Weber's force law for real finite-size elastic particles is here derived from the fundamental empirical laws of classical electrodynamics, i.e. Gauss's laws, Amp?re's law, Faraday's law, and Lenz's law, assuming Galilean invariance. The rearrangement of the elastic charge density within the finite-size moving particle to produce a minimum in potential energy under the stress of induction forces is seen to be the physical origin of so-called ?relativistic effects'. The derived version of Weber's force law appears to be fully ?relativistic' without any reference to Einstein's special relativity theory. It satisfies Newton's third law, conservation of energy and Mach's principle. Furthermore it incorporates finite-size particle effects, such as self-induced fields, which are missing from point- particle theories such as Maxwell's equations, Einstein's special relativity theory, and quantum mechanics. The most general form of the force law appears capable of describing fully ?relativistic' radiation and radiation-reaction effects as well as many other higher order time derivative effects. From this derivation it appears that Einstein's special relativity theory, as well as the use of retardation for non-radiation fields in electrodynamics, are not proper physical theories, but rather mathematical theories cleverly contrived to imitate the self-field effects of real finite-size elastic particles to order v in the Galilean transformation.
Reprinted in Galilean Electrodynamics, V14, N1, pp. 3-10 (2003).
