Relativistically invariant Bohmian trajectories of photons

Abstract

Bohmian mechanics is a nonlocal hidden-variable interpretation of quantum theory which predicts that particles follow deterministic trajectories in spacetime. Historically, the study of Bohmian trajectories has been restricted to nonrelativistic regimes due to the widely held belief that the theory is incompatible with special relativity. Here we derive expressions for the relativistic velocity and spacetime trajectories of photons in a Michelson-Sagnac-type interferometer. The trajectories satisfy quantum-mechanical continuity, the relativistic velocity addition rule. Our new velocity equation can be operationally defined in terms of weak measurements of momentum and energy. We finally propose a modified Alcubierre metric which could give rise to these trajectories within the paradigm of general relativity.

Non-local temporal interference

“…Due to the non-locality of Bohmian dynamics, there is no obvious and agreed-upon way to achieve a relativistic extension of it, especially for systems with more than one particle [124][125][126] . However, there are various proposals for this purpose 72,[127][128][129][130][131][132] . Therefore, using particles with relativistic speeds, the same kind of experiment could be used to probe these proposals.…”