Justifying Born’s Rule Pα = |Ψα|2 Using Deterministic Chaos, Decoherence, and the de Broglie–Bohm Quantum Theory

In this work, we derive Born’s rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to an environment made of “qubits” (i.e., Bohmian pointers), we show that entanglement together with deterministic chaos leads to a fast relaxation from any statis...

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Autor principal:	Aurélien Drezet
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	quantum probability pilot-wave mechanics entanglement deterministic chaos Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/473ca24e127e497fa693f04ace7eb9ed
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spelling	oai:doaj.org-article:473ca24e127e497fa693f04ace7eb9ed2021-11-25T17:29:05ZJustifying Born’s Rule <i>P<sub>α</sub></i> = \|Ψ<i><sub>α</sub></i>\|<sup>2</sup> Using Deterministic Chaos, Decoherence, and the de Broglie–Bohm Quantum Theory10.3390/e231113711099-4300https://doaj.org/article/473ca24e127e497fa693f04ace7eb9ed2021-10-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1371https://doaj.org/toc/1099-4300In this work, we derive Born’s rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to an environment made of “qubits” (i.e., Bohmian pointers), we show that entanglement together with deterministic chaos leads to a fast relaxation from any statistical distribution <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ρ</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></semantics></math></inline-formula> of finding a particle at point <i>x</i> to the Born probability law <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mo>\|</mo><mo>Ψ</mo><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>\|</mo></mrow><mn>2</mn></msup></semantics></math></inline-formula>. Our model is discussed in the context of Boltzmann’s kinetic theory, and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime.Aurélien DrezetMDPI AGarticlequantum probabilitypilot-wave mechanicsentanglementdeterministic chaosScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1371, p 1371 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	quantum probability pilot-wave mechanics entanglement deterministic chaos Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	quantum probability pilot-wave mechanics entanglement deterministic chaos Science Q Astrophysics QB460-466 Physics QC1-999 Aurélien Drezet Justifying Born’s Rule <i>P<sub>α</sub></i> = \|Ψ<i><sub>α</sub></i>\|<sup>2</sup> Using Deterministic Chaos, Decoherence, and the de Broglie–Bohm Quantum Theory
description	In this work, we derive Born’s rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to an environment made of “qubits” (i.e., Bohmian pointers), we show that entanglement together with deterministic chaos leads to a fast relaxation from any statistical distribution <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ρ</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></semantics></math></inline-formula> of finding a particle at point <i>x</i> to the Born probability law <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mo>\|</mo><mo>Ψ</mo><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>\|</mo></mrow><mn>2</mn></msup></semantics></math></inline-formula>. Our model is discussed in the context of Boltzmann’s kinetic theory, and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime.
format	article
author	Aurélien Drezet
author_facet	Aurélien Drezet
author_sort	Aurélien Drezet
title	Justifying Born’s Rule <i>P<sub>α</sub></i> = \|Ψ<i><sub>α</sub></i>\|<sup>2</sup> Using Deterministic Chaos, Decoherence, and the de Broglie–Bohm Quantum Theory
title_short	Justifying Born’s Rule <i>P<sub>α</sub></i> = \|Ψ<i><sub>α</sub></i>\|<sup>2</sup> Using Deterministic Chaos, Decoherence, and the de Broglie–Bohm Quantum Theory
title_full	Justifying Born’s Rule <i>P<sub>α</sub></i> = \|Ψ<i><sub>α</sub></i>\|<sup>2</sup> Using Deterministic Chaos, Decoherence, and the de Broglie–Bohm Quantum Theory
title_fullStr	Justifying Born’s Rule <i>P<sub>α</sub></i> = \|Ψ<i><sub>α</sub></i>\|<sup>2</sup> Using Deterministic Chaos, Decoherence, and the de Broglie–Bohm Quantum Theory
title_full_unstemmed	Justifying Born’s Rule <i>P<sub>α</sub></i> = \|Ψ<i><sub>α</sub></i>\|<sup>2</sup> Using Deterministic Chaos, Decoherence, and the de Broglie–Bohm Quantum Theory
title_sort	justifying born’s rule <i>p<sub>α</sub></i> = \|ψ<i><sub>α</sub></i>\|<sup>2</sup> using deterministic chaos, decoherence, and the de broglie–bohm quantum theory
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/473ca24e127e497fa693f04ace7eb9ed
work_keys_str_mv	AT aureliendrezet justifyingbornsruleipsubasubipsisubasubisup2supusingdeterministicchaosdecoherenceandthedebrogliebohmquantumtheory
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Justifying Born’s Rule <i>P<sub>α</sub></i> = |Ψ<i><sub>α</sub></i>|<sup>2</sup> Using Deterministic Chaos, Decoherence, and the de Broglie–Bohm Quantum Theory

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