Explosive astrophysical events at high redshift can be used to place severe limits on the fractional variation in the speed of light with frequency ( $\Delta c/c$), the photon mass ( $m_{\gamma }$), and the energy scale of quantum gravity ( $E_{\mathrm{QG}}$). I find $\Delta c/c<\mathrm{}6.3\mathrm{}\times {10}^{-21\mathrm{}}$ based on the simultaneous arrival of a flare in GRB 930229 with a rise time of $220\pm 30\mu \mathrm{s}$ for photons of 30 and 200 keV. The limit on $m_{\gamma }$ is $4.2\times {10}^{-44\mathrm{}}\mathrm{g}$ for GRB 980703 from radio to gamma ray observations. The limit on $E_{\mathrm{QG}}$ is $8.3\times {10}^{16}\mathrm{GeV}$ for GRB 930131 from 30 keV to 80 MeV photons.

• Received 29 October 1998

DOI:https://doi.org/10.1103/PhysRevLett.82.4964