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.
Bell’s theorem is a foundational result in quantum theory, demonstrating that no local hidden-variable model satisfying certain assumptions can reproduce quantum correlations. While mathematically correct within its formal framework, the theorem implicitly relies on a specific representational choice: measurement outcomes are modeled as scalar, commutative variables (±1). This assumption, though natural for flat and static configurations, is not mandated by physical necessity. In this work, we examine the consequences of relaxing this representational constraint when measurement outcomes arise as projections of states with nontrivial topology. We show that when physical correlations are naturally organized as elements of an S³-valued structure — such as those associated with spin and rotational degrees of freedom — the induced measurement algebra becomes noncommutative. Under these conditions, the key algebraic factorizations employed in Bell-type derivations no longer apply. We construct an explicit local, realistic model in which observable correlations reproduce the quantum expectation E(a, b) = − cos θ and violate the CHSH bound S ≤ 2, without invoking non-local interactions or superluminal influences. The effective S³×I structure arises not as a fundamental substrate, but as the natural geometric form taken by the actualization of physical processes within an underlying relational framework. Importantly, this structure was not introduced to address quantum entanglement specifically; it emerged independently in the study of cosmological expansion, emergent gravity, and mass generation. Its relevance to Bell-type correlations follows as a consequence of geometry, not as an ad hoc modification. These results suggest that quantum entanglement may reflect topological features of physical realization rather than intrinsic non-locality. Possible experimental implications and connections to geometric and substrate-based approaches to fundamental physics
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.
Bell's theorem is a conditional statement about theoretical models specified by a complete physical state
λ. It shows that models satisfying measurement independence and a stochastic Bell-locality (factorizability) condition obey Bell inequalities. Bell experiments, however, do not directly observe
λ or the
λ-conditioned probabilities appearing in that condition. They record analyzer settings, detector outcomes, and experimental metadata, from which they estimate operational joint distributions, marginals, correlations, and Bell statistics. We clarify the logical relationship between these two levels. The
λ-conditioned factorization identity cannot be directly evaluated at fixed
λ from the operational record alone. Nevertheless, by marginalizing over
λ under measurement independence, the model class implies observable inequalities that can be empirically violated. A Bell-inequality violation therefore excludes the corresponding Bell-local model class under the assumptions required for the inequality, but it does not by itself identify which latent assumption---measurement independence, parameter independence, or outcome independence---failed, nor does it uniquely determine an ontological interpretation. To illustrate this distinction concretely, we employ the Unified Quantum Mechanics formulation, in which the physical state is real, and the complex wavefunction is representational. We show that all four formulations of the dynamics---Schr\"odinger, Hilbert-transform, complex second-order, and real second-order---require the same two real initial functions
u0=u(0) and
u1=∂tu(0); the complex initial state is merely a repackaging of them, not additional physical information. We formulate the distinction as a three-level hierarchy: operational data, model-class exclusion, and ontological interpretation. The hierarchy separates experimental loopholes, which concern assumptions linking an actual experiment to an ideal Bell model, from the conceptual underdetermination of latent-variable conditional probabilities, which remains even in a loophole-free experiment. The result clarifies what Bell experiments establish without claiming that Bell-local models are empirically untestable. A Monte Carlo simulation illustrates the distinction between operational Bell-test results and latent-state factorization.
Bell–CHSH inequalities are commonly interpreted as demonstrating the incompatibility between quantum mechanics and local hidden-variable theories based on pre-existing measurement outcomes. In standard derivations of the CHSH inequality, however, it is implicitly assumed that all possible measurement settings can be assigned simultaneous values within a single global hidden-variable structure. In this paper, we reconsider the Bell–CHSH framework from the viewpoint of the Intrinsic Observability Framework (IOF). We argue that the central issue is not the experimental violation of the inequality itself, but the applicability of the global value assignment assumed in its derivation. In particular, the simultaneous definition of outcomes associated with incompatible measurement settings presupposes a common operational structure shared across all observational configurations. Within IOF, observable outcomes are not treated as globally pre-existing values independent of observational accessibility and decomposition structure. Instead, measurement outcomes are associated with operationally accessible configurations determined through observable–hidden relations. From this perspective, the global assignment required for the CHSH derivation is not operationally justified. We further show that this viewpoint remains fully consistent with the standard quantum-mechanical correlations observed in Bell-type experiments. The present analysis suggests that the Bell–CHSH inequality may be interpreted not as a direct contradiction between quantum mechanics and locality itself, but rather as a limitation of globally defined pre-existing value assignments across incompatible observational configurations.
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.