## The Principles of Quantum Mechanics.

Oxford: Clarendon Press, 1930.

First edition, and a fine copy with the dust-wrapper, of Dirac’s famous and hugely influential textbook, which “summarized the foundations of a new science, much of which was his own creation. It expressed the spirit of the new quantum mechanics, creating a descriptive language that we still use” (Brown, p. 381). “Physicists immediately hailed it a classic. *Nature* published a rhapsodic review by an anonymous reviewer who – to judge by the eloquence and sharp turn of phrase – may well have been Eddington. The author made clear that this was no ordinary account of quantum mechanics: ‘[Dirac] 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.’ The book eclipsed all the other texts on quantum mechanics written at about the same time – one by Born, another by Jordan – and became the canonical text on the subject in the 1930s. Pauli warmly praised it as a triumph and, although he worried that its abstraction rendered the theory too distant from experiment, described the books as ‘an indispensable standard work.’ Einstein was another admirer, writing that the book was ‘the most logically perfect presentation of quantum theory.’ *The Principles of Quantum Mechanics* later became Einstein’s constant companion: he often took it on vacation for leisure reading and, when he came across a difficult quantum problem, would mutter to himself, ‘Where’s my Dirac?’” (Farmelo, p. ?). The Nobel laureates “Abdus Salam and Eugene P. Wigner declared in their preface of a book commemorating Dirac’s seventieth birthday that: ‘Posterity will rate Dirac as one of the greatest physicists of all time. The present generation values him as one of its great teachers – teaching both through his lucid lectures as well as through his book *The Principles of Quantum Mechanics*. This exhibits a clarity and a spirit similar to those of the *Principia *written by a predecessor of his in the Lucasian Chair in Cambridge … Dirac has left his mark, not only by his observations … but even more by his human greatness … He is a legend in his own lifetime and rightly so’” (Brown, p. 381). Although not a rare book on the market, copies of the first edition of Dirac’s *Principles* in such fine condition as ours are rare – indeed, this copy hardly seems to have been opened – most copies having been studied closely by their owners.

“Although not well known to the general public, Paul Adrian 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 Einstein. Young Dirac made his first breakthrough in the fall of 1925 when he developed his own version of quantum mechanics known as *q*-number algebra, and over the next few years he established himself as a leading expert in the new quantum physics. In 1927-28 he made pioneering contributions to quantum statistics (Fermi-Dirac statistics), quantum electrodynamics, and relativistic quantum theory. The linear and relativistically-invariant wave equation for the electron that he published in early 1928 not only explained the electron’s spin and magnetic moment, but also, three years later, led to the prediction of antielectrons (positrons) and antiparticles more generally.

“Dirac’s genius was recognized early on. For example, he was part of the exclusive company of physicists invited to the famous Solvay conference in 1927. In 1930, at the unusually young age of 27, he was elected a fellow of the prestigious Royal Society, and the same year he published his monumental *Principles of Quantum Mechanics*. Two years later he was appointed Lucasian Professor of mathematics at Cambridge University, the chair once held by Isaac Newton and later by Stephen Hawking. Another high point of Dirac’s career came in 1933, when he was awarded the Nobel Prize in physics, sharing it with Erwin Schrödinger. Although Dirac’s scientific fame is closely linked to his fundamental contributions to quantum theory, and especially to those of the period 1925-34, he also dealt with other subjects, including cosmology, classical electron theory, and the general theory of relativity. Moreover, the influence of his ideas extended beyond physics, especially to mathematics (e.g. the Dirac *δ*-function, Dirac matrices, and Dirac operators). Paul Dirac remained Lucasian Professor until his retirement in 1969, when he joined the physics department of Florida State University in Tallahassee. He died in 1984, and in 1995 a commemorative stone carrying his name and equation was unveiled at a ceremony in Westminster Abbey.

“While still a Ph.D. student [at Cambridge], under the supervision of Ralph Fowler, Dirac was assigned to lecture on the new and exciting developments in quantum theory. The first course ever on quantum mechanics at a British University was given in the Easter term of 1926 … The following year, Dirac started giving a regular course on quantum mechanics, which he would continue to do until the 1960s” (Kragh (2013), pp. 249-250).

“Since the fall of 1927, Dirac had given a course of lectures on quantum mechanics at Cambridge. The content of these lectures formed the basis of his celebrated book *The Principles of Quantum Mechanics, *the first edition of which was published in the summer of 1930. The book was written at the request of Oxford University Press – and not, remarkably, Cambridge University Press – which was preparing a series of monographs in physics. The general editors of the series were two of Dirac’s friends, the Cambridge physicists Fowler and Kapitza. The author and science journalist James Crowther arranged the publication of Dirac’s book for Oxford University Press. ‘When I first called on Dirac,’ he recalled, ‘he was living in a simply furnished attic in St. John's College. He had a wooden desk of the kind which is used in schools. He was seated at this, apparently writing the great work straight off.’ Dirac started writing *Principles *in 1928, but because of his travels progress was slow. In January 1929, he wrote to Tamm:

‘The book is progressing with a velocity of about 10^{-8} Frenkel. I have started writing it again in what I hope is the final form and have written about 90 pages. I shall try hard to finish it before going to America. It is to be translated into German. Have you seen Weyl’s book on ‘Gruppentheorie und Quantenmechanik’? It is very clearly written and is far the most connected account of quantum mechanics that has yet appeared, although it is rather mathematical and therefore not very easy.’

“Van Vleck, at the time on sabbatical leave from the University of Wisconsin, visited Cambridge in March 1930 and was allowed to read the proof-sheets of Dirac's text. ‘What I have read so far I like very much,’ he wrote Dirac.

“*Principles *became a success. It went through several editions and translations and is still widely used … the first English edition sold two thousand copies … In the thirties, *Principles *was the standard work on quantum mechanics, almost achieving a position like that which Sommerfeld’s *Atombau und Spektrallinien *had before quantum mechanics. The nuclear physicist Philip A. Morrison recalled, with some exaggeration, that ‘everybody who had ever looked at books had a copy of Dirac.’ Unlike most other textbooks, *Principles *was not only of use to students in courses on quantum mechanics but was probably studied as much by experienced physicists, who could find in it a concise presentation of the mathematical principles of quantum mechanics, principles that were likely to be of eternal validity. When Heisenberg received the fourth edition of *Principles *in 1958, he gave Dirac the following fine compliment: ‘I have in the past years repeatedly had the experience that when one has any sort of doubt about difficult fundamental mathematical problems and their formal representation, it is best to consult your book, because these questions are treated most carefully in your book.’

“The book expressed Dirac’s personal taste in physics and possessed a style unique to its author. Regarded as a textbook, it was and is remarkably abstract and not very helpful to the reader wanting to obtain physical insight into quantum mechanics. Unlike most other modem textbooks. *Principles *is strictly ahistorical and contains very few references and no illustrations at all. Neither is there any bibliography or suggestions for further reading. The first edition did not even include an index.

“*Principles *was based on what Dirac called ‘the symbolic method,’ which ‘deals directly in an abstract way with the quantities of fundamental importance (the invariants. &c., of the transformations).’ This method. Dirac said, ‘seems to go more deeply into the nature of things.’ In accordance with the symbolic method, he wanted to present the general theory of quantum mechanics in a way that was free 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.’ Thanks to the wide distribution of the book. Dirac’s interpretation of quantum mechanics was disseminated to a whole generation of physicists, who through it learned about the formal aspects of the Copenhagen School’s views of the measurement process and the nature of quantum mechanical uncertainty …

“Although Dirac preferred an abstract or symbolic approach to physics, a kind of pictorial model appeared frequently in his works. But these models had very little in common with the traditional models of classical physics. Dirac used models, metaphors, and pictures to think about premature physical concepts and to transform vague ideas into a precise mathematical formalism . ‘One may,’ he stated in *Principles*, ‘extend the meaning of the word, ‘picture’ to include any *way of looking at the fundamental laws which makes their self-consistency obvious. *With this extension, one may gradually acquire a picture of atomic phenomena by becoming familiar with the laws of the quantum theory.’

“When Pauli reviewed *Principles *in 1931, he recommended it strongly. But he also pointed out that Dirac's symbolic method might lead to ‘a certain danger that the theory will escape from reality.’ Pauli complained that the book did not reveal the crucial fact that quantum mechanical measurement requires real, solid measuring devices that follow the laws of classical physics and is not a process that merely involves mathematical formulae. This was an important point in Bohr’s conception of the measurement process in quantum mechanics, a conception that Pauli shared. According to Bohr and his disciples, the classical nature of the measuring apparatus is crucial, but this point was not appreciated by Dirac.

“For all its qualities, *Principles *was not a book easily read or one that suited the taste of all physicists. It reflected Dirac’s aristocratic sense of physics and his neglect of usual textbook pedagogy. Ehrenfest studied it very hard, only to find it ‘ein greuliches Buch’ that was difficult to understand. ‘A terrible book – you can’t tear it apart!’ he is said to have exclaimed. In their reviews of *Principles, *both Oppenheimer and Felix Bloch emphasized its generality and completeness. Oppenheimer compared the book with Gibb’s *Elementary Principles in Statistical Mechanics *(1902) and warned that it was too difficult and abstract to be a suitable text for beginners in quantum theory” (Kragh (1990), pp. 76-79).

“Dirac expressed his philosophy in his preface to the first edition of *Principles* … He emphasized the ‘vast change’ that had taken place since the classical tradition, in which one could ‘form a mental picture in space and time of the whole scheme.’ Instead, the fundamental laws now ‘control a substratum of which we cannot form a mental picture without introducing irrelevancies.’ We are obliged to rely on the ‘mathematics of transformations,’ in which the ‘important things in the world appear as the invariants (or more generally the nearly invariants, or quantities with simple transformation properties) of these transformations.’

“Dirac noted that the required mathematics was not essentially different from that currently used by physicists. Instead of the usual method of coordinates or representations that Werner Heisenberg and Erwin Schrödinger used for instance, he preferred the symbolic method, which ‘deals directly in an abstract way with the quantities of fundamental importance.’ Dirac’s transformation theory, which he used to formulate the foundations of quantum theory, is really group theory, which physicists had used to treat particular problems in quantum mechanics, such as those of angular momentum and atomic spectra. He cautioned that, although *Principles *was very mathematical,

‘All the same 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. In this book I have tried to keep the physics to the forefront, by beginning with an entirely physical chapter and in the later work examining the physical meaning underlying the formalism wherever possible.’

“Thus, in the first chapter, ‘The Principle of Superposition,’ Dirac discusses its physics without using any equations. He begins by stating that ‘it is quite hopeless on the basis of classical ideas to try to account for the remarkable stability of atoms and molecules.’ ‘Classical electrodynamics forms a self-consistent and very elegant theory,’ but quantum mechanics is ‘even more elegant and pleasing than the classical theory.’ We see here immediately the high value that Dirac placed on mathematical beauty.

“Besides the stability of matter, Dirac considers the nature of light as requiring a departure from classical mechanics and electrodynamics (he appears to use these terms interchangeably). Since light exhibits interference and diffraction as well as causes the emission of photoelectrons, it consists of both waves and particles, which ‘should be regarded as two abstractions which are useful for describing the same physical reality’ … The difficulty of the conflict between the waves and corpuscles is, however, actually solved as soon as one can give an unambiguous answer to any experimental question. *The only object of theoretical physics is to calculate results that can be compared with experiment*....

“Dirac continues in Chapter I to discuss and generalize the concepts of superposition and indeterminacy. He defines the term ‘state’ as a ‘condition [that exists] throughout an indefinite period of time …’ ‘A system when once prepared in a given state, remains in that state so long as it remains undisturbed’ … Although superposition also occurs in classical wave theory, ‘*the superposition that occurs in quantum mechanics is of an essentially different nature from that occurring in the classical theory*. The analogies are therefore very misleading.’

“Dirac finally gives a general statement of the principle of superposition:

‘*We say that a state A may be formed by a superposition of states B and C when, if any observation is made on the system in the state A leading to any result, there is a finite probability for the same result being obtained when the same observation is made on the system in one (at least) of the two states B and C*. The Principle of Superposition says that any two states *B *and *C *may be superposed in accordance with this definition to form a state *A *and indeed an infinite number of different states *A *may be formed by superposing *B *and *C *in different ways. This principle forms the foundation of quantum mechanics. It is completely opposed to classical ideas, according to which the result of any observation is certain and for any two states there exists an observation that will certainly lead to two different results’ …

“To get a feeling for his style in the first edition, I quote the first paragraph of Chapter II, ‘Symbolic Algebra of States and Observables’:

‘We introduce certain symbols which we say denote physical things such as states of a system or dynamical variables. These symbols we shall use in algebraic analysis in accordance with certain axioms which will be laid down. To complete the theory we require laws by which any physical conditions may be expressed by equations between the symbols and by which, conversely, physical results may be inferred from equations between the symbols. A typical calculation in quantum mechanics will now be run as follows: One is given that a system is in a certain state in which certain dynamical variables have certain values. This information is expressed by equations involving the symbols that denote the state and the dynamical variables. From these equations other equations are then deduced in accordance with the axioms governing the symbols and from the new equations physical conclusions are drawn. 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 this connexion, contain a number of physical laws, which cannot conveniently be analyzed or even stated in any other way’ …

“In the last chapter of the first edition of *Principles*, ‘Relativity Theory of the Electron’, Dirac argued that it is ‘fairly certain’ that the transformation theory he developed earlier ‘will apply also to relativity treatments of dynamical systems.’ However, one would have to relate dynamical variables at a given time to those at another time, and these relations ‘would in general be very complicated and artificial, as they would require us to connect distant parts of space-time.’ The most straightforward way to deal with this difficulty would be to formulate a ‘purely field theory,’ but this ‘involves complicated mathematics and appears to be too difficult for practical application.’ In the special case of a single particle, however, one can introduce a (Schrödinger) wave function whose domain ‘becomes identical with the ordinary space-time continuum, and this circumstance makes possible an elementary treatment of the problem which cannot be extended to more general dynamical systems.’ He then derived the relativistic equation of the electron as he had done in his famous paper of 1928.

“Between the time that Dirac wrote the first and second editions of *Principles*, specifically in 1932 and 1933, he worked on the problem of relativistic quantum mechanics of several particles, publishing three papers that strongly influenced those whom Silvan S. Schweber has called the ‘Men Who Made’ QED, namely, Freeman Dyson, Richard Feynman, Julian Schwinger, and Sin-itiro Tomonaga” (Brown).

Brown, ‘Paul A. M. Dirac’s *The Principles of Quantum Mechanics*,’ *Physics in Perspective *8 (2006), pp. 381-407. Farmelo, *The Strangest Man. The Hidden Life of Paul Dirac, Quantum Genius*, 2009. Kragh, *Dirac. A Scientific Biography*, 1990. Kragh, ‘Paul Dirac and The Principles of Quantum Mechanics,’ Chapter 10 in: *Research and Pedagogy*: *A History of Quantum Physics through its Textbooks*, Badino & Navarro (eds.), 2013.

Large 8vo (237 x 155 mm), pp. x, 257, [1]. Original publisher’s cloth with dust-jacket (spine of jacket with a few scratches and minor loss at head). A fine copy in a near-fine dust-jacket, rare in this condition.

Item #5883

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Price:
$12,500.00
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