Volume 19: Pages 544-552, 2006)

Mass and Mass‐Energy Equation from Classical Mechanics Solution

J. X. Zheng‐Johansson ¹, P‐I. Johansson ²

¹Institute of Fundamental Physics Research, Nyköping, 611 93 Sweden

²Department of Neutron Research, Uppsala University, Nyköping, 611 82 Sweden

We establish and solve the classical wave equation for a particle formed from a massless oscillatory charge and the resulting electromagnetic waves of frequency ω in the vacuum. We obtain from its wave‐function solution the total energy of the particle wave to be Ε = ħ_cω, 2πħ_c being a function expressed in wave‐medium parameters and identifiable as the Planck constant. The source charge, hence the particle, may be generally traveling; ω thus depends on the particle's motion owing to its source‐motion resultant Doppler shift. The train of waves traveling as a whole at the finite velocity of light c has apparently an inertial mass m, and hence the Newtonian translational kinetic energy mc² = Ε, where m = ħ_cω/c². m is thereby in turn 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.

Keywords: nature and origin of mass, particle‐formation scheme, massless oscillatory elementary charge, electromagnetic wave‐train, vacuum structure, vacuum polarization and induced elasticity, vacuum factional force, first‐principles classical mechanics solutions, mass‐energy equation, de Broglie relations

Received: January 17, 2005; Published Online: December 15, 2008