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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,
Stephen
----- 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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- Re: Quantum Theory from Quantum Gravity Stephen Paul King
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