Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 2017

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.

Physical Review A, 2009

Is is shown here that the "simple test of quantumness for a single system" of arXiv:0704.1962 (for a recent experimental realization see arXiv:0804.1646) has exactly the same relation to the discussion of to the problem of describing the quantum system via a classical probabilistic scheme (that is in terms of hidden variables, or within a realistic theory) as the von Neumann theorem (1932). The latter one was shown by Bell (1966) to stem from an assumption that the hidden variable values for a sum of two non-commuting observables (which is an observable too) have to be, for each individual system, equal to sums of eigenvalues of the two operators. One cannot find a physical justification for such an assumption to hold for non-commeasurable variables. On the positive side. the criterion may be useful in rejecting models which are based on stochastic classical fields. Nevertheless the example used by the Authors has a classical optical realization.

Theoretical Computer Science, 2008

The seven papers in this special issue arose from the conference CiE 2006: Logical Approaches to Computational Barriers, held at the University of Wales Swansea in July, 2006. CiE 2006 was the second of a new series of conferences associated with the interdisciplinary network Computability in Europe.

2012

Abstract: We put forward a new take on the logic of quantum mechanics, following Schroedinger's point of view that it is composition which makes quantum theory what it is, rather than its particular propositional structure due to the existence of superpositions, as proposed by Birkhoff and von Neumann.

Synthese, 2012

This special issue is situated at the interface between Logic and the Foundations of Physics. This interface, though not as active as the logical foundations of mathematics, has long existed-with highlights such as "quantum logic", or studies of the general logical structure of physical theories. In recent years, more themes have come to the fore, and we may be witnessing a revival. The papers presented here emanate from a symposium held at the University of Utrecht in January 2008 with the aim of charting established as well as new connections between the two fields. One of the main questions discussed was whether and how modern techniques coming from logic, computer science and information theory might be combined with state-of-the-art insights in the philosophy of physics to gain a better understanding of the main foundational issues and open problems in modern physics. The success of this symposium has shown that there are several possible answers to this question. The invited papers in this issue present the reader with an overview of the main topics at play right now. A common

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Gödel incompleteness. I hypothesize that only computable and decidable (in Gödel's sense) structures exist, which alleviates the cosmological measure problem and may help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.

IT STAR Newsletter, 2013

An overview of the life of John von Neumann, analyzing the distribution of his publications and listing a few results having considerable impact in present day computing.

We discuss an apparent information paradox that arises in a materialist's description of the Universe if we assume that the Universe is 100% quantum. We discuss possible ways out of the paradox, including that Laws of Nature are not purely deterministic, or that gravity is classical. Our observation of the paradox stems from an interdisciplinary thought process whereby the Universe can be viewed as a " quantum computer ". Our presentation is intentionally nontechnical to make it accessible to as wide a readership base as possible.

When I first became fascinated with mathematics' tightly knit abstract structures, its prominence in physics and engineering reassured me. Mathematics' indisputable value in science made it clear that my preoccupation with its intangible expressions was not pathological. The captivating creative activity of doing mathematics has real consequences.

arXiv: History and Philosophy of Physics, 2018

Quantum mechanics predicts many surprising phenomena, including the two-slit interference of electrons. It has often been claimed that these phenomena cannot be understood in classical terms. But the meaning of "classical" is often not precisely specified. One might, for example, interpret it as "classical physics" or "classical logic" or "classical probability theory". Quantum mechanics also suffers from a conceptual difficulty known as the measurement problem. Early in his career, Hilary Putnam believed that modifications of classical logic could both solve the measurement problem and account for the two-slit phenomena. Over 40 years later he had abandoned quantum logic in favor of the investigation of various theories--using classical logic and probability theory--that can accomplish these tasks. The trajectory from Putnam's earlier views to his later views illustrates the difficulty trying to solve physical problems with alterations of...