A Theory of Electrons and Protons.

London: Harrison & Sons for the Royal Society, 1930.

First edition of Dirac’s prediction of anti-matter – although he did not accept it as such until a year later (see below) – and the advent of the dynamical view of the vacuum which was fundamental to the later development of quantum field theory. “The consensus among today’s scientists is that Dirac’s role in foreseeing the existence of the positron is one of the greatest achievements in science. In 2002, shortly after the centenary of Dirac’s birth, the theoretical physicist Kurt Gottfried went further: “Physics has produced other far-fetched predictions that have subsequently been confirmed by experiment. But Dirac’s prediction of anti-matter stands alone in being motivated solely by faith in pure theory, without any hint from data, and yet revealing a deep and universal property of nature”” (Farmelo, p. 226). “Dirac divided the initial wave equation into two simpler ones, each providing solutions independently. It now appeared that one of the solution systems required the existence of positive electrons having the same mass and charge as the known negative electrons. This initially posed considerable difficulty for Dirac’s theory, since positively charged particles were known only in the form of the heavy atom nucleus. This difficulty which at first opposed the theory has now become a brilliant confirmation of its validity. For later on, positive electrons, the positrons, whose existence was stipulated in Dirac’s theoretical investigation, have been found by experiment” (Nobel Prize Presentation Speech). Dirac shared the 1933 Nobel Prize in Physics with Schrödinger for “for the discovery of new productive forms of atomic theory.” OCLC lists only the copy at the University of Florida, where Dirac spent his final years and where many of his papers are held. No copies in auction records.

In 1928, Dirac published his discovery of the ‘Dirac equation’, his relativistic wave equation for the electron, which “ranks among the highest achievements of twentieth-century science” (Pais, p. 290). However, “it was clear to Dirac and several of his colleagues that the relativistic electron theory of 1928 led to strange consequences. The problem, sometimes referred to as the “± difficulty,” had its basis in the Dirac equation, which formally included solutions with negative energy. Contrary to the situation in classical physics, these could not be dismissed as nonphysical but had to be taken seriously – that is, somehow to be related to some objects of nature. In November 1929 Dirac believed he had found the solution to the problem. “There is a simple way of avoiding the difficulty of electrons having negative kinetic energy,” he wrote to Bohr, and continued: “[I]f the electron is started off with a +ve energy, there will be a finite probability of its suddenly changing into a state of negative energy and emitting the surplus energy in the form of high-frequency radiation… [I]f all states of –ve energy are occupied and also a few of +ve energy, those electrons with +ve energy will be unable to make transitions to states of –ve energy and will therefore have to behave quite properly… It seems reasonable to assume that not all states of negative energy are occupied, but that there are a few vacancies or ‘holes’ … [O]ne can easily see that such a hole would move in an electromagnetic field as though it had a +ve charge. These holes I believe to be protons.”

“Dirac’s proton-as-electron theory, published in 1930 [the present paper], assumed a world of negative energy states occupied by an infinite number of electrons governed by Pauli’s exclusion principle. Only the few unoccupied states, the “holes,” would appear as observable physical entities. But why would they appear as protons, two thousand times as heavy as electrons? There are two reasons for Dirac’s choice: For one thing, if protons and electrons were the only elementary particles – as almost all physicists believed at the time – there seemed to be no other possibility; for another thing, the hypothesis would be the realization of the age-old and, to Dirac, highly attractive “dream of philosophers.”

“Attractive or not, the hypothesis was universally met with skepticism and immediately ran into serious problems. For example, if the proton were the electron’s antiparticle (a name not yet introduced), [the electron and the proton] would supposedly annihilate… and calculations showed that the mean lifetime of matter would, in that case, be absurdly low, about 10-9 seconds. This argument alone was not sufficient to convince Dirac, but in the spring of 1931 he realized (as others had done) that the hole would have to have the same mass as the electron. In the new version, as it appeared in a remarkable paper in the Proceedings of the Royal Society [‘Quantised singularities in the electromagnetic field,’ Vol. 133, pp. 60-72], the antielectron was introduced for the first time as “a new kind of particle, unknown to experimental physics, having the same mass and opposite charge to an electron” … in 1931 the antielectron was a purely hypothetical particle, and most physicists declined to take Dirac’s theory seriously. It was only later that it became recognized as “perhaps the biggest jump of all big jumps in physics of our century,” as Heisenberg generously called it in 1973.

“The status of the antielectron… changed during 1932-33. At the California Institute of Technology, Carl Anderson, a former student of Millikan, noted in cloud chamber photographs from the cosmic radiation some tracks that he thought might be due to protons. In a later paper in March 1933, he suggested that he had discovered a positively-charged electron, or a “positron” as he called it” (Kragh, pp. 190-192).

As well as predicting the existence of antimatter, the present paper also transformed physicists’ view of the nature of ‘empty space’ – since it is not really empty, physicists refer to it as ‘the vacuum.’ “In Dirac’s proposal, the vacuum is full of negative-energy electrons. This makes the vacuum a medium, with dynamical properties of its own. For example, photons can interact with the vacuum. One thing that can happen is that if you shine a light on the vacuum, providing photons with enough energy, then a negative-energy electron can absorb one of these photons, and go into a positive-energy solution. The positive-energy solution would be observed as an ordinary electron, of course. But in the final state there is also a hole in the vacuum, because the solution originally occupied by the negative-energy electron is no longer occupied” (Wilczek, p. 55). This is the phenomenon of ‘pair-production,’ in which an electron-positron pair is created spontaneously. This dynamical view of the vacuum is fundamental to quantum field theory, developed starting in the mid-1930s, which enables the positron to be treated as a ‘real’ particle rather than the absence of a particle, and makes the vacuum the state in which no particles exist instead of an infinite sea of particles.

Graham Farmelo, The Strangest Man: The Hidden Life of Paul Dirac, Quantum Genius, 2009; Helge Kragh, Quantum generations, 1999; Abraham Pais, Inward bound, 1988; Frank Wilczek, ‘The Dirac equation,’ International Journal of Modern Physics A, Vol. 19 Supplement (2004), pp. 45-74. For a very detailed account of the genesis of this paper, see Kragh, Dirac: A scientific biography, 1990, pp. 87-103.

Pp. 360-365 in Proceedings of the Royal Society, Series A, Vol. 126, No. A801. The entire issue offered here. 8vo (254 x 177 mm), pp. v-viii, 183-365. Original printed wrappers. A very fine and unrestored copy.

Item #3519

Price: $2,200.00

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