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*From*: Spinozalens@aol.com*Date*: Tue, 26 Jan 2010 07:18:40 EST

Holographic Induced Gravity

A paper by Erik Verlinde is causing some excitement in the Physics world.

Notable physicists such as DR t'Hooft have expressed interest in the

Verlinde's proposal. As it turns out Verlinde's proposal follows along the same

path as the recent posts I did on the Holographic principle and gravity,

making this particularly interesting for me.

Verlinde has proposed that Gravity rather being a fundamental force in

nature is an emergent property of the information content of space time. The

basic idea is related to the M Theory formulation of the Ads/CFT

correspondence , which defines M theory as essentially a Holographic theory of

nature. Based on this model, both gravity and space time (dimensionality) are

emergent properties of nature. Because of this, the Verlinde model is not in

conflict with the Weinberg Witten Theorem. ( Genius Lubros Motl take note)

Because General Relativity unites geometry and gravity any emergent model of

gravity must also be an emergent model of space time.

The Verlinde proposal has it roots in the Ads/ CFT Correspondence which

was first proposed by the Argentine American Physicist Juan Maldacena This

proposal is also known as the Maldacena Duality, a duality between open and

closed strings related by a boundary. The Ads/CFT correspondence is

essentially the string theory realization of Sakharov's Induced Gravity theory

which models gravity as the sum over the action density of the vacuum state. In

the Ads/CFT correspondence , integrating over the open string states on a

boundary is equivalent as the exchange of closed string states. Therefore

integrating over the open strings on a boundary projects closed strings

into a D+1 space, where D is the number of dimensions of the boundary. This

leads naturally to the emergence of gravity and space. In this way the

open/closed string duality supports the interpretation of gravity as an emergent

property of nature resulting from the statistical tendency for physical

systems to evolve to a maximal entropy state. Therefore gravity is revealed to

be an Entropic Force, rather than a fundamental force of nature.

Entropic forces are effective macroscopic forces which originates by the

statistical tendency for many degrees of freedom to increases their entropy

to a maximum value, i.e. the Bekenstein bound.( This has implication for

the source of Dark Energy which might be viewed as the realization of a

comoving patch of space time at a maximum entropy. We know that in the comoving

patch of space time we inhabit the value of vacuum energy density assures a

saturated Bekenstein bound. )

Entropic forces are often invoked to model colloid physical systems, a

fact which again seems to relate to the basic approach Sakharov applied to

model gravity. An Entropic force points in the direction of increased entropy

and is proportional to temperature. We can write the basic equation for

this;

F= div[S]*k*T

Where S is entropy, k is the Boltzmann's constant and T is temperature.

This basic relationship allows us to derive both inertia and the gravity

field, resulting in the unity of gravitational and inertial mass, the

equivalence principle. We can easily derive the Newtonian equations directly from

the Bekenstein bound.

Given that;

E=hbar*c*S/(2*pi*R)

and

dE/dS= k*T = hbar*c/(2*pi*R)

Incorporating the Horizon

R=c^2/a

we get

dE/dT=k*T=a*hbar/(2*pi*c)

If we consider a Holographic screen, a particle of mass m that approaches

from the side at which space time has emerged will effect the entropy

content of the screen. This is essentially the analysis used by Bekenstein in

deriving his entropy bound.

Div[S] = 2*pi*E*/(hbar/c)= 2*pi*m*c/hbar

Applying this in the direction of travel

dS/dx= 2*pi*m*c/hbar

Given the one dimension Entropic force equation;

F= dS/dx*K*T

It is simple to derive the Newton inertial equation;

F=m*a

We can also apply the Entropic equation to a mass within a boundary. We

have;

N=A*c^3/(G*hbar)

Where N is the information content.

Based on the equipartion rule;

E=(1/2)*N*k*T

Allowing us to easily derive the Newtonian equation for gravity;

a=G*M/R^2

Based on this we can also relate the Hawking Temperature to the gravity

force of a black hole.

F=k*T_H*(dS(bh)/dR)

Of course all this is a somewhat heuristic formalism. But in my view the

work of Verlinde and others who have applied the Holographic principle to

gravity are getting at something very profound. The ideas described here are

beautiful in their simplicity and unity. Time will tell if this idea is the

paradigm change that some suspect it is.

Bob Zannelli

On the Origin of Gravity and the Laws of Newton

Authors: _Erik P. Verlinde_

(http://arxiv.org/find/hep-th/1/au:+Verlinde_E/0/1/0/all/0/1)

(Submitted on 6 Jan 2010)

Abstract: Starting from first principles and general assumptions Newton's

law of gravitation is shown to arise naturally and unavoidably in a theory

in which space is emergent through a holographic scenario. Gravity is

explained as an entropic force caused by changes in the information associated

with the positions of material bodies. A relativistic generalization of the

presented arguments directly leads to the Einstein equations. When space is

emergent even Newton's law of inertia needs to be explained. The

equivalence principle leads us to conclude that it is actually this law of inertia

whose origin is entropic.

_http://arxiv.org/PS_cache/arxiv/pdf/1001/1001.0785v1.pdf_

(http://arxiv.org/PS_cache/arxiv/pdf/1001/1001.0785v1.pdf)

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