This chapter introduces the special theory of relativity from a perspective that is appropriate for proceeding to the general theory of relativity later on, from Chapter 4 onwards. Several topics such as the manipulation of tensorial quantities, description of physical systems using action principles, the use of distribution function to describe a collection of particles, etc., are introduced in this chapter in order to develop familiarity with these concepts within the context of special relativity itself. Virtually all the topics developed in this chapter will be generalized to curved spacetime in Chapter 4. The discussion of Lorentz group in Section 1.3.3 and in Section 1.10 is somewhat outside the main theme; the rest of the topics will be used extensively in the future chapters.
The principles of special relativity
To describe any physical process we need to specify the spatial and temporal coordinates of the relevant event. It is convenient to combine these four real numbers – one to denote the time of occurrence of the event and the other three to denote the location in space – into a single entity denoted by the four-component object xi = (x0, x1, x2, x3) ≡ (t, x) ≡ (t, xα). More usefully, we can think of an event P as a point in a four-dimensional space with coordinates xi. We will call the collection of all events as spacetime.