by Ray Monk
Oppenheimer’s growing reputation at Göttingen – one is tempted to call it ‘mystique’ – was not, however, entirely based on Born’s high opinion of him. By the end of 1926, he was producing written work that was at least beginning to justify the things said about him by Compton and others. Most significant was an article he sent to Zeitschrift für Physik on Christmas Eve entitled ‘Zur Quantentheorie kontinuierlicher Spektren’ (‘On the Quantum Theory of Continuous Spectra’), which formed his PhD thesis and was, at twenty-five pages, one of the longest articles he ever published. The distinguished physicist Abraham Pais has described this article as ‘quite important’, since it introduced various mathematical techniques that are still in use. In particular, Oppenheimer devised for this article a method of calculating, in a quantum-mechanical way, the absorption of light by hydrogen, a method that is used even now for understanding the physical processes that occur in the interiors of stars. This, Pais emphasises, was ‘unexplored territory at the time’, and, as such, must be regarded as some kind of breakthrough, although, compared to the work of Dirac, Heisenberg, Jordan and Born, it was a fairly minor breakthrough, an application of the theory of quantum mechanics, rather than a fundamental step in the creation and development of that theory.
Paul Dirac, whom Oppenheimer venerated as a physicist perhaps more than any other except Niels Bohr, took a notoriously austere view of work that was not of the first importance. At St John’s College, he once crushed a fellow doctoral student, Robert Schlapp – who was then researching the reflection of X-rays from crystals – with the remark, ‘You ought to tackle fundamental problems, not peripheral ones.’ Later in life, when he gave a public lecture on ‘The Development of Quantum Mechanics’, Dirac conveyed the same attitude. Talking about the time just after the initial formulation of quantum mechanics, he remarked: ‘It was very easy in those days for any second-rate physicist to do first-rate work.’ What he meant, he explained, was that, once the mathematical techniques of quantum mechanics had been developed:
It was then an interesting game people could play to take the various models of dynamical systems, which we were used to in the Newtonian theory, and transform them into the new mechanics of Heisenberg . . . Whenever one solved one of the little problems, one could write a paper about it.
It is not entirely clear that Dirac would have regarded the topic of Oppenheimer’s PhD thesis as ‘one of the little problems’, but it seems entirely possible.
Oppenheimer was to get to know Dirac very well in the second half of his stay at Göttingen, since in February 1927 Dirac arrived in Göttingen and moved into the Cario family house, replacing the disgruntled Condon, who had left for Munich, hoping to receive from Arnold Sommerfeld the attention he had failed to receive from Born. ‘The most exciting time I had in Göttingen,’ Oppenheimer once said, ‘and perhaps the most exciting time in my life was when Dirac arrived and gave me the proofs of his paper on the quantum theory of radiation.’
It is unlikely that the excitement was reciprocated. Dirac was a notoriously solitary man. An interviewer once said to Dirac: ‘Oppenheimer indicates that, when he was in Göttingen, he thinks you saw as much or more of him than anyone else there.’ ‘That is so,’ Dirac replied. ‘We sometimes went for long walks together, although I had many walks alone.’ Though Oppenheimer often expressed his admiration for Dirac, there is, as far as I am aware, just one occasion on which Dirac is on record as expressing admiration for Oppenheimer, and that is a rather special case, since the occasion was Dirac’s acceptance of the J. Robert Oppenheimer Memorial Prize, an annual prize awarded by the University of Miami. ‘I am especially happy to be awarded the Oppenheimer Prize,’ Dirac said in his speech, ‘because I was a great friend and admirer of Oppenheimer.’ Strikingly, however, when he specifies the ‘admirable qualities’ that he saw in Oppenheimer, his emphasis is on expository gifts rather than on scientific achievement. His admiration for Oppenheimer, he makes clear, centres on his expertise ‘as a chairman for a discussion or a colloquium’.
Unlike Karl Compton, Dirac was not impressed by Oppenheimer’s knowledge of and interest in literature. On the contrary, he rather disapproved of it. Once he remarked to Oppenheimer: ‘I don’t see how you can work on physics and write poetry at the same time. In science, you want to say something nobody knew before, in words everyone can understand. In poetry, you are bound to say something that everybody knows already in words that nobody can understand.’
Dirac came to Göttingen from Bohr’s institute in Copenhagen, where he had been since September 1926, and where he had produced two pieces of fundamentally important work. The first laid the foundation for what is now known as ‘transformation theory’, showing how one can transform any statement of quantum physics written in Schrödinger’s wave theory into one written either in Heisenberg’s matrices or Dirac’s brackets. The second (the one Oppenheimer alludes to in the quotation above) established a new and important field of study: quantum electrodynamics, bringing quantum mechanics to bear on the understanding of electromagnetic radiation.
Though Oppenheimer’s work did not approach the importance of Dirac’s, at Göttingen the two were often associated with each other as young, brilliant theorists at the cutting edge of the new physics. In a letter to S.W. Stratton, president of the Massachusetts Institute of Technology, written on 13 February 1927, Born repeated the view he had earlier reported to the Rockefeller Foundation, that, among the Americans working at Göttingen, Oppenheimer stood out as being ‘quite excellent’. A few weeks later, the American physicist Earle Kennard wrote to a friend: ‘There are three young geniuses in theory here, each less intelligible to me than the others.’ The three were Oppenheimer, Jordan and Dirac.
American physicists were very keen to be kept abreast of theoretical developments in Europe because, as they were all aware, important things were happening so quickly that it was a constant battle to stay with the pace. As Edward Condon once put it: ‘Great ideas were coming out so fast during that period that one got an altogether wrong impression of the normal rate of progress in theoretical physics.’
In March 1927, Heisenberg published an article called ‘On the Intuitive Content of Quantum-theoretical Kinematics and Mechanics’, which contained the first expression of the idea that everyone now associates with quantum theory: the uncertainty principle. This states that there must always be some degree of uncertainty in our knowledge of quantum-mechanical systems, such as the interiors of atoms. Heisenberg showed that if quantum mechanics is correct (and, for the purpose of the article, Heisenberg used Dirac’s formulation of the theory, because that was the most general), then the more precise our determination of the position of a subatomic particle, the less precise will be our determination of its momentum, and vice versa. The reason for this is that subatomic particles, such as electrons, are so small that ordinary visible light will not be sufficient to fix their positions, because the wavelength of the light is much bigger than the particle. To fix the position of the particle more precisely, one would have to use electromagnetic radiation with much shorter waves (and therefore greater frequencies), such as gamma radiation. But these high-frequency waves carry great energy, enough to deflect, and thereby alter the momentum of, the electron. So, we can be precise about the position of an electron only by affecting (and thereby introducing some imprecision in the measurement of) its momentum, and we can only gain a precise measurement of its momentum if we use low-energy, low-frequency radiation, the wavelengths of which are too great for a precise determination of position.
A few months before Heisenberg’s uncertainty paper was published, Oppenheimer wrote a letter to George Uhlenbeck in Leiden, showing that he himself was giving at least some thought to fundamental questions about the interpretation of quantum mechanics. ‘My own feeling,’ he told Uhlenbeck, ‘is that, whereas it is often correct to regard ψ [the wave function] as a probability amplitude, this interpretation is not the most fundamental one. It seems to me that the problem
has entered a new stage now, & essentially because of Dirac’s last paper.’ He was right, of course, that the problem had entered – or was about to enter, after the publication of Heisenberg’s paper – a new stage. But, despite being shared by, among others, Einstein, Oppenheimer’s feeling that Born’s probabilistic interpretation of the wave function is not the most fundamental has not, so far, been justified; the search for a yet more fundamental interpretation still goes on.
Oppenheimer’s own research, as he outlined to Uhlenbeck, did not centre on this fundamental question of interpretation, but consisted rather in the kind of problem disparaged by Dirac: showing that quantum mechanics could be successfully applied to, as Oppenheimer put it, ‘such effects as polarization & depolarization of mercury resonance lines & impact radiation’. This work led to two papers, both of which were published in Zeitschrift für Physik, the journal most associated with the leading work in quantum mechanics.
Oppenheimer had been prompted to write to Uhlenbeck after meeting one of his colleagues, the experimental physicist E.C. Wiersma, who came to Göttingen to give a paper. Wiersma had evidently told Oppenheimer that Uhlenbeck had accepted a position at the University of Michigan, starting the following academic year. ‘I am very glad,’ Oppenheimer told Uhlenbeck. ‘I shall be going to America (Pasadena) next July & if you think of going at the same time & have no better plans, perhaps we might arrange to go together.’
Oppenheimer had, shortly before this, received a letter offering him one of the National Research Council postdoctoral fellowships. Given that he had not actually applied for such a fellowship and that he had not yet received his doctorate, this is a measure both of how far Oppenheimer’s reputation had spread by the spring of 1927 and of how keen American universities were at this time to attract physicists with expertise in quantum mechanics. His decision to use the fellowship to go to the California Institute of Technology (Caltech) in Pasadena shows how powerful the pull of the American South-west remained for him, as other prestigious universities were only too eager to attract him, not the least of which was Harvard.
On 3 April 1927, Oppenheimer’s old mentor at Harvard, Percy Bridgman – apparently unaware that Oppenheimer had already been offered an NRC fellowship – wrote to him, hoping to lure him back to Harvard. ‘From what I hear,’ Bridgman wrote, ‘I judge that you have your doctor’s degree already. I saw Fowler in Oxford last August, and he gave the most glowing account of the work you had been doing with him.’
Had you thought of applying for a National Research Fellowship for next year in case you are getting your degree? If this appeals to you at all I am sure that we would all be very glad indeed to have you at Harvard again and together with Kemble and Slaterfn23 you ought to make a team that would get some significant theoretical work done.
Perhaps in response to this approach, Oppenheimer changed his plans somewhat and arranged to spend his time as an NRC postdoctoral fellow first at Harvard and then at Caltech.
For now, though, he had to actually get his PhD, which, as everyone assumed, was purely a formality. The paper he had already published the previous December was accepted as a PhD dissertation, and a viva (an oral examination) was scheduled for 11 May, the examiners being Born and James Franck. Neither examiner had any doubt that Oppenheimer should pass and the examination was kept fairly short. Franck spent about twenty minutes asking Oppenheimer questions and, on leaving the examination room, was heard to say: ‘I’m glad that is over. He was on the point of questioning me.’ The dissertation was passed ‘with distinction’. One problem remained: officially, Oppenheimer was not even a student at Göttingen. He had, it seems, neglected to register. Remarkably, Born persuaded the authorities to overlook this arguably fundamental problem, on the extraordinarily implausible grounds of Oppenheimer’s poverty. ‘Economic circumstances,’ he wrote to the Prussian Ministry of Education, ‘render it impossible for Herr Oppenheimer to remain in Göttingen after the end of the summer term.’
Actually, by this time Born had a vested interest in ensuring that Oppenheimer did not spend more time than was necessary in Göttingen. The two had begun to collaborate and the partnership was proving to be, from Born’s point of view, extremely stressful. Working with Oppenheimer seemed to strip him of his self-belief and render him incapable of scientific work. ‘My soul was nearly destroyed by that man,’ he wrote to Paul Ehrenfest soon after Oppenheimer left; and, returning to the subject in another letter to Ehrenfest about a year later, he claimed that Oppenheimer’s ‘presence destroyed the last remnants of my scientific capabilities’. The nearest he came to explaining the destructive effect Oppenheimer had was his remark to Ehrenfest: ‘Through his manner to know everything better and to continue any idea you give him, he has paralysed all of us for three-quarters of a year.’ In other words, the problem with Oppenheimer was that he always wanted to be better than the people around him.
The most lasting fruit of the collaboration between Born and Oppenheimer was a published paper, ‘Zur Quantentheorie der Molekeln’ (‘On the Quantum Theory of Molecules’), which, though one of the least well known of Born’s works, is to this day the most frequently cited of all Oppenheimer’s publications. In the field of quantum chemistry it is considered a classic paper, and every undergraduate textbook in that field has a section on the paper’s central idea, which has become known as the ‘Born–Oppenheimer approximation’.
As Oppenheimer once put it, the purpose of the paper is to use quantum mechanics to explain ‘why molecules were molecules’. It was chemistry that had first attracted Oppenheimer to science, and one of his hopes for quantum mechanics was that it could be used to shed light on the fundamental nature of chemical compounds. His first paper, written while he was still in Cambridge, had sought to take an initial step in that direction; now, together with Born, he was determined to show how quantum mechanics could be extended from the understanding of atomic structures to the understanding of molecular structures. This was an extremely ambitious undertaking.
The calculation of the energy states of molecules is far more complicated than that of atoms, which is, in any case, immensely complicated – so complicated that it has only ever been done completely for the very simplest atoms, such as that of hydrogen, which consists of a single proton and a single electron. The complications arise from, among other things, the fact that the wave function at the heart of quantum mechanics describes a three-dimensional wave. The possible positions of an electron are envisaged in three dimensions, x, y, z, and so the associated wave of the electron – which, according to Born’s statistical interpretation of the theory, provides the probabilities of the electron being in any of the positions describable for possible values of x, y and z – is three-dimensional.
The electrons, these three-dimensional waves, are pictured as orbiting the nucleus, which is itself in motion, vibrating and rotating. The total energy of an atom is given by the energies of the electrons, together with the rotational and vibrational energies of the nucleus. With just one electron – as in the case of hydrogen – this is complicated enough, but with two or more electrons, it becomes dizzyingly complicated, since, with the introduction of each new electron, one has to take into account the forces operating between one electron and another and between the electrons and the nucleus. Now, consider a molecule, which is made up of two or more atoms, and one can see how the complications increase exponentially. Think, for example, of a molecule of water, which is made of two hydrogen atoms and an oxygen atom. Each hydrogen atom has a single electron, while each oxygen atom has eight electrons. So, there are three nuclei and ten electrons in the molecule. To calculate the total energy of the molecule, one has to calculate the energy of each electron, the energy of each of the three nuclei and the energy of the molecule itself, which, of course, will also be in motion.
What Born and Oppenheimer presented in their joint paper was a mathematical technique – which has since become a cornerstone of the entire discipline of quantum chemistry –
for calculating the energy of a molecule through a series of approximations. First, the energies of the electrons are calculated on the assumption that the nuclei are stationary. This is an approximation, but not a wild one, since the mass of the nucleus is so much greater than that of the electrons that, from the point of view of the electron, so to speak, the nucleus is stationary. Then, the vibrations of the nucleus are calculated, and finally the rotational energy of the molecule. Though each of these calculations is an approximation, the result is to turn what had previously been a completely impossible calculation into one that, though difficult, is at least possible, thereby enabling one to bring the insights of quantum mechanics to bear on the questions that had attracted Oppenheimer to science in the first place – questions about the fundamental nature of chemical substances.
The paper had a difficult gestation. Its first draft, produced by Oppenheimer during the Easter vacation of 1927, was only five pages long. ‘I thought this was about right,’ Oppenheimer later said. ‘It was very light of touch and it seemed to me all that was necessary.’ Born thought otherwise. He was, he later recalled, ‘horrified’ by Oppenheimer’s first draft and used his position as the senior partner to insist upon a more expansive rewrite. ‘I didn’t like it,’ Oppenheimer later said, ‘but it was obviously not possible for me to protest to a senior author.’
Because of the wrangling over presentation, and the rewriting it necessitated, the paper was not sent off for publication until the end of August 1927. In the meantime, in June, Edwin Kemble visited Göttingen and reported to a Harvard colleague:
Oppenheimer is turning out to be even more brilliant than we thought when we had him at Harvard. He is turning out new work very rapidly and is able to hold his own with any of the galaxy of young mathematical physicists here. Unfortunately Born tells me that he has the same difficulty about expressing himself clearly in writing which we observed at Harvard.
