RIVERHEADBOOKSAnimprintofPenguinRandomHouseLLC375HudsonStreetNewYork,NewYork10014

PublishedbyRiverheadBooks2018Copyright©2017byAdelphiEdizioniSPA,MilanoTranslationcopyright©2018bySimonCarnellandEricaSegreFirstpublishedinItalybyAdelphiEdizioniSPAunderthetitleL’ordinedeltempo2017EnglishtranslationpublishedsimultaneouslyinGreatBritainbyAllenLane,animprintofPenguinRandomHouseUKandintheUnitedStatesofAmericabyRiverheadBooks,animprintofPenguinRandomHouseLLCPenguinsupportscopyright.Copyrightfuelscreativity,encouragesdiversevoices,promotesfreespeech,andcreatesavibrantculture.Thankyouforbuyinganauthorizededitionofthisbookandforcomplyingwithcopyrightlawsbynotreproducing,scanning,ordistributinganypartofitinanyformwithoutpermission.YouaresupportingwritersandallowingPenguintocontinuetopublishbooksforeveryreader.

LibraryofCongressCataloging-in-PublicationData

Names:Rovelli,Carlo,author.|Segre,Erica,translator.|Carnell,Simon,translator.Title:Theorderoftime/CarloRovelli;translatedbyEricaSegreandSimonCarnell.Othertitles:Ordinedeltempo.EnglishDescription:FirstAmericanedition.|NewYork:RiverheadBooks,2018.|OriginallypublishedinItalian:L’ordinedeltempo(Milan:AdelphiEdizioni,2017).|Includesbibliographicalreferencesandindex.Identifiers:LCCN2017060293|ISBN9780735216105(hardcover)|ISBN9780735216129(ebook)Subjects:LCSH:Spaceandtime.|Time.|Presentism(Philosophy).|Cosmology.Classification:LCCQC173.59.S65R68132018|DDC530.11—dc23LCrecordavailableathttps://lccn.loc.gov/2017060293p.cm.

Version_1

FORERNESTO,BILO,ANDEDOARDO

CONTENTS

TitlePageCopyrightDedicationAuthor'sNote

PerhapsTimeIstheGreatestMystery

PartI THECRUMBLINGOFTIME1.LossofUnity2.LossofDirection3.TheEndofthePresent4.LossofIndependence5.QuantaofTime

PartII THEWORLDWITHOUTTIME6.TheWorldIsMadeofEvents,NotThings7.TheInadequacyofGrammar8.DynamicsasRelation

PartIII THESOURCESOFTIME9.TimeIsIgnorance10.Perspective11.WhatEmergesfromaParticularity12.TheScentoftheMadeleine13.TheSourceofTime

TheSisterofSleep

ImageCreditsNotesIndexAbouttheAuthor

Theversesthatopeneachchapter,unlessotherwiseindicated,arefromversionsofHorace’sOdestranslatedbyGiulioGalettoandpublishedinacharmingsmallvolumeentitledInquestobrevecerchio(Verona:EdizionidelPaniere,1980);EnglishtranslationsbyEricaSegreandSimonCarnell.

PERHAPSTIMEISTHEGREATESTMYSTERY

Eventhewordsthatwearespeakingnowthievingtimehasstolenaway,andnothingcanreturn.(I,11)

Istopanddonothing.Nothinghappens.Iamthinkingaboutnothing.Ilistentothepassingoftime.Thisistime,familiarandintimate.Wearetakenbyit.Therushof

seconds,hours,yearsthathurlsustowardlifethendragsustowardnothingness....Weinhabittimeasfishliveinwater.Ourbeingisbeingintime.Itssolemnmusicnurturesus,openstheworldtous,troublesus,frightensandlullsus.Theuniverseunfoldsintothefuture,draggedbytime,andexistsaccordingtotheorderoftime.InHindumythology,theriverofthecosmosisportrayedwiththe

sacredimageofShivadancing:hisdancesupportsthecoursingoftheuniverse;itisitselftheflowingoftime.Whatcouldbemoreuniversalandobviousthanthisflowing?Andyetthingsaresomewhatmorecomplicatedthanthis.Realityis

oftenverydifferentfromwhatitseems.TheEarthappearstobeflatbutisinfactspherical.Thesunseemstorevolveintheskywhenitisreallywewhoarespinning.Neitheristhestructureoftimewhatitseemstobe:itisdifferentfromthisuniform,universalflowing.Idiscoveredthis,tomyutterastonishment,inthephysicsbooksIreadasauniversitystudent:timeworksquitedifferentlyfromthewayitseemsto.InthosesamebooksIalsodiscoveredthatwestilldon’tknowhow

timeactuallyworks.Thenatureoftimeisperhapsthegreatestremainingmystery.Curiousthreadsconnectittothoseothergreatopenmysteries:thenatureofmind,theoriginoftheuniverse,thefateofblackholes,the

veryfunctioningoflifeonEarth.Somethingessentialcontinuestodrawusbacktothenatureoftime.Wonderisthesourceofourdesireforknowledge,1andthediscovery

thattimeisnotwhatwethoughtitwasopensupathousandquestions.Thenatureoftimehasbeenatthecenterofmylife’sworkintheoreticalphysics.Inthefollowingpages,Igiveanaccountofwhatwehaveunderstoodabouttimeandthepathsthatarebeingfollowedinoursearchtounderstanditbetter,aswellasanaccountofwhatwehaveyettounderstandandwhatitseemstomethatwearejustbeginningtoglimpse.Whydowerememberthepastandnotthefuture?Doweexistintime,

ordoestimeexistinus?Whatdoesitreallymeantosaythattime“passes”?Whattiestimetoournatureaspersons,tooursubjectivity?WhatamIlisteningtowhenIlistentothepassingoftime?Thisbookisdividedintothreeunequalparts.Inthefirst,Isummarize

whatmodernphysicshasunderstoodabouttime.Itislikeholdingasnowflakeinyourhands:gradually,asyoustudyit,itmeltsbetweenyourfingersandvanishes.Weconventionallythinkoftimeassomethingsimpleandfundamentalthatflowsuniformly,independentlyfromeverythingelse,fromthepasttothefuture,measuredbyclocksandwatches.Inthecourseoftime,theeventsoftheuniversesucceedeachotherinanorderlyway:pasts,presents,futures.Thepastisfixed,thefutureopen....Andyetallofthishasturnedouttobefalse.Oneafteranother,thecharacteristicfeaturesoftimehaveprovedtobe

approximations,mistakesdeterminedbyourperspective,justliketheflatnessoftheEarthortherevolvingofthesun.Thegrowthofourknowledgehasledtoaslowdisintegrationofournotionoftime.Whatwecall“time”isacomplexcollectionofstructures,2oflayers.Underincreasingscrutiny,inevergreaterdepth,timehaslostlayersoneafteranother,piecebypiece.Thefirstpartofthisbookgivesanaccountofthiscrumblingoftime.Thesecondpartdescribeswhatwehavebeenleftwith:anempty,

windsweptlandscapealmostdevoidofalltraceoftemporality.Astrange,alienworldthatisneverthelessstilltheonetowhichwebelong.Itislikearrivinginthehighmountains,wherethereisnothingbutsnow,rocks,andsky.OrlikeitmusthavebeenforArmstrongandAldrinwhenventuringontothemotionlesssandofthemoon.Aworldstrippedtoits

essence,glitteringwithanaridandtroublingbeauty.ThephysicsonwhichIwork—quantumgravity—isanattempttounderstandandlendcoherentmeaningtothisextremeandbeautifullandscape.Totheworldwithouttime.Thethirdpartofthebookisthemostdifficult,butalsothemostvital

andtheonethatmostcloselyinvolvesus.Inaworldwithouttime,theremuststillbesomethingthatgivesrisetothetimethatweareaccustomedto,withitsorder,withitspastthatisdifferentfromthefuture,withitssmoothflowing.Somehow,ourtimemustemergearoundus,atleastforusandatourscale.3

Thisisthereturnjourney,backtowardthetimelostinthefirstpartofthebookwhenpursuingtheelementarygrammaroftheworld.Asinacrimenovel,wearenowgoinginsearchofaguiltyparty:theculpritwhohascreatedtime.Onebyone,wediscovertheconstituentpartsofthetimethatisfamiliartous—not,now,aselementarystructuresofreality,butratherasusefulapproximationsfortheclumsyandbunglingmortalcreaturesweare:aspectsofourperspective,andaspects,too,perhaps,thataredecisiveindeterminingwhatweare.Becausethemysteryoftimeisultimately,perhaps,moreaboutourselvesthanaboutthecosmos.Perhaps,asinthefirstandgreatestofalldetectivenovels,Sophocles’OedipusRex,theculpritturnsouttobethedetective.Here,thebookbecomesafierymagmaofideas,sometimes

illuminating,sometimesconfusing.Ifyoudecidetofollowme,IwilltakeyoutowhereIbelieveourknowledgeoftimehasreached:uptothebrinkofthatvastnocturnalandstar-studdedoceanofallthatwestilldon’tknow.

PART1

THECRUMBLINGOFTIME

1 LOSSOFUNITY

Dancesofloveintertwinesuchgracefulgirlslitbythemoonontheseclearnights.(I,4)

THESLOWINGDOWNOFTIME

Let’sbeginwithasimplefact:timepassesfasterinthemountainsthanitdoesatsealevel.Thedifferenceissmallbutcanbemeasuredwithprecisiontimepieces

thatcanbeboughttodayontheinternetforafewthousanddollars.Withpractice,anyonecanwitnesstheslowingdownoftime.Withthetimepiecesofspecializedlaboratories,thisslowingdownoftimecanbedetectedbetweenlevelsjustafewcentimetersapart:aclockplacedonthefloorrunsalittlemoreslowlythanoneonatable.Itisnotjusttheclocksthatslowdown:lowerdown,allprocessesare

slower.Twofriendsseparate,withoneofthemlivingintheplainsandtheothergoingtoliveinthemountains.Theymeetupagainyearslater:theonewhohasstayeddownhaslivedless,agedless,themechanismofhiscuckooclockhasoscillatedfewertimes.Hehashadlesstimetodothings,hisplantshavegrownless,histhoughtshavehadlesstimetounfold....Lowerdown,thereissimplylesstimethanataltitude.

Isthissurprising?Perhapsitis.Butthisishowtheworldworks.Timepassesmoreslowlyinsomeplaces,morerapidlyinothers.Thesurprisingthing,perhaps,isthatsomeoneunderstoodthisslowing

downoftimeacenturybeforewehadclockspreciseenoughtomeasureit.Hisname,ofcourse,wasAlbertEinstein.Theabilitytounderstandsomethingbeforeit’sobservedisattheheart

ofscientificthinking.Inantiquity,AnaximanderunderstoodthattheskycontinuesbeneathourfeetlongbeforeshipshadcircumnavigatedtheEarth.Atthebeginningofthemodernera,CopernicusunderstoodthattheEarthturnslongbeforeastronautshadseenitdosofromthemoon.Inasimilarway,Einsteinunderstoodthattimedoesnotpassuniformlyeverywherebeforethedevelopmentofclocksaccurateenoughtomeasurethedifferentspeedsatwhichitpasses.Inthecourseofmakingsuchstrides,welearnthatthethingsthat

seemedself-evidenttouswerereallynomorethanprejudices.Itseemedobviousthattheskywasaboveusandnotbelow;otherwise,theEarthwouldfalldown.Itseemedself-evidentthattheEarthdidnotmove;otherwise,itwouldcauseeverythingtocrash.Thattimepassedatthesamespeedeverywhereseemedequallyobvioustous....Childrengrowupanddiscoverthattheworldisnotasitseemedfromwithinthefourwallsoftheirhomes.Humankindasawholedoesthesame.Einsteinaskedhimselfaquestionthathasperhapspuzzledmanyofus

whenstudyingtheforceofgravity:howcanthesunandtheEarth

“attract”eachotherwithouttouchingandwithoututilizinganythingbetweenthem?Helookedforaplausibleexplanationandfoundonebyimaginingthat

thesunandtheEarthdonotattracteachotherdirectlybutthateachofthetwograduallyactsonthatwhichisbetweenthem.Andsincewhatliesbetweenthemisonlyspaceandtime,heimaginedthatthesunandtheEartheachmodifiedthespaceandtimethatsurroundedthem,justasabodyimmersedinwaterdisplacesthewateraroundit.Thismodificationofthestructureoftimeinfluencesinturnthemovementofbodies,causingthemto“fall”towardeachother.4

Whatdoesitmean,this“modificationofthestructureoftime”?Itmeanspreciselytheslowingdownoftimedescribedabove:amassslowsdowntimearounditself.TheEarthisalargemassandslowsdowntimeinitsvicinity.Itdoessomoreintheplainsandlessinthemountains,becausetheplainsareclosertoit.Thisiswhythefriendwhostaysatsealevelagesmoreslowly.Ifthingsfall,itisduetothisslowingdownoftime.Wheretimepasses

uniformly,ininterplanetaryspace,thingsdonotfall.Theyfloat,withoutfalling.Hereonthesurfaceofourplanet,ontheotherhand,themovementofthingsinclinesnaturallytowardwheretimepassesmoreslowly,aswhenwerundownthebeachintotheseaandtheresistanceofthewateronourlegsmakesusfallheadfirstintothewaves.Thingsfalldownwardbecause,downthere,timeisslowedbytheEarth.5

Hence,eventhoughwecannoteasilyobserveit,theslowingdownoftimeneverthelesshascrucialeffects:thingsfallbecauseofit,anditallowsustokeepourfeetfirmlyontheground.Ifourfeetadheretothepavement,itisbecauseourwholebodyinclinesnaturallytowheretimerunsmoreslowly—andtimepassesmoreslowlyforyourfeetthanitdoesforyourhead.Doesthisseemstrange?Itislikewhen,watchingthesungoingdown

gloriouslyatsunset,disappearingslowlybehinddistantclouds,wesuddenlyrememberthatit’snotthesunthat’smovingbuttheEarththat’sspinning,andweseewiththeunhingedeyeofthemindourentireplanet—andourselveswithit—rotatingbackward,awayfromthesun.Weareseeingwith“mad”eyes,likethoseofPaulMcCartney’sFoolontheHill:thecrazedvisionthatsometimesseesfurtherthanourbleary,customaryeyesight.

TENTHOUSANDDANCINGSHIVAS

IhaveanenduringpassionforAnaximander,theGreekphilosopherwholivedtwenty-sixcenturiesagoandunderstoodthattheEarthfloatsinspace,supportedbynothing.6WeknowofAnaximander’sthoughtfromotherwriters.Onlyonesmalloriginalfragmentofhiswritingshassurvived—justone:

Thingsaretransformedoneintoanotheraccordingtonecessity,andrenderjusticetooneanotheraccordingtotheorderoftime.

“Accordingtotheorderoftime”(κατὰτὴντοῦχρόνουτάξιν).Fromoneofthecrucial,initialmomentsofnaturalsciencethereremainsnothingbuttheseobscure,arcanelyresonantwords,thisappealtothe“orderoftime.”Astronomyandphysicshavesincedevelopedbyfollowingthisseminal

leadgivenbyAnaximander:byunderstandinghowphenomenaoccuraccordingtotheorderoftime.Inantiquity,astronomydescribedthemovementsofstarsintime.Theequationsofphysicsdescribehowthingschangeintime.FromtheequationsofNewton,whichestablishthefoundationsofmechanics,tothoseofMaxwellforelectromagneticphenomena;fromSchrödinger’sequationdescribinghowquantumphenomenaevolve,tothoseofquantumfieldtheoryforthedynamicsofsubatomicparticles:thewholeofourphysics,andscienceingeneral,isabouthowthingsdevelop“accordingtotheorderoftime.”Ithaslongbeentheconventiontoindicatethistimeinequationswith

thelettert(thewordfor“time”beginswithtinItalian,French,andSpanish,butnotinGerman,Arabic,Russian,orMandarin).Whatdoesthiststandfor?Itstandsforthenumbermeasuredbyaclock.Theequationstellushowthingschangeasthetimemeasuredbyaclockpasses.Butifdifferentclocksmarkdifferenttimes,aswehaveseenabove,

whatdoestindicate?Whenthetwofriendsmeetupagainafteronehaslivedinthemountainsandtheotheratsealevel,thewatchesontheirwristswillshowdifferenttimes.Whichofthetwoist?Inaphysicslaboratory,aclockonatableandanotheronthegroundrunatdifferentspeeds.Whichofthetwotellsthetime?Howdowedescribethe

differencebetweenthem?Shouldwesaythattheclockonthegroundhasslowedrelativetotherealtimerecordedonthetable?Orthattheclockonthetablerunsfasterthantherealtimemeasuredontheground?Thequestionismeaningless.Wemightjustaswellaskwhatismost

real—thevalueofsterlingindollarsorthevalueofdollarsinsterling.Thereisno“truer”value;theyaretwocurrenciesthathavevaluerelativetoeachother.Thereisno“truer”time;therearetwotimesandtheychangerelativetoeachother.Neitheristruerthantheother.Buttherearenotjusttwotimes.Timesarelegion:adifferentonefor

everypointinspace.Thereisnotonesingletime;thereisavastmultitudeofthem.Thetimeindicatedbyaparticularclockmeasuringaparticular

phenomenoniscalled“propertime”inphysics.Everyclockhasitspropertime.Everyphenomenonthatoccurshasitspropertime,itsownrhythm.Einsteinhasgivenustheequationsthatdescribehowpropertimes

developrelativetoeachother.Hehasshownushowtocalculatethedifferencebetweentwotimes.7

Thesinglequantity“time”meltsintoaspiderweboftimes.Wedonotdescribehowtheworldevolvesintime:wedescribehowthingsevolveinlocaltime,andhowlocaltimesevolverelativetoeachother.Theworldisnotlikeaplatoonadvancingatthepaceofasinglecommander.It’sanetworkofeventsaffectingeachother.ThisishowtimeisdepictedinEinstein’sgeneraltheoryofrelativity.

Hisequationsdonothaveasingle“time”;theyhaveinnumerabletimes.Betweentwoevents,justasbetweenthetwoclocksthatareseparatedandthenbroughttogetheragain,thedurationisnotasingleone.8

Physicsdoesnotdescribehowthingsevolve“intime”buthowthingsevolveintheirowntimes,andhow“times”evolverelativetoeachother.*Timehaslostitsfirstaspectorlayer:itsunity.Ithasadifferent

rhythmineverydifferentplaceandpassesheredifferentlyfromthere.Thethingsofthisworldinterweavedancesmadetodifferentrhythms.IftheworldisupheldbythedancingShiva,theremustbetenthousandsuchdancingShivas,likethedancingfigurespaintedbyMatisse....

2 LOSSOFDIRECTION

IfmoregentlythanOrpheuswhomovedeventhetreesyouweretopluckthezitherthelife-bloodwouldnotreturntothevainshadow...Harshfate,butitsburdenbecomeslightertobear,sinceeverythingthatattemptstoturnbackisimpossible.(I,24)

WHEREDOESTHEETERNALCURRENTCOMEFROM?

Clocksmaywellrunatdifferentspeedsinthemountainsandintheplains,butisthisreallywhatconcernsus,ultimately,abouttime?Inariver,thewaterflowsmoreslowlynearitsbanks,fasterinthemiddle—butitisstillflowing....Istimenotalsosomethingthatalwaysflows—fromthepasttothefuture?Let’sleaveasidetheprecisemeasurementofhowmuchtimepassesthatwewrestledwithintheprecedingchapter:thenumbersbywhichtimeismeasured.There’sanother,moreessentialaspecttotime:itspassage,itsflow,theeternalcurrentofthefirstofRilke’sDuinoElegies:

TheeternalcurrentDrawsalltheagesalongwithit

Throughbothrealms,Overwhelmingtheminboth.9

Pastandfuturearedifferentfromeachother.Causeprecedeseffect.Paincomesafterawound,notbeforeit.Theglassshattersintoathousandpieces,andthepiecesdonotre-formintoaglass.Wecannotchangethe

past;wecanhaveregrets,remorse,memories.Thefutureinsteadisuncertainty,desire,anxiety,openspace,destiny,perhaps.Wecanlivetowardit,shapeit,becauseitdoesnotyetexist.Everythingisstillpossible....Timeisnotalinewithtwoequaldirections:itisanarrowwithdifferentextremities.

Anditisthis,ratherthanthespeedofitspassing,thatmattersmosttousabouttime.Thisisthefundamentalthingabouttime.Thesecretoftimeliesinthisslippagethatwefeelonourpulse,viscerally,intheenigmaofmemory,inanxietyaboutthefuture.Thisiswhatitmeanstothinkabouttime.Whatexactlyisthisflowing?Whereisitnestledinthegrammaroftheworld?Whatdistinguishesthepast,itshavingbeen,fromthefuture,itsnothavingbeenyet,inthefoldsofthemechanismoftheworld?Why,tous,isthepastsodifferentfromthefuture?Nineteenth-andtwentieth-centuryphysicsengagedwiththese

questionsandranintosomethingunexpectedanddisconcerting—muchmoresothantherelativelymarginalfactthattimepassesatdifferentspeedsindifferentplaces.Thedifferencebetweenpastandfuture,betweencauseandeffect,betweenmemoryandhope,betweenregretandintention...intheelementarylawsthatdescribethemechanismsoftheworld,thereisnosuchdifference.

HEAT

Itallbeganwitharegicide.OnJanuary16,1793,theNationalConventioninParissentencedLouisXVItodeath.Rebellionisperhapsamongthedeepestrootsofscience:therefusaltoacceptthepresentorderofthings.10AmongthosewhotookthefataldecisionwasafriendofRobespierrecalledLazareCarnot.CarnothadapassionforthegreatPersianpoetSaadiShirazi.CapturedandenslavedatAcrebythe

Crusaders,ShiraziistheauthorofthoseluminousversesthatnowstandattheentranceoftheheadquartersoftheUnitedNations:

AllofthesonsofAdamarepartofonesinglebody,Theyareofthesameessence.Whentimeafflictsuswithpain

InonepartofthatbodyAlltheotherpartsfeelittoo.

IfyoufailtofeelthepainofothersYoudonotdeservethenameofman.

Perhapspoetryisanotherofscience’sdeepestroots:thecapacitytoseebeyondthevisible.CarnotnameshisfirstsonafterSaadi.SadiCarnotisthusbornoutofpoetryandrebellion.Asayoungman,hedevelopsapassionforthosesteamenginesthatat

thestartofthenineteenthcenturyarebeginningtotransformtheworldbyusingfiretomakethingsturn.In1824,hewritesapamphletwiththealluringtitle“ReflectionsontheMotivePowerofFire,”inwhichheseekstounderstandthetheoreticalbasisofthefunctioningofthesemachines.Thelittletreatiseispackedwithmistakenassumptions:heimaginesthatheatisaconcreteentity—akindoffluidthatproducesenergyby“falling”fromhotthingstocold,justasthewaterinawaterfallproducesenergybyfallingfromabovetobelow.Butitcontainsakeyidea:thatsteamenginesfunction,inthefinalanalysis,becausetheheatpassesfromhottocold.Sadi’spamphletfindsitswayintothehandsof

afierce-eyed,austerePrussianprofessorcalledRudolfClausius.Itishewhograspsthefundamentalissueatstake,formulatingalawthatwasdestinedtobecomefamous:ifnothingelsearounditchanges,heatcannotpassfromacoldbodytoahotone.Thecrucialpointhereisthedifferencefrom

whathappenswithfallingbodies:aballmayfall,butitcanalsocomebackup,byrebounding,forinstance.Heatcannot.Thisistheonlybasiclawofphysicsthatdistinguishesthepastfrom

thefuture.

Noneoftheothersdoso.NotNewton’slawsgoverningthemechanicsoftheworld;nottheequationsforelectricityandmagnetismformulatedbyMaxwell.NotEinstein’sonrelativisticgravity,northoseofquantummechanicsdevisedbyHeisenberg,Schrödinger,andDirac.Notthoseforelementaryparticlesformulatedbytwentieth-centuryphysicists....Notoneoftheseequationsdistinguishesthepastfromthefuture.11Ifasequenceofeventsisallowedbytheseequations,soisthesamesequencerunbackwardintime.12Intheelementaryequationsoftheworld,13thearrowoftimeappearsonlywherethereisheat.*Thelinkbetweentimeandheatisthereforefundamental:everytimeadifferenceismanifestedbetweenthepastandthefuture,heatisinvolved.Ineverysequenceofeventsthatbecomesabsurdifprojectedbackward,thereissomethingthatisheatingup.IfIwatchafilmthatshowsaballrolling,Icannottellifthefilmis

beingprojectedcorrectlyorinreverse.Butiftheballstops,Iknowthatitisbeingrunproperly;runbackward,itwouldshowanimplausibleevent:aballstartingtomovebyitself.Theball’sslowingdownandcomingtorestareduetofriction,andfrictionproducesheat.Onlywherethereisheatisthereadistinctionbetweenpastandfuture.Thoughts,forinstance,unfoldfromthepasttothefuture,notviceversa—and,infact,thinkingproducesheatinourheads....Clausiusintroducesaquantitythatmeasuresthisirreversibleprogress

ofheatinonlyonedirectionand,sincehewasacultivatedGerman,hegivesitanametakenfromancientGreek—entropy:

Iprefertotakethenamesofimportantscientificquantitiesfromancientlanguages,sothattheymaybethesameinallthelivinglanguages.Ithereforeproposetocallentropythequantity(S)ofabody,fromtheGreekwordfortransformation:ἡτροπὴ.14

ThepageofthearticlebyClausiusinwhichheintroducesforthefirsttimetheconceptandtheword“entropy.”Theequationprovidesthemathematicaldefinitionofthevariationofentropy(S—S0)ofabody:thesum(integral)of

thequantityofheatdQleavingthebodyatthetemperatureT.

Clausius’sentropy,indicatedbytheletterS,isameasurableandcalculablequantity15thatincreasesorremainsthesamebutneverdecreases,inanisolatedprocess.Inordertoindicatethatitneverdecreases,wewrite:

ΔS≥0

Thisreads:“DeltaSisalwaysgreaterthanorequaltozero,”andwecallthis“thesecondprincipleofthermodynamics”(thefirstbeingtheconservationofenergy).Itsnubisthefactthatheatpassesonlyfromhotbodiestocold,nevertheotherwayaround.

Forgivemefortheequation—it’stheonlyoneinthebook.Itistheequationfortime’sarrow,andIcouldhardlyrefrainfromincludingitinmybookabouttime.Itistheonlyequationoffundamentalphysicsthatknowsany

differencebetweenpastandfuture.Theonlyonethatspeaksoftheflowingoftime.Behindthisunusualequation,anentireworldlieshidden.RevealingitwillfalltoanunfortunateandengagingAustrian,the

grandsonofawatchmaker,atragicandromanticfigure,LudwigBoltzmann.

BLUR

ItisBoltzmannwhobeginstoseewhatliesbehindtheequationΔS≥0,throwingusintooneofourmostdizzyingdivestowardunderstandingtheintimategrammarofourworld.

BoltzmannworksinGraz,Heidelberg,Berlin,Vienna,andtheninGrazagain.HelikedtoattributehisrestlessnesstothefactthathewasbornduringMardiGras.Hewasonlypartlyjoking,sincetheinstabilityofhischaracterwasrealenough,oscillatingasitdidbetweenelationanddepression.Hewasshortandstout,withdark,curlyhairandthebeardofaTaliban;hisgirlfriendcalledhim“mydearsweetchubbyone.”Itwashe,thisLudwig,whowasthelucklessherooftime’sdirectionality.SadiCarnotthoughtthatheat

wasasubstance,afluid.Hewaswrong.Heatisthemicroscopicagitationofmolecules.Hotteais

teainwhichthemoleculesareveryagitated.Coldteaisteainwhichthe

moleculesareonlyalittleagitated.Inanicecube,warmingupandmeltingmoleculesbecomeincreasinglyagitatedandlosetheirstrictconnections.Attheendofthenineteenthcentury,thereweremanywhostilldidnot

believeintheexistenceofmoleculesandatoms:Ludwigwasconvincedoftheirrealityandenteredthefrayonbehalfofhisbelief.Hisdiatribesagainstthosewhodoubtedtherealityofatomsbecamelegendary.“Ourgenerationwereatheartallonhisside,”remarkedoneoftheyounglionsofquantummechanicsyearslater.16Inoneofthesefierypolemics,ataconferenceinVienna,anotedscientist17maintainedagainsthimthatscientificmaterialismwasdeadbecausethelawsofmatterarenotsubjecttothedirectionalityoftime.Scientistsarenotimmunefromtalkingnonsense.Lookingatthesungoingdown,theeyesofCopernicushadseenthe

worldturning.Lookingataglassofstillwater,theeyesofBoltzmannsawatomsandmoleculesfrenziedlymoving.WeseethewaterinaglassliketheastronautssawtheEarthfromthe

moon:calm,gleaming,blue.Fromthemoon,theycouldseenothingoftheexuberantagitationoflifeonEarth,itsplantsandanimals,desiresanddespairs.Onlyaveinedblueball.Withinthereflectionsinaglassofwater,thereisananalogoustumultuouslife,madeupoftheactivitiesofmyriadsofmolecules—manymorethantherearelivingbeingsonEarth.Thistumultstirsupeverything.Ifonesectionofthemoleculesisstill,

itbecomesstirredupbythefrenzyofneighboringonesthatsettheminmotion,too:theagitationspreads,themoleculesbumpintoandshoveeachother.Inthisway,coldthingsareheatedincontactwithhotones:theirmoleculesbecomejostledbyhotonesandpushedintoferment.Thatis,theyheatup.Thermalagitationislikeacontinualshufflingofapackofcards:ifthe

cardsareinorder,theshufflingdisordersthem.Inthisway,heatpassesfromhottocold,andnotviceversa:byshuffling,bythenaturaldisorderingofeverything.Thegrowthofentropyisnothingotherthantheubiquitousandfamiliarnaturalincreaseofdisorder.ThisiswhatBoltzmannunderstood.Thedifferencebetweenpastand

futuredoesnotlieintheelementarylawsofmotion;itdoesnotresideinthedeepgrammarofnature.Itisthenaturaldisorderingthatleadstograduallylessparticular,lessspecialsituations.

Itwasabrilliantintuition,andacorrectone.Butdoesitclarifythedifferencebetweenpastandfuture?Itdoesnot.Itjustshiftsthequestion.Thequestionnowbecomes:why,inoneofthetwodirectionsoftime—theonewecallpast—werethingsmoreordered?Whywasthegreatpackofcardsoftheuniverseinorderinthepast?Why,inthepast,wasentropylower?Ifweobserveaphenomenonthatbeginsinastateoflowerentropy,it

isclearwhyentropyincreases—becauseintheprocessofreshuffling,everythingbecomesdisordered.Butwhydothephenomenathatweobservearoundusinthecosmosbegininastateoflowerentropyinthefirstplace?Herewegettothekeypoint.Ifthefirsttwenty-sixcardsinapackare

allredandthenexttwenty-sixareallblack,wesaythattheconfigurationofthecardsis“particular,”thatitis“ordered.”Thisorderislostwhenthepackisshuffled.Theinitialorderedconfigurationisaconfiguration“oflowentropy.”Butnoticethatitisparticularifwelookatthecolorofthecards—redorblack.ItisparticularbecauseIamlookingatthecolor.Anotherconfigurationwillbeparticularifthefirsttwenty-sixcardsconsistofonlyheartsandspades.Oriftheyarealloddnumbers,orthetwenty-sixmostcreasedcardsinthepack,orexactlythesametwenty-sixofthreedaysago....Oriftheyshareanyothercharacteristic.Ifwethinkaboutitcarefully,everyconfigurationisparticular,everyconfigurationissingular,ifwelookatallofitsdetails,sinceeveryconfigurationalwayshassomethingaboutitthatcharacterizesitinauniqueway.Justas,toitsmother,everychildisparticularandunique.Itfollowsthatthenotionofcertainconfigurationsbeingmore

particularthanothers(twenty-sixredcardsfollowedbytwenty-sixblack,forexample)makessenseonlyifIlimitmyselftonoticingonlycertainaspectsofthecards(inthiscase,thecolors).IfIdistinguishbetweenallthecards,theconfigurationsareallequivalent:noneofthemismoreorlessparticularthanothers.18Thenotionof“particularity”isbornonlyatthemomentwebegintoseetheuniverseinablurredandapproximateway.Boltzmannhasshownthatentropyexistsbecausewedescribethe

worldinablurredfashion.Hehasdemonstratedthatentropyispreciselythequantitythatcountshowmanyarethedifferentconfigurationsthatourblurredvisiondoesnotdistinguishbetween.Heat,entropy,andthe

lowerentropyofthepastarenotionsthatbelongtoanapproximate,statisticaldescriptionofnature.Thedifferencebetweenpastandfutureisdeeplylinkedtothis

blurring....SoifIcouldtakeintoaccountallthedetailsoftheexact,microscopicstateoftheworld,wouldthecharacteristicaspectsoftheflowingoftimedisappear?Yes.IfIobservethemicroscopicstateofthings,thenthedifference

betweenpastandfuturevanishes.Thefutureoftheworld,forinstance,isdeterminedbyitspresentstate—thoughneithermorenorlessthanisthepast.19Weoftensaythatcausesprecedeeffectsandyet,intheelementarygrammarofthings,thereisnodistinctionbetween“cause”and“effect.”*Thereareregularities,representedbywhatwecallphysicallaws,thatlinkeventsofdifferenttimes,buttheyaresymmetricbetweenfutureandpast.Inamicroscopicdescription,therecanbenosenseinwhichthepastisdifferentfromthefuture.*ThisisthedisconcertingconclusionthatemergesfromBoltzmann’s

work:thedifferencebetweenthepastandthefuturerefersonlytoourownblurredvisionoftheworld.It’saconclusionthatleavesusflabbergasted:isitreallypossiblethataperceptionsovivid,basic,existential—myperceptionofthepassageoftime—dependsonthefactthatIcannotapprehendtheworldinallofitsminutedetail?Onakindofdistortionthat’sproducedbymyopia?Isittruethat,ifIcouldseeexactlyandtakeintoconsiderationtheactualdanceofmillionsofmolecules,thenthefuturewouldbe“justlike”thepast?IsitpossiblethatIhaveasmuchknowledgeofthepast—orignoranceofit—asIdoofthefuture?Evenallowingforthefactthatourperceptionsoftheworldarefrequentlywrong,cantheworldreallybesoprofoundlydifferentfromourperceptionofitasthis?Allthisunderminestheverybasisofourusualwayofunderstanding

time.Itprovokesincredulity,justasmuchasthediscoveryofthemovementoftheEarthdid.ButjustaswiththemovementoftheEarth,theevidenceisoverwhelming:allthephenomenathatcharacterizetheflowingoftimearereducedtoa“particular”stateintheworld’spast,the“particularity”ofwhichmaybeattributedtotheblurringofourperspective.Lateron,Iwilldelveintothemysteryofthisblurring,toseehowitis

tiedtothestrangeinitialimprobabilityoftheuniverse.Fornow,Iwill

endwiththemind-bogglingfactthatentropy,asBoltzmannfullyunderstood,isnothingotherthanthenumberofmicroscopicstatesthatourblurredvisionoftheworldfailstodistinguish.Theequationthatstates

preciselythis20iscarvedonBoltzmann’stombinVienna,aboveamarblebustthatportrayshimasanaustereandsurlyfigure,suchasIdon’tbelieveheeverwasinlife.Manyyoungstudentsofphysicsgotovisithistomb,andlingertheretoponder.Andsometimestheoddelderlyprofessorofphysicsaswell.Timehaslostanotherofits

crucialcomponents:theintrinsicdifferencebetweenpastandfuture.Boltzmannunderstoodthatthereisnothingintrinsicabouttheflowingoftime.Thatitisonlytheblurredreflectionofamysteriousimprobabilityoftheuniverseatapointinthepast.ThesourceofRilke’s“eternal

current”isnothingotherthanthis.Appointedauniversityprofessoratjusttwenty-fiveyearsold;received

atcourtbytheemperorattheapexofhissuccess;severelycriticizedbythemajorityoftheacademicworld,whichdidnotunderstandhisideas;alwaysprecariouslybalancedbetweenenthusiasmanddepression:the“dearsweetchubbyone,”LudwigBoltzmann,willendhislifebyhanginghimself.HedoessoatDuino,nearTrieste,whilehiswifeanddaughterare

swimmingintheAdriatic.ThesameDuinowhere,justafewyearslater,Rilkewillwritehis

Elegy.

3 THEENDOFTHEPRESENT

ItopenstothisgentlebreezeofSpringthesealed-incoldofthestillseason,andtheboatsreturntothesea...Nowwemustbraidcrownswithwhichtoadornourheads.(I,4)

SPEEDALSOSLOWSDOWNTIME

Tenyearsbeforeunderstandingthattimeissloweddownbymass,21

Einsteinhadrealizedthatitwassloweddownbyspeed.22Theconsequenceofthisdiscoveryforourbasicintuitiveperceptionoftimeisthemostdevastatingofall.Thefactitselfisquitesimple.Insteadofsendingthetwofriendsfrom

thefirstchaptertothemountainsandtheplains,respectively,let’saskoneofthemtostaystillandtheotheronetowalkaround.Timepassesmoreslowlyfortheonewhokeepsmoving.Asbefore,thetwofriendsexperiencedifferentdurations:theonewho

movesageslessquickly,hiswatchmarkslesstimepassing;hehaslesstimeinwhichtothink;theplantheiscarryingtakeslongertogerminate,andsoon.Foreverythingthatmoves,timepassesmoreslowly.

Forthiseffecttobecomeperceptible,onemustmoveveryquickly.Itwasfirstmeasuredinthe1970s,usingprecisionwatchesonairplanes.23

Thewatchonboardaplanedisplaysatimebehindthatdisplayedbytheoneontheground.Today,theslowingdownoftimecanbeobservedinmanyphysicsexperiments.Inthiscase,too,Einsteinhadunderstoodthattimeslowsdownbefore

thephenomenonwasactuallymeasured—whenhewasjusttwenty-fiveyearsoldandstudyingelectromagnetism.Itturnedouttobeanotparticularlycomplexdeduction.Electricity

andmagnetismarewelldescribedbyMaxwell’sequations.Thesecontaintheusualtimevariabletbuthaveacuriousproperty:ifyoutravelatacertainvelocity,thenforyoutheequationsofMaxwellarenolongertrue(thatis,theydon’tdescribewhatyoumeasure)unlessyoucall“time”adifferentvariable:t´.24MathematicianshadbecomeawareofthiscuriousfeatureofMaxwell’sequations,25butnoonehadbeenabletounderstandwhatitmeant.Einsteingraspeditssignificance:tisthetimethatpassesifIstaystill,therhythmatwhichthingsoccurthatarestationary,likemyself;t´is“yourtime”:therhythmatwhichthingshappenthatmovewithyou.Thus,tisthetimethatmywatchmeasureswhenitisstationary,andt´isthetimethatyourwatchmeasureswhenitismoving.Nobodyhadimaginedpreviouslythattimecouldbedifferentforastationarywatchandonethatwasbeingmoved.Einsteinhadreadthiswithintheequationsofelectromagnetism,bytakingthemseriously.26

Amovingobjectthereforeexperiencesashorterdurationthanastationaryone:awatchmarksfewerseconds,aplantgrowsmoreslowly,ayoungmandreamsless.Foramovingobject,timecontracts.*Notonlyistherenosingletimefordifferentplaces—thereisnotevenasingletimeforanyparticularplace.Adurationcanbeassociatedonlywiththemovementofsomething,withagiventrajectory.“Propertime”dependsnotonlyonwhereyouareandyourdegreeof

proximitytomasses;itdependsalsoonthespeedatwhichyoumove.It’sastrangeenoughfactinitself,butitsconsequencesare

extraordinary.Holdontight,becauseweareabouttotakeoff.

“NOW”MEANSNOTHING

Whatishappening“now”inadistantplace?Imagine,forexample,thatyoursisterhasgonetoProximab,therecentlydiscoveredplanetthatorbitsastaratapproximatelyfourlight-years’distancefromus.WhatisyoursisterdoingnowonProximab?Theonlycorrectansweristhatthequestionmakesnosense.Itislike

asking“Whatishere,inBeijing?”whenweareinVenice.ItmakesnosensebecauseifIusetheword“here”inVenice,IamreferringtoaplaceinVenice,notinBeijing.Ifyouaskwhatyoursister,whoisintheroomwithyou,isdoingnow,

theanswerisusuallyaneasyone:youlookatherandyoucantell.Ifshe’sfaraway,youphoneherandaskwhatshe’sdoing.Buttakecare:ifyoulookatyoursister,youarereceivinglightthattravelsfromhertoyoureyes.Thelighttakestimetoreachyou,let’ssayafewnanoseconds—atinyfractionofasecond—therefore,youarenotquiteseeingwhatsheisdoingnowbutwhatshewasdoingafewnanosecondsago.IfsheisinNewYorkandyouphoneherfromLiverpool,hervoicetakesafewmillisecondstoreachyou,sothemostyoucanclaimtoknowiswhatyoursisterwasuptoafewmillisecondsago.Notasignificantdifference,perhaps.IfyoursisterisonProximab,however,lighttakesfouryearstoreach

youfromthere.Hence,ifyoulookatherthroughatelescope,orreceivearadiocommunicationfromher,youknowwhatshewasdoingfouryearsagoratherthanwhatsheisdoingnow.“Now”onProximabisdefinitely

notwhatyouseethroughthetelescope,orwhatyoucanhearfromhervoiceovertheradio.Soperhapsyoucansaythatwhatyoursisterisdoingnowiswhatshe

willbedoingfouryearsafterthemomentthatyouseeherthroughthetelescope?Butno,thisdoesnotwork:fouryearsafteryouhaveseenherthroughthetelescope,inhertime,shemightalreadyhavereturnedtoEarthandcouldbe(yes!thisisreallypossible!)tenterrestrialyearsinthefuture.But“now”cannotbeinthefuture...Perhapswecandothis:if,tenyearsago,yoursisterhadleftfor

Proximab,takingwithheracalendartokeeptrackofthepassageoftime,canwethinkthatnowforheriswhenshehasrecordedthattenyearshavepassed?No,thisdoesnotworkeither:shemighthavereturnedheretenofheryearsafterleaving,arrivingbackwhere,inthemeantime,twentyyearshaveelapsed.Sowhenthehellis“now”onProximab?Thetruthofthematteristhatweneedtogiveupaskingthe

question.27

ThereisnospecialmomentonProximabthatcorrespondstowhatconstitutesthepresenthereandnow.Dearreader,pauseforamomenttoletthisconclusionsinkin.Inmy

opinion,itisthemostastoundingconclusionarrivedatinthewholeofcontemporaryphysics.Itsimplymakesnosensetoaskwhichmomentinthelifeofyoursister

onProximabcorrespondstonow.Itislikeaskingwhichfootballteamhaswonabasketballchampionship,howmuchmoneyaswallowhasearned,orhowmuchamusicalnoteweighs.Theyarenonsensicalquestionsbecausefootballteamsplayfootball,notbasketball;swallowsdonotbusythemselvesearningmoney;soundscannotbeweighed.“Basketballchampions”referstoateamofbasketballplayers,nottofootballers.Monetaryprofitreferstohumansociety,nottoswallows.Thenotionof“thepresent”referstothingsthatareclosetous,nottoanythingthatisfaraway.Our“present”doesnotextendthroughouttheuniverse.Itislikea

bubblearoundus.Howfardoesthisbubbleextend?Itdependsontheprecisionwith

whichwedeterminetime.Ifbynanoseconds,thepresentisdefinedonlyoverafewmeters;ifbymilliseconds,itisdefinedoverthousandsofkilometers.Ashumans,wedistinguishtenthsofasecondonlywithgreat

difficulty;wecaneasilyconsiderourentireplanettobelikeasinglebubblewherewecanspeakofthepresentasifitwereaninstantsharedbyusall.Thisisasfaraswecango.Thereisourpast:alltheeventsthathappenedbeforewhatwecan

witnessnow.Thereisourfuture:theeventsthatwillhappenafterthemomentfromwhichwecanseethehereandnow.Betweenthispastandthisfuturethereisanintervalthatisneitherpastnorfutureandstillhasaduration:fifteenminutesonMars;eightyearsonProximab;millionsofyearsintheAndromedagalaxy.Itistheexpandedpresent.28ItisperhapsthegreatestandstrangestofEinstein’sdiscoveries.Theideathatawell-definednowexiststhroughouttheuniverseisan

illusion,anillegitimateextrapolationofourownexperience.29

Itislikethepointwheretherainbowtouchestheforest.Wethinkthatwecanseeit—butifwegotolookforit,itisn’tthere.IfIweretoask,“Arethesetwostonesatthesameheight?”in

interplanetaryspace,thecorrectanswerwouldbe:“It’saquestionthatdoesn’tmakesense,becausethereisn’tasinglenotionof‘sameheight’throughouttheuniverse.”IfIaskwhethertwoevents—oneonEarthandtheotheronProximab—arehappening“atthesamemoment,”thecorrectanswerwouldbe:“It’saquestionthatdoesn’tmakesense,becausethereisnosuchthingas‘thesamemoment’definableintheuniverse.”The“presentoftheuniverse”ismeaningless.

TEMPORALSTRUCTUREWITHOUTTHEPRESENT

GorgoisthewomanwhosavedGreecebyrealizingthatawax-coveredtabletsenttherefromPersiacarriedasecretmessageconcealedbeneaththewax:amessagethatforewarnedtheGreeksofaPersianattack.GorgohadasoncalledPleistarchus,fatheredbythekingofSparta,theheroofThermopylae:Leonidas.LeonidaswasGorgo’suncle,thebrotherofherfather,Cleomenes.Whobelongstothe“samegeneration”asLeonidas?Gorgo,whoisthemotherofhisson—orCleomenes,whoisthesonofthesamefather?Hereisadiagramforthosewho,likeme,havedifficultieswithgenealogy:

Thereisananalogybetweengenerationsandthetemporalstructureoftheworldasrevealedbyrelativity.ItmakesnosensetoaskifitisCleomenesorGorgowhois“ofthesamegeneration”asLeonidas,becausethereisnosingleconcept30of“samegeneration.”IfwesaythatLeonidasandhisbrotherare“ofthesamegeneration”becausetheyhavethesamefather,andthatLeonidasandhiswifeare“ofthesamegeneration”becausetheyhaveasontogether,wemustthereforesaythatthis“samegeneration”includesGorgoandherownfather!Thefilialrelationshipestablishesanorderbetweenhumanbeings(Leonidas,Gorgo,andCleomenescomeafterAnaxandridasandbeforePleistarchus),butnotbetweenanyhumans:LeonidasandGorgoareneitherbeforenorafterinrespecttoeachother.Mathematicianshaveatermfortheorderestablishedbyfiliation:

“partialorder.”Apartialorderestablishesarelationofbeforeandafterbetweencertainelements,butnotbetweenanytwoofthem.Humanbeingsforma“partiallyordered”set(nota“completelyordered”set)throughfiliation.Filiationestablishesanorder(beforethedescendants,aftertheforebears),butnotbetweeneveryone.Toseehowthisorderworks,weneedonlythinkofafamilytree,likethisoneforGorgo:

Thereisacone-shaped“past”madeupofherforebears,anda“future”conecomprisingherdescendants.Thosewhoareneitherancestorsnordescendantsremainoutsideofthecones.Everyhumanbeinghastheirownpastconeofancestorsandfuture

coneofdescendants.ThoseofLeonidasareshownbelow,alongsideGorgo’s:

Thetemporalstructureoftheuniverseisverysimilartothisone.Itisalsomadeofcones.Therelationof“temporalprecedence”isapartialordermadeofcones.31Specialrelativityisthediscoverythatthetemporalstructureoftheuniverseisliketheoneestablishedbyfiliation:itdefinesanorderbetweentheeventsoftheuniversethatispartial,notcomplete.Theexpandedpresentisthesetofeventsthatareneitherpastnorfuture:itexists,justastherearehumanbeingswhoareneitherourdescendantsnorourforebears.Ifwewanttorepresentalltheeventsintheuniverseandtheir

temporalrelations,wecannolongerdosowithasingle,universaldistinctionbetweenpast,present,andfuture,likethis:Wemustdosoinsteadbyplacingaboveandbeloweveryeventthe

conesofitsfutureandpastevents:

(Physicistshavethehabitinsuchdiagrams,Idon’tknowwhy,ofplacingthefutureaboveandthepastbelow—theoppositeofhowitisdoneingenealogicaltrees.)Everyeventhasitspast,itsfuture,andapartoftheuniversethatis

neitherpastnorfuture,justaseverypersonhasforebears,descendants,andotherswhoareneitherforebearsnordescendants.

Lighttravelsalongtheobliquelinesthatdelimitthesecones.Thisiswhywecallthem“lightcones.”Itiscustomary,asinthepreviousdiagram,todrawtheselinesatanangleofforty-fivedegrees,butitwouldbemorerealistictomakethemmorehorizontal,likethis:

Thereasonforthisisthat,atthescaletowhichweareaccustomed,theexpandedpresentseparatingourpastfromourfutureisextremelybrief(amatterofnanoseconds)andalmostimperceptible,asaresultofwhichitis“squashed”intoathinhorizontalbandweusuallycall“thepresent,”withoutanyqualification.Inshort,acommonpresentdoesnotexist:thetemporalstructureof

spacetimeisnotastratificationoftimessuchasthis:

Itis,rather,astructuremadeupentirelyoflightcones:

ThisisthestructureofspacetimethatEinsteinunderstoodwhenhewastwenty-fiveyearsold.Tenyearslater,hecomestounderstandthatthespeedatwhichtime

flowschangesfromplacetoplace.Itfollowsthatspacetimedoesnotreallyhavetheorderoutlinedabovebutcanbedistorted.Itnowlooksrathermorelikethis:

Whenagravitationalwavepasses,forexample,thesmalllightconesoscillatetogetherfromrighttoleft,likeearsofwheatblownbythewind.Thestructureoftheconescanevenbesuchthat,advancingalways

towardthefuture,onecanreturntothesamepointinspacetime,likethis:

Inthisway,acontinuoustrajectorytowardthefuturereturnstotheoriginatingevent,towhereitbegan.*32ThefirsttorealizethiswasKurtGödel,thegreattwentieth-centurylogicianwhowasEinstein’slastfriend,accompanyinghimonwalksalongthestreetsofPrinceton.Neartoablackhole,thelinesconvergetowardit,likethis:33

Thisisbecausethemassoftheblackholeslowstimetosuchadegreethat,atitsborder(calledthe“horizon”),timestandsstill.Ifyoulookclosely,youwillseethatthesurfaceoftheblackholeisparalleltotheedgesofthecones.So,inordertoexitfromablackhole,youwouldneedtomove(likethetrajectorymarkedindarkgrayinthefollowingdiagram)towardthepresentratherthantowardthefuture!Thisisimpossible.Objectscanonlymovetowardthefuture,asinthe

trajectoriesoutlinedinthediagraminwhite.Thisiswhatconstitutesablackhole:aninclinationofthelightconestowardtheinterior,markingahorizon,closingoffaregionofspaceinthefuturefromeverythingthatsurroundsit.Itisnothingotherthanthis.Itisthecuriouslocalstructureofthepresentthatproducesblackholes.

Morethanahundredyearshavepassedsincewelearnedthatthe“presentoftheuniverse”doesnotexist.Andyetthiscontinuestoconfoundusandstillseemsdifficulttoconceptualize.Everysooftenaphysicistmutiniesandtriestoshowthatitisn’ttrue.34Philosopherscontinuetodiscussthedisappearanceofthepresent.Today,thereareoftenconferencesdevotedtothesubject.Ifthepresenthasnomeaning,thenwhat“exists”intheuniverse?Is

notwhat“exists”preciselywhatishere“inthepresent”?Thewholeideathattheuniverseexistsnowinacertainconfigurationandchangestogetherwiththepassageoftimesimplydoesn’tstackupanymore.

4 LOSSOFINDEPENDENCE

Andonthatwavewewillallhavetonavigate,allwhoarenourishedbythefruitsoftheEarth.(II,14)

WHATHAPPENSWHENNOTHINGHAPPENS?

ItonlytakesafewmicrogramsofLSDtoexpandourexperienceoftimeontoanepicandmagicalscale.35“Howlongisforever?”asksAlice.“Sometimes,justonesecond,”repliestheWhiteRabbit.Therearedreamslastinganinstantinwhicheverythingseemsfrozenforaneternity.36Timeiselasticinourpersonalexperienceofit.Hoursflybylikeminutes,andminutesareoppressivelyslow,asiftheywerecenturies.Ontheonehand,timeisstructuredbytheliturgicalcalendar:EasterfollowsLent,andLentfollowsChristmas;RamadanopenswithHilalandcloseswithEidal-Fitr.Ontheother,everymysticalexperience,suchasthesacredmomentinwhichthehostisconsecrated,throwsthefaithfuloutsideoftime,puttingthemintouchwitheternity.BeforeEinsteintoldusthatitwasn’ttrue,howthedevildidwegetitintoourheadsthattimepasseseverywhereatthesamespeed?Itwascertainlynotourdirectexperienceofthepassageoftimethatgaveustheideathattimeelapsesatthesamerate,alwaysandeverywhere.Sowheredidwegetitfrom?Forcenturies,wehavedividedtimeintodays.Theword“time”derives

fromanIndo-Europeanroot—diordai—meaning“todivide.”Forcenturies,wehavedividedthedaysintohours.37Butformostofthosecenturies,however,hourswerelongerinthesummerandshorterinthewinter,becausethetwelvehoursdividedthetimebetweendawnandsunset:thefirsthourwasdawn,andthetwelfthwassunset,regardlessof

theseason,aswereadintheparableofthewinegrowerintheGospelaccordingtoMatthew.38Since,aswesaynowadays,duringsummer“moretime”passesbetweendawnandsunsetthanduringthewinter,inthesummerthehourswerelonger,andthehourswereshorterinwintertime.Sundials,hourglasses,andwaterclocksalreadyexistedintheancient

world,intheMediterraneanregionandinChina—buttheydidnotplaythecruelrolethatclocksdotodayintheorganizationofourlives.ItisonlyinthefourteenthcenturyinEuropethatpeople’slivesstarttoberegulatedbymechanicalclocks.Citiesandvillagesbuildtheirchurches,erectbelltowersnexttothem,andplaceaclockonthebelltowertomarktherhythmofcollectiveactivities.Theeraofclock-regulatedtimebegins.

Gradually,timeslipsfromthehandsoftheangelsandintothoseofthemathematicians—asisgraphicallyillustratedbyStrasbourgCathedral,wheretwosundialsaresurmounted,respectively,byanangel(oneinspiredbyearliersundialsfrom1200)andbyamathematician(onthesundialputtherein1400).

Theusefulnessofclockssupposedlyresidesinthefactthattheytellthesametime.Andyetthisideaisalsomoremodernthanwemightimagine.Forcenturies,aslongastravelwasonhorseback,onfoot,orincarriages,therewasnoreasontosynchronizeclocksbetweenoneplaceandanother.Therewasgoodreasonfornotdoingso.Middayis,bydefinition,whenthesunisatitshighest.Everycityandvillagehadasundialthatregisteredthemomentthesunwasatitsmidpoint,allowingtheclockonthebelltowertoberegulatedwithit,foralltosee.ButthesundoesnotreachmiddayatthesamemomentinLecceasitdoesinVenice,orinFlorence,orinTurin,becausethesunmovesfromeasttowest.MiddayarrivesfirstinVenice,andsignificantlylaterinTurin,andforcenturiestheclocksinVenicewereagoodhalfhouraheadofthoseinTurin.Everysmallvillagehaditsownpeculiar“hour.”AtrainstationinPariskeptitsownhour,alittlebehindtherestofthecity,asakindofcourtesytowardtravelersrunninglate.39

Inthenineteenthcentury,thetelegrapharrives,trainsbecomecommonplaceandfast,andtheproblemarisesofproperlysynchronizingclocksbetweenonecityandanother.Itisawkwardtoorganizetraintimetablesifeachstationmarkstimedifferently.ItisintheUnitedStatesthatthefirstattemptismadetostandardizetime.Initially,itisproposedtofixauniversalhourfortheentireworld.Tocall,forinstance,“twelveo’clock”themomentatwhichitismiddayinLondon,sothatmiddaywouldfallat12nooninLondonandaround6p.m.inNewYork.Theproposalisnotwellreceived,becausepeopleareattachedtolocaltime.In1883,acompromiseisreachedwiththeideaofdividingtheworldintotimezones,therebystandardizingtimeonlywithineachzone.Inthisway,thediscrepancybetweentwelveontheclockandlocalmiddayislimitedtoamaximumofaboutthirtyminutes.Theproposalisgraduallyacceptedbytherestoftheworldandclocksbegintobesynchronizedbetweendifferentcities.40

Itcanhardlybepurecoincidencethat,beforegainingauniversityposition,theyoungEinsteinworkedintheSwisspatentoffice,dealingspecificallywithpatentsrelatingtothesynchronizationofclocksatrailwaystations.Itwasprobablytherethatitdawnedonhim:theproblemofsynchronizingclockswas,ultimately,aninsolubleone.Inotherwords,onlyafewyearspassedbetweenthemomentatwhich

weagreedtosynchronizeclocksandthemomentatwhichEinstein

realizedthatitwasimpossibletodosoexactly.Formillenniabeforeclocks,ouronlyregularwayofmeasuringtime

hadbeenthealternationofdayandnight.Therhythmofdayfollowedbynightalsoregulatesthelivesofplantsandanimals.Diurnalrhythmsareubiquitousinthenaturalworld.Theyareessentialtolife,anditseemstomeprobablethattheyplayedakeyroleintheveryoriginoflifeonEarth,sinceanoscillationisrequiredtosetamechanisminmotion.Livingorganismsarefullofclocksofvariouskinds—molecular,neuronal,chemical,hormonal—eachofthemmoreorlessintunewiththeothers.41

Therearechemicalmechanismsthatkeeptoatwenty-four-hourrhythmeveninthebiochemistryofsinglecells.Thediurnalrhythmisanelementarysourceofourideaoftime:night

followsday;dayfollowsnight.Wecountthebeatsofthisgreatclock:wecountthedays.Intheancientconsciousnessofhumanity,timeis,aboveall,thiscountingofdays.Aswellasthedays,wethencounttheyearsandtheseasons,thecycles

ofthemoon,theswingsofapendulum,thenumberoftimesthatanhourglassisturned.Thisisthewayinwhichwehavetraditionallyconceivedoftime:countingthewaysinwhichthingschange.Aristotleisthefirstweareawareoftohaveaskedhimselfthequestion

“Whatistime?,”andhecametothefollowingconclusion:timeisthemeasurementofchange.Thingschangecontinually.Wecall“time”themeasurement,thecountingofthischange.Aristotle’sideaissound:timeiswhatwerefertowhenweask“when?”

“Afterhowmuchtimewillyoureturn?”means“Whenwillyoureturn?”Theanswertothequestion“when?”referstosomethingthathappens.“I’llreturninthreedays’time”meansthatbetweendepartureandreturnthesunwillhavecompletedthreecircuitsinthesky.It’sassimpleasthat.Soifnothingchanges,ifnothingmoves,doestimethereforeceaseto

pass?Aristotlebelievedthatitdid.Ifnothingchanges,timedoesnotpass—

becausetimeisourwayofsituatingourselvesinrelationtothechangingofthings:theplacingofourselvesinrelationtothecountingofdays.Timeisthemeasureofchange:42ifnothingchanges,thereisnotime.ButwhatisthenthetimethatIhearcoursinginthesilence?“Ifitis

darkandourbodilyexperienceisnil,”AristotlewritesinhisPhysics,“butsomechangeishappeningwithinthemind,weimmediatelysupposethat

sometimehaspassedaswell.”43Inotherwords,eventhetimethatweperceiveflowingwithinusisthemeasureofamovement:amovementthatisinternal....Ifnothingmoves,thereisnotime,becausetimeisnothingbuttheregisteringofmovement.Newton,instead,assumestheexactopposite.Inhismagnumopus,the

Principia,hewrites:

IdonotdefineTime,Space,PlaceandMotion,asbeingwellknowntoall.OnlyImustobserve,thatthecommonpeopleconceivethosequantitiesundernoothernotionsbutfromtherelationtheybeartosensibleobjects.Andthencearisecertainprejudices,fortheremovingofwhich,itwillbeconvenienttodistinguishthemintoAbsoluteandRelative,TrueandApparent,MathematicalandCommon.44

Inotherwords,Newtonrecognizesthatakindof“time”existsthatmeasuresdaysandmovements:theonetreatedbyAristotle(relative,apparent,andcommon).Buthealsocontendsthat,inadditiontothis,anothertimemustexist:“true”timethatpassesregardless,independentlyofthingsandoftheirchanges.Ifallthingsremainedmotionlessandeventhemovementsofoursoulsweretobefrozen,thistimewouldcontinuetopass,accordingtoNewton,unaffectedandequaltoitself:“true”time.It’stheexactoppositeofwhatAristotlewrites.“True”time,saysNewton,isnotdirectlyaccessible—onlyindirectly,

throughcalculation.Itisnotthesameasthatgivenbydays,because“thenaturaldaysaretrulyunequal,thoughtheyarecommonlyconsider’dasequal,andusedforameasureoftime:Astronomerscorrectthisinequalitythattheymaymeasurethecelestialmotionsbyamoreaccuratetime.”45

So,whoisright:AristotleorNewton?Twoofthemostacuteandprofoundinvestigatorsofnaturethattheworldhaseverseenareproposingtwooppositewaysofthinkingabouttime.Twogiantsarepullingusinoppositedirections.46

Timeisonlyawayofmeasuringhowthingschange,asAristotlewouldhaveit—orshouldwebethinkingthatanabsolutetimeexiststhatflowsbyitself,independentlyofthings?Thequestionweshouldreallybeaskingisthis:whichofthesetwowaysofthinkingabouttimehelpsustounderstandtheworldbetter?Whichofthetwoconceptualschemesismoreefficient?

Aristotle:Timeisnothingotherthanthemeasurementofchange.

Forafewcenturies,reasonseemedtocomedownonthesideofNewton.Newton’smodel,basedontheideaofatimeindependentofthings,hasenabledtheconstructionofmodernphysics—aphysicsthatworksincrediblywell.Anditassumesthattimeexistsasanentitythatrunsinawaywhichisuniformandimperturbable.Newtonwritesequationscontainingthelettertfortimethatdescribehowthingsmoveintime.47Whatdoesthislettermean?Doestindicatetimeshapedbythelongerhoursofsummerandtheshorteronesofwinter?Obviouslynot.Itindicatestimethatis“absolute,true,andmathematical,”assumedbyNewtontorunindependentlyofthingsthatchangeorthingsthatmove.

Newton:Thereisatimethatpassesevenwhennothingchanges.

Clocks,forNewton,aredevicesthatseek,albeitinamannerthatisalwaysimprecise,tofollowthisequalanduniformflowingoftime.Newtonwritesthatthis“absolute,true,andmathematical”timeisnotperceptible.Itmustbededuced,throughcalculationandobservation,fromtheregularityofphenomena.Newton’stimeisnottheevidencegiventousbyoursenses:itisanelegantintellectualconstruction.If,mydearcultivatedreader,theexistenceofthisNewtonianconceptoftimewhichisindependentofthingsseemstoyousimpleandnatural,it’sbecauseyouencountereditatschool.Becauseithasgraduallybecomethewayinwhichweallthinkabouttime.Ithasfilteredthroughschooltextbooksthroughouttheworldandendedupbecomingourcommonwayofunderstandingtime.Wehaveturneditintoourcommonsense.Buttheexistenceofatimethatisuniform,independentofthingsandoftheirmovementthattodayseemssonaturaltousisnotanancientintuitionthatisnaturaltohumanityitself.It’sanideaofNewton’s.Themajorityofphilosophershaveinfactrespondednegativelytothis

idea.Inastillcelebrated,furiouscounterblast,Leibnizdefendedthetraditionalthesisaccordingtowhichtimeisonlytheorderofevents,arguingthatthereisnosuchthingasanautonomoustime.Legendhasit

thatLeibniz,whosenameisstilloccasionallyspelledwitha“t”(Leibnitz),haddeliberatelydroppedtheletterfromhisnameinaccordancewithhisbeliefinthenonexistenceoftheabsoluteNewtoniantimet.48

BeforeNewton,timeforhumanitywasthewayofcountinghowthingschanged.Beforehim,noonehadthoughtitpossiblethatatimeindependentofthingscouldexist.Don’ttakeyourintuitionsandideastobe“natural”:theyareoftentheproductsoftheideasofaudaciousthinkerswhocamebeforeus.Butofthesetwogiants,AristotleandNewton,wasitreallyNewton

whowasright?Whatexactlyisthis“time”thatheintroduced,managingtoconvincetheentireworldthatitexists,onethatworkssobrilliantlywellinhisequationsandyetisnotthetimethatweperceive?Togetoutfrombetweenthesetwogiants,andinastrangewayto

reconcilethem,athirdwasneeded.Beforegettingtohim,however,abriefdigressiononspaceisinorder.

WHATISTHERE,WHERETHEREISNOTHING?

Thetwointerpretationsoftime(themeasureof“when”withregardtoevents,asAristotlewanted;theentitythatrunsevenwhennothinghappens,accordingtoNewton)canberepeatedforspace.Timeiswhatwespeakofwhenweask“when?”Spaceiswhatwespeakofwhenweask“where?”IfIask“WhereistheColiseum?”onepossibleansweris:“It’sinRome.”IfIask“Whereareyou?”apossibleanswermightbe:“Athome.”Toreplytothequestion“Whereissomething?”meanstoindicatesomethingelsethatisaroundthatthing.IfIsay“IntheSahara,”youwillvisualizemesurroundedbysanddunes.Aristotlewasthefirsttodiscussindepthandwithacuitythemeaning

of“space,”or“place,”andtoarriveataprecisedefinition:theplaceofathingiswhatsurroundsthatthing.49

Asinthecaseoftime,Newtonsuggeststhatweshouldthinkdifferently.ThespacedefinedbyAristotle,theenumerationofwhatsurroundseachthing,iscalled“relative,apparent,andcommon”byNewton.Hecalls“absolute,true,andmathematical”spaceinitself,whichexistsevenwherethereisnothing.

ThedifferencebetweenAristotleandNewtonisglaring.ForNewton,betweentwothingstheremayalsobe“emptyspace.”ForAristotle,itisabsurdtospeakof“empty”space,becausespaceisonlythespatialorderofthings.Iftherearenothings—theirextension,theircontacts—thereisnospace.Newtonimaginesthatthingsaresituatedina“space”thatcontinuestoexist,empty,evenwhendivestedofthings.ForAristotle,this“emptyspace”isnonsensical,becauseiftwothingsdonottouchitmeansthatthereissomethingelsebetweenthem,andifthereissomething,thenthissomethingisathing,andthereforeathingthatisthere.Itcannotbethatthereis“nothing.”Formypart,Ifinditcuriousthatboththesewaysofthinkingabout

spaceoriginatefromoureverydayexperience.Thedifferencebetweenthemexistsduetoaquirkyaccidentoftheworldinwhichwelive:thelightnessofair,thepresenceofwhichweonlybarelyperceive.Wecansay:Iseeatable,achair,apen,theceiling—andthatbetweenmyselfandthetablethereisnothing.Orwecansaythatbetweenoneandanotherofthesethingsthereisair.Sometimeswespeakofairasifitweresomething,sometimesasifitwerenothing.Sometimesasifitwerethere,sometimesasifitwerenotthere.Weareusedtosaying“Thisglassisempty”inordertosaythatitisfullofair.Wecanconsequentlythinkoftheworldaroundusas“almostempty,”withjustafewobjectshereandthere,oralternativelyas“completelyfull”ofair.Intheend,AristotleandNewtondonotengageinprofoundmetaphysics:theyareonlyusingthesetwodifferentintuitiveandingeniouswaysofseeingtheworldaroundus—takingornottakingairintoaccount—andtransformingthemintodefinitionsofspace.Aristotle,alwaystopoftheclass,wantstobeprecise:hedoesnotsay

thattheglassisempty;hesaysthatitisfullofair.Andheremarksthat,inourexperience,thereisneveraplacewhere“thereisnothing,notevenair.”Newton,lookingnotsomuchforaccuracyasforefficiencyoftheconceptualparadigmthatneedstobeconstructedinordertodescribethemovementofthings,thinksnotaboutairbutaboutobjects.Air,afterall,seemstohavelittleeffectonafallingstone.Wecanimaginethatitisnoteventhere.Asinthecaseoftime,Newton’s“containerspace”mayseemnaturalto

us,butitisarecentideathathasspreadduetotheenormousinfluenceof

histhought.Thatwhichseemsintuitivetousnowistheresultofscientificandphilosophicalelaborationsinthepast.TheNewtonianideaof“emptyspace”seemstobeconfirmedwhen

Torricellidemonstratesthatitispossibletoremovetheairfromabottle.Itsoonbecomesclear,however,thatinsidethebottlemanyphysicalentitiesremain:electricandmagneticfields,andaconstantswarmingofquantumparticles.Theexistenceofacompletevoid,withoutanyphysicalentityexceptamorphousspace,“absolute,true,andmathematical,”remainsabrillianttheoreticalideaintroducedbyNewtontofoundhisphysicson,forthereisnoscientific,experimentalevidencetosupportitsexistence.Aningenioushypothesis,perhapsthemostprofoundinsightachievedbyoneofthegreatestscientists—butisitonethatactuallycorrespondstotherealityofthings?DoesNewton’sspacereallyexist?Ifitexists,isitreallyamorphous?Canaplaceexistwherenothingexists?Thequestionisidenticaltotheanalogousoneregardingtime:does

Newton’s“absolute,true,andmathematical”timeexist,flowingwhennothinghappens?Ifitexists,isitsomethingaltogetherdifferentfromthethingsofthisworld?Isitsoveryindependentfromthem?Theanswertoallthesequestionsliesinanunexpectedsynthesisofthe

apparentlycontradictoryideasheldbythesetwogiants.Andtoaccomplishthis,itwasnecessaryforathirdgianttoenterthedance.*

THEDANCEOFTHETHREEGIANTS

ThesynthesisbetweenAristotle’stimeandNewton’sisthemostvaluableachievementmadebyEinstein.Itisthecrowningjewelofhisthought.TheansweristhatthetimeandspaceNewtonhadintuitedthe

existenceof,beyondtangiblematter,doeffectivelyexist.Theyarereal.Timeandspacearerealphenomena.Buttheyareinnowayabsolute;theyarenotatallindependentfromwhathappens;theyarenotasdifferentfromtheothersubstancesoftheworld,asNewtonhadimaginedthemtobe.WecanthinkofagreatNewtoniancanvasonwhichthestoryoftheworldisdrawn.Butthiscanvasismadeofthesamestuffthateverythingelseintheworldismadeof,thesamesubstancethatconstitutesstone,light,andair:itismadeoffields.Physicistscall“fields”thesubstancesthat,tothebestofour

knowledge,constitutetheweaveofthephysicalrealityoftheworld.

Sometimestheymaybegivenexoticnames:thefields“ofDirac”arethefabricofwhichtablesandstarsaremade.The“electromagnetic”fieldistheweaveofwhichlightismade,aswellastheoriginoftheforcesthatmakeelectricmotorsturnandtheneedleofacompasspointnorth.But—hereisthekeypoint—thereisalsoa“gravitational”field:itistheoriginoftheforceofgravity,butitisalsothetexturethatformsNewton’sspaceandtime,thefabriconwhichtherestoftheworldisdrawn.Clocksaremechanismsthatmeasureitsextension.Themetersusedformeasuringlengthareportionsofmatterthatmeasureanotheraspectofitsextension.Spacetimeisthegravitationalfield—andviceversa.Itissomething

thatexistsbyitself,asNewtonintuited,evenwithoutmatter.Butitisnotanentitythatisdifferentfromtheotherthingsintheworld—asNewtonbelieved—itisafieldliketheothers.Morethanadrawingonacanvas,theworldislikeasuperimpositionofcanvases,ofstrata,wherethegravitationalfieldisonlyoneamongothers.Justliketheothers,itisneitherabsolutenoruniform,norisitfixed:itflexes,stretches,andjostleswiththeothers,pushingandpullingagainstthem.Equationsdescribethereciprocalinfluencesthatallthefieldshaveoneachother,andspacetimeisoneofthesefields.*Thegravitationalfieldcanalsobesmoothandflat,likeastraight

surface,andthisistheversionthatNewtondescribed.Ifwemeasureitinmeters,wediscoverthattheEuclidiangeometrythatwelearnedatschoolapplies.Butthefieldcanalsoundulate,inwhatwecall“gravitationalwaves.”Itcancontractandexpand.Remembertheclocksinchapter1thatslowdowninthevicinityofa

mass?Theyslowdownbecausethereis,inaprecisesense,“less”gravitationalfieldthere.Thereislesstimethere.Thecanvasformedbythegravitationalfieldislikeavastelasticsheet

thatcanbepulledandstretched.Itsstretchingandbendingistheoriginoftheforceofgravity,ofthingsfalling,andprovidesabetterexplanationofthisthantheoldNewtoniantheoryofgravity.Lookagainatthefigureherewhichillustrateshowmoretimepasses

abovethanbelow,butimaginenowthatthepieceofpaperonwhichthediagramisdrawniselastic;imaginestretchingitsothatthetimeinthemountainsactuallybecomeselongated.Youwillobtainsomethingliketheimagebelow,whichrepresentsspace(theheight,ontheverticalaxis)

andtime(onthehorizontal)—but,now,the“longer”timeinthemountainseffectivelycorrespondstoagreaterlengthoftime.

Theimageaboveillustrateswhatphysicistscall“curved”spacetime.“Curved”becauseitisdistorted:distancesarestretchedandcontracted,justliketheelasticsheetwhenitispulled.Thisiswhythelightconeswereinclinedinthediagramsinchapter3.Timethusbecomespartofacomplicatedgeometrywoventogether

withthegeometryofspace.ThisisthesynthesisthatEinsteinfoundbetweenAristotle’sconceptionoftimeandNewton’s.Withatremendousbeatofhiswings,EinsteinunderstandsthatAristotleandNewtonarebothright.Newtonisrightinintuitingthatsomethingelseexistsinadditiontothesimplethingsthatweseemovingandchanging.TrueandmathematicalNewtoniantimeexists;itisarealentity;itisthegravitationalfield,theelasticsheet,thecurvedspacetimeinthediagram.ButNewtoniswronginassumingthatthistimeisindependentfromthings—andthatitpassesregularly,imperturbably,separately,fromeverythingelse.

Forhispart,Aristotleisrighttosaythat“when”and“where”arealwayslocatedinrelationtosomething.Butthissomethingcanalsobejustthefield,thespatiotemporalentityofEinstein.Becausethisisadynamicandconcreteentity,likeallthoseinreferencetowhich,asAristotlerightlyobserved,wearecapableoflocatingourselves.Allthisisperfectlycoherent,andEinstein’sequationsdescribingthe

distortionsofthegravitationalfieldanditseffectsonclocksandmetershavebeenrepeatedlyverifiedformorethanacentury.Butourideaoftimehaslostanotherofitsconstituentparts:itssupposedindependencefromtherestoftheworld.Thethree-handeddanceoftheseintellectualgiants—Aristotle,

Newton,andEinstein—hasguidedustoadeeperunderstandingoftimeandofspace.Thereisastructureofrealitythatisthegravitationalfield;itisnotseparatefromtherestofphysics,norisitthestageacrosswhichtheworldpasses.Itisadynamiccomponentofthegreatdanceoftheworld,similartoalltheothers,interactingwiththeothers,determiningtherhythmofthosethingsthatwecallmetersandclocksandtherhythmofallphysicalphenomena.Success,asever,isdestinedtobeshort-lived—evengreatsuccess.

Einsteinwritestheequationsofthegravitationalfieldin1915,andbarelyayearlateritisEinsteinhimselfwhoobservesthatthiscannotbethelastwordonthenatureoftimeandspace,becauseoftheexistenceofquantummechanics.Thegravitationalfield,likeallphysicalthings,mustnecessarilyhavequantumproperties.

5 QUANTAOFTIME

There’sanamphoraofoldwineinthehouseofnineyears’vintage.Thereisinthegarden,Phyllis,laurelforbraidingcrownsandmuchivy...Iinviteyoutocelebratethisdayinmid-April—afestiveoneforme,dearerthanmyownbirthday.(IV,11)

ThestrangelandscapeofthephysicsofrelativitythatIhavedescribedsofarbecomesevenmorealienwhenweconsiderquantaandthequantumpropertiesofspaceandoftime.Thedisciplinethatstudiestheseiscalled“quantumgravity,”andthis

ismyownfieldofresearch.50Thereisnotyetatheoryofquantumgravitythathasbeengenerallyacceptedbythescientificcommunity,orhasobtainedexperimentalsupport.Myscientificlifehasbeenlargelydedicatedtocontributingtotheconstructionofapossiblesolutiontotheproblem:loopquantumgravity,orlooptheory.Noteveryoneisbettingonthisturningouttobetherightsolution.Friendswhoworkonstringtheory,forinstance,arefollowingdifferentpaths,andthebattletoestablishwhoisrightisstillraging.Thisisgood—sciencealsogrowsthankstofiercedebates:soonerorlater,itwillbecomeclearwhichtheoryiscorrect,andperhapsitwillnotbelong.Divergencesofopinionregardingthenatureoftime,however,have

diminishedinthelastfewyears,andmanyconclusionshavebecomereasonablycleartomost.Whathasbeenclarifiedisthattheresidualtemporalscaffoldingofgeneralrelativity,illustratedinthepreviouschapter,alsofallsawayifwetakequantaintoaccount.

Universaltimehasshatteredintoamyriadofpropertimes,butifwefactorinthequanta,wemustaccepttheideathateachofthesetimes,inturn,“fluctuates”andisdispersedasinacloud—andcanhaveonlycertainvaluesandnotothers....Theycannolongermanagetoformthespatiotemporalsheetoutlinedinthepreviouschapters.Thethreefundamentaldiscoveriesthatquantummechanicshasledto

arethese:granularity,indeterminacy,andtherelationalaspectofphysicalvariables.Eachoneofthesedemolishesfurtherthelittlethatwasleftofourideaoftime.Let’sconsiderthemonebyone.

GRANULARITY

Thetimemeasuredbyaclockis“quantified,”thatistosay,itacquiresonlycertainvaluesandnotothers.Itisasiftimeweregranularratherthancontinuous.Granularityisthemostcharacteristicfeatureofquantummechanics,

whichtakesitsnamefromthis:“quanta”areelementarygrains.Aminimumscaleexistsforallphenomena.51Forthegravitationalfield,thisiscalledthe“Planckscale.”Minimumtimeiscalled“Plancktime.”Itsvaluecanbeeasilyestimatedbycombiningtheconstantsthatcharacterizephenomenasubjecttorelativity,gravity,andquantummechanics.52Together,thesedeterminethetimeto10-44seconds:ahundredmillionthofatrillionthofatrillionthofatrillionthofasecond.ThisisPlancktime:atthisextremelyminusculelevel,quantumeffectsontimebecomemanifest.Planck’stimeissmall,muchsmallerthananyactualclockistoday

capableofmeasuring.Itissoextremelysmallthatweshouldnotbeastoundedtodiscoverthat“downthere,”atsuchaminutescale,thenotionoftimeisnolongervalid.Whyshoulditbe?Nothingisvalidalwaysandeverywhere.Soonerorlater,wealwayscomeacrosssomethingthatisnew.The“quantization”oftimeimpliesthatalmostallvaluesoftimetdo

notexist.Ifwecouldmeasurethedurationofanintervalwiththemostpreciseclockimaginable,weshouldfindthatthetimemeasuredtakesonlycertaindiscrete,specialvalues.Itisnotpossibletothinkofdurationascontinuous.Wemustthinkofitasdiscontinuous:notassomething

thatflowsuniformlybutassomethingthatinacertainsensejumps,kangaroo-like,fromonevaluetoanother.Inotherwords,aminimumintervaloftimeexists.Belowthis,the

notionoftimedoesnotexist—eveninitsmostbasicmeaning.Perhapstheriversofinkthathavebeenexpendeddiscussingthe

natureofthe“continuous”overthecenturies,fromAristotletoHeidegger,havebeenwasted.Continuityisonlyamathematicaltechniqueforapproximatingveryfinelygrainedthings.Theworldissubtlydiscrete,notcontinuous.ThegoodLordhasnotdrawntheworldwithcontinuouslines:withalighthand,hehassketcheditindots,likethepainterGeorgesSeurat.Granularityisubiquitousinnature:lightismadeofphotons,the

particlesoflight.Theenergyofelectronsinatomscanacquireonlycertainvaluesandnotothers.Thepurestairisgranular,andso,too,isthedensestmatter.OnceitisunderstoodthatNewton’sspaceandtimearephysicalentitieslikeallothers,itisnaturaltosupposethattheyarealsogranular.Theoryconfirmsthisidea:loopquantumgravitypredictsthatelementarytemporalleapsaresmall,butfinite.Theideathattimecouldbegranular,thattherecouldbeminimal

intervalsoftime,isnotnew.ItwasdefendedintheseventhcenturybyIsidoreofSevilleinhisEtymologiae,andinthefollowingcenturybytheVenerableBedeinaworksuggestivelyentitledDeDivisionibusTemporum(“OntheDivisionsofTime”).Inthethirteenthcentury,thegreatphilosopherMaimonideswrites:“Timeiscomposedofatoms,thatistosayofmanypartsthatcannotbefurthersubdivided,onaccountoftheirshortduration.”53Theideaprobablydatesbackevenfurther:thelossoftheoriginaltextsofDemocrituspreventsusfromknowingwhetheritwasalreadypresentinclassicalGreekatomism.54Abstractthoughtcananticipatebycenturieshypothesesthatfindause—orconfirmation—inscientificinquiry.ThespatialsisterofPlancktimeisPlancklength:theminimumlimit

belowwhichthenotionoflengthbecomesmeaningless.Plancklengthisaround10-33centimeters:amillionthofabillionthofabillionthofabillionthofamillimeter.Asayoungmanatuniversity,Ifellinlovewiththeproblemofwhathappensatthisextremelysmallscale.Ipaintedalargesheetwith,atitscenter,inred,aglittering:

IhungitupinmybedroominBolognaanddecidedthatmygoalwouldbetotrytounderstandwhathappensdownthere,attheverytinyscalewheretimeandspaceceasetobewhattheyare—allthewaytotheelementaryquantaofspaceandtime.ThenIspenttherestofmylifeactuallytryingtoachievethis.

QUANTUMSUPERPOSITIONSOFTIMES

Theseconddiscoverymadebyquantummechanicsisindeterminacy:itisnotpossibletopredictexactly,forinstance,whereanelectronwillappeartomorrow.Betweenoneappearanceandanother,theelectronhasnopreciseposition,55asifitweredispersedinacloudofprobability.Inthejargonofphysicists,wesaythatitisina“superposition”ofpositions.Spacetimeisaphysicalobjectlikeanelectron.It,too,fluctuates.It,

too,canbeina“superposition”ofdifferentconfigurations.Theillustrationofstretchedtimeattheendofchapter4,forexample—ifwetakequantummechanicsintoaccount—shouldbeimaginedasablurredsuperpositionofdifferentspacetimes,moreorlessasshownbelow.

Similarly,thestructureoflightconesfluctuatesatallpointsthatdistinguishamongpast,present,andfuture.

Eventhedistinctionbetweenpresent,past,andfuturethusbecomesfluctuating,indeterminate.Justasaparticlemaybediffusedinspace,so,too,thedifferencesbetweenpastandfuturemayfluctuate:aneventmaybebothbeforeandafteranotherone.

RELATIONS

“Fluctuation”doesnotmeanthatwhathappensisneverdetermined.Itmeansthatitisdeterminedonlyatcertainmoments,andinanunpredictableway.Indeterminacyisresolvedwhenaquantityinteractswithsomethingelse.*Intheinteraction,anelectronmaterializesatacertainpoint.For

example,itcollideswithascreen,iscapturedbyaparticledetector,orcollideswithaphoton—thusacquiringaconcreteposition.Butthereisastrangeaspecttothismaterializationoftheelectron:the

electronisconcreteonlyinrelationtotheotherphysicalobjectsitisinteractingwith.56Withregardtoalltheothers,theeffectoftheinteractionisonlytospreadthecontagionofindeterminacy.Concretenessoccursonlyinrelationtoaphysicalsystem:this,Ibelieve,isthemostradicaldiscoverymadebyquantummechanics.*Whenanelectroncollideswithanobject—thescreenofanold

televisionsetwithacathoderaytube,forexample—thecloudofprobabilitywithwhichweconceivedofit“collapses”andtheelectronmaterializesatapointonthescreen,producingoneoftheluminousdotsthatgoesintothemakingofaTVimage.Butitisonlyinrelationtothescreenthatthishappens.Inrelationtoanotherobject,theelectronandscreenarenowtogetherinasuperpositionofconfigurations,anditisonlyatthemomentoffurtherinteractionwithathirdobjectthattheirsharedcloudofprobability“collapses”andmaterializesinaparticularconfiguration—andsoon.Itishardtotakeintheideathatanelectronbehavesinsuchabizarre

way.Itisevenmoredifficulttodigestthatthisisalsothewaytimeandspacebehave.Andyet,accordingtoalltheevidence,thisisthewaythequantumworldworks:theworldthatweinhabit.Thephysicalsubstratumthatdeterminesdurationandphysical

intervals—thegravitationalfield—doesnotonlyhaveadynamicinfluencedbymasses;itisalsoaquantumentitythatdoesnothavedeterminedvaluesuntilitinteractswithsomethingelse.Whenitdoes,thedurationsaregranularanddeterminateonlyforthatsomethingwithwhichitinteracts;theyremainindeterminatefortherestoftheuniverse.Timehasloosenedintoanetworkofrelationsthatnolongerholds

togetherasacoherentcanvas.Thepictureofspacetimes(intheplural)

fluctuating,superimposedoneabovetheother,materializingatcertaintimeswithrespecttoparticularobjects,providesuswithaveryvaguevision.Butitisthebestthatwehaveforthefinegranularityoftheworld.Wearepeeringintotheworldofquantumgravity.

—Letmereprisethelongdiveintothedepthsmadeinthefirstpartofthisbook.Thereisnosingletime:thereisadifferentdurationforeverytrajectory;andtimepassesatdifferentrhythmsaccordingtoplaceandaccordingtospeed.Itisnotdirectional:thedifferencebetweenpastandfuturedoesnotexistintheelementaryequationsoftheworld;itsorientationismerelyacontingentaspectthatappearswhenwelookatthingsandneglectthedetails.Inthisblurredview,thepastoftheuniversewasinacuriously“particular”state.Thenotionofthe“present”doesnotwork:inthevastuniversethereisnothingthatwecanreasonablycall“present.”Thesubstratumthatdeterminesthedurationoftimeisnotanindependententity,differentfromtheothersthatmakeuptheworld;itisanaspectofadynamicfield.Itjumps,fluctuates,materializesonlybyinteracting,andisnottobefoundbeneathaminimumscale....So,afterallthis,whatisleftoftime?

Yougottodeep-sixyourwristwatch,yougottotryandunderstand,Thetimeitseemstocaptureisjustthemovementofitshands...

57

Let’sentertheworldwithouttime.

PARTII

THEWORLDWITHOUTTIME

6 THEWORLDISMADEOFEVENTS,NOTTHINGS

Ogentlemen,thetimeoflifeisshort...Andifwelive,welivetotreadonkings.

Shakespeare,HenryIV,PartI(act5,scene2)

WhenRobespierrefreedFrancefrommonarchy,Europe’sancienrégimefearedthattheendofcivilizationitselfwasnigh.Whentheyoungseektoliberatethemselvesfromanoldorderofthings,theoldareafraidthatallwillfounder.ButEuropewasabletosurviveperfectlywell,evenwithoutthekingofFrance.Theworldwillgoonturning,evenwithoutKingTime.Thereis,nevertheless,anaspectoftimethathassurvivedthe

demolitioninflictedonitbynineteenth-andtwentieth-centuryphysics.DivestedofthetrappingswithwhichNewtoniantheoryhaddrapedit,andtowhichwehadbecomesoaccustomed,itnowshinesoutwithgreaterclarity:theworldisnothingbutchange.Noneofthepiecesthattimehaslost(singularity,direction,

independence,thepresent,continuity)putsintoquestionthefactthattheworldisanetworkofevents.Ontheonehand,therewastime,withitsmanydeterminations;ontheother,thesimplefactthatnothingis:thingshappen.Theabsenceofthequantity“time”inthefundamentalequationsdoes

notimplyaworldthatisfrozenandimmobile.Onthecontrary,itimpliesaworldinwhichchangeisubiquitous,withoutbeingorderedbyFatherTime;withoutinnumerableeventsbeingnecessarilydistributedingoodorder,oralongthesingleNewtoniantimeline,oraccordingtoEinstein’selegantgeometry.Theeventsoftheworlddonotformanorderlyqueue,liketheEnglish.Theycrowdaroundchaotically,likeItalians.Theyareevents,indeed:change,happening.Thishappeningisdiffuse,

scattered,disorderly.Butitishappening;itisnotstasis.Clocksthatrunatdifferentspeedsdonotmarkasingletime,butthehandsoneachclock

changeinrelationtotheothers.Thefundamentalequationsdonotincludeatimevariable,buttheydoincludevariablesthatchangeinrelationtoeachother.Time,asAristotlesuggested,isthemeasureofchange;differentvariablescanbechosentomeasurethatchange,andnoneofthesehasallthecharacteristicsoftimeasweexperienceit.Butthisdoesnotalterthefactthattheworldisinaceaselessprocessofchange.Theentireevolutionofsciencewouldsuggestthatthebestgrammar

forthinkingabouttheworldisthatofchange,notofpermanence.Notofbeing,butofbecoming.Wecanthinkoftheworldasmadeupofthings.Ofsubstances.Of

entities.Ofsomethingthatis.Orwecanthinkofitasmadeupofevents.Ofhappenings.Ofprocesses.Ofsomethingthatoccurs.Somethingthatdoesnotlast,andthatundergoescontinualtransformation,thatisnotpermanentintime.Thedestructionofthenotionoftimeinfundamentalphysicsisthecrumblingofthefirstofthesetwoperspectives,notofthesecond.Itistherealizationoftheubiquityofimpermanence,notofstasisinamotionlesstime.Thinkingoftheworldasacollectionofevents,ofprocesses,istheway

thatallowsustobettergrasp,comprehend,anddescribeit.Itistheonlywaythatiscompatiblewithrelativity.Theworldisnotacollectionofthings,itisacollectionofevents.Thedifferencebetweenthingsandeventsisthatthingspersistintime;

eventshavealimitedduration.Astoneisaprototypical“thing”:wecanaskourselveswhereitwillbetomorrow.Conversely,akissisan“event.”Itmakesnosensetoaskwherethekisswillbetomorrow.Theworldismadeupofnetworksofkisses,notofstones.Thebasicunitsintermsofwhichwecomprehendtheworldarenot

locatedinsomespecificpointinspace.Theyare—iftheyareatall—inawherebutalsoinawhen.Theyarespatiallybutalsotemporallydelimited:theyareevents.Oncloserinspection,infact,eventhethingsthataremost“thinglike”

arenothingmorethanlongevents.Thehardeststone,inthelightofwhatwehavelearnedfromchemistry,fromphysics,frommineralogy,fromgeology,frompsychology,isinrealityacomplexvibrationofquantumfields,amomentaryinteractionofforces,aprocessthatforabriefmomentmanagestokeepitsshape,toholditselfinequilibriumbefore

disintegratingagainintodust,abriefchapterinthehistoryofinteractionsbetweentheelementsoftheplanet,atraceofNeolithichumanity,aweaponusedbyagangofkids,anexampleinabookabouttime,ametaphorforanontology,apartofasegmentationoftheworldthatdependsmoreonhowourbodiesarestructuredtoperceivethanontheobjectofperception—and,gradually,anintricateknotinthatcosmicgameofmirrorsthatconstitutesreality.Theworldisnotsomuchmadeofstonesasoffleetingsounds,orofwavesmovingthroughthesea.Iftheworldwere,however,madeofthings,whatwouldthesethings

be?Theatoms,whichwehavediscoveredtobemadeupinturnofsmallerparticles?Theelementaryparticles,which,aswehavediscovered,arenothingotherthantheephemeralagitationsofafield?Thequantumfields,whichwehavefoundtobelittlemorethancodesofalanguagewithwhichtospeakofinteractionsandevents?Wecannotthinkofthephysicalworldasifitweremadeofthings,ofentities.Itsimplydoesn’twork.Whatworksinsteadisthinkingabouttheworldasanetworkofevents.

Simpleevents,andmorecomplexeventsthatcanbedisassembledintocombinationsofsimplerones.Afewexamples:awarisnotathing,it’sasequenceofevents.Astormisnotathing,it’sacollectionofoccurrences.Acloudaboveamountainisnotathing,itisthecondensationofhumidityintheairthatthewindblowsoverthemountain.Awaveisnotathing,itisamovementofwater,andthewaterthatformsitisalwaysdifferent.Afamilyisnotathing,itisacollectionofrelations,occurrences,feelings.Andahumanbeing?Ofcourseit’snotathing;likethecloudabovethemountain,it’sacomplexprocess,wherefood,information,light,words,andsoonenterandexit....Aknotofknotsinanetworkofsocialrelations,inanetworkofchemicalprocesses,inanetworkofemotionsexchangedwithitsownkind.Foralongtime,wehavetriedtounderstandtheworldintermsof

someprimarysubstance.Perhapsphysics,morethananyotherdiscipline,haspursuedthisprimarysubstance.Butthemorewehavestudiedit,thelesstheworldseemscomprehensibleintermsofsomethingthatis.Itseemstobealotmoreintelligibleintermsofrelationsbetweenevents.ThewordsofAnaximanderquotedinthefirstchapterofthisbook

invitedustothinkoftheworld“accordingtotheorderoftime.”Ifwedo

notassumeapriorithatweknowwhattheorderoftimeis—ifwedonot,thatis,presupposethatitisthelinearanduniversalorderthatweareaccustomedto—Anaximander’sexhortationremainsvalid:weunderstandtheworldbystudyingchange,notbystudyingthings.Thosewhohaveneglectedthisgoodadvicehavepaidaheavypricefor

it.TwoofthegreatswhofellintothiserrorwerePlatoandKepler,bothcuriouslyseducedbythesamemathematics.IntheTimaeus,Platohastheexcellentideaofattemptingtotranslate

intomathematicsthephysicsinsightsgainedbyatomistssuchasDemocritus.Buthegoesaboutitthewrongway:hetriestowritethemathematicsoftheshapeofatoms,ratherthanthemathematicsoftheirmovements.Heallowshimselftobefascinatedbyamathematicaltheoremwhichestablishesthattherearefive—andonlyfive—regularpolyhedra,theseones:

Andheattemptstoadvancetheaudacioushypothesisthatthesearetheactualshapesoftheatomsofthefiveelementarysubstancesthatinantiquitywerethoughttoformeverything:earth,water,air,fire,andthequintessenceofwhichtheheavensaremade.Abeautifulidea.Butcompletelymistaken.Theerrorliesinseekingtounderstandtheworldintermsofthingsratherthanevents.Itliesinignoringchange.Thephysicsandastronomythatwillwork,fromPtolemytoGalileo,fromNewtontoSchrödinger,willbemathematicaldescriptionsofpreciselyhowthingschange,notofhowtheyare.Theywillbeaboutevents,notthings.TheshapesofatomswillbeeventuallyunderstoodonlywithsolutionstoSchrödinger’sequationsdescribinghowtheelectronsinatomsmove.Eventsagain,notthings.Centurieslater,beforereachingthemomentousresultsobtainedinhis

maturity,theyoungKeplerfallsintothesameerror.Heaskshimselfwhatdeterminesthesizeoftheorbitsofplanetsandallowshimselftobe

seducedbythesametheoremthathadbewitchedPlato(it’sabeautifulone,nodoubtaboutthat).Keplerassumesthattheregularpolyhedradeterminethesizeoftheorbitsoftheplanets:iftheyareplacedoneinsidetheotherwithspheresbetweenthem,theradiiofthesesphereswillbeinthesameproportionastheradiioftheplanets.

Aniceidea,butcompletelywrongheaded.Onceagain,itlacksdynamics.WhenKeplermoveson,laterinlife,totacklethequestionofhowplanetsmove,thegatesoftheheavensopen.Wethereforedescribetheworldasithappens,notasitis.Newton’s

mechanics,Maxwell’sequations,quantummechanics,andsoon,tellushoweventshappen,nothowthingsare.Weunderstandbiologybystudyinghowlivingbeingsevolveandlive.Weunderstandpsychology(alittle,notmuch)bystudyinghowweinteractwitheachother,howwethink....Weunderstandtheworldinitsbecoming,notinitsbeing.“Things”inthemselvesareonlyeventsthatforawhileare

monotonous.58

Butonlybeforereturningtodust.Becausesoonerorlater,obviously,everythingreturnstodust.Theabsenceoftimedoesnotmean,therefore,thateverythingisfrozen

andunmoving.Itmeansthattheincessanthappeningthatweariestheworldisnotorderedalongatimeline,isnotmeasuredbyagiganticticktocking.Itdoesnotevenformafour-dimensionalgeometry.Itisaboundlessanddisorderlynetworkofquantumevents.TheworldismorelikeNaplesthanSingapore.Ifby“time”wemeannothingmorethanhappening,theneverythingis

time.Thereisonlythatwhichexistsintime.

7 THEINADEQUACYOFGRAMMAR

Goneisthewhitenessofsnow—greenreturnsinthegrassofthefields,inthecanopiesoftrees,andtheairygraceofspringiswithusagain.Thustimerevolves,thepassinghourthatstealsthelightbringsamessage:immortality,forus,isimpossible.Warmwindswillbefollowedbycold.(IV,7)

Usually,wecall“real”thethingsthatexistnow,inthepresent.Notthosewhichexistedonce,ormaydosointhefuture.Wesaythatthingsinthepastorthefuture“were”realor“willbe”real,butwedonotsaythey“are”real.Philosopherscall“presentism”theideathatonlythepresentisreal,

thatthepastandthefuturearenot—andthatrealityevolvesfromonepresenttoanother,successiveone.Thiswayofthinkingnolongerworks,however,ifthe“present”isnot

definedglobally,ifitisdefinedonlyinourvicinity,inanapproximateway.Ifthepresentthatisfarawayfromhereisnotdefined,what“isreal”intheuniverse?Diagramssuchastheonesthatwehaveseeninpreviouschapters

depictanentireevolutionofspacetimewithasingleimage:theydonotrepresentasingletimebutalltimestogether:

Theyarelikeasequenceofphotographsofamanrunning,orabookcontainingastorythatdevelopsovermanyyears.Theyareaschematicrepresentationofapossiblehistoryoftheworld,notofoneofitssingle,instantaneousstates.Thefirstdiagramillustrateshowweusedtothinkofthetemporal

structureoftheworldbeforeEinstein.Thesetofrealeventsnow,atagiventime,isshowningray:

Buttheseconddiagramprovidesabetterrepresentationofthetemporalstructureoftheworld,andinitthereisnothingthatresemblesapresent.Thereisnopresent.Sowhatisrealnow?Twentieth-centuryphysicsshows,inawaythatseemsunequivocalto

me,thatourworldisnotdescribedwellbypresentism:anobjectiveglobalpresentdoesnotexist.Themostwecanspeakofisapresentrelativetoamovingobserver.Butthen,whatisrealformeisdifferentfromthatwhichisrealforyou,despitethefactthatwewouldliketousetheexpression“real”—inanobjectivesense—asmuchaspossible.Therefore,theworldshouldnotbethoughtofasasuccessionofpresents.59

Whatalternativesdowehave?Philosopherscall“eternalism”theideathatflowandchangeare

illusory:present,past,andfutureareallequallyrealandequallyexistent.Eternalismistheideathatthewholeofspacetime,asoutlinedintheabovediagrams,existsalltogetherinitsentiretywithoutanythingchanging.Nothingreallyflows.60

Thosewhodefendthiswayofthinkingaboutreality—eternalism—frequentlyciteEinstein,whoinafamousletterwrites:

Peoplelikeuswhobelieveinphysics,knowthatthedistinctionbetweenpast,presentandfutureisonlyastubbornlypersistentillusion.61

Thisideahascometobecalledthe“blockuniverse”:theideathatitisnecessarytothinkofthehistoryoftheuniverseasasingleblock,allequallyreal,andthatthepassagefromonemomentoftimetothenextisillusory.Andsoisthis—eternalism,theblockuniverse—theonlywayleftforus

toconceiveoftheworld?Mustwethinkoftheworldwithpast,present,andfuturelikeasinglepresent,allexistinginthesameway?Thatnothingchanges,andthateverythingismotionless?Ischangeonlyanillusion?No,Ireallydon’tthinkso.Thefactthatwecannotarrangetheuniverselikeasingleorderly

sequenceoftimesdoesnotmeanthatnothingchanges.Itmeansthatchangesarenotarrangedinasingleorderlysuccession:thetemporalstructureoftheworldismorecomplexthanasimplesinglelinearsuccessionofinstants.Thisdoesnotmeanthatitisnonexistentorillusory.62

Thedistinctionbetweenpast,present,andfutureisnotanillusion.Itisthetemporalstructureoftheworld.Butthetemporalstructureoftheworldisnotthatofpresentism.Thetemporalrelationsbetweeneventsaremorecomplexthanwepreviouslythought,buttheydonotceasetoexistonaccountofthis.Therelationsoffiliationdonotestablishaglobalorder,butthisdoesnotmakethemillusory.Ifwearenotallinsinglefile,itdoesnotfollowthattherearenorelationsbetweenus.Change,whathappens—thisisnotanillusion.Whatwehavediscoveredisthatitdoesnotfollowaglobalorder.63

Let’sreturntothequestionwithwhichwebegan:What“isreal”?What“exists”?Theansweristhatthisisabadlyputquestion,signifyingeverything

andnothing.Becausetheadjective“real”isambiguous;ithasathousandmeanings.Theverb“toexist”hasevenmore.Tothequestion“Doesapuppetwhosenosegrowswhenheliesexist?”itispossibletoreply:“Ofcourseheexists!It’sPinocchio!”;or:“No,itdoesn’t,he’sonlypartofafantasydreamedupbyCollodi.”

Bothanswersarecorrect,becausetheyareusingdifferentmeaningsoftheverb“toexist.”Therearesomanydifferentusagesoftheverb,differentwaysinwhich

wecansaythatathingexists:alaw,astone,anation,awar,acharacterinaplay,thegod(orgods)ofareligiontowhichwedonotbelong,theGodofthereligiontowhichwedobelong,agreatlove,anumber....Eachoneoftheseentities“exists”and“isreal”inasensedifferentfromalltheothers.Wecanaskourselvesinwhatsensesomethingexistsornot(PinocchioexistsasaliterarycharacterbutnotasfarasanyItalianregisterofficeisconcerned),orifathingexistsinadeterminedway(doesaruleexistpreventingyoufrom“castling”inchess,ifyouhavealreadymovedthecastle?).Toaskoneselfingeneral“whatexists”or“whatisreal”meansonlytoaskhowyouwouldliketouseaverbandanadjective.64It’sagrammaticalquestion,notaquestionaboutnature.Nature,foritspart,iswhatitis—andwediscoveritverygradually.If

ourgrammarandourintuitiondonotreadilyadapttowhatwediscover,well,toobad:wemustseektoadaptthem.Thegrammarofmanymodernlanguagesconjugatesverbsinthe

“present,”“past,”and“future”tense.Itisnotwell-adaptedforspeakingabouttherealtemporalstructureofreality,whichismorecomplex.Grammardevelopedfromourlimitedexperience,beforewebecameawareofitsimprecisionwhenitcametograspingtherichstructureoftheworld.Whatconfusesuswhenweseektomakesenseofthediscoverythatno

objectiveuniversalpresentexistsisonlythefactthatourgrammarisorganizedaroundanabsolutedistinction—“past/present/future”—thatisonlypartiallyapt,hereinourimmediatevicinity.Thestructureofrealityisnottheonethatthisgrammarpresupposes.Wesaythatanevent“is,”or“hasbeen,”or“willbe.”Wedonothaveagrammaradaptedtosaythatanevent“hasbeen”inrelationtomebut“is”inrelationtoyou.Wemustnotallowourselvestobeconfusedbyaninadequate

grammar.ThereisatextfromtheworldofantiquitythatreferstothesphericalshapeoftheEarthinthefollowingway:

Forthosestandingbelow,thingsabovearebelow,whilethingsbelowareabove...andthisisthecasearoundtheentireearth.65

Onfirstreading,thephraseisamuddle,acontradictioninterms.Howisitpossiblethat“thingsabovearebelow,whilethingsbelowareabove”?Itmakesnosense.Itiscomparabletothesinister“Fairisfoulandfoulisfair”inMacbeth.ButifwerereaditbearinginmindtheshapeandthephysicsoftheEarth,thephrasebecomesclear:itsauthorissayingthatforthosewholiveattheAntipodes(inAustralia),thedirection“upward”isthesameas“downward”forthosewhoareinEurope.Heissaying,thatis,thatthedirection“above”changesfromoneplacetoanotherontheEarth.HemeansthatwhatisabovewithrespecttoSydneyisbelowwithrespecttous.Theauthorofthistext,writtentwothousandyearsago,isstrugglingtoadapthislanguageandhisintuitiontoanewdiscovery:thefactthattheEarthisasphere,andthat“up”and“down”haveameaningthatchangesbetweenhereandthere.Thetermsdonothave,aspreviouslythought,asingleanduniversalmeaning.Weareinthesamesituation.Wearestrugglingtoadaptourlanguage

andourintuitiontoanewdiscovery:thefactthat“past”and“future”donothaveauniversalmeaning.Instead,theyhaveameaningthatchangesbetweenhereandthere.That’sallthereistoit.Intheworld,thereischange,thereisatemporalstructureofrelations

betweeneventsthatisanythingbutillusory.Itisnotaglobalhappening.Itisalocalandcomplexonethatisnotamenabletobeingdescribedintermsofasingleglobalorder.AndwhataboutEinstein’sphrase“thedistinctionbetweenpast,

presentandfutureisonlyastubbornlypersistentillusion”?Doesitnotseemtosaythathethoughttheopposite?Evenifthiswerethecase,IamnotsurethatbecauseEinsteinhas

pennedsomephraseorotherweshouldtreatisastheutteranceofanoracle.Einsteinchangedhismindmanytimesonfundamentalquestions,anditispossibletofindnumerouserroneousphrasesofhisthatcontradicteachother.66Butinthisinstance,thingsareperhapsmuchsimpler.Ormoreprofound.EinsteincoinsthisphrasewhenhisfriendMicheleBessodies.Michele

hasbeenhisdearestfriend,thecompanionofhisthinkinganddiscussionssincehisdaysattheUniversityofZurich.TheletterinwhichEinsteinwritesthephraseisnotdirectedatphysicistsorphilosophers.ItisaddressedtoMichele’sfamily,andinparticulartohissister.Thesentencethatcomesbeforeitreads:

Nowhe[Michele]hasdepartedfromthisstrangeworldalittleaheadofme.Thatmeansnothing....

Itisnotaletterwrittentopontificateaboutthestructureoftheworld,it’saletterwrittentoconsoleagrievingsister.Agentleletter,alludingtothespiritualbondbetweenMicheleandAlbert.AletterinwhichEinsteinalsoconfrontshisownsufferingatthelossofhislifelongfriend;andinwhich,evidently,heisthinkingabouthisownapproachingdeath.Adeeplyemotionalletter,inwhichtheillusorinessandtheheartrendingirrelevancetowhichhealludesdonotrefertotimeasunderstoodbyphysicists.Theyarepromptedbytheexperienceoflifeitself.Fragile,brief,fullofillusions.It’saphrasethatspeaksofthingsthatliedeeperthanthephysicalnatureoftime.EinsteindiedonApril18,1955,onemonthandthreedaysafterthe

deathofhisfriend.

8 DYNAMICSASRELATION

Soonerorlatertheexactmeasurementofourtimewillresume—andwe’llbeontheshipthat’sboundforthebitterestshore.(II,9)

Howdoesonedescribeaworldinwhicheverythingoccursbutthereisnotimevariable?Inwhichthereisnocommontimeandnoprivilegeddirectioninwhichchangeoccurs?Inthesimplestway,thesamewaythatwehadthoughtabouttheworld

untilNewtonconvincedusallthatavariabletimewasindispensable.Todescribetheworld,thetimevariableisnotrequired.Whatis

requiredarevariablesthatactuallydescribeit:quantitiesthatwecanperceive,observe,andeventuallymeasure.Thelengthofaroad,theheightofatree,thetemperatureofaforehead,theweightofapieceofbread,thecolorofthesky,thenumberofstarsinthecelestialvault,theelasticityofapieceofbamboo,thespeedofatrain,thepressureofahandonashoulder,thepainofaloss,thepositionofthehandsonaclock,theheightofthesuninthesky...Thesearethetermsinwhichwedescribetheworld.Quantitiesandpropertiesthatweseecontinuouslychanging.Inthesechangesthereareregularities:astonefallsfasterthanafeather.Sunandmooncircleaftereachotherinthesky,passingbyeachotheronceamonth....Amongthesequantitiestherearesomethatweseechangingregularlywithrespecttoothers:thenumberofdays,thephasesofthemoon,theheightofthesunonthehorizon,thepositionofthehandsofaclock.Itisusefultoemploytheseaspointsofreference:let’smeetthreedaysafterthenextfullmoon,whenthesunisatitshighestinthesky.I’llseeyoutomorrow,whentheclockshows4:35.Ifwefindasufficientnumberofvariablesthatremainsynchronizedenoughin

relationtoeachother,itisconvenienttousetheminordertospeakofwhen.Thereisnoneedinanyofthistochooseaprivilegedvariableandcall

it“time.”Whatweneed,ifwewanttodoscience,isatheorythattellsushowthevariableschangewithrespecttoeachother.Thatistosay,howonechangeswhenotherschange.Thefundamentaltheoryoftheworldmustbeconstructedinthisway;itdoesnotneedatimevariable:itneedstotellusonlyhowthethingsthatweseeintheworldvarywithrespecttoeachother.Thatistosay,whattherelationsmaybebetweenthesevariables.67

Thefundamentalequationsofquantumgravityareeffectivelyformulatedlikethis:theydonothaveatimevariable,andtheydescribetheworldbyindicatingthepossiblerelationsbetweenvariablequantities.68

In1967,anequationaccountingforquantumgravitywaswrittenforthefirsttimewithoutanytimevariable.ThisequationwasdiscoveredbytwoAmericanphysicists—BryceDeWittandJohnWheeler—andtodayit’sknownastheWheeler–DeWittequation.69

Atfirstnoonecouldunderstandthesignificanceofanequationwithoutatimevariable,perhapsnotevenWheelerandDeWittthemselves.(Wheeler:“Explaintime?Notwithoutexplainingexistence!Explainexistence?Notwithoutexplainingtime!Touncoverthedeepandhiddenconnectionbetweentimeandexistence...isataskforthefuture.”70)Theissuewasdiscussedatgreatlength;therewereconferences,debates;riversofinkflowed.71Ithinkthatthedusthasnowsettledandthingshavebecomemuchclearer.Thereisnothingmysteriousabouttheabsenceoftimeinthefundamentalequationofquantumgravity.Itisonlytheconsequenceofthefactthat,atthefundamentallevel,nospecialvariableexists.Thetheorydoesnotdescribehowthingsevolveintime.Thetheory

describeshowthingschangeoneinrespecttotheothers,72howthingshappenintheworldinrelationtoeachother.That’sallthereistoit.BryceandJohnleftussomeyearsago.Iknewthembothandhadgreat

admirationandrespectforthem.InmystudyattheuniversityinMarseille,IhavehangingonthewallaletterthatJohnWheelerwrotetomewhenhebecameawareofmyfirstworkonquantumgravity.EverysooftenIrereaditwithamixtureofprideandnostalgia.Iwouldliketo

haveaskedhimmore,duringthehandfulofmeetingsthatwehadtogether.ThelasttimeIwenttoseehiminPrinceton,wetookalongwalktogether.Hespoketomewiththesoftvoiceofanoldman:Icouldnotmakeoutmuchofwhathesaidbutdidnotdaretoaskhimtoofrequentlytorepeatwhathewassaying.Nowheisnolongerwithus.Ican’tquestionhimanymore,ortellhimwhatIthink.Icannolongertellhimthatitseemstomethathisideasarecorrect,andthattheyhaveguidedmethroughoutalifetimeofresearch.IcannolongertellhimIbelievethathewasthefirsttocomeclosetotheheartofthemysteryofquantumgravity.Becauseheisnolongerhere—hereandnow.Thisistimeforus.Memoryandnostalgia.Thepainofabsence.Butitisn’tabsencethatcausessorrow.Itisaffectionandlove.Without

affection,withoutlove,suchabsenceswouldcauseusnopain.Forthisreason,eventhepaincausedbyabsenceis,intheend,somethinggoodandevenbeautiful,becauseitfeedsonthatwhichgivesmeaningtolife.Bryce,ImetinLondon,onthefirstoccasionthatIwenttoseekouta

groupworkingonquantumgravity.Iwasayoungnovice,fascinatedbythisarcanesubjectthatnooneinItalywasworkingon;hewasitsgrandguru.IhadgonetoImperialCollegetomeetupwithChrisIsham,andwhenIarrivedIwastoldthathewasonthetop-floorterrace.Sittingtogetheratasmalltableupthere,IfoundChrisIsham,KarelKuchar,andBryceDeWitt—thethreemainauthorswhoseideasIhadbeenstudyinginrecentyears.IremembervividlytheintenseimpressionIhadonseeingthemtherethroughtheglass,calmlydiscussingamongthemselves.Ididnotdaretointerrupt.TheyseemedtomelikethreegreatZenmastersexchangingunfathomabletruthsbetweenenigmaticsmiles.Theywereprobablyonlydecidingwheretogofordinner.Revisiting

andreflectingontheepisode,IrealizethatatthetimetheywereyoungerthanIamnow.This,too,istime:astrangeshiftingofperspective.Shortlybeforehedied,BrycegavealonginterviewinItaly,subsequentlypublishedinasmallbook.73AnditwasonlythenIbecameawarethathe’dfollowedmyworkmuchmoreclosely,andwithmoresympathy,thanIhadeversuspectedfromourconversationstogether,inwhichhewasmorepronetoexpresscriticismthanencouragement.JohnandBryceweremyspiritualfathers.Thirsting,Ifoundintheir

ideasfresh,clearwatertodrink.So,thankyou,John;thanks,Bryce.Ashumanbeings,welivebyemotionsandthoughts.Weexchangethem

whenweareinthesameplaceatthesametime,talkingtoeachother,lookingintoeachother’seyes,brushingagainsteachother’sskin.Wearenourishedbythisnetworkofencountersandexchanges.But,inreality,wedonotneedtobeinthesameplaceandtimetohavesuchexchanges.Thoughtsandemotionsthatcreatebondsofattachmentbetweenushavenodifficultyincrossingseasanddecades,sometimesevencenturies,tiedtothinsheetsofpaperordancingbetweenthemicrochipsofacomputer.Wearepartofanetworkthatgoesfarbeyondthefewdaysofourlivesandthefewsquaremetersthatwetread.Thisbookisalsoapartofthatweave....ButIhavedigressedandlostmythread.NostalgiaforJohnandBryce

hascausedmetodeviatefrommypath.AllIhadintendedtosayinthischapteristhattheyhaddiscoveredtheextremelysimplestructureoftheequationthatdescribesthedynamicsoftheworld.Itdescribespossibleeventsandthecorrelationsbetweenthem,andnothingelse.It’stheelementaryformofthemechanicsoftheworld,anditdoesnot

needtomention“time.”Theworldwithoutatimevariableisnotacomplicatedone.It’sanetofinterconnectedevents,wherethevariablesinplayadheretoprobabilisticrulesthat,incredibly,weknowforagoodparthowtowrite.Andit’saclearworld,windsweptandfullofbeautyasthecrestsofmountains;aridlybeautifulasthecrackedlipsoftheadolescentyouloved.

ELEMENTARYQUANTUMEVENTSANDSPINNETWORKS

Theequationsofloopquantumgravity74onwhichIworkareamodernversionofthetheoryofWheelerandDeWitt.Thereisnotimevariableintheseequations.Thevariablesofthetheorydescribethefieldsthatformmatter,

photons,electrons,othercomponentsofatomsandthegravitationalfield—allonthesamelevel.Looptheoryisnota“unifiedtheoryofeverything.”Itdoesn’tevenbegintoclaimthatit’stheultimatetheoryofscience.It’satheorymadeupofcoherentbutdistinctparts.Itseekstobe“only”acoherentdescriptionoftheworldasweunderstanditsofar.Thefieldsmanifestthemselvesingranularform:elementaryparticles,

photons,andquantaofgravity—orrather“quantaofspace.”These

Representationofthewebofelementarygrainsofspace

(orspinnetwork).

elementarygrainsdonotexistimmersedinspace;rather,theythemselvesformthatspace.Thespatialityoftheworldconsistsoftheweboftheirinteractions.Theydonotdwellintime:theyinteractincessantlywitheachother,andindeedexistonlyintermsoftheseincessantinteractions.Andthisinteractionisthehappeningoftheworld:itistheminimumelementaryformoftimethatisneitherdirectionalnorlinear.NordoesithavethecurvedandsmoothgeometrystudiedbyEinstein.Itisareciprocalinteractioninwhichquantamanifestthemselvesintheinteraction,inrelationtowhattheyinteractwith.Thedynamicoftheseinteractionsisprobabilistic.Theprobabilities

thatsomethingwillhappen—giventheoccurrenceofsomethingelse—caninprinciplebecalculatedwiththeequationsofthetheory.Wecannotdrawacompletemap,acompletegeometry,ofeverything

thathappensintheworld,becausesuchhappenings—includingamongthemthepassageoftime—arealwaystriggeredonlybyaninteractionwith,andwithrespectto,aphysicalsysteminvolvedintheinteraction.Theworldislikeacollectionofinterrelatedpointsofview.Tospeakoftheworld“seenfromoutside”makesnosense,becausethereisno“outside”totheworld.Theelementaryquantaofthegravitationalfield

existatthePlanckscale.TheyaretheelementarygrainsthatweavethemobilefabricwithwhichEinsteinreinterpretedNewton’sabsolutespaceandtime.Itisthese,andtheirinteractions,thatdeterminetheextensionofspaceandthedurationoftime.Therelationsofspatialadjacencytiethegrains

ofspaceintowebs.Wecallthese“spinnetworks.”Thename“spin”comesfromthemathematicsthatdescribethegrainsofspace.75Aringinthespinnetworkiscalleda“loop,”andthesearetheloopsthatgive“looptheory”itsname.Thewebs,inturn,transformintoeachotherindiscreteleaps,

describedinthetheoryasstructurescalled“spinfoam.”76

Theoccurrenceoftheseleapsdrawsthepatternsthatonalargescaleappeartouslikethesmoothstructureofspacetime.Onasmallscale,thetheorydescribesa“quantumspacetime”thatisfluctuating,probabilistic,

anddiscrete.Atthisscale,thereisonlythefrenziedswarmingofquantathatappearandvanish.

Representationofspinfoam.

ThisistheworldwithwhichIseekdailytocometoterms.Anunusualworld,butnotameaninglessone.InmyresearchgroupinMarseille,forexample,weareattemptingto

calculatethetimeneededforablackholetoexplodewhenitpassesthroughaquantumphase.

Duringthecourseofthisphase,insidetheblackholeandwithinitsimmediatevicinitythereisnolongerasingleanddeterminatespacetime.Thereisaquantumsuperpositionofspinwebs.Justasanelectroncanunfurlintoacloudofprobabilitiesbetweenthemomentitisemittedandthemomentitarrivesonascreen,passingthroughmorethanoneplace,sothespacetimeofthequantumcollapseofablackholepassesthroughaphaseinwhichtimefluctuatesviolently,thereisaquantumsuperpositionofdifferenttimes,andthen,later,areturntoadeterminedstateaftertheexplosion.Forthisintermediatephase,wheretimeiswhollyindeterminate,we

stillhaveequationsthattelluswhathappens.Equationswithouttime.Thisistheworlddescribedbylooptheory.AmIcertainthatthisisthecorrectdescriptionoftheworld?Iamnot,

butitistodaytheonlycoherentandcompletewaythatIknowoftothinkaboutthestructureofspacetimewithoutneglectingitsquantumproperties.Loopquantumgravityshowsthatitispossibletowritea

coherenttheorywithoutfundamentalspaceandtime—andthatitcanbeusedtomakequalitativepredictions.Inatheoryofthiskind,timeandspacearenolongercontainersor

generalformsoftheworld.Theyareapproximationsofaquantumdynamicthatinitselfknowsneitherspacenortime.Thereareonlyeventsandrelations.Itistheworldwithouttimeofelementaryphysics.

PARTIII

THESOURCESOFTIME

9 TIMEISIGNORANCE

Donotaskabouttheoutcomeofmydays,orofyours,Leuconoe—it’sasecret,beyondus.Anddon’tattemptabstrusecalculations.(I,11)

Thereisatimetobebornandatimetodie,atimetoweepandatimetodance,atimetokillandatimetoheal.Atimetodestroyandatimetobuild.77Uptothispoint,ithasbeenatimetodestroytime.Nowitistimetorebuildthetimethatweexperience:tolookforitssources,tounderstandwhereitcomesfrom.If,intheelementarydynamicoftheworld,allthevariablesare

equivalent,whatisthisthingthatwehumanscall“time”?Whatisitthatmywatchmeasures?Whatisitthatalwaysrunsforward,andneverbackward—andwhy?Itmaynotbepartoftheelementarygrammaroftheworld,butwhatisit?Therearesomanythingsthatarenotpartoftheelementarygrammar

oftheworldandthatsimply“emerge”insomeway.Forexample:

Acatisnotpartoftheelementaryingredientsoftheuniverse.Itissomethingcomplexthatemerges,andrepeatsitself,invariouspartsofourplanet.Agroupofboysonafielddecidetohaveamatch.Theyformteams.Thisishowweusedtodoit:thetwomostenterprisingwouldtaketurnschoosingtheplayerstheywanted,havingtossedacointoseewhowouldhavefirstpick.Attheendofthissolemnprocedure,thereweretwoteams.Whereweretheteamsbeforetheywerechosen?Nowhere.Theyemergedfromtheprocedure.Wheredo“high”and“low”comefrom—termsthataresofamiliarandyetarenotintheelementaryequationsoftheworld?FromtheEarththatissoclosetousandthatattracts.“High”and“low”emergeincertaincircumstancesintheuniverse,aswhenthereisalargemassnearby.Inthemountains,weseeavalleycoveredbyaseaofwhiteclouds.Thesurfaceofthecloudsgleams,immaculate.Westarttowalktowardthevalley.Theairbecomesmorehumid,thenlessclear;theskyisnolongerblue.Wefindourselvesinafog.Wheredid

thewell-definedsurfaceofthecloudsgo?Itvanished.Itsdisappearanceisgradual;thereisnosurfacethatseparatesthefogfromthesparseairoftheheights.Wasitanillusion?No,itwasaviewfromafar.Cometothinkofit,it’slikethiswithallsurfaces.ThisdensemarbletablewouldlooklikeafogifIwereshrunktoasmallenough,atomicscale.Everythingintheworldbecomesblurredwhenseencloseup.Whereexactlydoesthemountainendandwheredotheplainsbegin?Wheredoesthesavannahbeginandthedesertend?Wecuttheworldintolargeslices.Wethinkofitintermsofconceptsthataremeaningfulforus,thatemergeatacertainscale.Weseetheskyturningarounduseveryday,butwearetheoneswhoareturning.Isthedailyspectacleofarevolvinguniverse“illusory”?No,itisreal,butitdoesn’tinvolvethecosmosalone.Itinvolvesourrelationwiththesunandthestars.Weunderstanditbyaskingourselveshowwemove.Cosmicmovementemergesfromtherelationbetweenthecosmosandourselves.

Intheseexamples,somethingthatisreal—acat,afootballteam,highandlow,thesurfaceofclouds,therotationofthecosmos—emergesfromaworldthatatamuchsimplerlevelhasnocats,teams,upordown,nosurfacesofclouds,norevolvingcosmos....Timeemergesfromaworldwithouttime,inawaythathassomethingincommonwitheachoftheseexamples.Thereconstructionoftimebeginshere,intwolittlechapters—thisone

andthenext—thatarebriefandtechnical.Ifyoufindthemheavygoing,skipthemandgodirectlytochapter11.Fromthere,stepbystep,wewillgraduallyreachmorehumanthings.

THERMALTIME

Inthefrenzyofthermalmolecularmingling,allthevariablesthatcanpossiblyvarydosocontinuously.One,however,doesnotvary:thetotalamountofenergyinanyisolated

system.Betweenenergyandtimethereisaclosebond.Theyformoneofthosecharacteristiccouplesofquantitiesthatphysicistscall“conjugate,”suchaspositionandmomentum,ororientationandangularmomentum.Thetwotermsofthesecouplesaretiedtoeachother.Ontheonehand,knowingwhattheenergyofasystemmaybe78—howitislinkedtotheothervariables—isthesameasknowinghowtimeflows,becausetheequationsofevolutionintimefollowfromtheformofitsenergy.79Ontheother,energyisconservedintime,henceitcannotvary,evenwheneverythingelsevaries.Initsthermalagitation,asystem80passesthrough

alltheconfigurationsthathavethesameenergy,butonlythese.Thesetoftheseconfigurations—whichourblurredmacroscopicvisiondoesnotdistinguish—isthe“(macroscopic)stateofequilibrium”:aplacidglassofhotwater.Theusualwayofinterpretingtherelationbetweentimeandstateof

equilibriumistothinkthattimeissomethingabsoluteandobjective;energygovernsthetime-evolutionofasystem;andthesysteminequilibriummixesallconfigurationsofequalenergy.Theconventionallogicforinterpretingthisrelationistherefore:

time→energy→macroscopicstate81

Thatis:todefinethemacroscopicstate,wefirstneedtoknowtheenergy,andtodefineenergywefirstneedtoknowwhatistime.Inthislogic,timecomesfirstandisindependentfromtherest.Butthereisanotherwayofthinkingaboutthissamerelationship:by

readingitinreverse.Thatis,toobservethatamacroscopicstate,whichistosayablurredvisionoftheworld,maybeinterpretedasaminglingthatpreservesanenergy,andthisinitsturngeneratesatime.Thatis:

macroscopicstate→energy→time82

Thisobservationopensupanewperspective:inanelementaryphysicalsystemwithoutanyprivilegedvariablethatactslike“time”—where,ineffect,allthevariablesareonthesamelevelbutwecanhaveonlyablurredvisionofthemdescribedbymacroscopicstates.Agenericmacroscopicstatedeterminesatime.I’llrepeatthispoint,becauseitisakeyone:amacroscopicstate

(whichignoresthedetails)choosesaparticularvariablethathassomeofthecharacteristicsoftime.Inotherwords,atimebecomesdeterminedsimplyasaneffectof

blurring.Boltzmannunderstoodthatthebehaviorofheatinvolvesblurring,fromthefactthatinsideaglassofwaterthereisamyriadofmicroscopicvariablesthatwedonotsee.Thenumberofpossiblemicroscopicconfigurationsforwaterisitsentropy.Butsomethingfurtherisalsotrue:theblurringitselfdeterminesaparticularvariable—time.Infundamentalrelativisticphysics,wherenovariableplaysapriorithe

roleoftime,wecanreversetherelationbetweenmacroscopicstateand

evolutionoftime:itisnottheevolutionoftimethatdeterminesthestate,itisthestate—theblurring—thatdeterminesatime.Timethatisdeterminedinthiswaybyamacroscopicstateiscalled

“thermaltime.”Inwhatsensemayitbesaidtobeatime?Fromamicroscopicpointofview,thereisnothingspecialaboutit—itisavariablelikeanyother.Butfromamacroscopicone,ithasacrucialcharacteristic:amongsomanyvariablesallatthesamelevel,thermaltimeistheonewithbehaviorthatmostcloselyresemblesthevariableweusuallycall“time,”becauseitsrelationswiththemacroscopicstatesareexactlythosethatweknowfromthermodynamics.Butitisnotauniversaltime.Itisdeterminedbyamacroscopicstate,

thatis,byablurring,bytheincompletenessofadescription.Inthenextchapter,Iwilldiscusstheoriginofthisblurring,butbeforeIdo,let’stakeanotherstepbybringingquantummechanicsintoconsideration.

QUANTUMTIME

RogerPenroseisamongthemostlucidofthosescientistswhohavefocusedonspaceandtime.83Hereachedtheconclusionthatthephysicsofrelativityisnotincompatiblewithourexperienceoftheflowingoftimebutthatitdoesnotseemsufficienttoaccountforit.Hehassuggestedthatwhat’smissingmightbewhathappensinaquantuminteraction.84

AlainConnes,thegreatFrenchmathematician,haspointedoutthedeeproleofquantuminteractionattherootoftime.Whenaninteractionrendersthepositionofamoleculeconcrete,the

stateofthemoleculeisaltered.Thesameappliesforitsspeed.Ifwhatmaterializesfirstisthespeedandthentheposition,thestateofthemoleculechangesinadifferentwaythaniftheorderofthetwoeventswerereversed.Theordermatters.IfImeasurethepositionofanelectronfirstandthenitsspeed,itsstatechangesdifferentlythanifIweretomeasureitsvelocityfirstandthenitsposition.Thisiscalledthe“noncommutativity”ofthequantumvariables,

becausepositionandspeed“donotcommute,”thatistosay,theycannotexchangeorderwithimpunity.Thisnoncommutativityisoneofthecharacteristicphenomenaofquantummechanics.Noncommutativitydeterminesanorderand,consequently,agermoftemporalityinthe

determinationoftwophysicalvariables.Todetermineaphysicalvariableisnotanisolatedact;itinvolvesinteraction.Theeffectofsuchinteractionsdependsontheirorder,andthisorderisaprimitiveformofthetemporalorder.Perhapsitistheveryfactthattheeffectoftheseinteractionsdepends

ontheorderinwhichtheytakeplacethatisattherootofthetemporalorderoftheworld.ThisisthefascinatingideasuggestedbyConnes:thefirstgermoftemporalityinelementaryquantumtransitionsliesinthefactthattheseinteractionsarenaturally(partially)ordered.Conneshasprovidedarefinedmathematicalversionofthisidea:he

hasshownthatakindoftemporalflowisimplicitlydefinedbythenoncommutativityofthephysicalvariables.Duetothisnoncommutativity,thesetofphysicalvariablesinasystemdefinesamathematicalstructurecalled“noncommutativevonNeumannalgebra,”andConneshasshownthatthesestructureshavewithinthemselvesanimplicitlydefinedflow.85

Surprisingly,thereisanextremelycloserelationbetweenAlainConnes’sflowforquantumsystemsandthethermaltimethatIhavediscussedabove.Conneshasshownthat,inaquantumsystem,thethermalflowsdeterminedbydifferentmacroscopicstatesareequivalent,uptocertaininternalsymmetries,86andthat,together,theyformpreciselytheConnesflow.87Putmoresimply:thetimedeterminedbymacroscopicstatesandthetimedeterminedbyquantumnoncommutativityareaspectsofthesamephenomenon.Anditisthisthermalandquantumtime,Ibelieve,88thatisthe

variablethatwecall“time”inourrealuniverse,whereatimevariabledoesnotexistatthefundamentallevel.Theintrinsicquantumindeterminacyofthingsproducesablurring,

likeBoltzmann’sblurring,whichensures—contrarytowhatclassicphysicsseemedtoindicate—thattheunpredictabilityoftheworldismaintainedevenifitwerepossibletomeasureeverythingthatismeasurable.Boththesourcesofblurring—quantumindeterminacy,andthefact

thatphysicalsystemsarecomposedofzillionsofmolecules—areattheheartoftime.Temporalityisprofoundlylinkedtoblurring.Theblurringisduetothefactthatweareignorantofthemicroscopicdetailsofthe

world.Thetimeofphysicsis,ultimately,theexpressionofourignoranceoftheworld.Timeisignorance.AlainConneshascoauthoredwithtwofriendsashortsciencefiction

novel.Charlotte,theprotagonist,managestohaveforamomentatotalityofinformationabouttheworld,withoutblurring.Shemanagesto“see”theworlddirectly,beyondtime:

Ihavehadtheunheard-ofgoodfortuneofexperiencingaglobalvisionofmybeing—notofaparticularmoment,butofmyexistence“asawhole.”Iwasabletocompareitsfinitenatureinspace,againstwhichnooneprotests,withitsfinitenatureintime,whichisinsteadthesourceofsomuchoutrage.

Andthenreturningtotime:

Ihadtheimpressionoflosingalltheinfiniteinformationgeneratedbythequantumscene,andthislosswassufficienttodragmeirresistiblyintotheriveroftime.

Theemotionthatresultsfromthisisanemotionoftime:

Thisre-emergenceoftimeseemedtomelikeanintrusion,asourceofmentalconfusion,anguish,fearandalienation.89

Ourblurredandindeterminateimageofrealitydeterminesavariable,thermaltimethatturnsouttohavecertainpeculiarpropertieswhichbegintoresemblewhatwecall“time”:itisinthecorrectrelationwithequilibriumstates.Thermaltimeistiedtothermodynamics,andhencetoheat,butdoes

notyetresembletimeasweexperienceit,becauseitdoesnotdistinguishbetweenthepastandthefuture,hasnodirection,andlackswhatwemeanwhenwespeakofitsflow.Wehavenotyetreachedthetimeofourownexperience.Thedifferencebetweenthepastandthefuturethatissoimportantto

us:Wheredoesthatcomefrom?

10 PERSPECTIVE

Intheimpenetrablenightofhiswisdomagodclosesthestripofdaysthat’stocomeandlaughsatourhumantrepidation.(III,29)

Theentiredifferencebetweenpastandfuturemaybeattributedsolelytothefactthattheentropyoftheworldwaslowinthepast.90Whywasentropylowinthepast?InthischapterIwillgiveanaccountofanideathatprovidesapossible

answer,“ifyouwillhearmyanswertothisquestionanditsperhapsextravagantsupposition.”91Iamnotsurethatitisthecorrectanswer,butit’stheonewithwhichIhavebecomeenamored.92Itmightclarifymanythings.

WEARETHEONESTURNING!

Whateverwehumanbeingsmaybespecifically,indetail,weareneverthelesspiecesofnature,apartofthegreatfrescoofthecosmos,asmallpartamongmanyothers.Betweenourselvesandtherestoftheworldtherearephysical

interactions.Obviously,notallthevariablesoftheworldinteractwithus,orwiththesegmentoftheworldtowhichwebelong.Onlyaveryminutefractionofthesevariablesdoesso;mostofthemdonotreactwithusatall.Theydonotregisterus,andwedonotregisterthem.Thisiswhydistinctconfigurationsoftheworldseemequivalenttous.Thephysicalinteractionbetweenmyselfandaglassofwater—twopiecesoftheworld

—isindependentofthemotionofthesinglemoleculesofwater.Inthesameway,thephysicalinteractionbetweenmyselfandadistantgalaxy—twopiecesoftheworld—ignoreswhathappensindetailoutthere.Therefore,ourvisionoftheworldisblurredbecausethephysicalinteractionsbetweenthepartoftheworldtowhichwebelongandtherestareblindtomanyvariables.ThisblurringisattheheartofBoltzmann’stheory.93Fromthis

blurring,theconceptsofheatandentropyareborn—andthesearelinkedtothephenomenathatcharacterizetheflowoftime.Theentropyofasystemdependsexplicitlyonblurring.ItdependsonwhatIdonotregister,becauseitdependsonthenumberofindistinguishableconfigurations.Thesamemicroscopicconfigurationmaybeofhighentropywithregardtooneblurringandoflowinrelationtoanother.Thisdoesnotmeanthatblurringisamentalconstruct;itdependson

actual,existingphysicalinteractions.94Entropyisnotanarbitraryquantity,norasubjectiveone.Itisarelativeone,likespeed.Thespeedofanobjectisnotapropertyoftheobjectalone:itisa

propertyoftheobjectinrelationtoanotherobject.Thespeedofachildwhoisrunningonamovingtrainhasavaluerelativetothetrain(afewstepspersecond)andadifferentvaluerelativetotheground(ahundredkilometersperhour).Ifhismothertellsthechildto“Keepstill!,”shedoesnotmeanthattheyhavetothrowthemselvesoutofthewindowtostopinrelationtotheground.Shemeansthatthechildshouldstopwithregardtothetrain.Speedisapropertyofanobjectwithrespecttoanotherobject.Itisarelativequantity.Thesameistrueforentropy.TheentropyofAwithregardtoBcounts

thenumberofconfigurationsofAthatthephysicalinteractionsbetweenAandBdonotdistinguish.Clarifyingthispoint,whichfrequentlycausesconfusion,opensupa

seductivesolutiontothemysteryofthearrowoftime.Theentropyoftheworlddoesnotdependonlyontheconfigurationof

theworld;italsodependsonthewayinwhichweareblurringtheworld,andthisdependsonwhatthevariablesoftheworldarethatweinteractwith.Thatistosay,onthevariableswithwhichourpartoftheworldinteracts.Theentropyoftheworldinthefarpastappearsverylowtous.Butthis

mightnotreflecttheexactstateoftheworld:itmightregardthesubsetof

theworld’svariableswithwhichwe,asphysicalsystems,haveinteracted.Itiswithrespecttothedramaticblurringproducedbyourinteractionswiththeworld,causedbythesmallsetofmacroscopicvariablesintermsofwhichwedescribetheworld,thattheentropyoftheuniversewaslow.This,whichisafact,opensupthepossibilitythatitwasn’ttheuniverse

thatwasinaveryparticularconfigurationinthepast.Perhapsinsteaditisus,andourinteractionswiththeuniverse,thatareparticular.Wearetheoneswhodetermineaparticularmacroscopicdescription.Theinitiallowentropyoftheuniverse,andhencethearrowoftime,maybemoredowntousthantotheuniverseitself.Thisisthebasicidea.Thinkofoneofthegrandestandmostobviousphenomena:the

diurnalrotationoftheskies.Itisthemostimmediateandmagnificentcharacteristicoftheuniversearoundus:itturns.Butisthisturningreallyacharacteristicoftheuniverse?Itisnot.Ittookusthousandsofyears,butintheendwemanagedtounderstandtherevolvingoftheheavens:weunderstoodthatitiswewhoturn,nottheuniverse.TherotationoftheheavensisaperspectiveeffectduetoourparticularwayofmovingonEarth,ratherthanamysteriouspropertyofthedynamicsoftheuniverse.Somethingsimilarmightbetruefortime’sarrow.Thelowinitial

entropyoftheuniversemightbeduetotheparticularwayinwhichwe—thephysicalsystemthatwearepartof—interactwithit.Weareattunedtoaveryparticularsubsetofaspectsoftheuniverse,anditisthisthatisorientedintime.Howcanaparticularinteractionbetweenusandtherestoftheworld

determinealowinitialentropy?It’ssimple.Takeapackoftwelvecards,sixredandsixblack.Arrange

itsothattheredcardsareallatthefront.Shufflethepackalittleandthenlookfortheblackcardsthathaveendedupamongtheredones.Beforeshuffling,therearenone;after,some.Thisisabasicexampleofthegrowthofentropy.Atthestartofthegame,thenumberofblackcardsamongtheredinthefirsthalfofthepackiszero(theentropyislow)becauseithasstartedinaspecialconfiguration.Butnowlet’splayadifferentgame.First,shufflethepackinarandom

way,thenlookatthefirstsixcardsandcommitthemtomemory.Shufflealittleandlooktoseewhichothercardshaveendedupamongthefirstsix.Atthestart,therewerenone,thentheirnumbergrew,asitdidinthepreviousexample,togetherwiththeentropy.Butthereisacrucial

differencebetweenthisexampleandthepreviousone:atthebeginningofthisone,thecardswereinarandomconfiguration.Itwasyouwhodeclaredthemtobeparticular,bytakingnoteofwhichcardswereinthefronthalfofthepackatthebeginningofthegame.Thesamemaybetruefortheentropyoftheuniverse:perhapsitwasin

noparticularconfiguration.Perhapswearetheoneswhobelongtoaparticularphysicalsystemwithrespecttowhichitsstatecanbeparticular.Butwhyshouldtherebesuchaphysicalsystem,inrelationtowhich

theinitialconfigurationoftheuniverseturnsouttobespecial?Becauseinthevastnessoftheuniverse,thereareinnumerablephysicalsystems,andtheyinteractwitheachotherinwaysthatareevenmorenumerous.Amongthese,throughtheendlessgameofprobabilitiesandhugenumbers,therewillsurelybesomethatinteractwiththerestoftheuniversepreciselywiththosevariablesthatfoundthemselveshavingaparticularvalueinthepast.Itishardlysurprisingthatthereare“special”subsetsinauniverseas

vastasours.Itisnotsurprisingthatsomeonewinsthelottery:someonewinsiteveryweek.Itisunnaturaltoassumethattheentireuniversehasbeeninanincredibly“special”configurationinthepast,butthereisnothingunnaturalinimaginingthattheuniversehaspartsthatare“special.”Ifasubsetoftheuniverseisspecialinthissense,thenforthissubset

theentropyoftheuniverseislowinthepast,thesecondlawofthermodynamicsobtains;memoriesexist,tracesareleft—andtherecanbeevolution,life,andthought.Inotherwords,ifintheuniversethereissomethinglikethis—andit

seemsnaturaltomethattherecouldbe—thenwebelongtothatsomething.Here,“we”referstothatcollectionofphysicalvariablestowhichwecommonlyhaveaccessandbymeansofwhichwedescribetheuniverse.Perhaps,therefore,theflowoftimeisnotacharacteristicoftheuniverse:liketherotationoftheheavens,itisduetotheparticularperspectivethatwehavefromourcornerofit.Butwhyshouldwebelongtooneofthesespecialsystems?Forthe

samereasonthatapplesgrowinnorthernEurope,wherepeopledrinkcider,andgrapesgrowinthesouth,wherepeopledrinkwine;orthatIwasbornwherepeoplehappentospeakmynativelanguage;orthatthe

sunwhichwarmsusisattherightdistancefromus—nottoocloseandnottoofaraway.Inallthesecases,the“strange”coincidencearisesfromconfusingthecausalrelations:itisn’tthatapplesgrowwherepeopledrinkcider,itisthatpeopledrinkciderwhereapplesgrow.Putthisway,thereisnolongeranythingstrangeaboutit.Similarly,intheboundlessvarietyoftheuniverse,itmayhappenthat

therearephysicalsystemsthatinteractwiththerestoftheworldthroughthoseparticularvariablesthatdefineaninitiallowentropy.Withregardtothesesystems,entropyisconstantlyincreasing.There,andnotelsewhere,therearethetypicalphenomenaassociatedwiththeflowingoftime:lifeispossible,togetherwithevolution,thought,andourawarenessoftimepassing.There,theapplesgrowthatproduceourcider:time.Thatsweetjuicethatcontainsalltheambrosiaandallthegalloflife.

INDEXICALITY

Whenwedoscience,wewanttodescribetheworldinthemostobjectivewaypossible.Wetrytoeliminatedistortionsandopticalillusionsderivingfromourpointofview.Scienceaspirestoobjectivity,toasharedpointofviewaboutwhichitispossibletobeinagreement.Thisisadmirable,butweneedtobewaryaboutwhatweloseby

ignoringthepointofviewfromwhichwedotheobserving.Initsanxiouspursuitofobjectivity,sciencemustnotforgetthatourexperienceoftheworldcomesfromwithin.Everyglancethatwecasttowardtheworldismadefromaparticularperspective.Takingthisfactintoaccounthelpstoclarifymanythings.Itclarifies,

forinstance,therelationbetweenwhatageographicalmaptellsusandwhatweactuallysee.Inordertocomparethemapwithwhatwesee,itisnecessarytoaddacrucialpieceofinformation:wemustidentifyonthemapourexactlocation.Themapdoesnotknowwhereweare,atleastwhenitisnotfixedintheplacethatitrepresents—likethosemapsinmountainvillagesshowingroutesthatcanbewalkedwithareddotnexttowhichiswritten:“YouAreHere.”Astrangephrase:howcanamapknowwhereweare?Wemightbe

lookingatitfromafar,throughbinoculars.Instead,itshouldsay“I,amap,amhere,”withanarrownexttothereddot.Butthereisalsosomethingcuriousaboutatextthatreferstoitself.Whatisit?

Itiswhatphilosopherscall“indexicality”:thecharacteristicofcertainwordsthathaveadifferentmeaningeverytimetheyareused,ameaningdeterminedbywhere,how,when,andbywhomtheyarebeingspoken.Wordssuchas“here,”“now,”“I,”“this,”“tonight”allassumeadifferentmeaningdependingonwhouttersthemandthecircumstancesinwhichtheyareuttered.“MynameisCarloRovelli”istrueifIsayit,butuntrueifsomeoneelsenotalsocalledCarloRovelliusesthesamephrase.“NowitisSeptember12,2016”isaphrasethat’strueatthemomentthatIamwritingthisbutwillbefalsejustafewhourslater.Theseindexicalphrasesmakeexplicitreferencetothefactthatapointofviewexists,thatapointofviewisaningredientineverydescriptionoftheobservableworldthatwemake.Ifwegiveadescriptionoftheworldthatignorespointofview,thatis

solely“fromtheoutside”—ofspace,oftime,ofasubject—wemaybeabletosaymanythingsbutwelosecertaincrucialaspectsoftheworld.Becausetheworldthatwehavebeengivenistheworldseenfromwithinit,notfromwithout.Manythingsthatweseeintheworldcanbeunderstoodonlyifwetake

intoaccounttheroleplayedbypointofview.Theyremainunintelligibleifwefailtodoso.Ineveryexperience,wearesituatedwithintheworld:withinamind,abrain,apositioninspace,amomentintime.Ourbeingsituatedintheworldisessentialtounderstandingourexperienceoftime.Wemustnot,inshort,confusethetemporalstructuresthatbelongtotheworldas“seenfromtheoutside”withtheaspectsoftheworldthatweobserveandwhichdependonourbeingpartofit,onourbeingsituatedwithinit.95

Inordertouseageographicalmap,itisnotenoughtolookatitfromtheoutside:wemustknowwherewearesituatedinrelationtowhatitrepresents.Inordertounderstandourexperienceofspace,itisnotenoughtothinkofNewtonianspace.Wemustrememberthatweseethisspacefrominsideit,thatwearelocalized.Inordertounderstandtime,itisnotenoughtothinkofitfromoutside:itisnecessarytounderstandthatwe,ineverymomentofourexperience,aresituatedwithintime.Weobservetheuniversefromwithinit,interactingwithaminuscule

portionoftheinnumerablevariablesofthecosmos.Whatweseeisablurredimage.Thisblurringsuggeststhatthedynamicoftheuniversewithwhichweinteractisgovernedbyentropy,whichmeasuresthe

Universalmanatthecenterofthecosmos,inLiberDivinorumOperumbyHildegardof

Bingen(1164–70).

amountofblurring.Itmeasuressomethingthatrelatestousmorethantothecosmos.Wearegettingupdangerously

closetoourselves.WecanalmosthearTiresias,inOedipus,saying:“Stop!Oryouwillfindyourself”...OrHildegardofBingen,whointhetwelfthcenturyseekstheabsoluteandendsupbyputting“universalman”atthecenterofthecosmos.Butbeforegettingtothis“us,”

anotherchapterisrequired,toshowhowthegrowthinentropy—perhapsonlyaneffectofperspective—mightgiverisetotheentire,vastphenomenonoftime.Letmesummarizethehard

groundcoveredinthelasttwochapters,inthehopethatIhavenotalreadylostallmyreaders.Atthefundamentallevel,theworldis

acollectionofeventsnotorderedintime.Theseeventsmanifestrelationsbetweenphysicalvariablesthatare,apriori,onthesamelevel.Eachpartoftheworldinteractswithasmallpartofallthevariables,thevalueofwhichdetermines“thestateoftheworldwithregardtothatparticularsubsystem.”AsmallsystemSdoesnotdistinguishthedetailsoftherestofthe

universebecauseitinteractsonlywithafewamongthevariablesoftherestoftheuniverse.TheentropyoftheuniversewithrespecttoScountsthe(micro)statesoftheuniverseundistinguishablebyS.Theuniverseappearsinahigh-entropyconfigurationwithrespecttoS,because(bydefinition)therearemoremicrostatesinhigh-entropyconfigurations,thereforeitismorelikelytohappentobeinoneofthesemicrostates.Asexplainedabove,thereisaflowassociatedwithhigh-entropy

configurations,andtheparameterofthisflowisthermaltime.ForagenericsmallsystemS,entropyremainsgenerallyhighalongtheentire

flowofthermaltime,perhapsjustfluctuatingupanddown,because,afterall,wearedealingherewithprobabilities,notfixedrules.ButamongtheinnumerablesmallsystemsSthatexistinthis

extraordinarilyvastuniversewherewehappentolive,therewillbeafewspecialonesforwhichthefluctuationsoftheentropyhappentobesuchthatatoneofthetwoendsoftheflowofthermaltimeentropyhappenstobelow.ForthesesystemsS,thefluctuationisnotsymmetrical:entropyincreases.Thisgrowthiswhatweexperienceastheflowingoftime.Whatisspecialisnotthestateoftheearlyuniverse:itisthesmallsystemStowhichwebelong.I’mnotsureifwearedealingwithaplausiblestory,butIdonotknow

ofanybetterones.Thealternativeistoacceptasagivenofobservationthefactthatentropywaslowatthebeginningoftheuniverse,andtoleaveitatthat.96

ItisthelawannouncedbyClausius,ΔS≥0,anddecipheredbyBoltzmannthatisguidingus:entropyneverdecreases.Havinglostsightofit,insearchofthegenerallawsoftheworld,werediscoveritasapossibleperspectiveeffectforparticularsubsystems.Let’sbeginagainfromthere.

11 WHATEMERGESFROMAPARTICULARITY

Whydothetallpineandthepalepoplarintertwinetheirbranchestoprovidesuchsweetshadeforus?Whydoesthefleetingwaterinventbrightspiralsintheturbulentstream?(II,9)

ITISENTROPY,NOTENERGY,THATDRIVESTHEWORLD

AtschoolIwastoldthatitisenergythatmakestheworldgoround.Weneedtogetenergy—forexample,frompetroleum,fromthesun,orfromnuclearsources.Energymakesourenginesrun,helpsplantstogrow,andcausesustowakeupeverymorningfullofvitality.Butthereissomethingthatdoesnotaddup.Energy—asIwasalsotold

atschool—isconserved.Itisneithercreatednordestroyed.Ifitisconserved,whydowehavetoconstantlyresupplyit?Whycan’twejustkeepusingthesameenergy?Thetruthisthatthereisplentyofenergyanditisnotconsumed.It’s

notenergythattheworldneedsinordertokeepgoing.Whatitneedsislowentropy.Energy(beitmechanical,chemical,electrical,orpotential)transforms

itselfintothermalenergy,thatistosay,intoheat:itgoesintocoldthings,andthereisnofreewayofgettingitbackfromtheretoreuseittomakeaplantgrow,ortopoweramotor.Inthisprocess,theenergyremainsthesamebuttheentropyincreases,anditisthiswhichcannotbeturnedback.Thesecondlawofthermodynamicsdemandsit.Whatmakestheworldgoroundarenotsourcesofenergybutsources

oflowentropy.Withoutlowentropy,energywoulddiluteintouniform

heatandtheworldwouldgotosleepinastateofthermalequilibrium—therewouldnolongerbeanydistinctionbetweenpastandfuture,andnothingwouldhappen.NeartotheEarthwehavearichsourceoflowentropy:thesun.The

sunsendsushotphotons.ThentheEarthradiatesheattowardtheblacksky,emittingcolderphotons.Theenergythatentersismoreorlessequaltotheenergythatexits;consequently,wedonotgenerallygainenergyintheexchange.(Gainingenergyintheexchangeisdisastrousforus:itisglobalwarming.)Butforeveryhotphotonthatarrives,theEarthemitstencoldones,sinceahotphotonfromthesunhasthesameenergyastencoldphotonsemittedbytheEarth.Thehotphotonhaslessentropythanthetencoldphotons,becausethenumberofconfigurationsofasingle(hot)photonislowerthanthenumberofconfigurationsoften(cold)photons.Therefore,thesunisacontinualrichsourceoflowentropyforus.Wehaveatourdisposalanabundanceoflowentropy,anditisthisthatallowsplantsandanimalstogrow,enablesustobuildmotorsandcities—andtothinkandtowritebookssuchasthisone.Wheredoesthelowentropyofthesuncomefrom?Fromthefactthat,

inturn,thesunisbornoutofanentropicconfigurationthatwasevenlower:theprimordialcloudfromwhichthesolarsystemwasformedhadevenlowerentropy.Andsoon,backintothepast,untilwereachtheextremelylowinitialentropyoftheuniverse.Itisthegrowthofthisentropythatpowersthegreatstoryofthe

cosmos.Buttheincreaseintheentropyoftheuniverseisnotrapid,likethe

suddenexpansionofgasinabox:itisgradual,ittakestime.Evenwithagiganticladleittakestimetostirsomethingasbigastheuniverse.Aboveall,thereareobstaclesandcloseddoorstoitsgrowth—passageswhereitoccursonlywithgreatdifficulty.Apileofwood,forexample,lastsalongtimeifleftalone.Itisnotina

stateofmaximumentropy,becausetheelementsofwhichitismade,suchascarbonandhydrogen,arecombinedinaveryparticularmanner(“ordered”)togiveformtothewood.Entropygrowsiftheseparticularcombinationsarebrokendown.Thisiswhathappenswhenwoodburns:itselementsdisengagefromtheparticularstructuresthatformwoodandentropyincreasessharply(firebeing,infact,amarkedlyirreversibleprocess).Butthewooddoesnotstarttoburnonitsown.Itremainsfora

longtimeinastateoflowentropy,untilsomethingopensadoorthatallowsittopasstoastateofhigherentropy.Apileofwoodisinanunstablestate,likeapackofcards,butuntilsomethingcomesalongtomakeitdoso,itdoesnotcollapse.Thissomethingmight,forinstance,beamatchtolightaflame.Theflameisaprocessthatopensachannelthroughwhichthewoodcanpassintoastateofhigherentropy.Therearesituationsthatimpedeandhenceslowdowntheincreaseof

entropythroughouttheuniverse.Inthepast,forinstance,theuniversewasbasicallyanimmenseexpanseofhydrogen.Hydrogencanfuseintohelium,andheliumhasahigherentropythanhydrogen.Butforthistohappen,itisnecessaryforachanneltobeopened:astarmustigniteforhydrogentobegintoburnthereintohelium.Whatcausesstarstoignite?Anotherprocessthatincreasesentropy:thecontractionduetogravityofoneofthelargecloudsofhydrogenthatsailthroughoutthegalaxy.Acontractedcloudofhydrogenhashigherentropythanadispersedone.97

Butthecloudsofhydrogenaresovastthattheytakemillionsofyearstocontract.Onlyaftertheyhavebecomeconcentrateddotheymanagetoheatuptothepointthattriggerstheprocessofnuclearfission.Theignitionofnuclearfissionopensthedoorthatallowsthefurtherincreaseinentropy:hydrogenburningintohelium.Theentirehistoryoftheuniverseconsistsofthishaltingandleaping

cosmicgrowthofentropy.Itisneitherrapidnoruniform,becausethingsremaintrappedinbasinsoflowentropy(thepileofwood,thecloudofhydrogen...)untilsomethingopensadoorontoaprocessthatfinallyallowsentropytoincrease.Thegrowthofentropyitselfhappenstoopennewdoorsthroughwhichentropycanincreasefurther.Adaminthemountains,forinstance,retainswateruntilitisgraduallyworndownovertimeandthefreedwaterescapesdownhillonceagain,causingentropytogrow.Overthecourseofthisirregulartrajectory,largeorsmallportionsoftheuniverseremainisolatedinrelativelystablesituationsforperiodsthatcanbeveryprolonged.Livingbeingsaremadeupofsimilarlyintertwinedprocesses.

Photosynthesisdepositslowentropyfromthesunintoplants.Animalsfeedonlowentropybyeating.(Ifallweneededwasenergyratherthanentropy,wewouldheadfortheheatoftheSahararatherthantowardournextmeal.)Insideeverylivingcell,thecomplexwebofchemicalprocessesisastructurethatopensandclosesgatesthroughwhichlow

entropycanincrease.Moleculesfunctionasthecatalyststhatallowtheprocessestointertwine;or,conversely,theyputabrakeonthem.Theincreaseofentropyineachindividualprocessiswhatmakesthewholethingwork.Lifeisthisnetworkofprocessesforincreasingentropy—processesthatactascatalyststoeachother.98Itisn’ttrue,asissometimesstated,thatlifegeneratesstructuresthatareparticularlyordered,orthatlocallydiminishentropy:itissimplyaprocessthatdegradesandconsumesthelowentropyoffood;itisaself-structureddisordering,nomoreandnolessthanintherestoftheuniverse.Eventhemostbanalphenomenaaregovernedbythesecondlawof

thermodynamics.Astonefallstotheground.Why?Oneoftenreadsthatit’sbecausethestoneplacesitself“inastateoflowerenergy”thatitendsuplowerdown.Butwhydoesthestoneputitselfintoastateoflowerenergy?Whyshoulditloseenergyifenergyisconserved?TheansweristhatwhenthestonehitstheEarth,itwarmsit:itsmechanicalenergyistransformedintoheat.Andthereisnowaybackfromthere.Ifthesecondlawofthermodynamicsdidnotexist,ifheatdidnotexist,ifthereexistednomicroscopicswarming,thestonewouldreboundperpetually;itwouldneverlandandbestill.Itisentropy,notenergy,thatkeepsstonesonthegroundandthe

worldturning.Theentirecomingintobeingofthecosmosisagradualprocessof

disordering,likethepackofcardsthatbeginsinorderandthenbecomesdisorderedthroughshuffling.Therearenoimmensehandsthatshuffletheuniverse.Itdoesthismixingbyitself,intheinteractionsamongitspartsthatopenandcloseduringthecourseofthemixing,stepbystep.Vastregionsremaintrappedinconfigurationsthatremainordered,untilhereandtherenewchannelsareopenedthroughwhichdisorderspreads.99

Whatcauseseventstohappenintheworld,whatwritesitshistory,istheirresistiblemixingofallthings,goingfromthefeworderedconfigurationstothecountlessdisorderedones.Theentireuniverseislikeamountainthatcollapsesinslowmotion.Likeastructurethatverygraduallycrumbles.Fromthemostminuteeventstothemorecomplexones,itisthis

danceofever-increasingentropy,nourishedbytheinitiallowentropyoftheuniverse,thatistherealdanceofShiva,thedestroyer.

TRACESANDCAUSES

Thefactthatentropyhasbeenlowinthepastleadstoanimportantfactthatisubiquitousandcrucialforthedifferencebetweenpastandfuture:thepastleavestracesofitselfinthepresent.Tracesareeverywhere.Thecratersofthemoontestifytoimpactsin

thepast.Fossilsshowtheformsoflivingcreaturesfromlongago.Telescopesshowhowfaroffgalaxieswereinthepast.Bookscontainourhistory;ourbrainsswarmwithmemories.Tracesofthepastexist,andnottracesofthefuture,onlybecause

entropywaslowinthepast.Therecanbenootherreason,sincetheonlysourceofthedifferencebetweenpastandfutureisthelowentropyofthepast.Inordertoleaveatrace,itisnecessaryforsomethingtobecome

arrested,tostopmoving,andthiscanhappenonlyinanirreversibleprocess—thatistosay,bydegradingenergyintoheat.Inthisway,computersheatup,thebrainheatsup,themeteorsthatfallintothemoonheatit;eventhegoosequillofamedievalscribeinaBenedictineabbeyheatsalittlethepageonwhichhewrites.Inaworldwithoutheat,everythingwouldreboundelastically,leavingnotrace.100

Itisthepresenceofabundanttracesofthepastthatproducesthefamiliarsensationthatthepastisdetermined.Theabsenceofanyanalogoustracesofthefutureproducesthesensationthatthefutureisopen.Theexistenceoftracesservestomakeitpossibleforourbraintodisposeofextensivemapsofpastevents.Thereisnothinganalogoustothisforfutureones.Thisfactisattheoriginofoursensationofbeingabletoactfreelyintheworld:choosingbetweendifferentfutures,eventhoughweareunabletoactuponthepast.Thevastmechanismsofthebrainaboutwhichwehavenodirect

awareness(“IknownotwhyIamsosad,”mumblesAntonioatthebeginningofTheMerchantofVenice)havebeendesignedduringthecourseofevolutioninordertomakecalculationsaboutpossiblefutures.Thisiswhatwecall“deciding.”Sincetheyelaboratepossiblealternativefuturesthatwouldfollowifthepresentwereexactlyasitisexceptforsomedetail,wearenaturallyinclinedtothinkintermsof“causes”thatprecede“effects”:thecauseofafutureeventisapasteventsuchthatthe

futureeventwouldnotfollowinaworldthatwasexactlythesameexceptforthiscause.101

Inourexperience,thenotionofcauseisthusasymmetricalintime:causeprecedeseffect.Whenwerecognizeinparticularthattwoevents“havethesamecause,”wefindthiscommoncause102inthepast,notinthefuture.Iftwowavesofatsunamiarrivetogetherattwoneighboringislands,wethinkthattherehasbeenaneventinthepastthathascausedboth.Wedonotlookforitinthefuture.Butthisdoesnothappenbecausethereisamagicalforceof“causality”goingfromthepasttothefuture.Ithappensbecausetheimprobabilityofacorrelationbetweentwoeventsrequiressomethingimprobable,anditisonlythelowentropyofthepastthatprovidessuchimprobability.Whatelsecould?Inotherwords,theexistenceofcommoncausesinthepastisnothingbutamanifestationoflowentropyinthepast.Inastateofthermalequilibrium,orinapurelymechanicalsystem,thereisn’tadirectiontotimeidentifiedbycausality.Thelawsofelementaryphysicsdonotspeakof“causes”butonlyof

“regularities,”andthesearesymmetricalwithregardtopastandfuture.BertrandRussellnotedthisinafamousarticle,writingemphaticallythat“Thelawofcausality...isarelicofabygoneage,surviving,likethemonarchy,onlybecauseitiserroneouslysupposedtodonoharm.”103Heexaggerates,ofcourse,becausethefactthatthereareno“causes”atanelementarylevelisnotasufficientreasontorenderobsoletetheverynotionofcause.104Atanelementaryleveltherearenocatseither,butwedonotforthisreasonceasetobotherwithcats.Thelowentropyofthepastrendersthenotionofcauseaneffectiveone.Butmemory,causesandeffects,flow,thedeterminednatureofthe

pastandtheindeterminacyofthefuturearenothingbutnamesthatwegivetotheconsequencesofastatisticalfact:theimprobabilityofapaststateoftheuniverse.Causes,memory,traces,thehistoryitselfofthebecomingoftheworld

thatunfoldsnotonlyacrosscenturiesandmillenniaofhumanhistorybutinthebillionsofyearsofthegreatcosmicnarrative—allthisstemssimplyfromthefactthattheconfigurationofthingswas“particular”afewbillionyearsago.105

And“particular”isarelativeterm:itisparticularinrelationtoaperspective.Itisablurring.Itisdeterminedbytheinteractionsthata

physicalsystemhaswiththerestoftheworld.Hencecausality,memory,traces,thehistoryofthehappeningoftheworlditselfcanonlybeaneffectofperspective:liketheturningoftheheavens;aneffectofourpeculiarpointofviewintheworld....Inexorably,then,thestudyoftimedoesnothingbutreturnustoourselves.

12 THESCENTOFTHEMADELEINE

Happyandmasterofhimselfisthemanwhoforeverydayofhislifecansay:“TodayIhavelived;tomorrowifGodextendsforusahorizonofdarkcloudsordesignsamorningoflimpidlight,hewillnotchangeourpoorpasthewilldonothingwithoutthememoryofeventsthatthefleetinghourwillhaveassignedtous.”(III,29)

Letusturntoourselves,then,andtotheroleweplayinrelationtothenatureoftime.Aboveallelse,whatareweashumanbeings?Entities?Buttheworldisnotmadeupofentities,itismadefromeventsthatcombinewitheachother...Sowhat,then,am“I”?IntheMilindaPañha,aBuddhisttextwritteninPaliinthefirst

centuryofourera,NāgasenarepliestothequestionsofKingMilinda,denyinghisexistenceasanentity:106

KingMilindasaystothesageNāgasena:Whatisyourname,Master?Theteacherreplies:IamcalledNāgasena,ogreatking;Nāgasenaisnothingbutaname,adesignation,anexpression,asimpleword:thereisnopersonhere.

Thekingisastonishedbysuchanextreme-soundingassertion:

Ifnopersonexists,whoisitthenwhohasclothingandsustenance?Wholivesaccordingtothevirtues?Whokills,whosteals,whohaspleasures,wholies?Ifthereisnolongeranactor,neitheristheregoodorevilanylonger.

Andhearguesthatthesubjectmustbeanautonomousbeingthatisnotreducibletoitscomponentparts:

IsitthehairsthatareNāgasena,Master?Isitthenailsortheteethorthefleshorthebones?Isitthename?Isitthesensations,theperceptions,theconsciousness?Isitnoneofthesethings?

Thesagerepliesthat“Nāgasena”iseffectivelynoneofthesethings,andthekingseemstohavewonthediscussion:ifNāgasenaisnoneofthese,thenhemustbesomethingelse—andthissomethingelsewillbethepersonNāgasenawhothereforeexists.Butthesageturnshisownargumentagainsthim,askingwhata

chariotconsistsof:

Arethewheelsthechariot?Istheaxle?Isthechassisthechariot?Isthechariotthesumofitsparts?

Thekingrepliescautiouslythatcertainly“chariot”refersonlytotherelationshipamongtheensembleofwheels,axle,andchassis,totheirworkingtogetherandinrelationtous—andthattheredoesnotexistanentity“chariot”beyondtheserelationsandevents.Nāgasenatriumphs:inthesamewayas“chariot,”thename“Nāgasena”designatesnothingmorethanacollectionofrelationsandevents.Weareprocesses,events,compositeandlimitedinspaceandtime.But

ifwearenotanindividualentity,whatisitthatfoundsouridentityanditsunity?Whatmakesitso—thatIamCarlo—andthatmyhairandmynailsandmyfeetareconsideredpartofme,aswellasmyangerandmydreams,andthatIconsidermyselftobethesameCarloasyesterday,thesameastomorrow;theonewhothinks,suffers,andperceives?Therearedifferentingredientsthatcombinetoproduceouridentity.

Threeoftheseareimportantfortheargumentofthisbook:

1.Thefirstisthateveryoneofusidentifieswithapointofviewintheworld.Theworldisreflectedineachoneofusthrougharichspectrumofcorrelationsessentialforoursurvival.107Eachofusisacomplexprocessthatreflectstheworldandelaboratestheinformationwereceiveinawaythatisstrictlyintegrated.108

2.Thesecondingredientonwhichouridentityisbasedisthesameasforthechariot.Intheprocessofreflectingtheworld,weorganizeitintoentities:weconceiveoftheworldbygroupingandsegmentingitasbestwecaninacontinuousprocessthatismoreorlessuniformandstable,thebettertointeractwithit.WegrouptogetherintoasingleentitytherocksthatwecallMontBlanc,andwethinkofitasaunifiedthing.Wedrawlinesovertheworld,dividingitintosections;weestablishboundaries,weapproximatetheworldbybreakingitdownintopieces.Itisthestructureofournervoussystemthatworksinthisway.Itreceivessensorystimuli,elaboratesinformationcontinuously,generatingbehavior.Itdoessothroughnetworksofneurons,whichformflexibledynamicsystemsthatcontinuouslymodifythemselves,seekingtopredict109—asfaraspossible—theflowofinformationintake.Inordertodothis,thenetworksofneuronsevolvebyassociatingmoreorlessstablefixedpointsoftheirdynamicwithrecurringpatternsthattheyfindintheincominginformation,or—indirectly—intheproceduresofelaborationthemselves.Thisiswhatseemstoemergefromtheverylivelycurrentresearchonthebrain.110Ifthisisso,then“things,”like“concepts,”arefixedpointsintheneuronaldynamic,inducedbyrecurringstructuresofthesensorialinputandofthesuccessiveelaborations.Theymirroracombinationofaspectsoftheworldthatdependsonrecurrentstructuresoftheworldandontheirrelevanceintheirinteractionswithus.Thisiswhatachariotconsistsof.Humewouldhavebeenpleasedtoknowaboutthesedevelopmentsinourunderstandingofthebrain.Inparticular,wegroupintoaunifiedimagethecollectionofprocesses

thatconstitutesthoselivingorganismsthatareotherhumanbeings,becauseourlifeissocialandwethereforeinteractagreatdealwiththem.Theyareknotsofcauseandeffectthataredeeplyrelevantforus.Wehaveshapedanideaofa“humanbeing”byinteractingwithotherslikeourselves.Ibelievethatournotionofselfstemsfromthis,notfrom

introspection.Whenwethinkofourselvesaspersons,Ibelieveweareapplyingtoourselvesthementalcircuitsthatwehavedevelopedtoengagewithourcompanions.ThefirstimagethatIhaveofmyselfasachildisthechildthatmy

mothersees.Weareforourselvesinlargemeasurewhatweseeandhave

seenofourselvesreflectedbacktousbyourfriends,ourloves,andourenemies.Ihaveneverbeenconvincedbytheidea,attributedtoDescartes,that

theprimaryaspectofourexperienceisawarenessofthinking,andthereforeofexisting.(EventheattributionoftheideatoDescartesseemswrongtome:CogitoergosumisnotthefirststepintheCartesianreconstruction,itisthesecond.ThefirstisDubitoergocogito.Thestartingpointofthereconstructionisnotahypotheticalapriorithatisimmediatetotheexperienceofexistingasasubject.It’sarationalisticaposteriorireflectiononthefirststageoftheprocessinwhichDescarteshadarticulatedastateofdoubt:logicdictatesthatifsomeonedoubtssomething,theymusthavethoughtaboutit.Andthatiftheycanthink,thentheymustexist.Itissubstantiallyaconsiderationmadeinthethirdperson,notinthefirst,howeverprivatetheprocess.ThestartingpointforDescartesisthemethodicaldoubtexperiencedbyarefinedintellectual,notthebasicexperienceofasubject.)Theexperienceofthinkingofoneselfasasubjectisnotaprimary

experience:itisacomplexculturaldeduction,madeonthebasisofmanyotherthoughts.Myprimaryexperience—ifwegrantthatthismeansanything—istoseetheworldaroundme,notmyself.Ibelievethatweeachhaveaconceptof“myself”onlybecauseatacertainpointwelearntoprojectontoourselvestheideaofbeinghumanasanadditionalfeaturethatevolutionhasledustodevelopduringthecourseofmillenniainordertoengagewithothermembersofourgroup:wearethereflectionoftheideaofourselvesthatwereceivebackfromourkind.

3.Butthereisathirdingredientinthefoundationofouridentity,anditisprobablytheessentialone—itisthereasonthisdelicatediscussionistakingplaceinabookabouttime:memory.Wearenotacollectionofindependentprocessesinsuccessivemoments.Everymomentofourexistenceislinkedbyapeculiartriplethreadtoourpast—themostrecentandthemostdistant—bymemory.Ourpresentswarmswithtracesofourpast.Wearehistoriesofourselves,narratives.Iamnotthismomentarymassoffleshreclinedonthesofatypingtheletteraonmylaptop;IammythoughtsfullofthetracesofthephrasesthatIamwriting;Iammymother’scaresses,andtheserenekindnesswithwhichmyfathercalmly

guidedme;Iammyadolescenttravels;Iamwhatmyreadinghasdepositedinlayersinmymind;Iammyloves,mymomentsofdespair,myfriendships,whatI’vewritten,whatI’veheard;thefacesengravedonmymemory.Iam,aboveall,theonewhoaminuteagomadeacupofteaforhimself.Theonewhoamomentagotypedtheword“memory”intohiscomputer.TheonewhojustcomposedthesentencethatIamnowcompleting.Ifallthisdisappeared,wouldIstillexist?Iamthislong,ongoingnovel.Mylifeconsistsofit.Itismemorythatsolderstogethertheprocesses,scatteredacrosstime,

ofwhichwearemade.Inthissenseweexistintime.ItisforthisreasonthatIamthesamepersontodayasIwasyesterday.Tounderstandourselvesmeanstoreflectontime.Buttounderstandtimeweneedtoreflectonourselves.ArecentbookbyDeanBuonomenodevotedtoresearchonthe

functioningofthebrainisentitledYourBrainIsaTimeMachine.111Itdiscussesthemanywaysinwhichthebraininteractswiththepassageoftimeandestablishesbridgesbetweenpast,present,andfuture.Toalargeextent,thebrainisamechanismforcollectingmemoriesofthepastinordertousethemcontinuallytopredictthefuture.Thishappensacrossawidespectrumoftimescales,fromtheveryshorttotheverylong.Ifsomeonethrowssomethingatustocatch,ourhandmovesskillfullytotheplacewheretheobjectwillbeinafewinstants:thebrain,usingpastimpressions,hasveryrapidlycalculatedthefuturepositionoftheobjectthatisflyingtowardus.Furtheralongthescale,weplantseedsothatcornwillgrow.Orinvestinscientificresearchsothattomorrowitmightresultinknowledgeandnewtechnology.Thepossibilityofpredictingsomethinginthefutureobviouslyimprovesourchancesofsurvivaland,consequently,evolutionhasselectedtheneuralstructuresthatallowit.Wearetheresultofthisselection.Thisbeingbetweenpastandfutureeventsiscentraltoourmentalstructure.This,forus,isthe“flow”oftime.Thereareelementarystructuresinthewiringofournervoussystem

thatimmediatelyregistermovement:anobjectthatappearsinoneplaceandthenimmediatelyafterwardinanotherdoesnotgeneratetwodistinctsignalsthattravelseparatelytowardthebrain,butasinglesignalcorrelatedwiththefactthatwearelookingatsomethingthatismoving.Inotherwords,whatweperceiveisnotthepresent,whichinanycase

makesnosenseforasystemthatfunctionsonascaleoffinitetime,butrathersomethingthathappensandextendsintime.Itisinourbrainsthatanextensionintimebecomescondensedintoaperceptionofduration.Thisintuitionisanancientone.SaintAugustine’sruminationsonit

haveremainedfamous.InBookXIoftheConfessions,Augustineaskshimselfaboutthenature

oftimeand,despitebeinginterruptedbyexclamationsinthestyleofanevangelicalpreacherthatIfindquitetiresome,hepresentsalucidanalysisofourcapacityforperceivingtime.Heobservesthatwearealwaysinthepresent,becausethepastispastandthereforedoesnotexist,andthefuturehasyettoarrive,soitdoesnotexisteither.Andheaskshimselfhowwecanbeawareofduration—orevenbecapableofevaluatingit—ifwearealwaysonlyinapresentthatis,bydefinition,instantaneous.Howcanwecometoknowsoclearlyaboutthepast,abouttime,ifwearealwaysinthepresent?Hereandnow,thereisnopastandnofuture.Wherearethey?Augustineconcludesthattheyarewithinus:

Itiswithinmymind,then,thatImeasuretime.Imustnotallowmymindtoinsistthattimeissomethingobjective.WhenImeasuretime,Iammeasuringsomethinginthepresentofmymind.Eitherthisistime,orIhavenoideawhattimeis.

Theideaismuchmoreconvincingthanitseemsonfirstreading.Wecansaythatwemeasuredurationwithaclock.Buttodosorequiresustoreaditattwodifferentmoments:thisisnotpossible,becausewearealwaysinonemoment,neverintwo.Inthepresent,weseeonlythepresent;wecanseethingsthatweinterpretastracesofthepast,butthereisacategoricaldifferencebetweenseeingtracesofthepastandperceivingtheflowoftime—andAugustinerealizesthattherootofthisdifference,theawarenessofthepassingoftime,isinternal.Itisintegraltothemind.Itisthetracesleftinthebrainbythepast.Augustine’sexpositionoftheideaisquitebeautiful.Itisbasedonour

experienceofmusic.Whenwelistentoahymn,themeaningofasoundisgivenbytheonesthatcomebeforeandafterit.Musiccanoccuronlyintime,butifwearealwaysinthepresentmoment,howisitpossibletohearit?Itispossible,Augustineobserves,becauseourconsciousnessisbasedonmemoryandonanticipation.Ahymn,asong,isinsomewaypresentinourmindsinaunifiedform,heldtogetherbysomething—by

thatwhichwetaketimetobe.Andhencethisiswhattimeis:itisentirelyinthepresent,inourminds,asmemoryandasanticipation.Theideathattimemightexistonlyinthemindcertainlydidnot

becomedominantinChristianthought.Infact,itisoneofthepropositionsexplicitlycondemnedashereticalbyÉtienneTempier,theBishopofParis,in1277.Inhislistofbeliefstobecondemned,thefollowingcanbefound:

Quodevumettempusnichilsuntinre,Sedsoluminapprehensione.112

Inotherwords:“[Itishereticaltomaintainthat]theageandtimedonotexistinrealitybutonlyinthemind.”Perhapsmybookisslidingtowardheresy....ButgiventhatAugustinecontinuestoberegardedasasaint,Idon’tsupposethatIshouldbetooworriedaboutit.Christianity,afterall,isquiteflexible....ItmayseemeasytorefuteAugustinebyarguingthatthetracesofthe

pastthathefindswithinhimselfmaybethereonlybecausetheyreflectarealstructureoftheexternalworld.Inthefourteenthcentury,forinstance,WilliamofOckhammaintainedinhisPhilosophiaeNaturalisthatmanobservesboththesky’smovementsandtheoneswithinhimselfandthereforeperceivestimethroughhiscoexistencewiththeworld.Centurieslater,EdmondHusserlinsists—rightly—onthedistinctionbetweenphysicaltimeand“internalconsciousnessoftime”:forasoundnaturalistwishingtoavoiddrowningintheuselessvorticesofidealism,theformer(thephysicalworld)comesfirst,whilethelatter(consciousness)—independentlyofhowwellweunderstandit—isdeterminedbythefirst.Itisanentirelyreasonableobjection,justsolongasphysicsreassuresusthattheexternalflowoftimeisreal,universal,andinkeepingwithourintuitions.Butifphysicsshowsusinsteadthatsuchtimeisnotanelementarypartofreality,canwecontinuetooverlookAugustine’sobservationandtreatitasirrelevanttothetruenatureoftime?Inquiryintoperceptionoftheinternalratherthanexternalnatureof

timerecursfrequentlyinWesternphilosophy.KantdiscussesthenatureofspaceandtimeinhisCritiqueofPureReason,andinterpretsbothspaceandtimeasaprioriformsofknowledge—thatistosay,thingsthatdonotjustrelatetotheobjectiveworldbutalsotothewayinwhicha

subjectapprehendsit.Buthealsoobservesthatwhereasspaceisshapedbyourexternalsense,thatistosay,byourwayoforderingthingsthatweseeintheworldoutsideofus,timeisshapedbyourinternalsense,thatistosay,byourwayoforderinginternalstateswithinourselves.Onceagain:thebasisofthetemporalstructureoftheworldistobesoughtinsomethingthatcloselyrelatestoourwayofthinkingandperceiving,toourconsciousness.ThisremainstruewithouthavingtogettangledupinKantiantranscendentalism.HusserlreprisesAugustinewhenhedescribestheshapingof

experienceintermsof“retention”—using,likehim,themetaphoroflisteningtoamelody113(theworld,inthemeantime,hasbecomebourgeois,withmelodiesreplacinghymns):inthemomentthatwehearanote,thepreviousnoteis“retained,”thenthatonealsobecomespartoftheretention—andsoon,runningthemtogetherinsuchawaythatthepresentcontainsacontinuoustraceofthepast,becominggraduallymoreblurred.114Itisbywayofthisprocessofretention,accordingtoHusserl,thatphenomena“constitutetime.”ThediagramonthefollowingpageisHusserl’s:thehorizontalaxisfromAtoErepresentstimepassing;theverticalaxisfromEtoA’representsthe“retention”ofmomentE,wheretheprogressivesubsidenceleadsfromAtoA’.Phenomenaconstitutetimebecause,atthemoment,E,P’,andA’exist.TheinterestingpointhereisthatthesourceofthephenomenologyoftimeisnotidentifiedbyHusserlinthehypotheticalobjectivesuccessionofphenomena(thehorizontalline)butratherinmemory(similartoanticipation,called“protention”byHusserl),thatistosay,bytheverticallineinthediagram.Mypointisthatthiscontinuestobevalid(inanaturalphilosophy)eveninaphysicalworldwherethereisnophysicaltimegloballyorganizedinalinearwaybutonlytracesgeneratedbyvaryingentropy.

InthewakeofHusserl,MartinHeideggerwrites—asfarasmyloveoftheclarityandtransparencyofGalileo’swritingallowsmetodecipherthedeliberateobscurityofHeidegger’slanguage—that“timetemporalizesitselfonlytotheextentthatitishuman.”115Forhimalso,timeisthetimeofmankind,thetimefordoing,forthatwithwhichmankindisengaged.Evenif,afterward,sinceheisinterestedinwhatbeingisforman(for“theentitythatposestheproblemofexistence”116),Heideggerendsupbyidentifyingtheinternalconsciousnessoftimeasthehorizonofbeingitself.Theseintuitionsofthedegreetowhichtimeisinherenttosubjectivity

remainsignificantalsotoanysoundnaturalismthatseesthesubjectaspartofnatureandisnotafraidtospeakabout“reality”andtostudyit—whileatthesametimeacknowledgingthatourunderstandingandourintuitionareradicallyfilteredbythewayinwhichthatlimitedinstrument—ourbrain—works.Thisbrainispartofthatrealitythatconsequentlydependsontheinteractionbetweenanexternalworldandthestructureswithwhichthemindoperates.Butthemindistheworkingofourbrain.What(little)weare

beginningtounderstandofthisfunctioningisthatourentirebrainoperatesonthebasisofacollectionoftracesofthepastleftinthe

synapsesthatconnectneurons.Synapsesarecontinuallyformedintheirthousandsandthenerased—especiallyduringsleep,leavingbehindablurryreflectionofthatwhichhasactedonournervoussysteminthepast.Ablurredimage,nodoubt—thinkofhowmanymillionsofdetailsoureyesseeeverymomentthatdonotstayinourmemory—butonewhichcontainsworlds.Boundlessworlds.TheyarethoseworldsthattheyoungMarcelrediscovers,bewildered,

everymorning,inthefirstpagesofRemembranceofThingsPast,inthevertigoofthemomentwhenconsciousnessemergeslikeabubblefromunfathomabledepths.117ThatworldofwhichvastterritoriesarethenrevealedtohimwhenthetasteofthemadeleinebringsbacktohimtheflavorofCombray.Avastworld,amapofwhichProustslowlyunfoldsduringthecourseofthethreethousandpagesofhisgreatnovel.Anovel,itshouldbenoted,thatisnotanarrativeofeventsintheworldbutanaccountofwhat’sinsidethememoryofasingleperson.Fromthefragranceofthemadeleineatthebeginning,tothelastword—“time”—ofitsfinalpart,“TimeRegained,”thebookisnothingbutadisordered,detailedmeanderingamongthesynapsesofMarcel’sbrain.Proustfindsalimitlessspaceandanincrediblethrongofdetails,

fragrances,considerations,sensations,reflections,re-elaborations,colors,objects,names,looks,emotions...allwithinthefoldsofthebrainbetweentheearsofMarcel.Thisistheflowoftimefamiliarfromourexperience:itisinsidetherethatitnestles,insideofus,intheutterlycrucialpresenceoftracesofthepastinourneurons.Proustcouldnotbemoreexplicitonthismatter,writinginthefirst

book:“Realityisformedonlybymemory.”118Andmemory,initsturn,isacollectionoftraces,anindirectproductofthedisorderingoftheworld,ofthatsmallequationwrittenearlier,ΔS≥0,theonethattellsusthestateoftheworldwasina“particular”configurationinthepastandthereforehasleft(andleaves)traces.“Particular,”thatis,perhapsonlyinrelationtoraresubsystems—ourselvesincluded.Wearestories,containedwithinthetwentycomplicatedcentimeters

behindoureyes,linesdrawnbytracesleftbythe(re)minglingtogetherofthingsintheworld,andorientedtowardpredictingeventsinthefuture,towardthedirectionofincreasingentropy,inaratherparticularcornerofthisimmense,chaoticuniverse.

Thisspace—memory—combinedwithourcontinuousprocessofanticipation,isthesourceofoursensingtimeastime,andourselvesasourselves.119Thinkaboutit:ourintrospectioniseasilycapableofimaginingitselfwithouttherebeingspaceormatter,butcanitimagineitselfnotexistingintime?120

Itiswithrespecttothatphysicalsystemtowhichwebelong—duetothepeculiarwayinwhichitinteractswiththerestoftheworld,thankstothefactthatitallowstracesandbecausewe,asphysicalentities,consistofmemoryandanticipation—thattheperspectiveoftimeopensupforus,likeoursmall,litclearing.121Timeopensupourlimitedaccesstotheworld.122Time,then,istheforminwhichwebeings,whosebrainsaremadeupessentiallyofmemoryandforesight,interactwiththeworld:itisthesourceofouridentity.123

Andofoursufferingaswell.Buddhasummedthisupinafewmaximsthatmillionsofhuman

beingshaveadoptedasthefoundationsoftheirlives:birthissuffering,declineissuffering,illnessissuffering,deathissuffering,unionwiththatwhichwehateissuffering,separationfromthatwhichweloveissuffering,failuretoobtainwhatwedesireissuffering.124It’ssufferingbecausewemustlosewhatwehaveandareattachedto.Becauseeverythingthatbeginsmustend.Whatcausesustosufferisnotinthepastorthefuture:itishere,now,inourmemory,inourexpectations.Welongfortimelessness,weendurethepassingoftime:wesuffertime.Timeissuffering.Suchistime,andbecauseofthiswearefascinatedandtroubledbyit

inequalmeasure—andperhapsbecauseofthis,too,dearreader,mybrother,mysister,youareholdingthisbookinyourhands.Becauseitisnothingbutafleetingstructureoftheworld,anephemeralfluctuationinthehappeningoftheworld,thatwhichiscapableofgivingrisetowhatweare:beingsmadeoftime.Thattowhichweoweourbeing,givingusthepreciousgiftofourveryexistence,allowingustocreatethefleetingillusionofpermanencethatistheoriginofalloursuffering.ThemusicofStraussandthewordsofHofmannsthalsingofthiswith

devastatingdelicacy:125

Irememberalittlegirl...Buthowcanthatbe...

OnceIwasthatlittleResi,andthenonedayIbecameanoldwoman?...IfGodwillsitso,whyallowmetoseeit?

Whydoesn’thehideitfromme?Everythingisamystery,suchadeepmystery...

Ifeelthefragilityofthingsintime.Fromthebottomofmyheart,Ifeelweshouldclingtonothing.

Everythingslipsthroughourfingers.Allthatweseektoholdontodissolves.

Everythingvanishes,likemistanddreams...Timeisastrangething.

Whenwedon’tneedit,itisnothing.Then,suddenly,thereisnothingelse.

Itiseverywherearoundus.Alsowithinus.Itseepsintoourfaces.

Itseepsintothemirror,runsthroughmytemples...BetweenyouandIitrunssilently,likeanhourglass.

Oh,QuinQuin.SometimesIfeelitflowinginexorably.

SometimesIgetupinthemiddleofthenightandstopalltheclocks...

13 THESOURCEOFTIME

PerhapsGodhasmanymoreseasonsinstoreforus—orperhapsthelastistobethiswinterthatguidesbackthewavesoftheTyrrhenianSeatobreakagainsttheroughpumicecliffs.Youmustbewise.Pourthewineandencloseinthisbriefcircleyourlong-cherishedhope.(I,11)

Westartedoutwiththeimageoftimethatisfamiliartous:somethingthatflowsuniformlyandequallythroughouttheuniverse,inthecourseofwhichallthingshappen.Withtheideathatthereexiststhroughoutthecosmosapresent,a“now”thatconstitutesreality.Thepastforeveryoneisfixed,isgone,havingalreadyhappened.Thefutureisopen,yettobedetermined.Realityflowsfromthepast,throughthepresent,towardthefuture—andtheevolutionofthingsbetweenpastandfutureisintrinsicallyasymmetrical.This,wethought,isthebasicstructureoftheworld.Thisfamiliarpicturehasfallenapart,hasshownitselftobeonlyan

approximationofamuchmorecomplexreality.Apresentthatiscommonthroughoutthewholeuniversedoesnot

exist(chapter3).Eventsarenotorderedinpasts,presents,andfutures;theyareonly“partially”ordered.Thereisapresentthatisneartous,butnothingthatis“present”inafar-offgalaxy.Thepresentisalocalizedratherthanaglobalphenomenon.Thedifferencebetweenpastandfuturedoesnotexistinthe

elementaryequationsthatgoverneventsintheworld(chapter2).It

issuesonlyfromthefactthat,inthepast,theworldfounditselfsubjecttoastatethat,withourblurredtakeonthings,appearsparticulartous.Locally,timepassesatdifferentspeedsaccordingtowhereweareand

atwhatspeedweourselvesaremoving.Thecloserwearetoamass(chapter1),orthefasterwemove(chapter3),themoretimeslowsdown:thereisnosingledurationbetweentwoevents;therearemanypossibleones.Therhythmsatwhichtimeflowsaredeterminedbythegravitational

field,arealentitywithitsowndynamicthatisdescribedintheequationsofEinstein.Ifweoverlookquantumeffects,timeandspaceareaspectsofagreatjellyinwhichweareimmersed(chapter4).Buttheworldisaquantumone,andgelatinousspacetimeisalsoan

approximation.Intheelementarygrammaroftheworld,thereisneitherspacenortime—onlyprocessesthattransformphysicalquantitiesfromonetoanother,fromwhichitispossibletocalculateprobabilitiesandrelations(chapter5).Atthemostfundamentallevelthatwecurrentlyknowof,therefore,

thereislittlethatresemblestimeasweexperienceit.Thereisnospecialvariable“time,”thereisnodifferencebetweenpastandfuture,thereisnospacetime(PartTwo).Westillknowhowtowriteequationsthatdescribetheworld.Inthoseequations,thevariablesevolvewithrespecttoeachother(chapter8).Itisnota“static”world,ora“blockuniverse”whereallchangeisillusory(chapter7):onthecontrary,oursisaworldofeventsratherthanofthings(chapter6).Thiswastheoutwardlegofthejourney,towardauniversewithout

time.Thereturnjourneyhasbeentheattempttounderstandhow,fromthis

worldwithouttime,itispossibleforourperceptionoftimetoemerge(chapter9).Thesurprisehasbeenthat,intheemergenceoffamiliaraspectsoftime,weourselveshavehadaroletoplay.Fromourperspective—theperspectiveofcreatureswhomakeupasmallpartoftheworld—weseethatworldflowingintime.Ourinteractionwiththeworldispartial,whichiswhyweseeitinablurredway.Tothisblurringisaddedquantumindeterminacy.Theignorancethatfollowsfromthisdeterminestheexistenceofaparticularvariable—thermaltime(chapter9)—andofanentropythatquantifiesouruncertainty.

Perhapswebelongtoaparticularsubsetoftheworldthatinteractswiththerestofitinsuchawaythatthisentropyislowerinonedirectionofourthermaltime.Thedirectionalityoftimeisthereforerealbutperspectival(chapter10):theentropyoftheworldinrelationtousincreaseswithourthermaltime.Weseetheoccurrenceofthingsorderedinthisvariable,whichwesimplycall“time,”andthegrowthofentropydistinguishesthepastfromthefutureforusandleadstotheunfoldingofthecosmos.Itdeterminestheexistenceoftraces,residues,andmemoriesofthepast(chapter11).Wehumanbeingsareaneffectofthisgreathistoryoftheincreaseofentropy,heldtogetherbythememorythatisenabledbythesetraces.Eachoneofusisaunifiedbeingbecausewereflecttheworld,becausewehaveformedanimageofaunifiedentitybyinteractingwithourkind,andbecauseitisaperspectiveontheworldunifiedbymemory(chapter12).Fromthiscomeswhatwecallthe“flowing”oftime.Thisiswhatwearelisteningtowhenwelistentothepassingoftime.Thevariable“time”isoneofmanyvariablesthatdescribetheworld.It

isoneofthevariablesofthegravitationalfield(chapter4):atourscale,wedonotregisterquantumfluctuations(chapter5),henceitispossibletothinkofspacetimeasdetermined,asEinstein’sgreatmollusk;atourscale,themovementsofthemolluskaresmallandcanbeoverlooked.Hencewecanthinkofspacetimeasbeingasrigidasatable.Thistablehasdimensions:theonethatwecallspace,andtheonealongwhichentropygrows,calledtime.Inoureverydaylifewemoveatlowspeedsinrelationtothespeedoflightandsowedonotperceivethediscrepanciesbetweenthedifferentpropertimesofdifferentclocks,andthedifferencesinspeedatwhichtimepassesatdifferentdistancesfromamassaretoosmallforustodistinguish.Intheend,therefore,insteadofmanypossibletimes,wecanspeak

onlyofasingletime:thetimeofourexperience—uniform,universal,andordered.Thisistheapproximationofanapproximationofanapproximationofadescriptionoftheworldmadefromourparticularperspectiveashumanbeingswhoaredependentonthegrowthofentropy,anchoredtotheflowingoftime.Weforwhom,asEcclesiastes126

hasit,thereisatimetobebornandatimetodie.Thisistimeforus:amultilayered,complexconceptwithmultiple,

distinctpropertiesderivingfromvariousdifferentapproximations.

Manydiscussionsoftheconceptoftimeareconfusedbecausetheysimplydonotrecognizeitscomplexandmultilayeredaspect.Theymakethemistakeofnotseeingthatthedifferentlayersareindependent.ThisisthephysicalstructureoftimeasIunderstandit,afteralifetime

ofrevolvingaroundit.Manypartsofthisstoryaresolid,othersplausible,othersstillare

guesseshazardedinanattemptatunderstandingthewhole.Practicallyallthethingsrecountedinthefirstpartofthebookhave

beenascertainedfrominnumerableexperiments:theslowingdownoftimeaccordingtoaltitudeandspeed;thenonexistenceofthepresent;therelationbetweentimeandthegravitationalfield;thefactthattherelationsbetweendifferenttimesaredynamic,thatelementaryequationsdonotrecognizethedirectionoftime;therelationbetweenentropyandblurring.Allthishasbeenwellascertained.127

Thatthegravitationalfieldhasquantumpropertiesisasharedconviction,albeitonecurrentlysupportedonlybytheoreticalargumentsratherthanbyexperimentalevidence.Theabsenceofthetimevariablefromthefundamentalequations,as

discussedinPartTwo,isplausible—butontheformoftheseequationsdebatestillrages.Theoriginoftimepertainingtoquantumnoncommutativity,ofthermaltime,andthefactthattheincreaseinentropywhichweobservedependsonourinteractionwiththeuniverseareideasthatIfindfascinatingbutarefarfrombeingconfirmedorwidelyaccepted.Whatisentirelycredible,inanycase,isthegeneralfactthatthe

temporalstructureoftheworldisdifferentfromthenaïveimagethatwehaveofit.Thisnaïveimageissuitableforourdailylife,butit’snotsuitableforunderstandingtheworldinitsminutefolds,orinitsvastness.Inalllikelihood,itisnotevensufficientforunderstandingourownnature,becausethemysteryoftimeintersectswiththemysteryofourpersonalidentity,withthemysteryofconsciousness.Themysteryoftimehasalwaystroubledus,stirringdeepemotions.So

deepastohavenourishedphilosophiesandreligions.Ibelieve,asHansReichenbachsuggestsinoneofthemostlucidbooks

onthenatureoftime,TheDirectionofTime,thatitwasinordertoescapefromtheanxietytimecausesusthatParmenideswantedtodenyitsexistence,thatPlatoimaginedaworldofideasthatexistoutsideofit,

andthatHegelspeaksofthemomentinwhichtheSpirittranscendstemporalityandknowsitselfinitsplenitude.Itisinordertoescapethisanxietythatwehaveimaginedtheexistenceof“eternity,”astrangeworldoutsideoftimethatwewouldliketobeinhabitedbygods,byaGod,orbyimmortalsouls.*Ourdeeplyemotionalattitudetowardtimehascontributedmoretotheconstructionofcathedralsofphilosophythanhaslogicorreason.Theoppositeemotionalattitude,thevenerationoftime—HeraclitusorBergson—hasgivenrisetojustasmanyphilosophies,withoutgettingusanynearertounderstandingwhattimeis.Physicshelpsustopenetratelayersofthemystery.Itshowshowthe

temporalstructureoftheworldisdifferentfromourperceptionofit.Itgivesusthehopeofbeingabletostudythenatureoftimefreefromthefogcausedbyouremotions.Butinoursearchfortime,advancingincreasinglyawayfrom

ourselves,wehaveendedupbydiscoveringsomethingaboutourselves,perhaps—justasCopernicus,bystudyingthemovementsoftheheavens,endedupunderstandinghowtheEarthmovedbeneathhisfeet.Perhaps,ultimately,theemotionaldimensionoftimeisnotthefilmofmistthatpreventsusfromapprehendingthenatureoftimeobjectively.Perhapstheemotionoftimeispreciselywhattimeisforus.Idon’tthinkthereismuchmorethanthistobeunderstood.Wemay

askfurtherquestions,butweshouldbecarefulwithquestionsthatitisnotpossibletoformulateproperly.Whenwehavefoundalltheaspectsoftimethatcanbespokenof,thenwehavefoundtime.Wemaygestureclumsilytowardanimmediatesenseoftimebeyondwhatwecanarticulate(“Fine,butwhydoesit‘pass’?”),butIbelievethatatthispointwearemerelyconfusingmatters,attemptingillegitimatelytotransformapproximatewordsintothings.Whenwecannotformulateaproblemwithprecision,itisoftennotbecausetheproblemisprofound:it’sbecausetheproblemisfalse.Willwebeabletounderstandthingsbetterinthefuture?Ithinkso.

Ourunderstandingofnaturehasincreasedvertiginouslyoverthecourseofcenturies,andwearecontinuingtolearn.Weareglimpsingsomethingaboutthemysteryoftime.Wecanseetheworldwithouttime:wecanperceivewiththemind’seyetheprofoundstructureoftheworldwheretimeasweknowitnolongerexists—liketheFoolontheHillwhoseestheEarthturnwhenheseesthesettingsun.Andwebegintoseethatweare

time.Wearethisspace,thisclearingopenedbythetracesofmemoryinsidetheconnectionsbetweenourneurons.Wearememory.Wearenostalgia.Wearelongingforafuturethatwillnotcome.Theclearingthatisopenedupinthisway,bymemoryandbyanticipation,istime:asourceofanguishsometimes,butintheendatremendousgift.Apreciousmiraclethattheinfiniteplayofcombinationshasunlocked

forus,allowingustoexist.Wemaysmilenow.Wecangobacktoserenelyimmersingourselvesintime—inourfinitetime—tosavoringtheclearintensityofeveryfleetingandcherishedmomentofthebriefcircleofourexistence.

THESISTEROFSLEEP

Thebriefarcofourdays,OSestius,preventsusfromlaunchingprolongedhopes.(I,4)

InthethirdpartofthegreatIndianepictheMahābhārata,apowerfulspiritnamedYaksaaskstheoldestandwisestofthePandava,Yudhistira,whatisthegreatestofallmysteries.Theanswergivenresoundsacrossmillennia:“Everydaycountlesspeopledie,andyetthosewhoremainliveasiftheywereimmortals.”128

IwouldnotwishtoliveasifIwereimmortal.Idonotfeardeath.Ifearsuffering.AndIfearoldage,thoughlesssonowthatIamwitnessingthetranquilandpleasantoldageofmyfather.Iamafraidoffrailty,andoftheabsenceoflove.Butdeathdoesnotalarmme.ItdidnotscaremewhenIwasyoung,andIthoughtatthetimethatthiswasbecauseitwassucharemoteprospect.Butnow,atsixty,thefearhasyettoarrive.Ilovelife,butlifeisalsostruggle,suffering,pain.Ithinkofdeathasakintoawell-earnedrest.Thesisterofsleep,Bachcallsit,inhismarvelouscantataBWV56.Akindlysister,whowillcomequicklytoclosemyeyesandcaressmyhead.Jobdiedwhenhewas“fullofdays.”It’sawonderfulexpression.I,too,

wouldliketoarriveatthepointoffeeling“fullofdays,”andtoclosewithasmilethebriefcirclethatisourlife.Icanstilltakepleasureinit,yes;stillenjoythemoonreflectedonthesea,thekissesofthewomanIlove,herpresencethatgivesmeaningtoeverything;stillsavorthoseSundayafternoonsathomeinwinter,lyingonthesofafillingpageswithsymbolsandformulae,dreamingofcapturinganothersmallsecretfromamongthethousandsthatstillsurroundus....Iliketolookforwardtostilltastingfromthisgoldenchalice,tolifethatisteeming,bothtenderand

hostile,clearandinscrutable,unexpected....ButIhavealreadydrunkdeepofthebittersweetcontentsofthischalice,andifanangelweretocomeformerightnow,saying,“Carlo,it’stime,”Iwouldnotasktobeleftevenlongenoughtofinishthissentence.Iwouldjustsmileupathimandfollow.Ourfearofdeathseemstometobeanerrorofevolution.Many

animalsreactinstinctivelywithterrorandflightattheapproachofapredator.Itisahealthyreaction,onethatallowsthemtoescapefromdanger.Butit’saterrorthatlastsaninstant,notsomethingthatremainswiththemconstantly.Naturalselectionhasproducedthesebigapeswithhypertrophicfrontallobes,withanexaggeratedabilitytopredictthefuture.It’saprerogativethat’scertainlyusefulbutonethathasplacedbeforeusavisionofourinevitabledeath,andthistriggerstheinstinctofterrorandflight.Basically,Ibelievethatthefearofdeathistheresultofanaccidentalandclumsyinterferencebetweentwodistinctevolutionarypressures—theproductofbadautomaticconnectionsinourbrainratherthansomethingthathasanyuseormeaning.Everythinghasalimitedduration,eventhehumanraceitself.(“TheEarthhaslostitsyouthfulness;itispast,likeahappydream.Noweverydaybringsusclosertodestruction,todesert,”asVyasahasitintheMahābhārata.129)Fearingthetransition,beingafraidofdeath,islikebeingafraidofrealityitself;likebeingafraidofthesun.Whateverfor?Thisistherationalversion.Butourlivesarenotdrivenbyrational

arguments.Reasonhelpsustoclarifyideas,todiscovererrors.Butthatsamereasonalsoshowsusthatthemotivesbywhichweactareinscribedinourintimatestructureasmammals,ashunters,associalbeings:reasonilluminatestheseconnections,itdoesnotgeneratethem.Wearenot,inthefirstplace,reasoningbeings.Wemayperhapsbecomeso,moreorless,inthesecond.Inthefirstinstance,wearedrivenbyathirstforlife,byhunger,bytheneedtolove,bytheinstincttofindourplaceinhumansociety....Thesecondinstancedoesnotevenexistwithoutthefirst.Reasonarbitratesbetweeninstinctsbutusestheverysameinstinctsasprimarycriteriainitsarbitration.Itgivesnamestothingsandtothisthirst,itallowsustoovercomeobstacles,toseethingsthatarehidden.Itallowsustorecognizetheinnumerableinefficientstrategies,mistakenbeliefs,andprejudicesthatwehave.Ithasdevelopedtohelpusunderstandthatthetrackswefollow,thinkingthattheywillleadtothe

antelopeswearehunting,areinfactfalsetrails.Butwhatdrivesusisnotreflectingonlife:itislifeitself.Sowhatreallydrivesus?Itisdifficulttosay.Perhapswedonotknow

entirely.Werecognizemotivationsinourselves.Wegivenamestothesemotivations,andwehavemanyofthem.Webelievethatwesharesomeofthemwithotheranimals;othersonlywithhumankind—andothersstillwithsmallergroupstowhichweseeourselvesasbelonging.Hungerandthirst,curiosity,theneedforcompanionship,thedesiretolove,beinginlove,thepursuitofhappiness,theneedtofightforapositionintheworld,thedesiretobeappreciated,recognized,andloved;loyalty,honor,theloveofGod,thethirstforjusticeandliberty,thedesireforknowledge...Wheredoesallthiscomefrom?Fromthewaythatwearemade,from

whatwehappentobe.Wearetheproductsofalongselectionprocessofchemical,biological,andculturalstructuresthatatdifferentlevelshaveinteractedforalongtimeinordertoshapethefunnyprocessthatweare.Aboutwhichweunderstandverylittle,byreflectingonourselves,bylookingatourselvesinthemirror.Wearemorecomplexthanourmentalfacultiesarecapableofgrasping.Thehypertrophyofourfrontallobesisconsiderable,andhastakenustothemoon,allowedustodiscoverblackholes,andtorecognizethatwearecousinsofladybugs.Butitisstillnotenoughtoallowustoexplainourselvesclearlytoourselves.Wearenotevenclearaboutwhatitmeans“tounderstand.”Weseethe

worldandwedescribeit:wegiveitanorder.Weknowlittleoftheactualrelationbetweenwhatweseeoftheworldandtheworlditself.Weknowthatwearemyopic.Webarelyseejustatinywindowofthevastelectromagneticspectrumemittedbythings.Wedonotseetheatomicstructureofmatter,northecurvatureofspace.Weseeacoherentworldthatweextrapolatefromourinteractionwiththeuniverse,organizedinsimplistictermsthatourdevastatinglystupidbrainiscapableofhandling.Wethinkoftheworldintermsofstones,mountains,clouds,andpeople,andthisis“theworldforus.”Abouttheworldindependentofusweknowagooddeal,withoutknowinghowmuchthisgooddealis.Ourthinkingispreytoitsownweakness,butevenmoresotoitsown

grammar.Ittakesonlyafewcenturiesfortheworldtochange:fromdevils,angels,andwitchestoatomsandelectromagneticwaves.Ittakesonlyafewgramsofmushroomsforthewholeofrealitytodissolvebefore

oureyes,beforereorganizingitselfintoasurprisinglydifferentform.Itonlytakestheexperienceofspendingtimewithafriendwhohassufferedaseriousschizophrenicepisode,afewweekswithherstrugglingtocommunicate,torealizethatdeliriumisavasttheatricalequipmentwiththecapacitytostagetheworld,andthatitisdifficulttofindargumentstodistinguishitfromthosegreatcollectivedeliriumsofoursthatarethefoundationsofoursocialandspirituallife,andofourunderstandingoftheworld.Aside,perhaps,fromsolitude—andthefragilityofthosewhodetachthemselvesfromthecommonplaceorderofthings...130Thevisionofrealityandthecollectivedeliriumthatwehaveorganizedhasevolvedandhasturnedouttohaveworkedreasonablywellingettingustothispoint.Theinstrumentsthatwehavefoundfordealingwithitandattendingtoithavebeenmany,andreasonhasrevealeditselftobeamongthebestofthese.Itisprecious.Butitisonlyaninstrument,apincer.Weuseittohandleasubstance

thatismadeoffireandice:somethingthatweexperienceaslivingandburningemotions.Thesearethesubstancesofwhichwearemade.Theypropelusandtheydragusback,andwecloakthemwithfinewords.Theycompelustoact.Andsomethingofthemalwaysescapesfromtheorderofourdiscourses,sinceweknowthat,intheend,everyattempttoimposeorderleavessomethingoutsidetheframe.Anditseemstomethatlife,thisbrieflife,isnothingotherthanthis:

theincessantcryoftheseemotionsthatdriveus,thatwesometimesattempttochannelinthenameofagod,apoliticalfaith,inaritualthatreassuresusthat,fundamentally,everythingisinorder,inagreatandboundlesslove—andthecryisbeautiful.Sometimesitisacryofpain.Sometimesitisasong.Andsong,asAugustineobserved,istheawarenessoftime.Itistime.It

isthehymnoftheVedasthatisitselfthefloweringoftime.131IntheBenedictusofBeethoven’sMissaSolemnis,thesongoftheviolinispurebeauty,puredesperation,purejoy.Wearesuspended,holdingourbreath,feelingmysteriouslythatthismustbethesourceofmeaning.Thatthisisthesourceoftime.Thenthesongfadesandceases.“Thesilverthreadisbroken,the

goldenbowlisshattered,theamphoraatthefountainbreaks,thebucketfallsintothewell,theearthreturnstodust.”132Anditisfinelikethis.We

cancloseoureyes,rest.Thisallseemsfairandbeautifultome.Thisistime.

IMAGECREDITS

Here,here,here,here,andhere:©Peyo-2017LicensedthroughI.M.P.S(Brussels)—www.smurf.com

Here:LudwigBoltzmann,lithographbyRodolfFenzi(1989)©HultonArchive/GettyImages

Here(right-handside):JohannesLichtenberger,sculpturebyConradSifer(1493),sundialoftheCathedralofStrasbourg©GiliardiPhotoLibrary

Here:bustofAristotle©DeAgostini/GettyImages

Here:IsaacNewton,sculpturebyEdwardHodgesBaily(1828),afterLouis-FrançoisdeRoubiliac(1751),NationalPortraitGallery,London©NationalPortraitGallery,London/FotoScala,Florence

Here:ThomasThiemann,DynamicofQuantumSpinFoam,seenthroughtheeyesofanartist©ThomasThiemann(FAUErlangen),MaxPlanckInstituteforGravitationalPhysics(AlbertEinsteinInstitute),MildeMarketingScienceCommunication,exozeteffects

Here:HildegardvonBingen,LiberDivinorumOperum,CodexLatinus1942(XIIIcentury),c.9r,BiblioteccaStatale,Lucca©FotoScala,Florence—bycourtesyoftheMinistryofCulturalHeritageandActivities

NOTES

PERHAPSTIMEISTHEGREATESTMYSTERY

1.Aristotle,MetaphysicsI.2.982.

2.Thelayeringofthenotionoftimeisdiscussedindepth,forexample,inJ.T.Fraser,OfTime,Passion,andKnowledge(NewYork:Braziller,1975).

3.ThephilosopherMauroDoratohasinsistedonthenecessitytorendertheelementaryconceptualframeworkofphysicscoherentwithourexperience;seeMauroDorato,Checos’èiltempo?(Rome:Carocci,2013).

1.LOSSOFUNITY

4.Thisistheessenceofthetheoryofgeneralrelativity.AlbertEinstein,“DieGrundlagederalgemeinenRelativitätstheorie,”AnnalenderPhysik49(1916):769–822.

5.Intheapproximationofaweakfield,themetricscanbewrittends2=(1+2ϕ(x))dt²–dx²,whereϕ(x)isthepotentialofNewton.Newtoniangravityfollowsfromthesolemodificationofthetemporalcomponentofthemetricsgoo,thatis,fromthelocalslowingdownoftime.Thegeodesicsofthesemetricsdescribethefallofbodies:theybendtowardthelowestpotentiality,wheretimeslows.(Theseandsimilarnotesareforthosewhohavesomefamiliaritywiththeoreticalphysics.)

6.CarloRovelli,Checos’èlascienza:LarivoluzionediAnassimandro(Milan:Mondadori,2011);Englishtranslation,TheFirstScientist:AnaximanderandHisLegacy(Chicago:Westholme,2011).

7.Forexample:(ttable−tground)=gh/c2tgroundwherecisthespeedoflight,g=9.8m/s

2istheaccelerationofGalileo,andhistheheightofthetable.

8.Theycanalsobewrittenwithasinglevariable,t,the“temporalcoordinate,”butthisdoesnotindicatethetimemeasuredbyaclock(determinedbyds,notbydt)andmaybechangedarbitrarilywithoutchangingtheworlddescribed.Thistdoesnotrepresentaphysicalquantity.Whatclocksmeasureisthepropertimealongalineoftheuniverseγ,givenbytγ=∫γ√gab(x)dx

adxb.Thephysicalrelationbetweenthisquantityandgab(x)isdiscussedfurtheron.

2.LOSSOFDIRECTION

9.RainerMariaRilke,DuineserElegien,inSämtlicheWerke,vol.1,I,vv.83–85(Frankfurt:Insel,1955).

10.TheFrenchRevolutionwasanextraordinarymomentofscientificvitalityinwhichthebasesofchemistry,biology,analyticmechanics,andmuchelsewerefounded.Thesocialrevolutionwenthandinhandwiththescientificone.ThefirstrevolutionarymayorofPariswasanastronomer;LazareCarnotwasamathematician;Maratconsideredhimselftobe,aboveallelse,aphysicist.AntoineLavoisierwasactiveinpolitics.ThemathematicianJoseph-LouisLagrangewashonoredbythedifferentgovernmentsthatsucceededeachotherinthattormentedandmagnificentmomentinthehistoryofhumanity.SeeSteveJones,RevolutionaryScience:TransformationandTurmoilintheAgeoftheGuillotine(NewYork:Pegasus,2017).

11.Changingwhatisopportune:forinstance,thesignofthemagneticfieldintheequationsofMaxwell,chargeandparityofelementaryparticles,etc.ItistheinvarianceunderCPT(Charge,Parity,andTimereversalsymmetry)thatisrelevant.

12.TheequationsofNewtondeterminehowthingsaccelerate,andtheaccelerationdoesnotchangeifIprojectafilmbackward.Theaccelerationofastonethrownupwardisthesameasthatofafallingstone.IfIimagineyearsrunningbackward,themoonturnsaroundtheEarthintheoppositedirectionbutappearsequallyattractedtotheEarth.

13.Theconclusiondoesnotchangebyaddingquantumgravity.Ontheeffortstofundtheoriginofthedirectionoftime,see,forexample,H.D.Zeh,DiePhysikderZeitrichtung(Berlin:Springer,1984).

14.RudolfClausius,“ÜberverschiedenefürdieAnwendungbequemeFormenderHauptgleichungendermechanischenWärmetheorie,”AnnalenderPhysik125(1865):353–400;390.

15.Inparticularasaquantityofheatthatescapesfromabodydividedbytemperature.Whentheheatescapesfromahotbodyandentersacoldone,thetotalentropyincreasesbecausethedifferenceintemperaturemakesitsothattheentropyduetoheatthatescapesislessthanthatowedtotheheatthatenters.Whenallthebodiesreachthesametemperature,theentropyhasreacheditsmaximum:equilibriumhasbeenreached.

16.ArnoldSommerfeld.

17.WilhelmOstwald.

18.Thedefinitionofentropyrequiresacoarsegraining,thatistosay,thedistinctionbetweenmicrostatesandmacrostates.Theentropyofamacrostateisdeterminedbythenumberofcorrespondingmicrostates.Inclassicthermodynamics,thecoarsegrainingisdefinedthemomentitisdecidedtotreatsomevariablesofthesystemas“manipulable”or“measurable”fromoutside(thevolumeorpressureofagas,forinstance).Amacrostateisdeterminedbyfixingthesemacroscopicvariables.

19.Thatistosay,inadeterministicmannerifyouoverlookquantummechanics,andinaprobabilisticmannerifyoutakeaccountofquantummechanicsinstead.Inbothcases,inthesamewayforthefutureasforthepast.

20.S=klogW.Sistheentropy,Wisthenumberofmicroscopicstates,orthecorrespondingvolumeofphasespace,andkisjustaconstant,todaycalledBoltzmann’sconstant,thatadjuststhe(arbitrary)dimensions.

3.THEENDOFTHEPRESENT

21.Generalrelativity(A.Einstein,“DieGrundlagederalgemeinenRelativitätstheorie,”op.cit.).

22.Specialrelativity(AlbertEinstein,“ZurElektrodynamikbewegterKörper,”AnnalenderPhysik17[1905]:891–921).

23.J.C.HafeleandRichardE.Keating,“Around-the-WorldAtomicClocks:ObservedRelativisticTimeGains,”Science177(1972):168–70.

24.Thatdependsasmuchontasonyourspeedandposition.

25.Poincaré.Lorentzhadtriedtogiveaphysicalinterpretationtot,butinaquiteconvolutedway.

26.EinsteinfrequentlymaintainedthattheexperimentsofMichelsonandMorleywereofnoimportanceinallowinghimtoarriveatspecialrelativity.Ibelievethistobetrue,andthatitillustratesanimportantfactorinthephilosophyofscience.Inordertomakeadvancesinourunderstandingoftheworld,itisnotalwaysnecessarytohavenewdata.CopernicushadnomoreobservationaldatathanPtolemy:hewasabletodeduceheliocentrismfromthedataavailabletoPtolemybyinterpretingitbetter—asEinsteindidwithregardtoMaxwell.

27.IfIseemysisterthroughatelescopecelebratinghertwentiethbirthdayandsendheraradiomessagethatwillarriveonhertwenty-eighthbirthday,Icansaythatnowishertwenty-fourthbirthday:halfwaybetweenwhenthelightdepartedfromthere(20)andwhenitreturned(28).It’saniceidea(notmine:it’sEinstein’sdefinitionof“simultaneity”).Butthisdoesnotdefineacommontime.IfProximabismovingaway,andmysisterusesthesamelogictocalculatethemomentsimultaneoustohertwenty-fourthbirthday,shedoesnotobtainthepresentmomenthere.Inotherwords,inthiswayofdefiningsimultaneity,ifformeamomentAinherlifeissimultaneouswithamomentBinmine,thecontraryisnotthecase:forher,AandBarenotsimultaneous.Ourdifferentspeedsdefinedifferentsurfacesofsimultaneity.Noteveninthiswaydoweobtainanotionofacommon“present.”

28.Thecombinationofeventsthatareatspacelikedistancefromhere.

29.AmongthefirsttorealizethiswasKurtGödel;see“AnExampleofaNewTypeofCosmologicalSolutionsofEinstein’sFieldEquationsofGravitation,”ReviewsofModernPhysics21(1949):447–50.Inhisownwords:“Thenotionof‘now’isnothingmorethanacertainrelationbetweenacertainobserverandtherestoftheuniverse.”

30.Transitive.

31.Eventheexistenceofarelationofpartialordermightbetoostrongwithregardtoreality,ifclosedtemporalcurvesexist.Onthissubjectsee,forexample,MarcLachièze-Rey,Voyagerdansletemp:LaPhysiquemoderneetlatemporalité,(Paris:EditionsduSeuil,2013).

32.Thefactthatthereisnothinglogicallyimpossibleabouttravelstothepastisdemonstratedclearlyinanengagingarticlebyoneofthegreatphilosophersofthelastcentury:DavidLewis,“TheParadoxesofTimeTravel,”AmericanPhilosophicalQuarterly13(1976):145–52,reprintedinThePhilosophyofTime,eds.R.LePoidevinandM.MacBeath(Oxford:OxfordUniversityPress,1993).

33.ThisistherepresentationofthecausalstructureofablackholemetricinEddington-Finkelsteincoordinates.

34.Amongthedissentingvoices,therearethoseoftwogreatscientistsforwhomIhaveaparticularfriendship,affection,andadmiration:LeeSmolin(TimeReborn[Boston:HoughtonMifflinHarcourt,2013])andGeorgeEllis(“OntheFlowofTime,”FqxiEssay,2008,https://arxiv.org/abs/0812.0240;“TheEvolvingBlockUniverseandtheMeshingTogetherofTimes,”AnnalsoftheNewYorkAcademyofSciences1326[2014]:26–41;HowCanPhysicsUnderlietheMind?[Berlin:Springer,2016]).Bothinsistthattheremustexistaprivilegedtimeandarealpresent,evenifthesearenotcapturedbycurrentphysics.Scienceislikeaffection:thosewhoaredearesttousarethosewithwhomwehavetheliveliestdisagreements.AnarticulatedefenseofthefundamentalaspectoftherealityoftimecanbefoundinRobertoM.UngerandLeeSmolin,TheSingularUniverseandtheRealityofTime(Cambridge,UK:CambridgeUniversityPress,2015).ThepointofviewofSmolinandEllisisdefensible.Butisitfruitful?Thechoiceisbetweenforcingthedescriptionoftheworldsothatitadaptstoourintuition,orlearninginsteadtoadaptourintuitiontowhatwehavediscoveredabouttheworld.Ihavefewdoubtsthatthesecondstrategyisthemostfruitfulone.

4.LOSSOFINDEPENDENCE

35.Ontheeffectsofdrugsontimeperception,seeR.A.Sewelletal.,“AcuteEffectsofTHConTimePerceptioninFrequentandInfrequentCannabisUsers,”Psychopharmacology226(2013):401–13;thedirectexperienceisastonishing.

36.ValtteriArstila,“TimeSlowsDownduringAccidents,”FrontiersinPsychology3(2012):196.

37.Inourcultures.Thereareotherswithaprofoundlydifferentnotionoftime:D.L.Everett,Don’tSleep,ThereareSnakes,(NewYork:Pantheon,2008).

38.Matthew20:1–16.

39.PeterGalison,Einstein’sClocks,Poincaré’sMaps(NewYork:Norton,2003),p.126.

40.AnexcellentpanoramichistoryofthewayinwhichtechnologyhasprogressivelymodifiedourconceptoftimecanbefoundinAdamFrank,AboutTime:CosmologyandCultureattheTwilightoftheBigBang(NewYork:FreePress,2001).

41.D.A.Golombek,I.L.Bussi,andP.V.Agostino,“Minutes,DaysandYears:MolecularInteractionsamongDifferentScalesofBiologicalTiming,”PhilosophicalTransactionsoftheRoyalSociety.SeriesB:BiologicalSciences369(2014).

42.Timeis:“numberofchange,withregardtobeforeandafter”(Aristotle,PhysicsIV.219b2;seealso232b22‒3).

43.Aristotle,Physics,trans.RobinWaterfield,withanintroductionandnotesbyDavidBostock(Oxford:OxfordUniversityPress,1999),p.105.

44.IsaacNewton,PhilosophiaeNaturalisPrincipiaMathematica,BookI,def.VIII,scholium.

45.Ibid.

46.AnintroductiontothephilosophyofspaceandoftimecanbefoundinB.C.vanFraassen,AnIntroductiontothePhilosophyofTimeandSpace(NewYork:RandomHouse,1970).

47.Newton’sfundamentalequationisF=md2x/dt2.Notethattimetissquared:thisreflectsthefactthattheequationdoesnotdistinguishtfrom‒t,thatistosay,itisthesamebackwardorforwardintime,asIexplaininchapter2.

48.Curiously,manycontemporarymanualsofthehistoryofsciencepresentthediscussionbetweenLeibnizandtheNewtoniansasifLeibnizweretheheterodoxfigurewithaudaciousandinnovativerelationistideas.Inreality,theoppositewasthecase:Leibnizdefended(withanewwealthofarguments)thedominanttraditionalunderstandingofspace,whichfromAristotletoDescarteshadalwaysbeenrelationist.

49.Aristotle’sdefinitionismoreprecise:theplaceofathingistheinnerboundaryofthatwhichsurroundsthething,anelegantandrigorousdefinition.

5.QUANTAOFTIME

50.IspeakofthisinmoredepthinRealityIsNotWhatItSeems,trans.SimonCarnellandEricaSegre(NewYork:RiverheadBooks,2017).

51.ItisnotpossibletolocateadegreeoflibertyinaregionofitsphasespacewithinavolumesmallerthanthePlanckconstant.

52.Thespeedoflight,theNewtonconstantandthePlanckconstant.

53.Maimonides,TheGuideforthePerplexedI.73.106a.

54.WecantrytoinferthethoughtofDemocritusfromthediscussionsofAristotle(forexample,inPhysicsIV.213),buttheevidenceseemsinsufficienttome.SeeDemocrito.Raccoltadeiframmenti,interpretazioneecommentariodiSalomonLuria(Milan:Bompiani,2007).

55.UnlessthedeBroglie-Bohmtheoryistrue,inwhichcaseithasit—buthidesitfromus.Whichisperhapsnotsodifferentintheend.

56.CarloRovelli,“RelationalQuantumMechanics,”InternationalJournalofTheoreticalPhysics35(1996):1637,http://arxiv.org/abs/quant-ph/9609002.Seealso:“TheSkyIsBlueandBirdsFlyThroughIt,”http://arxiv.org/abs/1712.02894.

57.GratefulDead,“WalkintheSunshine.”

6.THEWORLDISMADEOFEVENTS,NOTTHINGS

58.NelsonGoodman,TheStructureofAppearance(Cambridge,MA:HarvardUniversityPress,1951).

7.THEINADEQUACYOFGRAMMAR

59.Foropposingviews,seenote34.

60.IntheterminologyofacelebratedarticlebyJohnMcTaggart(“TheUnrealityofTime,”Mind,N.S.17(1908):457–74;reprintedinThePhilosophyofTime,LePoidevinandMacBeath),thisisequivalenttodenyingtherealityoftheA-series(theorganizationoftimeinto“past-present-future”).Themeaningoftemporaldeterminationswouldthenbereducedtoonlythe

B-series(theorganizationoftimeinto“before-it,after-it”).ForMcTaggart,thisimpliesdenyingtherealityoftime.Tomymind,McTaggartistooinflexible:thefactthatmycarworksdifferentlyfromhowI’dimagineditandhowI’doriginallydefineditinmyheaddoesnotmeanthatmycarisnotreal.

61.LetterbyEinsteintothesonandsisterofMicheleBesso,March1955,inAlbertEinsteinandMicheleBesso,Correspondence,1903–1955(Paris:Hermann,1972).

62.TheclassicargumentfortheblockuniverseisgivenbythephilosopherHilaryPutnaminafamousarticlepublishedin1967(“TimeandPhysicalGeometry,”JournalofPhilosophy64(1967):240–47).PutnamusesEinstein’sdefinitionofsimultaneity.Aswehaveseeninnote27,iftheEarthandProximabmovewithrespecttooneanother,saytheyareapproachingeachother,aneventAonEarthissimultaneous(foranearthling)toaneventBonProximab,whichinturnissimultaneous(forthoseonProximab)toaneventConEarth,thatisinthefutureofA.Putnamassumesthat“beingsimultaneous”implies“beingrealnow,”anddeducesthattheeventinthefuture(suchasC)isrealnow.TheerroristoassumethatEinstein’sdefinitionofsimultaneityhasanontologicalvalue,whereasitisonlyadefinitionofconvenience.Itservestoidentifyarelativisticnotionthatmaybereducedtothenonrelativisticonethroughanapproximation.Butnonrelativisticsimultaneityisanotionthatisreflexiveandtransitive,whereasEinstein’sisnot,henceitmakesnosensetoassumethatthetwohavethesameontologicalmeaningbeyondtheapproximation.

63.ThatthediscoverybyphysicsoftheimpossibilityofpresentismimpliesthattimeisillusoryisanargumentputforwardbyGödelin“ARemarkabouttheRelationshipbetweenRelativityTheoryandIdealisticPhilosophy,”inAlbertEinstein:Philosopher-Scientist,ed.P.A.Schlipp(Evanston,IL:LibraryofLivingPhilosophers,1949).Theerroralwaysliesindefiningtimeasasingleconceptualblockthatiseitherallthereornotthereatall.ThepointisdiscussedlucidlybyDorato,Checos’èiltempo?,p.77.

64.See,forinstance,W.V.O.Quine,“OnWhatThereIs,”ReviewofMetaphysics2(1948):21–38,andthefinediscussionofthemeaningofrealityinJ.L.Austin,SenseandSensibilia(Oxford:ClarendonPress,1962).

65.DeHebdomadibusofBoethiusII.24,citedinC.H.Kahn,AnaximanderandtheOriginsofGreekCosmology(NewYork:ColumbiaUniversityPress,1960),pp.84–85.

66.SomeexamplesofimportantargumentswhereEinsteinhasstronglysupportedathesisthathelaterchangedhismindabout:1.Theexpansionoftheuniverse(firstridiculed,thenaccepted);2.Theexistenceofgravitationalwaves(firsttakenasobvious,thenrejected,thenacceptedagain);3.Theequationsofrelativitydonotadmitsolutionswithoutmatter(along-defendedthesisthatwasabandoned—rightlyso);4.NothingexistsbeyondthehorizonofSchwarzschild(wrong,thoughperhapshenevercametorealizethis);5.Theequationsofthegravitationalfieldcannotbegeneral-covariant(assertedintheworkwithGrossmannin1912;threeyearslater,Einsteinarguedtheopposite);6.Theimportanceofthecosmologicalconstant(firstaffirmed,thendenied—havingbeenrightthefirsttime.)...

8.DYNAMICSASRELATION

67.ThegeneralformofamechanicaltheorythatdescribesthedevelopmentofasystemintimeisgivenbyaphasespaceandaHamiltonianH.EvolutionisdescribedbytheorbitsgeneratedbyH,parametrizedbythetimet.Thegeneralformofamechanicaltheorythatdescribesthe

evolutionsofvariablewithrespecttoeachotherisinsteadgivenbyaphasespaceandaconstraintC.TherelationsbetweenthevariablesaregivenbytheorbitsgeneratedbyCinthesubspaceC=0.Theparametrizationoftheseorbitshasnophysicalmeaning.Adetailedtechnicaldiscussioncanbefoundinchapter3ofCarloRovelli,QuantumGravity(Cambridge,UK:CambridgeUniversityPress,2004).Foraconcisetechnicalaccount,seeCarloRovelli,“ForgetTime,”FoundationsofPhysics41(2011):1475–90,https://arxiv.org/abs/0903.3832.

68.AnaccessibleaccountofloopquantumgravitycanbefoundinRovelli,RealityIsNotWhatItSeems(op.cit.).

69.BryceS.DeWitt,“QuantumTheoryofGravity.I.TheCanonicalTheory,”PhysicalReview160(1967):1112–48.

70.J.A.Wheeler,“HermannWeylandtheUnityofKnowledge,”AmericanScientist74(1986):366–75.

71.J.ButterfieldandC.J.Isham,“OntheEmergenceofTimeinQuantumGravity,”inTheArgumentsofTime,ed.J.Butterfield(Oxford:OxfordUniversityPress,1999),pp.111–68(http://philsci-archive.pitt.edu/1914/1/EmergTimeQG=9901024.pdf);Zeh,DiePhysikderZeitrichtung;CraigCallenderandNickHuggett,eds.,PhysicsMeetsPhilosophyatthePlanckScale(Cambridge,UK:CambridgeUniversityPress,2001);SeanCarroll,FromEternitytoHere:TheQuestfortheUltimateTheoryofTime(NewYork:Dutton,2010).

72.ThegeneralformofaquantumtheorythatdescribestheevolutionofasystemintimeisgivenbyaHilbertspaceandtheHamiltonianoperatorH.TheevolutionisdescribedbySchrödinger’sequationiħ∂tΨ=HΨ.TheprobabilityofmeasuringapurestateΨatimetafterhavingmeasuredastateΨ′isgivenbythetransitionamplitude⟨Ψ|exp[–iHt/ħ]|Ψ′⟩.ThegeneralformofaquantumtheorythatdescribestheevolutionofthevariableswithrespecttooneanotherisgivenbyaHilbertspaceandWheeler-DeWittequationCΨ=0.TheprobabilityofmeasuringthestateΨafterhavingmeasuredthestateΨ′isdeterminedbytheamplitude⟨Ψ|∫dtexp[iCt/ħ]|Ψ′⟩.Adetailedtechnicaldiscussioncanbefoundinchapter5ofRovelli,QuantumGravity(op.cit.).Foraconcisetechnicalversion,seeRovelli,“ForgetTime”(op.cit.)

73.BryceS.DeWitt,Sopraunraggiodiluce(Rome:DiRenzo,2005).

74.Therearethree:theydefinetheHilbertspaceofthetheorywheretheelementaryoperatorsaredefined,whoseeigenstatesdescribethequantaofspaceandtheprobabilityoftransitionsbetweenthese.

75.SpinisthequantitythatenumeratestherepresentationsofthegroupSO(3),thegroupofspatialsymmetry.Themathematicsthatdescribesthespinnetworkshasthisfeatureincommonwiththemathematicsofordinaryphysicalspace.

76.TheseargumentsarecoveredindetailinRovelli,RealityIsNotWhatItSeems.(op.cit.).

9.TIMEISIGNORANCE

77.Ecclesiastes3:2–4.

78.Moreprecisely,theHamiltonianH,thatis,theenergyasafunctionofpositionandspeed.

79.dA/dt={A,H},where{,}arethePoissonbracketsandAisanyvariable.

80.Ergodic.

81.TheequationsaremorereadableinthecanonicalformationsofBoltzmannthaninthemicrocanonicalformtowhichImakereferenceinthetext:thestateρ=exp[‒H/kT]isdeterminedbytheHamiltonianHthatgeneratesevolutionoftime.

82.H=‒klog[ρ]determinesaHamiltonian(uptoamultiplicativeconstant),andthusa“thermal”time,startingfromthestateρ.

83.RogerPenrose,TheEmperor’sNewMind(Oxford:OxfordUniversityPress,1989);also,Penrose,TheRoadtoReality(London:Cape,2004).

84.Inthelanguageofquantummechanicsmanuals,itisconventionallyreferredtoas“measure.”Onceagain,thereissomethingmisleadingaboutthislanguage,inasmuchasitspeaksaboutphysicslaboratoriesratherthanspeakingabouttheworld.

85.ThetheoremofTomita-TakesakishowsthatastateonavonNeumannalgebradefinesaflow(aone-parameterfamilyofmodularautomorphisms).Conneshasshownthattheflowsdefinedbydifferentstatesareequivalentuptointernalautomorphisms,andthereforedefineanabstractflowdeterminedonlybythenoncommutativestructureofalgebra.

86.Theinternalautomorphismsofthealgebrareferredtointheabovenote.

87.InavonNeumannalgebra,thethermaltimeofastateisexactlythesameasTomita’sflow!ThestateisKMSwithrespecttothisflow.

88.SeeCarloRovelli,“StatisticalMechanicsofGravityandtheThermodynamicalOriginofTime,”ClassicalandQuantumGravity10(1993):1549–66;AlainConnesandCarloRovelli,“VonNeumannAlgebraAutomorphismsandTime-ThermodynamicsRelationinGeneralCovariantQuantumTheories,”ClassicalandQuantumGravity11(1994):2899–918.

89.AlainConnes,DanyeChéreau,andJacquesDixmier,LeThéâtrequantique(Paris:OdileJacob,2013).

10.PERSPECTIVE

90.Therearemanyconfusedaspectstothisquestion.Anexcellent,cogentcritiquecanbefoundinJohnEarman,“The‘PastHypothesis’:NotEvenFalse,”StudiesinHistoryandPhilosophyofModernPhysics37(2006):399–430.Inthetext,“lowinitialentropy”isintendedinthemoregeneralsensethat,asEarmanarguesinthisarticle,isfarfrombeingwellunderstood.

91.FriedrichNietzsche,TheGayScience(Cambridge,UK:CambridgeUniversityPress,2001),v–354.

92.ThetechnicaldetailscanbefoundinCarloRovelli,“IsTime’sArrowPerspectival?”inThePhilosophyofCosmology,eds.K.Chamchametal.(Cambridge,UK:CambridgeUniversityPress,2017),https://arxiv.org/abs/1505.01125.

93.Intheclassicalformulationofthermodynamics,wedescribeasystembyspecifyinginthefirstplacesomevariablesonwhichweassumewecanactfromtheoutside(movingapiston,forexample),orwhichweassumewecanmeasure(arelativeconcentrationofcomponents,forxample).Thesearethe“thermodynamicvariables.”Thermodynamicsisnotatruedescription

ofthesystem;itisadescriptionofthesevariablesofthesystem—thosethroughwhichweassumeweareabletointeractwiththesystem.

94.Forexample,theentropyoftheairinthisroomhasavaluetakenfromairasahomogeneousgas,butitchanges(diminishes)ifImeasureitschemicalcomposition.

95.AcontemporaryphilosopherwhohasshedlightontheseaspectsoftheperspectivalnatureoftheworldisJenannT.Ismael,TheSituatedSelf(NewYork:OxfordUniversityPress,2007).Ismaelhasalsowrittenanexcellentbookonfreewill:HowPhysicsMakesUsFree(NewYork:OxfordUniversityPress,2016).

96.DavidZ.Albert,inTimeandChance(Cambridge,MA:HarvardUniversityPress,2000),proposestoelevatethisfacttoanaturallaw,andcallsit“pasthypothesis.”

11.WHATEMERGESFROMAPARTICULARITY

97.Thisisanothercommonsourceofconfusion,becauseacondensedcloudseemsmore“ordered”thanadispersedone.Itisn’t,becausethespeedofthemoleculesofadispersedcloudareallsmall(inanorderedmanner),while,whenthecloudcondenses,thespeedsofthemoleculesincreaseandspreadinphasespace.Themoleculesconcentrateinphysicalspacebutdisperseinphasespace,whichistherelevantone.

98.See,inparticular,StuartA.Kauffman,HumanityinaCreativeUniverse(NewYork:OxfordUniversityPress,2016).

99.Theimportanceoftheexistenceofthisramifiedstructureofinteractionsintheuniversefortheunderstandingofthegrowthoflocalentropyisdiscussed,forinstance,byHansReichenbach,inTheDirectionofTime(Berkeley:UniversityofCaliforniaPress,1956).Reichenbach’stextisfundamentalforwhoeverhasdoubtsabouttheseargumentsorisinterestedinpursuingtheminmoredepth.

100.Onthepreciserelationbetweentracesandentropy,seeReichenbach,TheDirectionofTime,inparticularthediscussionontherelationamongentropy,traces,andcommoncause,andAlbert,TimeandChance.ArecentapproachcanbefoundinD.H.Wolpert,“MemorySystems,ComputationandtheSecondLawofThermodynamics,”InternationalJournalofTheoreticalPhysics31(1992):743–85.

101.Onthedifficultquestionofwhat“cause”meanstous,seeNancyCartwright,HuntingCausesandUsingThem:ApproachesinPhilosophyandEconomics(Cambridge,MA:CambridgeUniversityPress,2007).

102.“Commoncause,”inReichenbach’sterminology.

103.BertrandRussell,“OntheNotionofCause,”ProceedingsoftheAristotelianSociety,N.S.13(1912–1913):1–26.

104.Cartwright,HuntingCausesandUsingThem.

105.Foraluciddiscussiononthequestionofthedirectionoftime,seeHuwPrice,Time’sArrowandArchimedes’Point(Oxford:OxfordUniversityPress,1996).

12.THESCENTOFTHEMADELEINE

106.MilindaPañha(TheQuestionsofKingMilinda)II.1,inT.W.RhysDavids,SacredBooksoftheEast,vol.XXXV(Oxford:ClarendonPress,1890).

107.CarloRovelli,Meaning=Information+Evolution,2016,https://arxiv.org/abs/1611.02420.

108.G.Tononi,O.Sporns,andG.M.Edelman,“AMeasureforBrainComplexity:RelatingFunctionalSegregationandIntegrationintheNervousSystem,”ProceedingsoftheNationalAcademyofSciencesUSA91(1994):5033–37.

109.JakobHohwy,ThePredictiveMind(Oxford:OxfordUniversityPress,2013).

110.See,forexample,V.Mante,D.Sussillo,K.V.Shenoy,andW.T.Newsome,“Context-dependentComputationbyRecurrentDynamicsinPrefrontalCortex,”Nature503(2013):78–84,andtheliteraturecitedinthisarticle.

111.DeanBuonomano,YourBrainIsaTimeMachine:TheNeuroscienceandPhysicsofTime(NewYork:Norton,2017).

112.LaCondemnationparisiennede1277,ed.D.Piché(Paris:Vrin,1999).

113.EdmundHusserl,VorlesungenzurPhänomenologiedesinnerenZeitbewusstseins(Halle:Niemeyer,1928).

114.Inthecitedtext,Husserlinsiststhatthisdoesnotconstitutea“physicalphenomenon.”Toanaturalist,thissoundslikeastatementofprinciple:hedoesnotwanttoseememoryasaphysicalphenomenonbecausehehasdecidedtousephenomenologicalexperienceasthestartingpointofhisanalysis.Thestudyofthedynamicsofneuronsinourbrainshowshowthephenomenonmanifestsitselfinphysicalterms:thepresentofthephysicalstateofmybrain“retains”itspaststate,andthisisgraduallymorefadedthefartherawaywearefromthatpast.See,forexample,M.JazayeriandM.N.Shadlen,“ANeuralMechanismforSensingandReproducingaTimeInterval,”CurrentBiology25(2015):2599–609.

115.MartinHeidegger,“EinführungindieMetaphysik”(1935),inGesamtausgabe,vol.XL,p.90(Frankfurt:Klostermann,1983).

116.MartinHeidegger,SeinundZeit(1927),inGesamtausgabe,vol.II,passim(Frankfurt:Klostermann,1977);trans.BeingandTime.

117.MarcelProust,DucôtéduchezSwann,inÀlaRecherchedutempsperdu,vol.I(Paris:Gallimard,1987),pp.3–9.

118.Ibid.,p.182.

119.G.B.Vicario,Iltempo.Saggiodipsicologiasperimentale(Bologna:IlMulino,2005).

120.Theobservation,aquitecommonone,canbefound,forexample,intheintroductiontoJ.M.E.McTaggart,TheNatureofExistence,vol.I(Cambridge,UK:CambridgeUniversityPress,1921).

121.Lichtung,perhaps;inMartinHeidegger,Holzwege(1950),inGesamtausgabe,vol.V,passim(Frankfurt:Klostermann,1977).

122.ForDurkheim,oneofthefoundersofsociology,liketheothergreatcategoriesofthought,theconceptoftimehasitsoriginsinsociety—andinparticularinthereligiousstructurethatconstitutesitsprimaryform;inLesFormesélémentairesdelaviereligieuse(Paris:Alcan,1912).Ifthiscanbetrueforcomplexaspectsofthenotionoftime—forthe“moreexternal

layers”ofthenotionoftime—itseemstomedifficulttoextendittoincludeourdirectexperienceofthepassageoftime:othermammalshavebrainsroughlysimilartoours,andconsequentlyexperiencethepassageoftimelikewedo,withoutanyneedforasocietyorareligion.

123.Onthefoundationalaspectoftimeforhumanpsychology,seeWilliamJames’sclassicThePrinciplesofPsychology(NewYork:HenryHolt,1890).

124.MahāvaggaI.6.19,inRhysDavids,SacredBooksoftheEast,vol.XIII(1881).FortheconceptsrelatingtoBuddhism,IhavedrawnparticularlyonHermannOldenburg,Buddha(Milan:Dall’Oglio,1956).

125.HugovonHofmannstahl,DerRosenkavalier,actI.

13.THESOURCEOFTIME

126.Ecclesiastes3:2.

127.Foralighthearted,engagingbutinformedexpositionoftheseaspectsoftime,seeCraigCallenderandRalphEdney,IntroducingTime(Cambridge,UK:IconBooks,2001).

THESISTEROFSLEEP

128.MahābhārataIII.297.

129.Ibid.,I.119.

130.A.Balestrieri,“Ildisturboschizofreniconell’evoluzionedellamenteumana.Pensieroastrattoeperditadelsensonaturaledellarealtà,”Comprendre14(2004):55–60.

131.RobertoCalasso,L’ardore(Milan:Adelphi,2010).

132.Ecclesiastes12:6–7.

INDEX

Thepagenumbersinthisindexrefertotheprintedversionofthisbook.Thelinkprovidedwilltakeyoutothebeginningofthatprintpage.Youmayneedtoscrollforwardfromthatlocationtofindthecorrespondingreferenceonyoure-reader.

acceleration,17n,216n7,216n12Albert,DavidZ.,226–27n96Anaxandridas,46,47Anaximander,11,14–15,100–101Aristotle,63–66,69–71,77,78,84,97,220–21nn48–49,221n54astronomy,14,65,102atomism,86atoms,29,85,99,101–2,210AugustineofHippo,180–83,212

Bach,JohannSebastian:BWV56cantata,206Bede,theVenerable,85Beethoven,Ludwigvan:MissaSolemnis,212Besso,Michele,114–15blackholes,54–55,127blockuniverse,109,195,222n62Boltzmann,Ludwig,27–36,136,145,157,225n81Boltzmann’sconstant,217n20brain,153,166,167,176,179,180,182,186,189,207,210andfearofdeath,207–8frontallobes,207,209neurons.Seeneurons/neuralstructuresandProust,188synapses,107,108

Buddha,190

Carnot,Lazare,22–23,216n10Carnot,(NicolasLéonard)Sadi,23,28causeandeffect,20,21,33,168–69,176changeandcomplexity,109–10relations,eventsandworlddynamicswithoutatimevariable,117–28,195–96timeasmeasurementofchange,andAristotle’sspace,63–79,97timewhennothingchanges,63–4,72andworldasnetworkofevents,95–104,195

Clausius,Rudolf,23–25,157

equationofentropy,27,157,188–89CleomenesI,45–46,47clocks,15,59–63,67,74,96–97,197,216n8andeffectofspeedontime,40n,197slowedbyamass/gravitationalfield,9–13,75–77synchronizationof,61–62

Connes,Alain,138–42,225n85consciousness,63,173,182–87,199–203internalconsciousnessoftime,183,186

continuity,84,96Copernicus,Nicolaus,11,201,218n26

death,206fearof,206,207–8

delirium,collective,211Democritus,85,101,221n54Descartes,René,176–77,220–21n48DeWitt,Bryce,119,121–22,124diurnalrhythms,62–63Dorato,Mauro,215n3Duino,36Durkheim,Émile,229n122

Earman,J.,226n90Ecclesiastes,131,198Einstein,Albert,10–12,37–40,44,52–53,197,218n26,223n66andBesso,114–15generaltheoryofrelativity,16andthegravitationalfield,74–79,195onillusionoftime,108–9,114simultaneity,218n27,222n62specialrelativitytheory,48,218n26atSwissPatentOffice,61

electrons,85,87,89–90,124,138Ellis,George,219n34energy,159–60conservationof,27,135–36,159thermal.Seeheatandthermaltime,134–37.Seealsothermaltime

entropy,25–36,136,143,145–51,155–57,159–66,196–97,198,217n15,217n20,226n94andblurring,21–36,135–37,144–51,154,155–57,199Clausius’sequation,25–27,157,188–89andcoarsegraining,217n18indistantpast,143,146–51,161,163–64,167,169increase,161–66,189,196,217n15low,31–32,143,146–51,156–57,160–63,167,169,196andperspective,147–50secondlawofthermodynamics,23–28,149,160,165

eternalism,108–9.Seealsoblockuniverseevents

relations,eventsandlooptheorywithoutatimevariable,117–28worldasnetworkof,95–104,195

evolution,207–10

fearofdeath,206,207–8flowoftime,1,2–3,193–97andcauseandeffect,20,21,33,168–69Durkheim,religionand,229n122heat,entropy,andourblurredvisionof,25–36,135–37,145–51,154,156–57,199inHindumythology,2internalconsciousnessof,183,186andparticularity,16,30–34,91,146–51,162,170,188–89,194,196,198past,future,andthearrowoftime,19–36,146–51,194,195,196andrelativity,138.Seealsorelativityslowedbyamass,9–13,76–77,194,197,198slowedbyspeed,37–40,194,197,198sourceofRilke’seternalcurrent,20–36andthestructureofspacetime,48–56,73–79,106–7,109,184andsubjectivity/identity/consciousness,3,5,20–21,57–58,63,171–92,199–202.Seealso

perspectiveFrenchRevolution,22,216n10

Gödel,Kurt,53,218–19n29,222–23n63Gorgo,queenofSparta,45–46,47–48grammarofchange,97–104inadequacyof,105–15,132–34

granularity,quantummechanics,83–85,124–25spinnetworks,126,127,224–25n75

gravitationalfield,74–79,90,124,195,197,198–99andgranularity,83,124–25

HamiltonianH,223–24n67,224n72,225nn81–82heat,22–26,160,165andentropy.Seeentropythermaltime,134–38,139–40,142,196,225n87thermodynamics.Seethermodynamics

Hegel,GeorgWilhelmFriedrich,200Heidegger,Martin,84,186,200nhelium,163Hilbertspace,224n72,224n74HildegardofBingen,154–55Hindumythology,1,17,166,205,208Hofmannstahl,Hugovon:DerRosenkavalier,191–92Hume,David,176Husserl,Edmund,183,184–86,228n114hydrogen,163

identity,171–92,199impermanence,97.Seealsochange

indeterminacy,quantummechanics,87–89,124–28,140,196andblurring,140–42,170

indexicality,151–55Isham,Chris,121–22IsidoreofSeville,85Ismael,JenannT.,226n95

Job,206

Kant,Immanuel,184Kepler,Johannes,101–3Kuchar,Karel,121–22

Lagrange,Joseph-Louis,216n10Lavoisier,Antoine,216n10Leibniz,GottfriedWilhelm,68,220–21n48LeonidasI,45–46,47light,41,50,74cones,50–55,77,88granularityof,85,124andindeterminacyinquantummechanics,88photons,85,124,160–61

looptheory/loopquantumgravity,82,85,124–28Lorentz,Hendrik,218n25LouisXVI,22

Mahābhārata,205,208Maimonides,85Marat,Jean-Paul,216n10Maroun,Samy,219n34mass,timeslowedby,9–13,76–77,194,197,198Matthew,Gospelof,58Maxwell’sequations,14,39–40,103,216n11McTaggart,John,221–22n60memory/memories,21,121,149,166,169–70,196identity,timeand,178–92

MilindaPañha,172–73music,182,184,191–92,212

nervoussystem,175,179–80,187neurons/neuralstructures,62,175–76,180,188,202,228n14Newton,Isaac,64–69,69–76,77–78,117equations,14,67,216–17n12mechanics,14,103PhilosophiaeNaturalisPrincipiaMathematica,183

Newtoniangravity,215n5noncommutativityquantum,138–40,199VonNeumannalgebra,139,225n85,225n87

nostalgia,120,123,202

nuclearfission,163

Ockham,Williamof,183

Parmenides,200partialorder,46–48,139,219n31particularity,16,30–34,91,146–51,162,170,188–89,194,196,198pasttraces,166–67,181,183,187,196–97.Seealsomemory/memoriesPenrose,Roger,137–38perspective,4,5,122,143–57,196–97blurring,21–36,135–37,140–41,144–51,154,170,196,199andentropy,146–57.Seealsoentropy:andblurringandindexicality,151–55andparticularity.Seeparticularitysubjectivity/identity/consciousnessandtime,3,5,20–21,57–58,63,171–92,199–202

photons,85,124,160–61photosynthesis,164Planckconstant,221nn51–52Plancklength,85–86Planckscale,83,125–26Plancktime,83Plato,101,102,200Pleistarchus,45–46,47prediction,175,179–80,189,207andlooptheory,85,128

present,33,43–44,193–94meaninglessnessof“now,”andlossofthepresent,37–56,107–8,194temporalstructureofuniversewithoutthepresent,45–56,106–7,109–10

presentism,106,108,222–23n63probability,quantummechanics.Seeindeterminacy,quantummechanicspropertime,16,40,216n8Proust,Marcel,188Putnam,Hilary,222n62

quantumfieldtheory,15quantumgravity,4,81,91,119–20loopquantumgravity,82,85,124–28

quantummechanics,14,79,81–92,103,195andgranularity,83–85,124–25andindeterminacy.Seeindeterminacy,quantummechanicsandloopquantumgravity,82,85,124–28noncommutativity,138–40andquantaoftime,81–92.Seealsoquantumtimequantumsuperpositionsoftimes,87–88relationality,89–90andrelativity,81–83,138

quantumtime,138–42spinfoamand“quantumspacetime,”126

reality,1–2,74,78,99

andtheblockuniverse,109,222n62collectivedeliriumandourvisionof,211andinadequacyofgrammar,105–15andmemory,178–92.Seealsomemory/memoriesrelations,eventsandworlddynamicswithoutatimevariable,117–28,195–96

reason,208–9Reichenbach,Hans,200,227nn99–100relationalityquantummechanics,89–90relations,eventsandworlddynamicswithoutatimevariable,117–28,195–96

relativity,14–17,46,145andexperienceofflowoftime,138generaltheoryof,15–16andquantummechanics,81–83,138.Seealsoquantummechanicsspecial,48,218n16

Rilke,RainerMaria:DuinoElegies,20,36Russell,Bertrand,169

SaadiShirazi,22–23Schrödingerequations,14–15,102,224n72Shiva,1,17,166simultaneity,218n27,222n62slowingoftime,9–13,37–40,76,194,197,198Smolin,Lee,219n34Sophocles:OedipusRex,5spacetimeandAristotle,63–79,97curved,77,210“emptyspace,”70–71andeternalism,108–9.Seealsoblockuniversefluctuations,88–90granularity,83–85,124–25gravitationalfield.Seegravitationalfieldlossof,95–128,195andquantummechanics.Seequantummechanicsspinfoamand“quantumspacetime,”126.Seealsolooptheory/loopquantumgravitystructureof,48–56,73–79,106–7,109,184,197–98“true”timeandNewton’sspace,65–79

specialrelativitytheory,48,218n26speed,145acceleration,17n,216n7,216–17n12timeslowedby,37–40,194,197

spinnetworks,126,127,224–25n75spinfoam,126StrasburgCathedral,59Strauss,Richard:DerRosenkavalier,191–92stringtheory,82suffering,115,190–91,206sundials,59–61synapses,107–8

Tempier,Étienne,182temporalprecedence,48thermaltime,134–38,139–40,142,196,222n87thermodynamicssecondlawof,21–28,149,160,165andthermaltime,137,142.Seealsothermaltimevariables,226n93

timeabsence,andequationswithoutatimevariable,96,117–28,195,199,220n47Anaximanderandtheorderof,14–15,100–101arrowof,19–36,147–50,194,195,196Augustineon,180–83clock-regulated,59–63.Seealsoclocksclosedlines,53nanddiurnalrhythms,62–63dividingandmeasuring,58–64Einsteinonillusionof,108–9,114andemotion,141,200–201,211–12andeternalism,108–9.Seealsoblockuniverseflowof.Seeflowoftimeandgrammar.Seegrammargranularityof,85–86andthegravitationalfield,74–79,90,124,195,197,198–99.Seealsogravitationalfieldandheat.Seeheatinternalconsciousnessof,183–86lossofdirection,19–36,194,195lossofindependence,57–79lossofthepresent,37–56,107–8,194lossofunity,9–17asmeasurementofchange,andAristotle’sspace,63–79,97andmemory.Seememory/memoriesmodificationofstructureof,9–13multilayeredaspectof,3,198multiplemeaningsof,17nmysteryof,1–5,199–202andnetworkofrelations,89–91.Seealsorelationalitywhennothingchanges,63–64,72Plancktime,83propertime,16,40,216n8quantumsuperpositionsoftimes,87–88.Seealsoquantummechanicsquantumtime.Seequantumtimeandrelativity.Seerelativitysourcesof,193–203spacetime.Seespacetimestandardized,61–62assuffering,190–91temporalstructureofuniversewithoutthepresent,46–56,106–7,109thermal,134–38,139–40,142,196,222n87tracesofthepast,166–67,181,183,187,196–97.Seealsomemory/memories

“true”timeandNewton’sspace,65–79Tomita–Takesakitheorem,225n85

universalman,154–55

Wheeler,John,119–21,122,124Wheeler–DeWittequation,119,224n72

ABOUTTHEAUTHOR

CarloRovelli,anItaliantheoreticalphysicist,istheheadofthequantumgravitygroupattheCentredePhysiqueThéoriqueofAix-MarseilleUniversité.HeisoneofthefoundersoftheloopquantumgravitytheoryandauthoroftheinternationalbestsellerSevenBriefLessonsonPhysics,RealityIsNotWhatItSeems,andTheOrderofTime.RovellilivesinMarseille,France.

What’snextonyourreadinglist?

Discoveryournextgreatread!

Getpersonalizedbookpicksandup-to-datenewsaboutthisauthor.

Signupnow.

*Grammaticalnote:Theword“time”hasseveralmeaningslinkedtoeachotherbutdistinctfromoneanother:1.“Time”isthegeneralphenomenonofthesuccessionofevents(“Theinaudibleandnoiselessfootoftime”);2.“Time”indicatesanintervalinthissuccession(“Tomorrow,andtomorrow,andtomorrow,/Creepsinthispettypacefromdaytoday,/Tothelastsyllableofrecordedtime”);or3.itsduration(“Ogentlemen,thetimeoflifeisshort”);4.“Time”canalsoindicateaparticularmoment(“Timewillcomeandtakemyloveaway”;oftenthecurrentone(“Thetimeisoutofjoint”);6.“Time”indicatesthevariablethatmeasuresduration(“Accelerationisthederivativeofspeedwithrespecttotime”).Inthisbook,Iemployeachofthesemeaningsfreely,justasincommonusage.Incaseofanyconfusion,pleasereferbacktothisnote.

*Strictlyspeaking,thearrowoftimecanalsomanifestitselfinphenomenathatarenotlinkeddirectlytoheatbutsharecrucialaspectswithit—forinstance,intheuseofretardedpotentialsinelectrodynamics.Whatfollowsappliesalsoforthesephenomena—inparticular,theconclusions.Ipreferherenottooverloadthediscussionbybreakingitdownintoallitsdifferentsubcases.

*Thereareafewmoredetailsgivenonthispointinchapter11.

*ThepointisnotthatwhathappenstoacoldteaspooninacupofhotteadependsonwhetherIhaveablurredvisionofitornot.Whathappenstothespoonandtoitsmoleculesaswell,obviously,doesnotdependonhowIviewit.Itjusthappens,regardless.Thepointisthatthedescriptionintermsofheat,temperature,andthepassageofheatfromteatospoonisablurredvisionofwhathappens,andthatitisonlyinthisblurredvisionthatastartlingdifferencebetweenpastandfutureappears.

*“Inmotion”inrelationtowhat?Howcanwedeterminewhichofthetwoobjectsmoves,ifmotionisonlyrelative?Thisisanissuethatconfusesmany.Thecorrectanswer(rarelygiven)isthis:inmotionrelativetotheonlyreferenceinwhichthepointinspacewherethetwoclocksseparateisthesamepointinspacewheretheygetbacktogether.Thereisonlyasinglestraightlinebetweentwoeventsinspacetime,fromAtoB:it’stheonealongwhichtimeismaximum,andthespeedrelativetothislineistheonethatslowstime.Iftheclocksseparateandarenotbroughttogetheragain,thereisnopointaskingwhichoneisfastandwhichoneisslow.Iftheycometogether,theycanbecompared,andthespeedofeachonebecomesawell-definednotion.

*The“closedtemporallines,”wherethefuturereturnsustothepast,aretheonesthatfrightenthosewhoimaginethatasoncouldgoontokillhismotherbeforehisownbirth.Butthereisnologicalcontradictionentailedbytheexistenceofclosedtemporallinesorjourneystothepast;wearetheoneswhocomplicatethingswithourconfusedfantasiesaboutthesupposedfreedomofthefuture.

*Ihavebeencriticizedfortellingthehistoryofscienceasifitwerejusttheresultoftheideasofafewbrilliantmindsratherthanthepainstakingworkofgenerations.It’safairenoughcriticism,andIapologizetothegenerationswhohavedoneandaredoingthenecessarywork.MyonlyexcuseisthatIamnotattemptingadetailedhistoricalanalysisorscientificmethodology.Iamonlysynthesizingafewcrucialsteps.Slow,technical,cultural,andartisticadvancesmadebyinnumerableworkshopsofpaintersandartisanswerenecessarybeforetheSistineChapelwaspossible.Butintheend,itwasMichelangelowhopaintedit.

*TheroutebywhichEinsteinarrivedatthisconclusionwasalongone:itdidn’tendwiththewritingoftheequationsofthefieldin1915butcontinuedinhistortuouseffortstounderstanditsphysicalsignificance,causinghimintheprocesstochangehisideasrepeatedly.Hewasconfusedinparticularregardingtheexistenceofsolutionswithoutmatter,andbywhethergravitationalwaveswererealornot.Heachievesdefinitiveclarityonlyinhislastwritingsand,inparticular,inthefifthappendix,“RelativityandtheProblemofSpace,”whichwasaddedtothefiftheditionofRelativity:TheSpecialandGeneralTheory(Methuen:London,1954).Thisappendixcanbereadathttp://www.relativitybook.com/resources/Einstein_space.html.Forcopyrightreasons,thisappendixisnotincludedinmosteditionsofthebook.Amorein-depthdiscussioncanbefoundinchapter2ofmyQuantumGravity(Cambridge,UK:CambridgeUniversityPress,2004).

*Thetechnicaltermforinteractionusedinthiscontext,“measure,”ismisleadingbecauseitseemstoimplythatinordertocreatereality,weneedanexperimentalphysicistinawhitecoat.

*I’mmakingusehereoftherelationalinterpretationofquantummechanics,whichistheoneImyselffindleastimplausible.Theobservationsthatfollow,inparticularthelossofaclassicspacetimesatisfyingEinstein’sequations,remainvalidineveryotherinterpretationthatIknowof.

*ThereissomethingextremelyinterestingaboutthefactthatthisobservationbyReichenbach,inafundamentaltextforthetreatmentoftimebyanalyticalphilosophy,soundssoclosetoideasfromwhichHeidegger’sreflectionstems.Thesubsequentdivergenceisenormous:Reichenbachsearchesinphysicsforthatwhichweknowabouttimeintheworldofwhichwearepart,whileHeideggerconcernshimselfwithwhattimeisintheexistentialexperienceofhumanbeings.Thetworesultantimagesoftimearecompletelydifferentfromeachother.Aretheynecessarilyincompatible?Whyshouldtheybe?Theyexploretwodifferentproblems:ontheonehand,theeffectivetemporalstructuresoftheworldthatrevealthemselvestobeprogressivelymorethreadbareaswewidenourgaze;ontheother,thefoundationalaspectthatthestructureoftimehasforus,forourconcretesenseof“beingintheworld.”