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Bell's Inequality and its Implications in the Dynamic Metric Topology (DMT) Framework: Non-Local Conservation of the CHSH Parameter against Scalar Field Friction

Yassin Tanan

Published Apr 11, 2026• 0 citations
Publisher

Abstract

The current paradigm of quantum computing is severely limited by stochastic decoherence, conventionally modeled as an irreversible and probabilistic collapse of the wavefunction. This paper introduces the Dynamic Metric Topology (DMT) framework, postulating that decoherence is not inherently stochastic, but rather the result of a deterministic,topological friction between the spinorial phase of entangled particles and the pseudo-Riemannian manifold of the background scalar field, quantified by an impedance threshold of H˜ = 114.12 GeV. We demonstrate that the DMT framework does not rely on local hidden variables,strictly adhering to Bell’s Theorem by operating on the global topological manifold connecting entangled states. Furthermore, we show that applying an active topological phase compensation prevents the degradation of the CHSH inequality parameter, theoretically locking the system at the Tsirelson bound (|S| = 2√ 2) and preserving macroscopic entanglement.

DOI
10.5281/zenodo.19513797

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The current paradigm of quantum computing is severely limited by stochastic decoherence, conventionally modeled as an irreversible and probabilistic collapse of the wavefunction. This paper introduces the Dynamic Metric Topology (DMT) framework, postulating that decoherence is not inherently stochastic, but rather the result of a deterministic,topological friction between the spinorial phase of entangled particles and the pseudo-Riemannian manifold of the background scalar field, quantified by an impedance threshold of H˜ = 114.12 GeV. We demonstrate that the DMT framework does not rely on local hidden variables,strictly adhering to Bell’s Theorem by operating on the global topological manifold connecting entangled states. Furthermore, we show that applying an active topological phase compensation prevents the degradation of the CHSH inequality parameter, theoretically locking the system at the Tsirelson bound (|S| = 2√ 2) and preserving macroscopic entanglement.
Recent breakthroughs in many-body quantum dynamics have unexpectedly revealed that the growth of entanglement entropy and quantum decoherence strictly follow the Kardar-Parisi-Zhang (KPZ) universality class, an equation originally formulated to describe macroscopic stochastic surface growth. In this paper, we theoretically bridge this empirical observation with the Dynamic Metric Topology (DMT) framework. We demonstrate that the macroscopic "roughness" governed by the KPZ equation in quantum spin systems is not driven by fundamentally stochastic noise, but by a deterministic topological friction between the spinorial phase and the scalar field pseudo-Riemannian manifold. By explicitly mapping the KPZ non-linear growth term to the DMT scalar impedance threshold at H˜ = 114.12 GeV via the fine structure constant (α), we provide a unified tensorial master equation. This integration redefines quantum noise as an uncompensated metric drag, providing a definitive proof through the deterministic evolution of Bell’s inequality parameters.
Abstract This paper proposes a local-deterministic completion of quantum entanglement by identifying the instantaneous phase of rotating electric field vectors as the primary hidden variable. We demonstrate that the observed violation of the Bell-CHSH inequality is not a signature of non-locality, but a natural consequence of the Intensity-Phase doubling mechanism inherent in Maxwellian electrodynamics. Through analytical derivation and discrete-time numerical integration, it proves that the correlation of synchronized transverse waves—governed by the quadratic nature of Malus’s Law \(\:\left(\varvec{I}\:\propto\:\:{\varvec{E}}^{2}\right)\)—generates the exact quantum correlation function  E(Δ θ )=  Cos(2Δ θ )\:E\left(\varDelta\:\theta\:\right)=\:\:Cos(2\varDelta\:\theta\:)E(Δθ)=Cos(2Δθ). We resolve the long-standing discrepancy regarding measurement angles by showing that the maximum violation of the CHSH inequality  (S=22)\:(S=2\sqrt{2})(S=22​) occurs at a physical polarizer setting of  22.5∘ \:22.5^\circ\:22.5∘, which corresponds to a  45∘ \:45^\circ\:45∘, shift in the internal field phase . By distinguishing between mechanical rotation and field-space geometry, this model saturates the Tsirelson bound while strictly maintaining Einsteinian locality and causality. This framework suggests that the "spooky action" of entanglement is a manifestation of temporal phase-locking between the source and the detector, providing a fully realistic and Maxwellian interpretation of Bell-type statistics.
The term Bell's theorem refers to a set of closely related results which imply that quantum mechanics is incompatible with local hidden variable theories. Bell's inequality is the statement that if measurements are performed independently on two space-like separated particles of an entangled pair, the assumption that outcomes depend on hidden variables implies an upper bound on the correlations between the outcomes. Quantum mechanics predicts correlations which violate this upper bound. The CHSH inequality is a specific Bell inequality in which classical correlation (i.e. if local hidden variables exist) can take the maximum value of 2. Quantum mechanics violates this bound, allowing for a higher bound on the correlation, which can take the maximum value 222\sqrt{2}22​, known as the Tsirelson bound. Popescu and Rohrlich showed that the assumption of relativistic causality allows for an even higher bound on the CHSH correlation, this value being 4. Why is the bound coming from causality higher than the Tsirelson bound? Are there relativistic causal dynamical theories which violate the Tsirelson bound? In the present paper we answer this question in the affirmative. We show that the pre-quantum theory of trace dynamics, from which quantum theory is emergent as a thermodynamic approximation, permits the CHSH correlation to take values higher than 222\sqrt{2}22​. We interpret our findings to suggest that quantum theory is approximate, and emergent from the more general theory of trace dynamics.
This paper provides a conservative reinterpretation of quantum entanglement within the Scalar Temporal Field Ontology (STFO), in which time is represented as a strictly monotonic scalar field τ(x). Entangled systems are shown to be correlated not through superluminal influence or hidden-variable dynamics, but through shared temporal history established during joint preparation along τ. Measurement outcomes arise through local temporal decoherence and stabilization of macroscopic record sectors, while observed Bell correlations reflect non-factorizable global structure in τ-ordered histories. The account preserves local causality—no dynamical interaction exceeds the speed of light—while admitting an ontologically global temporal structure. The framework respects Bell’s theorem and the no-communication theorem, reproduces all empirical predictions of quantum mechanics, and remains fully consistent with prior STFO results on probability and wavefunction collapse.
Quantum entanglement is widely regarded as the most puzzling feature of quantum theory, apparently violating local realism through nonlocal correlations between spacelike-separated particles. Although violations of Bell inequalities are experimentally confirmed, their standard theoretical explanation relies on wavefunction collapse or nonlocal hidden variables. In this work, we present an alternative explanation based on Trembling Spacetime Relativity Theory (TSRT). In this framework, intrinsic metric fluctuations generate proper-time-synchronized geodesic ensembles whose deterministic trajectories give rise to statistical correlations across spacetime. Measurement outcomes are reinterpreted as geometric responses to these fluctuating backgrounds, without invoking quantum collapse or nonlocal influence. We show that the Clauser–Horne–Shimony–Holt (CHSH) inequality can be violated deterministically within a locally causal geometric structure. These violations emerge as macroscopic imprints of shared spacetime curvature, not quantum superposition. The resulting correlation function reproduces quantum predictions at short ranges but decays with separation—yielding testable deviations in long-baseline and gravitationally modulated experiments. TSRT thus offers a realist, Lorentz-invariant, and falsifiable account of entanglement grounded in the causal structure of spacetime.
The prediction of wavefunction collapse and quantum decoherence in solid-state quantum processors, such as superconducting transmon lattices, relies heavily on the stochastic Lindblad master equation and empirical T1 and T2 relaxation times. While these thermodynamic and statistical frameworks effectively estimate the aggregate probability of quantum error over time, they fail to deterministically define the exact spatial boundary where localized environmental coupling triggers an irreversible collapse of the superposition state. This paper introduces a strict continuum framework for quantum information science. By modeling the topological quantum state as a dynamic kinematic balance between the spatial capacity for phase entanglement (phase coherence) and the localized rate of classical measurement (environmental coupling), we derive a universal critical decoherence radius (Rcollapse). We demonstrate that wavefunction collapse is not a probabilistic decay over time, but an exact deterministic limit where localized environmental perturbation strictly overpowers the advective phase-distributing capacity of the surrounding topological geometry. We propose a blueprint for Absolute Topological Qubit Scaling to guarantee infinite coherence, bypassing massive software-based error-correction overheads.