Gravitational Causality and the Self-Stress of Photons

TL;DR

This paper investigates quantum causality in gravitational systems by analyzing photon self-stress and phase shifts, showing that asymptotic causality is preserved at first post-Minkowskian order, but local causality may be violated due to quantum effects.

Contribution

It introduces a quantum analysis of photon self-stress and causality in gravitational interactions beyond the classical limit using on-shell methods.

Findings

Asymptotic causality is maintained at first post-Minkowskian order.

The sign of the gauge coupling's beta function relates to time delay in scattering.

Quantum effects may violate local causality by extending photon time delays.

Abstract

We study causality in gravitational systems beyond the classical limit. Using on-shell methods, we consider the one-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.