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A Derivation Of Quantum Mechanics

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Posted by Richard Ruquist on November 19, 2003 15:16:06 UTC

Since this forum has been concerned with quantum mechanics, [lately in analogy with christianity, and earlier as a result of DrDick's derivation of Schroedinger's equation from data with various symmetries in a flat spacetime]

I think some of you may be interested that the Schroedinger equation has been derived from Loop Quantum Gravity, which at the same time derives spacetime. That is spacetime is not assumed as in Stafford's Theory. The abstract and a link to the paper are given below.

Quantum Theory from Quantum Gravity
Authors: Fotini Markopoulou, Lee Smolin
Comments: 17 pages, 2 eps figures
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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