Electromagnetism: Maxwell Equations, Wave Propagation and Emission

Chapter 13

Special Relativity and Electrodynamics

Until the end of the 19^th Century, classical mechanics was confirmed by all experiments and nobody dared to think that this might not be the case in electromagnetism. However, several experiments have shown some contradictions between classical mechanics and electromagnetic phenomena, especially the propagation of light. In fact, as we shall see in this chapter, Maxwell’s equations, which are the basic laws of electromagnetism, are not in accordance with the Galilean invariance, which is one of the basic principles of classical mechanics. Several attempts have been made, without success, to modify Maxwell’s equations in order to make them agree with classical mechanics. Lorentz adopted the opposite strategy and proposed to modify classical mechanics by replacing the Galilean transformation by the now-called Lorentz transformation. In 1905, Einstein analyzed the basic concepts of space and time, and formulated the special theory of relativity. The Lorentz transformation resulted straightforwardly from this analysis. Up to now, all the consequences of this theory have been verified experimentally.

The special theory of relativity and the general theory of relativity, both formulated by Einstein, are new perceptions of physics and the Universe with very important consequences. Special relativity is used to study high-velocity (thus high-energy) phenomena. All fundamental physical theories must be formulated in accordance with relativity ...