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Bohmian mechanics has garnered significant attention as an interpretation ofquantum theory since the paradigmatic experiments by Kocsis et. al. [Science332, 6034 (2011)] and Mahler et. al. [Sci. Adv. 2, 2 (2016)], which inferredthe average trajectories of photons in the nonrelativistic regime. Theseexperiments were largely motivated by Wiseman's formulation of Bohmianmechanics, which grounded these trajectories in weak measurements. Recently,Wiseman's framework was extended to the relativistic regime by expressing thevelocity field of single photons in terms of weak values of the photon energyand momentum. Here, we propose an operational, weak value-based definition forthe Bohmian "local mass" of relativistic single particles. For relativisticwavefunctions satisfying the scalar Klein-Gordon equation, this mass coincideswith the effective mass defined by de Broglie in his relativistic pilot-wavetheory, a quantity closely connected with the quantum potential that isresponsible for Bohmian trajectory self-bending and the anomalous photoelectriceffect. We demonstrate the relationship between the photon trajectories and themass in an interferometric setup.

How the result of a measurement of a photon's mass can turn out to be 100