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.
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.