Dynamical origin of quantum probabilities

By A. Valentini, H. Westman. Proceedings of the Royal Society A, 2004

221 citations recorded by the source corpus.

We study the origin of the Born probability rule ρ = |ψ|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 ρ ≠ |ψ|2 of particle positions, evolves towards the quantum distribution to high accuracy. The relaxation process ρ→|ψ|2 is quantified in terms of a coarse–grained H–function (equal to minus the relative entropy of ρ with respect to |ψ|2), which is found to decrease approximately exponentially over time, with a time constant that accords with a simple theoretical estimate.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/21d14ff82ef0111db3b7d912cd85d2f0cb863724

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Citations in the corpus

Do We Really Understand Quantum Mechanics? (2012, background): “See [636, 637] for more recent numerical simulations along the same line.”
The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations require fine-tuning (2012, background): “It is argued that one can still recover the standard distribution of conﬁgurations on a coarse-grained scale as a result of dynamical evolution [22].”
Bohmian Mechanics (2009, background): “It has further been suggested [13, 66] that this phenomenon may explain the |ψ|(2) distribution.”
Meaning of the wave function (2010, background): “tsch 1999); while for Bohm’s hidden variables theory, this problem is reflected in the quantum equilibrium hypothesis, which is still left for justification (see e.g. Dürr, Goldstein and Zanghì 1992; Valentini and Westman 2005). In a word, these realistic interpretations are plagued by the thorny pr”