Tests of quantum gravity from observations of γ-ray bursts

The recent confirmation that at least some gamma-ray bursters (GRBs) areindeed at cosmological distances raises the possibility that observations ofthese could provide interesting constraints on the fundamental laws of physics.Here we demonstrate that the fine-scale time structure and hard spectra of GRBemissions are very sensitive to the possible dispersion of electromagneticwaves in vacuo with velocity differences $\delta v \sim E/E_{\QG}$, assuggested in some approaches to quantum gravity. A simple estimate shows thatGRB measurements might be sensitive to a dispersion scale $E_{QG}$ comparableto the Planck energy scale $E_{P} \sim 10^{19}$ GeV, sufficient to test some ofthese theories, and we outline aspects of an observational programme that couldaddress this goal