Justifying Born’s Rule <i>P_α</i> = |Ψ<i>_α</i>|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 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 ρ(x) of finding a particle at point x to the Born probability law |Ψ(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.

Keywords

• quantum probability
• pilot-wave mechanics
• entanglement
• deterministic chaos