Quantum contextuality and its ontological meaning are very controversial issues, and they relate to other problems concerning the foundations of quantum theory. I address this controversy and stress the fact that contextuality is a universal topological property of quantum processes, which conflicts with the basic metaphysical assumption of the definiteness of being. I discuss the consequences of this fact and argue that generic quantum potentiality as a real physical indefiniteness has nothing in common with (...) the classical notions of possibility and counterfactuality, and that also it reverses, in a way, the classical mirror-like relation between actuality and definite possibility. (shrink)

In this paper we attempt to analyze the physical and philosophical meaning of quantum contextuality. We will argue that there exists a general confusion within the foundational literature arising from the improper “scrambling” of two different meanings of quantum contextuality. While the first one, introduced by Bohr, is related to an epistemic interpretation of contextuality which stresses the incompatibility of measurement situations described in classical terms; the second meaning of contextuality is related to a (...) purely formal understanding of contextuality as exposed by the Kochen–Specker theorem which focuses instead on the constraints of the orthodox quantum formalism in order to interpret projection operators as preexistent or actual properties. We will show how these two notions have been scrambled together creating an “omelette of contextuality” which has been fully widespread through a popularized “epistemic explanation” of the KS theorem according to which: The measurement outcome of the observableAwhen measured together withBor together withCwill necessarily differ in case\, and\. We will show why this statement is not only improperly scrambling epistemic and formal perspectives, but is also physically and philosophically meaningless. Finally, we analyze the consequences of such widespread epistemic reading of KS theorem as related to statistical statements of measurement outcomes. (shrink)

Hardy and Unruh constructed a family of non-maximally entangled states of pairs of particles giving rise to correlations that cannot be accounted for with a local hidden-variable theory. Rather than pointing to violations of some Bell inequality, however, they pointed to apparent clashes with the basic rules of logic. Specifically, they constructed these states and the associated measurement settings in such a way that the outcomes satisfy some conditionals but not an additional one entailed by them. Quantum mechanics avoids (...) the broken ‘if …then …’ arrows in such Hardy–Unruh chains, as we call them, because it cannot simultaneously assign truth values to all conditionals involved. Measurements to determine the truth value of some preclude measurements to determine the truth value of others. Hardy–Unruh chains thus nicely illustrate quantum contextuality: which variables do and do not obtain definite values depends on what measurements we decide to perform. Using a framework inspired by Bub and Pitowsky and developed in our book Understanding Quantum Raffles (co-authored with Michael E. Cuffaro), we construct and analyze Hardy–Unruh chains in terms of fictitious bananas mimicking the behavior of spin-1/2 particles. (shrink)

It is proposed a critique of existing interpretations of quantum mechanics, both anti-realistic and realistic, and, in particular, the Copenhagen interpretation, the interpretations with hidden variables, the metaphysical interpretation of H. Everett’s interpretation, the many-worlds interpretation by D. Wallace, QBism by C. Fuchs, D. Mermin and R. Schack, the relational interpretation by C. Rovelli, neo-Kantian and phenomenological interpretations by M. Bitbol, the informational interpretation by A. Zeilinger, the Nobel Prize Winner in Physics 2022, and others. As is known compared (...) to classical physics, quantum mechanics is a new physical paradigm. The author argues that from a philosophical point of view quantum mechanics is an anomaly within the paradigm of (post)modern philosophy. A new approach to understanding quantum mechanics and resolving its paradoxes, rejecting the assumptions and prejudices of (post)modern philosophy, is proposed – contextual quantum realism (CQR). It is a moderately deflationary approach that combines elements of (neo-)Copenhagen, informational and realist interpretations and recognizes the possibility of knowing the things themselves. From the point of view of CQR, the measurement problem – the basic problem of philosophy of quantum mechanics – is a pseudo-problem . (shrink)

We present a formal theory of contextuality for a set of random variables grouped into different subsets corresponding to different, mutually incompatible conditions. Within each context the random variables are jointly distributed, but across different contexts they are stochastically unrelated. The theory of contextuality is based on the analysis of the extent to which some of these random variables can be viewed as preserving their identity across different contexts when one considers all possible joint distributions imposed on the (...) entire set of the random variables. We illustrate the theory on three systems of traditional interest in quantum physics. These are systems of the Klyachko–Can–Binicioglu–Shumovsky-type, Einstein–Podolsky–Rosen–Bell-type, and Suppes–Zanotti–Leggett–Garg-type. Listed in this order, each of them is formally a special case of the previous one. For each of them we derive necessary and sufficient conditions for contextuality while allowing for experimental errors and contextual biases or signaling. Based on the same principles that underly these derivations we also propose a measure for the degree of contextuality and compute it for the three systems in question. (shrink)

We outline the rationale and preliminary results of using the State Context Property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used, and combined to generate meaning. The quantum formalism was developed to cope with problems arising in the description of (1) the measurement process, and (2) the generation of new states with new properties when particles become entangled. Similar problems arising with concepts motivated the formal (...) treatment introduced here. Concepts are viewed not as fixed representations, but entities existing in states of potentiality that require interaction with a context---a stimulus or another concept---to `collapse' to observable form as an exemplar, prototype, or other (possibly imaginary) instance. The stimulus situation plays the role of the measurement in physics, acting as context that induces a change of the cognitive state from superposition state to collapsed state. The collapsed state is more likely to consist of a conjunction of concepts for associative than analytic thought because more stimulus or concept properties take part in the collapse. We provide two contextual measures of conceptual distance---one using collapse probabilities and the other weighted properties---and show how they can be applied to conjunctions using the pet fish problem. (shrink)

The book explores the variety of meanings of contextuality across different disciplines, with the emphasis on quantum physics and on psychology. Keywords: Contextuality; Quantum Physics; Psychology.

The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valuation in quantum mechanics as exemplified, in particular, by Kochen–Specker’s theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event algebras. We show explicitly that the latter category is equipped with an object (...) of truth values, or classifying object, which constitutes the appropriate tool for assigning truth values to propositions describing the behavior of quantum systems. Effectively, this category-theoretic representation scheme circumvents consistently the semantic ambiguity with respect to truth valuation that is inherent in conventional quantum mechanics by inducing an objective contextual account of truth in the quantum domain of discourse. The philosophical implications of the resulting account are analyzed. We argue that it subscribes neither to a pragmatic instrumental nor to a relative notion of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature. (shrink)

Причина квантовых корреляций - запутанная волновая функция. Коррелирующие квантовые события не автономны, а определены в контексте их наблюдения. Независимо от средств их идентификации нет никаких событий. Редукция волновой функции в «процессе измерения» не реальный физический процесс, требующий своего объяснения, а переход в контекст измерения конкретного значения физической величины. Соответственно, измерение - не физическое взаимодействие, приводящее к изменению состояния системы, а идентификация контекстуальной физической реальности. Проблема измерения, или проблема применения квантовой теории к реальности, возникает в результате смешения категорий идеального, к которой (...) относится теория, и реального, к которой относится её применение. Она устраняется логически. Проблема - инстанциация витгенштейновской проблемы следования правилу. Роль витгенштейновского правила (нормы), «измеряющего» физическую реальность в рамках языковой игры его применения, играет квантовая теория. (shrink)

In his recent paper, C. Fuchs formulates QBism in the form of eight postulates. We criticise QBism as an anti-realist position and propose an alternative – contextual quantum realism (QCR). 1. A quantum state is not “an agent’s personal judgement” (QBism), nor is it subjective (QBism), but objective (QCR). It describes not the current experience (QBism), but a state of a physical system in context (QCR). 2. A quantum measurement is a (literally) measurement of quantum reality (...) (QCR), rather than an agent’s action upon its external world (QBism). It can only be regarded as an action in the sense in which a cognitive Wittgensteinian language game is an action (QCR). 3. The result of a quantum meas- urement is objective, though context-sensitive (QCR), rather than subjective (QBism), personal to the agent performing the action (QBism). 4. The quantum formalism is normative (QCR and QBism) and at the same time descriptive (QCR). The wave function tells us what to expect and how a quantum experiment should be conducted (i.e. plays the role of a norm), and also describes the state of a quantum system in context (QCR). 5. Unitary evolution is objective (QCR), not subjective (QBism). It does not express an agent’s degrees of belief (QBism). 6. Probability 1 is ontic (QCR), not an agent’s maximum degree of subjective certainty without ontic content (QBism). 7. In general, measurement outcomes are not predetermined (QCR and QBism), i.e. “unperformed measurements have no outcomes” (for QCR, this is an analytical judgement; for QBism this is a thesis), but they are predeter- mined in the case of probabilities 1 and 0 (QCR). In the case of probabilities 0 and 1, one can speak of performed measurements (QCR). 8. Quantum theory is a universal Wittgen- steinian rule (norm), i.e. a rule (norm) rooted in experience, reality (QCR). It can be used by any competent subject (QCR and QBism). We illustrate the difference between QCR and QBism on the example of how they treat “Wigner’s friend” thought experiment and consider their attitude to phenomenology. (shrink)

Quantum theory is a probabilistic theory that embodies notoriously striking correlations, stronger than any that classical theories allow but not as strong as those of hypothetical ‘super-quantum’ theories. This raises the question ‘Why the quantum?’—whether there is a handful of principles that account for the character of quantum probability. We ask what quantum-logical notions correspond to this investigation. This project isn’t meant to compete with the many beautiful results that information-theoretic approaches have yielded but rather (...) aims to complement that work. (shrink)

Following an article by John von Neumann on infinite tensor products, we develop the idea that the usual formalism of quantum mechanics, associated with unitary equivalence of representations, stops working when countable infinities of particles (or degrees of freedom) are encountered. This is because the dimension of the corresponding Hilbert space becomes uncountably infinite, leading to the loss of unitary equivalence, and to sectorisation. By interpreting physically this mathematical fact, we show that it provides a natural way to describe (...) the “Heisenberg cut”, as well as a unified mathematical model including both quantum and classical physics, appearing as required incommensurable facets in the description of nature. (shrink)

In a recent paper Griffiths [38] has argued, based on the consistent histories interpretation, that Hilbert space quantum mechanics is noncontextual. According to Griffiths the problem of contextuality disappears if the apparatus is “designed and operated by a competent experimentalist” and we accept the Single Framework Rule. We will argue from a representational realist stance that the conclusion is incorrect due to the misleading understanding provided by Griffiths to the meaning of quantum contextuality and its relation (...) to physical reality and measurements. We will discuss how the quite general incomprehension of contextuality has its origin in the ''objective-subjective omelette'' created by Heisenberg and Bohr. We will argue that in order to unscramble the omelette we need to disentangle, firstly, representational realism from naive realism, secondly, ontology from epistemology, and thirdly, the different interpretational problems of QM. In this respect, we will analyze what should be considered as Meaningful Physical Statements within a theory and will argue that Counterfactual Reasoning -considered by Griffiths as ''tricky''- must be accepted as a necessary condition for any representational realist interpretation of QM. Finally we discuss what should be considered as a problem in QM from a representational realist perspective. (shrink)

In this article we discuss the contextual character of quantum mechanics in the framework of modal interpretations. We investigate its historical origin and relate contemporary modal interpretations to those proposed by M. Born and W. Heisenberg. We present then a general characterization of what we consider to be a modal interpretation. Following previous papers in which we have introduced modalities in the Kochen-Specker theorem, we investigate the consequences of these theorems in relation to the modal interpretations of quantum (...) mechanics. (shrink)

A logically complete interpretation of quantum mechanics is given in terms of a theory of quantum processes.

We propose that whatever quantity controls the Heisenberg uncertainty relations it should be identified with an effective Planck parameter. With this definition it is not difficult to find examples where the Planck parameter depends on the region under study, varies in time, and even depends on which pair of observables one focuses on. In quantum cosmology the effective Planck parameter depends on the size of the comoving region under study, and so depends on that chosen region and on time. (...) With this criterion, the classical limit is expected, not for regions larger than the Planck length, \, but for those larger than \^{1/3}\), where H is the Hubble parameter. In theories where the cosmological constant is dynamical, it is possible for the latter to remain quantum even in contexts where everything else is deemed classical. These results are derived from standard quantization methods, but we also include more speculative cases where ad hoc Planck parameters scale differently with the length scale under observation. Even more speculatively, we examine the possibility that similar complementary concepts affect thermodynamical variables, such as the temperature and the entropy of a black hole. (shrink)

A critique of phenomenological interpretation of quantum Bayesianism (QBism) is offered, in particular, the position of M. Bitbol and L. de La Tremblay, which removes remnants of scientific realism from QBism and adopts a radically phenomenological first person point of view. It is shown that phenomenological view of quantum mechanics cannot explain cognition of quantum reality and behavior of real quantum systems, because the ultimate reality for phenomenology is autonomous phenomena, which, in fact, do not exist. (...) Our proposed contextual quantum realism (CQR) does not invert, as the mentioned authors do, but rejects, the traditional relation between experience and reality. By reinterpreting QBism, our CQR removes remnants of phenomenology from it, but in such a way as not to fall into the other extreme – metaphysical realism. (shrink)

This paper introduces an extension of the de Broglie-Bohm-Bell formulation of quantum mechanics, which includes intrinsic particle degrees of freedom, such as spin, as elements of reality. To evade constraints from the Kochen-Specker theorem the discrete spin values refer to a specific basis – i.e., a single spin vector orientation for each particle; these spin orientations are, however, not predetermined, but dynamic and guided by the wave function of the system, which is conditional on the realized location values of (...) the particles. In this way, the unavoidable contextuality of spin is provided by the wave function and its realized particle configuration, whereas spin is still expressed as a local property of the individual particles. This formulation, which furthermore features a rigorous discrete-time stochastic dynamics, allows for numerical simulations of particle systems with entangled spin, such as Bohm’s version of the EPR experiment. (shrink)

In this paper we attempt to analyze the physical and philosophical meaning of quantum contextuality. In the first part we will argue that a general confusion within the literature comes from the improper "scrambling" of two different meanings of quantum contextuality. The first one is related to an epistemic interpretation of contextuality, introduced by Bohr, which stresses the incompatibility of quantum measurements. The second, is related to an ontic notion of contextuality, exposed through (...) the Kochen-Specker theorem, which focuses on the constraints to discuss about actual properties within the orthodox formalism of QM. We will show how these two notions have been scrambled together creating an "omelette of contextuality" which has been fully widespread through a popularized "epistemic explanation" of the KS theorem according to which: The outcome of the observable A when mea- sured together with B or together with C will necessarily differ in case [A,B] = [A,C] = 0, and [B,C] ̸= 0. We will show why this statement is not only improperly scrambling epistemic and ontic perspectives, but is also physically and philosophically meaningless. In the second part of the paper, we will analyse the relation between ‘classical contexts’ and QM. We will show that three accepted presuppositions found within the orthodox literature are, in general, false. Namely: that quantum contextuality does not preclude an objective description of physical reality, that the choice of a context restores a classical description of reality, and that the choice of a context is a necessary condition for accounting for empirical statements in QM. (shrink)

In standard quantum mechanics, a state vector \ may belong to infinitely many different orthogonal bases, as soon as the dimension N of the Hilbert space is at least three. On the other hand, a complete physical observable A is associated with a N-dimensional orthogonal basis of eigenvectors. In an idealized case, measuring A again and again will give repeatedly the same result, with the same eigenvalue. Let us call this repeatable result a modality \, and the corresponding eigenstate (...) \. A question is then: does \ give a complete description of \? The answer is obviously no, since \ does not specify the full observable A that allowed us to obtain \; hence the physical description given by \ is incomplete, as claimed by Einstein, Podolsky and Rosen in their famous article in 1935. Here we want to spell out this provocative statement, and in particular to answer the questions: if \ is an incomplete description of \, what does it describe? is it possible to obtain a complete description, maybe algebraic? Our conclusion is that the incompleteness of standard QM is due to its attempt to describe systems without contexts, whereas both are always required, even if they can be separated outside the measurement periods. (shrink)

The semantics underlying the propositional structure of Hilbert space quantum mechanics involves an inherent ambiguity concerning the impossibility of assigning definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. Although the preceding Kochen-Specker result forbids a global, absolute assignment of truth values to quantum mechanical propositions, it does not exclude ones that are contextual. In this respect, the Bub-Clifton “uniqueness theorem” is utilized for arguing that truth-value definiteness is consistently restored (...) with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a suitable “preferred” observable. It is suggested that the most natural choice of the latter, especially for confronting the problem of truth valuation in quantum mechanics, results in the determinateness of the observable to be measured. An account of truth of contextual correspondence is thereby provided that is appropriate to the quantum domain of discourse. The resulting account of truth is compatible with a realist conception of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature. (shrink)

The semantically ambiguous nature of the sign and aspects of non-classicality of elementary matter as described by quantum theory show remarkable coherent analogy. We focus on how the ambiguous nature of the image, text and art work bears functional resemblance to the dynamics of contextuality, entanglement, superposition, collapse and decoherence as these phenomena are known in quantum theory. These quantumlike properties in linguistic signs have previously been identified in formal descritions of e.g. concept combinations and mental lexicon (...) representations and have been reported on in the literature. In this approach the informationalized, communicated, mediatized conceptual configuration—of e.g. the art work—in the personal reflected mind behaves like a quantum state function in a higher dimensional complex space, in which it is time and again contextually collapsed and further cognitively entangled. The observer–consumer of signs becomes the empowered ‘produmer’ creating the cognitive outcome of the interaction, while loosing most of any ‘classical givenness’ of the sign. These quantum-like descriptions are now developed here in four example aesthetic signs; the installation Mist room by Ann Veronica Janssens, the installation Sections of a happy moment by David Claerbout, the photograph The Falling Man by Richard Drew and the documentary Huicholes. The Last Peyote Guardians by Vilchez and Stefani. Our present work develops further the use of a previously developed quantum model for concept representation in natural language. In our present approach of the aesthetic sign, we extend to individual—idiosyncratic—observer contexts instead of socially shared group contexts, and as such also include multiple idiosyncratic creation of meaning and experience. This irreducible superposition emerges as the core feature of the aesthetic sign and is most critically embedded in the ‘no-interpretation’ interpretation of the documentary signal. (shrink)

Topos quantum theory represents a whole new approach to the formalization of non-relativistic quantum theory. It is well known that TQT replaces the orthomodular quantum logic of the traditional Hilbert space formalism with a new intuitionistic logic that arises naturally from the topos theoretic structure of the theory. However, it is less well known that TQT also has a dual logical structure that is paraconsistent. In this paper, we investigate the relationship between these two logical structures and (...) study the implications of this relationship for the definition of modal operators in TQT. (shrink)

According to a standard view, quantum mechanics is a contextual theory and quantum probability does not satisfy Kolmogorov’s axioms. We show, by considering the macroscopic contexts associated with measurement procedures and the microscopic contexts underlying them, that one can interpret quantum probability as epistemic, despite its non-Kolmogorovian structure. To attain this result we introduce a predicate language L, a classical probability measure on it and a family of classical probability measures on sets of μ-contexts, each element of (...) the family corresponding to a measurement procedure. By using only Kolmogorovian probability measures we can thus define mean conditional probabilities on the set of properties of any quantum system that admit an epistemic interpretation but are not bound to satisfy Kolmogorov’s axioms. The generalized probability measures associated with states in QM can then be seen as special cases of these mean probabilities, which explains how they can be non-classical and provides them with an epistemic interpretation. Moreover, the distinction between compatible and incompatible properties is explained in a natural way, and purely theoretical classical conditional probabilities coexist with empirically testable quantum conditional probabilities. (shrink)

Durant toute sa vie intellectuelle, Karl Popper a accusé Niels Bohr d’avoir défendu des thèses subjectivistes à propos de la mécanique quantique et d’avoir introduit le concept de sujet au sein de la physique. Or, cette accusation va à l’encontre des textes de Bohr. L’objectif de cet article est de montrer que, dans sa restitution même des positions de Bohr, Popper n’a pas pris au sérieux une thèse centrale défendue par Bohr, qu’on appelle « la contextualité des phénomènes quantiques», et (...) qui a pour conséquence de modifier en profondeur l’acte de mesure et la constitution de l’objet en mécanique quantique. Nous essayons de montrer que c’est cette difficulté dans la restitution des positions de Bohr qui l’a amené à porter son accusation de subjectivisme à l’encontre de Bohr. (shrink)

We presented a contextual statistical model of the probabilistic description of physical reality. Here contexts (complexes of physical conditions) are considered as basic elements of reality. There is discussed the relation with QM. We propose a realistic analogue of Bohr’s principle of complementarity. In the opposite to the Bohr’s principle, our principle has no direct relation with mutual exclusivity for observables. To distinguish our principle from the Bohr’s principle and to give better characterization, we change the terminology and speak about (...) supplementarity, instead of complementarity. Supplementarity is based on the interference of probabilities. It has quantitative expression trough a coefficient which can be easily calculated from experimental statistical data. We need not appeal to the Hilbert space formalism and noncommutativity of operators representing observables. Moreover, in our model there exists pairs of supplementary observables which cannot be represented in the complex Hilbert space. There are discussed applications of the principle of supplementarity outside quantum physics. (shrink)

In this paper we present a new categorical approach which attempts to provide an original understanding of QM. Our logos categorical approach attempts to consider the main features of the quantum formalism as the standpoint to develop a conceptual representation that explains what the theory is really talking about —rather than as problems that need to be bypassed in order to allow a restoration of a classical “common sense” understanding of what there is. In particular, we discuss a solution (...) to Kochen-Specker contextuality through the generalization of the meaning of global valuation. This idea has been already addressed by the so called topos approach to QM —originally proposed by Isham, Butterfiled and D ̈oring— in terms of sieve-valued valuations. The logos approach to QM presents a different solution in terms of the notion of intensive valuation. This new solution stresses an ontological reading of the quantum formalism and the need to restore an objective conceptual representation and understanding of quantum physical reality. (shrink)

This book provides an interdisciplinary perspective on one of the most fascinating and important open questions in science: What is quantum mechanics talking about? Quantum theory is perhaps our best confirmed physical theory. However, despite its great empirical effectiveness and the subsequent technological developments that it gave rise to in the 20th century, from the interpretation of the periodic table of elements to CD players, holograms and quantum state teleportation, it stands even today without a universally accepted (...) interpretation. The novelty of the book comes from the multiple viewpoints and subjects investigated by a group of researchers from Europe and North and South America. (shrink)

It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default, sheaf theory, topos theory, and non-standard or signed probabilities. In this paper we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability. In particular, we propose that if we assume the ontological thesis that (...) quantum particles or properties can be indistinguishable yet different, no contradiction arising from a Kochen-Specker-type argument appears: when we repeat an experiment, we are in reality performing an experiment measuring a property that is indistinguishable from the first, but not the same. We will discuss how the consequences of this move may help us understand quantum contextuality. (shrink)

Realist interpretations of quantum mechanics presuppose the existence of elements of reality that are independent of the actions used to reveal them. Such a view is challenged by several no-go theorems that show quantum correlations cannot be explained by non-contextual ontological models, where physical properties are assumed to exist prior to and independently of the act of measurement. However, all such contextuality proofs assume a traditional notion of causal structure, where causal influence flows from past to future (...) according to ordinary dynamical laws. This leaves open the question of whether the apparent contextuality of quantum mechanics is simply the signature of some exotic causal structure, where the future might affect the past or distant systems might get correlated due to non-local constraints. Here we show that quantum predictions require a deeper form of contextuality: even allowing for arbitrary causal structure, no model can explain quantum correlations from non-contextual ontological properties of the world, be they initial states, dynamical laws, or global constraints. (shrink)

We define a family of ‘no signaling’ bipartite boxes with arbitrary inputs and binary outputs, and with a range of marginal probabilities. The defining correlations are motivated by the Klyachko version of the Kochen-Specker theorem, so we call these boxes Kochen-Specker-Klyachko boxes or, briefly, KS-boxes. The marginals cover a variety of cases, from those that can be simulated classically to the superquantum correlations that saturate the Clauser-Horne-Shimony-Holt inequality, when the KS-box is a generalized PR-box (hence a vertex of the ‘no (...) signaling’ polytope). We show that for certain marginal probabilities a KS-box is classical with respect to nonlocality as measured by the Clauser-Horne-Shimony-Holt correlation, i.e., no better than shared randomness as a resource in simulating a PR-box, even though such KS-boxes cannot be perfectly simulated by classical or quantum resources for all inputs. We comment on the significance of these results for contextuality and nonlocality in ‘no signaling’ theories. (shrink)

This self-contained essay collection is published to commemorate half a century of Bell's theorem. Like its much acclaimed predecessor "Quantum [Un]Speakables: From Bell to Quantum Information" (published 2002), it comprises essays by many of the worlds leading quantum physicists and philosophers. These revisit the foundations of quantum theory as well as elucidating the remarkable progress in quantum technologies achieved in the last couple of decades. Fundamental concepts such as entanglement, nonlocality and contextuality are described (...) in an accessible manner and, alongside lively descriptions of the various theoretical and experimental approaches, the book also delivers interesting philosophical insights. The collection as a whole will serve as a broad introduction for students and newcomers as well as delighting the scientifically literate general reader. (shrink)

The recently established universal uncertainty principle revealed that two nowhere commuting observables can be measured simultaneously in some state, whereas they have no joint probability distribution in any state. Thus, one measuring apparatus can simultaneously measure two observables that have no simultaneous reality. In order to reconcile this discrepancy, an approach based on quantum logic is proposed to establish the relation between quantum reality and measurement. We provide a language speaking of values of observables independent of measurement based (...) on quantum logic and we construct in this language the state-dependent notions of joint determinateness, value identity, and simultaneous measurability. This naturally provides a contextual interpretation, in which we can safely claim such a statement that one measuring apparatus measures one observable in one context and simultaneously it measures another nowhere commuting observable in another incompatible context. (shrink)

A stream of conscious experience is extremely contextual; it is impacted by sensory stimuli, drives and emotions, and the web of associations that link, directly or indirectly, the subject of experience to other elements of the individual's worldview. The contextuality of one's conscious experience both enhances and constrains the contextuality of one's behavior. Since we cannot know first-hand the conscious experience of another, it is by way of behavioral contextuality that we make judgements about whether or not, (...) and to what extent, a system is conscious. Thus we believe that a deep understanding of contextuality is vital to the study of consciousness. Methods have been developed for handling contextuality in the microworld of quantum particles. Our goal has been to investigate the extent to which these methods can be used to analyze contextuality in conscious experience. (shrink)

Paul Busch has emphasized on various occasions the importance for physics of going beyond a merely instrumentalist view of quantum mechanics. Even if we cannot be sure that any particular realist interpretation describes the world as it actually is, the investigation of possible realist interpretations helps us to develop new physical ideas and better intuitions about the nature of physical objects at the micro level. In this spirit, Paul Busch himself pioneered the concept of “unsharp quantum reality”, according (...) to which there is an objective non-classical indeterminacy—a lack of sharpness—in the properties of individual quantum systems. We concur with Busch’s motivation for investigating realist interpretations of quantum mechanics and with his willingness to move away from classical intuitions. In this article we try to take some further steps on this road. In particular, we pay attention to a number of prima facie implausible and counter-intuitive aspects of realist interpretations of unitary quantum mechanics. We shall argue that from a realist viewpoint, quantum contextuality naturally leads to “perspectivalism” with respect to properties of spatially extended quantum systems, and that this perspectivalism is important for making relativistic covariance possible. (shrink)

Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modelling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The (...) second, 'quantum entanglement', allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision. (shrink)

We propose a new quantum ontology, in which properties are the fundamental building blocks. In this property ontology physical systems are defined as bundles of type-properties. Not all elements of such bundles are associated with definite case-properties, and this accommodates the Kochen and Specker theorem and contextuality. Moreover, we do not attribute an identity to the type-properties, which gives rise to a novel form of the bundle theory. There are no “particles” in the sense of classical individuals in (...) this ontology, although the behavior of such individuals is mimicked in some circumstances. This picture leads in a natural way to the symmetrization postulates for systems of many “identical particles”. (shrink)

I assess various proposals for the source of the intuition that there is something problematic about contextuality, ultimately concluding that contextuality is best thought of in terms of fine-tuning. I then argue that as with other fine-tuning problems in quantum mechanics, this behaviour can be understood as a manifestation of teleological features of physics. Finally I discuss several formal mathematical frameworks that have been used to analyse contextuality and consider how their results should be interpreted by (...) scientific realists. In the course of this discussion I obtain several new mathematical results—I demonstrate that preparation contextuality is a form of fine-tuning, I show that measurement contextuality can be explained by appeal to a global constraint forbidding closed causal loops, and I demonstrate how negative probabilities can arise from a classical ontological model together with an epistemic restriction. (shrink)

Noncontextual hidden variables theories, assigning simultaneous values to all quantum mechanical observables, are inconsistent by theorems of Gleason and others. These theorems do not exclude contextual hidden variables theories, in which a complete state assigns values to physical quantities only relative to contexts. However, any contextual theory obeying a certain factorisability conditions implies one of Bell's Inequalities, thereby precluding complete agreement with quantum mechanical predictions. The present paper distinguishes two kinds of contextual theories, ‘algebraic’ and ‘environmental’, and investigates (...) when factorisability is reasonable. Some statements by Fine about the philosophical significance of Bell's Inequalities are then assessed. (shrink)

In 1976, I met John Bell several times in CERN and we talked about a possible violation of optical theorem, purity tests, EPR paradox, Bell’s inequalities and their violation. In this review, I resume our discussions, and explain how they were related to my earlier research. I also reproduce handwritten notes, which I gave to Bell during our first meeting and a handwritten letter he sent to me in 1982. We have never met again, but I have continued to discuss (...) BI-CHSH inequalities and their violation in several papers. The research stimulated by Bell’s papers and experiments performed to check his inequalities led to several important applications of quantum entanglement in quantum information and quantum technologies. Unfortunately, it led also to extraordinary metaphysical claims and speculations which in our opinion John Bell would not endorse today. BI-CHSH inequalities are violated in physics and in cognitive science, but it neither proved the completeness of quantum mechanics nor its nonlocality. Quantum computing advantage is not due to some magical instantaneous influences between distant physical systems. Therefore one has to be _cautious in drawing-far-reaching philosophical conclusions from Bell’s inequalities_. The true resource for quantum computing is contextuality and not nonlocality. (shrink)