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, μ → e + γ, whose branching ratio increases as b γ where γ 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 based on observations of horizontal air showers with ne ≥ 5×10 . 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) To test by experiments the limits of validity of Lorentz invariance or indeed any of the fundamental principles of physics we need a theoretical model which assumes a specific form for the violation and makes predictions of physical phenomena which can be searched for by the experiments [25]. The recent model of Coleman and Glashow incorporates tiny departures from Lorentz invariance which do not also respect flavor conservation [1]. One of the signatures of such a flavor non conservation is the transition μ → e + γ whose rate increases rapidly with the energy of the muon as measured in a preferred frame such as the one in which the 2.7K universal