QED and the man who didn׳t make it: Sidney Dancoff and the infrared divergence

Sidney Dancoff׳s paper “On Radiative Corrections for Electron Scattering” is generally viewed in the secondary literature as a failed attempt to develop renormalized quantum electrodynamics (QED) a decade early, an attempt that failed because of a mistake that Dancoff made. I will discuss Dancoff׳s mistake and try to reconstruct why it occurred, by relating it to the usual practices of the quantum field theory of his time. I will also argue against the view that Dancoff was on the verge of developing renormalized QED and will highlight the conceptual divides that separate Dancoff׳s work from the QED of the late 1940s. I will finally discuss how the established view of Dancoff׳s paper came to be and how the reading of this specific anecdote relates to more general assessments of the conceptual advances of the late 1940s (covariant techniques, renormalization), in particular to their assessment as being conservative rather than revolutionary.     

The twin origins of renormalization group concepts

This paper traces the origin of renormalization group concepts back to two strands of 1950s high energy physics: the causal perturbation theory programme, which gave rise to the Stueckelberg-Petermann renormalization group, and the debate about the consistency of quantum electrodynamics, which gave rise to the Gell-Mann-Low renormalization group. Recognising the different motivations that shaped these early approaches sheds light on the formal and interpretive diversity we find in contemporary renormalization group methods.     

Some philosophical aspects of particle physics

The paper is concerned with explaining some of the principal theoretical developments in elementary particle physics and discussing the associated methodological problems both in respect of heuristics and appraisal. Particular reference is made to relativistic quantum field theory, renormalization, Feynman diagram techniques, the analytic S-matrix and the Chew — Frautschi bootstrap.     

A Bayesian reconstruction of the methodology of scientific research programmes

The paper is concerned with explaining some of the principal theoretical developments in elementary particle physics and discussing the associated methodological problems both in respect of heuristics and appraisal. Particular reference is made to relativistic quantum field theory, renormalization, Feynman diagram techniques, the analytic S-matrix and the Chew — Frautschi bootstrap.     

Understanding as explanatory knowledge: The case of Bjorken scaling

In this paper, we develop and refine the idea that understanding is a species of explanatory knowledge. Specifically, we defend the idea that S understands why p if and only if S knows that p, and, for some q, S’s true belief that q correctly explains p is produced/maintained by reliable explanatory evaluation. We then show how this model explains the reception of James Bjorken’s explanation of scaling by the broader physics community in the late 1960s and early 1970s. The historical episode is interesting because Bjorken’s explanation initially did not provide understanding to other physicists, but was subsequently deemed intelligible when Feynman provided a physical interpretation that led to experimental tests that vindicated Bjorken’s model. Finally, we argue that other philosophical models of scientific understanding are best construed as limiting cases of our more general model.     

Spacetime Visualisation and the Intelligibility of Physical Theories

This paper argues that spacetime visualisability is not a necessary condition for the intelligibility of theories in physics. Visualisation can be an important tool for rendering a theory intelligible, but it is by no means a sine qua non. The paper examines the historical transition from classical to quantum physics, and analyses the role of visualisability (Anschaulichkeit) and its relation to intelligibility. On the basis of this historical analysis, an alternative conception of the intelligibility of scientific theories is proposed, based on Heisenberg's reinterpretation of the notion of Anschaulichkeit.     

On conceptual issues in classical electrodynamics: Prospects and problems of an action-at-a-distance interpretation

Some conceptual issues in the foundations of classical electrodynamics concerning the interaction between particles and fields have recently received increased attention among philosophers of physics. After a brief review of the debate, I argue that there are essentially two incompatible solutions to these issues corresponding to F.A. Muller's distinction between the extension and the renormalization program. Neither of these solutions comes free of cost: the extension program is plagued with all problems related to extended elementary charges, the renormalization program works with point charges but trades in the notorious divergences of the field energies. The aim of this paper is to bring back into the discussion a third alternative, the action-at-a-distance program, which avoids both the riddles of extended elementary charges as well as the divergences although it admittedly has other problems. It will be discussed, why action-at-a-distance theories are actually not a far cry from particle–field theories, and I will argue that the main reasons for rejecting action-at-a-distance theories originate in certain metaphysical prejudices about locality and energy conservation. I will broadly suggest how these concepts could be adapted in order to allow for action at a distance.     

Drawing scales apart: The origins of Wilson's conception of effective field theories

This article traces the origins of Kenneth Wilson's conception of effective field theories (EFTs) in the 1960s. I argue that what really made the difference in Wilson's path to his first prototype of EFT are his long-standing pragmatic aspirations and methodological commitments. Wilson's primary interest was to work on mathematically interesting physical problems and he thought that progress could be made by treating them as if they could be analyzed in principle by a sufficiently powerful computer. The first point explains why he had no qualms about twisting the structure of field theories; the second why he divided the state-space of a toy model field theory into continuous slices by following a standard divide-and-conquer algorithmic strategy instead of working directly with a fully discretized and finite theory. I also show how Wilson's prototype bears the mark of these aspirations and commitments and clear up a few striking ironies along the way.     

John Wheeler’s Desert Island: The conservatism of non-empirical physics

This paper argues that non-empirical physics, as paradigmatically embodied by string theory, is a conservative research program, in spite of appearances. John Wheeler's 1950s research program of "daring conservatism" is identified as another non-empirical research program that checks all the same boxes as string theory. This case study is used to further analyze the connection between conservatism and a non-empirical approach. It is concluded that the prime difficulty of non-empirical physics is not that it involves unbridled speculation, but that the lack of empirical input prevents it from achieving revolutionary progress.     

From aether impulse to QED: Sommerfeld and the Bremsstrahlen theory

The radiation that is due to the braking of charged particles has been in the focus of theoretical physics since the discovery of X-rays by the end of the 19th century. The impact of cathode rays in the anti-cathode of an X-ray tube that resulted in the production of X-rays led to the view that X-rays are aether impulses spreading from the site of the impact. In 1909, Arnold Sommerfeld calculated from Maxwell׳s equations the angular distribution of electromagnetic radiation due to the braking of electrons. He thereby coined the notion of “Bremsstrahlen.” In 1923, Hendrik A. Kramers provided a quantum theoretical explanation of this process by means of Bohr׳s correspondence principle. With the advent of quantum mechanics the theory of bremsstrahlung became a target of opportunity for theorists like Yoshikatsu Sugiura, Robert Oppenheimer, and–again–Sommerfeld, who presented in 1931 a comprehensive treatise on this subject. Throughout the 1930s, Sommerfeld׳s disciples in Munich and elsewhere extended and improved the bremsstrahlen theory. Hans Bethe and Walter Heitler, in particular, in 1934 presented a theory that was later regarded as “the most important achievement of QED in the 1930s” (Freeman Dyson). From a historical perspective the bremsstrahlen problem may be regarded as a probe for the evolution of theories in response to revolutionary changes in the underlying principles.     

The non-relativistic limits of the Maxwell and Dirac equations: the role of Galilean and gauge invariance

The aim of this paper is to illustrate four properties of the non-relativistic limits of relativistic theories: (a) that a massless relativistic field may have a meaningful non-relativistic limit, (b) that a relativistic field may have more than one non-relativistic limit, (c) that coupled relativistic systems may be “more relativistic” than their uncoupled counterparts, and (d) that the properties of the non-relativistic limit of a dynamical equation may differ from those obtained when the limiting equation is based directly on exact Galilean kinematics. These properties are demonstrated through an examination of the non-relativistic limit of the familiar equations of first-quantized QED, i.e., the Dirac and Maxwell equations. The conditions under which each set of equations admits non-relativistic limits are given, particular attention being given to a gauge-invariant formulation of the limiting process especially as it applies to the electromagnetic potentials. The difference between the properties of a limiting theory and an exactly Galilean covariant theory based on the same dynamical equation is demonstrated by examination of the Pauli equation.     

Transcendental philosophy and mathematical physics

This paper explores the relationship between Kant’s views on the metaphysical foundations of Newtonian mathematical physics and his more general transcendental philosophy articulated in the Critique of pure reason. I argue that the relationship between the two positions is very close indeed and, in particular, that taking this relationship seriously can shed new light on the structure of the transcendental deduction of the categories as expounded in the second edition of the Critique.     

String theory,Einstein, and the identity of physics: Theory assessment in absence of the empirical

String theorists are certain that they are practicing physicists. Yet, some of their recent critics deny this. This paper argues that this conflict is really about who holds authority in making rational judgment in theoretical physics. At bottom, the conflict centers on the question: who is a proper physicist? To illustrate and understand the differing opinions about proper practice and identity, we discuss different appreciations of epistemic virtues and explanation among string theorists and their critics, and how these have been sourced in accounts of Einstein's biography. Just as Einstein is claimed by both sides, historiography offers examples of both successful and unsuccessful non-empirical science. History of science also teaches that times of conflict are often times of innovation, in which novel scholarly identities may come into being. At the same time, since the contributions of Thomas Kuhn historians have developed a critical attitude towards formal attempts and methodological recipes for epistemic demarcation and justification of scientific practice. These are now, however, being considered in the debate on non-empirical physics.     

Edison and science: a curious result

In November 1875, Thomas Edison made the sensational announcement that he had discovered a new force of nature, etheric force. It was to emerge some years later that the phenomenon Edison described was a form of wireless transmission, but Edison failed both to advance his theory and to exploit his discovery in new inventions. I contrast Edison’s approach to doing science with what he did when inventing, and also with the approach used by his principal scientific opponents. This contrast reveals that he failed, not so much because he was an inventor who did science badly, but because when he ventured into scientific theory-making he abandoned key techniques that made him America’s most successful inventor. From this I argue that we can identify artefact creation processes in science that parallel the process of invention, and that Edison failed because his opponents created better artefacts.     

I ain’t afraid of no ghost

This paper criticizes the traditional philosophical account of the quantization of gauge theories and offers an alternative. On the received view, gauge theories resist quantization because they feature distinct mathematical representatives of the same physical state of affairs. This resistance is overcome by a sequence of ad hoc modifications, justified in part by reference to semiclassical electrodynamics. Among other things, these modifications introduce ”ghosts”: particles with unphysical properties which do not appear in asymptotic states and which are said to be purely a notational convenience. I argue that this sequence of modifications is unjustified and inadequate, making it a poor basis for the interpretation of ghosts. I then argue that gauge theories can be quantized by the same method as any other theory. On this account, ghosts are not purely notation: they are coordinates on the classical configuration space of the theory—specifically, on its gauge structure. This interpretation does not fall prey to the standard philosophical arguments against the significance of ghosts, due to Weingard. Weingard’s argumentative strategy, properly applied, in fact tells in favor of ghosts’ physical significance.     

Genesis of Karl Popper's EPR-like experiment and its resonance amongst the physics community in the 1980s

I present the reconstruction of the involvement of Karl Popper in the community of physicists concerned with foundations of quantum mechanics, in the 1980s. At that time Popper gave active contribution to the research in physics, of which the most significant is a new version of the EPR thought experiment, alleged to test different interpretations of quantum mechanics. The genesis of such an experiment is reconstructed in detail, and an unpublished letter by Popper is reproduced in the present paper to show that he formulated his thought experiment already two years before its first publication in 1982. The debate stimulated by the proposed experiment as well as Popper's role in the physics community throughout 1980s is here analysed in detail by means of personal correspondence and publications.     

To envision a new particle or change an existing law? Hypothesis formation and anomaly resolution for the curious case of the β decay spectrum

This paper addresses the question of how scientists determine which type of hypothesis is most suitable for tackling a particular problem by examining the historical case of the anomalous β spectrum in early nuclear physics (1927–1934), a puzzle that occasioned the most diverse hypotheses amongst physicists at the time. It is shown that such determinations are most often implicitly informed by scientists' individual perspectives on the structural relations between the various elements of the theory and the problem at hand. In addition to this main result, it is suggested that Wolfgang Pauli's neutrino idea may well have been an adaptation of Ernst Rutherford's original and older neutron idea, which would provide evidence that the adaptation of older ideas is a more common practice than is often thought.     

Einstein׳s Equations for Spin 2 Mass 0 from Noether׳s Converse Hilbertian Assertion

An overlap between the general relativist and particle physicist views of Einstein gravity is uncovered. Noether׳s 1918 paper developed Hilbert׳s and Klein׳s reflections on the conservation laws. Energy-momentum is just a term proportional to the field equations and a ‘curl’ term with identically zero divergence. Noether proved a converse “Hilbertian assertion”: such “improper” conservation laws imply a generally covariant action.Later and independently, particle physicists derived the nonlinear Einstein equations assuming the absence of negative-energy degrees of freedom (“ghosts”) for stability, along with universal coupling: all energy-momentum including gravity׳s serves as a source for gravity. Those assumptions (all but) imply (for 0 graviton mass) that the energy-momentum is only a term proportional to the field equations and a symmetric “curl,” which implies the coalescence of the flat background geometry and the gravitational potential into an effective curved geometry. The flat metric, though useful in Rosenfeld׳s stress-energy definition, disappears from the field equations. Thus the particle physics derivation uses a reinvented Noetherian converse Hilbertian assertion in Rosenfeld-tinged form.The Rosenfeld stress-energy is identically the canonical stress-energy plus a Belinfante curl and terms proportional to the field equations, so the flat metric is only a convenient mathematical trick without ontological commitment. Neither generalized relativity of motion, nor the identity of gravity and inertia, nor substantive general covariance is assumed. The more compelling criterion of lacking ghosts yields substantive general covariance as an output. Hence the particle physics derivation, though logically impressive, is neither as novel nor as ontologically laden as it has seemed.     

Defining disposition concepts: A brief history of the problem

The aim of this paper is twofold. Firstly, I give a brief account of the history of the debate on the problem of defining disposition concepts from its beginning in the late 1920s until today. This account is divided into four parts, corresponding with 2, 3, 4 and 5 of the paper, each of which deals with a major period of the debate. Section 2 reports up to the mid-1950s. Section 3 deals with important contributions to the discussion between 1955 and 1958. However, the progress made around that time was far ahead of the logical theory and techniques which were needed for foundational reasons and for a better understanding of the basic notions. Some logical techniques appropriate for that aim were developed in the late 1960s and early 1970s. Though not uncontroversial, those logical techniques resulted in improvements of the insights gained in the mid-1950s; I shall report on those logical techniques and their application to the problem of defining disposition concepts in Section 4. In the early 1990s, however, the whole tradition of defining disposition concepts in terms of conditionals has been challenged by some strong counter-examples which are treated in Section 5. Finally, the second of the aims of this paper is explored in Section 6, in which I sketch very briefly the current stage of the debate by discussing and evaluating the most recent approaches to the subject.