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 = ħcω, 2πħc 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 = ħcω/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