Probability in relativistic Bohmian mechanics of particles and strings

TL;DR

This paper discusses a relativistic Bohmian mechanics framework for particles and strings, highlighting its well-defined probability density, potential deviations from standard quantum predictions, and the necessity of a preferred spacetime foliation.

Contribution

It introduces a relativistic Bohmian approach for particles and strings, addressing probability densities and potential experimental deviations from conventional quantum theory.

Findings

Probability density remains well-defined despite backward-in-time trajectories.

The theory predicts subtle deviations from standard quantum mechanics.

Extension to many particles or strings requires a preferred spacetime foliation.

Abstract

Even though the Bohmian trajectories given by integral curves of the conserved Klein-Gordon current may involve motions backwards in time, the natural relativistic probability density of particle positions is well-defined. The Bohmian theory predicts subtle deviations from the statistical predictions of more conventional formulations of quantum theory, but it seems that no present experiment rules this theory out. The generalization to the case of many particles or strings is straightforward, provided that a preferred foliation of spacetime is given.