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 ${rm E_{QG}}gtrsim 1.5times 10^{16}$ 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.
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