It has been long conjectured that a signature of quantum gravity will be Lorentz invariance violation (LIV) that could be observed at energies much lower than the Planck scale. One possible signature of LIV is an energy-dependent speed of photons. This can be tested with a distant transient source of very high-energy photons. We explore time-of-flight limits on LIV derived from LHAASO’s observations of tens of thousands of TeV photons from GRB 221009A, the brightest gamma-ray burst of all time. For a linear ($n=1$) dependence of the photon velocity on energy, we find a lower limit on the subluminal (superluminal) LIV scale of $5.9(6.2)E_{\mathrm{pl}}$. These are comparable to the stringent limits obtained so far and as an independent bound obtained from a different redshift confirm their robustness. For a quadratic model ($n=2$, corresponding to $d=6$ SME operators), the limits, which are currently the best available with the time-of-flight method, are $5.8(4.6)\times {10}^{-8}{E}_{\mathrm{pl}}$. Our analysis uses the LHAASO data in the 0.2–7 TeV range. Higher energy data would enable to improve our limits.

中文翻译：

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GRB 221009A 的洛伦兹不变性违规限制

长期以来，人们一直猜测量子引力的特征将是洛伦兹不变性破坏（LIV），可以在远低于普朗克尺度的能量下观察到。 LIV 的一个可能特征是光子的能量依赖速度。这可以用遥远的高能光子瞬态源进行测试。我们根据 LHAASO 对来自 GRB 221009A（有史以来最亮的伽马射线暴）的数万个 TeV 光子的观测，探索了 LIV 的飞行时间限制。对于线性 ($n=1$）光子速度对能量的依赖性，我们发现亚光速（超光速）LIV 尺度的下限为$5.9（6.2）{乙}_{\mathrm{PL}}$。这些与迄今为止获得的严格限制相当，并且从不同红移获得的独立界限证实了它们的稳健性。对于二次模型 ($n=2$，对应于$d=6$中小企业运营商），当前飞行时间法的最佳可用限制是$5.8（4.6）\times {10}^{-8}{乙}_{\mathrm{PL}}$。我们的分析使用 0.2–7 TeV 范围内的 LHAASO 数据。更高的能量数据将有助于提高我们的极限。