Foundations of statistical mechanics and the status of the Born rule in de Broglie-Bohm pilot-wave theory

TL;DR

This paper critically examines two approaches to the Born rule in de Broglie-Bohm theory, arguing that the typicality approach is flawed and advocating for an empirical, experiment-based perspective on quantum equilibrium.

Contribution

It clarifies the conceptual issues with the typicality approach and promotes an empirical stance on the foundations of statistical mechanics in pilot-wave theory.

Findings

The typicality approach is inherently circular and misleading.

Restricting to equilibrium causes misunderstandings about quantum principles.

An empirical approach is preferable for understanding quantum nonequilibrium.

Abstract

We compare and contrast two distinct approaches to understanding the Born rule in de Broglie-Bohm pilot-wave theory, one based on dynamical relaxation over time (advocated by this author and collaborators) and the other based on typicality of initial conditions (advocated by the 'Bohmian mechanics' school). It is argued that the latter approach is inherently circular and physically misguided. The typicality approach has engendered a deep-seated confusion between contingent and law-like features, leading to misleading claims not only about the Born rule but also about the nature of the wave function. By artificially restricting the theory to equilibrium, the typicality approach has led to further misunderstandings concerning the status of the uncertainty principle, the role of quantum measurement theory, and the kinematics of the theory (including the status of Galilean and Lorentz invariance). The restriction to equilibrium has also made an erroneously-constructed stochastic model of particle creation appear more plausible than it actually is. To avoid needless controversy, we advocate a modest 'empirical approach' to the foundations of statistical mechanics. We argue that the existence or otherwise of quantum nonequilibrium in our world is an empirical question to be settled by experiment.