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Reinterpreting Non-Locality: A Geometric Hypothesis of Quantum Entanglement in a Constrained 3+1+2 Manifold

Changho Cho

Published Sep 18, 2026• 0 citations
Publisher

Abstract

Abstract Standard quantum mechanics often describes entanglement as a non-local correlation, presenting persistent conceptual conflicts with relativistic causality. This paper proposes a heuristic geometric hypothesis within a constrained 3+1+2 multitemporal manifold, reinterpreting entanglement not as superluminal information transfer, but as a deterministic consequence of topological continuity across extra transverse-time dimensions. Within this theoretical framework, we hypothesize two distinct geometric mechanisms depending on particle topology. For massless bosons, modeled as open helical solitons, entanglement is proposed as the continuous bifurcation of a single phase-wavefront. This macroscopic splitting conceptually accounts for the energy bisection and wavelength doubling observed in spontaneous parametric down-conversion (SPDC), as the overarching topological tension is distributed across two macroscopic projections while remaining unbroken in the extra dimensions. Conversely, for massive fermions, which are modeled as closed topological rigid bodies, we propose that macroscopic spatial separation (Δx ≠ 0) can mathematically coexist with coordinate overlap in the 2D transverse-time plane (Δτ = 0). It is hypothesized that these rigid particles are strictly meshed together at a singular coordinate within the transverse-time dimension. This direct interlocking is strictly governed by the Pauli exclusion principle, which mandates that the two topological "gears" must mesh with opposite, complementary rotations to avoid metric rupture. Furthermore, SL(4,ℝ) tensor projections mathematically guarantee that this shared geometric state persists independently of any macroscopic spatial distancing. Finally, we suggest that "wave-function collapse" can be reinterpreted as a forced geometric alignment induced by macroscopic mass ("phase-anchors"). We hypothesize that quantum superposition arises from the transverse-time fluctuations of low-mass particles. Upon contact with a phase-anchor, the Pauli exclusion principle dictates a temporary structural meshing that synchronizes the particle's mass with the macroscopic cluster. This instantaneously forces the fluctuating particle to align with the overarching Meta-Time axis, deterministically halting the superposition and severing the entanglement.

DOI
10.5281/zenodo.22821308

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Abstract Standard quantum mechanics often describes entanglement as a non-local correlation, presenting persistent conceptual conflicts with relativistic causality. This paper proposes a heuristic geometric hypothesis within a constrained 3+1+2 multitemporal manifold, reinterpreting entanglement not as superluminal information transfer, but as a deterministic consequence of topological continuity across extra transverse-time dimensions. Within this theoretical framework, we hypothesize two distinct geometric mechanisms depending on particle topology. For massless bosons, modeled as open helical solitons, entanglement is proposed as the continuous bifurcation of a single phase-wavefront. This macroscopic splitting conceptually accounts for the energy bisection and wavelength doubling observed in spontaneous parametric down-conversion (SPDC), as the overarching topological tension is distributed across two macroscopic projections while remaining unbroken in the extra dimensions. Conversely, for massive fermions, which are modeled as closed topological rigid bodies, we propose that macroscopic spatial separation (Δx ≠ 0) can mathematically coexist with coordinate overlap in the 2D transverse-time plane (Δτ = 0). It is hypothesized that these rigid particles are strictly meshed together at a singular coordinate within the transverse-time dimension. This direct interlocking is strictly governed by the Pauli exclusion principle, which mandates that the two topological "gears" must mesh with opposite, complementary rotations to avoid metric rupture. Furthermore, SL(4,ℝ) tensor projections mathematically guarantee that this shared geometric state persists independently of any macroscopic spatial distancing. Finally, we suggest that "wave-function collapse" can be reinterpreted as a forced geometric alignment induced by macroscopic mass ("phase-anchors"). We hypothesize that quantum superposition arises from the transverse-time fluctuations of low-mass particles. Upon contact with a phase-anchor, the Pauli exclusion principle dictates a temporary structural meshing that synchronizes the particle's mass with the macroscopic cluster. This instantaneously forces the fluctuating particle to align with the overarching Meta-Time axis, deterministically halting the superposition and severing the entanglement.
In standard quantum mechanics, wave-function collapse and superposition are formulated as fundamental postulates devoid of underlying deterministic geometric mechanisms. Building upon a previously established constrained SO(3,3) spacetime framework, where a dynamic topological constraint field kinematically suppresses negative-norm ghost states, this paper proposes a purely geometric interpretation of quantum phenomena. We hypothesize that microscopic leakage into transverse-time dimensions—previously viewed as a threat to unitarity—is the fundamental geometric origin of quantum superposition. Specifically, we conceptualize quantum orbitals as the spatial projection of temporal desynchronization, superposition as transverse-time phase interference, and wave-function collapse as a forced kinematic synchronization driven by macroscopic phase-anchors. This framework translates quantum uncertainty into multi-temporal geometry while rigorously preserving macroscopic unitarity without requiring ad-hoc collapse postulates.
For nearly a century, the Copenhagen interpretation has constrained quantum mechanics to a probabilistic framework, treating wave-function collapse stochastically and quantum entanglement as a non-local correlation devoid of geometric causality. This paper proposes a purely theoretical paradigm shift. We present a mathematical ansatz wherein fundamental particles are modeled as stable topological solitons within an Einstein-Cartan spacetime imbued with micro-torsion (T_micro). Applying the unitary phase inversion operator I_SU(2), we hypothesize non-locality as an artifact of lower-dimensional projection. This establishes a purely deterministic, geometric framework intended to resolve the wave-particle duality and demystify quantum entanglement through topological continuum, operating strictly within the bounds of general relativistic quantum gravity.
Quantum entanglement has long been characterized by Albert Einstein as "spooky action at a distance," challenging the classical understanding of locality and causality due to its apparent instantaneous interaction across vast spatial separations. In this paper, we resolve this paradox through the theoretical framework of Holographic Hologram-Holographic Quantum Mechanics (H3QM). We postulate that vacuum space is not an empty continuous manifold, but rather a discrete, tightly packed three-dimensional network of physical gears at the Planck scale. Under this framework, quantum entanglement is no longer interpreted as the superluminal transmission of information, but as the rigid topological locking of microscopic gears within the same kinematic chain. By applying topological winding and classical gear mechanics to the fundamental structure of space, we demonstrate that entangled particles act as mechanically linked endpoints of a unified spatial structure. This geometric paradigm provides a deterministic, local, and causal explanation for entanglement, seamlessly integrating quantum non-locality with geometric mechanics. Note: This deposit includes the full paper in English (en-US), Traditional Chinese (zh-TW), and Simplified Chinese (zh-CN).
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.
ABSTRACT The emergence of quantum entanglement correlations across spatially separated measurement regions renders the interpretation of the relationship between quantum mechanics and relativistic causality a core problem in quantum foundations [Einstein et al., 1935; Bell, 1964]. In this study, two entangled particles are modeled not as two independent physical objects in Minkowski spacetime, but as a joint quantum state in configuration space. The relative space and time coordinates of the joint state are defined via: and the ideal space-time correlation limit assumed in the model is expressed as: This limit is not a general definition of quantum entanglement, but an idealized geometric assumption representing strong correlation in the relative coordinates of the joint state within the proposed model. In this approach, physical spacetime is treated as a geometric structure representing the projection of the joint quantum state onto observable spacetime coordinates. To ensure the projection is Lorentz-covariant, the light-like interval: is employed as the constitutive geometric condition of the model. This condition is accepted not as a mandatory Minkowski interval between physical measurement events, but as the mathematical postulate of the proposed projection geometry. The dynamic scale parameter of the model is grounded in total relativistic quantum energy instead of rest mass, establishing a dimensionless Planck-scaling factor defined as: To encompass both massive and massless systems, quantum energy density is defined via the energy density component of the stress-energy tensor relative to an observer. The required consistency condition for covariant energy-momentum conservation is derived in its general form. Furthermore, modeling the proposed geometric effect as a dimensionless metric perturbation yields a phenomenological first-order geometric phase correction defined as: where is the energy-dependent reduced wavelength. Under fixed and finite , the vanishing of the proposed correction in the low-energy regime relative to the Planck scale () demonstrates that the geometric effect added by the model to standard low-energy quantum mechanics becomes negligible. This study proposes a testable theoretical model aimed at explaining the spatiotemporal correlations of quantum entanglement within a Lorentz-covariant, energy-scaled, and phenomenological geometric framework.
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.