Although not well known to the general public, Paul Adrien Maurice Dirac hardly needs to be introduced to physicists and historians of science. Born in Bristol in 1902 as a Swiss citizen—his father was Swiss and Paul only acquired British nationality in 1919—he became one of the most important theoretical physicists ever. His impact on modern physics may even have been greater than that of
Dirac’s genius was recognized early on. For example, he was part of the exclusive company of physicists invited to the famous
While still a Ph.D. student, under the supervision of
The content of Dirac’s early lectures formed the basis of the textbook that appeared in the summer of 1930, and which he subsequently used for his course. Given the scarcity of suitable textbooks in quantum mechanics at the time, and that Dirac had already prepared extensive lecture notes on the subject, it was natural for him to transform and update these into a proper textbook. Indeed, with respect to both structure and content there is a great deal of similarity between his lecture notes of 1927–28 and his textbook. Moreover, it was important for Dirac to present the principles of the new quantum mechanics in the way he thought they should be presented, namely as a concise and coherent symbolic calculus that allowed comparison between calculated quantities and those found experimentally. To him, the new physics was basically a formal scheme that allowed the calculation of experimental results, while it had nothing to say about ontological questions. The proper way of presenting quantum mechanics must necessarily be abstract, he wrote, for the new theory is “built up from physical concepts which cannot be explained in terms of things previously known to the student, which cannot even be explained adequately in words at all” (Dirac 1930). It was this abstract picture of quantum mechanics that Principles conveyed to its readers.
The idea of writing a textbook was not Dirac’s, but seems to have come from James Gerald Crowther, a science journalist three years older than Dirac. This also accounts for the fact that the book was published by Oxford University Press and not, as would otherwise have been natural, by Cambridge University Press. Crowther, who had joined Oxford University Press in 1924 as representative for scientific and technical books, established a close relationship with physicists at the Cavendish Laboratory, including
It should be kept in mind that there were very few British books on quantum theory at the time. According to a catalogue issued by the British Science Guild, in 1930 there were only fourteen British books on quantum topics, and many of them were translations from German or bound collections of lectures.^{4} Although Principles was not the first book on quantum theory in Britain, it was one of the first. Dirac started writing the book in 1928, but due to travels and a busy scientific schedule—much of it occupied with the consequences of his new theory of the electron—progress was slow. By February 1930 the galley proofs of the book were ready, and about half a year later it appeared in the bookshops as the first volume in the Oxford International Series of Monographs on Physics. The preface was dated 29 May 1930, and the price was 17 shillings and 6 pence.
Principles of Quantum Mechanics became a great (and probably surprising) success, with the first edition selling about two thousand copies. The translations, and especially those in German and Russian, sold even better. The book quickly established itself as the standard work on quantum mechanics, not only used by students as a textbook but also by many experienced physicists. The mathematician HarishChandra recalled that he, while an undergraduate of Allahabad University in India, came across a copy of the 1930 edition in the university’s library. “[I] was immediately fascinated by it,” he said. “The exposition was so lucid and elegant that it gave me the illusion of having understood most of it and prompted in me a strong desire to devote my life to theoretical physics” (HarishChandra 1987, 34).^{5} Principles came out in a substantially rewritten second edition in 1935, and still later editions appeared in 1947 and 1958, with reprints in 1967, 1971, 1974, and 1984. The third and fourth editions differed from the one of 1935 mainly in Dirac’s use of the socalled “bracket” notation that he had developed in 1939 and which makes use of quantum states labeled as, for example, and (called a “bra vector” and a “ket vector”) (Dirac 1939; HarishChandra 1987, 34).^{6}
Principles was an enduring success. Paperback reprints of the fourth edition appeared as late as 1993, and the book is still in demand, eighty years after it was first published. The American physicist Philip Morrison exaggerated when he said that “everybody who had ever looked at books had a copy of Dirac,” but as far as physicists were concerned, it may have been close to the truth (Weiner 1972, 131). In this essay, I shall be concerned with the first two editions only, those of 1930 and 1935.
Dirac’s book on the principles of quantum mechanics was translated into German (1930), French (1931), Russian (1932), and Japanese (1936), and possibly into some other languages as well. The German translation, made by Werner Bloch, was arranged at an early time, as evidenced by a letter from Dirac to his Russian colleague Igor Tamm of January 1929, and it appeared only shortly after the English edition.^{7} Dirac, who knew German well, checked the translation.
With good connections to physicists in the Soviet Union, Dirac was also actively involved in bringing out a Russian translation of his book. In the summer of 1930, while attending a conference in Kharkov, he brought the corrected proof sheets with him and handed them over to the Russian theorist
Abstract and mostly concerned with foundational matters, Principles had little to say about the many applications of quantum mechanics. To make up for this deficiency, Dirac added, on the request of Ivanenko, an extra chapter in which he covered various approximation methods, such as those developed by
Sommerfeld’s supplementary volume Wellenmechanischer Ergänzungsband appears as a collection of solutions of a series of particular problems; de Broglie’s book Introduction à l’étude de la mécanique ondulatoire is only an introduction, devoted mainly to the transition from classical to quantum mechanics; Born and Jordan’s Elementare Quantenmechanik is an exposition of a deliberately restricted part of the material that is amenable to analysis by a special method (Schrödinger’s equation does not appear in the book); finally, Frenkel’s Einführung in die Wellenmechanik is the most accessible of the books for reading but, like all the others, does not give an exposition of the system of quantum mechanics. It is the exposition of the system that Dirac’s book gives, truly in the highest form, free from all provincialism, […] In our view, the book that is closest in nature, Weyl’s Gruppentheorie und Quantenmechanik—highly regarded by Dirac—is significantly inferior to Dirac’s book, on account of both the superfluous mathematical formalism and the actual style of the exposition.^{9} (Dalitz 1995, 473)
In 1930 theoretical physics in Japan was beginning to develop under the leadership of
The Principles of Quantum Mechanics was widely reviewed in the physics journals, in almost all cases positively and in some enthusiastically. It was a common feature of the reviews to praise the book for its directness, generality, and completeness. Some found it to be elegant. In a review of the German translation, the young Swiss physicist (and later Nobel laureate)
When
Dirac’s book was reviewed anonymously in Nature alongside two other works on quantum theory,
He bids us throw aside preconceived ideas regarding the nature of phenomena and admit the existence of a substratum of which it is impossible to form a picture. We may describe this as the application of “pure thought” to physics, and it is this which makes Dirac’s method more profound than that of other writers. […] He introduces a new attitude of mind towards the investigation of Nature, and the interest lies in watching the development of progress of his ideas. There can be no doubt that his work ranks as one of the high achievements of contemporary physics.
Other reviews of Dirac’s book appeared in journals not read by the majority of physicists.
The physicist and philosopher
Finally, it is worth mentioning that
Dirac, to whom, in my opinion, we owe the most logically perfect presentation of this theory, rightly points out that it appears, for example, to be by no means easy to give a theoretical description of a photon that shall contain within it the reasons that determine whether or not the photon will pass a polarizer set obliquely in its path. (Einstein 1931, 73)
Compared with other textbooks in theoretical physics, the format of the first edition of Principles was unusual. With no illustrations and no index, it was not a readerfriendly work. Again in contrast to other books on quantum mechanics, it was completely ahistorical and contained almost no references to the research literature. To be precise, altogether it included twelve references in its 264 pages. Dirac admitted in his preface that his chosen way of representation had “necessitated a complete break from the historical line of development,” but this he considered to be an advantage rather than a disadvantage. Although a considerable part of Principles was based on Dirac’s own works and discoveries, there was no indication at all of which parts were his own contributions, nor were there any references to them. While some scientists use the medium of the textbook to communicate and advertise their own work, this was not the case with Dirac. Readers unacquainted with the development of quantum physics would not guess that most of the sections on transformation theory, the function, radiation theory, and relativistic quantum mechanics were, in fact, about and based on the author’s own works. This kind of anonymity does not imply that Principles was a neutral presentation of an accepted theory. Dirac clearly had an agenda in writing the book, namely to disseminate what he thought were the basic principles and proper methods of quantum mechanics. He wanted to shape a theory which had not yet found its final shape.
The book was basically divided in two parts of about equal size. The first part dealt with the principles and general formalism, followed by applications of the theory, including perturbation theory, collision problems, quantum statistics, and radiation theory. It ended with a chapter on the new relativistic theory of the electron. Dirac’s original exposition is illustrated by
In the preface to the edition of 1930, Dirac stressed the abstract and unvisualizable nature of quantum mechanics and how different it was from classical physics. The aim of physics in the classical tradition was “to make assumptions about the mechanism and forces connecting […] observable objects, to account for their behavior in the simplest possible way.” But the new developments, not only in quantum mechanics but also in relativity theory, had demonstrated that “nature works on a different plane.” Nature’s fundamental laws, Dirac said, “do not govern the world as it appears in our mental picture in any very direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies.” Contrary to other works on quantum theory, which were based on the method of either matrix mechanics or wave mechanics, Dirac chose a more general representation. This representation, which he called the symbolic method, was harder to learn but “seems to go more deeply into the nature of things.”
The first chapter, on “The Principle of Superposition,” was purely qualitative, involving no mathematics. He carefully discussed the meaning of superposition by illustrating it with the case of polarization of light, emphasizing that “the superposition that occurs in quantum mechanics is of an essentially different nature from that occurring in the classical theory” (Dirac 1930, I, 11).^{13} Another very important term was the concept of “state,” which he defined as referring to the condition of a system being independent of time, that is, to a region of fourdimensional spacetime and not to threedimensional space. “A system, when once prepared in a given state, remains in that state as long as it remains undisturbed,” he wrote (I, 9). He further stated that if an observation is made on a system in any given state, “the result will not in general be determinate, i.e., if the experiment is repeated several times under identical conditions several different results may be obtained” (I, 10).
In the second edition of 1935, Dirac used the term “state” in a different sense, namely, to denote the condition of a physical system at a given time and not for all time. That is, he used it in a threedimensional, nonrelativistic sense, which might seem to be a retrograde step compared with the definition given in the first edition. However, Dirac motivated the change by arguing that it made the exposition clearer and also that “the fundamental ideas of the present quantum mechanics are in need of serious alterations at just this point” (II, v). He undoubtedly had in mind the problems of formulating a consistent relativistic theory of quantum electrodynamics with which he and other physicists were struggling at the time. Dirac perceived these problems to be so serious that he was willing to sacrifice the relativistic theory and perhaps even such a fundamental principle as the conservation of energy. As he wrote in a paper of early 1936:
The second, somewhat enlarged edition of Principles retained the basic structure of the first edition, but was written in a less abstract and symbolic form. “This should make the work suitable for a wider circle of readers,” Dirac said, adding that “the reader who likes abstractness for its own sake may prefer the style of the first edition” (II, v). Upon receiving a copy of the new edition, Heisenberg expressed his satisfaction with the work being “more human [menschlicher] than earlier,”^{14} a response shared by many other physicists. For example, the American physicist
Yet, not all reviewers were impressed by the pedagogical quality of the new, more menschlich edition.
At the time Dirac completed Principles, in early 1930, he was much occupied with the “± difficulty” that arose from his relativistic wave equation, namely, how to interpret the negativeenergy solutions in physical terms. In the final chapter of Principles, Dirac presented his new theory of the electron much as he had presented it in 1928. In dealing with the states formally referring to negative energies, he proposed that the antielectrons—unoccupied holes in the sea of negative energy states—were protons. The unifying idea of identifying antielectrons with protons, and thus reducing all matter to one elementary particle, appealed greatly to him. But of course he realized that it was hard “to account for the very considerable observed differences between electrons and protons, in particular their different masses.” In the very last sentence of the book he stated optimistically: “Possibly the solution of this difficulty will be found in a better understanding of the nature of interaction” (I, 257).
This did not happen. In 1931 Dirac famously predicted the existence of positive electrons, which were subsequently discovered in cosmic rays and known as positrons. Much of the discussion in the second edition was identical with the one in the first, except that “proton” was now replaced by “positron.” Concerning the negativeenergy solutions, Dirac wrote that they referred to “a new kind of particle having the mass of an electron and opposite charge. Such particles have been observed experimentally and are called positrons” (II, 271).
Contrary to the presentation of quantum mechanics by
Among the things not included in either of the editions was the complementarity principle, which played such an important role in Heisenberg’s contemporary Physikalische Prinzipien der Quantentheorie. It was the purpose of
The symbolic method which was such a characteristic feature of Principles, the first edition in particular, was a main reason why many readers found the book difficult to understand. The method was based on “certain symbols which we say denote physical things [… and which] we shall use in algebraic analysis in accordance with certain axioms” (I, 18). Dirac wanted to present the general theory of quantum mechanics in a way that was as free as possible from physical interpretation:
One does not anywhere specify the exact nature of the symbols employed, nor is such specification at all necessary. They are used all the time in an abstract way, the algebraic axioms that they satisfy and the connexion between equations involving them and physical conditions being all that is required. The axioms, together with their connexions, contain a number of physical laws, which cannot conveniently be analyzed or even stated in any other way. (ibid.)
Dirac’s philosophy of physics, in the form that implicitly permeated much of his book, was markedly instrumentalist and abstract. Quantum physics was presented as a formal scheme that allowed the calculation of experimental results, and there was nothing more to it. In his lecture notes from 1927–28, he emphasized that the new theory “deals essentially only with observable quantities, a very satisfactory feature.” Moreover: “[t]he theory enables one to calculate only observable quantities […] and any theories which try to give a more detailed description of the phenomena are useless.”^{17} The same message was spelled out in Principles, in both the first and the second edition. For example: “[t]he description which quantum mechanics allows us to give is merely a manner of speaking which is of value in helping us to deduce and to remember the results of experiments and which never leads to wrong conclusions” (I, 5). He added, significantly: “[o]ne should not try to give too much meaning to it.” In his review of the book,
A mathematical machine is set up, and without asserting or believing that it is the same as Nature’s machine, we put in data at one end and take out the results at the other. As long as these results tally with those of Nature, […] we regard the machine as a satisfying theory. But so soon as a result is discovered not reproduced by the machine, we proceed to modify the machine until it produces the new result as well. (LennardJones 1931, 505–506)
This was Dirac’s view of quantum theory, but it was not shared by LennardJones who wanted a “rather more ambitious” object for theoretical physics. He deplored that the quantum theorist, at least according to Dirac, “must for ever abandon any hope of providing a satisfying description of the whole course of phenomena.” In this respect,
Dirac, never much of a philosopher, was in general agreement with the
Although one can reasonably label Dirac, at the time he wrote Principles, a quantum instrumentalist, there are more grounds to doubt that he shared the positivistic view of physics that characterized
Regarding Dirac’s later advocacy of mathematical beauty as a royal road to progress in fundamental physics, it is noteworthy that, in the early 1930s, he still considered mathematics more from the perspective of an engineer than a mathematician. Although quantum mechanics, as presented in Principles, was said to be “essentially mathematical,” this referred only to the formalism. “All the same,” Dirac wrote, “the mathematics is only a tool and one should learn to hold the physical ideas in one’s mind without reference to the mathematical form” (I, vi). Indeed, while many physicists and students found Dirac’s book heavily mathematical, mathematicians were unimpressed by the way he used mathematics. “Dirac permits himself a number of mathematical liberties,” wrote the mathematician
The dissatisfaction of contemporary mathematicians with Dirac’s methods was expressed by
While Dirac presents his reasoning with admirable simplicity and allows himself to be guided at every step by physical intuition—refusing at several places to be burdened by the impediment of mathematical rigor—von Neumann goes at his problems equipped with the nicest of modern mathematical tools and analyses it to the satisfaction of those whose demands for logical completeness are most exacting.^{20}
Contrary to
As I have indicated, Principles was a difficult work and not pedagogical in the ordinary sense. Dirac based it to a large extent on his lectures of 1927–29 and, after having completed it, used it for the lectures on quantum mechanics he gave over most of the next four decades. During the 1930s, there was another regular lecture course on quantum physics in Cambridge, given by Alan Wilson in the fall (Michaelmas) term, while Dirac gave his lectures in the spring (Lent) term. Wilson’s course was more practically oriented, based on applications of the Schrödinger equation (Wilson 1984).
Although Dirac did not specifically refer to his book as a textbook, in the preface to the first edition he did mention students, and he seems to have regarded it as both a textbook and an exposition of the principles of quantum theory aimed at physicists. I doubt if he gave much thought to the intended readership. Because of Dirac’s lectures, which closely followed his book, Principles exerted considerable influence on a generation of Cambridge physicists. “His influence was not very great as a teacher,”
I do not know how much and at which levels Principles was used as a textbook outside Cambridge, but my guess is that it was not widely used for lectures or in the classroom. Even if this guess were right, however, it was much used by physicists, both young and more experienced. The number of copies sold speaks for itself. It rarely happens that textbooks are cited in research papers, but Principles was an exception to the rule. In the physics papers of the 1930s, there were many references to Dirac’s book, which probably exerted a greater influence on research physicists than students.
In the early stages of a new science, discipline, or research field, textbooks play an important role by legitimating the field and formulating the principles on which it builds. Whether explicitly or implicitly, the first generation of textbooks articulate the constitutive features of the new research field, which is particularly important in changes of a more revolutionary nature, such as quantum mechanics. Because the field is not yet fully consolidated, early textbooks may differ considerably in their understanding of the field, both as to content and methodology. It is almost inevitable that what an author presents has the character of a partisan text, at least in the sense that the book reflects the author’s view of the new field of science.^{22} Dirac’s Principles of Quantum Mechanics was far from polemical, but it was nonetheless a textbook that conveyed a view of quantum mechanics that may well be called partisan or even personal.
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 (1936). Does Conservation of Energy Hold in Atomic Processes?. Nature 137: 298299
 (1939). A New Notation for Quantum Mechanics. Proceedings of the Cambridge Philosophical Society 35: 416418
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[1]
On Dirac’s life and science, see (Dalitz and Peierls 1986; Kursunoglu and Wigner 1987; Kragh 1990). Dirac’s private life is covered in detail in (Farmelo 2009). On Dirac as Lucasian Professor, see (Kragh 2003). Other secondary sources can be found in these works.
[2]
The content of Dirac’s course in 1927–28 appears in his notes for “Lectures on Modern Quantum Mechanics,” (AHQP).
[3]
On the relationship between Crowther and Dirac, see (Farmelo 2009). The Oxford book series came to include several important monographs on physics, from the 1930s and later. Early examples are George Gamow, Constitution of Atomic Nuclei and Radioactivity (1931), John H. Van Vleck, The Theory of Electric and Magnetic Susceptibilities (1932), and Richard C. Tolman, Relativity, Thermodynamics and Cosmology (1934). The series continues to this very day, comprising a total of about 150 titles.
[4]
The total number of physics books was 424, of which 39 were on relativity theory. In 1925 there were only 3 books on quantum topics. See (Williamson 1987, 10).
[5]
HarishChandra became Dirac’s research student in 1945. After having obtained his Ph.D. in 1947 and doing some work in theoretical physics, he moved to the United States, where he changed from physics to mathematics.
[6]
On the third and fourth editions, see (Brown 2006).
[7]
Dirac to Tamm, 3 January 1929, quoted in (Kragh 1990, 79). The letter is reproduced in full in (Kojevnikov 1993, 18–19). Dirac mentioned to Tamm Hermann Weyl’s Gruppentheorie und Quantenmechanik (1928), which he praised as “very clearly written and […] far the most connected account of quantum mechanics that has yet appeared.” But he also pointed out that Weyl’s book was “rather mathematical and therefore not very easy.”
[8]
The Russian translation of the second edition of Principles included a similar warning from the publisher, namely that “P. Dirac […] makes some philosophical and methodological generalizations that contradict the only true scientific method of cognition–dialectical materialism.” Full translations of the prefaces of the Russian editions appear in (Dalitz 1995, 471–478).
[9]
Yakov Frenkel’s book appeared in 1932 in an English edition as Wave Mechanics: Elementary Theory (1932). Ivanenko also mentioned “a short introduction by Haas” that existed in a Russian translation, a reference to the Austrian physicist Arthur E. Haas’s Materiewellen und Quantenmechanik (1928).
[10]
The element of closed nature or selfconsistency seems also to have impressed Paul Ehrenfest, who allegedly found it to be “ein greuliches Buch” that was difficult to understand. “A terrible book—you can’t tear it apart,” he supposedly said according to the recollections of Adriaan Fokker (Kragh 1990, 79).
[11]
Koopman, a student of George D. Birkhoff, did work on ergodic theory, dynamical systems, mathematical physics, and later operations research. Yet another review, by the Italian physicist Franco Rasetti, appeared in Scientia 51 (1932, 371). See also the reviews quoted below.
[12]
The first English textbook in quantum mechanics, George Birtwistle’s The New Quantum Mechanics (1928) used “eigenfunction” and “eigenwert.”
[13]
References to the first edition are denoted by “I”, those to the second edition by “II”.
[14]
Heisenberg to Dirac, 27 March 1935, quoted in (Brown 2006, 388).
[15]
Koopman agreed that the second edition was not more suitable as a textbook on quantum theory than the first one: B. O. Koopman, Bulletin of the American Mathematical Society 42 (1936, 472–474). Given the completely ahistorical nature of Principles, it is remarkable that the second edition received an extensive review in Isis, the journal of the History of Science Society. See H. T. Davis, Isis 25 (1936, 493–496).
[16]
AHQP, interview by Thomas S. Kuhn of 14 May 1963. On Dirac and complementarity, see (Heilbron 1985; Kragh 1990, 81–84). Principles was not alone in ignoring complementarity: Among 43 textbooks on quantum mechanics published between 1928 and 1937, 40 included a treatment of the uncertainty principle, but only eight of them mentioned the complementarity principle.
[17]
Notes for “Lectures on Modern Quantum Mechanics” (AHQP).
[18]
Bokulich (2008) argues that Dirac sided with Einstein in the debate over the interpretation of quantum mechanics, and that he did so even in the early phase of the debate. However, her evidence is unconvincing as it is limited to some of Dirac’s writings from the 1960s and 1970s.
[19]
Birkhoff to Edwin Kemble, 3 March 1933, quoted in (Kragh 1990, 279).
[20]
Quoted in (Jammer 1966, 367). On Dirac’s pragmatic use of mathematics, see (Bueno 2005).
[21]
Interview with Mott in 1963 (AHQP). Quoted in (Kragh 1990, 253).
[22]
For the case of early textbooks in quantum chemistry, see (Gavroglu and Simões 2000).
Table of Contents
1 Pedagogy and Research. Notes for a Historical Epistemology
of Science Education
Massimiliano Badino, Jaume Navarro
2 Sorting Things Out: Drude and the Foundations of Classical Optics
Marta Jordi Taltavull
3 Max Planck as Textbook Author
Dieter Hoffmann
4 Dissolving the Boundaries between Research and Pedagogy: Otto Sackur’s Lehrbuch der Thermochemie und Thermodynamik
Massimiliano Badino
5 Fritz Reiche’s 1921 Quantum Theory Textbook
Clayton A. Gearhart
6 Sommerfeld’s Atombau und Spektrallinien
Michael Eckert
7 Kuhn Losses Regained: Van Vleck from Spectra to
Susceptibilities
Charles Midwinter, Michel Janssen
8 Max Born’s Vorlesungen über Atommechanik, Erster Band
Domenico Giulini
9 Teaching Quantum Physics in Cambridge: George Birtwistle and His Two Textbooks
Jaume Navarro
10 Paul Dirac and The Principles of Quantum Mechanics
Helge Kragh
11 Quantum Mechanics in Context:
Pascual Jordan's 1936 Anschauliche Quantentheorie
Don Howard
12 Epilogue: Textbooks and the Emergence of a Conceptual Trajectory
David Kaiser
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