This essay considers and evaluates recent results and arguments from classical chaotic systems theory and non-relativistic quantum mechanics that pertain to the question of whether our world is deterministic or indeterministic. While the classical results are inconclusive, quantum mechanics is often assumed to establish indeterminism insofar as the measurement process involves an ineliminable stochastic element, even though the dynamics between two measurements is considered fully deterministic. While this latter claim concerning the Schrödinger evolution must be qualified, the former fully depends (...) on a resolution of the measurement problem. Two alleged proofs that nature is indeterministic, relying, in turn, on Gleason's theorem and Conway and Kochen's recent 'free will theorem', are shown to be wanting qua proofs of indeterminism. We are thus left with the conclusion that the determinism question remains open. (shrink)

A new proof of the impossibility of reconciling realism and locality in quantum mechanics is given. Unlike proofs based on Bell's inequality, the present work makes minimal and transparent use of probability theory and proceeds by demonstrating a Kochen-Specker type of paradox based on the value assignments to the spin components of two spatially separated spin-1 systems in the singlet state of their total spin. An essential part of the argument is to distinguish carefully two commonly confused types of contextuality; (...) we call them ontological and environmental contextuality. These in turn are associated with two quite distinct senses of nonlocality. We indicate the relevance of our treatment to other related discussions in recent literature on the philosophy of quantum mechanics. (shrink)

It has long been recognized that a local hidden variable theory of quantum mechanics can in principle be constructed, provided one is willing to countenance pre-measurement correlations between the properties of measured systems and measuring devices. However, this ‘conspiratorial’ approach is typically dismissed out of hand. In this article I examine the justification for dismissing conspiracy theories of quantum mechanics. I consider the existing arguments against such theories, and find them to be less than conclusive. I suggest a more powerful (...) argument against the leading strategy for constructing a conspiracy theory. Finally, I outline two alternative strategies for constructing conspiracy theories, both of which are immune to these arguments, but require one to either modify or reject the common cause principle. Introduction The incompleteness of quantum mechanics Hidden variables Hidden mechanism conspiracy theories Existing arguments against hidden mechanisms A new argument against hidden mechanisms Backwards-causal conspiracy theories Acausal conspiracy theories Conclusion. (shrink)

I insist that I was able to raise my hand, and I acknowledge that a law would have been broken had I done so, but I deny that I am therefore able to break a law. To uphold my instance of soft determinism, I need not claim any incredible powers. To uphold the compatibilism that I actually believe, I need not claim that such powers are even possible. My incompatibilist opponent is a creature of fiction, but he has his prototypes (...) in real life. He is modeled partly after Peter van Inwagen and partly on myself when I first worried about van Inwagen's argument against compatibilism. (shrink)

The Free Will Theorem of Conway \& Kochen on the one hand follows from uncontroversial parts of modern physics and elementary mathematical and logical reasoning, but on the other hand seems predicated on an undefined notion of free will. Although Conway and Kochen informally claim that their theorem supports indeterminism and, in its wake, a libertarian agenda for free will, inferring the former from the Free Will Theorem is a \emph{petitio principii}. Of course, this also considerably weakens the case for (...) the latter. A recent reformulation of the Free Will Theorem due to Cator and the author uses a mathematically precise formulation of the idea that experimentalists freely choose their settings even in a deterministic world, and thence construes the theorem as providing constraints on determinism. In the present paper we argue that the concept of free will used in this version of the theorem is essentially the one proposed by Lewis, also known as `local miracle compatibilism'. To do so, we give a mathematical reformulation of this idea, which we believe to be well within its spirit and which may be of independent interest. On this double reformulation the Free Will Theorem shows that local miracle compatibilism contradicts the parts of modern physics used in its assumptions. Therefore, although the intention of Conway and Kochen was to support free will through their theorem, what they actually achieved is the opposite: a well-known, philosophically viable version of free will now turns out to be incompatible with physics! (shrink)

This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are (...) covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence. (shrink)

On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. We show that this result is robust, and deduce that neither hidden variable theories nor mechanisms of the GRW type for wave function collapse can be made relativistic and causal. We also establish the (...) consistency of our axioms and discuss the philosophical implications. (shrink)

Bell’s theorem is purported to demonstrate the impossibility of a local “hidden variable” theory underpinning quantum mechanics. It relies on the well-known assumption of ‘locality’, and also on a little-examined assumption called ‘statistical independence’ (SI). Violations of this assumption have variously been thought to suggest “backward causation”, a “conspiracy” on the part of nature, or the denial of “free will”. It will be shown here that these are spurious worries, and that denial of SI simply implies nonlocal correlation between spacelike (...) degrees of freedom. Lorentz-invariant theories in which SI does not hold are easily constructed: two are exhibited here. It is conjectured, on this basis, that quantum-mechanical phenomena may be modeled by a local theory after all. (shrink)

The Bayesian approach to quantum mechanics of Caves, Fuchs and Schack is presented. Its conjunction of realism about physics along with anti-realism about much of the structure of quantum theory is elaborated; and the position defended from common objections: that it is solipsist; that it is too instrumentalist; that it cannot deal with Wigner's friend scenarios. Three more substantive problems are raised: Can a reasonable ontology be found for the approach? Can it account for explanation in quantum theory? Are subjective (...) probabilities on their own adequate in the quantum domain? The first question is answered in the affirmative, drawing on elements from Nancy Cartwright's philosophy of science. The second two are not: it is argued that these present outstanding difficulties for the project. A quantum Bayesian version of Moore's paradox is developed to illustrate difficulties with the subjectivist account of pure state assignments. (shrink)

One of the most interesting programs in the foundations of quantum mechanics is the realist quantum logic approach associated with Putnam, Bub, Demopoulos and Friedman (and which is the focus of my own research.) I believe that realist quantum logic is our best hope for making sense of quantum mechanics, but I have come to suspect that the usual version may not be the correct one. In this paper, I would like to say why and to propose an alternative.

This paper involves one crucial assumption; namely, that the statistical predictions of quantum mechanics for Bell's variant of the EPR experiment will continue to be verified as detector efficiencies are improved and the need for coincidence counters is eliminated. This assumption entails that any hidden-variables theory for quantum mechanics must violate Bell's inequality--the inequality derived in Bell (1964). It is shown here that four locality conditions are involved in the derivation of Bell's inequality; and that a violation of any of (...) the four locality conditions will either entail the existence of superluminal influences or the existence of superluminal signals (superluminal influences that can be used to transmit information), if conspiratorial theories can be ruled out. The attempts so far to rule out conspiratorial theories are all found to be rather dubious, but there are other considerations developed here that rule them out convincingly. Finally, it is demonstrated that violations of each of the four locality conditions can be used to transmit information superluminally, if certain auxiliary conditions are satisfied. This is of particular interest because one of these conditions corresponds to a condition dubbed "completeness" by Jon Jarrett. Jarrett and others have suggested that violations of completeness cannot be used to send information superluminally. Demonstrating otherwise is, perhaps, the most significant result obtained in this paper. (shrink)

The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR experiment. That assumption is one of the premises of Bell’s theorem. I first argue that only a premise to the effect that what determines the choice of the measurement settings is independent of what determines the past state of the measured system is needed for the (...) derivation of Bell’s theorem. Determinism as such does not undermine that independence . Only entanglement could do so. However, generic entanglement without collapse on the level of the universal wave-function can go together with effective wave-functions for subsystems of the universe, as in Bohmian mechanics. The paper argues that such effective wave-functions are sufficient for the mentioned independence premise to hold. (shrink)

Bell’s Theorem from Physics 36:1–28 (1964) and the (Strong) Free Will Theorem of Conway and Kochen from Notices AMS 56:226–232 (2009) both exclude deterministic hidden variable theories (or, in modern parlance, ‘ontological models’) that are compatible with some small fragment of quantum mechanics, admit ‘free’ settings of the archetypal Alice and Bob experiment, and satisfy a locality condition akin to parameter independence. We clarify the relationship between these theorems by giving reformulations of both that exactly pinpoint their resemblance and their (...) differences. Our reformulation imposes determinism in what we see as the only consistent way, in which the ‘ontological state’ initially determines both the settings and the outcome of the experiment. The usual status of the settings as ‘free’ parameters is subsequently recovered from independence assumptions on the pertinent (random) variables. Our reformulation also clarifies the role of the settings in Bell’s later generalization of his theorem to stochastic hidden variable theories. (shrink)