A Local-Ether Wave Equation and the Consequent Electromagnetic Force Law

Abstract

_—The local-ether wave equation incorporating a nature frequency and the electric scalar potential is presented, from which the electrostatic force in conjunction with the inertial mass is derived. It is found that the inertial mass of a charged particle originates from the temporal variation of the associated matter wave. Further, the wave equation is extended by connecting the scalar potential to the augmentation operator which in turn is associated with the momentum operator and the velocity of source particles. From this local-ether wave equation, a first-order time evolution equation is derived, which in turn leads to the electromagnetic force law based on the augmented potentials. Under the low-speed condition, this law reduces to the modified Lorentz force law.