Professor of Physics, Harvard University. Why do science Ask deep and fundamental questions about...
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Professor of Physics, Harvard University
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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
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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
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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
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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
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The best route? The best route?
Model Building: adventure travel through world of ideas
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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?
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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”)”)
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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
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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
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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
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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!
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Geometric objects of extra Geometric objects of extra dimensionsdimensions
Build them up sequentiallyBuild them up sequentially
Difficult to picture higher-dimensional analog…
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Salvador Dali’s Salvador Dali’s Corpus HypercubusCorpus Hypercubus
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Hypercube ProjectionsHypercube Projections
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FLATLAND: EDWIN A ABBOTT, A2, Narrated by A Square
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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?
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Flatlander’s View of SphereFlatlander’s View of Sphere
A Flatlander would see a series of disks that grew larger and then smaller
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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!
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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…
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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
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Hose Across Football Field
1 Dimensional
Can see 2D or 3D with small probe
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Curled-up DimensionCurled-up Dimension
Entire universe is curled up!
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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
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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
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Branes can trap particles and Branes can trap particles and forcesforces
Stuck on a brane like a bead on a wire
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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.
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D-Branes: Where Open Strings D-Branes: Where Open Strings EndEnd
Particles and forces stuck on branes—not gravity!
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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
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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
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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
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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.
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““Multiverse”Multiverse”
Different type of parallel world—different forces, life, etcDifferent type of parallel world—different forces, life, etc
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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.
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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
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All Based on Warped GeometryAll Based on Warped Geometry
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Warped SpacetimeWarped Spacetime
But all of spacetime can be warped as well!
Matter and energy warp spacetime
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GravitationGravitation
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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!
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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
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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
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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!
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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!
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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
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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
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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-
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Hierarchy ProblemHierarchy Problem
Need “fine-tuning” to get very differentmasses
Key issue in particle physics today
One that will be resolved at LHC
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““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
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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
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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!
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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
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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
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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
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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
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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
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Atlas Experiment: finds fingerprintsAtlas Experiment: finds fingerprints
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I was there…I was there…
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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
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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
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Hidden riches in the universeHidden riches in the universe