|Slight energy dependences in the speed of light can accumulate over time,|
allowing for possible detection or exclusion of such effects. Highly energetic
photons emitted e.g. by a supernova are in particularly useful for such studies.
Predictions for possible Lorentz violations are a key area of interesting phenomenology in quantum gravity. Within loop quantum gravity, it has not been possible so far to reliably extract predictions for Lorentz violations. Existing claims were based on simplified toy models inspired by LQG, but not implied. This situation hasn’t changed so far, but there is an interesting development which hints at which order we might expect such Lorentz violations to be found.