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The development of quantum electrodynamics until 1947: the historical background of Julian Schwinger’s work on QED

JAGDISH MEHRA and KIMBALL A. MILTON

in Climbing the Mountain: The Scientific Biography of Julian Schwinger

Prior to 1947, Julian Schwinger had not worked in quantum electrodynamics (QED), apart from his first unpublished paper ‘On the interaction of several electrons’. Before joining the City College of ... More

Prior to 1947, Julian Schwinger had not worked in quantum electrodynamics (QED), apart from his first unpublished paper ‘On the interaction of several electrons’. Before joining the City College of New York, he had already studied Paul Dirac's The principles of quantum mechanics, first published in 1930. As a freshman at CCNY, Schwinger studied the recently published papers on quantum field theory of Dirac, Werner Heisenberg, Wolfgang Pauli, Enrico Fermi, J. Robert Oppenheimer, and others; he absorbed all that was being done in this field. However, he maintained his interest in quantum field theory, and had more exposure to the subject when he went to the University of California at Berkeley to work with Oppenheimer for two years. This chapter deals with Schwinger's work on QED, Dirac's theory of radiation and relativistic theory, relativistic quantum mechanics, the infinities in QED, earlier attempts to overcome the infinities in QED, and earlier experimental evidence for the deviations from Dirac's theory of the electron.Less

Paul Dirac and the Magic of Large Numbers

Helge Kragh

in Masters of the Universe: Conversations with Cosmologists of the Past

In the 1930s Paul Dirac was awarded the Nobel Prize in Physics for his fundamental contributions to quantum mechanics, and he also proposed a new cosmological theory based on the hypothesis that the ... More

In the 1930s Paul Dirac was awarded the Nobel Prize in Physics for his fundamental contributions to quantum mechanics, and he also proposed a new cosmological theory based on the hypothesis that the constant of gravitation decreases slowly in time. That theory did not win acceptance, but its foundation in what Dirac called the “large number hypothesis” played a considerable role in the development of cosmological thought. The main theme of CCN’s interview with Dirac, which took place in 1963, was this principle, the associated cosmological model, and the possibility of testing it by means of experiment. Dirac was optimistic, arguing that his old theory had survived several attempts to shoot it down. The interview also covered the role of antiparticles and magnetic monopoles in cosmology.Less

Forming the Canon

Dean Rickles

in Covered with Deep Mist: The Development of Quantum Gravity (1916-1956)

This chapter charts the early development of the canonical quantum gravity (that is, the quantization of the gravitational field in Hamiltonian form). What we find in this period include: the ... More

This chapter charts the early development of the canonical quantum gravity (that is, the quantization of the gravitational field in Hamiltonian form). What we find in this period include: the establishment of a procedure for quantizing in curved spaces; the first expressions for the Hamiltonian of general relativity; recognition of the existence and importance of constraints (i.e. the generators of infinitesimal coordinate transformations); a focus on the problem of observables (and the realisation of conceptual implications in defining these for generally relativistic theories), and a (template of a) method for quantizing the theory. Although it commenced relatively early, the canonical approach was slow in its subsequent development. This had two sources: (1) it required the introduction of tools and concepts from outside of quantum gravity proper (namely, the constraint machinery and the parameter formalism); (2) by its very nature, it is highly rigorous in a conceptual sense, demanding lots of groundwork to be established, in terms of the structure of physical observables, before the actual issue of quantization can even be considered. Work was further complicated by the fact that these two sources of difficulty happened to be entangled. Particular emphasis is placed on the parameter formalism of Paul Weiss.Less

Dirac’s Derivation of the Relativistic Wave Equation: Electron Spin and Antimatter

Jim Baggott

in The Quantum Cookbook: Mathematical Recipes for the Foundations for Quantum Mechanics

The problem of electron spin was in some way connected with special relativity. Dirac’s fascination with relativity and his already burgeoning reputation made the search for a fully relativistic form ... More

The problem of electron spin was in some way connected with special relativity. Dirac’s fascination with relativity and his already burgeoning reputation made the search for a fully relativistic form of the new quantum mechanics irresistible. An important clue was available in a treatment that Pauli had published in 1927, in which he had represented the spin angular momemtum operators as 2 × 2 Pauli spin matrices. Dirac presumed that a proper relativistic wave equation could be derived simply by extending the spin matrices to a fourth member, but quickly realized this couldn’t be the answer. As he played around with the equations, in 1928 he found that he needed 4 × 4 matrices, instead. This allowed him to derive a relativistic wave equation, and to show that electron spin was indeed the result. The two extra solutions were subsequently shown to belong to the positron. Dirac had discovered antimatter.Less

Introduction

Thomas Ryckman

in The Reign of Relativity: Philosophy in Physics 1915-1925

The general theory of relativity (GTR) brought a revolutionary transformation in philosophical as well as physical outlook. The philosopher Mortiz Schick, student of Max Planck, played a pivotal role ... More

The general theory of relativity (GTR) brought a revolutionary transformation in philosophical as well as physical outlook. The philosopher Mortiz Schick, student of Max Planck, played a pivotal role in fashioning the received view that GTR implied the untenability of any type of Kantian philosophy. Schlick’s assessment ignored the philosophically motivated contributions to GTR by Hermann Weyl and Arthur Eddington. Paul Dirac in 1931 recognized the significance of a new method of a priori mathematical speculation in theoretical physics, tying it to Eddington (and to Weyl).Less

Introductory Considerations

John von Neumann

Nicholas A. Wheeler (ed.)

in Mathematical Foundations of Quantum Mechanics: New Edition

This chapter presents the origins of the transformation theory and related concepts. It shows how, in 1925, a procedure initiated by Werner Heisenberg was developed by himself, Max Born, Pascual ... More

This chapter presents the origins of the transformation theory and related concepts. It shows how, in 1925, a procedure initiated by Werner Heisenberg was developed by himself, Max Born, Pascual Jordan, and a little later by Paul Dirac, into a new system of quantum theory—the first complete system of quantum theory which physics has possessed. A little later Erwin Schrödinger developed the “wave mechanics” from an entirely different starting point. This accomplished the same ends, and soon proved to be equivalent to the Heisenberg, Born, Jordan, and Dirac system. On the basis of the Born statistical interpretation of the quantum theoretical description of nature, it was possible for Dirac and Jordan to join the two theories into one, the “transformation theory,” in which they make possible a grasp of physical problems which is especially simple mathematically.Less

Dirac, Von Neumann, and the Derivation of the Quantum Formalism: State Vectors in Hilbert Space

Jim Baggott

in The Quantum Cookbook: Mathematical Recipes for the Foundations for Quantum Mechanics

The evolution of quantum mechanics through the 1920s was profoundly messy. Some physicists believed that it was necessary to throw out much of the conceptual baggage that early quantum mechanics ... More

The evolution of quantum mechanics through the 1920s was profoundly messy. Some physicists believed that it was necessary to throw out much of the conceptual baggage that early quantum mechanics tended to carry around with it and re-establish the theory on much firmer ground. It was at this critical stage that the search for deeper insights into the underlying reality was set aside in favour of mathematical expediency. All the conceptual problems appeared to be coming from the wavefunctions. But whatever was to replace them needed to retain all the properties and relationships that had so far been discovered. Dirac and von Neumann chose to derive a new quantum formalism by replacing the wavefunctions with state vectors operating in an abstract Hilbert space, and formally embedding all the most important definitions and relations within a system of axioms.Less

Stephen Hawking: The Scientific Sublime Embodied

Alan G. Gross

in The Scientific Sublime: Popular Science Unravels the Mysteries of the Universe

Lucy Hawking has had the good fortune of being the daughter of the most famous living physicist; she has had the better fortune of having been a teenager ... More

Lucy Hawking has had the good fortune of being the daughter of the most famous living physicist; she has had the better fortune of having been a teenager before Stephen Hawking became famous, a time when he was known and respected only by other theoretical physicists. In this less hectic time, he was just a father, a man with a disability, to be sure, but not a disabled man, a sufferer from Lou Gehrig’s disease who defied the odds. Who could view as disabled a man who zipped through the streets of Cambridge in a Formula 1 electric wheelchair driven at reckless speeds and, on one occasion at least, almost disastrous consequences? Hawking is now, perhaps, the most famous physicist since Einstein. While his work significantly expands the territory of the scientific sublime, his life embodies that sublime. This is not the ethical sublime that Rachel Carson, the subject of the next chapter, embodies; it is not a code of conduct. Rather, it is our firm sense that we are dealing with an extraordinary human being who has overcome daunting challenges to become an impressive virtual presence, a man who, alone among contemporary scientists, is a star, nay, a superstar. Confined to a wheelchair, he towers above us, an exemplar, a demonstration of just how deep a deep-seated commitment to science can be. But is he any good at physics? Is it all hype? His heroes—Galileo, Newton, and Einstein—are models he cannot hope to emulate. Those on whom he consistently relies—Werner Heisenberg, Paul Dirac, and Richard Feynman—are clearly his superiors. True, he is an elite physicist honored by his peers, but he is more a Dom than a Joe DiMaggio, excellent, though not the very best. As he says himself, “To my colleagues am just another physicist.” But his professional reputation hardly matters, because, as he asserts with characteristic good humor: . . . To the wider public I became possibly the best-known scientist in the world. This is partly because scientists, apart from Einstein, are not widely known rock stars, and partly because I fit the stereotype of a disabled genius. I can’t disguise myself with a wig and dark glasses—the wheelchair gives me away. . . . Less

Heisenberg’s Derivation of the Pauli Exclusion Principle: The Stability of Matter and the Periodic Table

Jim Baggott

in The Quantum Cookbook: Mathematical Recipes for the Foundations for Quantum Mechanics

Despite the success of Schrödinger’s description of the H-atom, it became apparent that the spectrum of the simplest multi-electron atom—helium—could not be so readily explained. And the spectra of ... More

Despite the success of Schrödinger’s description of the H-atom, it became apparent that the spectrum of the simplest multi-electron atom—helium—could not be so readily explained. And the spectra of other atoms showed ‘anomalous’ splitting in a magnetic field. In 1920 Sommerfeld introduced a fourth quantum number. A few years later Pauli was led to the inspired conclusion that the electron must have a curious ‘two-valuedness’ characterized by a quantum number of ½, and went on to discover the exclusion principle. Perhaps this is because the electron possesses a self-rotation, leading to the notion of electron spin, potentially explaining why each orbital can accommodate only two electrons. Heisenberg traced this behaviour back to the symmetry properties of the wavefunctions. By observing which transitions in the spectrum of helium are allowed and which are forbidden, we can deduce the generalized Pauli principle, from which the exclusion principle follows.Less