ALSOBYANILANANTHASWAMY

TheEdgeofPhysics

TheManWhoWasn’tThere

AnimprintofPenguinRandomHouseLLC

375HudsonStreetNewYork,NewYork10014

Copyright©2018byAnilAnanthaswamyPenguinsupportscopyright.Copyrightfuelscreativity,encouragesdiversevoices,promotesfreespeech,andcreatesavibrantculture.Thankyouforbuyinganauthorizededitionofthisbookandforcomplyingwithcopyrightlawsbynotreproducing,scanning,ordistributinganypartofitinanyformwithoutpermission.YouaresupportingwritersandallowingPenguintocontinuetopublishbooksforeveryreader.

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Portionsofchapters5and6appearedinNewScientistmagazine.Bohmiantrajectoriesinchapter6reproducedwithpermissionfromChrisDewdney.ThedeBroglie-Bohmandthemany-interactingworldstrajectoriesintheepiloguereproducedwithpermissiongrantedbyHowardWisemanonbehalfofhiscoauthors.

Illustrationscredit:RoshanShakeelLIBRARYOFCONGRESSCATALOGING-IN-PUBLICATIONDATANames:Ananthaswamy,Anil,author.Title:Throughtwodoorsatonce:theelegantexperimentthatcapturestheenigmaofourquantumreality/

AnilAnanthaswamy.Description:NewYork,NewYork:Dutton,animprintofPenguinRandomHouseLLC,[2018]|Includes

bibliographicalreferencesandindex.Identifiers:LCCN2018008272|ISBN9781101986097(hardcover)|ISBN9781101986110(ebook)|

Subjects:LCSH:Quantumtheory—Popularworks.|Wavetheoryoflight—Popularworks.|Reality—Popularworks.

Classification:LCCQC174.123.A532018|DDC530.12—dc23LCrecordavailablehttps://lccn.loc.gov/2018008272

Whiletheauthorhasmadeeveryefforttoprovideaccuratetelephonenumbers,Internetaddresses,andothercontactinformationatthetimeofpublication,neitherthepublishernortheauthorassumesanyresponsibilityforerrorsorforchangesthatoccurafterpublication.Further,thepublisherdoesnothaveanycontroloveranddoesnotassumeanyresponsibilityforauthororthird-partywebsitesortheircontent.

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Tomyparents

Allowmetoexpressnow,onceandforall,mydeeprespectfortheworkoftheexperimenterandforhisfighttowringsignificantfactsfromaninflexibleNature...[which]sayssodistinctly“No”andsoindistinctly“Yes”toourtheories.

—HermannWeyl,Germanmathematician,1885–1955

CONTENTS

ALSOBYANILANANTHASWAMY

TITLEPAGE

COPYRIGHT

DEDICATION

EPIGRAPH

PROLOGUETheStoryofNatureTauntingUs

1.THECASEOFTHEEXPERIMENTWITHTWOHOLESRichardFeynmanExplainstheCentralMystery

2.WHATDOESITMEAN“TOBE”?TheRoadtoReality,fromCopenhagentoBrussels

3.BETWEENREALITYANDPERCEPTIONDoingtheDoubleSlit,OnePhotonataTime

4.FROMSACREDTEXTSRevelationsaboutSpookyActionataDistance

5.TOERASEORNOTTOERASEMountaintopExperimentsTakeUstotheEdge

6.BOHMIANRHAPSODYObviousOntologyEvolvingtheObviousWay

7.GRAVITYKILLSTHEQUANTUMCAT?TheCaseforAddingSpacetimeintotheMix

8.HEALINGANUGLYSCARTheManyWorldsMedicine

EPILOGUEWaysofLookingattheSameThing?

NOTES

ACKNOWLEDGMENTS

INDEX

ABOUTTHEAUTHOR

T

Prologue

THESTORYOFNATURETAUNTINGUS

heofficeissimplythemostunclutteredofanyphysicist’sofficeIhaveeverseen.There’sachairalongsideasmalltable,withnothingonit.Nobooks,

nopapers,nolamp,nocomputer,nothing.Asofagracestheoffice.Largewindowsoverlookasmalllake,thetreesaroundwhicharebare,exceptforafewstragglersthatareholdingontotheirfallfoliage,defyingtheapproachingwinterinthispartofOntario,Canada.LucienHardyputshislaptoponthetable—pointingoutthathedoesmostofhisworkincafésandfiguresthatallheneedsinhisofficeisacafé-likesmalltabletosetdownhislaptop.

Thereistheobligatoryblackboard,takingupmostofonewallofhisoffice.Itdoesn’ttakelongforHardytospringupandstartchalkingitupwithdiagramsandequations—somethingthatmostofthequantumphysicistsImeetseeminclinedtodo.

Westarttalkingaboutsomeesotericaspectofquantumphysics,whenhestopsandsays,“Istartedoffthewrongway.”Toresetourdiscussion,hesays,“Imagineyouhaveafactoryandtheymakebombs.”Hehasmyattention.

Hewritestwonamesontheblackboard:ElitzurandVaidman.HeistalkingaboutsomethingcalledtheElitzur-Vaidmanbombpuzzle.NamedaftertwoIsraeliphysicists,thepuzzleexemplifiesthecounterintuitivenatureofthequantumworldinwaysthatnon-physicistscanappreciate.Itconfoundsphysiciststooinnosmallmeasure.

Theproblemgoessomethinglikethis.There’safactorythatmakesbombsequippedwithtriggers.Thetriggersaresosensitivethatasingleparticle,anyparticle,evenaparticleoflight,cansetthemoff.There’sabigdilemma,however.Thefactory’sassemblylineisfaulty.It’schurningoutbothgoodbombswithtriggersandbadbombswithouttriggers.Hardywritesthemas“good”and“bad”andquipsaboutthequotationmarks:“Obviously,youmayhaveadifferentmoralperspectiveonit.”

haveadifferentmoralperspectiveonit.”Thetaskistoidentifythegoodbombs.Thismeanshavingtocheckwhether

thebombshavetriggers.Butexaminingeachbombisn’tthecorrectstrategy,becauseinordertodoso,you’dneedtoshinelightonit,howeverfaint,andthatwouldcauseagoodbombtoexplode.Theonlyonesleftunexplodedwouldbethedudswithouttriggers.

So,howdoesonesolvethisproblem?Ifithelps,weareallowedoneconcession:wecandetonatesomebombs,aslongasweareleftwithsomegood,undetonatedbombs.

Fromoureverydayexperienceofhowtheworldworks,thisisanimpossibleproblemtosolve.Butthequantumworld—theworldofverysmallthingslikemoleculesandatomsandelectronsandprotonsandphotons—behavesinbizarreways.Thephysicsthatgovernsthebehaviorofthismicroscopicworldiscalledquantumphysicsorquantummechanics.Andwecanusequantumphysicstofindgoodbombswithoutsettingthemoff.Evenwithasimplesetup,it’spossibletosalvageabouthalfthegoodbombs.Itinvolvesusingamodernvariationofa200-year-oldexperiment.

Calledthedouble-slitexperiment,itwasfirstdoneintheearly1800stochallengeIsaacNewton’sideasaboutthenatureoflight.Theexperimenttookcenterstageagainintheearlytwentiethcentury,whentwoofthefoundersofquantumphysics,AlbertEinsteinandNielsBohr,grappledwithitsrevelationsaboutthenatureofreality.Inthe1960s,RichardFeynmanextolleditsvirtues,sayingthatthedouble-slitexperimentcontainedallofthemysteriesofthequantumworld.Asimplerandmoreelegantexperimentwouldbehardtofind,theworkingsofwhichahighschoolstudentcangrasp,yetprofoundenoughinitsimplicationstobewilderbrainslikeEinstein’sandBohr’s,aconfusionthatcontinuestothisday.

Thisisthestoryofquantummechanicsfromtheperspectiveofoneclassicexperimentanditssubtle,sophisticatedvariations(includingonethat,aswe’llsee,solvestheElitzur-Vaidmanbombpuzzle),whetherthesevariationsarecarriedoutasthoughtexperimentsbyluminousmindsorpainstakinglyperformedinthebasementlabsofphysicsdepartments.It’sthestoryofnaturetauntingus:catchmeifyoucan.

R

1

THECASEOFTHEEXPERIMENTWITHTWOHOLES

RichardFeynmanExplainstheCentralMystery

Thereisnothingmoresurreal,nothingmoreabstractthanreality.

—GiorgioMorandi

ichardFeynmanwasstillayearawayfromwinninghisNobelPrize.Andtwodecadesawayfrompublishinganendearingautobiographicalbookthat

introducedhimtonon-physicistsasastraight-talkingscientistinterestedineverythingfromcrackingsafestoplayingdrums.ButinNovember1964,tostudentsatCornellUniversityinIthaca,NewYork,hewasalreadyastarandtheyreceivedhimassuch.Feynmancametodeliveraseriesoflectures.Strainsof“FaraboveCayuga’sWaters”rangoutfromtheCornellChimes.TheprovostintroducedFeynmanasaninstructorandphysicistparexcellence,butalso,ofcourse,asanaccomplishedbongodrummer.Feynmanstrodeontothestagetothekindofapplausereservedforperformingartists,andopenedhislecturewiththisobservation:“It’sodd,butintheinfrequentoccasionswhenIhavebeencalleduponinaformalplacetoplaythebongodrums,theintroducerneverseemstofinditnecessarytomentionthatIalsodotheoreticalphysics.”

Byhissixthlecture,Feynmandispensedwithanypreamble,evenatoken“Hello”totheclappingstudents,andjumpedstraightintohowourintuition,whichissuitedtodealingwitheverydaythingsthatwecanseeandhearandtouch,failswhenitcomestounderstandingnatureatverysmallscales.

Andoften,hesaid,it’sexperimentsthatchallengeourintuitiveviewoftheworld.“Thenweseeunexpectedthings,”saidFeynman.“Weseethingsthatare

world.“Thenweseeunexpectedthings,”saidFeynman.“Weseethingsthatareveryfarfromwhatwecouldhaveimagined.Andsoourimaginationisstretchedtotheutmost—not,asinfiction,toimaginethingswhicharen’treallythere.Butourimaginationisstretchedtotheutmostjusttocomprehendthosethingswhicharethere.Andit’sthiskindofasituationthatIwanttotalkabout.”

Thelecturewasaboutquantummechanics,thephysicsoftheverysmallthings;inparticular,itwasaboutthenatureoflightandsubatomicbitsofmattersuchaselectrons.Inotherwords,itwasaboutthenatureofreality.Dolightandelectronsshowwavelikebehavior(likewaterdoes)?Ordotheyactlikeparticles(likegrainsofsanddo)?Turnsoutthatsayingyesornowouldbebothcorrectandincorrect.Anyattempttovisualizethebehaviorofthemicroscopic,subatomicentitiesmakesamockeryofourintuition.

“Theybehaveintheirowninimitableway,”saidFeynman.“Which,technically,couldbecalledthe‘quantum-mechanical’way.Theybehaveinawaythatislikenothingthatyouhaveeverseenbefore.Yourexperiencewiththingsthatyouhaveseenbeforeisinadequate—isincomplete.Thebehaviorofthingsonaverytinyscaleissimplydifferent.Theydonotbehavejustlikeparticles.Theydonotbehavejustlikewaves.”

Butatleastlightandelectronsbehavein“exactlythesame”way,saidFeynman.“Thatis,they’rebothscrewy.”

Feynmancautionedtheaudiencethatthelecturewasgoingtobedifficultbecauseitwouldchallengetheirwidelyheldviewsabouthownatureworks:“Butthedifficulty,really,ispsychologicalandexistsintheperpetualtormentthatresultsfromyoursayingtoyourself‘Buthowcanitbelikethat?’Whichreallyisareflectionofanuncontrolled,butIsayutterlyvain,desiretoseeitintermsofsomeanalogywithsomethingfamiliar.Iwillnotdescribeitintermsofananalogywithsomethingfamiliar.I’llsimplydescribeit.”

Andso,tomakehispointoverthecourseofanhourofspellbindingoratory,Feynmanfocusedonthe“oneexperimentwhichhasbeendesignedtocontainallofthemysteryofquantummechanics,toputyouupagainsttheparadoxesandmysteriesandpeculiaritiesofnature.”

Itwasthedouble-slitexperiment.It’sdifficulttoimagineasimplerexperiment—or,aswe’lldiscoveroverthecourseofthisbook,onemoreconfounding.Westartwithasourceoflight.Placeinfrontofthesourceasheetofopaquematerialwithtwonarrow,closelyspacedslitsoropenings.Thiscreatestwopathsforthelighttogothrough.Ontheothersideoftheopaquesheetisascreen.Whatwouldyouexpecttoseeonthescreen?

Theanswer,atleastinthecontextoftheworldwearefamiliarwith,dependsonwhatonethinksisthenatureoflight.Inthelateseventeenthcenturyandalloftheeighteenthcentury,IsaacNewton’sideasdominatedourviewoflight.Hearguedthatlightwasmadeoftinyparticles,or“corpuscles,”ashecalledthem.Newton’s“corpusculartheoryoflight”waspartlyformulatedtoexplainwhylight,unlikesound,cannotbendaroundcorners.Lightmustbemadeofparticles,Newtonargued,sinceparticlesdon’tcurveorbendintheabsenceofexternalforces.

Inhislecture,whenFeynmananalyzedthedouble-slitexperiment,hefirstconsideredthecaseofasourcefiringparticlesatthetwoslits.Toaccentuatetheparticlenatureofthesource,heurgedtheaudiencetoimaginethatinsteadofsubatomicparticles(ofwhichelectronsandparticlesoflightwouldbeexamples),weweretofirebulletsfromagun—which“comeinlumps.”Toavoidtoomuchviolentimagery(whatwithbombsintheprologue,andathoughtexperimentwithgunpowdertocome),let’simagineasourcethatspewsparticlesofsandratherthanbullets;weknowthatsandcomesinlumps,thoughthelumpsaremuch,muchsmallerthanbullets.

First,let’sdotheexperimentwitheithertheleftslitortherightslitclosed.

First,let’sdotheexperimentwitheithertheleftslitortherightslitclosed.Let’stakeitthatthesourceisfiringgrainsofsandathighenoughspeedsthattheyhavestraighttrajectories.Whenwedothis,thegrainsofsandthatgetthroughtheslitsmostlyhittheregionofthescreendirectlybehindtheopenslit,withthenumberstaperingoffoneitherside.Thehighertheheightofthegraph,themorethenumberofgrainsofsandreachingthatlocationonthescreen.

Now,whatshouldweseeifbothslitsareopen?Asexpected,eachgrainofsandpassesthroughoneortheotheropeningandreachestheotherside.Thedistributionofthegrainsofsandonthefarscreenissimplythesumofwhatgoesthrougheachslit.It’sademonstrationoftheintuitiveandsensiblebehaviorofthenon-quantumworldofeverydayexperience,theclassicalworlddescribedsowellbyNewton’slawsofmotion.

Tobeconvincedthatthisisindeedwhathappenswithparticlesofsand,let’sorientthedevicesuchthatthesandisnowfallingdownontothebarrierwithtwoslits.Ourintuitionclearlytellsusthattwomoundsshouldformbeneaththetwoopenings.

Turningtheexperimentbacktoitsoriginalposition,let’sdispensewiththesandandconsiderasourcethat’semittinglight,andassumethatlight’smadeofNewtoniancorpuscles.Informedbyourexperimentwithsandparticles,we’dexpecttoseetwostripsoflightonthescreen,onebehindtherightslitandonebehindtheleftslit,eachstripoflightfadingofftothesides,leadingtoadistributionoflightthatissimplythesumofthelightyou’dgetpassingthrougheachslit.

Well,that’snotwhathappens.Light,itseems,doesnotbehaveasifit’smadeofparticles.

EvenbeforeNewton’stime,therewereobservationsthatchallengedhistheoryoftheparticlenatureoflight.Forexample,lightchangescoursewhengoingfromonemediumtoanother—say,fromairtoglassandbackintoair(thisphenomenon,calledrefraction,iswhatallowsustomakeopticallenses).Refractioncan’tbeeasilyexplainedifyouthinkoflightasparticlestravelingthroughairandglass,becauseitrequirespositinganexternalforcetochangethedirectionoflightwhenitgoesfromairtoglassandfromglasstoair.Butrefractioncanbeexplainediflightisthoughtofasawave(thespeedofthewavewouldbedifferentinairthaninglass,explainingthechangeindirectionaslightgoesfromonetypeofmaterialtoanother).ThisisexactlywhatDutchscientistChristiaanHuygensproposedinthe1600s.Huygensarguedthatlightisawave

ChristiaanHuygensproposedinthe1600s.Huygensarguedthatlightisawavemuchlikeasoundwave,andsincesoundwavesareessentiallyvibrationsofthemediuminwhichtheyaretraveling,Huygensarguedthatlighttooismadeofvibrationsofamediumcalledetherthatpervadesthespacearoundus.

Thiswasaserioustheoryputforthbyanenormouslygiftedscientist.Huygenswasaphysicist,astronomer,andmathematician.Hemadetelescopesbygrindinglenseshimself,anddiscoveredSaturn’smoonTitan(thefirstprobetolandonTitan,in2005,wasnamedHuygensinhishonor).HeindependentlydiscoveredtheOrionnebula.In1690,hepublishedhisTraitédelaLumière(TreatiseonLight),inwhichheexpoundedhiswavetheoryoflight.

NewtonandHuygenswerecontemporaries,butNewton’sstarshonebrighter.Afterall,hehadcomeupwiththelawsofmotionandtheuniversallawofgravitation,whichexplainedeverythingfromthearcofaballthrownacrossafieldtothemovementofplanetsaroundthesun.Besides,Newtonwasapolymathofconsiderablerenown(asamathematician,hegaveuscalculus,andevenventuredintochemistry,theology,andwritingbiblicalcommentaries,nottomentionallhisworkinphysics).Itwasnowonderthathiscorpusculartheoryoflight,despiteitsshortcomings,overshadowedHuygens’sideasoflightbeingwavelike.It’dtakeanotherpolymathtoshowupNewtonwhenitcametounderstandinglight.

—ThomasYounghasbeencalled“TheLastManWhoKnewEverything.”In1793,barelytwentyyearsofage,heexplainedhowoureyesfocusuponobjectsatdifferentdistances,basedpartlyonhisowndissectionofanox’seyes.Ayearlater,onthestrengthofthatwork,YoungwasmadeaFellowoftheRoyalSociety,andin1796hebecame“doctorofphysic,surgery,andmidwifery.”Whenhewasinhisforties,YounghelpedEgyptologistsdeciphertheRosettastone(whichhadinscriptionsinthreescripts:Greek,hieroglyphics,andsomethingunknown).Andinbetweenbecomingamedicaldoctor,gettingsteepedinEgyptology,andevenstudyingIndo-Europeanlanguages,Youngdeliveredoneofthemostintriguinglecturesinthehistoryofphysics.ThevenuewastheRoyalSocietyofLondon,andthedate,November24,1803.Youngstoodinfrontofthataugustaudience,thistimeasaphysicistdescribingasimpleandeleganthomespunexperiment,which,inhismind,hadunambiguouslyestablishedthetruenatureoflightandprovedNewtonwrong.

“TheexperimentsIamabouttorelate...mayberepeatedwithgreatease,wheneverthesunshines,”Youngtoldtheaudience.

Wheneverthesunshines.Youngwasn’toverstatingthesimplicityofhisexperiment.“Imadeasmallholeinawindow-shutter,andcovereditwithapieceofthickpaper,whichIperforatedwithafineneedle,”hesaid.Thepinholeletthrougharayoflight,asunbeam.“Ibroughtintothesunbeamaslipofcard,aboutone-thirtiethofaninchinbreadth,andobserveditsshadow,eitheronthewall,oronothercardsheldatdifferentdistances.”

Iflightismadeofparticles,Young’s“slipofcard”wouldhavecastasharpshadowonthewallinfront,becausethecardwouldhaveblockedsomeoftheparticles.Andifso,Newtonwouldhavebeenprovedright.

If,however,lightismadeofwaves,asHuygensclaimed,thenthecardwouldhavemerelyimpededthewaves,likearockimpedesflowingwater,andthewavewouldhavegonearoundthecard,takingtwopaths,oneoneithersideofthecard.Thetwopathsoflightwouldeventuallyrecombineatthewalloppositethewindowshuttertocreateacharacteristicpattern:arowofalternatingbrightanddarkstripes.Suchstripes,alsoknownasinterferencefringes,arecreatedwhentwowavesoverlap.Crucially,thecentralfringewouldbebright,exactlywhereyou’dexpectadarkshadowiflightweremadeofparticles.

Weknowaboutinterferencefromoureverydayexperienceofwavesofwater.Thinkofanoceanwavehittingtwoopeningsinacoastalbreakwall.Newwavesemergefromeachopening(aprocesscalleddiffraction)andtravelonward,wheretheyoverlapandinterferewitheachother.Inregionswherethecrestsofbothwavesarriveatthesametime,there’sconstructiveinterferenceandthewaterisatitshighest(analogoustobrightfringesoflight);andinregionswherethecrestfromonewavearrivesatthesametimeasthetroughoftheother,thewavescanceleachotheroutandthere’sdestructiveinterference(correspondingtodarkfringes).

Youngsawsuchopticalinterferencefringes.Specifically,sincehewasworkingwithsunlight,whichcontainslightofallcolors,hesawacentralregionthatwasflankedbyfringesofcolors.Thecentralregion,uponcloserinspection,wasseentobemadeoflightanddarkfringes.Thenumbersofthesefringesandtheirwidthsdependedonhowfarawaythepinholeinthewindowshutterwasfromthescreenorwall.Andthemiddleofthecentralregionwasalwayswhite(abrightfringe).Hehadshownthatlightiswavelike.

Theremusthavebeendisbeliefintheaudience,forYoungwasgoingagainstNewton’sideas.EvenbeforeYoung’slecture,articleswrittenanonymouslyintheEdinburghReviewhadbeenheavilycriticalofhiswork.Theauthor,whoturnedouttobeabarristernamedHenryBrougham(hebecameLordChancellorofEnglandin1830),wasscathing,callingYoung’swork“destituteofeveryspeciesofmerit”and“theunmanlyandunfruitfulpleasureofaboyishandprurientimagination.”

Itwasanythingbut.Soonenough,Young’sideasgotfurthersupportfromotherphysicists.Hisexperimentledtowhat’snowcalledthedouble-slitexperimentandwasinfactthefirstformulationofit—theverysameexperimentwhosevirtuesFeynmanextolledduringhislectureatCornell.Inthemorestandarddouble-slitexperiment,Young’ssunbeamisreplacedbyasourceoflight.Andinsteadofa“slipofcard”placedinthesunbeam’spathtocreatetwopathsforthelight,thedouble-slitexperimentcreatestwopathsoflightbylettingthelightfallonanopaquebarrierwithtwonarrowslitsoropeningsthroughwhichthelightcanpass.Andonthescreenonthefarside,youseeaninterferencepattern,essentiallyfringessimilartowhatYoungsawonthewalloppositethewindowshutter(ifthescreenisaphotographicplate,orapieceofglasscoatedwithphotosensitivematerial,thentheimagecanbethoughtofasafilmnegative:darkregionswillformwherethefilmisbeingexposedtolight).Youdon’tseejusttwostripstaperingaway,whichyou’dexpectiflightbehavedasifitcameinlumps.It’sbehavinglikeawave.

So,wellbeforequantumphysicswasevenagleaminanyone’seyes,YounghadseeminglysettledthedebatebetweenNewtonandHuygens(despiteskepticswhocontinuedtofavorNewton).YoungcamedowninfavorofHuygens’slight-is-a-waveidea.Andsothingsstooduntilthequantumrevolution.

—Therevolutionbeganwithbewilderingdiscoveriesintheearly1900s,includingAlbertEinstein’s1905assertionthatlightshouldbethoughtofasbeingmadeofparticles,becauseitwastheonlywaytoexplainaphenomenonknownasthephotoelectriceffect(whichhelpsusconvertsunlightintoelectricity,givingusthetechnologyofsolarpanels).Theseparticlesoflightcametobecalledphotons.Foranygivenfrequencyorcoloroflight,aphotonoflightisthesmallestunitofenergy,anditcannotbedividedanyfurther:thelightcannotcomewithanylessenergythancontainedinonephoton.Einstein’sargumentissomewhatinvolved,butfornow,ifweaccepttheideathattherearecertainsituationsinphysicswhereyouhavetotreatlightasmadeofparticles,thenthe

situationsinphysicswhereyouhavetotreatlightasmadeofparticles,thenthedouble-slitexperimentstartschallengingourintuitivesenseofreality.

Feynmanspokeofthedouble-slitexperimentasembodyingthe“centralmystery”ofquantummechanics.Toshowwhy,hereplacedthegunshootingbullets(or,inourcase,grainsofsand)withasourceofelectrons.Everyoneinthe1960sknewthatelectronscameinlumps.Theyareoneofthemanytypesofelementaryparticlesthatmakeupthesubatomicworld,includingphotons.We’llusephotonsinsteadofelectrons.Thefactthattheexperiment,itsresults,anditsimplicationsdon’tchangewhetherweareusingphotons,whichareparticlesoflightwithoutanymass,orelectrons,whichareparticlesofmatterwithsomemass,leadstoitsownsetofmystifyingquestions.AsFeynmansaid,botharescrewyinthesameway.

Here’swhathappensifyouusephotons.Unlikewhatwegotwithparticlesofsand,youdon’tgettwobandsoflightonthescreen.Instead,yougetfringes,similartotheinterferencepatternthatYoungobserved,suggestingthatphotonsarebehavinglikewaves.Togetasharplydefinedsetoffringes,it’sbesttouselightofonecolor.Sothesourcecanbe,say,streamingoutanintensebeamofphotonsofredlightthatpassthroughthedoubleslit.

Whenbothslitsareopen,yougettheinterferencepattern,suggestingthatlight(whichweknownowismadeofparticles)isgoingthroughbothslits.Butifyoucloseoneofthetwoslits(doesn’tmatterwhichone),theinterferencepatterndisappears,clearlysuggestingthatlightisgoingthroughonlyoneslitandthere’snothingforittointerferewith.

Theexperiment,however,reallystartsmessingwithourmindswhenweconsiderasourcethatemitsonephotonatatime.We’llcometothewaysinwhichphysicistsinventedsourcestodothat.Itwasn’tpossiblein1964,whenFeynmanwasgivinghislecture.Fornow,let’sassumewehavesuchasourceinhand.Ifso,eachphotongoesthroughtheapparatus,andwemakesurethere’sonlyonephotonpassingthroughthesetupatatime.Thephotonhitsthephotographicplateonthefarsideandcreatesaspot.Ifweletenoughspotsaccumulate,ourintuitionsaysthatthesephotonsshouldactlikegrainsofsandandlineupbehindeachslit.Thereshouldbenointerferencepattern.

We’dbewrong.Asithappens,eventhougheachphotonseemstobelandingatsomerandomposition,fringesemergewhenenoughphotonshavemadetheirmarkonthephotographicplate.Eachphotonmakesadarkspotontheplate;placeswherethephotonsmostlylandbecomedarkstripes,andfringesbuildupovertime.

Thisissomewhatcurious.It’sclearthatwecangetaninterferencepatternwhenonewaveinterfereswithanother.Butourphotonsaregoingthroughtheapparatusonebyone.There’snointerferencebetweenonephotonandthenext,orthefirstphotonandthetenth,andsoon.Eachphotonisonitsown.Nonetheless,eachphotonismostlylandingonthephotographicplateatthosepositionsthateventuallybecomeregionsofconstructiveinterferenceandmostlyavoidingthoseplacesthatbecomeregionsofdestructiveinterference.Weget

interferencefringes.It’sasifeachphotonisexhibitingwavelikebehavior,asifit’sinterferingwithitself.

Thisishappeningeventhoughwecreateeachphotonasaparticle,anddetectitonaphotographicplateasaparticle:theresultsseemtosuggestthatbetweenthecreationanddetection,eachparticleactslikeawave,andsomehowgoesthroughbothslitssimultaneously.Howelsedoyouexplaintheinterferencepattern?

Ifthat’snotmysteriousenough,considerwhathappensifwetrytofindoutwhichslitaphotongoesthrough(ourintuition,afterall,saysthatitsurelywentthroughjustoneslit,notboth).Sayyouhaveamechanismfordetectingthepassageofaphotonthroughoneortheotherslitwithoutdestroyingthephoton.Ifyoudothat,theinterferencepatterngoesaway(meaningthephotonstopsbehavinglikeawaveandstartsactinglikeaparticle)—andyougetapatternthat’ssimplythesumofthe“lumps”goingthrougheachslit.Stoptryingtosneakapeekatthephoton’spathanditgoesbacktobehavinglikeawave—theinterferencepatternreemerges.

There’syetanotherwaytoappreciatethismystery.Whenyouarenotlookingatthephotons’paths,individualphotonsalmostnevergotocertainplacesonthephotographicplate—theplacesthateventuallybecomeregionsofdestructiveinterference.Butifyoustartmonitoringtheirpaths,theywillgototheverylocationsthattheyotherwiseshun.What’sgoingon?

Thecuriousbehaviorcontinues.Ifyouweretofiregrainsofsandatthedoubleslit,andifyoukneweverythingabouttheinitialconditionsofeachgrainofsand(itsinitialvelocity,theangleatwhichitleavesthesandgun,etc.),youcanpredictusingNewton’slawsexactlywherethegrainofsandwillenduponthescreenoppositethedoubleslit,takingintoaccountanydeflectionsduetotheinteractionwiththeslits.Thisishowphysicsissupposedtowork.Butyoucan’tdothatwithphotons(orelectrons,oranythingquantummechanicalforthatmatter).

Evenifyouhavealltheinformationaboutasinglephotonasitleavesthesourceandgoestowardthedoubleslit,youcanonlycalculatetheprobabilityofthephotonlandingonacertainpartofthephotographicplate.Forexample,thephotoncouldlandatanyoneofthemanyregionsofconstructiveinterference—butthere’snowaytotellexactlywhereanyparticularphotonwillgo.Nature,atitsdeepest,seemsinherentlynondeterministic.Orisitmerelyhidingitssecrets,andwehaven’tdugdeepenoughyet?

Thequestionspileup.Betweentheproductionofthephotonanditseventualdetection,bothproofsofitsparticlenature,thephotonostensiblybehaveslikea

detection,bothproofsofitsparticlenature,thephotonostensiblybehaveslikeawaveifwechoosenottolookatwhichpathittakes,andasaparticleotherwise.Doesthephoton“know”wearelookingatitswavenatureorparticlenature?Ifso,how?Andcanwefoolthephoton,say,bynotrevealingourhanduntilithascrossedthedoubleslitasawave,andonlythenchoosingtoseewhichslititwentthrough,thusexaminingitsparticle-likebehavior?

Maybethereisasimpleranswer:thatthephotonisalwaysaparticleandalwaysgoesthroughoneortheotherslit.Andsomethingelse,somethingthatourstandardtheoriesdon’taccountfor,goesthroughbothslitstoproducethewavelikebehavior.Inthatcase,whatisthatsomething?

Ifitcrossedyourmindthathumanconsciousnessissomehowinvolvedincausingthephotontobehaveonewayortheother,youwouldn’tbealoneinthinkingso.Asoftenhappenswhenconfrontedwithtwomysteries(inthiscasetheoddbehaviorofthequantumworldandtheinexplicablenatureofconsciousness),it’salmosthumannaturetowanttoconflatethetwo.

It’dbetwentyyearsonfromFeynman’slectureatCornellthatthedouble-slitexperimentwouldbedoneusingsinglephotons.Itwasanexampleofhow,fromYoung’seffortsintheearly1800stomodernversions,physicistscontinuetousethedouble-slitexperimenttounderstandthenatureofreality.Theexperimenthasn’tchangedinitsconceptualsimplicityformorethantwohundredyears,butithasbecometechnologicallymoreandmoresophisticated,asexperimenterskeepthinkingofcleverwaystotricknatureintorevealingitsprofoundestsecrets.

Q

2

WHATDOESITMEAN“TOBE”?

TheRoadtoReality,fromCopenhagentoBrussels

Theideaofanobjectiverealworldwhosesmallestpartsexistobjectivelyinthesamesenseasstonesortreesexist,independentlyofwhetherornotweobservethem...isimpossible.

—WernerHeisenberg

uantumphysicshasbeenwithusforaboutacentury.Butforalmosttwocenturiesbeforethebirthofquantumphysics,ourideasofhownature

worksweregovernedbylawsdiscoveredbyIsaacNewton.HeelucidatedhislawsinthePrincipia,anastonishingtreatisepublishedin1687.CrucialtotheNewtonianconceptionofnaturewasthatitwasmadeofparticlesofmatterwhosedynamicsweregovernedbytheforcesactinguponthem,includingthemutuallyattractiveforceofgravity.Lighttoowasregardedashavingparticlenature,thoughthiswasdebated.Huygens,Young,andotherschallengedthis,arguingforlight’swavenature.So,whiletheNewtonianuniversewasoneofparticlesofmatter,lightstoodapart,itsplaceinthecategoriesofthingsthatmakeuptheworld—theontologyoftheworld—somewhatunclear.

AFrenchprinceandphysicist,LouisdeBroglie,centurieslater,wouldrecountthistimeinthehistoryofphysicsrathereloquently:“WhenLightreachesusfromthesunorthestarsitcomestotheeyeafterajourneyacrossvastspacesvoidofMatter.ItfollowsfromthisthatLightcancrossemptyspacewithoutdifficulty...itisnotboundupwithanymotionofMatter.Henceadescriptionofthephysicalworldwouldremainincompleteunlesswewereto

addtoMatteranotherrealityindependentofit.ThisentityisLight.NowwhatisLight?Whatisitsstructure?”

AsdeBrogliewrote,suchquestionswereloominglargeinthe1860s,whenScottishscientistJamesClerkMaxwelldevelopedthemathematicalfoundationforphysiciststostartthinkingoflightasawave.

Maxwell’sworkfirstinvolvedunifyingelectricityandmagnetism,whichuntilthenhadbeenviewedasseparateforces,intooneforce.BuildingonearlierworkbytheEnglishphysicistandchemistMichaelFaraday,Maxwellcameupwithatheorycombiningelectricityandmagnetism,andpredictedthattheymoveasoneelectromagneticwave.HepresentedtheseideasonDecember8,1864,totheRoyalSocietyofLondon.Theontologyofnaturehadchanged.Inadditiontoparticles,itnowincludedelectromagneticfields—oscillationsofenergy—thatmovedatthespeedoflight.Particleswerelocalized,butfieldswerediffuseandcouldspreadandexertaninfluencefar,farfromwheretheyoriginated.

Maxwellarguedthatlighttooisanelectromagneticwave.Buthisideasmetwithsomeresistance.Whilephysicistscouldimagineelectromagneticwavesmovingthroughamedium,suchasawire,theyhadtroubleenvisaginglightasanelectromagneticwavemovingthroughthevacuumofspace,asitwouldhaveto.

Butevenbeforequestionsaboutthenatureoflightcouldbeanswered,Maxwell’shypothesisaboutelectromagnetismhadtobeproved.In1879,thePrussianAcademyofSciences(inBerlin)putoutacallforwhatcametobecalledtheBerlinPrizeproblem.TheprizewasforexperimentallyverifyingMaxwell’sideas.EntrieswereduebyMarch1,1882,withthewinnertobeawarded100ducats(aducatwaseitheragoldorasilvercoinusedinEuropeduringtheMiddleAges,andevenintothenineteenthandearlytwentiethcenturies).OneofthescientiststhoughtmostlikelytowintheprizewastheprodigiouslytalentedGermanphysicistHeinrichHertz.Thatyear,Hertzconsideredtheproblembutgaveuponit,forhecouldseenoclearexperimentalwayforward.“Butinspiteofhavingabandonedthesolutionatthattime,Istillfeltambitioustodiscoveritbysomeothermethod,”helaterwrote.

Noonewontheprizein1882.Hertz,however,injustafewyearssolvedthepuzzle.Hedesignedan

experimentthatprovedMaxwellcorrect.Theexperimentinvolvedbuildingatransmitterofelectromagneticwaves,andareceiver—andshowingthattheseinvisiblewavesdidindeedexistandcouldpropagatethroughair.Hertzhadinadvertentlydiscoveredradiowaves.

Whenaskedabouttheusefulnessofsuchwaves,Hertzreportedlysaid,“It

Whenaskedabouttheusefulnessofsuchwaves,Hertzreportedlysaid,“Itisofnousewhatsoever.ThisisjustanexperimentthatprovesMaestroMaxwellwasright.Wejusthavethesemysteriouselectromagneticwavesthatwecannotseewiththenakedeye.Buttheyarethere.”

Hertz’sexperimentsvalidatedMaxwell’stheoryofelectromagnetism.Eventually,itwouldbecomeclearthatlighttooisanelectromagneticwave.Itconsistsofanelectricfieldandamagneticfield,whicheachvibrateinmutuallyperpendicularplanes.Andlightitselftravelsinadirectionthatisperpendiculartoboththeconstituentelectricandmagneticfields.Thefrequencyofvibration,orthefrequencyoftheelectromagneticwave(ν),turnsouttobeequaltothevelocityoflight(c)dividedbyitswavelength(λ).

Butwhiledoingthisexperiment,Hertzstumbleduponanothercuriousphenomenonthatwould,withinadecade,challengethelight-is-a-waveargument.Thephenomenonisnowcalledthephotoelectriceffect.Whenlightfallsoncertainmetals,itcanejectelectrons.Mostimportant,foragivenmetal,theelectronsareejectedonlywhenthelightisaboveathresholdfrequency

theelectronsareejectedonlywhenthelightisaboveathresholdfrequencyuniquetothatmetal.Belowthatfrequency,regardlessofhowmuchlightfallsonthemetal,noelectronsareejected.Abovethethresholdfrequency,twothingshappen.Oneisthatthenumberofelectronsejectedincreasesastheintensityoftheincidentlightincreases.Theotheristhatincreasingthefrequencyofthelightincreasestheenergyoftheejectedelectrons.

Hertz,however,hadseenonlyglimmersofthisphenomenon.Hisreceiver,whichwasinterceptinginvisibleradiowaves,workedbetterwhenitwasilluminatedbylight,comparedtowhenitwasindarknessinsideanenclosure.Theradiowaveshadnothingtodowiththelight,yetsomethingaboutthelightwasinfluencingthereceiver.InaletterhewrotetohisfatherinJuly1887,Hertzwascharacteristicallymodestabouthisfinding:“Tobesure,itisadiscovery,becauseitdealswithacompletelynewandverypuzzlingphenomenon.Iamofcourselesscapableofjudgingwhetheritisabeautifuldiscovery,butofcourseitdoespleasemetohearotherscallitthat;itseemstobethatonlythefuturecantellwhetheritisimportantorunimportant.”

It’snotsurprisingthatwhatHertzhadobservedcouldnotbeexplainedatthetime.Physicistswereyettodiscoverelectrons,letaloneunderstandthephotoelectriceffectinallitsintricacies.Evenaslateastheearly1890s,ourconceptionofrealitywasthatatomswerethesmallestconstituentsofthematerialworld,butthestructureoftheatomwasstillunknown.ThediscoveryoftheelectronandotherimportantmilestoneslayonthepathfromHertztoEinsteintoquantummechanics.

Hertz,sadly,didn’tlivetoseeanyofthem.HediedonJanuary1,1894.AnobituaryinthejournalNaturerecountedhislastdays:“Achronic,andpainful,diseaseofthenosespread...andgraduallyledtobloodpoisoning.Hewasconscioustothelast,andmusthavebeenawarethatrecoverywashopeless;butheborehissufferingswiththegreatestpatienceandfortitude.”Hertzwasonlythirty-seven.Hismentor,HermannvonHelmholtz(whowouldhimselfdielaterthatyear)wroteintheprefacetoHertz’smonographThePrinciplesofMechanics:“HeinrichHertzseemedtobepredestinedtoopenuptomankindmanyofthesecretsthatnaturehadhithertoconcealedfromus;butallthesehopeswerefrustratedbythemalignantdiseasewhich...robbedusofthispreciouslifeandoftheachievementswhichitpromised.”

—ThesecretsofnaturethatHertzwouldsurelyhavehelpeddiscovercamethickandfast.Thefirstonewasthediscoveryoftheelectron,thankstosomethingcalledacathoderaytube.Thetube—essentiallyasealedglasscylinderwith

calledacathoderaytube.Thetube—essentiallyasealedglasscylinderwithelectrodesoneitherend,andfromwhichmuchoftheairhadbeenremoved—wasascientificcuriosityinthemid-nineteenthcentury.Whenahighvoltagewasappliedacrosstheelectrodes,thetubewouldlightup,andscientistsreveledinshowingtheseofftolayaudiences.Soon,physicistsdiscoveredthatpumpingoutmoreair,butnotallofit,revealedsomethingdramatic:raysseemedtoemergefromthenegativeelectrode(thecathode)andstreakacrosstothepositiveelectrode(theanode).

ThreeyearsafterHertz’sdeath,theEnglishphysicistJ.J.Thomson,usingaseriesofelegantexperiments,showedunequivocallythattheserayswereconstituentsofmatterthatweresmallerthanatoms,andtheirtrajectoriescouldbebentbyanelectricfieldinwaysthatprovedtherayshadnegativecharge.Thomsonhaddiscoveredtheelectron.He,however,calledthemcorpuscles.Thomsonspeculatedthesewereliterallybitsofatoms.Noteveryoneagreedwithhispronouncements.“Atfirsttherewereveryfewwhobelievedintheexistenceofthesebodiessmallerthanatoms,”hewouldlatersay.“IwaseventoldlongafterwardsbyadistinguishedphysicistwhohadbeenpresentatmylectureattheRoyalInstitutionthathethoughtIhadbeen‘pullingtheirlegs.’”

Suchdoubtsaside,Thomsonchangedourconceptionoftheatomforever.Meanwhile,afterHertzhadmadehisinitialdiscoveryofthephotoelectric

effect,hisassistant,PhilippLenard,tookupthecause.Hewasafantasticexperimentalist.Hisexperimentsclearlyshowedthatultravioletlightfallingonmetalsproducedthesamekindofparticlesasseeninthecathoderaytubes:electrons.Crucially,thevelocityoftheseelectrons(andhencetheirenergy)didnotdependontheintensityoftheincidentlight.Lenard,however,wasadodgytheoristandmadeahashoftryingtoexplainwhy.

EnterEinstein.In1905,Einsteinwroteapaperonthephotoelectriceffect.Inthispaper,hereferredtoworkbytheGermanphysicistMaxPlanck,whofiveyearsearlierhaddrawnfirstbloodinthetusslebetweenclassicalNewtonianphysicsandthesoon-to-be-formulatedquantummechanics.Planckwastryingtoexplainthebehaviorofcertaintypesofobjectscalledblackbodies,whichareidealizedobjectsinthermalequilibriumthatabsorballtheradiationandradiateitbackout.Iftheelectromagneticenergybeingemittedisinfinitelydivisibleintosmallerandsmalleramounts,asitisinclassicalphysics,thusmakingforaseamlesscontinuum,thenthepredictionsmadebytheorywereatoddswithexperimentaldata.Somethingwasnotquiterightwithclassicalnotionsofenergy.

Tosolvethepuzzle,Planckarguedthatthespectrumoftheblackbody

Tosolvethepuzzle,Planckarguedthatthespectrumoftheblackbodyelectromagneticradiationcouldbeexplainedonlyifonethoughtofenergyascominginquanta,whicharethesmallestunitsofenergy.Eachunitisaquantum,andthisquantumisafloor:foragivenfrequencyofelectromagneticradiation,youcannotdividetheenergyintopacketsanysmaller(thewayyoucannotdivideadollarintoanythingsmallerthanacent).Usingthisassumption,Planckbeautifullyexplainedtheobservations.Theideaofthequantumwasborn.

WhileEinsteindidnotfullyembracePlanck’sideasinhis1905papertoexplainthephotoelectriceffect,hewouldeventuallydoso.Einsteinarguedthatsincelightiselectromagneticradiation,ittoocomesinquanta:thehigherthefrequencyofthelight,thehighertheenergyofeachquantum.Thisrelationislinear—doublingthefrequencydoublestheenergyofthequantum.Einstein’sclaimaboutlightcominginquantawascrucialtounderstandingthephotoelectriceffect,inwhichlightfallingonametalcansometimesdislodgeanelectronfromanatomofthemetal.Foranygivenmetal,saidEinstein,anelectroncanbefreedfromthemetal’ssurfaceonlyiftheincidentquantumoflighthasacertainminimumamountofenergy:anythingless,andtheelectronsstayput.Thisexplainswhyelectronsneverleavethemetalsurfaceiftheincidentlightisbelowathresholdfrequency:thequantumofenergyistoolow.Anditdoesnotmatteriftwoquantaputtogetherhavethenecessaryamountofenergy.Theinteractionbetweenlightandanatomofmetalhappensonequantumatatime.So,justpumpingmoreandmorequantabelowthethresholdfrequencyhasnoeffect.

Withthistheory,Einsteinalsopredictedthattheejectedelectronswillgetmoreenergetic(orhavegreatervelocities)asthefrequencyoftheincidentlightincreases.Thereismoreenergyineachquantumoflight,andthisimpartsastrongerkicktotheelectron,causingittoflyoutofthemetalatagreaterspeed—apredictionthatwouldsoongetexperimentallyverified.

Einstein’sprofoundclaimherewasthatlightismadeofsmall,indivisibleparticles,wheretheenergyofeachparticleorquantumdependsonthefrequencyorcolorofthelight.Theoddthing,ofcourse,isthattermslikefrequencyandwavelengthrefertothewavenatureoflight,andyettheseweregettingtiedtotheideaoflightasparticles.Adisturbingdualitywasbeginningtoraiseitshead.Thingsweregettingconfusing.

BothLenardandEinsteingotNobelPrizesfortheirwork,Lenardin1905forhis“workoncathoderays,”andEinsteinin1921,forexplainingthe

photoelectriceffectusingPlanck’squantumhypothesis.Lenard,however,becamedeeplyresentfuloftheaccoladesgiventoEinsteinfortheorizingaboutwhatLenardregardedashisresult.Lenardwasananti-Semite.In1924,hebecameamemberofHitler’sNationalSocialistparty.InfrontofhisofficeatthePhysicsInstituteinHeidelberg,thereappearedasignthatread:“EntranceisforbiddentoJewsandmembersoftheso-calledGermanPhysicalSociety.”LenardviciouslyattackedEinsteinandhistheoriesofrelativity,withundisguisedracismandanti-Semitism.“EinsteinwastheembodimentofallthatLenarddetested.WhereLenardwasamilitaristicnationalist,Einsteinwasapacifisticinternationalist...Lenarddecidedthatrelativitywasa‘Jewishfraud’andthatanythingimportantinthetheoryhadbeendiscoveredalreadyby‘Aryans,’”PhilipBallwroteinScientificAmerican.

InthemidstofterriblesocialunrestandunhingedideologiesacrossEurope,thequantumrevolutionwassetinmotion.

—Asthingsstoodin1905,electronswereconstituentsofatoms(butitwasstillunclearwhetherthatwasthefullstoryaboutthemakeupofatoms).Plus,therewereelectromagneticfields,whichweredescribedbyMaxwell’sequations.Thesecameinquanta.Itwasclearthatlighttooisanelectromagneticwave,whichcameinquantaandthesequantacouldbethoughtofasparticles.Microscopicrealitydidnotmakeawholelotofsense.

J.J.Thomson,meanwhile,hadaquestionhewantedanswered.Whatwouldhappenwhenafewquantaoflightwentthroughasingleslit(ratherthantwoslits)?In1909,ayoungscientistnamedGeoffreyIngramTaylorstartedworkingwithThomsonathislaboratoryinCambridge.TaylordecidedtodesignanexperimenttotryandanswerThomson’squestion.Theanswerresonateswithinquantummechanicseventoday,andisparticularlyrelevantforthestoryofthedouble-slitexperiment.

Pictureasourceoflightthatshinesonanopaquesheetwithasingleslit.Ontheothersideoftheopaquesheetisascreen.Again,ournaiveexpectationisthatwe’llseeasinglestripoflightonthescreen.Instead,whatappeararefringes(albeitadifferentpatternthanseenwiththedoubleslit.Inthecaseofasingleslit,thefringescanbeexplainedbythinkingofeachpointintheopeningorapertureoftheslitasasourceofanewwave.Thesewavestheninterferewitheachother,leadingtowhat’scalledadiffractionpattern).It’sanotherproofthatlightbehaveslikeawave.Whenthere’slotsoflight,theresultsareeasytoexplain:lightisanelectromagneticwave,andsoweshouldseefringes.

explain:lightisanelectromagneticwave,andsoweshouldseefringes.Butgiventhatlightalsocomesinquanta,orparticles,Thomsonwantedto

understandthesingle-slitphenomenonwhentheintensityoflightfallingonthesingleslitisturnedwaydown,sothatonlyafewquantaoflightgothroughtheslitatanyonetime.Now,ifthescreenonthefarsideisaphotographicplatethatrecordseachquantumoflight,thenovertime,wouldoneseeinterferencefringes?Thomsonarguedthatthereshouldbeblurryfringes,becauseinordertogetsharpfringes,numerousquantashouldarrivesimultaneouslyatthescreenandinterfere.Reducingthequantareachingthescreenatthesametimetoatrickleshouldreducetheamountofinterferenceandhencethesharpnessofthefringes,Thomsonhypothesized.

Taylorwasinhistwentiesandstartingoutonhiscareerasanexperimentalphysicist.Hechosethisexperimentasthesubjectofhisfirstscientificpaper,butoddly,herecalledyearslater,“Ichosethatprojectforreasonswhich,Ifear,hadnothingtodowithitsscientificmerits.”Consequently,heperformedtheexperimentinthechildren’splayroomofhisparents’home.Tocreateasingleslit,hestuckmetalfoilontoapieceofglassand,usingarazorblade,etchedaslitinthemetalfoil.Forasourceoflightheusedagasflame.Betweentheflameandtheslit,heplacedmanylayersofdarkenedglass.Taylorcalculatedthatthelightfallingonthesingleslitwassofaintthatitwasequivalenttoacandleburningamileaway.Ontheothersideoftheslit,Taylorplacedaneedle,whoseshadowhecapturedonaphotographicplate.Thelight—ostensiblyjustafewquantaatatime—passedthroughtheslitandlandedonthephotographicplate.Whatwouldtheplaterecordafterweeksofexposuretothefaintlight?

Taylor’smind,meanwhile,waselsewhere.Hewasbecominganaccomplishedsailor.Hesetuphisexperimentsothathecouldgetenoughofanexposureonthephotographicplateaftersixweeks.“Ihad,Ithinkratherskillfully,arrangedthatthisstagewouldbereachedaboutthetimewhenIhopedtostartamonth’scruiseinalittlesailingyachtIhadrecentlypurchased,”hesaid.Duringthelongeststretchoftheexperiment,inwhichthephotographicplatewasexposedforthreemonths,Taylorreportedlywentawaysailing.

Afterthatthree-month-longexposure,Taylorsawinterferencefringes—assharpasifthephotographicplatehadbeenexposedtomoreintenselightforaveryshorttime.Thomsonwasprovedwrong.Taylorneverfolloweduponthisnegativeresult.Ifhehad,hemighthaveplayedanimportantroleinthedevelopmentofquantummechanics—forhisresultswerehintingattheoddbehaviorofphotons.Insteadofpursuingthisanyfurther,Taylorchangeddirectionsandwentontomakeseminalcontributionstootherfieldsofphysics,

directionsandwentontomakeseminalcontributionstootherfieldsofphysics,particularlyfluidmechanics.

—Thomson,however,wasn’tdonebeingamentor.Intheautumnof1911,ayoungDanishscientistnamedNielsBohrcametoworkwithThomson.Soonthereafter,BohrmovedtoManchestertostudywithNewZealand–bornBritishphysicistErnestRutherford,whowasprobingthestructureoftheatom.Rutherford’sworkhadestablishedthattheatom,besideshavingelectrons,alsohasapositivelychargednucleus.Calculationsshowedthatmuchofthemassoftheatomisinthenucleus.Whatemergedwasanewpictureofanatom:negativelychargedelectronsorbitingapositivelychargednucleus,thewayplanetsorbitthesun.

Almostimmediately,physicistsrealizedthatthismodelhadseriousshortcomings.Newton’slawsmandatedthatorbitingelectronshadtobeaccelerating,iftheyweretoremainintheirorbitswithoutfallingintothenucleus.AndMaxwell’sequationsshowedthatacceleratingelectronsshouldradiateelectromagneticenergy,thusloseenergyandeventuallyspiralintothenucleus,makingallatomsunstable.Ofcourse,that’snotwhathappensinnature.Themodelwaswrong.

AninterimsolutioncamecourtesyoftheyoungBohr.In1913,Bohrproposedthattheenergylevelsofelectronsorbitinganucleusdidnotchangeinacontinuousmanner,andalsothattherewasalimittothelowestenergylevelofanelectroninanatom.Bohrwasarguingthattheorbitsoftheelectronsandhencetheirenergylevelswerequantized.Foranygivennucleus,there’sanorbitwiththelowestpossibleenergy.Thisorbitwouldbestable,saidBohr.Ifanelectronwereinthislowest-energyorbit,itcouldnotfallintothenucleus,becausetodoso,it’dhavetooccupyevensmallerorbitswithlowerandlowerenergies.ButBohr’smodelprohibitedorbitswithenergiessmallerthanthesmallestquantumoforbitalenergy.Therewasnowherelowerfortheelectrontofall.Andapartfromthisstable,lowest-energyorbit,anatomhasotherorbits,whicharealsoquantized:anelectroncannotgofromoneorbittoanotherinacontinuousfashion.Ithastojump.

TogetasenseforhowweirditmusthavebeenforphysicistsintheearlytwentiethcenturytounderstandBohr’sadhocclaims,imagineyouaredrivingyourcarandwanttogofrom10to60milesperhour.Inananalogytothewayelectronsbehaveinorbits,thecarjumpsfrom10mphto60mphinchunksof10mph,withoutgoingthroughanyoftheintermediatespeeds.Moreover,nomatterhowhardyoubrake,youcannotslowthecardowntobelow10mph,forthat’s

howhardyoubrake,youcannotslowthecardowntobelow10mph,forthat’sthesmallestquantumofspeedforyourcar.

Bohralsoarguedthatifanelectronmovesfromahigh-energytoalow-energyorbit,itdoessobyemittingradiationthatcarriesawaythedifferenceinenergy;andtojumptoanorbitwithhigherenergy,anelectronhastoabsorbradiationwiththerequisiteenergy.

Topreventelectronsfromlosingenergywhileorbitingthenucleus,whichtheywouldhavetoaccordingtoMaxwell’stheory,Bohrarguedthattheelectronsexistedinspecial“stationary”states,inwhichtheydidnotradiateenergy.Theupshotofthissomewhatarbitrarypostulatewasthatanotherpropertyofelectrons,theirangularmomentum,wasalsoquantized:itcouldhavecertainvaluesandnotothers.

Itwasallterriblyconfounding.Nonetheless,therewereconnectionsemergingbetweentheworkofPlanck,Einstein,andBohr.Planckhadshownthattheenergyofelectromagneticradiationwasquantized,wherethesmallestquantumofenergy(E)wasequaltoanumbercalledPlanck’sconstant(h)multipliedbythefrequencyoftheradiation(v),producinghisfamousequationE=hv.Einsteinshowedthatlightcameinquanta,andtheenergyofeachquantumorphotonwasalsogivenbythesameequation,E=hv(wherevreferstothefrequencyofthelight).

WhileBohrhadshownthattheenergylevelsinatomswerequantized,it’dtakehimadecadeorsomoretoacceptthatwhenelectronsjumpedenergylevels,theradiationgoinginorcomingoutoftheatomwasintheformofquantaoflight(Bohrinitiallyinsistedthattheradiationwasclassical,wavelike).

ButwhenBohrdidacceptEinstein’sideaoflightquanta,hesawthattheabsorbedoremittedenergyofthephotonswasgivenby,again,E=hv.(Bohrwasn’ttheonlybignameresistingEinstein’sideas.Thenotionoflightbeingquantizedwashardtostomachforphysicists,giventhesuccessofMaxwell’sequationsofelectromagnetismindescribingthewavenatureoflight.Forinstance,Planck,whenhewasenthusiasticallyrecommendingEinsteinforaseatinthePrussianAcademyofSciencesin1913,slippedinthiscaveataboutEinstein:“Thathemightsometimeshaveovershotthetargetinhisspeculations,asforexampleinhislightquantumhypothesis,shouldnotbecountedagainsthimtoomuch.”)

Still,theevidencefornature’spredilectionforsometimesactinglikewavesandsometimeslikeparticlescontinuedtogrow.In1924,LouisdeBroglie,inhisPhDthesis,extendedthisrelationshiptoparticlesofmattertoo,andprovidedamoreintuitivewaytoenvisionwhytheorbitsofelectronsarequantized.Matter,

moreintuitivewaytoenvisionwhytheorbitsofelectronsarequantized.Matter,saiddeBroglie,alsoexhibitedthesamewave-particledualitythatEinsteinhadshownforlight.Soanelectroncouldbethoughtofasbothawaveandaparticle.Andatomstoo.Nature,itseems,didnotdiscriminate:everythinghadwavelikebehaviorandparticle-likebehavior.

TheideahelpedmakesomesenseofBohr’smodeloftheatom.Now,insteadofthinkingofanelectronasaparticleorbitingthenucleus,deBroglie’sideasletphysiciststhinkoftheelectronasawavethatcirclesthenucleus,theargumentbeingthattheonlyallowedorbitsarethosethatlettheelectroncompleteonefullwavelength,ortwo,three,four,andsoon.Fractionalwavelengthsarenotallowed.

Itwasclearbythenthatphysicswasundergoingaprofoundtransformation.Physicistswerebeginningtoexplainpreviouslyinexplicablephenomena,usingtheseideasofquantizedelectromagneticradiation,quantizedelectronorbits,andthelike,atleastforthesimplestatom,thatofhydrogen,whichhasoneelectronorbitingthenucleus.Morecomplexatomswerenotsoeasilytamed,evenwiththesenewconcepts.Still,whatwasbeingexploredwastheverystructureofreality—howatomsbehaveandhowtheelectronsinsideatomsinteractwiththeoutsideworldviaradiation,orlight.Butthesuccessesnotwithstanding,thepuzzleswerealsomounting.

Whilenature’sdiscontinuityanddiscretenessatthesmallestscaleswasbecomingevermoreobvious,therewasthepuzzlingissueofitsconcomitantwavenature,emblematicofclassicalcontinuity.And,probablymostdisturbingly,therewasthequestionofindeterminism.ItwasclearthattherearenaturalphenomenathatdonotfollowtheclockworkdeterminacyofNewton’sclassicalworld.Take,forexample,radioactivity:nothingaboutthecurrentstateofaradioactiveatomletsyoupredictexactlywhenit’llemitarayofradioactivity.Theprocessisunpredictable,stochastic.Thiswentagainstthetenetsofthescienceofthetime,accordingtowhichfullknowledgeofasystemshouldletyoupredictwithprecisionsomefutureeventinvolvingthatsystem.Themicroscopicworldseemedtobeoperatingwithadifferentsetofrules.

Butitwasn’tobviouswhattheseruleswere.Whatphysicslackedwasanoverarchingframeworkthatbroughtthesedisparateelementstogether.Allthatchangedduringthemidtolate1920s,wheninafewfeverishyears,brilliantmindsforgednotonebuttwoframeworksfortheorizingabouttheworldatsmallscales.Thiseffortwouldculminateinoneofthemostcelebratedscientificconferencesinhistory—theFifthSolvayInternationalConferenceonElectronsandPhotonsheldinOctober1927inBrussels,Belgium.Themoment,captured

inanow-iconicphotographtakenbyBelgianphotographerBenjaminCouprie,showsalltwenty-nineattendees,somestandinginthebackrowstillintheirtwentiesandyettobecomefamous,somealreadysoandseatedinthefrontrow,includingEinstein,Planck,andMarieCurie,andalmosteveryoneelseinbetweenwhomatteredtotheemergingfieldofquantumphysics.Iftheyweren’talreadyNobelPrizewinners,manywouldgoontowin—turningseventeenofthetwenty-nineintoNobellaureates.

—“Thelakes”ofCopenhagenarefivereservoirsthatstretchcrescent-shapednotfarfromthecitycenter.Walkalongthenorthernendoftheselakes,gopastastretchofshorelinedwithhorsechestnuttrees,downacoupleofblocksalonganalleynamedIrmingersgade,andyoucomeup,quitesuddenly,onanunassumingbuilding:theNielsBohrInstitute.Whenitwasfoundedin1921byBohr,itwascalledtheInstituteofTheoreticalPhysics.BohrhadmovedfromManchestertotheUniversityofCopenhagen,wherehebecameaprofessorin1916atjustthirty-oneyearsofage.Hethenlobbiedhardandgotthefundstobuildaninstitutefortheoreticalphysics.Andforafewdecades,theinstitutebecameacauldronwheregreatmindsstewedovertheevolvingfieldofquantumphysics,underBohr’sdeeplyengagedgaze.

OneofthesegreatmindswasayoungGermanphysicistnamedWernerHeisenberg.BohrfirstmetHeisenbergatGöttingen,Germany,inJune1922.Bohrwastheretotalkaboutthecurrentunderstandingofthemodeloftheatomandthevariousoutstandingproblemsyettobesolved.Duringthetalk,Heisenberg,stillatwenty-year-oldstudentinhisfourthsemester,questionedBohrwithsuchclaritythatasuitablyimpressedBohrtookHeisenbergforawalkafterwardtodiscussatomictheory.HealsoinvitedHeisenbergtoCopenhagen,anditwastherein1924thatHeisenbergrealized,afterdiscussionswithBohrandothers,that“perhapsitwouldbepossibleoneday,simplybycleverguessing,toachievethepassagetoacompletemathematicalschemeofquantummechanics.”Thewordmechanicsreferstophysicsthatcanexplainhowsomethingchangeswithtimeundertheinfluenceofforces.

Heisenberg’sinsightwasprophetic.Inthespringof1925,sufferingfromseverehayfever,hedecampedtoHelgolandintheNorthSea,arockyislanddevoidofpollen.There,betweenlongwalksandcontemplatingGoethe’sWest-östlicherDivan,hedevelopedtheearlymathematicsthatwouldbecomethebasisformodernquantumtheory.Heisenbergrecalledlater,“Itwasalmost

threeo’clockinthemorningbeforethefinalresultofmycomputationslaybeforeme...Icouldnolongerdoubtthemathematicalconsistencyandcoherenceofthekindofquantummechanicstowhichmycalculationspointed.Atfirst,Iwasdeeplyalarmed.Ihadthefeelingthat,throughthesurfaceofatomicphenomena,Iwaslookingatastrangelybeautifulinterior,andfeltalmostgiddyatthethoughtthatInowhadtoprobethiswealthofmathematicalstructuresnaturehadsogenerouslyspreadoutbeforeme.Iwasfartooexcitedtosleep,andso,asanewdaydawned,Imadeforthesoutherntipoftheisland,whereIhadbeenlongingtoclimbarockjuttingoutintothesea.Inowdidsowithouttoomuchtrouble,andwaitedforthesuntorise.”

Heisenbergwroteuphiswork,showeditfirsttoWolfgangPauli(anotherofthebrilliantyoungminds)andthentoMaxBorn(anequallybrilliantbutamorefatherlyfigureinhisforties,withwhomHeisenbergwasdoinghispostdoctoralwork).BornimmediatelyrealizedtheimportofHeisenberg’spaper.“Ithoughtthewholedayandcouldhardlysleepatnight...InthemorningIsuddenlysawthelight,”hewouldsay.

WhatBornrealizedwasthatthesymbolsHeisenbergwasmanipulatinginhisequationsweremathematicalobjectscalledmatrices,andtherewasanentirefieldofmathematicsdevotedtothem,calledmatrixalgebra.Forexample,Heisenberghadfoundthattherewassomethingstrangeabouthissymbols:whenentityAwasmultipliedbyentityB,itwasnotthesameasBmultipliedbyA;theorderofmultiplicationmattered.Realnumbersdon’tbehavethisway.Butmatricesdo.Amatrixisanarrayofelements.Thearraycanbeasinglerow,asinglecolumn,oracombinationofrowsandcolumns.Heisenberghadbrilliantlyintuitedawayofrepresentingthequantumworldandaskingquestionsaboutitusingsuchsymbols,whilebeingunawareofmatrixalgebra.

Inafewfreneticmonths,Born,alongwithHeisenbergandPascualJordan,developedwhat’snowknownasthematrixmechanicsformulationofquantumphysics.InEngland,PaulDiracsawthelighttoowhenheencounteredHeisenberg’swork,andhetoo,inaseriesofpapers,independentlyaddedtremendousinsightandmathematicstotheformulationanddevelopedthe“Diracnotation”that’sstillinusetoday.

Mostimportant,itwasclearthattheformalismworked.Forexample,thepositionof,say,anelectron,isrepresentedbyamatrix.Thepositioninthiscaseiscalledanobservable.Thematrixthendictatesallthepossiblepositionsinwhichtheelectroncanbefound,orobserved.Theformalismimplicitlyallowsfortheelectrontobeonlyincertainpositionsandnotinothers.Andthereisnosenseofacontinuouschangefromonepositiontoanother.Discreteness,or

senseofacontinuouschangefromonepositiontoanother.Discreteness,orjumpsfromonestatetoanother,isbakedintomatrixmechanics.

Induecourse,physicistswereabletousetheformalismtocalculate,forexample,theenergylevelsofelectronsinatoms,explaintheradiationemittedbyglowingbitsofsodiumorothermetals,understandhowsuchspectralemissionscouldbesplitintoslightlydifferentfrequenciesundertheinfluenceofamagneticfield,andbetterunderstandthehydrogenatomitself.

Butitwasn’tobviouswhytheformalismworked.Whatdidthesematricesmapto,physicallyspeaking?Theelementsofthesematricescouldbecomplexnumbers(acomplexnumberhasarealpartandanimaginarypart;theimaginarypartisarealnumbermultipliedbythesquarerootof-1andisimaginarybecause√-1doesn’texistyetturnsouttobeincrediblyusefulincertainkindsofmathematics).Howcouldthephysicalworldberepresentedbythingsthatcouldonlybeimagined?Wereweattheverylimitofhumanunderstanding?Wasaclearunderstandingpossible?

Matrixmechanicsdoesnotallowphysiciststothinkofelectronsashavingclear,fixedorbits,eveniftheyarequantized.Onecandescribeanelectron’squantumstateusingasetofnumbers,carryoutawholelotofmatrixmanipulationstopredictthingslikespectralemissions,butwhatyouloseistheabilitytovisualizetheelectron’sorbitinthewaythatonecanvisualize,say,Earth’sorbitaroundthesun.

Plus,theformalismdealsinprobabilities.IfaparticleisinstateAandyoumeasuretoseeifit’sstateA,then,ofcourse,themathsaysyou’llfindtheparticleinstateAwith100percentcertainty.Thesamegoesfor,say,stateB.Butmatrixmechanicssaysthataparticlecanbeinsomeintermediatestate,wherethestateisxpartsAandypartsB.Now,ifyoutryandpredictwhetheryou’llfindtheparticleinstateAorstateB,100percentcertaintyaboutrealityisnolongerpossible.

Matrixmechanicsletsyoucalculateonlytheprobabilitiesofoutcomesofmeasurements.So,foranelectronwhosestateisxpartsAandypartsB,sayyouwanttoseeiftheparticleisinstateA.ThemathsaysthattheprobabilityoffindingtheparticleinstateAisx2.Similarly,ifyouchecktoseeiftheparticleisinstateB,theprobabilityyou’llfinditinstateBisy2.(Theterminologygetstweakedalittlebitwhenyouallowxandytobecomplexnumbers,butfornow,it’seasytoseewhatrulesxandyhavetofollow:theprobabilitieshavetoadduptoone,sox2+y2shouldequal1.)

Thefactthatwearenowdealinginprobabilitiesisnot,presumably,becausewedonotknowenoughabouttheparticle.Matrixmechanicssaysyouhaveall

theinformationyoucanpossiblyhave.Yet,ifyoutakeamillionidenticallypreparedparticlesinthesamestate(thesamecombinationofstatesAandB)andperformamillionidenticalmeasurements,then,onaverage,x2numberoftimesyouwillfindtheparticleinstateA,y2ofthetimeyou’llfinditinstateB.Butyoucanneverpredicttheansweryou’llgetforanysingleparticle.Youcanonlytalkstatistically.Nature,itseems,isnotdeterministicinthequantumrealm.

Recallthatsomethingsimilarhappenswiththedoubleslit.Wecannotpredictwhereexactlyasinglephotonwilllandonthescreen—wecanonlyassignprobabilitiesforwhereitmightgo.

Soonafterthesephenomenaldevelopments,anAustrianphysicistnamedErwinSchrödinger,whosestatusasafoundingmemberofquantumphysicswasyettobeestablished,expressedhisdismayat,evendistastefor,Heisenberg’smatrixmechanics.Hesaidhewas“discouraged,ifnotrepelled”bywhathesawas“verydifficultmethodsoftranscendentalalgebra,defyinganyvisualization.”

Thebattlelineswerebeingdrawn.Waveversusparticle,continuousversusdiscrete,oldversusnew.Schrödinger’sdistasteledhimtodevelopaformidableold-schoolalternativetotheupstart,matrixmechanics—onethatseemedtorestorefaithintheclassicalwayofthinkingaboutnature.

—WhenLouisdeBrogliewrotehis1924thesisonthewave-particledualityofmatter,SchrödingerwasalreadyaprofessoroftheoreticalphysicsattheUniversityofZurich,andcomparedtotheyounggeniuseselsewhereinEurope,hewaspracticallyanoldman,approachingforty.ButforyearsSchrödingerhadbeendelvingintothesamequestionsthathadbeentormentingeveryone.SchrödingerlearnedofdeBroglie’sworkwhenhereadareferencetoitinapaperbyEinstein.ThinkingofmatteraswavesmadesensetoSchrödinger’sclassicallyintuitivemind,andheacknowledgedasmuchinalettertoEinstein,datedNovember3,1925:“AfewdaysagoIreadwiththegreatestinteresttheingeniousthesisofLouisdeBroglie,whichIfinallygotholdof.”Schrödingerwantedtodescribethemotionofelectronsaroundthenucleusbythinkingofthemaswaves.InsteadofHeisenberg’smatrixmechanics,Schrödingerwantedwavemechanicsforelectrons.

IfHeisenberg’ssolosojournatHelgolandhasbecomequantumphysicslore,sohasSchrödinger’sownburstofcreativityinisolation—well,almostinisolation.ANewYorkTimesbookreviewcapturesthisperiodinSchrödinger’slife:“AfewdaysbeforeChristmas,1925,Schrödinger...tookoffforatwo-

and-a-half-weekvacationatavillaintheSwissAlpinetownofArosa.LeavinghiswifeinZurich,hetookalongdeBroglie’sthesis,anoldViennesegirlfriend(whoseidentityremainsamystery)andtwopearls.Placingapearlineacheartoscreenoutanydistractingnoise,andthewomaninbedforinspiration,Schrödingersettoworkonwavemechanics.WhenheandthemysteryladyemergedfromtherigorsoftheirholidayonJan9,1926,thegreatdiscoverywasfirmlyinhand.”

Withinweeks,SchrödingerpublishedhisfirstpaperintheAnnalenderPhysik.Threemorepapersfollowedinquicksuccession,andSchrödingerturnedtheworldofHeisenbergandBornupsidedown.Suddenly,physicistshadanintuitivewayofunderstandingwhatwasostensiblyhappeningtoanelectroninahydrogenatom.Schrödingerhadcomeupwithhisnoweponymouswaveequation,whichtreatedtheelectronasawave,andshowedhowthiswavewouldchangeovertime.Itwaswavemechanics.Itwasalmostclassicalphysics,excepttherewerecuriousandconsequentialdifferences.

Inclassicalphysics,solvingawaveequationfor,say,asoundwavecangiveyouthepressureofthesoundwaveatacertainpointinspaceandtime.SolvingSchrödinger’swaveequationgivesyouwhat’scalledawavefunction.Thiswavefunction,denotedbytheGreekletterψ(psi,pronounced“sigh”),issomethingquitestrange.Itrepresentsthequantumstateoftheparticle,butthequantumstateisnotasinglenumberorquantitythatreveals,forexample,thattheelectronisatthispositionatthistimeandatthatpositionatanothertime.Rather,ψisitselfanundulatingwavethathas,atanygivenmomentintime,differentvaluesatdifferentpositions.Evenmoreweirdly,thesevaluesarenotrealnumbers;rather,theycanbecomplexnumberswithimaginaryparts.Sothewavefunctionatanyinstantintimeisnotlocalizedinaregionofspace;rather,itisspreadout,it’severywhere,andithasimaginarycomponents.TheSchrödingerequation,then,allowsyoutocalculatehowthestateofthequantumsystem,ψ,changeswithtime.

Schrödingerthoughtthewavefunctionprovidedawaytovisualizewhatwasactuallyhappeningtoelectronsorotherinhabitantsofthequantumworld.ButthisviewwaschallengedwithinmonthsofSchrödinger’spapersbeingpublished,whenMaxBornrealizedthatSchrödingerwaswrongaboutthemeaningofthewavefunction.

Inacoupleofseminalpaperspublishedinthesummerof1926,Bornshowedthatwhenelectronscollideandscatter,theresultingwavefunctionthatrepresentsthestateoftheelectronsonlyencodestheprobabilityoffindingthe

electronsinonestateoranother.IttookBornacoupleoftriestogetitright,butheshowedthatifψisthewavefunctionofanelectron,andifitcanbewritten,forexample,intermsoftwodifferentpossiblestatesoftheelectron,ψAandψB,suchthatψ=x.ψA+y.ψB,thenallyoucandoiscalculatetheprobabilitythatyou’llfindtheelectroninstateAorstateBwhenyoudoameasurement.(TheprobabilityoffindingtheelectroninstateAisgivenbythesquareoftheamplitudeofx,alsocalledthesquareofthemodulusofx,denotedas|x|2,andtheprobabilityoffindingitinstateBisgivenby|y|2.Ifxis,say,arealnumber,themodulus|x|issimplyitsabsolutevalue:ifit’spositivetostartwith,itremainspositive;ifit’snegative,thenwemultiplyitby-1;squaringitgivesusapositivenumber.Ofcourse,xandycanbecomplexnumbers,andcalculatingthemodulusofacomplexnumberisabitmorecomplicated,butinessence,whenyoutakethemodulus-squaredofacomplexnumber,youagaingetanumberthatispositiveandreal,withoutanyimaginaryparts.)

Bornhad,itseemedatfirstblush,castdoubtoncausality,theunderpinningofdeterministicclassicalphysics,whichsaysanygiveneffecthasacause.Givenaninitialstateofanelectron,standardquantummechanicscannotdefinitivelysaywhattheelectron’snextstatewillbe.Onecanonlycalculatetheprobabilityofanelectrontransitioningtosomenewstate,usingwhatcametobecalledtheBornrule.Anelementofrandomness,orstochasticity,becameanintegralpartofthelawsofnature.AsBornputit,“Themotionofparticlesfollowsprobabilitylawsbuttheprobabilityitselfpropagatesaccordingtothelawofcausality.”

Andthereitwas—oneinterpretationofthewavefunction.It’saprobabilitywave.Schrödinger’sequationletsyoucalculatehowthiswavechangeswithtimedeterministically,butasitevolvesandtakesondifferentshapes,what’schangingaretheprobabilitiesoffindingthequantumsysteminvariousstates.

Ifthissoundsliketheprobabilitiesofmatrixmechanics,youarenotmistaken.Schrödingerhimself,inanotherstrokeofinsight,showedthatwavemechanicsandmatrixmechanicsaremathematicallyequivalent(inhindsight,itwasamathematiciancalledJohnvonNeumannwhowouldreallyprovetheequivalenceafewyearslater).Ratherthanseethisasavalidationofmatrixmechanics,Schrödingerclaimedvictoryforwavemechanics,consideringhisapproachtobecorrectandarguingthatanythingthatwascalculatedusingmatrixmechanicscouldbecalculatedusingwavemechanics.Theadvantageofwavemechanics,inSchrödinger’sopinion,wastheideathatnatureevenatthesmallestscaleswascontinuous,notdiscrete.Therewerenoquantumjumps.

Heisenberg,meanwhile,wasn’tenamoredofSchrödinger’sideas.HewrotetoPauli,complainingthathefoundthem“abominable,”callingit“Mist”(whichisGermanforrubbish,manure,dung,ordroppings).PaulihimselfalludedtoZüricherLokalaberglauben(localZurichsuperstitions,anallusiontothecitywhereSchrödingerworked).Schrödinger,unsurprisingly,wasn’tpleasedbyPauli’sassertions.Pauli,inturn,triedtoappeaseSchrödingerbysaying,“Don’ttakeitasapersonalunfriendlinesstoyoubutlookontheexpressionasmyobjectiveconvictionthatquantumphenomenanaturallydisplayaspectsthatcannotbeexpressedbytheconceptsofcontinuumphysics.Butdon’tthinkthatthisconvictionmakeslifeeasyforme.Ihavealreadytormentedmyselfbecauseofitandwillhavetodosoevenmore.”

ThetormentthesetitansfeltoverthenatureofrealitycontinuedwhenSchrödingervisitedCopenhagenandmetBohrfortheveryfirsttime.

—DecadesafterSchrödinger’svisittoCopenhageninSeptember1926,Heisenbergwouldrecounttheintensityoftheirmeetings:“ThediscussionbetweenBohrandSchrödingerbeganattherailwaystationinCopenhagenandwascarriedoneverydayfromearlymorningtilllateatnight.SchrödingerlivedatBohr’shousesothatevenexternalcircumstancesallowedscarcelyanyinterruptionsofthetalks.AndalthoughBohrasarulewasespeciallykindandconsiderateinrelationswithpeople,heappearedtomenowlikearelentlessfanatic,whowasnotpreparedtoconcedeasinglepointtohisinterlocutorortoallowhimtheslightestlackofprecision.Itwillscarcelybepossibletoreproducehowpassionatelythediscussionwascarriedonfrombothsides.”

SopassionatelythatevenafterSchrödingerfellsickandwasbedriddenwithafeverandcold,thehostdidnotrelent.Bohrturnedupathisbedsidetodebatequantumphysics,evenasBohr’swife,Margrethe,tookcareofSchrödinger.

ThedebatebetweenBohrandSchrödingerwasaforetasteoffuturedebatesthatBohrwouldhavewithEinsteinabouthowtothinkaboutthesmallestconstituentsofreality(atthetime,electronsandphotons).Itwasaclashoftwowaysofthinking.AsWalterMoorewritesinhisbookSchrödinger:LifeandThought,“Schrödingerwasa‘visualizer’andBohrwasa‘nonvisualizer,’onethoughtintermsofimagesandtheotherintermsofabstractions.”

SchrödingerleftCopenhagen,butHeisenbergwasstilltheretoserveasBohr’sdebatingpartner.Heisenbergwasnowlivinginanatticapartmentattheinstitute,anditwastherethatBohrwouldturnuplateatnighttocontinuetheirarguments.Andthoughthetwoweremostlyonthesamesideofthedebate,they

arguments.Andthoughthetwoweremostlyonthesamesideofthedebate,theystillhaddifferences:Bohrwantedtomakewave-particledualism—theideathatnaturehastwofacesandonlyshowsoneortheotheratanyonetime—akeycomponentofanyinterpretationofreality;Heisenbergputhis“trustinthenewlydevelopedmathematicalformalism,”toseewhatmeaningsitsuggested,ratherthanpresupposinganyparticularviewofreality.

Theyfrettedaboutmakingsenseofexperiments,includingthedoubleslit.AsHeisenbergwouldsay,“Likeachemistwhotriestoconcentratehispoisonmoreandmorefromsomekindofsolution,wetriedtoconcentratethepoisonoftheparadox,andthefinalconcentrationwassuchexperimentsliketheelectronwiththetwoholes...Theywerejustakindofquintessenceofwhatwasthetrouble.”

BytheendofFebruary1927,theirdiscussionsatanimpasse,BohrwentofftoskiinNorway.Heisenbergtootooktimeforhimself.Hewroteofoneextraordinarynightwhensomethingclarified:“IwentforawalkintheFælledpark,whichliesbehindtheinstitute,tobreathethefreshairandcalmdownbeforegoingtobed.Onthiswalkunderthestars,theobviousideaoccurredtomethatoneshouldpostulatethatnatureallowedonly[those]experimentalsituationstooccurwhichcouldbedescribedwithintheframeworkoftheformalismofquantummechanics.Thiswouldapparentlyimply,asonecouldseefromthemathematicalformalism,thatonecouldnotsimultaneouslyknowthepositionandvelocityofaparticle.”

Heisenberghaddiscoveredtheuncertaintyprinciple.Theformalismofquantummechanicshaspairsofobservablequantities,suchasthepositionandmomentumofaparticle,wheretryingtodetermineonewithincreasingprecisionmeansthatyouincreasetheimprecisionofthevaluesyouobtainfortheother.So,ifyouknowexactlywhereaparticleis,youhaveverylittleideaofitsmomentum,andviceversa.Thisrelationextendstootherpairsofquantities,suchasenergyandtime.

(WhenIvisitedtheNielsBohrInstitute,IwentuptotheattictoseeHeisenberg’slivingquarters.Hisapartmentwasbeingusedbybuilderstostoreair-conditioningequipment.Acartooncaptioned“AthomewiththeHeisenbergs”wasstuckonthebathroomdooroutsidetheapartment,withMrs.Heisenbergsaying,“Ican’tfindmycarkeys,”andMr.Heisenbergreplying,“Youprobablyknowtoomuchabouttheirmomentum.”)

Bohr,meanwhile,becameevermoreconvincedthatwhathecalledtheprincipleofcomplementaritywasattheheartofquantummechanics:thatwavenatureandparticlenaturearecomplementaryaspectsofreality,andthatit’sour

natureandparticlenaturearecomplementaryaspectsofreality,andthatit’sourchoiceofexperimentthatrevealsoneortheother,butneverbothatthesametime.Hethoughtthattheuncertaintyprinciplewasoneoutcomeofthebroaderprincipleofcomplementarity.

Elsewhere,Einsteinwasgrowingdeeplyconcernedaboutsuchinterpretationsofthequantumformalism,andbuildinghimselfuptowardaprofoundintellectualdebatewithBohr,adebatethatwouldshapethefutureofquantummechanics.Einsteinhadapredilectionforconjuringupthoughtexperimentstomakeapoint—andoneoftheseinvolvedthedouble-slitexperiment.HebroughtitupattheFifthSolvayConference.

—HistoryhasoftenportrayedEinsteinandBohrasgiantsinbattle,slashingateachotherwiththeirrespectiveintellectualmight.Butoftenwhatgetslostintheretellingistheenormousrespectandaffectionthatthetwohadforeachother.EinsteinandBohrmetforthefirsttimeinBerlininApril1920.ImpressedbyBohr,EinsteinwrotetohiminMay,fromAmerica,beginninghisletterwiththesewords:“DearMr.Bohr:Themagnificentgiftfromtheneutralworld,wheremilkandhoneystillflow,givesmeawelcomeoccasiontowritetoyou.Notofteninlifehasaperson,byhismerepresence,givenmesuchjoyasyou.Iunderstandwhy[Paul]Ehrenfestissofondofyou.”BohrwrotebackinJune,saying,“Tomeetyou,andtalkwithyou,wasoneofthegreatestexperiencesIhaveeverhad.”

Thismutualadmirationunderpinnedtheirrelationship,despitetheirstrongdisagreementsoverquantummechanics.

TheirfriendlysalvoswerefiredinearnestattheFifthSolvayConferenceinBrussels.Thiswasagrandbattleofideas,thelikesofwhichoccurinfrequentlyenoughinsciencetobeetchedinculturalmemoryasmomentsthatchangedourunderstandingofourplaceintheuniverse.Sometimestheindividualsdebatinghavebeenseparatedbytheinterveningcenturies,aswasthecasewithCopernicus,whointhesixteenthcenturyarguedagainsttheGreekastronomerandmathematicianPtolemy’sancienttheorythatEarthisatthecenterofthesolarsystem.Copernicusputthesunatthecenter.Sometimes,it’soneperson’sfightagainstanemergingconsensus,aswasthecaseinthe1950swithEnglishastronomerFredHoyle’sincreasinglyisolatedstandforasteady-stateuniverse,whentheoryandevidencewerebothpointingtoanexpandingcosmosthatbeganinabigbang.Andattimes,theantagonistsdebatedthenatureofscientificprogressitself,ashappenedbetweenphilosophersKarlPopperandThomas

Kuhn.Popper,impressedbyEinstein’sworkonrelativity,arguedthatscienceprogressesinincrements;scientistscomeupwithhypothesestoexplainphenomena,hypothesesthattheythentrytheirbesttofalsify.Kuhnwouldbeinfluencedbythegoings-onattheFifthSolvayConferenceandarguedthatsciencemostlymovesalonginthemannersuggestedbyPopper,withscientistsworkingwithinanacceptedparadigm,untilanomalies—thingsthatcannotbeexplainedwithinthecurrentwayofthinking—pileup,bringingsciencetothebrinkofcrisis,causinganupheavalandadramaticparadigmshift.

ThedebatesattheFifthSolvayConferencesetthestageforjustsuchashift.Bohr,Heisenberg,andPauliweremakingacaseforwhateventuallycametobecalledtheCopenhageninterpretationofquantummechanics.Accordingtothem,theonlyaspectsofrealitythatyoucouldknowaboutwerethosethatwereallowedbytheformalism.Forexample,youcouldaskabouttheprobabilityoffindinganelectronsomewhere,butyoucouldn’taskwhatpathittooktogetthere,becausethereisnothinginthemaththatcapturesanelectron’spath.It’dtakeanotherfiveyearsforthemathtobecomesophisticated,thankstoJohnvonNeumann,butthenewviewofrealitywastakinghold.Takenatitsmostextreme,theCopenhageninterpretationisanti-realist:itdeniesanynotionofrealitythatexistsindependentofobservation.Moreimportant,theproponentswereclaimingthatthemathematicalformalismiscomplete,andthatthereisnothingmoretosayaboutreality.

Thiswas,ofcourse,amassiveshiftinourwayofthinking.Untilthen,ourtheoriessaidsomethingconcreteaboutanaturalworldthatexistsregardlessofobservation.Einstein,arealist,arguedthatthemathematicalformalismofquantummechanicswasincompleteanddidnotpaintafullpictureofreality.

TheSolvayConferencewasbeingheldattheInstituteofPhysiologyintheheartofBrussels.“However,withalltheparticipantsstayingattheHotelMetropole,itwasinitselegantartdecodiningroomthatthekeenestargumentstookplace...Theacknowledgedmasterofthethoughtexperiment,Einsteinwouldarriveatbreakfastarmedwithanewproposalthatchallengedtheuncertaintyprincipleandwithitthemuch-laudedconsistencyoftheCopenhageninterpretation.Theanalysiswouldbeginovercoffeeandcroissants.ItcontinuedasEinsteinandBohrheadedtotheInstituteofPhysiology,usuallywithHeisenberg,PauliandEhrenfesttrailingalongside.Astheywalkedandtalked,assumptionswereprobedandclarifiedbeforethestartofthemorningsession...DuringdinnerbackattheMetropole,BohrwouldexplaintoEinsteinwhyhislatestthoughtexperimenthadfailedtobreakthelimitsimposedbythe

uncertaintyprinciple.EachtimeEinsteincouldfindnofaultwiththeCopenhagenresponse,buttheyknew,saidHeisenberg,‘inhishearthewasnotconvinced.’”

Atthecenterofoneoftheirmindgameswasthedouble-slitexperiment.Einsteinimaginedanelectronthatfirstpassesthroughasingleslit,andthenencountersadoubleslit,andeventuallyendsupsomewhereatthecenterofthefarscreen.InEinstein’soriginalthoughtexperiment,thesingleslitcouldmoveupanddown,whilethedoubleslitwasfixed,butphysicistssincethenhavereimaginedthesetupwiththesingleslitheldinplace,andthedoubleslitastheonethatcanmoveupordownasit’sbuffetedbytheparticlesgoingthroughtheslits.WhileconceptuallyidenticaltoEinstein’simaginedapparatus,thenewerversioniseasiertograsp.

Consideranelectronthatgoesthroughthesingleslit,thenthroughthedoubleslit,andthenlandsatthecenterofthefarscreen.UsingEinstein’sanalysis,iftheelectronwentthroughthelowerslit,thenit’dhavehadtochangedirectionsandmoveupwardtogettothecenterofthescreen.Thiswouldimpartadownwardkicktotheslititself.Andiftheelectronwentthroughtheupperslit,it’dimpartanupwardkicktotheslit.So,bymeasuringthemomentumtransfer,

oneshouldbeabletotellwhichslittheelectronwentthrough,saidEinstein.Hispointwasthateventhoughoneobservestheinterferencepattern,whichdemonstratestheelectron’swavenature,measuringtheslit’smomentumtellsusabouttheelectron’spathonitswaytothefarscreen,thusrevealingitsparticlenature.Thetwoaspectsofrealityarenotmutuallyexclusive,heclaimed,andthefactthatquantummechanicsdidnothavetheformalismtocapturethatfactmeantthatitwassomehowincomplete.

Bohrwasstumpedforabit,butsooncamebackwitharetort(inadditiontocomingupwiththedrawingsthatinvolvedboltingtheapparatustoabaseandotherpracticalthings).Hepointedoutthatiftheslitcanmovewhentheelectronpassesthrough,andifwecanmeasurethemomentumtransferwithprecision,thenwe’llhaveimpreciseknowledgeaboutitslocation(thankstoHeisenberg’suncertaintyprinciple).Now,ifyoudothecalculationsofwheretheelectronslandonthefarscreen,takingintoaccounttheuncertaintyabouttheslit’sposition,itturnsouttheinterferencepatterngetssmudged.Tryingtofindoutwhichslittheelectronwentthrough,byallowingtheslitstomove,destroysitswavenature.Wecanseetheelectronseitherasparticlesoraswaves,notbothatthesametime.

Thiswas,ofcourse,athoughtexperiment.Therewasnowaytoimplementsuchanexquisitelyengineeredexperimentinthe1920s,togetinformationabouttheparticle’spathwithoutdestroyingtheparticle.It’dtakealmostacenturyofefforttocarryoutavariationofthisthoughtexperiment.ItturnsoutthatBohrwasrightinthisregard:it’simpossibletodupenature.(However,physicistsandhistoriansreadingBohr’swritingswouldpointoutlaterthatBohr’sargumentsweresomewhatinscrutable,sooneshouldbecircumspectaboutunqualifiedclaimsthat“Bohrwasright”—nonetheless,asexperimentalevidencegoes,itwentagainstEinsteinonthiscount.)TheexperimentalsoshowedthatcomplementarityisaseeminglymorepowerfulprinciplethanmaybeevenBohrimagined.

Suchvictoriesinhand,BohrandcompanystartedgivingconcreteshapetotheCopenhageninterpretationanditsanti-realistviewofnature.Inthedouble-slitexperiment,theCopenhageninterpretationmakesnoclaimastothepathoftheparticlethroughtheapparatusand,somewouldsay,evendeniesthatsuchapathexists.

EinsteinandBohrcontinuedsparringoverwhatquantummechanicswastellingusaboutreality.Wasquantumphysicsthewholestory?Wasthemathematicalformalismthatdescribedthestatisticalbehaviorofthesubatomic

worldacompletedescriptionofreality?Orwasthereahiddenrealitythatthemathwasn’tcapturing?Bohrmetaphoricallyshruggedhismassiveshouldersandinsistedtherewasnohiddenreality.

Bohr,forhispart,keptreturningtothedouble-slitexperimenttomakephilosophicalpoints,sometimesinfuriatinghisaudience.HendrikCasimir,ayoungphysicistwhohadcometoworkwithBohr,wroteaboutaconversationwithBohrandDanishphilosophersHaraldHøffdingandJørgenJørgensen.TheywereallattheCarlsbergmansion(theerstwhileresidenceofthefounderoftheCarlsbergbrewery).Bohrwastalkingaboutthedouble-slitexperimentdonewithelectrons.Someonequipped,“Buttheelectronmustbesomewhereonitsroadfromsourcetoobservationscreen.”Bohrpointedoutthattheanswerdependsonwhatonemeansbythephrasetobe.AnexasperatedJørgensenretorted:“Onecan,damnit,notreducethewholeofphilosophytoascreenwithtwoholes.”

ButBohrwasn’tbeingflippant.Whatdoesitmeantobesomethinginthequantumrealm?Opinionsdifferdramatically.Andtheexperimentwithtwoholes,despiteJørgensen’sprotestations,remainsatthecenterofthesehistoric,differingscientificandphilosophicalarguments.

T

3

BETWEENREALITYANDPERCEPTION

DoingtheDoubleSlit,OnePhotonataTime

Theelectron,asitleavestheatom,crystallisesoutofSchrödinger’smistlikeagenieemergingfromhisbottle.

—ArthurEddington

he2014NobelPrizewinnerforchemistry,StefanHell,duringhisNobelbanquetspeech,recalledthe1933NobelPrizewinnerErwinSchrödingeras

saying,“Itisfairtostatethatwearenotgoingtoexperimentwithsingleparticlesanymorethanwewillraisedinosaursinthezoo.”

Hell,speakingeighty-oneyearsafterSchrödinger’scomment,quipped,“Now,ladiesandgentlemen,whatdowelearnfromthis?First.ErwinSchrödingerwouldneverhavegoneontowriteJurassicPark...Second.AsaNobelLaureateyoushouldsay‘thisorthatisnevergoingtohappen,’becauseyouwillincreaseyourchancestremendouslyofbeingremembereddecadeslaterinaNobelbanquetspeech.”

ThereferencetodinosaursandSchrödinger’sskepticismofsingle-particleexperimentscameupwhenImetAlainAspect,aFrenchexperimentalphysicistattheInstitutd’OptiqueinPalaiseau,asuburbofParis.Aspect,infact,pioneeredsomeofthefirstexperimentsdonewithsinglephotons,includingthefirst-everdouble-slitexperimentdonebysendingsinglephotonsthroughtheapparatus.Itwasapivotalmomentinthemorethanhalf-a-century-longstoryofquantumphysics,onethatgavecredencetoallthetheorizingthathadcomebefore,whilelayingthefoundationforsimilar,moresophisticatedexperimentstocome.

Whenwemetmorethantwenty-fiveyearsafterhehadannouncedthe

Whenwemetmorethantwenty-fiveyearsafterhehadannouncedtheresultsofhispioneeringexperiments,Aspectspokeasanelderstatesmanofquantumphysics;thecombinationofhisFrench-accentedEnglishandluxurious,grayingmustacheremindedmeofthefictionaldetectiveHerculePoirotinAgathaChristiemysteries(withapologiestoAspect;Poirot,ofcourse,isBelgian).

Intheearly1970s,Aspectfinishedhismaster’sdegreeandwenttoCameroon,Africa,toteachschoolchildren,aspartofhismandatoryFrenchmilitaryservice.WhileinCameroon,hismindwasonphysics.Hecouldn’tshakethefeelingthattherewassomethinglackinginwhathehadlearned.Allthephysicshehadbeentaught—thingslikeoptics,electromagnetism,andthermodynamics—dealtwiththeclassical,continuous,anddeterministicworldofNewton,Maxwell,andEinstein.Heknewlittleaboutthephysicsofthemicroscopicquantumworldofparticlesandatoms.Whenheheardtalkofhowanatomjumpsfromoneenergyleveltoanotherbyemittingorabsorbingaphotonoflight,hecouldn’tunderstandhow.“IknewIwasmissingsomething,”hesaid.

So,Aspectboughtanewlypublishedbook,simplytitledQuantumMechanics(onethatwouldbecomeahighlyregardedtextbook,andoneoftheauthorsofwhich,ClaudeCohen-Tannoudji,wouldbecomeAspect’sPhDthesisadvisorandwouldalsowintheNobelPrizein1997).Aspectreadthebookfromcovertocover,orasheputit,“frompageoneto,Idon’tknow,page1,300.”Hewashooked.

WhenhereturnedtoFrancein1974,Aspectcameuponadecade-oldpaperbyJohnBell,aNorthernIrishphysicistworkingatCERN(EuropeanOrganizationforNuclearResearch),theparticlephysicslabnearGeneva,Switzerland.Bellwasn’tyetfamousforhis1964paper,whichcontainedatheoremthatisnowregardedashissignaturecontribution.WhenAspectreadthepaper,whichhedidinatwo-hoursitting,hesaidtohimself,“Thisisunbelievable...it’sfantastic.”HerealizedthatBell’spaperofferedawayofresolvinganargumentoverthenatureofrealitythathadsoconsumedEinsteinandBohr(othershadrealizedittoo,butforyoungAspectitwasarevelation).

Bell’s’64theoremmadeitpossibletoexperimentallyaddressthequestionposedbyEinstein:weretherelocalhiddenvariablestodescribepropertiesofquantumsystemsthatweren’tthereinthestandardformalismofquantummechanics,variablesthatinEinstein’sopinionwouldturnquantummechanicsintoacompletedescriptionofreality?Thewordlocalreferstoelementsof

realitythatcannotinfluenceeachotheranyfasterthanthespeedoflight:localvariablesarebitsofmathematicsinourtheoriesthatrepresentthisreality,andhiddenlocalvariablesrefertovariablesthatare,well,absentfromtheformalism.Bellwasparticularlyinterestedinlocality.WhilesomephysicistshadalreadydoneexperimentsbasedonBell’sideas,theresultsweren’tconclusive.InAspect’seyes,theseexperimentshadfailedtocomeclosetotheidealexperimentdemandedbyBell’stheorem.Hefelthecoulddoabetterjob.

ButAspecthadsomedoubts.Forone,hehadyettostartonhisPhD.Wasthistherightprojectforadoctoralthesis?AspectwenttoCERNtomeetBellforadvice,andBellreassuredtheyoungAspectthathewasontherighttrack.ButBellalsowarnedAspectthatthetopicwasconsideredbymanyas“crackpotphysics.”Almostnoonedoubtedthecompletenessofquantummechanics.Sowhybothertestingit?Bell,worriedfortheFrenchman’scareer,askedAspectifhehadapermanentjob.“Idid.Itwasasmallposition,butitwaspermanent,”AspectrecalledtellingBell.“Theycouldnotfireme,Iwassuretogetasalaryeachmonth.”

AspectreturnedtoFranceandembarkedonanexperimentthatisnowregardedasthefirsttoallbutruleoutaclassofso-calledhiddenrealitytheories.Toaccomplishhisfeat,Aspectdevelopedthetechnologytogeneratesingleparticlesoflight,orphotons,whichcouldbesentintohisapparatusoneatatime.TheuseofsinglephotonscaughtRichardFeynman’sattention.In1984,AspectwasinvitedtoCaltechtospeakabouthistestsofBell’stheorem.Feynmanwasinattendance.“EverybodyexpectedtoseeFeynmandestroythisyoungFrenchguypretendingtosettleaquestionthatdidn’texist,”saidAspect.

DuringtheQ&AsessionthatfollowedAspect’stalk,FeynmanamiablyaskedifAspectcouldusesinglephotonstoperformanolder,moreclassicexperimentinquantummechanics,onethatFeynmanhadhighlightedinhisowntalksandlecturesasonethatbestprobedthemysteriesattheheartofquantummechanics:thedouble-slitexperimentdonewithsingleparticles.Aspectrespectfullyrepliedthatastudentofhis,PhilippeGrangier,wasonthecasebackinParis.

FromthetimeYoungdidhissunbeamexperimentin1801andthroughthedevelopmentofquantummechanics,noonehadactuallydonethedouble-slitexperimentwithsinglephotons.UntilAspectcamealong,nooneevenknewhowtogeneratesinglephotonsandbesurethattherewasonlyonephotonintheapparatusatanygiventime.“Ordinarysourcesdonotemitwell-separatedsinglephotons.Inadischargelamp,inabulb,oreveninalaser,youhavealways

zillionsofatomssimultaneouslyemittingphotons,”saidAspect.“Asaresult,whatyougetisanensembleofphotons,andthisensembleofphotonshasallthepropertiesthatcanbedescribedbyclassicalelectromagneticwaves.”

Forexample,wenowknowthatGeoffreyIngramTaylor’sdetectionofinterferencefringes,whichwasdonewithlightsofaintthatitwaslikeplacingacandleamileaway,wasnottheresultofsinglephotonshittingthephotographicplate.Taylorusedsomethingcalledacoincidencedetector,whichrequiresatleastfourphotonstohitthedetectoratthesametimetocreateasignalbigenoughtoberecorded.

Toappreciatehowdifficultitistogetphotonsoneatatimefromasourceoflight,considerthis:youhavea100-wattlampandyouaremonitoringthenumberofphotonsreachingasquareopening,onecentimetertoaside,placedonemeterfromthelamp.Arough-and-readycalculation(byGiancarloGhirardiinSneakingaLookatGod’sCards)revealsthatabout24millionbillionphotonswillpassthroughthatone-square-centimeteropeningeverysecond.That’s24quadrillionphotons.Gettingsinglephotonswouldrequireatechniquesubstantiallydifferentfromjustturningdownalampordimmingthelightfromacandle.Aspectdevelopedsuchatechnique.Andwhenhecarriedoutthedouble-slitexperimentwithsinglephotons,classicalphysicshadnosay;onlyquantummechanicscouldexplaintheresults.

—WhilesinglephotonsproveddifficulttotameuntilAspectcamealong,physicistsweren’tbidingtheirtime,waitingfortechnologytocatchup.Therewereotherparticlestoworkwith.RecallthatFeynmanhadfocusedonthedouble-slitexperimentdonewithsingleelectrons.Heemphasized,however,thatitwassimplyathoughtexperiment.In1961–1962,FeynmangaveaseriesoflecturestofreshmenandsophomoresatCaltech,whichwerepublishedayearlaterasathree-volumeset.Init,hesaidaboutsingleelectroninterference:“Thisexperimenthasneverbeendoneinjustthisway.Thetroubleisthattheapparatuswouldhavetobemadeonanimpossiblysmallscaletoshowtheeffectsweareinterestedin.”Feynmanhadnowayofknowingthattheimpossiblehadbeenaccomplishedin1961—inGermany,theresultsbeingpublishedinGerman.

The1961experimenthaditsrootsinworkdonebyGottfriedMöllenstedtattheUniversityofTübingen.Möllenstedtinventedauniquedevicetosplitabeamofelectronsintotwoandthengetthemtointerfere,analogoustoThomasYoungusingathincardtosplithissunbeam.Thedeviceiscalledanelectronbiprism.

usingathincardtosplithissunbeam.Thedeviceiscalledanelectronbiprism.Möllenstedtcameupontheideaaccidentally.Intheearly1950s,hewasusinganelectronmicroscope,withathintungstenwirestretchedacrosstheobjectivelensofthemicroscope.Möllenstedtnoticedthatwhenthetungstenwiredevelopedacharge,thiscausedtwoimagestobeformed,asifthemicroscopewasseeingdouble.Möllenstedtrealizedthatthechargedwirewascausingthemicroscope’selectronbeamtopart,creatingthetwoimages.Couldsuchachargedwirebeusedtoseeinterferencefringesbysplittinganelectronbeamandlettingitrecombine?

MöllenstedtandhisstudentHeinrichDükertookonthetask.Forathinwire,theyinitiallyusedgold-platedstrandsofspidersilk(apparently,Möllenstedt“keptacollectionofspidersaroundthelaboratoryforthispurpose”).Eventually,theduofiguredouthowtogold-platequartzwiresonlyabout3micronsindiameter(humanhair,forcomparison,isabout100micronsthick).Theychargedthewirebyapplyingavoltagetoit,andplacedthewireinthepathofabeamofelectrons.Theelectrons,deflectedbythewire’scharge,curvedaroundthewireandeventuallyrecombined.Thiswasconceptuallyidenticaltoadouble-slitexperiment:theelectronscouldtakeoneoftwopaths,astheywouldiftheyencounteredtwoslits.

However,despiteusing“powerfuloptics,”theteamdidnotseeanyfringesatfirst—theywerejusttoosmall,justasFeynmanhadfeared.Butwhentheyexposedaphotographicplatetotheelectronsfor30secondsandthenlookedatthephotograph,usingapowerfulopticalmicroscope,theysaw“fineinterferencefringes.”Thiswasin1954.Inapaperpublishedsoonafter,inNaturwissenschaften,theycomparedtheirfringestoopticalfringesseenearlierbytheFrenchphysicistAugustin-JeanFresnel.Thejournal’seditor,whilepraisingMöllenstedtandDüker,alsopointedoutthat“ThomasYounghadproduced[such]...interferencestenyearsbeforeFresnel.”

It’seasytounderstatetheimportanceofthiswork.Electrons—whichareparticlesofmatter—areproducinginterferencefringes,whichareaphenomenonassociatedwithwaves.ThiswasexactlywhatLouisdeBrogliehadpostulatedin1924:thatmatter,andnotjustlight,exhibitedwave-particleduality.Usingnothingbutthevalueofthevoltageappliedtothequartzwire,thegeometryoftheapparatus,andtheobservedfringes,MöllenstedtandDükerprovedcorrectdeBroglie’sformulaformatterwaves,whichsaysthatthewavelengthofaparticle,λ,equalsPlanck’sconstant,h,dividedbytheparticle’smomentum,p(soλ=h/p).Theequationisaudacious:theleft-handsidedealswiththe

propertiesofwaves,andtheright-handsidewithpropertiesofparticles.Youcouldn’taskforamoresuccinctexpressionofwave-particleduality.MöllenstedtwrotetodeBroglie,anddeBrogliereplied,“Itwas...agreatpleasuretoseethatyouhaveobtainedanewandparticularlybrilliantproofoftheformula.”

Möllenstedt’syoungGermanstudent,ClausJönsson,watchedtheseexperimentsbeingdone.By1961,Jönssonperformedaformaldouble-slitexperimentwithelectrons,thesameyearthatFeynmanstartedtalkingofhisthoughtexperimentsatCaltech.JönssonwroteuphisreportsinGerman;it’dtakeyearsfortheworktobetranslatedintoEnglish,explainingwhyFeynmancontinuedtoregarditasanexperimentinthoughtonly.

Buttheseexperimentsthusfarweredonewithmanyelectronspassingthroughthedoubleslit(orpassingbythechargedwire)atthesametime.Theexperimentwithsingleelectronstooksomewhatlonger.Anddifferentteamsclaimthecreditforpullingitoff:onein1974,andthenextin1989.Conceptually,theexperimentsweresimilartoMöllenstedtandDüker’s,exceptfortheguaranteethatonlyoneelectronwasgoingthroughtheapparatusatanyonetime(whetherthisactuallyhappenedisthesourceofdisputebetweenthetwoteams).

In1974,ItalianphysicistsPierGiorgioMerli,GianFrancoMissiroli,andGiulioPozziinBologna,Italy,recordedonatelevisionmonitorthearrivaloftheelectronsaftertheyhadgonepastthebiprism.Toobservetheinterferencepatternwiththenakedeyerequiredsomefancyopticsthatmagnifiedthefringesafewhundredtimes.TheItaliansalsohadtodeveloptechnologyfor“storing”theelectronsthatarrivedatthemonitorforafewminutessothatonecouldseethefringesoncealltheelectronshadbeencollected—otherwisethespotcreatedbythefirstelectronwouldhavelongvanishedbythetimethelastelectronarrived.Theteammadea16mmmovieofthefringestakingshapeonthemonitor;themovieevenwonanawardattheSeventhInternationalScientificandTechnicalMovieFestivalheldinBrusselsin1976.

In1989,AkiraTonomuraandcolleaguesatHitachiinJapandidasimilarexperiment,withanextremelywellcontrolledsourceofelectrons.Tonomura’steamalsocreatedtechnologytorecordelectronsonascreenthewayonecanrecordparticlesoflightonaphotographicplate:onebyone,tobuildupanimageovertime.Thisway,theydidn’thavetostorethefirstelectronuntilthelastonearrived.TheHitachiteam’sfilmoftheelectronshittingthescreen(theactualelapsedtimewastwentyminutes,butthefilmisspedup)isoneofthemostfascinatingshortfilmsinthehistoryofphysics.Electronsappearasdotsonthescreen,seeminglyatrandom,butsoonenoughthefringesbuildup,amagical

thescreen,seeminglyatrandom,butsoonenoughthefringesbuildup,amagicaldemonstrationofsingle-particleinterference.Themoviebeliesthechallengetheexperimentersfaced:theentireequipment,includingtheelectronsourceandthebiprism,hadtobeheldunerringlystabletheentiretime;hadanythingmovedevenfractionsofamicron,itwouldhavedestroyedthefringes.

Alittleoveradecadelater,PhysicsWorldpublishedanarticletocelebratethefactthatthedouble-slitexperimentdonewithsingleelectronswasvoted“themostbeautifulexperiment”inphysics.Itfailedtomentionthe1974Italianeffort,promptingaletterofprotestfromtheItalianteam.PhysicsWorldupdateditsarticle,includingtheItalianteam’sletterandTonomura’sreplyarguingfortheJapaneseteam’splaceinhistory:“Webelievethatwecarriedoutthefirstexperimentinwhichthebuild-upprocessofaninterferencepatternfromsingleelectroneventscouldbeseeninrealtimeasinFeynman’sfamousdouble-slitgedankenexperiment.Thiswasunderthecondition,weemphasize,thattherewasnochanceoffindingtwoormoreelectronsintheapparatus.”

Thereis,however,nodoubtaboutwhowasthefirsttotestthedoubleslitwithsinglephotons.

—Thedouble-slitexperimentthatAspectandGrangierdidinParisstartswithapieceofglassthatreflectshalfthelightthatfallsonit,andtransmitstheotherhalf.Thisisactuallyafairlycommonoccurrencewithglass.Thinkofsittinginatrainthat’sracingthroughthecountrysideatnight.Ifit’scompletelydarkoutsideandyouarelookingatthewindowpane,youwillseetheinsideofthecarriagereflectedintheglass.Butwhenthetrainpassesbysomelightedbuildingsoutside,youseethebuildingswhilesimultaneouslyseeingyourownreflectionintheglass.Thewindowpaneisbothreflectingandtransmittinglight.Inlabs,suchglassiscalledabeamsplitterorahalf-silveredorsemi-transparentmirror(albeittheglassdoesitsjobfarmorepreciselythanyouraveragewindowpane),andasthenamesuggests,itsplitsabeamoflightintotwo.Halftheenergyofthewaveisreflectedandhalfistransmitted.

Somethingfunnyhappenswhentheincidentlightismadeofjustonephoton,thesmallestindivisibleunitoflight.Itcan’tbesplitfurtherintotwohalves.Sotheincidentphotonwillbeeithertransmittedorreflectedasonewhole.Let’sputphotondetectorsD1andD2,oneattheendofeachbeam.Sincethephotontravelsundivided,ifthephotonisreflected,thenD1clicks,andifit’stransmitted,D2clicks.Bothdetectorsneverclickatthesametime:thephotondoesindeedbehaveasanindivisibleunitofenergy.

Turnsoutthatifyousendlotsandlotsofphotons,oneatatime,intothe

Turnsoutthatifyousendlotsandlotsofphotons,oneatatime,intothebeamsplitter,thenonaverage,halfthetimeD1willclick,andhalfthetimeD2willclick.There’sanimportantobservationherethatwillbecomemoreandmorerelevant:onecanneverpredictwithcertaintywhatagivenphotonwilldo.Foreachphoton,wecanassignonlyaprobabilityfortheoutcome—it’lleithergotoD1withprobabilityof0.5ortoD2withaprobabilityof0.5.

Theimmediatereactiontothisfromourclassicallyattunedmindsistosay,well,thefactthatwecan’tpredictwhatthephotonwilldomusthavesomethingtodowithourlackofknowledgeaboutthecompletestateofthephoton.ItwasasimilarargumentthatinitiallypromptedEinsteintothinkthattheremustbesomehiddenvariables.

Forexample,whenweflipacoin,weassignaprobabilityofone-halftotheoutcomethatit’lllandheads,andone-halfthatit’llcomeuptails.Butthereasonwecannotpredictwithcertaintywhetheracoinwillcomeupheadsortailsisbecausewedon’tknoweverythingthereistoknowaboutthecoin’sinitialconditions(theangleatwhichit’sflipped,theinitialvelocity,etc.);ifwehadfullknowledgeoftheinitialconditions,knowledgethatcouldbeencodedwithadditionalvariables,wecouldinprinciplepredicttheoutcome.

Couldsomethingsimilarbeatworkwiththephotons?Whatifthereweresomeattributesofthephotonthatweren’tbeingcapturedinthemathematicalformalism?Andifweknewthevaluesofthesehiddenvariables,thencouldwenotpredictwithcertaintywhateachphotonwoulddo?

Puttingasideconcernsabouthiddenvariablesfornow,let’smaketheexperimentalsetupabitmoreinteresting.Let’sputfullyreflectingmirrorsinthepathsofthebeamssothatthebeamsareturnedatrightangles,towardeachother.D1andD2arestillattheendsofthesebeams.Whatcanweexpectifwesendtensofthousandsofphotons,oneatatime,intotheapparatus?

Well,nothingdifferent.Allwe’vedoneisincreasethedistancetraveledbythephotons,butnothingelsehaschanged.SoD1stillclickshalfthetime,andD2halfthetime.

Tocomplicatethingsfurther,let’saddasecondbeamsplitter,exactlyatthepointwherethepathsofthetwobeamscross.Now,aphotonreachingthesecondbeamsplitterwillbeeitherreflectedortransmitted.

Basedonwhatweknow,wecananalyzewhat’sexpectedofeachphotonthatenterstheapparatus.Aphotonthat’sreflectedbythefirstbeamsplitterandthentransmittedbythesecondbeamsplitterendsupatD1.Let’scallthisphotonrt.Thephotonthat’stransmittedfirstandreflectednextalsoarrivesatD1.Thisphotonistr.SophotonsthattakethepathsrtandtrreachD1.Similarly,rrandttendupatD2.

Whathappensthen,ifwesend10,000photons,oneatatime,intotheapparatus?Weknowfrompreviousexperimentsthathalfofthephotonswouldbesentonewaybythefirstbeamsplitterandhalftheotherway(speakingalways,onaverage).So5,000photonswouldtakepathRand5,000wouldtakepathT(thefateofanygivenphoton,however,isstillnotforustopredictwithcertainty).Atthesecondbeamsplitter,the5,000thattookpathRshouldbesplitinhalfagain;2,500shouldgotoD1and2,500shouldgotoD2.Thesameanalysisholdsforthe5,000photonsthattookpathT.Totalthemupandournaivebutperfectlylogicalconclusionisthat5,000photonsshouldreachD1and5,000shouldreachD2.

Bynow,ifourmindsaregettingusedtoquantumstrangeness,weshouldn’tbesurprisedtolearnthatthat’snotwhathappens.Addingthesecondbeamsplitterhasprofoundimplications.Beforethesecondbeamsplitterwasinplace,itwasclearwhenD1clickedthatthephotonhadcomethroughpathR,andifD2clicked,thephotoncameviaT.Now,withthetwobeamsplittersinplace,aphotonreachingD1couldhavetakeneitherpathrtortr,andaphotonreachingD2couldhavetakeneitherpathrrortt.IfyoudetectaphotonatD1,there’sno

waytotellwhichpathittook.ThesamegoesforaphotondetectedatD2.Thetwopaths,foranygivenphoton,havebecomeindistinguishable.Thisisexactlywhathappensinadoubleslit.Onceaphotonlandsonthefarscreen,there’snowaytotellwhichslitthephotoncamethrough.Ifnothingabouttheexperimentalsetupmakesthephotontakeoneortheotherpath,themathematicalformalismsaysthatittakesbothpaths,inamannerofspeaking.Nowthatweknowasmuch,canwefigureoutwhathappenstothe10,000photons?

Theclueisinthenameoftheapparatussketchedabove.It’scalledaMach-Zehnderinterferometer,afterLudwigMach(sonofthephysicistErnstMach)andLudwigZehnder.In1892,MachimprovedaninstrumentthatZehnderhaddesignedayearearlierforopticsexperiments(theyweren’tthinkingofsingle-particlequantummechanicsatthetime).TheMach-Zehnderinterferometerisaspecialcaseofadouble-slitexperiment.Lightcantakeoneoftwopaths(analogoustogoingthroughoneslitortheother)andtheninterferewhenthepathsrecombineinthesecondbeamsplitter(oratthelocationofthescreeninthecaseoftheclassicdoubleslit).Conceptually,anythingyoucandowithaclassicdoubleslit,youcandowithaMach-Zehnderinterferometer:modernexperimentalphysicists,whentheysaytheyareperformingadouble-slitexperiment,areinalllikelihoodusingthisinterferometer.It’sanexperimentalist’sdelight.“It’sjustsmarter,”Aspecttoldme.

Whyinterferencehappens,especiallywhenwesendoneparticleatatimeintotheapparatus,isacuriousphenomenon.It’sexactlywhatAspectandGrangierstudiedwhentheybuiltsuchaninterferometer.

First,histeamhadtoensurethattherewasonlyonephotonpassingthroughtheirexperiment.Theybeganbyusingcarefullycalibratedlaserstoexciteatomsofcalciumtoahigherenergylevel.Suchanexcitedatomfallsbackdowntoitspreviousstatebyemittingtwophotons,thefirstoneagreenphotonatawavelengthof551.3nanometers(onenanometerequals10-9meters),followedalmostimmediatelybyabluephotonat422.7nanometers.Sothere’sagreen-bluepair,followedbynothing,thenanothergreen-bluepair,thennothing,andsoon.Thepairsarewellseparatedintime.“Good,I’mgoingtousethisseparationintime,”Aspectrecalledthinking.

Thegreenphotonheraldsthearrivalofthebluephoton.Sotheteamusedthegreenphotontogettheirdetectorsreadyforthearrivalofthebluephoton,whichwouldcomewithinnanoseconds.Thecrucialthinghereisthattherewillbeoneandonlyonebluephotonintheapparatusatthatpointintime.“Theprobabilityofhavingasecondbluephotonduringthattimewaspeanuts,”said

Aspect.Theinitialtestwastosendthebluephotonthroughthefirstbeamsplitter,withoutthesecondbeamsplitterinplace.SothephotongoestoeitherD1orD2.QuantumtheorysaysthatonlyoneofD1orD2shouldclickforagivenphoton.Thispartoftheexperimentwassuccessful.Thebluephotonalwaysarrivesatoneortheotherdetector—andit’sclearwhichpathittook.Thetwodetectorsneverclicktogether.Thephotonalwaystravelsasanundividedwhole;itbehaveslikeaparticle.

Itwastimetotestthephoton’swavenature.Theteamaddedthesecondbeamsplitter.Nowthetwopathsbecomeindistinguishable.Andso,justasThomasYoungobservedinterferencewithhissplitsunbeam,AspectandGrangiersawittoo.

Butwhat’sthemeaningofinterferenceinaMach-Zehndersetupforasinglephoton?Forabeamoflight,weknowthatconstructiveinterferenceresultsinabrightfringe,anddestructiveinterferenceresultsinadarkfringe(nolight).Itturnsoutthatintheinterferometer,whenthetwopathsareofequallengthandyousendinphotonsonebyone,theyallgotoD1,andnonegotoD2.SoD1representsconstructiveinterferenceandD2representsdestructiveinterference.Ourearliernaiveanalysisofthe10,000photons—thathalfshouldreachD1andtheotherhalfshouldreachD2—iswrong.All10,000photonsreachD1andnonearriveatD2.

—Theonlywaytoexplaintheresultistothinkoflightasawave.Whenthewaveencountersabeamsplitter,thewavesplits;halfgoesintoonearmoftheinterferometer,andhalfintotheotherarm.Zoomingintothestructureofthebeamsplitter(whichhasafinitethickness),onecanseethatwhenawaveisreflected,ittravelsdifferentlythroughtheglasscomparedtoawavethat’stransmitted.

Whenthewavelengthofthelightandthicknessofthebeamsplitterarechosencorrectly,thiscancausethereflectedwavetolagbehindthetransmittedwavebyaquarterofawavelength.

Addinonemorereflectionatthesecondbeamsplitter,andthewavethat’sreflectedtwice,rr,nowlagsbehindthewavethat’stransmittedtwice,tt,byhalfawavelength.BothrrandttreachD2.SothecrestofonewavearrivesatD2atthesametimeasthetroughoftheother.That’sdestructiveinterference.YougetdarknessatD2.

ThesameanalysisshowsthatthertandtrpathsarriveatD1withtheirwavesinsync,thecrestsofbothwavesreachingatthesametime.Thewavesaresaidtobeinphase.That’sconstructiveinterference.AllthelightreachesD1.

That’saperfectlyfineexplanationforlightcomposedoflotsofphotonsandactinglikeanelectromagneticwave:it’seasytoconceptualizehalfthewavegoingonewayandtheotherhalftheotherwayandthenrecombiningtoproducetheinterferenceeffects.Butexactlythesamethinghappenswhenyousendinsinglephotons.WeseemtobegettingconstructiveinterferenceatD1(all10,000photons,henceallthelight,reachingD1),anddestructiveinterferenceatD2(nophotons,hencenolight,gettingtoD2).

Thisisallverystrange.Forinterferencetohappen,awavehastosplitintotwoandthenrecombine.Canthathappentoasinglephoton?Whenweaddthesecondbeamsplitter,eachphotonseemstobesplitting,goingthroughbotharmsoftheinterferometerandrecombining.But—andit’sworthponderingthistothepointofpain—weknowthataphotoncannotsplitintotwo,forit’sanindivisibleunitoflight.Whatthenisgoingthroughbotharmsoftheinterferometer(orthroughbothslitsofadouble-slitsetup)?Diggingfurtherrevealsexactlywhythequantumworldissoconfounding.

Let’sgobacktothefullMach-Zehndersetupandmakeonesmallchange:blockoneofthearmstopreventanyphotonsfromgoingthrough.Let’sstartwithblockingarmR.Whatcanweexpect?

Twothingshappen.First,thenumberofphotonsthatmakeittothesecondbeamsplitterishalved.Byblockingonearm,wearepreventinghalfthephotonsfromgettingthroughtothedetectors.

Butsomethingelsehappensthat’sfarmorepuzzling.Withouttheblockinplace,weknowthatallphotonsleavingthesecondbeamsplittergotoD1.However,withtheblockinplace,whilethenumberofphotonsreachingthesecondbeamsplitterisreducedtohalf,halfoftheonesthatdogetpastthesecondbeamsplittergotoD1andtheotherhalftoD2.RepeattheexperimentbyblockingarmT,andyouwillgetthesameresults.Theblock,whetherit’sinarmRorT,islikeadetector:weknowwithcertaintythatthephotonsthatreachthesecondbeamsplitteraretravelingthroughtheunblockedarmoftheinterferometer.Thereisnoindistinguishabilityanymore,thephotonsactlikeparticles,andthereisnointerference,leadingtothe50-50splitatD1andD2.

Withthesecondbeamsplitterinplaceandnothingblockingthephoton’spath,eachphotonisdoingsomethingthatisimpossibletointuitivelyunderstand.It’sinastateofquantumsuperposition.AsphilosopherDavidAlbertofColumbiaUniversitywritesinhisbookQuantumMechanicsandExperience,thetermsuperpositionis“justanameforsomethingwedon’tunderstand.”(AndtheaboveanalysisisinspiredbyasimilaranalysisofaslightlydifferentsysteminAlbert’sbook.)

Thephotonisinasuperpositionoftwostates,onestateinwhichitgoesthroughonepath,andanotherstateinwhichitgoesthroughanotherpath.Butthisisnotthesameassayingitwentthroughbothpaths,orthatitwentthroughonlyoneortheotherpath,orthatitwentthroughneitherpath.

“Thedouble-slitexperimentisusuallyusedtoestablishthattherecanbesituationsinwhichitmakesnosensetoask,say,whichslittheparticlewentthrough,”AlberttoldmewhenwemetathishomeinNewYorkCity.“Therefailstobeafactofthematteraboutwhichslittheparticlewentthrough.Askingwhichslittheparticlewentthroughis[like]askingaboutthemaritalstatusofthenumberfiveortheweightingramsofCatholicism.Thisissomethingphilosopherscallacategorymistake.”

Nonetheless,there’sinterference.Whatisitthatinterferes?Interferencehastodowithquantumsuperposition,andthestoryofhowquantumobjectsendupin,andfalloutof,superpositionis“themostunsettlingstoryperhaps,tohaveemergedfromanyofthephysicalsciencessincetheseventeenthcentury,”writesAlbert.

—ErwinSchrödingerwasparticularlyunsettledbyquantumsuperposition,andsowasEinstein,andtheycameupwithsomemorbidthoughtexperimentstomaketheirpointthattakingquantummechanicsasitiscouldresultinuntenablemacroscopicrealities.Indoingso,theyweretakingdirectaimatsomeofthekeytenetsoftheCopenhageninterpretation.

TaketheMach-Zehnderinterferometer.Accordingtotheformalism,beforeoneofthedetectorsclicks,signalingthearrivalofaphoton,thephotonisinasuperpositionoftwostates,oftakingonepathandtheotherpath.Thewavefunctionofthephotonissaidtobeinasuperpositionoftwostates,whereonestaterepresentsitsprogressalongonepath,andtheotherstateitsprogressalongtheotherpath.Usingthiswavefunction,wecancalculatetheprobabilitythatit’llbefoundatD1oratD2,which,incidentally,turnsouttobe1and0,

respectively,whenthelengthofthepathstoD1andD2areexactlythesame.Creatingsmalldifferencesinthelengthsofthepathscanchangetheseprobabilities.Accordingtothestandardview,thephotonhasnodefiniteposition—thewavefunctionisspreadout—untilthere’sameasurement.ThemeasurementatD1orD2causesthewavefunctiontocollapsetoonedefinitevalue:thephotonshowsupatoneofthedetectors.

Theonusofcollapsingthewavefunctionfallsonthemeasurementdevice,whichisassumedtobesomemacroscopic,classicalapparatus.ButtheCopenhageninterpretationdoesnotreallydefinetheexactmeaningofameasurement.Howbigdoesthemeasurementdevicehavetobetocountasclassical?Where’stheboundarybetweenthequantumandtheclassical?Suchquestionsleadtotheso-calledmeasurementproblem.

Toappreciatejusthowdeepthisproblemruns,let’sassumethemeasuringdevicesarealsosomethingquantummechanical—saytheyarethemselvesparticlesthatinteractwiththephotonandsomehowchangestatetorecordthearrivalofthephoton.Ifoneweretosimplyfollowthemathematics,somethingweirdhappens.Thewavefunctionofthephotonevolvesuntilitisinasuperpositionofhavinggonethroughbothpaths,whichrecombineatthesecondbeamsplitter.Thenitinteractswiththemeasurementdevice,whichisitselfaquantummechanicalparticle.Thewholesystemthenendsupinasuperposition,mathematicallyspeaking,ofastateinwhichthephotonhasreachedthemeasuringparticleD1andD1haschangedstateandthephotonhasreachedthemeasuringparticleD2andD2haschangedstate.Tocollapsethewavefunctionoftheentiresystemsothatwecanfigureoutexactlywherethephotonwent,we’llhavetodoyetanothermeasurement,withsomeostensiblyclassicalapparatus,todeterminethestateofD1andD2.

Whatifeverypieceofapparatuswechooseobeysthelawsofquantummechanics,suchthattheentiresetupalwaysremainsinsuperposition,anditstotalwavefunctionnevercollapses?Williteventuallyrequireaconscioushumantocauseacollapse,toseewherethephotonwent?

TheCopenhageninterpretation,whileitdoesnotinvoketheneedforhumanconsciousness,nonethelessdemandsaclassicalmeasurement.Thecorollaryisthatthequantumstateofasystemisadequatelyandindeedcompletelycapturedbythewavefunction,andsincethewavefunctionletsyoucalculateonlytheprobabilityoffindingthesysteminsomestate,anddoesnotcorrespondto,say,wherethephotonactuallyis,realitydoesnotexistinanymeaningfulsenseindependentofmeasurementwithaclassicalapparatus.

EinsteinandSchrödingerwerebothdeeplydisturbedbysuchanti-realist

EinsteinandSchrödingerwerebothdeeplydisturbedbysuchanti-realistideas.EinsteinpointedouthisconcernsinalettertoSchrödinger.Inathoughtexperiment,Einsteinimaginedsomegunpowderthatcanspontaneouslycombustbecauseofquantummechanicalgoings-onandhasacertainprobabilityofexplodingwithinayear,andacertainprobabilityofnotexploding.Thesystemstartsoffwithawell-definedwavefunction,meaningitisinadefinitestate.Butbecauseit’saquantumsystem,thewavefunctionevolvesaccordingtotheSchrödingerequation,intosomethingthateventuallyputsthegunpowderinaquantumsuperpositionofhavingexplodedandnothavingexploded.Ofcourse,macroscopically,inourunderstandingoftheworldatlarge,thisisabsurd.Thegunpowdershouldeitherexplodeornot,whetherwelookatitornot.EinsteinwrotetoSchrödinger,saying,“Throughnoartofinterpretationcanthisψ-function[wavefunction]beturnedintoanadequatedescriptionofarealstateofaffairs;[for]inrealitythereisjustnointermediarybetweenexplodedandnot-exploded.”

Schrödingerendeduprefiningthisthoughtexperiment,makingtheseemingabsurditystarker.HewrotetoEinstein,saying,“IamlongpastthestagewhereIthoughtthatonecanconsidertheψ-functionassomehowadirectdescriptionofreality.InalengthyessaythatIhavejustwrittenIgiveanexamplethatisverysimilartoyourexplodingpowderkeg.”Hethenwentontodescribetheexperiment,anelaborateversionofwhichappearedinhispublishedpaper.

“Acatisshutupinasteelchamber,togetherwiththefollowingdiabolicalapparatus(whichonemustkeepoutofthedirectclutchesofthecat):inaGeigertubethereisatinymassofradioactivesubstance,solittlethatinthecourseofanhourperhapsoneatomofitdisintegrates,butalsowithequalprobabilitynotevenone;ifitdoeshappen,the[Geiger]counterrespondsandthrougharelayactivatesahammerthatshattersalittleflaskofprussicacid.Ifonehasleftthisentiresystemtoitselfforanhour,thenonewillsaytohimselfthatthecatisstillliving,ifinthattimenoatomhasdisintegrated.Thefirstatomicdisintegrationwouldhavepoisonedit.Theψ-functionoftheentiresystemwouldexpressthissituationbyhavingthelivingandthedeadcatmixedorsmearedout(pardontheexpression)inequalparts.”

Butsurelythecatiseitheraliveordead,notinsomeweirdmixtureofboth?Atleastthat’sourclassicalintuition.Notsosaysthestandardviewofquantummechanics.TheparadoxarisesbecauseintheCopenhageninterpretation,thewavefunctionofthetotalsystemremainsinasuperpositionofcat-deadandcat-alivestates,untilsomethingclassicalinteractswiththesystem.Saysomeoneopensthesteelchamberandtakesalook,atwhichpointthewavefunctionofthe

entiresystemcollapsestooneortheother.Thecatwillbefoundeitherdeadoralive.

Quantummechanicsasksustosuspenddisbeliefandholdontosomecounterintuitivenotionsofrealityforlongenoughtobeabletoappreciatethebizarrenessofthesubatomicworld.Forexample,evenifSchrödinger’sthoughtexperimentwiththecat-in-a-steel-boxstretchescredulity,asitshould(itwasafterallanexerciseintryingtodemonstratethepossibleincompletenessofquantummechanics),itisalsoareminderofsomethingthat’strueofthequantumworld:superpositionexists,atleastinthestandardview.

Ifitdidnot,youcouldnotexplaintheinterferencepatternseeninadouble-slitexperimentdonewithsingleparticles.InAspectandGrangier’sMach-Zehndersetup,untileachphotonwasdetected,itwasinasuperpositionofhavingtakenbothpaths.Mathematically,here’swhatishappeningintheMach-Zehnderexperiment.Thereisonewavefunctionthatdescribesthestateofthephotongoingviaonepath,andanotherwavefunctionforthestateofthephotongoingviatheotherpath.Thefinalwavefunctionisalinearcombinationofthetwowavefunctions,whichletsyoucalculatetheprobabilitiesofdetectionatD1orD2(ψtotal=a1.ψD1+a2.ψD2,wheretheprobabilityoffindingthephotonatD1isgivenbythemodulus-squaredofa1,andtheprobabilityoffindingitatD2isthemodulus-squaredofa2.Thetotalprobabilityhastoadduptounity,so|a1|2+|a2|2=1.Theexactvaluesfora1anda2dependonthepathlengthsoftheinterferometer,whethertheyareidenticalorslightlydifferent).

Intheearlydaysofquantummechanics,itwasoftensaidthattheinterferencepatternappearsbecauseaparticleinterfereswithitself(toparaphrasePaulDirac).Butthatturnsouttobeasomewhatlimitedviewofwhat’shappening.Themoreprofoundrealizationisthatwhatarereallyinterferingaretwodifferentstatesofthesystem.Inthecaseofaninterferometerwithtwopaths,thetwostatesarethetwopossiblepathsforeachphoton.Ifthereweremultiplepossiblestatesorpathsforthephoton,sayyouhadfiveslitsinsteadoftwo,thenthesuperpositionwouldinvolvethephotongoingthroughallfiveslits,andaverydifferentinterferencepatternwouldemergeonthefarscreen.

Whetherit’stheMach-Zehnderinterferometerwithtwowell-definedpossiblepaths,oranapparatuswithfiveslits,thestandardquantumformalismmakesitimpossibletovisualizethepathofanindividualphoton—therearenoequationstocalculatetrajectories.TheCopenhageninterpretationofthisformalisminsiststhatsuchtrajectoriesdon’texist.Infact,thenotionofthepathhasnomeaning,justasthenotionofanelectron’sorbitaroundthenucleushas

hasnomeaning,justasthenotionofanelectron’sorbitaroundthenucleushasnomeaning.Ifrealismistheideathattheworldobjectivelyexistsoutthere,withwell-definedproperties,evenifwearenotprivytothem,thentheCopenhagenviewisanti-realist.Initstelling,theonlyworldwecantalkofdefinitivelyistheonethatrevealsitselfuponmeasurement;talkingaboutanythingelseismeaningless.

Aspect,forone,isholdingouthopeforpartofEinstein’sdream.“I’mreallysittingonthesideofEinstein,”hetoldme.“Ithinkthereisarealworld.”Meaningarealityindependentofobservers,experiments,andexperimentalists.Fornow,Aspectiswillingtoacceptquantummechanicsforwhatit’ssayingabouttheworld.“Theworldisnotassimpleasonecouldthink.Butphysicistsweresmartenoughtodevelopmathematicaltoolstorenderanaccountofwhathappens.”

—Theimpossibilityoftalkingaboutexactlywhat’shappeningtoaquantumsystem—sayaphotonworkingitswaythroughaMach-Zehnderinterferometer—withintheconfinesoftheCopenhageninterpretationwashighlightedbytheoreticalphysicistJohnWheelerinthelate1970sandearly1980s,mostcreativelybyhisuseofthemetaphorofthe“greatsmokydragon.”Wheelerimagined,andgotsomeonetosketchforhim,adragonwhoseheadandtailareclearlyvisible.Thetailrepresentstheunambiguousquantumstateofthephotonthatisabouttoenteraninterferometer.TheheadrepresentsthedefinitedetectionofthephotonateitherdetectorD1orD2.Butthedragon’sbodyisfuzzy,ambiguous,smoky,hencethename.“Whatthedragondoesorlookslikeinbetween[theheadandthetail]wehavenorighttospeak[of],”wroteWheelerandhiscolleagueWarnerMiller.Thedragon’sblurrybody,ofcourse,representsthestateofthephotonasitwindsitswaythroughtheinterferometer(ifitdoesthatatall).

Wheeler,likeEinstein,lovedthoughtexperiments.Theonemostassociatedwithhimbearshisname:Wheeler’sdelayed-choiceexperiment.It’sanexperimentthat’seasytoconceptualize,nowthatweknowofAspectandGrangier’s1985experimentdonewithsinglephotons,usingaMach-Zehnderinterferometer.Wheeler,ofcourse,thoughtofitbeforeanyonehaddonesuchexperiments.

Thedelayed-choiceexperimentbringsintostarkreliefBohr’scomplementarityprinciple.Bohrarguedthatthewavenatureandparticlenatureofaquantumsystemaremutuallyexclusivewaysoflookingatreality:whatyou

ofaquantumsystemaremutuallyexclusivewaysoflookingatreality:whatyouobservedependsontheexperimentalsetup,andyoucannothavebothtypesofsetupsinthesameexperiment.Andifyoutrytodoboth(asEinsteintriedtowithhisthoughtexperimentwiththedoubleslit),thenBohr’sclaimwasthattheuncertaintyprincipleensuresthatyoucannotseetheinterferencepattern(theactualexplanation,it’llturnout,ismoreinvolvedthanBohrunderstood).

Soaquantumsystemhastwofaces.Butwhendoesit“decide”toshowonefaceortheother?Isthatevenalegitimatequestion?Wheelertookonthequestionindramaticfashion.HisthoughtexperimentusestheMach-Zehnderinterferometer,inwhichweobservethephoton’sparticlenaturewhenwedon’thavethesecondbeamsplitterinplace(D1andD2eachclickhalfthetime)andweobservethephoton’swavenaturewhenthesecondbeamsplitterisinplace(there’sinterference,andD1clicksallthetime,andD2neverdoes).

Here’swhatWheelerproposed.Whatifwedelaythechoiceofwhetherornottoputinplacethesecondbeamsplitteruntilafterthephotonhasgonepastthefirstbeamsplitterandthusenteredtheinterferometer?Howdoesthephoton“know”whattodoinsidetheinterferometer?Atthemomentitencountersthefirstbeamsplitter,let’ssaythereisnosecondbeamsplittertomeasurethewavenature.Fromallweknowthusfar,thephotonshouldgothrougheitheronearmortheother,asaparticle.AfterthephotonisonitswaytoeitherD1orD2,weinsertthesecondbeamsplitterandmakethetwopathsindistinguishable.Theexperimentalsetupisnowlookingforthephoton’swavenature.What’sthephotontodo?Suddenlydecidethatithastogointoasuperpositionoftakingbothpathsanddisplayinterference?

Youcanalsodotheopposite.Letthephotonentertheinterferometerwiththesecondbeamsplitterinplace—sonowitisinasuperpositionofgoingthroughbothpaths,whichmeanseventuallyit’llendupatD1,notatD2.Butlet’stakeoutthesecondbeamsplitterjustbeforethephotonencountersit.Ifwecontinuethinkingintermsofonepathtakenorbothpathstaken,thephotonhastosomehowdoextremecalisthenicsandappeartotakeonlyoneoftwopaths,andthusrevealitsparticlenature,andendupateitherD1orD2.It’sasifthephotonisgoingbackintimeandundoingwhatithaddone.AsWheelerwrote:“Onedecideswhetherthephoton‘shallhavecomebyonerouteorbybothroutes’afterithas‘alreadydoneitstravel.’”

Theitalicizationof,ortheuseofscarequotesaround,wordsandphraseslikeseems,knows,asifisdeliberate—theyhighlightthefactthatourclassicalnotionsandthelanguageweusetotalkaboutthemfailuswhendealingwiththe

quantumworld,atleastwhenwelimitourselvestothestandardformalismandtheCopenhageninterpretation.

WhenAspectdidthesinglephotondouble-slitexperimentin1985,hewasawareofWheeler’sthoughtexperiment,andhewasawarethathisMach-ZehndersetuphadsomeofthenecessaryingredientsfortestingWheeler’sideas.Still,“atthattimeIwasnotdreamingofdoingtheexperiment,”Aspecttoldme.

Thereasonbeingthatthedelayed-choiceexperimentistechnicallyfarmorechallenging.InAspect’sinitialexperiment,eacharmoftheMach-Zehnderinterferometerwasabout6meterslong,whichisthedistancefromthefirstbeamsplittertooneofthedetectors.Aphotontakesonlyabout20nanosecondstocoverthatdistance.Totrickthephotonafterithadenteredtheinterferometer,Aspect’steamwouldhavehadhardlyanytimetoeitherinsertorremovethesecondbeamsplitter.Itseemedimpossible.

Whynotjustincreasethelengthoftheinterferometer?Sayto50meters?Thatwouldgiveoneabout165nanosecondstodothedirtydeed.It’snoteternity,butnotanimpossiblysmallintervaloftimeeither.

“I’mgoingtoteachyousomethingaboutoptics,”saidAspect,andproceededtoexplainwhygoinglongwasnotanoptionin1985.Theirsourceofsinglephotonsthenwasnotpoint-like.Itwasasifthephotonswerecomingoutnotfromapinholebutfromanopeningwithalargerdiameter.Inopticsexperiments,youoftenneedlensestocorralphotonstowardyourdetectors.Andifthesourceisnotpoint-like,thelightcandiverge,makingitnecessarytobuildbiggerandbiggerlenses,whichgetprohibitivelyexpensiveandtechnologicallyinfeasible.“Sixmeterswasalreadyaproblem,becausemysourcewasnotexactlypoint-like,butIcouldsolveit,”saidAspect.“But50meterswasoutofthequestion.”Thatwouldhaverequiredlensesseveralmetersindiameter.

AspecthadtowaittwentyyearsbeforethetechnologycaughtuptowherehecoulddoWheeler’sdelayed-choiceexperimentjustasWheelerhadintended.Otherteams,meanwhile,haddoneversionsoftheexperiment,butAspectwasafteritsessenceanddidnotwanttoleaveanythingtointerpretation.“Itwasclearformein2005thatthetechnologyhadreachedapointwhereyoucan[do]anexperimentwhichisveryclosetotheidealschemeofWheeler,”hesaid.

By2005,Aspecthadasourceofsinglephotonsthatwasmuchmorepoint-like,andhewasabletobuildaninterferometerwitharmlengthsof48meters—enoughtimetoinsertorremovethesecondbeamsplitterafterthephotonhadpassedthefirstbeamsplitter.

Andwhattheyobservedwasthattherewasnofoolingthephoton.Ifthesecondbeamsplitterwasnotthere,itbehavedlikeaparticle,otherwiseitactedlikeawave.Itdidnotmatterwhenthesecondbeamsplitterwasinserted.

RecallthattheinitialargumentsbetweenBohrandEinsteinastowhyonecannotobservethewavenatureandparticlenaturesimultaneouslyhadtodowithBohr’sassertionthattheactofobservationsomehowdisturbedtheapparatus,smearingouttheinterferencepattern.Complementaritywastheoutcomeoftheuncertaintyprinciple.

Butthedelayed-choiceexperimentdemonstratesthatcomplementarityisadeeperprinciple,deeperthanprobablyBohrrealized.InAspect’s2005experiment(theresultswerepublishedinFebruary2007),thephotonasitgoespastthefirstbeamsplitterisstilltoofarawayfromthelocationofthesecondbeamsplittertobeinfluencedbythedecisionbeingmadeatthedistantlocation.Inthelanguageofspecialrelativity,thesetwoeventsarespace-likeseparated,sothereisnoquestionofanydisturbanceduetomeasurement;nothingthatisbeingdoneneartheoutputstagecaninfluencethephoton.Andyet,thephotonshowsonlyonefaceortheother.

“Bohr’sstatementthatitisthemeasurementthatdetermineswhatyouobserveetc....shouldnotbetakeninatoonaive[manner].Itismoresubtlethanthat,”saidAspect.

Justhowsubtlewouldbecomeabundantlyclearwithanevenmoreaudaciousversionofthedelayed-choiceexperiment:theso-calleddelayed-choicequantumeraserexperiment.ThisistodistinguishitfromWheeler’soriginalidea,inwhichthesecondbeamsplitterisaclassical,macroscopicdevice.It’seitherthereornotthere.Whatiftheexperimentnotonlydelayedthechoiceofwhethertolookfortheparticlenatureorthewavenatureofphotonsbutallowedforthatchoicetobeerased?Whatwouldthephotondo?

Tounderstandthedelayed-choicequantumeraserexperimentinvolvesgoingback,yetagain,toEinstein’sobjectionstoquantumphysics.Forallhisworkonthespecialandgeneraltheoriesofrelativityandthephotoelectriceffect,Einstein’smostcitedpaperisonehewrotein1935,identifyingaweirdpropertyofquantumsystems(whichhewouldlaterrefertoas“spookyactionatadistance”).It’sapropertythatSchrödingeralsoidentifiedinthesameyear,andhecalleditentanglement.Ifquantumsuperpositionexhibitedbysingleparticleswasthefirstmysterythrownupbyquantummechanics,thenentanglement,whichinvolvestwoormoreparticles,wassomethingevenmoreprofound,andforEinstein,fundamentallymoredisturbing.Aspectcallsthedevelopmentsthatfollowed—includingexperimentalvariationsofthedoubleslitthatoutdideven

followed—includingexperimentalvariationsofthedoubleslitthatoutdidevenWheeler’sthoughtexperiments—thesecondquantumrevolution.“[It]hastodowithrealizingthatentanglementisdramaticallydifferent,”hesaid.

T

4

FROMSACREDTEXTS

RevelationsaboutSpookyActionataDistance

Nonlocalityforcesustoextendtheconceptualtoolboxweusetotalkaboutnature’sinnerworkings.

—NicolasGisin

imMaudlincanvividlyrecallthemomentthestrangenesshithim.Itwasmorethanthreedecadesago.Hewasinhissenioryearofcollege,whenhe

cameacrossaScientificAmericanarticletitled“TheQuantumTheoryandReality”bytheoreticalphysicistBernardd’Espagnat.Ithadaratherlongandunwieldlysubtitle—“TheDoctrineThattheWorldIsMadeUpofObjectsWhoseExistenceIsIndependentofHumanConsciousnessTurnsOuttoBeinConflictwithQuantumMechanicsandwithFactsEstablishedbyExperiment”—togowithsomefifteen-oddpagesoftext,equations,andillustrations.Prettyheavygoing.Maudlinreaditthoroughlyenoughtobeflooredbytheimplications.“Myroommatessaidlaterthattheyknewsomethingwasstrange,becauseIjustkept...holdingthismagazineandpacingaroundincirclesintheroom,”saidMaudlin,aphilosopherofscienceatNewYorkUniversity.WeweresittinginthesparinglyfurnishedlivingroomofhisNewYorkapartment.AframedprintofartworkbyCroatianartistDaninoBozicgracedonewall—asitdoesthecoverofoneofMaudlin’sbooks,TheMetaphysicswithinPhysics.Twothin,tallwoodenfigures—carvingsmadebytheNyamwezipeopleofTanzania—stoodinonecorner.Inthattastefullyausteresetting,Maudlincasthismindbacktothed’Espagnatarticle.Hesaidhe’dnowtakeissuewithsomeofthethingsthatd’Espagnatwrote,butreadingitthenasastudent,“itwasclear

enoughthatyoucouldseesomethingverystrangewasgoingon[withquantummechanics],thatitwasasharpenoughresultthatyoucouldn’tgetoutofit.”

TheScientificAmericanarticlehadadetailedexpositionofJohnBell’s1964paper,theverysamepaperthatinspiredAlainAspecttoembarkonhisexperimenttosettleadebatebetweenEinsteinandBohr.Inthearticle,d’EspagnatarguedthatEinstein’sideas(enshrinedinhistheoriesofrelativity)andquantummechanicswereatodds,andthatAspect’sexperimenttotestBell’stheorem,whichhadyettobedone,wouldsettletheissue.Einsteinbecameawareofthistensionbetweenhistheoriesandquantummechanicswellbeforealmostanyoneelse.

Tomakehiscaseatthe1927SolvayConference,Einsteintookthecaseofaparticlegoingthroughaholeinascreen.Withcharacteristichumility,he“firstapologizedfornothavinggonedeeplyintoquantummechanics.”Then,withcharacteristicinsight,hegaveanastuteanalysisofwhatwaspuzzlinghim.Accordingtotheformalism,theparticle’swavefunctiongoesthroughthehole,diffracts,andspreadsoutsemi-spherically,andonecancalculatetheprobabilityoffindingtheparticleatanyonelocationonthesurfaceofthisspreadinghemisphere.Now,let’ssayadetectoratsomedistancefromtheholedetectstheparticle.Thisisthesameassayingthatthespread-outwavefunctioncollapsesuponmeasurement.Ifoneinterpretsthewavefunctionasacompletedescriptionofthestateoftheparticleandasadescriptionofwhat’sactuallyhappening(andnotmerelyastatementaboutourstateofknowledge,orlackthereof,ofreality),thenitseemsthattheparticle,whichwasitselfspreadout,getslocalized.Ifso,Einsteinmadethepointthatthislocalization,ortheunequivocalappearanceoftheparticleatonelocation,ishappeningsimultaneouslywiththeindisputabledisappearanceoftheparticlefromallotherlocations.It’saviolationoftheprincipleoflocality,whichsaysthatifsomethingishappeninginoneregionofspacetime,itcannotinfluencesomethingelsehappeninginanotherregionofspacetimeanyfasterthanthespeedoflight.Thecollapseofthewavefunction,inthiswayofthinkingaboutit,isinstantaneousandpatentlynonlocal.Eventhisearlyinthehistoryofquantummechanics,Einsteinwasawarethatthisseemingnonlocality,whichimpliedsimultaneityofactions,wasinconflictwithhisowntheoryofspecialrelativity.

ButamoreseminalanalysiswastocomefromEinsteinandtwocolleagues.ToEinstein’schagrin,theworldlearnedofthisnotthroughtheusualchannelsofscientificdiscoursebutviaanalmosttabloid-likereportinTheNewYorkTimes.

EINSTEINATTACKSQUANTUMTHEORYscreamedtheheadlineonMay4,1935.AccordingtoTheNewYorkTimes,Einsteinandhistwoyoungercollaborators,BorisPodolskyandNathanRosen,hadshownthatquantummechanicswasn’tcompleteandthatitneededaugmenting.

EinsteinfoundoutthatPodolskyhadleakedinformationabouttheirupcomingpapersometwoweeksinadvanceofitspublicationinPhysicalReview,andEinsteincomplainedtotheTimes,saying,“Ideprecateadvancepublicationofanyannouncementinregardto...[scientific]mattersinthesecularpress.”(Decadeslater,physicistDavidMerminwouldquip,“IfTheNewYorkTimesisthesecularpress,itfollowsthatthesacredtextisthePhysicalReview.”)

Nonetheless,theelegantfour-page-longpaper,publishedonMay15,1935,wasaslowlyunfoldingseismiceventwhoseaftershockscontinuetoshakeupquantumphysicstothisday.KnownastheEPRpaperintheliterature(forEinstein-Podolsky-Rosen),ithaditsrootsinateatimeconversationbetweenEinsteinandRosenaboutthequantumstateoftwoparticlesaftertheyhaveinteractedwitheachother.Itturnsoutthatpost-interaction,thereisnoseparatewavefunctiontodescribeeachparticle;rather,theyaredescribedwithone,jointwavefunction.Theparticlesaresaidtobeentangled.Einsteinfiguredthatentangledparticleswouldallowhimtostrengthenhisargumentabouttheincompletenessofquantumtheory.DespitehisseemingdefeatatthehandsofBohrattheFifthSolvayConference,givingtheroundtotheCopenhageninterpretation,EinsteinwasfarfromdonedebatingBohr.

CentraltotheEPRargumentistheassumptionthatnatureislocal.Itseemsaprettyintuitiveidea,butittookEinstein’stheoryofgeneralrelativitytobringlocalityintosharpfocus.BeforeEinstein,Newtonhadobfuscatedlocalitybysuggestingthatgravitationalinfluenceswereinstantaneous.InNewtoniangravity,ifthesunweretosomehowdisappear,theEarthwouldbeimmediatelyinfluencedbythechangesinthegravitationalfield.Einstein’sgeneralrelativityshowedthatgravityistheoutcomeofthewarpingofspacetimebythepresenceofmatter(thewayaheavyballplacedonatautsheetofrubberdentsthesheet),andanychangestothecurvatureofspacetimecausedbymattercanpropagateonlyatthespeedoflight.SoitwilltakeEarthabouteightminutestonoticetheabsenceofthesun’sgravitationalpull,wereittodisappear.LocalityisessentialtoEinstein’srelativity.

Besideslocality,Einsteinhadlonghelddeartheideaof“realism”anditshowedupintheEPRpaper,whichbeginswiththesewords:“Anyseriousconsiderationofaphysicaltheorymusttakeintoaccountthedistinctionbetween

considerationofaphysicaltheorymusttakeintoaccountthedistinctionbetweentheobjectivereality,whichisindependentofanytheory,andthephysicalconceptswithwhichthetheoryoperates.Theseconceptsareintendedtocorrespondwiththeobjectivereality,andbymeansoftheseconceptswepicturethisrealitytoourselves.”

ForEinstein,therealworldexistsindependentofourobservations.Realismcanbesharpenedtoastatementaboutourphysicaltheories,to

arguethatvariablesinthetheoriescorrespondtoactualphysicalreality.Completenessofatheory,inthisregard,dependsonithavingenoughrelevantvariablestocaptureallofphysicalreality(forexample,variablesforaparticle’spositionandmomentum,whichwouldallowustocalculateitstrajectory,ifaparticlehasone,thatis).

Andindeed,oneoftheargumentsEPRusedtomaketheirpointthatquantummechanicsisincompleteinvolvedasomewhatcomplicatedthoughtexperimentthatrequiredmeasuringthepositionandmomentumofentangledparticles.Sixteenyearslater,in1951,physicistDavidBohmwouldillustratetheEPRargumentusingasimplerthoughtexperiment.Withhindsight,it’seasiertounderstandtheissueusingBohm’sclearerexample.

Imagineaparticlewithzerospinthatdecaysintotwoidenticalparticlesthatmoveawayfromeachother.Theconservationofangularmomentumdictatesthattheparticlesmustbespinninginoppositedirections,sothatthetotalspinstilladdsuptozero.Assumethattheparticles,AandB,aremovingawayfromeachotheralongtheX-axis(theleft-rightdirectiononthispage).Quantummechanicssaysthatthetwoparticlesareentangledintheirspin.

Let’sfirsttakeparticleA.IfyouweretomeasurethespinoftheparticlealongtheXdirection,youcanpredictonlytheprobabilityoftheoutcome.It’llbeeitherUPorDOWN.ThesameholdstrueifyouweretomeasurethespinintheYdirection(theup-downdirectiononthispage)ortheZdirection(anaxisgoinginandoutofthispage),orinanyarbitrarydirection.

ThisisalsothecaseifyouweretomeasureonlythespinofparticleBinanyarbitrarilychosendirection.There’sabsolutelynowayofpredictingwithcertaintytheresultofthemeasurement.

NowcomesthepartthatbotheredEinstein.AandBareentangled.So,ifyouweretomeasureA’sspinintheXdirection,andfindittobeUP,thequantumformalismtellsyouwithabsolutecertaintythatBwillhaveaspinofDOWNintheXdirection.Youdon’thavetomeasureBtoknowittobeso,butifyoudothemeasurement,itwillbeso.IfAismeasuredfirst,thenthefateofB’sspinissealed,andviceversa,aslongasyoumeasurethespinsofboth

particlesinthesamedirection,sayalongtheX-axis.It’sasifwhatwedidatthelocationofparticleAinstantlyinfluencedparticleB—aformofapparentnonlocality.

TheEPRargumentexplicitlyassumedlocality,makingsuchinfluencesimpossible.Withthisassumption,EPRcouldmakeanargumentfortheexistenceoftherealityofthespinofparticleB:“If,withoutinanywaydisturbingasystem,wecanpredictwithcertainty(i.e.,withprobabilityequaltounity)thevalueofaphysicalquantity,thenthereexistsanelementofphysicalrealitycorrespondingtothisphysicalquantity”[italicsinoriginal].

That’sexactlywhatthemeasurementofparticleAachieves.Iftheworldislocal,thenwhatwedoatthelocationofparticleAcannotdisturbparticleB.YetwecannowinstantlypredictwithcertaintythevalueofthespinofparticleB,nomatterhowfarawayBisfromA.SoparticleBmusthavehadthatvaluebeforethemeasurementatA.Andifaparticlehasapropertywhosevaluedoesnotdependonameasurement,thenit’spossibletohaveavariableinthetheorythatcapturesthatproperty.Youcanseewherethisisgoing.Allquantummechanicshasisawavefunctionthattellsyoutheprobabilityofoutcomesofmeasurements;itdoesnothavesuchhiddenvariables(say,forthepositionofaparticle;thefactthatavariableforthepositionofaparticlewouldbecalledhiddenwas“apieceofhistoricalsilliness,”wroteBell).

TheEPRpapertriumphantlyconcludedthat“thewavefunctiondoesnotprovideacompletedescriptionofphysicalreality.”Theydidnotaddresswhatacompletetheorywouldlooklikebutsaid,“Webelieve,however,thatsuchatheoryispossible.”

Anysuchtheorythataugmentsthewavefunctionwithadditionalvariablescametobecalledahiddenvariabletheory.TheironyoftheEPRpaperwasthatafewyearsearlier,in1932,JohnvonNeumannhadostensiblyprovedthatanytheorythatcouldreplicatetheexperimentalsuccessesofquantumtheorycouldnothavehiddenvariables.ThosewhosworebytheCopenhagentakeonthequantumworldwereonlytoohappytoacceptvonNeumann’sproof.

Somuchsothatonephilosopher’sprotestationswerelosttotheworld.GreteHermannwasaGermanphilosopher,and“thefirstandonlyfemaledoctoralstudent”ofEmmyNoether,aformidablemathematicianwhoseworkunderpinsmuchofmodernphysics.Hermannstraddledtheworldsofphilosophyandmathematicswithease.In1935,shepublishedapaperinaGermanjournalinwhichsheshowedthatvonNeumann’sproofwasincorrect.“AthoroughexaminationoftheproofofvonNeumannreveals...thatinhisargumentation

hemakesanassumptionwhichisequivalenttothestatementhewantstoprove,”shewrote.“Therefore,theproofiscircular.”

EvenEinstein,around1938,isreportedtohavesaidoftheassumptionHermannidentified:“Whyshouldwebelieveinthat?”Einstein,ofcourse,wasincreasinglybeingthoughtofasacurmudgeonlyoldmanwhowasholdingontohispreciousideasofrealism,locality,andattimesevendeterminism.Though,tobefairtoEinstein,thelackofdeterminismdidnotoverlybotherhim.Theoverusedquoteofhisinpopularculture,that“Goddoesnotplaydicewiththeworld,”misrepresentshisstandontheissue.Hecertainlydid,duringtheearly1920s,expressconcernsabouttheindeterminatenatureofthequantumworld,sayingthathefoundtheidea“intolerable,”andifitweretrue,he“wouldratherbeacobbler,orevenanemployeeofagaminghouse,thanaphysicist.”Butasquantummechanicsmatured,Einsteinbackedofffromhisdisavowalofindeterminism.Itwasanaspectofrealityhewaswillingtoaccept.Notsowithanti-realismandnonlocality.Inanycase,itwaseasyfortheyoungercrowdtobedismissiveofEinstein’sviewsashegrewolder.

ThereasonswhyHermann’sworknevergainedwidespreadattentionarelessclear.PublishinginanobscureGermanphilosophyjournaldidn’thelp.Butthat’snottheentireexplanation,sinceHeisenbergandhiscolleagueswereawareofherwork.Maybe,swayedbytheirownideas,theyoverlookedtheimplicationsofHermann’sclaims.Politicalaffiliationssupposedlyplayedapart.Ormaybeitwasthesexismofthetime,arguesphilosopherPatriciaShipley,butadds,“Ifthathadsomethingtodowithit,Idon’tthinkitwastheprimaryreason,itcouldhavebeenasecondaryreason.”

ItwasDavidBohmwho,in1952,ayearafterhereworkedEinstein’sEPRargumentintoasimplerthoughtexperiment,implicitlyunderminedvonNeumann’sproofbyconstructingahiddenvariabletheory.Decadeslater,JohnBellwouldsay,“In1952,Isawtheimpossibledone,”referringtoBohm’sformulationthatwentagainstvonNeumann’simpossibilityproof.

InaninterviewwithOmnimagazinein1988,Bellwasscathing:“ThevonNeumannproof,ifyouactuallycometogripswithit,fallsapartinyourhands!Thereisnothingtoit.It’snotjustflawed,it’ssilly.Ifyoulookattheassumptionsmade,itdoesnotholdupforamoment.It’stheworkofamathematician,andhemakesassumptionsthathaveamathematicalsymmetrytothem.Whenyoutranslatethemintotermsofphysicaldisposition,they’renonsense...TheproofofvonNeumannisnotmerelyfalsebutfoolish.”

UnimpressedbyvonNeumann’sproof,butinspiredbyBohmandEinstein,BellsawawaytoturntheEPRargumentintoatestofquantummechanics.The

BellsawawaytoturntheEPRargumentintoatestofquantummechanics.Theresultwashis1964paper,withhiseponymoustheorem.

Here’sonedescriptionofanexperimentbasedonBell’stheorem.It’saslightvariationofBohm’sEPRthoughtexperimentbutiscloserinspirittowhatexperimentalistslikeAspectactuallydo.Itinvolvesphotonsoflightandapropertycalledpolarization.

Wesawearlierthatlightisanelectromagneticwave,soit’sgotanoscillatingelectricfieldandanoscillatingmagneticfield.Polarizationhastodowiththeplaneinwhichtheelectricfieldisvibratingrelativetothedirectioninwhichthelightistraveling.Forexample,iflightismovingalongtheXdirection(again,lefttorightonthepage),thentheelectricfieldcouldbeoscillatingintheX-Yplane(up-down).Ifso,thelightissaidtobeverticallypolarized.IftheelectricfieldisvibratingintheX-Zplane(in-out),thelightishorizontallypolarized.Butthosearenottheonlyallowedvalues:theelectricfieldcanvibrateinanyplanethat’satanarbitraryangletothevertical—thisistheso-calledangleofpolarization.Also,theangleofpolarizationcanholdsteadyasthelighttravels,oritcankeepchanging.Individualphotonsoflight,whicharepulsesof

travels,oritcankeepchanging.Individualphotonsoflight,whicharepulsesofelectromagneticwaves,arealsopolarized.

Imaginenowasourcethatspitsouttwophotonsentangledintheirpolarizationthatstartmovingawayfromeachothertowardtwoobservers,AliceandBob.Alicedoesoneoftwomeasurementsonthephoton:shecheckstoseewhetherthephotonispolarizedeitherintheAdirectionorintheBdirection.Quantummechanicstellsusthatforeachtypeofmeasurement,she’llgeteitheraYESoraNOforananswer.Similarly,Bobcheckstoseeifhisphotonispolarizedinoneoftwodirectionsofhischoosing,say,CorD.Theyrepeatthisformany,manypairsofphotonsthatcomefromthesource.

Crucially,foreachphotonpair,AliceandBobmaketheirmeasurementsindependentlyofeachother:neitherknowsthedirectiontheotherischoosingforthemeasurement.

Now,ifthephotonsthatleavethesourcearenotentangled,theoutcomesofmeasurementsdonebyAlicewillhavenocorrelationwiththeoutcomesofmeasurementsdonebyBob,beyondwhat’sexpectedbyrandomchance.

Butweknowthatthephotonsareentangledandquantummechanicssaystheyaredescribedbythesamewavefunction(asfarastheirpolarizationisconcerned).So,foragivenentangledpairofphotons,ifAliceweretomeasureherphoton’spolarizationinsomedirectionandgetananswerofYES,thenwecanpredictwithcertaintythatifBobmeasureshisphotoninthesamedirection,he’llgetananswerofNO,andviceversa.

Here’swhereBell’stheoremcomesin.FormeasurementsinwhichthepolarizationdirectionsusedbyAliceandBobarenotthesame,BellcalculatedtheamountofcorrelationthatonecanexpectifEinsteinwascorrectinhisassertionthattheremustbeahiddenvariabletheorythatunderpinsquantummechanicsandalsoobeysthelawsoflocality.ThecorrelationisameasureofhowmanytimesAliceandBobwouldhavegotcontradictoryanswers.

BellshowedthatifEinsteiniscorrect,thecorrelationhastobelessthanorequaltoacertainamount(henceit’scalledtheBellinequalitytest).Morespecifically,Bellshowedthatifquantummechanicsiscorrectandthemeasurementofaphoton’spolarizationbyAlicedoesinstantlyinfluencethestateofBob’sphoton(andviceversa),thentheamountofcorrelationshouldexceedthatthreshold,thusviolatingtheinequality.Ifso,thequantumworldwouldbemanifestlynonlocal.

SoonafterBellpublishedhistheorem,experimentalistsstartedtestingtheinequality.Thesewerenotvariationsofthedouble-slitexperiment,buttheirfindingswouldhavetremendousimportforunderstandingthedoubleslit’sessentialmystery.AmongtheforerunnerswhodidsuchBellexperimentswere,

essentialmystery.AmongtheforerunnerswhodidsuchBellexperimentswere,mostnotably,StuartFreedmanandJohnClauserattheUniversityofCalifornia,Berkeley,RichardHoltandFrancisPipkinatHarvardUniversity,andEdwardFryandRandallThompsonatTexasA&MUniversity.By1976,atotalofsevensuchexperimentshadbeendone,andwhiletwooftheseexperimentsdisagreedwithquantummechanics(inthattheydidnotviolatetheBellinequality),theconsensuswasthatquantummechanicswascorrect.Theworld,atitsmostfundamental,seemednonlocal.

ItwasthenthatayoungAspectcameintothepicture.HerealizedthattheidealexperimentasimaginedbyBellhadyettobedoneusingsinglepairsofentangledphotonsinsuchawaythatthemeasurementsoneachpairofphotonswerespace-likeseparated(sothattherewasnowaythatnaturecould,throughsomeunknownmechanism,letAliceandBobknowofeachother’s

someunknownmechanism,letAliceandBobknowofeachother’smeasurementsettingsanyfasterthanthespeedoflight).Thismeantchoosingthesettingsforthemeasurementdevices—thedirectioninwhichtomeasurethepolarization(AorBforAlice,CorDforBob)—ontheflyateitherend.Thesettings,literally,hadtobechosenwhilethephotonswereinflightfromthesourcetothedetectors.

Theotherchallengewas“tobuildasourceofentangledphotonswhichwouldbeabletodeliverenoughpairsofentangledphotonspersecond,”Aspecttoldme.“Attheend,anyexperimentboilsdowntothesignal-to-noiseratio.”

Asmentionedearlier,Aspectsucceededinbuildingsuchasource(itwasthetechnologyhe’dlateruseforthesinglephotondouble-slitexperiment).“Ittookmefiveyears.By1980,Ihadafantasticsourceofentangledphotons.Itwasbyfarthebestsourceofentangledphotonsintheworld,”hesaid.“WhatClauserwoulddoinoneday,whatFrywoulddoinonehour,Icoulddoinoneminute.”

Withthemassofstatisticsandthespace-likeseparationbetweenAlice’sandBob’smeasurements,Aspectwasabletoshow—unequivocally—thattheBellinequalityisviolatedbyquantummechanics.Thereremainedsubtle,nitpickywaysinwhichAlice’smeasurementscouldinfluenceBob’sdeviceandviceversa,butthosewereforthepurists.Formostphysicists,Aspect’sexperimenthadsealedthedeal.TheexperimentmadeAspectastarofthelecturecircuit(andbroughthimintouchwithFeynman).“ItallowedmetopropagatetheideathatBell’stheoremwasreallysomethingveryimportant,andthatyes,Bell’sinequalitiesareviolated,sothereissomethinginentanglementwhichgoesbeyondallourideasofhowtheworldworks,”Aspectsaid.

Thatsomethingisnonlocality.ThiswasasetbackforEinstein’shopeforalocal,realistichiddenvariabletheory.Heneverlivedtoseetheresultsoftheseexperiments,andonecanonlywonderhowhe’dreacttothegrowingrealizationamongmanyfollowersofstandardquantummechanicsthatrealityisnonlocal.He’dwritetoMaxBorninaletterdatedMarch3,1947,“Icannotseriouslybelieveinit[quantumtheory]becausethetheorycannotbereconciledwiththeideathatphysicsshouldrepresentarealityintimeandspace,freefromspookyactionsatadistance.”Einsteindiedin1955.

—UnderthegazeofthetallNyamwezifigures,inhisapartmentoverlookingoneofNewYork’sgreenestsquares,TimMaudlinexplainedwhyentanglementandnonlocalitymakethedouble-slitexperimentevenmoreintriguingthanmere

wave-particleduality.Withhishandshemimedthewavefunctionsplittingintotwoparts,onegoingthroughoneslitandtheotherthroughthesecondslit.Thesetwoparts,astheyspreadoutfromeachslit,evolveindependentlyandeventuallyinterfere.Tocalculatetheprobabilityoffindingtheparticleatsomelocationawayfromthetwoslits,youhavetotakeintoaccountalinearsuperpositionofthesetwowavefunctions.Saythecombinedwavefunctionhitsaphotographicplate.Theparticleappearssomewhereonthatplate:itgetslocalized.Butatalltheotherlocationsonthephotographicplatewheretheparticlehadanonzeroprobabilityofexisting,nothinghappens.Thesearesimultaneouseventsandnonlocal.

“Howpuzzlingisthat?”saidMaudlin.Dothisforparticleafterparticle,andaninterferencepatternemergesonthe

photographicplate.Thestandardanalysisofthedouble-slitexperimentusuallyhighlightstheappearanceofthispatternasemblematicofthemysteryofquantummechanics.Inonesense,itundoubtedlyis.Eachspotthattheparticlemakesonaphotographicplateisindicativeofbothsomethingdelocalized—thewavefunction?—goingthroughbothslits,andthenonlocaleventsthatresultintheparticleseeminglyappearingatonelocationonthephotographicplate,andsimultaneouslydisappearingfromeverywhereelse.

ButtoMaudlin,themysteryofthedoubleslitisevenmorepronouncedwhenonetriestodetectwhichslittheparticlegoesthrough.Theinterferencepatterngoesaway.Butwhy?It’sbecausethesystembeingusedtodetecttheparticleasitgoesthroughthedoubleslitbecomesentangledwiththeparticle.“Schrödingersaidthatwhatwasreallynewaboutquantummechanicswasentanglement,”saidMaudlin.“Andsofromthatpointofview,thereally[surprising]quantummechanicaleffectisthedisappearanceoftheinterference.”

Thedouble-slitexperimentdoesn’tmerelyembodywave-particleduality,the“centralmystery,”asFeynmansaid;itincorporatesentanglementtoo.Oncephysicistsbeganappreciatingthis,itmadepossibleanewwaveofdouble-slitexperiments,eachprobingdeeperintothemysteriesofthequantumworld.Itmadepossiblethedelayed-choicequantumeraserexperiment.

E

5

TOERASEORNOTTOERASE

MountaintopExperimentsTakeUstotheEdge

Theseexperimentsareamagnificentaffronttoourconventionalnotionsofspaceandtime.Somethingthattakesplacelongafterandfarawayfromsomethingelseneverthelessisvitaltoourdescriptionofthatsomethingelse.Byanyclassical—commonsense—reckoning,that’s,well,crazy.Ofcourse,that’sthepoint:classicalreckoningisthewrongkindofreckoningtouseinaquantumuniverse.

—BrianGreene

xperimentalquantumphysicistspreferlabbenchesandtightlycontrolledenvironments.Soit’shighlyunusualthatsomeofthemostintriguing

experimentsinquantummechanicshavebeendoneatopmountainsintheCanaryIslands,anarchipelagojustoffthecoastofnorthwesternAfrica.Onaclearday,fromthesummitofRoquedelosMuchachos,the2,400-meter-highmountainonthesmallislandofLaPalma,onecanseestraightacrossthebluewatersoftheAtlanticOceantothetopsofthevolcanicmountainsonTenerife,thearchipelago’sbiggestisland,about144kilometersaway.Theexperiments,however,havetobedoneafterthesunhassetandthemoonisstillbelowthehorizon,withonlytheMilkyWayspreadacrossthenightsky.Theforebodingdarknessisessential,fortheexperimentsinvolvesendingsinglephotonstowardTenerife’sMountTeide,intheshadowofwhichatelescopehasitssightstrainedonthephotonsourceatLaPalma.

ThedrivingforcebehindtheseexperimentsistheAustrianphysicistAntonZeilinger.HeandAlainAspectarecompatriots.Bothforgedtheirreputationsasclear-thinkingexperimentalistsataboutthesametime(andwererecognizedfor

clear-thinkingexperimentalistsataboutthesametime(andwererecognizedfortheireffortsin2010,whentheywon,alongwithJohnClauser,theWolfPrizeinPhysics).ButZeilingerandAspectcouldn’tbefurtherapartwhenitcomestointerpretingquantumphysics.Aspect,aswesawinthepreviouschapter,leanstowardbeingarealistinthemoldofEinstein.ZeilingertakesafterBohr.

“Allquantummechanicsgivesusisprobabilitydistributionsforpossiblemeasurementresults,”hetoldme.TheirtestsofBell’sinequality(Zeilinger’steamdidmoresophisticatedversionsofAspect’spioneeringexperiment)haveshownthatthereisnolocalhiddenrealitythatquantummechanicsisfailingtocapture.Theprobabilitiesoneobserves,intheCopenhagenview,don’tseemtobetheoutcomeoflackofinformationthewayprobabilitiesofoutcomesinclassicalphysicsof,say,athrowofdicearetheresultofincompleteinformation.TheCopenhagenfollowersregardprobabilitiesasintrinsictoquantummechanics.

“Andthatisamazing,”saidZeilingerwhenImethimathisofficeonBoltzmanngasseinVienna,Austria,afewdaysafterImetAspectinParis.Zeilinger’sofficeisashortwalkfromtheDonaukanal,awaterwayoftheriverDanube.Theregionreeksofhistory.Thereare,ofcourse,thestreetnames:BoltzmanngasseforLudwigBoltzmann,astalwartoflate-nineteenth-centuryphysicsandakeyfigurebehindthedevelopmentofthekinetictheoryofgasesandstatisticalmechanics,bothofwhichleanedheavilyonprobabilitytheory.AfewdoorsawayfromZeilinger’sbuildingistheErwinSchrödingerInternationalInstituteforMathematicsandPhysics,which,beforeitmovedtoBoltzmanngassein1996,washousedinSchrödinger’shomeafewhundredmetersawayonPasteurgasse,astreetnamedafterLouisPasteur.Iftheinfluenceofscience,especiallyphysicsandmathematics,isoverwhelming,therearetheSigmundFreudandtheStraussmuseums,eachaboutaten-minutewalkaway.

Andsoitwasthatinabuildingonastreetnamedafteramanwhoputprobabilitiesintoclassicalphysics,Zeilingerexpressedwondermentatprobability’sroleinquantumphysics.“Howcanthatbe?Howcanwejusthaveprobabilitydistributionsandnothingbehindit?”

Thenintheverynextbreath,hesaid,“Theprobabilitiesaretherealitywehave.Thereisnothingbehindit.Theprobabilityisnotaboutahiddenreality...fullstop.”Headdedhe’sprobablya“non-realist”butsaidhehateslabels.“Theyaresillycategories,”hesaid.

ButdespitegoingagainstEinstein’sviews,Zeilingerprofessedenormousrespectforhisimpactonquantumphysics.“SometimespeoplebelittleEinstein’s

contribution,whichiswrong,”saidZeilinger.Einstein,moreoftenthannot,isrecalledasraisingconcernsaboutaspectsofquantummechanicsthatdidnotmake,well,classicalsense.ButEinsteindidmorethanthat.“Hepointedthefingeratthesethingsnotbecauseassomepeoplesayhedidnotunderstandquantummechanics,”saidZeilinger,butbecauseheunderstooditverywell.ZeilingermusedaboutwhatEinsteinwouldhavemadeoftheirexperiments.“I’dgivealottohearhiscommentsaboutthissituation,”hesaid.Withalightlaugh,hesaidhe’daskEinstein,“Youknowourresults,whatdoyousay?”

Attheleast,Einsteinwouldlikelyhavebeenenthralledbytheexperimentsdoneonmountaintops,givenhisownpenchantforhikingintheSwissAlps(in1913,hecrossedthenearly1,800-meter-highMalojaPassonfoot,withMarieCurieandherdaughtersforcompany).Onemountaintopexperiment,aparticularlyintricateandinvolvedvariantofthedouble-slitexperimentdonebyZeilingerandhisteam,combinedthetwoelementsofquantummechanicsthatmadeEinsteininsistonthetheory’sincompleteness:wave-particledualityandnonlocality.Theoriginsofthislineofinquirylieinathoughtexperimentdreamtupbyaphysicistwhocametobecalledthe“QuantumCowboy,”forhispioneeringresearchonthenatureofrealityandbeefcattleproduction.

—DuringtheAmericanCivilWar,aconfederateofficernamedRobertP.SaltercultivatedcottononafarmthatliesmidwaybetweenHoustonandDallas.Heboughtgunswiththecottonhegrew.Today,MarlanScullystudiessustainablefarmingonpartsofthathistoricfarm.“ThemysteryisnotthatI’minterestedinfarming,butthatI’minterestedinquantumphysics”hasbeenScully’sresponsetoquestionsaboutwhyaquantumphysicisttookupfarming.ScullygrewupinruralWyomingandmarriedintoafarmingfamily.

HewenttoYaletodohisgraduatestudies,wherehepursuedthegreatexperimentalistWillisLambnearlyeveryday.“AdumbkidfromWyoming,Ididn’tknowthattheNobelPrizephysicistatYalewasn’tthereforme.”Lambalwaysobligedwithhistime.AfterhisPhD,ScullycontinuedasaninstructoratYale.WithintwoyearshemovedtoMIT,andthensoonaftertotheUniversityofArizona.AdecadelaterhemovedtotheUniversityofNewMexico,andwhenhewasthere,hecollaboratedwithKaiDrühl,apostdocbasedinMunich,Germany,tocomeupwithoneofthemostfamousthoughtexperimentsinquantumphysics:thequantumeraser.

The“quantumeraserisqualitatively,conceptually,intellectually,muchdeeperthantheYoung[double-slit]experiment,”Scullytoldmeduringaphone

deeperthantheYoung[double-slit]experiment,”Scullytoldmeduringaphoneconversation.Still,atitscore,itisyetanothertypeofdouble-slitexperiment,albeitaverysophisticatedone.

ScullyandDrühltargetedakeyaspectofthedebatebetweenEinsteinandBohr:whetherornotexperimentsthemselvesdisturbquantumsystemsinwaysthatenforcecomplementarity.Intheearlydaysoftheirdeliberations,Bohrhadarguedthattheuncertaintyprinciplewouldpreventusfromseeingthewavenatureandtheparticlenatureofrealitysimultaneously.Thesewerecomplementaryaspectsthatwereforeverseparatedbytheclumsinessofourclassicalmeasurements,andtheuncertaintyprinciplewastheenforcer.ButasAspectshowedwithhisimplementationofWheeler’sdelayed-choiceexperiment,evenwhenyoucouldnotpointthefingeratdisturbancescausedbythemeasuringapparatusandhenceattheuncertaintyprinciple,complementaritystillreigned.Itwasadeeperprinciplethananyonehadrealized.ScullyandDrühlpushedtheargumentmuchfurther.

Theyimaginedcollectinginformationaboutwhichslitaparticlegoesthroughwithoutdisturbingtheparticle.Theparticlecontinuestodowhatitnormallydoes,andyetsomehow,itleavesbehindinformationaboutthepathittakesthroughthedoubleslit.Accordingtoquantummechanics,themerepresenceofsuchinformationshoulddestroytheinterferencepattern.Asifthatisn’tsurprisingenough,ScullyandDrühlthenaskedadeeperquestion:Whatifthisinformationiserased?Willtheinterferencepatterncomeback?

Withtheirthoughtexperiment,theduowastryingtorefinethenotionofmeasurementinquantumphysics.Inthe1930s,JohnvonNeumanndevelopedtherigorousmathematicalformalismforquantummechanics(intheverybookinwhichhesupposedlyprovedthattherecanbenohiddenvariabletheories).Thisformalismemergedfromaxiomsthatgavemeasurementscenterstage:measurementscausedawavefunctiontocollapse.Buttherewasnoprecisedefinitionofwhatconstitutesameasurement.Bohr,forexample,merelydivideduptheworldintothebigandsmall,andmeasurementapparatuseswere“big,”whilethethingstheyweremeasuringwere“small.”Theboundarybetweentheclassicalandthequantumwasentirelyunclear—nothingintheformalismsuggestedwheresuchaboundarymightlie.

Yet,thepracticaluseofthetheoryimpliedsuchaboundary.Aquantumsystem,describedbyitswavefunction,evolvesaccordingtotheSchrödingerequationandthensuddenly,uponmeasurement,thewavefunctioncollapses.Theprocessofcollapsedoesnotfollowthesamelawsastheonesgoverningtheevolutionofthewavefunction.Infact,thereisnolaw,sotospeak,thatgoverns

evolutionofthewavefunction.Infact,thereisnolaw,sotospeak,thatgovernscollapse.It’ssomethingadhoc,attributedtomeasurement.Soaparticlethat,untilthemeasurement,wasinasuperpositionofmultiplestatesisreducedtobeinginjustoneofthemanypossiblestates.Whatisitthatdetermineswhenandhowthiscollapsehappens?

Thisquestionwaspushedto,somewouldsay,itslogicalconclusionbyEugeneWigner,aNobelPrize–winningphysicistandvonNeumann’scontemporaryatPrincetonUniversityintheearlytomid-1930s.Wigner,afteracarefulanalysisofvonNeumann’sformalism,concludedthatthelawsofquantummechanicsdidnotdrawalinebetweenthequantumandtheclassical.Everything—thequantumsystem,themeasuringapparatus,everything—shouldevolveaccordingtothesamelaws.Theonlything,hereasoned,thatcouldberesponsibleforthecollapseofthewavefunctionwasconsciousness.Theactofperceptionbyaconsciousobserver,Wignerargued,isthenailinthecoffinforthewavefunction.In1961,hewrote:“Whentheprovinceofphysicaltheorywasextendedtoencompassmicroscopicphenomena,throughthecreationofquantummechanics,theconceptofconsciousnesscametotheforeagain:itwasnotpossibletoformulatethelawsofquantummechanicsinafullyconsistentwaywithoutreferencetotheconsciousness.”Butby1970,Wignerchangedhismind,doubtinghisownclaimsofconsciousnessplayingaroleincausingcollapse.

VeryfewphysiciststodayputstockinWigner’sideas.ScullyandDrühltooweren’tconcernedaboutconsciousnessanditsrole;theywantedasharperunderstandingofmeasurementandthenatureofcollapse.Theyaskedwhethermeasurementcoulditselfbesomethingquantummechanical.Ifso,themeasurementdevicewouldalsoevolveaccordingtotheSchrödingerequation.Itswavefunctionwouldnotcollapse,andsocouldbemadetoreverseitsevolutioninamannerthatundidthemeasurement.“Weproposeandanalyzeanexperimentsuchthatthepresenceofinformationaccessibletoanobserverandthesubsequent‘eraser’ofthisinformationshouldqualitativelychangetheoutcomeofourexperiment.”

Theydesignedtheirthoughtexperimenttoshowthatonecouldinprincipleacquirewhich-wayinformationaboutaphoton’spaththroughadoubleslitbyusinganentangledpartnerphoton.Aslongasthiswhich-wayinformation(orthewelcher-weginformation,inGerman)remainsaccessibletoanobserver,nointerferencecanbedetectedinthepatternsmadebythephotonsgoingthroughthedoubleslit.Butifthisinformationweretobeerased,ScullyandDrühl

showedthatonewouldobserveinterference.Theirpaperonthequantumeraserwaspublishedin1982.

By1995,Zeilingerandcolleaguescarriedoutaversionofthequantumeraserexperiment,asdidafewotherteams,butnoneoftheexperimentswerequitetheidealgedankenexperimentthatScullyandDrühlwereafter.ScullyeventuallyjoinedhandswithYoon-HoKimoftheUniversityofMarylandinBaltimore,andhiscolleagues,andinJanuary2000theypublishedtheresultsofanexperimentthatwasclosestinspirittotheoriginalidea.

Theexperimentusesanatomthatcanbemadetoemitentangledphotonswhenhitwithalaserpulse.Imaginetwosuchatoms,AandB.Eachatomemitsapairofphotons.Theatomsarearrangedsuchthatoneoftheentangledpairofphotonsgoestowardascreen.Let’scallitthe“system”photon.BothAandBcanemitasystemphoton.Thetwoatomsareplacedsidebyside,suchthattheirsystemphotonsappeartobecomingthroughadoubleslit.Sothedoubleslitinthisscenarioisvirtual;allwehavearethetwoatomssendingoutsystemphotons.Ifallwehadweresystemphotonsandwehadnootherinformation(soignoringtheentangledphotonsfornow),thenthesystemphotonswouldcreateaninterferencepatternonthescreen.That’sbecauseanysystemphotonthatlandsonthescreencouldhavecomefromeitheratomAoratomB,orfromoneortheotherslit(assumingwehavenowayoftellingwhichatomthephotoncamefrom).

Butthat’snotallwehave.Foreachsystemphotonthatanatomemits,itemitsanotherphotonintheoppositedirection;let’scallitthe“environment”photon,whichisentangledwithitssystemphoton.Theenvironmentphotoncontainsinformationaboutwhichatom(oranalogously,whichslit)thesystemphotoncamefrom.Thekeynowistoeitherpreserveordestroythisinformation,andseewhathappenswiththesystemphotonthatlandsonthescreen.Doesitactlikeawaveoraparticle?

TakeapairofphotonsemittedbyatomA.Thesystemphotongoestowardtherightofthescreen,whereit’srecordedonaphotographicplate.Theenvironmentphotonheadslefttowardasetofbeamsplittersdesignedtoeitherpreserveorerasethewhich-wayinformation.ItfirstencountersbeamsplitterBSA.AtBSA,thephotoncanbeeithertransmittedtoadetectorD3orreflectedtowardanotherbeamsplitter,BS,whereuponitcanbereflectedtoD1ortransmittedtoD2.Similarly,anenvironmentphotonfromatomBwillendupatD1orD2orD4.

It’sclearthatD3willclickonlyiftheenvironmentphotoncamefromatom(slit)A.SoaclickatD3constituteswhich-wayinformationaboutitspartnersystemphoton(notethatthisinformationisobtainedwithoutphysically

systemphoton(notethatthisinformationisobtainedwithoutphysicallydisturbingthesystemphotoninanyway).Similarly,ifD4clicks,weknowthecorrespondingsystemphotoncamefromatom(slit)B.

However,onceanenvironmentphotongetsreflectedateitherBSAorBSBandthengoespastthecentralbeamsplitterBSandhitseitherdetectorD1orD2,it’simpossibletotellwhetheritcamefromatom(slit)AorB,becauseenvironmentphotonsfrombothatoms(slits)cantriggereitherD1orD2.Thewhich-wayinformationforthecorrespondingsystemphotoniserased.

Nowimaginethatyouhavecollectedthepatternmadebyalargesetofsystemphotons,andtheclicksmadebytheenvironmentphotons.IfyouconsideronlythoseenvironmentphotonsthatendedupatD3andD4,andlookedatthepatternthatthecorrespondingsystemphotonsmadeonthephotographicplate,youdon’tseeaninterferencepattern.That’sbecauseforeachofthosephotons,weknowwhichslititcamethrough.Wegetparticle-likebehavior.

ButifyoulookatthepatternmadeonlybythosesystemphotonswhosecorrespondingenvironmentphotonsweredetectedatD1,somethingstrangehappens:youseeinterferencefringes.ThesamegoesforenvironmentphotonsdetectedatD2.ThedetectionatD1orD2haserasedthewhich-wayinformation.Atthephotographicplate,there’snowaytotellwhetherthecorrespondingsystemphotonscamefromtheleftortherightslit.Thepathsbecomeindistinguishable,settingthestageforsuperpositionandforinterference.

Oneofthemostastonishingfactsaboutthequantumeraserexperimentisthattheactoferasingthewhich-wayinformationcanbedelayedforanarbitrarylengthoftime.Saythesystemphotonsweredetectedalmostimmediatelyonthescreenandtheirpositionsrecorded.Theenvironmentphotons,however,wereallowedtotravel,maybeforkilometers,beforetheywentthroughthevariousbeamsplittersandonwardtothedetectors.Ifyouanalyzedthepatternsmadebyallthesystemphotonswhilealltheenvironmentphotonswerestillinflight,youwouldnotseeanyinterference(because,inprinciple,youstillhaveaccesstowhich-wayinformation).

Butoncetheenvironmentphotonsencounterthebeamsplittersandhitthefinaldetectors,andifyouthenselectivelyanalyzethemeasurementsalreadymadeofthesystemphotons,youwillseesomethingentirelydifferent.PickonlythoseenvironmentphotonsthatreachD3orD4andchecktheircorrespondingsystemphotons—youwillnotseeaninterferencepattern.ButpickthosesystemphotonswhosecorrespondingenvironmentphotonscausedeitherD1orD2to

click—andhenceerasedthewhich-wayinformation—andyouwillseeaninterferencepattern.Wasthepatternalwaysthere?Ordiditreappear?

Iftheideaofwaitingandwaitingbeforechoosingwhattodowiththeenvironmentphotonsseemsliketheoreticalfantasy,noonebotheredtotellsomephysicistsinAustria.AlittlemorethanadecadeafterScullyandYoon-HoKimdidtheirexperiment,ZeilingerandcolleagueswerereadytotestsuchfantasiesacrossthemountaintopsonLaPalmaandTenerife.

—Thedelayed-choicequantumeraserexperimentdonebyZeilinger’steamisamongthemostsophisticatedofallthevariationsofthedouble-slitexperiment.RupertUrsin,onceastudentofZeilinger’s,nowaseniormemberoftheteam,recalledthetravailsoftheseven-hourflightfromViennatotheCanaries.Theywerecarryingalmosttwo-thirdsofatonofequipment.ForEuropeansusedtoborderlesstravel,gettingtheequipmentpastcustomsinLaPalmawasn’ttrivial.“Believeitornot,theCanariesareoutsideoftheEuropeanUnion,”Ursintoldme,soundingsomewhatmiffed.Actually,theislandsareanautonomouspartofSpainbutstillrequirecustomschecksfortaxreasons.

TheteamhadalogisticscompanylugtheequipmentuptothesummitofRoquedelosMuchachos,wherethescientistsproceededtosetupanextremelysensitiveexperiment.Theybeganworkingcheektojowl.“Youbetterhavegoodfriendsbeforeyoustart[suchan]experiment,becauseyou’llhatethemwhenyoufinishtheexperiment,”Ursinsaid.

Theexperiment,inprinciple,ismuchthesameastheonedescribedintheprevioussection.Butthepracticaldetailsdifferenormously.Theexperimentwasspreadovertwophysicallocations:oneatopthemountaininLaPalmaandtheothernearMountTeideinTenerife,144kilometersawayasthecrow—orinthiscase,thephoton—flies.MostoftheequipmentwasatLaPalma,includingasourceofentangledphotons.

Inthepreviousexperiment,twoatomswerepositionedsuchthatwhenoneoftheatomsemittedapairofentangledphotons,thesystemphotonbehavedasifitcamethroughadoubleslit,andtheenvironmentphotonwenttheotherway,carryinginformationaboutwhich(virtual)slitthesystemphotoncamethrough.IntheCanaryIslandsexperiment,thereisonlyonesourceofentangledphotons.Itemitsasystemphotonandanenvironmentphoton.ThesystemphotonissentintoaMach-ZehnderinterferometeratLaPalmaandisdetectedimmediatelyateitherdetectorD1ordetectorD2.Thefirstbeamsplitterintheinterferometeris

somewhatdifferentfromthebeamsplitterswehaveseensofar;insteadofrandomlysendingaphotononewayortheother,thisso-calledpolarizingbeamsplitter(PBS)sendsthephotononewayifit’s,say,horizontallypolarized,andtheotherwayifit’spolarizedvertically(thereareexperimentalsubtletiesaboutwhatisdonetothephotonafteritcrossesthePBS,butwecanleavethataside).So,ifyouknowthepolarizationofthephoton,youknowwhichpathittakesthroughtheinterferometer.

Theentangledenvironmentphoton,however,issenttowardatelescopeatTenerife.Thephotonsareentangledintheirpolarizationstates.ThepolarizationoftheenvironmentphotoncanbeusedtotellwhichpaththesystemphotontakesthroughtheinterferometeratLaPalma.Orthepolarizationoftheenvironmentphotoncanbescrambled,whichistantamounttoerasingthewhich-wayinformationaboutthecorrespondingsystemphoton.Thisisthequantumeraserpartoftheexperiment.

Thedelayed-choicepartcomesinbecausethedecisiontoeraseornottoeraseismadeonlywhentheenvironmentphotonreachesTenerife—wellafterthepartnersystemphotonhasbeendetectedatLaPalma,andthuswellafterithasostensiblyalreadybehavedlikeawaveoraparticle.

TopreciselycontrolthelengthofthetwoarmsoftheinterferometeratLaPalma,theteamusedthevibrationsofatinypiezoelectriccrystal.Suchdelicatecontrolishardenoughinatemperature-controlledlabinthebasementofauniversitybuilding.OnRoquedelosMuchachos,itwasaphenomenalfeat.Thelaboratorywasessentiallyasteelshippingcontainerthatwasbeingbuffetedbywindsandwassubjecttoconstantday-nighttemperaturefluctuations.“Tostabilizesuchaninterferometerinamountainhut[at]2,500metersaltitudeisnoteasy,”saidUrsin.“Thisisnotaniceenvironment.”

HiscolleagueXiao-SongMa,whowasalsothenastudentofZeilinger’s,recalledhowoncesomeonemerelyopenedthedooroftheshippingcontainerandtheresultingacousticvibrationschangedtheinterferencepatterns.Sowhatdidtheyhavetodotoensurethatthetestbedwasstableandfreeofnoise?“Everything,literallyeverything,”Matoldme.“Eventhebreathofahumanbeingorastampofthefeetinthelabwill...[destroy]theinterference.”

Thenumerousbeachesontheislandssomewhatmadeupforthestressofworkingonthesummits.Theteamwouldworkthroughthenightandgotobedatsunrise,sleepforafewhours,andthenheadtoabeachintheafternoon.IaskedUrsinaboutwhichbeachtheyfrequented.“Allofthem,”hequipped.Theydidprefer,however,twoinTenerife:LasTeresitas,anartificialbeachbuiltofsandbroughtoverfromtheSaharaDesert,withswayingpalmsandcalmwatersmadepossiblebyabreakwater,andcontrastingly,ElBollullo,oneoftheisland’sbestnaturalbeaches.

Buttheyhadtogetbacktothesummitbeforesunsetandstartexperimentingalloveragain.

TransmittingtheenvironmentphotonfromLaPalmaanddetectingitatTenerifewasaseriouschallenge.Theworkofaimingthesourceatthereceivingtelescopehadtobedoneinnearcompletedarkness.Whiletheentanglement

telescopehadtobedoneinnearcompletedarkness.Whiletheentanglementbetweenthesystemandenvironmentphotonscouldsurvivealltheopticalequipment(lenses,mirrors,andthelike),itcouldn’tsurvivemoonlight,letalonesunlight.ThephotonsfromthemoonwouldinteractwiththeenvironmentphotonsastheyflewtoTenerife,causingthemtolosetheirentanglementwiththesystemphotons.Sotheresearchersworkedwithonlystarsforcompanyinanotherwisedarksky.

ToreceivethephotonattheObservatoriodelTeideinTenerife,theteamusedtheEuropeanSpaceAgency’sopticalgroundstation,withits1-metertelescope,ordinarilyusedforcommunicatingwithsatellites.Nearcompletedarknesswasessential.Once,oneofUrsin’scolleaguesstoodnearthesource,smokingacigarette.TheinfraredphotonsfromtheglowingcigaretteatLaPalmacompletelysaturatedthereceiveronTenerife,overwhelmingthesignaloftheloneenvironmentphoton.

Suchsensitivitycouldbeundonebyoneofnature’smostmajesticevents:Saharansandstorms.MassivestormsoffinedustblowingofftheSaharaDesertcanengulftheCanaryIslands,obscuringevennormalvisibility,letalonethekindneededtodosingle-photonexperimentsinthedeadofnight.

Butwhentheairisclear,then,underthecoverofdarkness,thetelescopeatTenerifereceivesthephoton.It’stimenowtoeitherretainthewhich-wayinformationoreraseit.Thedecisiontoeraseornottoeraseisbasedontheoutputofaquantumrandomnumbergenerator.

Ifitoutputsa“0,”theenvironmentphoton’spolarizationisleftuntouchedandthephotonpreservesthewhich-wayinformationaboutitscorrespondingsystemphotonatLaPalma.ThephotonthenpassesthroughapolarizingbeamsplitterandendsupatD3ifhorizontallypolarized,andD4ifverticallypolarized.Becauseofentanglement,weknowthatthecorrespondingsystemphotonwouldhavebeenoppositelypolarizedandthusweknowwhichpathittookatLaPalma.

Butiftherandomnumbergeneratoroutputsa“1,”theenvironmentphoton’spolarizationisscrambled,andthewhich-wayinformationencodedintheenvironmentphotoniserased.Ithasnowa50percentchanceofgoingtoD3anda50percentchanceofgoingtoD4.There’snowaytotellwhethertheenvironmentphotonwashorizontallyorverticallypolarizedandsothere’snowaytotellwhichpaththecorrespondingsystemphotontookatLaPalma.

TheutterlyconfoundingaspectofthisexperimentisthatthemeasurementsatTenerife—erasingthewhich-wayinformationorotherwise—aredonesome0.5milliseconds(aneternityforlight)afterthesystemphotonhasgonethroughtheMach-ZehnderinterferometerandhiteitherdetectorD1orD2atLaPalma.TheeventsatTenerifeandLaPalma,accordingtospecialrelativity,shouldhavenocausalinfluenceoneachother.Quantummechanicsbegstodiffer—ifoneisrelyingontraditionalnotionsofspaceandtime.

Wearenowcomingtotheheartofthisexperiment.Thisintricateversionofthedouble-slitexperimentcombinesallthemysteriousaspectsofquantummechanics:randomness,wave-particleduality,andevenentanglement.

Forthoseenvironmentphotonsthatwereleftuntouched,ifyoulooknowattheclicksmadeatD1orD2bythecorrespondingsubsetofsystemphotonsatLaPalma,you’llfindthattherewasnointerference;theyactedlikeparticles:halfofthemwouldhavegonetoD1andhalftoD2whenthetwoarmsoftheinterferometerwereofequallength(theexperimenterschangedthelengthofoneofthepathsinsmallincrementscontinuously,leadingtodifferentphotoncountsatD1andD2,butthat’sadetailwecanputaside).

Butforthoseenvironmentphotonswhosewhich-wayinformationwaserasedoncetheenvironmentphotonsweredetectedatTenerife,thecorrespondingsystemphotonsatLaPalmashowedwavelikebehavior:allthosephotonsendedupatD1andnoneatD2whenthepathlengthswereequal.

Thisisworthreiterating.ThemeasurementoneachsystemphotonatLaPalmaisdone0.5millisecondsbeforeanythingisdonetothepartnerenvironmentphotonatTenerife.Thedataonthesystemphotonisalreadyinthebag,sotosay.Onlylaterdowefindthatasubsetofthesephotonsendsupactinglikeparticles,goingthroughoneortheotherarmoftheinterferometer,andanothersubsetactslikewaves,witheachphotonendingupinasuperpositionoftakingbothpaths.AndbecausethedeterminationofwhichsubsetdoeswhatisuptothequantumrandomnumbergeneratoratTenerife,ifyoudidmultiplerunsofthisexperiment,eachtimeadifferentsubsetofphotonswouldshowinterference.

Forthosedisturbedbytheimplicationsofthestandardwayofthinking

Forthosedisturbedbytheimplicationsofthestandardwayofthinkingaboutquantummechanics,thisexperimentraisesthestakes.First,complementaritycannotbeovercome.Second,entangledorspookyactionatadistance,hencenonlocality,seemstobearealphenomenon.AndastestsofBell’sinequalityhadalreadyshowed,ifquantummechanicsiscomplete,thisseemstoimplysuperluminalorfaster-than-lightsignaling.Otherwise,what’sbeingdoneinTenerifetotheenvironmentphotoncannothaveaneffectontheoutcomeatLaPalma.

However,thereisadeeperprincipleatstakehere.Quantummechanicsisnotonlyaskingustogiveupnotionsoflocalityin3-Dspacebutournotionsoftimetoo.TheeventsatTenerife,inourusualwayofthinking,happenlaterintime,yetstillinfluencetheoutcomeofmeasurementsatLaPalma,eventhougheachmeasurementatLaPalmaisdoneanddustedwellbeforethepartnerenvironmentphotonreachesTenerife.

Languagefailsusatthispoint.Hereandthere,pastandfuturedon’tquitework.

IaskedUrsinifthismadehimthinkaboutinterpretationsofquantummechanics—thevariousattemptstounderstandwhatmaybehappeningatthemostbasiclevelofrealitythatgobeyondtheCopenhageninterpretation.Ursin,however,isinterestedinharnessingtheweirdnessofquantummechanicsfortechnologicaluses.Interpretationsareforoldfogies.“Iamtheyounggeneration,thenextgenerationofquantumphysicists,”hesaid.“Thisisonlyaquestionwhichisinterestingforgray-hairedpeople,butIdon’thavesomanygrayhairs.”

Thisishardlyamodern-dayresponse.EvenduringthetimesofNielsBohr,whenBohrwaspersistentinhisexplorationsaboutthenatureofreality,theyoungerphysicistsaroundhim,withtheexceptionofcourseofHeisenbergandPauli,weremorenonchalant.TheDanishphysicistChristianMøller,whowasNielsBohr’sassistantatonetime,said:“Althoughwelistenedtohundredsandhundredsoftalksaboutthesethings,andwewereinterestedinit,Idon’tthink...thatanyofuswerespendingsomuchtimewiththisthing...Whenyouareyoungitismoreinterestingtoattackdefiniteproblems.Imeanthiswassogeneral,nearlyphilosophical.”

HearingUrsintalkalsobroughttomindsomethingJohnWheelerwroteinoneofhispapers.HequotedGertrudeSteinonmodernart(possiblyerroneously):“Itlooksstrangeanditlooksstrangeanditlooksverystrange,andthenitsuddenlydoesn’tlookstrangeatallandyoucan’tunderstandwhatmadeitlookstrangeinthefirstplace.”Forayoungergenerationraisedonthemysteriesofquantummechanics,thestrangenessmaybepassé.

Xiao-SongMa,however,whoisofthesamegenerationasUrsin,hasphilosophicalconcerns.Whilehedoesn’tdismisstheCopenhageninterpretation,hehopesexperimentscanleadustobetterones.“Ihopetherewillbesomemoreintuitiveinterpretationsofquantumphysics[thatare]moreinvolvedthanCopenhagen,”hetoldme.He’sbackinChinacreatingevermoresophisticatedexperimentstofurtherexposetheapparentstrangenessofthequantumworld.

Forhimandothersofhisilk,Wheeler’sownwordsareasalve:“Thefinalstoryoftherelationbetweenthequantumandtheuniverseisunfinishedbusiness.Wecanwellbelievethatwewillfirstunderstandhowsimpletheuniverseiswhenwewillrecognizehowstrangeitis.”

—OneofthekeytenetsoftheCopenhageninterpretationistheideaofthecollapseofthewavefunction,whichostensiblyhappenswhenweperformameasurementusingclassicalinstruments.Thesemeasurementsareconsideredirreversibleandtheyimplyaboundarybetweenthequantumandtheclassical.Thequantumeraserexperimentpushesustoreexamineournotionsofwhatconstitutesameasurement(andhencecollapse)andtheexistenceofaquantum-classicalboundary.

TaketheenvironmentphotonintheCanaryIslandsexperiment.Itcontainsinformationaboutwhichpaththesystemphotontookthroughtheinterferometer.MeasuringtheenvironmentphotoninTenerifeinvolvedasiliconavalanchephotodiode,whichdetectsaphotonbyturningitintoanelectricalsignalinvolvingbillionsofelectrons.Thewavefunctionofthesystem-environmentphotonpairissaidtohavecollapsedatthatpoint.

Butgiventhattherehasneverbeenanexperimentthathasfoundanyphysicalevidenceofthisprocessofcollapse,it’sunclearwhatcollapseactuallymeans.Experimentally,whatoneisdoingismakingmeasurementsandpredictingthelikelyoutcomes,andifthosestatisticsareborneoutoveranumberofidenticalexperiments,quantummechanicsclaimscollapsehappenedineachrunoftheexperiment.Butdidit?

Quantummechanicsdoesn’tclaimcollapsewhentheenvironmentphotonisinflight.Buttheoretically,onecouldargueforcollapse,becauseaslongastheenvironmentphotoncontainswhich-wayinformationthatcanbeextracted,thesystemphotonisgoingtobehavelikeaparticle.Theonlydifferencehereisthatthecollapsecanbereversed,becausetheenvironmentphotonisitselfquantummechanical.Onecanerasethewhich-wayinformation,thusundoingwhatcouldhavebeenthoughtofasacollapseofthewavefunction.

havebeenthoughtofasacollapseofthewavefunction.It’stheinteractionoftheenvironmentphotonwiththephotodiodethat

createsasituationwheretheinformationisnowentangledwithbillionsofelectrons.It’simpossibletoreversethequantumstatesofallthoseelectrons.Thisdoeshavethewhiffofanactualcollapse.

Consider,however,ascenarioinwhichtheenvironmentphotoninteractswithasingleatomanddepositsitsinformationintheenergystateoftheatom.Suchanatom,ifheldinisolation,isaquantummechanicalobject,anditsstatecanbereversedinprincipleandtheinformationerased,andanyearliercollapseundone.Whycan’twetreattheinteractionwiththeenvironmentphotonandtheatomastheboundaryatwhichthewavefunctioncollapses?Well,becausethisparticularmeasurement,usinganatom,isreversible.

“IfIreplacethemacroscopicdetectorwithamicroscopic[detector]thatphysicallyIdoknowhowtoreversetheevolutionof,thenyoucanshow,‘Oh,look,collapseneverhappened,’”saidAephraimSteinbergwhenImethimattheUniversityofToronto.Steinbergisahighlyregardedexperimentalistwhoisequallyateasewiththetheoreticalandphilosophicalaspectsofquantummechanics.“That’sthemotivationofthequantumeraser.”Iftheinformationintheenvironmentphotonhadactuallycausedacollapseofthesystemphoton’swavefunction,thennothingcouldbringbacktheinterference.Butthequantumeraserallowsyoutodoso.

Theonlywaytotestwhetheranactualcollapsehappens,thusmakingitimpossibletoreversethestateofthesystem,istodoanexperimentwherequantummechanicsclaimsthereisacollapse—suchaswhenaphotonhitsaphotodiodeandcausesanavalancheofelectrons—andthenreversetheprocess,andsomehowerasethewhich-wayinformationencodedinallthoseelectrons,andthenchecktoseeiftheinterferencefringescomeback.

Iftheinterferencedoesn’tcomeback,thenonecouldrightfullysaythatthewavefunctiondidcollapse.Butsuchanexperimenthasneverbeendone,andislikelynevergoingtobedone,becauseitinvolvesthenear-impossibletaskofreversingtheevolutionofmacroscopicsystemsandthenlookingforinterference.It’dbeliketryingtounscrambleanegg.

So,eitheronehastosaythatcollapsesometimeshappens,butourtechnologiesareunabletotestifthecollapsepermanentlydestroysinterference,oronehastosaythatthewavefunctioncontinuestoevolveaccordingtotheSchrödingerequation(thewavefunctionnowinvolvesnotjustthesystem-environmentphotonpairbutthestatesofthebillionsofelectronstheyengenderedaswell)—andthatthereisnorealcollapse.

engenderedaswell)—andthatthereisnorealcollapse.ThesearethekeystumblingblocksoftheCopenhageninterpretationand

indeedofthestandardformulationofquantummechanics.Whatconstitutesameasurement?Whereistheboundarybetweentheclassicalandthequantum?Whatdoesitmeantosaythatthewavefunctioncollapses?There’sanevenmorebasicquestionstaringatusfromwithintheformalism:Isthewavefunctionreal?Doesithave—asphilosophersliketosay—“ontological”reality?

—LevVaidmancanstillrecallhis1991meetingwithAvshalomElitzur.Vaidmanwasworkinginwhatwasforhimafive-year“dead-end”programatTelAvivUniversity,whichinvolveddoingresearchandteachinghighschoolstudents.Elitzur,likeVaidman,wasinhisthirties.ButElitzurneverfinishedhighschoolandinsteadstartedteachinghimselfquantumphysics,amongothersubjects(inhisrésumétoday,thereareonlytwoentriesundertheheading“Education,”oneofwhichis“Autodidact”).ItwaswhilehewasstillastudentstudyingphilosophyofsciencewithnohighschooldiplomaorundergraduateorgraduatedegreetohisnamethatElitzurcametoVaidmanandposedaseriousquestion:canquantummechanicsbeusedtofindobjectswithoutinteractingwiththem?

AsElitzurandVaidmanfiguredout,theanswerisyes,andtheprinciplesbehinditwerefirstidentifiedin1960,byGermanphysicistMauritiusRenninger.

Considerasourceofsinglephotonsaimedatabeamsplitter.ThephotonwillgotowardeitherdetectorD1orD2.ButunlikethesetupwesawearlierwhenbuildinguptoaMach-Zehnderinterferometer,thearmlengthsinthis

setupareunequal,withD2beingmuch,muchfartherawaythanD1,sothatittakes,say,1secondtoreachD1but5secondstoreachD2.Quantummechanicssaysthat,untilthere’sameasurementateitherD1orD2,thewavefunctionofthephotonwillbeinasuperpositionofhavingtakenbothpaths.IfonesecondlaterthephotonisdetectedatD1,thewavefunctioncollapses;thephotonisnowatD1andnotatD2.NowconsiderthecasewhenthephotonisdetectedatD2.Thedetectorwillclickafter5seconds.Buthere’stheintriguingaspectofthisexperiment:after1second,ifD1hasn’tclicked,weknowthatthephotonhasgonetheotherwayandisheadedtoD2.Thenegativeresult(thenondetectionatD1after1second)isalreadygivingusinformationthatthephotonwillreachD2:thewavefunctionhaspotentiallyalreadycollapsed,eventhoughtheactualmeasurementatD2isyettooccur.It’sthesimplestexampleofaninteraction-freemeasurement.

ElitzurandVaidmanappliedthisprincipletosolvewhat’snowcalledtheElitzur-Vaidmanbombproblem,whichweencounteredintheprologue.It’stimetorevisitit.There’safactorythat’smakingbombswithtriggerssosensitivethatevenasinglephotonhittingthetriggercancausethebombtoexplode.Butthefactoryproducessomedudswithnotriggers.Thetaskathandistoseparatethedudsfromthegoodbombs.Youareallowedtoblowupsomebombsintheprocess.Ofcourse,lookingatthebombtoseeifithasatriggerisoutofthequestion,becauselookinginvolvesshininglight,andthatwouldresultinadetonation.Turnsoutthedoubleslitoritsspecialcase,theMach-Zehnderinterferometer,istailor-madeforthetask.

Imaginethebomb(dudorlive)alongsideoneofthearmsoftheinterferometer.Thelivebombhasatrigger,andit’sthetriggerthatliesinaphoton’spathandobstructsthepath.Adudhasnotrigger,andhencedoesnotimpedethepath.Forargument’ssake,let’salsoassumethatonecanphysicallypickupandmovethesebombsaroundwithoutexplodingthem:it’sjustphotonsthatcanblowthemup(maybetheyarebeinghandledbyrobotsinadarkroom).

Thedudsareeasytofind.Theinterferometerfunctionsasifthere’snoobstructioninanyofthepaths,sothephotonswillbeinsuperpositionoftakingbothpathsandtherewillbeinterference.Ifyousendamillionphotons,onebyone,intotheinterferometer(withtoday’stechnologies,thatcanbedoneinnotimeatall),allofthemwillendupatdetectorD1andnonewillgotodetectorD2.

Now,ifthere’salivebombinoneofthepaths,thingschange.Thebombactslikeawhich-waydetectororasensorfortellingwhichpaththephotontakesthroughtheinterferometer.Sothephotonsaregoingtoactlikeparticles:eachphotonisgoingtogothrougheitherpathaorpathb(whichhasthebomb).Therearethreepossibleoutcomes:

Oneisthatthephotontakespathb,encountersthetrigger,anddetonatesthebomb.That’sthat,then—thebombislost,andsoistheinterferometer;let’sassumethatwecanbuildonemoreinajiffyandstartalloveragain.

Nowsaythephotontakespathaandencountersthesecondbeamsplitter.Becausethephotonisnowactingasaparticle,ithasa50-50chanceofexitingthrougheitherarmofthesecondbeamsplitter.SohalfthetimethephotonwillgotoD1.Thisisthesecondoutcome.Unfortunately,D1alsoclicksinthecaseofadudbomb,sotheresultisinconclusive.Werepeatwithmorephotonsforadifferentresult.

Thethirdoutcomeisthekey.Thephotontakespatha,goesthroughthesecondbeamsplitter,andendsupatD2.Thisisaclearsignthatthere’salivebombobstructingoneoftheinterferometerpaths.Weknowthatifbothpathsareunobstructed,wegetinterference—whichmeansallphotonsgotoD1andnever

toD2.ButifD2clicks,asinthisthirdscenario,that’sbecausethereisnointerference.Thephotonistakingonepathortheother,becausesomethingisactinglikeawhich-waymeasurement—inthiscasethelivebomb.Wehaveessentiallydetectedthepresenceofthelivebombwithoutblowingitup.

Theprobabilitiesoftheoutcomeswithalivebombinplaceareeasytocompute.Halfthetime,alivebombwillcausetheinterferometertoblowup.One-quarterofthetime,thephotonwillendupatD1—buttheinformationisuseless.One-quarterofthetime,thephotonendsupatD2:weknowwehavealivebombinpathb.Quantummechanicshasallowedustodosomethingthatisimpossibletodowithclassicalphysics:wehavedistinguishedalivebombfromadudwithoutlookingatit.

Todaytheideaofinteraction-freemeasurementshasbecomerelativelycommonplace.In1991,itsimportancewasfarfromobvious.ElitzurandVaidmanbegancirculatingpreprintsoftheirpaperonthetopic(withasectionon“Howtotestabombwithoutexplodingit”),andalsosentittoPhysicalReviewLetters.Theygotbackarefereereportsayingthatwhilethepaperwasinteresting,itwasn’tthekindofworkthatPRLusuallypublished.PhysicsLettersAalsorejectedit(thetheneditorofthejournaltoldVaidmanlaterthattheunnamed,nay-sayingreferee“wasaverybigshot”).

Thepaperdidseethelightofdayin1993inanothersomewhatlessprestigiousjournal,buttheideagainedprominencewhenRogerPenrosewroteaboutitinhis1994book,ShadowsoftheMind.GiventhatElitzurandVaidmanworkedinIsrael,Penroserathercheekilysuggestedthattheexperimentcouldbecooptedforbuildingwhathecalledthe“Shabbosswitch,”tohelpthoseoftheJewishfaithobserveShabbat,whichstartsjustbeforesunsetonFridayandendsaftersunsetonSaturday.Duringthisperiod,strictadherentsarenotsupposedtolightafireoreventurnonappliances.Penrose’sShabbosswitchcouldhelpsomeoneturnonapplianceswithoutactuallydoingit.ImaginereplacingthebombintheElitzur-Vaidmanexperimentwithyourfinger.Halfthetime,aphotonenteringtheinterferometerwillhityourfinger,andnothinghappens.Butone-quarterofthetime,aphotonwillgothroughtheotherpath,thusnotinteractwithyourfinger,andreachdetectorD2,whichcouldthenflipaswitchandturnonanappliance.“Surely...itcanbenosintofailtoreceivethephotonthatactivatestheswitch!”wrotePenrose.

Jokesaside,interaction-freeexperimentshighlightthedisturbingconceptualquestionsthrownupbynotionsofcollapse.Whenthere’salivebombinonearmoftheinterferometer,standardquantummechanicssaysthatthewavefunctionofthephotoncollapses—makingthephotonactlikeaparticleand

wavefunctionofthephotoncollapses—makingthephotonactlikeaparticleandgothroughonearmortheother.Halfthetime,thephotonmeetsthebombandblowsthewholethingup.Theotherhalfofthetime,ittakesthebomb-freepath,whichallowsustoinferthepresenceofabombintheotherarm.Butnothinginteractedwiththebomb.Whatdoescollapsemeaninthiscontext?

ThecollapseofawavefunctionhasbuiltintoitthetwoelementsthatbotheredEinstein:randomnessandactionatadistance,withthelatterconcerninghimmuch,muchmorethanthelackofdeterminism.Inthestandardformalism,whenawavefunctioncollapses,wecanonlyassignprobabilitiestotheoutcomesofthecollapse.Theoutcomeisinherentlyrandom.Also,whenthewavefunctioninvolvestwoormoreparticlesthathaveinteractedatsomepoint,meaningtheyareentangled,thenthecollapseofthewavefunctionduetoameasurementononeparticleaffectstheentangledpartnersinstantaneously—makingtheinfluencenonlocal.“Collapsehasnonlocalityandrandomness,”Vaidmantoldme.“Thisistheonlyphenomenoninquantummechanicswhichhasthesetwoproperties.”JustlikeEinstein,Vaidmanisbotheredbysuchatheory.He’dratherseeanalternativetakeshape.“Ithinkatheorywithoutaction-at-a-distanceandwithoutrandomnessisamuchbettertheory.”

ForVaidman,interaction-freemeasurementsaretheclearestindicationthatanytheorythatinvokesameasurement-inducedcollapseofthewavefunctioncannotbethecorrecttheory.He’snottheonlyonetothinkso.Comingupwithalternativeinterpretationsortheoriestoexplaintheexperimentalobservationshasconsumedthemindsofasmallsubsetofquantumtheorists,atrendthatbeganwithEinsteinandhisinsistencethattheremustbeatheorythatisbothlocalandrealistic.WhileEinstein’sparticulardesireforalocalrealistictheoryorlocalhiddenvariabletheoryhasbeenrefutedbytheexperimentsdonebyClauser,Aspect,Zeilinger,andothers,therearealternativesverymuchintherunningand,somewouldsay,gainingground,becausethesimpleMach-Zehnderinterferometerand,byextension,thedouble-slitexperimentcontinuetoproduceglaringparadoxes.

—LucienHardy,whomwemetintheprologue,wasaPhDstudentintheearly1990swhenhesawapreprintoftheElitzur-Vaidmanbombpaper.ThiswasbeforethedaysofthearXivInternetserver(whereauthorsthesedaysuploadtheirpreprintsforeveryonetoread)—yougottoreadapreprintifitwassenttoyou.“Fortunately,theyhadsentapreprinttomysupervisor,EuanSquires,andEuanshowedmethispreprint,andwebothgotveryexcited,”Hardytoldme.

Euanshowedmethispreprint,andwebothgotveryexcited,”Hardytoldme.IntheElitzur-Vaidmanthoughtexperiment,thebombisitselfaclassical

device.Whatif,thoughtHardy,thebombisquantummechanical?Whatwouldconstituteaquantummechanicalexplosion?Oncethethoughtenteredhismind,itdidn’ttakehimlongtodeviseanexperimentwithtwoMach-Zehnderinterferometers,inwhichanexplosionhappenswhenanegativelychargedelectronmeetsitspositivelychargedanti-particle,apositron.

Thesetupisessentiallytwointerferometersplacedsidebyside(seenextpage).Thefirstoneisforelectrons:asourceshootselectronsoneatatimeintotheinterferometer,whichhavethechoiceoftakingpatha-orb-(“-”heredenotestheelectron’snegativecharge).Thesecondoneisforpositrons,whichcangoalonga+orb+.Theinterferometersarearrangedsuchthatpathb-oftheelectronandpathb+ofthepositroncrossjustbeforetheyhittheirrespectivefullyreflectingmirrors.Thewholesetup,inprinciple,isbuilttoexactingstandards,sothatifanelectronandapositronleavetheirrespectivesourcesatexactlythesametime,andiftheelectronhappenstotakepathb-andthepositronpathb+,thenthetwoparticleswillencountereachotheratthepointwheretheirpathsintersect.Thisisarecipeforanexplosion:aparticleanditsanti-particlewhenbroughttogetherwillannihilateintopureenergy.

Let’sstartbyanalyzingtheelectroninterferometer,whileignoringitspositroncounterpart.Weknowthatelectronsaregoingtoactlikewaves,soallofthemwillendupindetectorC-(“C”forconstructive,“-”fornegativecharge),whilenonewillreachD-.Similarly,ifyouconsideronlythepositroninterferometer,independentoftheelectrons,allthepositronswillreachC+,andnonewillreachD+.

Butputthemsidebysideasshown,andsuddenly,thewavenatureoftheelectronsandpositronssometimesdisappears.That’sbecausewenowhaveawhich-waydetectorbuiltintotheconfigurationofthetwointerferometers:it’stheequivalentofhavingalivebombinonearmofeachinterferometer.

First,let’stacklecaseswhentheelectronsandpositronsbehavelikewaves.Foranelectron,thishappenswhenthepositrongoesthroughpatha+.Inthissituation,there’snoimpedimenttotheelectron’sprogressthroughitsinterferometer,soit’llbeinasuperpositionoftakingpathsa-andb-,andconsequentlyendsupatdetectorC-.Similarly,whenanelectrontakespatha-,thecorrespondingpositronswillendupatC+.

Buttherearetimeswhentheelectronsandpositronswillactlikeparticles.Takethecaseofthepositrongoingthroughpathb+.Fortheelectroninterferometer,thepositron’spresenceinpathb+isthesameashavingadetectorinpathb-,sotheelectronisgoingtoactlikeaparticleandtakepatha-orpathb-withequalprobability.Ifittakesb-,thentheelectronencountersthepositronandannihilates.Butifittakesa-,thenatthefinalbeamsplitter,it’sgoingtogotoeitherC-orD-.Whenitwasactinglikeawave,theelectronwouldnevergotoD-.SoifanelectronmakesittoD-,it’sasignalthattherewas

apositroninpathb+.Anelectronisableto“sense”thepresenceofapositronwithoutactuallyencounteringit—aninteraction-freemeasurement.

Sincethetwointerferometersaresymmetric,yougetthesameresultifyouanalyzethepositronsideofthings.Ifanelectronisinpathb-,thenapositroncanendupateitherC+orD+;ifapositronmakesittoD+,itsignifiestherewasanelectroninpathb-.

Hardywasnotdone,however.Themathematicalformalism,heshowed,predictsthatone-sixteenthofthetime,onaverage,D+andD-willclicksimultaneously.Soifyoudidtheexperimentamilliontimes,thiswillhappenabout62,500times.Andthispresentsaparadox.

Here’swhy.Fromthepointofviewofanelectron,ifD-clicks,itmeansthatapositronwasinpathb+.Fromthepositron’sperspective,ifD+clicks,anelectronwasinpathb-.So,whenD+andD-goofftogether,itmeansthattheelectronwasinb-andthepositroninb+,atleastaccordingtoclassicallogic.Which,recall,istheoriginalrecipeforanannihilation.Butintheseone-sixteenthsofthecases,thereisnoannihilation:theelectronmakesittoD-andthepositrontoD+,withoutanattendantexplosion.

Ifallthisfeelsabitlikegedankenmumbojumbo,andyoucryout,“Surely,thiscan’thappeninareallabexperiment,”youwouldbewrong.Anearlyexactreplicaofthisexperiment,usingphotonsandtheirpolarizations,wasdonebyDirkBouwmeesterattheUniversityofCaliforniaatSantaBarbaraandhiscolleagues.Theyusedphotonsbecausetechnologydoesn’texisttodotheexperimentwithelectronsandpositrons.

Hardy’sparadoxisreal.Buttheparadoxarisesbecausewearetalkingandthinkingclassicallyofspaceandtime,ofparticlestakingthisorthatpath,andreachingthisorthatdetector.Naturehasitsowninimitablewayofdoingthings.

D+andD-gooffsimultaneouslysometimesbecause,accordingtotheformalismofquantummechanics,theparticlesaresomewhatentangledjustbeforetheyhittheirrespectivefinalbeamsplitters.What’sevenmoreastonishingisthattheentanglementisbetweenanelectronandapositronthatcamefromdifferentsources.Inthepreviousexperiments,whentwophotonswereentangled,theyhadbeenemittedbythesameatom,orhadinsomewayinteractedandgottenentangled.Notsointhiscase.

Soifweholdontolocalrealism—thebedrockofclassicalphysics—andgivealocaldescriptionintermsofparticlestakingactualpaths,thenweendupwithHardy’sparadox.Butletgooflocalrealismandwearefacedwithanunavoidableconclusion:“Quantumtheoryisnonlocal,”saidHardy.Hispaper,

asithappened,waspublishedin1992inphysics’premierjournal,PhysicalReviewLetters(whichhadrejectedElitzurandVaidmanin1991);theironyisthatHardy’sworkwasinspiredbytheElitzurandVaidmanpaperthatwasyettoseethelightofdayinapeer-reviewedjournal.Inhispaper,HardyacknowledgedtheIsraeliduo’spaperasa“TelAvivReport,1991.”In1994,physicistDavidMerminwrotethatHardy’sthoughtexperimenttodemonstratenonlocalityis“simplerandmorecompelling”thantestsofBell’stheorem:“[It]standsinitspristinesimplicityasoneofthestrangestandmostbeautifulgemsyettobefoundintheextraordinarysoilofquantummechanics.”

Theexperimentsinthischapterillustratethecounterintuitivenatureofthequantumworld,evenmoresothanthewave-particledualityweencounteredearlier.Butwhatwillbecomeclearintheforthcomingchaptersisthatphrasesandwordslikewave-particleduality,nonlocality,spookyactionatadistance,superpositionofbeinghereandthere,therandomnessofnature,nondeterminism—thesearewaysofthinkingaboutwhat’shappeninginthequantumrealmwhenthemathematicalformalismisinterpretedaccordingtotheCopenhageninterpretation.Otherinterpretations,sometimeswithdifferentformalisms,sometimesjustreinterpretationsofthesameformalism,giveusaverydifferentviewofthequantumunderworld.

Attheheartoftheformalismsisthewavefunction.Whatdowemakeofit?Doesitmerelyrepresentourknowledgeaboutthequantumworld,makingitepistemic?Orisitsomethingreal(aspotentiallyevidencedbyinteraction-freemeasurements,whichsuggestthatit’sthewavefunctionthat’s“sensing”thebomb,forexample),makingthewavefunctionakeyingredientofrealityandpartoftheontologyoftheworld?Andregardlessofwhetherit’sontologicalorepistemic,whatdoesonemakeofthewavefunction’scollapse?

Assuccessfulasquantummechanicsisasatheory—andit’sbyfarthemostsuccessfulphysicaltheorywehave—suchquestionscontinuetohauntthosewhopondertheveryessenceofreality.Forthem,someofwhomaregray-haired,it’snotenoughtoharnessquantummechanicstobuildbettertechnology,to“shutupandcalculate,”asthesayinggoes.Amongtheearliestthinkerslookingforadeeperdescriptionofreality,ofcourse,wereEinsteinanddeBroglie.Afterthem,thefirstphysicisttoseriouslytackletheconceptualdifficultiesoftheCopenhageninterpretationbyformulatingahiddenvariabletheorywasanAmericanphysicistwhobrieflyworkedalongsideEinsteinatPrincetonbeforehewashoundedoutofanAmericasteepedinMcCarthy-eraparanoia.

I

6

BOHMIANRHAPSODY

ObviousOntologyEvolvingtheObviousWay

There’sanentirelydifferentwayofunderstandingallthisstuff(awayofbeingabsolutelydeviantaboutit,awayofbeingpolymorphouslyhereticalagainstthestandardwayofthinking,awayoftearingquantummechanicsallthewaydownandreplacingitwithsomethingelse).

—DavidAlbert

t’snosmallironythatoneofthestrongestmovesagainsttheCopenhageninterpretationwasmadebyastudentofRobertOppenheimer.Bestknownto

theworldasthescientificdirectoroftheManhattanProject,theUSefforttobuildtheatomicbomb,OppenheimerwasastrongproponentofNielsBohr’sviewofthequantumworld.HefoundedthefirstschooloftheoreticalphysicsintheUnitedStatesandtaughtquantummechanicsattheUniversityofCalifornia,Berkeley,where“BohrwasGodandOppiewashisProphet.”AyoungDavidBohmcametodohisPhDwithOppenheimerandwasprobablydeeplyinfluencedbyOppenheimer’sevangelismofBohr’sideas.ButtherewasalreadyahintofarebelinBohm’sbehavior.

WorldWarIIwasdevastatingcountries,andAmericawasbuildingthebomb.BohmbecameamemberoftheCommunistPartyandgotinvolvedwithunionactivities—whichmeantthathecouldnotgetthesecurityclearancenecessarytodefendhisthesis,whichwasonatopicconsideredsensitiveenoughtobeclassified.Eventually,BohmgothisPhD,butonlyafterOppenheimerreassuredUCBerkeleythathisstudent’sthesisdeservedadegreewithoutthecustomarydefense.

SoonafterhegothisPhD,PrincetonUniversitygaveBohmajob(afterall,

SoonafterhegothisPhD,PrincetonUniversitygaveBohmajob(afterall,hewasoneofthebrightestofthecropofyoungAmericantheorists,and“probablyOppenheimer’sbeststudentatBerkeley”).Bohmbeganteachingquantumphysics.Butsoonhispastcaughtupwithhim.In1949,theHouseUn-AmericanActivitiesCommitteesubpoenaedhimtoappearbeforeCongressandtalkabouthisandhiscolleagues’communistconnections.Bohmrefused,andpleadedtheFifth.ThiswascontemptofCongress:Bohmwasindicted,arrested,butthenreleasedonbail.Acourtsubsequentlyacquittedhim,butthedamagewasdone.Princetonsuspendedhimandbarredhisaccesstouniversityfacilities,andwhenhiscontractcameupforrenewalin1951,theydemurred.

ButBohmhadn’tbeensittingonhishands.In1951,hepublishedoneofthemostlucidtextbooksonquantummechanics,QuantumTheory,inwhichheelegantlyexplainedtheCopenhagenviewpoint(thebookwasaresultofhispedagogicaleffortsatPrinceton).ItwasalsothebookinwhichBohmreformulatedtheEinstein-Podolsky-Rosen(EPR)thoughtexperiment,crystallizingitsessencebetterthanEinsteinhimself.Afterthebookcameout,BohmandEinsteinmetanddiscussedquantummechanics,adiscussionthatplayedakeyroleinBohm’sevolvingviewsaboutthenatureofreality.

Butbeforehecoulddothat,hiscareertookaturnfortheworse.WhenhiscontractatPrincetonwasn’trenewed,BohmknewhisdaysasanacademicintheUnitedStateswerenumbered.HemovedtoBrazilinOctober1951,whereacoterieofformerPrincetongraduatesgothimanacademicappointmentattheUniversityofSãoPaolo,withrecommendationsfromnolessthanEinsteinandOppenheimer.BohmwaslookingforwardtocollaboratingwithphysicistsinEurope,butthosehopesweredashedwhentheUSStateDepartmentconfiscatedhispassport.BohmwasnowofficiallyinexileinBrazilandhewouldstaythereuntil1955,whenhewouldleaveforIsrael.

Inthemeantime,Bohmpublishedapaperthatchallengedtheanti-realiststanceoftheCopenhagencrowd.Itseemedtocomeoutoftheblue,butinhindsight,his1951textbookcontainedhintsofhisradicalruminations.Inthebook,heopenlydiscussedtheideaofhiddenvariables.Usingthelawsofthermodynamicstomakehispoint,hearguedthatthereasonwhywehavetodealwithprobabilitiesofoutcomesinthermodynamicsisbecausewedon’thavecompleteknowledgeofthepropertiesof,say,theunderlyingmoleculesofsomegas.Variablesthatcapturethesepropertieswouldconstitutehiddenvariables.Couldtheprobabilitiesthatariseinquantumtheory—forexampletheprobabilityoffindinganelectronhereorthere—besimilarlytheoutcomeofnotknowingenoughaboutvariablesthatcapturethepropertiesofsomehiddenlayer

knowingenoughaboutvariablesthatcapturethepropertiesofsomehiddenlayerofreality?

Eventhoughheraisedtheseissuesinthebook,Bohmwasn’tyetconvincedthattheCopenhageninterpretationneededrethinking.“Untilwefindsomerealevidenceforabreakdown[ofquantumtheory]...itseems,therefore,almostcertainlyofnousetosearchforhiddenvariables.Instead,thelawsofprobabilityshouldberegardedasfundamentallyrootedintheverystructureofmatter,”hewrote.SoBohm,whileponderingheresies,wasstillespousingBohr’sviewsinhisbook(thewayZeilingerstilldoes).Infact,Bohm’sbookwasnot“onlyorthodoxintheCopenhagensensebutoneoftheclearestandfullest,mostpenetratingandcriticalpresentationsoftheCopenhagenvieweverpublished.”Heevenwentsofarastosaythatthe“generalconceptualframeworkofthequantumtheorycannotbemadeconsistentwiththeassumptionofhiddenvariables.”HeusedtheEPRresulttomakehiscase.AsEinstein,Podolsky,andRosenhadpointedout,theirthoughtexperimentsuggestedthatunderassumptionsoflocality,boththemomentumandpositionoftwoentangledparticleswouldhaveclearlydefinedvalues—butthiswouldcontradicttheuncertaintyprinciple,whichBohmcalled“oneofthemostfundamentaldeductionsofthequantumtheory.”

Therefore,Bohmconcluded,“notheoryof...hiddenvariablescanleadtoalloftheresultsofthequantumtheory.”

Butallthatchangedayearlater.In1952,BohmpublishedhisseminalpaperinPhysicalReview,titled“ASuggestedInterpretationoftheQuantumTheoryinTermsof‘Hidden’Variables.”(Thepaperacknowledgesonlyoneperson:“TheauthorwishestothankDr.Einsteinforseveralinterestingandstimulatingdiscussions.”)ItwasthefirstandclearestexampleofatheorythatBohmhimselfhadsaidcouldnotbeconceived.ItalsoimplicitlyshowedthatJohnvonNeumannhadbeenwrong:itwaspossibletocomeupwithatheorywithhiddenvariablesthatcouldexplainexperimentalobservationsinquantumphysicsandrecoverrealismanddeterminism.

—It’sinthenatureofthedebateaboutquantumtheorythattheproponentsoftheCopenhagenviewarenotparticularlyvocal.Theydon’thavetobe.Theyhavehistoryontheirside.NielsBohr,WernerHeisenberg,WolfgangPauli,andmanyothergiantsoftheoreticalphysicshavealreadyarguedthecasefortheCopenhageninterpretation.Butforsometheoriststhinkingaboutthefoundationsofquantummechanics,it’sfarfromadonedeal.Theyhaveto,however,raise

theirvoicestomakethemselvesheard,andtheyareusuallyfarmorepassionatethantheadherentstotheorthodoxy.SheldonGoldsteinisnoexception.

AswithBohm,GoldsteintoobeganhiscareeradvocatingBohr’sviews.HewasstudyingatYeshivaUniversityinNewYorkinthelate1960sandearly’70s.“IwasafairlystrongdefenderoftheCopenhageninterpretation,totheextentthatIunderstoodit,”GoldsteintoldmewhenwemetatRutgersUniversityinNewJerseyonamiserablyrainyday.Heinvitedmeintohislong,narrowoffice—onesideofwhichwaslinedwithbookshelvesfilledwithbooksonquantummechanics.Throughthelargewindowsatthefarendoftheoffice,Icouldseethegrayskyandtheoccasionalskeinofgeeseflyingpast.StucktothebookshelveswereclippingsofnewspaperarticlesaboutAlanSokal,aNewYorkUniversityprofessorwhoin1996dupedasocialstudiesjournalintopublishingwhatturnedouttobegibberish,toproveapointthatsuchjournalswouldpublishnonsense.AwhiteT-shirthungfromoneofthebookshelves;ithadanimageofBohm,withthewordsDavidBohm,Keepin’itreal.Goldsteinsatdownonhisswivelchair,leanedback,andputhislegsuponthetable,claspedhishandsbehindhishead,andproceededtotalkfortwohours,gettinguponlytoscribbleequationsontheblackboardortograbamuch-thumbedcopyofSpeakableandUnspeakableinQuantumMechanicsbyJohnBell,itsdustjacketintatters,andquoteentireparagraphstome.

“IwantedBohrandHeisenbergandorthodoxquantumtheorytoberight,andEinsteintobewrong,”hesaid.

“Youwantedthat?”Iasked.“Yeah,IwantedEinsteintobewrong,”saidGoldstein.“I’mnottooproud

ofthat,bytheway.Iwasexcitedaboutthequantumrevolution,andEinsteinwaspresentedassomebodywhowantedtogobacktoold-fashionedclassicalwaysofthought.Hejustcouldn’tgetwiththenewmodesofthinking;hewastooold.”

GoldsteinthenexpressedsomeremorseforthosethoughtsaboutEinstein.“Ithinkthatwasveryunfair,butanyway,that’swhatIthoughtthen,”hesaid.“YoucouldsayIwasn’tsmartenoughtoseewhatabunchofcrapthatwas,soIswallowedit.IthoughtifIlearnedthemathematicsbetterandlookedintoitcarefully,Iwouldreallyunderstanditalloneday.[But]themoreIlearned,themoreclearitbecamethatwewereallhoodwinked.”

Strongwords,butnotunusualfromthosewhohavedevelopedadistastefortheorthodoxy.

AsGoldsteinprobedfurtherintothemathematicsofstandardquantumtheory,hewasunabletomakesenseofwhatit’sabout.Whatarethefundamentalentitiesofreality?Isitatheoryaboutparticles?Isitaboutwaves?Isitatheoryofmeasurementsandobservations?Isitatheoryofwavefunctions?Isthewavefunctionontic(meaningitissomething)orisitepistemic(inthatthewavefunctionrepresentsourknowledgeaboutsomething);isthewavefunctionobjectiveorsubjective?

Goldsteinwasn’tdoneexpressinghisconcernsaboutorthodoxquantummechanics.“Arethereparticlesbeforeyoulook?Dotheyhavepositionsbeforeyoulook?Accordingtotextbookquantummechanics,presumablynot.Thenwhatdoyouhavebeforeyoulook?Ordoeslookingcreatereality?Isthatclearfromtheusualtheory,textbooktheory?No,it’snot.”

Goldsteinusedthedouble-slitexperimenttofurthermakehispointaboutthe“reality”ofthewavefunction.“Idon’tseehowyoucanunderstandtheinterferenceunlessyoutakeseriouslythatyouhaveawavefunction,anobjectivethingintheworld,whichhasthesetwopieces,onegoingthroughtheupperslit,andonegoingthroughthelowerslit,andtheyinterferewitheachother,”hesaid.

DisenchantedwiththeCopenhageninterpretation,GoldsteinturnedtoworkbyamathematicalphysicistatPrincetonnamedEdwardNelson,whohadproposedatheorycalledstochasticmechanicstoarriveatarealistictheoryofthequantumrealm.Thetheoryhadactualparticlesinit,withpositionsandmomenta,andtheseparticleswerebeingrandomlybuffetedbythewavefunction—resultinginasortofBrownianmotion.Itwasn’tdeterministicanditreproducedtheresultsofstandardquantumtheory,albeitaftermanymathematicalcontortions.GoldsteinfounditenticingbutsoonrealizedthatitwastoocomplicatedandthattherewassomethingsimplerhidinginNelson’sproposal.

Andevenashestartedfiguringoutthesimpleridea,hehadavaguenotionthat“therewasthisguyDavidBohm”whohadproposedadeterministicformulationofquantumtheory,onewithhiddenvariables.Goldsteindiscoveredthattheideathathewasplayingwith—makingNelson’sstochasticmechanicssimpleranddeterministic—wasexactlywhatBohmhadalreadyclearlyelucidated.HerewasanalternativetotheCopenhagenviewofthings:adeterministictheoryofparticlesthatmovearoundbecauseofinteractionswiththewavefunction,whichinturnisa“real”thingandevolvesaccordingtotherulesoftheSchrödingerequation.

Bohm’stheoryhasadefiniteontology:theworldismadeofparticlesandwavefunctions,evenifwavefunctionsarenot“physical”inthesensethat

wavefunctions,evenifwavefunctionsarenot“physical”inthesensethatparticlesarephysical,butnonethelessarereal,objectiveaspectsofnature.Aparticlehasadefinitepositionatalltimes,whichmeansithasatrajectory—indirectcontraventionoftheCopenhagenviewofreality.Theparticleis“guided”bythewavefunction,andthusinfluencednotjustbytheusualforces(suchaselectromagnetism),butbya“quantumpotential,”anewforcefeltbytheparticlebecauseofitsinteractionswithitswavefunction.Moreover,thetheoryisdeterministic:givenaparticle’spositionanditswavefunction,youcanpredicttheparticle’spositionatsomelatertime.Andevenmoreemphatically,theparticle’strajectoryisobjectivereality—itexistsindependentofanobserver.

Andwhatofhiddenvariables?InBohm’stheory,themuch-malignedhiddenvariablesarenothingotherthanthepositionsofparticles.TothosewhothinkBohmisright,it’sanironythatthisratherobviouspropertyhastobecalled“hidden”:it’scalledsobecauseitdoesn’tappearinthestandardformalismofquantummechanics,unless“observed.”

—JustasGoldsteindiscoveredthathisnascentideashadalreadybeenworkedoutbyBohm,Bohmwoulddiscoverthathistheorywasn’tentirelynoveleither.LouisdeBroglie,theyoungFrenchprincewhomweencounteredearlier,hadmadethefirstclearattemptatatheorythatincorporatedbothrealismanddeterminism,backinthe1920s.Recallthatin1924,deBrogliecameupwiththetheorythatparticlesofmattersuchaselectronshadwavelikeproperties.Thenin1927,deBrogliepresentedanotherradicalideaattheFifthSolvayConferenceinBrussels—thatrealityismadeofparticlesandthattheseparticlesarebeingguidedbya“pilotwave,”whichbehaveslikeawavefunctionandevolvesaccordingtoaformoftheSchrödingerequation.SodeBrogliewasproposingthatrealityisn’twaveorparticle,asBohrwasarguing,butratherit’swaveandparticle.AttheSolvaymeeting,WolfgangPauli—whosidedwithBohr—rippedintodeBroglie’stheory,claimingtopointoutcertainexperimentalsituationsthatitcouldn’texplain.AdishearteneddeBrogliegaveuponthepilot-wavetheory,andactuallybecameasupporteroftheCopenhageninterpretation.

Until,thatis,Bohmenteredthepicture.Bohm,unawareofdeBroglie’swork,hadreinventedthetheory,butwithfargreaterconceptualandmathematicalclarity.EinsteinandPaulibothalertedhimtodeBroglie’swork.Pauli,inparticular,raisedsomeofthesameissuesthathehadbroughtupafterdeBroglie’spresentationinBrussels.ButBohm,unlikedeBroglie,didnotbackdown.HerevisedhisdrafttoaddressPauli’sconcernsandsentittoPauli,who

down.HerevisedhisdrafttoaddressPauli’sconcernsandsentittoPauli,whoapparentlydidnotreaditbecauseitwastoolong.Bohmwasn’tamused.HesentPauliarathersternnote:“IfIwriteapaperso‘short’thatyouwillreadit,thenIcannotanswerallofyourobjections.IfIanswerallofyourobjections,thenthepaperwillbetoo‘long’foryoutoread.Ireallythinkthatitisyourdutytoreadthesepaperscarefully.”

AsforgivingdeBrogliehisdue,Bohmdidsosomewhatreluctantly.Inhis1952paper,heacknowledgedthathehadbeenalertedtodeBroglie’sworkafterhehadcompletedhispaper,andthatdeBrogliehadabandonedhisapproachfollowingcriticismfromPauliandafterdeBrogliehadhimselfrealizedwhathetooktobesomeofthetheory’sshortcomings.“AlloftheobjectionsofdeBroglieandPaulicouldhavebeenmetifonlydeBrogliehadcarriedhisideastotheirlogicalconclusion,”wroteBohm.

HeputthisargumentrathermorecolorfullyinalettertoPauli:“Ifonemanfindsadiamondandthenthrowsitawaybecausehefalselyconcludesthatitisavaluelessstone,andifthisstoneislaterfoundbyanothermanwhorecognizesitstruevalue,wouldyounotsaythatthestonebelongstothesecondman?Ithinkthesameappliestothisinterpretationofthequantumtheory.”

ToBohm’scredit,hedidpushtheideastotheirlogicalconclusionandtheresultwasthefirstdeterministic,realistic,hiddenvariablequantumtheory.AsBellsubsequentlysaid,Bohmhaddonetheimpossible.

Today,thepilot-wavetheoryisoftenreferredtoasthedeBroglie-Bohmtheory.DeBroglie,oncehebecameacquaintedwithBohm’swork,lefttheCopenhagencampandstartedworkingonavariantofhisownideacalledthedouble-wavesolution,somethinghehadstartedonin1926buthadgivenupasbeingtoodifficult.

Afterdecadesinexile,boththedeBroglie-Bohmpilot-wavetheory(whichGoldsteinfavors)anddeBroglie’sdouble-wavesolutionaregettingsomeattentionandevensupport.Thelatterfromanunlikelygroupofresearchersstudyinghowdropletsofsiliconeoilbounceonavibratingsurfaceofthesameoil.What,youmightask,hasthatgottodowithquantumphysics?

—Asagraduatestudent,JohnBushfeltthesameannoyancewithquantummechanicsashedidwithSundayschoolgrowingupinLondon,Ontario,Canada.Thereweresomequestionsthatwereoff-limitswhenitcametoreligion.Unfortunatelyforhim,heencounteredsimilarattitudeswhenlearningquantummechanicsandtheCopenhageninterpretation.“Youaretellingmethattheparticledoesn’texistunlessyouobserveit?”he’dask.Theinstructorwould

theparticledoesn’texistunlessyouobserveit?”he’dask.Theinstructorwouldgo,“Youcan’taskthatquestion.”BushfelthewasbackinSundayschool.

ItwasgallingtoBushthathumanobserverscouldsomehowbeheldresponsibleforcreatingquantumreality.Itstillgallshim.“Thisisthelatestinthelonglineofepichumanintellectualfolliesthathaveresultedfrommanputtinghimselfatthecenteroftheuniverse,”hesaidwhenwemetathisofficeatMIT.“Itstrikesmeasnonsense.”

Disillusionedwithquantummechanics,Bushendedupstudyingfluidmechanics.Littledidheknowthathischosenfieldwouldleadhimbacktoquantummechanics.Theimpetuscamefromthe2006workoftwoFrenchresearchers,YvesCouderandEmmanuelFort.Theyhadconjuredacurioussetup.Imagineapetridishfilledwithsiliconeoilthat’sbeingvibratedupanddown.Theseverticalvibrationsofthebathofoilarekeptbelowwhat’scalledtheFaradaythresholdforthefluid.Abovethisthreshold,wavesformonthesurface,butbelowthethreshold,thesurfaceremainssmooth,eventhoughthereisvibrationalenergyinthefluid.Theresearchersdiscoveredthatiftheyletamillimeter-sizedropletofthesameoilfallontothevibratingsurface,thedropletwouldkeepbouncingandbeginwanderingacrossthesurface.

Here’swhy.Athincushionofairbetweenthedropletandthesurfacepreventsthedropletfromcoalescingintotheoilbath.Uponfirstimpact,thevibratingsurfacegivesthedropletaverticalkick,causingittobounceup.Theimpactalsocreatesasmallwaveonthebathsurface.Whenthedropletfallsbackontothesurface,itencountersthiswave.Thistime,thedropletgetsbothahorizontalandaverticalkick,andtheprocessnowkeepsrepeating.Thedropletstarts“walking”overthesurface,guidedbytheverywaveitcreatesandsustainswitheachbounce.Thewavedictatesthedroplet’sspeedanddirection.

TheanalogywiththetheoriesofdeBroglieandBohmishardtoignore.Thedropletisaparticlebeingguidedbyitspilotwave.Whatelsecanonedoatthisstagebutcarryoutaversionofthedouble-slitexperiment?

CouderandFortdidjustthat.Theymadeabarrierwithtwoopeningsandsubmergeditfractionsofamillimeterbelowtheoilsurface,suchthatanythingmovingonthesurfacewouldbeinfluencedbythebarrier.Thesubsurfacebarriermadeforadoubleslit.Whenthewalkingdropletapproachedthebarrier,itwentoveroneortheotheropening(likeaparticlegoingthroughoneslitortheother).Theattendantpilotwave,however,spannedbothopeningsandthuswentoverboth.Whenthewaveemergedontheothersideofthesubmergedbarrier,itwasnowtheoutcomeoftheinteractionbetweentwodiffractedwaves,eachinfluencedbyonesubsurfaceslit.Thismorecomplexwavenowguidedthe

influencedbyonesubsurfaceslit.Thismorecomplexwavenowguidedthebouncingdropletawayfromthebarrier.Foreachrunoftheexperiment,thedropletwenttoadifferentlocationonthefarside.Theresearcherscollectedseventy-fivesuchtrajectories,andtheirinitialanalysisshowedthatthedropletsweregoingtosomeplacesandnottoothers—suggestiveofaninterferencepattern.Despitethereonlyeverbeingoneparticle-likedropletintheapparatusatanyonetime,itsaccompanyingpilotwavewascausingthedroplettobehaveasawave.Ifyoudidn’tknowaboutthepilotwave,you’dthinkthedroplethadgonethroughbothslitsandwasinterferingwithitself.

HadCouderandFortdoneanactualdouble-slitexperimentusingabouncingdropletofsiliconeoil?Hadtheyfoundaclassicalanalogueofwhathappensinthequantumworld?Otherteamsracedtoduplicatetheresults,butfailed.OneteamwasledbyTomasBohr,NielsBohr’sgrandson,attheTechnicalUniversityofDenmarknearCopenhagen.AnotherwasledbyJohnBushandhisteamatMIT.TheirresultsrevealedinadequaciesintheexperimentdonebyCouderandFort.BohrandcolleaguesshowedthattheFrenchteam’sstatisticswereinadequate—seventy-fivetrajectorieswerejusttoofewtomakestrongclaimsaboutwhatthedropletsweredoing.AndBush’steampointedoutthattheFrenchexperimenthadn’tbeenadequatelysealedofffromenvironmentalinfluences,sothedroplet’spatternsonthesurface,forexample,mayhavebeenaffectedbyambientaircurrents.

WhentheMITresearchersdidamorerigorousversionoftheexperiment,theydidnotseethedouble-slitinterferencepattern.Nordidtheyseethekindofdiffractionpatternsexpectedwhenaparticlegoesthroughasingleslit.Theyattributethisto“boundaryconditions”:theinteractionofthedropletsandthewaveswiththewallsofthepetridish,forexample,makingitdifficulttoreproducetheconditionsthatwouldbeexperiencedby,say,aphotongoingthroughadoubleslit,wheretherearenosuchboundaryeffects.Maybefutureexperimentalistscancomeupwithwalking-dropletsetupsthatnegateanyeffectsofphysicalboundaries.“Ourresultsdonotclosethedooronthequestfordiffractionandinterferenceofwalkingdroplets,”Bush’steamconcludedinoneofitspapers.

ButBushtoldmethattheydoseethekindofmysteryhighlightedbyRichardFeynman’sanalysisofthedouble-slitexperiment.Inthequantummechanicalversion,whenbothslitsareopen,theparticlegoestocertainplacesonthefarsideandnottoothers.Closeoneoftheslits,andthebehavioroftheparticlechanges,asiftheparticlesensestheclosingofoneslit.Theclassicalwalkingdropletdoesthesame,eventhoughitdoesnotexactlyreplicatean

interferencepatterninwhereitgoesanddoesnotgo.It’sfairtosaythatthedroplet,whichisgoingoveronlyoneopeninginthebarrierortheother,nonethelesscan“sense”whetherbothslitsareopenornot.“Oursystemhasthatfeature,ifthat’sthemystery,”saidBush.

Bushthinksthewalking-dropletsetupisanimportantclassicalanalogueofaquantummechanicalsystem.Theymaynothavereplicatedthedouble-slitexperimentyet,buttheyareseeingphenomenathataretoosuggestivetoignore.Forexample,whentheyfollowtheseeminglychaoticmovementsofadropletinthecircularbath,overtimeitsstatisticsresemblethoseofanelectronmovinginsideaquantummechanicalcorralofatoms.

BushexplainsthisresultusingdeBroglie’sdouble-wavesolution.DeBroglierevisitedthisidea,whichhehadabandonedafterthe1927SolvayConference,whenBohmrevitalizedthesinglepilot-wavetheoryin1952.Thedouble-wavesolutioniswhatitsays:therearetwowavesinvolvedinguidingaparticle.Oneisalocalizedwave,andtheparticleiscenteredonthatwaveandisguidedbyit.Thisparticle-wavecombinationgivesrisetoanotherwavethatbehaveslikethewavefunctioninorthodoxquantummechanics.

AccordingtoBush,thevibratingoilbathandthewalkingdropletphysicallyreplicatethistwo-wavesystem.Thebouncingdropletcreatesandsustainsthepilotwave.Thiswaveislocalizedandthedropletiscenteredonthewave.Theinteractionofthedropletandpilotwavewiththegeometryofthevibratingsurfacealsocreatesanotherwavepatternwhosepropertiesemergeovertimeandmimicthoseofawavefunction.“NowwehaveamacroscopicrealizationofthephysicalpicturesuggestedbydeBroglie,anditexhibitsmanyoftheallegedlyinscrutablefeaturesofquantummechanics,”Bushtoldme.“That’sahellofacoincidence.”

There’sachancethatthat’sallitmightbe:acoincidence.Bushisn’toverlyconcerned.ThemainthrustofhisargumentisthatphysicistshavetochallengetheCopenhageninterpretation,andanythingthatgetsthemtodothatisworththeeffort.“That’swhyI’mabelieverinthisventure,evenifitssoleresultistogetyoungpeopletoquestiontheirviewsonquantummechanics,”Bushsaid.

Tootherquantumphysicists,eventhosewhoareanti-Copenhagen,theideathataclassicalsystemcanreplicateallthefeaturesofquantummechanicsisahardsell.Goldstein,forone,thinksthatthewalkingdropletscanneverreplicatethekeyfeaturethatdistinguishesthequantumworldfromtheclassical:nonlocality,whichdependsonthewavefunctionthat,forasystemoftwoormoreparticles,doesn’tliveinthefamiliarthree-dimensionalspaceofphysicalthings.

things.

—GoldsteinhasanacronymfortheBohmianviewofthequantumworld(a“terribleacronym,”heacknowledged):OOEOW.Itstandsforthe“obviousontologyevolvingtheobviousway.”SinceBohmcameupwithhisformulationofquantumtheoryin1952,therehavebeenmanytweakstothetheory,mostnotablybyBohmhimselfincollaborationwithBasilHiley,whoworkedwithBohmduringthefinalphaseofBohm’scareeratBirkbeckCollegeinLondon(BohmmovedfromIsraeltotheUKandstayedput).OtherswhohavecontributedtothegrowingunderstandingofBohm’sideasincludeEnglishphysicistPeterHollandandtheteamofGoldstein,DetlefDürr,andNinoZanghi.Whilethedetailsdiffer(andcontentiouslyso),theessenceiscapturedbyGoldstein’sacronym.DürrcoinedthetermBohmianmechanics.It’satermthatHileydoesnotlike,butwe’llsticktoitinthischapter,toavoidgettingtangledupinthesubtletiesofthedifferentpointsofview.So,accordingtoBohmianmechanics,thequantumworldconsistsofparticleswithdefinitepositionsandawavefunctionthatguidestheseparticles.IfyouhaveasystemofNparticles,eachparticlehasaposition.Thereis,however,onlyonewavefunction,andeachparticleisbeinginfluencedbyit.Theparticleshavecoordinatesinthree-dimensionalspace,butthewavefunctiondoesn’toperateinthesame3-Dspace.Instead,itdoessoinsomethingphysicistscallconfigurationspace.Takejusttwoparticles.Eachparticlehasacoordinatein3-Dspacethatdescribesitsposition(x1,y1,z1forparticle1andx2,y2,z2forparticle2).Thewavefunctionforthetwoparticles,however,needsallsixnumbers(x1,x2,y1,y2,z1,z2)todescribethestateofthesystem,andthushastocontendwithsixmathematicaldimensions.Theactualpositionsofthetwoparticlesin3-Dspacecorrespondtoonepointinthe6-Dconfigurationspace.

It’seasytoseehowthenumberofdimensionsoftheconfigurationspacequicklymushroomsasthenumberofparticlesincreases—makingitimpossibletovisualize.Nonetheless,nomatterhowmanyparticlesthereareinthesystem,theirindividualpositionsin3-Dspaceultimatelycorrespondtojustonepointinthe3N-dimensionalconfigurationspace,whereNisthenumberofparticles.

Despitethismathematicalabstraction,thewavefunctionisrealinBohmianmechanics.ItpropagatesinconfigurationspaceandevolvesaccordingtotheSchrödingerequation.Anditsimultaneouslyexertsaninfluenceoneachandeveryparticle.Thewavefunctiondeterminesthetrajectoryofeveryparticle.Andbecausethisinteractionbetweenthewavefunctionandtheparticlesisnottaking

becausethisinteractionbetweenthewavefunctionandtheparticlesisnottakingplacein3-Dspacebutwithintheconfinesofconfigurationspace,theinteractionisinstantaneous.ThisishownonlocalityisbuiltintotheveryfabricofBohmianmechanics.Manyhavearguedthatthisprofoundnonlocality(aparticleinsomedistantgalaxy,inprinciple,isinstantlyinfluencingaparticlehereonEarth)makesBohm’sideasuntenable.EventhoughBohmwasawareofthenonlocalitybuiltintohistheory,itwasJohnBellwhowasthefirsttogiveitseriousthought.Hewonderedifhecouldgetridofit.“Heprovedyoucouldn’t,”Goldsteinsaid.

ThetestsofBell’sinequalitycarriedoutbyClauser,Aspect,Zeilinger,andothershaveruledoutlocalhiddenvariabletheories.Thecorrelationsintheoutcomesofmeasurementscarriedouton,say,twoentangledparticlescannotbeexplainedbytheoriesthatpositlocalhiddenvariables,meaningvariablesthatarenotpresentinstandardquantumtheoryandwhosevaluesevolveinalocalmanner,unaffectedbywhat’shappeningatadistance.Thesetests,however,donotruleoutnonlocalhiddenvariabletheories,ofwhichBohmianmechanicsisanexample.Thepositionofaparticle,thehiddenvariableinthetheory,isnonlocallyinfluencedbythepositionsofallotherparticles,mediatedbythewavefunction.BellwaskeenlyawarethathistheoremdidnotaddressnonlocaltheoriessuchasBohm’s.“Infact,Bellrepeatedlystressedthatanyseriousversionofquantummechanics,andevenorthodoxquantummechanics,mustbenonlocal,”Goldsteintoldme.

So,eventhoughorthodoxquantummechanicswinsoutwhenit’spittedagainstlocalhiddenvariabletheories,theoutcomeofatusslebetweentheorthodoxyandBohmianmechanicsisfarfromresolved.IthasprovenimpossibletoexperimentallydisproveBohm’sideas,becausethetheorymakesexactlythesamepredictionsasorthodoxquantumtheory.

Bohmianmechanicsmakesacaseforitselfinotherways.Someaspectsofquantumtheory,whichareaxiomaticinstandardquantummechanics,canbederivedinBohmianmechanics.Forexample,theuncertaintyprinciplecanbeshowntobeanoutcomeofnotknowingenoughabouttheexactinitialconditionsofasystem.So,despitethefactthatBohmianmechanicsisdeterministic,inadequateknowledgecanmakeprecisepredictionsimpossible.Thisisnotunlikechaostheoryinclassicalmechanics:asmallinitialperturbationcanleadtowildlydifferenteventualoutcomesintheevolutionofachaoticsystem(suchasweather),makingthesystemappearnondeterministic.Infact,evenwithallthechallengestoaccurateweatherprediction,itisnonethelessadeterministicsystem.

Eventhecollapseofthewavefunction,whichissuchabugbearinstandardquantumtheory—inthatwedon’tknowwhatitreallymeansorwhetheraphysicalcollapseactuallyhappens—canbededucedinBohmianmechanics.ConsiderSchrödinger’scat.Itcanbedescribedbythepositionsofthe“N”particlesthatmakeupthecatanditswavefunction.InSchrödinger’sthoughtexperiment,whenthecatendsupinasuperpositionofbeingdeadandalive,orthodoxquantummechanicsrequiresameasurement(orobservation)tocollapsethewavefunctionfromitsstateofsuperpositiontooneinwhichthecatiseitherdeadoralive.InBohmianmechanics,theoverallsystemendsupineitheracat-deadorcat-alivestateregardlessofmeasurement.TheNparticlesthatmakeupthecatwillbeinoneconfigurationortheother.Theobservermerelydiscoversthestate.Thereisnocollapseofthewavefunction.Thepartofthewavefunctionthatcapturesthecat-deadstateandthepartofthewavefunctionthatcapturesthecat-alivestatedivergeinconfigurationspaceandnolongerinfluenceeachother.Thereisaneffectivecollapse—butnothingthatismysterious.Thephysicalprocessisclearlymappedoutbywhathappenstotheparticlesthatmakeupthecat.Inaddition,ifonefocusesonwhatshouldberegardedasthewavefunctionofthecataftertheexperiment,onefindsanactualcollapseandnotmerelyaneffectiveone.

“SoBohmianmechanicsisnotarepudiationoftherulesofquantummechanics,”saidGoldstein.“It’ssimplyaclarificationofthem.Youunderstandwheretheycomefrom,youunderstandmoreclearlywhattheysay.”

Despitesuchclaims,supportforBohm’sideaswashardtocomeby.ThosewhofavoredtheorthodoxinterpretationevenpointedoutthattheverystrengthsofBohmianmechanics—itsclearontologyandthefactthatparticleshavetrajectories—wereleadingtoproblems.Theseproblemswerelaidbareusing—whatelse?—thedouble-slitexperiment.TheoristsclaimedthatthetrajectoriespredictedbyBohmianmechanicstodescribeparticlespassingthroughthedouble-slitapparatusmadenosense.Theydubbedthemsurreal,atermtheyusedtoderideBohmianmechanics.

Forexperimentalists,provingtheexistenceofsuchsurrealtrajectorieswasgoingtobeachallenge.Firsttheyhadtofindawaytodeterminetrajectoriesingeneral,beforetheycouldfocusonsurrealones.Itrequiredawholenewwayofthinkingaboutmeasuringtrajectories.Afterall,traditionalquantummechanicseschewedtheverynotionoftrajectories.

—Bohmianmechanics,however,saysthatparticleshavewell-definedtrajectories.

Bohmianmechanics,however,saysthatparticleshavewell-definedtrajectories.ChrisDewdneycanrecallthefirsttimehesawthetrajectoriesofparticlesgoingthroughadoubleslit.Itwasthelate1970s.HehadjustappliedtodoaPhDwithDavidBohmatBirkbeckCollege.BasilHileyrepliedinsteadandsaidhe’dtakeonDewdneyashisstudent.“Okay,closeenough,”Dewdneyrecalledthinking.

Whilehewaslookingaroundforathesistopic,DewdneystumbledonabookatalocalbookstoreonquantummechanicsbyFrederikBelinfante,whichhadachapteronBohm’shiddenvariabletheory.BelinfantesuggestedthepossibilityofcalculatingtheBohmiantrajectoriesofparticlesinatwo-slitexperiment.Dewdneyrecalledbeingpuzzled.“Ithought,‘Thisisverystrange.’AtBirkbeck,nobodywastalkingaboutthis,”hesaid,despitethefactthatBohmhimselfwasatBirkbeck.DewdneytalkeditoverwithHileyandChrisPhilippidisinacoffeeloungeatBirkbeck,andtheydecidedtoplotthetrajectories.Today,oursmartphoneswouldmakequickworkofsuchcalculations.Butfourdecadesago,theyneededasupercomputer,especiallyforthegraphics.Theprogrammingwasdoneusingpunchcards.Youhadtosubmitthecardsandwait.Theresultscamebackinasmallfilmcanister.“Youhadtogetthemprintedorholdthemuptothelight,”saidDewdney,whoisnowattheUniversityofPortsmouthintheUK.Andwhentheydid,theparticletrajectorieswereclearlyvisible.“Itwasamazing,totallyamazing,”Dewdneytoldme.Aparticlewentthroughoneslitortheother,andthenzigzaggeditswaytothescreenonthefarside.Takentogether,trajectoriesbunchedupinwaysthateventuallymimickedaninterferencepattern.

Thetriopublishedapapershowingthetrajectoriesin1979,butmeasuringthemremainedapipedream.“Mostlyeveryoneinthecommunityhadbelievedthatthesearetrajectoriesthatyoucannotdirectlymeasure,”experimentalistAephraimSteinbergoftheUniversityofTorontotoldme.

That’sbecauseatraditional“strong”measurement,whichostensiblycollapsesthewavefunctionofthethingbeingmeasured,destroysthecoherentsuperpositionoftheparticle.Theparticleisirrevocablydisturbed,evendestroyed,byastrongmeasurement.

So,findingaparticle’spossibletrajectoryusingsuchmeasurementsisanimpossibility.Thinkofhowdifferentthisisfromdeterminingthepathof,say,carsonahighway.Ifyouputcamerasevery100meterstorecordthepassingofcars,theinformationfromthesecamerascanbeusedtoreconstructthetrajectoriesofthecarsmovingpast.Butifyoutrytodothisforphotonsorelectrons,itdoesn’twork.Eachstrongmeasurementthattriestofindoutthelocationofaparticlegivestheparticlesuchakickthatitnolongergoeswhereitwouldhavegonehadtherebeennomeasurement.There’sreallynowaytomeasuretrajectoriesofparticlesusingstrongmeasurementswithoutalteringthem.

In1988,YakirAharonov(oneofBohm’sstudents),alongwithDavidAlbertandLevVaidman,cameupwithatheoryofwhattheycalled“weakmeasurements.”Whatifonedoesn’ttrytofindouttheprecisevalueofsomepropertyofaquantumsystembut,rather,probesiteversogently,soastonotdisturbtheparticle,allowingittocontinueonitstrajectoryasifnothinghappened?Itturnsoutthattheoutcomeofanysuchindividualmeasurementisratheruseless.Theuncertaintyinthemeasurementmeanstheresultcouldbewidelyoffthemark.ButAharonovandcolleaguesshowedthatifyoudosuchmeasurementsonalargeensembleofidenticallypreparedparticles,thenalthougheachmeasurementaloneisn’trevelatory,takentogethertheyare.Theteamarguedthattheaveragevalueofallmeasurements—say,inthiscase,ofaparticle’sposition—isanindicationofitsaverageposition.

There’splentyofcontroversyaboutwhetherthisaveragevalueisindeedgivingyouanyrelevantinformationaboutaparticle’sproperty.Butsomephysicistssawinweakmeasurementsawaytomeasureparticletrajectories.In2007,HowardWisemanofGriffithUniversityinBrisbane,Australia,showedthatyoucoulduseweakmeasurementstoseeminglymeasurethepositionsandmomentaofparticlesmovingthroughadouble-slitapparatus.Theideaissimple:youtakehundredsofthousandsorevenmillionsofidenticallypreparedparticlesandsendthemthroughthedoubleslitonebyone,andyouperformweakmeasurements,say,atdifferentlocationsbetweenthedoubleslitandthescreenwheretheinterferenceisobserved.Theseweakmeasurementscanthenbeusedtoreconstructthetrajectoriesofparticlestraversingtheapparatus.“Itmustbe

emphasized,”wroteWiseman,“thatthetechniqueofmeasuringweakvaluesdoesnotallowanexperimenter...tofollowthepathofanindividualparticle.”Thatwouldbeaviolationoftherulesofquantummechanics.Nonetheless,onecould,inprinciple,reconstructaveragetrajectories.

UntilWiseman’spaper,theideaofmeasuringtrajectorieshadbeenanathema,buthisworkchangedminds.AephraimSteinberg’steamtookonthetask.Asalwayswithsuchexperiments,itinvolvedsomeverysophisticatedoptics.Evenso,conceptually,theexperimentiseasytounderstand.Steinberg’steamsendseachphotonintoabeamsplitter,whichsteersthephotonintooneopticalfiberoranother,withequalprobability.Thefibersaresetuptohitamirroredprismthatreflectsthephotonsatrightangles(withtheleftfiberhittingtheleftprismandtherightfiberhittingtherightprism).Theneteffectofthisarrangementisthetwoprismsactastwoslits.ACCDcameraplacedonthefarsideoftheprismsrecordsthephotons.Foreachphotonthatlandsonthecamera,thereisnowaytotellwhichprism(orslit)itcamefrom.Thisindistinguishabilityleadstointerference,whichiscapturedbythecamera.

TheinnovationwasinablockofcalcitecrystalplacedbetweenthedoubleslitandtheCCDcamera.Thephotonshavetotraversethecalcitecrystal,whichhasthepropertyofrotatingtheangleofpolarizationofthephotonmovingthroughit.Bycarefullyaligningthecrystal,it’spossibletousethischangeinthe

photon’sangleofpolarizationtogetasenseofthedirectioninwhichthephotonismoving,relativetothemidline.Thisisaweakmeasurement:thechangeinpolarizationistantamounttocatchingawhiffofthepropagationdirectionwithoutdestroyingthephoton.It’sameasureoftheangleatwhichthephotonistravelingandhenceaproxyforitsmomentum.Ofcourse,thentoactuallymeasurethechangeinpolarizationrequiresastrongmeasurement,whichdestroysthephoton.

So,toreconstructentiretrajectories,Steinberg’steamperformedaseriesofsuchmeasurementsonawholeensembleofidenticalphotonsasthephotonspassedfromthedoubleslittothecamera.Thesewereweakmeasurements,sotheywereaveragevaluescomputedforalargenumberofphotons.Themeasurementswererepeatedfordifferentlocationsbetweenthedoubleslitandthecamera,byplacingthecalcitecrystalatvaryingdistancesfromthedoubleslit,eachtimeinaplaneparalleltotheplaneoftheslits.Thesegavetheaveragemomentaoftheparticlesineachplane.

Therewasonemoremeasurementofrelevance:thepositionofthephotonasitcrossedtheplaneofthecalcitecrystal.OpticswereusedtocapturetheimageofeachphotonontheCCDcameraasitpassedthroughthecrystal.Thiswasusedtocalculatethepositionsofthephotons.“Theimportantthingisthatwecan’tfollowanygivenphotonfromplanetoplane,butineachplanewecancorrelatepositionwithdirection,”saidSteinberg.So“ineachplane,weconstructamapofmomentumversusposition,andthenconnectthe‘arrows’tobuilduptrajectories.”

Thenetresultwasthattheresearcherswereabletoreconstructtheaveragetrajectoriesofthephotons.Theseeminglyimpossiblehadbeendone.ThereconstructedtrajectorieslookedverymuchlikethesimulatedBohmiantrajectories.Ithastobepointedoutthatonecanarriveatthesamepredictionsusingstandardquantummechanics,soit’simpossibletousetheexperimenttosaywhichinterpretationiscorrect.Butdespitesimilarpredictions,thetwointerpretationshaveentirelydifferentthingstosayaboutthenatureofreality:inBohmianmechanics,particlesandtheirtrajectoriesexistindependentofobservation,whereasinstandardquantummechanicstheactofobservationcreatesreality.

In2011,PhysicsWorldnamedSteinberg’sexperimenttheBreakthroughoftheYear,andsaid,“TheteamisthefirsttotracktheaveragepathsofsinglephotonspassingthroughaYoung’sdouble-slitexperiment—somethingthatSteinbergsaysphysicistshadbeen‘brainwashed’intothinkingisimpossible.”

NoteveryoneisconvincedthatSteinberg’steamhasactuallyreconstructed

NoteveryoneisconvincedthatSteinberg’steamhasactuallyreconstructedBohmiantrajectories.OnenaysayerisBasilHiley,whoisnowprofessoremeritusandstillactive.HileycontendsthattheBohmiantrajectoriesshowninhis1979paperwithDewdneyandPhilippidisarefornonrelativisticparticlesthataremovingfarslowerthanthespeedoflight.Photonsaremasslessparticlesthatmoveatthespeedoflightandsoarerelativistic.Particlesofmatter,suchasatoms,arenonrelativistic.HileyarguesthatSteinberg’sexperimentwithphotonsisnotthecorrectonetoreconstructparticletrajectories—eventhoughhe’simpressedwiththeexperimentitself.

Toverifythetrajectoriesfornonrelativisticparticles,HileyhasteamedupwithRobertFlackandhisteamatUniversityCollegeLondon(UCL),andtheyareworkingontheirowndouble-slitexperiment.HileyandFlackhavechosentoworkwithargonatoms.Theideafortheirexperimentcameaboutafewyearsago,whenthetwohappenedtomeetoverbreakfastataconferenceinSweden.TheybeganchattingaboutpossiblytestingBohm’sideas,andFlack(anexperimentalist)said,“Ithinkwecouldhaveago.”

Butit’sbeenahardslog.“SometimesIwishIhadn’tsaidthat,”jokedFlackwhenImethimandHileyintheirlabinthebasementofthephysicsdepartmentatUCL.

“Comeon,Rob,youknow,it’smadeyourlifeworthliving,”Hileybanteredback.

Theexperimentinvolvesfirstcreatingacloudofargonatomsinanexcited,metastablestate(meaningtheyarestableinthisstateforabout100seconds),andbeamtheseatomstowardadoubleslit.Aftergoingthroughthetwoslits,andbeforetheyhitadetector,theatomshavetopassthroughamagneticfield.AndjustasinSteinberg’sexperiment,wheretheangleofthepathofthephotonsthroughthecalcitecrystalisreflectedinachangeintheangleofpolarizationofthephotons,thepaththeargonatomstakethroughthemagneticfieldisalsoreflectedincertaininternalpropertiesoftheatoms.Thisisaweakmeasurement.Aseriesofsuchweakmeasurementscanthenbeusedtoreconstructthetrajectoriesoftheatoms.Intheory.

Theteamisstillworkingongettingtheexperimentupandrunning.Icouldn’thelpbutcommentonhowworkmanlikethesequantumphysicsexperimentslook.Opticalbenches,vacuumpumps,lasers,mirrors,andthelikestrewnabouteverywhere(theexperimentalistswouldpointoutthateverythingisratherpreciselypositioned).Thewholeplacelookslikeamechanic’sshop,albeitaverycleanonewithnogrease,anditbeliestheprofundityofwhat’sbeingtested:theunderpinningsofreality.“Asatheoretician,Ididn’tthinkI’dlivetoseethedaywhentheBohmtheorywasbeingtestedeffectively,”Hiley

livetoseethedaywhentheBohmtheorywasbeingtestedeffectively,”Hileysaid.

—Eventhoughsome,likeHiley,maydisagreewithSteinberg’sexperiment,theaveragetrajectoriesmeasuredbySteinberg’steambroughtoutoneaspectratherclearly:thepathsofthephotonsdidnotcrossthemidlineofthedouble-slitapparatus.Thephotonsgoingthroughtheleftslitendeduponthelefthalfofthefarscreenorcamera,andthosegoingthroughtherightslitarrivedattherighthalfofthedetector.Thepathswouldconvergenearthemiddle,butnevercross.

Whilethetrajectorieswereinlinewithwhat’sexpectedfromBohmianmechanics,therewasonenaggingconcernyettobeaddressed.In1992,MarlanScullyandhiscolleagues(dubbedESSW,aftertheinitialsofthefourteammembers),arguedthatBohmianmechanicspredictedsomethingratherstrange.Ifyoucouldputadetectorneartheslitsthatcouldsomehowtellwhichslittheparticlewentthroughwithoutdestroyingtheparticle,ESSWshowedthatinsomecasesthedetectorneartheleftslitwouldfire,buttheparticlewouldendupattherighthalfofthefarscreen.AccordingtoBohmianmechanics,aparticlethathittherighthalfofthescreencouldhaveoriginatedonlyintherightslit,becausethetrajectorycannotcrossthemidline.So,then,whywasthemathshowingthatsometimes,eventhoughtheparticlehittherighthalfofthescreen,theleftslitdetectorfired?ESSWcausticallycalledthisout.“Tersely:Bohmtrajectoriesarenotrealistic,theyaresurrealistic,”theywrote.

“Tothem,thiswasakindofreductioadabsurdumfortheBohminterpretation,”Steinbergsaid.Overtheyears,manyresearchers(includingHiley)pointedoutvariousproblemswiththeESSWanalysis.Bohmianmechanicsitselfkeptbeingtweaked,withphysicistsdevelopingdifferentversionsofit,butthequestionofsurrealtrajectoriesneverquitewentaway.“Inessence,withanyoftheseversionsoftheBohminterpretation,youcanfindsituationswhereonedetectorfires,buttheBohmmodelhasthetrajectoriesgoingthroughtheother[slit],”saidSteinberg.SurrealtrajectorieswereaknockagainstthecorrectnessofBohm’sideas.

Steinberg’steamsteppeduptheirgame,bringingmoresophisticatedexperimentaltechniquestotheopticalbench.Theywantedtoknow:couldsurrealtrajectoriesdestroyBohm’sideas?

—Asanexperimentalist,Steinbergisagnosticabouttheoreticalinterpretationsof

Asanexperimentalist,Steinbergisagnosticabouttheoreticalinterpretationsofquantummechanics.Evenso,giventheESSWtakeonsurrealtrajectories,SteinbergwasconcernedaboutthevalidityofBohmianmechanics.Thisdespitethefactthatthetheorycamewithcertainadvantages.First,itrestoresdeterminism.“Toalotofpeople,thestandardinterpretationofquantummechanics,whichisverymathematicalandabstract,givesupdeterminism,andtheydon’tunderstandwhyyouwouldgiveitupifyoudon’thaveto,”saidSteinberg.“Theysaythatit’ssuchanimportantphilosophicalassumptionthatifyoushowedmethatitwasincontradictiontoreality,I’dgiveitup,butotherwiseI’llbendoverbackwardstokeepit.”Bohmianmechanicskeepsdeterminismintact.

Second,itmakesnonlocalitymoreexplicit.TestsofBell’sinequalityclearlyshowthatthequantumworldisnonlocal.“Inthestandardtheory,thenonlocalitylooksmysterious,itlookslikethisspookyactionatadistance,whereasintheBohmianmechanics,itshowsupexactlyintheequationsofmotion,”saidSteinberg.It’sclearhowthemotionofanygivenparticleisinstantlyinfluencedbyotherparticles.It’sbuiltintothemathematics.

Ofcourse,BohmianmechanicsmesseswiththeeleganceofSchrödinger’sideas,inwhichthereisjustthequantumstateofthesysteminquestion(givenbythewavefunction)thatevolvesaccordingtotheSchrödingerequation.“Youcanthinkofitasbeingaparticleorawave,butitiswhatitis,”saidSteinberg.“InBohmianmechanics,everythingbecomestwothings.Everythingisaparticleandawave.Youhavedoubledthenumberofentitiesoutthere.Thatdoesn’treallydisturbme,butit’sanargumentsomepeoplemake.”

WhatdiddisturbSteinberg,though,weresurrealtrajectories.“IalsosharedtheESSWintuitionthatthesetrajectoriesdidn’tmakeanysense,”Steinbergtoldme.It“wasoneofthethingsthatusedtomakemelessenamoredoftheBohmianpicture.”Aftertheirtourdeforce2011paperonaveragetrajectoriesofphotonsgoingthroughadoubleslit,itwastimetotesttheESSWclaimaboutsurrealtrajectories.

Itrequiredasmallbutsignificanttweaktotheirearlierexperiment.Insteadofaphotonsourcethatgeneratedsinglephotons,theybeganusingasourcethatgeneratedapairofentangledphotons.Thesephotonsareentangledintheirpolarization.Thephotonsarepolarizedinthehorizontal-verticalbasis,soifonephotonismeasuredandfoundtobepolarizedinthehorizontaldirection,thentheotherphotonwillbeverticallypolarized,andviceversa.

Let’scalloneoftheentangledphotonsthesystemphoton.Thisissentthroughthesamekindofsetupthatwasusedtomeasureaveragetrajectories.

throughthesamekindofsetupthatwasusedtomeasureaveragetrajectories.Theonlydifferencebeingthatinsteadofusingastandardbeamsplitter,theyusedapolarizingbeamsplitter(PBS)tosteeraverticallypolarizedphotonintotheleftopticalfiberandhencetheleftslitofthevirtualdoubleslit,andthehorizontallypolarizedphotontotherightslit.Aswesawinearlierexperiments,thepolarizationisconvertedintoapath.

Theotherphotonisthe“probe”photon:itcontainstheinformationneededtoprobewhichwaythesystemphotonwent,withoutdisturbingthesystemphoton.

Therearemyriadthingsonecannowdowiththissetup.Forinstance,ifonesimplymeasuredtheprobephoton’spolarizationinthehorizontal-verticalbasisandgoteitherhorizontalorverticalasananswer,itimmediatelyrevealswhichpathitspartnersystemphotontookthroughthedoubleslit.So,forallthoseprobephotonsthataremeasuredinthehorizontal-verticalbasis,the

probephotonsthataremeasuredinthehorizontal-verticalbasis,thecorrespondingsystemphotonsthatgothroughthedoubleslitdon’tshowanyinterference,becauseweknowwhichpaththeytookandsotheyactlikeparticles.

Butifyoumeasuretheprobephoton’spolarizationinthe+45-degreedirection,thingschange.Themeasurementinvolvessendingtheprobephotonthrougha+45-degreepolarizer:eitheritcomesout(inwhichcase,it’spolarizedata+45-degreeangle)oritdoesn’t.Crucially,theinformationaboutwhetheritwasoriginallyhorizontallyorverticallypolarizedisnowerased.Themathsaysthatnowit’sequallylikelytobehorizontallyorverticallypolarized.Consequently,thecorrespondingsystemphotonisalsoequallylikelytobehorizontallyorverticallypolarized,andsoendsupinasuperpositionofgoingthroughtheleftandrightslits.Takentogether,suchsystemphotonsshowaninterferencepatternontheCCDcamera.

ThisisessentiallyMarlanScully’squantumeraserexperiment.Steinberg’steamhadlotsmoretodobesideserasethewhich-way

information.Forstarters,theybeganmeasuringtheaveragetrajectoriesofthesystemphotonsthroughthedoubleslit.Butforeachweakmeasurementtheymadeonasystemphoton,courtesyofthecalcitecrystal,theyalsomeasuredtheprobephoton,toseeifitwaspolarizedatsomegivenangle.Whateffectdidthispolarizationmeasurementhaveonthesystemphotontravelingthroughthedoubleslit?

Theteamfoundthattheirchoiceofpolarizationangleforthemeasurementoftheprobephotonhadanimmediateeffectonthesystemphoton:itstrajectorywasaltered(asdeterminedviameasurementsovermany,manyparticles).“Sowedirectlyseethatthisisanonlocaltheory,”saidSteinberg.“Wecan’treallypredictwhatthesetrajectoriesarewithoutpayingattentiontothe[probe]photon.”

Itwasnowfinallytimetoaskthebigquestion:weresometrajectoriessurreal?Toanswerthequestion,theybeganstudyingthetrajectoriesofthesystemphotons,andforeachtrajectory,theylookedatthepolarizationoftheprobephotonatvariouspointsinthetrajectoryofthesystemphoton.Didthepolarizationchangewiththetrajectory?

Theanswerwasaclearyes.Sayasystemphoton’strajectorystartedoffattheleftslit.Theprobephoton’spolarizationwouldbevertical.Butasthesystemphotonmovedthroughtheapparatus,theprobephoton’spolarizationkeptchanging:anotherdemonstrationofthenonlocalinteractionbetweenthetwophotons.AndthereweresituationswhenthesystemphotonthatbeganitsjourneyattheleftslitwouldreachthelefthalfoftheCCDcamerascreen,buttheprobephotonwouldendina50-50mixofbeinghorizontallyandverticallypolarized:itspolarizationwasequallylikelytobehorizontalorvertical.Moretothepoint,sincethepolarizationoftheprobephotonisanindicationofwhichslitthesystemphotontook,theprobephotonwouldsometimesindicatethatthesystemphotontooktheleftslitandatothertimesindicateittooktherightslit,eventhoughtheBohmiantrajectoryclearlyshowedthatthesystemphotonstartedattheleftslitandremainedinthelefthalfoftheapparatus,nevercrossingthemidline.

crossingthemidline.ThiswasthesurrealtrajectoryESSWhadtheoreticallyidentified.Except,to

them,ithadmadenosense,becausetheBohmiantrajectorieswereatoddswiththeinformationinthewhich-waydetector.ButSteinberg’sexperimentshowsthatthesystemphoton,asit’smovingfromtheslittothescreen,isnonlocallyinfluencingthepolarizationstateoftheprobephoton:it’snonlocallyinfluencingthewhich-waydetector.So,sometimes,attheendofthesystemphoton’strajectory,theprobephoton’spolarizationmayhavechanged,say,fromhorizontaltovertical,leadingonetoerroneouslyinterpretthatthesystemphotonwentthroughtherightslit,nottheleftone.Ifyoudidn’tknowofthenonlocalinteractionbetweenthephotons,youwouldseetheresultsasaknockagainstBohmianmechanics,asESSWdid.Steinberg’steamisarguingthatBohmianmechanicsisconsistentanddefensible,andcan’tberuledoutbasedontheESSWargument.

Theprobephotonshowsthecorrectpolarizationvaluewhenthesystemphotonisneartheslits,butsometimes,atthemomentthesystemphotonhitstheCCDcamera,theprobephoton’spolarizationitselfhaschanged,duetononlocality.Sothetrajectoryissurrealoruntenableonlyifyouthinkthewhich-waydetector’sfinalvaluewasalwaysitsvalue.That’sclearlynotthecase.

Whilethefindingsremaincontroversial(partlybecausethereareafewdifferentversionsofBohm’stheoryandpartlybecauseofthedebateoverthemeaningofweakmeasurements),forsome,includingSteinberg,thefactthatsurrealtrajectorieshaveaperfectlysensibleexplanationmakesitpossibletothinkofBohmianmechanicsasaviablealternativetotheCopenhageninterpretation.Theexperimentshowsthatitcannotberuledout,yet.

Ofcourse,thesameexperimentalresultscanbepredictedusingstandardquantumtheory.“Itcertainlydoesn’tcomedownononesideortheother,”saidSteinberg.“Thebestthingexperimentslikethiscandoistoremindpeoplethatthe[Bohmian]interpretationexists—peoplewhohadeitherforgottenorneverknewaboutit—andshowthemthatalthoughitmightsoundmysteriouswhenyoufirsthearitdescribed,thesehiddentrajectoriesarerelatedinaverystraightforwardwaytothingsyoucaneasilyimaginegoingintoalabandmeasuring.”

IttookyearsforBohmtogetoutofexilefromBrazilandreachtheUK,butit’stakenevenmoretimeforhisideastostartbeingtreatedasvalidandworthyofsuchexperimentation.“It’saninterpretationthathasn’tgottenenoughattention,peoplearen’tawareofit,andwewant...tobringitbacktoitsrightfulplaceamongallotherinterpretations,”Steinbergsaid.

PhilosopherDavidAlbertthinksthecoldshoulderBohm’sideasreceived

PhilosopherDavidAlbertthinksthecoldshoulderBohm’sideasreceivedwasinnosmallmeasureduetothepoliticsofthetime.“AlargepartofthestoryofthereceptionofBohm’stheoryhastodowiththefactthatwhenhewasinthemiddleofproposingthisherefusedtotestifybeforetheUn-AmericanActivitiesCommitteeandwashoundedoutofthecountry.AlotofthereceptionofBohm’stheoryistiedupwiththat,”saidAlbert.“Scienceisaveryhumanendeavor,andthehistoryoffoundationsofquantummechanicsareaparticularlyvividexampleofthis.”

EventheriseoftheCopenhageninterpretation,Albertargued,couldbeseeninthelightofthe“crisisofrepresentation”thatengulfedliteratureinthelate1800sandearly1900s.Couldlanguagecaptureobjectivereality?Modernistliteraturesaidno:itplayedwithperspective,highlightinguncertaintiesandambiguitiesinherentinanyoneviewoftheworld.Itwas“inspiredbythemodernrealizationoftheobserver’sroleinbothcreatingandcurtailingtheworldofperception”andledto,atitsextreme,“theviewthatthereisnotrueworld,sinceeverythingisbut‘aperspectivalappearancewhoseoriginliesinus.’”

“Literarymodernismwassupposedtobearesponsetothecrisisofrepresentationinliterature.Physicswantedtohaveitscrisisofrepresentationtoo,”saidAlbert.Anditgotone,whenquantumphysicsclaimedthat“thereisn’tanysuchthingastellingtheflat-footed,objective,truestoryofwhat’shappeningtotheparticleinbetweenthismeasurementandthatmeasurement.”

Bohm’sideascertainlychallengethisview.GoldsteinismorethanawarethattherumblingsaboutBohm’sideasaregrowing.“Afterdecadesanddecades,peoplearetakingBohmianmechanicsalittlebitmoreseriously,”hetoldme.“Therewasatimewhenyoucouldn’teventalkaboutit,becauseitwasheretical,itwasn’tCopenhagen.Therewasakindofpoliticalcorrectnessaboutphysics.ItprobablystillisthekissofdeathforaphysicscareertobeactuallyworkingonBohm,butmaybethat’schanging.”

ButasmuchasBohm’srealist,nonlocaltheoryappealstosome,thereareothersforwhomitholdslesssway.EvenSteinberg,whoseexperimentsareresponsibleforshiningafavorablelightonBohmianmechanics,remainsquietlyskepticalofBohm’sideas.OneproblemforSteinbergisthatBohmianmechanicsprivilegespositionoverotherpropertiesofaparticle:it’sonlypositionthatgetsthehonorofbeingassociatedwithahiddenvariable.Butwhataboutaparticle’sspinoritspolarization?Thetheorytreatsthesedifferently,anddoesn’taccordthemthesamekindofhiddenvariableasitdoesposition.“ImustadmitIalwaysfoundthatdistasteful,”saidSteinberg.“BecausebythetimeI

admitIalwaysfoundthatdistasteful,”saidSteinberg.“BecausebythetimeIwasraisedinquantummechanics,Ididn’tseeanythingthatspecialaboutposition.Thereshouldbeoneconsistenttreatmentofallkindsofmeasurements.Ifyourmeasuringdeviceusespolarization,thereshouldbeadifferenthiddenvariablethatcorrespondstopolarization.”

Goldsteinthinksotherwiseaboutaccordingpositiontheprideofplaceasahiddenvariable.“Iregarditasverymuchavirtuethatonedoesnotneedtohaveadditionalreifiedobservablesinordertofullyunderstandwhatisgoingoninanyquantummeasurement,”hesaid.“Positionsuffices.PeoplehaveindeedproposedaddingBohmianversionsoftheotherobservables.Theresultisuglyandtheeffortratherpointless.”

WhileGoldsteinstronglyfavorsBohmianmechanics,Steinberg’sholdingoutforsomethingmorethaneitherorthodoxquantummechanicsorBohmianmechanics.“I’mmostattractedtothepossibilityofusdiscoveringsomethingbeyondquantummechanicsthatresolvestheseproblemsbysayingthatthiswasn’tthecompletetheorytobeginwith,”hetoldme.“I’mwaiting.”

RogerPenrose,atheoreticalphysicistatOxfordUniversityintheUK,sharesSteinberg’sviewthatquantummechanicsmaybeincomplete.“Quantummechanicsisaprovisionaltheory,”hetoldmewhenImethimathishome.SittinginhisbucolicbackyardontheoutskirtsofOxford,Penroseproceededtoexplainwhygravity(whichwehaveignoredthusfarinourattemptsatunderstandingthequantumworld)mayhavesomethingtodowithfixingquantummechanics(atleastinthemindsofthosewhothinkitneedsfixing).Andasalways,itbeganwithadiscussionofthedoubleslit.Thistime,however,insteadofaparticlegoingthroughtwoslits,Penrosetalkedofacatwalkingthroughtwodoorsatonce.

T

7

GRAVITYKILLSTHEQUANTUMCAT?

TheCaseforAddingSpacetimeintotheMix

Auniversitystudentattendinglecturesongeneralrelativityinthemorningand...onquantummechanicsintheafternoon,mightbeforgivenforconcludingthathisprofessorsarefools,ortheyhaven’ttalkedtoeachotherforatleastacentury.

—CarloRovelli

hedayI’msupposedtomeetRogerPenroseatOxfordUniversity,hehastostayhome.SoIreceiveinstructionstogettohishouse—amapthathedrew

byhandalmosttwodecadesagoforguestscomingtohishousewarmingparty,andwhichhehasbeenupdatingeversince,astheneighborhoodchangesaroundhim.Thehigh-levelmapofwherehelivesnearOxfordisatadifferentscale,butisinformativeenough,andthere’sevenadetailed,zoomed-indrawingoftheroadsandhouseswithinafewhundredmetersofhishome(frommacroscaletomicroscale,Ithinktomyself).Itcontainswarnings:“Fancyblockedentrance(notus!),”“Imposingoldhouse,NOTus,”“Smartblockedentrance.NOTUS.”Andanarrowpointingtohishouse,saying,“Ourbrokendownentrance.”

Penrose’spenchantfordrawingbyhandisobviouswhenhegivestalks.Eschewingsophisticatedpresentationswithgraphicsandanimations,hestillreliesonanoverheadprojector,oftentimesusingmultiplehand-drawntransparenciestoprojectasingleimage,eachtransparencymeticulouslydrawnandannotatedindifferentcolors.Hethencarefullyfiddlesaroundwiththem,stackingthem,slidingthemaround,untilacomplexstoryemerges—likeacatinasuperpositionofbeingaliveanddeadatthesametime.

Amathematicalphysicist,Penroseisbestknownforhisworkongeneral

Amathematicalphysicist,Penroseisbestknownforhisworkongeneralrelativityandcosmology,particularlyonsingularitiesthatoccurinsideblackholesoratthebigbang,theplacesinthecosmoswhereourknownlawsofphysicsbreakdown.Suchbreakdownshappenpartlybecausethephysicsofintensegravitationalfieldshastocoexistwiththephysicsofthemicroscale.Generalrelativity,whichisatheoryofgravityonlargescales,hastoconfrontquantummechanics.Butsofar,gravityhasstubbornlyresistedsuccumbingtoquantization,unliketheotherthreefundamentalforcesofnature(thequantumoftheelectromagneticforceisthephoton,butthereisnoobservedquantumofthegravitationalforce).There’saconsensusview,however,amongthosestrivingforatheoryofquantumgravitythatit’sgeneralrelativitythathastomakewayinthistussleforsupremacy,andthatquantummechanicscancontinueuntouchedforthemostpart.

Penrose,however,thinksdifferently.“Therehastobegiveonbothsides,”hetoldme.“It’snotasthoughonewinsovertheother;it’sgottobeaneven-handedmarriage.”Andthatunion,saidPenrose,meansfixingwhathethinksiswrongwithquantummechanics.“Thetroublewithquantummechanics[isthat]...itdoesn’treallymakesense,”hesaid.

Hepausedbeforecontinuing.“Ishouldn’tappealtoauthorityhere,yousee,”hesaid.“You’vegotauthoritiesonbothsides.”Still,hepointedoutthatEinstein,Schrödinger,deBroglie,andevenDiractoanextenthadallfeltthatsomethingwasnotquiterightwithquantummechanics.Schrödingermagnifiedhisuneasewithhiseponymouscat—athoughtexperimentthat’saclearaffronttoourclassicalsensibilities.

Toillustratetheabsurdity,PenrosehashisownversionofSchrödinger’scat,a“morehumaneversion,”hequipped.Thecatisinoneroomandisconfrontedwithtwodoorsthatleadtoanotherroom.Themechanismthatopensoneortheotherdoorisquantummechanical.Penroseimaginesaphotongoingthroughabeamsplitter—ifit’sreflecteditopenstheleftdoor;ifit’stransmitteditopenstherightdoor.Thisresultsinthesystembeinginasuperpositionof“leftdooropen,rightdoorclosed”and“rightdooropen,leftdoorclosed.”Ifthecatgoesthrougheitherdoor,itgetssomefood,butunlikethedouble-slitexperiment,wheretheparticleentersasuperpositionofgoingthroughbothslitssimultaneously,ourclassicalsensibilitysaysthatthecatcannotgothroughbothdoorsatonce.But“quantummechanically,you’dhavetoconsiderthatbothalternativescoexistinordertogettherightanswer,”saidPenrose.

Treatingthecatquantummechanicallyleadstothewavefunctionofthecatgoingthroughbothdoorsinakindofsuperpositionofmotions.AccordingtotheCopenhageninterpretation,someinteractionwithaclassicalsystemthatcanbeconsideredanactofmeasurement,suchasaCCTVcamerarecordingthecat’sentry,wouldthencollapsethewavefunctionandshowthecatgoingthroughoneortheotherdoor.Aswithmostphysicistswhohavetroublewithquantummechanics,Penrosefindstheideathatmeasurementisnecessarytocollapsethewavefunctionimplausible.

Onewayoutofthismessisifthereisacleardividebetweenthequantumandtheclassical—andsothecatisalwaysaclassicalobjectandcannotbetreatedquantummechanically.Penrosehashadaradicalideafordecadesthatsuchadivideexistsanditcomesaboutbecauseofthespontaneouscollapseofthewavefunctionwithoutnecessitatingameasurement,explainingwhyanobjectaslargeasasuperposedcatwouldremaininasuperpositionforonlyasmall,smallfractionofasecondbeforecollapsingintooneclassicalstate.InthecaseofSchrödinger’scat,Penrose’stheorycouldcauseacollapseofthetotalsystem,sothecatwouldbeeitherdeadoralivealmostinstantly.

Thesolutioninvolvesgravityandmakesroughpredictionsaboutwherewemightfindtheclassical-quantumboundary.“Youhavegottolooknotattheimpactthatquantummechanicshasongravity,buttheimpactgravityhasonquantummechanics,”hesaid.

OnthatrathernippyEnglishafternoon,sittingatawoodentableonadeckinhisbackyard,Penrosetookoffhisglassesandplacedthemonthetable.Glasseshavemass,andaccordingtogeneralrelativity,theywillwarporcurvespacetimeintheirvicinity.Gravityisthecurvatureofspacetime:themoremassivetheobject,thegreaterthecurvature(blackholesreallyputadentinspacetime,apairofglasses,notsomuch).Butiftheglasseswereinasuperpositionofbeingintwoplaces—Penrosemovedthembackandforthforhisshow-and-tell—thentheglassesatonelocationwouldwarpspacetimeoneway,andanotherwayatthesecondlocation.“Now,therefore,youhaveasuperposition[of]twoslightlydifferentspacetimes,”hesaid.Andthat,saidPenrose,isanunstablesituationthatdestroysthesuperpositionrapidlyifthemassdisplacementislarge.

Sayyouhaveanexperimentinwhichyouhaveputalittlelumpofmaterialinasuperpositionofbeingintwodifferentplaces,saidPenrose.“I’dclaimthatthesuperpositionwillspontaneouslybecomeoneortheotherinatimescalewhichyoucancalculate,roughly.”

AccordingtoPenrose,asuperpositionoftwospacetimescreateswhathecallsa“blister”inthefour-dimensionalvolumeofspacetime.WhenthatblistergrowstoonePlanckunitinfourdimensions,wherethreeofthosearespacedimensions(onePlancklengthequalsabout10-35meters)andoneisthedimensionoftime(onePlancktimeisoftheorderof10-43seconds),thesuperpositionwillspontaneouslycollapsetoonestateortheother.

Forhispairofglasses,suchablisterinspacetimewouldforminfarlessthanonePlancktime.“It’dbeinstantaneous,”saidPenrose.Thatiswhyweneverseemacroscopicobjectsinasuperpositionofstates,whereasforsubatomicparticles,suchaspacetimeblisterwouldtakepracticallyforevertoresolveitselfintoonesideortheother.“Itcouldbeabouttheageoftheuniverse.”

Penrosehasanotherwayofthinkingwhathappenswhentwospacetimeconfigurationsareinsuperposition.Takehisglassesagain.Theyhaveapropertycalledgravitationalself-energy,whichistheenergyrequiredtoholdthesystemtogetheriftherewerenootherforces,inaconfigurationresemblingapairofglasses.Thisis,ofcourse,trueofallmatter,notjustPenrose’sglasses.Now,iftheglassesareinasuperpositionofbeingintwoplaces,thenthere’sanuncertaintyaboutthegravitationalself-energyofthesystem.PenrosethenresortstooneofHeisenberg’suncertaintyrelations,todowithsimultaneousmeasurementsofenergyandanintervaloftime:themorepreciselyyouknowtheenergyofasystem,thelesssureyouareofthetimeinterval,andviceversa.Byapplyingthisuncertaintyrelationtotheuncertaintyinthegravitationalself-energyofthesysteminsuperposition,Penroseestimatesthetimeintervalforwhichthesuperpositioncanbestablebeforecollapsingtooneortheotherstate.Admittingtoabitof“hand-waving,”Penrosesaid,“Ican’tsaywhenit’llhappenandIcan’tsaywhichit’lldo,butIcangiveyouanestimate.”

AsconvincedasPenroseisofhisideathatgravitymustplayaroleinthecollapseofthewavefunction,theresponsefromphysicistsandphilosophersprobingthefoundationsofquantummechanicshasbeentepid.It’sprobablybecausehe’sproposingmodifyingquantummechanics—particularlythewaythewavefunctionevolvesaccordingtotherulesoftheSchrödingerequation.Thegravitationallyinducedcollapseofthewavefunctionmessesupthisratherbeautifulpicture.Butthenitdoesprovideanexplanationforwhythereexistsaboundarybetweenthequantumandtheclassical.

JohnBellalwaysfoundthisboundary,unspecifiedbutimplicitintheCopenhageninterpretation,verytroubling.Afterall,evenaso-calledclassicalmeasurementapparatusconsistsofatomsandmolecules,eachofwhichonits

measurementapparatusconsistsofatomsandmolecules,eachofwhichonitsownisregardedasquantummechanical,butanagglomerationofanunspecifiednumberofatomsandmoleculeshastobeatsomepointregardedasaclassicalobject.Bellobjectedtowhathecalleda“shiftysplit”betweenthetwoworlds.Penrose’swork,whileitmesseswiththeelegantevolutionofthewavefunction,givesareasonforwhythissplitmightexistinthefirstplace.

Penroseispuzzledbypeople’sobjectionstomodifyingquantummechanics.HepointsoutthatNewtonianmechanicslastedalotlongerthanquantummechanicshas.“Peoplewereprettyconvincedthatthatwasapicturethatwasgoingtostickforever,”saidPenrose.Yetitdidn’t.Andthattoodespitenotsufferingfromanymeasurementparadox.“SoIdon’tseewhypeoplearesocompletelyconvincedby[quantummechanics].”

Gravity-inducedcollapseofthewavefunctioncanbeseenasoneexampleofamoregeneralizedsolutiontothemeasurementproblem.In1986,aroundthesametimethatPenroseandothers,includingmostprominentlytheHungarianphysicistLajosDiósi(whocametotheseideasatouchearlierthanPenrose),wereformulatingideasaboutgravity’srole,threephysicists,GiancarloGhirardi,AlbertoRimini,andTullioWeber,cameupwithanotherwayofmodifyingquantummechanics.

GRW,asthetheoryiscalled,changesthewaythewavefunctionsofparticlesevolve.RatherthanbeingcompletelygovernedbytheSchrödingerequation,GRWaddsacomponenttothedynamicsofthewavefunctionthatcausesittocollapseatrandom.Butthecollapseisnotinducedbygravity,àlaDiósi-Penrose,orbyameasurement,asintheCopenhageninterpretation.Rather,itissomethingspontaneous,andanelementalaspectofnature.Itcausesthewavefunctionofaparticletogofrombeingspreadouttobeingrelativelylocalized.Mathematically,thediffusewavefunction,whichsaysthattheparticlecanbeinmanydifferentlocationsatonce,ismultipliedbyanotherfunction.Thinkofthisfunctionassomethingthatismostlyzeroatallphysicallocationsbutatonelocationrapidlyrisestoacertainpeak.Thenetresultofthismultiplicationistocollapsethewavefunction,leavingtheparticleroughlylocalizedatonepointinspaceandtime.

Tomimicthepredictionsofquantummechanics,GRWhastoensuretwothings.One,thatsuchspontaneouscollapsesareextremelyrareforindividualparticles,sothattheycanremaininsuperpositionofstatesforanymeasurablelengthoftime.Two,thatforalargecollectionofparticles,say,thosethatmakeupacat,thecollapseofthewavefunctionisnearcertain,sothatthecatisalwaysfoundinsomemacroscopicallyidentifiablestateandnotinasuperposition.In

theirearliestversionsofthetheory,GRWshowedhowtosetupthetheorysothatitcouldtakealmost100millionyearsforasingleparticletocollapse,whereasamacroscopicobjectwithabout1020particleswouldcollapsealmostinstantly(afewtensofnanosecondsorless,butestimatesvary).

Asalwayswithmodificationstoquantummechanics,peoplefoundflawswiththeGRWmodel,whichotherstriedfixingwithfurthertweaks.Forexample,theGRWmodeldoesn’tdealwellwithalargecollectionofparticleswithidenticalproperties(sayabunchofelectrons,whichcannotbedistinguishedfromoneanother).Anotherversionofspontaneouscollapsefixesthisproblem.Andofcourse,theparametersoftheGRWmodelcanthemselvesbefine-tunedinanadhocmannertosuittheoutcomeofexperiments—somethingthatbothersnaysayers.Nonetheless,thebasicideabehindallthesemodelsisstillthesame:aspontaneouscollapseofthewavefunctionthathasnothingwhatsoevertodowithmeasurement.“Thecollapseissomethingthatisoccurringallthetimetoeveryparticle,atrandom,withacertainfixedprobabilityperunittime,”saidphilosopherDavidAlbert,whohasasoftspotfortheGRWtheory.“Thereisnoneedtotalkaboutmeasurements,oranythinglikethat.Thereisnoneedtouseanyofthesewords.”

EvenJohnBellwassuitablyimpressedwhenhefirstencounteredthetheory.“AnyembarrassingmacroscopicambiguityintheusualtheoryisonlymomentaryintheGRWtheory.Thecatisnotbothdeadandaliveformorethanasplitsecond,”hewrote.

MoreimportantforBell,collapsetheorieshadthemathematicstobackupclaimsofcollapse.Hesaidthey“haveacertainkindofgoodness...Theyarehonestattemptstoreplacethewoollywordsbyrealmathematicalequations—equationswhichyoudon’thavetotalkaway—equationswhichyousimplycalculatewithandtaketheresultsseriously.”

Someexperimentalistsaredoingexactlythat.Whetherit’sPenrose’stheoryorGRW-liketheories,theyallmakepotentiallytestablepredictionsaboutwheretheboundarybetweenthequantumandtheclassicalmightlie.Andeventhoughthepredictedboundaryseemsoutofreachoftoday’sexperiments,it’snotstoppingMarkusArndt,anexperimentalistinVienna,fromlookingforit.He’sdoingthatbysendinglargerandlargermolecules(notjustphotonsorelectronsoratoms)throughsomecomplicatedversionsofthedoubleslitandmakingtheminterfere.Thedayhecanconclusivelyclaimthatmoleculesofacertainsizedon’tinterferebecauseoftheirsize—meaningtheycan’tremaininacoherentsuperpositionofsimultaneouslytakingtwopaths—hewillhavefoundnature’sdividingline.Fornow,he’shappyclaimingthathisteamhasworkedwiththe

dividingline.Fornow,he’shappyclaimingthathisteamhasworkedwiththebiggest“Schrödinger’scat”evertoconfronttwodoorsatonce.

—Schrödinger’scathasbecomecodeforamacroscopicobjectthatcanremaininasuperpositionofmultiplestates.ForArndt,themoleculesheworkswitharesuchobjects.Whiletheyarecertainlynowherenearasbigaseventhesmallestpossiblecat,withthemassof10,000protons,theyarethelargestmacroscopicobjectsthathavethusfarbeenseeninsuperpositiongoingthroughadoubleslit.“IamclaimingthatwehavethebiggestSchrödingercat,”Arndttoldme,tongueincheek.TocountasSchrödinger’scat,aquantumsystemshouldbe“somethingthatshouldbereallymacroscopic;itshouldbeatleastaswarmasacatanditshouldcontainabiomolecule.”TheobjectsthatArndthasputintosuperpositionarecertainlymacroscopic,andtheycontainbiomolecules.Butunlikeacatthat’satroomtemperature,forexperimentalreasons,Arndt’smoleculesaremuchhotter.“Arealcatwouldbedeadbythen,”hequipped.

Arndt’sinterestinsuchexperimentsbeganwhenhewasapostdocwithJeanDalibardattheÉcoleNormaleSupérieureinParis(Dalibard,asastudentinthe1980s,hadworkedwithAlainAspectontestsofBell’sinequality,butthendidseminalworkonhisown,particularlyontrappingatomsinplaceusinglasersandmagneticfields).TheParisteamdemonstratedthevalidityofdeBroglie’sideasofmatter-waveduality,usingcesiumatoms.

ArndtcontinuedhispostdocphasewithAntonZeilinger,firstinInnsbruck,Austria,andthenmovedwithZeilingertotheUniversityofVienna,andnowrunshisownlabsonBoltzmanngasse.AmongthemanyexperimentsArndt’sgroupisdoing,onewithparticularrelevancetoquestionsaboutthefoundationsofquantummechanicshastodowithmolecularinterferometry:doingadvancedvariantsofthedouble-slitexperimentwithlargemoleculesandnanoparticles.Zeilinger,inhisearlydays,hadbeenpartofateamthatdemonstratedadouble-slitexperimentwithsingleneutrons,themostmassiveparticletobetestedinthe1970s.Soonphysicistsbeganshowingthatatomscouldbeplacedinsuperpositionofstatesandmadetointerfere.In1991,JürgenMlynekandcolleaguesinKonstanz,Germany,sentheliumatomsthroughtwo1-micrometer-wideslits,about8micrometersapart,andsawtheatomsinterfere.(Thehistoryofatominterferometryisrich.OtherprominentnamesincludeDavidPritchardatMIT,whoshowedin1983thatatomscouldbediffractedatgratings,andFujioShimizuattheUniversityofTokyo,whoreportedin1992adouble-slit

experimentdonewithneonatoms.)Sincethen,ithasbecomearaceofsorts,withtheattentionshiftingtomolecules,toseewhocanbellthebiggestSchrödinger’scat.

Thekeyissuewithgettingmoleculestointerfereistoensurethattheydon’thitanystrayparticlesduringtheexperiment.Ifamoleculeinteractswithaphoton,oranelectron,oranairmolecule,themoleculebeingtestedgetsentangledwiththeenvironment.Whatstartsoffinastateofcoherenceundergoesdecoherence.“Insuchasetting,Icannotdetect[thewhich-wayinformation],buttheenvironmentcan,”saidArndt.Inprinciple,themerepresenceofwhich-wayinformationintheenvironmentisenoughtomakeamessofthesuperposition.Thebestwaytoavoiddecoherence,then,istocarryouttheentireexperimentinavacuumchamber.

In1999,Zeilinger,Arndt,andtheirteamwerethefirsttodoamulti-slitexperimentwithlargemoleculesconsistingofsixtycarbonatomseach—astableformofcarbonthathadbeenidentifiedin1985andnamedbuckminsterfullerene,orbuckyball,becauseithasthesegmented3-DshapeofthegeodesicdomeinventedbyBuckminsterFuller.Abuckyballisabout1nanometerindiameter,andwhenflyinginamolecularbeamataspeedof200meters/second,ithas—accordingtodeBroglie’sequationrelatingthewavelengthofaparticletoitsmomentum—awavelengththat’sabout350timessmallerthanthesizeofthemolecule.Asobjectsgetmoremassive,theirdeBrogliewavelengthsgetsmallerandsmaller,andit’soneofthereasonswhywedon’tobservethewavenatureofsuchobjectsinordinaryencounters.However,accordingtoquantummechanics,theirwavenatureshouldbeapparentwhentheygothroughadoubleslit,onemoleculeatatime.TheresearchersshowedthattheC60moleculescouldindeedbeputintoasuperpositionoftakingtwopathsatonceandmadetointerfere.

Aswiththeexperimentwithsinglephotons,Arndtisquicktostressthattheinterferencebeingobservedintheseexperimentsisaquantummechanicaleffectatthelevelofsinglemolecules.Amoleculecanbedescribedbyawavefunctionforitscenterofmass.Theamplitudeofthewavefunctionatdifferentpointsinspaceletsuscalculatetheprobabilityoffindingthemoleculeatthoselocations.Eachmoleculethatgoesthroughthedoubleslithastohaveawavefunctionsimilartotheothermoleculestoensurethattheinterferencepatternthatdevelopsovertimeaddsup;otherwisethepatterncangetfuzzyornotformatall.

Gettingphotonsorelectronsorneutronstohavesimilarwavefunctionsisrelativelyeasy.Notsoformolecules:youhavetogetthemallmovinginthe

relativelyeasy.Notsoformolecules:youhavetogetthemallmovinginthesamedirectionatthesamevelocity.Adauntingtask,sinceunlikeatomsofgas,“moleculesdon’tliketofly,”saidArndt.Theyaremorelikelytosticktosurfaces,toeachother,doanythingbutgofromthesourcetothedoubleslitandbeyond.

Togetthemtoleavetheirsources,themoleculeshavetobeheatedorotherwiselaunched,butnotinwayssuchthattheirinternalthermalenergymakesinterferenceimpossible.Allofwhich,astheteamhasgonetobiggermolecules,hasmeantresortingtosomeseriouschemistryanddesigningcustommoleculesthathavestableinternalbondsbetweentheatomsthatmakeupeachmolecule,andyetthemoleculesarenotdrawntoeachother;theyarenot“sticky.”Theteam’sbesteffortsofar,intermsofmoleculesgoingthroughamulti-slitarrangement,isawhopper:it’sabespokemoleculewith284carbonatoms,190hydrogenatoms,320fluorineatoms,4ofnitrogen,and12sulfuratoms.That’s810atomsinonemoleculewithatotalatomicweightof10,123.ThemoleculewassynthesizedbyateamledbyMarcelMayor,oftheUniversityofBasel,inSwitzerland.ThehighfluorinecontentactslikeaTeflonshell—preventingthemoleculesfromstickingtoeachothertooreadily.

Whenthesemoleculesleavethesource,theyhaveatemperatureofabout220Celsius—whichwouldkillacat.

Catsormolecules,thetaskistoputthewavefunctionofthemacroscopicobjectintoasuperpositionofstates.Inthiscase,tofirstgeteachmolecule’swavefunctiononthesamepage,thebeamhastobecollimatedinboththehorizontalandverticaldirections,whichsimplyinvolveslettingthemoleculespassthroughnarrowopeningsandselectingonlyabouttheoneintenmillionthatmakeitthrough.Now,themoleculesaremovinginanarrowbeam,buttheystillmighthaveverydifferentvelocities,andhencedifferentwavefunctions.Sothemoleculesarefurtherfiltered—theyhavetogothroughthreenarrowslitsthatareplacedatdifferentdistancesandheights,suchthatatrajectorythatpassesthroughthesethreeslitstracesaparabola.Imaginethrowingaball.It’lltravelinaparabolicarc,theshapeofwhichwilldependonthespeedatwhichyouthrowtheball.Orinversely,foranygivenparabolicarc,allballswiththattrajectoryhavethesamespeed.Arndtandcolleaguestookadvantageofthissimplefact.Theyarrangedthethreeslitssothatallthemoleculesthatgetthroughthemwouldfollowthesameparabolicpath,andsohaveadefinitevelocitywhentheyexit.Nowtheyhadacollimatedbeamofmoleculeswithsimilarvelocities(withinabout10to15percentofoneanother)—andhencesimilarwavefunctions.

Therewasanotherbighurdletocrosstogetthesemoleculestointerfere.Foraparticletobeinasuperpositionofgoingthroughbothpaths,itswavefunctionhastospreadoutenoughtospantwoslits.Forthekindsofdistancestraveledonlaboratorybenches,thisisnotanissueforparticlessuchasphotonsandelectrons.Butnotsoforamolecule:it’dhavetotravelalongdistanceforitswavefunctiontospreadoutenough,makingforanimpossibleexperiment.SoArndt’steamdeployedatrick.Theymadethemoleculesfirstconfrontanarrayofextremelynarrowsingleslits.Thiscausesdiffractionateachoftheseslits,andthewavefunctionstartsspreadingrapidlyontheothersideofeachslit.Nowwhenthewavefrontreachesagratingwithmultipleslitsnottoofaraway,it’swideenoughtoencounteratleasttwoslitsatthesametimeandenterintoasuperposition.Togetasenseforjusthowsmallthedimensionsinvolvedare,thetwoslitsareonly266nanometersacross(aboutahundredthousandtimessmallerthanthewidthofahumanhair).Toensurethatthemoleculeshaveachanceofhittingtheslits(there’snowaytosteerthempreciselytoanyonelocation),theteamilluminatesamulti-slitgratingwithamolecularbeamjustonemillimeteracrossthatspansabout4,000slits.Anyonemolecule’swavefunctionwillhitonlytwoadjacentslitsoutofthese4,000—soeffectively,eachmoleculeseesonlyadoubleslit.

Onefinalchallengeremained:detectingwherethemoleculeslandaftercrossingthedoubleslit.Withaphoton,thisisrelativelyeasy.Aphotographicplatecanregisterahit.Moleculesarelumberingbeastscomparedtophotons.“Ifthey[land]ontoasurface,theystartrollingaround,andiftheydothat,theysmeartheinterferencepattern,”saidArndt.“Soyouhavetomakesurethatthemoleculesarebound,wherevertheyhitthesurface.”

Thismeantdesigningspecialsurfacestocapturemoleculesandmakethemstickthelanding.Onesolutiontheteamcameupwithwassomethingcalledreconstructedsilicon,whichisessentiallyultra-puresiliconwithnakedchemicalbondsonthesurface,likesomanyarmswaitingtoentrapmolecules.Thegiantmoleculeslandonthesiliconsurfaceandbond.Overtime,thesemoleculespileupatvariouslocationsalongthesiliconscreen.

Butunlikeaphotographicplate,thepatternmadebythemoleculesisnotvisibletothenakedeye.Arndt’steamhadtostudythesurfaceusingascanningelectronmicroscope—andwhattheysawwasaninterferencepattern.Moleculesamassedinareasthatmadeupbrightfringes,withfewerinlocationsthatmadeupthedarkfringes.

It’sworthreiteratingthatthemoleculesarenotinterferingwitheachother.Thisissinglemoleculeinterference:inthelanguageofstandardquantum

Thisissinglemoleculeinterference:inthelanguageofstandardquantummechanics,eachmoleculeendsupinasuperpositionofgoingthroughtwoslitsatthesametime,andthesetwostatesinterfere,causingthemoleculetogotolocationsthatendupasbrightfringesandavoidplacesthatbecomedarkfringes.

“Thisisthemostpictorialrepresentationoftheweirdnessofquantumphysics,thatyoucanseethings[behaving]asiftheywereinvariousplacesatthesametime,”saidArndt.“Ofcourse,itgetsmoreandmorecounterintuitive,atleastpsychologically,ifthingsbecomebiggerandbiggerandmorecomplexinternally.Itrelatestothequestion:whycanInotbeintwoplacesatthesametime?”

Theambiguouslanguagethat’sneededtotalkaboutwhat’shappeningisnotsurprising.Themoleculesareparticles,individual“things,”andyettheexperimenthastoacknowledgenotonlytheirdeBrogliewavelengthsbutalsoeachmolecule’swavefunction,andthespreadingoutofthewavefunction.Treatingmoleculesasrealparticles,withrealtrajectories,whileawavefunctionisgoingthroughbothslits,hasBohmianovertones.

“Tobehonest,ifyouarelookingat[these]matterwaves,occasionallyyouthinkasaBohmian.It’sveryhardtoavoid,”Arndtsaid.“Whenwedescribeourinterferometers,wearealwaysthinkingoftheentiretyoftheparticle,itsmass,electricalproperties,andinternaldynamics,etc.Wheneveritinteractswithagrating,it’salwaysthereasanentireparticleandyetitmusthavehadinformationaboutseveralslits,somehow.Inthiscontext,it’smoreintuitivetothinkthere’sapilotwavedrivingtheparticlearound.ThatfitsmostnicelywithBohm’stheory.”

ButthinkinginBohmiantermsisnottheVienneseway.“ViennadoesnothaveatraditionofappreciatingtheroleofthedeBroglie-Bohmmechanics,”Arndttoldme.Nowonder,giventhatthepatriarchoftheVienneseschoolofquantummechanics,AntonZeilinger,isastrongnon-realistinthetraditionofNielsBohrandtheCopenhagenschoolofthought.

ArndtisquicktopointoutthatdespitehistendencytothinkinBohmiantermsformatterwaves,he’sanon-realistwhenitcomestothedynamicsoftheinternalstatesofmolecules,inthatthesestatesdon’texistuntilwemeasurethem.Besides,whathe’sreallyafteristodiscernifthereisaquantum-classicalboundarythat’spredictedeitherbyPenrose’sgravitationalcollapsetheoryorbyanyofthemanyflavorsoftheGRWcollapsetheory.Neitherprediction,unfortunately,iswithineasyreach.ArndtrecalledtheearlydaysoftheGRWtheory,whenitwasthoughtthatmolecularinterferometerswouldseecollapseandhencefindtheboundarybetweenthequantumandtheclassical,with

moleculesatabout109,orabillion,atomicmassunits.Experimentalistscoulddreamoftestingthetheory.Subsequently,sometheoristsrevisedthetargettoabout1016atomicmassunits,makingthetheoryextremelydifficulttofalsify.“Theoristshaveasimplelife,”saidArndt.“Theycanchangetheirparameters.”

Lifeisn’tassimpleforexperimentalists.Ifthemoleculesgetbigger,theyhavetobemadetomoveslower;otherwisetheirdeBrogliewavelengthwillgetsosmallthatit’dbeimpossibletomakefine-enoughslitstoseeinterference.Andeveniftheycouldfigureouthowtomakemoleculesflyslowly,there’syetanotherproblemtoconfront.Slowermoleculeswilltakelongertogetthroughthedouble-slitapparatus,andwhenthemoleculesareinflightforlonger,Earth’srotationstartsbecominganissue.Themoleculesareflyingstraightthroughthevacuum,decoupledfromeverything,andiftheirtimeofflightismorethanafewseconds,thevacuumchamberandthegratingswouldhavemovedenoughduetoEarth’srotationthattheentireexperimentgoesoutofalignment.

Arndt’scalculationsshowthattheycanexperimentintheirlabwithmoleculesofupto108atomicmassunits,whichisabout10,000timesmorethanthecurrentrecord.Theyareevenexperimentingwithsourcesofbiologicalsamples,likethetobaccomosaicvirus,whichhasasizeofabout107atomicmassunits.That’s“intherangeofwhatyoucoulddoinourlab,hypothetically,”saidArndt.Buttheviruseshaven’tcooperated.“Wehadmanydifferenteffortstolaunchthemandeachtimetheybrokeapart.”

Onewaytogotobiggermassesisbyusingmetalorsiliconnanoparticles.ExperimentswithlargerparticleswouldneedtonegatetheeffectofEarth’sgravityandhencewouldhavetobedoneeitherinspace(averyexpensiveproposition)ormorelikelyinadroptower,aspecialtowerfromwhichenoughairhasbeenpumpedouttoletobjectsfree-fallwithoutanyairresistance,effectivelymimickingconditionsinouterspaceforafewseconds.There’sa146-meter-hightowerinBremen,Germany,builtspeciallyforsuchexperiments.Inprinciple,afullysealedvacuumchamberthatencapsulatesthedouble-slitexperimentcanbedroppeddownthetower,andduringfreefall—forabout4seconds—themoleculesandtheexperimentwon’texperienceEarth’sgravity,andthuseverythingwouldremaininalignment.

Whileverifyingcollapsetheorieswithsuchexperimentsremainsadistantdream,Arndthasn’truledoutseeingmodificationsoftheestablishedevolutionofquantumsystemsatmassscalessmallerthanpredictedbyeitherPenrose’sorGRW-liketheories.“Theexperimentalistinmesays,‘Well,whoknows?’Themodelsaremadeupbycleverpeopleandnobodyknowswhethertheyaretrue.Itmaywellbethatsomethinghappenswellbefore.Nooneknows.Soone

Itmaywellbethatsomethinghappenswellbefore.Nooneknows.Sooneshouldjustdotheexperiments,seewhathappens.”

Ifnothinghappens—meaningmoleculesremaininsuperpositionandtheircoherenceispreserved—thenit’stellingusthatthereisnoquantum-classicalboundary,atleastatthemassscalesbeingprobedbytheexperiment.Ontheotherhand,“if[coherence]isnotpreserved,it’samajordiscovery,”saysArndt.“Ineithercase,youwin.”

—Itmayproveimpossibletodotheclassicaldouble-slitexperimentwithmoleculeslargeenoughtofindevidenceforcollapse,especiallyatthemassrangespredictedbyPenrose’stheory.Butwhatifanelementoftheexperimentalapparatusitselfcanbeputintoasuperpositionofstates?BesideshavingaphotongothroughonearmortheotherofaMach-Zehnderinterferometer,whatifoneofthemirrorsusedintheinterferometercouldbemadesmallenoughtobeputintoasuperpositionofbeingatoneplaceoranother.It’sanalogoustoputtingoneoftheslitsinthedouble-slitexperiment—whichwehaveuntilnowconsideredtobeamacroscopic,classical,andimmovablepartoftheapparatus—intoasuperpositionoftwopositions.Thiswouldhaveaverystrangeimpactonthephotongoingthroughtheinterferometer.Notonlyisitconfrontingtwoslitsatonce,butit’sasifoneofthoseslitsisitselfintwodifferentpositions.ItturnsoutthatthistypeofinterferometerisideallysuitedtotestingPenrose’scollapsetheory.

DirkBouwmeester,aDutchexperimentalist,hasbeenworkingononesuchexperimentformorethanadecade,anideafirstsuggestedtohimbyPenrosehimself.WhenBouwmeesterwasworkingonhisPhDintheNetherlands,hebecameinterestedincertainsolutionsofMaxwell’sequationsofelectromagnetism,inwhichlightgoesaroundinknots.HerealizedthatwhathewasstudyingwascloselytiedtoPenrose’sworkontwistortheory(oneofPenrose’ssignaturecontributionstotheoreticalphysics).Intwistortheory,themostfundamentalthingsinnaturearenotparticlesbutraysoflight,ortwistors.BouwmeesterwasstillastudentwhenPenrosecametotheNetherlandstogiveatalk.Bouwmeesternabbedhimafterwardtodiscusstwistors.PenrosewasgettingreadytoleaveandsuggestedBouwmeestercomewithhimtotheairportandtheytalkontheway.Asithappened,“itwasterriblybadweatherandtheflightwasdelayed,andweendeduptalkingabitlonger.ThatwasthefirsttimeImethim,”Bouwmeestertoldme.

ThatinteractionledBouwmeestertoapplyforapostdocatOxford

ThatinteractionledBouwmeestertoapplyforapostdocatOxfordUniversity.AfterayearstudyingtwistortheoryatOxford,BouwmeestermovedtoInnsbruck,Austria,toworkwithZeilingeronquantumteleportationandentanglement.Withthatexperienceinhand,BouwmeestercamebacktoOxfordtosetuphisownquantumopticslaboratory.ItwasduringthissecondstintatOxfordthatPenrosewalkedintohislabonedayandsaid:“Ihavethisexperimentthatweneedtodo.”

Itwasthestrangestthing.Penrosehadplansfordoinganinterferometryexperimentinspace,whichinvolvedthreesatellites.Itgoessomethinglikethis.Ononesatellite,“A,”youfirstsendanX-rayphotonthroughabeamsplitter.Thephotonendsupinasuperpositionofbeingreflectedandtransmitted.Thereflectedphotonissentonitswaytoanothersatellite,“B,”abouttenthousand

reflectedphotonissentonitswaytoanothersatellite,“B,”abouttenthousandmilesaway.Thetransmittedphoton,whichisstillonsatelliteA,goestowardatinymirror.Themirrorisattachedtoacantilever,sothatitcanmoveifsomethinghitsit.Themirrorissosmall,andtheX-rayphotonhassomuchenergy,thatevenasthephotonimpactsthemirrorandisreflectedatrightangles,itdisplacesthemirrorasmidgen.Thisphotontooisnowsentofftowardanothersatellite,“C,”whichisasimilardistanceawayfromAasisB(notethattechnicallyit’dbequiteeasytohavesatellitesBandCcombinedintoonesatellite;it’dmaketheexperimentcheapertoo).

Quantummechanicssaysthatthephotonisinasuperpositionoftakingtwopaths.Notjustthat,thetinymirrorisalsoinasuperposition—ofbeingdisplacedornot-displaced,ofbeingintwolocations,barelyabout10-13metersapart,abouthalfwaybetweenthesizeofanatomicnucleusandtheatomitself(theprecisedisplacementdependsonthetypeofmirrorandcantilever).

Thephotonpathsreachthetwosatellites,eachofwhichhasarigidmirrorthatbouncesthephotonrightbacktothefirstsatellite.ThephotonbouncedoffsatelliteBcomesbacktothebeamsplitter.ThephotonbouncedoffsatelliteC,beforeitcanreachthebeamsplitter,hastoagainencounterthemirrorthatithadpreviouslydisplaced.Thedistancebetweenthesatellitesandthestiffnessofthecantileverissetsuchthatthemovingmirrorisbacktoitsoriginalpositionatexactlythesametimethereturningphotonencountersit.Themomentumfromthemirroristransferredbacktothephoton,reflectingitatrightanglestowardthebeamsplitter.Themirrorgoesbacktobeingatrest.

ThetwophotonpathsaredesignedsuchthatthereflectionsfromsatellitesBandCbothreachthebeamsplitterattheexactsameinstant.Soifthephotonisstillinasuperpositionofhavingtakenbothpaths,thenthetwopathswillconstructivelyinterfere,andthephotonwillexitthebeamsplittertowarddetectorD1.Crucially,thephotonwillneverexittowarddetectorD2,becausethatdirectionrepresentsdestructiveinterference.

IfthisisawfullyreminiscentofinterferenceinaMach-Zehnderinterferometer,thatintuitionisnotoffthemark.Thisisyetanotherwaytomaketwopathsthatlightcantakeinterfere:thisparticulararrangementiscalledaMichelsoninterferometer(withatinyPenrosevariationthrownin—themovablemirror).

Okay,sowhygotoallthistrouble?Whyallthefussaboutusingsatellitesinspace?Forone,thevacuumofspaceensuresthatthereisverylittlechanceofthephotonorthemirrorhittingstrayparticles,aninteractionthatwillleadtodecoherenceandlossofsuperposition.Also,thevastdistancesbetweenthesatellitesensurethatthephotonremainsinsuperpositionforalongenoughtime.

satellitesensurethatthephotonremainsinsuperpositionforalongenoughtime.Thislongso-calledcoherencetimeisnecessarytotestPenrose’sideas.

AccordingtoPenrose,thesizeofthetiny,movablemirrormakesallthedifferenceastowhetherornotthephotonevergoestodetectorD2.WhenthephotonisinasuperpositionofheadingtowardsatellitesBandC,themirrorisinasuperpositionofbeingdisplacedandnot-displaced.Penrose’sgravitationalcollapsetheorysaysthatthehigherthemassofthemirror,thefasterit’llcollapseintoonepositionortheother.

Let’ssaythatthecollapseneverhappensinthetimeittakesforthephotontoreturntothebeamsplitterandhitoneofthedetectors.Inthatcase,thephotonwillcomebackinacoherentsuperpositionofhavingtakentwopathsandhitdetectorD1.

Butifthemirror’squantumstateweretocollapsebeforethephotonreachesthedetectors,thenthephotonwillalsocollapseintohavingtakenonepathortheother.That’sbecausethewavefunctionsofthemirrorandthephotonareentangled,andtheirfatesaretiedupwitheachother.Ifsuchacollapsehappenswhenthephotonisstillenroute,thenthephotonwillarriveatthebeamsplitterhavingtakenoneortheotherpath,notinasuperpositionofhavingtakenbothpaths.Itactslikeaparticle.Thereisnointerference.SothephotonhasanequalchanceofgoingtoD1orD2.

Foragivenmassofthemirror,ifyoudidthisexperimentamilliontimes,andthephotonalwayswenttoD1,thenyoucansaythatthemirrornevercollapsed.ButifhalfthetimethephotonendedupatD2,themirrorhascollapsedineachrunoftheexperiment.ThisbecomesawaytoverifyPenrose’sideasofthecollapseofmacroscopicobjectsduetogravity—andfindthemassscaleatwhichcollapsehappens.

WhenPenrosewalkedintoBouwmeester’slab,hewaskeenonactuallydoingthisexperimentinspace.HeknewpeopleatNASA;hethoughttheycouldpullitoff.BouwmeesterhadtobringthediscussionbackdowntoEarth.“Myinitialreactionwas—it’saveryinterestingproblemtoworkon,butmyexpertiseisinoptics,”Bouwmeestertoldme.“Let’sseeifwecandesignsomethingthatfitsonanopticaltable.”

Andtheycameupwithasolution,withhelpfromatalentedpostdocnamedChristophSimonandagiftedPhDstudent,WilliamMarshall.SittinginhisofficeattheUniversityofCalifornia,SantaBarbara,in2017,Bouwmeestershowedmeapicturetakenin2001ofthefourofthemstandinginfrontofanopticalbench.“That’sme,”saidBouwmeester,pointingtoayouthfulversionofhimself.AndpointingtoPenrose,hesaid,“Rogerdoesn’tchange,butIdo.”

himself.AndpointingtoPenrose,hesaid,“Rogerdoesn’tchange,butIdo.”Indeed,PenroselookednodifferentfromwhenImethimmorethanfifteenyearsafterthepicturewastaken.

Theproblemtheyneededtosolve,todotheexperimentonanopticalbenchonEarth,wasessentiallytheonethatPenrosesolvedbygoingupintospace:howtokeepthephotoninasuperpositionforasufficientlylongtimetowitnessanypotentialcollapseofthemovablemirror’ssuperposition.OnEarth,theyneededtostoreaphotonawhilebeforelettingitcomebackintotheinterferometerandheadtowardthebeamsplitter.Oneoptionwastostorethephotoninanopticalcavity,whichisessentiallymadeoftwoextremelyhighqualityconcavemirrorsalignedsuchthatthephoton,onceitentersthecavity,keepsbouncingbackandforthbetweenthemirrorsandthen,atsomerandomtime,leaksoutagain.It’sawayofstoringthephotonforacertainlengthoftime.

Sothephoton’sjourneytosatellitesBandCisreplacedbytwoopticalcavities,eachholdingontothephotonforawhile,asifitweretraveling10,000milesandback.Theopticalcavitythatreplacesthepartofthephotonpathwiththemovablemirrorissomewhatunique.Inthiscavity,oneofthemirrorsistinyandsuspendedonacantileverarm.Bouwmeesterdecidedtouseopticalandinfraredphotons—it’seasiertomakehigh-qualitymirrorsforthemthanitisforX-rayphotons,whichPenrosehadusedinhisoriginalthoughtexperiment.Thephotonsbouncebetweenthetwomirrorsinsidetheopticalcavity.Thiscreatesa“radiationpressure”thatisstrongenoughtodisplacethemovablemirror.This

“radiationpressure”thatisstrongenoughtodisplacethemovablemirror.Thisphenomenonisitselfquitecurious.Quantummechanicallyspeaking,thephotonisnotlocalized.It’sallovertheplaceinsidethecavity,andovertime,itsdelocalizedpresencecreatesthenecessarypressuretopushatthemirror.

Now,justasthephotonisinasuperpositionofbeingintwoarmsoftheinterferometer,themovablemirrorendsupinasuperpositionofbeingdisplacedandnot-displaced.

Atsomerandommoment,thephotonleaksoutofthecavityandheadsbacktowardthebeamsplitter.Whathappensnextdependsonwhetherthephoton,andindeedtheentiresystem(includingthemovablemirror),isstillinacoherentstateofsuperpositionorhascollapsedtooneortheotherstate.

Iftheentiresystemisstillinsuperposition,thephoton’stwostateswillinterfere.Sinceoneofthepathlengthsisfixed,theinterferencepatternwilldependonthepositionofthemovablemirrorattheexacttimethephotonleaksout—itdictatesthedistancetraveledbythephotoninthearmoftheinterferometerwiththemovablemirror.Theinterferencepatterncreatedovermanyrunsofthisexperiment—detectedasthenumberofclicksatdetectorsD1andD2—willhaveasignaturethat’stiedtothemovablemirror’soscillations.

Butifthemirror’ssuperpositionhascollapsed,thephotonwillactlikeaparticleandhasanequalchanceofheadingtowardD1orD2.AswithPenrose’sspace-basedexperiment,monitoringthestatisticsofthedetectionsatD1andD2cantelluswhetherthetinymirrorhasremainedinsuperpositionornot.

Thefundamentaltaskathandinsuchanexperimentistoputamacroscopicobjectintosuperpositionandkeepittherelongenoughtodoanexperiment.Whentheywrotetheirpaperin2002,BouwmeesterandPenroseclaimedthatatinymirrorcouldbeputintoasuperpositionofbeingattwolocationsifonecouldcombinethestate-of-the-arttechnologiesforeachpieceofthepuzzle.“That’sstilltrue,butitisextremelyhardtocombinestate-of-the-artlowtemperaturephysicswithstate-of-the-artopticswithstate-of-the-artmechanicalfabricationandsoforth,”Bouwmeestersaid.“That’sbasicallywhatwehavebeenworkingoneversince.”

Itturnsoutthatnoneoftheseissuesistrivial.Farfromit.Firsttheyhadtolearnhowtofabricatemirrorsseveralordersofmagnitudesmallerthanagrainofsand.Onetechniqueinvolvedusingafocusedbeamofionstocutoutamirrorandthenglueittoatipofacantilever,tomakeitmovable;themirrorwassosmallandsohardtocontrolthatoftentimesit’dflipduringthefabricationprocessandgetgluedupsidedown.Evenifitwasrightsideup,suchamirror

wasstilltoolarge.Theteamfiguredouthowtomakesmallermirrorscantileveredatthetipofsliversofsiliconnitride.Theyalsohadtomakethesemirrorsunbelievablycold.Otherwisethethermaljigglingofthemoleculesofthemirrorwouldbesuchthattheimpactofasinglephotonwouldhavenodiscernibleeffect.Sothemirrorshadtobecooleddowntobringthemtotheirquantumgroundstate—whichmeantachievingtemperaturesbelow1millikelvin.“That’sridiculouslylowforacryogenicsexperiment,”saidBouwmeester.Butgettingthingssocoldmeansusingdilutionrefrigerators,pumpscirculatinghelium,andthelike—allsourcesofvibrationthatcouldrenderthewholeexercisefutile.And,therefore,theyhadtodevelopmultiplesystemstodampenvibrations.Ofcourse,allofthishastobedoneinsideavacuumchamber.“Intheendthisapparatuscostsseveralmillions,”saidBouwmeester.Allforatinymirrorthatstayssocoldandquietthatitcanbepushedaroundbyaphotonandendupinasuperpositionoftwopositions,onepositionthat’sbarelyafewhundredatomicwidthsawayfromtheother.

“Youfirsthavetoprovethatyoucancreateaquantumsuperpositionofamacroscopicobjectbeforeyoucaninvestigateitsdecoherence,”saidBouwmeester.“Intheend,wearestillquitefarawayfromit.[But]thedevelopmentshavebeenenormous.”

Decoherencespecificallyreferstothelossofcoherentsuperpositionofaquantummechanicalsystemduetoitsinteractionwiththeenvironment,suchthatitendsupinsomeclassicalstate.Penrose’sideasandGRW-likecollapsetheoriesarenottheoriesaboutdecoherence:theyexplicitlyadvocatecollapse,whichleadstodecoherence.

Aswetalked,BouwmeesteradmittedthatdespitebeinginspiredbyPenrose’sideastocarryoutsuchdifficultexperiments,hethinkstheexperimentswillmostlikelynotseeanycollapseofquantumsuperpositionsofmoreandmoremassiveobjects,aslongastheobjectsarewell-enoughisolatedfromtheirenvironmentstopreventdecoherence.Inwhichcase,Bouwmeestersaysthathe’dbeforcedtotakeseriouslytheideathatthereisnoquantum-classicalboundary,thatwavefunctionsevolveandthereisnocollapse.Differentpartsofthewavefunctioncontinueevolving,andastheyinteractwiththeirenvironment,theybehaveasifdecoherencehassetin,makingitdifficultifnotimpossibletogettheseparatelyevolvingwavefunctionstointeract.“Theybecomeindependentandthereisnointerferenceanymore,”saidBouwmeester.“Butthisisratherstrange,becausethenyouarereallybacktoSchrödinger’scat.”

Yes,backtothepoorcat,butinasubtlydifferentway.Insteadofbeingademonstrationoftheabsurdityofquantummechanics,itbecomesanunflinching

demonstrationoftheabsurdityofquantummechanics,itbecomesanunflinchingexplorationofitsimplications.Inthiswayofthinking,Bouwmeesterishintingattheargumentthatboththedeadcatandthelivecatexist,andsodoessomeonewhohasseenadeadcatandsomeonewhohasseenalivecat.Theyaretwodistinctminds,andtherearepossiblytwodifferentworldsthatthesetwomindsinhabit,whichdon’tinteractanymore.“That’snotaridiculouswayoflookingatthings,”hesaid.“Youjusthavetogothroughquantummechanicsforalittlewhiletounderstandhowelegantandsimpleitactuallyis.”

Somephysiciststakethesimplicityandeleganceofquantummechanicstoheart,suchasthestraightforwardevolutionofthewavefunctionaccordingtoSchrödinger’sequationandtheattendantsuperpositions,andrefusetoaddanythingtoitsformalism,eventhenotionofcollapseduetomeasurement,whichisamodificationoftheSchrödingerevolution.Andtheyendupwithastartlingconclusion:superpositionsofsystemsthatcannotinterferewitheachotheranymorenoweachexistintheirownright.Theidealeadsustoanotionof“manyworlds,”whereeverypossibilityexistssomewhere.ForBouwmeester,ifexperimentslikehisneverseecollapse,evenasthemacroscopicobjectsinsuperpositionkeepgettingbiggerandbigger,that’sasign.“InthatcaseIamreallygoingtotakethemanyworldsinterpretationseriously,”hesaid.

BouwmeesterfirstrealizedjusthowearnestlysomephysicistsregardthemanyworldsinterpretationwhenhemetLevVaidman(ofElitzur-Vaidmanbombpuzzlefame)onabusinChina,ontheirwaytoaconference.Vaidmanhasfamouslywritteninoneofhispapers,“Thecollapse[ofthewavefunction]...issuchanuglyscaronquantumtheory,thatI,alongwithmanyothers,amreadyto...denyitsexistence.Thepriceisthemany-worldsinterpretation(MWI),i.e.,theexistenceofnumerousparallelworlds.”

“HewasratherupsetwhenImethim,”Bouwmeestersaid,speakingattheInstituteforQuantumComputinginWaterloo,Canada.Vaidman,itseems,hadbeentryingtogetapatentapprovedforawatchthatwouldhelphimmakeadifficult“yesorno”lifedecision.Thewatchwouldhaveasinglephotonsource.Thephotonwouldgothroughabeamsplitterandbedetectedbyoneoftwosingle-photondetectorsinsidethewatch.Ifoneofthemclicks,thewatchsays“YES,”doit;iftheotherclicks,thewatchsays“NO,”don’t.Vaidman’spointbeingthatnomatterwhatdecisionyoumake,youcanresteasybecauseyouknowthatinanotherbranchofthewavefunction,youhavedonetheopposite.

OnepersonwholikelywouldhavebeenunfazedbyVaidman’swatchisHughEverettIII,amathematicianandquantumtheoristwhofirstadvocated,inhisPhDthesisin1957,takingthecollapse-freeevolutionofthewavefunctionseriously,asawayofsolvingthemeasurementproblem.Histhesisledto

seriously,asawayofsolvingthemeasurementproblem.Histhesisledtopossiblythemostunsettlingsolutiontotheparadoxofthedouble-slitexperimentyetentertained—themanyworldsinterpretation.

I

8

HEALINGANUGLYSCAR

TheManyWorldsMedicine

Actualitiesseemtofloatinawiderseaofpossibilitiesfromoutofwhichtheywerechosen;andsomewhere,indeterminismsays,suchpossibilitiesexist,andformapartofthetruth.

—WilliamJames

fthereisoneplacethatcouldbesaidtohaveharboredahandfulofquantumdissenters—thosewhofoundtheCopenhageninterpretationproblematic,if

notdistasteful—it’dhavetobePrinceton,NewJersey.Einstein,theoriginaldissenter,cametotheInstituteforAdvancedStudyin1933andlivedouttherestofhislifethere,andremainedforeveroftheopinionthatquantummechanicswasn’tcomplete.DavidBohm,whocametoPrincetonUniversityin1946,startedthinkingcontrarianviewsthere,beforegoingintoexileinBrazilin1951,fromwherehepublishedhishiddenvariabletheory.SoonafterBohmleftPrinceton,amathematicallymindedyoungmannamedHughEverettIII,havingjustgottenabachelor’sdegreeinchemicalengineering,cametoPrincetonUniversityin1953andby1955hadbegunworkingonhisPhDinquantumphysics.HissupervisorwasJohnWheeler.ThoughWheelerwasastaunchsupporterofNielsBohrandtheCopenhageninterpretation,Wheeler’sprotégéwouldturnouttobeoneofthemostimaginativeofthenonconformists.

Wheelerputalotofstockintakingtheequationsofphysicsseriouslyandseeingwheretheyledus.SoonafterEinsteincameupwithhisgeneraltheoryofrelativity,solutionsofhisequationswerepointingphysiciststowardtopologicalstructuresinspacetimethattaxedcommonsense.Inthe1960s,Wheelerwould

cointhetermsblackholeandwormholeforsuchstructures.Butevenearlier,Wheeler’sattitudelikelyrubbedoffonEverett—andhe’dapplyittothemathematicsofquantumphysics.

Itstartedwithtakingseriouslythewavefunctionanditsevolution,inallitssimplicityandelegance.TheessenceofEverett’sthinkingwasthatthewavefunctionisallthereis:auniversalwavefunctionfortheentireuniverse,whichdescribestheuniverseasbeinginasuperpositionofanynumberofclassicalstates,andthiswavefunctionandthesuperpositionsevolvecontinuously,deterministically,andforever.

Everett’sintuitionwasinformedbytheneedtodoawaywiththemeasurementproblem.By1955,hehadidentifiedwhathethoughtofasthekeyissuewiththequantumformalismtheninvogue.Ifthestateofaquantumsystematanyinstantisgivenbythewavefunctionpsi,ψ,thenEverettpointedoutthattherearetwoprocessesthatgovernit.First,thewavefunctionevolvesintimeaccordingtoSchrödinger’sequation,acompletelydeterministicprocess.Butuponmeasurement,thewavefunctionabruptlychangestoadefinitestatewithsomeprobabilitythatcanbecalculated—aso-calledprobabilisticjump.Everettfoundthisuntenable.

Heaskedifthesetwoprocesseswerecompatiblewitheachother.Morespecifically,heasked,“Whatactuallydoeshappenintheprocessofmeasurement?”

Consideraphotonthatgoesthroughabeamsplitter.Accordingtostandardquantummechanics,itgoesintoasuperpositionofbeingintwopaths.Thewavefunctionofthephotonatthispointisalinearcombinationoftwo

wavefunctions,oneinwhichthephotontakesthereflectedpath,andtheotherinwhichittakesthetransmittedpath.(Aswesawearlier,ifψ=a.ψref+b.ψtr,wherethecoefficients“a”and“b”arecomplexnumbers,thenthesquareofthemodulusofa,or|a|2,istheprobabilityoffindingthephotoninthereflectedpath,and|b|2theprobabilityoffindingitinthetransmittedpath.Ifthebeamsplitterisbuilttoreflecthalfthelightandtransmithalfthelight,thentheprobabilitiesareeachequalto0.5.)

Now,ifyouhavedetectorsD1andD2,oneattheendofeachpath,thenforeachphotonthatgoesthroughthebeamsplitter,we’llgetaclickateitherD1orD2.IntheCopenhageninterpretation,becausethedetectorsaresomehowmagicallytreatedasclassicalobjects,themeasurementcausesthecollapseofthewavefunction,andthephotonislocalizedateitherD1orD2.Recallthatinthe1960s,EugeneWignertoofoundthisdistinctionbetweenthequantumandtheclassicalratherarbitrary,andarguedthatit’stheconsciousnessofanobserverthatcausesthecollapse.

Everetttookadifferenttack.Ifyoufollowthemathandtreatthedetectorsquantummechanicallytoo,thentheentireapparatusendsupinasuperpositionofD1clickingandD2clicking.Whyjustthedetector?Whynotalsotreattheobserverquantummechanically?Ifso,theobserverendsupinasuperpositionof

hearingD1clickandhearingD2click.AccordingtoEverett,ifyouconsideronlyapartofthiswavefunctioninwhichD1clicks,youareleftwithadefiniteobserverwhohearstheclick.AndexamininganotherpartofthewavefunctionrevealsadefiniteobserverwhohearsD2click.“Inotherwords,theobserverhimselfhassplitintoanumberofobservers,eachofwhichseesadefiniteresultofthemeasurement,”hewrote.

WhatEverettwasproposingisthatthereisnocollapseofthewavefunctionandhencenomeasurementproblem.Allpossibilitiesexist(andwe’llsooncometowhatexistmightmean,again).Inthesimplecaseofabeamsplitterandtwodetectors,weendupwithtwoobservers,eachofwhomhearsoneofthedetectorsclick.

Nowthinkofanobserverinoneofthosebranches.Havingobserved,say,D1click,theobserversendsanotherphotonthroughthesamebeamsplitter.Again,theobserversplits,intoonewhohearsD1clickandonewhohearsD2click.There’snocollapse,noprobabilisticjump,justthecontinuingevolutionofthewavefunction.Thisprocesscanbecarriedonadinfinitum—andwegetatreelikestructureofobservers.Ifyoufollowanyonebranchofthistree,youwillfindanobserverwhohearsthedetectorsclick,forexample,inthefollowingsequence:D1,D1,D2,D1,D2,D1,D1,D2...;orD1,D1,D1,D2,D1,D2,D1,D1...;oraseeminglyrandomcombinationofD1sandD2s.

So,eventhoughthereisnoprobabilisticjumpoccurringinanyonesuchsequenceofdetections—inthesenseofthewavefunctioncollapsingrandomlytooneorotherstate—foreachobserveritseemsasifD1orD2clicksrandomly,andthusthereisaperceptionofacollapsetoonestateortheother.Everettarguedthat“foralmostallofthe‘branches’ofhis‘lifetree,’”anobserverwouldhearD1orD2clickingatafrequencythatwouldtallywiththeprobabilitiesgivenbytheinitialsuperposition,providedofcourseonecarriedoutthisexperimentenoughtimes(it’dturnouttobenotquitesosimple).

Everettwasproposingatheorythatwascontinuous(therewerenorealjumps,justapparentjumps)andcausal,becauseeverythingevolveddeterministicallyaccordingtotherulesoftheSchrödingerequation.Yet,foranygivenobserver,thetheoryisdiscontinuousbecauseoftheperceivedjumpsinstates,andthejumpsareseeminglyrandom.Thetheory,Everettwrote,“canlayclaimtoacertaincompleteness,sinceitappliestoallsystems,ofwhateversize...Theprice,however,istheabandonmentoftheconceptoftheuniquenessoftheobserver,withitssomewhatdisconcertingphilosophicalimplications.”

Heevencameupwithananalogytodrivehomethepoint:“Onecanimagineanintelligentamoebawithagoodmemory.Astimeprogressestheamoebaisconstantlysplitting,eachtimetheresultingamoebashavingthesamememoriesastheparent.Ouramoebahencedoesnothavealifeline,butalifetree.Thequestionoftheidentityornonidentityoftwoamoebasatalatertimeissomewhatvague.Atanytimewecanconsidertwoofthem,andtheywillpossesscommonmemoriesuptoapoint(commonparent)afterwhichtheywilldivergeaccordingtotheirseparatelivesthereafter...Thesameistrueifoneacceptsthehypothesisoftheuniversalwavefunction.Eachtimeanindividualsplitsheisunawareofit,andanysingleindividualisatalltimesunawareofhis‘otherselves’withwhichhehasnointeractionfromthetimeofsplitting.”

WheelerwasimpressedbyEverett’swork,andyethehadseriousreservationsaboutthese“disconcertingphilosophicalimplications.”EverettwastakingontheCopenhageninterpretation,andassuch,Wheeler—whoadmiredNielsBohr—wantedtodiscussEverett’sworkwiththoseinCopenhagen.ButWheelerhadconcernsaboutsplittingobserversandamoebas.“IamfranklybashfulaboutshowingittoBohrinitspresentform,valuable&importantasIconsiderittobe,becauseofpartssubjecttomysticalmisinterpretationsbytoomanyunskilledreaders,”WheelertoldEverett.

Everettavoidedsomeofthese“mystical”overtonesinhisthesis,especiallythebitaboutsplittingamoebas,andthensubmittedittoWheelerin1956.Whileexpoundinghisideasingreatdetailandwithmathematicalrigor,henonethelesstookaimatBohrandtheCopenhageninterpretation,callingitconservativeandovercautious(quitetheirony,whenyouconsiderthattheCopenhagenview,initsextreme,saysthatrealitydoesn’texistuntiloneobservesit).“Wedonotbelievethattheprimarypurposeoftheoreticalphysicsistoconstruct‘safe’theoriesatseverecostintheapplicabilityoftheirconcepts,whichisasterileoccupation,buttomakeusefulmodelswhichserveforatimeandarereplacedastheyareoutworn,”wroteEverett.HecriticizedtheCopenhageninterpretationforrelyingonaformof“objectionable”dualism,splittingtheworldintotheclassicalandthequantum,andascribingtotheclassicalworldarealitythatitdeniedtothequantum.

Asexpected,Everett’sthesiswasreceivedrathercoldlyinCopenhagen.AnAmericanphysicist,AlexanderStern,whowasinCopenhagenatthetime,organizedaseminarinMay1956inwhichhe,NielsBohr,andothersdiscussedEverett’sideas.SternwrotealettertoWheeleraweeklater,inwhichhedetailedthecriticismsoftheCopenhagencrowd,takingissueparticularlywithEverett’sideaofauniversalwavefunction.SternsaidthatEverett’sideas“lack

ideaofauniversalwavefunction.SternsaidthatEverett’sideas“lackmeaningfulcontent”andsaidthatsomeaspectswerea“matteroftheology.”

Wheelerwrotebackalmostimmediately,andwasevensomewhatapologetic.“IwouldnothaveimposeduponmyfriendstheburdenofanalyzingEverett’sideas,norgivensomuchtimetopastdiscussionsoftheseideasmyself,ifIdidnotfeelthattheconceptof‘universalwavefunction’offersanilluminatingandsatisfactorywaytopresentthecontentofquantumtheory.”HethenbothpraisedEverettandmischaracterizedhisposition:“...thisveryfineandableandindependentlythinkingyoungmanhasgraduallycometoacceptthepresent[Copenhagen]approachtothemeasurementproblemascorrectandselfconsistent,despiteafewtracesthatremaininthepresentthesis,draftofapastdubiousattitude[italicsmine].”

Everettdidnosuchthing.Hedidreworkhisthesisintoaversionthatwasalmostthree-quartersshorter(Wheelerhadaskedhimtomakeit“javelinproof”);hetookoutthesharpestattacksagainsttheCopenhageninterpretation,includinghisdenunciationofthemeasurementproblem,andrecasthisviewsaboutquantummechanicsasawaytosolvetheproblemofreconcilinggeneralrelativitywithquantummechanicsintoatheoryofquantumgravity.Buttheunderlyingmathematicalformalismsinthelongandshortversionsofthethesiswereessentiallythesame.HisviewsontheCopenhageninterpretationhadnotchanged,somethingthatbecameabundantlyclearinacorrespondencewiththetheoreticalphysicistBryceDeWitt.

DeWitthadeditedtheissueofReviewsofModernPhysicsinwhichEverett’sshortenedthesishadappeared.DeWittwouldlatersayaboutEverett’spaper:“Iwasstunned,Iwasshocked.”DeWittwrotetoWheeler,raisingsomeconcerns,includingtheissueofthesplittingofobservers:“Icantestifytothisfrompersonalintrospection,ascanyou.Isimplydonotbranch.”WheelerforwardedthelettertoEverett.

Inhisreply,EverettcalledtheCopenhageninterpretation“hopelesslyincomplete”and“aphilosophicmonstrositywitha‘reality’conceptforthemacroscopicworldanddenialofthesameforthemicrocosm.”

Everettalsoclearlyoutlinedwhathappenstothevariousmacroscopicsuperpositionsintheuniversalwavefunction:“Fromtheviewpointofthetheory,allelementsofasuperposition(all‘branches’)are‘actual,’noneanymore‘real’thananother.Itiscompletelyunnecessarytosupposethatafteranobservationsomehowoneelementofthefinalsuperpositionisselectedtobeawardedwithamysteriousqualitycalled‘reality’andtheotherscondemnedtooblivion.Wecanbemorecharitableandallowtheotherstocoexist—theywon’tcauseanytroubleanywaybecausealltheseparateelementsofthesuperposition

causeanytroubleanywaybecausealltheseparateelementsofthesuperposition(‘branches’)individuallyobeythewaveequationwithcompleteindifferencetothepresenceorabsence(‘actuality’ornot)ofanyotherelements.”Inotherwords,toanswerDeWitt,oneversionof“you”doesnotinteractwithanyotherversionof“you”aftersplitting,soyoucanneverfeelyourselfsplitting.

Butamoreseeminglypreposterousideawaswaitinginthewingstobeunleashed:thatsomehoweachsplittingiscausingtheuniverseitselftodivideintoparallelworlds.EverettwouldbringuptheideaataconferenceinOctober1962inCincinnati,Ohio.Amongtheparticipantsweremanyluminaries,includingNathanRosen,BorisPodolsky,PaulDirac,AbnerShimony,andEugeneWigner.Everettwastheretoo.Theattendeesbeganraisingtheuncomfortablequestionofparalleluniverses.Atonepoint,Shimonysaidthattheideathatallmacroscopicsuperpositionscontinuetoexist,evenforasingleobserver,hadstrangeconsequences.“Itseemstomethatifthisisthecase,therearetwopossibilities.Thetwopossibilitiesinvolveawareness.Onepossibilityisthatordinaryhumanawarenessisassociatedwithoneofthesebranchesandnotwiththeothers.Thenthequestionbecomes,howdoesyourformalismpermitthissolution?Theotherpossibilityisthatawarenessisassociatedwitheachbranch.”

Podolskysaid,“Somehoworotherwehaveheretheparalleltimesorparallelworldsthatsciencefictionlikestotalkaboutsomuch.Everytimeadecisionismade,theobserverproceedsalongoneparticulartimewhiletheotherpossibilitiesstillexistandhavephysicalreality.”TowhichEverettreplied,“Yes,it’saconsequenceofthesuperpositionprinciplethateachseparateelementofthesuperpositionwillobeythesamelawsindependentofthepresenceorabsenceofoneanother.Hence,whyinsistonhavingacertainselectionofoneoftheelementsasbeingrealandalloftheotherssomehowmysteriouslyvanishing?”

Aftersomeback-and-forth,ShimonysaidtoEverett,“YoueliminateoneofthetwoalternativesIhadinmind.Youdoassociateawarenesswitheachoneofthese.”Everettconcurred:“Eachindividualbranchlookslikeaperfectlyrespectableworldwheredefinitethingshavehappened,”hesaid.ThiswasabouttheonlyinstanceinwhichEverettexplicitlyacknowledgedthenotionofmultipleworlds.

ItwasDeWittwhoeventuallygavecredencetotheideaofmanyworlds.InanarticleforPhysicsTodayin1970,DeWittexplainedthenewinterpretation,inwhichauniverseisrepresentedbyasinglewavefunction.“Thisuniverseis

constantlysplittingintoastupendousnumberofbranches,allresultingfromthemeasurementlikeinteractionsbetweenitsmyriadsofcomponents.Moreover,everyquantumtransitiontakingplaceoneverystar,ineverygalaxy,ineveryremotecorneroftheuniverseissplittingourlocalworldonearthintomyriadsofcopiesofitself.”

DeWittwouldlaterrememberhisownastonishmentattherealization:“IstillrecallvividlytheshockIexperiencedonfirstencounteringthismultiworldconcept.Theideaof10100+slightlyimperfectcopiesofoneselfallconstantlysplittingintofurthercopies,whichultimatelybecomeunrecognizable,isnoteasytoreconcilewithcommonsense.Hereisschizophreniawithavengeance.”

Despitehisshockandawe,DeWittwasaconvertandhe’dplayamajorroleinproselytizingEverett’sinterpretation,whichgoesbymanynamesnow,butwe’llrefertoitasEverett’smanyworldsorsimplythemanyworldsinterpretation.

—ThefirstthingthatgreetsyouastheelevatordoorsopenonthefourthflooroftheDowns-LauritsenLaboratoryofPhysicsatCaltechisagiantmuralofFeynmandiagrams—thekindofsquigglydrawingsthatFeynmanwoulddrawonpapernapkinstovisualizetheinteractionofparticles.IwastheretomeettheoreticalphysicistSeanCarroll,aproponentofthemanyworldsinterpretation.WeweremidwaythroughourdiscussionaboutquantummechanicswhenCarrolldecidedhewasgoingtosplittheworld.

HisiPhonehasanappcalledtheUniverseSplitter,whichisaversionofthewatchthatVaidmanwantedtopatent—onethatwillhelpyoumakeupyourmindwhenconfrontedwithadifficultYESorNOdecision.Thereisnowrongdecision,for—intheEverettianview—thereexistsauniverseinwhichtheappsuggestsadifferentdecision.Sowhyworry?

Carrollfireduptheapp,withitsdefaultchoicesofwhattodo:TakeachanceorPlayitsafe(wecouldhavetypedinsomethingelse,butwestuckwiththosechoices).Carrollpressedabuttonthatsaid,ominously,“SplitUniverse.”TheappsentacommandtoalabsomewherenearGeneva,Switzerland,whereasinglephotonwassentthroughabeamsplitter.“IfyoubelieveinEverett,thereisaworldinwhichthephotongoesleftandaworldinwhichthephotongoesright,”saidCarroll.

Afewsecondslater,theresultcameback.“Ah,weareintheuniversewherewehavetotakeachance.”AndtheactofsayingaloudthewordsTakeachance

(andpresumablythewordsPlayitsafeinanotherworld)hadsplittheuniverseirreconcilably(we’llcometowhyinamoment).“Nowtherearejusttwocopiesofme.”

Andpresumablyme,Ithought.Wasthisrealorsurreal?WhatIhadwitnessedwasanexperimentalrealizationofonepartofthe

Mach-Zehnderinterferometer,whichbecomesastrangelysimplethingtobeholdinthemanyworldsinterpretation.

Considerfirstaconfigurationwithjustthefirstbeamsplitter,andnothingelse.TheEverettianviewisthatthewavefunctionoftheuniversenowhastwocomponents:oneinwhichthephotonistransmitted,andoneinwhichthephotonisreflected(let’sassumefornowthatthisistheonlyquantumchoicebeingexercisedintheentireuniverse).Sofar,boththeCopenhageninterpretationandthemanyworldsinterpretationareinsync.ThesystemisnowinasuperpositionofthosestatesandcontinuestoevolveaccordingtotheSchrödingerequation.

Ifwenowputdetectorsattheendsofeachpath,thetwointerpretationsgiveuswildlydifferentviewsofreality.

IntheCopenhagenviewofthings,oneofthedetectorsclicks.Ifthemeasurementapparatusisconsideredclassical,thenthatclick,sotosay,isthesoundofthewavefunctioncollapsing.

Forawhile,physiciststhoughttheyhadcomeupwithawaytoexplainthiscollapsewithoutresortingtomagic.Let’ssaythedetectorcanalsobetreatedasaquantummechanicalobject.Ifit’snotkeptcompletelyisolated,thedetectoreventuallystartsinteractingwithitsenvironment,mainlythroughotherambientphotonsandairmoleculesbouncingoffit,andthedetectorbecomesentangledwiththeenvironment.It’smathematicallyimpossibletodescribethiscomplicatedinteraction.So,whatquantummechanicsdoesistodescribethecombinedstateofthephotonandthedetectorusingsomethingcalledadensitymatrix—basically,amathematicalformalismthatignorestheenvironment.Beforetheinteractionwiththeenvironment,thephotonandthedetectorsareinadefinitestateof“thephotonisreflectedandD1clicks”and“thephotonistransmittedandD2clicks.”Aftertheinteractionwiththeenvironment,thequantumformalismsaysthatthesystemisinastateofeither“thephotonwasreflectedandD1clicked”or“thephotonwastransmittedandD2clicked,”butwedon’tknowwhich.Thelattersituationnowrepresentsastatethatencodesourignoranceofwhathappened.

“Ifyouignoretheenvironment,thebestyoucansayaboutyourquantumsystemandthemeasuringapparatusisthattheyareinamixedstate,describedbyadensitymatrix,”saidCarroll.

byadensitymatrix,”saidCarroll.ThedensitymatrixallowsyoutocalculatetheprobabilitythatD1clickedor

D2clicked(0.5each,forthisexperiment).Inthiscase,theprobabilitieslooklikeclassicalprobabilities,inthattheyaregroundedinourignorance.Theprocessofinteractionwiththeenvironmentiscalleddecoherence,andthefactthattheresultantdensitymatrixletsyoucalculatethecorrectprobabilitiesledphysiciststothinkthatdecoherence—whenitwasfirstproposed—actuallycausedthecollapseofthewavefunctionandthussolvedthemeasurementproblem.Butthatexcitementwasshort-lived.Decoherence,whileitsaysthatthecombinationofaquantumsystemandthemeasuringapparatusevolvestolooklikeasysteminaprobabilisticmixtureofclassicalstates,doesn’treallyexplainwhy.

Intheclassicalworld,whenweuseprobabilitiestotalkaboutthestateofasystem,it’sbecauseweareignorant,butthesystemnonethelessisinsomedefinitestate,andthereisnothingelseit’sinteractingwith.Inthequantumworld,theprobabilitiescalculatedusingthedensitymatrixaresomewhatdifferent.Itappearsasifweareignorantoftheexactstate,butunliketheclassicalstate,thequantumstatebeingdescribedbythedensitymatrixisnotadefinitestate.We’dhavetoconsidertheentanglementwiththeoutsideworldtodescribethequantumstateinitsentirety,andthedensitymatrixdoesn’tdothat.

Sothetheoryofdecoherencecomestantalizinglyclosetomakingsenseofcollapse,butfails.TheCopenhageninterpretationdropstheballatthispoint,whereasthemanyworldsinterpretationpicksitupandrunswithit.

Accordingtomanyworlds,bothD1andD2click,eachintheirownbranchofthewavefunction.Thisclickingandtheconsequentinteractionswiththeirlocalenvironmentsleadtoentanglementanddecoherence.Oncedecoherencesetsin,thetwoworldsbeginevolvingindependently,butstillaccordingtotheSchrödingerequation.However,thetwobranchesoftheevolvingwavefunctionarenowimpossibletorecombine.“Theenvironmentsattachedtoeachdecoherentbranchareorthogonaltoeachother,whichmeansthattherewillneverbeanyinterference,”saidCarroll.So,fromthepointofviewofanyonebranchofthewavefunction,“alltheotherbranchesarestillthere,theyarejustexponentiallyhardtofind.”

Butlet’ssaythatyoudidnotputdetectorsD1andD2attheendofeachpathcomingoutofthebeamsplitter,thusavoidingdecoherence.Then,inprinciple,it’spossibletorecombinethetwoworldsbybringingthetwopathstogetheratasecondbeamsplitter.ThatisexactlywhathappensinaMach-Zehnderinterferometer.InordertocalculatetheprobabilityoffindingthephotonatD1orD2,afteritcrossesthesecondbeamsplitter,wehavetotakeintoaccountthatitwentthroughbothpaths,adifferentworldforeachpath.

intoaccountthatitwentthroughbothpaths,adifferentworldforeachpath.ThisisreminiscentofFeynman’sapproachtosolvingthepuzzleofthe

double-slitexperiment,orquantummechanicsmoregenerally.Feynmancameupwithwhathecalledthepathintegralformulationofquantummechanics.Inthisapproach,aparticleapproachingadoubleslitcanstillbetreatedclassically—inthatitgoesthroughoneortheotherslit,butinordertocalculatetheprobabilitythatitlandsonaparticularplaceonthefarscreen,youhavetolettheparticletakeeverypossiblepathfromthetwoslitstothescreen.Thesepathsincludeallsortsofsquigglytrajectoriesthatdon’tmakeanyclassicalsense.Eachofthesepathsisassignedaweightthatdictatesitscontributiontothefinalprobability.

“Whatquantummechanicstellsusfundamentallyabouthowtothinkabouttheuniverseisthatinordertocalculatetheprobabilityofsomethinghappeningwehavetoaddtheamplitudesforallthedifferentwaysitcouldoccur,”AephraimSteinbergtoldme.Whenyoudothat,yougetinterference.“TheinsightthatFeynmanhadwastorealizethatwhat’sreallyinterferingaretwodifferentstatesoftheuniverse.Andinthesimplestcase,thosetwostatesmightonlydifferbywhereasingleparticleis.Istheelectronintheupperpathorthelowerpath?”

WhileFeynman’spathintegralapproachisatoolforcalculatingtheprobabilitiesofexperimentaloutcomesinthisworld,themanyworldsapproachtakesthisideaofdifferentstatesoftheuniverserathermoreliterally.Andthis,accordingtoCarroll,iswhatmakesitstakeonrealityveryappealing,andunderstandingthedoubleslitabreeze,assuming,ofcourse,thatyouarenotperturbedbytheideaofnewbranchesofthewavefunctionandhencenewworldsappearingateveryquantumforkintheroad.“Thereisaheavypsychologicalpricetopay,andthequestionis,howmuchdoesthatbotheryou?”saidCarroll.“Doesn’tbothermeatall.”

HeisfarmorebotheredbytheCopenhageninterpretation.Take,forinstance,Bohr’slanguagethat’susedtodescribethedouble-slitexperiment:ifwedon’tcollectwhich-wayinformation,thephotonbehaveslikeawave;ifwedo,itbehaveslikeaparticle.“Allthatiscompletenonsense,”saidCarroll.

AsanEverettian,Carrollthinkssimplyintermsofawavefunctionthatsplitsintotwocomponentsatabeamsplitter,andeachcontinuestoevolveaccordingtotheSchrödingerequation.Ifthere’snodecoherence,thenthosetwopartsofthewavefunctioncanbemadetointerfere.“Ifyoudon’tentanglethephotonasitmovesthroughtheslits,thenyou’llseetheinterferencepattern,becausethat’sthesolutionoftheSchrödingerequation,”saidCarroll.

thesolutionoftheSchrödingerequation,”saidCarroll.There’snodoublespeak,sotosay,aboutthephotonshowingitswavenature

orparticlenature.It’sjustthewavefunctionevolvinganddoingitsthing—andthewavefunctionrepresentsthequantumstateofreality.“Manyabstractthinkingphysicistsare...impressedbytheunderlyingmathematicalbeautyandeleganceofEverett,”saidCarroll.“Physicistsaresuckersformathematicalbeautyandelegance.”

There’scertainlyamathematicalsimplicitytothemanyworldsidea.There’sjustthewavefunctionanditsevolution.Noaddedingredients(suchashiddenvariables)orungainlynonlineardynamics(suchasstochasticcollapseàlaPenroseorGRW)orCopenhagen-likemagictoinducecollapse.

ThispointwasbroughthomevividlywhenIvisitedphilosopherDavidWallace,whoseofficeisaboutfifteenmilesawayfromCarroll’s,attheUniversityofSouthernCalifornia,LosAngeles.Wallace,whohadpreviouslyworkedwithDavidDeutschattheUniversityofOxford,hadjustmovedtoCalifornia.AndlikeDeutsch,Wallaceisastrongproponentofthemanyworldsinterpretation.Hebeganhisacademiccareerasatheoreticalphysicistbutthenswitchedtophilosophy(whentheoreticalphysics“startedtosoundalittlebittoopractical,”he’sknowntojoke).Andasaphilosopher,hewasseducedbyEverett’smanyworldsinterpretation.

“Tome,oneofthemostattractivethingsabouttheEverettinterpretationisthatitdoesn’tcommityoutoarevisionaryprojectinphysics,”Wallacetoldme.“I’mveryskepticalthatarevisionaryprojectwouldsucceed.”

Tomakehiscase,Wallacetoreapageoffhisyellow,linedwritingpad,andsketcheda2-Dcoordinatesystem,withtheX-axisrepresenting“Changethephysics?”andtheY-axisrepresenting“Changethephilosophy?”.ThepositivepartofeachaxisrepresentedYESandthenegativepartrepresentedNO.

ThephysicsherereferstotheevolutionofaphysicalsystemaccordingtothestandardSchrödingerequation.Thephilosophyreferstothewaywedoscience:standardscientificrealism,theideathatourtheoriesareanobjective,observer-independentdescriptionoftherealitythatisoutthere.

HecrosshatchedthequadrantthatinvolvedYESforboth.“Nobodywouldwanttodobothofthem,socrossoutthatbox,”hesaid.

CopenhagenandQuantumBayesianism(QBism)wentintotheNO,YESquadrant:theydon’tchangethephysics,buttheychangethephilosophy,becausetheinterpretationsarenotobserver-independent(howeveryoudefineanobserver).Copenhagendoesinvolveacollapse,whichisnon-Schrödingerevolution,butsinceitdoesclaimalawforhowthathappens,onecanarguethatitdoesnotmodifythephysics.

Bohmianmechanics,GRW,andPenrose’scollapsetheoryallmodifythephysics,eitherbyaddinghiddenvariablesorbyaddingnewdynamicsthatinterrupttheSchrödingerevolutionofasystem,causingittocollapse.Buttheyleavethephilosophyalone.

Everettmodifiesneitherthephysicsnorthephilosophy.“ThissoundsweirdforsomethingascrazyastheEverettinterpretation,buttheattractionformeisthatit’sextremelyconservative,”saidWallace.

—

—Ifthemanyworldsinterpretationissuchathingofbeautyandelegance,thenhowcomenoteveryoneissoldontheidea?Forstarters,there’stheobviousdiscomfortwiththethoughtof,well,manyworlds.ThiswasvoicedearlyinthelifeoftheEverettinterpretation,mostnotablybyAbnerShimonyattheOctober1962meetinginCincinnati,Ohio.Shimonysaid,“IthinkoneshouldinvokeOccam’srazor:Occamsaidthatentitiesoughtnottobemultipliedbeyondnecessity.Andmyfeelingisthatamongtheentitieswhicharen’ttobemultipliedunnecessarilyarehistoriesoftheuniverse.Onehistoryisquiteenough.”Changethewordhistoriestoworlds,andtheobjectiongetsevenmoretrenchant.

Ofcourse,theproponentsthinkthatthenaysayershaveappliedOccam’srazortothewrongissue.ThephysicistPaulDaviesonceaskedDavidDeutsch,“Sotheparalleluniversesarecheaponassumptionsbutexpensiveonuniverses?”Deutschsaid,“Exactlyright.Inphysicswealwaystrytomakethingscheaponassumptions.”

Wallaceisofthesameopinion.Yes,theEverettianinterpretationarguesfortheexistenceofmanyhistories,worlds,universes(howeveryouwanttothinkofwhat’shappening).“Butthecrucialthingisthatyoudidn’taddthatmaterialtotheunderlyingequation.Youjustinterpretedtheequationsthatway,”saidWallace.“Idon’tthinkthereisaparticularlydefensiblescientificprinciplethatsaysthatfewerthingsarebetter.Thereisaverydefensiblescientificprinciplethatsayssimplerthingsarebetter.Themanyworldsinterpretationmathematicallyisuncontentiouslysimplerthananyof[theother]modifications.”

Andfromacosmologicalpointofview,theideathatthemanyworldsinterpretationrequirestoomuchstuffisalsobattedawaybyCarrollandWallace.Carroll,whoisacosmologist,likesthinkingintermsofawavefunctionfortheentireuniverseanditsevolutionindependentofobservers—itallowshimtodealwiththephysicsofthebigbangandblackholes,forexample.Also,cosmologiststhinkthatourunobserveduniverseisinanycasefar,farlargerthanwhatwecanseethroughourtelescopes.“Wearealready,inphysics,committedtoincrediblylargeamountsofstuff,”saidWallace.What’ssomemoreofthesame?

Thereareotherargumentsindefenseofmanyworlds.Inthemathematicalformalismofquantummechanics,aquantumstatecanberepresentedbyavectorinacoordinatesystemcalledtheHilbertspace.Avectorin2-Dspaceisa

directedarrowthatbeginsattheorigin(0,0)andgoestoapoint(X,Y).Similarly,avectorin3-Dspacebeginsattheoriginandendsatsomepoint(X,Y,Z).AvectorinHilbertspaceisconceptuallythesame,exceptit’sdimensionalitycanbeenormous.AndintheEverettianway(orindeedwhenyoucontemplatethestateoftheentireuniverseinanyinterpretation),thewavefunctionoftheuniverseisavectorintheHilbertspacefortheentireuniverse,andthedimensionalityofthisabstractmathematicalspaceismind-bogglinglylarge.“Itcouldbeinfinite,buteveninthemostpessimisticreadings,itissomethinglikeetothepowerof10120,whichisjustanenormouslycrazynumber,”saidCarroll(whereeequals2.72,approximately).“There’splentyofroomformany,manybranchings.Wearenowhereneardone.”

Schrödingerevolutionmerelytellsyouhowthequantumstateoftheuniverse,representedbyonevectorinthisHilbertspace,changestoanothervector.Soifawavefunctiondenotedbyonevectorsplitsintotwovectors,doeseachvectorrepresentaphysicaluniverse?“Peoplefretaboutthat,butIthinkit’sfine.Ihavenotroublethinkingofthemasuniverses,”saidCarroll.“Theyarenotlocatedinourphysicalspace,theyareseparatecopiesofourphysicalspace,locatedinHilbertspace.”

Similarargumentsarealsousedagainstthosewhosaythatthemanyworldsinterpretationfloutslawsofconservationofenergy.Wheredoestheenergyforthenewphysicalbranchescomefrom?Well,alltheseworlds/universesexistinHilbertspace—notinphysicalspace—sothequestionisabitillposed.NobellaureateFrankWilczekhasargued,forinstance,that“iftheotheruniversesareinaccessible,theycannotbesourcesorsinksofenergy.”

ToCarroll,worryingaboutthenumberofworldsisfruitless.“Let’sgrowupandmovebeyondthat,”hesaid.

That’sbecausethereareotherseeminglymorepressingandlegitimateconcernsabouttheEverettianview.Oneisabouttryingtofigureoutwhatexactlyhappenswhenauniversesplits.Saywesendaphotonthroughabeamsplitterandleteachpathdecohere,resultingintwoseparateworlds.Doestheentireuniversesplitintotwoeverywhereatthesameinstant(andwhatdoesthatmean,giventhatEinstein’srelativityabolishedthenotionofauniversal“now”)ordoesitstartsplittingatthepointwherethedecoherencehappensnearthebeamsplitter,andmoveoutwardatthespeedoflight?Opinionsdiffer,andthere’snoconsensus,evenamongthosewhoarenottroubledbytheideaofmanyworlds.

PerhapsthemostwellknownconcernabouttheEverettianviewhastodowiththemeaningofprobability,whichiscontestedinphysicsandsciencein

withthemeaningofprobability,whichiscontestedinphysicsandscienceingeneral.Butitcomestotheforeinthemanyworldsinterpretation.“Itjustbringsintotheopentheinherentlymysteriousnatureofprobability,”saidWallace.

Let’ssayyousetupaMach-Zehnderinterferometerwithpathlengthssuchthatifyousentphotonsonebyoneintotheinterferometer,75percentofthemwillendupatdetectorD1and25percentatdetectorD2(recallthatthedifferenceinpathlengthscanbetunedtogetthisresult).Thewavefunctionofthephotonafterithascrossedthetwobeamsplitterscanbewrittenasalinearcombinationoftwowavefunctions(ψ=a.ψD1+b.ψD2,whereaandbareamplitudes,and|a|2equals0.75and|b|2equals0.25,andthesenumbersaretobetakenastheprobabilitiesofdetectingthephotonatD1andD2,respectively,theso-calledBornrule).“Thequestioniswhydoamplitudes-squaredgetinterpretedasprobabilitiesofanything?”saidCarroll.

IntheCopenhageninterpretation,that’sjustbydecree:randomnessisinherentinrealityandtheBornrulegivesustheprobabilitiesofmeasurementoutcomes.InBohmianmechanics,eventhoughtheentireevolutionofthequantumsystemisdeterministic,theprobabilitiesarisebecauseweareuncertainoftheinitialconditions.Incollapsetheories,thereisirreduciblerandomnessinthedynamicsofaquantumsystemandthereisreallysomethingstochastichappeningatthemicroscale,regardlessofmeasurement.

Inthemanyworldsinterpretation,thewatersgetmuddiedsomewhat.InEverett’soriginalview,eachtimeyousendthephotonintoour75-25-tunedinterferometer,theuniversesplitsintotwo:oneinwhichD1clicksandD2doesn’t,andanotherinwhichD2clicksandD1doesn’t.SoinoneworldD1clickswithaprobabilityof1,andintheotherworldD2clickswithaprobabilityof1.Significantly,bothworldsarereal.Thenwhat’sonetomakeoftheprobabilitiesof0.75and0.25assignedtotheseoutcomesbyquantummechanics?Onetackistoimaginethattheexperimentcontinuesineachnewbranchoftheuniverse,andsplittingcontinuestoo,creatingmorebranches.Afteralarge,potentiallyinfinitenumberofobservations,onecanlookatthefrequencyofclicksofD1andD2ineachbranchandask:dothefrequenciescomeclosetotheidealof75percentforD1and25percentforD2?Notquite.“Itdoesn’tworkifyoujustcountuptheworlds,”saystheAustralianphysicistHowardWiseman,whoseworkweencounteredinthecontextofweakmeasurementsandBohmiantrajectories.“Inthevastmajorityofworlds,therelativefrequenciesarenothinglikethequantumprobabilities.”Everettusedasleightofhandtoarguethatsomeoftheseworldsshouldbedisregarded—an

argumentthatreliesontheBornrule.Intheremainingworlds,givenanextremelylargenumberofobservations,probabilitiescanbethoughtofasfrequencyofoutcomes.“Butthenwhathappenedtotheideathatallworldsareequallyreal?”saysWiseman.“Howcomeyouarenoweffectivelythrowingawayalmostallofthem,asiftheyarenotasgoodastheothers?”

He’snottheonlyonetroubledbythiswayoflinkingfrequencyofoutcomestoprobabilityinthemanyworldsscenario.CarrollandWallacearetoo.

Carrollsuggestsonewayout:thinkofprobabilityassomethingsubjective.CarrollandphilosopherCharles“Chip”Sebenshavearguedthat|a|2and|b|2shouldbeinterpretedasnumbersthatrepresentouruncertaintyabouttheoutcomeofameasurement.So,asinclassicalphysics,probabilitieshereareduetoourignorance,exceptinthiscasetheignoranceisaboutsomethingquitedramatic:wedon’tknowwhichbranchofthewavefunctionweareon.Let’ssayyoudidonerunoftheexperiment,sendingonephotonthroughtheinterferometer.D1clicksinonebranchandD2clicksintheotherbranchofthewavefunction,decoherenceensues,andyou’llsoonenoughfindyourselfinabranchoftheuniverseinwhicheitherD1clickedorD2clicked.“Thebranchinghappensfirst,becausedecoherenceisvery,veryfast,onmicroscopictimescales,[of]10-20secondsorless.Thereisalwaysaperiodoftimeinwhichthebranchinghasoccurredandtherearetwocopiesofyou,butthosetwocopiesareexactlythesame,becausetheydon’tknowwhatbranchtheyareonyet,”saidCarroll.Thus,eventhoughtherearetwocopiesofyou,foraverytinytimeperiod,thosetwocopiesareignorantaboutthebranching,andit’sthisignorancethatexplainstheoutcomesofexperimentsintermsofprobabilities.CarrollandSebenshaveshownthatinthatbriefmoment,post-decoherence,ifyouweretoassignprobabilitiestoD1clickingorD2clicking,undercertainsimpleassumptions,you’dendupwith|a|2and|b|2,respectively:whichistheBornrule.“There’sarealworld,”butweareuncertainaboutwhereweareinthatrealworld,saidCarroll.

There’syetanotherwaytothinkofprobabilitiesinmanyworlds.Wallaceusesdecisiontheory,anapproachpioneeredbyDavidDeutsch,whichisthestudyofthereasonsbehindthechoicesonemakesorthebetsoneplaces.Ifyouweredoingtheaboveexperimentandhadtobetontheoutcomeofthemeasurement,then,accordingtoWallace,therationalthingforyoutodobeforetheexperimentistotreat|a|2and|b|2asprobabilitiestoplaceyourbetsonwhichbranchofthewavefunctionyou’llfindyourselfin,oncetheexperimentiscomplete.That’swhatarationalagentwoulddo:trusttheBornrule.Wallace

hastriedtoderivetheBornruleusingdecisiontheory,bymakingcertainseeminglysimpleandacceptableassumptions.Forexample,ifthewavefunctionoftheuniverseweretochangeonlybyasmallamount,yourbettingstrategyshouldonlychangebyasmallamount.

Noteveryoneisconvincedofthisapproach.Theaboveassumption“wouldbereasonablewithnormalphysicalquantities.[But]isthatreasonablewhenwetalkofthewavefunctionoftheuniverse?It’ssuchabizarrething.Howcanwegetourheadsaroundwhatthisthingreallyis?”saidWiseman.“It’scertainlynotjustathingthatweareexperiencingintheworld.It’sactuallydescribingusandsimultaneouslyallourpossiblefutures.I’mjustnotconvincedthatthatproblem[ofprobability]hasbeensolved,despitetheworkthathasbeendoneonit.That’sreallyinmymindthebiggestproblemwiththemanyworldsinterpretation,whichhasbeentheproblemwithitallalong.Everettwascertainlyawareofthisproblem.”

Ifnothingelse,themanyworldsinterpretationundeniablyquestionsourunderstandingofthemeaningofprobabilitiesinquantummechanics.

Theadherentsofmanyworldsarenottheonlyonesfussingaboutthemeaningofprobability.Ourfinalinterpretation—atfirstcalledQuantumBayesianism,butnowknownasQBism—initiallygotitsnamefromtheBayesruleofprobability(namedafteraneighteenth-centurystatisticianandtheologian,ThomasBayes).NotonlyistheissueofprobabilityfrontandcenterinQBism,butitbringstheobserverbackintothemix,claimsthatprobabilitiesaresubjective(personaltoeachobserver),andthrowsupquestionsaboutwhatquantumstates(thevectorsinHilbertspace)sayaboutobjectivereality.QBism,“ratherthanrelinquishingtheideaofreality...[says]thatrealityismorethananythird-personperspectivecancapture.”

—WhenChristopherFuchswasaresearcheratthePerimeterInstituteinWaterloo,Canada,heandhiswife,Kiki,boughtanenormoushouseandrefurbishedit.Thepreviousownerhadbeenawomanwhodiedinhernineties.Thehousehadasmallroomwhereshehadwatchedtelevisionanddrankandsmokedheavily,evidencedbytheburnmarksonthewoodenfloornexttothecouch.ChrisFuchsthoughttheroomwouldbeperfectforalibrarywithfloor-to-ceilingbookshelves,soKikiFuchsdesignedone.Sheremovedbyhandthenicotine-soakedburlapwallpaper,commoninhousesbuiltinthelatenineteenthcentury,andhadtheroomcleanedup.Thentheygotacarpentertobuildthebookshelves(madeofquartersawnoak,becausebothChrisFuchsandthecarpenterfeltthat

(madeofquartersawnoak,becausebothChrisFuchsandthecarpenterfeltthatthe1886housedeservednothingless)andstockeditwithFuchs’sfavoritebooksonphilosophy,mostlyonAmericanpragmatism(bythelikesofWilliamJamesandJohnDewey).ButtherewasonesectionofthelibrarydedicatedtothemodernAmericanphilosopherDanielDennett.Itwasn’tthatFuchsadmiredDennett’sphilosophy—quitetheopposite.“ThereasonDennettwastherewasnotbecauseI’masupporterorinterestedinhiminanyway,butratherIseehimastheenemy,”Fuchstoldme.“Youshouldknowyourenemy.”

Dennettisawell-knownmaterialistwhohaslongarguedthattheperceivedimmaterialityofconsciousnessisanillusion.Fuchswantstotakeourconsciousexperienceseriously—astanceheattributestoWilliamJames’sphilosophy.FuchshasalsobeenheavilyinfluencedbyJohnWheeler(withwhomhestudiedattheUniversityofTexasatAustin).WheelerwasastaunchadvocateofBohr’svisionofquantummechanicsandtheCopenhageninterpretation,thestrongversionofwhicharguestheobservercannotbeseparatedfromthatwhichisobserved.ForBohr,theobserverwassomemacroscopicexperimentalsetup.Wheelersometimeswentfurtherinhisspeculations,wonderingwhethertheentiretyofexistencecamedowntoindividualquantumphenomena,eachofwhichwaslinkedtoanobserver,sothatweendupwithauniverse“builtonbillionsuponbillionsofelementaryquantumphenomena,thoseelementaryactsofobserver-participancy.”

ThealternativestotheCopenhageninterpretationwehaveseensofar—Bohmianmechanics,collapsetheories,manyworlds—allremovetheobserverfromthemix(amovethatDennettwouldlikelyapplaud).Fuchs,however,hitchedhiswagontoBohrandWheeler.Hewantstobringtheobserverbackintoreckoning.HisreadingofWheeler’sworksinparticularledhimtothinkingaboutwhatitmeansforsomethingtobeintrinsicallyrandom(whichthequantumworldis,accordingtotheCopenhageninterpretation,makingtheprobabilitiesweassigntotheoutcomesofmeasurementsanobjectivepartofreality).“Thatledmetothinkaboutprobabilitytheory,”FuchstoldmeaswesatattheUniversityofMassachusettsBoston,hisnewacademichomeafterhemovedtherefromWaterloo(ironically,BostonisjustafewmilesawayfromDennett’shometurfatTuftsUniversityinMedford).

Fuchs’stusslewiththemeaningofprobabilityinquantummechanicsbeganinearnestwhenhewasdoinghisPhDwithCarltonCavesattheUniversityofNewMexicoinAlbuquerque.Atthetime,Fuchswasa“frequentist”—someonewhothinksprobabilitiesareobjectivemeasuresofthetendenciesofthingsto

happen,tendenciesthatbecomeapparentifyoudothosethingsaverylarge,possiblyinfinite,numberoftimes.Caves,however,wasaBayesian.Inthiswayofthinking,probabilityisnotanobjectivepropertyofthings.Rather,it’sastatementaboutthepersonassessingthelikelihoodofsomethinghappeningandassigningitaprobability:theprobabilityincorporatestheideathatthepersonisuncertainforwhateverreason,yetmuststillmakethebestdecisionspossibleinlightofthatuncertainty.QuantumBayesianismwasofficiallybornin2002,withthefirstpaperbyCaves,Fuchs,andRüdigerSchack.Thenameprovedamouthful(andbesides,thetermBayesianismcausedcontroversy,giventhemanydivisionswithinBayesianprobabilitytheoryaboutthemeaningoftheterm),soFuchseventuallyshortenedittoQBism,leavingtheBtostandforitself.Itprovedamarketingmasterstroke.QBismhasaringtoit.

QBismchallengednotionsaboutthemeaningofthewavefunction.Thedebateoverthestatusofthewavefunctionhasbeenattheheartofalltheinterpretationswehaveseenthusfar.Itcanbebroadlythoughtofintwoways:eitherthatthewavefunctionrepresentsourknowledgeofthequantumsystem,soitisepistemic,andtheoriesthattakethisstancearecalledpsi-epistemic;orthatthewavefunctionispartofrealityitself,andtheoriesofthispersuasionarecalledpsi-ontic(forontology).

TheCopenhageninterpretation,whichdoesn’taccordanyrealitytothequantumworldbeyondwhatismanifestduringobservation,ispsi-epistemic.Thewavefunctioncontainsenoughknowledgeforustomakeprobabilisticpredictionsabouttheoutcomesofexperiments.Also,nohiddenvariablesareneededtocompletethetheory.

Therearepsi-epistemicmodelsthatdonottakeananti-realistposition,inthattheyaccordarealitytothequantumworld,butnonethelessarguethatthewavefunctionisnotapartofthisrealworld;rather,itisaboutourknowledgeofthatworld.Einsteinisthoughttohavebeenaproponentofthisviewofquantummechanics.

ThealternativestotheCopenhageninterpretationexaminedsofar—thedeBroglie-Bohmtheory,collapsetheories,andthemanyworldsinterpretation—areallrealistaboutthewavefunction.Theyargueforanobjectiveworldouttherethatexistsindependentofobservers.Inotherwords,thereisanontologyofthequantumworld,andthewavefunctionispartofthisontology,makingthesealternativespsi-ontic.

Butinallthesecases,thequantumstate(givenbythewavefunction),whetherit’sepistemicorontic,isassociatedwiththequantumsystem—

somethingthatallobserverscanobjectivelyagreeupon.QBismtakesaradicallydifferentstance.“We’dsay:innaturetherearen’tanythingscalledquantumstates,”Fuchssaid.“Theyjustaren’toutthere.”

QBismisdefinitelypsi-epistemic,butthewavefunctionisassociatedwitheachindividualobserverstudyingaquantumsystem,notwiththequantumsystem.SoifI’mmakingaquantummeasurement,thewavefunctionIuseforthequantumsystemencodesmyexpectationsfortheconsequencesoftheactionI’mabouttotakeonit.Theseexpectationsaredictatedbymybeliefsaboutthesystem.

Sotakeaphotongoingthroughabeamsplitter.Ifyou,theagent,hadnoideaofwhatabeamsplitterdoes,thenyoumightassociateawavefunctiontothephotonasitgoespastthebeamsplitterthatencodesyouruncertainty.Thewavefunctionisalinearcombinationoftwocomponents(thetransmittedandthereflectedpaths).Let’ssayyouassignaprobabilityof1/3forfindingthephotonindetectorD1andof2/3forfindingitindetectorD2.Thisisthesameasassigningamplitudesof1/√3and√2/√3tothereflectedandtransmittedpartsofthewavefunction,sothatsquaringtheamplitudesgivesyoutherespectiveprobabilities.

Butexperience—sayofdoingtheexperimentoverandoveragainorunderstandingthephysicsofthebeamsplitterorreadingtextbooksortalking

understandingthephysicsofthebeamsplitterorreadingtextbooksortalkingwithyourcolleagues—wouldtellyouthattheseprobabilitiesarewrong.You’dupdatethewavefunctionuntilitaccuratelyrepresentsyourbeliefthatthephotonwillgotoD1halfthetimeandD2halfthetime.ThisideacanbeextendedtothefullMach-Zehnderinterferometerand,byextension,tothedoubleslit,thoughtheargumentationgetsmoreinvolved.Regardlessofthecomplexityofthesystem,thekeyideahereisthattheprobabilitiesyouassigntotheoutcomesofexperimentsarecontingentuponyourpersonalsetofbeliefsaboutwhatmighthappen.

“AllofthisispersonalBayesianprobability,”saidFuchs.“TheBayesiannotionisthatyouwritedownaprobabilityassignmentasameasureofwhatyoucan’tpredict.Youmightwritedownaprobabilityassignmentjustbecauseyoudon’thaveallthefacts.[It’s]notanobjectivefeatureofthings,it’sratherastatementaboutthepersonmakingthe[prediction].”

SomephysicistshavearguedthatQBismissimplyCopenhageninsheep’sclothing.ButFuchsvehementlydisagrees.HepointsoutthatintheCopenhageninterpretation,thewavefunctionisassociatedwiththequantumsystembeingstudied,andremovingtheobserverdoesn’tremovethewavefunction:itstillexists,independentoftheobserver,asanobjective,epistemicstatementaboutthesystem.NotsoinQBism.Removetheobserverandthereisnoquantumstate,nowavefunctiontotalkof.Moreover,Copenhagenisanti-realist.QBismisnot,accordingtoFuchs.Itdoesnotdenythatthereisarealworldoutthere.Allitdoesisstate,unequivocally,thatthequantumstatesintheformalismarenotabouttherealworldbutaboutourbeliefsabouttherealworld.Theyaresubjective,notobjective.

Whatdoesallthisachieve,however?Forone,thewholeissueofthecollapseofthewavefunctionbecomes,well,anonissue.Thereisnothingphysicalthatiscollapsing.Allthathappensisthatyouupdateyourbeliefsabouttheworld:thewavefunction,whichquantifiesyourexpectations,changes.Nothingphysicalhappened(notethatthesameargumentcanbemadeforanypsi-epistemictheory—thatthecollapsehasnothingtodowiththephysicalsystem,butrather,it’saboutthechangeinourknowledgeofthesystem).

“ForQBism,youdon’tneedaphysicalstoryanymore,”saidFuchsabouttheneedtoexplaincollapse.“Insteadyousaythis:Itookanactionthatledtoaconsequence,andbecauseoftheconsequenceIbelievenewthings.ThethingsIbelievearecapturedbythismathematicalsymbol,ψ.BecauseIbelievenewthings,instantaneously,uponthenewexperience,thismathematicalobjectchangesinstantaneously.”

changesinstantaneously.”Asfarasinterpretationsoralternativetheoriesofthequantumworldgo,

QBismisoneofthenewestkidsontheblock,anditgoesagainstthegrainformostphysicists,whoshrinkfromtheideaofpersonalizingscience.Forawhile,exceptforFuchsandShack,therewerefewtakers.ButQBismgotaboostwhenDavidMermin,ahighlyregardedsolidstatephysicistatCornellUniversityinIthaca,NewYork,cameonboard.

“WhatreallyappealedtomeaboutQBismwasthatitgaveacontextinwhichCopenhagenmademoresense,andgaveanexplanationofwhyCopenhagenwassohardtograsp,”MermintoldmewhenImethimathisofficeinIthacaonablustery,bitinglycoldwinter’sday.“Becausewhateverybodywasdoingwaswhatscientistshadbeentaughttodoalmostforever,whichwastoconstructanunderstandingoftheexternalworldthatmadenoreferencewhatsoevertothepeoplewhoaretryingtounderstandit.Andalotoftheclumsy,awkwardthingsaboutCopenhageninvolvedtryingtoobjectifythingsthataren’tobjective,thataresubjectiveandpersonal.”

QBismlaysitselfopentochargesofsolipsism,whichistheargumentthattheonlythingthatisrealiswhatIexperience.AccordingtoMermin,thereisafallacyinsucharguments.Wehavelanguagetocommunicatewitheachotheraboutourprivateexperiences—includingthelanguageofscienceandmathematics—andthismakesoursubjectiveexperienceasharedreality.

Nonetheless,thereisnothinglikeanobjectivethird-personviewofrealityinQBism.Thishasimplicationsforquestionsaboutwhethertheuniverseislocalornonlocalorwhetherthereisaquantum-classicaldivide—theotheraxesalongwhichwecansortoutthevariousinterpretations.Takenonlocality.Copenhagenarguesthatthequantumworldisnonlocalbutprovidesnoexplanationsforwhyitmightbeso.Itjustis.ThedeBroglie-Bohmtheoryresortstononlocalhiddenvariablestoexplainnonlocality.Collapsetheoriesarenonlocal,inthattheytakethewavefunctionseriously—andthecollapseofthewavefunction(whetherithappensstochasticallyasinGRWorbecauseofgravityasintheDiósi-Penrosetheories)isanonlocalevent.Andaccordingtosomeproponentsofthemanyworldsinterpretation,theuniverseislocal.QBismsayssotoo.Andbothofthemresorttosimilarargumentstoarguewhy.

RecallAlainAspect’sexperimentaboutAliceandBobdoingmeasurementsonentangledphotonsandfindingcorrelationsthatimplyinstantaneousactionatadistancebetween,say,Alice’smeasurementsandBob’sphotons,orviceversa.SoifAliceandBobmakemeasurements,andtheirmeasurementshavedefiniteoutcomes,thenwhenanalyzedfromathird-personperspective,these

measurementoutcomesarecorrelatedinwaysthatcannotbeexplainedwithouttheassumptionofnonlocality.Butthethird-personperspectivedoesn’tmakesenseinthemanyworldsinterpretation.InhisbookTheEmergentMultiverse,DavidWallacearguesthatwhenitcomestomanyworlds,“fromthethird-personperspectivefromwhichBell’stheoremisnormallydiscussed,noexperimenthasanyuniquedefiniteoutcomeatall.”

Wallaceexplains:“Fromtheperspectiveofagivenexperimenter,ofcourse,herexperimentdoeshaveaunique,definiteoutcome,evenintheEverettinterpretation.ButBell’stheoremrequiresmore:itrequiresthatfromherperspective,herdistantcolleague’sexperimentalsohasadefiniteoutcome.ThisisnotthecaseinEverettianquantummechanics—not,atanyrate,untilthatdistantexperimententersherpastlightcone.”MeaningthattheinstantatwhichonecantalkaboutmeasurementsbyAliceandBobinthesamebreathiswhenonegetsaccesstotheother’sworld—whichcannothappenfasterthanthespeedoflight.

OnthewhiteboardinhisofficeinBoston,FuchsdrewcartoonsforAliceandBobtoexplainwhyQBismtakesasomewhatsimilarstance.“Thisisabitlikemanyworlds,whichI’llbehonestabout,”hesaid.InbothQBismandmanyworlds,fromAlice’sperspective,there’snoclickonBob’sdetectorandviceversa.Bell’sanalysis,however,insiststhattherebeaclickonbothsides,asseenfromathird-personperspective.Thisisn’tpossibleinQBism.It’sonlyafterAlicewalksovertoBob—whichcannothappenfasterthanthespeedoflight—andBob’sresultsbecomepartofherexperiencethatshecanupdateherbeliefsaboutwhathashappened.Butuntilthen,thereisnonotionofcorrelationsbetweentheresultsobtainedbyAliceandBob.“Quantummechanics,intheQBistinterpretation,cannotassigncorrelations,spookyorotherwise,tospace-likeseparatedevents,sincetheycannotbeexperiencedbyanysingleagent.QuantummechanicsisthusexplicitlylocalintheQBistinterpretation.Andthat’sallthereistoit.”

There’sasimilardismissaloftheideaofthequantum-classicaldivideinQBism.IntheCopenhageninterpretation,thereisadividethatexistsbydiktat.Therearesomethingsthatarequantumandothersthatareclassical,butwithoutanysolidexplanationforwhythatmightbeso.Explanationsusingdecoherencegetuspartwaytounderstandingwhyquantumstatesmightendupasclassical,buttheydon’tcompletethejob.InthedeBroglie-Bohmtheory,thereisnodivide.Thereisalwaysafactofthematterastowheretheparticlesthatmakeupanyobjectare,howeverbigorsmalltheobject.Collapsetheoriesargueforan

emergentdividethatisbroughtaboutbythestochasticprocessofcollapseitself.Themanyworldsinterpretationdoesnotdistinguishbetweentheclassicalandthequantum—thewavefunctionisallthereis,evolving,forever.QBism,ontheotherhand,asksustorethinktheverynotionsofwhatwemeanbythequantumandtheclassical,giventhatthesetermsareusuallytalkedaboutfromanimpersonal,objectivethird-personperspective.“Scienceisabouttheinterfacebetweentheexperienceofanyparticularpersonandthesubsetoftheworldthatisexternaltothatparticularuser...ItiscentraltotheQBistunderstandingofscience,”wroteDavidMermininhisessay“WhyQBismIsNottheCopenhagenInterpretationandWhatJohnBellMightHaveThoughtofIt.”So,inQBism,whatonethinksof(and“one”heremeansaparticularperson)asclassicalorquantumhassimplytodowithone’sbeliefsabouttheworldoutside.

Ifallthismakesourheadsreel,weshouldrestassuredthatwearenottheonlyonessuffering.Physicistswhoaredeeplyimmersedinthesequestionsarenotimmunetobeingflummoxed.ThereareexpertsonBohmianmechanicswhoprofesstobeingcluelessaboutQBism,QBistswhothinkcollapsetheoriesaremisguided,collapsetheoristswhoclaimthemanyworldstheoryisextravagantnonsense,andadvocatesofmanyworldswhodismissBohmianmechanicsasunnecessarilycontrived.And,ofcourse,allthosewhoworkonalternativeinterpretationsofquantummechanicsthinkCopenhagenshouldbeconsignedtothedustbinofhistory.AndtheCopenhagenfolks,well,theyareyettobedecisivelyknockeddownfromtheirsomewhatloftyperch.

Someyoungminds—àlaHeisenbergwhenhewastwenty-four—mightcutthroughthisclutter.There’sinsightinacommentthatAntonZeilingermadetoFuchs,afterFuchshadgivenatalkonQBismthatwasn’tterriblywellreceivedinFuchs’sownestimation.FuchsthoughtthattheveteranAlainAspect,whowasintheaudience,hadwrittenhimoff“asanutcase.”EvenMermin,awell-wisher,walkeduptoFuchsandsaid,“Weneedtotalk.Thatwastheworsttalkyou’veevergiven.”Zeilingersaid,“Greattalk!”towhichMerminresponded,“No,itwasn’t!”Fuchsrecalled(inhiswritings)thatZeilingerlookedpastMerminandaddressedhimdirectly:“YouknowwhatIwoulddowhenIwasyoung,beingdismissedbytheoldprofessorsonthefrontrowsoftheseminar?IwouldnotlooktothemasIspoke,butrathertothebackrowswheretheyoungstudentsweresitting.Theyweretheonesreadytohearsomethingnew.”

—Itmightwelltakesomeonenew,young,andunbiasedtomakeincontrovertiblesenseofthequantumworld.Imetphysicistswhoaredeeplyconvincedthatthey

senseofthequantumworld.Imetphysicistswhoaredeeplyconvincedthattheyareonthecorrectpath,astheymustbetosummontheenergyneededtodevoteanentirelifetimetothepursuitofthenatureofreality.Imetphysicistswhoremaindissatisfiedwiththestatusquo,uncommittedtoanyonepath,astheyshouldbetodiscernanycracksinthefoundationsofquantummechanics.Surely,allinterpretationsandformalismscan’tbesimultaneouslycorrect.Maybeoneofthemis,maybenoneare.Or,tantalizingly,maybetheyarealltouchingthetruthintheirownwayandgivingusglimpsesofadeeperreality.Ifso,thecrackswillletthelightthrough,andwe’llbebetterabletotellwhetheritgoesthroughtwodoorsatonce.Ornot.

D

Epilogue

WAYSOFLOOKINGATTHESAMETHING?

uringthelate1970sandearly’80s,WernerErhard,thefounderofest,organizedaseriesofphysicsconferences,usingthewealthfromhisself-

helpempiretoindulgehisfascinationforphysics.“Theestfoundation’sphysicsconferencesattractedstarafterstarofthephysicsfirmament,”wroteDavidKaiserinhisbookHowtheHippiesSavedPhysics:Science,Counterculture,andtheQuantumRevival.OneofthesestarswasLeonardSusskind,atheoreticalphysicistatStanfordUniversity.Oneevening,SusskindwashavingdinnerwithRichardFeynmanandSidneyColemanatErhard’shomeinSanFrancisco.Erhardhadalsoinvitedtwoyoungphilosopherstothedinner.“Theywerespoutingallsortsofphilosophicalverbiage,academicstylephilosophicalverbiage...whichitwasclearthatFeynmanhadnopatiencewithandhetookthemapart.Itwascruel.Idon’tknowhowtodescribewhathedidtothem.Withsimplewords,hetookapinandpuncturedtheirballooninawaythatyoumightcallugly,butthesavinggraceisthattheyweretotallyenchantedbyhim,”Susskindtoldme.

Butdespitehisdistasteforbloviatingphilosophers,Feynman“waspossiblythemostphilosophicalofallthephysicistsIeverknew,”saidSusskind.

ThissideofFeynmanwasclearlyevidentduringhislecturesatCornell.Inonetalk,heaskedhisaudiencetoconsidertwotheories,AandB,whichhavedifferenttakesonthenatureofrealitybutwhicharemathematicallyequivalent,makethesameempiricalpredictions,andareimpossibletotellapartexperimentally(hecouldhavebeentalkingabouttheCopenhageninterpretationandBohmianmechanics,buthewasn’t—hewasmakingageneralpoint).Feynmanarguedthatit’simportanttounderstandthatthephilosophiesbehindAandBcanleadusindifferentdirectionseveniftheyareindistinguishableatsomestageofthescientificprocess.

“Inordertogetnewtheories,thesetwothingsareveryfarfromequivalent.

“Inordertogetnewtheories,thesetwothingsareveryfarfromequivalent.Becauseonegivesamandifferentideasthantheother,”saidFeynman.

Forexample,itmightbepossibletomakeatinytweaktoAthatisn’tpossiblewithB.Inwhichcase,Acanleadtoaverydifferenttheoryafterthechange.“Inotherwords,althoughtheyareidenticalbeforetheyarechanged,therearecertainwaysofchangingonewhichlooknatural,whichdon’tlooknaturalintheother.Therefore,psychologicallywemustkeepallthetheoriesinourhead,”saidFeynman.“Andeverytheoreticalphysicistthat’sanygoodknowssixorsevendifferenttheoreticalrepresentationsforexactlythesamephysicsandknowsthattheyareallequivalentandthatnobodyisevergoingtobeabletodecidewhichoneisrightatthatlevel...buthekeepstheminhishead,hopingthatthey’llgivehimdifferentideas.”

InBrisbane,Australia,HowardWisemantriestodoexactlythat:keepthedifferentinterpretationsofquantummechanicsinmind,andseewhatemerges.Oneobviousintuitionisthatthesetheoriesandinterpretationsareeachshiningalightonadifferentaspectofthesamereality.“Alotofprogressinphilosophyofsciencehasbeenmadebyshowingthatthingswhichwerethoughtofasbeingseparateareactuallyjustdifferentwaysoflookingatthesamething,”Wisemantoldme.

Thisapproach,whenappliedtoquantummechanics,isprovidingsomesurprisinginsights.TakecollapsetheoriesandahiddenvariabletheorylikeBohmianmechanics—twoverydifferentviewsofthenatureofreality.InBohmianmechanics,ifyouconsideratwo-particlesystem,thewavefunctionisafunctionoftwovariables,thepositionofparticleAandthepositionofparticleB;theseparticlesalsohaveactualpositions,thehiddenvariablesinthetheory.Now,hypothetically,ifyouknewtheexactpositionofparticleA(whichinpracticeyoucannot,butlet’sgowiththeargument)youcanplugthatintotheequationsandthewavefunctionreduces—oreffectivelycollapses—toafunctionofonevariable,thepositionofparticleB.

ThisinspiredWisemantothinkofcollapsetheories—inwhichthewavefunctionstochasticallycollapsesatsomerateatdifferentpointsinspacetime—astheoriesinwhichthewavefunctionisentangledwithsomeotherlargesystemwithhiddenvariablesthatweareunawareof.Changestothevaluesofthesehiddenvariables,unbeknownsttous,caninfluencethewavefunctionofthesystemwearestudying—anditcanseemlikethewavefunctionissubjecttostochasticcollapses.Inthiswayofthinkingaboutcollapsetheories,theybecomehiddenvariabletheories,exceptthatthevariablesare,well,trulyhidden—andweareprivyonlytotheireffects.

WisemanhasalsofoundwaysofconnectingBohmianmechanicstotheideaofmanyworlds.TakeasingleparticlegoingthroughadoubleslitinBohmianmechanics.Ifyouknewitsexactinitialpositionandvelocity,youcouldpredictitsexacttrajectorythroughtheapparatus.Butinordertotallywiththeprobabilisticpredictionsofquantummechanics,Bohmianmechanicsaddsadashofuncertaintytoourknowledgeabouttheinitialstateoftheparticle.Itsstartingpositionisgivenbyaprobabilityfield,meaningtheparticlecouldbeinoneofmanylocations,withadifferentprobabilityforeachstartingposition.It’slikeimaginingavirtualensembleofparticleswhosestartingpositionsaredictatedbythisprobabilityfield,givenbythemodulus-squaredofthewavefunction.Therealparticleisinoneofthosepositions,wejustdon’tknowwhich.Now,asthisvirtualensembleevolvesthroughthedoubleslit,Bohmianmechanicsgivesusavirtualensembleoftrajectories,but,ofcourse,onlyoneofthemisreal—andforonerunoftheexperiment,we’llseetheconsequenceofonesuchtrajectory.We’llfindtheparticlelandingsomewhereonascreen,anoutcometowhichwecouldhaveassignedonlyacertainprobability.Andifyoudothisexperimentoverandoveragain,withthesamevirtualensembleofparticles,you’llgetaslewoftrajectories,whichtakentogetherformaninterferencepattern.

Whencontemplatingthisvirtualensemble,Wisemanwondered:whatifthisvirtualensembleisreal,inthateveryparticleexists,butinadifferentworld?Eachparticleisinfluencedbythoseinitslocalsurroundings(someregionsaremoredensewithparticlesthanothers).Thenthewayeachparticlemovesisdictatedbyinteractionswithitsimmediateneighbors,likestarlingsinamurmuration.Crucially,youdon’tneedawavefunctiontodeterminehowanygivenparticlemoves.“Whenthatideaoccurredtome,itwaslike,wow!”Wisemansaid.

HeandhiscolleaguesDirk-AndréDeckertandMichaelHallpostulatedaparticularmany-worldforcelawforthissituation,thendidsimulations.First,theyusedBohmianmechanics—wavefunction,hiddenvariables,andall—toplottrajectoriesofparticlesgoingthroughadoubleslit.Next,theytreatedeachparticletrajectoryasbeingtheoutcomeofitsinteractionswithotherparticlesthatexistinotherworlds,withoutresortingtothemathematicsoftheevolutionofthewavefunction.Theresultstheyobtainedareeerilysimilar.

“That’sjustaboutthetheoryforoneparticle,”saidWiseman.“Ofcourse,theuniverseisnotoneparticle.”

Inamany-particlesystem,whileeachparticleexistsin3-Dspace,thewavefunctionexistsinconfigurationspace.Anygivendistributionofparticlesin3-Dspacecorrespondstoonepointintheconfigurationspace.Thisonepoint

3-Dspacecorrespondstoonepointintheconfigurationspace.Thisonepointrepresentsaworld.InBohmianmechanics,ourknowledgeabouttheinitialconfigurationofparticlesissubjecttouncertainty—andthisuncertaintycorrespondstoaprobabilisticdistributionofpointsinconfigurationspace,oravirtualensembleofworlds.Bohmianmechanicssaysthereisonerealworldwhoseevolutioncanbedescribedbytheevolutionofthewavefunction,subjecttothisinitialuncertainty.Justasinthecaseofthesingleparticlein3-Dspacebeinginfluencedbyotherparticlesinotherworlds,Wiseman’sargumentisthatyoucantreatthisvirtualensembleofpointsinconfigurationspaceasacollectionofrealworlds.Anygivenworldinteractswiththeotherworldsinconfigurationspace,andthisinteractionislocal,withnearbyworldsinfluencingeachothermorethandistantworlds.

Thishasenormousconsequences.Forexample,alocalinteractioninconfigurationspacecanappearnonlocalin3-Dspace.“Sothat’swherethenonlocalityofquantummechanicswouldcomefrom,”saidWiseman.He’sdubbedthisstill-nascentidea“manyinteractingworlds”(todistinguishitfromtheEverettianmanyworldsidea).It’sanexampleofhowthebehaviorofthequantummechanicalworldemergesfromthedynamicsofadeeperreality.Buthe’scertainlynotclaimingthatthisiswhat’shappeninginthequantumworld.Theexerciseistomakethepointthattherearemyriadwaysofexplainingquantumphenomena,someofwhichareonstrongermathematicalfootingthanothers,andeachhasitsownsetofproblems,whetherit’sthemeasurementproblemintheCopenhageninterpretation,ortheproblemofpotentialconflictswithspecialrelativityinBohmianmechanics(nottomentionthedistasteforhiddenvariablesintheeyesofsome),ortheadhocnatureofstochasticcollapseincollapsetheories,ortheproblemofexplainingprobabilityinEverett’smanyworlds.

Anddependingonwhichaxisyouchooseforanalyzingthequantumworld,

Anddependingonwhichaxisyouchooseforanalyzingthequantumworld,thetheoriesandinterpretationsfallintodifferentbins,makingforstrangebedfellows.

Takedeterminism.ThedeBroglie-Bohmtheory,theEverettianmanyworldsinterpretation,andWiseman’smanyinteractingworldsaredeterministic;Copenhagenandcollapsetheoriesarenot.QBismdoesn’tsayanythingaboutwhetherornottherealworldisdeterministic.

Whataboutrealism?Well,deBroglie-Bohm,collapse,manyworlds,andmanyinteractingworldsareallrealist.Copenhagenisnot.QBismisrealist,withthecaveatthatthewavefunctionisnotaboutthisreality.

Whataboutclaimsthatthereisnothingbutthewavefunction?Manyworldsandcollapsetheoriessayyes.DeBroglie-Bohmsaysno(becausethetheoryhashiddenvariablesbesides).Thereisnowavefunctioninmanyinteractingworlds.InCopenhagen,thewavefunctionrepresentsthequantumworld,butthereistheclassicalworldtocontendwith.InQBism,thestatusofthewavefunctionisentirelysubjective(it’spersonaltooneobserver).

Thenthere’sthewholeissueoflocalityversusnonlocality.Fromthepointofviewofour3-Dworld,thetheoriesofdeBroglie-Bohm,collapse,andmanyinteractingworldsareallnonlocal.There’ssomedisputeaboutthestatusoftheEverettianmanyworldsinterpretationinthisregard,butopinionstendtowarditbeinglocal.Copenhagenisobscure:ifyoutakethewavefunctiontoberepresentativeofsomethingoutthere,thenit’snonlocal,elseyoucandismissconcernsofnonlocalitybysayingthatallonedoesismakemeasurements,comparethemtoresultsofotherexperiments,findcorrelations,andthat’sthat(there’snoattempttoexplainthecauseofthecorrelations).QBism,aswesawearlier,dismissesnonlocality.

Therearefinerdistinctionstobemade,butthemessageisclear:there’snowaytoclassifythesetheoriesinaconsistentmanner.It’sastrongcluethatourunderstandingofthequantumworldisstillupforgrabs.Andit’sverylikelythatfurtherattemptsatclarificationwillinvolvethedouble-slitexperimentinsomeformortheother.

Andnowheredoesthisbecomemoreapparentthaninexperimentsbeingdonetoverifyoneofthekeyassumptionsofquantummechanics:theBornrule.Asoneprominenttheoristhassaid,“IfBorn’srulefails,everythinggoestohell.”Allofthevariousmathematicalformalismsforexplainingthequantumworld,ultimately,aredesignedtoanswerwhy,whenwedoexperimentslikethedoubleslit,wegettheoutcomeswedo.Aphotongoesthroughthedoubleslit,itswavefunctionsplits,evolves,recombines,andsoon.Eventually,thewavefunctioncanbewrittendownasalinearcombinationofdifferent

wavefunctioncanbewrittendownasalinearcombinationofdifferentwavefunctions(oneforeachpaththephotontakes),eachevolvingaccordingtotherulesoftheSchrödingerequation.Thephotonissaidtobeinasuperpositionoftakingallpossiblepaths.TheBornrulesaysthattheprobabilityoffindingthephotonatanygivenlocationisgivenbythemodulus-squaredofthevalueofthewavefunctionatthatlocation.But“theBornRuleisconjecture,”saidUrbasiSinha,formerlyoftheInstituteforQuantumComputingatWaterloo,Canada,andnowoftheRamanResearchInstituteinBengaluru,India.“ThereisnoformalproofoftheBornRule.”

Ofcourse,therearemanyquantummechanicalphenomenathatagreewiththeoreticalpredictionstoastonishingprecision,butthesepredictionsallassumethevalidityoftheBornrule.Now,SinhaandhercolleaguesaretryingtodirectlytesttheBornrule—using,whatelse,thedouble-slit(orsometimesthetriple-slitexperiment,whichmakessomemeasurementssharperbutisconceptuallyidenticaltodoingtheexperimentwithtwoslits).Takeaphotongoingthroughthedoubleslit.AccordingtoFeynman’spathintegralapproach,tocalculatetheprobabilityoffindingthephotonat,say,thecenterofthescreen,youhavetoconsidertheclassicalpaths(whichgothroughoneslitortheother)andnonclassicalpaths,suchasonethatstartsoffgoingthroughoneslit,theninstantlyturnstowardtheotherslit,andthengoestowardthescreen.

Sinha’steamcalculatedtheexpectedintensityoflightatthecenterofthescreen,giventhemostdominantclassicalandnonclassicalpathsthephotoncantakethroughtheapparatus.Thenextstepwastofigureouttheexpectedchangeinintensityifthenonclassicalpathisblocked(whichcanbedonebyplacingabafflethroughoneslit—thispreventsthephotonfromtakingitsunusualslit-huggingroute.Thebaffleisthin,sothereisstillroomoneithersideofitforaphotontakingtheclassicalpathtogothroughtheslit).ThemeasuredintensityissensitivetotheexactformulationoftheBornrule.Istheprobabilityequaltothesquareoftheamplitudeofthewavefunction?Orisitequaltotheamplituderaisedtosomenumber2+δ,whereδrepresentsatinydeviation?ManyteamsbesidesSinha’sareaskingsuchquestions.“Evenasmalldeviationwillchangemanythings,”Sinhatoldme.

WhiletheBornrulehasheldupsofartoacertainlevelofprecision,theexperimentalistsaretighteningthescrews.IftheycanshowthattheBornruleneedstweaking,itwillcreateanopening,givingtheoristsessentialcluesonhowtoproceedtowardthecorrectquantummechanicalviewofnature.Theexperimentsalsohighlightthatthedoubleslit,asimplecontraptionifevertherewasone,continuestoconcealsomecentralprinciplethatanimatesreality.

wasone,continuestoconcealsomecentralprinciplethatanimatesreality.

AsFeynmanputitinhisCornelllecture:“Any...situationinquantummechanics,itturnsout,canalwaysbeexplainedafterwardsbysaying‘Yourememberthecaseoftheexperimentwiththetwoholes?’”

Physicshasyettocompleteitspassagethroughthedouble-slitexperiment.Thecaseremainsunsolved.

NOTES

“Allowmetoexpressnow”:CarlC.GaitherandAlmaE.Cavazos-Gaither,eds.,Gaither’sDictionaryofScientificQuotations(NewYork:Springer,2008),502.

“Thereisnothingmoresurreal”:SiriHustvedt,“TheDramaofPerception:LookingatMorandi,”YaleReview97,no.4(Oct2009):20–30.

ButinNovember1964:http://www.cornell.edu/video/playlist/richard-feynman-messenger-lectures.“It’sodd,butintheinfrequentoccasions”:FeynmanMessengerLectures,Lecture1,“Lawof

Gravitation,”http://www.cornell.edu/video/richard-feynman-messenger-lecture-1-law-of-gravitation.“Thenweseeunexpectedthings”:FeynmanMessengerLectures,Lecture6,“ProbabilityandUncertainty:

TheQuantumMechanicalViewofNature,”http://www.cornell.edu/video/richard-feynman-messenger-lecture-6-probability-uncertainty-quantum-mechanical-view-nature.

“Theybehaveintheirowninimitableway”:Ibid.“Thatis,they’rebothscrewy”:Ibid.“Butthedifficulty”:Ibid.“oneexperimentwhichhasbeendesigned”:Ibid.let’sorientthedevice:TheBritishphysicistJimAl-Khalilihasusedthesameideatodemonstratethe

double-slitexperimentdonewithparticles,https://youtu.be/A9tKncAdlHQ?t=125.“TheLastManWhoKnewEverything”:AndrewRobinson,TheLastManWhoKnewEverything

(London:OneWorld,2007).“doctorofphysic,surgery,andmidwifery”:Ibid.,51.“TheexperimentsIamabouttorelate”:ThomasYoung,“TheBakerianLecture:Experimentsand

CalculationsRelativetoPhysicalOptics,”PhilosophicalTransactionsoftheRoyalSocietyofLondon94(1804):1–16.

“Imadeasmallholeinawindow-shutter”:Ibid.“Ibroughtintothesunbeam”:Ibid.Youngsawsuchopticalinterferencefringes:Ibid.HenryBrougham:https://www.britannica.com/biography/Henry-Peter-Brougham-1st-Baron-Brougham-

and-Vaux.“destituteofeveryspecies”:WhippleMuseumoftheHistoryofScience,

http://www.sites.hps.cam.ac.uk/whipple/explore/models/wavemachines/thomasyoung/#ref_2.“Theideaofanobjectiverealworld”:WernerHeisenberg,PhysicsandPhilosophy(London:Penguin

Books,2000),83.Heelucidatedhislaws:https://www.aps.org/publications/apsnews/200007/history.cfm.“WhenLightreachesusfromthesun”:LouisdeBroglie,MatterandLight:TheNewPhysics,trans.W.

H.Johnston(NewYork:W.W.Norton&Co.,1939),27.HepresentedtheseideasonDecember8,1864:J.ClerkMaxwell,“ADynamicalTheoryofthe

ElectromagneticField,”PhilosophicalTransactionsoftheRoyalSocietyofLondon155(1865):459–512.

In1879,thePrussianAcademyofSciences:D.Baird,R.I.Hughes,andA.Nordmann,eds.,HeinrichHertz:ClassicalPhysicist,ModernPhilosopher(Dordrecht,NL:SpringerScience,1998),49.

“Butinspiteofhavingabandoned”:Ibid.“Itisofnousewhatsoever”:AndrewNorton,ed.,DynamicFieldsandWaves(Bristol:CRCPress,2000),

83.“Tobesure,itisadiscovery”:JosephF.Mulligan,“HeinrichHertzandPhilippLenard:Two

DistinguishedPhysicists,TwoDisparateMen,”PhysicsinPerspective1,no.4(Dec1999):345–66.“Achronic,andpainful,disease”:“HeinrichHertz,”editorialinNature49,no.1264(Jan18,1894):265.“HeinrichHertzseemedtobepredestined”:Mulligan,“HeinrichHertzandPhilippLenard.”wasascientificcuriosity:https://history.aip.org/history/exhibits/electron/jjrays.htm.“Atfirsttherewereveryfew”:http://history.aip.org/exhibits/electron/jjelectr.htm.Hisexperimentsclearlyshowedthat:Mulligan,“HeinrichHertzandPhilippLenard.”WhileEinsteindidnotfullyembracePlanck’sideas:AbrahamPais,“EinsteinandtheQuantum

Theory,”ReviewsofModernPhysics51,no.4(Oct1979):863–914.“EntranceisforbiddentoJews”:Mulligan,“HeinrichHertzandPhilippLenard.”“Einsteinwastheembodiment”:PhilipBall,“How2Pro-NaziNobelistsAttackedEinstein’s‘Jewish

Science’”excerpt,February13,2015,https://www.scientificamerican.com/article/how-2-pro-nazi-nobelists-attacked-einsteins-jewish-science-excerpt1/.

Thomsonarguedthatthereshouldbeblurryfringes:GeorgeK.Batchelor,TheLifeandLegacyofG.I.Taylor(Cambridge:CambridgeUniversityPress,1996),40.

“Ichosethatprojectforreasons”:Ibid.Tocreateasingleslit:Ibid.,41.“Ihad,Ithinkratherskillfully,arranged”:Ibid.Taylorreportedlywentawaysailing:SidneyPerkowitz,SlowLight:Invisibility,Teleportation,andOther

MysteriesofLight(London:ImperialCollegePress,2011),68.Afterthatthree-month-longexposure:GeorgeK.Batchelor,TheLifeandLegacyofG.I.Taylor,41.it’dtakehimadecadeorsomore:GöstaEkspong,“TheDualNatureofLightasReflectedintheNobel

Archives,”https://www.nobelprize.org/nobel_prizes/themes/physics/ekspong/.“Thathemightsometimeshaveovershot”:WalterIsaacson,Einstein:HisLifeandUniverse(NewYork:

Simon&Schuster,2007),100.Themoment,capturedinanow-iconicphotograph:ParticipantsoftheFifthSolvayCongress,

https://home.cern/images/2014/01/participants-5th-solvay-congress.BohrfirstmetHeisenberg:JagdishMehra,Einstein,PhysicsandReality(Singapore:WorldScientific,

1999),94.HealsoinvitedHeisenbergtoCopenhagen:GinoSegré,FaustinCopenhagen:AStrugglefortheSoulof

Physics(NewYork:VikingPenguin,2007),116.“perhapsitwouldbepossibleoneday”:JagdishMehra,GoldenAgeofTheoreticalPhysics,vol.2

(Singapore:WorldScientific,2001),648.There,betweenlongwalksandcontemplating:Ibid.,650.“Itwasalmostthreeo’clockinthemorning”:Ibid.,651.“Ithoughtthewholeday”:Ibid.,652.“discouraged,ifnotrepelled”:Ibid.,840.“AfewdaysagoIread”:WalterMoore,Schrödinger:LifeandThought(Cambridge:Cambridge

UniversityPress,2015),192.“AfewdaysbeforeChristmas”:DickTeresi,“TheLoneRangerofQuantumMechanics,”reviewof

WalterMoore’sSchrödinger:LifeandThought,January7,1990,http://www.nytimes.com/1990/01/07/books/the-lone-ranger-of-quantum-mechanics.html.

“Themotionofparticlesfollowsprobability”:AbrahamPais,“MaxBorn’sStatisticalInterpretationofQuantumMechanics,”Science218(Dec17,1982),1193–98.

HewrotetoPauli,complaining:Moore,Schrödinger,221.ZüricherLokalaberglauben:Ibid.“Don’ttakeitasapersonalunfriendliness”:Ibid.

“ThediscussionbetweenBohrandSchrödinger”:Ibid.,226.“Schrödingerwasa‘visualizer’”:Ibid.,228.“trustinthenewlydeveloped”:StefanRozental,ed.,NielsBohr:HisLifeandWorkasSeenbyHis

FriendsandColleagues(Amsterdam:North-HollandPublishing,1967),104.“Likeachemistwhotriestoconcentrate”:JørgenKalckar,ed.,NielsBohrCollectedWorks,vol.6

(Amsterdam:North-Holland,1985),15.“Iwentforawalk”:Rozental,NielsBohr,105.“DearMr.Bohr”:LéonRosenfeldandJ.RudNielsen,eds.,NielsBohrCollectedWorks,vol.3

(Amsterdam:North-Holland,1976),22.“Tomeetyou”:Ibid.“However,withalltheparticipants”:ManjitKumar,Quantum:Einstein,Bohr,andtheGreatDebate

abouttheNatureofReality(NewYork:Norton,2011),273.physicistssincethenhavereimagined:Theillustrationoftherecoilingdoubleslitisinspiredbyadrawing

inP.Bertetetal.,“AComplementarityExperimentwithanInterferometerattheQuantum-ClassicalBoundary,”Nature411(May10,2001):166–70.

“Buttheelectronmustbesomewhere”:JorritdeBoer,ErikDal,andOleUlfbeck,eds.,TheLessonofQuantumTheory(Amsterdam:North-Holland,1986),17.

“Theelectron,asitleavestheatom”:ArthurEddington,TheNatureofthePhysicalWorld(NewYork:MacmillanCompany,1929),199.

“Itisfairtostatethatwearenot”:StefanHell,NobelBanquetSpeech,December10,2014,https://www.nobelprize.org/nobel_prizes/chemistry/laureates/2014/hell-speech_en.html.

“Now,ladiesandgentlemen”:Ibid.adecade-oldpaperbyJohnBell:J.S.Bell,“OntheEinsteinPodolskyRosenparadox,”PhysicsPhysique

Fizika1,no.2(Nov1,1964):195–200.Taylorusedsomethingcalledacoincidencedetector:WilliamM.Honig,DavidW.Kraft,andEmilio

Panarella,eds.,QuantumUncertainties:RecentandFutureExperimentsandInterpretations(NewYork:PlenumPress,1987),339.

Arough-and-readycalculation:ThecalculationappearsinGiancarloGhirardi,SneakingaLookatGod’sCards:UnravelingtheMysteriesofQuantumMechanics(Princeton:PrincetonUniversityPress,2005),16.

“Thisexperimenthasneverbeendone”:RichardP.Feynman,RobertB.Leighton,andMatthewSands,TheFeynmanLecturesonPhysics,vol.1,NewMillenniumEdition(NewYork:BasicBooks,2011),37–5.

Möllenstedtnoticedthatwhenthetungsten:EdgarVölkl,LawrenceF.Allard,andDavidC.Joy,eds.,IntroductiontoElectronHolography(NewYork:SpringerScience,1999),3.

“keptacollectionofspiders”:RobertCrease,ThePrismandthePendulum:TheTenMostBeautifulExperimentsinScience(NewYork:RandomHouse,2004),197.

theteamdidnotseeanyfringesatfirst:Völkl,Allard,andJoy,eds.,IntroductiontoElectronHolography,5.

“ThomasYounghadproduced”:Ibid.“Itwas...agreatpleasuretosee”:Ibid.,7.In1974,Italianphysicists:PierGiorgioMerli,GianFrancoMissiroli,andGiulioPozzi,“OntheStatistical

AspectofElectronInterferencePhenomena,”AmericanJournalofPhysics44,no.306(1976):306–7.themovieevenwonanaward:https://www.bo.imm.cnr.it/users/lulli/downintel/electroninterfea.html.In1989,AkiraTonomuraandcolleagues:A.Tonomuraetal.“DemonstrationofSingleElectronBuildup

ofanInterferencePattern,”AmericanJournalofPhysics57,no.117(1989):117–20.“Webelievethatwecarriedout”:Lettertoeditor,“TheDouble-SlitExperimentwithSingleElectrons,”

PhysicsWorld(May2003):20.Suchanexcitedatomfallsback:AlainAspect,PhilippeGrangier,andGérardRoger,“ExperimentalTests

ofRealisticLocalTheoriesviaBell’sTheorem,”PhysicalReviewLetters47,no.7(Aug17,1981):

460–63.“justanameforsomething”:DavidAlbert,QuantumMechanicsandExperience(Cambridge,MA:

HarvardUniversityPress,1994),11.“themostunsettlingstoryperhaps”:Ibid.,1.Einsteinimaginedsomegunpowder:ArthurFine,TheShakyGame:Einstein,RealismandtheQuantum

Theory(Chicago:UniversityofChicagoPress,1986),78.“Throughnoartofinterpretation”:Ibid.“Iamlongpastthestage”:Ibid.,82.“Acatisshutupinasteelchamber”:Moore,Schrödinger,308.aparticleinterfereswithitself:PaulDirac,ThePrinciplesofQuantumMechanics(Oxford:OUP,1958),

9.“greatsmokydragon”:WarnerA.MillerandJohnA.Wheeler,“Delayed-ChoiceExperimentsandBohr’s

ElementaryQuantumPhenomenon,”S.Kamefuchietal.,eds.,ProceedingsoftheInternationalSymposiumonFoundationsofQuantumMechanics(Tokyo:PhysicalSocietyofJapan1984),140–52.

“Whatthedragondoes”:Ibid.“Onedecideswhetherthephoton”:JohnWheelerandWojciechZurek,eds.,QuantumTheoryand

Measurement(Princeton:PrincetonUniversityPress,1983),183.aninterferometerwitharmlengthsof48meters:VincentJacquesetal.,“ExperimentalRealizationof

Wheeler’sDelayed-ChoiceGedankenExperiment,”Science315,no.5814(Feb16,2007):966–68.Einstein’smostcitedpaper:DennisOverbye,“QuantumTrickery:TestingEinstein’sStrangestTheory,”

NewYorkTimes,December27,2005,http://www.nytimes.com/2005/12/27/science/quantum-trickery-testing-einsteins-strangest-theory.html.

“Nonlocalityforcesus”:NicolasGisin,QuantumChance:Nonlocality,TeleportationandOtherQuantumMarvels(Cham,Switzerland:Springer,2014),32.

“firstapologizedfornothaving”:AndrewWhitaker,Einstein,BohrandtheQuantumDilemma:FromQuantumTheorytoQuantumInformation(Cambridge:CambridgeUniversityPress,2006),203.

Einsteinmadethepointthatthislocalization:Ibid.EINSTEINATTACKSQUANTUMTHEORY:KellyDevineThomas,“TheAdventandFalloutofEPR,”IAS:

TheInstituteLetter(Fall2013):13.“Ideprecateadvancepublication”:Ibid.“IfTheNewYorkTimesisthesecularpress”:DavidMermin,OppenheimerLecture,Universityof

California,Berkeley,March17,2008,https://youtu.be/ta09WXiUqcQ?t=833.elegantfour-page-longpaper:AlbertEinstein,BorisPodolsky,andNathanRosen,“CanQuantum-

MechanicalDescriptionofPhysicalRealityBeConsideredComplete?”PhysicalReview47(May15,1935):777–80.

teatimeconversationbetweenEinsteinandRosen:Thomas,“AdventandFalloutofEPR.”Sixteenyearslater,in1951:DavidBohm,QuantumTheory(NewYork:DoverPublications,1989),611.“If,withoutinanyway”:Einstein,Podolsky,andRosen,“Quantum-MechanicalDescription.”“apieceofhistoricalsilliness”:Fine,ShakyGame,57.“thefirstandonlyfemaledoctoralstudent”:EliseCrullandGuidoBacciagaluppi,eds.,GreteHermann

—BetweenPhysicsandPhilosophy(Dordrecht:Springer,2016),4.“AthoroughexaminationoftheproofofvonNeumannreveals”:HaraldAtmanspacherandChristopher

A.Fuchs,eds.,ThePauli-JungConjecture:AndItsImpactToday(Exeter,UK:ImprintAcademic,2014),ebook.

“Whyshouldwebelieveinthat?”:Ibid.“wouldratherbeacobbler”:Isaacson,Einstein,324.“Ifthathadsomethingtodowithit”:CrullandBacciagaluppi,GreteHermann,184.“In1952,Isawtheimpossibledone”:OlivalFreireJr.,TheQuantumDissidents:Rebuildingthe

FoundationsofQuantumMechanics(1950–1990)(Heidelberg:Springer-Verlag,2015),66.“ThevonNeumannproof”:CharlesMannandRobertCrease,“JohnBell,”Omni,May1988,88.

“Icannotseriouslybelieve”:JürgenAudretsch,EntangledSystems:NewDirectionsinQuantumPhysics(Weinheim,Wiley-VCH,2007),130.

“Theseexperimentsareamagnificentaffront”:BrianGreene,TheFabricoftheCosmos:Space,Time,andtheTextureofReality(NewYork:VintageBooks,2005),199.

recognizedfortheireffortsin2010:“WhereCreditisDue,”editorialinNaturePhysics(Jun1,2010),https://www.nature.com/articles/nphys1705.

washousedinSchrödinger’shome:https://www.esi.ac.at/material/Evaluation2008.pdf.in1913,hecrossedthenearly1,800-meter-highMalojaPass:AliceCalaprice,DanielKennefick,and

RobertSchulmann,AnEinsteinEncyclopedia(Princeton:PrincetonUniversityPress,2015),89.natureofrealityandbeefcattleproduction:“PhysicistDesignsPerfectAutomotiveEngine,”

ScienceDaily(Feb27,2003),https://www.sciencedaily.com/releases/2003/02/030227071656.htm.“ThemysteryisnotthatI’minterested”:VimalPatel,“CowsMeetQuantum,LifelongLearningonthe

BanksoftheBrazos,”TexasA&MUniversityScienceNews,November21,2013,http://www.science.tamu.edu/news/story.php?story_ID=1141#.WTOOvO-0k7Y.

“AdumbkidfromWyoming”:InterviewofMarlanScullybyJoanBromberg,July15and16,2004,NielsBohrLibrary&Archives,AmericanInstituteofPhysics,CollegePark,MD,www.aip.org/history-programs/niels-bohr-library/oral-histories/32147.

“Whentheprovinceofphysicaltheory”:WheelerandZurek,QuantumTheoryandMeasurement,169.Butby1970,Wignerchangedhismind:ArtHobson,TalesoftheQuantum:UnderstandingPhysics’

MostFundamentalTheory(NewYork:OxfordUniversityPress,2017),201.“Weproposeandanalyzeanexperiment”:MarlanO.ScullyandKaiDrühl,“QuantumEraser:A

ProposedPhotonCorrelationExperimentConcerningObservationand‘DelayedChoice’inQuantumMechanics,”PhysicalReviewA25,no.4(Apr1982):2208–13.

Zeilingerandcolleagues:ThomasJ.Herzogetal.,“ComplementarityandtheQuantumEraser,”PhysicalReviewLetters75,no.17(Oct23,1995):3034–37.

Scullyeventuallyjoinedhands:Yoon-HoKimetal.,“Delayed‘Choice’QuantumEraser,”PhysicalReviewLetters84,no.1(Jan3,2000):1–5.

“Althoughwelistenedtohundreds”:Freire,TheQuantumDissidents,20.“Itlooksstrange”:WheelerandZurek,QuantumTheoryandMeasurement,185.“Thefinalstoryoftherelation”:AlwynVanderMerwe,WojciechHubertZurek,andWarnerAllen

Miller,eds.,BetweenQuantumandCosmos:StudiesandEssaysinHonorofJohnArchibaldWheeler(Princeton:PrincetonUniversityPress,2017),10.

GermanphysicistMauritiusRenninger:A.Cardoso,J.L.Cordovil,andJ.R.Croca,“Interaction-FreeMeasurements:AComplexNonlinearExplanation,”JournalofAdvancedPhysics4,no.3(Sep2015):267–71.

Thepaperdidseethelightofday:AvshalomElitzurandLevVaidman,“QuantumMechanicalInteraction-FreeMeasurements,”FoundationsofPhysics23,no.7(Jul1993):987–97.

“Surely...itcanbenosintofail”:RogerPenrose,ShadowsoftheMind:ASearchfortheMissingScienceofConsciousness(Oxford:OxfordUniversityPress,1996),269.

Anearlyexactreplicaofthisexperiment:WilliamIrvine,JuanHodelin,ChristophSimon,andDirkBouwmeester,“RealizationofHardy’sThoughtExperimentwithPhotons,”PhysicalReviewLetters95(Jul15,2005):030401–4.

Hispaper:LucienHardy,“QuantumMechanics,LocalRealisticTheories,andLorentz-InvariantRealisticTheories,”PhysicalReviewLetters68,no.20(May18,1992):2981–4.

“simplerandmorecompelling”:DavidMermin,“QuantumMysteriesRefined,”AmericanJournalofPhysics62,no.10(Oct1994):880–7.

“standsinitspristinesimplicity”:Ibid.“There’sanentirelydifferentway”:DavidAlbert,QuantumMechanicsandExperience,134.Hefoundedthefirstschooloftheoreticalphysics:RobertSanders,“Conference,ExhibitsProbeScience

andPersonalityofJ.RobertOppenheimer,FatheroftheAtomicBomb,”UCBerkeleyNews,April13,

2004,https://www.berkeley.edu/news/media/releases/2004/04/13_oppen.shtml.“BohrwasGodandOppiewashisProphet”:Freire,TheQuantumDissidents,26.OppenheimerreassuredUCBerkeley:Ibid.“probablyOppenheimer’sbeststudentatBerkeley”:Ibid.Princetonsuspendedhim:Ibid.,28.“Untilwefindsomerealevidence”:Bohm,QuantumTheory,115.“onlyorthodoxintheCopenhagen”:KarlPopper,QuantumTheoryandtheSchisminPhysics:Fromthe

PostscripttotheLogicofScientificDiscovery(NewYork:Routledge,2013),36.“generalconceptualframeworkofthequantumtheory”:Bohm,QuantumTheory,115.“oneofthemostfundamental”:Ibid.,623.“notheoryof...hiddenvariables”:Ibid.becauseitwastoolong:Freire,TheQuantumDissidents,31.“IfIwriteapaper”:Ibid.“Alloftheobjections”:DavidBohm,“ASuggestedInterpretationoftheQuantumTheoryinTermsof

‘Hidden’Variables,”PhysicalReview85,no.2(Jan15,1952):166–79.“Ifonemanfindsadiamond”:Freire,TheQuantumDissidents,32.Theimpetuscamefrom:YvesCouderandEmmanuelFort,“Single-ParticleDiffractionandInterference

ataMacroscopicScale,”PhysicalReviewLetters97(Oct13,2006):154101–4.“Ourresultsdonotclosethedoor”:GiuseppePucci,DanielHarris,LuizFaria,andJohnBush,“Walking

DropletsInteractingwithSingleandDoubleSlits,”JournalofFluidMechanics835(Jan25,2018):1136–56.

Thetriopublishedapapershowingthetrajectories:ChrisPhilippidis,ChrisDewdney,andBasilHiley,“QuantumInterferenceandtheQuantumPotential,”IlNuovoCimentoB52,no.1(Jul1979):15–28.

In1988,YakirAharonov:YakirAharonov,DavidAlbert,andLevVaidman,“HowtheResultofaMeasurementofaComponentoftheSpinofaSpin-1/2ParticleCanTurnOuttoBe100,”PhysicalReviewLetters60(Apr4,1988):1351–54.

“Itmustbeemphasized”:HowardWiseman,“GroundingBohmianMechanicsinWeakValuesandBayesianism,”NewJournalofPhysics9(Jun2007):165.

“Theteamisthefirsttotrack”:HamishJohnston,“PhysicsWorldRevealsItsTop10Breakthroughsfor2011,”PhysicsWorld(Dec16,2011),http://physicsworld.com/cws/article/news/2011/dec/16/physicsworld-reveals-its-top-10-breakthroughs-for-2011.

“Tersely:Bohmtrajectoriesarenotrealistic”:Berthold-GeorgEnglert,MarlanScully,GeorgSüssmann,andHerbertWalther,“SurrealisticBohmTrajectories,”ZeitschriftfürNaturforschungA47,no.12(1992),1175–86.

Itrequiredasmallbutsignificant:DylanMahleretal.,“ExperimentalNonlocalandSurrealBohmianTrajectories,”ScienceAdvances2,no.2(Feb19,2016):e1501466.

“inspiredbythemodernrealization”:LouisSass,MadnessandModernism:InsanityintheLightofModernArt,Literature,andThought(Cambridge,MA:HarvardUniversityPress,1994),31.

“Auniversitystudentattendinglectures”:CarloRovelli,RealityIsNotWhatItSeems:TheJourneytoQuantumGravity(NewYork:RiverheadBooks,2017),148.

Penroseimaginesaphoton:RogerPenrose,Fashion,Faith,andFantasyintheNewPhysicsoftheUniverse(Princeton:PrincetonUniversityPress,2016),162.

“shiftysplit”:JohnBell,“Against‘Measurement,’”PhysicsWorld3,no.8(Aug1990):33.theHungarianphysicist:LajosDiósi,“AUniversalMasterEquationfortheGravitationalViolationof

QuantumMechanics,”PhysicsLettersA120,no.8(Mar16,1987):377–81.threephysicists:GiancarloGhirardi,AlbertoRimini,andTullioWeber,“UnifiedDynamicsfor

MicroscopicandMacroscopicSystems,”PhysicalReviewD34,no.2(Jul15,1986):470–91.“Anyembarrassingmacroscopicambiguity”:JohnBell,SpeakableandUnspeakableinQuantum

Mechanics(Cambridge:CambridgeUniversityPress,1989),204.

“haveacertainkindofgoodness”:JohnBellquotedinGiancarloGhirardi,SneakingaLookatGod’sCards:UnravelingtheMysteriesofQuantumMechanics(Princeton:PrincetonUniversityPress,2005),415.

“Theyarehonestattempts”:Ibid.In1991,JürgenMlynekandcolleagues:O.CarnalandJ.Mlynek,“Young’sDouble-SlitExperimentwith

Atoms:ASimpleAtomInterferometer,”PhysicalReviewLetters66,no.21(May27,1991):2689.atomscouldbediffractedatgratings:PhilipMoskowitz,PhillipGould,SusanAtlas,andDavid

Pritchard,“DiffractionofanAtomicBeambyStanding-WaveRadiation,”PhysicalReviewLetters51,no.5(Aug1,1983):370.

adouble-slitexperimentdonewithneonatoms:FujioShimizu,KazukoShimizu,andHiroshiTakuma,“Double-SlitInterferencewithUltracoldMetastableNeonAtoms,”PhysicalReviewA46,no.1(Jul1,1992):R17.

In1999,Zeilinger,Arndt,andtheirteam:MarkusArndtetal.,“Wave–ParticleDualityofC60Molecules,”Nature401(Oct14,1999):680–82.

it’sabespokemolecule:SandraEibenbergeretal.,“Matter–WaveInterferenceofParticlesSelectedfromaMolecularLibrarywithMassesExceeding10,000amu,”PhysicalChemistryChemicalPhysics15(Jul8,2013):14696-700.

There’sa146-meter-hightowerinBremen:https://www.zarm.uni-bremen.de/en/drop-tower/general-information.html.

Penrosehadplans:RogerPenrose,“WavefunctionCollapseasaRealGravitationalEffect,”inMathematicalPhysics2000,ed.A.Fokas,A.Grigoryan,T.Kibble,andB.Zegarlinski(London:ImperialCollegePress,2000),266–82.

HeknewpeopleatNASA:https://youtu.be/mvHg5PcXb6k?t=45.Whentheywrotetheirpaper:WilliamMarshall,ChristophSimon,RogerPenrose,andDirk

Bouwmeester,“TowardsQuantumSuperpositionsofaMirror,”PhysicalReviewLetters91,no.13(Sep23,2003):130401.

“Thecollapse[ofthewavefunction]”:SimonSaunders,JonathanBarrett,AdrianKent,andDavidWallace,eds.,ManyWorlds?:Everett,QuantumTheory,andReality(Oxford:OxfordUniversityPress,2010),582.

“HewasratherupsetwhenImethim”:DirkBouwmeesterspeakingattheInstituteforQuantumComputinginWaterloo,Ontario,Canada,May2013,https://youtu.be/g7RqLbqDr4U?t=387.

“Actualitiesseemtofloat”:WilliamJames,TheWilltoBelieve:AndOtherEssaysinPopularPhilosophy(NewYork:LongmansGreenandCo,1907),151.

Wheeler’sattitudelikelyrubbed:TranscriptofconversationbetweenHughEverettandCharlesMisner,inHughEverettIII,TheEverettInterpretationofQuantumMechanics:CollectedWorks1955–1980withCommentary,ed.JeffreyA.BarrettandPeterByrne(Princeton:PrincetonUniversityPress,2012),309.

“Whatactuallydoeshappen”:Everett,TheEverettInterpretation,65.“Inotherwords,theobserver”:Ibid.,67.“foralmostallofthe”:Ibid.,69.“canlayclaimtoacertain”:Ibid.“Onecanimagineanintelligent”:Ibid.,69–70.“Iamfranklybashful”:Ibid.,71.“Wedonotbelieve”:Ibid.,153.“objectionable”dualism:Ibid.AnAmericanphysicist,AlexanderStern:Ibid.,214.“lackmeaningfulcontent”:Ibid.,215.“matteroftheology”:Ibid.,217.“Iwouldnothaveimposed”:Ibid.,219.

“thisveryfineandable”:Ibid.“javelinproof”:Ibid.,212.“Iwasstunned,Iwasshocked”:InterviewofBryceDeWittandCecileDeWitt-MorettebyKennethW.

Ford,February28,1995,NielsBohrLibrary&Archives,AmericanInstituteofPhysics,OralHistories,https://www.aip.org/history-programs/niels-bohr-library/oral-histories/23199.

“Icantestifytothis”:Everett,TheEverettInterpretation,246.“hopelesslyincomplete”:Ibid.,255.“aphilosophicmonstrosity”:Ibid.“Fromtheviewpointofthetheory”:Ibid.,254.aconferenceinOctober1962inCincinnati,Ohio:AtranscriptoftheconferenceisavailableinEverett,

TheEverettInterpretation,270.“Itseemstomethatifthisisthecase”:Everett,TheEverettInterpretation,273.“Somehoworotherwehavehere”:Ibid.“Yes,it’saconsequence”:Ibid.,274.“Youeliminateoneofthetwo”:Ibid.,275.“Eachindividualbranch”:Ibid,276.“Thisuniverseisconstantlysplitting”:BryceDeWitt,“QuantumMechanicsandReality,”PhysicsToday

23,no.9(Sep1970):30.“Istillrecallvividlytheshock”:Ibid.UniverseSplitter:https://itunes.apple.com/us/app/universe-splitter/id329233299.“startedtosoundalittlebittoopractical”:DavidWallace,“TheEmergentMultiverse:ThePluralityof

Worlds—QuantumMechanics,”February21,2015,https://youtu.be/2OoRdyn2M9A?t=183.“Ithinkoneshouldinvoke”:Everett,TheEverettInterpretation,278.“Sotheparalleluniversesarecheap”:PaulDaviesandJulianBrown,eds.,TheGhostintheAtom

(Cambridge:CambridgeUniversityPress,1993),84.“iftheotheruniverses”:FrankWilczek,“RemarksonEnergyintheManyWorlds,”Centerfor

TheoreticalPhysics,MIT,Cambridge,Massachusetts,July24,2013,http://frankwilczek.com/2013/multiverseEnergy01.pdf.

probabilityassomethingsubjective:CharlesSebensandSeanCarroll,“Self-LocatingUncertaintyandtheOriginofProbabilityinEverettianQuantumMechanics,”BritishJournalforthePhilosophyofScience69,no.1(Mar1,2018):25–74.

“ratherthanrelinquishing”:ChristopherA.Fuchs,“OnParticipatoryRealism,”June28,2016,https://arxiv.org/abs/1601.04360.

“builtonbillionsuponbillions”:JohnWheelerparaphrasedinIbid.QuantumBayesianism:CarltonCaves,ChristopherFuchs,andRüdigerSchack,“QuantumProbabilities

asBayesianProbabilities,”PhysicalReviewA65,no.2(Jan4,2002):022305.Einsteinisthoughttohave:MatthewLeifer,“IstheQuantumStateReal?AnExtendedReviewofψ-

ontologyTheorems,”Quanta3,no.1(Nov2014):72.notethatthesameargument:Ibid.“fromthethird-personperspective”:DavidWallace,TheEmergentMultiverse:QuantumTheory

accordingtotheEverettInterpretation(Oxford:OxfordUniversityPress,2012),310.“Fromtheperspectiveofagivenexperimenter”:Ibid.“Quantummechanics,intheQBistinterpretation”:ChristopherFuchs,DavidMermin,andRüdiger

Schack,“AnIntroductiontoQBismwithanApplicationtotheLocalityofQuantumMechanics,”November20,2013,https://arxiv.org/pdf/1311.5253.pdf.

“Scienceisabouttheinterface”:DavidMermin,“WhyQBismIsNottheCopenhagenInterpretationandWhatJohnBellMightHaveThoughtofIt,”September8,2014,https://arxiv.org/pdf/1409.2454.pdf.

“asanutcase”:ChristopherFuchs,ComingofAgewithQuantumInformation:NotesonaPaulianIdea(Cambridge:CambridgeUniversityPress,2011),Kindleedition.

“Weneedtotalk”:Ibid.

“Greattalk!”:Ibid.“No,itwasn’t!”:Ibid.“YouknowwhatIwoulddo”:Ibid.“Theestfoundation’sphysicsconferences”:DavidKaiser,HowtheHippiesSavedPhysics:Science,

Counterculture,andtheQuantumRevival(NewYork:Norton,2011),189.Inonetalk,heaskedhisaudiencetoconsidertwotheories:RichardFeynmanMessengerLectureson

theCharacterofPhysicalLaw,Lecture7,“SeekingNewLaws,”November1964,http://www.cornell.edu/video/richard-feynman-messenger-lecture-7-seeking-new-laws.

“Inordertogetnewtheories”:Ibid.“Inotherwords,althoughtheyareidentical”:Ibid.ThisinspiredWiseman:JayGambettaandHowardWiseman,“InterpretationofNon-Markovian

StochasticSchrödingerEquationsasaHiddenVariableTheory,”PhysicalReviewA68(Dec9,2003):062104.

Theresultstheyobtainedareeerilysimilar:MichaelHall,Dirk-AndréDeckert,andHowardWiseman,“QuantumPhenomenaModeledbyInteractionsbetweenManyClassicalWorlds,”PhysicalReviewX4(Oct23,2014):041013.

“IfBorn’srulefails”:W.H.Zurek,quotedinUrbasiSinhaetal.,“ATripleSlitTestforQuantumMechanics,”PhysicsinCanada66,no.2(Apr/Jun2010):83.

sometimesthetriple-slit:G.Rengarajetal.,“MeasuringtheDeviationfromtheSuperpositionPrincipleinInterferenceExperiments,”November20,2017,https://arxiv.org/abs/1610.09143.

Orisitequaltotheamplitude:RahulSawantetal.,“NonclassicalPathsinQuantumInterferenceExperiments,”PhysicalReviewLetters113,no.12(Sep19,2014):120406.

“Any...situationinquantummechanics”:FeynmanMessengerLectures,Lecture6,“ProbabilityandUncertainty:TheQuantumMechanicalViewofNature,”http://www.cornell.edu/video/richard-feynman-messenger-lecture-6-probability-uncertainty-quantum-mechanical-view-nature.

ACKNOWLEDGMENTS

IrememberbeingthrilledbyGaryZukav’sDancingWuLiMasterswhenIreaditinthe1980s.Themysteriesofquantumphysicscamealive.Thebookhad,ofcourse,adescriptionofthedouble-slitexperiment,besidesalotelse.Then,asajournalist,Itoostartedwritingstoriesaboutquantummechanicsandencounteredtheiconicexperimentateveryturn.Anideatookshape:astoryaboutquantumphysicstoldfromtheperspectiveofthedouble-slitexperiment.Butitremainedonabackburnerforyears.

Thankstomyeditor,StephenMorrow,forseeingthepossibilitiesandmakingmerevisittheideaandthenseeingthebookthroughtotheend.ThanksalsotoMadelineNewquistandothersatDuttonandtomyagent,PeterTallack,fortheirhelpinmakingthishappen.

Abooklikethisneedsanillustrator.ThankstomyfriendAjaiNarendranforintroducingmetoRoshanShakeel.Roshanturnedmyhalf-bakedsketchesintoclean,sharpdrawingsthatwonderfullycomplementthewords.I’mgratefultoRoshanforhisunflaggingefforts,andtoAjaiforsupportingandencouragingbothmeandRoshan.

I’mgratefulalsotoRobSunderland,LisRasmussen,FelicityPors,andtherestofthestaffattheNielsBohrArchiveinCopenhagen,Denmark,foralltheirhelpinaccessinghistoricaldocuments.

Ileanedheavilyonphysiciststoexplainquantummechanicstome.Theytookthetime,eitherinpersonorbyphoneoremail,toenlightenmeonthemanyconceptualissuesthatmakequantumphysicssoconfoundingandenthralling;manyreadpartsofthebookandcaughterrorsandsuggestedchanges.I’mgratefulto(inorderofthechapters):LucienHardy,AlainAspect,PhilippeGrangier,DavidAlbert,TimMaudlin,AntonZeilinger,MarlanScully,RupertUrsin,Xiao-SongMa,LevVaidman,SheldonGoldstein,JohnBush,TomasBohr,ChrisDewdney,BasilHiley,AephraimSteinberg(formanydiscussionsandmeetingsovertheyears),RoderichTumulka,RogerPenrose,MarkusArndt,DirkBouwmeester,SeanCarroll,DavidWallace,HowardWiseman,ChrisFuchs,DavidMermin,DavidKaiser,LeonardSusskind,UrbasiSinha,John

Fuchs,DavidMermin,DavidKaiser,LeonardSusskind,UrbasiSinha,JohnSipe,andNealAbraham.

I’mespeciallygratefultoJohnBushforvettingalmostallthechapters.Hisenthusiasmwasinfectious.AndaspecialthankstoAntoineTilloyforreadingandcommentingonthewholebook.ThanksalsotomyfriendsSriramSrinivasanandVarunBhattafortheirinput.Mostofall,thankstoAdamBeckerforhissupportthroughoutthewritingofthisbook—includinganimateddiscussionsoverinnumerablecoffeesandlunchesinBerkeley—andforcatchingsomeerrorsinthefinaldraft.

Anyerrorsthatremainare,ofcourse,myresponsibility.ThankstoBanuandRameshforhostingmeformonthsinArlingtonand

Amherst,asIwentaboutmeetingthecoterieofquantumphysicistsontheUSEastCoast;toCarolineSidiforhostingmeinParis;toGitaSuchakformakingmefeelathomeinLondon;andtoRaoAkellaforhelpfindingquotesfortheepigraphs.Andlast,butbynomeansleast,mythankstomyfamilybackinIndiafortheirsupport,particularlymyparents.

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.

Albert,David,79–80,182–83,195anti-particles,141–44Arndt,Markus,195–205Aspect,AlainandBell’stheorem,102,105–6andBohmianmechanics,164andDalibard,196andnonlocality–relativityconflict,94andQBism,250,253andquantumeraser,110–11,113,140andsingle-particleexperiments,60–64,68,74–75,84–86,88–91

Ball,Philip,32Bayes,Thomas,242–43Bayesianprobability,248.SeealsoQuantumBayesianism(QBism)beam-splittersandBohmianmechanics,170–71,177anddecision-makingapp,216andmanyworldstheories,228,228–33,229,238–39andPenrose’sthoughtexperiment,189–90andQBism,247,247andquantumeraser,118–20,123,126,134,137,143–44andsingle-particleexperiments,64–65,68–75,75–80superpositionmirrorin,207–12anduniversalwavefunction,219–21,220SeealsoMachZehnderinterferometers

Belinfante,Frederik,167Bell,John,61–62,94,101–2.SeealsoBell’stheoremBell’stheoremandBohmianmechanics,164,176

andmolecularinterferometry,196andnonlocality–relativityconflict,94andQBism,251–52andquantumeraser,110,128,144andsingle-particleexperiments,61–62testingof,102–6

Bohm,David(andBohmianmechanics)backgroundandearlyworks,147–51debateonBohmianmechanics,181–85deBroglie-Bohmtheory,156–57,203,246,250,252,260,261–62anddeBroglie’sdouble-wavesolution,161anddissentonCopenhageninterpretation,217andEPRargument,98andESSWargument,175–77andGoldstein,151–52,154hiddenvariabletheoryof,101–2influenceofBohmianmechanics,162–66andmanyworldstheories,235,239–40,261–62andmolecularinterferometry,202–3andparticletrajectoryresearch,166–67,168,172–75,179–81,180andphilosophicalimplications,235andpilot-wavetheory,155–58andQBism,244,250–53

Bohr,NielsandBell’stheorem,61andBohmianmechanics,147–48,150–52,155andEinstein,52–58andFifthSolvayconference,40andmanyworldstheories,233andmodelsofatomicstructure,35–38andmolecularinterferometry,203andnonlocality–relativityconflict,94andoriginofdouble-slitexperiment,3andQBism,244andquantumentanglement,96andquantumeraser,110,113–14,129andSchrödinger,49–52andsingle-particleexperiments,86,89–90anduniversalwavefunction,222–23andWheeler,218

Bohr,Tomas,159Born,Max,41–42,46–48,107,239–42,263–64Bornrule,48,239–42,263–64,265Bouwmeester,Dirk,143–44,206,210–11,213–16Bozic,Danino,94Broglie,LouisdeandBohmianmechanics,155–58,161deBroglie-Bohmtheory,156–57,203,246,250,252,260,261–62andmolecularinterferometry,196,198,202–4andproblemswithquantummechanics,189

andquantumeraser,146andsingle-particleexperiments,66andwave-particleduality,24,38,45–46

Brougham,Henry,15Bush,John,157,159–61

Carroll,Sean,227–28,230–34,237–41Casimir,Hendrik,58causality.Seedeterminism/indeterminismCaves,Carlton,245classicalphysicsandcausality,48classical-quantumboundary,190,192,195,203,205,214,250,252andindeterminism,39andphotoelectriceffect,26–27andwave-particlenatureoflightdebate,23–24

Clauser,John,104,106,110,164Cohen-Tannoudji,Claude,61Coleman,Sidney,255collapseofwavefunctionsandBohmianmechanics,165–69andfutureofquantumresearch,257–58gravitationalcollapsetheory,190–93,203–6,209andmanyworldstheories,215–16,230–31,234–35,239,261–62andnonlocality–relativityconflict,95andQBism,244,246,248–50,252–53andquantumeraser,114–16,130–35,139–40,145andsingle-particleexperiments,80–81,83spontaneouscollapse,190–91,193–95andsuperpositionmirrorinterferometer,209–12,214–15anduniversalwavefunction,220–21

complementarity,52,57,86,90,113–14,128complexnumbers,43–44,47–48configurationspace,163,259–61constructiveinterference,14,20–21,75,77,141,208CopenhageninterpretationofquantummechanicsandBohmianmechanics,147–51,153–57,159,161–62,182–83dissentingopinionson,217–18andEPRargument,96,100andhiddenvariabletheory,146andmanyworldstheories,229,231,233–35,235,239,261–62andmolecularinterferometry,203originof,54–57andPenrose’sthoughtexperiment,190andQBism,244,246,248–50,252–53andquantumeraser,110,129–30,133,145andsingle-particleexperiments,80–81,83,85,88andspontaneouscollapse,192,193anduniversalwavefunction,219–20,222–25

Copernicus,Nicolaus,53“corpusculartheoryoflight,”8,11,29Couder,Yves,158–59Couprie,Benjamin,39Curie,Marie,39,112

Dalibard,Jean,196Davies,Paul,236de-Broglie-Bohmtheory,156–57,203,246,250,252,260,261–62Deckert,Dirk-André,259decoherence,197–98,209,214,230–31,233,238,241,252delayed-choiceexperiments,86–91,108,113,121,123Dennett,Daniel,243–45densitymatrices,230–31d’Espagnat,Bernard,93–94destructiveinterference,14,20,75–77,208determinism/indeterminismandBohmianmechanics,151,153–56,165,169,176andEPRargument,100–101andfirstdouble-slitexperiments,21andmanyworldstheories,239,261–62andmatrixmechanics,44–45andquantumeraser,139,145andradioactivity,39andsingle-particleexperiments,60anduniversalwavefunction,218–19,221andwavemechanics,48

Deutsch,David,234,236,241Dewdney,Chris,166,173DeWitt,Bryce,224–27Diósi,Lajos,193Dirac,Paul,42,84,189,225doubleinterferometerexperiments,140–44double-wavesolution,157,161Drühl,Kai,113–16Düker,Heinrich,65–66Dürr,Detlef,162

Eddington,Arthur,59Ehrehfest,Paul,52–53,55Einstein,AlbertandAspect’seducation,60–61andBell’stheorem,104,106–7andBohmianmechanics,148–52,155andBohr-Schrödingerdiscussions,50debateswithBohr,52–58anddissentingopinionsonCopenhageninterpretation,217–18andEPRargument,100–102andFifthSolvayconference,39–40

andmanyworldstheories,238andmodelsofatomicstructure,37–38andnonlocality–relativityconflict,94–98andoriginofdouble-slitexperiment,3andphotoelectriceffect,16–17,27,29–32andproblemswithquantummechanics,189andQBism,246andquantumeraser,110–12,113,139–40andsingle-particleexperiments,70,80,82,85–86,89–91andwave-particledualityofmatter,45

electromagnetismandBell’stheorem,102–3andBohmianmechanics,154andBouwmeester’sworkonMaxwell’sequations,206electromagneticfields,26,26,32electromagneticwaveviewoflight,24–26,33,63,103andMaxwell’sequations,32,35andmodelsofatomicstructure,37–38andphotoelectriceffect,26–27,29–30andquantaoflight,32–33andquantumgravitytheories,188andsingle-particleexperiments,63,77andwave-particlenatureoflightdebate,24–26

electronsdiscoveryof,28–31anddoubleinterferometerexperiments,140–44andFeynmanondouble-slitexperiment,6andfirstdouble-slitexperiments,18andmatrixmechanics,42–45andmodelsofatomicstructure,36–37andoriginoftheCopenhageninterpretation,54–58andphotoelectriceffect,17andwavemechanics,45–48wave-particleduality,6–7

Elitzur,Avshalom,2,133–35,138,144ElitzurVaidmanbombpuzzle,2–3,135,135–40,136,142,145,216entanglement,quantumandBell’stheorem,103–7,105andBohmianmechanics,150,164,177–78,178andBouwmeester’swork,206andEPRargument,96,98andmanyworldstheories,229,231,233Maudlinon,107–8andmolecularinterferometry,197andQBism,250andquantumeraser,116–17,121–23,125–28,131,139,144andsingle-particleexperiments,91andstochasticcollapsetheories,257andsuperpositionmirrorinterferometer,209

EPR(Einstein-Podolsky-Rosen)paper,96–102,149–50

Erhard,Werner,255ESSWtheory,175,176–77,181Everett,Hugh,III,216,218–28,233–40,242,251,261–62

Faraday,Michael,24Feynman,RichardandBell’stheorem,106andBohmianmechanics,160andfirstdouble-slitexperiments,15–18,22andmanyworldstheories,227,232onopen-mindedness,255–56andoriginofdouble-slitexperiment,3andpathintegralformulation,232,264onsignificanceofdouble-slitexperiment,3–9,108,266andsingle-particleexperiments,62–66,68

FifthSolvayInternationalConferenceonElectronsandPhotons(1920),39,52–58,155Flack,Robert,173–74Fort,Emmanuel,158–59Freedman,Stuart,104Fresnel,Augustin-Jean,65–66Fry,Edward,104,106Fuchs,Christopher,243–46,248–49,251,253

generalrelativity,96–97,187–88,190,224Ghirardi,Giancarlo,63–64,193Gisin,Nicolas,93Goethe,JohannWolfgangvon,41Goldstein,Sheldon,151–55,157,162,164,166,183–84Grangier,Philippe,63,68,74–75,84,86gravity,23,96–97Greene,Brian,109GRWtheory,193–95,203,205,214,235

Hall,Michael,259Hardy,Lucien,1–2,140,143–44Heisenberg,Wernerandatomictheory,40–42andBohmianmechanics,151–52onBohr-Schrödingerdiscussions,49–52andHermann’swork,101andmatrixmechanics,44–46onobjectivityatquantumscales,23andoriginoftheCopenhageninterpretation,54–56andQBism,253andquantumeraser,129andspontaneouscollapsetheories,192

Hell,Stefan,59–60Helmholtz,Hermannvon,28Hermann,Grete,100–101

Hertz,Heinrich,25–29hiddenvariablesandBell’stheorem,104,106–7andBohmianmechanics,149–51,154–56,164,167,182,184dissentonCopenhageninterpretation,217andEPRargument,99–101andfutureofquantumresearch,257–58,259andmanyworldstheories,233–35,261–62andQBism,246,250andquantumeraser,114,140,146andsingle-particleexperiments,61–62,70–71

Hilbertspace,237–38,243Hiley,Basil,162,166–67,173–74,174–75Høffding,Harald,58Holland,Peter,162Holt,Richard,104Hoyle,Fred,53Huygens,Christiaan,12–14,16,23–24

incompletenesstheorem,112interaction-freemeasurements,135,138–39,143,145

James,William,217,244Jordan,Pascual,42Jørgensen,Jørgen,58

Kaiser,David,255Kuhn,Thomas,53–54

Lamb,Willis,113LaPalma-Tenerifeexperiments,110,121–29,122,126laserinterferometers,74–75.SeealsoMachZehnderinterferometersLenard,Philipp,29,32locality/nonlocality,93–107andBohmianmechanics,150,161–64,176,179–81,183andmanyworldstheories,261–62Maudlinon,107–8andQBism,250–51andquantumeraser,112,128,139,144–45andSchrödinger’swavemechanics,47andsingle-particleexperiments,62andspontaneouscollapse,194andsuperpositionmirrorinterferometer,212anduniversalwavefunction,220andwave-particlenatureoflightdebate,24

Ma,Xiao-Song,124,130Mach,Ludwig,73MachZehnderinterferometers

andmanyworldstheories,228,231–32,239andmolecularinterferometry,205andQBism,248andquantumeraser,123,127,134–41andsingle-particleexperiments,73–75,78,80,84–88andsuperpositionmirrorinterferometer,208–9

manyworldstheories,261–262,215–16,226–36,235,250,260Marshall,William,210matrixmechanics,42–45,48Maudlin,Tim,93–94,107Maxwell,JamesClerk,24–26,37,60,206Maxwell’sequations,32,35–37,206Mayor,Marcel,199measurementproblems,218–21,224,226,230–31,261Merli,PierGiorgio,67Mermin,David,96,144,249,252–53Miller,Warren,86Missiroli,GianFranco,67Mlynek,Jürgen,197molecularinterferometry,196–205Möllenstedt,Gottfried,64–67Møller,Christian,129Moore,Walter,50Morandi,Giorgio,3

Nelson,Edward,153–54Newton,Isaac,3,8,12–13,16,23,39Newtonianphysics,10–11,21,23–24,39.SeealsoclassicalphysicsNielsBohrInstitute,40Noether,Emmy,100

Oppenheimer,Robert,147–48

paralleluniversetheories,225.Seealsomanyworldstheoriespathintegralformulation,232Pauli,Wolfgang,41,49,54–55,129,151,155–56Penrose,Roger,138–39,184–85,187–93,195,203,205–7,209–14,235Philippidis,Chris,167,173photoelectriceffect,16–17,26–27,29–32,31,32,91pilot-wavetheory,155–59,161,203Pipkin,Francis,104Planck,Max,29–32,37–39,66,191Planck’sconstant,66Podolsky,Boris,96,225,226polarizedoflight,102,102–6,105,123,125–27,126,143,171,174,177–81,180,184polarizingbeamsplitter(PBS),123,126,126,177,178Popper,Karl,53–54positrons,141–44Pozzi,Giulio,67

Pritchard,David,197probabilityanddensitymatrices,230–31andfirstdouble-slitexperiments,21andmanyworldstheories,230–32,239–43andmatrixmechanics,44–45andoriginoftheCopenhageninterpretation,57andquantumeraser,110–11,139andSchrödinger’swavemechanics,47–48andsingle-particleexperiments,70–75,80–81anduniversalwavefunction,219,221

psi-epistemicandpsi-ontictheories,245–46,249

quanta,30,32–34,37QuantumBayesianism(QBism),235,235,242–43,245–46,248–54,262quantumeraserexperiments,113–21,121–30,130–33,133–40,140–46,179quantumgravity,188,224

radiation,38–39,43randomnessandrandomizationandBohmianmechanics,153electromagneticwaveviewoflight,103andfirstdouble-slitexperiments,19andmanyworldstheories,239andQBism,244andquantumeraser,123,125–28,126,139–40,145andSchrödinger’swavemechanics,48andsingle-particleexperiments,68andspontaneouscollapse,193,195andsuperpositionmirrorinterferometer,211–12anduniversalwavefunction,221Seealsostochasticity

realist-anti-realistinterpretationsandBell’stheorem,106andBohmianmechanics,149,151,183andEPRargument,97,100–101andESSWargument,175andGoldstein’swork,153andmanyworldstheories,234,261–62andmolecularinterferometry,203andoriginoftheCopenhageninterpretation,54,57andpilot-wavetheory,155–56andQBism,246,248andquantumeraser,110–11,140,144andsingle-particleexperiments,82,85

relativity,94–97,173,187–88,190,224,238,261Renninger,Mauritius,134Rimini,Alberto,193Rosen,Nathan,96,225

Rovelli,Carlo,187Rutherford,Ernest,35

Salter,RobertP.,112Schack,Rüdiger,245,249Schrödinger,Erwin,49–50andBohmianmechanics,154–55,163,165,176andBornRule,263cat-in-a-boxthoughtexperiment,83–84,164–66,189–90,215developmentofwavemechanics,45–49onentanglement,108andmanyworldstheories,229,231,233–35,238andmatrixmechanics,44–45andmolecularinterferometry,196–97andquantumeraser,111,114,116,133andsingle-particleexperiments,59–60,80,82,91andspontaneouscollapse,192–93anduniversalwavefunction,219,221–22

Scully,Marlan,112–16,175,179Sebens,Charles“Chip,”240–41Shimizu,Fujio,197Shimony,Abner,225–26,236Shipley,Patricia,101Simon,Christoph,210single-particleexperiments,59–91Aspect’sexperiment,60–64beam-splittingexperiments,64–65,68–75,75–80Schrödinger’sskepticismof,59–60singlemoleculeinterference,202single-photonsensitivity,2,21–22technologicaladvancesrequiredfor,64–68thoughtexperimentson,80–85andWheeler’sdelayedchoiceexperiment,85–91SeealsoElitzurVaidmanbombpuzzle

single-slitexperiments,33–35Sinha,Urbasi,263,264Sokal,Alan,151–52spacetimecurvature,190–91specialrelativity,95,261spinofparticles,98–99,184spontaneouscollapsetheories,190–95“spookyactionatadistance,”91,107,128,145,176Squires,Euan,140Stein,Gertrude,130Steinberg,Aephraim,132,167,170–79,181–85,232Stern,Alexander,223stochasticity,39,48,153–54,234,239,257,261superposition,quantumandBohmianmechanics,165,169,179

andBornRule,263entanglementandnonlocality,107andmanyworldstheories,229andmolecularinterferometry,196–202,205Penrose’sthoughtexperiment,188–90andquantumeraser,115,120,128,134,136,142,145Schrödinger’scatthoughtexperiment,83–84,215single-particleexperiments,79–85,87,91andspontaneouscollapse,190–92,194superpositionmirrorinterferometer,207–13anduniversalwavefunction,218–21,225–26

surrealtrajectories,166,175–77,179,181–82Susskind,Leonard,255–56

Taylor,GeoffreyIngram,33–35,63thermodynamics,149,238Thompson,Randall,104Thomson,J.J.,28–29,32–34,35Tonomura,Akira,67–68twistortheory,206

uncertaintyprincipleandBohmianmechanics,150,164–65,169andBohr-Schrödingerdiscussions,51–52andCopenhageninterpretation,54–57andfutureofquantumresearch,258–59andmanyworldstheories,241andQBism,245,247andquantumeraser,113–14andsingle-particleexperiments,86,90andspontaneouscollapse,192

universalwavefunctiontheory,218–27Ursin,Rupert,121,129–30

Vaidman,Lev,2,133–35,138–40,144,169,215–16,227virtualdouble-slitexperiment,117,117–18,122,171,177virtualensemblesofparticles,258–59,261VonNeumann,John,48,54,100–102,114–15,151

walkingdropletexperiments,158–62Wallace,David,234,236–37,239–42,251wavefunctionsandBell’stheorem,103–4andBohmianmechanics,153–55,161–68,176entanglementandnonlocality,107–8andEPRargument,99–100andfutureofquantumresearch,257–59,262–64andmanyworldstheories,215–16,228–31,233,237–39,241–42andmolecularinterferometry,198–202

andnonlocality–relativityconflict,94–98andPenrose’sthoughtexperiment,189–90andQBism,245–50,252andquantumeraser,114–16,130–35,139–40,145andSchrödinger’swavemechanics,46–48andsingle-particleexperiments,80–84andspontaneouscollapse,192–95andsuperpositionmirrorinterferometer,209,214–15universalwavefunctiontheory,218–27

wave-particledualityandBohr-Schrödingerdiscussions,50andFeynmanondouble-slitexperiment,6–7andfirstdouble-slitexperiments,17–22andphotoelectriceffect,31andquantumeraser,112,127,145andSchrödinger’swavemechanics,45–49andsignificanceofthedouble-slitexperiment,108andvirtualdouble-slitexperiment,117–18

“weakmeasurement,”169–72,171,174,179,182,240Weber,Tullio,193Wheeler,John,85–91,113,129–30,218,222–24,244which-way(welcher-weg)informationandBohmianmechanics,179,181andmanyworldstheories,233andmolecularinterferometry,197–98andquantumeraser,116,118–20,123,125,127–28,131–32,136–37,141–42

Wigner,Eugene,115,220,225Wilczek,Frank,238Wiseman,Howard,170,240,242,257–59,261WorldWarII,148

Yoon-HoKim,116,120–21Young,Thomas,13–16,17,22–24,63,75,112,173Young’sexperimentwithsunlight,13–16

Zanghi,Nino,162Zeilinger,AntonandBohmianmechanics,150,164andBouwmeester’swork,206andmolecularinterferometry,196–98,203andQBism,253andquantumeraser,110–12,116,120–21,124,140

Zender,Ludwig,73

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

AnilAnanthaswamyisanaward-winningjournalistandformerstaffwriteranddeputynewseditorfortheLondon-basedNewScientistmagazine.

HehasbeenaguesteditorforthesciencewritingprogramattheUniversityofCalifornia,SantaCruz,andorganizesandteachesanannualsciencejournalismworkshopattheNationalCentreforBiologicalSciencesinBengaluru,India.HeisafreelancefeatureeditorfortheProceedingsoftheNationalAcademyofScience’sFrontMatter.HecontributesregularlytoNewScientist,andhasalsowrittenforNature,NationalGeographicNews,Discover,Nautilus,Matter,TheWallStreetJournal,andtheUK’sLiteraryReview.Hisfirstbook,TheEdgeofPhysics,wasvotedbookoftheyearin2010byPhysicsWorld,andhissecondbook,TheManWhoWasn’tThere,wonaNautilusBookAwardin2015andwaslonglistedforthe2016PEN/E.O.WilsonLiteraryScienceWritingAward.

TavoladeiContenuti-"TOC"ALSOBYANILANANTHASWAMYCONTENTSPrologueTHESTORYOFNATURETAUNTINGUS1THECASEOFTHEEXPERIMENTWITHTWOHOLESRichardFeynmanExplainstheCentralMystery2WHATDOESITMEAN“TOBE”?TheRoadtoReality,fromCopenhagentoBrussels3BETWEENREALITYANDPERCEPTIONDoingtheDoubleSlit,OnePhotonataTime4FROMSACREDTEXTSRevelationsaboutSpookyActionataDistance5TOERASEORNOTTOERASEMountaintopExperimentsTakeUstotheEdge6BOHMIANRHAPSODYObviousOntologyEvolvingtheObviousWay7GRAVITYKILLSTHEQUANTUMCAT?TheCaseforAddingSpacetimeintotheMix8HEALINGANUGLYSCARTheManyWorldsMedicineEpilogue

WAYSOFLOOKINGATTHESAMETHING?NOTESACKNOWLEDGMENTSINDEXABOUTTHEAUTHOR