  The effect of quantum gravity can bring a tiny light speed variation which is
detectable through energetic photons propagating from gamma ray bursts (GRBs)
to an observer such as the space observatory. Through an analysis of the
energetic photon data of the GRBs observed by the Fermi Gamma-ray Space
Telescope (FGST), we reveal a surprising regularity of the observed time lags
between photons of different energies with respect to the Lorentz violation
factor due to the light speed energy dependence. Such regularity suggests a
linear form correction of the light speed $v(E)=c(1-E/E_{\rm LV})$, where $E$
is the photon energy and $E_{\rm LV}=(3.60 \pm 0.26) \times 10^{17}~ \rm GeV$
is the Lorentz violation scale measured by the energetic photon data of GRBs.
The results support an energy dependence of the light speed in cosmological
space.
