Recently, there was a rapid communication published in Phys.Rev.D (PRD 83, 021502), titled "Gravity is not an entropic force", that claimed that an experiment performed in 2002 with ultra cold neutrons in a gravitational field, disproves Verlinde's entropic approach to gravity.
The neutrons experiment gave results consistent with the predictions of Newtonian gravity for the lowest energy state.
As I understand it, the author claims that the fact that Verlinde's entropic force comes from a thermodynamic process that is irreversible (or approximately reversible), leads to non-unitarity in the evolution of quantum systems. The non-unitarity then exponentially suppresses the eigenfunctions, predicting results very much different than the Newtonian. Thus, that experiment is in contradiction to what is expected if Verlinde's approach is correct.
My questions are,
- First of all, is there anything else essential that I am missing?
- Is there any response to that argument?
- Is that a fatal problem with Verlinde's entropic approach?
- Is that a fatal problem for any entropic approach?
Updates on the discussion:
- There is also this recent comment arxiv.org/abs/1104.4650
- Once more: gravity is not an entropic force arxiv.org/abs/1108.4161
Best Answer
This question has introduced me to the whole "entropic force" area which has several papers during 2010. I see that there are references to "entropic force" explanations for Coulomb's law and other areas too. Here is a link to a simple introduction to these ideas.
The Verlinde paper and others however are deriving Newtons Law, Einstein's GR etc as classical theories. The underlying formulation of course being a stochastic behaviour of unknown microstates. Despite the presence of $\hbar$ and the motivation from the Black Hole area formulae the Verlinde paper does not introduce an explicit link with quantum mechanics. Thus there is no derivation of Schrodinger's equation and no introduction of $\Psi$.
The Kobakhidze paper says "One starts with a "holographic screen” S which contains macroscopically large number of microscopic states which we denote as $\left|i(z)\right\rangle$, $i(z) = 1, 2, ...,N(E(z), z).$ The screen is then described by the mixed state
$$\rho(z)=\sum p_{i(z)}\left|i(z)\rangle \langle i(z)\right|$$
However Verlinde does not explicitly introduce microstates as quantum states, with density matrices etc, although this is a tempting extension.
Now it might be that this is the only sensible quantum development of the stochastic basis of the "entropic idea", but Verlinde has not taken it. So what is disproved is a theory that Verlinde has not written down.
Having said this, there is a resemblance between "entropy" and the idea of introducing "stochastics" into quantum theory. One such attempt is known as "Stochastic Electrodynamics" (link to Wikipedia). As you will see from the summary this has had successes with e.g. the Unruh effect, but problems modelling genuine quantum phenomena.
I dont know whether anyone has considered combining the two areas directly.