  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 mainly 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 and the relativistic velocity addition rule. Our
new velocity equation is 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.
