Justifying Born's rule $P_\alpha=|\Psi_\alpha|^2$ using deterministic chaos, decoherence, and the de Broglie-Bohm quantum theory

Aurélien Drezet

doi:10.3390/e23111371

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arXiv · 2109.09353

Justifying Born's rule $P_\alpha=|\Psi_\alpha|^2$ using deterministic chaos, decoherence, and the de Broglie-Bohm quantum theory

Aurélien Drezet

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Abstract

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 a environement made of "qubits" (i.e., Bohmian pointers) we show that entanglement together with deterministic chaos lead to a fast relaxation from any statistitical distribution $\rho(x)$ (of finding a particle at point $x$) to the Born probability law $|\Psi(x)|^2$. 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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Aurélien Drezet. 2021-09-20. Justifying Born's rule $P_\alpha=|\Psi_\alpha|^2$ using deterministic chaos, decoherence, and the de Broglie-Bohm quantum theory. https://doi.org/10.3390/e23111371

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