The Special Theory of Relativity

Abstract

In our development of electromagnetic theory the hypothesis of a Galilean transformation was assumed. This is a transformation from one coordinate system to another where the reference frame moves rigidly with a constant velocity with no rotation. Newton’s laws of mechanics are invariant under such a transformation. But a Galilean transformation predicts that the velocity of light should be different in the two reference systems. Are not Newton’s laws of mechanics therefore incorrect? The answer to this question led to a new and revolutionary system of mechanics, relativity theory, developed by Albert Einstein. Actually Einstein formulated two relativity theories: the special theory which does not account for gravitational effects, and the general theory which reformulates mechanics in the setting of a time—space whose curvature represents the effect of the gravitational field. The general theory is much more revolutionary and entirely a product of Einstein’s genius, whereas other investigators such as Poincaré and Lorentz were skirting around the edges of the special theory. Indeed, Poincaré would have discovered the special theory if he had just made the leap of physical intuition that Einstein did. In this chapter we shall be concerned only with the special theory, since this deals with electromagnetic and optical phenomena.