  Bohmian mechanics has garnered significant attention as an interpretation of
quantum theory since the paradigmatic experiments by Kocsis et. al. [Science
332, 6034 (2011)] and Mahler et. al. [Sci. Adv. 2, 2 (2016)], which inferred
the average trajectories of photons in the nonrelativistic regime. These
experiments were largely motivated by Wiseman's formulation of Bohmian
mechanics, which grounded these trajectories in weak measurements. Recently,
Wiseman's framework was extended to the relativistic regime by expressing the
velocity field of single photons in terms of weak values of the photon energy
and momentum. Here, we propose an operational, weak value-based definition for
the Bohmian "local mass" of relativistic single particles. For relativistic
wavefunctions satisfying the scalar Klein-Gordon equation, this mass coincides
with the effective mass defined by de Broglie in his relativistic pilot-wave
theory, a quantity closely connected with the quantum potential that is
responsible for Bohmian trajectory self-bending and the anomalous photoelectric
effect. We demonstrate the relationship between the photon trajectories and the
mass in an interferometric setup.
