning.Theintentmatters:informationinthissenserequiresbeingswiththeintentionofconveyingmeaning.Forarealist,whowantstoknowwhattheworldisbeyondwhatpeopleknoworunderstand,thisisnotausefulideatoapplytotheatomicworld.*

AlessprecisedefinitionofinformationwasgivenbyGregoryBateson,anEnglishanthropologist,whocalledit“adifferencethatmakesadifference.”Thisideaissometimesexpressedinsteadas“adistinctionwhichmakesadifference.”Thisisdirectlyapplicabletophysics,wherewemighttranslateitas“Ifdifferentvaluesofaphysicalobservableleadtomeasurablydifferentfuturesofaphysicalsystem,thatobservablecanbeconsideredtoconstituteinformation.”Putthisway,almosteveryphysicalobservablepotentiallyconveysinformation.Thisdefinitionwouldimplythat“information”ispresenteverytimethevaluesoftwophysicalvariablesarecorrelated.Butthereisnothingprofoundaboutthis,unlessitistheappreciationoftheinterdependenceofthedifferentcomponentsofthephysicalworld.Andwealreadyhavemeasuresofcorrelation.Wecanrenamethese“information,”butachangeofnamesthatweakensthespecificityofanideaismorelikelytoresultinconfusionthanitistobringaboutrevolutioninourconceptionoftheworld.

ComputersprocessinformationinShannon’ssense.Theytakeaninputsignalfromasenderandapplytoitanalgorithm,whichtransformsitintoanoutputsignaltobereadbyareceiver.Suchcontextsareveryspecial.Thechoiceofanalgorithmtobeembodiedisacrucialpartofthedefinitionofacomputation.Mostphysicalsystemsarenotcomputers,andtheprocessbywhichtheinitialdataatonetimeevolvetothedataatalatertimecannotalwaysbeexplainedintermsoftheapplicationofanalgorithmorasequenceoflogicaloperations.

Someauthorsappeartoconfuseandconflatethetwodefinitionsofinformation,whichtemptsthemintowantingtodescribenatureasacomputerandtherelationbetweenstatesoftheworldatdifferenttimesasacomputation.Iamnotconvincedthatsucharadicalhypothesisisjustified.

Thisisnottosaythatsomephysicalsystemscannotbemodeledtosomedegreeofapproximationbyacomputation,whichisagaintriviallytrue.Youcandefineapproximationstothemainequationsofphysics,suchasthoseofgeneralrelativityorquantummechanics,whichcanbecodedasalgorithms,whicharethenrunonadigitalcomputer.Thisisoftenaveryusefulwaytogetapproximatesolutionstotheequations.Butthereisalwaysanapproximationinvolved.

Thesoundasymphonyorchestramakescanbecapturedbyadigitization,toanapproximatedegree,butthisalwaysinvolvesanapproximation,whichtruncatestherangeoffrequencies.Thefullexperienceoflisteningtotheorchestraliveisneverfullyconveyed,whichiswhythereisstillanaudienceforperformanceaswellasamarketforvinyl,purelyanalogrecordings.Itisthesameforphysics:adigitizationofEinstein’sequationscanbeveryuseful,butitnevercapturesallthattheequationsdo.

Evenifphysicsisnotingeneralcomprehensibleasinformationprocessing,itmaybeassertedthatthequantumstaterepresentsnotthephysicalsystem,buttheinformationwehaveaboutthesystem.Rule2certainlymakesitseemtobethecase,becausethewavefunctionchangesabruptlyjustwhenwegainnewinformationaboutthesystem.Butifthewavefunctionrepresentstheinformationwehaveaboutasystem,thentheprobabilitiesquantummechanicspredictsmustbeseenassubjective,bettingprobabilities.ThisviewpointcanbedevelopedbyunderstandingRule2asanupdaterulebywhichoursubjectiveprobabilitiesforfutureexperimentschangeasameasurementismade.ThisiswhatiscalledquantumBayesianism.5

—ARATHERELEGANTAPPROACH,whichalsoseesthequantumstateasconveyinginformationthatonesystemhasaboutanother,iscalledrelationalquantumtheory.Accordingtothisview,whichsitsbetweenoperationalismandaformofrealism,quantumstatesareassociatedwith

splitsoftheuniverseintotwoparts,observerandobserved,andrepresentwhattheformercanknowofthelatter.Thisideahaditsrootsinquantumgravity,andaroseoutofconversationsbetweenLouisCrane,CarloRovelli,andmeintheearly1990s.

Ourinspirationwasaveryelegantbodyofmathematicaldescriptionsofverysimplifiedcosmologies,whichCraneandothermathematicianshaddeveloped,calledtopologicalfieldtheories.Inthesetheoriesthereisnoquantumdescriptionofawholeuniverse.Thereisnoquantumstatedescribingtheuniverseasawhole.Instead,thereisaquantumstateforeachwayofdividingtheuniverseintotwosubsystems.Thesecanbethoughtofascarryingtheinformationthatanobserverononesideofthedividecouldhaveaboutthequantumsystemontheotherside.

ThisremindedusofBohr’sinsistencethatquantummechanicsrequiresasplitoftheworldintotwoparts,oneclassical,theotherquantum,andthatanysplitwilldo.ThemodelsCraneandothermathematicianshadstudiedtookBohr’sphilosophyastepfurther,forthereweretwoquantumstatesforeveryboundary—oneforeachside.Thisisbecausetherearetwowaystoreadeachsplit.IfAlicelivesononesideandBoblivesontheother,thenAlicewillseeherselfasaclassicalobserver,measuringaquantumBob,butBobwillseethingstheotherwayaround.

Themodelswereverysimple,sothattherewasonlyonequestionthatcouldbeasked,whichwas:Howsimilarwerethetwoviews?WhatistheprobabilitythatAlice’squantumdescriptionofBobwillbethesameasBob’squantumdescriptionofAlice?Themathematicianssetuptheirtheoriessothattheanswerwasthesamehowevertheuniversewassplit.Inthatcase,theprobabilityofoneside’sviewresemblingtheotherside’sviewmeasuressomethinguniversal,whichwouldcharacterizehowthatuniverseisconnected,i.e.,whatmathematicianscalltheuniverse’stopology.Thisiswhytheywerecalledtopologicalfieldtheories.

CranebroughtthesemodeluniversestoRovelli’sandmyattentionbecausehesawthatthemathematicalstructuresinvolvedcouldbeextendedtoencompassloopquantumgravity.Heturnedouttoberightaboutthat,butthatisanotherstory.Cranealsoproposedthatthenewmathematicsofferedawaytoextendquantummechanicstotheuniverseasawhole.Hewasrightaboutthattoo,andtheresultwasrelationalquantumtheory.

Wewereeachinspiredtoapplythisideatoquantumtheoryingeneral,andweeachpublishedaversionofit.6Rovelli’sformulationwasthemostgeneral,andhasbecomethebestknown,soI’lldescribehisformulationoftheidea.

Bohrtaughtthatquantumphysicistsmustspeakalwaysoftwoworlds.Weobserversliveintheclassicalworld,buttheatomswestudyliveinaquantumworld.Thetwoworldssatisfydifferentrules.Inparticular,objectsinthequantumworldcanexistinsuperpositions,butobservablepropertiesofthingsintheclassicalworldalwaystakesharpvalues,andsocannotbesuperposed.Bohr’spointisthatbothworldsarenecessaryforscience.

Theinstrumentsweusetomanipulateandmeasuretheatomsliveat,andinasensedefine,aboundarybetweenthemandus.Bohremphasizedthattheplacementofthisboundaryisarbitrary,andcouldbedrawndifferentlyfordifferentpurposes,solongasitdividestheworldintotwodomains.

LetusthinkoftheSchrödinger’scatexperiment.Onewaytodrawtheboundaryistoconsidertheatomandphotonasthequantumsystem,keepingtheGeigercounterandcatintheclassicalworld.Inthispicturetheatommayexistinasuperposition,buttheGeigercounterwillalwaysshowadefinitestate—eitherYES,itsawaphoton,orNO,itdidnot.Butwecanredrawtheboundary,includingthedetectorinthequantumworld.Inthispicture,thecatisalwayseitherdeadoralive,buttheGeigercountermaybeinanentangledsuperpositionwiththeatom.Or,andthiswasSchrödinger’spoint,youcaninsteaddrawtheboundarytocoincidewiththewallsofthebox,sothecatisnowalsopartofthequantumsystemandcanexistinentangledsuperpositionswiththeatomandGeigercounter.Theclassicalworldthenincludesafriendofours,Sarah,whoopenstheboxandlooksin.Sarah,wepresume,ismacroscopicandclassicalandsocanbetreatedasalwaysbeinginadefinitestate.Fromherviewpoint,Sarahexperiencesherselftobeontheclassicalsideoftheboundary,so,accordingtoher,shealwaysseesthecattobeeitheraliveordead.

EugeneWignersuggestedwetakethisfableonestepfurtherandconsiderthatthequantumsystemincludesalsoourfriendSarah,togetherwiththebox,thecat,andthebox’sothercontents.*Iremainoutsidetheboundary,soIseeSarahbecomepartofasuperpositionof

entangledstates.InonepartofthesuperpositionthecatisaliveandSarahseesittobealive,whileinanotherpartofthesuperpositionthecatisdeadandsheseesittobedead.

Thuswehavefivedifferentwaystodividetheworldintoquantumandclassical,wherebyquantumwemeanitcouldbeinasuperposition,whileclassicalmeansthatphysicalquantitiesalwayshavedefinitevalues.Thesedifferentdescriptionsappeartodisagreewitheachother.WeseeSarahtobeinasuperpositionwhereasshealwaysseesherselftobeinadefinitestate.

Rovelli’sproposalisthattheseareallequallycorrect,partialdescriptionsoftheworld.Allarepartofthetruth.Eachgivesavaliddescriptionofapartoftheworld,definedbyaboundary.IsSarahtrulyinasuperposition,ordoesshedefinitelyseeandhearalivecat?Rovelliwouldliketonothavetochoosebetweenthese.Heinsiststhatadescriptionofphysicaleventsandprocessesisalwaysmadewithrespecttosomeparticularwayofdrawingtheboundarybetweenquantumandclassical.Hepositsthatallwaysofdrawingtheboundaryareequallyvalidandallarepartofthetotaldescription.

Simplyput,Rovelliwouldsaythatitistrue,fromSarah’spointofview,thatthecatisalive,anditisalsotrue,frommypointofview,thatSarahisentangledinasuperpositionof“seeingdeadcat”and“seeinglivecat.”

Isthereanytruththatisnotqualifiedbyapointofview?MyunderstandingisthatRovelliwouldsayno.InthestoryasI’vetoldit,SarahandIagreethatsheopenedtheboxandinspectedthecat,evenifwedon’tagreeontheoutcome.ButitcouldhavebeenthecasethatSarah’sdecisiontoopentheboxdependedontheoutcomeofaquantumeventsuchasthedecayofanunstableatom,inwhichcaseImaydescribeSarahasbeinginasuperpositionofhavinglookedintheboxandnot.ButSarahwillexperienceoneortheother.

Noticethatthereisaweakkindofconsistency,inthatmydescriptionofSarahdoesnotprecludehers.Noticealso—andthisiscentral—thateverywayofdrawingaboundarysplitstheworldintotwoincompleteparts.Thereisnoviewoftheuniverseasawhole,asiffromoutsideofit.Thereisnoquantumstateoftheuniverseasawhole.

Ifrelationalquantumtheoryhadaslogan,itwouldbe“Manypartialviewpointsdefineasingleuniverse.”

Thisproposalcanbeseenthroughvariouslenses.Apragmaticoperationalistseeseachwaytodividetheworldintwowithaboundaryasdefiningasystemthatcanbetreatedwithquantummechanics.Eachchoiceresultsinadescription,whichcontainsalltheinformationthatanobserverontheclassicalpartoftheboundarycanhaveaboutthequantumsystemontheothersideoftheboundary.Forsuchanoperationalist,thecollectionofquantumstatescontainstheinformationthatanobservercanhaveateachlevel,definedbyaboundarythatsetsherapart.Eachobserverusesaquantumstatetocodetheinformationtheyhaveaboutthesystemontheothersideoftheirboundary;thesedifferentstatesaredifferentbecausetheyaredescriptionsofdifferentsubsystems.

Seenthroughthisoperationallens,relationalquantummechanicshassomethingincommonwithEverett’soriginalrelativestateinterpretation.Eachdescribestheworldintermsofcontingentstatementsthatcodecorrelationsbetweendifferentsubsystems,whichareestablishedwhentheyinteract.

ButthisisnotthewaythatRovelliseesrelationalquantummechanics.Rovelliwantstocallhisviewrealism,butitmeanssomethingdifferentfromnaiverealism,asIhaveusedthetermsofar.Forhim,realityconsistsofthesequenceofeventsbymeansofwhichasystemononesideofaboundarymaygaininformationaboutthepartoftheworldontheotherside.Thus,wecansaythatRovelliisarealistaboutcausation.Thisrealityisdependentonachoiceofboundary,becausewhatisadefiniteevent—somethingthatdefinitelyhappenedforoneobserver—couldbepartofasuperpositionforanother.Thus,Rovelli’srealismisdifferentfromnaiverealism,accordingtowhichwhatisrealconsistsofeventsthatallobserverswilluniversallyagreetookplace.

Rovellideniesthatthatkindofnaiverealismispossibleinourquantumworld,soheproposesweadopthisradicallydifferentversionofrealism,accordingtowhichwhatisrealisalwaysdefinedrelativetoasplitoftheworldthatdefinesanobserver.RovelliusesverydifferentwordsthanBohr,andachievesaformulationwhichismoreprecise,butthetwoemployasimilarlogic,whichdeniesthepossibilityofnaiverealismaboutquantumsystems.

—

ANOTHERAPPROACHWHICHDENIESthatnaiverealismispossibleisbasedonelevatingthecategoryofthepossible—thingsthatmightbetrue—totheworldofthereal.Naively,whenwesaythatsomethingispossible,suchasthatmyson’slizardmightbecomepregnantinthenextyear,wemeanitisamongthethingsthatmighthappen.Whensomethingpossiblehappensitbecomespartofthereal;buttillthenitisnotreal.

Languageandlogicreflecttheverydifferentstatusofthepossible,anddistinguishitfromthereal.Thelawoftheexcludedmiddlesaysthatsomethingrealcannotsimultaneouslyhaveapropertyandnothaveit.Ourneighbor’sbunnyrabbitcannotbebothgrayandnotgray.Butpossiblestatesofaffairshavenosuchconstraint.Therabbitourfriendwillbuyatthepetstorenextweekmightpossiblybeblackanditalsomightpossiblybewhite.

Inreallifetheactualandthepossiblehaveanasymmetricrelation.Therealexistenceofourneighbor’sdaughtermakesarabbitapossiblefuturepetfortheirfamily.Sowhatispossibleisinfluencedbywhatisreal.Butknowledgeofthepossible,whilehelpful,isnotstrictlyspeakingnecessaryforworkingoutwhatwillbereal;totheextentthatthelawsofNewtonianphysicsaredeterministic,allyouneedtopredicttheactualfutureisacompletedescriptionoftheactualpresent.

—SEVERALWRITERS,beginningwithHeisenbergandincludingmyteacherAbnerShimony,haveproposedthattheworldofthepossiblehastobeincludedaspartofreality—becauseinquantumphysicsthepossibleinfluencesthefutureoftheactual.ThisviewhasbeenrecentlydevelopedbymyfriendStuartKauffman,incollaborationwithRuthKastnerandMichaelEpperson.7

Thereisnowaytodescribethisviewthatdoesn’tcausesometensionwithordinarylanguageusage,butkeepanopenmindandI’llaimtobeclear.Westartbystatingthattherearetwowaysforacircumstancetobereal.Itcanbeactual,whichmeansthatitispartoftheworldinthesamewaythataNewtonianparticlehasadefiniteposition.Butsomethingrealcanalsobe“possible”or“potential”;thisisthestatusweassigntopropertiesthataresuperposedinthewavefunction,suchasaleftisthavingequalcatanddogpreference,oraparticlewhichcouldgothrough

theleftslitortherightslit,orSchrödinger’scatbeingbothaliveanddead.

Thingsthatarerealbutpossibledon’tobeythelawoftheexcludedmiddle,buttheyaretobeconsideredpartoftherealbecausetheycaninfluencetheactual.Thisis,accordingtothisperspective,whatisdifferentandnewaboutquantumphysics.AccordingtoKauffmanandhiscoauthors,experimentsareprocessesthatconvertpotentialitiestoactualities.Thus,Schrödinger’scatispotentiallyaliveandpotentiallydead,notinthesenseofsomethingthatisoneortheother,butaboutwhichweareignorant,andnotinthesenseofsomeundeterminedstateofaffairs,butbecauseitsactualrealityconsistsofthispotentialityforoneoranothertoberealizedbyanexperiment.

Thefactthatexperimentplaysadistinctroleinconvertingthepossibletotheactual,withprobabilitiesgivenbytheBornrule,isenoughtotellusthatthisisnotanaivelyrealistperspective,i.e.,adescriptionoftheworldasitwouldbeinourabsence,inwhichexperimentcannotplayanyrole.Butitisadirection,perhaps,tobedeveloped,ifrealismfails.

Hereisawaywemightdeveloptheviewthatthepossibleispartofthereal.Bringintime,andletustaketheviewthatthepresentmomentandthefloworpassageofmomentsarerealandfundamental.*PartofwhatImeanbythisisthatthereisanobjectivedistinctionbetweenthepast,present,andfuture.Insuchaview,thepresentisreal.Thepresentconsistsofeventswhichhavehappened,butwhichhaveyettogiverisetothefutureeventsthatwillbetheirreplacements.

Thepastconsistsofthoseeventswhichwereoncepresentandreal.Theynolongerexist,althoughtheirpropertiescanbecapturedandrememberedinpresentlyexistingstructures.

Thefutureisnotreal.Moreover,thefutureisslightlyopen,inthesensethatrarenoveleventswithnovelpropertiesmayhappeneveryonceinawhile.(Seemyprincipleofprecedencebelow.)Butifforamomentweignorethatpossibility,thentheredoesexistinthepresentafinitesetofpossiblenextsteps,whicharepossiblenexteventsandtheirproperties.

Giventhepresentstateoftheworld,noteverythingcanhappeninthenexttimestep.ThoseeventsthatmightbenextKauffmancallstheadjacentpossible.Thepossiblenear-futureeventsthatmakeupthe

adjacentpossiblearenotyetreal,buttheydefineandconstrainwhatmightbereal.

TheadjacentpossibleofSchrödinger’scatincludesalivecatandadeadcat.Itdoesnotincludeabrontosaurusoranaliendog.Sotheelementsoftheadjacentpossiblehaveproperties,evenifthelawoftheexcludedmiddledoesnotapplytothem.Asobjectswithproperties,therearefactsofthematteraboutthem.Thisisthesenseinwhichwemaysaythatasmallpartofthepossiblemaybeconsideredreal.

Thisstartstomakesense.Noteverythingthatispossibleisreal.Butasmallpartofthepossiblehasdefinitepropertiesthatjustifyassigningittoanewcategoryoftherealandpossible.

—THEREAREALSORECENTDEVELOPMENTSonthemagicalrealismside.Backinthe1990sJulianBarbourproposedaquantumtheoryofcosmologythathasmanymomentsratherthanmanyworlds.8ThishasbeenrevivedinarecentproposalbyHenriqueGomes.Aswearenotconcernedwithtechnicaldetails,I’lldescribetheoriginalapproachofBarbour,butmostofwhatI’llhavetosayappliestoGomes’sversion9,aswellasmorerecentworkofBarbourandhiscollaborators.

Amoment,forthem,isaconfigurationoftheuniverseasawhole.Theseconfigurations,accordingtoBarbourandGomes,arerelationalconfigurations,whichcodealltherelationsthatcanbecapturedinamoment,suchasrelativedistancesandrelativesizes.

Weseemtoexperiencetimepassingasasmoothflowofmoments.Barbourinsiststhatthepassageoftimeisanillusionandthatrealityconsistsofnothingbutavastpileofmoments,eachaconfigurationofthewholeuniverse.Younowareexperiencingamoment.Nowyouareexperiencingadifferentmoment.AccordingtoBarbour,bothmomentsexisteternallyandtimelessly,inthepileofmoments.Realityisnothingbutthisfrozencollectionofmomentsoutsidetime.Eachexperienceofamomentalsoexiststimelessly—aspartofitsmoment.Thefleetingaspectofamomentisinrealityjustanaspectofthemoment,afeatureithaseternally.

Themomentsallcoexist,andeachisaconfigurationofthewholeuniverse.Butthereisanimportantwaytheycandiffer.Thepilecanhave

morethanonecopyofaconfiguration,andthenumberofcopiesmayvaryfrommanycopiestononeatall.

Barbourhypothesizesthatweareequallylikelytobeexperiencinganyofthemomentsinthepile.Butsincesomearemorecommonthanothers,thereisstructuretoourexperience,aswearemostlikelytoexperiencethemorecommonmoments.

Thecollectionofmomentsisstructuredsothatthemostcommonmomentsarethoseconfigurationsthat,tosomedegreeofapproximation,canbestrungtogetherasiftheywereahistoryoftheuniversegeneratedbyalaw.Thisgivesustheillusionthatlawsareacting,buttherearenolawsgeneratinghistories,andindeednohistory.Realityisjustthevastcollectionofmoments.

Barbourhypothesizesthatthemostcommonmomentscontainstructureswhichspeaktousofothermoments.Abook,evenwhilefrozenforeverinamoment,maytellstoriesthatareonlycomprehensibleasasequenceofeventsthatplayedoutovertime.Abookhasapublicationdate,whichreferencesahappyevent(atleastforitsauthor)sometimeinthepast.Anditwasbroughtintoexistencebyaprintingcompany,apublishingcompany,andapapermill,eachofwhichhasahistory,whichevokesmorestories.

Barbourcallsobjectslikebooks,whichcontaineternallyfrozen,momentarystructuresthatarepointerstoothermoments,timecapsules.Anythingthatis,orcontains,arecord,suchasaDVDoravideofile,isatimecapsule.Soitcanbeanybuiltstructureormanufacturedobject.Indeed,itcanbeanylivingthing.

Formostofus,thefactthatthenaturalworldischock-fulloftimecapsulesisevidencethattimeisrealandfundamental.Eventsareorderedintimebecausepasteventscausepresentevents.ButaccordingtoBarbour,eventheimpressionwehaveoflivingwithinaflowofmomentsisanillusion.Allthememories,records,andrelicswehavethatgivetheimpressionthattherewasapastare,infact,aspectsofapresentmoment.Eachmomentliveseternallyinthepileofmoments.

Anunorderedpileofmoments,whichisallthatmakesupaBarbourianuniverse,mighteasilycontainfewmomentswithtimecapsules.Whythenisalmosteverymomentofouruniversefullofthem?

Toelucidateourworld,Barbourhastoexplainwhatdetermineswhichconfigurationsarecommon,havingmanycopiesinthepile,andwhich

arelesscommon,oraltogetherabsent.Thisisdictatedbyanequation,whichistheonlylawthatactstostructurethepile.Itdoessobychoosingwhichconfigurationsarerepresentedinthepile,andbyhowmanycopies.ThisisaversionofSchrödinger’sequation,butonewithnoexplicitreferencetotime.ItiscalledtheWheeler-DeWittequation;wecancallitRule0.Thisequationchoosesassolutionspilesofmomentswhicharepopulatedbythosethatcanbestrungtogethertopermittheillusionofhistorytoemerge.

Ifthisisright,thenthepassageoftimeisanillusion,whichisduetoapresentmomentcontainingtheexperienceofmemoriesofthepast.Causalityisalsoanillusion.

These“manymoments”theoriesarerealist,inthattheytakeastandonwhatisreal,whichisthetimelesscollectionofmoments.Butthesetheoriesarebeyondnaiverealisminthattheypositarealworldenormouslydifferentfromthetime-boundworldweexperience,inwhichweperceiveasuccessionofmoments,oneatatime.

ThelessonIdrawfromthesetheoriesisthattoextendquantummechanicstoatheoryofthewholeuniverse,wehavetochoosebetweenspaceandtime.Onlyonecanbefundamental.Ifweinsistonbeingrealistsaboutspace—asBarbourandGomesdo—thentimeandcausationareillusions,emergentonlyatthelevelofacoarseapproximationtothetruetimelessdescription.Orwecanchoosetoberealistsabouttimeandcausation.Then,likeRovelli,wehavetobelievethatspaceisanillusion.

Thereismuchmorethatcouldbesaidabouttheserecentnon-realistandmagical-realistperspectives.Butthebottomlineisthatifyourinterestispragmatic,andyouwanttousequantumtheorytounderstandquestionsotherthanthosearisingfromquantumfoundations,anyofthesewillservetoframeyourcalculationsandtheexplanationsyoudrawfromthem.Butifyouwanttosolvethemeasurementprobleminawaythatgivesadetaileddescriptionofwhatgoesoninanindividualphysicalprocess,nothingbutarealistdescriptionwilldo.

T

THIRTEEN

Lessons

hemainmessageofthisbookisthathoweverweirdthequantumworldmaybe,itneednotthreatenanyone’sbeliefincommonsenserealism.Itispossibletobearealistwhilelivinginthequantum

universe.However,simplyaffirmingrealismisnotenough.Arealistwantsto

knowthetrueexplanationforhowtheworldworks.Therewouldbenosenseinbelievingthattheworldhasadetailedexplanation,andnotbeinginterestedinwhatthatexplanationis.Thusthenextquestiontoaskiswhetheranyoftheavailablerealistversionsofquantumphysicsarecompellingastrueexplanationsoftheworld.Thatis,arewedone,ordowehavemoreworkahead?Unfortunately,Ibelievetheansweristhat,sofar,noneofthewell-developedoptionsareconvincing.Alltherealistapproachesthathavesofarbeenstudiedhaveseriousdrawbacks.Toexplainwhy,letmereviewtheavailableoptions,withafocusonthestrengthsandweaknessesofeach.

PILOTWAVETHEORY

Pilotwavetheorycompletesquantummechanicsbyprovidingadditionaldegreesoffreedomwhich,togetherwiththewavefunction,fullyspecifywhatisgoingoninanindividualphysicalsystem.Thesearetheparticletrajectories.Wecalledthesehiddenvariables,butthatisperhapsnotthebestwaytotalk,astheparticlesare,afterall,whatisobserved.Abetterwaytodescribetheoptionsistousetheterm“beables,”assuggestedbyJohnBell.Realistswantatheorytotakeastandaboutwhatreallyexists;

thesearethebeables.Inpilotwavetheorythewavesandparticlesarebothbeables.

Pilotwavetheorysolvesthemeasurementproblem,becausetheparticlealwaysexistsanditisalwayssomewhere.Whenanexperimentaldevicelooksfortheparticle,itfindsitwhereitis.

Theequationsofpilotwavetheoryaredeterministicandreversible,whicharguesforthecompletenessofthetheory.Probabilityisexplainedbyourignoranceoftheinitialpositionsoftheparticles,justlikeinotherapplicationsofprobabilitytophysics.TheBornrule,therelationshipbetweenprobabilityandthesquareofthewavefunction,isexplainedbythedemonstrationthatthisistheonlystableprobabilitydistribution,andallothersevolvetoit.

Inaddition,pilotwavetheoryiscompleteandunambiguous.Someoftheothermodificationsofquantummechanicscomewithnewfreeparameters,whichmaybeadjustedtohidevariousembarrassmentsandprotectthetheoryfromexperimentaldisproof.Pilotwavetheoryhasnoadditionalparametersandallowsnochoicestobemade.Thisisaveryimportantpointinitsfavor.

Becauseitgivesaclean,unambiguous,andexplicitdescriptionofthequantumbeables,pilotwavetheorycontinuestobeapopularoptionwithinthesmallcommunityofquantumrealists.Partlythisisbecausethereremainsalottodotodeveloptheapplicationsofthetheory.Itisonethingtodemonstrategenerallythatthepredictionsofpilotwavetheoryandconventionalquantummechanicswilloftenagree,butitisanothertoseehowthisworksoutindetail.Physicistsliketohavewell-definedproblemstoworkout,andpilotwavetheoryoffersnoshortageofthese.

Therearechallengesforpilotwavetheory.Ifitistoreplacequantummechanics,itmustdosoinallthecontextsinwhichtheusualtheoryworks.Thisincludesrelativisticquantumfieldtheory,whichisthebasisofthestandardmodelofparticlephysics.Therehasbeengoodworkdoneonthis,butimportantquestionsremainunresolved.Therehavealsobeenveryinterestingexplorationsofpilotwavetheoryappliedtoquantumgravityandcosmology,butthesearefarfromdefinitive.

Butthemostimportantaimofresearchinpilotwavetheorymustbetodiscoverandopenupdomainswhereexperimentswilldistinguishthe

newtheoryfromtheolderone.HerethereisexcitingworkbeingdoneonthecosmologicalscalebyAntonyValentiniandothers.

Atthesametime,thereareseveralreasonspilotwavetheoryisnotentirelyconvincingasatruetheoryofnature.Oneistheemptyghostbranches,whicharepartsofthewavefunctionwhichhaveflowedfar(intheconfigurationspace)fromwheretheparticleisandsolikelywillneveragainplayaroleinguidingtheparticle.TheseproliferateasaconsequenceofRule1,butplaynoroleinexplaininganythingwe’veactuallyobservedinnature.Becausethewavefunctionnevercollapses,wearestuckwithaworldfullofghostbranches.Thereisonedistinguishedbranch,whichistheoneguidingtheparticle,whichwemaycalltheoccupiedbranch.Nonetheless,theunoccupiedghostbranchesarealsoreal.Thewavefunctionofwhichtheyarebranchesisabeable.

TheghostbranchesofpilotwavetheoryarethesameasthebranchesintheManyWorldsInterpretation.InbothcasestheyareaconsequenceofhavingonlyRule1.UnliketheManyWorldsInterpretation,pilotwavetheoryrequiresnoexoticontologyintermsofmanyuniverses,orasplittingofobservers,becausethereisalwaysasingleoccupiedbranchwheretheparticleresides.Sothereisnoproblemofprinciple,noristhereaproblemofdefiningwhatwemeanbyprobabilities.Butifonefindsitineleganttohaveeverypossiblehistoryoftheworldrepresentedasanactuality,thatsiniscommontoManyWorldsandpilotwavetheory.

AperceptivereadermightbetroubledbythissimilaritytotheManyWorldsInterpretation.AssumingthatitsproponentsdosucceedingivingEverettianquantummechanicsasensiblephysicalinterpretationviadecoherence,subjectiveprobabilities,andtheworks,couldn’tweapplyexactlythesameinterpretationtothebranchingwavefunctionofpilotwavetheory—andsimplyignoretheparticles?Theanswerisyes,youcanignoretheparticles,andthenyouaresquarelybackinEverett’smultiverse.Thisbringsupahidden,perhapsunconsciousassumptionmadebytheadherentsofpilotwavetheory,whichisthattherealitythatweobserversperceiveandmeasureiscomposedofmatterconstructedfromtheparticlesofpilotwavetheory.

Justbecauseboththeparticlesandthewavesarebeablesinpilotwavetheorydoesnotmakethemequivalent.Tomakesenseofpilotwavetheorywemustprivilegetheparticlesandpostulatethattheworldwe

perceiveconsistsoftheparticles.Thewavesarethereinthebackground,buttheirroleistoguidetheparticles—theyarenotperceiveddirectly,andonlyaffectourobservationsthroughtheirroleasguides.

Fromthepointofviewofeitherexplainingorpredictingtheworld,theghostbranchesplaylittleroleinpilotwavetheory.Theprobabilitythataghostbranchofamacroscopicsystemwillinterferewiththeoccupiedbranch,changingthefutureofthatsystem,istrulytiny.Itistemptingthentointroducesomemechanismtoprunebacktheghostbranches.Thiswouldbeacombinationofpilotwavetheoryandspontaneouscollapsemodels.Iamnotawareofanyworkinthisdirection,butitseemsaninterestingavenuetoexplore.

Thisbringsupanotherissuewithpilotwavetheory,whichisthatthereisanasymmetryofcauses.Thewavefunctionguidestheparticle,buttheparticlehasnoinfluencebackonthewavefunction.Thisisunlikethewaycausesworkinordinaryphysics.Innature,andsoinmostofphysics,causesareusuallyreciprocal.Everythingyoupushonpushesback.ThisisduetoNewton’sthirdlaw,whichstatesthateveryactionismetbyanequalandoppositereaction.Itisthenverystrangethattheparticlecannotinfluencethewavefunction.Thelackofareciprocaleffectstronglysuggestssomethingismissing.

Eveniftheghostbranchescanoftenbeignored,theycan’talwaysbe.Somecleverexperimentshavebeendevisedwhichshowthatthebranchofthewavefunctionwhichtheparticledoesn’ttakecaninfluencethefutureasmuchastheoccupiedbranches.1Thesetrickycasesinvolvetwoquantumparticleswhichinteractwitheachother,suchasanatomandaphoton.

Accordingtopilotwavetheory,theatomisbothaparticleandawave.Let’scallthemtheatom’sparticleandtheatom’swave.Thephotonisalsoaparticleandawave,and,likewise,we’llcallthemthephoton’sparticleandthephoton’swave.Ineachcase,thewaveguidestherespectiveparticle.Butsupposewesetthingsupsothatthephotonistocollidewiththeatom.Whichentityinteractswithwhich?

Youmightbetemptedtosupposethattheatom’sparticlecollideswiththephoton’sparticle.Butthatturnsouttobewrong.Thetwoparticlesareeachinvisibletotheother.Theywilleasilypassrightthrougheachother.Instead,whathappensisthatthetwowavesinteractandscatteroffeachother.Then,asthewavesretreatfromtheircollision,theatom’s

wavepullstheatom’sparticlewithit,whilethephoton’swavelikewisepullsthephoton’sparticleaway.

Butwhetherawavefunctionscattersanotherwavefunctiondoesn’tdependatallonwhetheritisanoccupiedbranchoraghostbranch.Thishassomeprettyweirdconsequences,buttheyareequallyweirdforconventionalquantummechanicsandpilotwavetheory.Forexample,itcanappearthataparticlebouncesofftheemptyghostbranchofanotherparticle’swavefunction.

Thefactthatwavefunctionsbounceoffwavefunctionsdoesn’tcountagainstpilotwavetheory.Indeed,itshowsthatthetheoryworkseveninsuchcounterintuitivesituations;thisshouldstrengthenourconfidenceinit.Butitteachesusthecost,whichistogiveupcomfortablepicturesinwhichtheparticlesarethemainstoryandtheghostbranchesarediscounted.

Thefactthattheparticlesareguidedbythewavefunctionshasotherweirdconsequences,oneofwhichisthatthemotionstheparticlesmakeinresponsetotheirguidancebythewavefunctionfailtoconservemomentumandenergy.TheparticlesbehavelikeUFOsinbadsciencefictionmovies—forexample,theycansitstillforhours,whichiswhattheydoinstatesofdefiniteenergy,andsuddenlyjumpupandrunawayinresponsetochangesintheguidingwavefunction.

ThisdidnotshockdeBroglie,anditdoesn’tperturbhismodernfollowers,suchasValentini.Theyunderstandithastobethatway,becausepartoftheguidanceequation’sjobistobendthepathsofparticlesaroundobstaclesandthroughslits,toreproducethediffractionoflight,andaparticlethataltersitsdirectionwithoutcollidingwithanotherparticleisonethatchangesitsmomentum.ButthiswasadealbreakerforEinsteinand,Iwouldguess,ithasbeenforothers.

Ifoneaveragesasystemthatisinquantumequilibriumovermanypossibletrajectoriesoftheparticles,thenonaveragemomentumandenergyareconserved.ThisisonereasonI’vecometofavorformulationsinwhichtheprobabilitiesrefertoensemblesofparticlesthatreallyexist.Iwillbediscussingtheseinthenextchapter.

Pilotwavetheoryoffersabeautifulpictureinwhichparticlesmovethroughspace,gentlyguidedbyawave,whichalsoflowsinspace.Therealityisabitlessintuitive.Whenappliedtoasystemofseveralparticles,thewavefunctiondoesn’tflowthroughspace;itflowsonthe

configurationspace,whichismultidimensionalandthushardtovisualize.And,asI’veemphasized,theparticlesarenotyourgrandmother’slittleroundspheres—theyreacttothingsnearandfar,includingsuddennonlocalinfluencestransmittedthroughtheguidanceequation.Still,theparticlescandonothingelseifpilotwavetheoryistoreproducetheresultsofquantummechanics.

Athirdproblemwithpilotwavetheoryisthatthereisastrongtensionwithrelativitytheory.Thisisbecauseofnonlocality.TheexperimentaltestsofBell’srestrictiontellusthatanyattempttogobeyondthequantum,togiveadescriptionofindividualeventsandprocesses,mustexplicitlyincorporatenonlocality.

Thisnonlocalitymustsomehowbecodedintothepilotwavetheory,becausethattheoryisacompletionofquantummechanicsandagreeswithitspredictions.Andindeed,nonlocalityisbuiltin.Howcanthatbe?Letusconsiderasystemoftwoentangledparticles,whichareverydistantfromeachother.Thesecretisthatthequantumforcethatoneparticleexperiencesdependsonthepositionoftheotherparticle.Thisdependenceremainsevenifthetwoparticlesareveryfarfromeachother.

Asaresult,ifonecouldfollowthetrajectoriesoftheindividualquantumparticles,onecouldseethatentangledparticlesareinfluencingeachothernonlocally(i.e.,atadistance).Becausewenormallymeasureonlyaveragepositionsandaveragemotions,thisincessantnonlocalinfluenceiswashedoutbytherandomnessofthequantummotions.Butitisthereexplicitlyinthewaythewavefunctionguidestheparticles,andonecancontemplateexperimentswhichmightbeabletoobserveit.

Thealertreadermaybehearingalarmbellsgoingoff.Thisnonlocalcommunicationofforcesoveradistancerequiresustoobjectivelyspeakofeventsthataredistantfromeachother,butarenonethelesssimultaneous.Suchaninstantaneouseffectatadistancedirectlycontradictsspecialrelativity,whichtellsusthatthereisnoabsolutenotionofsimultaneityfordistantevents.Thisisindeedaproblem,andasaresultthereisatensionbetweenspecialrelativityandpilotwavetheory.

Inparticular,theguidanceequation,whichisthesourceofthenonlocalforces,isinconsistentwithrelativity.Itrequiresforitsdefinitionapreferredframeofreference,whichdefinesanabsolutenotionofsimultaneity.Inpractice,theconflictisbluntedbecausetherandomness

ofquantumphysicsimpliesthat,solongasonestaysinquantumequilibrium,*onecannotdirectlyobservethenonlocalcorrelationsinanexperiment.Norcanwesendinformationfasterthanlight.Ifwedon’tlooktoocloselyatwhatishappeninginindividualsystems,pilotwavetheorymaintainsanuneasycoexistencewithrelativity.Butthenagain,thewholepointofpilotwavetheoryisthatitenablesustolookmoreclosely.

Atthepresenttimethereisworkinprogressaimedatextendingpilotwavetheorytorelativisticfieldtheory,sowecannotgiveadefinitivepictureastohowthistensionbetweenrelativityandpilotwavetheoryresolves.2

WAVE-FUNCTIONCOLLAPSE

Thespontaneouscollapsehypothesisalsoservesuswellasarealistdescriptionofthequantumworldintermsofbeables.Accordingtothispicture,therearenoparticles—onlywaves—butthosewavesoccasionallyinterrupttheirsmoothflowtosuddenlycollapseintoparticle-likeconcentrations.Fromthere,thewaveflowsandspreadsoutagain.Becausethewavehasthispeculiarbehavior,itmimicsparticleswhenneeded,andthusistheonlybeable.

Thecollapsemodelsalsosolvethemeasurementproblem,becausethecollapseofthewavefunctionispositedtobearealphenomenon.Foratomicsystemsthisisrare.Buttherateofcollapsegrowsrapidlywiththesizeandcomplexityofthesystem,sothereisnochanceforsuperpositionsandentanglementstosurviveformacroscopicsystems.Superpositionsandentanglementsaredestroyedbythecollapses,andsoarelimitedtotheatomicdomain.Thissolvesthemeasurementproblem,becausethewavefunctionsofthemeasuringinstrumentsarealwayscollapsedsomewheredefinite.Italsogetsridoftheghostbranches.

Thepilotwavetheoryandspontaneouscollapsemodelsarenotjusttwodifferentinterpretationsofquantummechanics.Theyaredistincttheories,whicheachmakesomepredictionsthatdifferfromthoseofquantummechanics.Yetwhenitcomestothebehaviorofatomsandmolecules,theyagreewitheachother,andwithconventionalquantummechanics,tomuchbetterprecisionthantheexperimentscandetect.So,

upuntilthispointtheycannotbedistinguishedexperimentallyfromeachotherorfromquantummechanics.Pilotwavetheory,however,predictsthatsuperpositionandentanglementareuniversalandshouldbeinprincipledetectibleinanysystem,nomatterhowlargeorcomplex.Thisischallengingtotestexperimentally,becauseonehastofightthetendencyforasystemofmanyparticlestodecohere,asthemanyinteractionswiththesystem’senvironmentrandomizethephases*ofthewavefunction.Inprincipleitcanbedone,and,indeed,experimentalistsarecontinuallyexpandingthedomainofquantumphenomena.

Butifthewavefunctionundergoesspontaneouscollapse,assoonasthathappensthegameisup.Ifspontaneouscollapseisright,noexperimentalistwilleverbeabletosuperposetwowavefunctionsofalarge,complexsystem.

Anotherdifferencebetweenspontaneouscollapseandpilotwavetheoryliesintheirattitudetowardtime.Thelawsofpilotwavetheoryarereversibleintime,justlikethelawsofNewtoniandynamics.Spontaneouscollapseisirreversible,likethelawsofthermodynamics.

Thetheoriesofwave-functioncollapsehavesomeofthesamedrawbacksaspilotwavetheory.Inparticular,thecollapseisinstantaneous,buttakesplaceeverywhereatonce,creatingasevereconflictwithrelativity.Aswithpilotwavetheory,thepreciselawrequiresapreferredframeofreferencetobespecifiedandthereforecontradictsrelativitytheory.And,asinthatcase,thereissomeworkthatindicatesthattheconflictcanbemanaged,sothatinthedomainwherethetheoryagreeswithquantummechanics,theviolationsofrelativitytheoryareverysmall.

Anotherdrawbackofsomecollapsemodelsisthefact,alreadymentioned,thatenergyisnotconserved.Stillanotheristhatthisdefectcanbeminimizedbytuningafreeparameter.Tomyunderstanding,theabilitytotuneparameterstoensureagreementwithanexperimentisaweakness,asitsuggeststhetheoryiscontrivedtohideanessentialtensioninitsconstruction.

Indeed,collapsemodelscomeinseveralversions,andthereissomefreedomtomodifythemandtunenewparameters.Thatiswhytheyarecalledmodels,whilepilotwavetheory,havingnofreedomtoadjustanything,isatheory.

Amongthevariousissueswehavediscussed,itisimpressivethatallthehiddenvariabletheorieswhichhavebeenproposedconflictwithspecialrelativity.Thereasonissimple.Ifonewantsacompletedescriptionofindividualprocesses,thatdescriptionmust,becauseoftheexperimentaltestsofBell’srestriction,benonlocal,andthatrequiresapreferredsimultaneity.Averagingoverindividualcasesgivesoneprobabilities,andsincetheseagreewiththeprobabilitiespredictedbyquantummechanics,thereisnomanifestcontradictionwithspecialrelativity,becauseinformationcannotbesentfasterthanlight.Butforarealisttheconflictisnonethelesspresentbecauserealityismadeofindividualcases.Weseethisclearlyinpilotwavetheoryandinspontaneouscollapsemodels.

Norcanoneescapethisdilemmabygivinguptheambitionofgoingbeyondquantummechanics,fortheconflictispresentinquantummechanicsitself.WhenthewavefunctioncollapsesfollowingRule2,itdoessoeverywhereatonce.

Noprobleminphysicshasgivenmemorepain,andkeptmeupmorenights,thanthisconflictbetweencommonsenserealismappliedtotheatomicdomainandtheprinciplesofspecialrelativity.

Tomymind,themostimportantreasontobeskepticalaboutbothpilotwavetheoryandcollapsemodelsisthattheymakelittlecontactwiththeotherbigquestionsinphysics,suchasquantumgravityandunification.

Atminimum,bothapproachesprovideproofofconceptthatwecanberealistsaboutquantumphysics.Butneitherhastheringoftruth.Thereismoreworktodotodiscoverarealistcompletionofquantummechanicsthatavoidsthepitfallsoftheexistingtheorieswhileofferingsolutionstotheotherkeyquestionsinphysics,andsogivesusaplatformonwhichtorebuildphysics.

—THEREHAVEBEENSOMEnewproposalsofrealistquantumtheories,noneofwhichare,tomymind,completelyconvincingeither.Buttheycontainsomeintriguingideas.

RETROCAUSALITY

Arecentrealistapproachtoquantummechanicsisretrocausality,whichsupposesthatcausaleffectscangobackwardaswellasforwardintime.Usuallytheeffectfollowsthecause,but,theproponentsofthisviewargue,sometimestheeffectprecedesthecause.Byzigzaggingbackwardandforwardintime,achainofcausationscanappearnonlocal,asweseeinfigure10onthefollowingpage.Thetrickiseasy.Ifwecangobackwardintimeatlightspeed,andthenforward,wecanendupataneventsimultaneouswith,butfarfrom,wherewestarted.Soinatheorywithcausationbothinthefutureandinthepast,wecanaimtoexplainnonlocalityandentanglement.

ThiskindofapproachhasbeenadvocatedbyYakirAharonov3andcolleagues.Anotherversion,calledthetransactionalinterpretation,hasbeenproposedbyJohnCramerandRuthKastner.4HuwPricehaspublishedanargumentthatanytime-symmetricversionofquantummechanicsmustrelyonretrocausality.5

FIGURE10.RETROCAUSALITYThetwoatomstraveltothefuture,onetotheleftandonetotheright.ButacausalinfluencecantravelfromthelocationmarkedatomBbacktothepointinthepastfromwhichtheatomsoriginated,andthenforwardtothepointatatomA.ThustheeffectatatomAappearstobesimultaneouswithitscauseatatomB.

APPROACHESBASEDONHISTORIES

Anancientideaholdsthatwhatisfundamentallyrealisnotthings,butprocesses;notstates,buttransitions.Thisboldideaunderliesseveralapproachestoquantumphysics.TheyarisefromadiscoveryRichardFeynmanmadewhilehewasstillaPhDstudent.Feynmanformulatedanalternativewayofexpressingquantummechanicsthateschewsthedescriptionofnatureinwhichquantumstateschangecontinuouslyintime.Instead,wecomputetheprobabilityforthesystemtomakeatransitionbetweenanearlierconfigurationandalaterconfiguration.Wedothisbyconsideringallthepossiblehistoriesthatmighthavetakenthesystembetweenthetwoconfigurations.Thetheoryassignstoeachhistoryaquantumphase,*andtofindthewavefunctionforthetransition,weaddupthesephasesforallthepossiblehistories.Thenwetakethesquaretogettheprobability,asinBorn’srule.

AsFeynmanproposedit,thisisjustaschemetocalculateprobabilitiesinquantummechanics.ButRafaelSorkinproposesthatthisisthebasisofarealistquantumtheory,inwhichthebeablesarehistories.Thecatch(youshouldknowbynowtherealwaysisacatch)isthatonehastouseanonstandardquantumlogictotalkaboutwhatisrealaboutthosehistories.6

AverydifferentuseismadeofhistoriesbyMurrayGell-MannandJamesHartle,7whomaintainthattherealityweexperienceisjustoneofmanyequallyconsistentandequallyrealhistories.Theideaisthatifdifferenthistoriesdecohere,theycan’tbesuperposed;thustheycanbethoughtofasalternativehistories.Gell-MannandHartle,alongwithRobertGriffithsandRolandOmnès,formulatedthisideaastheconsistenthistoriesapproachtoquantummechanics.8AkeyresultofthisapproachwasthatahistoryobeyingNewton’slawsofclassicalphysicswouldbepartofafamilythatwoulddecohere.Thesedecoherenthistoriescouldbetreatedasiftheywerealternativerealhistories.However,theconversewasshownnottobethecasebyFayDowkerandAdrianKent,whodemonstratedthattherearemanyclassesofhistoriesthatdecoherewhicharenotrelatedtoNewtonianphysics.9

Noneofthesehistory-basedtheoriessatisfymydesiretohaveanaivelyrealistdescriptionoftheworld.Ihavenothingagainstarealisminwhichwhatisrealisprocessesratherthanstates,happen-ablesrather

thanbeables.ButintheapproachesI’vejustmentioned,youendupcomputingnotwhathappened,butonlytheprobabilitiesforwhathappened.AndtherelationshipbetweenthehistoriespositedbythetheoryandtheprobabilitiesweobservearealwaysrelatedbyBorn’srule,whichsuggeststhatthosehistoriesrepresentpossibilitiesandnotactualities.

MANYINTERACTINGCLASSICALWORLDS

Hereisanothercontemporaryrealistformulationofquantumphysics.10

Assumethatourworldisclassical,butitisjustoneofaverylargenumberofclassicalworlds,whichexistsimultaneously.Theseworldsaresimilartoeachother,inthattheyhavethesamenumbersandkindsofparticles.Buttheydifferastothepositionsandtrajectoriesoftheparticles.

AlltheseworldsobeyNewton’slaws,withasinglechange,whichisthat,inadditiontotheusualforcesbetweentheparticlesinasingleworld,thereisanewkindofforce,whichinvolvesaninteractionbetweentheparticlesinthedifferentworlds.

Whenyouthrowaball,itrespondstotheforcefromyourarmaswellasthegravitationalattractionoftheEarth.Atthesametime,alargenumberofsimilarcopiesofyou,eachintheirownworld,throwsaball.Eachoftheseballshasaslightlydifferentstartingpointandtrajectory.Thedifferentballsreachouttoeachotherfromtheirseparateworldsandinteractwitheachother.Thesenew,inter-worldforcesaretiny,buttheresultisthateachballisjiggledabitasittravels.Youonlyobservetheballinyouruniverse,soyoucan’taccountindetailforthejiggles.Thusthereappearstobearandomfluctuationwhichslightlydisturbstheflightofyourball.Theresultisthatyouhavetointroducearandom,probabilisticelementintoanypredictionsyoumaymakeofyourball’smotion.Thisprobabilisticdescriptionisquantummechanics.

Thisiscalledthemanyinteractingworldstheory.Tomakeitworkoutindetail,youhavetochoosetheforcesbetweentheworldsverycarefully.Togetquantummechanicstoemerge,thatforcemustbeunlikeanyforceweknowabout.Ithastoinvolvetripletsofworlds,sothereisa

jiggleonyourballwhichdependsonwheretwootherballsare,eachintheirownworlds.

Onegreatadvantageofthisformulationisthatit’sbeenextremelyusefulasabasisfordetailedandhighlyaccuratecomputercalculationsofthechemistryofmolecules.11

Iamnotgoingtosuggestwetakethisasaseriousproposalaboutnature.Butitservesasanotherexampleofarealistversionofquantumphysics.

SUPERDETERMINISM

NoteveryoneworkingonquantumfoundationsacceptstheconclusionofBell’stheoremthatlocalityisviolatedinnature.Thereareseveralloopholes,mostofwhichhavebeenruledoutbyexperiment.Oneloopholewhichisnotaseasytoruleoutisbasedonanideacalledsuperdeterminism.RecallAspectandcolleagues’experimentdisprovingBelllocality,whichwetalkedaboutinchapter4.Twoobservers,distantfromeachother,eachchooseadirectionalongwhichthepolarizationofthephotonontheirsidewillbemeasured.Theproofthatlocalityisviolatedreliesonanassumptionthatthesetwochoicesaremadeindependently.

But,strictlyspeaking,thetwoeventsinwhichthesechoicesaremadearebothinthecausalfutureofsomeeventsintheirpast.Wejusthavetogobackintimefarenoughuntilwefindeventswhosecausalfuturesincludebotheventswhenthechoicesofwhichpolarizationtomeasureweremade.Sowecouldincludesucheventsinthepast,whosecausalfutureincludesthewholeexperiment,asnecessarypartsoftheexperiment.Youcouldthenimaginethattheangleschosenoneachsidewerebothspecifiedbysomeonesettingupverycarefullytheinitialconditionsinthepastofboth.Thephilosophyofsuperdeterminismassertsthattheuniverseevolvesdeterministicallysothatallsuchcorrelationswerefixedlongago,inthebigbang.

Severalphysicistshaveproposedthatifweassumethattheinitialstateoftheuniversewaschosenextremelydelicately(bywhateveragencycanberecognizedassettingtheinitialconditions),alltheentangledpairsthatwouldeverbemeasuredcouldbedeterminedtobesetupinsucha

wayastomimictheresultsthatareusuallytakenasconfirmingnonlocality.Thoseresultsthenshouldbereadasconfirmationsofsuperdeterminismratherthannonlocality.Oneisthenfreetoproposealocalhiddenvariabletoexplainquantummechanics.ProposalslikethishavebeenmadebyGerard’tHooft,12amongothers.

Gerard’tHooftisatrulygreatscientist,whoinhistwentieswassinglehandedlyresponsibleforagoodportionofthekeyresultsthatwentintotheconstructionofthestandardmodel.Iwasveryfortunatetotakeacoursefromhimingraduateschool,andI’vealwayslookeduptohimpersonally.Formanyyearshehasbeenclaimingtohaveconstructedadeterministicandlocalhiddenvariabletheorybasedonacellularautomaton,whichisamodelofacomputer.IfIunderstandcorrectly,itworksforspecialcases;butheclaimsamoregeneralvaliditybasedonanappealtosuperdeterminism.But,detailsaside,betweennonlocalityandsuperdeterminismIamwillingtobetthatpursuingtheformerwillbringusclosertothetruth.Isaythiswithsomeregret,astherearefewtheoristsofhisgenerationwhomIadmiremorethanGerard’tHooft.

GOINGBEYONDPILOTWAVETHEORYANDCOLLAPSEMODELS

TheconclusionIcometoisthatnoneoftheproposalsforarealistquantumtheorythatI’vepresentedsofarareentirelycompelling.Somearecaptivating,butnonehaveeitherexperimentalsupportorthekindofeleganceorcompletenessthatcan,foratime,substituteforthatdecisiveexperiment.SoifyouwanttojoinEinstein,deBroglie,Schrödinger,Bohm,andBell,andgobeyondthestatisticaldescriptionofquantumtheorytoadescriptionofbeablesthatwilltelluswhatexactlyishappeningineachindividualquantumprocess,staywithus,forwearenotyetdone.

Aretherelessonstotakewithusaswemovebeyondpilotwavetheoryandcollapsemodels?Indeedthereare.Themostimportantlessonwecanlearnfromthesuccessesofthecollapsemodelsandpilotwavetheoryisthatthewavefunctioncapturesanelementofphysicalreality.Let’sseehowthisconclusioncomesabout.

Thepilotwavetheoryassertsthateverythingintheuniversehasadualexistence—asaparticleandasawave.Thissolvesthemeasurementproblembecauseitkeepstheparticle.Anditdoessoinawaythatincorporatessuperposition,entanglement,andalltheirweirdconsequencesbecauseitkeepsthewave.Butisitright?Iarguedthatimpressiveasitis,ithasseveredrawbacks.Thisbringsustoournextoption:togobeyondpilotwavetheorytoinventanewtheoryofbeables.

Pilotwavetheorysucceedsbecauseitpositsthatbothparticlesandwavesarereal.Butisthisreallynecessary?Mighttherebeatheorythataccomplisheswhatpilotwavetheorydoeswhichdoesn’trequirethedoubledontology?Thiswouldalsoresolvetheissueofthelackofreciprocityinthetheory.

Itwouldbeextremelyinterestingiftherewerewaystoreproducethesuccessesofpilotwavetheorythathadjustoneclassofbeablesandnottwo.Wavesorparticles,butnotboth.Orsomethingelseentirely.

Asafirsttry,wecanaskwhathappensifwestartwithpilotwavetheoryanddropeitherthewavesortheparticles.

Ifwedroptheparticles,wenolongersolvethemeasurementproblem—unlessweradicallyalterthebehaviorofthewavebyhypothesizingspontaneouscollapse.SodroppingtheparticlesleadsbacktoeithercollapsemodelsortheManyWorldsInterpretation.

Wenexttrytodropthewavefunction,butkeeptheparticles.Whatthenisgoingtoguidetheparticles?Howarewetoexplaininterferenceifwehaveonlyparticles?Mightwe,forexample,recoverthewavefunction’sguidancebygivingtheparticlesstrangenewproperties?

Severalphysicistsandmathematicianshavetriedtoinventatheoryofbeableswithjusttheparticles,butnonehavesucceeded.Thisisalongstory,withsomefascinatinginsandouts,buttheconclusionissimple:thewavefunctionappearstocaptureanessentialaspectofreality.13TheclosesttosuccessIknowofisanapproachbythemathematicianEdwardNelsoncalledstochasticquantummechanics.FormanyyearsIthoughtthiswastherightway,butthenIunderstooditrequiresalargeamountoffine-tuningtoavoidinstabilities.

Thisconclusionisupheldbyarecentanalysisbythreespecialistsinquantuminformationtheory,MatthewPusey,JonathanBarrett,andTerryRudolph,whogaveanewargumenttotheeffectthatthequantumstatecannotbemerelyarepresentationofinformationanobserverhas

aboutasystem.Itmustbephysicallyreal,orrepresentsomethingreal.14

Soweseemtohaveonlytwochoices:keepthewavefunctionitselfasabeable,asitisinpilotwavetheoryandcollapsemodels,orfindanotherbeablethatcaptures,insomedifferentform,thephysicalrealitywhichthewavefunctionrepresents.

I

FOURTEEN

First,Principles

wentintophysicshopingtocontributetosolvingthetwogreatquestionsEinsteinposedinhisautobiographicalnotes:unitingquantumphysicswithspacetimeandmakingsenseofquantum

physics.Despitetheeffortsofmanybrilliantpeopleoverthemorethanhalfa

centurysinceEinsteinwrotehisautobiographicalnotes,thesetwoproblemsremainunsolved.Itisworthtakingsometimetoaskwhy.

Thisquestionhasbeenonmymind.LatelyIfindmyselfwonderingifwehavebeengoingaboutcompletingEinstein’stwinrevolutionsallwrong.Weinventtheories,suchasloopquantumgravity,stringtheory,pilotwavetheory,andothers,butthesedonotgodeepenough.Theorieslikethesearemodels,whichembodyourideasaboutnature,buttheyarenotthedeepestorpurestexpressionsofthoseideas.

Modelsexemplifyideas,butofteninasimplifiedform,whichallowstheideas’essentialfeaturesandimplicationstoshinethrough.ThegameMonopolyisamodelofcapitalism.Nonscientistsoftenfailtoappreciatehowusefulmodelscanbe—exactlybecausetheyareincompleteandleavethingsout—whenoneisinthestageofexploringtheimplicationsofanidea.

Ideasaboutnaturearemostpurelyexpressedaseitherhypothesesorprinciples.Ahypothesisisasimpleassertionaboutnature,whichiseithertrueorfalse.“Matterisnotinfinitelydivisiblebecauseitismadeofatoms”isahypothesis.Sois“Lightisawavetravelingthroughtheelectricandmagneticfields.”Bothofthesehypothesesturnedouttobetrue,butthehistoryofscienceislitteredwiththosethatprovedfalse.

Aprincipleisageneralrequirementthatrestrictstheformthatalawofnaturecantake.“Itisimpossibletodoanyexperimentthatcan

determineanabsolutesenseofrest,ormeasureanabsolutevelocity”isaprinciple.

Einsteinknewwhathewasdoingwhenheintroducedspecialrelativity:hebeganhis1905paperwithtwoprinciplesanddeducedconsequencesdirectlyfromthem.ItisworthnotingthattheideaofunifyingspaceandtimeintoasingleentitycalledspacetimewasnotpartofEinstein’soriginalconceptionofrelativity.TheideaofspacetimewasintroducedtwoyearslaterbyhisteacherHermannMinkowskiasamodelwhichexemplifiedEinstein’sprinciples.

Theproblemwithskippingthestageofprinciplesandhypothesesandgoingrighttomodelsisthatwecanloseourway.It’seasytogettrappedinamicroscopicfocuswhiletryingtoworkoutthedetailsofthosemodels.AsFeynmanoncetoldme,“Makeeveryquestionyouaskinresearchaquestionaboutnature.Otherwiseyoucanwasteyourlifeinworkingouttheminutiaeoftheoriesthatmostlikelywillneverhaveanythingtodowithnature.”Evenworse,wegetcaughtupinpettycompetitionsandacademicturfbattlesbetweentheadherentsofdifferentmodels.

Einsteinexpressedthislessonbyinsistingthatwedistinguishtwokindsoftheories.Principletheoriesarethosethatembodygeneralprinciples.Theyrestrictwhatispossible,buttheydon’tsufficeforthedetails.Thosearesuppliedbythesecondkindoftheory,whichhecalledconstitutivetheories.Thesedescribeparticularparticlesorspecificforcesthatnaturemayormaynotcontain.Specialrelativityandthermodynamicsareprincipletheories.Dirac’stheoryoftheelectronandMaxwell’stheoryofelectromagnetismareconstitutivetheories.

So,myconclusionisthatweneedtobackofffromourmodels,postponeconjecturesaboutconstituents,andbeginagainbytalkingaboutprinciples.

Ourstrategywillthenbetoproceedtoourgoalofinventinganewfundamentaltheoryinfoursteps:first,principles;second,hypotheses(whichmustsatisfytheprinciples);third,models(whichillustratepartialimplicationsoftheprinciplesandhypotheses);thenlast,completetheories.Puttingprinciplesbeforetheoriesraisesaninterestingquestion:Wheredoyoufindalanguagetostatetheprinciples,andacontexttomotivateandcritiquethem?Youdon’twanttousethelanguageofexistingtheoriesbecausethewholepointoftheexerciseistogetbeyond

them.EinsteinwouldneverhaveinventedgeneralrelativityhadherestrictedhimselftoreasoningwithinthelanguageofNewtonianphysics.

Mathematicscansometimesprovidenewideasandstructures,andsoisoftenahelp.Butnewmathematicsisusuallynotenoughtoinventnewphysics;otherwiseBernhardRiemannorWilliamKingdonCliffordwouldhaveinventedgeneralrelativity.Thisiswhereaknowledgeofphilosophycanbetheessentialelement,becauseapersonwithaphilosophicaleducationhasintheirtoolboxaplethoraofideasandmethodscomingfromthewholehistoryofhumanbeings’attemptingtothinkaboutthefundamentalsofourdescriptionoftheworld.Andwhenitcomestobasicquestionslikethenatureofspaceandtime,thathistoryisrichwithusefulargumentsandstrategiestobetriedout.SoEinsteinwasnotalonewhenhefacedtheneedfornewnotionsofspaceandtime.ItwasasifhecarriedGalileo,Newton,Leibniz,Kant,andMachinhisbackpocketandwasabletoconversewiththemandbenefitfromtheirinsights.Similarly,agoodknowledgeofPlato,Kant,andothersgaveHeisenbergalanguagetogobeyondNewtonianparticles.

Thetwentiethcenturysawafloweringofphilosophyinphysics,whichhasfurtherenrichedthestorehouseofusefulideasandarguments.Philosophyisindeedalivingtradition,andiftherewasatimewhenphilosophersofphysicslaggedbehindintechnicalmasteryofphysics,thattimeislongover.SoIwillnotapologizeforgoingbothtothesagesofthepastandtoourcontemporaryphilosopherstofindlanguage,contexts,andideastoframemysearchfornewprinciplesofphysics.

Startingwithprincipleshasanimmediateconsequence,whichisthatwerealizethatquantumgravityandquantumfoundationsaredifferentsidesofasingleproblem.Whenphysiciststrytosolvequantumgravitywithoutregardtotheproblemsofquantumfoundations,andviceversa,wearetakingthewrongapproach.Thesetwoproblemsaredeeplyrelated.Onereasonisthatbecauseofquantumnonlocality,goingbeyondquantummechanicsmeansgoingbeyondspacetime.

SoIwillproceedbyputtingforwardprincipleswhichcombinequantumphenomenawithspacetime.Afterwehaveagoodsetofprinciples,thenextstepwillbetoframehypothesesabouthowtheyarerealized.

Ouraimistocombinequantumphysicsandspacetimeattheleveloffundamentalprinciples.Ibelievetherightprinciplestoshapethis

unificationarethefollowing:

PRINCIPLESFORFUNDAMENTALPHYSICS

1.Backgroundindependence.

Aphysicaltheoryshouldnotdependonstructureswhicharefixedandwhichdonotevolvedynamicallyininteractionwithotherquantities.Thisisakeyconcept,whichtakessomeunpacking.

Allphysicaltheoriestodatedependonstructureswhicharefixedintimeandhavenopriorjustification;theyaresimplyassumedandimposed.Oneexampleisthegeometryofspace,inalltheoriespriortogeneralrelativity.InNewtonianphysics,thegeometryofspaceissimplyfixedtobeEuclideanthree-dimensionalgeometry.It’sarbitrary;itdoesn’tchangeintime,itcan’tbeinfluencedbyanything.Henceitisnotsubjecttodynamicallaw.

InNewton’stime,Euclid’swastheonlygeometryknown,sohehadnoalternativeanddidn’tneedtoseekajustificationforchoosingit.Butinthenineteenthcentury,CarlFriedrichGauss,NicholasLobachevsky,andRiemanndiscoveredaninfinitudeofalternategeometries.Anyfundamentaltheorythatcomesaftertheirworkmustjustifythechoiceitmakesforthegeometryofspace.Theprincipleofbackgroundindependencerequiresthatthechoiceismadenotbythetheorist,butbythetheory,dynamically,asapartofsolvingthelawsofphysics.

Non-dynamical,fixedstructuresdefineafrozenbackgroundagainstwhichthesystemweareinterestedinevolves.Iwouldmaintainthatthesefrozenstructuresrepresentobjectsoutsidethesystemwearemodeling,whichinfluencethesystembutdonotthemselveschange.(Orwhosechangesaretooslowtobenoticed.)Hencethesefixedbackgroundstructuresareevidencethatthetheoryinquestionisincomplete.

Itfollowsthatanytheorywithfixedexternalstructurescanbeimprovediftheexternalelementscanbeunfrozen,madedynamical,andbroughtinsidethecircleofmutuallyinteractingphysicaldegreesoffreedom.ThiswasthestrategythatledEinsteintogeneralrelativity.ThegeometryofspaceandtimeisfrozeninNewtonianphysics,anditisalsofrozeninspecialrelativity.Inthesetheories,thespacetimegeometry

providesanabsoluteandfixedbackgroundagainstwhichmeasurementsaredefined.Generalrelativityunfreezesgeometry,makingitdynamical.

Thisisturningouttobeamultistageprocess,becauseourtheorieshavelayersoffrozenelements,whichwerelaiddown,likelayersofsedimentation,duringthelongandcomplexhistoryofoursubject.Generalrelativityunfreezessomeaspectsofgeometry,butdeeperstructures,suchasdimensionandstructuresneededtodefinethecontinuousnumbersordefinearateofchange,remainfrozen.Sogeneralrelativity,beautifulasitis,cannotbetheendofoursearch,andwillrequirefurthercompletion.

Eachstepextendstherangeofthetheory.Itfollowsthattheonlycompletetheoryofphysicsmustbeacosmologicaltheory,fortheuniverseistheonlysystemwhichhasnothingoutsideofit.Atheoryofthewholeuniversemustthenbeverydifferentfromtheoriesofpartsoftheuniverse.Itmusthavenofixed,frozen,timelesselements,astheserefertothingsoutsidethesystemdescribedbythetheory.Itmustbefullybackgroundindependent.

Thisrecognitionthatacosmologicaltheorycannotbeachievedbyjustscalingupourcurrenttheories,butmustbearadicallynewkindoftheory,isthemostimportantlessonlearnedsofarinthesearchforacompletionofEinstein’stwinrevolutions.*

Itfollowsthatquantummechanicscannotbeatheoryofthewholeuniversebecauseittoohasfixedelements.Theseincludetheobservablesofthesystemandvariousrelationstheyhave,aswellasthestructurethatgivesrisetoprobabilities.*

Thisimpliesthatthereisnowavefunctionoftheuniverse,becausethereisnoobserveroutsidetheuniversewhocouldmeasureit.Thequantumstateis,andmustremain,adescriptionofpartoftheuniverse.

Wethenseektocompletequantumtheorybyeliminatingbackgroundstructures.Wedothisbyexposingandthenunfreezingthebackgroundandgivingitdynamics.Inotherwords,ratherthanquantizinggravityweseektogravitizethequantum.Wemeanbythattheprocessofidentifyingandunfreezingthoseaspectsofquantumtheorywhicharearbitraryandfixed,makingthemsubjecttodynamicallaws.Turningthisaround,wehopetounderstandthechallengingfeaturesofquantumphysicsasconsequencesofseparatingtheuniverseintotwoparts:thesystemwe

observe,andtherest,containingtheobserverandtheirmeasuringinstruments.

Closelyrelatedtobackgroundindependenceisanotherkeyidea:thattheobservablesofphysicaltheoriesshoulddescriberelationships.

Leibniz,Mach,andEinsteintaughtustodistinguishabsolutenotionsofspaceandtimefromrelationalnotions.Wesaythatlocationinspaceisabsolutewhenthereisafixedmeaningtowheresomethingis.Arelativelocationisdefinedwithreferencetosomethingelse.Threeblockssouthofthesupermarketisarelativelocation.Similarly,anabsolutetimeismeaningfulwithoutreferencetoanythingelse,whilerelationaltimeisalwaysdefinedbyitsrelationtoanothereventorsetofevents.

Thisleadstooursecondprinciple:

2.Spaceandtimearerelational.

Arelationalobservable,orproperty,isonethatdescribesarelationshipbetweentwoentities.Inatheorywithoutbackgroundstructures,allpropertiesthatrefertolocationinspaceortimeshouldberelational.Background-independenttheoriesspeaktousaboutnaturethroughrelationalobservables.

Thethirdprincipletellsusnothingisleftout.

3.Principleofcausalcompleteness.

Ifatheoryiscomplete,everythingthathappensintheuniversehasacause,whichisoneormorepriorevents.Itisneverthecasethatthechainofcausestracesbacktosomethingoutsidetheuniverse.

OurnextprinciplewasintroducedbyEinstein,inhispapersongeneralrelativity.

4.Principleofreciprocity.

Thisprinciplestatesthatifanobject,A,actsonasecondobject,B,thenBmustalsoactbackonA.

Thereisonemoreoftheseprinciples,anditisbothsubtleandpowerful.

5.Principleoftheidentityofindiscernibles.

Thisstatesthatanytwoobjectsthathaveexactlythesamepropertiesareinfactthesameobject.

Puttingtheminorder,wehavefivecloselyrelatedprinciples:

1. Theprincipleofbackgroundindependence2. Theprinciplethatspaceandtimearerelational3. Theprincipleofcausalcompleteness4. Theprincipleofreciprocity5. Theprincipleoftheidentityofindiscernibles

Theseareallaspectsofasingleprinciple,whichLeibnizcalledtheprincipleofsufficientreason.Thisstatesthateverytimeweidentifysomeaspectoftheuniversewhichseeminglymightbedifferent,wewilldiscover,onfurtherexamination,arationalreasonwhyitissoandnototherwise.

Forexample,givenpresentknowledge,itseemsthatspacemighthavemoreorlessthanthreedimensions.(BythisImeanthethreelargedimensionsthatweseearoundus;thisdoesn’tcounthypotheticaltiny,“rolled-up”dimensionsperceivableonlyonasubatomicscale.)Thisisbecauseallourcurrenttheories,includinggeneralrelativityandquantummechanics,wouldalsomakesenseinaworldwithadifferentnumberofspatialdimensions.Leibniz’sprincipleofsufficientreasonadvisesusthatthismustbebecauseourcurrenttheoriesareincomplete.Wemustseektocompleteourtheories,andonesignofsuccesswillbewhenwefindoutwhythenumberoflargespatialdimensionsisthree.*

LeibnizbelievedwecoulduncoverarationalexplanationforeveryapparentchoiceGodmightseemtohavemadeinthecreationoftheuniverse.Hespokeofthestateinwhichthisunderstandingwouldbeachievedasoneofhaving“sufficientreason.”Hisprincipleofsufficientreasonstatesthattheuniversecanbecompletelyunderstood.

EachoftheprinciplesI’vestatedexpressesthisidea.Forexample,wecouldaskwhytheuniversecameintobeingwhereitwasandnottenmeterstotheleft.Buteverythingwouldhavehappenedjustthesameway,sothiscan’tbeameaningfulquestion.Therefore,absolutepositionismeaningless;onlyrelativepositionismeaningful.Ascientistwhoaspirestoberationalmustbearelationalist.

Ourtheoriesexpresstheseprinciplesincompletely,butovertimetherehasbeenacleartrendtowardtheoriesthatexplainmore.Eachtimeweexplainafeatureoftheworldinawaythatlimitsthechoiceacreatormighthavehad,weeliminatesomeofthearbitrarinessweformerlyperceivedinthedesignoftheworld.Asweunderstandtheworldbetter,itappearstoustobemorerational.Thishappenseachtimewediscoverahiddenunity.AgoodexampleofthiswasMaxwell’sdiscoverythatlight,electricity,andmagnetismarenotseparatephenomena,butaredifferentaspectsofasingleforce.Thisdiscoveryshowsusthataworldcouldnotexistthathasmagnetismbutnoelectricforces.Andweunderstandthatanyworldwithelectricityandmagnetismmustalsohavelight.

Idonotknowifacompleteunderstandingofnaturewilleverbeattained.ButIdobelievethatourgoalshouldbetoalwaysprogresstowardevermorecompleteunderstanding,whichmeansweseekalwayslessarbitrarinessandmorerationality.HenceIwouldproposeweseekevermoresufficientreason.

Ibelievetheprogressofscienceismeasuredbysuchincreasesinourunderstandingofnature.

SpecialrelativityisanimprovementoverNewtonianphysics,andgeneralrelativity,byembracingapurelyrelationalspacetimegeometry,isanimprovementonboth.WecanalsosaythatquantummechanicssatisfiestheprincipleofreciprocitybetterthanNewtonianmechanics,butthatpilotwavetheorycomesstillclosertosufficientreasonbecauseitexplainsthingsquantummechanicsleavesunexplained,suchaswhyindividualeventstakeplacewhereandwhentheydo.

But,asI’vealreadymentioned,pilotwavetheoryfailstosatisfyanotherofourprinciples:Einstein’sprincipleofreciprocity.Thepilotwaveguidestheparticle,buttheparticlehasnoeffectbackonthewave.Sowestillhavesomedistancetogo.

Theprincipleofsufficientreasonadvisesuswecandobetter.

Howshallwethinkofspaceandtimeinthisnewworldofrelations?TwochaptersagoIdrewalessonfromasurveyofapproachestoquantumfoundations,whichisthatspaceandtimecannotbothbefundamental.Onlyonecanbepresentatthedeepestlevelofunderstanding;theothermustbeemergentandcontingent.Thisseemsultimatelytobeforcedonusbythenonlocalityofentanglement,whichleadstoatensionbetweenrealistapproachestoquantummechanicsandspecialrelativity.Thelatterunifiesspaceandtimeintospacetime,whichtheexperimentaltestsofBell’srestrictionsuggestistranscendedinindividualquantumprocesses.Iwouldthenliketosuggestthatthetensionisresolvedbymakingoneofthepairspace/timefundamental,whiletheotherisanemergentandapproximatedescription,ultimatelyakindofillusion.Formanyreasons,somedescribedhere,somethesubjectofearlierbooks,1Ichoosetofocusonthehypothesisthattimeisfundamental,whilespaceisemergent.

Thisisasfarasprinciplestakeus.Thenextstepistoframehypotheses.Iproposethreehypothesesaboutwhatliesbeyondspacetimeandbeyondthequantum:

Time,inthesenseofcausation,isfundamental.Thismeanstheprocessbywhichfutureeventsareproducedfrompresentevents,calledcausation,isfundamental.

Timeisirreversible.Theprocessbywhichfutureeventsarecreatedfrompresenteventscan’tgobackward.Onceaneventhashappened,itcan’tbemadetoun-happen.*

Spaceisemergent.Thereisnospace,fundamentally.Thereareeventsandtheycauseotherevents,sotherearecausalrelations.Theseeventsmakeupanetworkofrelationships.Spacearisesasacoarse-grainedandapproximatedescriptionofthenetworkofrelationshipsbetweenevents.

Thismeansthatlocalityisemergent.Nonlocalitymustthenalsobeemergent.

Iflocalityisnotabsolute,ifitisthecontingentresultofdynamics,itwillhavedefectsandexceptions.Andindeed,thisappearstobethecase:howelsearewetounderstandquantumnonlocality,particularlynonlocal

entanglement?These,Iwouldhypothesize,areremnantsofthespacelessrelationsinherentintheprimordialstage,beforespaceemerges.Thus,bypositingthatspaceisemergentwegainapossibilityofexplainingquantumnonlocalityasaconsequenceofdefectswhichariseinthatemergence.2

Thecombinationofafundamentaltimeandanemergentspaceimpliesthattheremaybeafundamentalsimultaneity.Atadeeperlevel,inwhichspacedisappearsbuttimepersists,auniversalmeaningcanbegiventotheconceptofnow.Iftimeismorefundamentalthanspace,thenduringtheprimordialstage,inwhichspaceisdissolvedintoanetworkofrelations,timeisglobalanduniversal.Relationalism,intheforminwhichtimeisrealandspaceisemergent,istheresolutionoftheconflictbetweenrealismandrelativity.

Let’sgiveanametothisversionofrelationalism,whichemphasizestherealityandirreversibilityoftimeandthefundamentalityoftheflowofpresentmoments.Let’scallittemporalrelationalism.Wecancontrastitwitheternalistrelationalism,whichinvestigatesthehypothesisthatspaceisfundamental,buttimeisemergent.

RELATIONALHIDDENVARIABLES

Wethusseekacompletionofquantummechanicswhichisbackgroundindependentandrelational,andwhichisframedinaworldwheretimeisfundamentalandspaceisemergent.Ifitinvolveshiddenvariables,thesemustexpressrelationsbetweenparticles.Thus,thehiddenvariablesdonotgiveusamorecompletedescriptionofanindividualelectron;theymustdescriberelationswhichholdbetweenoneelectronandotherelectrons.Wecancalltheserelationalhiddenvariables.

Indeed,whatismorerelationalthanthedeepestandsubtlestofthequantummysteries,whichisentanglement?Arelationalformulationofquantumphysicswillstartbyputtingentanglementfirst.If,aswehypothesized,spaceisemergent,distanceinspacemustbederivativeofmorefundamentalrelations.Perhapsthismorefundamentalrelation,fromwhichspaceemerges,isentanglement.*

Thehiddenvariablesinpilotwavetheoryarethetrajectoriesoftheparticles.Theyarenotrelational;theydoinfactjustgiveusmore

informationabouteachoftheparticles,individually.However,thereisalreadyalargedoseofrelationalisminpilotwavetheory.Thisisinherentinthefactthatforasystemofmorethanoneparticle,thewavefunctionlivesnotinordinaryspace,butinthespaceofconfigurationsofthetotalsystem,whichconsistsofseveralparticles.Thisis,asIexplainedinchapter8,necessarytoincorporateentanglement.

Ifirstformulatedtheconceptofarelationalhiddenvariabletheory,includingthehypothesisthatspaceisderivativeofmorefundamentalrelations,especiallyentanglement,earlyinmycareer.Iwroteup3aformulationofarelationalhiddenvariabletheoryin1983;thiswasthefirstofseveralsuchefforts.4

My1983theorywasbasedonasimpleidea.Supposeyouhaveasystemofparticlesinspace.Inanabsolutedescription,youcodeinthelocationofeachparticleindividuallybygivingcoordinatesinspace.Thesecoordinatesareabsolute;theyrefertoanobserveroutsidethesystem—forNewtonthiswasGodhimself.Inarelationaldescriptionyoucoulduseonlytherelativedistancesbetweeneachpairofparticles.Thesenolongerdependonreferencetoanobserveroutsidethesystem.

Thereisarelativedistancebetweeneverypairofparticles.Hence,therelativedistancescanberepresentedasatableofnumbers.Theentry“10downand47over”givesthedistancebetweenthe10thand47thparticles.Anothernameforsuchatableofnumbersisamatrix.Inmyrelationalhiddenvariabletheory,thehiddenvariablesweresuchamatrix.My1983theoryutilizedalargematrixofcomplexnumberstodescribeasystemofmanyparticleslivinginatwo-dimensionalspace.Whenthenumberofparticleswaslarge,theprobabilitiesforthemotionoftheparticleswereapproximatelydescribedbySchrödinger’sequation.

FIGURE11.Amatrixisatableofnumbers,madeupofrowsofcolumns.

Therearebynowseveralproposalsthatgobeyondthequantumbystartingwithpilotwavetheoryandtradinginthewavefunctionforadeeperstructuredescribedintermsofmatrices.RelationalhiddenvariablestheoriesbasedonmatriceshavealsobeenproposedbyStephenAdler5andArtemStarodubtsev.6

Amatrixassignsanumbertoeverypairofparticles.Anotherstructurethatdoessoisagraph,whichisasimplestructurebuiltofpoints,connectedbylines.Eachpairofpointsiseitherconnectedbyalineornot.Wecanassignaonetothepairiftheyareconnectedandazeroiftheyarenot,andthenwehaveamatrixrepresentingthesamestructure.

Graphsandmatricesarethusbothwaystoexpressthehypothesisthatthefundamentalbeablesunderlyingphysicsareanetworkofrelations.Theserelationsmayexpressquantumentanglementandnonlocality.

Thereisnopurermodelofasystemofrelationsthanagraphornetwork.Interestinglyenough,networksareubiquitousinthoseapproachestoquantumgravitywhichareinaccordwiththeprincipleofbackgroundindependence.Theseincludeloopquantumgravity,causalsets,andcausaldynamicalrelations.Thissuggeststwoexcitingdeepeningsofourhypotheses:First,spaceemergesfromthe

fundamentalnetwork.Second,quantumphysicsarisesfromnonlocalinteractionsleftoverwhenspaceemerges.

However,networksfituneasilyintospace,if“nearby”intheemergentspaceistocorrespondwith“nearby”inthenetwork.Thereasonissimple:considertwopointsinthegraph,eachcorrespondingtoapointintheemergentspace.Supposetheyarefarawayfromeachotherinspaceandalsofarawayonthegraph.Butnowaddalinktothegraphdirectlyconnectingthosetwopoints.Allofasuddentheyareneighborsonthegraph,butstillfarawayfromeachotherwhenconsideredintermsoftheemergentspace.

InourworkwithFotiniMarkopoulou,wecalledsuchconnectionsdefectsoflocality.Theylooklikenarrowwormholes.Weshowedthattheywillbecommoninloopquantumgravity.7Thisledustoanotherpaperwherewederivedquantummechanicsfromaveragingoverthenonlocalinteractionswhichmightarisefromsuchdefectsoflocality.8Abittongueincheek,wecalledthis“QuantumTheoryfromQuantumGravity.”*

FIGURE12.DISORDEREDLOCALITY(A)Alatticeofpoints,embeddedinspace,whichwecalllocalbecausepointswhicharefarawayintermsofstepsonthelatticearefarawayinthespaceitisembeddedin.(B)Byaddinganewlinkthatconnectsfarawaypoints,wedisruptlocalitybecausetheconnectedpointsarestillfarawayinspace,butareonlyonestepapartonthelattice.

—IMETRICHARDFEYNMANONLYafewtimes,butontwooccasionshewaskindenoughtoaskaboutmywork.Eachtimeherespondedthesameway.HelistenedcarefullyandthensuggestedthattheideaIdescribedtohimwasn’tcrazyenoughtohaveachancetowork.WhatIbelievehemeantbythatwasthatmyideadidn’tgodeepenough.Inanycase,thatishowIfeelaboutmyearlierattemptstomakearelationalhiddenvariabletheorybasedonmatricesandnetworks.Theysolvetheproblemofgivingacompletionofquantummechanicsatatechnicallevel,butinotheraspectstheycomeupshort.OnewaytotellisthattheSchrödingerequationonlycomesoutasapredictionofthetheoryifyouhammerouttheimperfectionsandfine-tunetheequations.

Togodeeperintotherelationalidea,wecangobacktoLeibnizforinspiration.Leibnizsketchedapurelyrelationalviewoftheuniverseinashortbook,TheMonadology,9writtenin1714.SinceweareinterestedonlyingettinginspirationfromLeibniz,wedon’tcaretoaccuratelyreproducehisvision.Wearefreetocreativelymisinterprethisbook.HereisonesuchloosereadingofTheMonadology.

WeshallcalltheelementsofarelationalmodeloftheuniversenadsbecausetheyareonlypartiallyinaccordwithLeibniz’selements,whichhecalledmonads.Nadshavetwokindsofproperties:intrinsicproperties,whichbelongtoeachindividualnad,andrelationalproperties,whichdependonseveralofthenads.Anadicuniversemaybepicturedasagraph,withtherelationalpropertiesrepresentedbylabelsonlinksthatconnectpairsofnads.

Itisnotacoincidencethatsofarthispictureaccordswiththedescriptionoftheworldgiveninloopquantumgravity.There,astateoftheworldisdescribedbyagraphwithlabelsonit.

Eachnadhasaviewoftheuniverse,whichsummarizesitsrelationswiththerest.Onewaytotalkabouttheviewsisintermsofneighborhoods(orzones)ofthegraph.Let’stalkabouttheviewofanadcalledSam.ConsiderthenadsonestepawayinthegraphfromSam:theyarethefirst,ornearest,neighbors.ThefirstneighborhoodconsistsofSamandhernearestneighbors,togetherwiththerelationstheyshare,whichareindicatedonthelinksbetweenthem.

ToconstructSam’ssecondneighborhood,addinthenadstwostepsawayfromher,andalltheirrelationswitheachotherandwiththeirneighborswhoareonestepaway(whoarealsoincluded).Andsoon.TheseneighborhoodsconstituteSam’sviewsofheruniverse.

WecancompareSam’sviewstotheviewsofanothernad—let’scallhimSue.SamandSuehaveidenticalfirstandsecondneighborhoods,whichistosay,wecouldn’ttellthemapartifwecanonlyseethatfar.

Butletuspositthatourrelational,nadicuniverseobeysLeibniz’sprincipleoftheidentityofindiscernibles.ThenSam’sandSue’sneighborhoodsmustdifferatsomepoint;otherwisetheywouldhaveidenticalviews,whichisforbiddenbythatprinciple.Thisimpliestheremustbesomenumberofstepsatwhichthetwoneighborhoodsdiffer.WecallthatnumberthedistinctionofSueandSam.

FIGURE13.ThefirstandsecondneighborhoodsofSamandSue,definedbytheconnectivityofthegraphtheyinhabit,areidentical,butthethirdandhigherneighborhoodsdistinguishthem.

Leibnizpositedthattheactualuniverseisdistinguishedfrommanypossibleuniversesby“havingasmuchperfectionaspossible.”Ifwestripthisofitspoeticorallegoricalmeaning,whatLeibnizisdoingispositingthatthereissomeobservablequantitywhichislargerintherealuniversethaninalltheotherpossibleuniverses.Thisisshockinglymodern,asitanticipatesamethodforformulatinglawsofnaturethatwasdevelopedlaterandonlycameintofruitionduringthetwentiethcentury.Thequantitythatismaximized,whichLeibnizcalled“perfection,”wecallanaction.

Feynmanlikedtoemphasizethatabeautifulfeaturethelawsofphysicsenjoyisthattheycanbeformulatedinseveraldifferentways.Theseseem,atfirst,tobeverydifferent,butwhenyouknowthembetteryoucometounderstandthattheyareallequivalenttoeachother.IcanillustratethiswithNewton’slawsofmotionandgravity.Thesedescribethemotionoftheplanets,moons,andotherbodiesinthesolarsystem.Onewaytodescribethelawsisbyspecifyinghowthepositionsofthesebodieschangeintime.Thisisusuallydonebysettingtheiraccelerationsequaltothesumofthegravitationalforcesfromtheotherbodies,dividedbythemasses.

Butanotherwaytospecifythesamelawsistodelineateasetofquantitiesthatarefixed,anddon’tchangeastheplanetsmove,suchastheirtotalenergy.Athirdway,equivalenttothefirsttwo,istosaythattheplanetsmoveinsuchawaythatacertainquantityismadeaslargeaspossible.Wecallthistheaction;*Leibnizcalleditperfection.

Leibniztellsuswhatgoesintothe“perfection.”Hedefinedaworldwith“asmuchperfectionaspossible”tobeonehaving“asmuchvarietyaspossible,butwiththegreatestorderpossible.”

WhatdoesLeibnizmeanhereby“variety”?IbelievethatLeibnizmeantthattheviewsofthedifferentmonadsshoulddifferasmuchaspossible.Sobymaximizingperfection,Leibnizmeansweshouldmaximizethevarietyofdifferentviews.

Inspiredbythispicture,JulianBarbourandIconstructednumericalmeasuresofthevarietyinherentinasystemofrelations.10Wenoticedthatasvarietyincreases,lessinformationisneededtopickoutanddistinguisheachviewfromtheothers.Thatis,everythingelsebeingequal,wepreferworldswhereanypairofnadshasneighborhoodswhichdifferatasmallnumberofsteps.

ForLeibniz,sufficientreasonhadtobefoundedonanotionofmaximalperfection.

Andthis[sufficient]reasoncanbefoundonlyinthefitness,orinthedegreesofperfection,thattheseworldspossess....Thisinterconnection(oraccommodation)ofallcreatedthingstoeachother,andeachtoalltheothers,bringsitaboutthateachsimplesubstancehasrelationsthatexpressalltheothers,andconsequently,thateachsimplesubstanceisaperpetual,livingmirroroftheuniverse.

Hethenreachesforametaphortodescribethis,andcomesupwiththedifferentviewsofacity.

Justasthesamecityviewedfromdifferentdirectionsappearsentirelydifferent,and,asitwere,multipliedperspectively,injustthesamewayithappensthat,becauseoftheinfinitemultitudeofsimplesubstances,thereare,asitwere,justasmanydifferentuniverses,whichare,nevertheless,onlyperspectivesonasingleone.11

ThisisindeedametaphorthatJaneJacobswouldhaveappreciated,asitcapturesanotionofurbandiversitychampionedbyherandembracedbyphilosophersofthecity,suchasRichardFlorida,since.

Thisurbanmetaphorinspiresahypothesisabouthowspaceandlocalitybreakdown.Ifyoustandnexttomeandwebothlookout,byvirtueofourproximitywehavesimilarviewsoftherestoftheuniverse.Ourviewscannotbeidentical,becausewecannotcoincide,byvirtueofboththePauliexclusionprincipleandtheidentityofindiscernibles.Buttheclosertoeachotherwestand,themoresimilarareourviews.

Becauseweareclosetoeachother,wecaninteracteasily,andindeed,thecloserwestandthehigheristheprobabilitythatweinteractthroughaninterchangeofquantasuchasphotons.Thisisbasicallywhatwemeanwhenwesayphysicalinteractionsarelocal.

Butsupposewehavethisbackward.Whatifweinteractwithhighprobabilityexactlybecauseourviewsaresimilar?Supposethatthe

probabilityforustointeractincreaseswiththeincreasingsimilarityofourviews,anddecreasesifourviewsbegintodiffer.

Ifthisisright,thenthefundamentalrelationdetermininghowoftenweinteractishowsimilarourviewsare—anddistanceinspaceisderivativefromthat.

Now,forbig,clunkythingslikeourselves,madeupofvastnumbersofatoms,thisisasfarasitgoes.Butconsiderwhatittakesforatomstohavesimilarviews.Atomshavemanyfewerdegreesoffreedom,hencefewerrelationalproperties.Soatomswhicharefarawayfromeachotherinspacemaystillhavesimilarneighborhoods,justbecausetherearevastlyfewerconfigurationstheirlocalneighborhoodscouldtake.Thissuggeststhatperhapssimilaratoms,withthesameconstituentsandsimilarsurroundings,interactwitheachotherjustbecausetheyhavesimilarviews.

Theseinteractionswouldbehighly,highlynonlocal.Butinmyrecentwork,Ihaveshowedthatthiscouldbethebasisofquantumphysics.12

Considerahydrogenatominawatermoleculedancingintheairinfrontofme.Thishasafirstneighborhoodconsistingofanoxygenatom,andasecondneighborhoodconsistingofthewholemolecule.Thesameistrueofeveryhydrogenatominawatermoleculeeverywhereintheuniverse.SoIamgoingtotrustmyrelationalinstinctsandtakethecrazystepofpositingthatalltheseatomsareinteractingwitheachother,justbecausetheirviewsaresimilar.Morespecifically,Iwillpositthattheinteractionsacttoincreasethedifferencesbetweentheseatoms’views.Thiswillgoonuntilthesystemhasmaximizedthevarietyofviewstheatomshaveoftheuniverse.

Inarecentpaper,IshowedthatthehypothesisofmaximalvarietyleadstotheSchrödingerequation,andhencetoquantummechanics.ThishappensbecausethereturnsouttobeamathematicalsimilaritybetweenthevarietyandBohm’squantumforce.Asaresult,Bohm’squantumforceactstoincreasethevarietyofasystem.Itdoessobymakingtheneighborhoodsofallthedifferentparticlesasdifferentfromeachotheraspossible.

Inthisapproachtheprobabilitiesinquantummechanicsrefertoanensemblethatreallyexists,theensembleofallsystemswithsimilarviews.Thisisarealensemble,inthattheelementsarenotlocatedinourimagination;theyare,eachandeveryone,apartofthenaturalworld.

Thisisinaccordwiththeprinciplesofcausalcompletenessandreciprocity.

ThiswasthebasisofarelationalhiddenvariabletheoryIproposed,whichIcalledtherealensembleformulationofquantummechanics.Fromit,IcouldderivetheSchrödingerformulationofquantummechanicsfromaprinciplethatmaximizesthevarietypresentinrealensemblesofsystemswithsimilarviewsoftheuniverse.

Onthetechnicalside,thistheoryborrowsfromthemanyinteractingclassicaluniversestheoryIdescribedinthelastchapter,onlytheensembleofsimilarsystemsdoesnotcomefromotheruniversesparalleltoourown;insteadtheyaresimilarsystemsfarawayindistantregionsofourownsingleuniverse.

Inthistheory,thephenomenaofquantumphysicsarisefromacontinualinterplaybetweenthesimilarsystemsthatmakeupanensemble.Thepartnersofanatominmyglassofwaterarespreadthroughtheuniverse.Theindeterminismanduncertaintiesofquantumphysicsarisefromthefactthatwecannotcontrolorobservethosedifferentsystems.Inthispicture,anatomisquantumbecauseithasmanynearlyidenticalcopiesofitself,spreadthroughtheuniverse.

Anatomwithitsneighborhoodhasmanycopiesbecauseitisclosetothesmallestpossiblescale.Itissimpletodescribe,asithasfewdegreesoffreedom.Inabiguniverseitwillhavemanynearcopies.

Large,macroscopicsystemssuchascats,machines,orourselveshave,bycontrast,avastcomplexity,whichtakesagreatdealofinformationtodescribe.Eveninaverybiguniverse,suchsystemshavenocloseorexactcopies.Hence,catsandmachinesandyouandIarenotpartofanyensemble.Wearesingletons,withnothingsimilarenoughtointeractwiththroughthenonlocalinteractions.Hencewedonotexperiencequantumrandomness.Thisisasolutiontothemeasurementproblem.

Thistheoryisnew,and,asisthecasewithanynewtheory,itismostlikelywrong.Onegoodthingaboutitisthatitwillmostlikelybepossibletotestitagainstexperiment.Itisbasedontheideathatsystemswithagreatmanycopiesintheuniversebehaveaccordingtoquantummechanics,becausetheyarecontinuallyrandomizedbynonlocalinteractionswiththeircopies.

Iarguedthatlargecomplexsystemshavenocopies,andhencearenotsubjecttoquantumrandomness.Butcanweproducemicroscopic

systems,madefromasmallnumberofatoms,whichalsohavenocopiesanywhereintheuniverse?Suchsystemswouldnotobeyquantummechanics,inspiteofbeingmicroscopic.

Wehavethecapabilitytodojustthatusingthetoolsofquantuminformationtheory.Indeed,asufficientlylargequantumcomputershouldbeabletoproducestatesinvolvingenoughentangledqubitsthattheyareveryunlikelytohaveanynaturalcopiesanywhereintheobservableuniverse.Thissuggeststhattherealensembletheorycanbefalsifiedbymakingalargequantumcomputerthatworksexactlyaspredictedbyquantummechanics.

Scienceprogresseswhenweinventfalsifiabletheories,eveniftheresultisthattheygetfalsified.Itiswhentheoristsinventnon-falsifiabletheoriesthatsciencegetsstuck.

Andwhataboutsystemswithsmallnumbersofcopies?Thesebehaveneitherquantummechanicallynordeterministically.Theywillhavetoexhibitbehaviorofanewkindwhichisneitherclassicalnorquantum.Thiswillgiveusfurtheropportunitiestotestthisnewtheory.*

THEPRINCIPLEOFPRECEDENCE

Therealensembletheorydependsonasystembeingabletorecognizeandinteractwithothersystemswhicharesimilartoit,inthesensethattheyhaveasimilarviewoftheuniverseofrelations,nomatterwheretheyareintheuniverse.Accordingtothishypothesis,similarityordifferenceofviewsismorefundamentalthanspace;spaceemergestodescribetheroughordercreatedbysimilarityofviews.Twosystemsmayinteractiftheirviewsaresimilarenough.Oftenthatreflectstheirbeingnearbyinspaceandtime,butnotalways,anditisthelattercasesthatunderliequantumphenomena.

Whathappensifweapplythisviewpointtosystemsatdifferenttimes?Mightasysteminteractwithsystemsinthepastthathavesimilarviews?Ifthisispossible,wecanusetheinfluenceofthepastonthepresenttofindanewunderstandingofwhatthelawsofnatureare.Thisleadstoanovelidea,whichIcalltheprincipleofprecedence.13

Toexplainitinsimpleterms,ithelpstouseoperationalterminology,inwhichaquantumprocessisdefinedbythreesteps.Thefirstisits

preparation,whichpickstheinitialstate.Nextwehaveanevolution,duringwhichitchangesintimeaccordingtoRule1.Attheendwehaveameasurement,whichisgovernedbyRule2.Wehaveseveralchoicesaboutwhatwemeasure,butwhicheverwechoose,severaldifferentoutcomesarepossible.Quantummechanicspredictsthattheprobabilitiesforthesedifferentoutcomeswilldependonthepreparation,theevolution,andthechoiceofwhatwemeasure.Ifweknowtheforcesactingonthesystemduringtheevolution,wecanuseRules1and2topredicttheprobabilitiesofthedifferentoutcomes.

Itiscommontobelievethat,oncetheenvironmentofthesystemisfixed,Rule1evolvesthesystemintimeasdictatedbythefundamentallaws.Theselawsarepresumednottochangeintime.Asaconsequence,wecansaythefollowing.Foreveryquantumsystemwestudyinthepresent,definedbyaspecificpreparation,evolution,andmeasurement,therewillbeacollectionofsimilarsystemsinthepast.Thesearesimilarinthesensethattheyhadthesamepreparation,evolution,andmeasurementasourpresentsystem.Now,thefactthatthelawsdon’tchangeimpliesthattheprobabilitiesfordifferentoutcomesalsodon’tchange.

Asaresultwecansaythat

Theprobabilitiesfordifferentoutcomestoresultinthepresentexperimentarethesameasifwepickedrandomoutcomesfromthecollectionofpastsimilarinstances.*

Wecancallthisthelawofprecedents.NowIwouldliketomakeasimplebutradicalproposal.Thelawof

precedentsisusuallyunderstoodtobeaconsequenceoftheexistenceofunchanginglaws.Butactually,thislawofprecedentsisallweneedoflaw.Wecanpositthatthereisnolawexceptthelawofprecedents.Insteadoftheabove,wepositthat

Theprobabilitiesfordifferentoutcomestoresultinthepresentexperimentarearrivedatbypickingrandomoutcomesfromthecollectionofpastsimilarinstances.

BythisIpostulatethataphysicalsystemhasaccesstotheoutcomesofsystemswithsimilarpreparations,evolutions,andmeasurementsinitspast(wecallthese“similarsystems,”forshort).Ourhypothesisisthen

Aphysicalsystem,whenfacedwithachoiceofoutcomesofameasurement,willpickarandomoutcomefromthecollectionofsimilarsystemsinthepast.

Thislawofprecedentsguaranteesthatmostofthetime,thepresentwillresemblethepast,inthattheprobabilitiesforthevariouspossibleoutcomesofthesameexperimentwillbeunchanged.

Ifthisisright,theappearancethatatomsaregovernedbyunchanginglawsisanillusioncreatedbythefactthattheuniverseisoldenoughandbigenoughthatthereisampleprecedentformostsituationsanatomwillfinditselfin.

Butwhatiftherearenoprecedents?Whatifweprepareaquantumstatewhichhasneversofarexistedinthehistoryoftheuniverse?Ifwemakeameasurementofit,howwillwedetermineitsoutcome,iftherearenopastsimilarinstancestoreferto?

Idon’tknowtheanswertothisquestion.Thiscouldbeand,Ihope,willbeaquestionforexperimentalphysics.Thestandardbeliefinatimelessfundamentallawhasnoproblemmakingaprediction,byapplyingtheknownlawtothenewsituation.Iftheexperimentsalwaysconfirmthatanswer,wecandeducethattheprincipleofprecedenceiswrong.However,ifprecedenceisthekeytolawfulness,thentheresponsetoanovelsituation,anovelquantumstate,willbenovel.

Aftermanyrepetitionsprecedencebuildsup,andtherewillnolongerbesurprises.Thetransition,though,fromnoveltytoprecedenceshouldbeopentoexperimentalinvestigation.

Thesiteforsuchinvestigationsisagainlikelytobelaboratorieswhereexperimentalistsarepreparingentangledstatesofseveralatoms.Suchstateswillatsomepointsoonbecomplexenoughthatitwouldbesafetodeducetheyhavenoprecedentsinthehistoryoftheuniverse.Soverysoonitoughttobecomepossibletotesttheprincipleofprecedenceexperimentally,andperhapsdiscovertheprocessbywhichprecedencebuildsup.

E

FIFTEEN

ACausalTheoryofViews

achofustheoristshashisorhercommitments:theguessesaboutnatureyouarewillingtobetyourcareeron.Personally,Iamarealist,arelationalist,and,indeed,atemporalrelationalist.I

believethatquantummechanicsisincompleteandaimtoconstructarealisttheoryaccordingtotheprinciplesoftemporalrelationalism,whichcanstandasasimultaneouscompletionofquantummechanicsandgeneralrelativity.Ihavehopesthatthistheorywillnotonlyresolvethepuzzlesinthefoundationsofquantumtheory,butwillleadtothediscoveryoftherightquantumtheoryofgravity,aswellasaddressmysteriesincosmologyandparticlephysicscomingfromtheuniverse’sapparentfreedomtochoosebothlawsandinitialconditions.

InthisclosingchapterI’dliketodescribeonepathwemighttaketoreachthisgoal,andthentellyouaboutsomeveryrecentworkthatbringsusafewstepsalongthispath.

Thisisatheoryofnads,ofthesortI’vebeendescribing,withtwoadditionalideas.First,wetakeseriouslyLeibniz’sideathatwhatisrealinapurelyrelationaldescriptionoftheworldistheviewsthateachnadhasoftherestoftheuniverse.Theviewsdon’trepresentwhatisreal;theyarewhatisreal.Thismeansthattheviewsthemselvesarethedynamicaldegreesoffreedom,theprotagonistsofourstory.ThisindeedbringsournadsclosertowhatLeibnizcalledmonads(althoughtherearestillsomedifferences).

Buttowhatexactlydothenadscorrespondintheworldwearefamiliarwith,andofwhatdotheirviewsconsist?

Ifwewantacorrespondencewithgeneralrelativity,itisnaturaltopresumethatthenadsareevents.Inrelativitytheory,eventsarethingsthathappenatasingleplaceandtime.Theyarefundamentaltogeneral

relativity’spictureoftheworld.Youcanthinkofthemasmomentswhensomethingchangesatoneplace:forexample,twoparticlescollidingmakeanevent.Aworldmadeofeventsisaworldinwhich“tobecome”ismorefundamentalthan“tobe.”

Ifthenadsareevents,whatdotherelationsbetweenthemdescribe?Theshortansweriscausation.Eventscauseotherevents.

Eacheventiswovenintothehistoryoftheuniversethroughrelationswiththeotherevents,whichexpresswhicheventsmightbeacauseofwhich.Thesecausalrelationschartthehistoryofprocessesofchange.

Wecanextracthowtheserelationsworkfromgeneralrelativity.Giventhatcausescanpropagateonlyatthespeedoflightorless,wesaythataneventBisinthecausalpastofanotherevent,A,ifaphysicalcausecouldhavetraveledatthespeedoflightorlessfromBtoA.Ifthisrelationholds,thenconditionsatBmighthavecontributedtocausingconditionsatA.

UnderthesameconditionwealsosaythatAisinthecausalfutureofB.

Givenanytwoevents,AandB,weusuallyrequireofgeneralrelativitythatonlyoneofthefollowingthreethingsmustbetrue.EitherAisinthecausalfutureofB,orBisinthecausalfutureofA,ortheyarecausallyunrelatedbecausenosignaltravelingatthespeedoflightorlesscouldhavepassedbetweenthem.ThisrulesoutclosedcausalloopsinwhichAisinboththecausalfutureandcausalpastofB.Exotichistorieswithclosedcausalloopsarefuntospeculateabout,buttheyraisepuzzlesandparadoxes.Iseenoreasontopresumeclosedcausalloopsarepartofnature,especiallyasIwanttopresumethatcausationisfundamental,andfundamentallyirreversible.*

FIGURE14.Asetofdiscreteevents,connectedbycausallinks.

Ifwesaywhatthecausalrelationsarebetweeneverypairofevents,wearedescribingtheuniverseintermsofitscausalstructure.

Accordingtogeneralrelativity,spacetimeconsistsofacontinuousinfinityofevents.Instead,Ifollowsomeofthepioneersofquantumgravity,whohypothesizethenadstobeadiscretesetoffundamentalevents.Discretemeanstheycanbecounted,whetherthecountisfiniteorinfinite.Wewillalsorequirethateveniftheirtotalnumbersareinfinite,thereisafinitenumberwithinanyfinitevolumeofspaceandfiniteintervaloftime.Thisgreatlysimplifiesthings.

Ataminimum,wewillwanttoascribecausalrelationstothenads.Theseworkjustlikecausalrelationsingeneralrelativity.Givenanytwonads,AandB,eitherAisinthecausalfutureofB,orBisinthecausalfutureofA,ortheyarecausallyunrelated.Asetofnadstogetherwith

theircausalrelationsisamodelofwhatadiscreteorquantumspacetimemightbelike.

Sincethenadsareadiscreteset,theircausalrelationsarediscreteaswell.Wecancountbackwardandforwardindiscretecausalsteps.Eachnadhasitsimmediatecausalpast,whichconsistsofthosenadsonestepbackfromitintothepast.

Itisthennaturaltothinkofnadsintermsofametaphorofparentage.NadCmighthavehadtwoparents,AandB;thenwecanthinkofCastheeventdefinedbythemeetingoftwocauses,onefromAandonefromB.TracingtheancestryofCbackthroughAandBtotheirparents,andbeyond,givesusanetworkofcausesstretchingdeepintothepast.Cinturnmighthavetwoprogeny,DandE,whichitinfluences.

Atthispoint,wehaveinfrontofusapossibilityofbreathtakingsimplicity.Wecansupposethattheeventswhichmakeupthehistoryoftheworldhavefundamentallyonlythesecausalrelations.Allotherentitiesandallotherpropertiesinnaturearetobederivedfromalargebutdiscretesetofeventswhoseonlypropertyiswhichcauseswhich.ThisradicalsuggestionwasmadebyRafaelSorkin,1anddevelopedinclosecollaborationwithagroupoffriendsandenthusiasts.Theycallitthecausalsettheory.

Acausalsetissimplyadiscretesetonwhichtherearedefinedonlycausalrelations,satisfyingtheconditionthataneventisneveritsowncause.OnealsorequiresthatgivenanytwoeventsAandB,onlyafinitenumberofeventsareinboththecausalfutureofBandthecausalpastofA.

Iadmiretheambitionandradicalpurityofcausalsettheory.Itisacompletelyrelationaldescriptionofspacetime,inwhicheacheventisdefinedcompletelyintermsofitsplaceinthenetworkofcausalrelations.

Oneverygoodfeatureisthatthegeometryofaspacetimecan,toagoodapproximation,becapturedbyacausalset.Thisisdonebyamethodanalogoustohowpollsofourpoliticalviewsaretaken.Ratherthanaskeveryone’sviews,thoseofasmall,randomlychosensamplearequeried.Similarly,onecanpickoutarandomsampleofeventsinaspacetimeandrecordtheircausalrelationswitheachother.Onelosesalotofinformation,butifonepicksaneventpersomefixedvolumeofspaceandunitoftime,onegetsarepresentationofthecausalrelationswhichisaccuratedowntothatscale.

However,Sorkinandhiscollaboratorshypothesizethatthereverseisalsothecase.Theybelievethehistoryoftheuniverseis,atitsmostfundamental,adiscretecausalset,fromwhichemerges,onasufficientlylargescale,theillusionofacontinuousspacetime.Justlikealiquidappearstouscontinuousbutisactuallymadeupofdiscreteatoms,theeventsofthecausalsetwouldconstitutetheatomsofspacetime.

Onegreatsuccessofthecausalsettheoryisthatitpredictedtheroughvalueofthecosmologicalconstant.Sorkinderivedthispredictionbeforethecosmologicalconstantwasmeasured.2Itwastheonlyapproachtoquantumgravitytodoso.

Thecausalsethypothesisisoneofseveralcompetinghypothesesconcerningthepropertiesofspacetimeatoms.Comparedtotheothers,suchasspinfoammodels,itenjoysthegreatadvantageofitsuttersimplicity,inthattheonlypropertiesofeventsaretheircausalrelations.Thisgreatlynarrowsdownthepossibleformsthatafundamentallawofspacetimeatomscouldtake.

Thisradicalsimplicityisalsobehindaveryformidableobstaclethatthisapproachfaces,whichiscalledtheinverseproblem.AsIsaidearlier,givenacontinuousspacetime,wecaneasilysampleitseventstofindacausalset.Butthereverseisalmostneverthecase.Intheworldofpossiblecausalsets,almostnoneprovideanapproximatedescriptionofaspacetime,withthreedimensionsofspace.Thismakesitseemasifthereismoretoaspacetimethanaroughdescriptionofanetworkofcausalrelations.

Quantumgravity,ortheproblemofunderstandingspacetimewithinquantumtheory,hascertainlyprovedtobeaformidablechallenge.Ithelpstoputthechallengeofdiscoveringtheatomsofspacetimeinperspectivebycomparingitwiththehistoryofthehypothesisthatmatterismadeofatoms.

Inthecaseofmatter,thechallengesfacingatomistsinthenineteenthandearlytwentiethcenturiesweretwofold.First,theyneededtodiscoverthefundamentallawsthatgoverntheatoms.Second,theyhadtodeducefromthosefundamentallawstheroughpropertiesweperceivemattertohave.Theyhadtounderstandhowtheillusionsofsolids,liquids,andgasesariseasconsequencesofthemorefundamentalatomiclaws.Theoristsofquantumgravityfacethesametwochallenges.

Weshouldbemindfuloftwolessonsfromthehistoryoftheoriginalatomichypothesis.Thefirstisthatprogressonthefirstchallenge—thatofdiscoveringthelawsofatomicphysics—didn’tbegintobemadeuntilwehadexperimentsthatcouldverifythatatomsreallyexistedandrevealtoussomeoftheirproperties.

Historyalsoteachesusthatthesecondchallenge—derivingthebulkpropertiesofthevariousphasesofmatter—maybeeasiertoaddressthanthefirst.Halfacenturybeforewebegantomakerealprogressonuncoveringthelawsofatomicphysics,afewpioneershadalreadymadesubstantialprogressonthesecondchallenge.Thereasonisthatthebehaviorofmatterinbulkturnsoutnottodependverymuchonthedetailsofatomicphysics.Oneneededtoknowonlythatthereareatomsandthattheyinteractbyforcesthatareshort-range(i.e.,couldonlyactoverashortdistance).

Thislessonistakentoheartbysomequantumgravitytheoristswhoseektoderivethelawthatgovernsspacetimeonamacroscopicscale,namelygeneralrelativity,fromsimplehypothesesabouttheatomsofspacetime.ThisdirectionwaspioneeredbyTedJacobson,3andithassucceededtoasignificantdegree.Thismakesitlikelythattheknownlawsofphysics,whichoperateonscaleswecanobserve—muchlargerthanthefundamentalPlanckscale—don’tdependverymuchonthelawsthatgoverntheatomsofspacetime.

Thisisbadbecauseitmeansthattheknownlawsholdfewclueswhichmighthelprevealthetrulyfundamentallaws.Indeed,thereare,itwouldseem,justtwoclues.Thefirsthastodowithhowinformationflowsthroughspacetime,andisthefollowing:Toderivegeneralrelativityfromthepropertiesofhypotheticalatomsofspacetime,onemustpositthatthereisamaximumrateatwhichinformationmayflowthroughasurfaceinspace.Thisrateofinformationflowcannotbegreaterthantheareaofthatsurface,whencountedupinfundamentalPlanckunits.*Thisiscalledthe(weak4)holographichypothesis.*

Ifthisholographichypothesisisfundamental,thenithastomakesensetospeakofaflowofinformationallthewaydownatthetinyscaleswherequantumgravityoperates.Butinformationisinfluence,asisexpressedbydefiningitasthedistinctionthatmakesadifference.Soaflowofinformationdefines(ordependson)acausalstructure.Thustheholographichypothesisrequiresthatwemusthaveacausalstructureto

guide,orexpress,theflowsofinformation.Thisisonereasontobelievethatcausalstructureisfundamental.

ThesecondclueisthattoderivegeneralrelativityfollowingJacobson’sargument,wehavetokeeptrackoftheflowsofenergythroughthesamesurfaces.Thissuggeststhatenergyisafundamentalquantitythatmakessenseallthewaydowntothelevelofthefundamentalevents.ThegreatinsightofJacobsonisthentohaverealizedthat,mostfundamentally,theequationsofgeneralrelativityencodearelationshipbetweenflowsofenergyandflowsofinformation,bothflowsbeingguidedbythecausalstructure.

Becauseofthefirstclue,Ifavorthehypothesisthatthehistoryoftheuniversecontainsasetofeventsandtheircausalrelations,i.e.,thattheuniverseisacausalset.But,becauseoftheinverseproblem,Idonotbelievetheradicalhypothesisthattheonlypropertieseventsenjoyarecausalrelations.Iamwillingtobelievethatthecausalrelationsaretheonlyrelationalpropertiesneeded,butIbelievetheremustbefurtherproperties,whichareintrinsictotheevents.Thesecondclueleadsmetopositthatamongtheseintrinsicproperties,eventsareendowedwithenergy,whichflowsbetweenthem,followingthecausalrelations.

Ithenwouldproposethateacheventhasacertainquantityofenergy,andthatenergyistransmittedfrompasteventstofutureeventsalongthecausalrelations.Anevent’senergyisthesumoftheenergiesreceivedfromtheeventsinitsimmediatecausalpast.Thatenergyisdividedupandtransmittedtotheeventsinitsimmediatecausalfuture.Inthiswaythelawofconservationofenergy,accordingtowhichenergyisnevercreatedordestroyed,isrespected.

Specialrelativitytellsusthatenergyisunifiedwithmomentum,soIwouldhavemomentumpropagatedfrompasteventstofutureeventsaswell.IncollaborationwithMarinaCortês,Iinventedacausalsetmodelwhichincorporatesflowsofenergyandmomentum,whichwecallanenergeticcausalset.5

Thehistoryoftheuniverse,accordingtoanenergeticcausalsetmodel,consistsofeventswhichareeachthecausesoffutureevents,towhichtheytransfersomeenergyandmomentum.Butthereisnospacetime,fundamentally;thereisjustthediscretesetofeventsconnectedbycausalrelations,withtheeventsandtherelationsendowedwithenergyandmomentum.

Oneearlysuccessofthisapproachwasasolutiontotheinverseproblem.Atleastinsimplecasesinwhichspaceandtimeeachhaveonedimension,wewereabletoderivetheemergenceofspacetimedirectlyfromtheenergeticcausalsetmodels.

—ITISTIMEwetalkedaboutenergy.

Eachofthemajorphysicaltheories,fromNewtonianphysicsdownthroughgeneralrelativityandontoquantumfieldtheory,hasequationsofmotionthattellhowsomeentitychangesintime.ForNewton,thatentityisthepositionofaparticle,whileforquantumfieldtheoryitisthevalueofafieldateverypointinspace.Itishighlysignificantthatalltheseequationsofmotionshareacommonstructure.Thereisaconfigurationvariable—thepositionsoftheparticlesorthevaluesofthefields.Thentherearecertainadditional,dynamicalquantities,whicharecalledsobecausetheycomeintothelawsthattellhowtheparticlesmovearoundorhowthefieldsoscillate.Themostimportantofthesearemomentumandenergy.

Eachparticlecarriesacertainquantityofenergyandmomentum.Whentwoparticlesinteract,theyexchangesomeoftheirenergyandmomentum.Onemaygainabit,whiletheotherloses,solongasthetotalenergyandtotalmomentumareconserved.

Thestructureofthesetheoriesisalwaysthesame:therearetwofundamentalequations.Thefirsttellshowthepositionsoftheparticleschangeintime,inawaythatdependsontheparticles’momentum.*Thesecondequationtellshowthemomentumchangesintime,andthisdependsontheparticles’positions.Sothetwoquantities,positionandmomentum,areintertwined;thechangeofonedependsontheother.Wesaythattwoquantities,relatedinthisway,aredual.Positionandmomentumaredual.Soaretheelectricandmagneticfields.

Ibelievethatthefactthatthispatternofdualequationsisuniversalinphysicsisadeeppropertyofnature.Itisalsorestrictedtophysics.Othersciencesdescribesystemsthatchangeintime,suchascomputersorecosystemsormarketsororganisms.Theyeachhavetheirequations.Butinnoneofthesecasesdotheequationshavethisdualstructureinvolvingconfigurationvariables,momenta,andenergy,thelattertwoofwhichare

conservedintotal.ThisisonereasonIdon’tthinkit’sveryhelpfultoimaginethatthephysicaluniverseisacomputer.

Theconservationofmomentumisimportantforanotherreason.Itexplainstheprincipleofinertia,whichisthedeepestprincipleofphysicssofarposited.

Whyistherethisduality,involvingconfigurationandmomentumvariables?Whyistheworldsuchthatenergyandmomentumareconserved?Thereisanoldanswertothesequestions,whichisbasedonadeeptheoremofEmmyNoether,whichsheprovedin1915.Itinvolvesthenotionofsymmetry,whichisatransformationthatchangesasysteminsomewaythatdoesn’tchangethelawsofmotion.Rotationsaresymmetries,asaretranslationsinspaceandtime;solongastheentiresystemisrotatedortranslatedtogether,thenthelawsofmotionareunaffected.Noether’stheoremstatesthatforeverysymmetryinnaturethatisbasedonatransformationthatvariescontinuously,thereisaconservedquantity.Symmetryinspaceimpliesthatmomentumisconserved.Symmetryintimeexplainstheconservationofenergy.*

Thissuggeststhatspaceisfundamental,whileenergyandmomentumareemergentpropertiesofspace,reflectingitssymmetries.Thisisastandardview,butIbelievethereverseisclosertothetruth.

WhileNoether’stheoremreflectsatrueinsight,itcannotapplytoafundamentaltheory.Thisisbecausewerequirethatthefundamentaltheorysatisfytheprincipleoftheidentityofindiscernibles.Butthatprincipleimpliesthattherearenosymmetriesinnature.Thinkofabodythatisinvariantunderarotation,suchasasphereoracylinder.Thefactthatitissymmetricalmeansthatitisunchangedbyarotation.Thatis,anobservercannottellthedifferencebetweenthebodybeforeandafteritisrotated.Butthisistruebecausethereareonthebodycirclesofpoints,whichareallidenticaltoeachother.Similarly,aninfinitestraightlineisinvariantunderatranslationalongitslengthbecauseundersuchatranslation,eachpointistakentoanotherpointwithidenticalproperties.Ineachcaseweseethattheexistenceofasymmetrymeanstherearedistinctpointswithidenticalproperties,whichviolatestheprinciple.

Symmetriesarepropertiesoffixedbackgrounds,andtheoccurrenceofasymmetryinatheoryisaclearsignthatthattheoryisbackgrounddependent.Asymmetryisanoperationthattranslatesorrotatesthesystemwearestudying,withrespecttothebackground,whichisleft

unchanged.Symmetriescharacterizeasystemthathasbeenisolatedfromalargeruniverse,andarisefromwhatisignoredinthatisolation.

Wehavepositedthatthefundamentaltheoryisbackgroundindependent,whichmeanstherearenosymmetries.Thisinturnmeansthatwecannotregardenergyandmomentum,andtheirconservation,asemergentfromthepropertiesofspace.Butwestillhavetoexplainwhyenergyandmomentumplaytheubiquitousroletheydointhestructureoftheequationsofphysics.

Further,wehavehypothesizedthatspaceisnotpresentatthefundamentallevelinnature,butisemergent.Soifwewantenergyandmomentumtoplayaroleinphysics,thereseemstobenoalternativebuttoputtheminatthebeginning.

WhatwewantisaninverseofNoether’stheorem,whichassumesthatenergyandmomentumandtheirconservationarefundamental,andtellsustheconditionsunderwhichspacemayemergeasanapproximatedescriptionofsubsystemsofthewhole.

Soweareleftwithapictureinwhichcausalrelations,energy,andmomentumarefundamental.Energeticcausalsetsareaworkingoutofthispicture.

TheenergeticcausalsetmodelsrealizetheprinciplesandhypothesesoftemporalrelationalismthatIintroducedinthepreviouschapterwithinaconcreteframework.Intheseprinciples,time,inthesenseofthecontinualbecomingofthepresentmoment,isfundamentaltonature.Indeed,ourexperienceoftime’spassageistheonethingwedirectlyperceiveabouttheworldwhichistrulyfundamental.Alltherest,includingtheimpressionthatthereareunchanginglaws,isapproximateandemergent.Thisview,andthecaseforit,hadbeendevelopedduringalongcollaborationwithRobertoMangabeiraUnger.Animportantconsequenceisthatthelawsofnature,ratherthanbeingtimeless,evolveintime.Thisreversesthebelief,commonamongphysicists,thattimeisnotpresentinthemostfundamentallaws,butratheremergesfromthoselaws.Instead,wearguethattime,inthesenseofthepresentmomentanditspassage,isfundamental,whilethelawsareemergentandsubjecttochange.

MarinaCortêsinsistedthatthelawsatthemostfundamentallevelmustbeirreversible,intwosenses.First,thelawsarenotthesameifyoureversethedirectionoftime.Ifyoutakeavideoofalawfulprocess,you

donotgetanotherlawfulprocessbyplayingitbackward.Thisdirectlycontradictsawidelyheldbeliefthatthelawsofnatureareunchangedifyoureversethedirectionoftime.

Butalltheknownfundamentallaws,includingquantummechanics,generalrelativity,andthestandardmodel,areinvariantundersuchatimereversal.*Theremustbemore-fundamentallaws,whicharenotreversible.Thisraisestwochallenges:First,canweinventcandidatesforanirreversiblefundamentallaw?Second,mightithappenthatreversiblelawsemergeasanapproximationtomorefundamentalirreversiblelaws?Thesewerethequestionswhichenergeticcausalsetmodelswereinventedtoaddress.

Cortêsalsoinsistedonadeepersenseinwhichatheorythattakeseventsasprimaryisirreversible.Aneventissomethingthathappens.Aswestatedabove,oncesomethinghappensitcannotun-happen.However,theeffectofaneventcanbereversed.IfaneventchangesAtoB,itcanbefollowedbyaneventthatchangesBbacktoA.Butthatmakesahistorywithtwoevents.Onceaneventhashappeneditisinthepast,andthatfactcannotbeerasedbyafutureevent,evenifthatfutureeventreversestheeffectoftheoriginalevent.

Thisthoughtledustoviewthepassageoftimeasaprocessbywhichneweventsaresteadilycreatedfrompresentevents.Whilewemaygivediversemeaningstotheword“time,”wepositedthatthepassageoftimeexpressesanactiveprocessofcreationandthatthis“activityoftime”isthecreationofnovelevents,eachoneaftertheother.

Morespecifically,weinventedseveralmodels,forthepurposesofmakingaconcreterealizationofourprinciplesandhypotheses.Inonemodelwestudied,eacheventiscreatedfromtwo“parent”events,andthen,inturn,becomestheparentoftwo“child”events.

Ateachstageintheprocessthereisavanguardofevents,whichhavebeencreatedbuthaveyettohavehadalltheirchildren.Theseeventsmakeupwhatwecall“thepresent,”astheyaretheeventsthatwillstillinfluencethefuture.

Thisprocessofthecontinualbecomingofeventscreatesahistory.Onceaneventhashaditsfullallotmentofchildren,itmaynolonger

playadirectroleincreatingthefuture,sowesayitisinthepast.Eachpasteventhasacausalpast,consistingofthoseprioreventsthathavedirectlyorindirectlyinfluencedit.Itscausalfutureisthecontinually

growingsetofeventsitdirectlyorindirectlyinfluences.Thus,thepasthasthestructureofacausalset.

Wenextaddedenergyandmomentum,makingourmodelofagrowingfutureanenergeticcausalset.Eacheventhasatotalenergyandatotalmomentum,whicharethesumsofthoseoftheirparents.Thesearedividedupandpasseddowntotheirchildren.

Tocompletethismodel,wemustanswertwoquestions.Howdoestheprocessthatcreatesneweventsoutofpresentevents,whichwecalledtheactivityoftime,choosewhichpairofpresenteventswillbethenextparentsofanovelevent?Second,howdoeventsdistributeenergyandmomentumtotheirchildren?Toanswerthesequestions,weneedtoprescribearuleforthecreationofnewevents.

InchoosingthisrulewewereguidedbytwooftheprinciplesIenunciatedearlier.Thetheoryshouldbebackgroundindependent,whichinthiscontextmeansthatthedifferenteventsshouldbenamed,orlabeledordistinguished,onlybydynamicallycreatedstructures.Moreover,thesestructuresshouldnotrefertotheorderinwhichtheeventswerecreated.Theserequirementsaresatisfiedifeventsarelabeledordescribedonlybythestructureoftheircausalpasts.

Thismakesitnaturaltoinvoketheidentityofindiscerniblesasoursecondprinciple.Ifeventsaredistinguishedbytheircausalpasts,thenthecausalpastofeacheventmustbeunique.Theeventcreationruleshouldthenensurethateacheventitcreateshasacausalpastdifferentfromalltheotherssofarcreated.

InthemodelsIstudiedwithCortês,wefoundtwoveryinterestingresults.Thefirst,alreadymentioned,isthattheinverseproblemappearstobesolved,inthatthereemergesaspacetimeintowhichtheeventsandtheircausalrelationscanbemapped.Wealsofoundthatthesystemsbegininaverytime-asymmetricanddisorderedphase,whichevolvestoaphasethatisorderedandapproximatelytimesymmetric.*

Wethuslearnedanimportantlessonfromtheenergeticcausalsetmodels,whichisthattime-reversiblelawscanemergefrommorefundamental,irreversiblelaws.Thiscontradictsthewaymostphysiciststhinkaboutirreversibility.

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WEBEGANinthelastchapterwithfiveprinciples,whichareallwaysofexpressingLeibniz’sprincipleofsufficientreason,andthreehypotheses,whichexpressthefundamentalandirreversiblecharacteroftimeandthecontrasting,emergent,andcontingentnatureofspace.Thetheoryweseek,whichwouldcompleteEinstein’stwinrevolutions,Ibelievemaybetheconsistentexpressionofallofthese.But,beforegoingallthewaythere,weintroducedseveralmodels,whichwerenotmeanttobethecompletetheory,butratherexplorationsofsomeaspectsitmayhavebyapplyingonlyasubsetoftheprinciples.

Therealensembleformulationisarelationalhiddenvariabletheory.Itisnotafullapplicationoftheprinciples,asitissituatedinafixedbackgroundoftimeandspace,butotherwiseittakestheprincipleoftheidentityofindiscerniblesextremelyseriouslywhenitpostulatesthattwoevents,whichhavethesameviewoftheuniverse,aretobeidentified.Ithenpostulatedthatthereasontwobodiesinteractmorestronglywhentheyarenearerinspaceisinfactthattheirviewsoftherestoftheuniversearesimilar.Thatis,Iproposetoexplaintheprincipleoflocalityasarisingfromadeeperprincipleofsimilarityofviews.Toensurethattheidentityofindiscerniblesisrealized,weintroduceaforcebetweensubsystemsthatseekstoincreasetheirdistinctiveness,ormaximizetheoverallvariety.This,asIdescribedearlier,leadstoaderivationofquantummechanics.

Energeticcausalsetsaremodelsofdiscreteorquantumuniversesthatexplorethehypotheseswemadeaboutspaceandtime.Inparticular,theyembodytheideathatthereisnobackgroundspaceorspacetime.Instead,theytaketobefundamentalanactive,irreversiblenotionoftimeandcausation,aswellasenergyandmomentum.Spacetime,andspace,areemergentandcontingent.

Thenextstepistomarrythesetwomodels,givingusarelationalhiddenvariabletheorythatisalsobackgroundindependent,andwhichrealizesthehypothesisthatspaceandlocalityareemergent.

Thesetwomodelsstartedasseparateresearchprograms,buttheysharedamotif,whichisthecentralroleplayedbythesimilaritiesanddifferencesamongevents.Bothmodelstaketheseasfundamental,whilelocalityisdemotedtoanaccidentalandemergentaspectofnature.Itslowlydawnedonmethattheseweredifferentperspectivesonasingle

picture,andsoonesummerdayIsatdownandopenedafreshnotebooktoseeifIcouldtellthefullstory.

Itwasimmediatelyclearthattheprotagonistofthisnewstoryistheview.Thatis,thebasicvariablesarenothingbuttheviewsoftheuniverseseenfromeachevent.SoIbeganbyfashioninganapproachtophysicsinwhichtheseviewsarefundamental,ratherthanderivedfromamorebasicstructure.Inthisnewperspective,thefundamentallawsinvolvedirectlyonlytheviewsandtheirdifferences.Icallthistheorythecausaltheoryofviews.6

Theviewofaneventisnothingbuttheinformationavailabletoitfromitscausalpast.Theviewintothepastofaneventislikethesky;itiswhatyouseewhenyoulookaround.Becausethespeedoflightisfinite,lookingaroundmeanslookingback,intoyourpast.

Theviewofanevent,asIusethewordhere,isentirelyrealandhasnothingtodowithopinion.*InthetheoryIamdescribing,whatisrealandobjectiveintheworldistheinformationavailableateacheventmakingupthehistoryoftheworld,comingtothateventfromitscausalpast.

Lookup!Yourviewoftheworldislikeafilmprojectedonatwo-dimensionalsphere,whichwecallthesky.Theviewofaneventinamodelwiththree(emergent)dimensionsofspacewillthenberepresentedasatwo-dimensionalspherethatwecalltheevent’ssky.Whataneventseesonitsskyistheeventsdirectlyinitscausalpast.Moreprecisely,itseestheenergyandmomentumcomingfromeachofitsparentevents.Eachparentshowsupasacoloredpointonthatevent’ssky.Eachofthesepointsrepresentsaquantumofenergyandmomentumthathasarrivedfromapastevent.Thelocationofeachpointontheskyrecordsthedirectionofthemomentum,whilethecolorindicatesthemagnitudeoftheenergyreceived.

Thenextstepissimple:hypothesizethatallthattheuniverseconsistsofistheseskies—eachonetheviewofsomeevent.Ratherthanconstructtheviewsfromthecausalrelations,reversethingsandderivethecausalrelationsandeverythingelsefromtheviews.Thiscanworkbecauseinformationcontainedinthetotalityofviewsisenoughtoreconstructthecausalrelationsandhencethefullhistory.

Asintherealensembletheory,thelawsincludetherequirementthatthevarietyofalltheseviewsismaximized.Thishasasimilareffectof

leadingtothequantumforce.Usingthis,onecanderivequantummechanicsasanapproximationtothetheory.

Hereisaone-sentencesummaryofthistheory:theuniverseconsistsofnothingbutviewsofitself,eachfromaneventinitshistory,andthelawsacttomaketheseviewsasdiverseaspossible.

Fromherethestoryunfoldsverymuchlikethatoftherealensembletheory.Similarviewsinteractwitheachother,asaresultofthemandatetoevolveinthedirectionofevermorediversity.Thisleadstotheemergenceofspaceandoflocalityinthatspace.Nonlocalityalsoemergesasinteractionswhicharedistantintheemergentspacebutnearbyintermsofsimilarityofviews.Finally,asintherealensembleformulation,quantummechanicsarisesfromthesenonlocalinteractionsasanapproximatedescriptionofthedynamicsofviews.

Thecausaltheoryofviewsisthenaroutetoacompletionofquantummechanics.Itisarealistcompletion,becauseitisatheoryofbeables,whicharetheviewsthemselves.Mostimportant,itdemonstratesthatasinglefundamentaltheorycanbeatthesametimeacompletionofquantummechanicsandanatomicmodelofspacetime.Itcanexplaintheemergenceofbothlocalityandnonlocality,ofbothspacetimeandquantummechanics.

Thistheoryisstillonlypartofthestory,andthereisstillmuchtolearnaboutit,butitisawaytheworldmightbe.

—FORUSREALISTS,quantummechanicscannotbethefinalstory.Thereisstillmuchtodiscover.Nonetheless,Iremainconfidentthatnatureiscomprehensible.Iamoptimisticthattheuniversalpowerofreasoningthateachofushas,togetherwithourvastpowersofimaginationandourabilitytoinventnovelideas,willsufficetocomprehendtheuniverse.Iamespeciallyhopefulaboutafutureinwhichourindividualpowersarecombinedanddisciplinedbyourparticipationinthescientificcommunity.WhileIfindmyselfattimesdeeplyfrustratedbyourlackofdefiniteprogressonfundamentalphysicsduringthislasthalfcentury,Iamoptimisticaboutthelongrun.Iamconfidentthatinthefutureourdescendantswillknowvastlymoreaboutnaturethanwedo.

Iamalsosurethattheanswertothequestionsthathavebedeviledusfornearlyacenturywillbesimple,andexpressedintermsofelegant

hypothesesandprinciplesofthekindIhaveputforwardhere.ItwouldbefortunateindeedifwealreadyhaveamongourlibraryofideastheanswertohowtocompleteEinstein’stwinrevolutions.Butifwedon’t,Ihavenodoubtourdescendantswill,solongaswekeepthegreatadventureofsciencealive.

E

EPILOGUE/REVOLUTIONS

NotetoSelfThetruthisoutthere.

—THEX-FILES

Never,never,never,never,nevergiveup.—DAVIDGROSS

insteintoldusthatwescientistsareopportunistswhoarewillingtobreaktherulesandbendthescientificmethodtoourpurposeofdiscoveringhownatureworks.Eachscientistislikean

entrepreneur,whohasacertainamountofcapitaltoinvest;foratheoreticalphysicistthatcapitalconsistsmainlyoftimeandattention.Themostimportantdecisionswemakearewhatproblemsweworkonandwhichapproacheswechoose.Whichnewpaperdowestudy,towhichconferencesdowetravel,and,oncethere,towhichtalksdowelisten?Therewardscomeindifferentforms:thethrillofdiscovery,theadmirationofone’speersandstudents,andalsoone’scareer,jobopportunities,andsalary.

Ifyouareinterestedonlyinapplyingtheknownlawsofphysicstobroadenourappreciationofhownatureworks,thisisagreatperiodtobeaphysicist.Beautifuldiscoverieslightthewayincondensedmattertheory,andwearedoingrealastronomyusinggravitationalwavestoseetheuniverse.Theseparadigmsareworking.Steadyprogressinmathematicsdrivesadvancesinmathematicalphysics,withtrulybrilliantpeopleleadingthewaytoabetterunderstandingofthemathematicalstructuresofourestablishedandnascenttheories.Advancesinexperimentaltechniqueareequallyimpressive,withMoore’slawpaying

offinexponentiallyincreasingrangeandaccuracyofastronomicalobservations.Thereisnothingwrongwithanyofthisexceptthatlittleofitaddressesthebigfoundationalpuzzles.Itisonlywhenwetrytoadvancetheprojectofdiscoveringthefundamentallawsandprinciplesthatweseemtobespinningourwheels.

Atthepresentmomentinfundamentalphysicsandcosmology,therearebasicallyonlytwowaystobet.Weeitherbetthatweknowallthefundamentalprinciples,orwebettherearebasicideasandprinciplesmissing.Themajorresearchprograms,suchasinflation,stringtheory,andloopquantumgravity,areallwaysofbettingthatweknowthebasicprinciplesoffundamentalphysics.Withnotableexceptions,workersinthesefieldstakeforgrantedthatthebasicprinciplesofquantumtheoryandrelativityaresoundandapplytothenewtheory.Manyofthepeoplewhoworkoutsidetheseprogramsaredoingsobecausetheybetthereismuchmoretobediscovered.Peoplelikeme,whodosomeofboth,arehedgingourbets.

Whenitcomestoquantummechanicswefacethesamechoice.Eitherwebetthatwehavethecompletetheoryinourhandsandjustneedtounderstanditbetter,orwebetthetheoryisincompleteinimportantways.TheCopenhageninterpretation,theoperationalinterpretations,Everettquantummechanics,andsoonareallwaysofbettingweknoweverythingimportantaboutquantumphenomena.Anyonewhofocusesexclusivelyononeoftherealistproposalssuchaspilotwavetheoryorspontaneouscollapseisbettingtheirfavoritetheorywillturnouttobethecorrectcompletionofquantummechanics.Ineithercase,thebetassumesthatweknowalltheprinciplesneededtounderstandnature.

Whataboutthoseofuswhoareconvincedthatacompletionisneeded,butarenotconvincedanyofthewell-studiedoneshavetheringoftruth?Howarewetobet?

Uptonow,myownbetshavefallenonbothsidesofthesedivides.Mymostsuccessfulbetsemployedideasandtechnicaltoolsfromparticlephysicstosolveproblemsinquantumgravity.Thiswasoneoftheroutesthatledtoloopquantumgravity.ButfromtimetotimeIwrotepapersreportingmyeffortstoinventrelationalhiddenvariabletheories.Andtheverybestofmyearlypaperswasanattempttoconnecttheprincipleofinertiatoquantumfoundations.AstheyearswentonIextendedmyfoundationaleffortstothelandscapeissue,whichledtomyworkonthe

natureoftime.Butmybread-and-butterworkremainsquantumgravity,boththephenomenologyofthetheoryandloopquantumgravity.

Abookprojectisakindofmentaltherapy,whichforcesyoutoexamineyourconfusedthoughtsandintuitionsanddevelopthemtotheirlogicalconclusions.SonowthatIhavewrittenabookwhicharguesthataradicallynewtheoryisneededtosolvethefoundationalissuesinphysicsandcosmology,whatamIgoingtodoaboutit?DoIkeeptothesamesafe,hedgedprogram,orgoalloutonanattempttosolvetherealproblems?

Tobetthatthetruthrequiressomethingasyetundiscovered,wemustspendourtimesearchingforthatunknowncompletion.Wecan’tjustsaildownoneshorelineandupanother.Weheadwest:outofsightofland,followingourowncompass,orthebestfacsimilethereofthatwecancobbletogetherfromtheclueswetakeseriously.

Thereisnomorereasonablebetthanthatourcurrentknowledgeisincomplete.Ineveryeraofthepastourknowledgewasincomplete;whyshouldourperiodbeanydifferent?Certainlythepuzzleswefaceareatleastasformidableasanyinthepast.Butalmostnoonebetsthisway.Thispuzzlesme.

Isuspectit’shardformanyphysiciststoimaginethatwearenotneartheendofoursearchfortheultimatelawsofnature.Wehavebeenraisedinacultureinwhichit’sallabouthavingtherightanswer,andweoweourcareerstohavingbeenthescientistswhohadthem.ButI’vealwayshadinmyheadanimageofhowmuchmorepeopleinthefuturewillknow,andhowsillyourclaimstoknowledgewilllooktothem.Thishasprobablymademealesseffectiveadvocateofmyownideas.

Sowhatdowedowiththepartlysuccessfulinventions,suchasloopquantumgravity?Atfirst,thediscoveryofanewpossibledirection,incompleteandwithoutexperimentalconfirmation(inotherwords,highlyvulnerabletocriticism,asmostnewtheoriesareatbirth),isveryworthourtimeandfocus.ThatX,howeverincompletelyformulated,issomethingthatjustmightbetrue,orbepartofthetruth,evenwithoutpositiveevidence,iscertainlygoodforadecadeofexamination.Butafterathirdormoreofacentury,duringwhichmanycareer-longeffortshavefailedtobudgemightbetrueanyclosertomustbetrue,isn’tittimetomoveon?YoumightthinkI’mrepeatingpolemicsfromthestringwars,butI’mthinking,withagreatdealofaffection,ofallofuswhoseyearsof

hardworkhavefailedtoyieldthebreakthroughswefantasizedabout.Includingmyself;especiallymyself.

Whydowewritemoreandmorepapersonapproacheswhosedeficiencieshavebeenobviousfordecades,andalmostnopapersproposingnewcompletionsofquantummechanics?Itisnotforlackofcaring,foreveryoneIknowwhoworksonquantumfoundationshaschosenthatriskypathbecausetheycarepassionatelyabouthownatureresolvesthemeasurementproblemandtheotherpuzzles.

I,forone,amtiredofarguingovertheinsandoutsandrelativemeritsoftheexistingapproaches,andthecleverfixesinventedtosaveanideathatisprettyobviouslycollapsingfrominsufficiency.SoIhaveadecisiontomake:Ieitherkeeponthepresentpath,whichwillenduponthetopofthatlowhilljustpastthenextvillage,orheaddownintotheswampstostumblealongunknownpathsinsearchofundiscoveredmountains.IfItaketheswamptrail,Iwillalmostcertainlyfail,butIhopetosendbackreportstointerestandinspirethosefewotherswhofeelintheirbonesthecostofourignorance,ofgivingupthesearchtoosoon.

EvenifI’mconvincedthatsomethingverynewisneeded,Ihavelittleideahowtosearchforscientifictruthexceptbybuildingonanexistingresearchprogram,usingawell-honedtoolkitandmethodology.Thisisresearchasitistaught,recognized,funded,andrewardedbytheacademiccommunity.Acommunity,Ishouldmention,thatitisnecessarytobeanactivepartoftogetyourworktakenseriouslybypeoplewhoknowenoughtoevaluateit.WhatwouldIputinmyresearchproposals,ifmyideasarenotexpressibleinthelanguageofanalreadyexistingandwidelyfollowedresearchprogram?WhatproblemsdoIsetformyPhDstudents,iftheyarenottocalculatesomethingusingtoolsdevelopedwithinagivenframework?DoItellmystudentstowakeupinthemorning,makecoffee,openablanknotebook,andstareatituntiladisheveledangelarriveswitharevelation?IsthatwhatIshoulddomyself?Howmanydays,weeks,months,years,howmanyincoherentscribbledpages,doItoleratebeforegivingup?

Itisnotjustthattotrytoinventawholenewphysicsisriskyformycareeranddamagingtomyemotionalstability.Idon’tevenknowhowtobegin.Almostnoonealivehasdonethat,inthewaythattherevolutionariesofacenturyagodid.Inmyexperiencethereislittleasterrifyingasputtingasidethebasicprinciplesthatformthefoundationof

ourunderstandingofhowwefitintonature—isn’tthatwhyitfeelscomfortingtoknowthem?

Itcertainlyiseasiertoworkwithinanexistingframework,totestthelimitsofwhatweknowfromtheinside,sotospeak.Wecandothiswhilekeepinganopenmindaboutthebasicprinciplesandlookingoutforopportunitiestomodifythoseprinciplesorevenintroducenewones.Evenmoreimportantistokeeponthelookoutfornewopportunitiestotesttheoriesagainstexperimentsandobservations.ThisiswhatIhavedoneformostofmycareer,andIventuretosaythisistrueaswellofmanywhoworkonthemainapproaches,suchasstringtheoryandloopquantumgravity.Whatwehavetoshowforthisisacollectionofbeautifulresults,whichmayormaynotleadtothetruestory,and,especiallyprecious,afewproposalsfornewprinciples,includingtheholographicprincipleandtheprincipleofrelativelocality.But,withallduerespecttothoseofuswhoinvestedmostofourtimeinreasonableapproachestothedevelopmentofreasonabletheories,itdoesnotseemtohavebeenenough,thistime.

Isaytomyself,I’lltakesuchrisksafterIgetmyPhD,afterIgetmypostdoc,aftermyfacultyposition,aftertenure.Buteventenured,senior,famousprofessorsmustapplyforresearchgrants,andthereisalwaysthatfancycareer-culminatingprize,orthatcomfortableandprestigiouschair.Sowe’lljustwaittillretirement.Thenwe’llbefreetotakethebigrisks.Well,assomeoneclosinginonthat,Icanreportthattheonlythingyoulearniscertain,asyourfiftiesandsixtiesrushby,everydaybusywithaschedulefullofseminars,facultymeetings,workingwithstudents,classes,reviewpanels,airplanes,hotels,andconferencetalks,isthatyouarenotimmortal.

Somaybeit’salluptoabrilliantstudentsomewhere,impossiblyarrogant,astheyoungEinsteinwas,butblindinglytalentedenoughtoabsorbtheessentialsofallwehavedone,beforeputtingthemtoonesideandconfidentlystartingover.

Afriendoncetoldmethattheacademicworldwasmodeledonmonasteries,whichweredesignedtoperpetuateoldknowledgewhileresistingthenew.EvenafterdecadesinthesystemIamamazedathowthefinemechanicsofthiswork.Thereisnoarguingwiththelogicofacademicfame,whichrewardseveryscientificsuccesswithdistractionsthatmakeithardertodomorescience,whileimposingenormous

disincentivestoputtingasidepolishingyourlegacytotakeonnewchallenges.

TheacademicworldisverywellsuitedtosupportwhatThomasKuhncallednormalscience.Thatisgreatuntilitbecomeslongpastduetocompletearevolution.

Tomyknowledge,fewhavestumbledonamajordiscoverybyaccident;mosttruebreakthroughswerefoundafteryearsandyearsofhard,unrewardingwork.Feynmansaidtodiscoversomethingnewyouhavetotakethetimetomakeeverymistakepossiblealongtheway.Andhesurelyknew.

SoIhavenobetteranswerthantofacetheblanknotebook.Wedohaverolemodels.Einsteindidit.Bohrdidit.DeBroglie,Schrödinger,andHeisenbergdidit,asdidBohmandBell.Theyeachfoundapathfromthatblankpagetoafoundationaldiscoverythatenlargedourunderstandingofhownatureworks.Startbywritingdownwhatyouareconfidentweknowforsure.Askyourselfwhichofthefundamentalprinciplesofthepresentcanonmustsurvivethecomingrevolution.That’sthefirstpage.Thenturnagaintoablankpageandstartthinking.

ACKNOWLEDGMENTS

Thisbookrepresentsalifetimeofwrestlingwiththepuzzlesofquantumfoundations,andIhavetothank,firstofall,HerbertBernstein,forhisrevolutionaryfreshmanquantummechanicscourse,formakingmethegraderinthecoursetomakesureIlearnedhowtosolvetheproblems,andformanyyearsoffriendshipsincethen.IngraduateschoolIwasfortunatetobeabletostudywithAbnerShimony,whohasbeenarolemodelforallofuswishingtobringtherigoranddepthofphilosophytotheexaminationoffoundationalproblemsinphysics.ForthatIhavetothankHilaryPutnam,whotoldmethatAbnerwouldbeabletoanswermyquestionsaboutquantumtheorythathewasn’tableto.

Ingraduateschoolandintheyearssince,Ihavebeenfortunatetomeetandconversewithsomeofthetrulydeepthinkerswhoinspireusstill:SteveAdler,YakirAharonov,BryceDeWitt,CécileDeWitt-Morette,FreemanDyson,PaulFeyerabend,RichardFeynman,JimHartle,Gerard’tHooft,ChrisIsham,EdwardNelson,RogerPenrose,LeonardSusskind,JohnArchibaldWheeler,andEugeneWigner.

ShortlyafterreceivingmyPhD,ImetJulianBarbour,whointroducedmetoLeibnizandMach,andhasbeenmymentorandguidetorelationalphilosophysince.MyphilosophicaleducationhascontinuedthroughconversationswithDavidAlbert,HarveyBrown,JimBrown,JeremyButterfield,JenannIsmael,andSteveWeinstein,amongmany.HenriqueGomes,SimonSaunders,RoderichTumulka,AntonyValentini,andDavidWallacehavebeenespeciallyhelpfulreadingandcommentingondraftsandpatientlyexplainingwhatIgotwrong.Allerrorsthatremainare,however,myresponsibility.

ThenIwantverymuchtothankthosewhohavebecomefriendsthroughoursharedworkonfoundationalproblems:StephonAlexander,GiovanniAmelino-Camelia,AbhayAshtekar,EliCohen,MarinaCortês,LouisCrane,JohnDell,AvshalomElitzur,LaurentFreidel,Sabine

Hossenfelder,TedJacobson,StuartKauffman,JurekKowalski-Glikman,AndrewLiddle,RenateLoll,JoãoMagueijo,RobertoMangabeiraUnger,FotiniMarkopoulou,andCarloRovelli.

ThebookhasbeenverymuchimprovedbyfeedbackfromKristaBlake,SaintClairCemin,DinaGraser,JaronLanier,andDonnaMoylan.IalsowanttothankKaćaBradonjićfortheillustrationsandformanywiseandhelpfulsuggestionsonthetext.

Forhelpfulconversationsandcorrespondenceonspecificpoints,ImustthankJimBaggott,JulianBarbour,FreemanDyson,OlivalFreire,StuartKauffman,MichaelNielsen,PhilipPearle,BillPoirier,CarloRovelli,andJohnStachel.AlexanderBlumandJürgenRennhelpedmetellatruestoryofthehistoryofquantummechanics.

IamextremelygratefultobepartofavibrantcommunityatthePerimeterInstituteforTheoreticalPhysicsfocusedonfoundationalphysics,whichgivesmeahomeandacontextformywork.Inadditiontothosealreadynamed,I’velearnedimmeasurablyovertheyearsfromGemmaDelasCuevas,BiancaDittrich,FayDowker,ChrisFuchs,LucienHardy,AdrianKent,RafaelSorkin,RobSpekkens,andmanyothers.IwishtothankMikeLazaridis,HowardBurton,andNeilTurokforincludingmeinthisadventureofalifetime,andalsogiveashout-outtoMichaelDuschenesandthewholePIstafffortheirintelligentanddedicatedwork.

Iamgratefultoseveralclassesofstudents,goingbackto“NatureLovestoHide”atHampshireCollege,whohavetakenvariousversionsofaquantumphysicsforpoetsclass,duringwhichItestedthepedagogicalstrategiesIusehere.Mostrecently,CamillaSinghallowedherselftobeatestcaseinanexperimenttoteachquantummechanicstoartists.

JohnBrockman,KatinkaMatson,andMaxBrockmanhavebeenmyliteraryagentsandfriendsforthemanyyearsIhavebeenwritingbooks.ScottMoyers,ChristopherRichards,andThomasPennhavebeengreateditors,andIamespeciallygratefultothemforinsistingthatIcouldwriteabetterbookthanIknew.IamproudtobeamongthemanywriterswhohavebenefitedfromthecriticaleyeofLouiseDennys.

Finally,IoweeverythingtoDinaGraserandKaiSmolin,whohavesupportedmethroughoutalltheupsanddownsofthisproject.

NOTES

Preface

1.J.S.Bell,“OntheEinsteinPodolskyRosenParadox,”Physics1,no.3(November1964):195–200.

Chapter1:NatureLovestoHide

EpigraphAlbertEinstein,“AReplytoCriticisms,”AlbertEinstein:Philosopher-Scientist,ed.P.A.Schillp,3rded.(Peru,IL:OpenCourtPublishing,1988).

1.EinsteintoMaxBorn,December4,1926,inTheBorn-EinsteinLetters:TheCorrespondenceBetweenAlbertEinsteinandMaxandHedwigBorn,1916–1955,withCommentariesbyMaxBorn,trans.IreneBorn(NewYork:WalkerandCo.,1971)88.

Chapter2:Quanta

1.TomStoppard,Arcadia:APlay,firstperformance,RoyalNationalTheatre,London,April13,1993;act1,scene1(NewYork:Farrar,StrausandGiroux,2008),9.

Chapter4:HowQuantaShare

EpigraphJohnArchibaldWheeler,QuantumTheoryandMeasurement,ed.J.A.WheelerandW.H.Zurek(Princeton:PrincetonUniversityPress,1983):194.

1.AlbertEinstein,BorisPodolsky,andNathanRosen,“CanQuantum-MechanicalDescriptionofPhysicalRealityBeConsideredComplete?,”PhysicalReview47,no.10(May15,1935):777–80.

2.AlainAspect,PhilippeGrangier,andGérardRoger,“ExperimentalTestsofRealisticLocalTheoriesviaBell’sTheorem,”PhysicalReviewLetters47,no.7(August1981):460–63;AlainAspect,JeanDalibard,andGérardRoger,“ExperimentalTestofBell’sInequalitiesUsingTime-VaryingAnalyzers,”PhysicalReviewLetters49,no.25(December1982):1804–7.

3.NielsBohr,“CanQuantum-MechanicalDescriptionofPhysicalRealityBeConsideredComplete?,”PhysicalReview48,no.8(October1935):696–702.

4.SimonKochenandE.P.Specker,“TheProblemofHiddenVariablesinQuantumMechanics,”JournalofMathematicsandMechanics17,no.1(July1967):59–87;JohnS.Bell,“OntheProblemofHiddenVariablesinQuantumMechanics,”ReviewsofModernPhysics38,no.3(July1966):447–52.

Chapter6:TheTriumphofAnti-Realism

EpigraphChristopherA.FuchsandAsherPeres,“QuantumTheoryNeedsNo‘Interpretation,’”PhysicsToday53,no.3(March2000):70–71,https://doi.org/10.1063/1.883004.

1.J.J.O’ConnorandE.F.Robertson,“LouisVictorPierreRaymondducdeBroglie,”http://www-history.mcs.st-andrews.ac.uk/Biographies/Broglie.html.

2.LouisdeBroglie,interviewbyThomasS.Kuhn,AndreGeorge,andTheoKahan,January7,1963,transcript,NielsBohrLibrary&Archives,AmericanInstituteofPhysics,CollegePark,MD,https://repository.aip.org/islandora/object/nbla:272502.

3.WernerHeisenberg,ThePhysicist’sConceptionofNature,trans.ArnoldJ.Pomerans(NewYork:HarcourtBrace,1958),15,29.

4.NielsBohr(1934),quotedinMaxJammer,ThePhilosophyofQuantumMechanics:TheInterpretationsofQuantumMechanicsinHistoricalPerspective(NewYork:JohnWileyandSons,1974),102.

Chapter7:TheChallengeofRealism:deBroglieandEinstein

1.GuidoBacciagaluppiandAntonyValentini,QuantumTheoryattheCrossroads:Reconsideringthe1927SolvayConference(Cambridge,UK:CambridgeUniversityPress,2009),235.

2.BacciagaluppiandValentini,487.3.GreteHermann,“DienaturphilosophischenGrundlagenderQuantenmechanik,”DieNaturwissenschaften23,no.42(October1935),718–21,doi:10.1007/BF01491142;GreteHermann,“TheFoundationsofQuantumMechanicsinthePhilosophyofNature,”trans.withanintroductionbyDirkLumma,TheHarvardReviewofPhilosophy7,no.1(1999):35–44.

4.JohnBell,“Interview:JohnBell,”interviewbyCharlesMannandRobertCrease,Omni10,no.8(May1988):88.

5.N.DavidMermin,“HiddenVariablesandtheTwoTheoremsofJohnBell,”ReviewsofModernPhysics65,no.3(July1993):805–6.

Chapter8:Bohm:RealismTriesAgain

EpigraphRoderichTumulka,“OnBohmianMechanics,ParticleCreation,andRelativisticSpace-Time:Happy100thBirthday,DavidBohm!,”Entropy20,no.6(June2018):462,arXiv:1804.08853v3.

1.DavidBohm,“ASuggestedInterpretationofQuantumTheoryinTermsof‘Hidden’Variables,1,”PhysicalReview85,no.2(January1952):166–79.

2.AlbertEinstein,quotedinWayneMyrvold,“OnSomeEarlyObjectionstoBohm’sTheory,”InternationalStudiesinthePhilosophyofScience17,no.1(March2003):7–24.

3.AlbertEinstein,quotedinE.DavidPeat,InfinitePotential:TheLifeandTimesofDavidBohm(NewYork:BasicBooks,1997),132.

4.AlbertEinstein,“ElementäreÜberlegungenzurInterpretationderGrundlagenderQuanten-Mechanik,”inScientificPapersPresentedtoMaxBorn(NewYork:Hafner,1953),33–40;quotedinMyrvold.

5.BenyaminCohen,“4ThingsEinsteinSaidtoCheerUpHisSadFriend,”FromtheGrapevine,June13,2017,https://www.fromthegrapevine.com/lifestyle/einstein-bohm-letters-winner-auction-israel.

6.WernerHeisenberg,quotedinMyrvold,“OnSomeEarlyObjections,”12.7.OlivalFreireJr.,“ScienceandExile:DavidBohm,theHotTimesoftheColdWar,andHisStruggleforaNewInterpretationofQuantumMechanics,”HistoricalStudiesonthePhysicalandBiologicalSciences36,no.1(September2005):1–34,https://arxiv.org/pdf/physics/0508184.pdf.

8.J.RobertOppenheimerremarkstoMaxDresden,inMaxDresden,H.A.Kramers:BetweenTraditionandRevolution(NewYork:Springer-Verlag,1987),133.AlsoquotedinF.DavidPeat’sInfinitePotential:TheLifeandTimesofDavidBohm(Reading,MA:Addison-Wesley,1996),whereheattributesthemtoDresden’s“remarksfromthefloorattheAmericanPhysicalSocietyMeeting,Washington,May,1989.Dresdenconfirmedthisversioninaninterviewwiththeauthor[Peat]immediatelyfollowingthatsessionandinalettertotheauthor.”(Quote,p.133;note,p.334.)

9.Peat,InfinitePotential,133.10.JohnNashtoJ.RobertOppenheimer,July10,1957,InstituteforAdvancedStudy,Shelby

WhiteandLeonLevyArchivesCenter,https://www.ias.edu/ideas/2015/john-forbes-nash-jr.11.LéonRosenfeldtoDavidBohm,May30,1952,quotedinLouisaGilder,TheAgeof

Entanglement:WhenQuantumPhysicsWasReborn(NewYork:AlfredA.Knopf,2008),216–17.

12.AntonyValentini,“Signal-Locality,Uncertainty,andtheSub-QuantumH-Theorem,1,”PhysicsLettersA156,nos.1–2(June1991):5–11;“2,”PhysicsLettersA158,nos.1–2(August1991):1–8.

13.AntonyValentiniandHansWestman,“DynamicalOriginofQuantumProbabilities,”ProceedingsoftheRoyalSocietyofLondonA461,no.2053(January2005):253–72,arXiv:quant-ph/0403034;EitanAbraham,SamuelColin,andAntonyValentini,“Long-TimeRelaxationinPilot-WaveTheory,”JournalofPhysicsA:MathematicalandTheoretical47,no.39(September2014):5306,arXiv:1310.1899.

14.AntonyValentini,“Signal-LocalityinHidden-VariablesTheories,”PhysicsLettersA297,nos.5–6(May2002):273–78.

15.NicolasG.UnderwoodandAntonyValentini,“AnomalousSpectralLinesandRelicQuantumNonequilibrium”(2016),arXiv:1609.04576;SamuelColinandAntonyValentini,“RobustPredictionsfortheLarge-ScaleCosmologicalPowerDeficitfromPrimordialQuantumNonequilibrium,”InternationalJournalofModernPhysicsD25,no.6(April2016):1650068,arXiv:1510.03508.

Chapter9:TheCollapseoftheQuantumState

1.DavidBohmandJeffreyBub,“AProposedSolutionoftheMeasurementProbleminQuantumMechanicsbyaHiddenVariableTheory,”ReviewsofModernPhysics38,no.3(July1966):453–69.

2.PhilipPearle,“ReductionoftheStateVectorbyaNonlinearSchrödingerEquation,”PhysicalReviewD13,no.4(February1976):857–68.

3.GiancarloGhirardi,AlbertoRimini,andTullioWeber,“UnifiedDynamicsforMicroscopicandMacroscopicSystems,”PhysicalReviewD34,no.2(July1986):470–91.

4.RoderichTumulka,“ARelativisticVersionoftheGhirardi-Rimini-WeberModel,”JournalofStatisticalPhysics125,no.4(November2006):821–40.

5.RogerPenrose,“GravitationalCollapseandSpace-TimeSingularities,”PhysicalReviewLetters14,no.3(January1965):57–59.

6.StephenW.HawkingandRogerPenrose,“TheSingularitiesofGravitationalCollapseandCosmology,”ProceedingsoftheRoyalSocietyA314,no.1519(January1970):529–48.

7.R.Penrose,“Time-AsymmetryandQuantumGravity,”inQuantumGravity2:ASecondOxfordSymposium,eds.C.J.Isham,R.Penrose,andD.W.Sciama(Oxford:ClarendonPress,1981),244;R.Penrose,“GravityandStateVectorReduction,”inQuantumConceptsinSpaceandTime,eds.R.PenroseandC.J.Isham(Oxford:ClarendonPress,1986),129;R.Penrose,“Non-localityandObjectivityinQuantumStateReduction,”inQuantumCoherenceandReality:In

Celebrationofthe60thBirthdayofYakirAharonov,eds.J.S.AnandanandJ.L.Safko(Singapore:WorldScientific,1995),238;R.Penrose,ShadowsoftheMind:ASearchfortheMissingScienceofConsciousness(Oxford:OxfordUniversityPress,1994);R.Penrose,“OnGravity’sRoleinQuantumStateReduction,”GeneralRelativityandGravitation28,no.5(May1996):581–600;I.FuentesandR.Penrose,“QuantumStateReductionviaGravity,andPossibleTestsUsingBose-EinsteinCondensates,”inCollapseoftheWaveFunction:Models,Ontology,Origin,andImplications,ed.S.Gao(Cambridge,UK:CambridgeUniversityPress,2018),187.

8.L.Diósi,“ModelsforUniversalReductionofMacroscopicQuantumFluctuations,”PhysicalReviewA40,no.3(August1989):1165–74;F.Károlyházy,“GravitationandQuantumMechanicsofMacroscopicBodies,”IlNuovoCimentoA42,no.2(March1966):390–402;F.Károlyházy,A.Frenkel,andB.Lukács,“OnthePossibleRoleofGravityintheReductionoftheWaveFunction,”inQuantumConceptsinSpaceandTime,109–28.

9.S.Bose,A.Mazumdar,G.W.Morley,H.Ulbricht,M.Toros,M.Paternostro,A.A.Geraci,P.F.Barker,M.S.Kim,andG.Milburn,“SpinEntanglementWitnessforQuantumGravity,”PhysicalReviewLetters119,no.24(December2017):240401,arXiv:1707.06050;C.MarlettoandV.Vedral,“GravitationallyInducedEntanglementbetweenTwoMassiveParticlesIsSufficientEvidenceofQuantumEffectsinGravity,”PhysicalReviewLetters119,no.24(December2017):240402,arXiv:1804.11315.

10.PhilipPearle,“ARelativisticDynamicalCollapseModel,”PhysicalReviewD91,no.10(May2015):105012,arXiv:1412.6723.

11.RodolfoGambiniandJorgePullin,“TheMontevideoInterpretationofQuantumMechanics:AShortReview,”Entropy20,no.6(February2015):413,arXiv:1502.03410.

12.StephenL.Adler,“GravitationandtheNoiseNeededinObjectiveReductionModes,”inQuantumNonlocalityandReality:50YearsofBell’sTheorem,eds.MaryBellandShanGao(Cambridge,UK:CambridgeUniversityPress,2016),390–99.

Chapter10:MagicalRealism

EpigraphBryceS.DeWitt,“QuantumMechanicsandReality:CouldtheSolutiontotheDilemmaofIndeterminismBeaUniverseinWhichAllPossibleOutcomesofanExperimentActuallyOccur?”PhysicsToday23,no.9(September1970):155–65.

1.HughEverettIII,“‘RelativeState’FormulationofQuantumMechanics,”ReviewsofModernPhysics29,no.3(July1957):454–62.

Chapter11:CriticalRealism

1.DavidDeutsch,“QuantumTheoryofProbabilityandDecisions,”ProceedingsoftheRoyalSocietyA455,no.1988(August1999):3129–37,arXiv:quant-ph/9906015.

2.DavidWallace,“QuantumProbabilityandDecisionTheory,Revisited”(2002),arXiv:quant-ph/0211104;Wallace,“EverettianRationality:DefendingDeutsch’sApproachtoProbabilityintheEverettInterpretation,”StudiesinHistoryandPhilosophyofSciencePartB:StudiesinHistoryandPhilosophyofModernPhysics34,no.3(September2003):415–39,arXiv:quant-ph/0303050;Wallace,“QuantumProbabilityfromSubjectiveLikelihood:ImprovingonDeutsch’sProofoftheProbabilityRule,”StudiesinHistoryandPhilosophyofSciencePartB:StudiesinHistoryandPhilosophyofModernPhysics38,no.2(June2007):311–32,arXiv:quant-ph/0312157;Wallace,“AFormalProofoftheBornRulefromDecision-TheoreticAssumptions”(2009),arXiv:quant-ph/0906.2718;SimonSaunders,“DerivationoftheBorn

RulefromOperationalAssumptions,”ProceedingsoftheRoyalSocietyA460,no.2046(June2004):1771–88,arXiv:quant-ph/0211138.

3.LawrenceS.Schulman,“NoteontheQuantumRecurrenceTheorem,”PhysicalReviewA18,no.5(November1978):2379–80,doi:10.1103/PhysRevA.18.2379.

4.StevenWeinberg,“TheTroublewithQuantumMechanics,”TheNewYorkReviewofBooks,January19,2017,https://www.nybooks.com/articles/2017/01/19/trouble-with-quantum-mechanics/.

Chapter12:AlternativestoRevolution

EpigraphLucienHardy,“ReformulatingandReconstructingQuantumTheory”(2011),arXiv:1104.2066.

1.RichardFeynman,“SimulatingPhysicswithComputers,”keynoteaddressdeliveredattheMITPhysicsofComputationConference,1981.PublishedinInternationalJournalofTheoreticalPhysics21,nos.6–7(June1982):467–88.

2.DavidDeutsch,“QuantumTheory,theChurch-TuringPrincipleandtheUniversalQuantumComputer,”ProceedingsoftheRoyalSocietyA400,no.1818(July1985):97–117.

3.JohnArchibaldWheeler,“Information,Physics,Quantum:TheSearchforLinks,”inProceedingsofthe3rdInternationalSymposium:FoundationsofQuantumMechanicsintheLightofNewTechnology,Tokyo,1989,eds.ShunichiKobayashietal.(Tokyo:PhysicalSocietyofJapan,1990),354–58.

4.JohnArchibaldWheeler,quotedinPaulDavies,TheGoldilocksEnigma,alsotitledCosmicJackpot(BostonandNewYork:HoughtonMifflin,2006),281.

5.ChristopherA.FuchsandBlakeC.Stacey,“QBism:QuantumTheoryasaHero’sHandbook”(2016),arXiv:1612.07308.

6.LouisCrane,“ClockandCategory:IsQuantumGravityAlgebraic?,”JournalofMathematicalPhysics36,no.11(May1995):6180–93,arXiv:gr-qc/9504038;CarloRovelli,“RelationalQuantumMechanics,”InternationalJournalofTheoreticalPhysics35,no.8(August1996):1637–78,arXiv:quant-ph/9609002;LeeSmolin,“TheBekensteinBound,TopologicalQuantumFieldTheoryandPluralisticQuantumCosmology”(1995),arXiv:gr-qc/9508064.

7.RuthE.Kastner,StuartKauffman,andMichaelEpperson,“TakingHeisenberg’sPotentiaSeriously”(2017),arXiv:1709.03595.

8.JulianBarbour,TheEndofTime:TheNextRevolutioninPhysics(Oxford:OxfordUniversityPress,1999).

9.HenriquedeA.Gomes,“BacktoParmenides”(2016,2018),arXiv:1603.01574.

Chapter13:Lessons

1.IamgratefultoAvshalomElitzurandEliCohenformanydiscussionsonthesekindsofcases.2.Forarecentreview,seeRoderichTumulka,“BohmianMechanics,”inTheRoutledgeCompaniontothePhilosophyofPhysics,eds.EleanorKnoxandAlastairWilson(NewYork:Routledge,2018),arXiv:/1704.08017.

3.YakirAharonovandLevVaidman,“TheTwo-StateVectorFormalismofQuantumMechanics:AnUpdatedReview,”inTimeinQuantumMechanics,vol.1,eds.J.GonzaloMuga,RafaelSalaMayato,andÍñignoEgusquiza,2nded.,LectureNotesinPhysics734(BerlinandHeidelberg:Springer,2008),399–447,arXiv:quant-ph/0105101v2.

4.JohnG.Cramer,“TheTransactionalInterpretationofQuantumMechanics,”ReviewsofModernPhysics58,no.3(July1986),647–87;Cramer,TheQuantumHandshake:Entanglement,NonlocalityandTransactions(Cham,Switzerland:SpringerInternational,

2016);RuthE.Kastner,“ThePossibilistTransactionalInterpretationandRelativity,”FoundationsofPhysics42,no.8(August2012):1094–113.

5.HuwPrice,“DoesTime-SymmetryImplyRetrocausality?HowtheQuantumWorldSays‘Maybe,’”StudiesinHistoryandPhilosophyofSciencePartB:StudiesinHistoryandPhilosophyofModernPhysics43,no.2(May2012),75–83,arXiv:1002.0906.

6.RafaelD.Sorkin,“QuantumMeasureTheoryandItsInterpretation,”inQuantumClassicalCorrespondence:Proceedingsofthe4thDrexelSymposiumonQuantumNonintegrability,DrexelUniversity,Philadelphia,USA,September8–11,1994,eds.Bei-LokHuandDaHsuanFeng(Cambridge,MA:InternationalPress,1997),229–51,arXiv:gr-qc/9507057.

7.MurrayGell-MannandJamesB.Hartle,“QuantumMechanicsintheLightofQuantumCosmology,”inProceedingsofthe3rdInternationalSymposium:FoundationsofQuantumMechanicsintheLightofNewTechnology,Tokyo,1989,321–43;Gell-MannandHartle,“AlternativeDecoheringHistoriesinQuantumMechanics,”inProceedingsofthe25thInternationalConferenceonHighEnergyPhysics,2–8August1990,Singapore,eds.K.K.PhuaandY.Yamaguchi,vol.1,1303–10(SingaporeandTokyo:SouthEastAsiaTheoreticalPhysicsAssociationandPhysicalSocietyofJapan,dist.WorldScientific,1990);Gell-MannandHartle,“TimeSymmetryandAsymmetryinQuantumMechanicsandQuantumCosmology,”inProceedingsoftheNATOWorkshoponthePhysicalOriginsofTimeAsymmetry,Mazagón,Spain,September30–October4,1991,eds.J.Halliwell,J.Pérez-Mercader,andW.Zurek(Cambridge,UK:CambridgeUniversityPress,1992),arXiv:gr-qc/9304023;Gell-MannandHartle,“ClassicalEquationsforQuantumSystems,”PhysicalReviewD47,no.8(April1993):3345–82,arXiv:gr-qc/9210010.

8.RobertB.Griffiths,“ConsistentHistoriesandtheInterpretationofQuantumMechanics,”JournalofStatisticalPhysics36,nos.1–2(July1984),219–72;Griffiths,“TheConsistencyofConsistentHistories:AReplytod’Espagnat,”FoundationsofPhysics23,no.12(December1993):1601–10;RolandOmnès,“LogicalReformulationofQuantumMechanics,1:Foundations,”JournalofStatisticalPhysics53,nos.3–4(November1988):893–932;Omnès,“LogicalReformulationofQuantumMechanics,2:InterferencesandtheEinstein-Podolsky-RosenExperiment,”ibid.,933–55;Omnès,“LogicalReformulationofQuantumMechanics,3:ClassicalLimitandIrreversibility,”ibid.,957–75;Omnès,“LogicalReformulationofQuantumMechanics,4:ProjectorsinSemiclassicalPhysics,”JournalofStatisticalPhysics57,nos.1–2(October1989):357–82;Omnès,“ConsistentInterpretationsofQuantumMechanics,”ReviewsofModernPhysics64,no.2(April1992):339–82.

9.FayDowkerandAdrianKent,“OntheConsistentHistoriesApproachtoQuantumMechanics,”JournalofStatisticalPhysics82,nos.5–6(March1996):1575–646,arXiv:gr-qc/9412067.

10.MichaelJ.W.Hall,Dirk-AndréDeckert,andHowardM.Wiseman,“QuantumPhenomenaModeledbyInteractionsbetweenManyClassicalWorlds,”PhysicalReviewX4,no.4(October2014):041013,arXiv:1402.6144.

11.BenhuiYang,WenwuChen,andBillPoirier,“RovibrationalBoundStatesofNeonTrimer:QuantumDynamicalCalculationofAllEigenstateEnergyLevelsandWavefunctions,”JournalofChemicalPhysics135,no.9(September2011):094306;GérardParlant,Yong-ChengOu,KisamPark,andBillPoirier,“Classical-likeTrajectorySimulationsforAccurateComputationofQuantumReactiveScatteringProbabilities,”invitedcontributionandleadarticle,specialissuetohonorJean-ClaudeRayez,ComputationalandTheoreticalChemistry990(June2012):3–17.

12.Gerard’tHooft,“Time,theArrowofTime,andQuantumMechanics”(2018),arXiv:1804.01383.

13.LeeSmolin,“CouldQuantumMechanicsBeanApproximationtoAnotherTheory?”(2006),arXiv:quant-ph/0609109.

14.MatthewF.Pusey,JonathanBarrett,andTerryRudolph,“OntheRealityoftheQuantum

State,”NaturePhysics8,no.6(June2012):475–78,arXiv:1111.3328.

Chapter14:First,Principles

1.LeeSmolin,TimeReborn:FromtheCrisisinPhysicstotheFutureoftheUniverse(NewYork:HoughtonMifflin,2013);RobertoMangabeiraUngerandLeeSmolin,TheSingularUniverseandtheRealityofTime:AProposalinNaturalPhilosophy(Cambridge,UK:CambridgeUniversityPress,2015);Smolin,“TemporalNaturalism,”invitedcontributiontospecialissueonCosmologyandTime,StudiesinHistoryandPhilosophyofSciencePartB:StudiesinHistoryandPhilosophyofModernPhysics52,no.1(November2015):86–102,arXiv:1310.8539.

2.FotiniMarkopoulouandLeeSmolin,“DisorderedLocalityinLoopQuantumGravityStates,”ClassicalandQuantumGravity24,no.15(July2007):3813–24,arXiv:gr-qc/0702044.

3.LeeSmolin,“DerivationofQuantumMechanicsfromaDeterministicNon-LocalHiddenVariableTheory,I.TheTwo-DimensionalTheory,”IASpreprintPRINT-83-0802(Princeton:InstituteforAdvancedStudy,August1983);Smolin,“StochasticMechanics,HiddenVariablesandGravity,”inQuantumConceptsinSpaceandTime,eds.RogerPenroseandC.J.Isham(OxfordandNewYork:ClarendonPress/OxfordUniversityPress,1986).

4.LeeSmolin,“MatrixModelsasNon-LocalHiddenVariablesTheories,”inQuoVadisQuantumMechanics?,eds.AvshalomC.Elitzur,ShaharDolev,andNancyKolenda,TheFrontiersCollection(BerlinandHeidelberg:Springer,2005),121–52;Smolin,“Non-LocalBeables,”InternationalJournalofQuantumFoundations1,no.2(April2015):100–106,arXiv:1507.08576.

5.StephenL.Adler,QuantumTheoryasanEmergentPhenomenon:TheStatisticalMechanicsofMatrixModelsasthePrecursorofQuantumFieldTheory(Cambridge,UK:CambridgeUniversityPress,2004);bookdraft,StatisticalDynamicsofGlobalUnitaryInvariantMatrixModelsasPre-QuantumMechanics(2002),arXiv:hep-th/0206120.

6.ArtemStarodubtsev,“ANoteonQuantizationofMatrixModels,”NuclearPhysicsB674,no.3(December2003):533–52,arXiv:hep-th/0206097.

7.MarkopoulouandSmolin,“DisorderedLocality.”8.FotiniMarkopoulouandLeeSmolin,“QuantumTheoryfromQuantumGravity,”PhysicalReviewD70,no.12(December2004):124029,arXiv:gr-qc/0311059.

9.GottfriedWilhelmLeibniz,TheMonadology,1714,inLeibniz:PhilosophicalWritings,ed.G.H.R.Parkinson,trans.MaryMorrisandG.H.R.Parkinson(London:J.M.Dent,1973).

10.JulianBarbourandLeeSmolin,“ExtremalVarietyastheFoundationofaCosmologicalQuantumTheory”(1992),arXiv:hep-th/9203041.

11.Leibniz,TheMonadology,paragraph57,inLeibniz,PhilosophicalWritings.12.LeeSmolin,“TheDynamicsofDifference,”FoundationsofPhysics48,no.2(February2018):

121–34,arXiv:1712.04799;Smolin,“QuantumMechanicsandthePrincipleofMaximalVariety,”FoundationsofPhysics46,no.6(June2016):736–58,arXiv:1506.02938;Smolin,“ARealEnsembleInterpretationofQuantumMechanics,”FoundationsofPhysics42,no.10(October2012):1239–61,arXiv:1104.2822.

13.LeeSmolin,“PrecedenceandFreedominQuantumPhysics”(2012),arXiv:1205.3707.

Chapter15:ACausalTheoryofViews

1.LucaBombelli,JoohanLee,DavidMeyer,andRafaelD.Sorkin,“Space-TimeasaCausalSet,”PhysicalReviewLetters59,no.5(August1987):521–24;Sorkin,“SpacetimeandCausalSets,”inRelativityandGravitation:ClassicalandQuantum(ProceedingsoftheSILARGVII

Conference,heldinCocoyoc,Mexico,December1990),eds.J.C.D’Olivoetal.(Singapore:WorldScientific,1991),150–73.

2.MaqboolAhmed,ScottDodelson,PatrickB.Greene,andRafaelSorkin,“EverpresentLambda,”PhysicalReviewD69,no.10(May2004):103523,arXiv:astro-ph/0209274.

3.TedJacobson,“ThermodynamicsofSpacetime:TheEinsteinEquationofState,”PhysicalReviewLetters75,no.7(August1995):1260,arXiv:gr-qc/9504004.

4.FotiniMarkopoulouandLeeSmolin,“HolographyinaQuantumSpacetime”(October1999),arXiv:hep-th/9910146;Smolin,“TheStrongandWeakHolographicPrinciples,”NuclearPhysicsB601,nos.1–2(May2001):209–47,arXiv:hep-th/0003056.

5.MarinaCortêsandLeeSmolin,“TheUniverseasaProcessofUniqueEvents,”PhysicalReviewD90,no.8(October2014):084007,arXiv:1307.6167[gr-qc];CortêsandSmolin,“QuantumEnergeticCausalSets,”PhysicalReviewD90,no.4(August2014):044035,arXiv:1308.2206[gr-qc];CortêsandSmolin,“SpinFoamModelsasEnergeticCausalSets,”PhysicalReviewD93,no.8(June2014):084039,arXiv:1407.0032;CortêsandSmolin,“ReversingtheIrreversible:FromLimitCyclestoEmergentTimeSymmetry,”PhysicalReviewD97,no.2(January2018):026004,arXiv:1703.09696.

6.Smolin,“TheDynamicsofDifference,”FoundationsofPhysics48,no.2(2018):121–34,arXiv:1712.04799.

Epilogue/Revolutions

EpigraphDavidGross,“ClosingRemarks,”Strings2003Conference,Kyoto,Japan,July6–11,2003,slide17,https://www.yukawa.kyoto-u.ac.jp/assets/contents/seminar/archive/2003/str2003/talks/gross.pdf.

GLOSSARY

Acceleration:Therateofchangeofvelocity.

Angularmomentum:Aconservedquantitythatmeasurestheamountofrotationorangularmotion.

Anti-realism:Aphilosophyaccordingtowhicheitherthereisnoobjective,universalreality,orifthereissuch,humanbeingscannothavecompleteknowledgeofit.

Atom:Thebasicunitofmatter,consistingofanucleus,whichcontainsprotonsandneutrons,surroundedbyelectrons.

Background:Ascientificmodelortheoryoftendescribesonlypartoftheuniverse.Somefeaturesoftherestoftheuniversemaybeincludedasnecessarytodefinethepropertiesofthatpartoftheuniversethatisstudied.Thesefeaturesarecalledthebackground.Forexample,inNewtonianphysicsspaceandtimearepartofthebackgroundbecausetheyaretakentobeabsolute.

Backgrounddependent:Atheory,suchasNewtonianphysics,thatmakesuseofabackground.

Backgroundindependent:Atheorythatdoesnotmakeuseofadivisionoftheuniverseintoapartthatismodeledandtherest,whichistakentobepartofthebackground.Generalrelativityissaidtobebackgroundindependentbecausethegeometryofspaceandtimeisnotfixed,butevolvesintimejustlikeanyotherfield,suchastheelectromagneticfield.

Bayesianprobability:Asubjectiveprobabilitywhichmeasuresaperson’sdegreeofbeliefaboutsomething.

Bell’stheorem:Statesthatinaworldwhichislocal,inthesensethatthechoiceofmeasurementsmadeononesystemneverinfluencestheprobabilitiesfortheoutcomeofmeasurementsmadeonadistantsystem,certaincorrelationsofmeasurementsarerestrictedbyaninequality.Thatinequalityisviolatedexperimentally.AlsocalledBell’srelationorBell’srestriction.

Bohmianmechanics:Anothernameforpilotwavetheory.

Causalsettheory:Anapproachtoquantumspacetimebasedonthehypothesisthatthehistoryoftheworldismadefromadiscretesetoffundamentaleventsandtheircausalrelations.

Causality:Theprinciplethateventsareinfluencedbythoseintheirpast.Inrelativitytheoryoneeventcanhaveacausalinfluenceonanotheronlyifenergyorinformationsentfromthefirstreachesthesecond.

Causalstructure:Becausethereisamaximumspeedatwhichenergyandinformationcanbetransmitted,theeventsinthehistoryoftheuniversecanbeorganizedintermsoftheirpossible

causalrelations.Todothis,oneindicates,foreverypairofevents,whetherthefirstisinthecausalfutureofthesecond,orviceversa,orwhetherthereisnopossiblecausalrelationbetweenthembecausenosignalcouldhavetraveledbetweenthem.Suchacompletedescriptiondefinesthecausalstructureoftheuniverse.

Classicalphysics:ThatpartofphysicsfromGalileothroughgeneralrelativity,priortothequantumtheory.

Collapseofthewavefunction:Thepostulatethatimmediatelyafteranobservertakesameasurementwhichrevealsadefinitevalueforsomeobservable,aquantumsystemtakesonthequantumstateassociatedtothatvalue.

Complementarityprinciple:PrincipleproposedbyBohrthatquantumsystemsadmitdifferentdescriptions,suchasparticleandwave,thatwouldcontradicteachotheriftheyhadtobeimposedsimultaneously.However,anygivenexperimentcanbedescribedusingoneortheother.

Conservedquantity:Apropertyofaphysicalsystemwhosetotalvalueneverchangesintimeasthesystemevolves.Examplesareenergy,momentum,andangularmomentum.

Consistenthistoriesapproach:Aninterpretationofquantummechanicsbasedonassigningprobabilitiestosetsofhistoriesthatdecoherefromeachother.

Contrarystate:SeeEinstein-Podolsky-Rosenstate.

DeBroglie–Bohmtheory:Anothernameforpilotwavetheory,namedforitstwoinventors.

Decoherence:Theprocessbywhichlargequantumsystems,containingmanydegreesoffreedom,incontactwithanenvironmentwhichintroducesrandomfluctuations,losetheirwaveproperties,duetothephasesofthewavesbecomingrandomized,andsoemergeasparticles.

Degreeoffreedom:Avariablequantity,describingonewayaphysicalsystemcanchange.

Determinism:Thephilosophythatthefuturestateofaphysicalsystemiscompletelydeterminedbythelawsofphysicsactingonthepresentstate.

Discreteness:Thepropertyofsomeobservablesofquantumsystems,suchastheenergyofanatom,totakevaluesrestrictedtoadiscretelist.

Dynamicalcollapsetheory:Aproposalthatcollapseofthewavefunctionisarealphysicalprocess.

Einstein-Podolsky-Rosen(EPR)state:Ajointstateoftwoparticleswhichcontainsnoinformationatallabouttheindividualparticles,butindicatesthatifanymeasurementismadeonboth,theresultswillbeopposite.Alsocalledthecontrarystate.

Energy:Aphysicalquantitygivingameasureoftheactivityofasystem,whosevalueispreservedintime.Energytakesseveralformsandcanbetransmutedamongthem,withthetotalvaluealwaysconserved.

Entanglement:Apropertyofaquantumstateoftwoormoresystems,wherethestateindicatesapropertysharedbythosesystemsthatisnotjustthesumofpropertiesheldbytheindividualparticles.TheEPRorcontrarystateisanexampleofanentangledstate.

Entropy:Ameasureofthedisorderofaphysicalsystem,whichisrelatedtotheinformationtrappedintheexactvaluesofitsmicroscopicdegreesoffreedom.

Event:Inrelativitytheory,somethingthathappensataparticularpointofspaceandmomentoftime.

Exclusionprinciple:InventedbyWolfgangPauli,itsaysthatnotwofermionscanbeinthesamequantumstate.

Field:Aphysicalsystemspreadoutinspace,withoneormoredegreesoffreedomperspacetimepoint.Theelectricandmagneticfieldsareexamples.

Fieldtheory:Aphysicaltheorythatdescribestheevolutionintimeofoneorseveralfields.Anexampleiselectrodynamics,wherethelawsofmotionofthefieldsarecalledtheMaxwellequations.

Force:InNewtonianphysics,thechangeinthemomentuminacollision.Alsoequaltotheaccelerationofabodytimesthemass.

Future:Thefuture,orcausalfuture,ofaneventconsistsofallthoseeventsthatitcaninfluencebysendingenergyorinformationtothem.

Hiddenvariable:Apropertyordegreeoffreedomofaquantumsystemthatisnotdescribedbyquantummechanics,butisneededtocompletethedescriptionofanindividualsystem.

Holographicprinciple:AconjecturedprinciplewhichlimitsthequantityofinformationcrossingasurfacetotheareaofthesurfaceinPlanckunits.

Information:Ameasureoftheorganizationofasignal.Itisequaltothenumberofyes/noquestionswhoseanswerscouldbecodedinthesignal.

Instrumentalism:Anapproachtosciencewhereintheroleoftheoryisonlytoprovideadescriptionofaphysicalsystemintermsofitsresponsestoexternallyimposedforcesconveyedbymeasuringinstruments.

Kochen-Speckertheorem:Atheoremthatshowsthatquantummechanicsiscontextual,whichmeansthatthevalueofanobservablecandependonachoiceofwhichothermeasurementsaremadeatthesametime.

Locality:Thepropertyofphysicallawthatsystemsareonlydirectlyinfluencedbywhatisnearbyinspaceandtime.

Loopquantumgravity:AnapproachtoquantumgravitybasedonaquantizationofEinstein’sgeneraltheoryofrelativity.

Manymomentsinterpretation:Thehypothesisthatwhatreallyexistsisavastcollectionofmoments,containingeverythingthatmighthavehappenedinthehistoryoftheuniverse.

ManyWorldsInterpretation:Aninterpretationofquantumtheoryaccordingtowhichthedifferentpossibleoutcomesofanobservationofaquantumsystemresideindifferentuniverses,allofwhichsomehowcoexist.

Mass:InNewtonianphysics,theinertialmassisameasureofthequantityofmatter,which,multipliedbyvelocity,givesaconservedquantitycalledthemomentum.

Matrix:Atableofnumbersorganizedintorowsandcolumns.

Matrixmechanics:Anapproachtoquantummechanicsinwhichobservablesarerepresentedbymatrices.

Momentum:Aquantitydefinedformovingparticles,whichisexchangedincollisionssoastoconservethetotal.InNewtonianphysicsitisequaltotheproductofthemassandvelocity.

Newtonianphysics:Aframeworkfordescribingandexplainingmotion,inventedbyIsaacNewtonandpresentedinhis1687bookPrincipiaMathematica,whichisbasedonthreelawsofmotion.

Nonlocality:Anyphenomenonwhichdoesnotsatisfytheprincipleoflocality,andsoinvolvesinfluencestransmittedbetweensystemsseparatedinspace.

Operationalism:Anapproachtoinstrumentalisminwhichonespecifiesforaphysicalsystemasetofoperationswhichincludehowitistobepreparedandhowitistobemeasured.

Pastorcausalpast:Foraparticularevent,allothereventsthatcouldhaveinfluenceditbysendingenergyorinformationtoit.

Photon:Aquantumoftheelectromagneticfield,whichcarriesanamountofenergyproportionaltothefrequencyofthefield.

Pilotwavetheory:Thefirstrealistapproachtoquantummechanics,inventedbyLouisdeBrogliein1927andreinventedbyDavidBohmin1952.Acompletedescriptionofanindividualsystemisgivenbybothawaveandaparticle,wheretheparticleisguidedbythewave.

Planck’sconstant:ThefundamentalquantityspecifyingthescaleatwhichtheeffectsofquantumphysicsdepartfromthoseofNewtonianphysics.Usuallyrepresentedash.Itcomesintotherelationshipsbetweentheenergyofaquantumandthefrequencyoftherelatedwave.

Planckenergy:AunitofenergyconstructedbymultiplyingPlanck’sconstant,h,Newton’sgravitationalconstant,G,andthespeedoflight,c,togetherintherightcombinationtogiveanenergy.Itisequaltotheenergyinonehundred-thousandthofagram.

Plancklength:Theunitoflengthsoconstructed;itisroughlytwentypowersoftensmallerthananatomicnucleus.

Planckmass:Theunitofmasssoconstructed,aboutonehundred-thousandthofagram.

Quanta(n.,pl.):Theparticlesideofthewave-particleduality.

Quantize(v.):TofollowanalgorithmthattakesasinputaclassicalorNewtoniantheoryandoutputsacorrespondingquantumtheory.Itisknownthatanysuchalgorithmishighlynon-unique.

QuantumBayesianism:Anapproachtoquantumfoundationsaccordingtowhichallusesofprobabilityinquantummechanicsaresubjective,bettingprobabilities.

Quantumcosmology:Thetheorythatattemptstodescribethewholeuniverseinthelanguageofquantumtheory.

Quantumequilibrium:Inahiddenvariabletheorysuchaspilotwavetheory,thestatisticaldistributionofparticlesinanensembleofsystemsisarbitrary.Whenitisequaltothesquareofthewavefunction,asisspecifiedinBorn’srule,thesystemissaidtobeinquantumequilibrium.

Quantumfieldtheory:Aquantumtheoryoffieldssuchastheelectricandmagneticfields.Thesearechallengingbecausetheymustincorporatespecialrelativityandalsobecausetheyhaveaninfinitenumberofdegreesoffreedom.

Quantumgravity:Thetheorywhichcombinesgeneralrelativityandquantumphysics.

Quantummechanics:Thetheoryofatomsandlightasdevelopedinthe1920s.

Quantumstate:Acompletedescriptionofanindividualsystemaccordingtoquantummechanics.

Realism:Thebeliefthatthereisanobjectivephysicalworldwhosepropertiesareindependentofwhathumanbeingsknoworwhichexperimentswechoosetodo.Realistsalsobelievethatthereisnoobstacleinprincipletoourobtainingcompleteknowledgeofthisworld.

Relationalism:Thephilosophythatallthepropertiesofelementaryobjectsoreventsarisefrominteractionsbetweenpairsorlargersetsofthem,andhencemeasuresharedproperties.

Relationalquantumtheory:Aninterpretationofquantumtheoryaccordingtowhichthequantumstateofaparticle,orofanysubsystemoftheuniverse,isdefinednotabsolutely,butonlyinacontextcreatedbythepresenceofanobserver,andbyadivisionoftheuniverseintoapartcontainingtheobserverandapartcontainingthatpartoftheuniversefromwhichtheobservercanreceiveinformation.Relationalquantumcosmologyisanapproachtoquantumcosmologywhichassertsthatthereisnotonequantumstateoftheuniverse,butasmanystatesastherearesuchcontexts.

Relativity,thegeneraltheoryof:Einstein’s1915theoryofgravitationinwhichthegravitationalforceisreplacedbythedynamicsofthespacetimegeometry.

Relativity,thespecialtheoryof:Einstein’s1905theoryofmotionandlightintheabsenceofgravity.

Retrocausality:Hypotheticalprocessesinwhichtheorderofcausesrunsbackwardrelativetotheglobaldirectionoftime.

Rule0:Thebasicdynamicalequationofquantumgravity,whichexpressestheabsenceofaglobaloruniversaltime.AlsocalledtheWheeler-DeWittequation.

Rule1:Thebasicdynamicalequationofquantummechanicsthatdescribeshowquantumstatesevolvewithrespecttotimeasmeasuredbyclocksoutsidethequantumsystem.AlsocalledtheSchrödingerequation.Rule1explainsthatgiventhequantumstateofanisolatedsystematonetime,thereisalawthatwillpredicttheprecisequantumstateofthatsystematanyothertime.

Rule2:Thelawthatprescribeshowaquantumstaterespondstoameasurement,whichistocollapseimmediatelyintoastatewithinwhichthemeasuredquantityhasaprecisevalue,thevaluethatthemeasurementproduced.Rule2explainsthattheoutcomeofameasurementcanonlybepredictedprobabilistically.Butafterward,themeasurementchangesthequantumstateofthesystembeingmeasured,byputtingitinthestatecorrespondingtotheresultofthemeasurement.Thisiscalledcollapseofthewavefunction.

Schrödinger’scatexperiment:AthoughtexperimentinwhichRule1impliesthatacatisinasuperpositionoftwodistinctmacroscopicstates:livinganddead.

Schrödinger’sequation:SeeRule1.

Secondlawofthermodynamics:Statesthattheentropyofanisolatedsystemwillmostprobablyincrease.

Speed:Therateofchangeofdistancewithtime.

Spin:Theangularmomentumofanelementaryparticlewhichisanintrinsicpropertyofit,independentofitsmotion.

Spinnetwork:Agraphwhoseedgesarelabeledbynumbersrepresentingspins.Inloopquantumgravityeachquantumstateofthegeometryofspaceisrepresentedbyaspinnetwork.

Standardmodelofparticlephysics:Aquantumfieldtheorywhichisourbestmodeloftheelementaryparticlesandtheirinteractions,exceptforgravity.

State:Inanyphysicaltheory,theconfigurationofasystemataspecifiedmomentoftime.

Stringtheory:Anapproachtoquantumgravitybasedonthehypothesisthatthefundamentalthingsintheworldareone-dimensional.

Symmetry:Anoperationbywhichaphysicalsystemmaybetransformedwithoutaffectingthefactthatitsstateisapossiblestateofthesystem.Twostatesconnectedbyasymmetryhavethesameenergy.

Uncertaintyprinciple:Aprincipleinquantumtheoryaccordingtowhichitisimpossibletomeasureboththepositionandmomentum(orvelocity)ofaparticle.

Velocity:Therateofchangeofpositionintime.

Wavefunction:Arepresentationofthequantumstateofasystem.

Wavemechanics:AformofquantummechanicsinventedbyErwinSchrödingerin1926.Latershowntobeequivalenttomatrixmechanics.

Wave-particleduality:Aprincipleofquantumtheoryaccordingtowhichonecandescribeelementaryparticlesasbothparticlesandwaves,dependingonthecontext.

FURTHERREADING

PopularBooksbytheInventorsofQuantumMechanics

Bell,J.S.SpeakableandUnspeakableinQuantumMechanics.2nded.IntroductionbyAlainAspect;twoadditionalpapers.Cambridge,UK:CambridgeUniversityPress,2004.

Bohm,David.WholenessandtheImplicateOrder.London:RoutledgeandKeganPaul,1980.Reprint,London:Ark/Routledge,2002.

Bohr,Niels.AtomicPhysicsandHumanKnowledge.NewYork:ScienceEditions,1961.Reprint,Mineola,NY:DoverPublications,2010.

Bohr,Niels.AtomicTheoryandtheDescriptionofNature:FourEssayswithanIntroductorySurvey.Cambridge,UK:CambridgeUniversityPress,1934,1961.Reprint,2011.

Bohr,Niels.“DiscussionwithEinsteinonEpistemologicalProblemsinAtomicPhysics.”InAlbertEinstein:Philosopher-Scientist,editedbyPaulArthurSchilpp,199–242.3rded.LibraryofLivingPhilosophers7.Peru,IL:OpenCourtPublishing,1988.

Einstein,Albert.AutobiographicalNotes.TranslatedandeditedbyPaulArthurSchilpp.Centennialed.Peru,IL:OpenCourtPublishing,1999.

Einstein,Albert.IdeasandOpinions.Reprinted.NewYork:BroadwayBooks,1995.

Heisenberg,Werner.PhilosophicalProblemsofQuantumPhysics.2nded.Woodbridge,CT:OxBowPress,1979.

Heisenberg,Werner.ThePhysicalPrinciplesoftheQuantumTheory.TranslatedbyCarlEckartandF.C.Hoyt.Mineola,NY:DoverPublications,1949.

Schrödinger,Erwin.WhatIsLife?WithMindandMatterandAutobiographicalSketches.ForewordtoWhatIsLife?byRogerPenrose.Cambridge,UK:Canto/CambridgeUniversityPress,1992.

BooksbyContemporaryContributors

Barbour,Julian.TheEndofTime:TheNextRevolutioninOurUnderstandingoftheUniverse.NewYork:OxfordUniversityPress,1999.

Carroll,Sean.TheBigPicture:OntheOriginsofLife,Meaning,andtheUniverseItself.NewYork:Dutton,2016.

Deutsch,David.TheBeginningofInfinity:ExplanationsthatTransformtheWorld.NewYork:Viking,2011.

Deutsch,David.TheFabricofReality:TheScienceofParallelUniverses—andItsImplications.NewYork:PenguinPress,1997.

Greene,Brian.TheHiddenReality:ParallelUniversesandtheDeepLawsoftheCosmos.NewYork:AlfredA.Knopf,2011.

Penrose,Roger.TheEmperor’sNewMind:ConcerningComputers,Minds,andTheLawsofPhysics.Reprinted.,withanewprefacebytheauthor.OxfordandNewYork:OxfordUniversityPress,1999.

Penrose,Roger.ShadowsoftheMind:ASearchfortheMissingScienceofConsciousness.OxfordandNewYork:OxfordUniversityPress,1994.

Rovelli,Carlo.TheOrderofTime.NewYork:RiverheadBooks,2018.//L’ordinedeltempo.Milan:AdelphiEdizioni,2017.

Rovelli,Carlo.RealityIsNotWhatItSeems:TheJourneytoQuantumGravity.NewYork:RiverheadBooks,2017.//Larealtànonècomeciappare:Lastrutturaelementaredellecose.Milan:RaffaelloCortinaEditore,2014.

Rovelli,Carlo.SevenBriefLessonsonPhysics.NewYork:RiverheadBooks,2016.//Settebrevilezionidifisica.Milan:AdelphiEdizioni,2014.

Tegmark,Max.OurMathematicalUniverse:MyQuestfortheUltimateNatureofReality.NewYork:AlfredA.Knopf,2014.

BiographiesofKeyFigures

Byrne,Peter.TheManyWorldsofHughEverettIII:MultipleUniverses,MutualAssuredDestruction,andtheMeltdownofaNuclearFamily.OxfordandNewYork:OxfordUniversityPress,2010.

Farmelo,Graham.TheStrangestMan:TheHiddenLifeofPaulDirac,MysticoftheAtom.NewYork:BasicBooks,2009.

Gribbin,John.ErwinSchrödingerandtheQuantumRevolution.Hoboken,NJ:JohnWileyandSons,2013.

Hoffmann,Banesh,withHelenDukas.AlbertEinstein:CreatorandRebel.NewYork:VikingPress,1973.

Klein,MartinJ.PaulEhrenfest.Vol.1:TheMakingofaTheoreticalPhysicist.NewYork:AmericanElsevier,1970.

Overbye,Dennis.EinsteininLove:AScientificRomance.NewYork:Penguin,2000.

Pais,Abraham.NielsBohr’sTimes:InPhysics,Philosophy,andPolity.Oxford,UK,andNewYork:ClarendonPress/OxfordUniversityPress,1991.

Pais,Abraham.SubtleistheLord:TheScienceandtheLifeofAlbertEinstein.Oxford,UK,andNewYork:OxfordUniversityPress,1982.Reprinted.,withanewforewordbyRogerPenrose,2005.

Peat,F.David.InfinitePotential:TheLifeandTimesofDavidBohm.Reading,MA:Addison-Wesley,1997.

HistoriesofQuantumPhysics

Bacciagaluppi,Guido,andAntonyValentini.QuantumTheoryattheCrossroads:Reconsideringthe1927SolvayConference.Cambridge,UK,andNewYork:CambridgeUniversityPress,2009.

Baggott,Jim.TheQuantumStory:AHistoryin40Moments.Oxford,UK,andNewYork:OxfordUniversityPress,2011.

Baggott,Jim.BeyondMeasure:ModernPhysics,Philosophy,andtheMeaningofQuantumTheory.Oxford,UK,andNewYork:OxfordUniversityPress,2004.

Forman,Paul.“WeimarCulture,Causality,andQuantumTheory,1918–1927:AdaptationbyGermanPhysicistsandMathematicianstoaHostileIntellectualEnvironment.”HistoricalStudiesinthePhysicalSciences,Vol.3(1971):1–115.Formanexpandedonhisoriginalargumentin:Forman,Paul.“Kausalität,Anschaulichkeit,andIndividualität,orHowCulturalValuesPrescribedtheCharacterandtheLessonsAscribedtoQuantumMechanics.”InSocietyandKnowledge:ContemporaryPerspectivesintheSociologyofKnowledgeandScience,editedbyNicoStehrandVolkerMeja,333–47.NewBrunswick,NJ:TransactionBooks,1984.

Gefter,Amanda.TrespassingonEinstein’sLawn:AFather,aDaughter,theMeaningofNothing,andtheBeginningofEverything.NewYork:BantamBooks,2014.

Gilder,Louisa.TheAgeofEntanglement:WhenQuantumPhysicsWasReborn.NewYork:AlfredA.Knopf,2008.

Gribbin,John.InSearchofSchrödinger’sCat:QuantumPhysicsandReality.NewYork:BantamBooks,1984.

Jammer,Max.ThePhilosophyofQuantumMechanics:TheInterpretationsofQuantumMechanicsinHistoricalPerspective.NewYork:JohnWileyandSons,1974.

Kaiser,David.HowtheHippiesSavedPhysics:Science,Counterculture,andtheQuantumRevival.NewYork:W.W.Norton,2011.

Kragh,Helge.QuantumGenerations:AHistoryofPhysicsintheTwentiethCentury.Princeton:PrincetonUniversityPress,1999.Reprint,2002.

Kuhn,ThomasS.Black-BodyTheoryandtheQuantumDiscontinuity,1894–1912.Chicago:UniversityofChicagoPress,1987.

Stone,A.Douglas.EinsteinandtheQuantum:TheQuestoftheValiantSwabian.Princeton:PrincetonUniversityPress,2013.

CollectionsofPapers

DeWitt,BryceSeligman,andNeillGraham,eds.TheManyWorldsInterpretationofQuantumMechanics.PrincetonSeriesinPhysics.Princeton:PrincetonUniversityPress,1973.Reprinted.:PrincetonLegacyLibrary,2015.

Saunders,Simon,JonathanBarrett,AdrianKent,andDavidWallace,eds.ManyWorlds?Everett,QuantumTheory,andReality.Oxford:OxfordUniversityPress,2010.

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

INDEX

Thepagenumbersinthisindexrefertotheprintedversionofthisbook.Thelinkprovidedwilltakeyoutothebeginningofthatprintpage.Youmayneedtoscrollforwardfromthatlocationtofindthecorrespondingreferenceonyoure-reader.

academiccommunity,277academiclife,94acceleration,297actuality,possibilityand,177–78,197–98,200,243adjacentpossible,201AgainstMethod(Feyerbend),173Aharonov,Yakir,118,216alternategeometry,229AmericanCommunistParty,115namplitude,138angularmomentum,77,263n,297anti-realism,xxvi,xxix,8,26,94,117,175ofBohr,106definitionof,297electronsand,85natureand,xxvphysicsand,xxvquantummechanicsand,xxi

approximations,192Arcadia(Stoppard),15Aspect,Alain,45,46,49,220assumptions,10astronomy,274atomicbomb,108atomiclaws,251–52,258atomicscale,xvii,xx,77,91atomicsystems,wavefunctionand,141,213atoms,xiv,xv,xvii,56,71behaviorof,129Bohron,93chemicalpropertiesof,3communicationbetween,46–47configurationspaceof,122–24,123,217–18copiesof,248decayof,125

definitionof,297densityof,73electronsand,78,83energyand,77–78ensembleof,59entanglementof,252freedomand,246gravityand,74Heisenbergon,87lawsof,251–52,258lightand,77–78locationof,5matterand,72measurementof,195moleculesand,3,246–47nucleusof,74observablesof,27photonsand,195,209–10pilotwavetheoryand,122propertiesof,xvi,5,6–7quantummechanicsand,6,62quantumstatesof,37–38quantumteleportation,186radiationand,52,93,125realismand,75retrocausality,216–17,217solarsystemand,74spacetime,257–59spectrumof,59–60,78statesof,49–51,60–61,77–78,146–47,152stationarystatesof,77superpositionof,4–5,6–7,50,139–40,146,152,156–57truetheoryof,xxiwaterand,xv

averages,62–63

backgroundscosmicmicrowave,121definitionof,297dependenceon,264,297independenceprinciple,229,264,267,297spacetimeand,269symmetryand,264

Barbour,Julian,201–3,244Bateson,Gregory,191Bayesianprobabilities,160–61,163,297beables,26–27,206–7,213,218,222,224,240beliefs,164,205Bell,John,xxviii,xxix,26,39,41,45,47–49,55,56,105,220hiddenvariablesand,184

restrictiontheorem,184,215,235,298Bernstein,Herbert,xxviii,25,27bigbang,221biochemistry,177biology,quantummechanicsand,3black-bodyradiation,79blackholes,75,134Bohm,David,xxix,105,107–8Bohrand,113communismand,114–15Einsteinand,108–11guidanceequationand,109measurementprocess,117Oppenheimerand,112pilotwavetheoryand,109,110,116,118Princetonand,113theoryof,109–12vonNeumannand,110

Bohmianmechanics.SeepilotwavetheoryBohr,Niels,xxi–xxii,xxvii,xxix,75anti-realismof,106onatoms,93Bohmand,113complementarityand,85–86,90educationof,77Einsteinand,8,78,102electronsand,84EPRand,47–48familyandbackgroundof,76Heisenbergand,90–91leadershipandinspirationof,117–18pilotwavetheoryand,102–3quantumtheoriesand,xxii,7–8,9splittingand,193–94

Boltzmann,Ludwig,71,71n,72nBorn,Max,8,34,81–83,86,88–91,100Born’srule,34,61,83,99–100,109,150,151n,177decisiontheoryand,167–69definition,206probabilitiesand,164,200,218Rule1and,171

boundarysplits,197Brownianmotionofmolecules,73Bub,Jeffrey,130buckyballs,24

causalcompletenessprinciple,232,247causalfuture,254–55,266–67causality,134,204,216–17,217,236,298causallinks,255

causalloops,255,255ncausalpast,254,261,266–67,301causalrelations,254–57,260–61,270causalsets,260–61,264–69causalsettheory,257–58,298causalstructure,256,260,298causaltheoryofviews,269–71circularmotion,77classicalmechanics,111,193–95,196classicalphysics,xx,30,298classicalstate,30classicalworlds,219–20climatechange,xxiv,178codes,48,185,186collapses.Seealsowave-functioncollapsegravityand,139–40models,beyond,222–24specialrelativityand,141spontaneous,131ofwavefunction,139,186

collapsetheorydynamical,299measurementproblemand,131–32,133,142,144–45noiseand,133pilotwavetheoryand,131theoryofrelativityand,133

collisions,20,73communication,46–47,189communism,114–15,115ncommutativity,18–20complementarity,84,101,114Bohrand,85–86,90consistencyof,90definitionof,298pilotwavetheoryand,101uncertaintyprincipleand,92–93

complexsystems,248computation,definitionof,192computers,191–92computerscience,quantumphysicsand,185configurationspace,122–24,123,217–18consciousness,xvconservationofmomentum,263consistenthistoriesapproach,218,298constitutivetheories,227contextuality,55–57continuousspontaneouslocalization(CSL),130–31contrarystates,38–43,45,123,298Copenhageninterpretation,94,97,107,112,113,117,184,274correlatedstates,51,145–47,146n,149

Cortês,Marina,265–67cosmicmicrowavebackground,121cosmology,201,207,230–31,253,302Crane,Louis,193–94creationruleofevents,267criticalrealism,154CSL.Seecontinuousspontaneouslocalizationcycles,268n

Dalibard,Jean,45Davisson,Clinton,81–82deBroglie,Louis,xxviii,12,78–81Einsteinand,81,103PhDthesisof,81,145pilotwavetheoryof,98–101,100Schrödingerand,82studentsof,118wave-particledualityand,83–84,103

deBroglie,Maurice,79deBroglie–Bohmtheory.SeepilotwavetheoryDebye,Peter,82decay,53,54decisiontheory,167–69,174decoherence,150n,154,175,208definition,155–56,299detectorsand,155historiesand,218ManyWorldsInterpretation,157nmeasurementand,159observationand,155,157quantumtheoryand,155randomnessand,155–56,159realismand,157Rule1and,158,159–60Schrödinger’scatand,156–57splittingproblemand,157wave-particledualityand,156

defectsoflocality,240degreeoffreedom,299density,29,30detectors,decoherenceand,155determinism,14–16,220–22,299deterministicdynamicalsystems,268nDeutsch,David,154,166–68,175,185Dewitt,Bryce,143diffraction,67,81–82,210dimensions,233,234nDirac,Paul,91,108discreteness,299disorderlocality,241

distinction,243doubleslitexperiment,67–68,68,72,98,199–200,210–11duality,ofreality,23–24dynamicalcollapsetheory,299

earlyuniverse,4earth,xivEinstein,Albert,xxvii,xxixautobiographicalnotesof,12,225Bohmand,108–11Bohrand,8,78,102contrarystatesand,43deBroglie,L.,and,81,103generalrelativityand,230lettertoBorn,8lightand,67localityand,44Maxwelland,69,70NobelPrizeof,8,72papersof,72–73pilotwavetheoryand,101–3,111quantummechanicsand,8–9quantumrevolutionof,8quantumtheoriesof,8realismand,84onreality,3relativity,theoryof,8,137,227spacetimeand,226specialrelativityand,226wave-particledualityand,83–84

Einstein-Podolsky-Rosen(EPR)state,45,47–49Einstein-Rosenbridge,240nelectricfield,40,68,262electricity,234electromagneticfield,189electromagneticradiation,40electromagnetism,227electrons,xvanti-realismand,85atomsand,78,83Bohrand,84chemicalpropertiesof,75defining,xvi,74diffractionand,81–82experimentaldevicesand,84–85Heisenbergon,87ofmatter,73–74momentumof,35orbits,74,77,83,92asparticles,79–80,82

perceptionof,84photonsand,69–70pilotwavetheory,98–101,100positionof,100propertiesof,xvi,xxviii,84quantummechanicsand,62statesof,78superpositionof,152wave-particledualityand,98–99aswaves,79–80,82,83

Elsasser,Walter,81energy,20atomsand,77–78causalrelationsand,261causalsetsand,264–65,267,269definitionof,299frequencyand,22,60,77–78informationand,260lawofconservationof,261oflight,74,183–84momentumand,21,261,262,264,267,270photonsand,69–70,77–78positionand,61specialrelativityand,261spectrumof,60–61

ensembleofatoms,59ensembleofsimilarsystems,247entanglement,38–39,43,57,188,221ofatoms,252forcodes,48definitionof,299elementaryparticlesand,5localityand,47Mach’sprincipleand,135nonlocal,xxviii,235ofphotons,45pilotwavetheoryand,214quantumcomputerand,248–49inquantumsystems,196retrocausalityand,216spaceand,238spacetimeand,135spinnetworksand,135superpositionand,195technology,48

entropy,120,159,177,191n,299epistemology,11Epperson,Michael,198EPR.SeeEinstein-Podolsky-Rosenstateeternalistrelationalism,237

ethicalquandaries,raisedbyEverett,176–77Euclid,229events,266,267,269–70,299Everett,Hugh,xxvii,145ethicalquandariesraisedby,176–77hypothesisof,165–71,175,176,178–80particlesand,148pilotwavetheoryand,148proofsof,151–52,151nquantummechanicsof,148nrealityand,165Rule2and,164–65

evolution,250exclusionprinciple,299existingframeworks,278experimentaldevices,electronsand,84–85experimentalinvestigation,252experimentalphysics,252experimentaltechniques,274

facts,xivfantasy,realityand,xiii,xix,xxiv,xxvFeyerabend,Paul,113,173Feynman,Richard,xxvii,184–85,217,241,279field,299fieldtheory,300Finkelstein,David,116firstlawofmotion,80–81force,300Forman,Paul,12freedom,atomsand,246frequencyenergyand,22,60,77–78lightand,69–71probabilities,161–64,165–66quantumstatesand,60resonant,60–61ofwaves,22,61

Fuchs,Chris,66fundamentallaws,252,265–66,274fundamentalphysics,principlesfor,229–37fundamentalsimultaneity,237future,200–201,266,300causal,254–55predicting,16–17,21,25,30,90,198

Gambini,Rodolfo,141gases,propertiesof,71Geigercounter,50–52,121,146,195geometry,136,229–30,234n,257

Germer,Lester,81Ghirardi,Rimini,andWeber(GRW),130,139ghostbranchesofpilotwavetheory,207–10wave-functioncollapseand,213

God,234,238Gomes,Henrique,201Grangier,Philippe,45gravity,xvii,xxvi,74,134,137,139–40Gross,David,273GRW.SeeGhirardi,Rimini,andWeberguidanceequation,99,109,210–11Gurdjieff,115,115n

Hardy,Lucien,183,186,187Heisenberg,Werner,xxii,xxix,18,85–92Hermann,Grete,104,106hiddenvariables,xxi,113,139,141,184,215,221,237–49,300histories,217–19,266,298holographichypothesis,260,278holographicprinciple,300HouseUn-AmericanActivitiesCommittee,108humanistacademics,xxivhydrogenatoms,77,78,83,89hydrogenbomb,xxvii

identityofindiscerniblesprinciple,233–37,242,245,263,268–69illusion,timeas,202–4indeterminism,248inertia,80–81,275informationcausalstructureand,260ascommunication,189computersand,191–92contextof,190definitionof,189,191,191n,192,300energyand,260entropyand,191nflowof,259–60languageand,189–90meaning,190–91measurementof,190particlesand,249nphysicsand,189,192–93relationalquantumtheoryand,193semanticsand,189–90spacetimeand,259–60speedoflightand,46,121universeand,189wavefunctionand,193,249n

instrumentalism,300interference,19,68,68,81–82,126,131inverseproblem,258irrationality,117irreversibility,158,214,236,236n,268

Jacobson,Ted,259Jordan,Pascual,88–89

Kabbalah,86Károlyházy,F.,130Kastner,Ruth,198Kauffman,Stuart,198Khrushchev,Nikita,114knowledge,xiii,9–12,271–72Kochen,Simon,56Kochen-Speckertheorem,56,300Krishnamurti,115,115n,116Kuhn,Thomas,279

Lakatos,Imre,174–75language,informationand,189–90laws.SeealsoRule0;Rule1;Rule2;thermodynamicsofatoms,251–52ofconservationofenergy,261ofexcludedmiddle,199–201offundamentalparticles,14ofnature,xix,92,226,243,250,265,276tophysicalsystems,applicationof,28–30ofphysics,15–16,25,273ofprecedents,251–52probabilitiesand,250unitary,31

Leibniz,241–42,268Lewis,David,163light,56,234.Seealsophotonsatomsand,77–78colorof,70–71doubleslitexperiment,67–68,68,72Einsteinand,67energyof,74,183–84frequencyand,69–71interferencepatternof,68natureof,67,75Newtonand,67,80asparticles,69,72,80propertiesof,70–71realismand,75travelinginstraightlines,67–68,68aswave,68,68,72,80

wave-particledualityand,84locality,10,41,55,269assumptionsaboutphysicsand,44–45defectsof,240definitionof,300disordered,241Einsteinand,44asemergent,236,271entanglementand,47natureand,45,46,57,220photonsand,44–45ofphysicalsystems,43physicsand,47,48quantummechanicsand,45,46spaceand,245

loopquantumgravity,136,137,194,240,278,300luck,scienceand,90–91

Mach’sprinciple,135macroscopicobjects,128macroscopicsystems,248magicalrealism,xxiii,xxv–xxvi,8,201magneticfields,68,262magnetism,234manyinteractingworldstheory,220manymomentstheory,202–4,300ManyWorldsInterpretation,xxiii,145,148,172decoherence,150n,154,157ndefinitionof,300Deutschand,175manyinteractingworldstheory,219–20measurementand,149moralityand,176–78multiverseand,xxv–xxvioutcomesofexperimentsin,150–52pilotwavetheoryand,208probabilitiesand,160problemswith,175quantumstatesand,152realismand,150,174splittingprocessin,149–50,150n,152,153–54

Markopoulou,Fotini,240mass,300mathematicallaws,9mathematics,227,274matrix,91,239,239,240,300,301matter,xiv,71,79–80,226atomsand,72behaviorof,259defining,xv,xvi

electronsof,73–74formsof,xvaswaves,5,23,84

Maxwell,JamesClerk,68,69,70,74,77measurement,17,250ofatoms,195contextualityand,55–56correlatedstatesand,149decoherenceand,159devices,5,52,64,87,89,91,131–32EPRand,48ofinformation,190instruments,128,129,213ManyWorldsInterpretationand,149ofmomentum,23nonlocalityand,42–43ofparticles,48,128positionand,23,61probabilitiesand,34,35processof,88–89,117quantummechanicsand,26,58–59quantumstatesand,34quantumtheoryand,34randomnessin,62–63realismand,65realityand,26Rule1and,33–34Rule2and,144superpositionand,64

measurementproblem,6–7,52,62–64,117collapsetheoryand,131–32,133,142,144–45pilotwavetheoryand,142,206quantumstatesand,34,187wave-functioncollapseand,213wave-particledualityand,223

Mermin,David,105metaphysics,xvi,xxiv–xxvmimeographs,135Minkowski,Hermann,226miracles,xivmistakes,279models,226molecules,3,5,6,73,246–47moments,201–4momentum,16,18,55angular,77,263n,297collisionsand,20conservationof,263definition,16n,20,301ofelectrons,35

energyand,21,261,262,264,267,270exchangeof,20measurementof,23ofparticles,22–23,262npositionand,90,262specialrelativityand,261symmetryand,263timeand,262uncertaintyprincipleand,21–22velocityand,20–21,21wavelengthand,xxviii,22

TheMonadology(Leibniz),241–42morality,176–78motion,80–81,111,141,244Moussouris,John,135nmultiverse,xxv,xxv–xxvi,178,179mysticism,xxiii,xxvi,115,118

nads,242–43,243,244,253–56naiverealism,xxii–xxiii,218Nash,John,113natureanti-realismand,xxvbehaviorof,xixascomputers,192contextualityof,56featuresof,xivknowledgeof,271–72localityand,45,46,57,220metaphysicsand,xviobjectivityand,85propertiesof,xxquantummechanicsand,xx,xxiii,3,6quantumstatesand,217realismand,xxiirelationshipwith,92religionand,xxivscienceand,85timeand,265understandingof,xiii,xviii

nearby,innetworks,240neighborhoods,242–43,243,244,246–47Nelson,Edward,223networks,240neutrinophysics,136newevolutionlaw,141Newton,Isaac,16,67,80–81Newtonianmechanics,16,111Newtonianphysics,301Newton’slaws,64,141,209,218,219,244

Noether,Emmy,104,104n,263,264noise,collapsetheoryand,133non-commutativityprinciple,17–20nonlocalentanglement,xxviii,235nonlocalinteractions,248,271nonlocality,49,56definitionof,301emergenceof,271asemergent,236measurementand,42–43particlesand,211–12retrocausality,216specialrelativityand,212speedoflightand,57

now,conceptof,237nuclearphysics,4nuclearwar,178nucleus,74,93

objectivity,11,30,85,166,168,171objects,6,139observables,26,27,231observation,155,157,166–67,188,193,231observer,193,238ontology,11operationalism,92,100,187,197,301operationalists,xxiiOppenheimer,J.Robert,108,112outcomesofexperimentsinManyWorldsInterpretation,150–52probabilitiesand,251Rule2and,172

Oxfordinterpretation,ofquantummechanics,154,160,169–70

paralleluniverses,145,148,247parity,136participation,observationand,188particles,4.Seealsowave-particleduality;wavesbehaviorof,21–22,211combining,32–33determinismand,14–15electronsas,79–80,82entanglementand,5Everettand,148guidanceequationand,211informationand,249nlawsoffundamental,14lightas,69,72,80manyinteractingworldstheory,219–20measurementof,48,128

momentumof,22–23,262nmotionof,111,141Newtonianmechanicsand,111nonlocalinfluenceson,211–12nonlocalityand,211–12photonsas,69physicalsystemsand,29pilotwavetheoryand,131,238positionof,22–23,34,119,199,262probabilitiesand,61,119superpositionof,4–5trajectoryof,23velocityof,23wavefunctionand,99–100,109,118–20,209,210wavesand,21–24,34,60,66,79–80,81,83–84,99–100,213

past,200,203,204,254,261,266,301Pauli,Wolfgang,89,93,112Pearle,Philip,130,141Penrose,Roger,122,133,134–39,238nperception,xx,xxiii,xxvii,9–10,84Peres,Asher,66perfection,243,244–45philosophy,11,228photoelectriceffect,72photons,40–41atomsand,195,209–10contrarystatesof,45correlatedstatesand,146definitionof,301electronsand,69–70energyand,69–70,77–78entanglementof,45localityand,44–45asparticles,69polarizationof,45,220specialrelativityand,47spectrographmeasurementsof,87superpositionof,50aswaves,69

physicalcollapsemodels,130physicalinteractions,246physicalsystems,28–30,43,192,251physicaltheories,229physicsanti-realismand,xxvassumptionsaboutlocalityand,44–45departments,quantumfoundationsand,184inearlyuniverse,175–76goalof,25Heisenbergon,86–87

informationand,189,192–93localityand,47,48Penroseand,135philosophyand,228realityand,3

pilotwavetheory,98–101,100beyond,222–24applicationsof,207atomsand,122Bohmand,109,110,116,118Bohrand,102–3challengesfor,207collapsetheoryand,131complementarityand,101definitionof,301Einsteinand,101–3,111entanglementand,214equationsof,206Everettand,148ghostbranchesof,207–10hiddenvariablesin,238inconsistencyof,104lessonsfrom,206–13ManyWorldsInterpretationand,208measurementproblemand,142,206particlesand,131,238probabilitiesin,119quantumcomputersand,174quantummechanicsand,101,121realismand,129,143–44,206–7reciprocityand,209,223relativisticfieldtheoryand,213researchaimfor,207reversibilityof,214Rule1and,101,116Rule2and,101specialrelativityand,212superpositionand,214theoryofrelativityand,211universeand,121wavefunctionand,125–26,210wave-particledualityand,142,208–10,222

Planck,Max,18,22,71,71n,183–84Planckenergy,301Plancklength,301Planckmass,301Planck’sconstant,22,77,301planets,74–75plasmaphysics,108Podolsky,Boris,43,44.SeealsoEinstein-Podolsky-Rosenstate

polarization,40,40–41,45,220Popper,Karl,191nposition,16,18,55definite,31,32ofelectrons,100energyand,61indefinite,31,32measurementand,23,61momentumand,90,262ofparticles,22–23,34,119,199,262probabilitiesand,34uncertaintyprincipleand,21–22

possibility,actualityand,177–78,197–98,200,243precedence,249–52preparation,250present,200,203,266pressure,29PrincetonUniversity,108,113principalprinciple,163principleofprecedence,249–52principleofrelativelocality,278principleofsufficientreason,233–35,268principlesforfundamentalphysics,229–37principletheories,227probabilities,29–30,117,145,247amplitudeand,138Bayesian,160–61,163,297beliefsand,164Born’sruleand,164,200,218Deutschand,166–68distributionfunction,119–20frequency,161–64,165–66historiesand,218–19lawsand,250ManyWorldsInterpretationand,160meaningof,160–61measurementand,34,35objectivityand,166,168,171outcomesand,251particlesand,61,119inpilotwavetheory,119positionand,34principalprinciple,163npropensity,164inquantummechanics,59,179–80quantumstatesand,34–35realismand,132–33Rule2and,150subjective,162,163n,170,172,174,193,208wavefunctionand,124,128,151,165

propensity,164proteins,24Puali,Wolfgang,104Pullin,Jorge,141

quanta,301quantization,137,302quantumBayesianism,187,193,302quantumblackholes,189quantumcomputers,48,159,174,185,188,248–49quantumcosmology,302quantumepistemologists,xxiiquantumequilibrium,120–21,143–44,211,212,302quantumforce,247quantumfoundations,13n,134,173,175,183–86,275quantumgravity,xvii,133,134,139,185,193,207,216,228,231,253,275challengesof,258–59definitionof,302loop,136,137,194,240,300nadsand,256networksand,240

quantuminformationtheory,185–86,188,248–49quantummechanics,xvianti-realismand,xxiargumentover,xixatomsand,6,62basicsof,xxviii–xxixbiologyand,3causaltheoryofviewsand,271classicalmechanicsand,193–95,196completionof,241,274–75conceptualproblemswith,xviiconventional,120definitionof,302determinismand,15Einsteinand,8–9electronsand,62essentialprincipleof,14ofEverett,148nfalsificationof,169gestationperiodof,183–84historyof,xviiincompletenessof,9,28,43,175,253localityand,45,46mathematicalstructureof,103matrixin,91measurementand,26,58–59mysteriesof,7,10–11natureand,xx,xxiii,3,6originof,83

Oxfordinterpretationof,154,160,169–70pilotwavetheoryand,101,121polarizationand,41predictionsfrom,61–62probabilitiesin,59,179–80propertiesexplainedby,58puzzlesof,10–11quantumcomputerand,249quantumphysicsand,xvirealensembleformulationof,247realismand,xxi,11–12,144realityand,xxiirejectionof,xxirestrictionand,45retrocausalityand,217spacetimeand,228spontaneouscollapsesand,143structureof,104successof,26superpositionand,37,138–39timeand,63,137universeand,28,159n,231

quantumphenomena,13nquantumphysics,xvi,xix,17–20,57,185quantumPoincarérecurrencetheorem,158,158nquantumspacetime,256quantumstates,30,302adding,32–33ofatoms,37–38definitionof,31frequencyand,60joint,32–33,37–38ManyWorldsInterpretationand,152measurementproblemand,34,187natureand,217asnonlinear,139operationalismand,197probabilitiesand,34–35superpositionand,32–33timeand,31universeand,193,197,231wavefunctionand,31n,32

quantumsuperposition,6quantumsystems,37,137–38,147,196quantumteleportation,186quantumtheory,xviii,xxi,12backgroundstructuresof,231Bohrand,xxii,7–8,9ofcosmology,201decoherenceand,155

definitionof,302ofEinstein,8generalrelativityand,136–38incompletenessof,274incorrect,xxvimeasurementand,34naturallawsand,92ofPenrose,134realismand,107,153restrictionand,46Rule1and,154Rule2and,172structureof,186unificationof,xxviuniverseand,27–28

qubit,187–88

radiation,xvii,52,56,79–80,93,125randomness,62–63,155–56,159,212,248rationality,234Raymond,LouisVictorPierre,78–79realensembleformulation,247,249n,268realensembletheory,249realism,xix–xx,26,180.Seealsoanti-realism;criticalrealismabandonmentof,66,97atomsand,75beliefsand,205decoherenceand,157definitionof,302Einsteinand,84failureof,200Heisenbergand,91lightand,75manymomentsand,204ManyWorldsInterpretationand,150,174measurementand,65naive,xxii–xxiii,197,218naturalworldand,xxiiobjectivityand,30ontologyand,11operationalismand,187Penroseand,139pilotwavetheoryand,129,143–44,206–7probabilitiesand,132–33quantummechanicsand,xxi,11–12,144quantumphysicsand,57quantumtheoryand,107,153relativityand,237Rovelliand,197Rule1and,145,149

specialrelativityand,215wave-particledualityand,89

realitydualityof,23–24Einsteinon,3elementsof,43–44Everettand,165fantasyand,xiii,xix,xxiv,xxvfundamental,xxiihistoriesand,218knowledgeand,12measurementand,26momentsand,202nadsand,253–54objectivityand,11old-fashionednotionsof,10parallel,xviiiphysicsand,3possibilityand,198quantummechanicsand,xxiisuperpositionand,147

reciprocity,209,223,232–33,235,247relationalhiddenvariables,237–49,241,269relationalism,237,253,265,302relationalmodel,ofuniverse,242relationalquantumtheory,193,197,302relationalspacetimegeometry,specialrelativityand,235relationships,231–32,236relativisticfieldtheory,pilotwavetheoryand,213relativity,general,9,93,227,229Einsteinand,230nadsand,254asnonlinear,138Penroseand,134–39planetsand,75quantumtheoryand,136–38solutionto,255nspacetimeand,256superpositionand,138

relativity,special,9,47,133,230,303collapseand,141Einsteinand,226energyand,261momentumand,261nonlocalityand,212pilotwavetheoryand,212quantumequilibriumand,121realismand,215relationalspacetimegeometryand,235

relativity,theoryof,xx,8,16,303

collapsesand,133collapsetheoryand,133ofEinstein,137,227equation,72pilotwavetheoryand,211spacetimeand,226speedoflightand,47wavefunctionand,142

religion,xxivrestriction,45,46,55,184,215,298retrocausality,216–17,217,303reversibility,158,214,268,268nRoger,Gérard,45rolled-updimensions,233Rosen,Nathan,43,44.SeealsoEinstein-Podolsky-RosenstateRosenfeld,Léon,113–14rotations,263–64,263nRovelli,Carlo,193–94,196,197Rule0,203,303Rule1,31–36,35n,54,54,63–64,99,121Born’sruleand,171decoherenceand,158,159–60definition,303lackof,148nmeasurementand,33–34pilotwavetheoryand,101,116quantuminformationtheoryand,188quantumtheoryand,154realismand,145,149reversibilityof,158Rule2and,64,129–31,141,158asuniversal,148nwavefunctionand,116,118

Rule2,35–36,35n,41–42,50,51,53–54,63–64,99definition,303Everettand,164–65inventionof,128irreversibilityof,158measurementand,144outcomesand,172pilotwavetheoryand,101probabilitiesand,150quantumtheoryand,172Rule1and,64,129–31,141,158wave-functioncollapseand,215

Rutherford,Erenst,74

Saunders,Simon,171Schrödinger,Erwinbackgroundof,82

deBroglie,L.,and,82equationof,31,239,241,247,303NobelPrizeof,83Schrödinger’scat,49–54,54,121–24,145–48,152,156–57,201wave-particledualityand,83–84

Schrödinger-Newtonlaw,141science,xix,xxiii–xxiv,xxiv–xxv,xxvi,27,85,90–91scientificmethod,273scientificmind,xivsecondlawofthermodynamics,159,303self-reference,28semantics,informationand,189–90senses,xivshadowtheory,xviiShannon,Claude,189,191nShimony,Abner,158,198Shore,Peter,185similarsystems,251solarsystem,xv,74,75,244SolvayConference,98,101–2,117Sorkin,Rafael,218,257–58soundwaves,98spaceconfiguration,122–24,123,217–18dimensionsof,233asemergent,236–37,238,264,269entanglementand,238asfundamental,263geometryof,229–30asillusion,204localityand,245networksand,240relationshipswithin,236

spacetime,xxvi,4addingtogether,138atoms,257–59backgroundsand,269causalityand,134causalrelationsand,257Einsteinand,226asemergent,269entanglementand,135generalrelativityand,256geometryof,130,134,257informationand,259–60inverseproblemand,258quantum,256quantummechanicsand,228relationalprincipleof,232theoryofrelativityand,226

wavefunctionand,140Specker,Ernst,56spectrograph,measurementsofphotons,87spectrum,59–61,78,83,89speed,303speedoflight,43,46–47,57,121.Seealsolocalityspin,303spinnetworks,135–36,238n,303splittingBohrand,193–94problem,152–54,157,174processinManyWorldsInterpretation,149–50,150n,152,153–54

spontaneouscollapses,131–33,141,143,213,214standarddeviation,62standardmodelofparticlephysics,304stars,4starvation,178states.Seealsoquantumstatesofatoms,49–51,60–61,77–78,146–47classical,30contrary,38–43,45,123,298correlated,51,145–47,146n,149definition,15,304ofelectrons,78superposing,32–33

stationarystates,77,87,92stochasticquantummechanics,223Stoppard,Tom,15stringtheory,189,234n,278,304subjectiveprobabilities,162,163n,170,172,174,193,208subjectivity,entropyand,191nsubsystemprinciple,26,27superdeterminism,220–22superposition,4–5ofatoms,6–7,50,139–40,146,152,156–57ofelectrons,152entanglementand,195generalrelativityand,138gravityand,140measurementand,64ofmolecules,6ofobjects,139ofparticles,4–5ofphotons,50pilotwavetheoryand,214quantum,6quantummechanicsand,37,138–39quantumstatesand,32–33ofquantumsystems,37,137–38realityand,147

Schrödinger’scat,49–53ofstates,32–33,196–97wavefunctionand,139–40,213

superpositionprinciple,33,137–39symmetry,104n,255n,263,263–64

’tHooft,Gerard,221–22technology,entanglement,48temperature,29,30temporalrelationalism,237,253,265thermodynamics,120,159,177,191n,214,303timecapsules,203causalityand,204,236asemergent,237eventsand,266gravityand,137,140asillusion,202–4irreversibilityof,236,236nlawsof,265lawsofnatureand,265momentsand,201–3momentumand,262natureand,265quantummechanicsand,63,137quantumstateand,31retrocausality,216–17,217

topologicalfieldtheories,193–94transactionalinterpretation,216–17truth,xx,xxvi,276–77Tumulka,Roderich,107Turingmachine,185twistortheory,136tyranny,178

uncertaintyprinciple,18–22,32,58,61,90,92–93,117,145,304Unger,RobertoMangabeira,265unification,216,229unificationofforces,xviiunitarylaw,31universalquantumcomputer,185universeascausalset,260chosenaspectof,221expansionof,4informationand,189livingmirrorof,245nadic,242–43,243observationand,166–67,231parallel,145,148,247

physicsinearly,175–76pilotwavetheoryand,121quantummechanicsand,28,159n,231quantumstatesand,193,197,231quantumtheoryand,27–28relationalmodelof,242theoryof,27wavefunctionand,231

Valentini,Antony,120,121,210variety,244,247velocity,20–21,21,23,81,262n,304views,causaltheoryof,269–71Vigier,Jean-Pierre,114vonNeumann,John,93–94,104–5,110

water,xvwavefunction,31n,32,99n,176atomicsystemsand,141,213beablesand,224definitionof,304informationand,193,249nparticlesand,99–100,109,118–20,209,210phasesof,214npilotwavetheoryand,125–26,210probabilitiesand,124,128,151,165Rule1and,116,118spacetimeand,140spontaneouscollapsesand,143squaring,99–100,100,151superpositionand,139–40,213theoryofrelativityand,142universeand,231

wave-functioncollapse,35–36,129–30,139,186definition,298drawbacksof,214–15ghostbranchesand,213lessonsfrom,213–16measurementproblemand,213Rule2and,215

wavelength,xxviii,22wavemechanics,304wave-particleduality,86,97–98deBroglie,L.,and,83–84,103decoherenceand,156definitionof,304doubleslitexperimentand,98,199–200,210–11Einsteinand,83–84electronsand,98–99lightand,84

measurementproblemand,223pilotwavetheoryand,142,208–10,222realismand,89Schrödingerand,83–84

wavesinelectricfield,40electronsas,79–80,82,83frequencyof,22,61heightof,34lightas,68,68,72,80matteras,5,23,84particlesand,21–24,34,60,66,79–80,81,83–84,99–100,213photonsas,69sumof,124

wavetheory,67Weinberg,Steven,179Weyl,Hermann,82–83Wheeler,JohnArchibald,xxvii,37,145,187–88Wheeler-DeWittequation,203Wigner,Eugene,195–96Wigner’sfriend,196nWitten,Edward,136Wittgenstein,Ludwig,72nWorldWarI,12wormholes,240,240n

X-rays,79–80

Young,Thomas,67–68

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

ABOUTTHEAUTHOR

LeeSmolinhasmadeinfluentialcontributionstothesearchforaunificationofphysics.HeisafoundingfacultymemberofthePerimeterInstituteforTheoreticalPhysics.HispreviousbooksincludeTimeReborn,TheTroublewithPhysics,andThreeRoadstoQuantumGravity.

*Anotetomyexpertreaders:Quantumfoundationsispresentlyaverylivelysubject,withmanyexcitingdevelopmentsbothexperimentalandtheoretical.Manyproposalscompetetoresolvethepuzzleswewillmeethere.Ishouldwarnthereaderthatourpaththroughthesefrontierswillbeanarrowone,andtherearemanyexcitingideasandresultsthatIdonotmentionhere.HadItriedtoreviewthewholefield,orincludeallthelatestsupremelycleveradvances,theresultwouldhavebeenalessaccessiblebook.Myfirstaimistointroducetheworldofquantumphenomena,notthefullspectrumofcompetinginterpretationsofthosephenomena.Iapologizeinadvancetothoseexpertswhodon’tfindtheirpreferredversionofquantumphysicshere,andencouragethemtowritetheirownbooks.Ialsoapologizetothehistorians.Iamnotascholar,andthestoriesItellarecreationmyths,handeddownfromteachertostudent,originating,insomecases,withthefoundersthemselves.

*Themetaphoroftheuniverseasacomputerishelpfulforillustratingdeterminism,butisonthewholemisleading,asIwillarguebelow.

*Momentumwillbedefinedshortly,butroughly,abody’smomentumisproportionaltobothitsspeedandmass.

*>means“islargerthan.”

*Whenawaverepresentsaquantumstate,wesometimescallitawavefunction.

*ButyouknewassoonasImentionedRule1thattherehadtobeasecondone.Ishouldpointoutthatinsometextbooks,Rules1and2areswitched.

*FormoreonhowPlanckmisappropriatedBoltzmann’smethods,seeThomasKuhn’sBlack-BodyTheoryandtheQuantumDiscontinuity,1894–1912,orawonderfulbiographyofPaulEhrenfestbyMartinKlein,bothlistedintheFurtherReadingsection.

*Unfortunately,thiscametoolateforBoltzmann,who,depressedathisfailuretoconvincehiscolleaguesoftherealityofatoms,committedsuicidethenextyear.Andasafootnotetoafootnote:ayoungViennesephysicsstudentcalledLudwigWittgensteinwassodismayedbynewsofBoltzmann’ssuicidethatheswitchedtophilosophy.

*Iamoversimplifyingabit.Theparticlefollowsapartofthewavefunctioncalleditsphase.

*AntonyValentinigavemeacopyofthatpaperofEinstein’sduringaspeechatmywedding,whichIpromptlylost.

*Noetherisoneofthegreatesttwentieth-centurymathematicians;amonghermanydiscoverieswasaseminaltheoremonsymmetryinphysics,whichwewillcometo.

*IfIcanbepermittedapurelypersonalremark,IamagrandchildofaMarxistwhoremainedalifelongmemberoftheAmericanCommunistPartylongafterthedreamhaddied,andIamalsothesonofseekerswhospentmanyyearsintheGurdjieffwork.Toalargeextent,theerrorsofmyparentsandgrandparentsinoculatedmeagainstfallinginlovewithorganizedseekers,runningaftervisionsoftranscendence.ItiseasyformetocriticizeBohmandothersofhisgenerationfortheastoundingnaivetétheyshowedinthefaceofthepeculiarcombinationofgenuinecompassionforhumansufferingandextraordinarydishonestyandnarcissismthatguruslikeGurdjieffandKrishnamurtisharedwiththe“revolutionary”leadersonthevanguardoftheleft.Butatthesametime,thereis,Ibelieve,theshadowofsomethingrealbehindtheteachingsofthelikesofGurdjieffandKrishnamurti,whobroughtdistillationsofEasternspiritualpracticestowesterners.

*WhichwascompletedinaPhDthesisofastudentofPenrose’scalledJohnMoussouris,whichalsoremainedunpublished,andwasalsopassedhandtohand.

*Noticethatthetwocontingentstatements,whichtogetherexpressthecontentofthecorrelatedstateIN-BETWEEN,donotrequireorimplythattheatomhasdecayed,releasingaphotonthatpassesthroughandtriggersthedetector.Ateachtime,itmayhavedecayedoritmayhaveyettodecay.ThisiswhyIreferto“thephoton’spossiblepassagethroughthedetector.”

*WecanthinkofEverettianquantummechanicsaspilotwavetheorywithouttheparticles.Inbothcases,thereisnoRule2;bothmakeRule1universal.Soinbothcases,thewavefunctioncontinuallybranches,creatingalternativehistories,suchastheoneswhereIstayedinLondonorperishedoffPeggy’sCovewiththeSwissairflight.Thedifferenceisthatpilotwavetheoryhasparticles,whichtakeonlyoneofthealternatebranches.

*ThereisanoperationalreadingofEverettthatseesthetheorypurelyasamethodforproducingsetsofcontingentstatementssuchasIdescribedabove,butmakesnoclaimstowhatisrealbeyondthat.ThisseemstomeaconsistentwaytoreadEverett’sthesis.(LeeSmolin,“OnQuantumGravityandtheManyWorldsInterpretationofQuantumMechanics,”inQuantumTheoryofGravity:EssaysinHonoroftheSixtiethBirthdayofBryceS.DeWitt,eds.StevenChristensenandBryceS.DeWitt[Bristol,UK:AdamHilger,1984].)

*Inthenextchapter,wewillseethatsomeexpertsarguethatsplittingrequiresamacroscopicprocesscalleddecoherence.Thishappensfarlessoften;thishastheeffectofdecreasing“vast”inthissentencetomerelyverylarge.

*Thatis,wavefunctionswithsmallamplitudes.

*Toputitmoreprecisely,whilethemeasureofallthosebrancheswithstatisticsnotobeyingtheBornrulegoestozero,inthelimitofaninfinitenumberoftrials,thenumberofthosebranchesdoesnot.

*WallaceandMyrvoldhavesinceleftOxford;Deutsch,Greaves,andSaundersremainasof2018.

*TheideathatdecoherencedefinesthebranchesintheManyWorldsInterpretationhadbeensuggestedearlierbyothersincludingHeinz-DieterZeh,WojciechZurek,MurrayGell-Mann,andJamesHartle.

*Indeed,theholographicprinciple(whichisdefinedonpages259–260)requiresthatanysystemthatcanbefitintoaboxwithwallsofafiniteareahasafinitenumberofstates.Thisiscertainlythecasewithanysystemofthekindwearediscussinghere—anatomicsysteminteractingwithameasuringinstrument.Onereplythatmightbegivenisthatweliveinanever-expandinguniverse,whichmayimplythatthedimensionofthestatespaceiscontinuallyexpanding,inwhichcasethereisnoPoincarérecurrence.Thisraisesseveralfascinatingissues.But,forthemoment,itisenoughtonotethatthisamountstoclaimingthatquantummechanicsmakessenseonlywhenappliedtotheuniverseasawhole.

*Notethatthisprinciplecannotbetakenasanendofthestoryofmakingsenseofprobabilities,becauseitisolatessomethingthatwewouldreallyliketounderstandfromfirstprinciples.Whatismissingisaconvincingargumentthatwouldcompelustolineupoursubjectiveprobabilitieswiththeobjectivechances.

*IncludingGreaves,Myrvold,andWallace.IshouldnotethattheyintroducelinesofargumentIhaven’tmentionedhere,aboutwhichexpertsdisagree,sothesituationissomewhatmorecomplexthantheoverviewIhavepresented.

*Myownviewastohowscienceworksandtheroleofindividualjudgmentsinformingaconsensusofthewholescientificcommunityisoutlinedinchapter17ofmybookTheTroublewithPhysics.

*Ratherthanjustrulingoutlocalhiddenvariabletheories.

*AtthispointIhavetomakeanaside,whichthenon-expertreadermayskip.AnexpertmightobjecttomycharacterizationofShannoninformationbypointingoutthatthatquantityisequaltothe

negativeoftheentropyofthemessage.Entropy,theywouldargue,isanobjective,physicalpropertyofnature,whichisgoverned(whenthesystemisinthermodynamicequilibrium)bythelawsofthermodynamics.Hence,byvirtueofitsconnectionwithentropy,Shannoninformationmustbeobjectiveandphysical.Iwouldanswerbymakingthreepoints.First,itischangesinthethermodynamicentropy,nottheentropyitself,that

comeintothelawsofthermodynamics.Second,asKarlPopperpointedoutyearsago,thestatisticaldefinitionofentropywhichShannoninformationisrelatedtoisnotacompletelyobjectivequantity.Itdependsonachoiceofcoarse-graining,whichprovidesuswithanapproximatedescriptionofthesystem.Theentropyoftheexactdescription,givenintermsoftheexactstate,isalwayszero.Theneedtospecifythisapproximationbringsanelementofsubjectivitytothedefinitionofentropy.Thisisseeninthedependenceoftheentropyofaquantumsystemonasplittingintotwosubsystems.Finally,theattributionofentropytoamessageisadefinition,whichdefinesentropyintermsofShannoninformation.

*Thisstepoftheargumentiscalled“Wigner’sfriend.”

*AsIargueinTimeReborn,andinTheSingularUniverseandtheRealityofTime,withRobertoMangabeiraUnger.

*WhichIdefinedbackinchapter8.

*Thephasesofawavefunctionreferstothelocationsofthepeaksandtroughs,andthepatternstheyform.

*Thatis,acomplexnumber.

*Formuchmoreonthispoint,seemybooks,TimeReborn,andTheSingularUniverseandtheRealityofTime,withRobertoMangabeiraUnger.

*Intechnicalterms,theobservablesalgebraandinnerproduct.

*Stringtheorydoesnotdothis;instead,itfixesthetotalnumberofdimensions,includingpossiblemicroscopicdimensions.Thatcouldbeagoodthing,ifitdidn’tgiveusinfinitechoicesforthegeometryandnumberofthesehypothesizedtinydimensions.

*Aneventcanbefollowedbyasecondeventthatreversestheactionofthefirst,butthenyouhavetwoevents;thisisnotequivalenttoaspacetimeinwhichneitherhappened.

*Thisisnotanewidea;asInotedinchapter9,RogerPenrosementioneditasmotivationforhisspinnetworksmodelintheearly1960s.

*JuanMaldacenaandLeonardSusskindhavesinceintroducedaversionofthisideatheycallER=EPR,whereERstandsforanEinstein-Rosenbridge,whichisawormholeconnectingtwopointsfarfromeachotherinspace(“CoolHorizonsforEntangledBlackHoles,”arXiv:1306.0533).

*Moreprecisely,thenegativeoftheaction.

*Inthisrealensembleformulation,theinformationinawavefunctionofaquantumsystemisspreadthroughouttheuniverse,codedintotheconfigurationsofthecopies.Akeyquestionishowmanycopiesasystemmusthavefortheinformationcodedintothecopiestobeadequatetoreproducetheinformationinthewavefunction.Thatinformationincreasesexponentiallywiththenumberofparticlesinthequantumsystem.Butthenumberofcopiesofasystemtheuniversewilllikelycontaindecreasesrapidlywiththenumberofparticlesthatmakeupthesystem.Sothereisasizeofasystembeyondwhichtheinformationinthecopiesdoesnotsuffice,withtheconsequencethateitherquantummechanicsbreaksdown,orthisapproachiswrong.Isuspectthatevenmodestquantumcomputerswillcrossthisline.

*I.e.,thosewiththesamepreparation,evolution,andmeasurement.

*SomerelativistspointtotheexistenceofsolutionstotheEinsteinequationswhichhaveclosedcausalloops.Idon’tthinkthishasanyforcebecausetheuniverseisdescribedbyatmostonesolutiontogeneralrelativity,andthatsolutionneednothaveeveryexoticbehaviorshowninothersolutions.Moredefinitively,thosesolutionswhichhaveclosedcausalloops(includingoneproposedbythegreatlogicianKurtGödel)areveryspecialinthattheyhavealotofsymmetry.Ifweimposetheprincipleoftheidentityofindiscernibles,thensolutionswithsymmetriesareexcluded.Thesesolutionsarealsounstableandcollapsetosingularitiesatthefaintesthintofaperturbation.

*ThesefundamentalunitsofareaareequaltotheproductofNewton’sgravitationalconstantandPlanck’sconstant.

*Formoreabouttheholographichypothesis,seemybookThreeRoadstoQuantumGravity.

*IntheNewtoniancase,themomentumofaparticleisproportionaltoitsvelocity.Theconstantofproportionalityisthemass.

*Androtationalsymmetryimpliestheconservationofangularmomentum.

*Fortheexperts,aCPTtransformation.

*Afewyearslaterweunderstoodthistwo-phasedbehaviorintermsofthedynamicsofageneralclassofdeterministicdynamicalsystems,withafinitenumberofpossiblestates.Suchsystemsevolvetocycles,andthetwophasesarethephaseofconvergencetoacyclefollowedbycyclicbehavior.Butacycleisreversible,becauseeacheventhasasinglechildandasingleparent.

*Ishouldwarnthereadernottobemisledbythecolloquialunderstandingofa“view”inwhichitstandsforthesubjectiveopinionofanindividual.

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