On the Modernisation of Weber’s Electrodynamics

Abstract

This work is an attempt to modernise Weber’s electrodynamics to make it compatible with the high-velocity regime, and with the existence of a limiting velocity, c. For this purpose, starting from the law of energy conservation and the mass–energy equivalence, new expressions for potential energy and for kinetic energy are derived jointly which are consistent with an ultimate velocity of the value of c. The new potential energy, already reported by Phipps, becomes Weber’s expression in the limit of low velocities. The new kinetic energy differs from the relativistic expression, but, like the latter, it also becomes the Newtonian expression in the limit of low velocities. New expressions for force and linear momentum are also derived which complete a new mechanics. Phipps’ potential energy and new kinetic energy are applied to the problem of two interacting charges in a radial motion and orbital motion. The new framework is also applied to the problem of a charge moving between the two plates of a charged capacitor, obtaining a result similar to that obtained by means of Maxwell–Lorentz electromagnetism and relativistic mechanics. The metaphysical considerations that clearly differentiate the conventional framework from the new framework proposed here are discussed.