Simply Dirac (eBook)

Helge Kragh (Autor)

eBook Download: EPUB

2016
119 Seiten
Simply Charly (Verlag)
978-1-943657-00-1 (ISBN)

Infos

'What a fantastic entrée into the life of Paul Dirac and the exotic world of Quantum Mechanics, of which he was one of the great pioneers. With its cast of some of the most important scientists of the modern age, this is both an entertaining and an enlightening read.'
-Michael White, Bestselling author of 39 books including Isaac Newton: The Last Sorcerer

Paul Dirac (1902-1984) was a brilliant mathematician and a 1933 Nobel laureate whose work ranks alongside that of Albert Einstein and Sir Isaac Newton. Although not as well known as his famous contemporaries Werner Heisenberg and Richard Feynman, his influence on the course of physics was immense. His landmark book, The Principles of Quantum Mechanics, introduced that new science to the world and his 'Dirac equation' was the first theory to reconcile special relativity and quantum mechanics. 

Dirac held the Lucasian Chair of Mathematics at Cambridge University, a position also occupied by such luminaries as Isaac Newton and Stephen Hawking. Yet, during his 40-year career as a professor, he had only a few doctoral students due to his peculiar personality, which bordered on the bizarre. Taciturn and introverted, with virtually no social skills, he once turned down a knighthood because he didn't want to be addressed by his first name. Einstein described him as 'balancing on the dizzying path between genius and madness.' 

In Simply Dirac, author Helge Kragh blends the scientific and the personal and invites the reader to get to know both Dirac the quantum genius and Dirac the social misfit. Featuring cameo appearances by some of the greatest scientists of the 20th century and highlighting the dramatic changes that occurred in the field of physics during Dirac's lifetime, this fascinating biography is an invaluable introduction to a truly singular man.

Textauszug

Quantum Wizard

Unknown to Dirac, in the summer of 1925 Werner Heisenberg had figured out the skeleton of a new and abstract “quantum mechanics” that promised to be fundamental, logically consistent, and not plagued by the difficulties of the existing quantum theory of atomic structure. Only eight months older than Dirac, Heisenberg was a graduate student of Max Born in Göttingen. Like Dirac, he had not yet obtained his Ph.D. degree.

The young German reasoned that a truly fundamental theory had to contain observable quantities only. By this criterion, electron orbits were no longer legitimate, whereas the frequencies of light emitted by atoms were. After all, who had ever observed an electron orbiting around a nucleus? Transforming this general idea into an abstract mathematical scheme, Heisenberg expressed physical quantities by arrays of symbols soon recognized to be matrices. One of the arrays might represent the position of an electron (Q) and another array its momentum (P, which equals mass times velocity). Heisenberg’s theory led to a mysterious law of multiplication according to which QP differed from PQ, that is, QP ≠ PQ. It was as if 3 × 2 was not always equal to 2 × 3, or that the two numbers do not “commute.” Noting the puzzling fact that in general physical quantities did not commute, Heisenberg, at first, thought it was a flaw in his theory that might disappear when it was further developed.

Heisenberg’s seminal paper was published in a German journal on September 18, 1925, but Dirac knew of it ahead of publication. In August, Heisenberg had sent proofs of his forthcoming paper to Ralph Fowler, who sent them on to Dirac with a note saying, “What do you think of this? I shall be glad to hear.” Dirac first thought that it was of no interest, but a closer study told him a different story. He now realized that far from being a flaw, the strange appearance of non-commuting physical variables was the key element in the new mechanics and, consequently, had to be understood. Some versions of classical mechanics, he remembered, operated with non-commuting variables, which indicated that Heisenberg’s idea might be expressed in formal analogy with classical theory. The crucial insight came to Dirac “in a flash” (as he recalled) one afternoon at the beginning of October. A couple of weeks later he had a paper ready with the ambitious title “The Fundamental Equations of Quantum Mechanics.” This was the first paper that mentioned the term “quantum mechanics” in its title and with a meaning recognizable by modern physicists.

Among the fundamental equations was a significant sharpening of Heisenberg’s non-commuting variables. PQ and QP did not only differ, but, according to Dirac, they differed by a precise amount given by the tiny constant of nature Max Planck had introduced in 1900: PQ – QP ~ h. Planck’s constant is tiny indeed (h = 6.6 × 10-34 in units of joule × second), which explains why position and momentum commute for a canon-ball but not for an electron. Dirac’s paper also contained a quantum analogue of the classical equation of motion, that is, an expression of how a physical quantity varies in time. Without an equation of motion, quantum mechanics would not be of much value, just as classical mechanics would be of little use without Newton’s second law of motion.

Even back in the 1920s, physics was a very competitive field (as it remains to this day). Dirac was aware that he was in competition with the German physicists, but the question of priority of the laws of quantum mechanics was not of great concern to him. Yet, he must have been disappointed when Heisenberg informed him in a letter of November 20 that most of the results in Dirac’s “extraordinarily beautiful paper” had already been derived by Born and another talented young Göttingen physicist, Pascual Jordan. The two Germans had extended and clarified Heisenberg’s theory, recognizing for the first time that it could be formulated in the language of matrix calculus. Consequently, the Göttingen approach to quantum mechanics was often referred to as “matrix mechanics.” In a lengthy follow-up paper known as the Dreimännerarbeit (“three-man paper”) Born, Heisenberg, and Jordan further developed matrix mechanics into what today is considered to be the first full exposition of quantum mechanics.

Dirac followed the development in Germany with interest but decided to pursue his own ideas. On their side, the German physicists were quick to appreciate the surprising progress made in Cambridge by the “Englishman working with Fowler”—this is how Heisenberg referred to Dirac in a letter of November 24 to his Austrian colleague Wolfgang Pauli. And this is what Born recalled: “The name Dirac was completely unknown to me. The author appeared to be a youngster, yet everything was perfect in its way and admirable.” The German-speaking physicists were not used to competition and especially not from their British counterparts.

The version of quantum mechanics that Dirac developed in 1926 was known as “q-number algebra,” indicating that it was essentially a mathematical theory that could be applied to problems of physics. Measurable properties are given by numbers read on an instrument—for instance, the weight of a body as read on a balance. They are ordinary or classical numbers that satisfy the law of commutation (3 × 2 is equal to 2 × 3). Quantum variables, on the other hand, do not satisfy the law. They are members of a new class of q-numbers with mathematical properties of its own. Q-numbers are queer. On this basis, Dirac established his abstract q-number algebraic theory. Given the theory’s thoroughly algebraic and unvisualizable character, it is remarkable that it may have been inspired by geometric considerations. Dirac later said that while he published in the algebraic style, he thought in terms of pictures and diagrams. “I prefer the relationships which I can visualize in geometric terms,” he noted.

Despite its apparent remoteness from physical reality, Dirac’s theory turned out to be equivalent to the matrix mechanics of the German physicists, and, as such, described the quantum world of atoms, molecules, and light. For example, Dirac succeeded in explaining the spectrum of hydrogen in accordance with Bohr’s old atomic theory. Symptomatic of the competitiveness of the period, Pauli did the same, using more cumbersome methods of matrix mechanics.

In early 1926, there were basically two versions of quantum mechanics, the Göttingen matrix mechanics, and Dirac’s q-number theory. The latter was very much Dirac’s own and rarely used by other physicists. When the Austrian physicist Erwin Schrödinger published his new “wave mechanics” a few months later, the number of versions grew to three. For a while, confusion increased as Schrödinger’s theory was quite different from the abstract schemes developed in Göttingen and Cambridge. It described particles and atomic phenomena in terms of a continuous wave function (ψ), which satisfied a classical-looking equation of motion soon known as the Schrödinger equation. The physical meaning of the wave function was a matter of some dispute until Born suggested the currently accepted interpretation, namely, that ψ is a measure of the probability of something happening. Dirac, at first, resented the new wave mechanics, which he thought was formulated in a too classical framework. “I definitely had a hostility to Schrödinger’s ideas,” he recalled. However, the hostility did not last long. When it was proved that wave mechanics was mathematically equivalent to matrix mechanics (and also to q-number algebra), Dirac adopted a more pragmatic attitude, often mixing elements of his own theory with those of Schrödinger’s.

As a result of his study of Schrödinger’s theory, in August of 1926 Dirac published an important paper in which he clarified the physical meaning of the mysterious ψ-function and used a generalized version of the Schrödinger equation to solve problems of physics. The most important result was a fundamental distinction between two classes of particles on the basis of their different wave functions. Some particles, such as electrons and protons, were characterized by “anti-symmetrical” wave functions, while other particles, including the light quantum or photon, could be described by “symmetrical” wave functions. The quantum behavior of the first class of particles was initially examined by the Italian physicist Enrico Fermi; they became known as Fermi-Dirac particles (contrary to the photon, which is a Bose-Einstein particle). Later, Dirac invented the more convenient names fermion and boson for the two kinds of particles—designations that have long been part of physicists’ general vocabulary. The latter name is a reference to the Indian physicist Satyendra Nath Bose whose idea was improved by Einstein. As Pauli later proved, all fermions have half-integral spin (½ for an electron) and all bosons feature integral spin (0 for a photon).

Dirac’s paper of August 1926 was widely recognized to be an important contribution to quantum mechanics, but also one that was very hard to understand. It had to be deciphered, line by line. Einstein was not the only one who had troubles with Dirac’s abstract and condensed style of writing. In an October 1926 letter to Bohr, Schrödinger expressed his admiration for Dirac’s paper,...

Produkt-Details

• Erscheint lt. Verlag: 29.8.2016
• Reihe/Serie: Great Lives
• Reihe/Serie: Great Lives
• Sprache: englisch
• Themenwelt: Literatur ► Biografien / Erfahrungsberichte
• Themenwelt: Sozialwissenschaften ► Politik / Verwaltung
• Schlagworte: Albert Einstein • Niels Bohr • Paul Dirac • Physics • quantum mechanics • Richard Feynman • Werner Heisenberg
• ISBN-10: 1-943657-00-9 / 1943657009
• ISBN-13: 978-1-943657-00-1 / 9781943657001