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Why the Hausdorff Dimension of Spacetime is D ≈ 2.7 A Critical Fractal Threshold in Unified Fractal Quantum Field Theory (UFQFT)

Authors: sogukpinar, haci;

Why the Hausdorff Dimension of Spacetime is D ≈ 2.7 A Critical Fractal Threshold in Unified Fractal Quantum Field Theory (UFQFT)

Abstract

Unified Fractal Quantum Field Theory (UFQFT) proposes that the fundamental structure of spacetimeis not characterized by an integer dimension but by a critical fractal Hausdorff dimension that governsthe formation of stable physical reality. In this framework, the Hausdorff dimension D does not representthe number of spatial dimensions but quantifies the degree of connectivity, confinement, and resonanceof unified energy (Φ) and charge (Ψ) fields within spacetime. We demonstrate that a critical thresholdat D≈2.7 uniquely permits the emergence of stable standing-wave resonances identified as elementaryparticles, while simultaneously allowing long-range interactions and a non-frozen temporal evolution.For D=3, field delocalization prevents confinement and particle formation, whereas for significantlylower values of D, excessive localization suppresses interaction range and halts dynamical evolution.The value D≈2.7 thus represents a geometric balance point between localization and dispersion, enablingquark confinement, lepton and photon propagation, and the continuous flow of time. Within this scheme,normal matter corresponds to resonances near the critical dimension, dark matter emerges fromsubcritical fractal regimes incapable of full particle formation, and dark energy arises as the asymptoticD→3 limit of delocalized field oscillations. The theory yields testable predictions for particle stabilitythresholds, mass hierarchies, confinement scales, and cosmological structure formation, offering aunified geometric explanation for matter, time, and the dark sector based on a single fractal paramet

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