Free Radicals - Michael Brooks [27]
In general, theorists are thought to be immune from the worst scientific misdemeanour, the one that tops Martinson’s table. Falsifying or ‘cooking’ research data – ‘counterfeiting the coin of science’, as David Goodstein has put it – is generally thought to be impossible for those who deal only in ideas. But that is simply not the case. Constructing a mathematical theory is not unlike performing an experiment. Every step requires attention to detail; one slip renders the whole endeavour invalid. You must watch carefully for unwarranted assumptions, for example: mathematical models are developed to deal with particular situations, and what applies in one scenario will not necessarily work for another. Just because a formula applies in one context, such as when moving at the speed of a train, that doesn’t mean that it applies in another – moving at something close to the speed of light. Einstein, ever the anarchist, refused to let such inconvenient details get in the way of a good idea.
In 1905, Einstein’s intuition told him something ‘jolly and beguiling’: that the mass of a body will change if it emits a pulse of light. This crystallised in his mind as the famous E = mc2 equation: the energy lost as the light pulse is equal to the change in mass multiplied by the square of the speed of light. But he never managed to prove it.
His first attempt – the 1905 paper published in September’s Annalen der Physik – contained a mistake. Einstein used a formula that applied only to slow-moving bodies. The description of fast-moving emitters of light required an entirely different approach. According to the physicist Hans Ohanian, this error ‘is the sort of thing every amateur mathematician knows to watch out for’, but Einstein didn’t bother with it. Generously, Ohanian suggests that Einstein’s mind must still have been exhausted from his work on special relativity, which had been finished only a couple of months before. But over the next forty-one years, Einstein made eight attempts at a proof of E = mc2. Not once did he manage it without inserting a fudge.
Take Einstein’s 1912 ‘proof’, for example. The approach he took was borrowed (without acknowledgement) from work done by another physicist, Max von Laue. In the process of trying to make it his own, Einstein had to admit to making a nonsensical assumption. One footnote reads, ‘To be sure, this is not rigorous.’ Mitigating his fudge, he suggests that the idea that the assumption won’t work out in his favour ‘seems so artificial that we will not dwell on this possibility at all’. This is not an attempt at fraud, or even a glossing-over of inconvenient truths. It is more like a mind-trick, an illusionist using the power of suggestion. If it was Newton’s style that Einstein copied when he fudged the mathematics, here he was borrowing Galileo’s tactic of bullying others into asking no questions.
The final attempt to prove E = mc2 came in 1934, when Einstein presented a ‘repaired’ proof of the equation to a gathering of scientists. A New York Times reporter was in attendance, and made it front page news. The writer gushed about Einstein’s talk: it was like ‘watching a Beethoven making the final draft of his Ninth Symphony’. Four hundred American scientists were given ‘the treat of watching him remodel his universe. A piece of chalk was his only tool.’ But the proof was still wrong – for the same reason that his first proof was wrong. The error had been pointed out years before by no less an authority than Max Planck, the creator of quantum theory, but Einstein had either not noticed or decided to ignore Planck’s advice.
It wasn’t as big a deal as the New York Times made out, anyway. Nobody in the know had been surprised by the equation, even back in 1905: the relation was known to exist for electrical energy, if not light. And by 1934 several mathematicians had already published ironclad proofs that stood in stark contrast to Einstein’s botched