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Dissolving the EPR Paradox: Quantum Entanglement as Topological Non-Separability in a Discrete Substrate

Néstor E Ramos

Published Oct 11, 2026• 0 citations
Publisher

Abstract

Quantum entanglement remains the most contentious phenomenon in modern physics, famously described by Einstein as "spooky action at a distance." The standard interpretation relies on the instantaneous collapse of a non-local wave function, a mechanism that blatantly challenges the speed-of-light limit, or alternatively, relies on "superdeterminism", a conceptual patch suggesting all variables were correlated since the Big Bang. We demonstrate that under the framework of Computational Finitism, the EPR paradox is entirely dissolved. By modeling the universe as a discrete, Modulo-9 causal graph, we prove that entangled particles are not independent objects communicating across space. Instead, they are a single, indivisible topological knot projected onto two spatial coordinates. We present a deterministic simulation (The Finitism Entanglement Automaton) that achieves 100.0% perfect anti-correlation without any signal propagation, ontological randomness, or faster-than-light communication. Entanglement is not magic; it is the macroscopic observation of a non-separable algebraic identity.

DOI
10.5281/zenodo.23298794

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Quantum entanglement remains the most contentious phenomenon in modern physics, famously described by Einstein as "spooky action at a distance." The standard interpretation relies on the instantaneous collapse of a non-local wave function, a mechanism that blatantly challenges the speed-of-light limit, or alternatively, relies on "superdeterminism", a conceptual patch suggesting all variables were correlated since the Big Bang. We demonstrate that under the framework of Computational Finitism, the EPR paradox is entirely dissolved. By modeling the universe as a discrete, Modulo-9 causal graph, we prove that entangled particles are not independent objects communicating across space. Instead, they are a single, indivisible topological knot projected onto two spatial coordinates. We present a deterministic simulation (The Finitism Entanglement Automaton) that achieves 100.0% perfect anti-correlation without any signal propagation, ontological randomness, or faster-than-light communication. Entanglement is not magic; it is the macroscopic observation of a non-separable algebraic identity.
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.
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.
Modern physics treats quantum entanglement, superluminal cosmic expansion, and the finite speed of light as separate domain-specific mysteries. We question the "spookiness" of entanglement but accept that space expands faster than light. We postulate c as a fundamental constant but rarely ask why it is finite. Computational Finitism resolves these tensions by reframing the universe not as a continuous container, but as a finite-state computational graph. In this substrate, entanglement is a shared topological state, expansion is a dynamic node insertion, and the speed of light is the maximum propagation rate of a causal update rule. These are not paradoxes; they are hardware constraints. This article not only demonstrates how a discrete, relationship-driven network unifies quantum and cosmological phenomena without invoking infinity, non-locality, or mystical postulates, but also makes falsifiable predictions.
Quantum Entanglement—the phenomenon where spatially separated particles exhibit instantaneous correlations—poses a fundamental challenge to the principle of locality central to General Relativity. The standard interpretation accepts "spooky action at a distance" (non-locality) as an irreducible feature of nature. In this work, we propose a geometric resolution based on Unified Field Dynamics (UFD). We postulate that the configuration space Q possesses a higher connectivity than the apparent 3D spatial manifold. Building on the UFD Soliton Model (where particles are topological knots), we demonstrate that entanglement corresponds to a state where two solitons share a common Topological Flux Line in the bulk of the configuration space. Although separated by a large geodesic distance in the emergent 3D metric, the solitons remain adjacent in the underlying high-dimensional topology of Q. This framework reinterprets the EPR paradox not as a violation of causality, but as a manifestation of Vacuum Connectivity. We show that this model is isomorphic to the ER=EPR conjecture (Entanglement = Einstein-Rosen Bridges) but derives the "bridges" naturally from the connectivity of the S^3 fiber bundle, eliminating the need for wormhole singularities.
The phenomenon of quantum entanglement, famously described by Einstein, Podolsky, and Rosen (EPR) as "spooky action at a distance," remains a fundamental mystery of quantum mechanics. In this monograph, we resolve the EPR paradox using Topological Quantum Chromodynamics (Topological QCD). We mathematically prove the ER=EPR conjecture without string theory, demonstrating that entangled particles are physically connected by microscopic Einstein-Rosen bridges formed within the Gravitational Spin Polarization Tensor Πab\Pi_{ab}Πab​. Bell's inequalities are geometrically violated not due to superluminal signaling, but because the topological distance between entangled particles through the spin network is strictly zero. The modified Lichnerowicz identity provides the geometric stability for these macroscopic quantum connections.
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.