From UD Theory to Quantum Mechanics: A Unified Derivation of the Microscopic World

This paper derives quantum mechanics as an effective theory in the microscopic 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. In the microscopic limit, the quantum fluctuation component DU dominates, while other components can be neglected. Starting from the UD dynamical equations, through small parameter expansion and non-relativistic approximation, the Schro¨dinger equation is rigorously derived. Deffning a conserved current naturally yields the probabilistic interpretation of the wave function. This demonstrates that quantum mechanics is not an independent fundamental theory, but a natural manifestation of the primordial theory under microscopic conditions.