GRAVITY AS AN EMERGENT FORCE Erik Verlinde University of Amsterdam - - PowerPoint PPT Presentation

GRAVITY AS AN EMERGENT FORCE

Erik Verlinde

University of Amsterdam

ICHEP conference, Paris , 22/07/10

Emergence

Current Paradigm

FUNDAMENTAL FORCES: carried by elementary particles

Emergence of Particles and Forces

Gravity as an Emergent Force

• At a microscopic scale Nature is described by

many degrees of freedom, most of which are invisible and at first sight irrelevant for the

• bserved macroscopic physics.
• Gravity arises due to the fact that the amount of

phase space volume (“information”) occupied by these microscopic degrees of freedom is influenced by the observable macroscopic variables, like the positions of material objects.

Black Hole Horizon

• Black hole thought experiments.

Considera particle gradually lowered in to a black hole. Classically, the energy associated with the particle gets redshifted, and vanishes when the particle is at the horizon. Penrose Christodoulou Bekenstein Hawking

Black Hole Entropy => Holographic Principle

S BH k B Ac

3

4Gh

Maximal information associated with a part of space can be encoded in a # of bits equal to the area in Planck units

ADS/CFT CORRESPONDENCE

EQUIVALENCE BETWEEN FIELD THEORY ON THE “BOUNDARY” AND GRAVITY IN THE “BULK” ONE SPACE DIMENSION EMERGES CORRESPONDING TO THE “SCALE” OF THE BOUNDARY THEORY. RADIAL EVOLUTION IS LIKE RENORMALIZATION GROUP FLOW.

Black Hole In AdS space Bulk description Thermal Heat Bath

T

Delocalized state gets thermalized by heath bath

Boundary description:

Particle gets lowered in to black hole

Hot CFT

Entropic force (wikipedia)

An entropic force is a macroscopic force whose properties are determined not by the character of an underlying microscopic force, but by the whole system's statistical tendency to increase its entropy.

Heat Bath Entropic Force Polymer

T

F T

xS

S(E, x) kB log (E, x)

Black Hole Horizon

• Thought experiment

dx dr 1 2GM / r

E m 1 2GM / r F dE dx GMm r

2

“stretched horizon” black hole

Black Hole Horizon

• Consistency with black

hole thermodynamics implies

F x TH SBH

TH g 2

S BH 2 m x

information is stored on holographic screens moving a particle over one Compton wavelength leads to one more bit of information

S 2 k B

x

m

x h mc

A HEURISTIC DERIVATION OF GRAVITY

S 2 k B mc h x

To get a force one needs a temperature. By taking that temperature to be the Unruh temperature

• ne finds Newton’s law of inertia

x

m

F x T S

T

k BT 1 2 ha c

F ma

In order to get an entropic force I need a temperature

T F

E Mc

2

1 2 k BT

Mc

2 / # bits

# bits Ac

3

Gh

F x T S

F GMm R

2

Holographic screens at equipotential (= equal redshift) surfaces

What about General Relativity?

Surface of constant redshift

k BT 1 2 h c

Komar mass => Einstein equation

dn c

3

Gh dA

dA 8 GM

log

a a

a

timelike Killing vector

T h 2 k B a c

h 2 k B

xS

mc

F ma

Rindler Horizon

F T

xS

ma

c v Suggestive link with QM: What is this velocity v ?

Cosmological Horizon

T h 2 k B a0 c

De Sitter Space

a0 c

2

Cosmological Horizon

T h 2 k B a

2

a 0

2

c

Cosmological Horizon

T h 2 k B a

2

a 0

2

c

h 2 k B dS dx mc a a

2

a 0

2

T h 2 k B dv dx

h 2 k B

xS

mv

v

2

2

Equipotential surface v = escape velocity

Born-Oppenheimer & Adiabatic theorem

i t (t) H x(t) (t) H x

n ( x)

E n (x)

n ( x)

Schroedinger eqn with H depending on infinitely slow variable Instantaneous eigenstates Adiabatic Reaction Force

F dE n dx ( x )

J pdq 2 nh

Semiclassically

F dE dJ dJ dx

Microscopic Fast Variables

Born-Oppenheimer & Entropic Force

x

Macroscopic Slow Variables

x

E

The system stays in an energy eigenstate

• f the fast variables( adiabatic theorem).

Born-Oppenheimer & Entropic Force

Macroscopic Slow Variables

x

E

( E , x) d E H ( , x)

d dx log E ( x ), x

Assuming eigenvalues don’t cross, the energy follows from

What lives on the screens?

According to string theory: open strings.

Integrating out the UV open strings produces closed strings in the emerged space.

Open closed string duality

(-1)

F

ds s

3/2 exp - s(m i 2 i

x

2)

(-1)

F m i d -2

ds s

(5 -d)/2 exp - s i

x

2

(-1)

F m i d -2

d˜ s dk exp

i

ikx ˜ s k

2

x

Open string one loop diagram Massless pole in dual channel

UV/IR correspondence

(-1)

F

ds s

3/2 exp - s(m i 2

1

i

x

2)

(-1)

F m i d -2

d˜ s dk exp

i

ikx ˜ s k

2

(-1)

F

ds s

3/2 exp - s(m i 2

1

i

x

2 )

Open string with UV cut off Closed string / gravity with UV cut off

Matrix description of gravity.

tr Ý X I

2 ` tr [ X I , X J ] 2

Ý z

2

(x y )

2 z 2

X x11 .. x1N z1 : :: : : x N 1 .. x NN z N z1

*

.. z N

*

yI

Matrix description of gravity.

X x11 .. x1N z1 : :: : : x N 1 .. x NN z N z1

*

.. z N

*

yI T

F

Gravity as an Emergent Force

• At a microscopic scale Nature is described by

many degrees of freedom, most of which are invisible and at first sight irrelevant for the

• bserved macroscopic physics.
• Gravity arises due to the fact that the amount of

phase space volume (“information”) occupied by these microscopic degrees of freedom is influenced by the observable macroscopic variables, like the positions of material objects.

Berry Phase and Crossing Eigenvalues

x

E

H z x iy x iy z v x r r B ˆ x 4 r x

2

Dirac monopool At the locus of coinciding eigenvalues

• ne can construct

Non-abelian Berry

A ij

i d j