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.     

Niels Bohr as philosopher of experiment: Does decoherence theory challenge Bohr׳s doctrine of classical concepts?

Niels Bohr׳s doctrine of the primacy of “classical concepts” is arguably his most criticized and misunderstood view. We present a new, careful historical analysis that makes clear that Bohr׳s doctrine was primarily an epistemological thesis, derived from his understanding of the functional role of experiment. A hitherto largely overlooked disagreement between Bohr and Heisenberg about the movability of the “cut” between measuring apparatus and observed quantum system supports the view that, for Bohr, such a cut did not originate in dynamical (ontological) considerations, but rather in functional (epistemological) considerations. As such, both the motivation and the target of Bohr׳s doctrine of classical concepts are of a fundamentally different nature than what is understood as the dynamical problem of the quantum-to-classical transition. Our analysis suggests that, contrary to claims often found in the literature, Bohr׳s doctrine is not, and cannot be, at odds with proposed solutions to the dynamical problem of the quantum–classical transition that were pursued by several of Bohr׳s followers and culminated in the development of decoherence theory.     

Heuristics versus norms: On the relativistic responses to the Kaufmann experiments

The aim of this article is to provide a historical response to Michel Janssen’s (2009) claim that the special theory of relativity establishes that relativistic phenomena are purely kinematical in nature, and that the relativistic study of such phenomena is completely independent of dynamical considerations regarding the systems displaying such behavior. This response will be formulated through a historical discussion of one of Janssen's cases, the experiments carried out by Walter Kaufmann on the velocity-dependence of the electron's mass. Through a discussion of the different responses formulated by early adherents of the principle of relativity (Albert Einstein, Max Planck, Hermann Minkowski and Max von Laue) to these experiments, it will be argued that the historical development of the special theory of relativity argues against Janssen's historical presentation of the case, and that this raises questions about his general philosophical claim. It will be shown, more specifically, that Planck and Einstein developed a relativistic response to the Kaufmann experiments on the basis of their study of the dynamics of radiation phenomena, and that this response differed significantly from the response formulated by Minkowski and Laue. In this way, it will be argued that there were, at the time, two different approaches to the theory of relativity, which differed with respect to its relation to theory, experiment, and history: Einstein's and Planck's heuristic approach, and Minkowski's and Laue's normative approach. This indicates that it is difficult to say, historically speaking, that the special theory of relativity establishes the kinematical nature of particular phenomena. Instead, it will be argued that the theory of relativity should not be seen as a theory but rather as outlining an approach, and that the nature of particular scientific phenomena is something that is open to scientific debate and dispute.     

Norton's material theory of analogy

In his book, The Material Theory of Induction, Norton argues that the quest for a universal formal theory or ‘schema’ for analogical inference should be abandoned. In its place, he offers the “material theory of analogy”: each analogical inference is “powered” by a local fact of analogy rather than by any formal schema. His minimalist model promises a straightforward, fact-based approach to the evaluation and justification of analogical inferences. This paper argues that although the rejection of universal schemas is justified, Norton's positive theory is limited in scope: it works well only for a restricted class of analogical inferences. Both facts and quasi-formal criteria have roles to play in a theory of analogical reasoning.     

How to put a black box in a showcase: History of science museums and recent heritage

Coping with recent heritage is troublesome for history of science museums, since modern scientific artefacts often suffer from a lack of esthetic and artistic qualities and expressiveness. The traditional object-oriented approach, in which museums collect and present objects as individual showpieces is inadequate to bring recent heritage to life. This paper argues that recent artefacts should be regarded as “key pieces.” In this approach the object derives its meaning not from its intrinsic qualities but from its place in an important historical event or development. The “key pieces” approach involves a more organic way of collecting and displaying, focussing less on the individual object and more on the context in which it functioned and its place in the storyline. Finally, I argue that the “key pieces” approach should not be limited to recent heritage. Using this method as a general guiding principle could be a way for history of science museums to appeal to today’s audiences.     

Von Neumann’s impossibility proof: Mathematics in the service of rhetorics

According to what has become a standard history of quantum mechanics, in 1932 von Neumann persuaded the physics community that hidden variables are impossible as a matter of principle, after which leading proponents of the Copenhagen interpretation put the situation to good use by arguing that the completeness of quantum mechanics was undeniable. This state of affairs lasted, so the story continues, until Bell in 1966 exposed von Neumann’s proof as obviously wrong. The realization that von Neumann’s proof was fallacious then rehabilitated hidden variables and made serious foundational research possible again. It is often added in recent accounts that von Neumann’s error had been spotted almost immediately by Grete Hermann, but that her discovery was of no effect due to the dominant Copenhagen Zeitgeist.We shall attempt to tell a story that is more historically accurate and less ideologically charged. Most importantly, von Neumann never claimed to have shown the impossibility of hidden variables tout court, but argued that hidden-variable theories must possess a structure that deviates fundamentally from that of quantum mechanics. Both Hermann and Bell appear to have missed this point; moreover, both raised unjustified technical objections to the proof. Von Neumann’s argument was basically that hidden-variables schemes must violate the “quantum principle” that physical quantities are to be represented by operators in a Hilbert space. As a consequence, hidden-variables schemes, though possible in principle, necessarily exhibit a certain kind of contextuality.As we shall illustrate, early reactions to Bohm’s theory are in agreement with this account. Leading physicists pointed out that Bohm’s theory has the strange feature that pre-existing particle properties do not generally reveal themselves in measurements, in accordance with von Neumann’s result. They did not conclude that the “impossible was done” and that von Neumann had been shown wrong.     

Inductive reasoning in the context of discovery: Analogy as an experimental stratagem in the history and philosophy of science

Building on Norton's “material theory of induction,” this paper shows through careful historical analysis that analogy can act as a methodological principle or stratagem, providing experimentalists with a useful framework to assess data and devise novel experiments. Although this particular case study focuses on late eighteenth and early nineteenth-century experiments on the properties and composition of acids, the results of this investigation may be extended and applied to other research programs. A stage in-between what Steinle calls “exploratory experimentation” and robust theory, I argue that analogy encouraged research to substantiate why the likenesses should outweigh the differences (or vice versa) when evaluating results and designing experiments.     

Truth may not explain predictive success,but truthlikeness does

In a recent paper entitled “Truth does not explain predictive success” (Analysis, 2011), Carsten Held argues that the so-called “No-Miracles Argument” for scientific realism is easily refuted when the consequences of the underdetermination of theories by the evidence are taken into account. We contend that the No-Miracles Argument, when it is deployed within the context of sophisticated versions of realism, based on the notion of truthlikeness (or verisimilitude), survives Held’s criticism unscathed.     

On the verge of <Emphasis Type="Italic">Umdeutung</Emphasis> in Minnesota: Van Vleck and the correspondence principle. Part two

This is the second installment of a two-part paper on developments in quantum dispersion theory leading up to Heisenberg’s Umdeutung paper. In telling this story, we have taken a 1924 paper by John H. Van Vleck in The Physical Review as our main guide. In this second part we present the detailed derivations on which our narrative in the first part rests. The central result that we derive is the Kramers dispersion formula, which played a key role in the thinking that led to Heisenberg’s Umdeutung paper. We derive classical formulae for the dispersion, emission, and absorption of radiation and use Bohr’s correspondence principle to construct their quantum counterparts both for the special case of a charged harmonic oscillator (Sect. 5) and for arbitrary non-degenerate multiply-periodic systems (Sect. 6). We then rederive these results in modern quantum mechanics (Sect. 7). This paper was written as part of a joint project in the history of quantum physics of the Max Planck Institut für Wissenschaftsgeschichte and the Fritz-Haber-Institut in Berlin. The authors gratefully acknowledge support from the Max Planck Institute for History of Science. The research of Anthony Duncan is supported in part by the National Science Foundation under grant PHY-0554660.     

Inventing paradigms,monopoly, methodology,and mythology at ‘Chicago’: Nutter,Stigler, and Milton Friedman

This paper aims to contribute to a better understanding of the formation of the so-called Chicago-school of economics; it does so by focusing on (i) previously unpublished correspondence between George Stigler and Thomas Kuhn as well as (ii) Warren Nutter’s The Extent of Enterprise Monopoly in the United States, 1899–1939. Nutter’s book started out as a (1949) doctoral dissertation at The University of Chicago, part of Aaron Director’s Free Market Study. Besides Director, O.H. Brownlee and Milton Friedman were closely involved with supervising it. It was published by The University of Chicago Press in 1951. The book was explicitly understood as belonging to the “Chicago School” (Dow & Abernathy, 1963). But by the time of Reder’s well known (1982) review paper Nutter does not figure at all. I argue that the Stigler-Kuhn correspondence helps us better understand why Nutter disappeared from sight. More important, by contrasting the work of Nutter with that of Harberger, the episode reveals how Milton Friedman’s methodological statements became the rhetoric for a paradigm that was committed to a very different approach than the one advocated by Nutter or Friedman.     

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.     

Complementarity,wave-particle duality,and domains of applicability

Complementarity has frequently, but mistakenly, been conflated with wave-particle duality, and this conflation has led to pervasive misunderstandings of Bohr's views and several misguided claims of an experimental “disproof” of complementarity. In this paper, I explain what Bohr meant by complementarity, and how this is related to, but distinct from, wave-particle duality. I list a variety of possible meanings of wave-particle duality, and canvass the ways in which they are (or are not) supported by quantum physics and Bohr's interpretation. I also examine the extent to which wave-particle duality should be viewed as an example of the sort of dualities one finds in, e.g., string theory. I argue that the most fruitful way of reading of Bohr's account complementarity is by comparing it to current accounts of effective theories with limited domains of applicability.     

The role of symmetry in the interpretation of physical theories

The symmetries of a physical theory are often associated with two things: conservation laws (via e.g. Noether׳s and Schur׳s theorems) and representational redundancies (“gauge symmetry”). But how can a physical theory׳s symmetries give rise to interesting (in the sense of non-trivial) conservation laws, if symmetries are transformations that correspond to no genuine physical difference? In this paper, I argue for a disambiguation in the notion of symmetry. The central distinction is between what I call “analytic” and “synthetic“ symmetries, so called because of an analogy with analytic and synthetic propositions. “Analytic“ symmetries are the turning of idle wheels in a theory׳s formalism, and correspond to no physical change; “synthetic“ symmetries cover all the rest. I argue that analytic symmetries are distinguished because they act as fixed points or constraints in any interpretation of a theory, and as such are akin to Poincaré׳s conventions or Reichenbach׳s ‘axioms of co-ordination’, or ‘relativized constitutive a priori principles’.     

The concept of intelligibility in modern physics (1948)

This is an English translation of Paul Feyerabend's earliest extant essay “Der Begriff der Verständlichkeit in der modernen Physik” (1948). In it, Feyerabend defends positivism as a progressive framework for scientific research in certain stages of scientific development. He argues that in physics visualizability (Anschaulichkeit) and intelligibility (Verständlichkeit) are time-conditioned concepts: what is deemed visualizable in the development of physical theories is relative to a specific historical context and changes over time. He concludes that from time to time the abandonment of visualizability is crucial for progress in physics, as it is conducive to major theory change, illustrating the point on the basis of advances in atomic theory.     

“Local–Global”: the first twenty years

This paper investigates how and when pairs of terms such as “local–global” and “im Kleinen–im Grossen” began to be used by mathematicians as explicit reflexive categories. A first phase of automatic search led to the delineation of the relevant corpus, and to the identification of the period from 1898 to 1918 as that of emergence. The emergence appears to have been, from the very start, both transdisciplinary (function theory, calculus of variations, differential geometry) and international, although the AMS-Göttingen connection played a specific part. First used as an expository and didactic tool (e.g. by Osgood), it soon played a crucial part in the creation of new mathematical concepts (e.g. in Hahn’s work), in the shaping of research agendas (e.g. Blaschke’s global differential geometry), and in Weyl’s axiomatic foundation of the manifold concept. We finally turn to France, where in the 1910s, in the wake of Poincaré’s work, Hadamard began to promote a research agenda in terms of “passage du local au general.”     

The case of the composite Higgs: The model as a “Rosetta stone” in contemporary high-energy physics

This paper analyses the practice of model-building “beyond the Standard Model” in contemporary high-energy physics and argues that its epistemic function can be grasped by regarding models as mediating between the phenomenology of the Standard Model and a number of “theoretical cores” of hybrid character, in which mathematical structures are combined with verbal narratives (“stories”) and analogies referring back to empirical results in other fields (“empirical references”). Borrowing a metaphor from a physics research paper, model-building is likened to the search for a Rosetta stone, whose significance does not lie in its immediate content, but rather in the chance it offers to glimpse at and manipulate the components of hybrid theoretical constructs. I shall argue that the rise of hybrid theoretical constructs was prompted by the increasing use of nonrigorous mathematical heuristics in high-energy physics. Support for my theses will be offered in form of a historical–philosophical analysis of the emergence and development of the theoretical core centring on the notion that the Higgs boson is a composite particle. I will follow the heterogeneous elements which would eventually come to form this core from their individual emergence in the 1960s and 1970s, through their collective life as a theoretical core from 1979 until the present day.