The Relative Masses of the Proton, Electron, and Helium Nucleus

Abstract

THEORETICAL considerations suggest that the square root of mass may be more interesting and important than mass itself in the case of the ultimate particles of matter. For in the modern theory of matter, electric charge is more fundamental than mass, and the dimensional formula for electric charge e is M1/2L3/2T^-1 in the electrostatic system. Thus e is proportional to M1/2. This appears in more definite form if we adopt the classical point of view that the mass of the ultimate particles is entirely of electromagnetic origin. According to the theory of relativity, energy and mass are related by the well-known equation E = mc². But if the energy E is entirely electromagnetic, E= ∫1/8π(F² + H²)dv, where Fand H are the electric and magnetic field intensities respectively. Thus m depends on the square of F and H, corresponding to the fact that it depends on the square of e. Carrying out this process yields the well-known formula