On the Relation between Mass and Charge: A Pure Geometric Approach

TL;DR

This paper presents a geometric model using absolute parallelism space to relate mass and charge, showing that a particle's mass can be entirely electromagnetic and dependent on charge, with implications for elementary particles like electrons.

Contribution

It introduces a new solution in generalized field theory within AP-space, demonstrating how mass can originate solely from electromagnetic charge and analyzing the physical meaning through dual schemes.

Findings

Mass has gravitational and electromagnetic contributions.

Charged particles can have mass entirely from electromagnetic origin.

The model excludes massless charged particles.

Abstract

A new solution of the field equations of the generalized field theory, constructed by Mikhail and Wanas in 1977, has been obtained. The geometric structure used, in the present application, is an absolute parallelism (AP)-space with spherical symmetry (type FIGI). The solution obtained represents a generalized field outside a charged massive central body. Two schemes have been used to get the physical meaning of the solution: The first is related to the metric of the Riemannian space associated with the AP-structure. The second is connected to a covariant scheme known as {\it{Type Analysis}}. It is shown that the dependence on both schemes for interpreting the results obtained, is more better than the dependence on the metric of the Riemannian space associated with the AP-structure. In General, if we consider the solution obtained as representing a geometric model for an elementary charged particle, then the results of the present work can be summarized in the following points. (i) It is shown that the mass of the particle is made of two contributions: The first is the gravitational contribution, and the second is the contribution due to the existence of charge. (ii) The model allows for the existence of a charged particle whose mass is completely electromagnetic in origin. (iii) The model prevents the existence of a charged massless particle. (iv) The electromagnetic contribution, to the mass, is independent of the sign of the electric charge. (v) It is shown that the mass of the electron (or a positron) is purely made of its charge.