Constraints on Lorentz invariance from the event KM3-230213A

Abstract: Lorentz invariance is the cornerstone of relativity theory. Its implications have been verified experimentally with a variety of approaches. The detection of a muon at extremely high energy detected by the ARCA detector in the Mediterranean sea, the most energetic particle directly measured up to date, allows to put additional constraints on Lorentz non-invariant theories. The prediction of some of those theories is that the lifetimes of particles in the laboratory frame 'decrease' rather than 'increase' with increasing $\gamma$. In this frame the sheer fact that the muon traversed the whole ARCA detector puts a lower limit on the muon lifetime in the laboratory frame, that implies upper limits on Lorentz violating parameters.