As many other theories about quantum mechanics, also this one is based on Nelson's idea of quantum mechanical effects in classical mechanics.
Unfortunately, Nelson's idea cannot explain all the quantum mechanical effects observed in nature. In order to apply Nelson's approach, we need that the velocity field is v=dS(x,t)/dx. This condition means that all the interference effects cannot be explained by Nelson's idea. By the way, it's worth noting that all the non-local effects of quantum mechanics are basically interference phenomena, so Nelson's idea reproduces only a "lesser quantum mechanics", that is local.
The same problem holds for this new paper.
A polemic consideration. If one understood the so called "many worlds interpretation", that is the Everett interpretation of quantum mechanics, he should be able to understand that the "lesser quantum mechanics" describes only a single world. The two ideas, or interpretations, cannot hold together!
Finally, it's time to note that many explanation of quantum mechanics in terms of statistical dynamics have been proposed, but none of them have been able to explain any experiment about quantum mechanics. Many people (including G. Parisi, for example) proposed a similarity between quantum field theory and classical statistical mechanics, but there's alwais a factor "i" that is wrong. There's a huge difference between diffusion equation and Schroedinger equation, though they differ only by a factor "i". I'm a supporter of many worlds theories, and I think that there are many experimental evidences of the real existence of different wave packets in interference experiments. This is in contrast with the "lesser quantum mechanics", where interference is not possible.
Best regards,
Doriano Brogioli
Saibal Mitra wrote:
http://arxiv.org/abs/gr-qc/0311059
*Authors:* Fotini Markopoulou <http://arxiv.org/find/gr-qc/1/au:+Markopoulou_F/0/1/0/all/0/1>, Lee Smolin <http://arxiv.org/find/gr-qc/1/au:+Smolin_L/0/1/0/all/0/1>
We provide a mechanism by which, from a background independent model
with no quantum mechanics, quantum theory arises in the same limit
in which spatial properties appear. Starting with an arbitrary
abstract graph as the microscopic model of spacetime, our ansatz is
that the microscopic dynamics can be chosen so that 1) the model has
a low low energy limit which reproduces the non-relativistic
classical dynamics of a system of N particles in flat spacetime, 2)
there is a minimum length, and 3) some of the particles are in a
thermal bath or otherwise evolve stochastically. We then construct
simple functions of the degrees of freedom of the theory and show
that their probability distributions evolve according to the
Schroedinger equation. The non-local hidden variables required to
satisfy the conditions of Bell's theorem are the links in the
fundamental graph that connect nodes adjacent in the graph but
distant in the approximate metric of the low energy limit. In the
presence of these links, distant stochastic fluctuations are
transferred into universal quantum fluctuations.
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