10th November 2000 at 00:00
e=mc2. By David Bodanis. Macmillan pound;14.99

In 1905 an obscure clerk in the patents office in Bern published a paper on what he termed the special theory of relativity. In an appendix, Albert Einstein explained some of this theory by an equation (later to be re-written as e=mc2) an expression of the theory so neat and elegant as to become as famous in its own right as its cloudy-haired composer. But what does it mean?

When film star Cameron Diaz tells an interviewer that one thing she would really like is to understand e=mc2, when the technology not only of death-dealing bombs but also of smoke alarms and hospital scanners is based on its understanding, and when our deepest theories of time and space from big bangs to black holes depend on its masterful illumination, how come so many of us are ignorant?

David Bodanis's witty and informative book can enlighten you painlessly. Briefly, Bodanis explains that the universe is not as it appears to our commonsense apprehension, not even as it seemed to be to Newton.

All matter (mass) is actually composed of atoms, which, in turn, are largely empty space in which tiny particles zoom around, held together by fields of energy. At the furthest edges of what is possible, if you speed up mass to the fastest speed that anything can travel (the speed of light), and then make atoms collide, you break the field and release the energy. As mass, so to speak, bangs into itself - as physicists say undergoes atomic fission - the impact is squared, which is why the equation means, "energy is equivalent to mass multiplied by the speed of light squared". That is, energy and mass are different forms of the same thing. From this, we can work out how everything began (all scrunched up in a big mass) and how it will end, ages hence (all spread out, energy spent). The proofs can be found in the book, on the website (www.davidbodanis.com) and in most physics textbooks.

Bodanis's contribution, easily accessible to GCSE students and above, is to enliven his explanation with stories. He uses the device of a biography of the equation to guide readers through a quick tour of maths, physics and 20th-century history. As he traces each component in the famous equation, even the = sign, he focuses on the scientists who pondered on the ideas, giving the unfolding comprehension human shape.

Thus, he traces the history of the idea that mass (m) contains latent energy (e) by focusing on the biographies of the chemist Antoine Lavoisier and his contemporaries in pre-Revolutionary-France, the intellectual lovers Emilie du Chatelet and Voltaire.

Lavoisier conducted one of the first experiments to see what happens when metal rusts. Answer: it gains weight. Du Chatelet was one of the first to work out that energy released when two objects impact is squared rather than added, a view first advanced by the German philosopher and mathematician Gottfried Wilhelm von Leibniz. Her findings informed Candide, Voltaire's satire on Leibniz. P> In his chapter on c - for celeritas, or speed (of light) - Bodanis outlines the sad saga of Michael Faraday and his mentor Humphry Davy, a snob who used the ideas of his apprentice, Faraday, then accused him of stealing them. With material like this, Bodanis scoops much of the recent history of physics into his story, showing how great discoveries build on previous work and drawing attention to the crucial but unpublicised gains made by female scientists as far back as the 18th century.

Rich in science, this book is also a-glitter with anecdote. The equation got its reputation for extreme difficulty, Bodanis tells us, because the New York Times reporter sent to a 1919 press conference did not understand a word: he was the golfing correspondent. Chaim Weizman, the first president of Israel, is also recorded as saying, after crossing the Atlantic with Einstein: "Einstein explained his theory to me every day, and soon I was completely convinced that he understood it."

Yet, in fact, the formula and its implications caught on quickly. The 1940s race to develop an atomic bomb reveals more about the contested frontier between politics, ethics and science than about pure physics. Bodanis relishes this stage of the story. From the neurotic American J Robert Oppenheimer to the vain and vengeful German Werner Heisenberg, from the dull bureaucrats of pre-war America to the brutal masters of the Third Reich, his account grips.

Bodanis suggests that it is also a scientific talent to have the nose for a discovery whose time has come. Consider, for instance, the chemist Otto Hahn. Hahn worked for much of the 1930s in the Berlin laboratory of Lise Meitner. But Meitner was a Jew and Hahn had her sacked and exiled to Norway. He went on to take the credit for discovering nuclear fission, though Meitner had not only grasped the concept first, but also devised the experiments that Hahn carried out and wrote up.

Science always interacts with the world of realpolitik. If there had not been a Second World War, the atomic bomb, foreshadowed in a letter from Einstein to President Roosevelt, might never have been invented. Without these bombs, the Cold War would not have had such a terrifying grip on the world. Yet the minutes of the meeting which decided to drop the bombs on Japan are uncannily similar to a story from Russian physicist Andrei Sakharov about Soviet high command. Allied attempts to sabotage Norwegian production of heavy water, necessary to build bombs, offer a moving saga of derring-do; they are counterpoised by the sobering accounts of the activities of the German chemical firm I G Farben, which bought Jewish women from Auschwitz for its fatal experiments.

Such are the building blocks of Bodanis's take on e=mc2. Peter Medawar, whose research into immunology won a Nobel Prize, called the researcher's knack of finding the right questions "art of the soluble". Bodanis has mastered that art, and the book fizzes in the reader's imagination.

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