A Revolution with No Revolutionaries The Planck-Einstein Equation for the Energy of a Quantum Graham Farmelo I 'Revolutions are celebrated when they are no longer dangerous.' Pierre Boulez, 13 January 1989, on the bicentennial celebrations of the French Revolution The twentieth century chose some undeserving characters to be its celebri­ ties, but it selected its favourite scientist with excellent taste. Albert Einstein, as brilliant at identifying fruitful scientific problems as he was at solving them, did more than anyone else in the most scientifically productive of cen­ turies to advance human knowledge. What a pity that his most truly revolutionary work is now so widely forgotten. If you were to ask people on the street to name Einstein's most famous contribution to science, they would probably cite his theory of relativity. This was a brilliant piece of work, to be sure, but it was not revolutionary, as Einstein often stressed. He had positioned himself squarely on the shoul­ ders of Newton and Galileo to produce a new theory of space, time and matter that meshed smoothly with their theories. Only once did Einstein depart radically from his predecessors' thinking, when he put forward a remarkable new idea ~bout the energy of light. Common sense tells us that light enters our eyes in a continuous stream. Scientists at the end of the nineteenth century seemed to confirm this 2 It Must be Beautiful A Revolution with No Revolutionaries 3 intuitive belief using their universally agreed wave picture of light, which a punctilious administrator, Einstein took every opportunity to avoid paper­ says that the energy of light is delivered smoothly, like the energy of water work; Planck was a family man, Einstein's home life was dysfunctional. waves sloshing against a harbour wall. But, as Einstein observed, 'common But the two also had much in common. They were both theoretical physi­ sense is that body of prejudice acquired before the age of eighteen'. He pro­ cists, a relatively new breed of scientist with an overwhelming interest in posed in 1905, when he was working as a patent examiner in Bern, that this understanding nature in terms of universal, overarching principles. The two picture of light is wrong and that the energy of light is delivered not contin­ men, both workaholics, heeded new experimental results, but they were uously but in discrete amounts, which he called quanta. Shortly afterwards, happiest when they were working in the laboratories inside their heads. he speculated that the energies of atoms in a solid are also quantized - only Both believed that scientific principles existed independent of human beings certain values of energy are possible. Again, this quantization of energy was and that new principles were out there waiting to be discovered. Like all contrary to common sense. The energy of motion of the apple that fell in good scientists, Planck and Einstein approached their work conservatively. Newton's garden appeared to increase gradually, not in a series of jumps. They were cautious about new experimental results, chary of innovations Einstein saw more clearly than anyone else that the submicroscopic that contradicted well-established theories, and mindful that if a new theory world is replete with quanta: nature is fundamentally granular, not smooth. is to be taken seriously, it must reproduce every success of its predecessors Although he was working alone when he came to these conclusions, he did and ideally make new predictions of its own. not pluck them from out of the blue. He was inspired by papers written by For both men, physics was their first love, music their second. Einstein a physicist twenty-one years his senior, Max Planck, then the dean of was fond of Bach, Mozart and Haydn, and loved to play the violin, which German physicists, working in Berlin. Planck had been the first to introduce he carried everywhere on his travels. Opinions differ on the quality of his the idea of energy quanta in the closing weeks of 1900, although it is not technique: his tone was 'beautifully delicate', according to the great violin clear whether he fully understood the implications of what he had done. teacher Shinichi Suzuki, but another authority said that he 'bowed like a One deceptively simple equation was especially perplexing to the quan­ lumberjack'. Whatever the truth about his musical gifts, Einstein did not tum pioneers. First written down by Planck but properly interpreted only take kindly to criticisms of his playing: 'Einstein got a lot more excited over later by Einstein, the equation relates the energy E of each quantum to its musical disputes than scientific disputes,' one of his acquaintances observed. frequency f: E = hf, where h is a fixed quantity that others later named after Planck was a much finer and more equable musician, a pianist good enough Planck. This was the first important new scientific equation of the century in later life to play duets with the great violinist Joseph Joachim. Planck (Kaiser Wilhelm II had decreed that 1900 was the first year of the twentieth loved the music of Joachim's friend and collaborator Brahms, and was also century, not the last of the nineteenth). High-school students now learn it by · especially fond of Schubert and Bach. rote and few of them puzzle over it, but it took the first quantum physicists When Planck, Einstein and their colleagues were laying the foundations almost twenty-five years to tease out its meaning. During this time, of quantum theory, they were also in the vanguard of the wider movement Einstein's work on the ideas behind theE= hf equation led him to become of modernism, consciously reinventing their subject, exploring the means the first person successfully to predict the existence of a fundamental par­ , and limits of classical techniques. 1 In this sense, they were similar to Igor ticle. In addition, he and others laid the foundations of a fully fledged ''Stravinsky in St Petersburg, Virginia Woolf in London, Pablo Picasso in quantum theory, arguably the century's most revolutionary scientific idea. Paris, Antonio Gaudf in Barcelona. But, unlike the artists, Planck and Albert Einstein and Max Planck dominate the story of this most intel­ Binstein were modernists despite themselves: neither set out to challenge lectually productive of equations. The two men were superficially very the foundations of their subject for its own sake. Whereas the artists were different. Planck was tall, gaunt and bald, whereas Einstein was muscular, free to create new forms to replace ones that seemed to them outdated, the just above average height and blessed with a resplendent mane of hair; scientists had no choice but to create new theories to replace those that had Planck was convivial with his peers, Einstein kept an intellectual distance .., been found irredeemably wanting. It was a tiny but troubling disparity from them; Planck was nationalistic, Einstein avowedly cosmopolitan and · · between experiment and theory that led to the quantum revolution. The liberal; Planck's politics were to the right, Einstein's to the left; Planck was trouble started in a few ovens in Berlin. 4 It Must be Beautiful A Revolution with No Revolutionaries 5 n the visible range, with higher and lower frequencies. Light is simply part of the spectrum of electromagnetic radiation. Berlin has never been a favourite destination for fins gourmets. They will Another of Maxwell's many interests was thermodynamics, the second concede, however, that it is at least now possible to buy a decent espresso great theory of physics to come of age towards the end of the nineteenth there, for example in one of the Einstein® coffee bars springing up all over century. The theory dealt with different forms of energy and the extent to the city. Although these smart establishments were not named after the which they can be converted into one another, for example, from the motion great physicist, the name above their front doors reminds us of the time a of a fly-wheel into heat; it was concerned only with bulk matter and said century ago when Berlin was not only Europe's fastest-growing and most nothing about the behaviour of the individual constituent atoms. The steam opulent city, 2 but the capital of physics. engines that powered the industrialization of western Europe were initially Shortly before the close of the Franco-Prussian War in 1871, Bismarck ·responsible for stimulating theoretical work on thermodynamics. By the made Berlin the capital of the victorious new Reich. The city - a bubbling middle of the nineteenth century, developments in the theory led to cultural stew since the glory days of the polymathic Prussian despot improvements in the technology, which itself led to refinements in the appa­ Frederick the Great a century before- was home to some of the world's ratus designed to test the theory. leading experimenters. Berlin was also the headquarters of an elite group of and electromae:netism. together with Newton's theoretical physicists, members of a new discipline that the more prestigious ··;:"-=on forces, is part of what we no'Y call 'classical Rhvsigs'. Not tliat its inven­ experimenters had begun to employ in the late 1860s to teach the forbid­ tors thought they were working in a classical tradition - they believed they dingly mathematical theories that were becoming increasingly fashionable. were simply doing physics. It was the emergence of the quantum theory of This community was at first ex-clusively male - women were admitted to Planck, Einstein and their colleagues that gave rise to this retrolabelling. universities in Berlin only from the summer of 1908.3 A century later, little Among the leading classical physicists in Germany was Rudolf Clausius, has changed: the overwhelming majority of theoretical physicists continue arguably the first theoretical physicist.