State Vector Reduction as a Shadow of a Noncommutative Dynamics

Abstract

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.

20 pages, LaTex, no figures

References in corpus (5)

• Towards Noncommutative Quantization of Gravity
• Topology at the Planck Length
• Emergence of Time
• Origin of Classical Singularities
• Einstein-Podolski-Rosen Experiment from Noncommutative Quantum Gravity

Cited by in corpus (5)

• Noncommutative Dynamics of Random Operators
• Noncommutative Unification of General Relativity and Quantum Mechanics
• Observables in a Noncommutative Unification of Quanta and Gravity. A Final Model
• Noncommutative Unification of General Relativity and Quantum Mechanics. A Finite Model
• Noncommutative regime of fundamental physics