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On the Mass Neutrino Phase along the geodesic line and the null line in curved and ﬂat spacetime

On the mass neutrino phase calculations along both the particle geodesic line and the photon null line, there exists a double counting, factor of 2, when comparing the geodesic phase with the null phase. Moreover, we compare the phase calculations among the same energy description, the same momentum description by means of the Minkowski diagram, and obtain the practical equivalence of these two descriptions. On the same velocity description, although it does not correspond to a reality of physical process, we still indicate its phase calculation in the Minkowski diagram, which has the same result as those of same energy and same momentum cases. Further, in the curved spacetime, we also prove the existence of the double counting of the geodesic phase to the null phase. Our conclusions are same as others’ results by the diﬀerent methods.