Paul Dirac and the Nobel Prize in Physics

Despite the success of the Bohr model and later improvements by Arnold Sommerfeld, it was clear that even the relatively simple spectrum of the helium atom was impenetrable to the QM developed and applied between 1900 and 1925. Heisenberg was the one who took the first, bold step of formulating a new QM by throwing the nonobservable Bohr atomic orbits overboard. Instead, Heisenberg’s QM was based on relationships between observables, such as position and momentum for an oscillator. Heisenberg’s groundbreaking paper³ was received by Zeitschrift für Physik on 29 July 1925 and published in December.

Dirac, then a doctoral student at the University of Cambridge, learned about the paper in advance of publication through his adviser Ralph Fowler, whom Heisenberg visited on his trip to the UK during the summer of 1925. Later that year Dirac came up with his own mathematical formulation of Heisenberg’s QM.⁴ Meanwhile in Germany, Max Born, Pascual Jordan, and Heisenberg were also working on a mathematical formulation to represent observables with matrices. In Austria, Schrödinger was inspired by Louis de Broglie’s concept of the electron’s wave nature and formulated his own wave mechanics.⁵ 

However, neither Heisenberg’s matrix mechanics nor Schrödinger’s wave mechanics incorporated the special theory of relativity. Another problem was that electron spin had been incorporated into the nonrelativistic quantum equations ad hoc, which resulted in a workable theory that could explain atomic spectra but provided no insight to the origin of spin.⁶ It was Dirac who took the decisive step⁷ in 1928. His bold idea of writing the wave equation in a relativistic invariant form that was linear in time had a profound impact on physics. That brilliant mathematical insight led to predictions of electron spin and magnetic moment without any ad hoc assumptions. By going from scalar equations to a matrix form, Dirac also introduced the beautiful mathematical formalism that preserves Lorentz invariance:

The introduced matrices α and β, now named after Dirac, act on the wavefunction of the electron. The electron can be written as a four-component spinor: two components for it as particle and antiparticle, and two components for its spin as a fermion. For massless particles, m = 0 and the relationship between energy and momentum, the Dirac dispersion, is E = cp. Subsequent extensions by Hermann Weyl and Ettore Majorana led to representations that are relevant for modern condensed-matter realizations of Weyl and Majorana fermions.

The seed of the prediction for the antiparticle is apparent from this equation. If the wavefunction of the observed electron required only two components with spin up and spin down, then why are two “unused” components of the spinor needed? Those unused components correspond to negative-energy solutions. At the time, negative-energy solutions were considered undesirable physics, but they predicted an antiparticle, or a positive electron in the terms of Dirac’s day. Dirac’s equation thus led to a clear prediction of antiparticles and antimatter, one of the great triumphs of physics in the 20th century.

Meanwhile, de Broglie was awarded the 1929 Nobel Prize in Physics for “his discovery of the wave nature of electrons,” a theoretical achievement the committee was not entirely sanguine about rewarding. As late as 1928, the committee still hesitated because the members felt the experimental evidence for de Broglie’s work was not sufficiently strong and rejected him in favor of experimentalist Owen Willans Richardson. One year later, however, the committee was convinced that the experimental demonstration of the wave nature of electrons was solid enough to award the prize to de Broglie.

The 1930 physics Nobel went to Chandrasekhara Raman for his work on the scattering of light known as Raman spectroscopy, an experimental achievement that created far less consternation among the committee members. Indeed, they were so confident in the value of Raman’s work that they nearly upheld Nobel’s wish to reward a discovery from “the preceding year”; Raman made his discovery in early 1928. But as the new decade began, pressure was mounting for the committee to award the prize to work on the new QM.

Untangling the reasons behind particular nominations—or their absence—is no easy task. The archives of the Nobel Prize in Stockholm are closely held, and access is granted selectively. Material older than 50 years is open, but only by application and only to historians of science. Newer material is available only to elected members of the Royal Swedish Academy of Sciences.

Furthermore, in contrast to the present-day practice of asking the international physics community to submit confidential expert reports about nominees, in the first six decades of the physics prize, the reports were mainly written by members of the committee and always in Swedish. The reports concerning the Nobel Prize nominees in 1932 and 1933, for example, were mostly written by committee member Carl Wilhelm Oseen, director of the Nobel Institute for Theoretical Physics in Stockholm. The international physics community is visible in the early 1930s only through the nomination letters, which were obviously important but varied in their level of detail.

If we look at nominations from the early 1930s, the following picture emerges. Between 1928 and 1933, the period when the committee was under the most pressure to choose a prize recipient who had worked on the new QM, Schrödinger received 41 nominations; Heisenberg, 29; and Dirac, just 3. The most interesting nominations came from two of the founding fathers of QM, Bohr and Einstein. Writing in Danish, Bohr nominated Heisenberg, arguing that he should be first in line to be recognized for the development of QM. He placed Schrödinger second behind Heisenberg, and never mentioned Dirac at all.⁸ 

Einstein’s nomination letter, shown in figure 2, was written from his summer house outside Berlin and is noteworthy in several ways.⁹ Einstein was not very active as a nominator, but when he did nominate someone, he had the committee’s ear. According to his letter, two men stood at the front of the line for a QM Nobel: Schrödinger and Heisenberg. They had worked independently, and Einstein argued that their work was of such importance that a shared prize should not be considered. Forced to make a recommendation about who should receive the prize first, Einstein put Schrödinger slightly ahead of Heisenberg. Once again, Dirac was not mentioned and, in fact, was never nominated by Einstein.

The date of Einstein’s letter, 30 September 1931, is peculiar. It was just barely a month before the Royal Swedish Academy of Sciences was scheduled to announce the 1931 prize. The deadline for nominations, 31 January, had long since passed. Einstein must have known his letter would not count as a nomination for 1931, only for 1932. We can only speculate about his motivation for sending the letter off-cycle, but there seems to have been a growing realization among physicists that the committee ought to acknowledge the new QM.

With such a large number of nominations for Heisenberg and Schrödinger, including from both Bohr and Einstein (albeit a late one), why not award the prize to one or both of them? And why did no one mention Dirac? The committee’s problem was how to reconcile a prize for the development of QM with Alfred Nobel’s will, which required a “discovery” or “invention” in the field of physics. Oseen, the only theorist on the committee, seems to have particularly struggled with that quandary. True, the new QM had systematized vast swaths of data in atomic physics, but had it led to any new experimental discoveries? In a report to the Nobel Committee dated 16 March 1929, Oseen’s conclusion was “no.”

Swedish chemist Theodor Svedberg, who had received the 1926 Nobel Prize in Chemistry, tried to help his physics colleagues by nominating Heisenberg in January 1930 for his work on the allotropic forms of hydrogen. In 1927 Heisenberg had predicted that molecular ortho-hydrogen (parallel nuclear spins) should be three times as abundant as para-hydrogen (antiparallel spins), and in 1929 the prediction was experimentally verified. That work was too close to chemistry for the members of the physics prize committee, but the citation for Heisenberg’s Nobel Prize mentions the allotropic forms of hydrogen.

Unable to agree on a prize for either Heisenberg or Schrödinger, but also unable to find candidates they preferred, the committee members ultimately decided to postpone awarding the 1931 physics prize. When deliberations for the 1931 and 1932 prizes resumed, they were still ambivalent about their most-nominated candidates, but support was building. Erik Hulthén, an experimentalist whose specialty was molecular spectroscopy, argued that there were now many experimental results, in particular for diatomic molecules, that could only be satisfactorily explained with the new QM. He also emphasized connections between phenomena in nuclear physics, such as radioactivity, and Heisenberg’s uncertainty principle.

Oseen, on the other hand, insisted that the new QM was nonrelativistic—an inexcusable omission, in his view. Dirac’s theory was relativistic, but Oseen thought it had insurmountable problems—namely, a lack of experimental verification. At the same time, the committee was still unable to identify anyone else who was more worthy of a Nobel Prize than Heisenberg and Schrödinger. Once again, the decision was postponed. The Nobel Prize for 1931 would therefore never be awarded; a prize can only be reserved until the following year.

Before 1933 Dirac received only one Nobel nomination, in 1929 by Hans Thirring at the University of Vienna. In 1933 he received two. One was from Czesław Białobrzeski at the University of Warsaw, who also nominated Heisenberg. The other was from William Lawrence Bragg, recipient of the 1915 Nobel Prize in Physics. Bragg’s nomination letter¹⁰ explicitly put Dirac on equal footing with Heisenberg and Schrödinger (see figure 3), and it prompted Oseen to write a long report¹¹ about Dirac, which he submitted to the committee in March 1933.

Oseen could not accept Dirac as an equal to Schrödinger and especially to Heisenberg. Was Dirac a scientific innovator of the same caliber as Nobel recipients Max Planck, Einstein, and Bohr? For Oseen, the answer was definitely no. He compared Dirac’s contributions with those of Born and Jordan in Germany. Their efforts to give a mathematical framework to Heisenberg’s QM were never seriously considered worthy of a Nobel Prize. Furthermore, Dirac’s 1928 paper had predicted not only the real physical states but also negative energy states in which the electron had positive charge. That charge, though, had never been observed. It is clear from Oseen’s report that Dirac was not initially a contender for either the 1932 or 1933 prize. He had done work that was correct but not first, and when he was first, he was not correct—or at least not confirmed.

But a remarkable finding was about to paint Dirac’s work in a new light. The same month that Oseen submitted his report about Dirac to the committee, US physicist Carl Anderson published a paper in Physical Review about his discovery of the positive electron.¹² Dirac’s theory had now made a prediction that had been experimentally verified.

The committee members did not change their stance immediately. At the committee’s June meeting, Heisenberg and Schrödinger were shortlisted, but Dirac was not. Anderson’s discovery, however, was stirring excitement among physicists. That summer, J. Robert Oppenheimer and Milton Plesset wrote a letter to Physical Review in which they suggested that pairs of negative and positive electrons could be created in the vicinity of a nucleus.¹³ By applying Dirac’s relativistic electron theory, they calculated the probability of pair production as a result of the gamma-ray irradiation of matter. The results were in fairly good agreement with experimental results published by Patrick Blackett and Giuseppe Occhialini earlier that year.¹⁴ Now Dirac’s theory had both qualitative confirmations and an approximate quantitative confirmation.

Those developments prompted Oseen to write an addendum to his March report for the committee’s meeting in September, at which it was expected to make its recommendations for the 1932 and 1933 Nobel Prizes in Physics. On 25 September 1933, the committee recommended that Heisenberg should receive the 1932 reserved prize and that Schrödinger and Dirac should be jointly awarded the 1933 prize “for the discovery of new productive forms of atomic theory.” In Oseen’s undated amendment, Dirac’s name was inserted by hand into the typewritten recommendation.¹⁵ 

The Royal Swedish Academy of Sciences followed the committee’s recommendation when it made the final decision on 9 November 1933 (see figure 4). In committee member Henning Pleijel’s presentation speech on 10 December, he said to Dirac, “The experimental discovery of the existence of the positron has in a brilliant way confirmed your theory.”¹⁶ The Swedish newspaper Dagens Nyheter reported the next day, “Then followed [after Heisenberg], one after the other, professor Schrödinger and young professor Dirac, who staggered down [the stairs] in a real old-fashioned professor’s white tie. But this didn’t prevent mama Dirac from being somewhat proud where she was sitting and stretching herself on the third row behind the high-sounding foreign ministers.”

We now know that Dirac’s elegant equation has applications in a wide range of fields, including materials science (see the box). Bragg was the first to suggest that Heisenberg, Schrödinger, and Dirac were equals as physicists. Posterity has confirmed his claim—and for some of us, Dirac is perhaps first among those equals.

We are thankful to the Royal Swedish Academy of Sciences for access to its Nobel archives and to Karl Grandin, head of the archives, for valuable comments. We are grateful to Konrad Kleinknecht for comments. Alexander Balatsky’s work was supported by the Villum Centre of Excellence for Dirac Materials, grant 11744, and Knut and Alice Wallenberg Foundation grant 2013.0096.

Mats Larsson is a professor in the department of physics at Stockholm University and a member of the Royal Swedish Academy of Sciences. Alexander Balatsky is a professor of physics at the Nordic Institute for Theoretical Physics in Stockholm and at the University of Connecticut in Storrs.