Gravitational causality and the self-stress of photons

We study causality in gravitational systems beyond the classical limit. Using on-shell methods, we consider the 1-loop corrections from charged particles to the photon energy-momentum tensor - the self-stress - that controls the quantum interaction between two on-shell photons and one off-shell graviton. The self-stress determines in turn the phase shift and time delay in the scattering of photons against a spectator particle of any spin in the eikonal regime. We show that the sign of the beta-function associated to the running gauge coupling is related to the sign of time delay at small impact parameter. Our results show that, at first post-Minkowskian order, asymptotic causality, where the time delay experienced by any particle must be positive, is respected quantum mechanically. Contrasted with asymptotic causality, we explore a local notion of causality, where the time delay is longer than the one of gravitons, which is seemingly violated by quantum effects.

Automated summary

We investigate the causality in gravitational systems beyond the classical limit. By employing on-shell methods, we examine the 1-loop corrections to the photon energy-momentum tensor caused by charged particles, which in turn influences the quantum interaction between two on-shell photons and one off-shell graviton. Our findings indicate that the principle of asymptotic causality is respected at the first post-Minkowskian order in quantum mechanics.