EXTRA DIMENSIONS: FLOUTING CONVENTIONAL WISDOM in Particle Physics and Cosmology. Lisa Randall Harvard University

Transcription

1 EXTRA DIMENSIONS: FLOUTING CONVENTIONAL WISDOM in Particle Physics and Cosmology Lisa Randall Harvard University

2 Everything you never wanted to know about extra dimensions But don t be afraid to ask TM Lisa Lisa Randall Harvard University, Radcliffe

3 Introduction: Standard Lore is that there are three dimensions of space Strong Evidence Detailed tests of gravity Force laws, more on this later It s obvious!

4 Not necessarily true! There can be more than 3 dimensions We actually don t (yet) know Need to distinguish what we take for granted and what has been verified Extra dimensions are not only permissible, but they can resolve puzzles of 3+1 dimensions

5 Outline Review gravity, notion of extra D Demonstrate viability of extra dimensions Curled up Even infinite ones (in warped space)! Why Particle Theorists Care Why Cosmologists Care

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7 Gravity Physical Experience Other forces compete with gravitational force of entire Earth! Gravitational force on Earth: a=9.8 m/sec 2 For later: paradoxically, gravity extremely weak

8 Newtonian Gravity F ~ 1/r 2 60 R e Many confirmations: Solar system Detailed gravity experiments

9 Inverse square law: 1/r 2 Easy to understand Force is isotropic Force lines uniformly distributed over the surface of a sphere F ~ 1/r 2 Notice connection to 3 spatial dimensions!

10 General Relativity Matter determines geometry Curved geometry introduces gravity Matter warps space- time Distorted space yields gravitational force

11 Not the end of the story Major physics revolutions of the last century General Relativity Large Scales Cosmological Incompatible! Quantum Mechanics Small scales Particles, electrons, quarks Classical stationary background vs. uncertainty and short distance String Theory reconciles the two cm cm cm cm cm cm

12 String Theory Expected to reconcile Quantum Mechanics and Gravity Only consistent with more than 3 dimensions of space! Generally need 9 (or more)! Very dramatic consequences But why don t we see them? String theorist: NOT do do extra dim dim exist exist Where are are they? Extra d? Sounds Interesting Nonstring theorist: Logical possibility Einstein doesn t pick pick out out 3D 3D

13 Rapid Intro to Xtra D Thinking about more than 3 D is done every day Most don t think of it that way One dimensional: hr/wk at work Multidimensional person: works, plays, reads, does sports, engages in in political activity (40, (40, 10, 10, 7, 7, 6, 6, 3) 3) # hours on on each activity 5 5 D: D: hard hard to to plot plot Database has has multidimensional information Dimension: number of of points to to specify the the person/thing

14 Dimensions of space Number of points needed to specify location of an object We are familiar with 3 (or less) We can only see projections of higher dimensions FLATLAND: EDWIN A ABBOTT, A 2, 2, Narrated Narrated by by A Square What is is it it?

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16 Geometric objects of extra dimensions Build them up sequentially

17 Hypercube Projections

18 Dimensions D: Number of points to specify location With space, also need metric Tells how you measure distance Inches, meters, miles, parsecs? And angles: is space flat or curved? Sphere vs. flat space Necessary in 3D, necessary in more

19 Compactification: : Curled up Dimensions If a dimensions is wound sufficiently tightly you won t see it e. g. Curled up to a very small circle Very intuitive; if sufficiently small, it doesn t look like it s there 2 D can 1 Dimensional see 2 or or 3D with small probe

20 Why does force law appear correct? 4 D r c For r>r c, F ~ 1/r 2 For r<r c, F ~ 1/r 2+n Don t see extra dimension at low energy or long distance But how big would the extra dimensions be?

21 Novel Way to Hide Dimensions LR, Sundrum An important ingredient in string theory was only recently recognized BRANES Like membranes in a higher dimensional space Play an essential role in string theory

22 BRANES electron quark Stuck on a brane like a bead on a wire Weaker bounds on extra dimensions size

23 BRANES Branes carry energy and momentum According to Einstein s General Relativity, this means branes bend surrounding space Geometry is warped 3+1 D branes with fifth additional dimension Dramatic curvature of space

24 Brane Localized Gravity Br ane Bulk Energy Energy, E Prob biggest near brane Prob finding graviton Tiny prob away

25 Localized Gravity Infinite Dim Compact Space Finite Dims The graviton is so strongly peaked near the brane that gravity doesn t leak away Graviton essentially bound to the brane Difference between exhaustion and locked door You stay indoors either way! Force law is correct because Force lines spread very asymmetrically Lines almost parallel to brane

26 Exciting but frustrating Exists something as dramatic as an infinite extra dimension but we don t know it! Can this be tested? Yes, if connected to Particle Physics (or Cosmology)

27 Hierarchy Problem Related to electroweak mass scale Where masses arise Must be much less than gravity mass scale Force Strong Electromag Weak Gravity Mediating Particle Gluon Photon W, Z Graviton Interaction strength 4 pi 1/3 1/2 E/10 19 GeV ~E/M Pl 17 order of mag difference Mass of particle GeV 0

28 Localized Gravity and the Hierarchy Suppose multiverse multiverse : two branes On one brane gravity is very strong On the other, gravity is very weak Geometry naturally explains hierarchy!! Gravity Brane Weak Weak Brane Brane Gravity is exponentially suppressed! e -35 ~ 10-17

29 Natural for gravity to be weak! If we live anywhere but the gravity brane, gravity will seem weak If we live on the weak brane gravity is so weak that the mass hierarchy is natural Gravity so weak because of small prob for graviton to be near the weak brane This scenario is testable at high energy colliders

30 Heralds of extra dimensions With extra dimensions, there are new (Kaluza- Klein) particles Carry momentum in extra dimensions Look to us like particles with mass characteristic of the extra-dimensional geometry Because of connection to hierarchy and weak mass physics, mass will be about 1000 GeV Precisely the energy that will be explored in upcoming collider experiments: LHC If we are very lucky, five-dimensional black holes and string states might also appear

31 Experimental Signal Kaluza-Klein particles Definite mass spectrum and spin -2 qq q KK particle e + e -

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34 Extra Dimensions and Unification Forces Strength of three nongravitational forces might be the same at high energy In that case, there could be a single unifying force at high energy (temperature) Never quite unifies with gravity however Except with larg(ish) ) extra dimension 4D 4D force H-W H-W RS RS Forces 5D 5D force unification

35 Bulk Unification Unification a feature of five-dimensional theory! Can calculate strength of coupling in bulk Find very natural to have unification Coupling strength energy Gravity energy

36 Bulk Calculation High E Low E

37 Extra Dimensions and Sequestering Extra dimensions introduce new possibilities for Particle Physics New parameters: size, curvature Also new tool: locality Field theory: Totalitarian Principle Everything interacts Not true with extra dimensions Particles don t interact

38 Extra Dimensions and Cosmology The problem of unexplained large numbers is even worse in cosmology The universe is extraordinarily big, smooth, homogeneous, isotropic Inflation is invoked to solve these problems With inflation, universe undergoes period of exponential expansion During this time, constant expansion rate

39 Requirements for Inflationary Potential Potential must be flat for a long time But inflation ends: phase where not flat And reheating: must interact with other fields

40 Alternative Idea: Don t have very flat potential Have large field value (greater than quantum gravity scale) Here no bizarre potentials required But need large field values Need lower energy than M Pl Only sensible with additional dimensions A nice candidate is particle associated with extra dimensional forces Potential very constrained if it wraps an extra dimension by locality

41 Inflation and Extra Dimensions Problem is that 3+1-dimensional physics doesn t give any obvious candidates to trigger expansion Turns problem of large numbers into a different problem of small numbers With extra dimensions, very natural inflationary physics Particle mediating force Winds around curled up up dimension Potential for for such a field field very very constrained

42 Predictions This model predicts significant (visible) deviation from flat spectrum Gravity waves that should be seen! Inflationary evidence for extra dimensions possible?!?

43 Infinite Extra Dimensions Give Radically Different Conception of Universe Black holes and gravity extend a bit into the fifth dimension Extremely small decay away from brane into the bulk higher dimensional space Natural scale for gravity depends on location! Evolution of universe involves more than 3 dimensions.

44 Even more dramatic possibility 5D 5D gravity Dimensionality depends on location! LR, Karch Could see different dimensions in different places Determined by gravity bound state in that region 4D 4D gravity 4D 4D gravity 5D 5D gravity

45 Conclusions Implications for : Particle Physics Theory PP Experiment General Relativity String Theory Cosmology: explore time-dependence Rich blossoming field Yet to understand all connections

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