State Vector Reduction as a Shadow of a Noncommutative Dynamics

Details State Vector Reduction as a Shadow of a Noncommutative Dynamics State Vector Reduction as a Shadow of a Noncommutative Dynamics

1999-06-17

arxiv.org/abs/hep-th/9906132v1

J.Math.Phys. 41 (2000) 5168-5179

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, LaTex, no figures

Scientific paper

10.1063/1.533400

A model, based on a noncommutative geometry, unifying general relativity with quantum mechanics, is further develped. It is shown that the dynamics in this model can be described in terms of one-parameter groups of random operators. It is striking that the noncommutative counterparts of the concept of state and that of probability measure coincide. We also demonstrate that the equation describing noncommutative dynamics in the quantum gravitational approximation gives the standard unitary evolution of observables, and in the "space-time limit" it leads to the state vector reduction. The cases of the spin and position operators are discussed in details.

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