WELL BEFORE THE CONTESTED EDITION of Flamsteed's Historia coelestis in 1712 brought that episode to a temporary conclusion, two new concerns, which would dominate Newton's life for more than five years, had imposed themselves upon him. In 1709, work began in earnest on a second edition of the Principia. In the spring of 1711, a letter from Leibniz to Hans Sloane, secretary of the Royal Society, inaugurated a heated controversy over claims of priority in the invention of the calculus. Moreover, a fourth problem of great import for Newton was also taking form. Already an ugly scene with Craven Peyton, the warden of the Mint, had signaled a deterioration of their relations which culminated in a major crisis in the Mint in 1714, when the battle with Leibniz was reaching its highest pitch. The Mint was the bedrock on which Newton's existence in London stood. Trouble there had to affect his whole life. In its intensity, the period from 1711 to 1716, succeeding more than a decade of relative calm, matched the great periods of stress at Cambridge, when his relentless pursuit of truth stretched him to the limit. The coincidence of these events, the demands they placed on Newton, may help to explain the furious episode with Flamsteed at Crane Court on 26 October 1711 and much else from these years not yet mentioned.

NEWTON SET OUT FOR CAMBRIDGE early in June 1661. There was no greater watershed in his life. Although he would return to Woolsthorpe infrequently during the next eighteen years, with two extended visits during the plague, spiritually he now left it, and what a later commentator has called the idiocy of rural life, once and for all. Three short years would put him beyond any possibility of return, though three more years, perhaps somewhat longer, had to pass before a permanent stay in Cambridge was assured. His accounts show that he stopped at Sewstern, presumably to check on his property there; and after spending a second night at Stilton as he skirted the Great Fens, he arrived at Cambridge on the fourth of June and presented himself at Trinity College the following day. If the procedures set forth in the statutes were followed, the senior dean and the head lecturer of the college examined him to determine if he was fit to hear lectures. He was admitted – although there is no record whatever of anything but the verdict, one feels constrained to add – “forthwith.” He purchased a lock for his desk, a quart bottle and ink to fill it, a notebook, a pound of candles, and a chamber pot and was ready for whatever Cambridge might offer.

CRISES RACKED THE INSTITUTION to which Newton moved in the spring of 1696. Indeed, the Mint was an institution within an institution within an institution, all three of which faced crises. The recoinage engaged every pinch of energy at the Mint. The Treasury, of which the Mint was a relatively minor department, devoted equal energy to devising temporary expedients and new machinery to cope with overwhelming financial needs caused by war with France. The English state and the revolutionary settlement it embodied balanced precariously on the outcome of the Treasury's efforts. In 1696, it was not clear that the financial demands of the war would be met. If they were not, if national bankruptcy ensued, the revolutionary settlement would undoubtedly collapse before a second Stuart restoration. In the larger crises of the government and its finances Newton was not involved beyond his concern as an Englishman committed to the revolution.

The narrower monetary crisis, which bedeviled the financial crisis by reaching a climax when it could least be tolerated, occupied him almost completely for more than two years. As the debasement of silver coinage reached disastrous proportions, the government under the leadership of Newton's friend Charles Montague, then Chancellor of the Exchequer, began to consider a recoinage as the only effective remedy.

Problem definition

The self-energy of the electron is the energy of the electromagnetic field which is generated by the electron in addition to the energy of the interaction of the electron with this field. Waller, Oppenheimer, and Rosenfeld calculated the self-energy of the free electron by means of the Dirac relativistic wave equation of the electron and the Dirac theory of the interaction between matter and light. They here used an approximation method which represents the self-energy in powers of the charge e. They found that the first term, which is proportional to e2, already becomes infinitely large. The essential reason for this is that the theory of the interaction of the electron with the electromagnetic field is built on the classical equations of motion of a point shaped electron whose self-energy, as is well known, also becomes infinite in classical theory.

In the present note, the expressions for the self-energy shall be derived without direct application of quantum electrodynamics, but by means of the Heisenberg radiation theory, which is linked much more closely to classical electrodynamics.

Introduction

In classical theory, the field strengths E and H become arbitrarily large in the neighborhood of the point-charge e, so that the integral over the energy density 1/8π(E2 + H2) diverges. To overcome this difficulty, one therefore assumes a finite radius r0 for the electron in classical electron theory. This radius is related to the mass m of the electron in the order-of-magnitude relation r0 ~ e2/mc2; the integral over the energy density is then of the order mc2. In quantum theory, not only this radius r0 but possibly also another length λ0 = h/mc, which is characteristic of the electron, plays a role in the self-energy. In a superficial consideration in terms of the correspondence principle, one would suspect that the self-energy of the point-like electron must also become infinite in quantum theory.

In fact, Oppenheimer and Waller have indeed shown that a perturbation method which proceeds in powers of e does not yield finite values for the self-energy. At first, it appears as if, in quantum theory also, only the introduction of a finite electron radius can provide a way out of this difficulty.

Jordan's 1926 results

Heisenberg wrote in (1929), that ‘the existence of the electron’ is as unintelligible to the wave mechanical theory as the ‘existence of the light quantum’ to Maxwell's theory. The fundamental problem for the light quantum was how it could produce interference. The fundamental problem concerning electricity was how quantization of electric charge could be deduced from the Schrödinger wave function because, according to wave mechanics, the total charge on a body is e∫Ψ*Ψd3r. How could the volume integral of the product of two wave functions be an integer?

Pascual Jordan approached this problem in the Dreimänner-Arbeit of 1926, coauthored with Born and Heisenberg, in the section entitled ‘Coupled harmonic oscillators. Statistics of wave fields’ (Born, Heisenberg and Jordan, 1926 – see letter of Heisenberg to Pauli of 23 October 1926, which confirms that Jordan wrote this section, in Pauli, 1979). Here the line of development begun by Bohr's coupling mechanism is explored further. Jordan cited the investigations of Ehrenfest (1906) and of Debye (1910) noting that neither of these approaches could include the important problem of the ‘coupling of distant atoms’ because they are semiclassical, mixing classical wave-theoretical notions with light quanta. Consequently, as Einstein (1925) had recognized, although Debye's method leads to Planck's formula, it gives the wrong result for the mean square fluctuations of cavity radiation in a volume element, yielding, instead of the expected two-term result (wave–particle duality of light), only the wave contribution.

Introduction

One of the well-known difficulties of quantum electrodynamics concerns the infinite self-energy of a charged particle. In addition, as is well known, there is also a divergent result of this theory which concerns the emission of light quanta of very low frequency.

Prior to and into the first decade of Niels Bohr's 1913 atomic theory, physicists dealt with physical systems in which the usual space and time pictures of classical physics were assumed trustworthy and so could be extrapolated to any sort of matter in motion, for example, electrons move like billiard balls and light behaves analogously to water waves. In the German scientific milieu this visual imagery was accorded a reality status higher than viewing merely with the senses and was referred to as ‘ordinary intuition [gewöhnliche Anschauung]’. Ordinary intuition is the visual imagery abstracted from phenomena that we have actually witnessed in the world of sense perceptions. The concept of ordinary intuition was much debated during 1923–27 by physicists like Niels Bohr, Werner Heisenberg, Wolfgang Pauli and Erwin Schrödinger, all of whom used this term with proper Kantian overtones, and all of whom lamented its loss in the new quantum mechanics.

Ordinary intuition is associated with the strong causality of classical mechanics. According to the law of causality, initial conditions (position and velocity or momentum and energy) can be ascertained with in-principle perfect accuracy. Consequently any system's continuous development in space and time can be traced with in-principle perfect accuracy using Newton's laws of motion and conservation of energy and momentum. Any limitations to the accuracy of measurements are assumed not to be intrinsic to the phenomena, that is they are interpreted to be systematic measurement errors that ideally can be made to vanish.

The intention of the present paper is to build the Dirac theory of the positron into the formalism of quantum electrodynamics. A requirement here is that the symmetry of nature in the positive and negative charges should from the very beginning be expressed in the basic equations of theory, and further that, except for the divergences which are caused by the well-known difficulties of quantum electrodynamics, no new infinities appear in the formalism, i.e. that the theory provides an approximation method for treating the group of problems which could also be treated according to the previous quantum electrodynamics. The latter postulate distinguishes the present attempt from the investigations of Fock, Oppenheimer and Furry, and Peierls, which it otherwise resembles; it is here rather closely connected with a paper by Dirac. Compared to Dirac's treatment, this paper emphasizes the significance of the conservation laws for the total system of radiation and matter, and the necessity of formulating the basic equations of the theory in a manner extending beyond the Hartree approximation.

Thus far, studies in the history of twentieth-century physics have focused on developments until 1927. Testimony to the vigor of this work is the rich secondary literature on the special and general theories of relativity and on quantum mechanics into its interpretive phase.

Historical research into the genesis of quantum electrodynamics is only just beginning. There are good reasons for this hiatus, chief among them being the complexity of the subject matter. The goal of this book is to provide a properly introduced corpus of primary source materials in English to physics researchers and students whose day-to-day activities preclude literature searches, and to historians and philosophers of science interested in the genesis of a theory that has been on the cutting edge of physics ever since P. A. M. Dirac's quantization of the radiation field in 1927: quantum electrodynamics.

Like the papers chosen for this volume, the Frame-setting essay emphasizes conceptual transformations during 1927–38, which carried physicists to the threshold of renormalization theory. For the most part the leaders in fundamental developments in quantum electrodynamics were the same physicists whose focus on conceptual matters led to the fully interpreted quantum mechanics in 1927: Niels Bohr, P. A. M. Dirac, Werner Heisenberg and Wolfgang Pauli. This constitutes the subject matter of Chapter 1 of the Frame-setting essay. Throughout Chapter 1 runs the metaphor of the harmonic oscillator representation for a bound electron, which found its highest development in the second-quantization methods discussed in Chapter 2.