A Bound on Violations of Lorentz Invariance

Recently Coleman and Glashow [1] have developed a model which allows the introduction of a small violation of Lorentz invariance. Observational signatures arise because this interaction also violates flavor conservation and allows the radiative decay of the muon, $\mu \to e + \gamma$, whose branching ratio increases as b $\gamma^4$ where $\gamma$ is the Lorentz factor of the muon with respect to the reference frame in which the dipole anisotropy of the universal microwave radiation vanishes. In this paper we place a bound of b$< 10^{-25}$ based on observations of horizontal air showers with $n_e \geq 5 \times 10^6$. With such small values of b the proposed radiative decay of the muon will not affect the functioning of the muon collider.(THIS IS A PRELIMINARY VERSION)