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

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Abstract
Observations of the distant and short γ-ray burst GRB 090510 with the Fermi Gamma-ray Space Telescope have provided an opportunity to test a central prediction of Einstein's special theory of relativity — the Lorentz invariance. This holds that all observers measure exactly the same speed of light in a vacuum, independent of photon energy. A key test of the violation of Lorentz invariance is a possible variation of photon speed with energy. Accumulated over cosmological light-travel times, even a tiny variation in photon speed should become observable — as for instance sharp features in the light curve of a γ-ray burst. No evidence for the violation of Lorentz invariance was found in the GRB 090510 spectrum, at least down to a limit of the Planck length divided by 1.2. This argues against quantum-gravity theories where the quantum nature of space–time linearly alters the speed of light with photon energy. Lorentz invariance — the postulate that all observers measure exactly the same speed of light in vacuum, independent of photon energy — is a cornerstone of Einstein's special relativity, but it has been suggested that it might break near the Planck scale. A possible variation of photon speed with energy is a key test for this proposed violation; here, by studying sharp features in γ-ray burst light-curves to look for even tiny variations in photon speed, no evidence for the violation of Lorentz invariance is found. 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, lPlanck ≈ 1.62 × 10-33 cm or EPlanck = MPlanckc2 ≈ 1.22 × 1019 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 energy1,2,3,4,5,6,7. Even a tiny variation in photon speed, when accumulated over cosmological light-travel times, may be revealed by observing sharp features in γ-ray burst (GRB) light-curves2. Here we report the detection of emission up to ∼31 GeV from the distant and short GRB 090510. We find no evidence for the violation of Lorentz invariance, and place a lower limit of 1.2EPlanck 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 lPlanck/1.2 on the length scale of the effect). Our results disfavour quantum-gravity theories3,6,7 in which the quantum nature of space–time on a very small scale linearly alters the speed of light.
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