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SDRIS: The Geometric Origin of Non-Locality - Deriving Quantum Entanglement from the Topological Folding of the Recursive Time-Slice

Jan Patrick Maier-Lutz

Published Jan 1, 2026• 1 citation
Publisher

Abstract

Paper 101 of the SDRIS Research Series Building upon the geometric derivation of forces (Paper 100), this work addresses the ontological mechanism of quantum non-locality. Abstract: The phenomenon of quantum entanglement challenges the principle of local realism, suggesting instantaneous information transfer across spacelike intervals. This paper proposes a geometric resolution within the Static-Dynamic Recursive Information Space (SDRIS) framework. We demonstrate that entanglement is not a dynamic transmission of signals through 3D-space ($v > c$), but a static topological identity in the embedding 5D-manifold ($\Delta x_{5D} = 0$). By modeling the 3D-universe as a lower-dimensional projection of a recursive information flux, we derive the quantum correlation function $|\psi\rangle$ as a deterministic consequence of a "Recursive EPR Bridge". We show that the "collapse" of the wavefunction is a global update of the pre-metric information source, occurring in recursive processing time ($\tau$) rather than metric time ($t$). This reinterpretation validates Bell's inequality violations while preserving causality, ultimately proving that spatial separation is an emergent artifact of dimensional reduction. Includes Computational Verification: This publication includes a Python simulation framework (SDRIS_Entanglement_Simulation_Code_v1.0.ipynb) that visualizes the 5D-topology and numerically validates the violation of Bell's inequalities against the geometric SDRIS prediction.

DOI
10.5281/zenodo.18115334

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Paper 101 of the SDRIS Research Series Building upon the geometric derivation of forces (Paper 100), this work addresses the ontological mechanism of quantum non-locality. Abstract: The phenomenon of quantum entanglement challenges the principle of local realism, suggesting instantaneous information transfer across spacelike intervals. This paper proposes a geometric resolution within the Static-Dynamic Recursive Information Space (SDRIS) framework. We demonstrate that entanglement is not a dynamic transmission of signals through 3D-space (v>cv > cv>c), but a static topological identity in the embedding 5D-manifold (Δx5D=0\Delta x_{5D} = 0Δx5D​=0). By modeling the 3D-universe as a lower-dimensional projection of a recursive information flux, we derive the quantum correlation function ∣ψ⟩|\psi\rangle∣ψ⟩ as a deterministic consequence of a "Recursive EPR Bridge". We show that the "collapse" of the wavefunction is a global update of the pre-metric information source, occurring in recursive processing time (τ\tauτ) rather than metric time (ttt). This reinterpretation validates Bell's inequality violations while preserving causality, ultimately proving that spatial separation is an emergent artifact of dimensional reduction. Includes Computational Verification: This publication includes a Python simulation framework (SDRIS_Entanglement_Simulation_Code_v1.0.ipynb) that visualizes the 5D-topology and numerically validates the violation of Bell's inequalities against the geometric SDRIS prediction.
Paper 102 of the SDRIS Research Series Following the geometric derivation of forces (Paper 100) and non-locality (Paper 101), this work addresses the origin of quantum probability. Abstract: The Born Rule, which states that the probability of a quantum measurement is proportional to the square of the wavefunction's amplitude (P=∣ψ∣2P = |\psi|^2P=∣ψ∣2), is one of the most fundamental yet least understood axioms of quantum mechanics. Standard theory treats it as an empirical postulate without a rigorous geometric derivation. In this paper, we derive the Born Rule as a necessary consequence of the Static-Dynamic Recursive Information Space (SDRIS) framework. We demonstrate that the "amplitude" ∣ψ∣|\psi|∣ψ∣ corresponds to the linear Euclidean length of the information vector in the 5-dimensional bulk, while the "probability" PPP corresponds to the interaction flux through the 3-dimensional projection interface. Since the information flux through a holographic boundary scales with the surface area (A∝r2A \propto r^2A∝r2) rather than the linear radius, the quadratic relationship is geometrically inevitable. Furthermore, we show that Wave-Particle Duality is resolved as an observational artifact: The "Wave" is the continuous rotation of the vector in the recursive time dimension (τ\tauτ), while the "Particle" is the discrete intersection of this vector with the static metric slice (ttt). Thus, quantum randomness is identified not as intrinsic indeterminism, but as the geometric cross-section of a higher-dimensional determinism. Includes Computational Verification: This publication includes a Python simulation (SDRIS_Born_Rule_Simulation_Code_v1.0.ipynb) that numerically validates the flux-projection mechanism, confirming that the measurement of a deterministic 5D-vector yields a statistical distribution strictly following the Born Rule.
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.
The Heisenberg Uncertainty Principle is conventionally interpreted as a fundamental limit of nature's precision or as a consequence of measurement disturbance. In this paper, we propose a structural reinterpretation within the Static-Dynamic Recursive Information Space (SDRIS) framework. We demonstrate that quantum uncertainty is mathematically isomorphic to the Time-Bandwidth Product in signal processing. By modeling the vacuum as a discrete information grid, we identify the uncertainty relation not as an intrinsic indeterminism of the object, but as a Representation Limit arising from the projection of infinite information onto a finite-bandwidth substrate. Key Results: Geometric Derivation: We derive the uncertainty inequality σxσk≥1/2\sigma_x \sigma_k \ge 1/2σx​σk​≥1/2 strictly from the properties of the Fourier Transform on a lattice, identifying the Planck constant ℏ\hbarℏ as the scaling parameter converting grid bandwidth into physical momentum (p=ℏkp = \hbar kp=ℏk). Numerical Verification: Included Python simulations (FFT) confirm that Gaussian wavepackets minimize the uncertainty product to exactly 0.50.50.5. This proves that "fuzziness" is effectively the compression artifact of a finite-resolution universe. Ontological Shift: The paper recovers the standard quantum mechanical limit while providing a rigorous geometric foundation based on discrete signal theory, removing the need for an axiomatic "indeterminacy principle." Includes: Full mathematical derivation (Fourier Duality). Python Simulation Notebook (102_18116715_SDRIS_Born_Rule_Simulation_Code_v1_0.ipynb) verifying the lower bound.
This work addresses a fundamental question raised by the 2022 Nobel Prize in Physics: What is the correct interpretation of Bell inequality violations? We construct a 10-dimensional dynamical framework where: 1. Spin-1/2 (s = 0.5000 exactly) emerges from the topological winding number of chaotic attractors 2. Bell inequality violations (|S| = 2.82, achieving 99.7% of the Tsirelson bound) arise from Möbius topology without superluminal signaling 3. Gravity emerges from metric distortion by the hierarchy dimension The central insight is that "non-locality in 3D is locality in 10D." Entangled particles are not two objects mysteriously connected—they are one object with two spatial projections sharing a twisted fiber in internal dimensions. This archive contains: - Main manuscript (PDF and LaTeX source) - Supplementary Information - Complete Python code for all numerical results - All figures - Reproducibility test suite (14/14 tests passing) Target journal: Foundations of Physics
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.
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.