Pilot-Wave Theories as Hidden Markov Models

TL;DR

This paper reinterprets de Broglie-Bohm pilot-wave theory as a hidden Markov model with latent variables, challenging traditional ontological views and addressing related theoretical challenges.

Contribution

It introduces a novel perspective by modeling the pilot wave as a hidden Markov model, providing new insights into the theory's underlying structure.

Findings

Pilot wave modeled as hidden Markov model with latent variables

Addresses challenges from gauge transformations and canonical transformations

Proposes a non-ontological interpretation of the pilot wave

Abstract

The original version of the de Broglie-Bohm pilot-wave theory, also called Bohmian mechanics, attempted to treat the wave function or pilot wave as a part of the physical ontology of nature. More recent versions of the de Broglie-Bohm theory appearing in the last few decades have tried to regard the pilot wave instead as an aspect of the theory's nomology, or dynamical laws. This paper argues that neither of these views is correct, and that the de Broglie-Bohm pilot wave is best understood as a collection of latent variables in the sense of a hidden Markov model, a construct that was not available when de Broglie and Bohm originally formulated what became their pilot-wave theory. This paper also discusses several other challenges for the ontological view of the pilot wave. One such challenge is due to Foldy-Wouthuysen gauge transformations, which connect up with the Deotto-Ghirardi ambiguity in the de Broglie-Bohm theory. Another challenge arises from the freedom to carry out canonical transformations in the wave function's own notion of phase space, as defined by Strocchi and Heslot.