  Violation of Lorentz invariance (VLI) has been suggested as an explanation of
the superluminal velocities of muon neutrinos reported by OPERA. In this note
we show that the amount of VLI required to explain this result poses severe
difficulties with the kinematics of the pion decay, extending its lifetime and
reducing the momentum carried away by the neutrinos. We show that the OPERA
experiment limits $\alpha = (v_\nu - c)/c < 4 \times 10^{-6}$. We then take
recourse to cosmic ray data on the spectrum of muons and neutrinos generated in
the earth's atmosphere to provide a stronger bound on VLI: $(v-c)/c <
10^{-12}$.
