Minimum electric charge of an extended electromagnetic field theory

Abstract

The hypothesis of a non-zero divergence of the electric field in vacuo and an associated extended Lorentz invariant formulation of Maxwell's equations provide steady-state solutions of the electromagnetic field. Among the solutions there are those of axisymmetric configurations having integrated field quantities which represent an equivalent electric charge q0, magnetic moment M0, mass m0, and angular momentum s0. All these quantities become finite and non-zero, at the same time as the corresponding characteristic radius can be allowed to shrink indefinitely, to correspond to the property of a "point charge". The present theoretical model includes relevant quantum conditions, and a condition of equipartition between electric and magnetic energy.The question is raised whether the obtained results could have a bearing on the physics of charged leptons, such as the electron. In comparison with observed electron data, the present approach thus yields correct signs of the quantities q0, M0, m0 and s0, the ratio M0 m0/q0 s0 is predicted to be of the order of unity as for measured data, a "point charge" of very small radial extension can be obtained, and a minimum charge |q0| ≅ 1.60 × 10−19 Coulomb is deduced from a simple iteration process, thereby differing at most by about one percent from the measured value of the electronic charge. This suggests that the electronic charge is not an independent constant of nature, but is a typical quantum number determined by the speed of light and Planck's constant. The present theory also fits the muon data, at least within one percent accuracy.