  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.
