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

ICHEP conference, Paris , 22/07/10 GRAVITY AS AN EMERGENT FORCE Erik Verlinde University of Amsterdam

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 observed 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 Penrose associated with the particle gets Christodoulou redshifted, and vanishes when Bekenstein Hawking the particle is at the horizon.

Black Hole Entropy 3 Ac S BH k B 4 G h => Holographic Principle 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.

Bulk description Particle gets lowered Black in to black hole Hole In AdS space Hot CFT Boundary description: Delocalized state gets Thermal T thermalized by heath bath Heat Bath

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.

F T x S Heat Bath T Entropic Force Polymer S ( E , x ) k B log ( E , x )

 Thought experiment Black Hole black hole Horizon dr dx 1 2 GM / r E m 1 2 GM / r “ stretched dE GMm F 2 horizon” dx r

 Consistency with black Black Hole hole thermodynamics Horizon implies F x T H S BH g T H S BH 2 m x 2

x A HEURISTIC DERIVATION m OF GRAVITY information is stored on holographic screens moving a particle over one Compton wavelength leads to one more bit of information mc h S 2 k B x S 2 k B x mc h

x 1 h a k B T 2 c m T To get a force one needs a temperature. By taking that temperature to be the Unruh temperature one finds Newton’s law of inertia F ma F x T S

GMm F F F x T S 2 R T In order to get an entropic force I need a temperature 2 / # bits 1 2 k B T Mc 2 E Mc 3 Ac # bits G h

Holographic screens at equipotential (= equal redshift) surfaces

What about General Relativity? 1 a h log k B T a 2 c a timelike Killing vector 3 c Surface of constant redshift dn dA G h dA 8 GM Komar mass => Einstein equation

Rindler F ma F T x S ma Horizon a h T 2 k B c h x S mc 2 k B Suggestive link with QM: c v What is this velocity v ?

Cosmological De Sitter Horizon Space a 0 h T 2 k B c 2 a 0 c

Cosmological Horizon 2 2 a a 0 h T 2 k B c

Cosmological Horizon 2 2 a a 0 h T 2 k B c dS a h mc 2 k B dx 2 2 a a 0

2 v 2 Equipotential dv h surface T 2 k B dx h x S mv 2 k B v = escape velocity

Born-Oppenheimer & Adiabatic theorem Schroedinger eqn with H depending on infinitely slow variable i ( t ) H x ( t ) ( t ) t Instantaneous eigenstates H x n ( x ) E n ( x ) n ( x ) Adiabatic Reaction Force Semiclassically dE n dE dJ F ( x ) F dx dJ dx J pdq 2 n h

Born-Oppenheimer & Entropic Force The system stays in an energy eigenstate Microscopic of the fast variables ( adiabatic theorem). Fast Variables Macroscopic x Slow Variables E x

Born-Oppenheimer & Entropic Force Assuming eigenvalues ( E , x ) d E H ( , x ) don’t cross, the d energy follows from Macroscopic log E ( x ), x 0 dx Slow Variables E x

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 ds F 2 2 ) (-1) 3/2 exp - s(m i x s 0 i Open string one loop diagram ds F m i d -2 2 (-1) (5 -d)/2 exp - s x s 0 i Massless pole in dual channel F m i d -2 2 d ˜ ˜ x (-1) s dk exp ikx s k 0 i

UV/IR correspondence ds 2 ) F 2 (-1) 3/2 exp - s(m i x 1 s i Open string with UV cut off ds 1 F 2 2 ) (-1) 3/2 exp - s(m i x s 0 i F m i d -2 2 d ˜ ˜ (-1) s dk exp ikx s k i Closed string / gravity with UV cut off

Matrix description of gravity. x 11 .. x 1 N z 1 : :: : : X x N 1 .. x NN z N * * z 1 .. z N yI 2 ` tr [ X I , X J ] Ý 2 tr X I 2 z 2 2 Ý z ( x y )

Matrix description of gravity. x 11 .. x 1 N z 1 : :: : : X x N 1 .. x NN z N * * z 1 .. 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 observed 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 z x iy r v H x E x iy z ˆ r x x Dirac B r monopool 2 4 x At the locus of coinciding eigenvalues one can construct A ij i d j Non-abelian Berry