A search in gamma-ray burst data for nonconstancy of the velocity of light

We discuss possible tests of the constancy of the velocity of light using d istant astrophysical sources such as gamma-ray bursters (GRBs), active gala ctic nuclei (AGNs), and pulsars. This speculative quest may be motivated by some models of quantum fluctuations in the spacetime background, and we di scuss explicitly how an energy-dependent variation in photon velocity delta c/c similar to -E/M arises in one particular quantum-gravitational model. We then discuss how data on GRBs may be used to set limits on variations in the velocity of light, which we illustrate using BATSE and OSSE observatio ns of the GRBs that have recently been identified optically and for which p recise redshifts are available. We show how a regression analysis can be pe rformed to look for an energy-dependent effect that should correlate with r edshift. The present data yield a limit M greater than or similar to 10(15) GeV for the quantum gravity scale. We discuss the prospects for improving this analysis using future data, and how one might hope to distinguish any positive signal from astrophysical effects associated with the sources.