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

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.

Submittted article

References in corpus (2)

• Chaos in de Broglie - Bohm quantum mechanics and the dynamics of quantum relaxation
• A causal and continuous interpretation of the quantum theory: About an original manuscript by David Bohm sent to Louis de Broglie in 1951