Action-Only Theory I: Mechanical Properties of the Vacuum and Scaling Laws of Physical Constants

This paper is Part I of the Action-Only Theory (AOT) trilogy, offering a mechanical interpretation of modern physics by treating the vacuum as a dilatant fluid with measurable impedance properties (μ₀, ε₀). We reveal structural relationships behind fundamental constants while preserving all experimental results. Three main achievements: (1) Relativity as fluid mechanics—the Lorentz factor is mathematically identical to the Prandtl-Glauert compressibility factor, with c as the vacuum jamming transition. (2) Fine-structure constant identity—the relation α = Z₀/ (2RK) is shown to be an exact impedance-matching condition, demystifying electromagnetic coupling. (3) Proton radius prediction—topological analysis (Borromean rings) yields R = 4ℏ/ (Mc) with zero free parameters, predicting Rₚ = 0. 8412 fm (0. 02% experimental agreement) and R_π/Rₚ = π/4 (0. 3% agreement). Parts II and III address operational foundations and cosmological implications, completing a unified mechanical framework.