The geometry of special relativity: a concise course by N. Dragon

Abstract

This book arises from several years of the author’s teaching special relativity; it gives an interesting, if idiosyncratic, overview of the subject. The first chapter sets the scene for the subsequent development, introducing the notion of space-time, ideal clocks and measuring rods, and the invariant nature of the speed of light. This is used to give a pictorial explanation of simultaneity, and how observers in relativemotionwill therefore disagree not only about whether two distinct events take place at the same place, but also whether they take place at the same time. This geometric and pictorial approach is developed in the next chapter in a rather sophisticated version of Bondi’s k-calculus. Using only elementary geometrical ideas and symmetry assumptions the standard kinematical results of special relativity are obtained: composition of velocities, time dilation and length contraction, the Doppler effect, and the standard (non-)paradoxes of the twins and the pole-in-barn (here, carin-garage) are given a clear and careful development. The discussion is also extended to the full four dimensional space-time, not confined to the two dimensional case. Chapter three builds on this by finding the relationship between inertial coordinate systems: the Lorentz transformation. With the Lorentz transformation in hand, one can now consider what a moving object actually looks like to a stationary observer. A particularly nice example is the argument in terms of aberration that a moving sphere presents a circular appearance to a stationary observer. This chapter is rounded off by the introduction of the dynamical quantities of energy and momentum. Up to this point, the arguments have used little, if any, mathematics beyond what might be met in high school, or the early part of the undergraduate curriculum of a