Wave propagation

Abstract

In the last chapter we formulated relativistically invariant forms for the law of conservation of momentum and energy. To follow a logical ordering we ought now to try to formulate the equivalent of the Newtonian equations of motion. As we indicated, however, this is by no means an easy task. The concept of action at a distance has to be abandoned and if one particle is to influence another, the information has to be conveyed from one to the other with a velocity whose maximum value is the velocity of light. The only forces we have considered in detail up until now have been electromagnetic ones. We have seen that the fields that are responsible for these forces are propagated through space as electromagnetic waves. This suggests that, at least as far as the electromagnetic forces are concerned, ‘action at a distance’ may be accomplished through the medium of waves propagating with the velocity of light. Therefore before we attempt to look for further dynamic laws, we will examine the propagation of waves as viewed from different inertial frames. We start by examining the propagation of waves in free space.