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Lorentz violation (LV) is predicted by some quantum gravity theories, wherephoton dispersion relation is modified, and the speed of light becomesenergy-dependent. Consequently, it results in a tiny time delay between highenergy photons and low energy ones. Very high energy (VHE) photon emissionsfrom cosmological distance can amplify these tiny LV effects into observablequantities. Here we analyze four VHE $\gamma$-ray bursts (GRBs) from Fermiobservations, and briefly review the constraints from three TeV flares ofactive galactic nuclei (AGNs) as well. One step further, we present a firstrobust analysis of VHE GRBs taking the intrinsic time lag caused by sourcesinto account, and give an estimate to quantum gravity energy $\sim 2 \times10^{17}$ GeV for linear energy dependence, and $\sim 5 \times 10^9$ GeV forquadratic dependence. However, the statistics is not sufficient due to the lackof data, and further observational results are desired to constrain LV effectsbetter.

Lorentz violation from cosmological objects with very high energy photon emissions