Professor of Physics, Harvard University

Why do scienceWhy do science

Ask deep and fundamental questions Ask deep and fundamental questions about world in which we liveabout world in which we liveAdvances in technology, medicine, way of Advances in technology, medicine, way of lifelifeTrain people to think analytically and Train people to think analytically and quantitativelyquantitativelyKeep the world interestingKeep the world interestingIt drives you crazy but it’s uniquely fun-It drives you crazy but it’s uniquely fun-And rewardingAnd rewarding

Scope of my area of physicsScope of my area of physics

I do theoretical particle physics, string theory, I do theoretical particle physics, string theory, and cosmologyand cosmologyParticle physics deals with the most basic Particle physics deals with the most basic structure of matterstructure of matterAnd nature’s fundamental lawsAnd nature’s fundamental lawsThose also have consequences at large scales: Those also have consequences at large scales: cosmologycosmologyCosmology deals with large scale structure of Cosmology deals with large scale structure of the universe and how it evolved this waythe universe and how it evolved this wayAnd at scales beyond which we can observe And at scales beyond which we can observe today: string theorytoday: string theory

At high energies: String TheoryAt high energies: String Theory

Theoretical problem of reconciling general Theoretical problem of reconciling general relativity (gravity, large scales)relativity (gravity, large scales)

With quantum mechanics (atomic scales)With quantum mechanics (atomic scales)

String theory, in which the fundamental String theory, in which the fundamental ingredients are oscillating, vibrating ingredients are oscillating, vibrating strings, is the leading candidatestrings, is the leading candidate

A quantum gravity (candidate) theory A quantum gravity (candidate) theory

Lower Energies?Lower Energies?

At lower energy scales, physical phenomena At lower energy scales, physical phenomena that we can study experimentallythat we can study experimentally

Understand basic elements of matter and their Understand basic elements of matter and their interactionsinteractions

New ideas might provide deeper connections New ideas might provide deeper connections among known physical quantities: masses, among known physical quantities: masses, forcesforces

These are theories we can experimentally testThese are theories we can experimentally test

The best route? The best route?

Model Building: adventure travel through world of ideas

Why are physicists thinking about Why are physicists thinking about extra dimensions?extra dimensions?

With extra dimensions we can:With extra dimensions we can: address problems that have baffled address problems that have baffled

physicists for yearsphysicists for years deduce connections we would otherwise deduce connections we would otherwise

missmiss

We wouldn’t understand why Inuits We wouldn’t understand why Inuits and Chinese people share common and Chinese people share common features without dimension of timefeatures without dimension of time

Could additional dimensions of Could additional dimensions of space show connections as space show connections as dimension of time already has?dimension of time already has?

Why extra dimensions now?Why extra dimensions now?

String theoryString theory: only makes sense with extra : only makes sense with extra dimensionsdimensions

Ten, eleven, ?? Ten, eleven, ??

What are the implications of the extra What are the implications of the extra ones?ones?

(String theory also introduces “(String theory also introduces “branesbranes”)”)

Spirit of InquirySpirit of Inquiry

We don’t know why there appear to be four We don’t know why there appear to be four spacetime dimensions spacetime dimensions No physical laws mandate thatNo physical laws mandate thatGeneral relativity works for any number of General relativity works for any number of dimensionsdimensionsMakes sense to explore alternativesMakes sense to explore alternativesTake up where Einstein left offTake up where Einstein left offWhat really are the consequences of our theory What really are the consequences of our theory of gravity when we stop straightjacketing of gravity when we stop straightjacketing ourselves to three spatial dimensionsourselves to three spatial dimensions

Best ReasonBest Reason

Seek a better understanding of our Seek a better understanding of our universeuniverse

And physical phenomena we observeAnd physical phenomena we observe

So what are (extra) dimensions?So what are (extra) dimensions?

We think about dimensions all the timeWe think about dimensions all the time We organize thoughts according to dimensionsWe organize thoughts according to dimensionsEven if we don’t explicitly think of it that wayEven if we don’t explicitly think of it that wayFor example, when buying a house, you’ll considerFor example, when buying a house, you’ll consider

sizesize locationlocation architecturearchitecture noise levelnoise level and the list goes onand the list goes on

You make this decision in a You make this decision in a multidimensional space.multidimensional space.

Each of the checked Each of the checked items is a dimensionitems is a dimension

More generally, we organize More generally, we organize categories of informationcategories of informationA database has multidimensional entries—categories of information

What about dimensions of space?What about dimensions of space?

??

•We are familiar with three dimensions: •x,y,z (up-down, forward-backward, left-right)•However, there may be more we don’t see!

Geometric objects of extra Geometric objects of extra dimensionsdimensions

Build them up sequentiallyBuild them up sequentially

Difficult to picture higher-dimensional analog…

Salvador Dali’s Salvador Dali’s Corpus HypercubusCorpus Hypercubus

Hypercube ProjectionsHypercube Projections

FLATLAND: EDWIN A ABBOTT, A2, Narrated by A Square

Flatland: Way to Imagine Flatland: Way to Imagine Dimensions of Dimensions of SpaceSpace

Suppose beings lived on a two-dimensional surface

How would they see three dimensions?

Flatlander’s View of SphereFlatlander’s View of Sphere

A Flatlander would see a series of disks that grew larger and then smaller

Ways to Think About Extra Ways to Think About Extra DimensionsDimensions

SlicesSlicesProjectionsProjectionsHologramHologramSuppress some dimensions when there is Suppress some dimensions when there is symmetrysymmetryAverage—when you can’t detect them, they Average—when you can’t detect them, they might as well not be theremight as well not be there

Best way: Math or Words—not Best way: Math or Words—not pictures!pictures!

Extra Dimensions in PhysicsExtra Dimensions in Physics

Theodor Kaluza proposed extra Theodor Kaluza proposed extra dimensions in 1919dimensions in 1919Einstein (referee) delayed publication for Einstein (referee) delayed publication for two yearstwo yearsInteresting idea, but what makes the other Interesting idea, but what makes the other dimension different?dimension different?Old answerOld answer: Extra dimensions can be : Extra dimensions can be rolled up to a tiny sizerolled up to a tiny sizeBut Also New Answers…But Also New Answers…

Compactification: Curled up Compactification: Curled up DimensionsDimensions

Oskar Klein proposed idea that dimension is Oskar Klein proposed idea that dimension is rolled up in 1926rolled up in 1926

If a dimension is wound sufficiently tightly If a dimension is wound sufficiently tightly you won’t see ityou won’t see it

e. g. Curled up to a very small circle e. g. Curled up to a very small circle

Very intuitive; if sufficiently tiny, it doesn’t Very intuitive; if sufficiently tiny, it doesn’t look like it’s therelook like it’s there

Hose Across Football Field

1 Dimensional

Can see 2D or 3D with small probe

Curled-up DimensionCurled-up Dimension

Entire universe is curled up!

New (1999) Way to Hide New (1999) Way to Hide DimensionsDimensions

Based on an important ingredient in “string” Based on an important ingredient in “string” theory whose importance was only theory whose importance was only recently recognizedrecently recognized

BRANESBRANES

Membrane-like objects in higher Membrane-like objects in higher dimensional spacedimensional space

Play an essential role in string theoryPlay an essential role in string theory

What’s New? BranesWhat’s New? Branes

Branes:Branes:

Distinguish Distinguish dimensions along dimensions along a brane from those a brane from those perpendicular to itperpendicular to it

Branes can trap particles and Branes can trap particles and forcesforces

Stuck on a brane like a bead on a wire

Water droplets on “shower brane”Water droplets on “shower brane”

Branes, like shower Branes, like shower curtains trap things curtains trap things (water droplets) on lower-(water droplets) on lower-dimensional surfaces. dimensional surfaces. Similarly, particles or Similarly, particles or strings can be confined to strings can be confined to a three-dimensional a three-dimensional brane sitting inside a brane sitting inside a higher-dimensional world. higher-dimensional world. Unlike the droplets on the Unlike the droplets on the curtain, particles would curtain, particles would be truly trapped: not free be truly trapped: not free to be anywhere. to be anywhere.

D-Branes: Where Open Strings D-Branes: Where Open Strings EndEnd

Particles and forces stuck on branes—not gravity!

Why not gravity?Why not gravity?

Gravity ---closed string: Gravity ---closed string: no ends!no ends!

Energy: all energy Energy: all energy interacts via gravityinteracts via gravity

Geometry: gravity Geometry: gravity connected to spacetimeconnected to spacetime

BraneworldsBraneworlds

Perhaps the stuff we know about (except Perhaps the stuff we know about (except gravity) is all trapped on a branegravity) is all trapped on a brane

Then we live in a Then we live in a braneworldbraneworld

BraneworldBraneworld

Drawn as 2D

Really 3D

And really

infinite

Higher-dimensional world in which particles and Higher-dimensional world in which particles and matter are stuck on a branematter are stuck on a brane

MultiversesMultiverses

If there can be one brane suspended in a If there can be one brane suspended in a higher-dimensional spacetime, higher-dimensional spacetime,

No denying the possibility of many more. No denying the possibility of many more. Braneworld scenarios often involve more Braneworld scenarios often involve more than a single brane. than a single brane.

MultiverseMultiverse is a cosmos with non- is a cosmos with non-interacting or only weakly interacting interacting or only weakly interacting pieces. pieces.

““Multiverse”Multiverse”

Different type of parallel world—different forces, life, etcDifferent type of parallel world—different forces, life, etc

Many PossibilitiesMany Possibilities

Universes with curled-up, warped, large, and Universes with curled-up, warped, large, and infinite dimensionsinfinite dimensionsSome of which contain a single brane and others Some of which contain a single brane and others of which have multiple branes housing unseen of which have multiple branes housing unseen worlds. worlds.

If extra dimensions are a physicist’s playground, If extra dimensions are a physicist’s playground, then then braneworldsbraneworlds—universes with some —universes with some particles trapped on a brane (or branes)—are particles trapped on a brane (or branes)—are the multi-faceted jungle gym.the multi-faceted jungle gym.

With branes, we’ve found:With branes, we’ve found:

New way to hide dimensionsNew way to hide dimensions

New way to explain weakness of gravityNew way to explain weakness of gravity

New concept of our place in the universeNew concept of our place in the universe

All Based on Warped GeometryAll Based on Warped Geometry

Warped SpacetimeWarped Spacetime

But all of spacetime can be warped as well!

Matter and energy warp spacetime

GravitationGravitation

RS2 Braneworld: new idea for RS2 Braneworld: new idea for hidden dimensionhidden dimension

(LR with Raman Sundrum)(LR with Raman Sundrum)

Gravity stays near the Gravity stays near the brane.brane.

Extra dimension can Extra dimension can be infinite!be infinite!

Localized Gravity:Localized Gravity:

Gravity is concentrated Gravity is concentrated near the branenear the brane

Tiny probability for gravity to leak away from brane

We solved equations for gravity and according We solved equations for gravity and according to Einstein’s General Relativityto Einstein’s General Relativity

All of spacetime is warpedAll of spacetime is warped

Force spreads very asymmetricallyForce spreads very asymmetricallyLines of gravitational force almost parallel to braneLines of gravitational force almost parallel to braneGravity doesn’t leak into extra dimension as you would Gravity doesn’t leak into extra dimension as you would expect without warpingexpect without warpingLocalized gravity: new way to hide dimensionsLocalized gravity: new way to hide dimensions

Gravitational Field Near Brane

Localized Gravity Infinite DimLocalized Gravity Infinite Dim

Compact Space Finite DimsCompact Space Finite Dims

Gravity is so strongly peaked near the brane that Gravity is so strongly peaked near the brane that gravity doesn’t leak awaygravity doesn’t leak away

Graviton essentiallyGraviton essentially bound bound to the brane to the brane

Not much difference between exhaustion and Not much difference between exhaustion and locked doorlocked door

You stay indoors either way!You stay indoors either way!

Summarize:Summarize:

Extra dimension can be infinite in sizeExtra dimension can be infinite in size

Without us knowing about itWithout us knowing about it

Because warped gravity spreads out in Because warped gravity spreads out in only three spatial dimensionsonly three spatial dimensions

---Not four (really, tiny amount in fourth)---Not four (really, tiny amount in fourth)

Alternative to rolled-up dimension!Alternative to rolled-up dimension!

Even More Dramatic: Locality of Four Dimensions

Why should you need to know about space far from the brane?

With Andreas Karch, found four-dimensional gravity near the brane

But higher-d everywhere else

Four-dimensional sinkhole

Exciting but frustratingExciting but frustrating

Could exist something as dramatic as an Could exist something as dramatic as an infinite extra dimension, pockets of lower-infinite extra dimension, pockets of lower-dimensional space, but we wouldn’t know dimensional space, but we wouldn’t know it!it!

Can a warped extra dimension be testedCan a warped extra dimension be tested??

Yes, if connected to Particle PhysicsYes, if connected to Particle Physics

Hierarchy Problem: One of the Hierarchy Problem: One of the biggest puzzles in particle physicsbiggest puzzles in particle physicsWhy is gravity so weak compared to the Why is gravity so weak compared to the other elementary forces?other elementary forces?

Might not seem weak but magnet can take on the entire Earth-

Hierarchy ProblemHierarchy Problem

Need “fine-tuning” to get very differentmasses

Key issue in particle physics today

One that will be resolved at LHC

““Fine-tuning” is unlikely:Fine-tuning” is unlikely:No artist so we need an No artist so we need an

explanationexplanation

Barnett Newman: Broken Obelisk

RS1 “Multiverse:”RS1 “Multiverse:”Warped Spacetime Geometry Like Warped Spacetime Geometry Like

BeforeBefore

•Now two branes

•Gravity still concentrated on Gravitybrane

•But we live on a second brane:

•The Weakbrane

If we live anywhere If we live anywhere but the Gravitybrane, but the Gravitybrane, gravity will seem gravity will seem weakweak

Small probability for Small probability for graviton to be near graviton to be near the Weakbranethe Weakbrane

Natural consequence Natural consequence of warped geometryof warped geometry

Natural for gravity to be weak!

Everything rescaled in warped Everything rescaled in warped geometry!geometry!

Can understand Can understand weakness of gravity as weakness of gravity as things being bigger and things being bigger and lighter on the lighter on the WeakbraneWeakbrane

Experimental Tests?Experimental Tests?

This scenario is testable This scenario is testable

Because of connection to mass and Because of connection to mass and weakness of gravity relative to other weakness of gravity relative to other known forcesknown forces, ,

Collider experiments will have the right Collider experiments will have the right energy to search for consequences of this energy to search for consequences of this theorytheory

CERN, LHC Ring: 2007CERN, LHC Ring: 2007

•Underground ring 27 km circumference located near GenevaUnderground ring 27 km circumference located near Geneva•Collide together two proton beams: make new particlesCollide together two proton beams: make new particles

KK Particles: Weak Scale KK Particles: Weak Scale Fingerprints of Extra DimensionsFingerprints of Extra Dimensions

With extra dimensions, there are new With extra dimensions, there are new Kaluza-Klein (KK)Kaluza-Klein (KK) particles particles

Travel and carry momentum in extra Travel and carry momentum in extra dimensionsdimensions

Look to us like particles with mass Look to us like particles with mass characteristic of the extra-dimensional characteristic of the extra-dimensional geometrygeometry

Experimental Signal: Can search Experimental Signal: Can search for extra dimensions!for extra dimensions!

Kaluza-Klein particlesKaluza-Klein particles

Definite mass Definite mass spectrum and “spin”-2spectrum and “spin”-2

Atlas Experiment: finds fingerprintsAtlas Experiment: finds fingerprints

I was there…I was there…

If extra dimensions solve the hierarchy If extra dimensions solve the hierarchy problem, we’ll know about it!problem, we’ll know about it!

And If we are very lucky, And If we are very lucky, five-dimensional five-dimensional black holes and string statesblack holes and string states might also might also appearappear

Entering a new era in physicsEntering a new era in physics

Every time we’ve explored smaller or Every time we’ve explored smaller or larger length scales, we’ve found new larger length scales, we’ve found new phenomena, new connectionsphenomena, new connectionsMany exciting new ideas for what we Many exciting new ideas for what we might discovermight discoverMore connections are there—we just have More connections are there—we just have to find themto find themSecrets of the universe are about to Secrets of the universe are about to unravelunravel

Hidden riches in the universeHidden riches in the universe