Relativistic Electromagnetism

Abstract

In this monograph, Maxwell’s equations were developed in Chapter 4 from the formulae for the electric and magnetic fields of a ‘point’ charge moving with uniform velocity. These formulae had been developed previously in Chapter 3, from Coulomb’s law taking the transformations of the theory of special relativity as axiomatic. This approach is the reverse of the historical approach. The theory of special relativity evolved from classical optics and electromagnetism, Maxwell’s equations were developed before the theory of special relativity. In 1905, Einstein¹ assumed as his first postulate that all the laws of physics, including the laws of electromagnetism, obeyed the principle of relativity. As his second postulate, Einstein could have assumed that the appropriate laws of electromagnetism were Maxwell’s equations. Instead, Einstein chose the principle of the constancy of the speed of light as his second postulate. (It is shown by Rosser^{2a, 15}, that, if it is assumed that Maxwell’s equations, are correct and obey the principle of relativity, the principle of the constancy of the speed of light follows.) After developing the Lorentz transformations, Einstein¹ went on to show that the Lorentz transformations did leave Maxwell’s equations invariant in mathematical form. This approach is developed in this chapter.