From special relativity, photon annihilation process $\gamma \gamma \to e^{+}{e}^{-}$ prevents cosmic photons with energies above a threshold to propagate a long distance in cosmic space due to their annihilation with low energy cosmic background photons. However, modifications of the photon dispersion relation from Lorentz invariance violation (LIV) can cause novel phenomena beyond special relativity to happen. In this paper, we point out that these phenomena include optical transparency, threshold reduction and reappearance of ultra-high energy photons in cosmic space. The recent observation of near and above PeV photon events by the LHAASO Collaboration reveals the necessity to consider the threshold anomalies. Future observations of above threshold photons from extragalactic sources can testify LIV properties of photons.

从狭义相对论，光子湮灭过程 $\gamma \gamma \to {\mathrm{电子}}^{+}{\mathrm{电子}}^{-}$阻止能量高于阈值的宇宙光子在宇宙空间中长距离传播，因为它们会被低能量的宇宙背景光子湮灭。然而，洛伦兹不变性违反 (LIV) 对光子色散关系的修改可能会导致超出狭义相对论的新现象发生。在本文中，我们指出这些现象包括光学透明、阈值降低和超高能光子在宇宙空间中的再现。LHAASO 合作组织最近对接近和高于 PeV 光子事件的观察揭示了考虑阈值异常的必要性。未来对来自河外源的高于阈值的光子的观察可以证明光子的 LIV 特性。