Violations of energy conservation and action uniqueness as sources for mass-energy waves

Abstract

Homogeneous wave equations satisfied by the 4-vector momentum density p (including the mass-energy density as its timelike component) are derived as a consequence of energy conservation and uniqueness of the action integral. These two conditions can be written respectively as the vanishing of the four-dimensional versions of the divergence and curl of p . The generation of such waves described by inhomogeneous wave equations is shown to be possible by violation of energy conservation, action uniqueness or both. In the case where energy is conserved but action uniqueness is violated by the presence of an electromagnetic field it is found that an Ansatz proportional to q( H ̄ + i E ̄ ) for the curl of p̄ leads to the correct Lorentz force term in Newton II modified by the presence of the electromagnetic field. This then implies that the D'Alembertian of the mass density is proportional to the square of the charge density. It is speculated that this may be applicable to the internal distributions of mass and charge of electrons, protons and neutrons as evidenced by electromagnetic stering experiments.