Can Bohmian mechanics be made relativistic?

TL;DR

This paper explores whether Bohmian mechanics can be formulated in a Lorentz-invariant way by covariantly determining the foliation from the wave function, potentially reconciling it with relativity.

Contribution

It proposes a covariant method to determine the foliation in Bohmian theories, aiming to preserve Lorentz invariance without extra absolute structures.

Findings

Foliation can be covariantly derived from the wave function.

Bohmian theories may be compatible with Lorentz invariance.

Discussion on the fundamental relativity of such formulations.

Abstract

In relativistic space-time, Bohmian theories can be formulated by introducing a privileged foliation of space-time. The introduction of such a foliation - as extra absolute space-time structure - would seem to imply a clear violation of Lorentz invariance, and thus a conflict with fundamental relativity. Here, we consider the possibility that, instead of positing it as extra structure, the required foliation could be covariantly determined by the wave function. We argue that this allows for the formulation of Bohmian theories that seem to qualify as fundamentally Lorentz invariant. We conclude with some discussion of whether or not they might also qualify as fundamentally relativistic.