  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.
