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Solution to the EPR Paradox Via Temporal Multiplexing and Impedance Addressing. The Communication Window in General Relativity as a Quantum Theory

Jonatan P. camargo

Published Jan 5, 2026• 0 citations
Publisher

Abstract

This work extends the geometric ontology established in the previous volumes of General Relativity as a Quantum Theory (RGTQ), volumes Vol.VI, Vol.VII, to resolve the fundamental problem of interaction selectivity and local coexistence in a globally connected spacetime lattice. Through the rigorous application of the \textit{Foundations of Spectral Physics} (FFE) to the dynamic metric, we mathematically deduce that the local energy density does not saturate the Planck volume due to a mechanism of **Geometric Temporal Multiplexing**. We demonstrate that quantum states with distinct harmonic frequencies ($n, 200n$) maintain phase orthogonality by sampling the lattice in disjoint time windows, analogous to 't Hooft's discrete automata. In the non-local regime, we derive the mechanism of **Impedance Addressing** to solve the selection problem in entanglement. Rejecting the transmission of superluminal signals, we prove that the EPR connection occurs through topological torsion channels where the effective metric is nullified for a specific resonance frequency. We deduce the analytical formula for this **Signature Frequency** ($f_{ent}$), modulating the natural carrier of the *Zitterbewegung* ($2mc^2/h$) by the path integral of the gravitomagnetic holonomy and the medium's impedance ($Z_{geom}$). This formalism unifies Couder's hydrodynamic path memory and De Broglie's phase coherence under a single variational principle. It is concluded that the universe preserves relativistic locality for energy transport ($v \leq c$), while sustaining instantaneous global connectivity for phase, governed strictly by the impedance matching of topological channels.

DOI
10.5281/zenodo.18153540

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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.
Este trabalho estende a ontologia geométrica estabelecida nos volumes anteriores da \textit{Relatividade Geral como Teoria Quântica, \cite{RGTQ}} (RGTQ), volumes Vol.VI, Vol.VII para resolver o problema fundamental da seletividade de interações e da coexistência local em um reticulado espaço-temporal globalmente conectado. Através da aplicação rigorosa dos \textit{Fundamentos da Física Espectral} (FFE) à métrica dinâmica, deduzimos matematicamente que a densidade de energia local não satura o volume de Planck devido a um mecanismo de **Multiplexagem Temporal Geométrica**. Demonstramos que estados quânticos com frequências harmônicas distintas (n,200nn, 200nn,200n) mantêm ortogonalidade de fase ao amostrarem o reticulado em janelas temporais disjuntas, análogo aos autômatos discretos de 't Hooft. No regime não-local, derivamos o mecanismo de **Endereçamento por Impedância** para solucionar o problema da seleção no entrelaçamento. Rejeitando a transmissão de sinais superluminais, provamos que a conexão EPR ocorre através de canais de torção topológica onde a métrica efetiva é anulada para uma frequência de ressonância específica. Deduzimos a fórmula analítica para esta **Frequência de Assinatura** (fentf_{ent}fent​), modulando a portadora natural do *Zitterbewegung* (2mc2/h2mc^2/h2mc2/h) pela integral de caminho da holonomia gravitomagnética e pela impedância do meio (ZgeomZ_{geom}Zgeom​). Este formalismo unifica a memória de caminho hidrodinâmica de Couder e a coerência de fase de De Broglie sob um único princípio variacional. Conclui-se que o universo preserva a localidade relativística para o transporte de energia (v≤cv \leq cv≤c), enquanto sustenta uma conectividade global instantânea para a fase, governada estritamente pelo casamento de impedância dos canais topológicos.
This paper formally extends the Pure Gauge-Topological Vacuum framework by providing a deterministic, geometric deconstruction of quantum entanglement and the Einstein-Podolsky-Rosen (EPR) paradox. By eradicating the continuous temporal dimension in favor of a discrete structure ordered by the Mapping Class Group and quantified by the Donaldson invariant, we demonstrate that non-locality does not require superluminal information propagation. Entanglement is reformulated via two convergent formalisms: the continuity of a macroscopic gauge connection shared across an extended cobordism, and the structural preservation of harmonic resonances governed by the Laplace-Beltrami operator on the Weil-Petersson hyperbolic lattice. Instantaneous correlations emerge as necessary algebraic conditions for minimizing the vacuum's thermoelastic tension and preserving global structural stability.
This Volume III develops a complete geometric formulation of quantum mechanics, demonstrating that quantum phenomena emerge from the very structure of spacetime. We demonstrate that Einstein's field equations—when interpreted in the spectral domain and taking phase coherence into account—already contain the entire structure of quantization. Quantum mechanics appears not as an axiom, but as a geometric consequence. Based on the experimental and mathematical results consolidated in Volumes~0, I, and II, the present work shows that quantization need not be postulated: it arises inevitably from three fundamental geometric elements—proper frequency, parallel transport, and phase coherence. The action appears as the phase accumulated along the worldline, and its discretization into coherence windows, derived without external hypotheses, naturally leads to the condition Sn=nhS_n = n hSn​=nh and to all associated quantum phenomenology. We derive the Schrödinger equation as the limit of short windows, obtain the commutator [x,p]=iℏ[x,p]=i\hbar[x,p]=iℏ from the incompatibility between spatiotemporal synchronizations, and reinterpret interference, propagators, and decoherence as spectral properties of parallel transport. The Hilbert space arises as the spectral space of the metric, observables correspond to generators of isometric deformations, while the collapse is understood as the geometric selection of coherent subspaces. The formalism extends to relativistic particles, spin, quantum statistics, the Dirac equation, harmonic oscillators, and field quantization, where spectral modes of the metric assume the role of particles: photons as harmonic 1-forms, weak modes as connections of 2-forms, gluons as 3-forms, and the Higgs as the fundamental scalar curvature mode. The reinterpretation of the Standard Model thus becomes a direct consequence of spectral geometry. The Volume culminates in the Central Theorem —Geometry = Quantization— showing that the entire quantum structure is a manifestation of the spectral granularity of spacetime. We conclude with experimental predictions and falsification criteria, as well as the conceptual framework necessary for Volume~IV, dedicated to the complete quantization of the metric within the same paradigm.
The incompatibility between General Relativity and Quantum Mechanics necessitates a reevaluation of spacetime ontology. This paper proposes a Discrete Dynamic Ledger (DDL) model, defining time as a sequence of discrete state-nodes within a directed acyclic graph. Based on Wheeler’s delayed-choice experiment, we argue that historical states lack absolute determinacy until retroactively fixed by present observations, and predictions based on past states are merely decohered "abandoned futures." We introduce "Local Causal Closure": entangled particles and the observer's physical operation share a single topological node in the fundamental ledger. Through partial trace and quantum channel formulations, it is demonstrated that this synchronization requires no superluminal signaling. The observer is strictly defined by the macroscopic irreversible physical entanglement (Lindblad decoherence) formed by the unification of decision and action, independent of consciousness. Integrating the Holographic Principle and the ER=EPR conjecture, a modified interference phase formula is derived at the Planck scale. Overwritten histories are shown to transform into a "Static Information Ground State"—an eternal stillness (Ataraxia) that preserves information without energy inflation.
This manuscript establishes the microscopic dynamics (Phase B) of the Information-Topological Register Model. Building upon the macroscopic derivation of gravity, mass-energy equivalence, and the Schwarzschild metric (Works 1-3), this paper resolves the conceptual conflict between continuous classical kinematic forces and the discrete quantum probability current. By formalizing physical matter as an objective, phase-encoded information amplitude within a 1D topological lattice, this framework moves beyond the epistemic limitations of the Copenhagen interpretation, aligning with an advanced, deterministically derivable formulation of pilot-wave dynamics. Key Derivations and Theoretical Milestones: • Phase-Encoded Kinematics: We demonstrate that the topological register does not operate via classical Newtonian forces (F=ma), but executes spatial address updates via phase-gradient descent: ∇ Im(ln Ψ). • The Topological Guidance Equation: We derive the exact dynamical law for multiparticle states. The quantum mechanical momentum is redefined as an emergent, guided vector field, deterministically regulated by a topological correlation scalar. • The Decoherence Limit: The model smoothly recovers classical, local field theory. As topological entanglement collapses (η → 0), the guidance momentum decays exponentially beyond the system's intrinsic coherence length. • Deterministic Resolution of the EPR Paradox: The framework provides a rigorous geometric solution to quantum non-locality. We analytically prove that at extreme entanglement (η → 1), the geometric distance parameter (d_geo) is mathematically annihilated from the dynamic equation. The "spooky action at a distance" is thus explained not as a physical anomaly, but as a systematic geometric requirement of the 1D information-topological background manifold. This paper formally concludes the synthesis of Information Topology and modern physics, providing an analytic bridge between local macroscopic isolation and non-local microscopic entanglement.