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We discuss possible tests of the constancy of the velocity of light usingdistant astrophysical sources such as gamma-ray bursters (GRBs), ActiveGalactic Nuclei (AGNs) and pulsars. This speculative quest may be motivated bysome models of quantum fluctuations in the space-time background, and wediscuss explicitly how an energy-dependent variation in photon velocity \deltac/ c \sim - E / M arises in one particular quantum-gravitational model. We thendiscuss how data on GRBs may be used to set limits on variations in thevelocity of light, which we illustrate using BATSE and OSSE observations of theGRBs that have recently been identified optically and for which preciseredshifts are available. We show how a regression analysis can be performed tolook for an energy-dependent effect that should correlate with redshift. Thepresent data yield a limit M \gsim 10^{15} GeV for the quantum gravity scale.We discuss the prospects for improving this analysis using future data, and howone might hope to distinguish any positive signal from astrophysical effectsassociated with the sources.Comment: 37 pages LaTeX, 9 eps figures included, uses aasms4.st

A Search in Gamma‐Ray Burst Data for Nonconstancy of the Velocity of Light