Time-space symmetry as a solution to the mass hierarchy of charged lepton generations

Based on an extended time-space symmetry, a cylindrical model of gravitational geometrical dynamics with two time-like extra-dimensions leads to a microscopic geodesic description of the curved space-time. Due to interaction of a Higgs-like cosmological potential with individual space-time fluctuations, the original time-space symmetry is spontaneously broken, inducing a strong time-like curvature and a weak space-like deviation curve. As a result, the basic Klein-Gordon-Fock equation of a free massive elementary particle was derived, which implies a duality between the quantum mechanics equation and a microscopic geodesic description in the frame of general relativity. Consequently, Heisenberg inequalities are determined explicitly by the space-time curvatures. Moreover, extending curvatures to higher time-like dimensional hyper-spherical surfaces than one of the basic common cylindrical configuration, we found reasonable mass ratios of all charged leptons and succeeded to fix the number of their generations to be three. Following to concepts of the standard cosmological model, a possible experimental verification of mass ratio variation is proposed.