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(Planck) approximate to 1.62 x 10(-33) cm or E-Planck = M(Planck)c(2) approximate to 1.22 x 10(19) 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(1-7). 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(2). Here we report the detection of emission up to similar 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(Planck) 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(Planck)/1.2 on the length scale of the effect). Our results disfavour quantum-gravity theories(3,6,7) in which the quantum nature of space-time on a very small scale linearly alters the speed of light.< Réduire