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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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
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| Acceso en línea: | https://doaj.org/article/473ca24e127e497fa693f04ace7eb9ed |
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| Sumario: | 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. |
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