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We constrain the possibility of a non-trivial refractive index in free space corresponding to an energy-dependent velocity of light:
c(
E)
≃
c
0(1
−
E/
M), where
M is a mass scale that might represent effect of quantum-gravitational space-time foam, using the arrival times of sharp features observed in the intensities of radiation with different energies from a large sample of gamma-ray bursters (GRBs) with known redshifts. We use wavelet techniques to identify genuine features, which we confirm in simulations with artificial added noise. Using the weighted averages of the time-lags calculated using correlated features in all the GRB light curves, we find a systematic tendency for more energetic photons to arrive earlier. However, there is a very strong correlation between the parameters characterizing an intrinsic time-lag at the source and a distance-dependent propagation effect. Moreover, the significance of the earlier arrival times is less evident for a subsample of more robust spectral structures. Allowing for intrinsic stochastic time-lags in these features, we establish a statistically robust lower limit:
M
>
0.9
×
10
16
GeV on the scale of violation of Lorentz invariance.