The de Broglie-Bohm weak interpretation

TL;DR

This paper introduces a restricted version of the de Broglie-Bohm interpretation focusing on unbound particles in physical space, arguing it avoids criticisms of the full interpretation and aligns with classical and experimental observations.

Contribution

It defines the weak de Broglie-Bohm interpretation, demonstrates its theoretical consistency with classical mechanics, and shows experimental compatibility with quantum phenomena.

Findings

Weak dBB interpretation avoids common criticisms

Wave function density converges to classical action as Planck constant approaches zero

Experimental results are compatible with particles having trajectories in the weak interpretation

Abstract

We define the de Broglie-Bohm (dBB) weak interpretation as the dBB interpretation restricted to particles in unbound states whose wave function is defined in the three-dimensional physical space, and the dBB strong interpretation as the usual dBB interpretation applied to all wave functions, in particular to particles in bound states whose wave function is defined in a 3N-dimensional configuration space in which N is the number of particules. We show that the current criticisms of the dBB interpretation do not apply to this weak interpretation and that, furthermore, there are theoritical and experimental reasons to justify the weak dBB interpretation. Theoretically, the main reason concern the continuity existing for such particles between quantum mechanics and classical mechanics: we demonstrate in fact that the density and the phase of the wave function of a single-particle (or a set of identical particles without interaction), when the Planck constant tends to 0, converges to the density and the action of a set of unrecognizable prepared classical particles that satisfy the statistical Hamilton-Jacobi equations. As the Hamilton-Jacobi action pilots the particle in classical mechanics, this continuity naturally concurs with the weak dBB interpretation. Experimentally, we show that the measurement results of the main quantum experiments (Young's slits experiment, Stern and Gerlach, EPR-B) are compatible with the de Broglie-Bohm weak interpretation and everything takes place as if these unbounded particles had trajectories. In addition, we propose two potential solutions to complete the dBB weak interpretation.