Origin of Mass. Mass and Mass-Energy Equation from Classical-Mechanics Solution

Abstract

We establish the classical wave equation for a particle formed of a massless oscillatory elementary charge generally also traveling, and the resulting electromagnetic waves, of a generally Doppler-effected angular frequency $\w$, in the vacuum in three dimensions. We obtain from the solutions the total energy of the particle wave to be $\eng=\hbarc\w$, $2π\hbarc$ being a function expressed in wave-medium parameters and identifiable as the Planck constant. In respect to the train of the waves as a whole traveling at the finite velocity of light $c$, $\eng=mc^2$ represents thereby the translational kinetic energy of the wavetrain, $m=\hbarc\w/c^2$ being its inertial mass and thereby the inertial mass of the particle. Based on the solutions we also write down a set of semi-empirical equations for the particle's de Broglie wave parameters. From the standpoint of overall modern experimental indications we comment on the origin of mass implied by the solution.