From UD Theory to Quantum Mechanics: The Spinor Projection and the Rigorous Emergence of Quantum Postulates

We derive the foundational postulates of quantum mechanics from the UD axioms. Starting from the four-aspect field structure, we construct the spinor projection = (Uᵤ + iUd, \; Dd + iDᵤ) ^T. The U (1) Noether current from the Dirac action gives the conserved probability density, and the global normalization axiom yields the Born rule. The Dᵤ field (U in matter) is continuous and linear, explaining wave-like phenomena such as interference. The Dd field (D in matter) is localized and determinate, explaining particle-like behavior and the absence of macroscopic superpositions. The measurement process is described by a coupling Hamiltonian derived from the UD interaction, which entangles the Dᵤ field with a macroscopic Dd apparatus, leading to dissipation of Dᵤ coherence and the Born rule without collapse. The U D duality implies the existence of antiparticles with opposite phase. All derivations are self-contained and logically inevitable.