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The Song of the Vacuum: Decoupling Wave-Particle Duality, Spin, Entanglement, and Cooper Condensates within the Pure Gauge-Topological Framework Yassin Tanan Independent Researcher, Torino,

Yassin Tanan

Published Jun 8, 2026• 0 citations
Publisher

Abstract

For nearly a century, contemporary physics has accepted wave-particle duality, electron spin, the Pauli exclusion principle, and quantum entanglement as abstract probabilistic axioms. This paper presents a profound shift in perspective, systematically translating these quantum mysteries into deterministic, concrete geometric properties of a structured vacuum. Operating within a four-dimensional hyperbolic topological lattice governed by the Weil-Petersson metric space, we eliminate classical pseudo-Riemannian curvature in favor of micro-scale Yang-Mills holonomy. By parsing the exact mathematical thresholds between the fluid Gauge Covariant Derivative and the rigid Topological Friction Tensor, we provide a unified physical mechanism that explains quantum behavior from the double-slit experiment to superconducting Cooper pairs without epistemological ambiguities.

DOI
10.5281/zenodo.20595496

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For nearly a century, contemporary physics has accepted wave-particle duality, electron spin, the Pauli exclusion principle, and quantum entanglement as abstract probabilistic axioms. This paper presents a profound shift in perspective, systematically translating these quantum mysteries into deterministic, concrete geometric properties of a structured vacuum. Operating within a four-dimensional hyperbolic topological lattice governed by the Weil-Petersson metric space, we eliminate classical pseudo-Riemannian curvature in favor of micro-scale Yang-Mills holonomy. By parsing the exact mathematical thresholds between the fluid Gauge Covariant Derivative and the rigid Topological Friction Tensor, we provide a unified physical mechanism that explains quantum behavior from the double-slit experiment to superconducting Cooper pairs without epistemological ambiguities.
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.
We propose a unified physical framework in which four-dimensional spacetime vacuum is the unique physical reality, and all quanta are its localized topological excitations. Matter particles correspond to stable knot-like configurations, while radiation quanta correspond to weak propagating ripples of the same substrate. From this single ontological commitment, we derive: (1) wave–particle duality is resolved—particle behavior belongs to the localized excitation, wave behavior to the disturbance field it generates in spacetime; (2) double-slit interference arises from coherent superposition between a quantum's newly sourced disturbance and its own historical disturbance field, not from ontological self-superposition; (3) the wave function is a statistical tool encoding ensemble distributions of trajectories modulated by disturbance feedback, and collapse is epistemic convergence rather than a physical process; (4) quantum entanglement corresponds to Planck-scale topological connectivity (microscopic Einstein–Rosen bridges), preserving relativistic causality; (5) gravity is the macroscopic accumulation of universal but individually weak quantum–vacuum couplings, explaining both its microscopic weakness and macroscopic dominance without requiring a graviton; (6) the four fundamental interactions are differentiated coupling modes of quanta to one spacetime vacuum field; and (7) apparent dark matter and dark energy are reinterpreted as collective topological curvature and large-scale vacuum self-relaxation, respectively. We formulate falsifiable predictions at both laboratory and cosmological scales, including disturbance–corpuscle separation interferometry, tunable decoherence threshold measurements, and galaxy rotation–topology correlations. The framework compresses the conventional axiomatic structure of quantum mechanics and cosmology into one master axiom and eliminates at least twenty-eight independent interpretive assumptions.
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.
The double-slit experiment remains the empirical foundation of wave–particle duality. While standard quantum mechanics successfully predicts interference patterns via wave-function evolution and attributes the loss of interference to “decoherence,” it lacks a physical ontology. The Copenhagen interpretation and subsequent models offer mathematical descriptions of probability without identifying the underlying mechanical cause. This paper asserts that quantum mechanics is not a departure from physical realism but the statistical consequence of subatomic hydrodynamics. Under the Quantum Vector Time Field (QVTF) framework, the vacuum is modelled not as an empty geometry but as a continuous, highly pressurised superfluid medium. Subatomic masses are defined as topological vortex-solitons that generate continuous pilot-waves through this medium. We demonstrate that double-slit interference is the strict result of classical hydrodynamic steering, and we define quantum “decoherence” not as mathematical entanglement but as the physical destruction of the guiding wave structure via turbulent injection of measurement probes. By treating the vacuum as a physical fluid, the epistemological paradoxes of quantum mechanics are resolved into deterministic mechanics.
This treatise delivers the definitive mathematical physics formulation to resolve the foundational quantum measurement paradox and wave-particle duality anomalies inherent in the classical Double-Slit Experiment. Traditional quantum mechanics relies on probabilistic wave-function collapse formalisms that introduce unphysical non-local discontinuities during detector interactions (t -> 0). Operating within the multi-dimensional framework of Trans-Planckian Horizon Lock Mechanics (TPHLM), we resolve these observational anomalies by executing a rigorous multi-loop tensor regularization under the global metric scale factor of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m). We prove that the apparent wave-to-particle transition is an artifact of localized Riemannian curvature constraints locked into the chrono-hydrodynamic mesh of the slit geometry. This framework satisfies absolute diffeomorphism Ward-Khandey identities, eliminating mathematical singularities across an absolute 0.0000000000000000% error baseline compatible with quantum supercomputing arrays.
Building upon the unified 4D geometry of the Causal Smoothing Framework, this paper resolves three foundational paradoxes of quantum mechanics: wave-particle duality in the double-slit experiment, the measurement problem (wave function collapse), and the origin of particle-antiparticle asymmetry. By defining particles as time-like topological knots (ds² < 0) and quantum fields as the deterministic causal smoothing of vacuum momentum fluxes along the null boundary (ds² = 0), this framework discards probabilistic observer-driven collapse. The double-slit experiment is analyzed under two distinct boundary conditions (continuous emission and single-particle emission), demonstrating that quantum statistics are simply the macroscopic interference of vacuum geometry guiding discrete knots through a chaotic ER=EPR substrate. Furthermore, the framework provides a strict geometric proof for why fermions require distinct antiparticles while gauge bosons act as their own antiparticles, rooted entirely in the chiral phase of the localized metric shear.