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 ~boutthe 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. 4 This quarrelsome man was the pio­ to be men. neering master of a mathematical approach to thermodynamics that It was as a leading member of Berlin's new scientific community that concentrated on seeking a few grand, overarching principles or axioms. It Planck conceived the concept of the energy quantum and wrote down the was crucial, he argued, that they should be logically consistent and that they E =hf equation. To understand Planck's work, we need to look at the two lead to results that agree with experiment. This top-down approach con­ great theories that seized the imagination of physicists in the latter half of trasted sharply with the traditional piecemeal style of doing mathematical the nineteenth century. The first was a unified mathematical treatment of physics, which involved writing down equations to describe a phenomenon electricity, magnetism and optics, set out in 1864 by James Clerk Maxwell, ·before seeing how well they accounted for experimental results. a Scottish physicist celebrated for his brilliance and versatility. Using a set Others had already established that energy can neither be created nor of equations that now bears his name, he demonstrated that visible light is destroyed- the first law of thermodynamics. But in 1850 Clausius was an electromagnetic wave that travels through an all-pervasive ether, in much ..aunong the first to fashion what became known as the second law, which the same way as a sound wave zips through air. Like any other wave, an ' . says, roughly speaking, that heat does not flow spontaneously from some­ electromagnetic wave has a wavelength and a corresponding frequency. thing cold to something hotter. This is plausible enough: a cold cappuccino You can think of the wavelength as the distance between any two consecu­ never warms up if it's left alone. Both thermodynamic laws appeared to be tive peaks of the wave, and the frequency as the number of times it jiggles absolute - to be universally valid, wherever and whenever they are checked. up and down every second. At the red end of the rainbow spectrum, light Although the two laws are superficially simple, Clausius had to deploy waves have a wavelength of seven ten-thousandths of a millimetre and an enormous amount of intellectual artillery to state them rigorously. His move up and down 430 trillion times a second, while at the violet end its mathematical and linguistic precision, together with the diamond-hard clar­ wavelength is rather shorter and its frequency is rather higher. Maxwell's ity of his reasoning, fascinated Max Planck when he was an impressionable theory correctly explained why there exist electromagnetic waves outside graduate student.5 Born in 1858 into a patriotic and affluent family of 6 It Must be Beautiful A Revolution with No Revolutionaries 7

scholars, lawyers and public servants, he was deeply imbued with conser­ Experimenters observe this cavity radiation by making a small hole in the vative values. Some of his early memories of political unrest were to stay side of the cavity, enabling a small amount of the radiation to escape. Some with him for his entire life, not least his witnessing as an eight-year-old the radiation from the surroundings enters the cavity, but it is soon absorbed, re­ sight of victorious Prussian and Austrian troops marching into his native emitted and reflected around the cavity so that it takes on the same town of Kiel after their defeat of Denmark. A diligent undergraduate, if not characteristics as the other radiation in the cavity. Because all of the radia­ an especially brilliant one, Planck had enjoyed a broad education in math­ tion from outside that passes through the hole is 'absorbed', the hole looks ematics, physics, philosophy and history. He also studied music, his black when it is viewed at room temperature, and the emerging radiation - principal hobby, and distinguished himself by composing a tuneful operetta a sample of the cavity radiation - is often called black-body radiation.6

performed at musical evenings in the homes of his professors. .· The question that fascinated physicists was: at any given temperature of the Unsure of which subject to pursue, he chose physics, no thanks to his cavity, what is the intensity of its radiation at each colour or, more rigor­ professor at the University of Munich, Philip von Jolly. In what ranks ously, at each wavelength? It was by answering this question that Planck among the most egregious howlers in the history of career counselling, von was led to the equation E =hf Jolly advised the twenty-year-old Planck against entering physics because One of Planck's research advisers had already proved that whatever the after the discovery of the two laws of thermodynamics, all that was left for law for the radiation's intensity turned out to be, it would depend on nei­ theoretical physicists to do was to tidy up the loose ends. With his trademark ther the size of the cavity nor its shape, nor on the material from which its conservatism, Planck touchingly replied that he wished only to deepen the walls were made. Such a law would be a classic example of what Planck foundations laid by his predecessors and that he had no wish to make any , called an 'absolute', something that 'will necessarily retain its impor­ new discoveries. As we shall see, the first wish was to be granted at the tance for all times and cultures, even for non-terrestrial and non-human expense of the second. ones'. Cavity radiation was not just of academic interest: it was important Planck fell in love with thermodynamics when he was working on his for Germany's lighting industry, one of the many flourishing branches of doctoral thesis and he became intrigued with the power and generality of its _the country's economy at a time when electrical and chemical technolo­ laws. He was, however, deeply uncomfortable about two aspects of the gies were revolutionizing capitalism. Always looking for sources of thermodynamic being championed by the leading Austrian theoretical ·illumination that gave out as much visible light and as little heat as pos­ physicist, the passionate and depressive Ludwig Boltzmann. First, Planck sible, engineers who were trying to design increasingly efficient electric was not convinced that matter was ultimately made of atoms: no one had lamps needed to know how much radiation their filaments emitted. The actually observed one, so perhaps they were nothing more than a convenient inore they knew about cavity radiation, the better equipped they would be fiction? He was also sceptical of Boltzmann's argument that the second law to produce better lamps of the kind invented in 1897 by the American of thermodynamics was true only statistically: that heat is overwhelmingly Thomas Edison. · likely - but not certain - to flow spontaneously from something hot to This was one of the problems under investigation at the lavishly equipped something colder. This lack of certainty was inimical to Planck's passion for · Physikalisch-Technische Reichsanstalt (the Imperial Institute of Physics absolutes, for incontestability, for certainty. Technology) in Charlottenburg, just outside Berlin, three miles from the One absolute did catch his eye. It concerned a problem so subtle that few ··university where Planck had been working since 1889. Funded jointly by scientists outside Berlin were concerned with it - and anyone outside sci­ German government and the industrialist Werner von Siemens, the ence could reasonably have dismissed it as laughably obscure. Imagine a Reichsanstalt was founded in the aftermath of the Franco-Prussian War completely sealed cavity, like an electric oven but with neither vents nor 1) to refine the art of making precise measurements and to set stan­ windows. Now suppose that the cavity is at a steady, uniform temperature. with which scientists and engineers could work. Mindful of the The walls of the cavity give out electromagnetic radiation, which bounces ·,potential economic benefits for the new Reich, the Reichsansta1t's founders

around inside the cavity, continually being reflected from the walls or being · set out to provide nonpareil research facilities that would be of practi~al absorbed and then re-emitted. benefit to German industry.7 Even its classically designed vP.llow-bnck. 8 It Must be Beautiful A Revolution with No Revolutionaries 9

buildings, located in almost nine acres of immaculate parkland, spoke of the intensity of cavityradiation institution's imperial ambitions. 1919'C German physicists had been working on cavity radiation for thirty years. 150 Their understanding could be handily summarized by simple mathematical laws that predicted the intensity of the radiation for every wavelength. 125 While two teams of Reichsanstalt experimenters were working on the prob­ lem, Planck was trying to understand the most successful of the radiation 100 laws, written down in March 1896 by his close friend Wilhelm 'Willy' Wien, one of the finest physicists at the Reichsanstalt. Wien was a charac­ 75 ter: the country-loving son of an East Prussian land owner, he had hoped to divide his time between physics and farming until a disastrous harvest 50 forced his father to sell the farm and made it necessary for the young Wien 25 to take up science as a full-time career. He was also a chauvinist and an anti­ Semitic reactionary. A few days after the end of World War I he led a group of volunteers, mainly war veterans, to shoot at communists and other left­ wavelength/micrometres ists in the streets ofWiirzburg and Munich, to prevent what he described as 'the Bolshevization of Germany'. Figure 1.1 The circular points on this graph were the seeds of quantum theory. Wien's cavity-radiation law successfully accounted for the intensity of the The solid curved lines show the prediction of the Wien law for cavity radiation at radiation at each colour, for a wide range of temperatures. Planck wanted to three temperatures; note that the earliest data (plotted as triangular points) were in understand his colleague's law using thermodynamics and electromagnet­ essentially perfect agreement with this law. Disturbed by the systematic disagreement between Wien's predictions and the new data, plotted here as ism, and he began with high hopes that he could understand cavity radiation circular points, Planck was led to propose a new law that fitted all the without having to assume the existence of atoms or by having to use a ver­ . experimental data. His attempts to understand the fundamental origin of his new sion of the second law of thermodynamics that involved probabilities rather law led him to the idea of energy quanta. than certainties. By the early summer of 1899, however, he had given up both of these preconceptions. He reluctantly concluded that he could under­ · data: Planck dashed off a postcard to Rubens telling him of his new cavity­ stand cavity radiation only if he accepted that atoms exist and if he embraced tadiation law and, twelve days later, presented the law for the first time in Boltzmann's statistical way of thinking. As he was correcting the proof of a ;public to a formal meeting of his Berlin colleagues, including Rubens. paper setting out the theory, the experimenters - 'the shock troops of sci­ ·Afterwards, Rubens returned to his laboratory and was able the next mom­ ence', as he called them- brought him some disturbing news: Wien's law . ing to give Planck a pleasant start to his weekend by confirming that his new appeared suddenly to be in trouble. It consistently underestimated the inten­ law had successfully accounted for his new data. To this day, no one has sity of cavity radiation, especially at long wavelengths, which new ·~meup with a law that better predicts the intensity of cavity radiation. equipment had only just enabled them to investigate (Figure 1.1). · On the very day that Planck first wrote down his cavity-radiation law, he On Sunday 7 October 1900 the Reichsanstalt experimenter Heinrich to try to understand it in terms of what was actually going on inside Rubens and his wife visited Planck and his family at their handsome oak­ ovens, initially using the laws of classical physics.8 He soon found that panelled villa in the GrUnewald, the smart Berlin suburb favoured by the had no choice but to use Boltzmann's statistical reasoning, which he had professoriate. The two physicists talked shop, and soon after the Rubenses i

~ A Revolution with No Revolutionaries 11 10 It Must be Beautiful this case Boltzmann's way of treating the energies of the atoms didn't work, But all scholars agree that Planck did correctly seize on the importance 11 so Planck had no choice but to abandon some of the assumptions of of his new constant h. He worked for several years to try to understand the classical physics that he had thought were the bedrock of his subject and do constant in terms of classical physics and he later wrote that many of his something that was desperately uncongenial to him- extemporize. It was as eolleagues mistakenly regarded his failure as a tragedy. He eventually came if Artur Rubinstein suddenly had to riff like Earl Hines. accept that he had discovered the latest of only a handful of truly funda­ During some eight weeks of the most strenuous work of his life, he constants- including the speed of light and the constant in Newton's found that he could derive his law only if he drastically modified of gravitation - which figure in the equations of physics, with values Boltzmann's statistical techniques and if he took one particularly strange cannot be derived. Such a discovery is extremely rare in the history of step. He had to divide the total energy of all the atoms vibrating in the •$Clence: since Planck saw the need for h, not a single new fundamental con­ oven's walls at each frequency into discrete amounts, each with an energy has been identified. given by the equation E = hf Here was the first appearance of the energy Planck's theory also featured a second constant k that related to quantum, the first suggestion that energy at the molecular level is funda­ '•Boltzmann's statistical theory, so Planck named it after him, with a gen- mentally different from energy on the everyday scale. erosity that he was to regret, as Boltzmann neither introduced it nor thought The notion of energy quanta flew in the face of what was at the time investigating its value. By comparing the predictions of his mathematical every scientist's understanding of energy. Energy was, like water, supposed with the Reichsanstalt cavity-radiation data, Planck found the value of to be available in any quantity - you can take water from the sea, or put it of the two constants. The measurement of the Boltzmann constant was back, in any amount you like. The idea that water could come only in defi­ tspecially pleasing for Planck, as it enabled him to make what was then the 12 nite quantal amounts, say cupfuls, contradicts everyday experience, yet this . accurate measurement of the mass of an atom. The value of the con­ is how energy apparently behaves at the molecular level. Could it be that, also subsequently enabled scientists to calculate the average energy of an 13 just as water ultimately comes in units of water molecules, energy funda­ in any substance anywhere in the universe, whatever its temperature. As strange as it might now seem, Planck was less excited by his quantum mentally comes in discrete quanta, in lumps? Planck first publicly presented his E =hf equation in a lecture. On Friday 14 and his E = hf equation than by the possibility the theory raised of December, shortly after five o'clock in the afternoon, he stood up to read a length, time and mass in terms of a new set of units that would short paper about his derivation of his cavity law to Berlin physicists at one of to use anywhere in the universe. Tradition and convenience leads the fortnightly meetings of the German Physical Society. It was with no fanfare on earth to measure length in metres or feet, to measure time in sec- or excitement that Planck first mentioned the E =hf equation during this talk. and mass in kilograms or pounds, but there is no fundamental reason His colleagues were, it appears, respectfully interested but underwhelmed. these units are better than any others. If history had turned out differ­ According to the conventional view, this presentation was Planck's unveil­ we lliight now be measuring length in units of the extent of Julius ing of the quantum idea to the world.9 Many quantum historians have been little finger, and measuring mass and time in terms of the weight of persuaded, however, that this account is simplistic, following the writings of and the time it took his heart to beat. the late philosopher and historian of science Thomas Kuhn. Planck wrote that quickly realized that the new constant h enabled him to set up he considered energy quantization 'a purely formal assumption, and I did not that are not at all arbitrary but emerge from the laws of nature. He saw give it much thought except for this: that I had to obtain a positive result, could calculate unique values of length, mass and time using special under any circumstances and at whatever cost'. Statements like this convinced lbinations ofthe new universal constant with two others, the speed of 14 Kuhn that in 1900 Planck did not appreciate the significance of energy quanta and Newton's gravitational constant. Planck reasoned that if these and that he did not believe that energies are quantized. Rather, Kuhn argued, constants have always been the same everywhere, then his calculated Planck believed along with everyone else that the atoms could have any energy of mass, length and time gave units that.are also valid everywhere in they liked, and that he was dividing these energies into quanta simply as a vP.rse and are therefore more natural than any set up by any earthly 10 mathematical device to make his calculations work out satisfactorily. no matter how august. Planck found that the unique value for 12 It Must be Beautiful A Revolution with No Revolutionaries 13 mass that emerged is about the mass of a giant amoeba (10--8 kilogrammes), Hans had been born, they had moved to a two-room apartment and for length it's about a trillionth of a trillionth of the width of an atom Einstein's job had been made permanent. Somehow, in the interstices of his oo-35 metres) and for time it's about 1(}43 second, about a millionth of a life at home and at the office, he was developing his ideas about light, trillionth of a trillionth of a trillionth of the time it takes you to blink. None relativity and also the molecular structure of matter, which he chose as the of these is convenient to use in everyday life, of course, but Planck saw that subject of his PhD thesis. In what we now realize was one of the most the essential new point was that it was not only some laws that had absolute, spectacular flowerings of talent in the history of science, all three of universal validity - a unique set of units did, too. ·Einstein's lines of research bore fruit in 1905.16 The first paper he published Most of Planck's colleagues regarded his cavity-radiation law as little that year, today recognized as his first great contribution to science, was more than a mathematical formula that happened to fit the data. Not one of about light quanta, an idea he described in a letter to a friend as 'very the Berlin physics Brahmins saw clearly the implications of Planck's work revolutionary'. and, in particular, of his new equation E =hf That was left to a young grad­ The paper was a gem. Although its language is temperate to the point of uate student, working mainly on his own, in Switzerland. understatement, its reasoning has the audacity of which only the most bril­ liant and unfettered young minds are capable. Einstein came straight to the point by gently asserting that, contrary to Maxwell's wave theory of light, m 'the energy of [a light ray emitted from a point source] is not distributed continuously over ever-increasing volumes of space but consists of a finite The poet Paul Valery made a point of keeping a notebook in his pocket to jot number of energy quanta localized at points of space that move without down his ideas. When he asked Einstein if he did the same, Einstein replied, dividing, and can be absorbed or generated only as complete units.' To fol­ 'Oh, that's not necessary,' before adding wistfully, 'It's so seldom I have lowers of Maxwell- and that included every leading physicist at the time - one.' He made that comment in the 1920s, when the most creative part of his this was abject heresy. career was drawing to a close. When it was beginning, twenty years before, Einstein then moved on to give Planck what amounted to a physics one wonders how much stationery he consumed. lesson, by demonstrating that the reasoning Planck had used to study his In the autumn of 1900, when Planck first wrote down his E = hf equation, cavity radiation was fatally flawed. Using simple mathematics, Einstein Einstein was in Zurich, eking out a living by giving private tutorials. 15 showed that the total energy of radiation in a cavity was infinite according Several years before, he had read about the problem of understanding cavity to classical physics. Had Planck realized this, he probably would have dis­ radiation and by the spring of 1901 he was familiar with Planck's work. carded his theory and not made his great discovery of energy quanta, as Einstein's reaction to it shows that he was already a special talent. No one Einstein later pointed out. Wary of Planck's formula for the intensity of else saw beyond the virtuosity of Planck's mathematical analysis and the cavity radiation, Einstein instead used Wien's earlier formula, which gave superficial success of his formula in explaining the Reichsanstalt data, but an excellent account of cavity radiation with short wavelengths or, equiva­ Einstein swiftly realized that revolution was afoot. He later wrote that, soon lently, high frequencies. Einstein noticed that the equation for the density of after the appearance of Planck's work, 'It was as if the ground had been this radiation is exactly the same as the corresponding equation for a gas of pulled out from under one, with no firm foundation anywhere, upon which quanta, when they are all bouncing around independent of one another. one could have built.' So- and here is his especially audacious step- Einstein suggested that the Einstein thought about the implications of Planck's work for almost four radiation described by Wien's law behaves as if it is a gas, whether or not it years before he published his revolutionary ideas about light - or, more gen­ is inside a cavity. The comparison also gave him a simple equation for the erally, radiation - and what happens when it interacts with matter. The energy of each 'quantum' in the gas of radiation: it was E = hf, where h is confident and cheerful young physicist had secured a well-paid job as a Planck's constant andfis the frequency of the radiation. patent examiner 'Expert Class ill' at the Swiss patent office in Bern and had Although Einstein's formula looks identical to Planck's, they say quite married a former student colleague. By the early autumn of 1904, their son different things: Einstein's applied to the energy of every light quantum, 14 It Must be Beautiful A Revolution with No Revolutionaries 15

whereas Planck's was about the special case of the energy of the atoms in a of peaks and troughs in brightness, and it is easy to explain this pat­ cavity when they interact with light. But Einstein had something else to say radiation is a wave. Otherwise, it is impossible. about this interaction: he proposed that matter absorbs or gives out radiation ;;,Einstein was well aware of this and he understood the force of the argu­ not in a continuous stream - as classical theory implied - but 'as if' but he was not going to be intimidated by inconvenient experimental (Einstein's words) the radiation consisted of quanta. So matter could absorb He completed his paper in mid-March and sent it to the world's lead- or give out one, thirty-seven or any other whole number of radiation quanta, · journal of physics research, Annalen der Physik, edited by Planck and but not two and a half or any other fractional number. Planck was a particularly effective editor: he rejected second-rate If radiation is delivered in quanta, why aren't we conscious of individual !)ftlissions but was happy to publish papers that were either orthodox or packets of energy entering our eyes? Although Einstein didn't address this provided they were well argued and logically consistent. question explicitly, he well knew the answer - each quantum has such a revolutionary paper was duly published a few months later. minuscule energy that the number of quanta entering our eyes is normally majority will always reject a truly revolutionary idea, because it is so vast that our brains cannot differentiate between their separate arrivals, so ifromprehensible in terms of the ideas it seeks to displace. So it was with they appear to arrive in a continuous stream. Each quantum of visible light paper, whose publication was totally ignored by the world's pro­ has only about a trillionth of the energy of the beat of a fly's wing and, as a physicists - all thousand or so of them - and by all other scientists result, an ordinary candle gives out about a billion trillion quanta every can hardly blame them: his ideas made no sense at all in terms of \} second - far too many for our eyes to be able to distinguish between them. which had passed every experimental test jt had ~enput Einstein concluded his paper by pointing out how his light-quantum u ...... -..-~ L •. ~- IE_ --n- ...~- T' Lr £ .._1_- of the idea could be tested experimentally. His most striking suggestion con­ a quantum

cerned another superficially obscure problem: of understanding what radiation's frequency, a concept that madesense ~~lyif the radiation happens when radiation is shone on a metal, the so-called photoelectric a wave. And who was this Albert Einstein, anyway? effect. The metal reflects and absorbs the radiation, but Einstein knew that Einstein was not downhearted. By January 1906 the papers he had writ­ experimenters had found that radiation could eject some of the electrons previous year had been published without quibble from Planck or in the metal. If the quantum picture of radiation is correct, Einstein and he had become 'Herr Doktor Einstein'. Although he was happy argued, then it is reasonable to suppose that each ejected electron is dis­ his eight-hour day at the patent office, he was getting itchy feet placed by a single radiation quantum with energy E =hf What is more, if seriously considered taking up a full-time career in school teaching.

the quantum surrenders all this energy to the electron, then the energy of - ... ~,.:le,he was thinking about the the emergent electron is simply equal to the energy of the radiation, quan­ and J>l,nr-lr'~<>w~;:t;'l tum, less the energy needed to fish out the electron from the metal. Einstein expressed this idea mathematically in what became known as his photoelectric law. Einstein called his view of light 'heuristic' - something put forward as an aid to learning - so he appeared to be hedging his bets about whether light quanta are real. It is easy to see why he did this - he was arguing that, in this case, the hallowed Maxwell theory of radiation was wrong and that radia­ tion behaved as quanta, not as waves. Yet if there was one thing that by the frequency. So the smallest energy the vibrating atom can physicists thought they knew about radiation, it was that it did behave as is E =hf, and it could also have the energy values 2hf, 3hf, 4hf etc. waves. And they had incontrovertible proof: .if an experimenter shines a was saying that the equation E = hf applies to every atom in a beam of light on a sufficiently narrow slit, the light is diffracted, or - to use it was not a mathematical subdivision of the total energy of all the a less formal term - spread out. Diffracted light often has a characteristic , as Planck had proposed. A Revolution with No Revolutionaries 17 16 It Must be Beautiful

In November 1906 Einstein showed how to· test this idea by considering Einstein's audience must have been as nonplussed as Schoenberg's were how solids absorb heat, something that classical physics was at a loss to at the premiere of his second quartet nine months before in nearby Vienna. explain. He pictured an idealized crystalline solid, its regularly spaced atoms ·.:planck, speaking for almost all his colleagues, noted respectfully that it was early to give up Maxwell's equations and he was reluctant 'to assume jiggling about with the same frequency, independently of each other in a light waves themselves to be atomistically constituted'. Planck had, three-dimensional array. Einstein knew that this picture was not completely softened his opposition to the quantum idea and had come to realistic because the atoms don't move independently, but he hoped that it was that when ·· ·· ··• ·· a simplification he could get away with. By also assuming that each atom's vibrational energy is quantized, he predicted that the average energy of the atoms in a solid falls slowly with temperature, until it is zero. His predictions agreed well with previously puzzling measurements taken twenty-five years 1909 Einstein handed in his notice at the patent office in order to before. This successful comparison, the first of only three instances in which Einstein published a graph to compare his theoretical predictions with exper­ up his first academic post as an extraordinary associate professor of iment, immediately gave credence to the emerging quantum theory. Because 1e0retical physics at Zurich University. He spent most of his time thinking radiation was not involved, physicists could be impressed without having to his favourite problem- understanding light quanta. He tried many dif­ wring their hands over the troubling contradictions with Maxwell's theory. approaches and even tried tinkering with Maxwell's equations, but to Mainly as a result of his relativity theory, Einstein's reputation had avail. The language he used to describe radiation quanta was invariably spread rapidly among physicists, many of them amazed to discover that the reumspect and he never went the whole hog and stated unequivocally author of this great theory was working eight hours a day in a patent office. the quanta exist; rather he talked of radiation behaving 'as if' its energy The first to recognize Einstein's talent was one of the theoreticians he most quantized. No wonder many of his colleagues thought his commit­ admired, Max Planck. The men first met in September 1909 at a conference to the quanta was half-hearted. in Salzburg, where Planck invited Einstein to take a few days off work at the those who had been struck by Einstein's ambivalence towards office to give what was to be his inaugural lecture to the luminaries of theo­ quanta was the American Robert Millikan, an enormously energetic retical physics. To their surprise, Einstein chose to speak not on his erimenter with a penchant for tackling the most pressing questions of the acclaimed and profoundly fashionable relativity theory, but on 'The nature 1912, during a six-month sabbatical from the University of Chicago, Berlin colleagues and spent a good deal of time with Planck, who and constitution of radiation'. His talk was a tour de force. In keeping with the tradition of Clausius, he his interest in measurements of fundamental constants. The two also concerned himself neither with experimental odds and ends nor with math­ radiation quanta and Planck made clear how vehemently he dis­ ematical detail, but with issues of high principle. His audience must have with Einstein's ideas. Like many visitors, Millikan was invited to the been startled to hear this new member of their fraternity: he did not give the ' home for one of their musical soirees. Planck accompanied a diffident presentation of the tyro, rather he took up the cudgels and set out of German lieder by his wife, and he improvised skilfully on the a new research manifesto on the nature of light. He took forward his already Millikan recalled forty years later. controversial ideas about radiation quanta when he argued that, like an was quick to see how important it was to do experiments that electron, every quantum travels in a specific direction - in technical lan­ shed light on how radiation ejects electrons from matter, the photo­ guage, it has momentum. For the first time. Einstein suggested publicly that effect. Although he didn't for a moment believe that Einstein's radiation consists of particles. He also pointed out that because relativity of the effect was correct, he appreciated that it made eminently r --.. theory had rendered the ether superfluous, it was no longer necessary to predictions that contrasted sharply with ones made by the compet­ think of radiation as existing in anything, but 'as something existing inde­ u.u;;uries. Here was an opportunity, if he could overcome the difficulties pendently, just like matter'. So important was the problem of understanding the experiments, to shed light on what leading physicists regarded most pressing problem of the day - understanding radiation. As soon radiation, in Einstein's view, that 'everyone should work on it'. 18 Must be Beautiful It A Revolution with No Revolutionaries 19

as he returned to Chicago, Millikan began his photoelectric experiments, a professional cellist, Einstein a little ragged in the soaring violin part, which were to take him three years to complete. maestro Planck revelling in the operatic second movement. The two great Meanwhile, Einstein's light quanta had attracted little interest and few · physicists enjoyed making music together; for the next eighteen years, advocates. In June 1913 Planck confidentially put his reservations in writ­ While they were fatally undermining the foundations of classical physics by ing when he and three of his Berlin colleagues proposed Einstein for the ·day, they liked nothing more than to explore the classical chamber canon by prestigious membership of the Prussian Academy of Sciences. In what was night. Not for them the musical revisionism and dissonance.of Berg's otherwise a cloying tribute to Einstein's achievements, Planck apologized ~eck,Stravinsky's Oedipus Rex and Strauss's Elektra. for his younger colleague's having 'gone overboard in his speculations' spring of 1915, Millikan had completed his photoelectric exper­ with this work, and he asked that this 'should not be held against him too lliad been amazed to find that Einstein's photoelectric law was much, for without occasional venture or risk no genuine innovation can be But that did not necessarily imply that his quantum picture of radi­ accomplished even in the most exact sciences'. Nor was Einstein wholly was right, Millikan pointed out.18 In the very first sentence of the complimentary about Planck, whom he described as 'stubbornly attached to in which he published his results, he wrote that Einstein's law 'cannot preconceived opinions that are undoubtedly false'. judgement be looked upon at present as resting upon any sort of sat­ Both of them, however, were intrigued by news from Copenhagen that llfactory theoretical foundation'. Millikan's results nonetheless gave -nenmark s bngtltest young physicist had successfully applied quantum ideas ;;-tional credence to the E =hf equation, as Einstein had used it when he to the structure of atoms. Niels Bohr, then a man of blazing ambition, had down his photoelectric law. elaborated on a popular picture of the atom as a tiny nucleus surrounded by The congenitally sceptical scientific community was not going to be orbiting electrons. In a trio of papers published in 1913, Bohr decreed that ~ed by a single piece of experimental evidence in favour of an equa­ the electrons in every atom could have only certain allowed orbits, that appeared flagrantly at odds with dozens of other experiments. 17 corresponding to the atom's characteristic energy values. Although it made physicists disputed Millikan's results and several groups spent years no sense in terms of classical physics, the theory explained at a stroke why and extending his results, although none of them found any seri- every atom gives out and absorbs light of certain characteristic wavelengths - 11$;4isagreement with Einstein's predictions. But that certainly did not they corresponded to quantum jumps between the atom's energy values. that radiation consisted of particles: the photoelectric-effect theory Better still, the theory made predictions that agreed with experiment: Bohr's the radiation's energy- it assumed nothing about the directions picture of the atom accounted wonderfully well for the wavelengths of the the quanta were travelling. To prove the particle model of radia­

light given out and absorbed by the lightest atom of all, the hydrogen atom. ~experimenterswould need to demonstrate that each radiation quantum This success quickly persuaded quantum theorists to focus their efforts on through space in a specific direction. Millikan's results, together with understanding atoms. Einstein thought carefully about this problem and ..-easing confidence in the underlying theory, convinced Einstein by later showed how ~ohr'smodel of the atom explained Planck's cavity­ particles of radiation really did exist. 'I do not doubt any more the radiation law, using a picture in which the radiation quanta, eacn with the of radiation quanta,' he wrote to a friend a few months later, energy E =h were given out and absorbed b toms in the cavity. I stand quite alone in this conviction', forgivably forgetting the Four months before the outbreak of World War I, Planck wooed instein of lesser scientists who were broadly in agreement with him. to Berlin from Prague, where he had been working for a year. Planck was stood when Einstein became a front-rank international rejoicing in the orgy of patriotism that preceded the war and later publicly in early November 1919, when British astronomers announced supported the German cause, while the pacifist Einstein deplored the con­ results appeared to confirm the superiority of Einstein's theory of flict, which he regarded as an international eruption of insanity. The two over Newton's. Exhausted and demoralized by the war, the world men put aside their political differences, however, and they became close. for the consolations of hero-worship. Within a few weeks of Einstein's arrival, Planck invited him to one of his once remarked that although his friends often flattered his talent, he musical evenings, where they played Beethoven's D major piano trio with knew that his younger colleague Mozart was far above him. Planck A Revolution with No Revolutionaries 21 20 It Must be Beautiful tbe cautious and the disbelieving. Two years of checking followed, but by believed the same thing about his relationship with Einstein whom he called the end of 1924 the consensus was that Compton's results were correct 'the new Copernicus'. Planck was therefore among those least surprised when and that he was right to say that his discovery entailed 'a revolutionary Einstein became that great rarity - a celebrity scientist. His work on relativ­ onange in our ideas regarding the process of scattering of electromagnetic ity - never his work on quanta - became the butt of jokes in nightclubs all waves'. The hegemony of Maxwell's wave picture of light was over. over Europe and, no doubt, a theme of modish chatter at Jay Gatsby's parties. ",unaware of Einstein's earlier thinking about the particle nature of radia­ Many people thought that Einstein was preoccupied by this work but the Compton did not mention Einstein when he wrote up his discovery truth is otherwise: he later wrote, 'I have thought a hundred times as much publication. But Einstein was pleased, as well he might have been- he about quantum theory as I have about general relativity theory.' become the first person successfully to predict the existence of a fun­ 'Einstein fever' gripped New York in April 1920, when the newly famous ~ntal particle. scientist sailed into the city to be greeted by thousands of cheering admir­ ~\:,ffulsteinons would have been a plausible name for the new particles but, ers lining the streets. Over in St Louis, the arguments over his particle :mercifully, no one suggested it. But in 1926 the American chemist Gilbert description of light were about to be settled in a series of experiments by 19 came up with an appellation that immediately proved popular. He Arthur Compton, one of the most talented young physicists in America. 1t m a now discredited paper in which he introduced the idea that Compton was thinking about the scattering of radiation waves by electrons, ;t'ildiation comes in atoms. He called these 'atoms' by a name now univer­ and he pictured it much like water waves bouncing off buoys in a harbour. used as a synonym for particles of radiation - photons. If this picture were correct, the wave's frequency would be the same after the scattering as it was before. Yet Compton found that the two frequencies were different: the radiation before the "Scattering had a higher frequency -- IV than it had afterwards. It was as if the mere act of scattering had turned blue light into red. After years of trying, Compton had not been able to explain [eanWhile, a few scientists outside the Planck-Einstein circle had used the this strange discovery, either by revising widely held assumptions about the equation to open another rich seam of the submicroscopic world. size and shape of the electron or by adapting the quantum picture of radia­ the cream of the world's physicists had been trying to understand tion. Then, in November 1922, the fog lifted. "._or whether - the equation applied to radiation, an obscure physicist The key to the problem, Compton realized, is that radiation quanta each in France made the astonishing suggestion in 1923 that it described have momentum, though he was unaware that Einstein had proposed this radiation but matter as well. It was this crucial insight that led several years before. So the radiation as well as the electron could be pic­ to modem quantum mechanics. 20 tured as particles and their collision was like a microscopic version of little-known physicist was Louis de Broglie, a thirty-year-old grad­ billiards. No slouch as a theorist, Compton quickly worked out the conse­ who had begun his scientific career in earnest only two years quences of this and found that his new theory accounted beautifully for the after he had been demobilized from military service in World War I. results of his experiments. The explanation hinged on the E = hf equation: · a taciturn and reflective man, was no ordinary scholar. He was the energy of the scattered X-ray photon is lower than the energy of the fide prince and a member of one of France's most illustrious fami­ original photon because some of the energy of the original photon is trans­ left-leaning great-great-grandfather Charles welcomed the French ferred to the electron. So it follows that the frequency of the scattered but was nevertheless condemned to the guillotine a month radiation should also be lower. Compton promptly announced his results the fall ofRobespierre).jJe Broglie graduated in history and law at three weeks before Christmas at a physicists' meeting in freezing Chicago. orbonne in 1913, but decided to take up a career in physics, thanks to The sensational news that radiation quanta really do behave as particles - of his brother Due Maurice de Broglie, a distinguished each with both energy and momentum - spread like a tsunami across the rimenter who was wealthy enough to fund a laboratory in his own usually calm waters of the international physics community. Louis's plans were interrupted after only a few months, when he was Like every truly remarkable observation, Compton's was doubted by 22 It Must be Beautiful A Revolution with No Revolutionaries 23

called up for military service. He later spent most of the war working fiisasser, a young physicist at Gottingen University in Germany, pointed out without special distinction as a radio engineer at the Eiffel Tower, after it lbat if de Broglie was right, a simple crystal should diffract a beam of had begun to be used as a post for wireless telegraphy. , ~Jeetronsshone on it. Elsasser calculated that if the electrons are accelerated De Broglie began his doctorate on quantum theory by working in his . 150 volts, they should have a wavelength of a tenth of a billionth of a brother's private laboratory in his multi-storey town house, two minutes' just less than the spacing of atoms in a typical metal. These are just walk from the Arc de Triomphe and a stone's throw from the Champs­ right conditions for diffraction, so if de Broglie was right, experimenters Elysees. While Compton was puzzling over his data in St Louis, Maurice de be able to detect peaks and troughs in the number of electrons that Broglie was inducting his brother into the latest experimental techniques . out from a crystal at different angles. Like water and light waves, and drawing his attention to the need for both wave and particle models of should also be diffracted. radiation. Louis later wrote that 'long conversations with my brother about man, you are sitting on a gold mine,' Einstein told Elsasser. the properties of X-rays ... led me to profound meditations on the need of the student was to be no more than a catalytic bystander when two always associating the aspects of waves with that of particles.' It was this perimenters brought his idea to fruition. In August 1926 they had the line of thought that led him to ask a profound question whose answer was fortune to attend a meeting in Oxford, where the theoretical ideas of to change the course of science: if electromagnetic waves can behave li).ce Broglie and Elsasser were in the air. The meeting was the annual con­ particles, can particles such as electrons behave like waves? of the British Association for the Advancement of Science, where Einstein had touched upon this theme a year or so before, but Louis de lllticmtistsmingle with each other and the public. Although the two experi­ Broglie's insight was deeper and more vivid. De Broglie later recalled did not meet at the conference, they both left thinking about how having a Eureka moment, much rarer in scientific reality than in folklore: might confirm de Broglie's ideas. Soon afterwards, they had closed the 'After long reflection in solitude and meditation, I sudsienly bad the idea, chapter of the E =hf story. duringJAugust] 1923, that the discovery made bYEinstein in 1905 should first of the experimenters was Clinton Davisson, a slight and rather be generalized to all material particles, notably to electrons.' De Broglie had man who had slowly built his reputation as an electron-scattering hit on the idea that the equation E =hfapplied to matter as well as to radi­ through work he had carried out at the Bell Telephone Laboratories ation. When Einstein used the equation to describe radiation, he had to Street in south Manhattan, a few blocks from the meat markets. 22 explain how the energy of a quantum could be linked to a property of a five years he had been pursuing a programme of routine but increasingly wave, its frequency. De Broglie had the opposite problem: everyone was omplished experiments to find out what happens when a beam of dec­ familiar with electrons and the idea of other particles of matter, but what on strikes a metal target. To smash things together like this may seem a earth was the wave associated with it? According to de Broglie, every par­ way of doing science, but experiments like these have proved espe­ ticle has some sort of associated matter wave. Using an analogy to the fruitful- witness the success of the post-World War IT atom-smashers. familiar formula E =hf, he wrote down a simple formula for the wavelength results were nothing special until April1925, when a liquid-air of the wave associated with a free particle, one with no net force acting on in his laboratory exploded, one of the most fortunate laboratory acci­ it.21 As the particle's momentum increases, its wavelength shortens, de in the history of science. Before the incident, Davisson's nickel target Broglie argued, and the size of the wavelength depended on the value of of a random patchwork of tiny crystals, but after he had treated it Planck's constant h. right the effects of the explosion, he inadvertently changed the nickel 'It looks crazy, but it's a completely sound idea,' Einstein told a colleague into virtually a single crystal. As soon as he used this new sample to j in December after he had read de Broglie's PhD thesis. It was all very well his electron beam, his results changed completely, but electron dif­ to have the master's imprimatur, but what did nature think of it? De Broglie was still not in evidence. had quickly seen that if matter has wave properties, then a beam of electrons Davisson had taken his results to the Oxford conference and had sailed should be spread out - diffracted - like a beam of light. It was, however, a with an inkling that quantum theory might explain his data. On student who saw most clearly how the theory could be checked. Walter eturnin_g to New York, he used de Broglie's theory to predict the location A RevoluUon wl~::~R~volutlonar;e, - ~--:,~ It Must be Beautiful 24 v of the diffraction peaks, but they were nowhere to be found. Undeterred, he and a colleague set out a detailed research programme designed to check are scientific revolutions, but there are no revolutionaries,' suggests once and for all whether electrons really were diffracted. His reward duly science historian Simon Schaffer. For him, it is undeniable that there are arrived in early January 1927, when he detected several pikestaff-plain asionally major shifts in the way scientists think about nature and study diffraction peaks. A few simple calculations demonstrated that they but he does not believe in the usual picture of the scientific innovator as occurred precisely where de Broglie's formula predicted, inspired by an hero who changes the way science is done after a flash of inspiration. analogy with the E = hf equation. Here was proof of something that barely one spearheads a scientific revolution on their own. Not Planck, not five years before no one had even contemplated - that particles of matter Einstein.' could be diffracted. Does the story of the energy quantum bear out Schaffer's view? There is Three thousand miles away, in the dour granitic city of Aberdeen, the doubt that this was a revolution - the acceptance of quantum theory English physicist George Paget Thomson was meanwhile doing similar a complete break from classical tradition. Planck and Einstein cer­ experiments with electron beams, but with much higher energies than deserve their reputations as great scientists, but can we attribute the Davisson was using.23 After Thomson had returned from the Oxford con­ of the quantum revolution solely to either of them? Scientists tradi­ ference, he began working with a student to try to detect electron regard Planck as the father of quantum theory but it is far from clear diffraction, not from a single crystal but from specially prepared thin films. he initially understood the extent of the changes in our thinking The experiments were strikingly successful: using a celluloid film, energy that his first quantum theory entailed, as Thomas Kuhn has Thomson observed a diffraction pattern whose shape was exactly as de For Kuhn, the quantum revolution began with Einstein. But is it Broglie's formula predicted. This observation completed a unique double regard him as a lone revolutionary? He undoubtedly drew heavily on for the Thomson family: George Paget Thomson discovered that the elec­ work, and for some fourteen years Einstein's advocacy of radiation tron was a wave, only twenty-eight years after his father 'J.J.' had was decidedly tentative. Even in 1924, when he was enthusing about discovered that it was a particle. And, as in so many father-son disagree­ importance of Compton's proof of the particle picture of radiation, ments, they were both right: the electron does behave like a particle when did not go the whole hog and say that the particles were real. He experimenters probe its interactions, whereas it behaves like a wave when in a newspaper article, '[The Compton experiment] proves that radi-

0 0 0 they study its propagation. ." • r discrete eneri!:Voroiectiles 0 0 .'Note: 'as if' 0 The upshot of all this is that both light and matter can behave like parti- view, it is best to think of the quantum revolution as the work cles and like waves. So ends theE= hfstory. Today's scientists routinely use revolutionary but of a disorganized junta. It had no manifesto, no the equation with scarcely a thought for the twenty-six years of work it took of loyalty, and some of those who belonged to it would have found to tease out its'ineaning. I tre equation 1soest Krtbwn for givmg the ene~ good deal more congenial under the ancien regime. It is not even clear of photons, not so much for the crucial role it played in stimulating debate the junta formed and who were its bona fide members. In addition to about the duality of matter. As de Broglie was the first to see, radiation and and Einstein, it would have to include de Broglie and a bevy of matter are both Janus-faced: they show their particle face in their interac­ tenters: the Reichsanstalt cavity-radiation experts who supplied tions, and their wave face in their propagation. All science students are with the crucial data; Robert Millikan, who verified Einstein's confused when they come across this duality, and you can hardly blame loelectric law; Arthur Compton, who first demonstrated the existence of them- it perplexed the world's best scientists for years. The problem's res­ and certainly Clinton Davisson and George Thomson, who proved olution came in the late 1920s, when physicists developed quantum theory ~'electronscan behave as waves. 24 into what became known as quantum fi theo ich made possible a junta had its share of dissidents, too. Millikan and Compton, for uni ed descnp o o radiatio and matter. Among all the forrni a e math­ did much of their great experimental work while refusing to eni!ilfcal syriitiols of quantum field tneory, tlle simple E = hf equation the quantum explanations they later espoused. No one fought harder remains, a pristine relic of quantum history. A Revolution with No Revolutionaries 27 26 It Must be Beautiful posterity.' Einstein composed those words at the Institute than Planck to preserve the heritage of classical physics, and it is a moot of of ,Advanced Study in Princeton, where he had lived since 1933, having fled point whether he ever fully signed up to all the implications of the quantum (iennany the previous December, seven weeks before the Nazis came to revolution. In 1927, two years after virtually the entire science community He never set foot in the country again. had accepted'triar=pnotons eXIst, Planckwrote a short article for the Franklin In the eyes of most of the world, Einstein was an authority capable of Institute in Philadelphia explaining why he still was not fully prepared to God a boost just by giving him a mention, as Saul Bellow later wrote. believe in them. Nor did he ever change his mind, so far as I know. for most of Einstein's fellow scientists he was by then an embarrassingly ·- Planck sii1endship wiih Einstem had afways been the -~losestrelationship in the junta, but the amity came to an end when Planck made an accomoda­ !~Pi-detachedfigure, obstinately refusing to accept the fully fledged quan­ theory that physicists had formulated in the 1920s. Einstein was, as tion with Hitler. They first met in 1933, shortly after Hitler became happy to work on his own, to be an intellectual loner. Music contin­ chancellor, and Planck made numerous concessions to the Nazi regime- he be a passion. Although he had given up playing the violin shortly after regularly gave the Hitler salute, lectured in halls decorated with swastikas, War II, the Juilliard Quartet did once persuade him to give an and made speeches in which he pointedly omitted the names of leading ll)l'Omptu performance when they visited him in his home in the autumn of Jewish physicists, including Einstein. Appalled as he was to see the FUhrer's corruption of the apparatus of state, Planck's devotion to the institutions of Asked to select a piece, Einstein unhesitatingly chose Mozart's soul­ minor quintet and played second violin, scarcely referring to the score. German physics, his patriotism and, arguably, his gullibility led him to make Planck was the Moses of quantum science, Einstein was its Joshua. increasingly more humiliating compromises. In many ways he behaved like his Mount Pisgah in Berlin, Planck saw the Promised Land and he led a character from an Ishiguro novel, as someone whose way of looking at the world we see gradually exposed as being more and more unequal to events. followers to it, but he could never make the journey himself. It was who took them there, though for him the journey was not yet over, Towards the end of the war, on the night of 15 February 1944, an air raid destroyed the GrUnewald suburb where Planck had lived for some fifty years. plain from his final words on radiation quanta, written in December : 'All these fifty years of brooding have brought me no nearer the His library, in which he probably first wrote down the E =hf equation, was destroyed along with the rooms in which he had made music with Einstein. to the question "What are light quanta?" Nowadays, every Tom, and Harry thinks he knows it, but he is mistaken.' To understand the Planck's stoicism was to be tested almost to breaking point: he had lost his elder son in the trenches of World War I, and both daughters in childbirth, ,.. properly, Einstein believed, quantum theory was not enough. years later, the theory has yet to be troubled by conflict with exper­ and his younger son was murdered by the Gestapo in February 1945. Death finally came to Planck, almost as a redemption, in October 1947, a let alone to be superseded. If, however, such a counter-revolution founding member, few months before what would have been his ninetieth birthday. At his com­ come, Einstein would be seen as its junta's l\lffiOusly vindicated. And his celebrity would be given another boost in memoration ceremony, on a bright spring day in GOttingen, chamber music by Bach, Brahms and Beethoven interspersed the eulogies. It is a safe bet that would appropriately underline his bravest contribution to science. the mourning physicists all thought of the photon as a particle like any other, yet Planck had never wholeheartedly been able to join them. The explanation may lie in words that he had written shortly before, in his autobiographical Acknowledgements notes: 'A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually friends and colleagues have given me valuable advice during the of this essay. It is a pleasure to give special thanks to David die, and a new generation grows up that is familiar with it.' !'IJ,