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We investigate the potential of short-baseline experiments in order to measure the dispersion relation of the (muon) neutrino, with a prospect of eventually measuring the neutrino mass. As a byproduct, the experiment would help to constrain parameters of Lorentz-violating effects in the neutrino sector. The potential of a high-flux laser-accelerated proton beam (e.g., at the upcoming ELI facility), incident on a thick target composed of a light element to produce pions, with a subsequent decay to muons and muon-neutrinos, is discussed. We find a possibility for a muon neutrino mass measurement of unprecedented accuracy.