Dear Saibal,
    A most interesting paper. It seems to me that Fotini and Lee are fooling themselves by being surprised that a quantized theory emerges when they start off with the requirement of a minimum length between the nodes of the graphs that they are using. Such an assumption will naturally lead to quantization since it is, in effect a form of quantization itself. I am disappointed that this was not noticed!
Kindest regards,
----- Original Message -----
Sent: Wednesday, December 01, 2004 8:39 PM
Subject: Quantum Theory from Quantum Gravity

Authors: Fotini Markopoulou, Lee Smolin

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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