We argue that for the proof of Bell's theorem no assumptions about realism or free will are necessary. The key formula \[E(AB|a,b) = \int A(a,b,λ)B(a,b,λ)ρ(λ) dλ\] follows from the logic of plausible reasoning (the objective Bayesian interpretation of probability theory) taken alone, without any further assumptions about realism. The space $Λ$, usually interpreted as some space of `hidden variables', can be constructed for an arbitrary `field of discourse' using Stone's theorem. The rejection of superdeterminism follows from logical independence -- the non-existence of information which suggest a dependence -- of the free decisions of the experimenters from everything else. To prove the Bell inequality it is, then, sufficient to reduce this to \[E(AB|a,b) = \int A(a,λ)B(b,λ)ρ(λ) dλ.\] This follows for space-like separated measurements from Einstein causality alone. So, the consequence of the violation of Bell's inequality is that Einstein causality has been empirically falsified, without any loopholes left. We consider and reject the idea of weakening the logic of plausible reasoning could be used to create a loophole. Finally, we discuss what can be used to replace Einstein causality. While weak (signal) Einstein causality holds, it follows either from a notion of strong causality or from human inability to prepare states which violate quantum uncertainty, which makes it uninteresting for fundamental considerations. A notion of strong causality has either unacceptable causal loops or requires a hidden preferred frame. Given that a hidden preferred frame is completely compatible with modern physics, it is argued that this choice is preferable.
We argue that for the proof of Bell's theorem no assumptions about realism or free will are necessary. The key formula [E(AB|a,b) = \int A(a,b,λ)B(a,b,λ)ρ(λ) dλ] follows from the logic of plausible reasoning (the objective Bayesian interpretation of probability theory) taken alone, without any further assumptions about realism. The space Λ, usually interpreted as some space of hidden variables', can be constructed for an arbitrary field of discourse' using Stone's theorem. The rejection of superdeterminism follows from logical independence -- the non-existence of information which suggest a dependence -- of the free decisions of the experimenters from everything else. To prove the Bell inequality it is, then, sufficient to reduce this to [E(AB|a,b) = \int A(a,λ)B(b,λ)ρ(λ) dλ.] This follows for space-like separated measurements from Einstein causality alone. So, the consequence of the violation of Bell's inequality is that Einstein causality has been empirically falsified, without any loopholes left. We consider and reject the idea of weakening the logic of plausible reasoning could be used to create a loophole. Finally, we discuss what can be used to replace Einstein causality. While weak (signal) Einstein causality holds, it follows either from a notion of strong causality or from human inability to prepare states which violate quantum uncertainty, which makes it uninteresting for fundamental considerations. A notion of strong causality has either unacceptable causal loops or requires a hidden preferred frame. Given that a hidden preferred frame is completely compatible with modern physics, it is argued that this choice is preferable.
Bell's theorem is 50 years old. Still there is a controversy about its implications. Much of it has its roots in confusion regarding the premises from which the theorem can be derived. Some claim that a derivation of Bell's inequalities requires just locality assumption, and nothing more. Violations of the inequalities are then interpreted as ``nonlocality'' or ``quantum nonlocality''. We show that such claims are unfounded and that every derivation of Bell's inequalities requires a premise -- in addition to locality and freedom of choice -- which is either assumed tacitly, or unconsciously, or is embedded in a single compound condition (like Bell's ``local causality''). The premise is equivalent to the assumption of existence of additional variables which do not appear in the quantum formalism (in form of determinism, or joint probability for outcomes of all conceivable measurements, or ``additional causes`'', or ``hidden variables'', ``complete description of the state'' or counterfactual definiteness, etc.). A certain irony is that perhaps the main message of violation of Bell's inequalities is that our notion of locality should be based on an operationally well-defined no-signalling condition, rather than on local causality.
This work offers a foundational, ontological re-examination of the Einstein-Podolsky-Rosen (EPR) paradox and the violation of Bell inequalities. It argues that the apparent "nonlocality" in quantum mechanics stems not from a physical mechanism of interaction, but from an inadequate ontological premise shared by classical reasoning and many interpretations of quantum theory. Core Thesis: The paradox arises from the implicit assumption that measurement outcomes in entangled systems represent independent, local facts that pre-exist or can be defined separately. The work rejects this premise. Instead, it proposes that entangled states describe indivisible ontological structures, where correlated outcomes are not separate entities to be coordinated, but inseparable aspects of a single whole. Key Conceptual Innovations: The JED Postulate (Ontological Simultaneity): The cornerstone of the framework. It posits a global constraint on the co-realization of facts: for an entangled state, individual outcomes cannot exist as autonomous facts. They can only be realized as elements of an admissible pair (e.g., {Alice+, Bob-} or {Alice-, Bob+}). This is not a temporal or causal constraint, but a structural condition for existence. Formalism of Frames and Admissibility Relations: The ontology is formalized using "frames" (sets of co-existing facts) and an "admissibility relation" R, which encodes the structure of an entangled state (e.g., for a singlet: R = {(+, -), (-, +)}). The JED postulate ensures that a frame containing one element of a related pair must contain its counterpart. The "Broken Mirror" Metaphor: A central heuristic. Entanglement is likened to a mirror broken into two complementary halves. The halves do not "communicate" to match; their perfect fit is a consequence of their common origin in a single act of breaking. Asking "which half appeared first?" or "how does one half know about the other?" is ontologically meaningless—there is no process that produces only one isolated half. Resolution of the EPR Paradox: The paradox dissolves because its first step—treating Alice's local outcome as an independent fact—is invalid within the JED ontology. There is no independent fact for locality to protect, hence no contradiction between correlations and relativistic locality. Interpretation of Bell's Theorem: The work reframes Bell's theorem. Its violation is not proof of nonlocality, but empirical evidence against the ontology of independent local facts. Bell's mathematics is correct, but its physical significance depends on ontological axioms that may not hold. The JED ontology provides a local, realistic (but not fact-local) framework consistent with the correlations. Distinction from Hidden Variables: The approach is explicitly not a hidden-variable theory. It introduces no hidden parameters λ governing individual outcomes. The relation R is a structural definition of the entangled whole, not a hidden cause of correlations. Probabilities are treated as a descriptive layer over the admissible ontological structures. Methodology: The work is developed in the spirit of the "pencil-case" methodology, constructing minimal ontological models to analyze the logical roots of physical puzzles without adding new dynamical mechanisms. Scope and Intent: The present work should be read as a contribution to the philosophy of physics: it does not aim at proposing a new physical theory, but at clarifying the ontological assumptions underlying existing formalisms. It seeks to shift the discussion from "how do the parts communicate?" to "what kind of whole do the parts constitute?" The formalism is shown to be logically consistent with the standard quantum correlation function (e.g., E(θ,φ) = -cos(θ-φ)), without deriving it, thereby separating the ontological question of admissibility from the empirical-statistical question of probability distribution. Keywords: EPR Paradox, Bell's Theorem
Bell’s [Physics 1 (1964) 195–200] theorem is popularly supposed to establish the nonlocality of quantum physics. Violation of Bell’s inequality in experiments such as that of Aspect, Dalibard and Roger [Phys. Rev. Lett. 49 (1982) 1804–1807] provides empirical proof of nonlocality in the real world. This paper reviews recent work on Bell’s theorem, linking it to issues in causality as understood by statisticians. The paper starts with a proof of a strong, finite sample, version of Bell’s inequality and thereby also of Bell’s theorem, which states that quantum theory is incompatible with the conjunction of three formerly uncontroversial physical principles, here referred to as locality, realism and freedom. Locality is the principle that the direction of causality matches the direction of time, and that causal influences need time to propagate spatially. Realism and freedom are directly connected to statistical thinking on causality: they relate to counterfactual reasoning, and to randomisation, respectively. Experimental loopholes in state-of-the-art Bell type experiments are related to statistical issues of post-selection in observational studies, and the missing at random assumption. They can be avoided by properly matching the statistical analysis to the actual experimental design, instead of by making untestable assumptions of independence between observed and unobserved variables. Methodological and statistical issues in the design of quantum Randi challenges (QRC) are discussed. The paper argues that Bell’s theorem (and its experimental confirmation) should lead us to relinquish not locality, but realism.
Local realism is now revitalized as a fully viable causal explanation of physical reality including empirical Bell violations according to detailed arguments provided at the link below. Meanwhile, by denying local realism in its account of EPR experiments, quantum theory requires a physical causal signal that is physically discontinuous, leaping out of spacetime from one locality and landing in another, like a fish leaping out of water. Quantum theory thus invokes a physical domain outside spacetime through which its causal signal is logically required to travel -- unobservable, unstoppable, and at infinite speed. It might be tempting to conclude that such domains and such signals are some sort of magic, except that would be exactly wrong. Even magic obeys local realism. A master magician, however, can provide a compelling illusion to the contrary. The causally complete local realistic model given by the article below argues compellingly that the antilocality claims of quantum physics reduce to such illusions. Please see main article: ** http://vixra.org/abs/1704.0078 ** Local Realism Explains Bell Violations (author Andrew P. Yake) - Claims to demonstrate that all empirical evidence taken to support quantum theory over local realism plausibly does the reverse. The article comprises 8 pages, 4 figures, 6 equations, 32 references, 1 graph of testable predictions, and 2 paragraphs that purport to expose how the Bell inequality misrepresents the local realistic predictions for the EPR experiment. Thoughtful feedback appreciated (apyake@gmail.com).
Local realism reduces to the proposition that every physical effect arises exclusively at the spacetime locality where the determinate properties of physical reality determine that it be so. The causal model of quantum theory, however, and thus all prospects for quantum computers, require that local realism is false. The essential argument favoring quantum beliefs is that local realism cannot explain empirical Bell violations, whereas quantum theory can. By contrast, the article cited below offers compelling evidence to the contrary. Furthermore, such alleged refutations of local realism are predicated on an interpretation of the Bell inequality that many researchers reject (the cited article provides specific references). Meanwhile, the causal model of quantum theory reduces to the quantum formalism itself, which distributes outcomes across separate localities without providing enough information to determine what those outcomes are. More specifically, depending on subtleties of interpretation, the quantum formalism requires either: (A) There exists a bit of physical information such that this bit exists as mutually exclusive states, or (B) there exists a bit of physical information such that this bit is not physically informed. They are both contradictions. Pick your poison. Or reconsider local realism. See ** http://vixra.org/abs/1704.0078 ** Local Realism Explains Bell Violations (author Andrew P. Yake) - for a demonstration that all empirical evidence taken to support quantum theory over local realism plausibly does the reverse. The article comprises 8 pages, 4 figures, 6 equations, 32 references, 1 graph of testable predictions, and 2 paragraphs that purport to expose how the Bell inequality misrepresents the local realistic predictions for the EPR experiment. Thoughtful feedback appreciated (apyake@gmail.com).
Bell's theorem states that no description of a Bell experiment can be simultaneously local, realistic in the sense of counterfactual definiteness, and free of conspiracy between settings and hidden state. The recent generation of experiments has confirmed the predicted violation of the CHSH inequality, so one of the assumptions must be abandoned. Which one, and how one reconstructs a coherent worldview after doing so, is a question on which many authors disagree. This paper is written by three such authors. All three reject both counterfactual definiteness and conspiratorial violation of statistical independence of setting choices and state. After a joint exposition of the classical half of Bell's theorem in the language of Pearl-style causal graphs, a joint summary of the loophole-free experiments, and a joint survey of the recent literature, each author states where they have presently arrived. Gill accepts irreducible and non-local quantum randomness and finds the choice between locality and realism a false dichotomy. In his later works, Bell derives counterfactual definiteness from classical local causality, and that is what has to go. The metaphysical concepts "realism", "locality", "causality" need to be reconsidered. Helland reconstructs the Hilbert-space formalism from a theory of accessible variables, and from this theory he concludes that every observer must be limited in a specific sense. Jongejan proposes a geometric hidden-variable construction in which the degree of violation of the CHSH inequality depends on the number of dimensions of space, Tsirelson's bound corresponding to three dimensions. The authors conclude with a discussion.