Dynamical Origin of Quantum Probabilities

2004/03/04 by Antony Valentini, Hans Westman · 7 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Statistical Mechanics and Entropy #gr-qc #hep-th #quant-ph

paper · pdf · doi:10.1098/rspa.2004.1394

published as Proc.Roy.Soc.Lond.A461:253-272,2005 · 25 pages, 10 figures

arxiv created 2004/03/04 · openalex publication_date 2004/10/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We study the origin of the Born probability rule rho = |psi|² in the de Broglie-Bohm pilot-wave formulation of quantum theory. It is argued that quantum probabilities arise dynamically, and have a status similar to thermal probabilities in ordinary statistical mechanics. This is illustrated by numerical simulations for a two-dimensional system. We show that a simple initial ensemble with a non-standard distribution rho not= |psi|² of particle positions evolves towards the quantum distribution to high accuracy. The relaxation process rho --> |psi|² is quantified in terms of a coarse-grained H-function (equal to minus the relative entropy of rho with respect to |psi|²), which is found to decrease approximately exponentially over time, with a time constant that accords with a simple theoretical estimate.

Citations

• On the Problem of Hidden Variables in Quantum Mechanics
• Characterizing Quantum Theory in Terms of Information-Theoretic Constraints

Cited by

• The paleoclassical interpretation of quantum theory
• Statistical anisotropy and cosmological quantum relaxation
• Contextuality, Fine-Tuning and Teleological Explanation
• Astrophysical and cosmological tests of quantum theory
• Mechanism for the suppression of quantum noise at large scales on expanding space
• Can the World Beshown to be Indeterministic after all?
• Antony Valentini [wikipedia]