Bell inequalities are commonly presented as abstract constraints derived from assumptions of locality and realism, while their violation in quantum mechanics is often regarded as a profound mystery. In this work I present an operational reconstruction of Bell correlations using a constraint-based framework in which all assumptions are made explicit and executable. By separating locality, factorization, signaling, contextuality, and nonlocal correlation into independently controllable components, I demonstrate numerically that Bell inequality violation arises if and only if joint probability factorizability is relaxed. Quantum correlations emerge as extremal, geometrically constrained solutions within a broader space of admissible correlations. No appeal is made to wavefunction collapse or Hilbert space axioms. The results clarify the precise content of Bell’s theorem and suggest that quantum nonlocality is best understood as a global consistency constraint rather than a dynamical influence.
Bell inequalities are commonly presented as abstract constraints derived from assumptions of locality and realism, while their violation in quantum mechanics is often regarded as a profound mystery. In this work I present an operational reconstruction of Bell correlations using a constraint-based framework in which all assumptions are made explicit and executable. By separating locality, factorization, signaling, contextuality, and nonlocal correlation into independently controllable components, I demonstrate numerically that Bell inequality violation arises if and only if joint probability factorizability is relaxed. Quantum correlations emerge as extremal, geometrically constrained solutions within a broader space of admissible correlations. No appeal is made to wavefunction collapse or Hilbert space axioms. The results clarify the precise content of Bell’s theorem and suggest that quantum nonlocality is best understood as a global consistency constraint rather than a dynamical influence.
Bell inequalities are commonly presented as abstract constraints derived from assumptions of locality and realism, while their violation in quantum mechanics is often regarded as a profound mystery. In this work I present an operational reconstruction of Bell correlations using a constraint-based framework in which all assumptions are made explicit and executable. By separating locality, factorization, signaling, contextuality, and nonlocal correlation into independently controllable components, I demonstrate numerically that Bell inequality violation arises if and only if joint probability factorizability is relaxed. Quantum correlations emerge as extremal, geometrically constrained solutions within a broader space of admissible correlations. No appeal is made to wavefunction collapse or Hilbert space axioms. The results clarify the precise content of Bell’s theorem and suggest that quantum nonlocality is best understood as a global consistency constraint rather than a dynamical influence.
Violations of Bell inequalities are commonly interpreted as evidence for either nonlocal dynamics or the failure of classical realism. In this work, we show that Bell-type correlations can arise without invoking superluminal influences, retrocausality, or local hidden variables, provided that the mapping between underlying configurations and observable outcomes is non-injective. We study a class of effective models in which multiple underlying states correspond to the same observable description. Such non-injective projections generically induce non-factorizable joint probability structures at the level of observables, even when the underlying description itself is fully local and deterministic. As a result, the statistical assumptions required to derive Bell inequalities are violated at the effective level, while locality is preserved at the underlying level. Within this framework, quantum correlations emerge as structural features of projected descriptions rather than as signatures of nonlocal causation. We clarify the precise assumption of Bell’s theorem that fails in this setting and show how classical behavior is recovered in regimes where the effective projection becomes approximately injective, suppressing nonlocal correlations through decoherence and environmental coarse-graining. Our results suggest that Bell inequality violations need not reflect a fundamental nonlocality of nature, but may instead indicate intrinsic information loss induced by non-injective mappings between underlying configurations and observable descriptions.
Violations of Bell inequalities are commonly interpreted as evidence for nonlocal influences or as constraints on realist descriptions. We show that the failure of Bell-type factorizability arises naturally when observable outcomes are obtained through a non-injective mapping from an underlying configuration space. In this setting, the standard factorization assumption can be viewed as an implicit requirement that observable variables admit a jointly factorizable completion at the underlying level. We demonstrate that this requirement need not hold when the mapping from underlying configurations to observables is many-to-one. The resulting breakdown of probabilistic factorization does not rely on superluminal dynamics or hidden causal influences, but follows from information loss under projection. Observable outcomes correspond to equivalence classes of underlying configurations, preventing the assignment of independent local variables. We illustrate this mechanism with an explicit toy model producing Bell–CHSH violations while preserving operational no-signalling and statistical independence of measurement settings. The model is not intended to reproduce quantum correlations quantitatively, and may exceed the Tsirelson bound; its role is to isolate the structural origin of the violation. This analysis does not contradict Bell’s theorem, but identifies a class of effective descriptions for which its factorizability assumption does not apply. The framework preserves locality at the underlying level, introduces no additional hidden-variable dynamics, and does not modify quantum mechanics. It clarifies how classical factorization is recovered in regimes where the effective mapping becomes approximately injective. In the operator language of quantum theory, the same mechanism admits a natural reformulation in terms of reduction to an effective observable subalgebra by a noncommutative conditional expectation.
This document is part of the Informational Mechanics (IM) framework and is published in the IM-D (Core Physics) series within the IM v0.3 corpus. The paper develops a structural account of quantum entanglement under regime-limited admissibility constraints. Rather than introducing new dynamics, hidden variables, or collapse mechanisms, it analyzes entanglement as a consequence of structural non-factorizability arising from bilinear composition and tensor minimality within admissible operator regimes. Building on IM-B004 (tensor minimality), IM-C004 (regime-conditional structural principles), and IM-E004 (operator-defined outcome weights), the analysis shows that Bell-inequality violations constrain classical factorizability assumptions without implying superluminal signaling or ontological inseparability. The account preserves the formal structure of quantum mechanics and treats locality and no-signaling conditions as operator-level constraints. No new axioms, empirical fits, or modifications to established physical theories are introduced. The contribution is classificatory and structural: it clarifies how entanglement and Bell correlations emerge within regime-bounded admissibility while explicitly identifying the structural assumptions under which the account would require revision.
We present a constraint-based axiomatization of quantum correla- tions that derives Bell statistics without invoking Hilbert space, wave functions, or causal mechanisms. Starting from five physically moti- vated axioms—rotational invariance, perfect anti-correlation, uniform marginals (no-signaling), smoothness, and extremality—we prove that the singlet correlation function E(ˆ a,ˆˆb) =−ˆa·b is uniquely deter- mined. The proof proceeds through functional equation analysis: the extremality axiom implies angle additivity, reducing the problem to Cauchy’s equation with boundary conditions. We derive the Tsirelson bound |S|≤2√2 directly from this correlation function without op- erator algebras, and show that CHSH violation follows as a theorem. The no-signaling condition emerges as a structural property of the con- straint, ensuring compatibility with relativistic causality. We extend the framework to tripartite systems, deriving GHZ correlations from analogous axioms and proving maximal Mermin inequality violation. The constraint interpretation dissolves the tension between entangle- ment and causality: correlations are neither caused nor explained by hidden variables—they are specified by the constraint structure itself. This framework recovers all quantum predictions while eliminating causation from the foundational ontology.
In a Bell test, the set of observed probability distributions complying with the principle of local realism is fully characterized by Bell inequalities. Quantum theory allows for a violation of these inequalities, which is famously regarded as Bell nonlocality. However, finding the maximal degree of this violation is, in general, an undecidable problem. Consequently, no algorithm can be used to derive quantum analogs of Bell inequalities, which would characterize the set of probability distributions allowed by quantum theory. Here we present a family of inequalities, which approximate the set of quantum correlations in Bell scenarios where the number of settings or outcomes can be arbitrary. We derive these inequalities from the principle of Information Causality, and thus, we do not assume the formalism of quantum mechanics. Moreover, we identify a subspace in the correlation space for which the derived inequalities give the necessary and sufficient conditions for the principle of Macroscopic Locality. As a result, we show that in this subspace, the principle of Information Causality is strictly stronger than the principle of Macroscopic Locality.