Constraining Lorentz Invariance Violation with Fermi

A cornerstone of special relativity is Lorentz Invariance, the postulate that all observers measure exactly the same photon speeds independently on the photon energies. However, a hypothesized structure of spacetime may alter this conclusion at ultra-small length scales, a possibility allowed in many of the Quantum-Gravity (QG) formalisms currently investigated. A generalized uncertainty principle suggests that such effects might occur for photon energies approaching the Planck energy, $E_{Planck}=M_{Planck} c^2 \simeq 1.22\times10^{19} GeV$. Even though all photons yet detected have energies $E_{ph}<<E_{Planck}$, even a tiny variation in the speed of light, when accumulated over cosmological light-travel times, may be revealed by high temporal-resolution measurements of sharp features in Gamma-Ray Burst (GRB) lightcurves. Here we report the results of a study using the emission from GRB 090510 as detected by \textit{Fermi}'s LAT and GBM instruments, that set unprecedented limits on the dependence of the speed of photons on their energy. We find that the mass/energy scale for a linear in energy dispersion must be well above the Planck scale, something that renders any affected QG models highly implausible.