A Geometrical Approach to Action-at-a-Distance Electrodynamics
Keywords: Geometry, Action-at-a-Distance, IAAD, Electrodynamics
This paper begins with a brief introduction to the trigonometry of the complex plane. We then present an intuitive, geometrical derivation of the relativistic addition of velocities, and of the electromagnetic interaction between two uniformly moving charged particles, based on 2 spatial + 1 temporal dimensional Minkowski diagrams [http://xxx.lanl.gov/abs/physics/0003008]. New physical insight is then obtained by a critical analysis of the concept of \'material point particle\'. We argue that this concept is incompatible with the force laws of action-at-a-distance electrodynamics. By complementing our mod?l with other results, we are led to a straightforward derivation of the principles underlying the electromagnetic interaction between two uniformly moving charged particles. An extension of our theory to the case of particles in arbitrary motion shows that we have to modify the Maxwell equations of the microscopic electromagnetic field, in order to accommodate a field-strength tensor which is no longer antisymmetric, Remarkably, the averaged macroscopic field still is described by an antisymmetric tensor. Future work will try to determine how our results are related to the tangential forces experimentally and theoretically studied by other authors [Physics Essays 12 (1) p.153].