Action-Only Theory III: The Connected Universe — Entanglement, Dimensionality, and Cosmological Implications

This paper is Part III, the culmination of the Action-Only Theory (AOT) trilogy. Applying the operational and fluid-dynamic framework developed in Parts I and II, we address global and macroscopic phenomena that have historically resisted local mechanical descriptions, ultimately unifying quantum non-locality and General Relativity under a single physical primitive: vacuum impedance. Three main theoretical achievements: (1) Entanglement as pre-spatial coupling—quantum non-locality is reframed without "spooky action at a distance. " Spatially separated entangled states are reinterpreted as coordinated localized events emerging from a single, undivided topological process, exposing pre-existing spatial distance as a geometric illusion. (2) Dimensional lock—the three-dimensionality of space is proposed not as an arbitrary background, but as a strict topological necessity. Three dimensions provide the unique geometric regime where knot-like localized excitations (particles) are both possible and stable against unwinding. (3) Gravity as kinematic refraction—the geometric curvature of General Relativity is operationally translated into a physical impedance gradient (∇Z). Mass exerts stress on the vacuum, causing objects and light to drift along paths of least rheological resistance (Fermat's principle). This preserves the exact mathematics of the metric tensor while replacing empty spacetime with a responding medium. Ultimately, AOT completes a unified mechanical framework by reducing the fundamental forces to one measurable property: electromagnetism is dictated by an impedance RATIO (α = Z₀/2RK), and gravity is dictated by an impedance GRADIENT (∇Z).