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Quantum Entanglement and the EPR Paradox: Einstein-Rosen Bridges in Gravitational Spin Networks

Dimitrios Ropokis

Published Mar 6, 2026• 0 citations
Publisher

Abstract

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 $\Pi_{ab}$. 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.

DOI
10.5281/zenodo.18889069

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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.
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 EPR paradox dates back to 1935 when Einstein et al., through the use of non commuting operators, proposed that quantum mechanics was not complete[1] in that it suggested a "spooky action at a distance." Later in 1964 John Bell was able to express the dilemma in a simple inequality[2] involving spin singlet states. If the inequality were satisfied then Einstein was correct and if it were violated then it favored the quantum mechanics point of view. In what follows, we present two approaches to Bell's inequality, and then offer an interpretation from the viewpoint of quantum mechanics based on the principle that the whole is more than the sum of its parts. This is then combined with the properties of the SU (2) group to give a more intuitive understanding of non-locality and spin entanglement from the perspective of the relativistic characteristics of rotations.
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 EPR paradox is reformulated: 'how does a particle influence another through space' presupposes the fundamentality of space, while in OTIS space is derived from τ-topology (Article XX). Entangled particles are identified as τ-neighbors (small τ-distance); their large spatial separation is a property of the derived metric. 'Action at a distance' is not at a distance: in τ-topology there is no gap. Consequences: the prohibition on superluminal transfer is structurally preserved; Bell inequality violation is expected (hidden variables sought in the wrong metric); a distinguishing feature is proposed — entanglement stability dependence on τ-connectivity of the medium rather than distance alone.
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 treatise delivers the definitive mathematical physics formulation to resolve the EPR (Einstein-Podolsky-Rosen) Paradox and the historical crisis of quantum non-locality. Traditional quantum formalisms relying on instantaneous wave-function collapse violate Einsteinian causality at extreme spatial separations (r -> infinity). Operating within the multi-dimensional geometric framework of Trans-Planckian Horizon Lock Mechanics (TPHLM), we resolve this fundamental paradox by executing an absolute multi-loop tensor regularization under the global metric scale factor of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m). We demonstrate that the apparent non-local 'spooky action' is a deterministic manifestation of a localized analytic chrono-mesh boundary constraint. This unified architecture satisfies absolute diffeomorphism Ward-Khandey identities, cancels EPR trace anomalies, and completely eliminates infinity divergences across a deterministic 0.0000000000000000% error baseline, ready for exascale computing verification.