  In a recent article [Foo et. al., Nature Comms. 13, 2 (2022)], we devised a
method of constructing the Lorentz-covariant Bohmian trajectories of single
photons via weak measurements of the photon's momentum and energy. However,
whether such a framework can consistently describe multiparticle interactions
remains to be seen. Here, we present a nontrivial generalisation of our
framework to describe the relativistic Bohmian trajectories of two interacting
photons exhibiting nonclassical interference due to their indistiguishability.
We begin by deriving the average velocity fields of the indistinguishable
photons using a conditional weak measurement protocol, with detectors that are
agnostic to the identity of the respective photons. We demonstrate a direct
correspondence between the operationally-derived trajectories with those
obtained using a position- and time-symmetrised multiparticle Klein-Gordon
wavefunction, whose dynamics are manifestly Lorentz-covariant. We propose a
spacetime metric that depends nonlocally on the positions of both particles as
a curvature based interpretation of the resulting trajectories. Contrary to
prior expectations, our results demonstrate a consistent trajectory-based
interpretation of relativistic multiparticle interactions in quantum theory.
