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the physics of extra dimensions

Joseph LykkenFermi National Accelerator Laboratory

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a revolution in physics

the physics of extra dimensions is a revolution in the making

like the quantum mechanics revolution of the 1920’s, it is the result of many new ideas (from many people) coming together to give a radically new picture of physics and of the universe

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the universe: traditional view

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the universe: a bigger view

extra dimensions of space

the rest is terra incognita

everything we know about is on this slice

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why do physicists think that there are extra dimensions of space?

what is the physics that hides extra dimensions?

how can experiments discover and explore extra dimensions?

questions for this talk

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why do physicists think that there are extra dimensions of space?

supermassive black hole inthe center of galaxy M87

Reason #1: string theory

particle physicists developed string theory tounderstand quantum gravity - to explain extremephysics such as goes on inside black holes

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string theory

in string theory, all the elementary particlesare merely different vibrations of asingle substance called strings.

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string theory

physicists have shown that quantum theoryonly allows one unique theory of quantumstrings… but there is a catch:

quantum strings need 9 spatial dimensions to wiggle in!

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why do physicists think that there are extra dimensions of space?

Reason #2: mysteries of particle physics

all ordinary matter is composed of justthree kinds of elementary particles.

but in particle accelerators we producemany more!

why do these extra particles exist,and why these particles but not others?

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in string theory the answer liesin the shape of the extra dimensions

determines how many ways the strings can vibrate,and thus whether there are 3, 12, or 137 kinds ofelementary particles.

particle physics data already in our hands is anencrypted map of the geography of extra dimensions.

slice of a6 dimensional Calabi-Yau space

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why do physicists think that there are extra dimensions of space?

Reason #3: the Big Bang

the three spatial dimensions thatwe see are changing – expanding

we don’t understand what is thedark energy driving the expansiontoday

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why do physicists think that there are extra dimensions of space?

Reason #3: the Big Bang

the three spatial dimensions thatwe see are changing – expanding

we don’t understand what drovecosmic inflation in the earlyuniverse

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why do physicists think that there are extra dimensions of space?

Reason #3: the Big Bang

the three spatial dimensions thatwe see are changing – expanding

we don’t understand whatthis was

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why do physicists think that there are extra dimensions of space?

Reason #3: the Big Bang

the three spatial dimensions thatwe see are changing – expanding

extra dimensions may be theextra ingredient that explainsthe history of the universe

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long ago philosopher Immanuel Kant gavea ~500 page proof that space and time area priori

however to make sense of quantum gravity,not to mention the Big Bang singularity,this cannot be true

in the real theory of everything,spacetime should be emergent.

emergent spacetime

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if extra spatial dimensions exist, they must be(for some reason) difficult to probe

physicists have uncovered several possibleexplanations:

hidden dimensions

the additional spatial dimensionsare compact and small

Nordstrom, Kaluza, and Klein, circa 1920Nordstrom, Kaluza, and Klein, circa 1920

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compact extra dimensionscompact extra dimensionswhat do we look for experimentally?…

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Kaluza-Klein modesKaluza-Klein modes

if spatial dimension is compactthen momentum in thatdimension is quantized: R

np =

from our point of view we see new massive particles!

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220

2

Rn

mm +=

pR1R2R3R4

0

∞→R

KK momentumtower of states

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how do we look for new massive particles?

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2121stst century particle physics century particle physics

Fermilab’s Tevatron is the highestenergy accelerator in the worldtoday.

beams of protons collide with beams ofantiprotons.antiprotons.

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physicists have uncovered several possibleexplanations:

hidden dimensions

it may be that not all particles(in a certain energy range)move, probe, or seethe same number of spatial dimensions

e.g. the Braneworld

brane-worldsbrane-worlds

Standard Model particles are trapped on a brane andStandard Model particles are trapped on a brane andcan’t move in the extra dimensionscan’t move in the extra dimensions

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if we are stuck on a brane world,only gravity tells us about the extra dimensions

this hides the extra dimensions quiteefficiently, since gravity effects are hard to measure

only the graviton (the force particle of gravity)can move off the brane into extra dimensions

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gravitonsgravitonsmay be our only probe of extra dimensions

but gravity is so weak that we have nevereven seen a graviton.

The gravitational attraction between two electrons isabout 1042 times smaller than the electromagneticrepulsion.

F=GF=GNNmelectronmelectron

r2

rmelectron melectron

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gravity gets stronger at extremely high energies(or short distances).

forc

e st

reng

th

energy

4d gravity

(4+n

)d gr

avity

it gets stronger at not-so-high energies(not-so-short distances) if there are extra dimensions….

extra dimensions change gravity

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2*

2 ~ +nnPlanck MRM

ADD braneworld modelsADD braneworld modelsArkani-Hamed, Dimopoulos, Dvali

assume that only gravity sees assume that only gravity sees nn largelarge extra extra compact dimensions with common size compact dimensions with common size R:R:

in ADD models in ADD models MM** ~ ~ 1 TeV,1 TeV,the energy reached by the Fermilab Tevatronthe energy reached by the Fermilab Tevatron

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fm 10~ 7,6

nm1~ 3mm1~ 2

Km10~ 1 9

Rn

RnRnRn

⇒=

⇒=⇒=⇒= Solar system

Pinhead

Gold atom

these are large extra dimensionsthese are large extra dimensions

we can test these models in experiments

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Force lawsForce laws

large extra dimensions appear at length scale Ras exchange of massive graviton KK modes,changing the gravitational force law

look for these deviationsin short-range gravity expts

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Gµν

fi

fj

gα

(n)

a gα(k1)

gβ(k2)b

agluon (becomes“jet” of hadrons)

graviton

quark

antiquark

if gravity gets stronger at high energies…then high energy gravitons may be produced in collider experiments:

these gravitons probably “escape”these gravitons probably “escape”into the extra dimensions into the extra dimensions

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Randall–Sundrumwarped space

zero mode graviton likes tozero mode graviton likes tobe near mother, but massivebe near mother, but massivemodes do notmodes do not

mother branemother brane

GG

5th dimension5th dimension5th dimension

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compactified space: R <~ 10-16 cm ADD braneworlds: R <~ 200 microns warped braneworld : R <= infinity!

the warped braneworlds hide theextra dimensions even more efficientlythan ADD braneworlds:

current experimental upper boundson the size of extra dimensions:

collider signals can also be dramatically different

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science fiction, science factscience fiction, science fact

although extra dimensions isalthough extra dimensions isa pretty weird concept,a pretty weird concept,physics has already producedphysics has already producedmany even weirder phenomenamany even weirder phenomena

the real leap of imaginationthe real leap of imaginationis designing experiments tois designing experiments toexplore the extra dimensions - if they exist.explore the extra dimensions - if they exist.

35Large Hadron Collider (CERN, 2007)

new accelerators for new physics

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new accelerators for new physics

Linear Collider

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emergent spacetime

a great theoretical challenge for the futureis to figure out where spacetime comes fromin the first place

spacetime must somehow arise “dynamically”,but what does dynamics mean without spacetime?

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what is a dimension, anyway?

a good starting point is to realize that, operationally,an extra dimension of space just means new degreesof freedom of a certain type (Kaluza-Klein modes).

but we already have discovered examples instring theory (e.g. AdS/CFT) where new degreesof freedom can be interpreted either as an extradimension or as new dynamics without anextra dimension!

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deconstructing dimensions

recently we have even discovered how to dothis in simple models that do not carry allthe heavy baggage of full-blown string theory

these “deconstruction models” are a first stepto a more dynamical understanding ofspacetime dimensions

particle theorists are learning to think differently…

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