Predetermined physical properties cannot manifest at the same time if they are mutually exclusive. As part of a single system, they become observable at different times, in sequence. In this case, pairwise detections in a narrow window of coincidence allow for maximal Bell violations (S=4 for the CHSH protocol), without room for doubt about the local nature of the process. This shows that a deeper description of physical reality is possible, as suggested by Einstein, Podolsky and Rosen. Though, a more inclusive definition of Realism is required, in order to account for Bohr’s Contextuality.
Predetermined physical properties cannot manifest at the same time if they are mutually exclusive. As part of a single system, they become observable at different times, in sequence. In this case, pairwise detections in a narrow window of coincidence allow for maximal Bell violations (S=4 for the CHSH protocol), without room for doubt about the local nature of the process. This shows that a deeper description of physical reality is possible, as suggested by Einstein, Podolsky and Rosen. Though, a more inclusive definition of Realism is required, in order to account for Bohr’s Contextuality.
A realization that came gradually in physics is that the ``elements of reality'' of Einstein, Podolsky, and Rosen are provably nonexistent. Specker initiated a line of thinking in 1960, observing that the outcomes of quantum measurements cannot reveal preexisting properties that are independent of which other measurements are performed. This review discusses the diverse current thinking on the problem of contextuality. The possibilities and problems with experimental verifications are discussed, and the violation of Bell inequalities can be viewed as a special case of contextuality.
Bell's theorem is popularly stated as the inconsistency of quantum theory with local realism. Realism is here formalized by the ontological models framework, where elements of reality are points of a measurable space and probabilities obey the Kolmogorov axioms. In the Bell scenario, locally causal ontological models posit a common cause supporting a global valuation, a joint assignment of outcomes to all measurements at once, across incompatible contexts. Within this notion of realism, Bell's theorem makes any realist explanation of the quantum predictions conspiratorial: any mechanism, whether superluminal, superdeterministic, or retrocausal, must be finely tuned so as never to manifest operationally. We redefine realism through a new ontological framework that generalizes the standard one. The elements of reality, which we call records, are no longer points but relational parts of a point-free generalization of a topological space (sublocales of a locale). A record shared by two incompatible contexts establishes the sameness of a measurement across them, without such pairwise identities composing into a global valuation, and the common cause is then a web of such records. Within this framework, Bell's no-go theorem becomes a go theorem: local causality, restated for records, is no longer at odds with the quantum statistics. This is possible because modularity, the inclusion-exclusion law of classical probability, fails across incompatible contexts, so that the probability theory generalizes Kolmogorov's. We exhibit explicit models reproducing several quantum strategies, including the optimal CHSH violation. More broadly, locally causal models of this kind attain every Bell-CHSH value up to the algebraic maximum. A realist explanation of the quantum predictions need not be conspiratorial; every causal influence posited by these models is reflected in the operational predictions.
Modern theoretical physics is built around two myths. The first one is that quantum observables are inseparable from the act of measurement. In some cases, this “observer effect” is supposed to be so strong that some qualities are mutually exclusive. Though, what is the difference between quantum contextuality and classical contextuality? This is where the second myth comes in. Objectively incompatible properties are treated as if they do not exist in classical physics. Instead, only two types of observables are considered: the ones that can occur at the same time as part of a single system, and the ones that are produced by measurement artifacts. As a result, we have a gap between two incomplete theories: a “quantum” theory without objective processes and a “classical” theory without mutually exclusive events. Together, they create the false impression that quantum entanglement is non-local. This is illustrated below with a clockwork mechanism for predetermined sequential properties. The system produces super-quantum Bell violations, as well as the features of quantum monogamy, in ideal experiments without loopholes. A separate illustration, with a classical fluid flow-splitter, is used to explain quantum-like Bell violations with independent and random measurement settings at remote stations. Objective contextuality is the missing piece of the quantum puzzle.
In quantum mechanics, nonlocality (a violation of a Bell inequality) is intimately linked to complementarity, by which we mean that consistently assigning values to different observables at the same time is not possible. Nonlocality can only occur when some of the relevant observables do not commute, and this noncommutativity makes the observables complementary. Beyond quantum mechanics, the concept of complementarity can be formalized in several distinct ways. Here we describe some of these possible formalizations and ask how they relate to nonlocality. We partially answer this question by describing two toy theories which display nonlocality and obey the no-signaling principle, although each of them does not display a certain kind of complementarity. The first toy theory has the property that it maximally violates the Clauser, Horn, Shimony, and Holt (CHSH) inequality, although the corresponding local observables are pairwise jointly measurable. The second toy theory also maximally violates the CHSH inequality, although its state space is classical and all measurements are mutually nondisturbing: if a measurement sequence contains some measurement twice with any number of other measurements in between, then these two measurements give the same outcome with certainty.
This short article concentrates on the conceptual aspects of the violation of Bell inequalities, and acts as a map to the 265 cited references. The article outlines (a) relevant characteristics of quantum mechanics, such as statistical balance and entanglement, (b) the thinking that led to the derivation of the original Bell inequality, and (c) the range of claimed implications, including realism, locality and others which attract less attention. The main conclusion is that violation of Bell inequalities appears to have some implications for the nature of physical reality, but that none of these are definite. The violations constrain possible prequantum (underlying) theories, but do not rule out the possibility that such theories might reconcile at least one understanding of locality and realism to quantum mechanical predictions. Violation might reflect, at least partly, failure to acknowledge the contextuality of quantum mechanics, or that data from different probability spaces have been inappropriately combined. Many claims that there are definite implications reflect one or more of (i) imprecise non-mathematical language, (ii) assumptions inappropriate in quantum mechanics, (iii) inadequate treatment of measurement statistics and (iv) underlying philosophical assumptions.
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.