A limit on the variation of the speed of light arising from quantum gravity effects

A cornerstone of Einstein's special relativity is Lorentz invariance---the postulate that all observers measure exactly the same speed of light in vacuum, independent of photon-energy. While special relativity assumes that there is no fundamental length-scale associated with such invariance, there is a fundamental scale (the Planck scale, l<SUB>Planck</SUB>~1.6210<SUP>-33</SUP>cm or E<SUB>Planck</SUB> = M<SUB>Planck</SUB>c<SUP>2</SUP>~1.2210<SUP>19</SUP>GeV), at which quantum effects are expected to strongly affect the nature of space-time. There is great interest in the (not yet validated) idea that Lorentz invariance might break near the Planck scale. A key test of such violation of Lorentz invariance is a possible variation of photon speed with energy. Even a tiny variation in photon speed, when accumulated over cosmological light-travel times, may be revealed by observing sharp features in gamma-ray burst (GRB) light-curves. Here we report the detection of emission up to ~31GeV from the distant and short GRB090510. We find no evidence for the violation of Lorentz invariance, and place a lower limit of 1.2E<SUB>Planck</SUB> on the scale of a linear energy dependence (or an inverse wavelength dependence), subject to reasonable assumptions about the emission (equivalently we have an upper limit of l<SUB>Planck</SUB>/1.2 on the length scale of the effect). Our results disfavour quantum-gravity theories in which the quantum nature of space-time on a very small scale linearly alters the speed of light.