  The delay in the arrival times between high and low energy photons from
cosmic sources can be used to test the violation of the Lorentz invariance
(LIV), predicted by some quantum gravity theories, and to constrain its
characteristic energy scale ${\rm E_{QG}}$ that is of the order of the Planck
energy. Gamma-ray bursts (GRBs) and blazars are ideal for this purpose thanks
to their broad spectral energy distribution and cosmological distances: at
first order approximation, the constraints on ${\rm E_{QG}}$ are proportional
to the photon energy separation and the distance of the source. However, the
LIV tiny contribution to the total time delay can be dominated by intrinsic
delays related to the physics of the sources: long GRBs typically show a delay
between high and low energy photons related to their spectral evolution
(spectral lag). Short GRBs have null intrinsic spectral lags and are therefore
an ideal tool to measure any LIV effect. We considered a sample of $15$ short
GRBs with known redshift observed by Swift and we estimate a limit on ${\rm
E_{QG}}\gtrsim 1.5\times 10^{16}$ GeV. Our estimate represents an improvement
with respect to the limit obtained with a larger (double) sample of long GRBs
and is more robust than the estimates on single events because it accounts for
the intrinsic delay in a statistical sense.
