Lisa Randall, Harvard University AA NewNew ViewView ofof WeakWeak ScaleScale PhysicsPhysics ManyMany newnew resultsresults inin theoreticaltheoretical physicsphysics SomeSome ofof thethe mostmost excitingexciting involveinvolve extraextra dimensionsdimensions ofof spacespace IntriguingIntriguing possibilitiespossibilities forfor ourour universe:universe: bothboth theoreticaltheoretical andand experimentalexperimental WarpedWarped geometrygeometry hashas particularlyparticularly interestinginteresting signatures:signatures: resonances!resonances! ExtraExtra dimensionsdimensions ofof spacespace couldcould bebe thethe nextnext bigbig discoverydiscovery atat CERNCERN SamplingSampling ofof whatwhat wewe nownow knowknow isis possiblepossible——inin physics!physics! BraneworldsBraneworlds andand MultiversesMultiverses ExtraExtra dimensionsdimensions cancan bebe infinitelyinfinitely large,large, yetyet bebe invisibleinvisible NewNew placeplace inin thethe universe:universe: threethree--dimensionaldimensional sinkholesinkhole ExtraExtra dimensionsdimensions cancan illuminateilluminate connections,connections, resolvingresolving puzzlespuzzles ofof aa 3+13+1 dimensionaldimensional worldworld WithWith testabletestable experimentalexperimental consequencesconsequences WhyWhy shouldshould suchsuch differentdifferent resultsresults connect?connect? HighHigh--energyenergy physicsphysics coverscovers anan enormousenormous rangerange ofof energiesenergies AtAt thethe highesthighest energies,energies, wewe needneed aa theorytheory ofof quantumquantum gravitygravity——aa theorytheory thatthat includesincludes quantumquantum mechanicsmechanics andand generalgeneral relativityrelativity StringString theory,theory, inin whichwhich thethe fundamentalfundamental ingredientsingredients areare oscillating,oscillating, vibratingvibrating strings,strings, isis thethe leadingleading candidatecandidate LowerLower Energies?Energies? AtAt lowerlower energyenergy scales,scales, therethere areare physicalphysical phenomenaphenomena thatthat wewe cancan studystudy experimentallyexperimentally UnderstandUnderstand basicbasic elementselements ofof mattermatter andand theirtheir interactionsinteractions NewNew ideasideas mightmight provideprovide deeperdeeper connectionsconnections amongamong knownknown physicalphysical quantities:quantities: masses,masses, forcesforces TheseThese areare theoriestheories wewe cancan experimentallyexperimentally testtest TheThe bestbest route?route? Model Building: adventure travel through world of ideas ExtraExtra DimensionsDimensions OneOne Route?Route? StringString theory:theory: extraextra dimensionsdimensions essentialessential LowerLower energies:energies: ExtraExtra dimensionsdimensions cancan illuminateilluminate connectionsconnections amongamong observableobservable phenomenaphenomena inin newnew waysways TheyThey areare afterafter allall aa possibilitypossibility fromfrom perspectiveperspective ofof generalgeneral relativityrelativity Plus:Plus: Bonus:Bonus: EvenEven shedshed lightlight onon purelypurely fourfour-- dimensionaldimensional physicsphysics ExtraExtra DimensionsDimensions inin PhysicsPhysics TheodorTheodor KaluzaKaluza proposedproposed extraextra dimensionsdimensions inin 19191919 EinsteinEinstein (referee)(referee) delayeddelayed publicationpublication forfor twotwo yearsyears InterestingInteresting idea,idea, butbut whatwhat makesmakes thethe otherother dimensiondimension different?different? OldOld answeranswer:: ExtraExtra dimensionsdimensions cancan bebe rolledrolled upup toto aa tinytiny sizesize ButBut AlsoAlso NewNew AnswersAnswers…… HoseHose AcrossAcross FootballFootball FieldField Oskar Klein proposed idea that dimension is rolled up in 1926 If a dimension is wound sufficiently tightly you won’t see it 1 Dimensional Can see 2D or 3D with small probe Very intuitive; if sufficiently tiny, it doesn’t look like it’s there CurledCurled--upup DimensionDimension Entire universe is curled up! NewNew (1999)(1999) WayWay toto HideHide DimensionsDimensions BasedBased onon anan importantimportant ingredientingredient inin ““stringstring”” theorytheory whosewhose importanceimportance waswas onlyonly recentlyrecently recognizedrecognized BRANESBRANES MembraneMembrane--likelike objectsobjects inin higherhigher dimensionaldimensional spacespace PlayPlay anan essentialessential rolerole inin stringstring theorytheory WhatWhat’’ss New?New? BranesBranes Branes:Branes: DistinguishDistinguish dimensionsdimensions alongalong aa branebrane fromfrom thosethose perpendicularperpendicular toto itit BranesBranes cancan traptrap particlesparticles andand forcesforces Stuck on a brane like a bead on a wire Particles stuck on a brane like beads on a wire DD--Branes:Branes: WhereWhere OpenOpen StringsStrings EndEnd Particles and forces stuck on branes—not gravity! WhyWhy notnot gravity?gravity? GravityGravity ------closedclosed string:string: nono ends!ends! Energy:Energy: allall energyenergy interactsinteracts viavia gravitygravity Geometry:Geometry: gravitygravity connectedconnected toto spacetimespacetime BraneworldBraneworld HigherHigher--dimensionaldimensional worldworld inin whichwhich particlesparticles andand mattermatter areare stuckstuck onon aa branebrane Drawn as 2D Really 3D And really infinite WithWith branes,branes, wewe’’veve foundfound warpedwarped geometrygeometry SolutionsSolutions thatthat provide:provide: NewNew wayway toto hidehide dimensionsdimensions NewNew wayway toto explainexplain weaknessweakness ofof gravitygravity NewNew conceptconcept ofof ourour placeplace inin thethe universeuniverse RS2RS2 BraneworldBraneworld—— NewNew wayway toto hidehide aa dimensiondimension (LR with Raman Sundrum) Extra dimension can be infinite in size! Spacetime is warped and gravity stays near the brane. LocalizedLocalized Gravity:Gravity: WarpedWarped GeometryGeometry We solved equations for gravity and according to Einstein’s General Relativity All of spacetime is warped GravityGravity isis concentratedconcentrated nearnear thethe branebrane Tiny probability for gravity to leak away from brane GravitationalGravitational FieldField NearNear BraneBrane Force spreads very asymmetrically Lines of gravitational force almost parallel to brane Gravity doesn’t leak into extra dimension as you would expect without warping Localized gravity: new way to hide dimensions ExtraExtra dimensiondimension cancan bebe infiniteinfinite inin sizesize WithoutWithout usus knowingknowing aboutabout itit BecauseBecause warpedwarped gravitygravity spreadsspreads outout inin onlyonly threethree spatialspatial dimensionsdimensions ------NotNot fourfour (really,(really, tinytiny amountamount inin fourth)fourth) AlternativeAlternative toto rolledrolled--upup dimension!dimension! EvenEven MoreMore Dramatic:Dramatic: LocalityLocality ofof FourFour DimensionsDimensions WhyWhy shouldshould youyou needneed toto knowknow aboutabout spacespace farfar fromfrom thethe branebrane?? WithWith AndreasAndreas KarchKarch,, foundfound fourfour--dimensionaldimensional gravitygravity nearnear thethe branebrane ButBut higherhigher--dd everywhereeverywhere elseelse FourFour--dimensionaldimensional sinkholesinkhole ExcitingExciting butbut frustratingfrustrating CouldCould existexist somethingsomething asas dramaticdramatic asas anan infiniteinfinite extraextra dimension,dimension, pocketspockets ofof lowerlower-- dimensionaldimensional space,space, butbut wewe wouldnwouldn’’tt knowknow it!it! CanCan aa warpedwarped extraextra dimensiondimension bebe testedtested?? Yes,Yes, ifif connectedconnected toto ParticleParticle PhysicsPhysics HierarchyHierarchy Problem:Problem: OneOne ofof thethe biggestbiggest puzzlespuzzles inin particleparticle physicsphysics WhyWhy isis gravitygravity soso weakweak comparedcompared toto thethe otherother elementaryelementary forces?forces? MightMight notnot seemseem weakweak butbut magnetmagnet cancan taketake onon thethe entireentire Earth-Earth- HierarchyHierarchy ProblemProblem Need “fine-tuning” to get very different masses Key issue in particle physics today One that will be resolved at LHC ““FineFine--tuningtuning”” isis unlikely:unlikely: NoNo artistartist soso wewe needneed anan explanationexplanation Barnett Newman: Broken Obelisk RS1RS1 ““MultiverseMultiverse::”” WarpedWarped SpacetimeSpacetime GeometryGeometry LikeLike BeforeBefore •Now two branes •Gravity still concentrated on Gravitybrane •But we live on a second brane: •The Weakbrane NaturalNatural forfor gravitygravity toto bebe weak!weak! IfIf wewe livelive anywhereanywhere butbut thethe GravitybraneGravitybrane,, gravitygravity willwill seemseem weakweak SmallSmall probabilityprobability forfor gravitongraviton toto bebe nearnear thethe WeakbraneWeakbrane NaturalNatural consequenceconsequence ofof warpedwarped geometrygeometry RescalingRescaling AcrossAcross FifthFifth DimensionDimension EverythingEverything rescaledrescaled inin warpedwarped geometry!geometry! Can understand weakness of gravity as things being bigger and lighter on the Weakbrane WhatWhat rescalingrescaling meansmeans:: AnythingAnything onon oror nearnear thethe WeakbraneWeakbrane hashas OrderOrder TeVTeV--scalescale massmass AnythingAnything localizedlocalized inin thethe bulkbulk hashas CorrespondinglyCorrespondingly exponentiallyexponentially biggerbigger massmass OnOn GravitybraneGravitybrane--backback toto PlanckPlanck--scalescale massesmasses ParticlesParticles inin bulkbulk Planck 106 TeV 1000 TeV TeV ExperimentalExperimental Tests?Tests? ConnectionConnection toto massmass andand weaknessweakness