From UD Theory to General Relativity: A Unified Derivation of Gravitational Theory

This paper derives general relativity as an effective theory in the macroscopic limit from a single fundamental axiom. The axiom is based on the universe originating from the critical state U = D, and through the logical necessity of “mutual containment”, the four-aspect structure UU , UD, DD, DU is derived. From the total normalization axiom and the principle of least action, the dynamical equations of UD theory are established. In the macroscopic limit, ignoring UD and DU , and deffning the scalar ffeld ϕ = C/E, the effective action reduces to a scalar-tensor form. Variation with respect to the metric yields the Einstein equations. In the weak-ffeld static limit, the theory reduces to Newtonian gravity and gives the post-Newtonian parameter γ − 1 ≈ −2.5 × 10 −6 , consistent with experimental results.