  We propose relativistic tests of quantum gravity using the gravitational
self-interaction of photons in a cavity. We demonstrate that this interaction
results in a number of quantum gravitational signatures in the quantum state of
the light that cannot be reproduced by any classical theory of gravity. We
rigorously assess these effects using quantum parameter estimation theory, and
discuss simple measurement schemes that optimally extract their signatures.
Crucially, the proposed tests are free of QED photon-photon scattering, are
sensitive to the spin of the mediating gravitons, and can probe the locality of
the gravitational interaction. These protocols provide a new avenue for
studying the quantum nature of gravity in a relativistic setting.
