Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo

The recent confirmation that gamma-ray bursters (GRBs) are indeed at cosmological distances raises the possibility that observations of these could provide interesting constraints on the fundamental laws of physics. In particular, the fine-scale time structure and hard spectra of GRB emissions are very sensitive to dispersion of electromagnetic waves in vacuo: $\delta v\sim E/E_{\QG}$, a possibility suggested in some approaches to quantum gravity. A simple estimate shows that GRB measurements might be sensitive to a dispersion scale $E_{\QG}\sim E_{\P}\sim 10^{19}$ GeV.