The Sobolev-Ozok Lattice Model: A Framework for Bridging General Relativity and Quantum Mechanics

The Sobolev–Ozok Lattice (SOL) model is a theoretical framework designed to bridge the gap between General Relativity and Quantum Mechanics by reformulating spacetime as a discrete lattice of Planck-scale cells. The model introduces the concept of coherence fields, where cell islands act as collective quantum states whose interactions mimic the effects of a metric tensor. Gravitational phenomena emerge from coherence-induced tension gradients rather than from continuous curvature, while quantum behavior is derived from local cell dynamics and phase alignment. 

 

The SOL model proposes a multi-order coherence structure, with k=1 terms governing large-scale interactions such as galaxy rotation curves, and k=2 terms describing local curvature effects consistent with General Relativity. The framework also incorporates energy conservation across cell islands, a mass bias favoring gravitational attraction, and the possibility of deriving fundamental constants (G, α, ħ, Λ) from first principles. 

 

This paper presents the mathematical formulation of the SOL model, its physical interpretations, and its implications for unifying the Standard Model of particle physics with gravitational theory. Potential applications include explanations for cosmological expansion, black hole properties, and quantum entanglement within a lattice-based spacetime framework.

 

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