by Manjit Kumar
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.
De Broglie realised that this ‘whole number’ condition restricted the possible electron orbits in the Bohr atom to those with a circumference that permitted the formation of standing waves. These electron standing waves were not bound at either end like those on a musical instrument, but were formed because a whole number of half-wavelengths could be fitted into the circumference of the orbit. Where there was no exact fit, there could be no standing wave and therefore no stationary orbit.
Figure 9: Standing waves of a string tethered at both ends
Figure 10: Standing electron waves in the quantum atom
If viewed as a standing wave around the nucleus instead of a particle in orbit, an electron would experience no acceleration and therefore no continual loss of radiation sending it crashing into the nucleus as the atom collapsed. What Bohr had introduced simply to save his quantum atom, found its justification in de Broglie’s wave-particle duality. When he did the calculations, de Broglie found that Bohr’s principal quantum number, n, labelled only those orbits in which electron standing waves could exist around the nucleus of the hydrogen atom. It was the reason why all other electron orbits were forbidden in the Bohr model.
When de Broglie outlined why all particles should be viewed as having a dual wave-particle character in three short papers in the autumn of 1923, it was not immediately clear what was the nature of the relationship between the billiard ball-like particles and the ‘fictitious associated wave’. Was de Broglie suggesting that it was akin to a surfer riding a wave? It was later established that such an interpretation would not work and that electrons, and all other particles, behaved exactly like photons: they are both wave and particle.
De Broglie wrote up his ideas in an expanded form and presented them as his PhD thesis in the spring of 1924. The necessary formalities of acceptance and its reading by the examiners meant that de Broglie did not defend his doctoral dissertation until 25 November. Three of the four examiners were professors at the Sorbonne: Jean Perrin, who had been instrumental in testing Einstein’s theory of Brownian motion; Charles Mauguin, a distinguished physicist working on the properties of crystals; and Elie Cartan, a renowned mathematician. The last member of the quartet was the external examiner, Paul Langevin. He alone was well versed in quantum physics and relativity. Before officially submitting his dissertation, de Broglie approached Langevin and asked him to look at his conclusions. Langevin agreed and afterwards told a colleague: ‘I am taking with me the little brother’s thesis. Looks far-fetched to me.’13
Louis de Broglie’s ideas may have been fanciful, but Langevin did not quickly dismiss them. He needed to consult another. Langevin knew that Einstein had publicly stated in 1909 that future research into radiation would reveal a kind of fusion of the particle and wave. Compton’s experiments had convinced almost everyone that Einstein had been right about light. It did after all appear to be a particle in collisions with electrons. Now, de Broglie was suggesting the same kind of fusion, wave-particle duality, for all of matter. He even had a formula that linked the wavelength of the ‘particle’ to its momentum p, =h/p where h is Planck’s constant. Langevin asked the physicist prince for a second copy of the dissertation and sent it to Einstein. ‘He has lifted a corner of the great veil’, Einstein wrote back to Langevin.14
The judgement of Einstein was enough for Langevin and the other examiners. They congratulated de Broglie for ‘having pursued with a remarkable mastery an effort that had to be attempted in order to overcome the difficulties in the midst of which the physicists found themselves’.15 Mauguin later admitted that he ‘did not believe at the time in the physical reality of the waves associated with grains of matter’.16 All Perrin knew for sure was that de Broglie was ‘very intelligent’.17 As for the rest he had no idea. With Einstein’s support, aged 32, he was no longer just Prince Louis Victor Pierre Raymond de Broglie, but had earned the right to call himself plain Dr Louis de Broglie.
Having an idea was one thing, but could it be tested? De Broglie had quickly realised in September 1923 that if matter has wave properties, then a beam of electrons should spread out like a beam of light – they should be diffracted. In one of his short papers written that year, de Broglie had predicted that a ‘group of electrons that passes through a small aperture should show diffraction effects’.18 He tried, but failed to convince any of the skilled experimentalists working in his brother’s private laboratory to put his idea to the test. Busy with other projects, they simply thought the experiments too difficult to perform. Already indebted to his brother Maurice for continually directing his ‘attention to the importance and the undeniable accuracy of the dual particulate and wave properties of radiation’, Louis did not pursue the matter.19
However Walter Elsasser, a young physicist at Göttingen University, soon pointed out that if de Broglie was right, a simple crystal would diffract a beam of electrons hitting it: since the spacing between adjacent atoms in a crystal would be small enough for an object the size of an electron to reveal its wave character. ‘Young man, you are sitting on a gold mine’, Einstein told Elsasser when he heard of his proposed experiment.20 It was not a gold mine, but something a bit more precious: a Nobel Prize. But as in any gold rush, one cannot wait too long before getting started. Elsasser did, and two others staked their claims first and grabbed the prize.
Thirty-four-year-old Clinton Davisson of the Western Electric Company in New York, later better known as the Bell Telephone Laboratories, had been investigating the consequences of smashing a beam of electrons into various metal targets when, one day in April 1925, a strange thing happened. A bottle of liquefied air exploded in his laboratory and broke the evacuated tube containing the nickel target that he was using. The air caused the nickel to rust. As a result of cleaning the nickel by heating it, Davisson had accidentally turned the array of tiny nickel crystals into just a few large ones, which caused electron diffraction. When he continued his experiments he soon realised that his results were different. Unaware that he had diffracted electrons, he simply wrote up the data and published it.
‘It seems impossible that we will be in Oxford a month from today – doesn’t it? We should have a lovely time – Lottie darling – It will be a second honeymoon – and should be sweeter even than the first’, Davisson wrote to his wife in July 1926.21 With the children being looked after by relatives back home, the Davissons could enjoy a much-needed break touring England before heading to Oxford and the British Association for the Advancement of Science conference. It was there that Davisson was astonished to learn that some physicists believed that the data from his experiment supported the idea of a French prince. He had not heard of de Broglie or his suggestion that wave-particle duality be extended to encompass all matter. Davisson was not alone.
Few people had read de Broglie’s three short papers because they had been published in the French journal Compte Rendu. Fewer still knew of the existence of the doctoral dissertation. On returning to New York, Davisson and a colleague, Lester Germer, immediately set about checking whether electrons really were diffracted. It was January 1927 before they had conclusive evidence that matter was diffracted, it did behave like wav
es, when Davisson calculated the wavelengths of the diffracted electrons from the new results and found they matched those predicted by de Broglie’s theory of wave-particle duality. Davisson later admitted that the original experiments were really ‘undertaken as a sort of sideline’ in the wake of others that he had been conducting on behalf of his employers, who were defending a lawsuit from a rival company.
Max Knoll and Ernst Ruska quickly utilised the wave nature of the electron with the invention in 1931 of the electron microscope. No particle smaller than approximately half the wavelength of white light can absorb or reflect light waves so as to make the particle visible through an ordinary microscope. However, with wavelengths more than 100,000 times smaller than that of light, electron waves could. The construction of the first commercial electron microscope began in England in 1935.
Meanwhile in Aberdeen, Scotland, the English physicist George Paget Thomson was carrying out his own experiments with electron beams as Davisson and Germer were busy conducting theirs. He too had attended the BAAS conference in Oxford where de Broglie’s work had been widely discussed. Thomson, who had a very personal interest in the nature of the electron, immediately began experiments to detect electron diffraction. But instead of crystals, he used specially prepared thin films that gave a diffraction pattern whose features were exactly as de Broglie predicted. Sometimes matter behaves like a wave, smeared over an extended region of space, and at others like a particle, located at a single position in space.
In a remarkable twist of fate, the dual nature of matter was embodied in the Thomson family. George Thomson was awarded the Nobel Prize for physics in 1937, together with Davisson, for discovering that the electron was a wave. His father, Sir J.J. Thomson, had been awarded the Nobel Prize for physics in 1906 for discovering that the electron was a particle.
Over a quarter of a century, the developments in quantum physics – from Planck’s blackbody radiation law to Einstein’s quantum of light, from Bohr’s quantum atom to de Broglie’s wave-particle duality of matter – were the product of an unhappy marriage of quantum concepts and classical physics. It was a union that by 1925 was increasingly under strain. ‘The more successes the quantum theory enjoys, the more stupid it looks’, Einstein had written as early as May 1912.22 What was needed was a new theory, a new mechanics of the quantum world.
‘The discovery of quantum mechanics in the mid-1920s,’ said the American Nobel laureate Steven Weinberg, ‘was the most profound revolution in physical theory since the birth of modern physics in the seventeenth century.’23 Given the pivotal role of young physicists in making the revolution that shaped the modern world, these were the years of knabenphysik – ‘boy physics’.
PART II
BOY PHYSICS
‘Physics at the moment is again very muddled; in any case, for me it is too complicated, and I wish I were a film comedian or something of that sort and had never heard anything about physics.’
—WOLFGANG PAULI
‘The more I think about the physical portion of the Schrödinger theory, the more repulsive I find it. What Schrödinger writes about the visualizability of his theory “is probably not quite right”, in other words it’s crap.’
—WERNER HEISENBERG
‘If all this damned quantum jumping were really here to stay, I should be sorry I ever got involved with quantum theory.’
—ERWIN SCHRÖDINGER
Chapter 7
SPIN DOCTORS
‘One wonders what to admire most, the psychological understanding for the development of ideas, the sureness of mathematical deduction, the profound physical insight, the capacity for lucid, systematic presentation, the knowledge of the literature, the complete treatment of the subject matter, or the sureness of critical appraisal.’1 Einstein was certainly impressed by the ‘mature, grandly conceived work’ he had just reviewed. It was difficult for him to believe that the 237-page article, with 394 footnotes, on relativity was the work of a 21-year-old physicist who had been a student, and just nineteen, when asked to write it. Wolfgang Pauli, later nicknamed ‘The Wrath of God’, was acerbic and regarded as ‘a genius comparable only with Einstein’.2 ‘Indeed from the point of view of pure science,’ said Max Born, his one-time boss, ‘he was possibly even greater than Einstein.’3
Wolfgang Pauli was born on 25 April 1900 in Vienna, a city still in the grip of fin de siècle anxiety while enjoying the good times. His father, also called Wolfgang, had been a physician, but abandoned medicine for science and in the process changed his family name from Pascheles to Pauli. The transformation was complete as he converted to Catholicism amid fears that the rising tide of anti-Semitism threatened his academic ambitions. His son grew up knowing nothing of the family’s Jewish ancestry. At university, when another student said that he must be Jewish, Wolfgang junior was astonished: ‘I? No. Nobody has ever told me that and I don’t believe that I am.’4 He learnt the truth from his parents during his next visit home. His father felt vindicated by the decision to assimilate when, in 1922, he was appointed to a coveted professorship and became the director of a new institute for medical chemistry at Vienna University.
Pauli’s mother, Bertha, was a well-known Viennese journalist and writer. Her circle of friends and acquaintances meant that Wolfgang and his sister Hertha, six years his junior, grew up accustomed to seeing leading figures from the arts as well as science and medicine at the family home. His mother, a pacifist and a socialist, exerted a strong influence on Pauli. The longer the First World War dragged on through his formative teenage years, ‘the keener became his opposition against it and, generally, against the whole “establishment”’, recalled a friend.5 When she died two weeks before her 49th birthday in November 1927, an obituary in the Neue Freie Presse described Bertha as ‘one of the few truly strong personalities among Austrian women’.6
Pauli was academically gifted but far from a model pupil, finding school unchallenging. He began having private tuition in physics to compensate. Before long, when bored by a particularly tedious lesson at school, he began reading Einstein’s papers on general relativity hidden under his desk. Physics had always loomed large in his young life in the form of the influential Austrian physicist and philosopher of science Ernst Mach, his godfather. For one who would later enjoy the company and friendship of the likes of Einstein and Bohr, Pauli said that contact with Mach, whom he last saw in the summer of 1914, was ‘the most important event in my intellectual life’.7
In September 1918 Pauli left what he called the ‘spiritual desert’ that was Vienna.8 With the Austria-Hungarian empire on the verge of extinction and Vienna’s past glories faded, it was the lack of top-flight physicists at the city’s university that he was lamenting. He could have gone almost anywhere, but went to Munich to study with Arnold Sommerfeld. Having recently turned down a professorship in Vienna, Sommerfeld had already been in charge of theoretical physics at Munich University for a dozen years when Pauli arrived. From the beginning, in 1906, Sommerfeld set out to create an institute that would be ‘a nursery of theoretical physics’.9 It was not as grand as the institute Bohr would soon create in Copenhagen, consisting as it did of only four rooms: Sommerfeld’s office, a lecture theatre, a seminar room, and a small library. There was also a large laboratory in the basement where in 1912 Max von Laue’s theory that X-rays were short-wavelength electromagnetic waves was tested and confirmed, bringing quick recognition to the ‘nursery’.
Sommerfeld was an exceptional teacher with the uncanny knack of setting his students problems that tested, but did not exceed, their abilities. Having already supervised more than his fair share of talented young physicists, Sommerfeld soon recognised Pauli as someone of rare and exceptional promise. He was a man not easily impressed, but in January 1919 a paper on general relativity written by Pauli before leaving Vienna had just been published. In his ‘nursery’ he had a first-year student, not yet nineteen years old, who was already regarded by others as an expert in relativity.
P
auli quickly became known, and feared, for his sharp and incisive criticism of new and speculative ideas. Some would later call him the ‘conscience of physics’ for his uncompromising principles. Stout with bulging eyes, he was every inch the Buddha of physics, albeit one with a biting tongue. Whenever he was lost deep in thought, Pauli unconsciously rocked back and forth. It was acknowledged far and wide that his intuitive grasp of physics was unmatched among his contemporaries and probably not even surpassed by Einstein. He judged his own work even more harshly than that of others. At times Pauli understood physics and its problems too well, and that hampered the free exercise of his creative powers. Discoveries that he might have made if his imagination and intuition had roamed a little more freely went instead to colleagues less talented and unconstrained.
The only person towards whom he was, and remained, diffident was Sommerfeld. Even as a celebrated physicist, whenever Pauli found himself in the presence of his former professor, those who had been on the receiving end of his sharp judgements were always amazed to see the ‘Wrath of God’ responding with ‘Ja, Herr Professor’, ‘Nein, Herr Professor’. They hardly recognised the man who had once ticked off a colleague: ‘I do not mind if you think slowly, but I do object when you publish more quickly than you think.’10 Or on another occasion saying of a paper he had just read: ‘It is not even wrong.’11 He spared no one. ‘You know, what Mr Einstein said is not so stupid’, he told a packed lecture theatre while still a student.12 Sommerfeld, sitting in the front row, would not have tolerated such a remark coming from any of his other students. But then he knew none of them would have uttered it. When it came to evaluating physics, Pauli was self-confident and uninhibited even in the presence of Einstein.