Entropic gravity and cosmology

[oldman]

Entropic gravity and cosmology

The considerable impact of Verlinde’s recent paper in which he suggests that gravity is nothing but an entropic force has familiarised many with this type of force.

Verlinde wrote:

An entropic force is an effective macroscopic force that originates in a system with many degrees of freedom by the statistical tendency to increase its entropy. The force equation is expressed in terms of entropy differences, and is independent of the details of the microscopic dynamics. In particular, there is no fundamental field associated
with an entropic force. Entropic forces occur typically in macroscopic systems such as
in colloid or bio-physics. Big colloid molecules suspended in an thermal environment
of smaller particles, for instance, experience entropic forces due to excluded volume
effects. Osmosis is another phenomenon driven by an entropic force. Perhaps the best
known example is the elasticity of a polymer molecule. A single polymer molecule can
be modeled by joining together many monomers of fixed length, where each monomer
can freely rotate around the points of attachment and direct itself in any spatial
direction. Each of these configurations has the same energy. When the polymer
molecule is immersed into a heat bath, it likes to put itself into a randomly coiled
configuration since these are entropically favored. There are many more such
configurations when the molecule is short compared to when it is stretched into an
extended configuration. The statistical tendency to return to a maximal entropy state
translates into a macroscopic force, in this case the elastic force.

The examples he mentions involve constituents in thermal equilibrium with a fluid heat
bath: a uniform liquid or, in the case of pressure --- also an entropic force --- a uniform
ideal gas.

In cosmology, the LCDM model is based on the cosmological principle that we are not
in any way specially situated in the universe. The model assumes that the universe’s
uniformly expanding spatial geometry is that of a homogeneous and isotropic everywhere gravitating cosmic fluid whose dynamics are ruled by general relativity. At first glance, therefore, gravity as an entropic force fits well into this scheme, based on a model fluid.

But the universe is not quite uniform. Wiltshire,
while discussing the modifications that he argues should be made to the perceived age of the universe and the perceived acceleration of expansion ---- because of inhomogeneities --- notes that:

At the present epoch... following the growth of complex structures from gravitational collapse, the universe is only statistically homogeneous if sampled on large scales of order 150–300 Mpc. A box of the size of statistical homogeneity may be as small as 100h−1 Mpc, where h is the dimensionless parameter related to the Hubble constant by H0 = 100h km sec−1 Mpc−1. ...If we include the numerous minivoids of smaller diameters, then the volume of thepresent universe is dominated by empty voids, while clusters of galaxies are spreadin a cosmic web of bubble-like sheets that surround the voids, and thin filaments that thread them.

I find puzzling the concept of gravity being treated as the same entropic force both in empty voids and deep inside galaxies, and get confused in trying to identifying the nature
of the heat bath which validates calling gravity an entropic force. Does the CMB perhaps act as a heat bath for gravity? And is there evidence that Newton's law of gravity (which Verlinde derives) is the same deep inside voids as it is deep inside galaxies?

 

[torquil]

Does the CMB perhaps act as a heat bath for gravity?

If I remember correctly, Penrose claims that the entropy of the radiation content in the universe is very small compared to that of black holes. If so, the CMB could not be considered a heat bath for gravity.

Anyway, is a heat bath necessary? After all, you can define entropy e.g. for a closed microcanonical system without a reference to any heat bath.

Torquil

 

[oldman]

If I remember correctly, Penrose claims that the entropy of the radiation content in the universe is very small compared to that of black holes. If so, the CMB could not be considered a heat bath for gravity.

Anyway, is a heat bath necessary? After all, you can define entropy e.g. for a closed microcanonical system without a reference to any heat bath.

Torquil

About the CMB, yes, I guess I was grasping at a straw. The examples used to illustrate the concept of "entropic force" --- colloids, osmosis, polymers, ideal gases --- all deal with pretty homogeneous systems equipped with "heat baths" , though. I can understand why classifying forces as "entropic" is appropriate here. But our present universe is so heterogeneous in a hierarchical way, ranging all the way from quarks to black holes, that I find the adjective "entropic" quite baffling when used for a force that rules such a mixed bag of stuff. Makes me unkindly suspect that all Verlinde is doing is reinventing wheels.

Especially when I look at papers like that of Jerzy Kowalski-Glikman (arXiv:1002.1035v1 [hep-th] 4 Feb 2010 ; A note on gravity, entropy, and BF topological field theory) in which it seems Faraday's lines of force are about to re-emerge in a much more sophisticated guise.

If only we could manipulate and experiment with gravity, as we so competently do with electromagnetism. Then there would be some hope of confirming theories of gravity with experiment and observation.