Amp?re proposed an equation for the force between current elements in 1823. Gauss and Weber suggested equations for the force between moving charges which are derived from scalar potentials and are consistent with the Amp?re equation. Grassmann derived an alternative equation for the force between current elements in 1845, which is often called the Lorentz force. This paper derives a time-variant generalization of this equation. It also proposes a new equation for the force between current elements that satisfies the basic criteria suggested by Gauss and Hertz.
This paper is based on the fundamental criteria for the electrodynamic equation suggested by Gauss. It considers the definitions of the electric field proposed by Neumann and by Hertz. The classical formulation utilizing Neumann's definition and Einstein's postulate on the velocity of light does not satisfy the criteria suggested by Gauss. A new electrodynamic equation is proposed, utilizing the Hertzian definition of the electric field and the universal time postulate on the velocity of light, which does satisfy the Gaussian criteria.
Maxwell?s theory was based on the idea of a stationary aether. When the concept of the aether became untenable, two obvious procedures suggested themselves:
- Keep Maxwell?s equations but replace the Galilean transformation by the Lorentz transformation,
- Keep Galilean relativity but replace Maxwell?s equations by an extension of the Amp?re-Gauss formulation.
The first of these procedures was chosen by Einstein in his celebrated paper of 1905. But there is no necessity for such a deinfication of Maxwell?s equations. The experimental results seem to be satisfied equally well by the second alternative (the ?new electrodynamics?) which eliminates the concept of a magnetic field, replaces the four equations of Maxwell by a singe force equation, and retains Galilean relativity.
The present paper consists of an examination of the experimental results and how they fit into the new electrodynamics. Simultaneity, astronomical aberration, the de Sitter effect, the Sagnac experiment, and the Kaufmann effect are considered. The attempt is made to show that the triumphs of Einstein?s restricted relativity are explicable also on the basis of Galilean relativity.