The biography of an equation- Review: E=mc squared, by David Bodanis

Submitted by Anon on 30 March, 2002 - 11:13

David Bodanis was inspired to write this book when he heard that the actor Cameron Diaz had said in an interview that she’d really like to understand what “E=mc squared” means. He decided to tackle the task himself, not by explaining how the equation came to be derived, but by treating it almost as a person: he decided to write the biography of an equation.

Its birth was in the Bern Patent Office, where its immediate parent, Albert Einstein, was languishing in exile from the academic world: his irreverent attitude to his teachers meant that he got bad references when he applied for academic posts. Its ancestors were the ideas of a varied bunch of bright sparks, who often had to fight against the dead weight of established authority or prejudice.

Young, working-class, Michael Faraday was to come up with one of these ideas. He was able to see the connection between electrical and magnetic energies, hitherto thought separate, because, perhaps, of his unorthodox religious views. He then saw his mentor, the more socially accepted Humphry Davy, try to steal his discovery, a common theme in science. The key idea that came from Faraday’s work was that all forms of energy are interchangeable, and the law of conservation of energy entered scientific orthodoxy. Einstein was later to overthrow this law.

The idea of mass as a theme unifying the apparently unrelated types of matter, such as gold and oxygen, or chalk and cheese, was also crucial. Newton had shown that all matter was affected by the force of gravity. Antoine Lavoisier, assisted by his wife Marie Anne, was able to show not only that, when iron burnt or rusted, it gained weight, but also that the surrounding air lost the same amount of weight. This pointed towards the existence of oxygen but also to the law of conservation of mass: Einstein was to overthrow that law, too.

By the end of the 19th century, it was apparent that mass could have energy but the idea that mass is energy was revolutionary. And the suggestion that the conversion factor was the speed of light squared (c squared) was super-revolutionary. But what was the speed of light, c? Previous attempts to measure it had often failed because, unlike the speed of sound, the time intervals to be measured were far to short to be detectable with the available clocks, even with the longest distances possible on Earth. It only takes about one ten thousandth of a second to reach the horizon, for example. The idea that it travelled at an infinite speed became dominant.

In the late 17th century, a young Danish astronomer, Roemer, proposed that a puzzling feature of the orbit of one of Jupiter’s moons could be explained by the different distances that light had to travel to Earth as Earth orbited round the Sun. He even estimated a speed for light close to the current known value. His work was rubbished by his boss, the prominent astronomer Cassini and his career stalled, another common theme in science.

In the mid-19th century, Maxwell took Faraday’s discovery of the inter-relationship of changing electric and magnetic fields further, by supposing a mutually perpetuating oscillation of fields. He realised that this would travel through empty space at the speed of light and in fact was light. This idea came with the corollary that the speed of light was determined by the nature of space and was not altered by the speed of the thing sending it out.

So we have a type of energy (light and all the things that behave like it, such as radio waves, ultra-violet and X-rays) that travels at an enormous but definite speed in space. We also have matter (mass) that can travel at different speeds. Surely, it should be possible to accelerate a piece of matter to c or even beyond. Newton’s laws did not rule this out. However, Einstein suggested that c was an absolute barrier beyond which nothing could go and, if you tried to expend energy accelerating some mass to c or beyond, what you actually succeeded in doing was increasing its mass! Einstein showed that the calculation of this increase of mass included the speed of light squared.

Now, expressions for kinetic energy (the energy of a moving object) include the factor of speed squared. Bodanis describes the role in establishing this fact of Emilie du Châtelet, a rich young woman of 18th century France who studied mathematics and the sciences and died giving birth to her child with Voltaire. She played a major part in replacing the previous notion of energy, which is what we now call momentum (including speed as a factor). The new definition explains, for instance, why the stopping distance for cars increases fourfold when the speed doubles.

Initially, after 1905, Einstein’s equation, and the theory of special relativity that contained it, were ignored. Gradually, it became more widely known and accepted, perhaps because it seemed to offer explanations for phenomena like radioactivity. In this, energy changes millions of times greater than those found in chemical reactions take place. Something like E=mc squared would be needed to explain these, as it would when contemplating the incredible concentration of mass in the nucleus of the atom, discovered at about the same time by Rutherford. Experimental verification of the predictions of Einstein’s theories of relativity helped, too.

One of the important consequences of E=mc squared was that the power source of the Sun could be explained. This could only happen after it had been shown that the Sun consists almost entirely of hydrogen and helium. Once again, discoveries by a woman (astronomer Cecilia Payne) were first dismissed and then appropriated by the established scientists. The hydrogen is in the process of being converted into helium with the loss of a little mass. The Sun is a gigantic nuclear fusion reactor converting four million tonnes of mass into energy every second.

The other important consequence was the discovery that it was possible to release locked-up energy from certain types of nuclei by splitting them. This was nuclear fission of atoms like uranium-235. Here, the prime mover was Lise Meitner, but, as a woman and as a Jew in Nazi Germany, she was forced into exile. Later, she was to see her former student and friend, the non-Jew Otto Hahn, receive the Nobel Prize for their joint work. Bodanis’ discussion of the development of the atom bomb by the US — and the failure of Nazi Germany to match it — is fascinating.

The book includes accounts of the lives and fates of other people mentioned, such as Lavoisier and Heisenberg, as well as 50 pages of notes (rather interesting, actually!) and suggestions for further reading. My only complaint is the use throughout of US units, which British readers educated since the 1970s may find confusing. I hope Cameron Diaz read it.

Les Hearn

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