Locomotion that trains the mind to think deep

Just over a century ago, Einstein formulated a theory of relativity in his 1905 paper On the electrodynamics of moving bodies . The term special relativity came into use later, when he had completed the theory of gravity known as general relativity. Special relativity rests on two postulates. As Einstein put it: "In electromagnetism as well as in mechanics, phenomena have no properties corresponding to the concept of absolute rest." This principle, first enunciated for mechanics by Galileo, was later incorporated into classical mechanics by Newton. Einstein extended the principle to electromagnetism, removing at a stroke the confusion caused by the then-widespread view that there is a preferred frame of reference for electric and magnetic behaviour, the frame in which the luminiferous ether was stationary.

Einstein's second postulate, that light in empty space moves with a velocity that is independent of the velocity of the source, is highly counterintuitive. It is from this principle of the constancy of the velocity of light that Einstein first realised that the nature of time involved wonderful subtleties.

Several of Einstein's predecessors had suspected that something was wrong with Newtonian physics. At the end of the 19th century, George FitzGerald and Hendrik Lorentz had independently suggested that bodies moving through the ether would contract and that clocks would slow. The mathematician Henri Poincare, writing and lecturing in 1900-04, came remarkably close to the special theory of relativity. However, these advances were in the context of explaining experimental results where ether enabled light to propagate in the first place. Einstein's paper is remarkably different.

Instead of accounting for experiments, he presented the theory for its beauty and the simplicity of the two postulates. Einstein was always reticent to acknowledge the contributions to relativity made by others.

The consequence of the two postulates, both of which are invariance principles, is that space and time have curious properties. In It's About Time , David Mermin explores how relativity works on a practical level using thought experiments involving (very long) trains and railway stations. A physical situation is set up, such as balls colliding, then the physics is examined from the point of view of an observer on the train and one on the station platform.

Consider, for example, the problem of synchronising two clocks that are known to run at identical speeds. If both clocks are brought to the centre of the train, they can be synchronised. Now move one to the front of the train and the other to the back. From the train's point of view both are showing the same time. But this is not true on the platform, where the reading of the front clock will lag behind that of the rear clock. This is time dilation, a real effect, not just a trick of the way we use language to describe the appearance of clocks. In particle accelerators, the internal clocks of unstable particles run much more slowly as they approach the velocity of light, and time dilation is crucially important to the operation of accelerators.

There are countless books on special relativity, so why do we need another one? Most relativity texts are aimed at first-year physics undergraduates.

But Mermin's premise is that everyone should know about relativity in order to understand the real nature of time. For almost 40 years Mermin has taught this course to non-science majors at Cornell University. What is remarkable in his approach is his reliance on developing the reader's skills to analyse events in more than one frame of reference. This is the key to understanding relativity: being able to translate with ease from one frame of reference (a moving train) to another (a station).

The normal experience for a physics undergraduate is to learn how to apply special relativity quantitatively to a variety of problems. Mermin does not take this line: his book has no worked examples or homework problems. The goal, in which the author succeeds completely, is to develop a thinking style in which the consequences of relativity can be appreciated, and understood, at a deeply philosophical level. The jacket blurb claims that the theory is "rigorously explained without advanced mathematics". In the last quarter of the book, the equations come thick and fast, although by that stage the novice reader has already learnt so much that the remaining chapters can be skipped. Professional physicists and undergraduates should find the book's highly original approach rewarding.

Simon Mitton is a fellow of St Edmund's College, Cambridge.