Special Relativity

This book can serve as a bridge between college-level introductions and advanced graduate-level books on special relativity. The book begins at an elementary level exposing and discussing in Chapter 1 and Chapter 2 the basic concepts normally contained in college-level expositions, including the Lorentz transformation. In Chapter 3 the student is introduced to the four-dimensional world view implied by the Lorentz transformations mixing time and space coordinates. Chapter 4 continues with the formalism of tensors, a topic usually avoided in lower-level courses. Chapter 5 introduces the essential concept of causality and details the application of the general formalism of tensors to Minkowski space. Chapter 6 discusses the relativistic mechanics of point particles, four-momentum and four-force, the equivalence between mass and energy, and some applications. An optional short Chapter 7 follows, in which measurements in Minkowski spacetime are discussed. Matter in Minkowski spacetime is discussed in Chapter 9. Here the energy-momentum tensor of a continuous distribution of mass-energy and its covariant conservation are introduced, and (optional) various energy conditions are presented. Angular momentum is discussed briefly. This part is followed by a discussion of the scalar field of perfect fluids and of the Maxwell field. Chapter 10 introduces general coordinates, covariant differentiation and geodesics and reformulates the previous material in arbitrary coordinate systems using covariant formulas.§Every chapter is supplemented by a section containing numerous exercises to practice the theory. These exercises constitute an essential part of the textbook. The solutions to approximately half of the exercises are presented at the end of the book.