dorsal/arxiv
View SchemaDynamical Origin of Quantum Probabilities
| Authors | Antony Valentini, Hans Westman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0403034 |
| URL | https://arxiv.org/abs/quant-ph/0403034 |
| DOI | 10.1098/rspa.2004.1394 |
| Journal | Proc.Roy.Soc.Lond.A461:253-272,2005 |
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.
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"abstract": "We study the origin of the Born probability rule rho = |psi|^2 in the de\nBroglie-Bohm pilot-wave formulation of quantum theory. It is argued that\nquantum probabilities arise dynamically, and have a status similar to thermal\nprobabilities in ordinary statistical mechanics. This is illustrated by\nnumerical simulations for a two-dimensional system. We show that a simple\ninitial ensemble with a non-standard distribution rho not= |psi|^2 of particle\npositions evolves towards the quantum distribution to high accuracy. The\nrelaxation process rho --\u003e |psi|^2 is quantified in terms of a coarse-grained\nH-function (equal to minus the relative entropy of rho with respect to\n|psi|^2), which is found to decrease approximately exponentially over time,\nwith a time constant that accords with a simple theoretical estimate.",
"arxiv_id": "quant-ph/0403034",
"authors": [
"Antony Valentini",
"Hans Westman"
],
"categories": [
"quant-ph",
"gr-qc",
"hep-th"
],
"doi": "10.1098/rspa.2004.1394",
"journal_ref": "Proc.Roy.Soc.Lond.A461:253-272,2005",
"title": "Dynamical Origin of Quantum Probabilities",
"url": "https://arxiv.org/abs/quant-ph/0403034"
},
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