Classical Electrodynamics and Theory of Relativity

Although relativistic electrodynamics is more than 100 year old, there is one neglected topic in its presentation and application: relativistic transformations of electromagnetic integrals. Whereas in theoretical and applied electrodynamics electric and magnetic fields are mainly expressed in terms of integrals over charge and current distributions, relativistic transformations are traditionally applied to point charges and elementary currents. The purpose of this paper is to...

Some key notions of line geometry are recalled, along with their application to mechanics. It is then shown that most of the basic structures that one introduces in the pre-metric formulation of electromagnetism can be interpreted directly in terms of corresponding concepts in line geometry. The results are summarized in a table.

A new approach to classical electrodynamics is presented, showing that it can be regarded as a particular case of the most general relativistic force field. In particular, at first it is shown that the structure of the Lorentz force comes directly from the structure of the three-force transformation law, and that E and B fields can be defined, which in general will depend not only on the space-time coordinate, but also on the velocity of the body acted upon. Then it is proved...

The axiomatic structure of the electromagnetic theory is outlined. We will base classical electrodynamics on (1) electric charge conservation, (2) the Lorentz force, (3) magnetic flux conservation, and (4) on the Maxwell-Lorentz spacetime relations. This yields the Maxwell equations. The consequences will be drawn, inter alia, for the interpretation and the dimension of the electric and magnetic fields.

Some pedagogical aspects of the formulation of electrodynamics independently of the system of units are commented. Only electrodynamics in vacuum is considered. It is pointed out the efficiency of using a notation system close to SI.

In this paper the proofs are given that the electric and magnetic fields are properly defined vectors on the four-dimensional (4D) spacetime (the 4-vectors in the usual notation) and not the usual 3D fields. Furthermore, the proofs are presented that under the mathematically correct Lorentz transformations (LT), e.g., the electric field vector transforms as any other vector transforms, i.e., again to the electric field vector; there is no mixing with the magnetic field vector...

This text aims to explain general relativity to geometers who have no knowledge about physics. Using handwritten notes by Michel Vaugon, we construct the bases of the theory.

In the invariant approach to special relativity (SR), which we call the ''true transformations (TT) relativity,'' a physical quantity in the four-dimensional spacetime is mathematically represented either by a true tensor or equivalently by a coordinate-based geometric quantity comprising both components and a basis. This invariant approach differs both from the usual covariant approach, which mainly deals with the basis components of tensors in a specific, i.e., Einstein's c...

The illuminating role of differential forms in electromagnetism is seldom discussed in the classroom. It is the aim of this article to bring forth some of the relevant insights that can be learnt from a differential forms approach to E\&M. The article is self-contained in that no previous knowledge of forms is needed to follow it through. The effective polarization of the classical vacuum due to a uniform gravitational field and of the quantum vacuum in the Casimir effect are...

In this article we have illustrated how is possible to formulate Maxwell's equations in vacuum in an independent form of the usual systems of units. Maxwell's equations, are then specialized to the most commonly used systems of units: International system of units (SI), Gaussian normal, Gaussian rational (Heaviside-Lorentz), C.G.S. (electric), C.G.S. (magnetic), natural normal and natural rational. Both, the differential and the integral formulations of Maxwell's equations in...