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
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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| Format: | Article |
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MDPI AG
2021-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/11/1371 |
| _version_ | 1797510429924130816 |
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| author | Aurélien Drezet |
| author_facet | Aurélien Drezet |
| author_sort | Aurélien Drezet |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T05:31:23Z |
| format | Article |
| id | doaj.art-473ca24e127e497fa693f04ace7eb9ed |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T05:31:23Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-473ca24e127e497fa693f04ace7eb9ed2023-11-22T23:14:00ZengMDPI AGEntropy1099-43002021-10-012311137110.3390/e23111371Justifying 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 TheoryAurélien Drezet0Institut NEEL, CNRS and Université Grenoble Alpes, F-38000 Grenoble, FranceIn 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.https://www.mdpi.com/1099-4300/23/11/1371quantum probabilitypilot-wave mechanicsentanglementdeterministic chaos |
| spellingShingle | 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 Entropy quantum probability pilot-wave mechanics entanglement deterministic chaos |
| 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_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_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_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 |
| topic | quantum probability pilot-wave mechanics entanglement deterministic chaos |
| url | https://www.mdpi.com/1099-4300/23/11/1371 |
| work_keys_str_mv | AT aureliendrezet justifyingbornsruleipsubasubipsisubasubisup2supusingdeterministicchaosdecoherenceandthedebrogliebohmquantumtheory |