by Ray Monk
Oppenheimer, who had not yet even begun work on his PhD thesis, managed, within a few weeks of returning from Corsica, to complete the paper that was to become his first publication. Its title was ‘On the Quantum Theory of Vibration-Rotation Bands’. On 24 May 1926, it was received by the Cambridge Philosophical Society, the venerable scientific society (established in 1819 ‘for the purpose of promoting scientific inquiry’) to which Oppenheimer had been elected as an ‘associate’ in January 1926, and was published in their Proceedings in July. Though he was later disparaging about it (‘That was a mess, that first paper’), the very fact that he was able, so soon after his severe problems during the winter, to write a publishable paper on a subject right at the cutting edge of advanced physical theory was a notable achievement.
The paper might be seen as one of the earliest contributions to the subject of ‘quantum chemistry’, in that it attempts to apply the new quantum mechanics of Heisenberg, Born, Jordan, Dirac and Schrödinger (all of whose papers are cited in it) to the understanding not of atoms, but of molecules. In particular, Oppenheimer seeks to show the applicability of Dirac’s version of the mathematics of quantum mechanics to the understanding of diatomic molecules; that is, molecules, like those of oxygen (O) and hydrogen (H), that consist of two atoms. The vibration and rotation of these molecules produce characteristic spectra of electromagnetic radiation, the frequencies of which Oppenheimer attempts in this paper to derive from within Dirac’s theory.
Compared with what Dirac was producing at this time, Oppenheimer’s first paper was a minor piece of work. It addresses a problem that is of secondary, rather than fundamental, importance, and, moreover, it has a weakness that would have been unthinkable in anything by Dirac: it contains mathematical errors. Nevertheless, its publication was enough to transform Oppenheimer from a failing experimental physicist to an up-and-coming theorist. When distinguished visitors came to Cambridge, Oppenheimer was now introduced to them as one of the Knaben leading the revolution in theoretical physics. When Paul Ehrenfest, the professor of physics at Leiden, came to Cambridge, for example, Oppenheimer remembers that ‘we went out on the river and talked about collision problems, Coulomb’s law . . . and so on’. A short while after Ehrenfest’s visit to Cambridge, Oppenheimer met him again, when he and other American physicists at Cambridge spent a week at the University of Leiden. There he met Ehrenfest’s young, but already famous, assistants, Samuel Goudsmit and George Uhlenbeck, who together had been the first to put forward the idea that electrons possess the property of spin. Oppenheimer’s reception among the theoretical physicists at Leiden recalls his acceptance by the literary ‘troika’ in New Mexico in 1922. Uhlenbeck remembers Oppenheimer as being a ‘very warm person’ who was ‘so involved in physics’ that it ‘was as if we were old friends because [we] had so many things in common’. Oppenheimer, for his part, recalls that it was ‘wonderful’ at Leiden and that he ‘realised then that some of the troubles of the winter had been exacerbated by the English customs’.
Back in Cambridge, Oppenheimer resumed his theoretical studies and began work on a second paper on quantum mechanics, this time on what is known as the ‘two-body problem’. This is, in general, the problem of providing a mathematical model of two bodies orbiting one another. Newton had provided a solution of this problem for classical physics, and Dirac and Schrödinger had investigated it from the point of view of quantum mechanics. Oppenheimer’s aim was to provide a more complete quantum-mechanical solution to this problem than had so far been achieved.
At the beginning of June 1926, while hard at work on this problem, Oppenheimer had one of the most memorable moments of his time at Cambridge – indeed, of his entire life – when he was introduced to Niels Bohr. Bohr, who was in England to receive the honour of being made a foreign member of the Royal Society, happened to be in Rutherford’s room at the Cavendish when Oppenheimer walked in. Rutherford, who by then looked upon Oppenheimer as a promising theorist rather than a distinctly unpromising experimentalist, immediately introduced him to Bohr. As custom and politeness demanded in such a situation, Bohr asked Oppenheimer what he was working on and, on being told that it was the two-body problem, asked him how it was going. ‘I’m in difficulties,’ Oppenheimer replied. ‘Are the difficulties mathematical or physical?’ Bohr asked. ‘I don’t know,’ Oppenheimer answered, prompting Bohr to remark: ‘That’s bad.’ The encounter made a deep and lasting impression on Oppenheimer. After meeting Bohr, he once said, ‘I forgot about beryllium and films and decided to try to learn the trade of becoming a theoretical physicist.’ Bohr’s question to him, he thought, was a very good one, a question that went right to the heart of his difficulties. ‘I thought it put a rather useful glare on the extent to which I became embroiled in formal questions without stepping back to see what they really had to do with the physics of the problem.’
Perhaps because of the arithmetical mistakes in his first paper, Oppenheimer took immense care to ensure that the mathematics in this second paper was free from error. Edsall remembers how, at Oppenheimer’s request, he spent hours one Sunday checking the figures in this paper, even though he himself had little idea what they meant. His reward was a footnote acknowledging his help while misspelling his name (‘I am indebted to Mr J.T. Edsahl for checking these calculations’). By the middle of July the paper was finished and it appeared that month in the Proceedings of the Cambridge Philosophical Society under the title ‘On the Quantum Theory of the Problem of the Two Bodies’.
By a fortuitous coincidence, this second paper brought Oppenheimer to the attention of one of the leading figures in quantum mechanics at the very point when he was making his greatest contribution to the subject. That figure was Max Born, who had already played a key role in the development of the matrix version of quantum mechanics and was on the brink of providing the definitive interpretation of the theory. A summary of that interpretation had been given in a short paper that Born published on 10 July 1926 called ‘Zur Quantenmechanik der Stossvorgänge’ (‘On the Quantum Mechanics of Collision Processes’). Ten days later, Born sent off a longer, more polished and refined paper with the same title to the journal Zeitschrift für Physik, and on 29 July – three days after the publication of Oppenheimer’s second paper – Born came to Cambridge to deliver this paper as a talk to the Kapitza Club with the English title ‘On the Quantum Mechanics of Collisions of Atoms and Electrons’. This paper was to have a profound impact on the way quantum mechanics was understood, addressing head-on exactly the question raised by Bohr’s brief discussion with Oppenheimer, the question about how one was to understand the physical reality that lay behind the mathematics of quantum mechanics.
The immediate aim of Born’s paper was to bring quantum mechanics to bear on the subject of how particles behave when they collide with each other; his more general intention was to provide an interpretation of the mathematical formulae of quantum mechanics. In both respects, his conclusions were startling, from both a physical and a philosophical point of view; so startling that many people, including Einstein, refused to accept them. Still more remarkable, especially in the light of Einstein’s resistance, is the fact that those conclusions became widely accepted and remain today the generally held view among scientists.
Regarding collisions, Born showed that quantum mechanics, unlike classical Newtonian mechanics, is non-deterministic. In Newtonian mechanics, what happens to one body after it collides with another (for example, a billiard ball hitting another billiard ball) is entirely determined by the laws of motion. So, if you repeat a collision (hit a billiard ball into another in exactly the same way), exactly the same thing will happen. If the ball deflected to the left the first time, it would deflect to the left every time you repeated the shot. In quantum mechanics, however, the situation is very different. According to Born, quantum mechanics allows identical experiments to have different outcomes: one time, the particle might be deflected to the left; another time, to the right. Any outcome is possible; s
ome outcomes, however, are more probable than others. It is this feature of quantum mechanics that persuaded Einstein that the theory could not possibly be right and prompted him to make his famous remark (in a letter to Born): ‘God does not play dice.’
The non-deterministic, probabilistic nature of quantum mechanics provided Born with an intriguing answer to the general question regarding the physical reality described by its equations, allowing him to decide between the particle-like ‘quanta’ described by the mathematics of Heisenberg and Dirac and the waves described by Schrödinger’s differential equations. Basically, he came down on the side of regarding electrons as particles, while providing an ingenious explanation for why Schrödinger’s wave mechanics ‘worked’. Schrödinger believed that the success of his wave functions showed that de Broglie was right – electrons are waves – and his problem was to explain why, in countless experiments (including the original experiments of J.J. Thomson back in the 1890s), electrons seemed to behave like particles. For Born, it was the other way round; electrons were particles (or at least discrete ‘quanta’) and what required explanation was why they seemed to behave like waves. His answer to this last question invoked the probabilistic nature of quantum theory that he had demonstrated in his analysis of collisions. The waves of de Broglie and Schrödinger, Born argued, had no physical reality. Rather, they were probability waves. What they described was the probability of an electron being in a particular place at a particular time. Quantum mechanics, according to Born, is unable to say definitely whether an electron is or is not at a particular place at a particular time; it can only say what the odds are that it is here or there. And this is not because of the limitations of our knowledge; it is an inherent feature of physical reality, linked to its non-deterministic nature. This ‘statistical interpretation of quantum mechanics’, as it became known, was quickly adopted by other leading physicists, most notably Heisenberg and Bohr (who famously defended it against Einstein on numerous occasions), and it was for discovering it that Born was awarded the Nobel Prize, though oddly not until 1954, more than twenty years after the same honour had been awarded to de Broglie, Heisenberg, Schrödinger and Dirac.fn22
Though Born had already sent his paper to the Zeitschrift, it had not yet been published when he came to Cambridge to deliver his talk to the Kapitza Club on 29 July 1926. When it was published, in September 1926, a footnote had been added, acknowledging the importance of Oppenheimer’s paper on the two-body problem. For a twenty-two-year-old research student who had not yet completed a PhD thesis, this was a significant feather in his cap. Born was evidently very impressed with Oppenheimer. In the second week of August, Born returned to England to read a paper at the annual meeting of the British Association for the Advancement of Science, which that year was held in Oxford. The paper, entitled ‘Physical Aspects of Quantum Mechanics’, was Born’s most direct statement yet on the question of how, in the light of quantum mechanics, we are to understand physical reality, and was responsible for spreading his idea of probability waves to theoretical physicists in Britain. When the paper was published in Nature the following year, it carried the following acknowledgement: ‘Translated by Mr Robert Oppenheimer. The author is very much obliged to Mr Oppenheimer for his careful translation.’
By the summer of 1926, then, Oppenheimer had not only established himself as a promising young theorist; he had become a collaborator with the person who at that time was leading the effort of the international community of physicists to understand the extraordinary world of quantum mechanics. He had, in fact, positioned himself where he had wanted to be: at the ‘centre’ of theoretical physics. His year at Cambridge had allowed him to achieve this, partly because it had enabled him to see that, in 1926, the centre of theoretical physics was not Cambridge, but Göttingen. The person to work with was not Ernest Rutherford, or even Niels Bohr, but rather Max Born. Accordingly, on 18 August 1926, a week after the meeting at Oxford, Oppenheimer wrote to Raymond Priestley, asking for permission to spend the following year at Göttingen, under the supervision of Born, who, Oppenheimer informed Priestley, was ‘particularly interested in the problems at which I hoped to work’. Reflecting on his decision to leave Cambridge for Göttingen, Oppenheimer later said that, though he ‘had very great misgivings about myself on all fronts’, he still felt determined to pursue his inclination to become a theoretical physicist: ‘Here was something I felt just driven to try.’
He may have had misgivings, but he must also have known that, in pursuing this inclination, he had every chance of meeting with success. He had never stood any chance of impressing the ‘tutors & the dukes’ of British high society, he would never have been invited to Garsington or to Pontigny, and he would never be described (as Blackett had been by I.A. Richards) as ‘a young Oedipus’, but he had succeeded in impressing one of the foremost quantum physicists in the world – an achievement that brought him not just near the centre of theoretical physics, but right inside it.
* * *
fn17 T.S. Eliot and Bertrand Russell.
fn18 It is impossible to tell how much of this story is true. Can one believe that Oppenheimer deliberately dropped his suitcase, intending it to hit the woman? Did he really kiss her? And, perhaps most improbably of all: can one really imagine him travelling third-class?
fn19 An alpha particle, as Rutherford was the first to establish, is a helium nucleus. It is (we now know, though this was not known before the discovery of neutrons in 1932) made up of two protons and two neutrons. What Rutherford and the physicists of the 1920s knew about alpha particles/helium nuclei was that they had an atomic weight of 4 and that they, like all nuclei, were positively charged. Chiefly, however, alpha particles were associated in the minds of the scientists of this period with what Rutherford had christened ‘alpha radiation’, which occurs when a radioactive element such as radium decays. The radioactive decay simply is the emission of alpha particles. As these particles include two protons, the decayed radium (atomic number 88) turns into radon (atomic number 86), and then, successively, into polonium (84) and lead (82).
fn20 Nitrogen has atomic number 7, so that when it absorbs a proton it becomes element number 8 – i.e. oxygen.
fn21 It is indicative of the attitude towards theoretical physics at Cambridge during this period that Fowler’s official position was college lecturer in mathematics.
fn22 As far as I know, no authoritative answer has been given as to why it took so long to award Born the Nobel Prize. Jeremy Bernstein has speculated that it is because, in 1933, when Heisenberg, Dirac and Schrödinger were honoured, it would have been natural to have included Born and Jordan, but Jordan was a member of the Nazi Party and unacceptable. Therefore the committee had to wait until they had a reason for giving it to Born alone. This might explain why Born did not receive the prize in 1933, but it hardly explains why he had to wait a further twenty-one years.
PART II
1926–1941
6
Göttingen
IN THE STARKEST contrast to his arrival in Cambridge just a year earlier, Oppenheimer arrived in Göttingen in the summer of 1926 in a state of almost unrestrained self-confidence. As Max Born put it, Oppenheimer seemed ‘conscious of his superiority’. In his autobiography Born complains several times about Oppenheimer’s arrogance, without appearing to recognise the central role he himself had played in nurturing it. Whereas at Cambridge, Oppenheimer arrived having been rejected by the leading physicist there, at Göttingen he arrived having been invited by the leading physicist there, who made no secret of the fact that he was extremely impressed with, and indeed a little intimidated by, Oppenheimer’s intelligence.
Though apparently unaware of what it revealed, Born tells a story that perfectly conveys the role he played in allowing, even encouraging, Oppenheimer to be ‘conscious of his superiority’. The story concerns Born’s most famous paper, ‘The Quantum Mechanics of Collision Processes’, the one that he read to the Kapitza Club in July 1926, when he first
met Oppenheimer. Born says that when he finished writing the paper, he showed it to Oppenheimer in order for him to check the difficult and involved calculations it contained. This must have been, I think, in August 1926, when Born returned to England to read the paper that Oppenheimer translated to the British Association for the Advancement of Science at Oxford. Born had by then received the proofs of ‘The Quantum Mechanics of Collision Processes’ from the Zeitschrift für Physik, and it is presumably these proofs that he showed to Oppenheimer. What would immediately have struck Oppenheimer, and boosted his confidence enormously, was the footnote Born added to the paper at the proof stage drawing attention to the importance of Oppenheimer’s work on the two-body problem. Born, who was self-critical to a fault, says that he asked Oppenheimer to check the calculations because ‘I was never very good at long calculations and always made silly mistakes.’ All his students knew this, he says, but Oppenheimer ‘was the only one frank and rude enough to say it without joking’. For, after he had checked the paper, Oppenheimer returned it to Born, saying, with an astonished expression: ‘I couldn’t find any mistake – did you really do this alone?’ ‘I was not offended,’ Born insists. ‘It actually increased my esteem for his remarkable personality.’
