Recently Cator and Landsman made a comparison between Bell’s Theorem and Conway and Kochen’s Strong Free Will Theorem. Their overall conclusion was that the latter is stronger in that it uses fewer assumptions, but also that it has two shortcomings. Firstly, no experimental test of the Conway–Kochen Theorem has been performed thus far, and, secondly, because the Conway–Kochen Theorem is strongly connected to the Kochen–Specker Theorem it may be susceptible to the finite precision loophole of Meyer, Kent and Clifton. In (...) this paper I show that the finite precision loophole does not apply to the Conway–Kochen Theorem. (shrink)

A widespread view among physicists is that Bell’s theorem rests on an implicit assumption of “classicality,” in addition to locality. According to this understanding, the violation of Bell’s inequalities poses no challenge to locality, but simply reinforces the fact that quantum mechanics is not classical. The paper provides a critical analysis of this view. First we characterize the notion of classicality in probabilistic terms. We argue that classicality thus construed has nothing to do with the validity of classical physics, nor (...) of classical probability theory, contrary to what many believe. At the same time, we show that the probabilistic notion of classicality is not an additional premise of Bell’s theorem, but a mathematical corollary of locality in conjunction with the standard auxiliary assumptions of Bell. Accordingly, any theory that claims to get around the derivation of Bell’s inequalities by giving up classicality, in fact has to give up one of those standard assumptions. As an illustration of this, we look at two recent interpretations of quantum mechanics, Reinhard Werner’s operational quantum mechanics and Robert Griffiths’ consistent histories approach, that are claimed to be local and non-classical, and identify which of the standard assumptions of Bell’s theorem each of them is forced to give up. We claim that while in operational quantum mechanics the Common Cause Principle is violated, the consistent histories approach is conspiratorial. Finally, we relate these two options to the idea of realism, a notion that is also often identified as an implicit assumption of Bell’s theorem. (shrink)

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by (...) identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with. I also identify similar oversight in the GHZ variant of Bell's theorem, invalidating its claim of having found an inconsistency in the premisses of the argument by EPR for completing quantum mechanics. Conceptually, the oversight in both Bell's theorem and its GHZ variant traces back to the oversight in von Neumann's theorem against hidden variable theories identified by Grete Hermann in the 1930s. (shrink)

Nonrelativistic quantum mechanics (QM) works perfectly well for all practical purposes. Once one admits, however, that a successful scientific theory is supposed not only to make predictions but also to tell us a story about the world in which we live, a philosophical problem emerges: in the specific case of QM, it is not possible to associate with the theory a unique scientific image of the world; there are several images. The fact that the theory may be compatible with distinct (...) ontologies, and that those ontologies may themselves be associated with a plurality of metaphysical approaches, gives rise to the problem of metaphysical underdetermination. This paper concludes that the available metametaphysical criteria fail to deliver objectivity in theory choice, and it puts forward its own criterion based on a tension between two methods of metaphysical inquiry: one that is closely related to science and another that is not. (shrink)

This thesis inquires what it means to interpret non-relativistic quantum mechanics (QM), and the philosophical limits of this interpretation. In pursuit of a scientific-realist stance, a metametaphysical method is expanded and applied to evaluate rival interpretations of QM, based on the conceptual distinction between ontology and metaphysics, for objective theory choice in metaphysical discussions relating to QM. Three cases are examined, in which this metametaphysical method succeeds in indicating what are the wrong alternatives to interpret QM in metaphysical terms. The (...) first two cases failed in doing so due to different kinds of underdetermination. In the third case, unlike underdetermination, where there are many choices to be made, a “null-determination” is proposed where there may be no metaphysical choices in the available metaphysical literature. Considering what has been discussed, an agnostic philosophic position is adopted concerning the possibility of interpreting QM from a scientific-realistic point of view. (shrink)

The principle of 'information causality' can be used to derive an upper bound---known as the 'Tsirelson bound'---on the strength of quantum mechanical correlations, and has been conjectured to be a foundational principle of nature. In this paper, however, I argue that the principle has not to date been sufficiently motivated to play this role; the motivations that have so far been given are either unsatisfactorily vague or else amount to little more than an appeal to intuition. I then consider how (...) one might begin to successfully motivate the principle. I argue that a compelling way of so doing is to understand it as a generalisation of Einstein's principle of the mutually independent existence---the 'being-thus'---of spatially distant things, interpreted as a special methodological principle. More specifically: I describe an argument, due to Demopoulos, to the effect that the quantum-mechanical no-signalling condition can be viewed as a generalisation, appropriate to an irreducibly statistical theory such as quantum mechanics, of the Einsteinian principle. And I then argue that a compelling way to motivate information causality is to in turn consider it as a further generalisation of the Einsteinian principle that is appropriate to a theory of communication. I nevertheless describe important obstacles that must yet be overcome if the project of establishing information causality as a foundational principle of nature is to succeed. (shrink)

Some recent work in the philosophy of quantum mechanics has suggested that quantum systems can be thought of as non-separable and therefore non-individual, in some sense, in Bell and E.P.R. type situations. This suggestion is set in the context of previous work regarding the individuality of quantal particles and it is argued that such entities can be considered as individuals if their non-classical statistical correlations are understood in terms of non-supervenient relations holding between them. We conclude that such relations are (...) strongly non-supervenient in Cleland's sense and note a possible connection between this idea and the realist quantum logic programme. (shrink)

Recent years have seen new general notions of contextuality emerge. Most of these employ context-independent symbols to represent random variables in different contexts. As an example, the operational theory of (Spekkens in Phys Rev A 71(5):52108, 2005) treats an observable being measured in two different contexts identically. Non-contextuality in this approach is the impossibility of drawing ontological distinctions between identical elements of the operational theory. However, a recent collection of work seeks to exploit context-dependent symbols of random variables to interpret (...) contextuality (Kujala et al. in Phys Rev Lett 115(15):150401, 2015; Dzhafarov and Kujala in Phys Scr T163:014009, 2014). This approach associates contextuality with the possibility of imposing a particular joint distribution on random variables recorded under different experimental contexts. This paper compares these two different treatments of random variables and highlights the limitations of the context-dependent approach as a physical theory. (shrink)

Quantum mechanics seems to portray nature as nonseparable, in the sense that it allows spatiotemporally separated entities to have states that cannot be fully specified without reference to each other. This is often said to implicate some form of “holism.” We aim to clarify what this means, and why this seems plausible. Our core idea is that the best explanation for nonseparability is a “common ground” explanation, which casts nonseparable entities in a holistic light, as scattered reflections of a more (...) unified underlying reality. (shrink)

Time-symmetric interpretations of quantum theory are often presented as featuring "retrocausal" effects in addition to the usual forward notion of causation. This paper examines the ontological implications of certain time- symmetric theories, and finds that no dynamical notion of causation applies to them, either forward or backward. It is concluded that such theories actually describe a static picture, in which the notion of causation is relegated to a descriptor of static relationships among events. In addition, these theories lead to an (...) epistemic rather than ontologically referring, realist view of quantum states. (shrink)

I argue that categorical realism, contrary to what most believe today, holds for quantum (and indeed for all) objects and substances. The main argument consists of two steps: (i) the recent experimental verification of the AB effect gives strong empirical evidence for taking quantum potentials as physically real (or substantival), which suggests a change of the data upon which any viable interpretation of quantum theory must rely, and (ii) quantum potentials may be consistently taken as the categorical properties of quantum (...) objects so that categorical realism can be restored. (shrink)

The use of probability theory is widespread in our daily life as well as in scientific theories. In virtually all cases, calculations can be carried out within the framework of classical probability theory. A special exception is given by quantum mechanics, which gives rise to a new probability theory: quantum probability theory. This dissertation deals with the question of how this formalism can be understood from a philosophical and physical perspective. The dissertation is divided into three parts. In the first (...) part, the formalism of quantum probability theory and its relation to quantum mechanics is presented. The second part considers the possibility of reformulating quantum probability theory to embed it within classical probability. Mathematically, this possibility overlaps with the possibility of the existence of hidden variables theories of quantum mechanics: theories that attempt to solve fundamental problems in quantum mechanics by introducing additional physical properties of systems. The conclusion of this part is that, although classical reformulations of quantum probability theory are formally possible, they offer little insight into the formalism of quantum probability theory itself. The third part regards a more direct investigation of quantum probability theory. A reformulation of quantum probability theory is obtained by constructing a quantum logic on the basis of empirical non-probabilistic predictions of quantum mechanics. In this reformulation quantum probability functions are conditional probability functions on an algebra of propositions about measurements and measurement outcomes. (shrink)

In this paper, I want to present a family of results that may seem to add up to a new proof of the impossibility of hidden variables. In fact, I very much doubt that that’s really what really emerges, but I think the results are nonetheless interesting because they help to sharpen the discussion of Jon Jarrett’s very useful decompostion theorem, in particular, of the condition he calls locality. Jarrett (1984) and Ballentine and Jarrett (1987) have suggested that the so-called (...) condition of locality is the one that provides the conceptual link between hidden variable theories and relativity: if locality is violated, so is relativity. On the other hand, a theory may violate the condition Jarrett calls completeness without running afoul of relativity. Now I agree with Jarrett and Ballentine about completeness, but I strongly suspect that we have quite a way to go before we really understand what would be involved in a violation of locality. (shrink)

I show why old and new claims on the role of counterfactual reasoning for the EPR argument and Bell’s theorem are unjustified: once the logical relation between locality and counterfactual reasoning is clarified, the use of the latter does no harm and the nonlocality result can well follow from the EPR premises. To show why, after emphasizing the role of incompleteness arguments that Einstein developed before the EPR paper, I critically review more recent claims that equate the use of counterfactual (...) reasoning with the assumption of a strong form of realism and argue that such claims are untenable. (shrink)

I show why old and new claims on the role of counterfactual reasoning for the EPR argument and Bell’s theorem are unjustified: once the logical relation between locality and counterfactual reasoning is clarified, the use of the latter does no harm and the nonlocality result can well follow from the EPR premises. To show why, after emphasizing the role of incompleteness arguments that Einstein developed before the EPR paper, I critically review more recent claims that equate the use of counterfactual (...) reasoning with the assumption of a strong form of realism and argue that such claims are untenable. (shrink)

Since he proved his theorem in 1982, Fine has been challenging the traditional interpretation of the experimental violation of the Bell Inequalities. A natural interpretation of Fine's theorem is that it provides us with an alternative set of assumptions on which to place blame for the failure of the BI, and opens to a new interpretation of the violation of the BI. Fine has a stronger interpretation for his theorem. He claims that his result undermines the traditional interpretation in terms (...) of local realism. The aim of this paper is to understand and to assess Fine's claim. We distinguish three different strategies that Fine uses in order to support his view. We show that none of these strategies is successful. Fine fails to prove that local realism is not at stake in the violation of the BI by quantum phenomena. (shrink)

Two types of contextual theories are distinguished and shown to be related. For theories of each type a criterion of locality is formulated which is weaker than the classical requirement of separability at spacelike intervals. The relations between the concepts of locality, realism, and ontic chance are discussed.

Based partly on proving that algebraic relativistic quantum field theory (ARQFT) is a stochastic Einstein local (SEL) theory in the sense of SEL which was introduced by Hellman (1982b) and which is adapted in this paper to ARQFT, the recently proved maximal and typical violation of Bell's inequalities in ARQFT (Summers and Werner 1987a-c) is interpreted in this paper as showing that Bell's inequalities are, in a sense, irrelevant for the problem of Einstein local stochastic hidden variables, especially if this (...) problem is raised in connection with ARQFT. This leads to the question of how to formulate the problem of local hidden variables in ARQFT. By giving a precise definition of hidden-variable theory within the operator algebraic framework of quantum mechanics, it will be argued that the aim of hidden-variable investigations is to determine those classes of quantum theories whose elements represent a statistical content that cannot be reduced in a given way. In some particular way to be stated, a proposition will be stated which distinguishes quantum field theories whose statistical content cannot be reduced without violating some relativistic locality principle. (shrink)

John S. Bell introduced the notion of beable, as opposed to the standard notion of observable, in order to emphasize the need for an unambiguous formulation of quantum mechanics. In the paper I show that Bell formulated in fact two different theories of beables. The first is somehow reminiscent of the Bohr views on quantum mechanics but, at the same time, is curiously adopted by Bell as a critical tool against the Copenhagen interpretation, whereas the second, more mature formulation was (...) among the sources of inspiration of the so-called Primitive Ontology (PO) approach to quantum mechanics, an approach inspired to scientific realism. In the first part of the paper it is argued that, contrary to the Bell wishes, the first formulation of the theory fails to be an effective recipe for addressing the ambiguity underlying the standard formulation of quantum mechanics, whereas it is only the second formulation that successfully paves the way to the PO approach. In the second part, I consider how the distinction between the two formulations of the Bell theory of beables fares vis-a-vis the complex relationship between the theory of beables and the details of the PO approach. (shrink)

My topics are two theses about quantum mechanics that are widely doubted but curiously tempting: value-definiteness and contextualism. Value-definiteness holds that every observable has a definite value; contextualism follows from value-definiteness, and claims that one Hermitian operator can represent many observables. In fact, contextualism is my deeper interest Although it is not a view with an army of defenders, it has a long history of discussion in the literature. (See, for example, Belinfante 1973, van Fraassen 1973, Shimony 1984, Redhead 1987). (...) The bulk of this paper will be concerned with a puzzle about degenerate operators that arises out of the standard accounts of contextualism. But before we get to the details, let us begin with a lurid example. (shrink)

J. S. Bell's classic 1966 review paper on the foundations of quantum mechanics led directly to the Bell nonlocality theorem. It is not widely appreciated that the review paper contained the basic ingredients needed for a nonlocality result which holds in certain situations where the Bell inequality is not violated. We present in this paper a systematic formulation and evaluation of an argument due to Stairs in 1983, which establishes a nonlocality result based on the Bell-Kochen-Specker “paradox” in quantum mechanics.

Quantum optics does not give a local explanation of the coincidence counts in spatially separated photodetectors. This is the case for a wide variety of phenomena, including the anticorrelated counting rates in the two channels of a beam splitter, the coincident counting rates of the two “photons” in an atomic cascade, and the “antibunching” observed in resonance fluorescence.We propose a local realist theory that explains all of these data in a consistent manner. The theory uses a completely classical description of (...) the electromagnetic field, but with boundary conditions of the far field that are equivalent to assuming a real fluctuating, zero-point field. It is related to stochastic electrodynamics similarly to the way classical optics is related to classical electromagnetic theory.The quantitative aspects of the theory are developed sufficiently to show that there is agreement with all experiments performed till now. (shrink)

To consider metaphysical claims a priori and devoid of empirical content, is a rather commonplace received opinion. This paper attempts an exploration of a contemporary philosophical heresy: it is possible to test metaphysical claims if they play an indispensable role in producing empirical success, i.e. novel predictions. To do so one, firstly, needs to express the metaphysical claims employed in the logico-mathematical language of a scientific theory, i.e. to explicate them. Secondly, one should have an understanding of what it is (...) to test and to verify or to falsify a metaphysical claim. Finally, one also need to consider the philosophical practice of testing a metaphysical claim. These three aspects are introduced in this paper and they are illustrated by means of the metaphysical concept of common cause and the principle of the common cause. (shrink)

http://dx.doi.org/10.5007/1808-1711.2008v12n1p49 The aim of this article is to offer a rejoinder to an argument against scientific realism put forward by van Fraassen, based on theoretical considerations regarding microphysics. At a certain stage of his general attack to scientific realism, van Fraassen argues, in contrast to what realists typically hold, that empirical regularities should sometimes be regarded as “brute facts”, which do not ask for explanation in terms of deeper, unobservable mechanisms. The argument from microphysics formulated by van Fraassen is based (...) on the claim that in microphysics the demand for explanation leads to a demand for the so-called hidden-variable theories, which “runs contrary to at least one major school of thought in twentieth-century physics”. It is shown here that this argument does not represent an insurmountable obstacle to scientific realism, not even when a series of important theoretical and experimental results against hidden-variable theories — and not merely a conflict with a certain school of thought—is taken into account. (shrink)

The notion of quantum supports introduced by Foulis, Piron, and Randall can be used to construct combinatorial versions of contextualist hidden-variable models for finite quantum logics. The original logic can be uniquely recovered from appropriate such models as a solution of a combinatorial inverse problem. One can thus set up a classical ontology for a finite quantum logics that completely specifies it. Computer studies are used to explore the ideas.

Fine has recently proved the surprising result that satisfaction of the Bell inequality in a Clauser-Horne experiment implies the existence of joint probabilities for pairs of noncommuting observables in the experiment. In this paper we show that if probabilities are interpreted in the von Mises-Church sense of relative frequencies on random sequences, a proof of the Bell inequality is nonetheless possible in which such joint probabilities are assumed not to exist. We also argue that Fine's theorem and related results do (...) not impugn the common view that local realists are committed to the Bell inequality. (shrink)

It was with some trepidation that I agreed to speak today, because of a strong doubt that I could say anything substantial not already to be found in the literature of the subject. I cannot say that this trepidation has been subsequently relieved: all I can claim to offer in this paper is a review of certain basic characteristics or themes in the quantum-mechanical situation (which by now should, I think, be thoroughly understood by everyone engaged with the matter), supplemented (...) by some rather general reflections on our philosophical predicament. In aid of these more general reflections, I shall indulge a proclivity for calling on historical matters—some fairly recent, some older, some ancient—which I hope may serve to place current issues in a useful perspective; and I ask your forgiveness for allowing myself to quote certain previous, but hitherto unpublished, remarks of my own. (shrink)