by Manjit Kumar
In February 1923 Bohr received a letter dated 21 January, from Arnold Sommerfeld, alerting him to the ‘most interesting thing that I have experienced scientifically in America’.95 He had swapped Munich, Bavaria for Madison, Wisconsin for a year and managed to escape the worst of the hyperinflation about to engulf Germany. It had been a shrewd financial move for Sommerfeld. To get an early glimpse of the work of Arthur Holly Compton before his European colleagues was an unexpected bonus.
Compton had made a discovery that challenged the validity of the wave theory of X-rays. Since X-rays were electromagnetic waves, a form of short-wavelength invisible light, Sommerfeld was saying that the wave nature of light, contrary to all the evidence in its favour, was in serious trouble. ‘I do not know if I should mention his results’, wrote Sommerfeld somewhat coyly, since Compton’s paper had not yet been published. ‘I want to call your attention to the fact that eventually we may expect a completely fundamental and new lesson.’96 It was a lesson that Einstein had been trying to teach with varying degrees of enthusiasm since 1905. Light was quantised.
Compton was one of America’s leading young experimenters. He had been appointed professor and head of physics at the University of Washington in St Louis, Missouri in 1920 at just 27. His investigations into the scattering of X-rays conducted two years later would be described as ‘the turning point in twentieth-century physics’.97 What Compton did was fire a beam of X-rays at a variety of elements such as carbon (in the form of graphite) and measure the ‘secondary radiation’. When the X-rays slammed into the target most of them passed straight through, but some were scattered at a variety of angles. It was these ‘secondary’ or scattered X-rays that interested Compton. He wanted to find out if there was any change in their wavelength compared to the X-rays that had struck the target.
He found that the wavelengths of the scattered X-rays were always slightly longer than those of the ‘primary’ or incident X-rays. According to the wave theory they should have been exactly the same. Compton understood that the difference in wavelength (and therefore frequency) meant the secondary X-rays were not the same as the ones that had been fired at the target. It was as strange as shining a beam of red light at a metal surface and finding blue light being reflected.98 Unable to make his scattering data tally with the predictions of a wavelike theory of X-rays, Compton turned to Einstein’s light-quanta. Almost at once he found ‘that the wavelength and the intensity of the scattered rays are what they should be if a quantum of radiation bounced from an electron, just as one billiard ball bounces from another’.99
If X-rays came in quanta, then a beam of X-rays would be similar to a collection of microscopic billiard balls slamming into the target. Although some would pass through without hitting anything, others would collide with electrons inside atoms of the target. During such a collision an X-ray quantum would lose energy as it was scattered and the electron sent recoiling from the impact. Since the energy of an X-ray quantum is given by E=h, where h is Planck’s constant and its frequency, then any loss of energy must result in a drop in frequency. Given that frequency is inversely proportional to wavelength, the wavelength associated with a scattered X-ray quantum increases. Compton constructed a detailed mathematical analysis of how the energy lost by the incoming X-ray and the resulting change in the wavelength (frequency) of the scattered X-ray was dependent upon the angle of scattering.
No one had ever observed the recoiling electrons that Compton believed should accompany the scattered X-rays. But then no one had been looking for them. When he did, Compton soon found them. ‘The obvious conclusion,’ he said, ‘would be that X-rays, and so also light, consist of discrete units, proceeding in definite directions, each unit possessing the energy h and the corresponding momentum h.’100 The ‘Compton effect’, the increase in wavelength of X-rays when they are scattered by electrons, was irrefutable evidence for the existence of light-quanta, which until then many had dismissed at best as science fiction. It was by assuming that energy and momentum are conserved in the collision between an X-ray quantum and an electron that Compton was able to explain his data. It was Einstein, in 1916, who had been the first to suggest that light-quanta possessed momentum, a particle-like property.
In November 1922 Compton announced his discovery at a conference in Chicago.101 However, although he sent his paper to the Physical Review just before Christmas, it was not published until May 1923 as the editors failed to understand the significance of its content. The avoidable delay meant that the Dutch physicist Pieter Debye beat Compton into print with the first complete analysis of the discovery. A former Sommerfeld assistant, Debye had submitted his paper to a German journal in March. Unlike their American counterparts, the German editors recognised the importance of the work and published it the following month. However, Debye and everyone else gave the talented young American the credit and recognition he deserved. It was sealed when Compton was awarded the Nobel Prize in 1927. By then, Einstein’s light-quantum had been rechristened the photon.102
There had been 2,000 at his Nobel lecture in July 1923, but Einstein knew that most of them had come to see rather than to listen to him. Sitting on the train as he made his way from Göteborg to Copenhagen, Einstein was looking forward to meeting a man who would listen to his every word and probably disagree. When he got off the train, Bohr was there to greet him. ‘We took the streetcar and talked so animatedly that we went much too far’, Bohr recalled almost 40 years later.103 Speaking in German, they were oblivious to the curious stares of fellow passengers. Whatever was discussed, as they rode back and forth missing their stop, it was sure to include the Compton effect, soon to be described by Sommerfeld as ‘probably the most important discovery that could have been made in the current state of physics’.104 Bohr was unconvinced and refused to accept that light was made up of quanta. It was he, not Einstein, who was now in the minority. Sommerfeld was in no doubt that ‘the death-knell of the wave theory of radiation’ had been sounded by Compton.105
Like the doomed hero in the westerns that he later liked to watch, Bohr was outnumbered as he made one last stand against the quantum of light. In collaboration with his assistant Hendrik Kramers and a visiting young American theorist, John Slater, Bohr proposed sacrificing the law of conservation of energy. It was a vital component in the analysis leading to the Compton effect. If the law was not strictly enforced on the atomic scale as it was in the everyday world of classical physics, then Compton’s effect was no longer incontrovertible evidence for Einstein’s light-quanta. The BKS proposal, as it became known (after Bohr, Kramers and Slater), appeared to be a radical suggestion but was in truth an act of desperation that showed how much Bohr abhorred the quantum theory of light.
The law had never been experimentally tested at the atomic level and Bohr believed that the extent of its validity remained an open question in processes such as the spontaneous emission of light-quanta. Einstein believed that energy and momentum were conserved in every single collision between a photon and an electron, while Bohr believed they were valid only as a statistical average. It was 1925 before experiments by Compton, then at Chicago University, and by Hans Geiger and Walther Bothe at the Physikalische-Technische Reichsanstalt, confirmed that energy and momentum were conserved in collisions between a photon and an electron. Einstein had been right and Bohr wrong.
Confident as ever, on 20 April 1924, more than a year before experiments silenced the doubters, Einstein eloquently summed up the situation for the readers of the Berliner Tageblatt: ‘There are therefore now two theories of light, both indispensable and – as one must admit today despite twenty years of tremendous effort on the part of theoretical physicists – without any logical connection.’106 Einstein meant that both the wave theory of light and quantum theory of light were in some way valid. Light-quanta could not be invoked to explain the wave phenomena associated with light, such as interference and diffraction. Conversely, a full explanation of Compton’s experiment and the photoelectric effect c
ould not be provided without recourse to the quantum theory of light. Light had a dual, wave-particle character, which physicists just had to accept.
One morning, not long after the article appeared, Einstein received a parcel with a Paris postmark. Opening it, he discovered a note from an old friend seeking his opinion of the accompanying doctoral thesis written by a French prince on the nature of matter.
Chapter 6
THE PRINCE OF DUALITY
‘Science is an old lady who does not fear mature men’, his father had once said.1 But he, like his elder brother, had been seduced by science. Prince Louis Victor Pierre Raymond de Broglie, a member of one of France’s leading aristocratic families, had been expected to follow in the footsteps of his illustrious forebears. The de Broglie family, originally from Piedmont, had served French kings as soldiers, statesmen and diplomats with high distinction since the middle of the seventeenth century. In recognition of the service he had rendered, an ancestor was given the hereditary title of Duc in 1742 by Louis XV. The Duke’s son, Victor-François, inflicted a crushing defeat on an enemy of the Holy Roman Empire and a grateful Emperor rewarded him with the title of Prinz. Henceforth, all of his descendants would be either a prince or a princess. So it was that the young scientist would one day be both a German prince and a French duke.2 It is an unlikely family history for the man who made a fundamental contribution to quantum physics, which Einstein described as ‘the first feeble ray of light on this worst of our physics enigmas’.3
The youngest of the four surviving children, Louis was born in Dieppe on 15 August 1892. In keeping with their elevated position in society, the de Broglies were educated at the ancestral home by private tutors. While other boys might have been able to recite the names of the great steam engines of the day, Louis could recite the names of all the ministers of the Third Republic. To the amusement of the family, he began giving speeches based upon the political coverage in the newspapers. With a grandfather who had been prime minister, before long ‘a great future as a statesman was predicted for Louis’, recalled his sister Pauline.4 It might have been the case had his father not died, in 1906, when he was fourteen.
His elder brother, Maurice, at 31, was now the head of the family. As tradition demanded, Maurice had pursued a military career but had chosen the navy rather than the army. At naval college he excelled at science. As a promising young officer he found a navy in a period of transition as it prepared for the twentieth century. Given his scientific interests, it was only a matter of time before Maurice became involved in attempts at establishing a reliable ship-to-ship wireless communication system. In 1902 he wrote his first paper on ‘radioelectric waves’ and, despite the opposition of his father, it strengthened his determination to leave the navy and devote himself to scientific research. In 1904, after nine years in the service, he quit the navy. Two years later his father was dead and he had to shoulder new responsibilities as the sixth Duc.
On Maurice’s advice, Louis was sent to school. ‘Having experienced myself the inconvenience of a pressure exercised on the studies of a young man I refrained from imparting a rigid direction to the studies of my brother, although at times his vacillations gave me some concerns’, he wrote almost half a century later.5 Louis did well in French, history, physics and philosophy. In mathematics and chemistry he was indifferent. After three years Louis graduated in 1909 at the age of seventeen, with both the baccalauréat of philosophy and that of mathematics. A year earlier Maurice had acquired his PhD under Paul Langevin at the Collège de France and set up a laboratory in his Parisian mansion on the rue Châteaubriand. Rather than seek employment in a university, the creation of a private laboratory in which to pursue his new vocation helped soften the disappointment of some of the family at a de Broglie abandoning military service for science.
Unlike Maurice, Louis at the time was set for a more traditional career as he studied medieval history at the University of Paris. However, the twenty-year-old prince soon discovered that the critical study of texts, sources and documents of the past held little interest for him. Maurice said later that his brother was ‘not far from losing faith in himself’.6 Part of the problem was a burgeoning interest in physics fostered by time spent with Maurice in the laboratory. The enthusiasm of his elder brother about his research on X-rays had proved contagious. However, Louis was consumed by doubts about his abilities that were aggravated by failing a physics exam. Was he, Louis wondered, destined to be a failure? ‘Gone the gaiety and high spirits of his adolescence! The brilliant chatter of his childhood has been muted by the depth of his reflections’, was how Maurice remembered the introvert he hardly recognised.7 Louis would become, according to his brother, ‘an austere and fairly untamed scholar’, who did not like leaving his own home.8
The first time Louis travelled abroad it was to Brussels in October 1911.9 He was nineteen. In the years since he left the navy, Maurice had become a much-respected scientist specialising in X-ray physics. When the invitation arrived to be one of the two scientific secretaries entrusted with the smooth running of the first Solvay conference, he readily accepted. Even though it was an administrator’s role, the chance to discuss the quantum with the likes of Planck, Einstein and Lorentz was just too tempting to forgo. The French would be well represented. Curie, Poincaré, Perrin, and his former supervisor Langevin would all be there.
Staying at the Hotel Metropole with all the delegates, Louis kept his distance. It was only after they returned and Maurice recounted the discussions about the quantum that took place in the small room on the first floor that Louis began taking an even greater interest in the new physics. When the proceedings of the conference were published, Louis read them and resolved to become a physicist. By then he had already swapped history books for those of physics, and in 1913 he obtained his Licence és Science, the equivalent of a degree. His plans had to wait as a year of military service beckoned. Despite the three Marshals of France that the de Broglies could boast, Louis entered the army as a lowly private in a company of engineers stationed just outside Paris.10 With Maurice’s help, he was soon transferred to the Service of Wireless Communication. Any hopes of a quick return to his study of physics evaporated with the outbreak of the First World War. He spent the next four years as a radio engineer stationed underneath the Eiffel Tower.
Discharged in August 1919, he deeply resented having spent six years, from the age of 21 to 27, in uniform. Louis was more determined than ever to continue down his chosen path. He was helped and encouraged by Maurice and spent time in his well-equipped laboratory following the research being done on X-rays and the photoelectric effect. The brothers had long discussions on the interpretation of the experiments being conducted. Maurice reminded Louis of ‘the educational value of the experimental sciences’ and ‘that theoretical constructions of science have no value unless they are supported by facts’.11 He wrote a series of papers on the absorption of X-rays while thinking about the nature of electromagnetic radiation. The brothers accepted that both the wave and particle theories of light were in some sense correct, since neither on its own could explain diffraction and interference and also the photoelectric effect.
In 1922, the year Einstein lectured in Paris at the invitation of Langevin and received a hostile reception for having remained in Berlin throughout the war, de Broglie wrote a paper in which he explicitly adopted ‘the hypothesis of quanta of light’. He had already accepted the existence of ‘atoms of light’ at a time when Compton had yet to make any sort of announcement concerning his experiments. By the time the American published his data and analysis of the scattering of X-rays by electrons and thereby confirmed the reality of Einstein’s light-quanta, de Broglie had already learned to live with the strange duality of light. Others, however, were only half-joking when they complained about having to teach the wave theory of light on Mondays, Wednesdays and Fridays, and the particle theory on Tuesdays, Thursdays and Saturdays.
‘After long reflection in solitude and meditation
,’ de Broglie wrote later, ‘I suddenly had the idea, during the year 1923, that the discovery made by Einstein in 1905 should be generalized by extending it to all material particles and notably to electrons.’12 De Broglie had dared to ask the simple question: if light waves can behave like particles, can particles such as electrons behave like waves? His answer was yes, as de Broglie discovered that if he assigned to an electron a ‘fictitious associated wave’ with a frequency and wavelength , he could explain the exact location of the orbits in Bohr’s quantum atom. An electron could occupy only those orbits that could accommodate a whole number of wavelengths of its ‘fictitious associated wave’.
In 1913, to prevent Rutherford’s model of the hydrogen atom from collapsing as its orbiting electron radiated energy and spiralled into the nucleus, Bohr had been forced to impose a condition for which he could offer no other justification: an electron in a stationary orbit around the nucleus did not emit radiation. De Broglie’s idea of treating electrons as standing waves was a radical departure from thinking about electrons as particles orbiting an atomic nucleus.
Standing waves can easily be generated in strings tethered at both ends, such as those used in violins and guitars. Plucking such a string produces a variety of standing waves with the defining characteristic that they are made up of a whole number of half-wavelengths. The longest standing wave possible is one with a wavelength twice as long as the string. The next standing wave is made up of two such half-wavelength units, giving a wavelength equal to the physical length of the string. The next is a standing wave consisting of three half-wavelengths, and so on up the scale. This whole number sequence of standing waves is the only one that is physically possible, and each has its own energy. Given the relationship between frequency and wavelength, this is equivalent to the fact that a plucked guitar string can vibrate only at certain frequencies beginning with the fundamental tone, the lowest frequency.
