It is argued that among possible nonlocal hidden-variable theories a particular class (called here “crypto-nonlocal” or CN) is relatively plausible on physical grounds. CN theories have the property that (for example) the two photons emitted in an atomic cascade process are indistinguishable in their individual statistical properties from photons emitted singly, and that in the latter case the effects of nonlocality are unobservable. It is demonstrated that all CN theories are constrained by inequalities which are violated by the quantum-mechanical predictions; (...) these inequalities bear no simple relation to Bell's inequalities, and an explicit example is constructed of a CN theory which violates the latter. It is also shown that while existing experiments cannot rule out general CN theories, they do rule out (subject to a few caveats such as the usual ones concerning the well-known “loopholes”) the subclass in which the photon polarizations are linear. (shrink)

It is shown here that Suarez (Found. Phys. 38:583, 2008) wrongly presents the assumptions behind the Leggett’s inequalities, and their modified form used by Groeblacher et al. (Nature 446:871, 2007) for an experimental falsification of a certain class of non-local hidden variable models.

Nonlocal “realistic” Leggett models can be considered refuted by the before-before experiment. “Single preferred frame” models are not refuted by this experiment but bear severe oddities.

It is shown that the before-before (or Suarez-Scarani) experiment refutes hidden variable models with a deterministic (“realistic”) nonlocal part, whereas experiments violating Leggett-type inequalities refute models with biased random local part. Therefore the claim that Gröblacher et al. (Nature 446:871–875, 2007) present “an experimental test of nonlocal realism” is misleading, and Marek Żukowski’s (Found. Phys. 38:1070, 2008) comment misses the point. A new experiment is suggested.

In his 2013 Foundations of Physics paper Mathias Egg claims to show that my critical arguments toward the foundational significance of Leggett’s non-local theories are misguided. The main motivation is that my argument would connect too strongly the Leggett original motivation for introducing this new class of theories with the foundational significance of these theories per se. Egg basically aims to show that, although it can be conceded that the Leggett original motivation relies on a mistaken view of the (...) original Bell theorem, the investigation on the Leggett theories does have a foundational meaning that can be disassociated from the view that Leggett himself has of of them. As a reply to Egg, I would like to argue here that, even if we assume to disentangle the Leggett view from the fate of the Leggett theories, there is still room to dispute the foundational significance of the Leggett ‘non-local realistic’ research program. (shrink)

In a recent paper, I have analysed and criticised Leggett and Garg’s argument to the effect that macroscopic realism contradicts quantum mechanics, by contrasting their assumptions to the example of Bell’s stochastic pilot-wave theories, and have applied Dzhafarov and Kujala’s analysis of contextuality in the presence of signalling to the case of the Leggett–Garg inequalities. In this chapter, I discuss more in general the motivations for macroscopic realism, taking a cue from Einstein’s criticism of the Bohm theory, then go on (...) to summarise my previous results, with a few additional comments on other recent work on Leggett and Garg. [To appear in: E. Dzhafarov, Contextuality from Quantum Physics to Psychology.]. (shrink)

We elaborate on a new interpretation of quantum mechanics which we introduced recently. The main hypothesis of this new interpretation is that quantum particles are entities interacting with matter conceptually, which means that pieces of matter function as interfaces for the conceptual content carried by the quantum particles. We explain how our interpretation was inspired by our earlier analysis of non-locality as non-spatiality and a specific interpretation of quantum potentiality, which we illustrate by means of the example of two interconnected (...) vessels of water. We show by means of this example that philosophical realism is not in contradiction with the recent findings with respect to Leggett’s inequalities and their violations. We explain our recent work on using the quantum formalism to model human concepts and their combinations and how this has given rise to the foundational ideas of our new quantum interpretation. We analyze the equivalence of meaning in the realm of human concepts and coherence in the realm of quantum particles, and how the duality of abstract and concrete leads naturally to a Heisenberg uncertainty relation. We illustrate the role played by interference and entanglement and show how the new interpretation explains the problems related to identity and individuality in quantum mechanics. We put forward a possible scenario for the emergence of the reality of macroscopic objects. (shrink)

The separable hidden variables theory (Bhave [1986]) of Aspect's [1982] four single channel polarizers is developed further to consider possible modified Aspect's experiment with four double channel polarizers. It is shown that Aspect's commutator is not a truly stochastic commutator, and that until such a truly stochastic commutator is devised, experiments based on Bell's inequalities (like those of Aspect's) cannot be adequate experimental tests of quantum nonseparability.

Laudisa (Found. Phys. 38:1110–1132, 2008) claims that experimental research on the class of non-local hidden-variable theories introduced by Leggett is misguided, because these theories are irrelevant for the foundations of quantum mechanics. I show that Laudisa’s arguments fail to establish the pessimistic conclusion he draws from them. In particular, it is not the case that Leggett-inspired research is based on a mistaken understanding of Bell’s theorem, nor that previous no-hidden-variable theorems already exclude Leggett’s models. Finally, I argue that the (...) framework of Bohmian mechanics brings out the importance of Leggett tests, rather than proving their irrelevance, as Laudisa supposes. (shrink)

Ernesto Laclau and Chantal Mouffe’s post-Marxist analysis pushed Gramsci’s anti-determinism to its limits, embracing a post-structuralist, discourse-centred politics. Mouffe’s subsequent programme for radical democracy has sought a renewed democratic left project. While radical democracy’s post-structuralism enables important insights into political subjectivity and antagonism in contemporary democracies, it also weakens its own critical and strategic capacity. By recuperating its Gramscian heritage, radical democracy could be more theoretically and politically effective. In contrast to discourses operating in an entirely open and contingent political (...) field, Gramscian theory offers a more realist – but non-determinist – account of the structural, enabling and constraining properties of ideologies. It also allows for a distinctive institutional space for society. Society is the site upon which political identities are articulated, and from which existing power relations are challenged. But a conception of society also points to the institutional limits to politics, notable by their absence in post-structuralism and radical democracy. (shrink)

Recent proposals to test Bell’s inequalities with entangled pairs of pseudoscalar mesons are reviewed. This includes pairs of neutral kaons or B-mesons and offers some hope to close both the locality and the detection loopholes. Specific difficulties, however, appear thus invalidating most of those proposals. The best option requires the use of kaon regeneration effects and could lead to a successful test if moderate K0 and k̄0 detection efficiencies are achieved.

The recursion-theoretic study of mathematical structures other thanωis now a field of much activity. Analysis and algebra are two such structures which have been studied for their effective contents. Studies in analysis began with the work of Specker on nonconstructive proofs in analysis [16] and in Lacombe's inspiring notes on relevant notions of recursive analysis [8]. Studies in algebra originated in the work of Frolich and Shepherdson on effective extensions of explicit fields [1] and in Rabin's study of computable fields (...) [15]. Equipped with the richness of modern techniques in recursion theory, Metakides and Nerode [11]–[13] began investigating the effective content of vector spaces and fields; these studies have been extended by Kalantari, Remmel, Retzlaff, Shore and others.Kalantari and Retzlaff [5] began a foundational inquiry into effectiveness in topological spaces. They consider a topological spaceXwith a countable basis ⊿ for the topology. The space isfully effective, that is, the basis elements are coded intoωand the operation of intersection of basis elements and the relation of inclusion among them are both computable. Similar to, the lattice of recursively enumerable subsets ofω, the collection of r.e. open subsets ofXforms a latticeℒunder the usual operations of union and intersection. (shrink)

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)

Violations of Bell's Inequality can only be reliably produced if some information about the apparatus setting on one wing is available on the other, requiring superluminal information transmission. In this paper I inquire into the minimum amount of information needed to generate quantum statistics for correlated photons. Reflection on informational constraints clarifies the significance of Fine's Prism models, and allows the construction of several models more powerful than Fine's. These models are more efficient than Fine claims to be possible (...) and work for the full range of possible analyzer settings. It also demonstrates that the division of theories into those that violate parameter independence and those that violate outcome independence sheds no light on the question of superluminal information transmission. (shrink)

Bell's inequality must be satisfied by a theory that can be based on local realistic variables. We derive such an inequality and show that it is violated by some quantum mechanical states. These states may be looked upon as pertaining to one particle.

A logical approach to Bell's Inequalities of quantum mechanics has been introduced by Abramsky and Hardy [2]. We point out that the logical Bell's Inequalities of [2] are provable in the probability logic of Fagin, Halpern and Megiddo [4]. Since it is now considered empirically established that quantum mechanics violates Bell's Inequalities, we introduce a modified probability logic, that we call quantum team logic, in which Bell's Inequalities are not provable, and prove a Completeness Theorem for this logic. For this (...) end we generalise the team semantics of dependence logic [7] first to probabilistic team semantics, and then to what we call quantum team semantics. (shrink)

RÉSUMÉ: Cet article examine les conséquences pour l’inégalité sexuelle au Canada des coupures gouvernementales dans les soins de santé et les services sociaux, et les évalue à l’aune de la jurisprudence relative à la Charte. L’auteure soutient que ce recul a en fait désavantagé les femmes d’une manière disproportionnée, et qu’on pourrait y voir, du point de vue de la Charte, une discrimination à leur endroit. Or les gouvernements n’ont offert aucune justification de ces effets discriminatoires qui satisferait aux critères (...) de la Charte en en montrant le caractère raisonnable dans une société libre et démocratique. Présenter l’action gouvernementale comme un exercice neutre de transfert de responsabilités vers les familles et les communautés ne saurait constituer une telle justification. (shrink)

Eight derivations of Bell’s inequality are given. First a simple and concrete derivation is given drawing on the full strength of the two hypotheses of locality and hidden variables. Two attempts at deriving Bell’s inequality without locality are made. They fail, but give valuable insight into the form which nonlocality must take in quantum physics. Arguments are given against this form of nonlocality. Ontological ideas which allow separation, realism, and locality in quantum mechanics are indicated. In the following (...) five derivations, a number of variants of the assumption of hidden variables are tried. Among the insights which these derivations give rise to are: Particles cannot be assumed to have spin or polarisation values for as much as one fixed direction. The classical picture of electromagnetic radiation is incompatible with QM. Heisenberg’s idea of potentiality in elementary particles is incompatible with QM. There is a weakest form of hidden variables, called realisability, which is sufficient to yield Bell’s inequality. Quantum states cannot be identified with physical states. The mathematical problem of the integration of quantum states into physical states is nontrivial. (shrink)

Wage inequality, including the college/high school education premium, has increased substantially in the United States. A key part of the most widely accepted explanation for this is that skill-biased technological change accelerated during this time. This article suggests that the impact of skill-biased technological change was closer to constant in the second half of the twentieth century. This leaves a large unexplained decrease in the college/high school education premium in the 1940s and a large unexplained increase in the 1980s. (...) The current article provides evidence that the upsurge and decline in union power during those respective periods provide a good explanation for these unexplained wage inequality changes. (shrink)

Instead of the usual asymptotic passage from quantum mechanics to classical mechanics when a parameter tended to infinity, a sharp boundary is obtained for the domain of existence of classical reality. The last is treated as separable empirical reality following d'Espagnat, described by a mathematical superstructure over quantum dynamics for the universal wave function. Being empirical, this reality is constructed in terms of both fundamental notions and characteristics of observers. It is presupposed that considered observers perceive the world as a (...) system of collective degrees of freedom that are inherently dissipative because of interaction with thermal degrees of freedom. Relevant problems of foundation of statistical physics are considered. A feasible example is given of a macroscopic system not admitting such classical reality.The article contains a concise survey of some relevant domains: quantum and classical Bell-type inequalities; universal wave function; approaches to quantum description of macroscopic world, with emphasis on dissipation; spontaneous reduction models; experimental tests of the universal validity of the quantum theory. (shrink)

After recalling proofs of the Bell inequality based on the assumptions of separability and of noncontextuality, the most general noncontextual contrapositive conditional probabilities consistent with the Aspect experiment are constructed. In general these probabilities are not all positive.

In this book Larry Temkin examines the concepts of equality and inequality, and addresses one particular question in depth: how can we judge between different sorts of inequality? When is one inequality worse than another? Temkin shows that there are many different factors underlying and influencing our egalitarian judgments and that the notion of inequality is surprisingly complex. He looks at inequality as applied to individuals and to groups, and at the standard measures of (...) class='Hi'>inequality employed by economists and others, and considers whether inequality matters more in a poor society than a rich one. The arguments of non-egalitarians are also examined. Temkin's book presents a new way of thinking about equality and inequality which challenges the assumptions of philosophers, welfare economists, and others concerned with these notions on a practical as well as a theoretical level. (shrink)

We show that a local theory conforming to the requirement of reducing to usual quantum mechanics for single-particle states and describing two-particle correlations in terms of mixtures violates the condition of perfect anticorrelation between spin components in the case of Bohm's version of EPR.

Temkin presents a new way of thinking about equality and inequality that challenges the assumptions of philosophers, welfare economists, and others, and has significant implications on both a practical and theoretical level.

RésuméCet article examine les conséquences pour l'inégalité sexuelle au Canada des coupures gouvernementales dans les soins de santé et les services sociaux, et les évalue à I'aune de la jurisprudence relative à la Charte. L'auteure soutient que ce recul a en fait désavantagé les femmes d'une manière disproportionnée, et qu'on pourrait y voir, du point de vue de la Charte, une discrimination à leur endroit. Or les gouvernements n'ont offert aucune justification de ces effets discriminatoires qui satisferait aux critères de (...) la Charte en en montrant le caractère raisonnable dans une société libre et démocratique. Présenter l'action gouvernementale comme un exercice neutre de transfert de responsabilités vers les families et les communautés ne saurait constituer une telle justification. (shrink)

In this paper I demonstrate that the quantum correlations of polarization observables used in Bell’s argument against local realism have to be interpreted as conditional quantum correlations. By taking into account additional sources of randomness in Bell’s type experiments, i.e., supplementary to source randomness, I calculate the complete quantum correlations. The main message of the quantum theory of measurement is that complete correlations can be essentially smaller than the conditional ones. Additional sources of randomness diminish correlations. One can say another (...) way around: transition from unconditional correlations to conditional can increase them essentially. This is true for both classical and quantum probability. The final remark is that classical conditional correlations do not satisfy Bell’s inequality. Thus we met the following conditional probability dilemma: either to use the conditional quantum probabilities, as was done by Bell and others, or complete quantum correlations. However, in the first case the corresponding classical conditional correlations need not satisfy Bell’s inequality and in the second case the complete quantum correlations satisfy Bell’s inequality. Thus in neither case we have a problem of mismatching of classical and quantum correlations. The whole structure of Bell’s argument was based on identification of conditional quantum correlations with unconditional classical correlations. (shrink)

It is argued that the long standing failure to show an uncontroversial, loophole-free, empirical violation of a Bell inequality should be interpreted as a support to local realism. After defining realism and locality, this as relativistic causality, the performed experimental tests of Bell’s inequalities are commented. It is pointed out that, without any essential modification of quantum mechanics, the theory might be compatible with local realism.

We make use of natural induction to propose, following John Ju Sakurai, a generalization of Bell's inequality for two spin s=n/2(n=1,2,...) particle systems in a singlet state. We have found that for any finite integer or half-integer spin Bell's inequality is violated when the terms in the inequality are calculated from a quantum mechanical point of view. In the final expression for this inequality the two members therein are expressed in terms of a single parameter θ. (...) Violation occurs for θ in some interval of the form (α,π/2) where α parameter becomes closer and closer to π/2, as the spin grows, that is, the greater the spin number the size of the interval in which violation occurs diminishes to zero. Bell's inequality is a relationship among observables that discriminates between Einstein's locality principle and the non-local point of view of orthodox quantum mechanics. So our conclusion may also be stated by saying that for large spin numbers the non-local and local points of view agree. (shrink)

In 1893, Schatunowsky showed that 30 is the largest number all of whose totatives are primes; we show that this result cannot be proved, in any form, in Chebyshev's theorem (Bertrand's postulate), even if all irreducibles are primes. Bonse's inequality is shown to be indeed weaker than Chebyshev's theorem. Schatunowsky's theorem holds in together with Bonse's inequality, the existence of the greatest prime dividing certain types of numbers, and the condition that all irreducibles be prime.

Jensen’s inequality is one of the fundamental inequalities which has several applications in almost every field of science. In 2003, Mercer gave a variant of Jensen’s inequality which is known as Jensen–Mercer’s inequality. The purpose of this article is to propose new bounds for Csiszár and related divergences by means of Jensen–Mercer’s inequality. Also, we investigate several new bounds for Zipf–Mandelbrot entropy. The idea of this article may further stimulate research on information theory with the help (...) of Jensen–Mercer’s inequality. (shrink)

The extended semantic realism (ESR) model proposes a new theoretical perspective which embodies the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) into a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide in this review an overall view on the present status of our research on this topic. We attain in a new, shortened way a mathematical representation of the generalized observables introduced by the ESR model and a generalization of the projection postulate of elementary (...) QM. Basing on these results we prove that the Bell-Clauser-Horne-Shimony-Holt (BCHSH) inequality, a modified BCHSH inequality and quantum predictions hold together in the ESR model because they refer to different parts of the picture of the physical world supplied by the model. Then we show that a new mathematical representation of mixtures must be introduced in the ESR model which does not coincide with the standard representation in QM and avoids some deep problems that arise from the representation of mixtures provided by QM. Finally we get a nontrivial generalization of the Lüders postulate, which is justified in a special case by introducing a reasonable physical assumption on the evolution of the compound system made up of the measured system and the measuring apparatus. (shrink)

We analyze the proof given by J. S. Bell of an inequality between mean values of measurement results which, according to him, would be characteristic of any local hidden-parameter theory. It is shown that Bell's proof is based upon a hypothesis already contained in von Neumann's famous theorem: It consists in the admission that hidden values of parameters must obey the same statistical laws as observed values. This hypothesis contradicts in advance well-known and certainly correct statistical relations in measurement (...) results: One must therefore reject the type of theory considered by Bell, and his inequality has no general meaning. (shrink)

This note presents a very simple way of interpreting the Gini coefficient of inequality, in `equivalent' welfare terms, as the proportion of a cake of given size going to the poorer of two individuals in a two-person cake-sharing problem.

By assuming a deterministic evolution of quantum systems and taking realism into account, we carefully build a hidden variable theory for Quantum Mechanics based on the notion of ontological states proposed by ’t Hooft. We view these ontological states as the ones embedded with realism and compare them to the quantum states that represent superpositions, viewing the latter as mere information of the system they describe. Such a deterministic model puts forward conditions for the applicability of Bell’s inequality: the (...) usual inequality cannot be applied to the usual experiments. We build a Bell-like inequality that can be applied to the EPR scenario and show that this inequality is always satisfied by QM. In this way we show that QM can indeed have a local interpretation, and thus meet with the causal structure imposed by the Theory of Special Relativity in a satisfying way. (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)