Explosive astrophysical events at high redshift can be used to place severe limits on the fractional variation in the speed of light with frequency ( Δc/c), the photon mass ( mγ), and the energy scale of quantum gravity ( EQG). I find Δc/c<6.3×10-21 based on the simultaneous arrival of a flare in GRB 930229 with a rise time of 220+/-30 μs for photons of 30 and 200 keV. The limit on mγ is 4.2×10-44 g for GRB 980703 from radio to gamma ray observations. The limit on EQG is 8.3×1016 GeV for GRB 930131 from 30 keV to 80 MeV photons.