Introduction to Spacetime: A First Course on Relativity

Abstract

When somebody gets hold of a book he or she tries first to infer from the title of that book what it is likely to be about. Thus, in the case at hand, it would be fair to assume that the book is an introductory course on special as well as general relativity. Therefore, to begin with, we have to mention what this book is really about. In spite of its title it is a book exclusively on special relativity. Then one is tempted to ask why yet another book on special relativity must have been written in view of the many already existing ones. In a sense, however, Laurent's book is one of a new generation in that it admits from the very outset that special relativity is by now well established in physics and, in particular, that it is no longer necessary to justify it from the insufficiencies of Newtonian mechanics. Therefore, the author treats special relativity in a very straightforward and adequate way, i.e. purely geometrically. Accordingly, it is expected that the reader is familiar with vector calculus at least in three-dimensional Euclidean space. The book consists of 18 chapters and is divided into three main parts. In the first main part headed `Principles. Basic Applications' ten chapters take turns in being aimed predominantly at either physics or mathematics. The first two chapters are devoted to the assumptions behind special relativity. While, for instance, the principle of maximal proper time is put at the very beginning, the resolution of the famous twin paradox comes out almost automatically. As one of the consequences of these assumptions the Lorentz transformation is derived from the constancy of the velocity of light. Except for the Michelson--Morley and the Hafele--Keating experiments as well as the Doppler shift and aberration, the experimental verification of the theory remains beyond the scope of the book. In a wider sense, however, chapter 9 on particle kinematics is highly valuable for an understanding of particle physics experiments. From a deeper point of view also chapter 10 is very informative in that it discusses the gedanken experiments on the rotating wheel and how to fit a car into a garage. All in all, in this first main part, forming about one half of the book, nearly all issues which usually belong to relativistic kinematics and dynamics are treated in a geometrical language. In the second main part headed `Tensors' tensor algebra and analysis are developed with regard to electrodynamics. Accordingly, spacetime volumes with and without metric and Gauss's law are discussed. Apart from an introductory motivation from the point of view of physics, the five chapters of this part are predominantly mathematical. One can get the feeling that more is done than would be necessary for special relativity. On the other hand, this pays off at the last when the reader wants to use this book as a preparatory reading for general relativity. The third main part is devoted to `Electrodynamics' with and without sources. The last three chapters of the book start with the scalar wave equation and end up with its solution by Lienard--Wiechert potentials, the geometric interpretation of which leads back to the light cone first discussed in chapter 6. The book is written in an elegant style which, at least as far as mathematics is concerned, could cause some difficulties for the novice but which, on the other hand, has the advantage that the reader is directly brought up to the original literature. All those who want to become acquainted with special relativity without the need of being convinced of its validity beforehand will find Laurent's book particularly useful. By emphasizing the geometric aspects of the theory the reader will get a deeper understanding of the characteristic traits of special relativity and its generalization to general relativity.