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Entanglement as p-adic Proximity: Deriving the ER=EPR Correspondence from the Recursive Tensor Network of SDRIS

@pm14552

Published Nov 21, 2025• 1 citation
Publisher

Abstract

The experimental violation of Bell's inequalities implies that the universe is non-local in Euclidean space. This paper applies the SDRIS framework [1-4] to resolve this paradox by proposing a fundamental change in topology. I demonstrate that the Recursive Dynamic Space ($D$) is isomorphic to the field of p-adic numbers ($\mathbb{Q}_p$), possessing an ultrametric topology. By modeling the recursion $R$ as a MERA Tensor Network (Multi-scale Entanglement Renormalization Ansatz), I show that spacetime geometry ($S$) emerges from the entanglement structure of the quantum state. Entangled particles are shown to be ``neighbors'' in the p-adic metric ($\delta_p \to 0$), rendering quantum correlations strictly local in the ontology, while appearing non-local only in the Archimedean projection.

DOI
10.5281/zenodo.17666952

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The experimental violation of Bell's inequalities implies that the universe is non-local in Euclidean space. This paper applies the SDRIS framework [1-4] to resolve this paradox by proposing a fundamental change in topology. I demonstrate that the Recursive Dynamic Space (DDD) is isomorphic to the field of p-adic numbers (Qp\mathbb{Q}_pQp​), possessing an ultrametric topology. By modeling the recursion RRR as a MERA Tensor Network (Multi-scale Entanglement Renormalization Ansatz), I show that spacetime geometry (SSS) emerges from the entanglement structure of the quantum state. Entangled particles are shown to be ``neighbors'' in the p-adic metric (δp→0\delta_p \to 0δp​→0), rendering quantum correlations strictly local in the ontology, while appearing non-local only in the Archimedean projection.
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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.
ppp-adic Distance, Finite Precision and Emergent Superdeterminism: A Number-Theoretic Consistent-Histories Approach to Local Quantum Realism
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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.
ABSTRACT For nearly a century, the phenomenon of Quantum Entanglement has challenged the logical foundations of physics, culminating in the conflict between Einstein’s "Local Realism" and Bohr’s "Non-Locality." The experimental violation of Bell’s Inequalities seemed to prove that particles communicate instantaneously across vast distances, defying the speed of light. This article proposes a resolution based on Elastic Tensor Mechanics (ETM). By redefining the elementary particle not as a static spatial object but as a dynamic temporal oscillator (a Hysteresis Cycle of the Discontinuum), we introduce the concept of Iso-Temporal Synchronization. We demonstrate that the "Hidden Variable" Einstein sought is not spatial, but temporal (Phase). Entanglement is thus reinterpreted not as a magical connection across space, but as a deterministic conservation of rhythm over time, restoring a logical causal structure to the universe. Keywords: Quantum Entanglement, EPR Paradox, Bell’s Theorem, Elastic Tensor Mechanics (ETM), Iso-Temporal Synchronization, Phase Memory, Local Realism.
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.