This paper describes a long-standing, though little-known, debate between Paul Dirac and Werner Heisenberg over the nature of scientific methodology, theory change, and intertheoretic relations. Following Heisenberg’s terminology, their disagreements can be summarized as a debate over whether the classical and quantum theories are “open” or “closed.” A close examination of this debate sheds new light on the philosophical views of two of the great founders of quantum theory.

In early 1927, Pascual Jordan published his version of what came to be known as the Dirac-Jordan statistical transformation theory. Later that year and partly in response to Jordan, John von Neumann published the modern Hilbert space formalism of quantum mechanics. Central to both formalisms are expressions for conditional probabilities of finding some value for one quantity given the value of another. Beyond that Jordan and von Neumann had very different views about the appropriate formulation of problems in the new (...) theory. For Jordan, unable to let go of the analogy to classical mechanics, the solution of such problems required the identification of sets of canonically conjugate variables, i.e., p’s and q’s. Jordan ran into serious difficulties when he tried to extend his approach from quantities with fully continuous spectra to those with wholly or partly discrete spectra. For von Neumann, not constrained by the analogy to classical physics and aware of the daunting mathematical difficulties facing the approach of Jordan ), the solution of a problem in the new quantum mechanics required only the identification of a maximal set of commuting operators with simultaneous eigenstates. He had no need for p’s and q’s. Related to their disagreement about the appropriate general formalism for the new theory, Jordan and von Neumann stated the characteristic new rules for probabilities in quantum mechanics somewhat differently. Jordan was the first to state those rules in full generality, von Neumann rephrased them and then sought to derive them from more basic considerations. In this paper we reconstruct the central arguments of these 1927 papers by Jordan and von Neumann and of a paper on Jordan’s approach by Hilbert, von Neumann, and Nordheim. We highlight those elements in these papers that bring out the gradual loosening of the ties between the new quantum formalism and classical mechanics. (shrink)

The ArgumentIn this paper I argue that Kuhn's and Hanson's notion of incommensurable paradigms is rooted in the rhetoric of finality of the Copenhagen dogma — the orthodox philosophical interpretation of quantum physics. I also argue that arguments for holism of a paradigm, on which the notion of the impossibility of its gradual modification is based, misinterpret the Duhem-Quine thesis. The history of science (Copernican, Chemical, and Quantum Revolutions) demonstrates fruitful selective appropriation of ideas from seemingly “incommensurable” paradigms (rather than (...) the impossibility of communication between their representatives). I argue in conclusion that such openness underlies scientific creativity, and that dialogue between different alternatives is indispensable for the growth of knowledge. (shrink)

Zuerst werden die Argumente rekonstruiert, die dafür sprechen, Einsteins Wort, dass Gott nicht würfelt, als Ausdruck eines überholten deterministischen Weltbildes anzusehen. Anschließend werden Forschungsergebnisse der letzten Jahrzehnte benannt, die für eine Neubewertung seiner Position zur dominanten Interpretation der Quantenmechanik sprechen. Den Abschluß bildet die Diskussion der Möglichkeiten einer Reinterpretation seines Satzes vom nicht würfelnden Gott.

For many among the scientifically informed public, and even among physicists, Heisenberg's uncertainty principle epitomizes quantum mechanics. Nevertheless, more than 86 years after its inception, there is no consensus over the interpretation, scope, and validity of this principle. The aim of this chapter is to offer one such interpretation, the traces of which may be found already in Heisenberg's letters to Pauli from 1926, and in Dirac's anticipation of Heisenberg's uncertainty relations from 1927, that stems form the hypothesis of finite (...) nature. Instead of a mere mathematical theorem of quantum theory, or a manifestation of "wave-particle duality", the uncertainty relations turn out to be a result of a more fundamental premise, namely, the inherent limitation on spatial resolution that follows from the bound on physical resources. The implication of this view are far reaching: it depicts the Hilbert space formalism as a phenomenological, "effective", formalism that approximates an underlying discrete structure; it supports a novel interpretation of probability in statistical physics that sees probabilities as deterministic, dynamical transition probabilities which arise from objective and inherent measurement errors; and it helps to clarify several puzzles in the foundations of statistical physics, such as the status of the "disturbance" view of measurement in quantum theory, or the tension between ontology and epistemology in the attempts to describe nature with physical theories whose formalisms include subjective probabilities. Finally, this view also renders obsolete the entire class of interpretations of quantum theory that adhere to "the reality of the wave function". (shrink)

We want to consider anew the question, which is recurrent along the history of philosophy, of the relationship between rationality and mathematics, by inquiring to which extent the structuration of rationality, which ensures the unity of its function under a variety of forms (and even according to an evolution of these forms), could be considered as homeomorphic with that of mathematical thought, taken in its movement and made concrete in its theories. This idea, which is as old as philosophy itself, (...) although it has not been dominant, has still been present to some degree in the thought of modern science, in Descartes as well as in Kant, Poincaré or Einstein (and a few other scientists and philosophers). It has been often harshly questioned, notably in the contemporaneous period, due to the failure of the logistic programme, as well as to the variety of “empirical” knowledges, and, in a general way, to the character of knowledges that show them as transitory, evolutive and mind-built. However, the analysis of scientific thought through its inventive and creative processes leads to characterize this thought as a type of rational form whose configurations can be detailed rather precisely. In this work we shall propose, first, a quick sketch of some philosophical requirements for such a research programme, among which the need for an harmonization, and even a conciliation, between the notions of rational (or rationality), of intuitive grasp and of creative thought. Then we shall examine some processes of creative scientific thought bearing on the knowledge and the understanding of the world, distinct from mathematics although keeping tight relations with them. Contemporary physical theories are privileged witnesses in this respect, for in them the rational thought of phenomena makes an intrinsic use of mathematical thought, which contributes to the structuration of the formers and to the expression of their concepts (which entails the physical contents of the latter). The General Theory of Relativity and the Quantum Theory are exemplar to this, as they directly reveal what can be called the “drag of physical thought par the mathematical form”, which makes possible to overcome the limitations of the physical knowledge previously adquired. This process is tightly related to the modalities and to the stucture of the rational thought underlying it. This is what we would like to show. DOI:10.5007/1808-1711.2011v15n2p303. (shrink)

A re-evaluation of the notion of vacuum in quantum electrodynamics is presented, focusing on the vacuum of the quantized electromagnetic field. In contrast to the ‘nothingness’ associated to the idea of classical vacuum, subtle aspects are found in relation to the vacuum of the quantized electromagnetic field both at theoretical and experimental levels. These are not the usually called vacuum effects. The view defended here is that the so-called vacuum effects are not due to the ground state of the quantized (...) electromagnetic field. Nevertheless it is possible to maintain an empirically demonstrable notion of vacuum state that is consistent with the interpretation of the formalism of the theory. (shrink)

Traditional nomological accounts of scientific explanation have assumed that a good scientific explanation consists in the derivation of the explanandum’s description from theory (plus antecedent conditions). But in more recent philosophy of science the adequacy of this approach has been challenged, because the relation between theory and phenomena in actual scientific practice turns out to be more intricate. This critique is here examined for an explanatory paradigm that was groundbreaking for 20th century physics and chemistry (and their interrelation): Bohr’s first (...) model of the atom and its explanatory relevance for the spectrum of hydrogen. First, the model itself is analysed with respect to the principles and assumptions that enter into its premises. Thereafter, the origin of the model’s explanandum is investigated. It can be shown that the explained “phenomenon” is itself the product of a host of modelling accomplishments that stem from an experimental tradition related to 19th century chemistry, viz. spectroscopy. The relation between theory and phenomenon is thus mediated in a twofold way: by (Bohr’s) theoretical model and a phenomenological model from spectroscopy. In the final section of the paper an account is outlined that nevertheless permits us to acknowledge this important physico-chemical achievement as a case of (nomological) explanation. (shrink)

I reinterpret Bohr's attitude towards quantum mechanical formalism and its empirical content, based on his understanding of the correspondence principle and its approximate applicability. I suggest that Bohr understood complementarity as a limitation imposed by the commutation relations upon the applicability of the idealizations which had grounded the use of the correspondence principle. By discussing this interpretation against the contemporary background of discussions regarding “naïve realism” about operators (as observables), I suggest that a Bohrian view on the empirical content of (...) quantum mechanical operators may provide a middle ground between complete contextualism and an untenable realism about quantum properties. (shrink)

This paper studies the notion of virtuality in the Bohr-Kramers-Slater theory of 1924. We situate the virtual entities of BKS within the tradition of the correspondence principle and the radiation theory of the Bohr model. We show how, in this context, virtual oscillators emerged as classical substitute radiators and were used to describe the otherwise elusive quantum transitions. They played an effective role in the quantum theory of radiation while remaining categorically distinct and ontologically separated from the quantum world of (...) the Bohr model. The notion of virtuality thus differs markedly from its counterpart in quantum mechanics or QFT. (shrink)

In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Using Bohr’s correspondence principle and Einstein’s quantum theory of radiation along with advanced techniques from classical mechanics, Van Vleck showed that quantum formulae for emission, absorption, and dispersion of radiation merge with their classical counterparts in the limit of high quantum numbers. For modern readers Van Vleck’s paper is (...) much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg’s Umdeutung paper. This makes Van Vleck’s paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself. (shrink)

This article examines the problem of the origins of the correspondence principle formulated by Bohr in 1920 and intends to test the correctness of the argument that the essential elements of that principle were already present in the 1913 “trilogy”. In contrast to this point of view, moreover widely shared in the literature, this article argues that it is possible to find a connection between the formulation of the correspondence principle and the assessment that led Bohr to abandon the search (...) for a Planck-type theory. In fact, a thorough examination of Bohr’s works shows that the birth of this principle coincided with the depletion of a research program whose origins may date back to Bohr’s stay at the Rutherford’s laboratory (summer 1912). Finally, this article argues that original program of research was abandoned when it became clear that Planck’s quantum hypothesis for the harmonic oscillator was not an adequate support for the theoretical architecture of atomic physics; namely, there was evidence enough to justify a most drastic conclusion, according to Bohr: “I do not think that a theory of the Planck type can be made logical consistent”. (shrink)

The laser, first operated in 1960, produced light with coherence properties that demanded explanation. While some attempted a treatment within the framework of classical coherence theory, others insisted that only quantum electrodynamics could give adequate insight and generality. The result was a sharp and rather bitter controversy, conducted over the physics and mathematics that were being deployed, but also over the criteria for doing good science. Three physicists were at the center of this dispute, Emil Wolf, Max Born’s collaborator on (...) a canonical text on optics as a branch of classical electromagnetism, Roy J. Glauber, a student of Julian Schwinger and a high-energy particle theorist, and Leonard Mandel, both experimentalist and theorist and versed in the physics of photodetection. The story told here is thus one of three distinct research trajectories and of the explosion that occurred when, pushed into the well-financed field of laser studies, these trajectories collided. (shrink)

PhD dissertation addressing what can be called conceptual-mathematical anomalies in quantum electrodynamics. This work can be seen as following the line of philosophy of physics studies of quantum field theory that started to emerge in a systematic way in the early eighties of last century. One example is Teller’s work on standard quantum electrodynamics.In this work, by following a historical approach, I will return to the standard version of quantum electrodynamics, which is the only one available when we want to (...) get numbers out to compare with experimental results. This work spins around two main vectors. One is the divergence of the S-matrix series expansion, the other is the spatio-temporal description of physical processes in the theory. (shrink)

Philosophical interpretations of theories generally presuppose that a theory can be presented as a consistent mathematical formulation that is interpreted through models. Algebraic quantum field theory (AQFT) can fit this interpretative model. However, standard Lagrangian quantum field theory (LQFT), as well as quantum electrodynamics and nuclear physics, resists recasting along such formal lines. The difference has a distinct bearing on ontological issues. AQFT does not treat particle interactions or the standard model. This paper develops a framework and methodology for interpreting (...) such informal theories as LQFT and the standard model. We begin by summarizing two minimal epistemological interpretation of non-relativistic quantum mechanics (NRQM): Bohrian semantics, which focuses on communicables; and quantum information theory, which focuses on the algebra of local observables. Schwinger's development of quantum field theory supplies a unique path from NRQM to QFT, where each step is conceptually anchored in local measurements. LQFT and the standard model rely on postulates that go beyond the limits set by AQFT and Schwinger's anabatic methodology. The particle ontology of the standard model is clarified by regarding the standard model as an informal modular theory with a limited range of validity. (shrink)

The idea of a canonical transformation emerged in 1837 in the course of Carl Jacobi's researches in analytical dynamics. To understand Jacobi's moment of discovery it is necessary to examine some background, especially the work of Joseph Lagrange and Siméon Poisson on the variation of arbitrary constants as well as some of the dynamical discoveries of William Rowan Hamilton. Significant figures following Jacobi in the middle of the century were Adolphe Desboves and William Donkin, while the delayed posthumous publication in (...) 1866 of Jacobi's full dynamical corpus was a critical event. François Tisserand's doctoral dissertation of 1868 was devoted primarily to lunar and planetary theory but placed Hamilton–Jacobi mathematical methods at the forefront of the investigation. Henri Poincaré's writings on celestial mechanics in the period 1890–1910 succeeded in making canonical transformations a fundamental part of the dynamical theory. Poincaré offered a mathematical vision of the subject that differed from Jacobi's and would become influential in subsequent research. Two prominent researchers around 1900 were Carl Charlier and Edmund Whittaker, and their books included chapters devoted explicitly to transformation theory. In the first three decades of the twentieth century Hamilton–Jacobi theory in general and canonical transformations in particular would be embraced by a range of researchers in astronomy, physics and mathematics. (shrink)

We analyze the evolution of EHRENFEST's thought since he proved the necessity of quanta in 1911 until the formulation of his adiabatic hypothesis in 1914. We argue that his research contributed significantly to the solution of critical problems in quantum physics and led to a rigorous definition of the range of validity of BOLTZMANN's principle.

This paper considers the importance of unification in the context of developing scientific theories. I argue that unifying hypotheses are not valuable simply because they are supported by multiple lines of evidence. Instead, they can be valuable because they guide experimental research in different domains in such a way that the results from those experiments inform the scope of the theory being developed. I support this characterization by appealing to the early development of quantum theory. I then draw some comparisons (...) with discussions of robustness reasoning. (shrink)

Authoritative appraisals have qualified this book as an “axiomatic” theory. However, given that its essential content is no more than an analogy, its theoretical organization cannot be axiomatic. Indeed, in the first edition Dirac declares that he had avoided an axiomatic presentation. Moreover, I show that the text aims to solve a basic problem (How quantum mechanics is similar to classical mechanics?). A previous paper analyzed all past theories of physics, chemistry and mathematics, presented by the respective authors non-axiomatically. Four (...) characteristic features of a new model of organizing a theory were recognized. A careful examination of Dirac’s text shows that it actually applied this kind of organization of a theory, confirming formally what Kronz and Lupher suggested through intuitive categories (pragmatism and rigour), i.e. Dirac’s formulation of Quantum mechanics represents a distinct theoretical approach from von Neumann’s axiomatic approach. However, since the second edition Dirac has changed his approach: although relying again on analogy, his theory refers to the axiomatic method. Some considerations on the odd paths which led to the present formulation of QM are added. They suggest that a new foundation of this theory needs to be found. (shrink)

The purpose of this dissertation is to contribute to our understanding of scientific theory pursuit by providing a detailed case study on the development of early quantum theory, from roughly 1900 to 1916. I first elaborate on why this case should be considered an instance of piecemeal pursuit by presenting the historical quantum conjectures that were being used in different contexts. These conjectures gave varied interpretations of quantization. By comparing these conjectures, I identify a general quantum postulate that captures the (...) underlying assumption common to all the cases. I argue that it is possible to consider a general postulate about quantization even when its proper application is ambiguous in a given context, and that the postulate can be separated from different elements of the framework being used to investigate it. I show that the quantum postulate can be deemed promising by analysing the support it gains using a Bayesian framework. I first defend the use of such a framework by considering the purported inconsistencies in Planck's introduction of his quantum conjecture and how we should handle these. I then explicate two cases of support for the postulate. First, I show how we can use a particular solution to the Bayesian problem of old evidence to interpret the support the quantum postulate received by accounting for phenomena that had no previous explanation. Finally, I show that the quantum postulate is also supported by a unification argument, where unification is interpreted as informational relevance between the different domains of inquiry. (shrink)

This paper considers the importance of unification in the context of developing scientific theories. I argue that unifying hypotheses are not valuable simply because they are supported by multiple lines of evidence. Instead, they can be valuable because they guide experimental research in different domains in such a way that the results from those experiments inform the scope of the theory being developed. I support this characterization by appealing to the early development of quantum theory. I then draw some comparisons (...) with discussions of robustness reasoning. (shrink)

The aim of this paper is to combine the intellectual and the psychosocial aspects. blurring the distinction between the conceptual and the anecdotal history of quantum mechanics. The full realization of the importance of such “anecdotal” factors leads to the revision of our understanding of the conceptual development itself. The paper concludes with the suggestion that a major part of numerous inconsistencies in the Copenhagen interpretation of quantum physics are of a psychosocial origin.

Niels Bohr’s “correspondence principle” is typically believed to be the requirement that in the limit of large quantum numbers (n→∞) there is a statistical agreement between the quantum and classical frequencies. A closer reading of Bohr’s writings on the correspondence principle, however, reveals that this interpretation is mistaken. Specifically, Bohr makes the following three puzzling claims: First, he claims that the correspondence principle applies to small quantum numbers as well as large (while the statistical agreement of frequencies is only for (...) large n); second, he claims that the correspondence principle is a law of quantum theory; and third, Bohr argues that formal apparatus of matrix mechanics (the new quantum theory) can be thought of as a precise formulation of the correspondence principle. With further textual evidence, I offer an alternative interpretation of the correspondence principle in terms of what I call Bohr’s selection rule. I conclude by showing how this new interpretation of the correspondence principle readily makes sense of Bohr’s three puzzling claims. (shrink)

In 1927, Paul Dirac first explicitly introduced the idea that electrodynamical processes can be evaluated by decomposing them into virtual (modern terminology), energy non-conserving subprocesses. This mode of reasoning structured a lot of the perturbative evaluations of quantum electrodynamics during the 1930s. Although the physical picture connected to Feynman diagrams is no longer based on energy non-conserving transitions but on off-shell particles, emission and absorption subprocesses still remain their fundamental constituents. This article will access the introduction and the initial reception (...) of this picture of subsequent transitions (PST) by conceiving of concepts, models, and their representations as tools for the practitioners. I will argue for a multi-factorial explanation of Dirac’s initial, verbally explicit introduction: the mathematical representation he had developed was highly suggestive and already partly conceptualized; Dirac was philosophical flexible enough to talk about transitions when no actual transitions, according to the general interpretation of quantum mechanics of the time, occurred; and, importantly, Dirac eventually used the verbal exposition in the same paper in which he introduced it. The direct impact of PST on the conception of quantum electrodynamical processes will be exemplified by its reflection in diagrammatical representations. The study of the diverging ontological commitments towards PST immediately after its introduction opens up the prehistory of a philosophical debate that stretches out into the present: the dispute about the representational and ontological status of the physical picture connected to the evaluation of the perturbative series of QED and QFT. (shrink)

In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck used Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum formulae for the emission, absorption, and dispersion of radiation. The paper is similar but in many ways superior to the well-known paper by Kramers and Heisenberg published the following year that is widely credited (...) to have led directly to Heisenberg's Umdeutung paper. As such, it clearly shows how strongly the discovery of matrix mechanics depended on earlier work on the application of the correspondence principle to the interaction of matter and radiation. (shrink)

This article discusses the meaning of the notion of virtuality in modern physics. To this end, it develops considerations on the introduction and establishment in nuclear physics of two independent concepts at the turn of the 1920s and 1930s: that of the virtual state, used in the context of neutron scattering studies, and that of the virtual transition, useful for the theoretical understanding of strong nuclear forces, which forms the basis of what are now called virtual particles. Their comparative analysis (...) highlights the theoretical nature of virtual entities and processes in modern physics. It also shows how the virtual has been associated with various purely physical attributes, leading to a form of polysemy of the term, from the beginning of the application of these concepts. (shrink)

Once one of the main protagonists of history of science, the historiography on quantum theory has recently gone through a process of reconfiguration of methods, research questions and epistemological framework. In this paper, I review the recent developments and propose some reflections on its future evolution.

The essential role of classical mechanics in the “old quantum theory” is well known. With the rise of a genuine quantum formalism, classical analogies remained a powerful heuristic tool. However, classical insights soon proved problematic, and in some cases, even counterproductive. The case of the implementation of quantum canonical transformations provides a distinguished case study for the historian studying the circumstances which led to the transformation theory of London, Dirac and Jordan. -/- The attempts to use canonical transformations in strict (...) analogy to classical practice met serious difficulties as soon as one tried to accommodate the action-angle scheme. At some point, the very consistency of quantization went addressed because of the unclear quantum equivalence of classically equivalent Hamiltonians. -/- The early attempts, often beset with ill-defined problems, are illustrative of the lack of understanding of the underlying mathematical scheme. The latter had to be properly appraised before the problem of the meaning of changing variables in quantum theory could be solved. This is why the latter proved instrumental in the discovery of transformation theory. -/- Some of the problems which arose then are still highly instructive from the foundational point of view, and worth to be rediscovered, beyond their historical interest. (shrink)

This paper re-evaluates the formative year of quantum mechanics—from Heisenberg’s first paper on matrix mechanics to Schrödinger’s equivalence proof—by focusing on the role of radiation in the emerging theory. We argue that the radiation problem played a key role in early quantum mechanics, a role that has not been taken into account in the standard histories. Radiation was perceived by the main protagonists of matrix and wave mechanics as a central lacuna in these emerging theories and continued to contribute to (...) the theoretical development and conceptual clarification of quantum mechanics. Studying the interplay between quantum mechanics and radiation, the paper provides an account of (a) how quantum mechanics was able to connect to its empirical basis in spectroscopy and (b) how Schrödinger’s equivalence proof emerged from his explorative calculations on the emission of radiation. (shrink)