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

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