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Quantum Holism from Geometric Projections

A.B.M Masum Billah Mim

Published Jun 2, 2026• 0 citations
Publisher

Abstract

This paper introduces a mathematically unified, fully local, and realistic framework for quantum entanglement by deriving non-local correlations directly from the global invariants of a smooth, inherently non-commutative operator field manifold. Moving away from background-dependent spacetime stress tensors, we establish a strict ontological hierarchy where the universe is governed by a global operator invariant constraint, formulated as an eigenvalue equation $(\hat{A} + \hat{B})|\Psi\rangle = \mathcal{I}|\Psi\rangle$. We resolve previous fragmentation in topological interpretations by explicitly constructing the operators $\hat{A}$ and $\hat{B}$ as localized spatial integrals of a quantized winding density operator $\hat{\Omega}_{\mathrm{top}}(x)$ and establishing their formal evaluation action on the state space. In a zero-baseline vacuum ($\mathcal{I}=0$), the states of localized field excitations are shown to be structural mirror images. Crucially, by modeling measurement as a geometric projection (the ``Shadow'' view), we provide the explicit algebraic derivation connecting the holistic state vector to the characteristic quantum cosine correlation $-\cos(\theta_1 - \theta_2)$. This framework naturally violates Bell's inequalities up to the Tsirelson bound ($2\sqrt{2}$) while strictly preserving local causality, offering a mathematically cohesive alternative to the Copenhagen probability collapse.

DOI
10.5281/zenodo.20500964

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In the Cosmology of the Quarkbase, quantum particles and photons are interpreted as excitations of an etheric plasma represented by the scalar or vector field Ψ(x,t). An experiment that, in standard quantum theory, produces an entangled pair instead generates in this framework a single non-local field excitation: a coherent combination of Ψ-modes correlated through conservation of momentum, spin, and polarization, as well as through the coupling topology between local sources (quarkbases). Local measurement acts as a projection on this extended excitation, producing the experimentally observed strong correlations without any exchange of causal signals between detectors. The Quarkbase formalism introduces explicit medium parameters —density ρp, compressibility K, and effective mass mΨ— that define physical scales such as the screening length λ = 1/mΨ. These quantities determine the spatial decay of entanglement visibility according to V(r) ∝ e⁻ʳ/λ / r, and the effective CHSH parameter becomes Seff = C(r) 2√2. Therefore, if the vacuum possesses a finite λ, Bell-type correlations should attenuate exponentially with distance, providing a falsifiable signature of a massive or screened etheric field. Mathematically, the framework reproduces the predictions of quantum field theory —Bell states, coincidence probabilities, CHSH violation— while offering an ontological interpretation in which entanglement arises from the geometry and coherence of the Ψ-field rather than from instantaneous nonlocal action. The theory therefore unifies microscopic quantum behavior with macroscopic medium dynamics, transforming questions about “collapse” and “nonlocality” into experimentally testable properties of the underlying ether-plasma.
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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 produces correlations that violate classical locality constraints while remaining fully consistent with relativistic no-signaling. Although standard quantum mechanics predicts these correlations with extraordinary empirical success, the ontological meaning of entangled states and the physical status of wave-function collapse remain deeply debated. This paper develops a speculative but structured informational interpretation in which entangled subsystems are modeled as multiple local realizations of a single shared informational identity within an underlying finite-capacity substrate. The framework is articulated through explicit postulates, density-matrix analysis, entanglement entropy, a toy realization scheme, and an informational identity operator acting on composite states. Within this view, nonlocal correlations arise not from superluminal causal influence but from ontological non-separability at the informational level. Measurement is interpreted as informational resolution: a reduction of degeneracy in the local realization of a shared informational structure. The irreversible stabilization of outcomes is then linked to thermodynamic cost through Landauer-type reasoning. The proposal is not advanced as a replacement for quantum mechanics, nor as a fully worked-out hidden-variable theory, but as an ontological scaffold intended to unify entanglement, collapse, and thermodynamic irreversibility within an informational perspective. Compatibility with Bell inequalities, decoherence, basis selection, and no-signaling is discussed in detail, together with limitations and possible routes toward future formalization and empirical relevance.
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.
A geometric interpretation of quantum entanglement as the polar structure of the electromagnetic closure sphere, deriving the Tsirelson bound as a consequence of spherical topology rather than quantum formalism. This paper proposes that quantum entanglement is not a correlation between two separate systems but the polar structure of a single spherically confined field. Every confined field — whether gravitational, electromagnetic, or strong — closes at a boundary defined by the universal condition C = g². This closure sphere is a global topological object with two poles. What we call an entangled pair is not two particles but two observers at opposite poles of one such sphere. From this picture, the non-locality of entanglement is not mysterious — it is the straightforward consequence of attempting to assign separate spatial addresses to the poles of a geometric object that has no spatial address of its own. Measurement defines an orientation globally, not locally. No signal passes. The Tsirelson bound — the maximum violation of Bell inequalities permitted by quantum mechanics — is shown to be a direct consequence of spherical geometry, independent of which force confines the field. All spheres in three dimensions have the same polar topology and the same maximum pole correlation