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American Journal of Physics

Vindications of Dirac’s electron, 1932–1934

Donald Franklin Moyer

Published Dec 1, 1981• 23 citations
Publisher

Abstract

This is the last of a three-part series. The first essay in the series described Dirac’s generalizations of quantum mechanics leading to his theory of the electron. The second essay surveyed evaluations of Dirac’s theory by other physicists, especially by Bohr who used Dirac’s speculations about negative energy electrons as evidence for the failure of quantum mechanics at nuclear dimensions. This essay shows how the material reality of positrons vindicated quantum mechanics and opened new paths for physics.

DOI
10.1119/1.12559

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Paul Dirac has been undoubtedly one of the central figures of the last century physics, contributing in several and remarkable ways to the development of quantum mechanics; he was also at the centre of an active community of physicists, with whom he had extensive interactions and correspondence. In particular, Dirac was in close contact with Bohr, Heisenberg and Pauli. For this reason, among others, Dirac is generally considered a supporter of the Copenhagen interpretation of quantum mechanics. Similarly, he was considered a physicist sympathetic with the positivistic attitude which shaped the development of quantum theory in the 1920s. Against this background, the aim of the present essay is twofold: on the one hand, we will argue that, analyzing specific examples taken from Dirac's published works, he can neither be considered a positivist nor a physicist methodologically guided by the observability doctrine. On the other hand, we will try to disentangle Dirac's figure from the mentioned Copenhagen interpretation, since in his long career he employed remarkably different—and often contradicting—methodological principles and philosophical perspectives with respect to those followed by the supporters of that interpretation. Quanta 2019; 8: 68–87.

arXiv:1911.02426•Quanta•Nov 10, 2019•4 citations
This is the last of a three-part series. The first essay in the series described Dirac’s generalizations of quantum mechanics leading to his theory of the electron. The second essay surveyed evaluations of Dirac’s theory by other physicists, especially by Bohr who used Dirac’s speculations about negative energy electrons as evidence for the failure of quantum mechanics at nuclear dimensions. This essay shows how the material reality of positrons vindicated quantum mechanics and opened new paths for physics.
Once I tried to teach some quantum mechanics to a class of law students, philosophers, and art historians. As an advertisement for the course I put together the most sensational quotations I could collect from the most authoritative practitioners of the subject. Heisenberg was a goldmine: “The concept of the objective reality of the elementary particles has thus evaporated…”; “the idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them … is impossible …” Feynman did his part too: “I think I can safely say that nobody understands quantum mechanics.” But I failed to turn up anything comparable in the writings of Bohr. Others attributed spectacular remarks to him, but he seemed to take pains to avoid any hint of the dramatic in his own writings. You don't pack them into your classroom with “The indivisibility of quantum phenomena finds its consequent expression in the circumstance that every definable subdivision would require a change of the experimental arrangement with the appearance of new individual phenomena,” or “the wider frame of complementarity directly expresses our position as regards the account of fundamental properties of matter presupposed in classical physical description but outside its scope.” I was therefore on the lookout for nuggets when I sat down to review these three volumes – a reissue of Bohr's collected essays on the revolutionary epistemological character of the quantum theory and on the implications of that revolution for other scientific and non-scientific areas of endeavor (the originals first appeared in 1934, 1958, and 1963.)
Meanwhile, on 18 September 1931, Heisenberg wrote to Bohr that ‘my work seems to be somewhat gray on gray’ (Pauli, 1985). By 1931 the bright future for quantum physics that seemed just over the horizon in the fall of 1927 paled with the formulation of relativistic quantum mechanics. Besides the as yet uninterpreted negative energy states, there was the electron's divergent self-energy and the continuous energy spectrum of β-particles in the supposedly two-body final state of nuclear β-decay, which implied that energy was not conserved in nuclear reactions (Bohr, 1932) and that perhaps quantum mechanics was not valid within the nucleus (to be discussed in Chapter 5). Measurement problems in a quantum theory of the electromagnetic field At the 20–25 October 1930 Solvay Conference, Bohr, Dirac, Heisenberg and Pauli concurred that fundamental difficulties in quantum electrodynamics might be clarified by investigating measurability of electromagnetic field quantities. Upon his return to Copenhagen from Brussels, Bohr continued discussing field measurements with Lev Landau, who happened to be visiting at Bohr's institute. In December 1930 Landau went on to Zürich, where he interested Pauli's assistant Rudolf Peierls in field measurements. Their deliberations led to a joint 1931 publication entitled ‘Extension of the uncertainty principle to relativistic quantum theory’ (Landau and Peierls, 1931). Measurement of an electric field can be accomplished through measuring the change in momentum of a charged test body placed in the field.
This book gives a detailed study of the development and the interpretation given to Niels Bohr's Principle of Correspondence. It also describes the role that this principle played in guiding Bohr's research over the critical period from 1920 to 1927. Quantum mechanics, developed in the 1920s and 1930s by Bohr, Heisenberg, Born, Schrödinger and Dirac, represents one of the most profound turning points in science. This theory required a wholly new kind of physics in which many of the principles, concepts and models representing reality, that had formed the basis of classical physics since Galileo and Newton, had to be abandoned. This book re-examines the birth of quantum mechanics, in particular examining the development of crucial and original insights of Niels Bohr.
Paul Dirac has been undoubtedly one of the central figures of the last century physics, contributing in several and remarkable ways to the development of quantum mechanics; he was also at the centre of an active community of physicists, with whom he had extensive interactions and correspondence. In particular, Dirac was in close contact with Bohr, Heisenberg and Pauli. For this reason, among others, Dirac is generally considered a supporter of the Copenhagen interpretation of quantum mechanics. Similarly, he was considered a physicist sympathetic with the positivistic attitude which shaped the development of quantum theory in the 1920s. Against this background, the aim of the present essay is twofold: on the one hand, we will argue that, analyzing specific examples taken from Dirac's published works, he can neither be considered a positivist nor a physicist methodologically guided by the observability doctrine. On the other hand, we will try to disentangle Dirac's figure from the mentioned Copenhagen interpretation, since in his long career he employed remarkably different—and often contradicting—methodological principles and philosophical perspectives with respect to those followed by the supporters of that interpretation. Quanta 2019; 8: 68–87.