While Bell’s theorem is traditionally seen as a total rejection of local classical models in quantum mechanics, this paper argues that such a conclusion relies on the narrow assumption of "joint definiteness." Bell’s derivation requires a single hidden state, λ, to account for all possible measurement outcomes simultaneously, which implies that the measurement apparatus remains microscopically unchanged regardless of its settings. However, because physical instruments are composed of matter, their internal microstates necessarily vary with the chosen settings, meaning the relevant hidden variables are setting-dependent. This physical reality prevents the formation of a global joint probability distribution, placing these types of models outside the mathematical constraints of Bell’s and Fine’s theorems. Consequently, the authors conclude that while Bell’s theorem remains mathematically sound, it only excludes hidden-variable models that ignore the setting-dependent nature of the measuring apparatus, leaving the door open for classical descriptions of physical reality.
While Bell’s theorem is traditionally seen as a total rejection of local classical models in quantum mechanics, this paper argues that such a conclusion relies on the narrow assumption of "joint definiteness." Bell’s derivation requires a single hidden state, λ, to account for all possible measurement outcomes simultaneously, which implies that the measurement apparatus remains microscopically unchanged regardless of its settings. However, because physical instruments are composed of matter, their internal microstates necessarily vary with the chosen settings, meaning the relevant hidden variables are setting-dependent. This physical reality prevents the formation of a global joint probability distribution, placing these types of models outside the mathematical constraints of Bell’s and Fine’s theorems. Consequently, the authors conclude that while Bell’s theorem remains mathematically sound, it only excludes hidden-variable models that ignore the setting-dependent nature of the measuring apparatus, leaving the door open for classical descriptions of physical reality.
This paper presents a conceptually simple account of the EPR argument and Bell’s theorem using entangled photon polarization experiments. It clarifies how quantum correlations arise from conditioning outcomes through fundamental properties of quantum entanglement that result in conditional probability structures rather than from superluminal influences or pre-existing particle properties. Building on this analysis, the paper explores the informational and philosophical consequences of Bell violations. Hidden-variable theories are shown to entail severe informational overhead by requiring microscopic labeling of otherwise indistinguishable particles, whereas quantum mechanics encodes structure economically through relational constraints on joint outcomes. A striking but rarely-emphasized feature of Bell-type experiments is that while traditionally the geometery of the apparatus used to carry out these experiments are aligned with each other, according to quantum mechanics the physical orientations of the apparatus have no physical meaning with respect to one another at the time of measurement. The geometry is defined only locally, relative to the laboratory in which the tests is set. The essay further argues that Bell’s theorem motivates a shift from object-centered classical realism toward a form of realism referred to as “Relational Realism” wherein correlations and informational structure are ontologically primary, while objects having individual properties are contextual and derivative. This perspective dissolves the traditional realism-versus-idealism dichotomy and situates quantum mechanics as a fundamentally relational theory of physical reality rather than an incomplete classical one.
Abstract. For unit vectors a, b, entanglement requires that spin measurements satisfy those just given for a≠b. Bell’s hidden variable quantum mechanical local particle with a=b cannot provide the values for a≠b and, hence, the values for an entangled particle system. The perception that any hidden variable quantum mechanical description of an entangled system of particles is non-local depends on Bell’s inappropriate definition of locality, which excludes entanglement for a distant particle, and the condition that a=b, which does not give the values for a≠b as required to give the quantum mechanical expectation values, when entanglement occurs for systems that are close, not distant, and ignores that entanglement is a local phenomenon. Expecting the condition a=b and a local particle analysis with no distant entangled particle to give the quantum mechanical result is absurd. Any disentanglement of once entangled particles moving apart sets the spin measurements at those given for a≠b if a≠b and those given for a=b if a=b. Any subsequent measurement of the set values agrees with those for a≠b if a≠b and those given for a=b if a=b just as if the particles are entangled still. In examples where Bell’s inequality is supposedly violated, the conditions for which the inequality is true are not met. There is no contradiction.
In quantum physics, the term ‘contextual’ can be used in more than one way. One usage, here called ‘Bell contextual’ since the idea goes back to Bell, is that if A , B and C are three quantum observables, with A compatible (i.e. commuting) with B and also with C , whereas B and C are incompatible, a measurement of A might yield a different result (indicating that quantum mechanics is contextual) depending upon whether A is measured along with B (the { A , B } context) or with C (the { A , C } context). An analysis of what projective quantum measurements measure shows that quantum theory is Bell non-contextual: the outcome of a particular A measurement when A is measured along with B would have been exactly the same if A had, instead, been measured along with C . A different definition, here called ‘globally (non)contextual’ refers to whether or not there is (non-contextual) or is not (contextual) a single joint probability distribution that simultaneously assigns probabilities in a consistent manner to the outcomes of measurements of a certain collection of observables, not all of which are compatible. A simple example shows that such a joint probability distribution can exist even in a situation where the measurement probabilities cannot refer to properties of a quantum system, and hence lack physical significance, even though mathematically well defined. It is noted that the quantum sample space, a projective decomposition of the identity, required for interpreting measurements of incompatible properties in different runs of an experiment using different types of apparatus, has a tensor product structure, a fact sometimes overlooked. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.
Quantum mechanics, despite its extraordinary success in describing microscopic phenomena, continues to raise foundational questions concerning measurement, nonlocality, and the nature of physical reality. These issues are exemplified by the Einstein-Podolsky-Rosen (EPR) paradox and the Bell inequality, which contrast quantum correlations with classical notions of locality and realism. In this work, we critically examine the assumptions underlying Bell’s theorem in light of the incompatible and contextual nature of quantum observables. We show that Bell’s constraint on simultaneous definite values for incompatible observables, together with the assumption of hidden variables, is not applicable to quantum mechanics itself, which is inherently nonclassical and contextual. When measurement is modeled as a local system-environment interaction within the framework of quantum decoherence, the resulting dynamics remain entirely local and unitary in the EPR scenario. Decoherence naturally selects pointer states and suppresses interference, giving rise to the appearance of wavefunction collapse consistent with quantum predictions. Importantly, the Bell correlations obtained in this framework reproduce the standard quantum results and are independent of both system-bath and inter-bath interactions, which affect only the rate of decoherence. Our analysis suggests that, in the EPR scenario, quantum mechanics can be both local and realistic when the wavefunction is treated as an ontic description of reality within the decoherence framework, offering a potential route toward a locally realistic quantum theory aligned with Einstein’s vision. This work contributes to a more rigorous foundation for quantum mechanics, providing insights that can accelerate progress in quantum computing and nanoenergy harvesting.
This paper examines no-hidden-variables theorems in quantum mechanics from the point of view of statistical mechanics. It presents a general analysis of the measurement process in the Boltzmannian framework that leads to a characterization of (in)compatible measurements and reproduces several features of quantum probabilities often described as “non-classical”. The analysis is applied to versions of the Kochen–Specker and Bell theorems to shed more light on their implications. It is shown how, once the measurement device and the active role of the measurement process are taken into account, contextuality appears as a natural feature of random variables. This corroborates Bell’s criticism that no-go results of the Kochen–Specker type are based on gratuitous assumptions. In contrast, Bell-type theorems are much more profound, but should be understood as nonlocality theorems rather than no-hidden-variables theorems. Finally, the paper addresses misunderstandings and misleading terminology that have confused the debate about hidden variables in quantum mechanics.
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.