Relativistic Bohmian mechanics without a preferred foliation

TL;DR

This paper proposes a relativistic Bohmian mechanics model that does not rely on a preferred foliation of spacetime, potentially resolving conflicts with relativity by considering all foliations equally valid.

Contribution

It introduces a novel approach where no law determines a preferred foliation, uniting all foliations into a single model, challenging previous assumptions of a covariant law.

Findings

The model unifies all foliations without a preferred one.

It suggests the absence of a preferred foliation reduces conflicts with relativity.

The approach is empirically equivalent to existing models.

Abstract

In non-relativistic Bohmian mechanics the universe is represented by a probability space whose sample space is composed of the Bohmian trajectories. In relativistic Bohmian mechanics an entire class of empirically equivalent probability spaces can be defined, one for every foliation of spacetime. In the literature the hypothesis has been advanced that a single preferred foliation is allowed, and that this foliation derives from the universal wave function by means of a covariant law. In the present paper the opposite hypothesis is advanced, i.e., no law exists for the foliations and therefore all the foliations are allowed. The resulting model of the universe is basically the "union" of all the probability spaces associated with the foliations. This hypothesis is mainly motivated by the fact that any law defining a preferred foliation is empirically irrelevant. It is also argued that the absence of a preferred foliation may reduce the well known conflict between Bohmian mechanics and Relativity.