The book is a philosophical refection on the possibility of mathematical history. Are poosible models of historical phenomena so exact as those of physical ones? Mathematical models borrowed from quantum mechanics by the meditation of its interpretations are accomodated to history. The conjecture of many-variant history, alternative history, or counterfactual history is necessary for mathematical history. Conclusions about philosophy of history are inferred.

According to what has become a standard history of quantum mechanics, von Neumann in 1932 succeeded in convincing the physics community that he had proved that hidden variables were impossible as a matter of principle. Subsequently, leading proponents of the Copenhagen interpretation emphatically confirmed that von Neumann's proof showed the completeness of quantum mechanics. Then, the story continues, Bell in 1966 finally exposed the proof as seriously and obviously wrong; this rehabilitated hidden variables and made serious foundational research possible. 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 more balanced story. Most importantly, von Neumann did not claim 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 conclusion was basically that hidden-variables schemes must violate the "quantum principle" that all physical quantities are to be represented by operators in a Hilbert space. According to this conclusion, hidden-variables schemes are possible in principle but 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 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. (shrink)

The publication of the EPR paper in 1935 prompted Heisenberg to draft a manuscript on the question of the completability of quantum mechanics. We give here the English translation of this manuscript with a brief introduction and bibliography.

The two major options on which the current debate on the interpretation of quantum mechanics relies, namely realism and empiricism, are far from being exhaustive. There is at least one more position available, which is metaphysically as agnostic as empiricism, but which shares with realism a committment to considering the structure of theories as highly significant. The latter position has been named transcendentalism after Kant. In this paper, a generalized version of Kant's method is used. This yields a reasoning that (...) one is entitled to call a transcendental deduction of some major formal features of quantum mechanics. (shrink)

This is a self-contained introduction to the Everett interpretation of quantum mechanics. It is the introductory chapter of Many Worlds? Everett, quantum theory, and reality, S. Saunders, J. Barrett, A. Kent, and D. Wallace, Oxford University Press.

This article focuses on two of the main problems raising interpretational issues in quantum mechanics, namely the notorious measurement problem and the equally important but not quite as widely discussed problem of the classical regime. The two problems are distinct, but they are both intimately related to some of the issues arising from entanglement and density operators. The article aims to be fairly non-technical in language, but modern in outlook and covering the chosen topics in more depth than most introductory (...) treatments. (shrink)

We explore the different meanings of “quantum uncertainty” contained in Heisenberg’s seminal paper from 1927, and also some of the precise definitions that were developed later. We recount the controversy about “Anschaulichkeit”, visualizability of the theory, which Heisenberg claims to resolve. Moreover, we consider Heisenberg’s programme of operational analysis of concepts, in which he sees himself as following Einstein. Heisenberg’s work is marked by the tensions between semiclassical arguments and the emerging modern quantum theory, between intuition and rigour, and between (...) shaky arguments and overarching claims. Nevertheless, the main message can be taken into the new quantum theory, and can be brought into the form of general theorems. They come in two kinds, not distinguished by Heisenberg. These are, on one hand, constraints on preparations, like the usual textbook uncertainty relation, and, on the other, constraints on joint measurability, including trade-offs between accuracy and disturbance. (shrink)

In this paper, we discuss various aspects of Heisenberg’s thought on hidden variables in the period 1927–1935. We also compare Heisenberg’s approach to others current at the time, specifically that embodied by von Neumann’s impossibility proof, but also views expressed mainly in correspondence by Pauli and by Schroedinger. We shall base ourselves mostly on published and unpublished materials that are known but little-studied, among others Heisenberg’s own draft response to the EPR paper. Our aim will be not only to clarify (...) Heisenberg’s thought on the hidden-variables question, but in part also to clarify how this question was understood more generally at the time. (shrink)

We review the famous no-hidden-variables theorem in von Neumann’s 1932 book on the mathematical foundations of quantum mechanics. We describe the notorious gap in von Neumann’s argument, pointed out by Hermann and, more famously, by Bell. We disagree with recent papers claiming that Hermann and Bell failed to understand what von Neumann was actually doing.

The paper presents a detailed interpretation of Edgar Wind’s Experiment and Metaphysics, a unique work on the philosophy of physics which broke with the Neo-Kantian tradition under the influence of American pragmatism. Taking up Cassirer’s interpretation of physics, Wind develops a holistic theory of the experiment and a constructivist account of empirical facts. Based on the concept of embodiment which plays a key role in Wind’s later writings on art history, he argues, however, that the outcomes of measurements are contingent. (...) He then proposes an anti-Kantian conception of a metaphysics of nature. For him, nature is an unknown totality which manifests itself in discrepancies between theories and experiment, and hence the theory formation of physics can increasingly approximate the structure of nature. It is shown that this view is ambiguous between a transcendental, metaphysical realism in Kant’s sense and an internal realism in Putnam’s sense. Wind’s central claim is that twentieth century physics offers new options for resolving Kant’s cosmological antinomies. In particular, he connected quantum indeterminism with the possibility of human freedom, a connection that Cassirer sharply opposed. (shrink)

Using the volume of her works and correspondence recently edited by K. Herrmann, I assess the significance of Grete Hermann's work.