  A lower bound on the light neutrino mass $m_\nu$ is derived in the framework
of a geometrical interpretation of quantum mechanics. Using this model and the
time of flight delay data for neutrinos coming from SN1987A, we find that the
neutrino masses are bounded from below by $m_\nu\gtrsim 10^{-4}-10^{-3}$eV, in
agreement with the upper bound $m_\nu\lesssim$ $({\cal O}(0.1) - {\cal O} (1))$
eV currently available. When the model is applied to photons with effective
mass, we obtain a lower limit on the electron density in intergalactic space
that is compatible with recent baryon density measurements.
