Parallel Universes - MIT Kavli Institute

1 To appearinScience andUltimateReality:FromQuantumto Cosmos, honoringJohnWheeler's90thbirthday, , ,& eds.,CambridgeUniversity Press(2003) Physics, Pennsylvania,Philadelphia,PA surveyphysicstheoriesinvolvingparallelun iverses,which forma naturalfour-levelhierarchy of multiversesallowingprogressivelygreaterd iversity. Level I: A genericpredictionofin ationis an in niteergodicuniverse,which containsHubblevolumesrealizingall initialconditions|includinganidenticalco py of youabout101029m away. Level II: Inchaoticin ation,otherthermalizedregionsmay have di erent physicalconstants, dimensionality andparticlecontent. LevelIII: In unitaryquantummechanics,otherbranchesof thewavefunctionaddnothingqualitativelyne w,which is ironicgiventhatthislevel IV:Othermathematicalstructuresgive di erent fundamentalequationsof questionisnotwhetherparalleluniversesexi st(Level I is theuncontroversialcosmologicalconcordanc emodel),buthow many discusshow multiversemodelscanbe falsi edandarguethatthereis a severe\measureproblem"thatmustbe solvedto make testablepredictionsat thereanothercopy of you readingthisarticle,decid-ingto putit asidewithout nishingthissentencewhileyouarereadingon?

2 A personlivingona planetcalledEarth,withmisty mountains,fertile eldsandsprawlingcities,in a solarsystemwitheight thispersonhasbeenidenticaltoyoursin everyrespect{ until now,thatis,whenyourdecisionto readonsignalsthatyourtwo lives ndthisideastrangeandimplausible,andI mustconfessthatthisis my gutreactiontoo. Yetit lookslike we willjusthave to live withit,sincethesimplestandmostpopularcos mologicalmodeltoday pre-dictsthatthispersonactuallyexistsin a noteven assumespec-ulative modernphysics,merelythatspaceis in niteandratheruniformly lledwithmatteras indicatedby simplya pre-dictionof theso-calledconcordancemodelof cosmology,which agreeswithallcurrent observationalevidenceandis usedas thebasisformostcalculationsandsimulation spresentedat ,alter-natives such as a fractaluniverse,a closeduniverseanda multiplyconnecteduniversehave beenseriouslychal-lengedby is thedistancethatlighthasbeenableto travel visibleobjectsarenow about4 1026metersaway , anda sphere Afteremittingthelight thatis now reachingus.}

3 Themostdistant thingswe canseehave recededbecauseof thecosmicexpansion,andarenow aboutabout40billionlight thisradiusde nesourobservableuniverse,alsocalledourHu bblevolume, ,theuniverseof yourabove-mentionedtwinis a sphereof thesamesizecenteredover there,noneof which we canseeor have any thesimplest(butfarfromtheonly) nitionof \universe",onemight ex-pectthenotionthatourobservableunivers eis merelyasmallpartof a larger\multiverse"to be forever in thedo-mainof theepistemologicalborderlinebetweenphysi csandmetaphysicsis de nedby whethera theoryis experimentallytestable,notby whetheritis weirdor involves thereforeex-pandedthefrontiersof physicsto incorporateever moreabstract(andat thetimecounterintuitive) conceptssuchasa roundrotatingEarth,anelectromagnetic eld,timeslowdownat highspeeds,quantumsuperpositions,curveds paceandblack thisar-ticle,it is becomingincreasinglyclearthatmultiversem odelsgroundedin modernphysicscanin factbe em-piricallytestable,predictive andfalsi ,asmany as fourdistincttypes of paralleluniverses(Figure1) have beendiscussedin therecent scienti cliterature,so thatthekey questionis notwhetherthereis a multi-verse(sinceLevel I is ratheruncontroversial),butratherhow many levelsit !

4 #"$ % & izon' (*),+.-#/%(10%2 Same laws of physics, different initial conditionsAssumptions:3547658498:;!<>=7?1@*;BA,; C>DFEHGF8@JIK? ::; C distributionEvidence: - Microwave background meaurements point to 65L? :>AB8496>8478:M; <>=N?*@*;,ABL? C>DF;1O> <P@*?*L; <.IKEFEB:QH47;1<R< - Simplest model S T TUK WV XF&K Y [Z\ ! 9XH]B ^B %_JX, % ` K W K % ' (*)B+.-#/*(*0%2 Same fundamental equations of physics, but perhaps GF86M6erent constants, particles and dimensionalityAssumption: Chaotic inflation occurredEvidence: - Inflation theory explains flat space, scale-invariant fluctuations, solves horizon problem and monopole problems and can naturally explain such bubbles - Explains fine-tuned parametersLevel 3: The Many a lds of Quantum Physics' (*),+>-#/*(*0%2 Same as level 2 Assumption: Physics unitaryEvidence: - Experimental support for unitary physics - bTG9cFdegfihj@*E,C5Ck;1<>=NEB47GF; 49@1; <.)))

5 L7 DHDF;1<.:5<S:Q7? : even quantum gravity is unitary - Decoherence experimentally verified - Mathematically simplest model S T TmK VnXF&K Y "o_JXF&K "o_JXH _ W 9XF K SXF Y ' (1)B+.-#/*(*0%2p86M6erent fundamental equations of physicsAssumption: Mathematical existence = physical existenceEvidence: - qr4FC.;1?1<PE,49?tsNL; ;*6M6ectiveness of math in physics - Answers Wheeler/Hawking question: "why these equations, not others"2I. LEVELI: REGIONSBEYONDOURCOSMICHORIZONL etusreturntoyourdistant spaceis in -niteandthedistributionof matteris su cientlyuniformonlargescales,theneven themostunlikelyevents musttake particular,therearein nitelymany otherinhabitedplanets,includingnotjuston ebutin nitelymany withpeoplewiththesameappearance,nameandm emoriesas ,therearein nitelymany otherregionsthesizeof ourobservableuniverse,whereeverypossible cosmichistoryis theLevel I I paralleluniversesAlthoughtheimplications mayseemcrazyandcounter-intuitive,thisspa tiallyin nitecosmologicalmodelis in factthesimplestandmostpopularoneonthemar ket today.)

6 It is partof thecosmologicalconcor-dancemodel,which agreeswithallcurrent observationalevidenceandis usedas thebasisformostcalculationsandsimulation spresentedat ,alternatives such as a fractaluniverse,a closeduniverseanda multiplyconnecteduniversehave beense-riouslychallengedby theLevel I mul-tiverseideahasbeencontroversial(inde ed,anassertionalongtheselineswas oneof theheresiesforwhich theVat-icanhadGiordanoBrunoburnedat thestake in 1600y),so letus reviewthestatusof thetwo assumptions(in -nitespaceand\su cientlyuniform"distribution).How largeis space?Observationally, thelower boundhasgrowndramatically(Figure2) withnoindicationofanupper allaccepttheexistenceof thingsthatwe cannotseebutcouldseeif we moved or waited,like similarstatus,sincetheobservableuniverse growsby a light-yeareveryyearaslight fromfurtheraway hastimeto reach usz.

7 Sincewe areall taught aboutsimpleEuclideanspacein school,it canthereforebe dif- cultto imaginehow spacecouldnotbe in nite|forwhatwouldliebeyondthesignsaying\ SPACEENDSHERE|MINDTHEGAP"? Yet Einstein'stheoryofgravity allowsspaceto be niteby beingdi erentlycon-nectedthanEuclideanspace,say withthetopologyofyBruno'sideashave sincebeenelaboratedby, , Brundrit(1979),Garriga& Vilenkin(2001b)andEllis(2002),allofwhomh ave thus thecosmicexpansioncontinuesto accelerate(currentlyan open question), four-dimensionalsphereor a doughnut so thattravel-ingfarin onedirectioncouldbringyouback backgroundallowssensitive testsof such nitemodels,buthassofarproducednosupportf orthem| atin nitemodels tthedata neandstronglimitshave addition,a spatiallyin niteuniverseis a genericpredictionof thecosmologicaltheoryof in ation(Gar-riga& Vilenkin2001b).

8 Thestrikingsuccessesof in a-tionlistedbelow thereforelendfurthersupporttotheideathat spaceis afterallsimpleandin nitejustas welearnedin uniformis thematterdistributionon largescales?In an\islanduniverse"modelwherespaceis in nitebutallthematteris con nedtoa niteregion,almostallmembersof theLevel I multiversewouldbe dead,con-sistingof nothingbutempty modelshavebeenpopularhistorically, originallywiththeislandbe-ingEarthandthe celestialobjectsvisibleto thenakedeye, andin theearly20thcenturywiththeislandbeingthe knownpartof theMilkyWay Galaxy. Anothernon-uniformalternative is a fractaluniverse,wherethemat-terdistribut ionis self-similarandallcoherent structuresin thecosmicgalaxydistributionaremerelya smallpartof even largercoherent bothbeendemolishedby recent ob-servationsas reviewedin Tegmark(2002).

9 Mapsof thethree-dimensionalgalaxydistributionha ve shownthatthespectacularlarge-scalestruct ureobserved(galaxygroups,clusters,superc lusters,etc.) gives way todulluniformity onlargescales,withnocoherent , imagineplacinga sphereof radiusRat variousrandomlocations,measuringhow much massMis enclosedeach time,andcomputingthevariationbetweenthem easurements asquanti edby theirstandarddeviation M. Therelative uctuations M=Mhave beenmeasuredto be of orderunity on thescaleR 3 1023m,anddroppingon hasfound M=Mas smallas 1%onthescaleR 1025m andcosmicmi-crowave backgroundmeasurements have establishedthatthetrendtowardsuniformity continuesall theway outtotheedgeof ourobservableuniverse(R 1027m),where M=M 10 5. Barringconspiracytheorieswheretheunivers eis designedtofool us,theobservationsthusspeakloudandclear: spaceas we know it continuesfarbeyondtheedgeof ourobservableuniverse,teemingwithgalaxie s, WhatareLevel I paralleluniverseslike?

10 Thephysicsdescriptionof theworldis traditionallysplitinto two parts:initialconditionsandlawsof physicsspecifyinghow niteuniversehasalwaysbeenapossibility, thelower limitonthesizeof paralleluniversesat Level I observe theexactsamelawsof physicsas we do,butwithdi erent initialconditionsthanthosein thattheinitialconditions(thedensitiesand motionsof di erent types of matterearlyon)werecreatedby quantum uctuationsduringthein- ationepoch (seesection3).Thisquantummechanismgenera tesinitialconditionsthatareforallpractic alpur-posesrandom,producingdensity uctuationsdescribedby whatmathematicianscallanergodicrandom youimaginegeneratinganensem-bleof Universes ,each withitsownrandominitialcon-ditions,thent heprobability distributionof outcomesina givenvolumeis identicalto thedistributionthatyougetby samplingdi erent volumesin a ,it meansthateverythingthatcouldin prin-ciplehave happenedheredidin ationin factgeneratesall possibleinitialconditionswithnon-zeropro bability, themostlikelyonesbeingal-mostuniformwith uctuationsatthe10 5level thatxStrictlyspeaking,therandom eldis ergodicif 1) Spaceis in nite,2) themass uctuations M=Mapproach zeroonlargescales(asmeasurements suggest)