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  1. Samson Abramsky & Lucien Hardy (2012). Logical Bell Inequalities. Physical Review A 85:062114-1 - 062114-11.
    Bell inequalities play a central role in the study of quantum nonlocality and entanglement, with many applications in quantum information. Despite the huge literature on Bell inequalities, it is not easy to find a clear conceptual answer to what a Bell inequality is, or a clear guiding principle as to how they may be derived. In this paper, we introduce a notion of logical Bell inequality which can be used to systematically derive testable inequalities for a very wide variety of (...)
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  2. Alexander Afriat, Altering the Remote Past.
    An abstract treatment of Bell inequalities is proposed, in which the parameters characterizing Bell’s observable can be times rather than directions. The violation of a Bell inequality might then be taken to mean that a property of a system can be changed by the timing of a distant measurement, which could take place in the future.
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  3. Arif Ahmed & Adam Caulton (2014). Causal Decision Theory and EPR Correlations. Synthese 191 (18):4315-4352.
    The paper argues that on three out of eight possible hypotheses about the EPR experiment we can construct novel and realistic decision problems on which (a) Causal Decision Theory and Evidential Decision Theory conflict (b) Causal Decision Theory and the EPR statistics conflict. We infer that anyone who fully accepts any of these three hypotheses has strong reasons to reject Causal Decision Theory. Finally, we extend the original construction to show that anyone who gives any of the three hypotheses any (...)
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  4. Robert Alicki (2009). On von Neumann and Bell Theorems Applied to Quantumness Tests. Foundations of Physics 39 (4):352-360.
    The issues, raised in Żukowski (arXiv:0809.0115v1, 2008), concerning the relevance of the von Neumann theorem for the single-system’s quantumness test proposed in Alicki and Van Ryn (J. Phys. A: Math. Theor. 41:062001, 2008) and performed for the case of single photon polarization in Brida et al. (Opt. Express 16:11750, 2008; arXiv:0811.3376, 2008) and the usefulness of Bell’s inequality for testing the idea of macroscopic quantum systems are discussed in some details. Finally, the proper quantum mechanical description of the experiment with (...)
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  5. Valia Allori (2013). Book Review Of: "Do We Really Understand Quantum Mechanics?" by Franck Laloë. [REVIEW] Notre Dame Philosophical Review.
  6. Frank Arntzenius (1994). Relativistic Hidden Variable Theories? Erkenntnis 41 (2):207 - 231.
    I show that for any quantum dynamics and any choice of observables as hidden variables an adequate hidden variable theory always exists. I argue that hidden variable theories have no more problems in reconciling non-locality with relativity than no-hidden-variable theories.
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  7. David Atkinson, Nonlocality Is a Nonsequitur.
    Nonlocality in quantum mechanics does not follow from nonseparability, nor does classical stochastic independence imply physical independence. In this paper an explicit proof of a Bell inequality is recalled, and an analysis of the Aspect experiment in terms of noncontextual, but indefinite weights, or improper probabilities, is given.
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  8. David Atkinson, Bell's Inequalities and Kolmogorov's Axioms.
    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.
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  9. Michael N. Audi (1973). Book Review:Perspectives in Quantum Theory: Essays in Honor of Alfred Lande Wolfgang Yourgrau, Alwyn Van Der Merwe. [REVIEW] Philosophy of Science 40 (2):323-.
  10. Tomek Bartoszyński, Andrzej Roslanowski & Saharon Shelah (2000). After All, There Are Some Inequalities Which Are Provable in ZFC. Journal of Symbolic Logic 65 (2):803-816.
    We address ZFC inequalities between some cardinal invariants of the continuum, which turned out to be true in spite of strong expectations given by [11].
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  11. Donald Bedford & Henry P. Stapp (1995). Bell's Theorem in an Indeterministic Universe. Synthese 102 (1):139 - 164.
    A variation of Bell's theorem that deals with the indeterministic case is formulated and proved within the logical framework of Lewis's theory of counterfactuals. The no-faster-than-light-influence condition is expressed in terms of Lewis would counterfactual conditionals. Objections to this procedure raised by certain philosophers of science are examined and answered. The theorem shows that the incompatibility between the predictions of quantum theory and the idea of no faster-than-light influence cannot be ascribed to any auxiliary or tacit assumption of either determinism (...)
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  12. Darrin W. Belousek (1999). Bell's Theorem, Nonseparability, and Spacetime Individuation in Quantum Mechanics. Philosophy of Science 66 (3):46.
    We first examine Howard's analysis of the Bell factorizability condition in terms of 'separability' and 'locality' and then consider his claims that the violations of Bell's inequality by the statistical predictions of quantum mechanics should be interpreted in terms of 'nonseparability' rather than 'nonlocality' and that 'nonseparability' implies the failure of spacetime as a principle of individuation for quantum-mechanical systems. We will argue that his argument for the first claim is less than compelling and that any argument for the second (...)
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  13. Enrico G. Beltrametti & Maciej J. Maczynski (1994). On Bell-Type Inequalities. Foundations of Physics 24 (8):1153-1159.
    A Bell-type inequality is defined as an inequality of the type 0⩽L⩽1,where L is a linear combination with real coefficients of probabilities p i and joint probabilities p ij ,p ijk ,...,p l ,...,n corresponding to n events. A general theorem on the validity of such inequalities in correspondence to physical assumptions about commutativity or noncommutativity is given. Examples and possible physical applications are discussed.
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  14. Yemima Ben-Menahem (1997). Dummett Vs Bell on Quantum Mechanics. Studies in History and Philosophy of Science Part B 28 (2):277-290.
  15. S. Bergia, F. Cannata & V. Monzoni (1985). Explicit Examples of Theories Satisfying Bell's Inequalities: Do They Miss Their Goal Prior to Contradicting Experiments? [REVIEW] Foundations of Physics 15 (2):145-154.
    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.
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  16. S. V. Bhave (1991). Bell's Inequalities and Quantum Non-Separability. British Journal for the Philosophy of Science 42 (4):541-545.
    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.
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  17. Tomasz Bigaj (2010). How to (Properly) Strengthen Bell's Theorem Using Counterfactuals. Studies in History and Philosophy of Science Part B 41 (1):58-66.
    Bell’s theorem in its standard version demonstrates that the joint assumptions of the hidden-variable hypothesis and the principle of local causation lead to a conflict with quantum-mechanical predictions. In his latest counterfactual strengthening of Bell’s theorem, Stapp attempts to prove that the locality assumption itself contradicts the quantum-mechanical predictions in the Hardy case. His method relies on constructing a complex, non-truth functional formula which consists of statements about measurements and outcomes in some region R, and whose truth value depends on (...)
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  18. Tomasz Bigaj (2010). How to Strengthen Bell's Theorem Using Counterfactuals. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (1):58-66.
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  19. Tomasz Bigaj (2007). Counterfactuals and Non-Locality of Quantum Mechanics: The Bedford–Stapp Version of the GHZ Theorem. Foundations of Science 12 (1):85-108.
    In the paper, the proof of the non-locality of quantum mechanics, given by Bedford and Stapp (1995), and appealing to the GHZ example, is analyzed. The proof does not contain any explicit assumption of realism, but instead it uses formal methods and techniques of the Lewis calculus of counterfactuals. To ascertain the validity of the proof, a formal semantic model for counterfactuals is constructed. With the help of this model it can be shown that the proof is faulty, because it (...)
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  20. Tomasz Bigaj (2006). Non-Locality and Possible Worlds. A Counterfactual Perspective on Quantum Entanglement. Ontos Verlag.
    This book uses the formal semantics of counterfactual conditionals to analyze the problem of non-locality in quantum mechanics. Counterfactual conditionals enter the analysis of quantum entangled systems in that they enable us to precisely formulate the locality condition that purports to exclude the existence of causal interactions between spatially separated parts of a system. They also make it possible to speak consistently about alternative measuring settings, and to explicate what is meant by quantum property attributions. The book develops the possible-world (...)
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  21. A. Bramon, R. Escribano & G. Garbarino (2006). Bell's Inequality Tests with Meson–Antimeson Pairs. Foundations of Physics 36 (4):563-584.
    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.
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  22. Thomas Breuer (2003). Another No‐Go Theorem for Hidden Variable Models of Inaccurate Spin 1 Measurements. Philosophy of Science 70 (5):1368-1379.
    Uncertainty about the actual orientation of the measurement device has been claimed to open a loophole for hidden variable models of quantum mechanics. In this paper I describe the statistics of inaccurate spin measurements by unsharp spin observables. A no‐go theorem for hidden variable models of the inaccurate measurement statistics follows: There is a finite set of directions for which not all results of inaccurate spin measurements can be predetermined in a non‐contextual way. In contrast to an earlier theorem (Breuer (...)
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  23. Thomas Breuer (2003). Another No-Go Theorem for Hidden Variable Models of Inaccurate Spin 1 Measurements. Philosophy of Science 70 (5):1368-1379.
    Uncertainty about the actual orientation of the measurement device has been claimed to open a loophole for hidden variable models of quantum mechanics. In this paper I describe the statistics of inaccurate spin measurements by unsharp spin observables. A no-go theorem for hidden variable models of the inaccurate measurement statistics follows: There is a finite set of directions for which not all results of inaccurate spin measurements can be predetermined in a non-contextual way. In contrast to an earlier theorem [Breuer, (...)
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  24. Thomas Breuer, A No-Go Theorem for Hidden Variable Models of Inaccurate Spin Measurements.
    Uncertainty about the actual orientation of the measurement device has been claimed to open a loophole for hidden variable models of quantum mechanics. In this paper I describe the statistics of inaccurate spin measurements by unsharp spin observables. If the inaccuracy is below a certain level, a no-go theorem for hidden variable models of the inaccurate measurement statistics follows: There are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate (...)
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  25. Harvey R. Brown & Christopher Gordon Timpson, Bell on Bell's Theorem: The Changing Face of Nonlocality.
    Between 1964 and 1990, the notion of nonlocality in Bell's papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations between separated beables. The proposition that standard quantum mechanics is itself nonlocal became divorced from the Bell theorem per se from 1976 on, although this important point is widely overlooked in the literature. In 1990, the year of his death, Bell would express serious misgivings about the mathematical (...)
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  26. Matthew J. Brown (2014). Quantum Frames. Studies in History and Philosophy of Science Part B 45 (1):1-10.
    The framework of quantum frames can help unravel some of the interpretive difficulties i the foundation of quantum mechanics. In this paper, I begin by tracing the origins of this concept in Bohr's discussion of quantum theory and his theory of complementarity. Engaging with various interpreters and followers of Bohr, I argue that the correct account of quantum frames must be extended beyond literal space–time reference frames to frames defined by relations between a quantum system and the exosystem or external (...)
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  27. Jeffrey Bub & Vandana Shiva (1978). Non-Local Hidden Variable Theories and Bell's Inequality. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:45-53.
    Bell's proof purports to show that any hidden variable theory satisfying a physically reasonable locality condition is characterized by an inequality which is inconsistent with the quantum statistics. It is shown that Bell's inequality actually characterizes a feature of hidden variable theories which is much weaker than locality in the sense considered physically motivated. We consider an example of non- local hidden variable theory which reproduces the quantum statistics. A simple extension of the theory, which preserves the non- local character, (...)
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  28. Jeremy Butterfield, Quantum Chance and Non-Locality.
    This is an excellent book, by one of the philosophy of quantum theory's brightest stars. It combines a clear presentation of determinism, probability and non-locality in several current interpretations of quantum theory, with a good deal of detailed analysis, both reporting other people's and Dickson's own results, and developing his own ideas|which are often heterodox, but always well-defended and thought-provoking. The treatment is often concise, especially when reporting standard material or others' results. There are also frequent changes of gear; both (...)
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  29. Jeremy Butterfield (2001). Book Review:Quantum Chance and Non-Locality: Probablity and Non-Locality in the Interpretations of Quantum Mechanics W. Michael Dickson. [REVIEW] Philosophy of Science 68 (2):263-.
  30. Jeremy Butterfield (1992). Bell's Theorem: What It Takes. British Journal for the Philosophy of Science 43 (1):41-83.
    I compare deterministic and stochastic hidden variable models of the Bell experiment, exphasising philosophical distinctions between the various ways of combining conditionals and probabilities. I make four main claims. (1) Under natural assumptions, locality as it occurs in these models is equivalent to causal independence, as analysed (in the spirit of Lewis) in terms of probabilities and conditionals. (2) Stochastic models are indeed more general than deterministic ones. (3) For factorizable stochastic models, relativity's lack of superluminal causation does not favour (...)
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  31. Adán Cabello (2005). Bell's Theorem Without Inequalities and Without Unspeakable Information. Foundations of Physics 35 (11):1927-1934.
    A proof of Bell’s theorem without inequalities is presented in which distant local setups do not need to be aligned, since the required perfect correlations are achieved for any local rotation of the local setups.
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  32. Charles B. Campbell, A 'Plausible' Showing After 'Bell Atlantic Corp. V. Twombly'.
    The United States Supreme Court's decision in Bell Atlantic Corp. v. Twombly is creating quite a stir. Suddenly gone is the famous loosey-goosey rule of Conley v. Gibson that a complaint should not be dismissed for failure to state a claim unless it appears beyond doubt that the plaintiff can prove no set of facts in support of his claim which would entitle him to relief.Now a complaint must provide enough facts to state a claim to relief that is plausible (...)
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  33. Michele Caponigro & Enrico Giannetto (2012). Epistemic Vs Ontic Classification of Quantum Entangled States? Discusiones Filosóficas 13 (20):137 - 145.
    In this brief paper, starting from recent works, we analyze from conceptual point of view this basic question: can be the nature of quantum entangled states interpreted ontologically or epistemologically? According some works, the degrees of freedom of quantum systems permit us to establish a possible classification between factorizables and entangled states. We suggest, that the "choice" of degree of freedom, even if mathematically justified introduces epistemic element, not only in the systems but also in their classification. We retain, instead, (...)
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  34. Eric Cator & Klaas Landsman (2014). Constraints on Determinism: Bell Versus Conway–Kochen. Foundations of Physics 44 (7):781-791.
    Bell’s Theorem from Physics 36:1–28 (1964) and the (Strong) Free Will Theorem of Conway and Kochen from Notices AMS 56:226–232 (2009) both exclude deterministic hidden variable theories (or, in modern parlance, ‘ontological models’) that are compatible with some small fragment of quantum mechanics, admit ‘free’ settings of the archetypal Alice and Bob experiment, and satisfy a locality condition akin to parameter independence. We clarify the relationship between these theorems by giving reformulations of both that exactly pinpoint their resemblance and their (...)
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  35. Eric G. Cavalcanti (2010). Causation, Decision Theory, and Bell's Theorem: A Quantum Analogue of the Newcomb Problem. British Journal for the Philosophy of Science 61 (3):569-597.
    I apply some of the lessons from quantum theory, in particular from Bell’s theorem, to a debate on the foundations of decision theory and causation. By tracing a formal analogy between the basic assumptions of causal decision theory (CDT)—which was developed partly in response to Newcomb’s problem— and those of a local hidden variable theory in the context of quantum mechanics, I show that an agent who acts according to CDT and gives any nonzero credence to some possible causal interpretations (...)
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  36. Eric G. Cavalcanti & Raymond Lal (2014). On Modifications of Reichenbach's Principle of Common Cause in Light of Bell's Theorem. Journal of Physics A: Mathematical and Theoretical 47 (42):424018.
    Bellʼs 1964 theorem causes a severe problem for the notion that correlations require explanation, encapsulated in Reichenbachʼs principle of common cause. Despite being a hallmark of scientific thought, dropping the principle has been widely regarded as much less bitter medicine than the perceived alternative—dropping relativistic causality. Recently, however, some authors have proposed that modified forms of Reichenbachʼs principle could be maintained even with relativistic causality. Here we break down Reichenbachʼs principle into two independent assumptions—the principle of common cause proper and (...)
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  37. Eric G. Cavalcanti & Howard M. Wiseman (2012). Bell Nonlocality, Signal Locality and Unpredictability (or What Bohr Could Have Told Einstein at Solvay Had He Known About Bell Experiments). Foundations of Physics 42 (10):1329-1338.
    The 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the assumptions of locality and determinism. On the other hand, the assumptions of signal locality plus predictability are also sufficient to derive Bell inequalities. This simple theorem, previously noted but published only relatively recently by Masanes, Acin and Gisin, has fundamental implications not entirely appreciated. Firstly, nothing can be concluded about the ontological assumptions of locality or determinism independently of each (...)
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  38. José L. Cereceda (1995). The Kochen-Specker Theorem and Bell's Theorem: An Algebraic Approach. [REVIEW] Foundations of Physics 25 (6):925-949.
    In this paper we present a systematic formulation of some recent results concerning the algebraic demonstration of the two major no-hidden-variables theorems for N spin-1/2 particles. We derive explicitly the GHZ states involved and their associated eigenvalues. These eigenvalues turn out to be undefined for N=∞, this fact providing a new proof showing that the nonlocality argument breaks down in the limit of a truly infinite number of particles.
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  39. G. K. Chesterton (2009). The Bell-Ringers. The Chesterton Review 35 (3-4):441-442.
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  40. G. K. Chesterton (2001). The Bell-Ringers. The Chesterton Review 27 (1):15-16.
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  41. Joy Christian, On the Fatal Mistake Made by John S. Bell in the Proof of His Famous Theorem.
    We explain the elementary mistake made by John S. Bell in the proof of his famous ``theorem.''.
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  42. Joy Christian, Proposed Macroscopic Test of the Physical Relevance of Bell's Theorem.
    A macroscopic experiment capable of detecting a signature of spinorial sign changes is discussed. If realized, it would determine whether Bell inequalities are satisfied for a manifestly local, classical system. By providing an explicitly local-realistic derivation of the EPR-Bohm type spin correlations, it is demonstrated why Bell inequalities must be violated even in such a manifestly local, macroscopic domain, just as strongly as they are in the microscopic domain. The proposed experiment has the potential to transform our understanding of the (...)
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  43. Joy Christian, Macroscopic Observability of Spinorial Sign Changes: A Simplified Proof.
    A macroscopic experiment capable of detecting a signature of spinorial sign changes is discussed. If realized, it would determine whether Bell inequalities are satisfied for a manifestly local, classical system. By providing an explicitly local-realistic derivation of the EPR-Bohm type spin correlations, it is demonstrated why Bell inequalities must be violated even in such a manifestly local, macroscopic domain, just as strongly as they are in the microscopic domain. The proposed experiment has the potential to transform our understanding of the (...)
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  44. Joy Christian, A Simplified Local-Realistic Derivation of the EPR-Bohm Correlation.
    We illustrate an explicit counterexample to Bell's theorem by constructing a pair of spin variables within S^3 that exactly reproduces the EPR-Bohm correlation in a manifestly local-realistic manner.
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  45. Joy Christian, Whither All the Scope and Generality of Bell's Theorem?
    In a recent preprint James Owen Weatherall has attempted a simple local-deterministic model for the EPR-Bohm correlation and speculated about why his model fails when my counterexample to Bell's theorem succeeds. Here I bring out the physical, mathematical, and conceptual reasons why his model fails. In particular, I demonstrate why no model based on a tensor representation of the rotation group SU can reproduce the EPR-Bohm correlation. I demonstrate this by calculating the correlation explicitly between measurement results A = +1 (...)
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  46. Joy Christian, Refutation of Richard Gill's Argument Against My Disproof of Bell's Theorem.
    I identify a number of errors in Richard Gill's purported refutation of my disproof of Bell's theorem. In particular, I point out that his central argument is based, not only on a rather trivial misreading of my counterexample to Bell's theorem, but also on a simple oversight of a freedom of choice in the orientation of a Clifford algebra. What is innovative and original in my counterexample is thus mistaken for an error, at the expense of the professed universality and (...)
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  47. Joy Christian, Refutation of Some Arguments Against My Disproof of Bell's Theorem.
    In a couple of recent preprints Moldoveanu has suggested that there are errors in my disproof of Bell's theorem. Here I show that this claim is false. In particular, I show that my local-realistic framework is incorrectly and misleadingly presented in both of his preprints. In addition there are a number of serious mathematical and conceptual errors in his discussion of my framework. For example, contrary to his claim, my framework is manifestly non-contextual. In particular, quantum correlations are understood within (...)
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  48. Joy Christian, Disproof of Bell's Theorem.
    We illustrate an explicit counterexample to Bell's theorem by constructing a pair of dichotomic variables that exactly reproduce the EPR-Bohm correlations in a manifestly local-realistic manner.
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  49. Joy Christian, Restoring Local Causality and Objective Reality to the Entangled Photons.
    Unlike our basic theories of space and time, quantum mechanics is not a locally causal theory. This well known fact was brought forth by Einstein, Podolsky, and Rosen in 1935. Today it is widely believed that any hopes of restoring local causality within a realistic theory have been undermined by Bell's theorem and its supporting experiments. By contrast, we provide a strictly local, deterministic, and realistic explanation for the correlations observed in two such supporting experiments performed at Orsay and Innsbruck. (...)
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  50. Joy Christian, Failure of Bell's Theorem and the Local Causality of the Entangled Photons.
    A counterexample to Bell's theorem is presented which uses a pair of photons instead of spin-1/2 particles used in our previous counterexamples. A locally causal protocol is provided for Alice and Bob, which allows them to simulate observing photon polarizations at various angles, and record their results as A=+/-1 in S^3 and B=+/-1 in S^3, respectively. When these results are compared, the correlations are seen to be exactly those predicted by quantum mechanics; namely cos 2(alpha - beta), where alpha and (...)
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