Brian Cox and Jeff Forshaw

WHY DOES E=mc²?

(And Why Should We Care?

Throughout, Cox and Forshaw emphasise that, like all scientific theories, relativity is not guaranteed to hold true for all time, despite its central importance in physics. Just as Einstein modified Newton's laws, so too his work may be modified in the future by new discoveries or insights. But so far it has successfully withstood all the challenges it has met; all its predictions have been fulfilled. All scientific theories are provisional, true only until they have been disproved.

The book starts with a discussion of space and time in Einstein's world and goes on to explain why the speed of light is an upper limit at which anything can move. The authors make it clear that the cosmic speed limit is not fixed by some kind of divine fiat but arises necessarily from the structure of space and time. This leads up to an account of Einstein's theory of special relativity, which they don't just describe but deduce from a chain of reasoning which is quite similar to that which Einstein himself used when he presented the theory. The implications are then explored in a chapter which looks at the Twins Paradox and other counter-intuitive results.

We then come to the famous equation that provides the title of the book. The authors emphasise the real meaning of this—the literal equivalence of mass and energy. Mass is not just a measure of the amount of stuff something contains, it is also a measure of the energy stored up in matter. But there is a mystery about where mass comes from, and this leads to a discussion of the elusive Higgs boson. If this particle exists it will account for the existence of mass; if it doesn't, the 'Standard Model' of the structure of matter will have to be revised. The Large Hadron Collider is expected to decide the question one way or the other in the quite near future.

To explain why the existence of mass is a problem the authors make a detour to describe the present understanding of the structure of matter. They print what they call the central equation which lies at the heart of the Standard Model of Particle Physics. This is an intimidating four-line affair bristling with symbols, but readers are not expected to understand it in detail but merely to get an overall impression. In explaining some of the implications of the forumula the authors make use of some of the celebrated Feynman diagrams of particle interaction; a fair amount of concentration is required at this point from readers to whom all this is new.

The final chapter tackles Einstein's general theory of relativity, which includes gravity. At this point the authors confess frankly that although the idea that gravity results from the warping of space-time is fairly easy to grasp the underlying mathematics is difficult, so there are no equations here and the theory is merely presented rather than derived, as in the case of special relativity.

This is an unusual way of presenting Einstein's ideas and it may not work for everyone, but readers who are prepared to take their time and think through the steps of the argument will probably be left with the feeling that they have glimpsed a little of the way in which real physicists think about their subject. At least, Cox and Forshaw think that this will be the case and they are well placed to make the judgement.

26 August 2011