An Illustrated Guide to Relativity
Tatsu Takeuchi
CAMBRIDGE UNIVERSITY PRESS 2010, 256 PAGES
PRICE (PAPERBACK) £16.99 ISBN 978-0-521-14100-0
An Illustrated Guide to Relativity explains Einstein’s Theory of Relativity but largely without the equations found in traditional texts. It does this mainly by means of space-time diagrams and cartoons. To an extent it succeeds although the diagrams themselves become quite complex in the more advanced parts of the book, particularly on Lorenz transformation.
Part I is entitled ‘Kinematics: Relativity without any equations’ although in fact some equations are given for reference in the end-notes of chapters. The basics of Newtonian physics are briefly summarised along with relative velocities. The problems arising from the ‘mystery of the speed of light’, the fact that it is constant regardless of themotion of the observer or the source, are well explained. This leads naturally to Einstein’s argument that the concept of events happening ‘at the same time’ depends on the frame of reference, in other words it is relative. Addition of velocities is explained through some simple examples. Here it would have been useful to have shown the equation (given in the end-notes) and its derivation. Some philosophical issues about cause and effect, the impossibility of exceeding the speed of light and time travel are then tackled. There is also a lucid exposition of some of the consequences of relativity, including the twin paradox and the Doppler effect in light (causing the red shift observed in receding galaxies). Some common misunderstandings about relativity are dispelled.
Part II consists of a series of challenging problems. First there are qualitative problems with solutions. These require application of the space-time diagrams and ask questions such as the order in which events are perceived to take place by different observers either stationary or inmotion. The examples used are entertaining with material drawn from sport (on an astronomical scale) as well as the expected space wars and supernovae. Further problems are quantitative, but the reader is exhorted to approach these from basic principles rather than simply apply equations. Solutions to the quantitative problems are given in the form of space-time diagrams with the interpretation left to the reader.
Part III is called ‘Dynamics: Relativity with a few equations’. This leads up to the famous equation E=mc2 and here equations cannot be avoided. In fact the level of physics is substantially more demanding in this section. Newtonian dynamics is briefly introduced along with concepts such as inertial mass and momentum. Unfortunately the derivation of E=mc2 is not entirely rigorous and in fact the notation gets rather confusing. The end-notes do go some way toward making things a bit clearer. The commentary around the topic is good however.
The author has set out ambitiously to make the Theory of Relativity accessible to non-scientists while at the same time having sufficient scientific content for physics students. Ostensibly this is done by minimising the maths, but in reality the maths is still there but in pictures not formulae. He just about succeeds in his aim, although a basic level of physics would be needed to follow the detail, particularly for Part III.
There is one minor practical quibble: the space-time diagrams are reasonably clear and readable, however they are not numbered. Usually it is obvious which diagram the text is referring to but not always, which can be confusing. Overall this fresh approach is entertaining and informative, particularly on the historical and philosophical aspects of the theory. There is something for the inquisitive reader whatever their current knowledge.
Francis McGonigal CMath MIMA
Birmingham City University
Mathematics Today December 2011
An Illustrated Guide to Relativity can be purchased at Amazon.co.uk
