Deriving an Electric Wave Equation from Weber’s Electrodynamics

Abstract

Weber’s electrodynamics presents an alternative theory to the widely accepted Maxwell–Lorentz electromagnetism. It is founded on the concept of direct action between particles, and has recently gained some momentum through theoretical and experimental advancements. However, a major criticism remains: the lack of a comprehensive electromagnetic wave equation for free space. Our motivation in this research article is to address this criticism, in some measure, by deriving an electric wave equation from Weber’s electrodynamics based on the axiom of vacuum polarization. Although this assumption has limited experimental evidence and its validity remains a topic of debate among researchers, it has been shown to be useful in the calculation of various quantum mechanical phenomena. Based on this concept, and beginning with Weber’s force, we derive an expression which resembles the familiar electric field wave equation derived from Maxwell’s equations.

Pseudo-Instantaneous Action-at-a-Distance with Weberian Potentials

“…Fukai, for example, showed in [36] that Weber's law is not only able to explain most of classical electrodynamics, but also to explain the propagation of radiation through a vacuum, for which only certain assumptions about the vacuum, which are common in quantum physics, need to be made. A similar line was followed by Li in [37], where, using Weber electrodynamics, and assuming a neutral but polarisable vacuum, he derived the wave equation, for waves propagating at speed c.…”