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Quantum Entanglement Solved by Topological Micro-Physics: Instantaneous State Synchronization via Angular Torsion Waves (OTA)

Pascal Moulin MOULIN

Published Dec 26, 2025• 0 citations
Publisher

Abstract

Quantum entanglement poses a fundamental challenge to causal locality by exhibiting instantaneous correlation between separated particles. This paper proposes that the paradox is resolved by the ontology of the **\textbf{Angular Unification Theory} ($\mathbf{\TAU}$)**. We redefine entanglement as a **\textbf{fundamental, non-local angular relationship}** maintained by an **\textbf{Angular Cohesion} Potential ($\mathbf{\LambdaCoh}$)** (Eq. II) within the network of **Dynamic Relational Quanta ($\mathbf{QRDs}$)**. The instantaneous state update following a measurement is ensured by **\textbf{Angular Torsion Waves} ($\mathbf{OTA}$)**. The $\mathbf{PR-TAU}$ 5.2 quantifies their propagation speed: $\mathbf{v}_{\mathbf{OTA}} \approx \mathbf{1.09 \times 10^{24} \ \text{m}\cdot\text{s}^{-1}}$. This velocity $\mathbf{v}_{\mathbf{OTA}} \gg c$ arises because $\mathbf{OTA}$ represent changes in the fundamental angular relationships that define spacetime itself, not kinetic energy transfer through it. $\mathbf{\TAU}$ thus provides a causal and topological explanation for entanglement, while preserving the validity of the locality principle for macroscopic energy transfers.

DOI
10.5281/zenodo.18061223

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The phenomenon of quantum entanglement, classically interpreted as "spooky action at a distance" due to the apparent instantaneous correlation of spatially separated systems, represents a profound epistemological crisis in modern physics. This letter resolves the EPR paradox by replacing the abstract concept of non-locality with deterministic continuum mechanics. By postulating a rigid, three-dimensional Euclidean vacuum modeled as a pre-tensioned fluid (epsilon0, mu0), entangled energetic nodes (photons) are demonstrated to remain physically connected via a continuous macroscopic torsion tube. The instantaneous synchronization of spin states during measurement is mathematically derived as the strict conservation of total angular momentum across this highly strained vacuum conduit. This classical mechanical approach eliminates the necessity of probability waves, proving that entanglement is an explicit manifestation of mechanical phase stiffness rather than a violation of the speed of light. Alternative explanation for quantum entanglement: Resolving the EPR paradox and non-locality through classical continuum mechanics, identifying entangled systems as mechanically coupled torsion tubes in a rigid Euclidean vacuum.
This study examines and resolves one of the most fundamental problems in quantum mechanics, the apparent non-locality arising from quantum entanglement (EPR paradox), utilizing the axiomatic model of Topological Network Dynamics (Phi-ND). The research demonstrates that the state change of entangled systems does not violate the causal speed limit of relativity. The framework establishes that entanglement is physically a topological phase transition (vertex-fusion) on a discrete, fundamental graph, whereas macroscopic three-dimensional Euclidean distance is merely the result of a lower-energy projection. Because the distance between the two entangled objects is strictly zero within the fundamental topological space, causal phase-state updating remains local and instantaneous, thereby preserving local realism and providing a definitive mathematical explanation for the violation of Bell's inequalities.
The phenomenon of quantum entanglement and its apparent non-locality have challenged the boundaries of classical physics and Einstein’s special relativity for nearly a century. Mainstream interpretations often rely on the ambiguous concept of ”spooky action at a distance” or superluminal communication. This paper completely dismantles the non-locality paradox by shifting the paradigm from a 3dimensional spatial background to an infinite-dimensional non-commutative supermanifold governed by Rough Operator Algebra (ROA) and the Seonggil Theory of Composite Torsion (STCT). We prove that entangled particles are not distinct entities separated by macroscopic distance, but are geometrically bound as a single ”Topological Knot” at a continuous fractional dynamic rank (ν) within the Hypertensor space. Furthermore, we demonstrate that wave-function collapse uponmeasurement is not a transmission of information, but a simultaneous geometric shadow cast by the Tensor Projection Operator (P_4D), triggered by a topological shockwave from the collision of macroscopic and microscopic roughness indices(α). Consequently, absolute quantum unitarity and local causality are flawlessly preserved without violating the speed of light limit.
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Following the geometric derivation of the Lepton Mass Spectrum in the first paper of this series (TTS I), this work addresses the dynamic origins of the "Stitching" mechanism to resolve the measurement problem and quantum non-locality. We postulate that Rest Mass is the physical manifestation of Temporal Zitterbewegung---a micro-oscillatory search for causal connectivity driven by the metric expansion of the underlying causal network. By treating the particle not as a point but as a temporal oscillator, we show that the spatial projection of this oscillation naturally generates a Feynman-like "Cone of Threads" (potential paths). We derive the Born Rule (P ∝ |Ψ|2) as the geometric cross-section of this causal search pattern. Furthermore, we demonstrate that Quantum Entanglement is not superluminal communication, but a Global Topological Constraint on a single bifurcated thread. The selection of a valid history at one endpoint instantaneously restricts the topological validity of the other, resolving the EPR paradox through geometric conservation laws while strictly preserving no-signaling constraints.