Relativistic transformations and the equivalence principle

Abstract

Abstract As a precursor of a discussion of invariance principles and symmetries in Chapter 3, we summarize in this chapter relativistic transformations and Lorentz invariance, the Equivalence Principle, and important solutions of the Einstein field equations of general relativity. These are central to our discussions of cosmology in later chapters. Readers familiar with these topics can skip to Chapter 3. The special theory of relativity, proposed by Einstein in 1905, involves transformations between inertial frames (IFs) of reference. An IF is one in which Newton’s law of inertia holds: a body in such a frame not acted on by any external force continues in its state of rest or of uniform motion in a straight line. Although an IF is, strictly speaking, an idealized concept, a reference frame far removed from any fields or gravitating masses approximates to such a frame, as does a lift in free fall on Earth. On the scale of experiments in high-energy physics at accelerators, gravitational effects are negligibly small and to all intents and purposes the laboratory can be treated as an IF. However, on the scale of the cosmos, gravity is the most important of the fundamental interactions. We list here the coordinate transformations, called Lorentz transformations, among IFs in special relativity. These are obtained from two assumptions: that the coordinate transformations should be linear (to agree with the Galilean transformations in the non-relativistic limit); and that the velocity of light c in vacuum should be the same in all IFs (as observed in numerous experiments).