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Quantum Entanglement as Virtual Domain Correlation: Resolving Non-Locality Through Dual Regulator Framework

Eric Needham

Published Jan 17, 2026• 0 citations
Publisher

Abstract

This paper presents a finite, regulator-based resolution of quantum entanglement, extending the Dual Regulator Framework to nonlocal correlations while preserving causality, locality of dynamics, and relativistic consistency. Entanglement is shown to arise entirely within the virtual domain, which lacks spatial topology and is regulated by the finite invariant Λφ=ln⁡(φ2),\Lambda_\varphi = \ln(\varphi^2),Λφ=ln(φ2), while decoherence and measurement occur exclusively in the real domain, regulated by the Resolution Gap (RG). Because entangled correlations never propagate through real spacetime, their strength is shown to be exactly independent of spatial separation, without invoking superluminal influence or observer-dependent collapse. Bell inequality violations are derived from domain structure alone. The framework predicts a finite correction to the standard Tsirelson bound arising from virtual-domain regulation, yielding a testable enhancement at high precision. No hidden variables, signaling mechanisms, or modifications to relativistic causality are introduced. Decoherence of entangled systems is shown to be additive across subsystems and governed by regulator ratios rather than ad hoc environmental postulates. The Born rule emerges from symmetric coupling across the virtual–real interface, consistent with prior papers in the series. A companion computational validation script numerically reproduces all constants and predicted correlation bounds using standard numerical libraries. All results are reproducible and contain zero adjustable parameters. This work constitutes Paper III in a planned sequence addressing foundational inconsistencies in quantum field theory, following finite resolutions of measurement and wave–particle duality. Licenses Creative Commons Attribution Non Commercial No Derivatives 4.0 International

DOI
10.5281/zenodo.18279931

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This paper presents a finite, regulator-based resolution of quantum entanglement, extending the Dual Regulator Framework to nonlocal correlations while preserving causality, locality of dynamics, and relativistic consistency. Entanglement is shown to arise entirely within the virtual domain, which lacks spatial topology and is regulated by the finite invariant Λφ=ln⁡(φ2),\Lambda_\varphi = \ln(\varphi^2),Λφ=ln(φ2), while decoherence and measurement occur exclusively in the real domain, regulated by the Resolution Gap (RG). Because entangled correlations never propagate through real spacetime, their strength is shown to be exactly independent of spatial separation, without invoking superluminal influence or observer-dependent collapse. Bell inequality violations are derived from domain structure alone. The framework predicts a finite correction to the standard Tsirelson bound arising from virtual-domain regulation, yielding a testable enhancement at high precision. No hidden variables, signaling mechanisms, or modifications to relativistic causality are introduced. Decoherence of entangled systems is shown to be additive across subsystems and governed by regulator ratios rather than ad hoc environmental postulates. The Born rule emerges from symmetric coupling across the virtual–real interface, consistent with prior papers in the series. A companion computational validation script numerically reproduces all constants and predicted correlation bounds using standard numerical libraries. All results are reproducible and contain zero adjustable parameters. This work constitutes Paper III in a planned sequence addressing foundational inconsistencies in quantum field theory, following finite resolutions of measurement and wave–particle duality. Licenses Creative Commons Attribution Non Commercial No Derivatives 4.0 International
Quantum entanglement produces correlations that violate classical locality constraints while remaining fully consistent with relativistic no-signaling. Although standard quantum mechanics predicts these correlations with extraordinary empirical success, the ontological meaning of entangled states and the physical status of wave-function collapse remain deeply debated. This paper develops a speculative but structured informational interpretation in which entangled subsystems are modeled as multiple local realizations of a single shared informational identity within an underlying finite-capacity substrate. The framework is articulated through explicit postulates, density-matrix analysis, entanglement entropy, a toy realization scheme, and an informational identity operator acting on composite states. Within this view, nonlocal correlations arise not from superluminal causal influence but from ontological non-separability at the informational level. Measurement is interpreted as informational resolution: a reduction of degeneracy in the local realization of a shared informational structure. The irreversible stabilization of outcomes is then linked to thermodynamic cost through Landauer-type reasoning. The proposal is not advanced as a replacement for quantum mechanics, nor as a fully worked-out hidden-variable theory, but as an ontological scaffold intended to unify entanglement, collapse, and thermodynamic irreversibility within an informational perspective. Compatibility with Bell inequalities, decoherence, basis selection, and no-signaling is discussed in detail, together with limitations and possible routes toward future formalization and empirical relevance.
Translator This paper reformulates quantum entanglement within the framework of Finite-Resolution Physics (FRP), a finite-coherence version of quantum theory derived from the Reflexive Monoid Algebra (RMA) hierarchy.All experimental predictions of entanglement—joint probabilities, Bell-inequality violations, and Born frequencies—remain identical to those of standard quantum mechanics.The difference lies in structure: entanglement is no longer a separate postulate about tensor-product Hilbert spaces but an algebraic phase-consistency relation (FR3) and typicality constraint (FR4) linking additive subsystems under finite resolution.This reinterpretation explains nonlocal correlations as boundary-level coherence, not superluminal influence, and describes decoherence as the loss of FR3 coherence, marking the transition from quantum (Qμ) to statistical (Sμ) regimes.The work provides a unified algebraic account of entanglement, nonlocality, and decoherence within a finite-resolution operational framework.
This work presents a minimal reinterpretation of quantum entanglement based solely on the causal structure inherent in relativistic spacetime. No new physical entities, parameters, or modifications to existing theories are introduced.The discussion remains entirely within the established frameworks of general relativity and quantum mechanics, with particular emphasis on Lorentz invariance and relativistic causality. The central idea is that the causal structure of spacetime is unique and invariant, while spatial separation corresponds to different references (foliations) to this structure rather than its duplication.Within this viewpoint, quantum entanglement is understood as a local readout of correlations already encoded in a shared causal structure, without invoking nonlocal influences or superluminal information transfer. This document is intended as a conceptual clarification and archival record rather than a proposal of a new theory.It is provided to preserve a logically consistent interpretation that may be of interest for future foundational discussions.
This is Paper 142 in the Anaxiomatic Mechanics / pq-Spacetime stack. It develops a finite mechanical account of quantum entanglement within pq-spacetime. Entanglement is identified with the persistence of a non-factorable family of admissible future histories. Two measurement regions can therefore appear as separate local systems in emergent spacetime while still remaining projections of one joint finite closure problem. Bell inequality violation follows because the joint outcomes are not generated by two independent local completion families. No-signalling is nevertheless preserved because complete changes to a distant measurement boundary do not alter the local marginal outcome weights. The paper establishes the Entanglement Closure Theorem and distinguishes microscopic non-factorability from observable entanglement after coarse-graining into stable measurement records. It also gives an explicit minimal singlet construction using two opposed history fibers carrying the relevant four-phase weights. The resulting finite ledger is antisymmetric, nonseparable, and exactly balanced at each local wing. Complete changes of basis on the distant side preserve those local marginals. Using the previously derived Hilbert-space and beta-Dirac bridges of pq-spacetime, the paper recovers the familiar spinor overlap law, the quantum singlet correlation, the maximal Bell-CHSH value, monogamy of maximal entanglement, and decoherence through environmental boundary enlargement. The analysis also explains why no preferred measurement ordering is required and why entanglement remains compatible with relativistic causality. The resulting picture is direct. Entangled systems do not exchange superluminal messages, carry classical answer sheets, or require a force acting across space. Their local outcomes arise from one shared finite admissibility structure whose joint correlations are nonlocal while its controllable local statistics remain causal. Entanglement is therefore physically real, nonclassical, and nonlocal in correlation, but not a signalling mechanism.
This paper proposes an ontological framework that resolves the apparent paradox of quantum entanglement without invoking faster-than-light signaling or violating the principle of locality in special relativity. The solution rests on a strict ontological separation between two levels of reality: (1) an existential level governed by a single, absolute, non-spatial existential time τ, where quantum information resides in unified superposed states; and (2) a cosmic level consisting of ordinary relativistic spacetime, where material systems are spatially separated and causality is preserved. Under this framework, entanglement represents a dual-layer phenomenon: existential–informational unity at the level of being, combined with cosmic–material separation at the level of appearance. Quantum correlations are thus explained not as superluminal influence, but as the manifestation in spacetime of a pre-unified informational structure in existential time. The framework preserves all mathematical formalism of standard quantum mechanics, remains fully consistent with special and general relativity, and offers a deep ontological grounding for the foundations of quantum theory
This paper proposes an ontological framework that resolves the apparent paradox of quantum entanglement without invoking faster-than-light signaling or violating the principle of locality in special relativity. The solution rests on a strict ontological separation between two levels of reality: (1) an existential level governed by a single, absolute, non-spatial existential time τ, where quantum information resides in unified superposed states; and (2) a cosmic level consisting of ordinary relativistic spacetime, where material systems are spatially separated and causality is preserved. Under this framework, entanglement represents a dual-layer phenomenon: existential–informational unity at the level of being, combined with cosmic–material separation at the level of appearance. Quantum correlations are thus explained not as superluminal influence, but as the manifestation in spacetime of a pre-unified informational structure in existential time. The framework preserves all mathematical formalism of standard quantum mechanics, remains fully consistent with special and general relativity, and offers a deep ontological grounding for the foundations of quantum theory.