On the lifetime of the muon state of the electron-muon mass doublet

Abstract

In a previous paper the electron and muon masses were derived by combining the author’s general relativistic derivation of the inertial masses of spinor particles from the geometrical field and his model of the « physical vacuum » (from a self-consistent field theory of electrodynamics) in terms of an ideal gas of electron-positron pairs in a particular state that was derived from the theory. It was predicted earlier that in this field theory spinor particles occur in mass doublets. In the electron-muon case, the observation of the « heavy electron » (muon) is a consequence of quadrupolar excitation of the physical vacuum of pairs—correspondingly altering the geometrical field in the vicinity of the observed electron, thereby making it more inertial. In this paper, the lifetime of the heavy electron in this physical vacuum will be determined, de-excitation occurring by the transferral of electromagnetic energy from this heavy electron to the pairs of the physical vacuum by means of a quadrupolar transition. To facilitate the calculation with time-dependent perturbation theory, use is made of Fermi’s multiple-meson production theory, and the improvisation of his theory for break-up reactions by the author. In this way, the ensuing quantitative analysis yields a lifetime for the heavy electron that is of the order of 2.09·10-6 s, which is within 5% of the observed muon decay rate. It is then shown how the present theory, in which electromagnetic variables are in terms of 2-component spinor fields, explains the reaction Μ → e++Ν in terms of a process that is purely electromagnetic and does not entail neutrinos.