Critical review of classical electrodynamics

Abstract

In this paper, we will review classical electrodynamics, where our main concern will be exclusively the propagation of electromagnetic waves in the vacuum and the interaction of these waves with free charges. We will examine the reasons why the classical Maxwell's equations are not complete and consistent. We will show that there are three kinds of waves propagating in the vacuum, namely, transverse waves, longitudinal waves, and helicoidal waves. We will particularly review the theoretical and experimental aspects of longitudinal waves whose existence seems to be proven.