Measurement-based Lorentz-covariant Bohmian trajectories of interacting photons

TL;DR

This paper extends a Lorentz-covariant Bohmian framework to describe interacting photons, demonstrating consistent trajectories for multiparticle quantum systems using weak measurements and a nonlocal spacetime metric.

Contribution

It introduces a novel method to derive relativistic Bohmian trajectories for two interacting photons, incorporating nonlocal spacetime curvature and confirming consistency with Lorentz covariance.

Findings

Derived average velocity fields for indistinguishable photons

Established correspondence with Lorentz-covariant Klein-Gordon wavefunction

Proposed a nonlocal spacetime metric for trajectory interpretation

Abstract

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.