Geometric gravitational origin of neutrino oscillations and mass-energy

Abstract

A mass-energy scale for neutrinos was calculated from the null cone curvature using geometric concepts. The scale is variable depending on the gravitational potential and the trajectory inclination with respect to the field direction. The proposed neutrino covariant equation provides the adequate curvature. The mass-energy at the Earth surface varies from a horizontal value 0.402 eV to a vertical value 0.569 eV. Earth spinor waves with winding numbers n show squared energy differences within ranges from 2.05 x 10*(-3) to 4.10 x 10*(-3) eV*2 for n=0,1 neutrinos and from 3.89 x 10*(-5) to 7.79 x 10*(-5) eV*2 for n=1,2 neutrinos. These waves interfere and the different phase velocities produce neutrino-like oscillations. The experimental results for atmospheric and solar neutrino oscillation mass parameters respectivelly fall within these theoretical ranges. Neutrinos in outer space, where interactions may be neglected, appear as particles travelling with zero mass on null geodesics. These gravitational curvature energies are consistent with neutrino oscillations, zero neutrino rest masses and Einstein's General Relativity and energy mass equivalence principle. When analyzing or averaging experimental neutrino mass-energy results of different experiments on the Earth it is of interest to consider the possible influence of the trajectory inclination angle.