Now the idea that gravity has a relation to thermodynamics is not new. It's been around since decades and has maybe most clearly been pointed out by Ted Jacobsen. I thus fail to see what's so particularly offensive about Verlinde's recent contribution. Jacobson's paper however is 15 years old, and not much seems to have come out of it, at least not that I know of. So I'll admit that I read Verlinde's paper feeling obliged to follow what's going on in my research area, thinking it's either wrong or meaningless or both.
In the course of my reading it became clearer to me what was the actual content of the paper. And what not. If you are interested, I have written up my notes and uploaded them here:
- Comments on and Comments on Comments on Verlinde’s paper “On the Origin of Gravity and the Laws of Newton”
Here is a short summary: With a suitable definition of quantities, describing gravity by a Newtonian potential or describing it as an entropic force in terms of an "entropy," "temperature" and "holographic screens" is equivalent. One can do it back and forth. The direction Verlinde has shown in his paper is the more difficult and more surprising one. That it works both ways relies on the particularly nice properties that harmonic functions have. Formally, one can also do this identification for electrostatics. In this case however one finds that the "temperature" can be negative and that the "entropy" can decrease without having to do work.
Some assumptions made in the paper are actually not necessary. For example, the equipartition theorem for "bits on the screen," and the explanation for why the change in entropy is proportional to the distance the particle is shifted. One doesn't actually need that. The equivalence works pretty well for the case of Newtonian gravity, but when it comes to General Relativity things are getting somewhat murky.
The biggest problem is that Verlinde's argument to show that gravity can be derived from a thermodynamical description already makes use of quantities that belong on the gravity side. To really show that gravity can be obtained from thermodynamics, one would have to express the gravitational quantities in terms of thermodynamical ones. Unfortunately, Verlinde does it the other way 'round. He also has to use a lot of previous knowledge from General Relativity. It does not seem entirely impossible to actually do this derivation, but there are some gaps in his argument.
In any case, let us consider for a moment these gaps can be filled in. Then the interesting aspect clearly is not the equivalence. The interesting aspect is to consider the thermodynamical description of gravity would continue to hold where we cannot use classical gravity, that it might provide a bridge to a statistical mechanics description of a possibly underlying more fundamental theory. The thermodynamical description might then be advantageous for example in regimes where effects of quantum gravity become strong. Maybe more banally, you might ask what's the gravitational field of a superposition state, a state that is neither "here" nor "there." It can't have a gravitational field in the classical sense. But the thermodynamical description might still work. However, the treatment Verlinde offers is purely classical. It's not even quantum particles in a classical background, it's classical particles in a classical background. So there's way to go.
Taken together, I can see the appeal. However, at the present level it is very unclear to me what the physical meaning of the used quantities is. I would like to add that Erik Verlinde has kindly replied to my queries and patiently clarified several points in his argument.
Update March 04: The notes are now on the arxiv:1003.1015v1 [gr-qc]