Lower Neutrino Mass Bound from SN1987A Data and Quantum Geometry

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 $m_{\nu }\lesssim$ $(\mathcal{O}(0.1)-\mathcal{O}(1))$ 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.