Derivation of Pauli Equation and its Bipartite Form based on Budiyono-Rohrlich Ontic Extension and Epistemic Restriction of Statistical Model of Quantum Mechanics

Abstract

In this report, we discuss a possible way to derive the Pauli equation of a spin−1/2 particle based on Budiyono-Rohrlich ontic extension and epistemic restriction axioms of a statistical model of quantum mechanics. Applying the conservation of energy and probability continuity equation, we show that for a pure quantum mechanical particle spin, the corresponding equation can be reconstructed by assuming the existence of separable probability distribution functions of spin. The associated particle spin is still considered as a pure quantum phenomenon which has no classical counterpart. We also discuss the possibility of constructing a bipartite Pauli equation of nonlocal interacting two spin−1/2 particles. We examine the corresponding necessary conditions for the separability of the Bell-like-states and Werner-like-states through the Peres–Horodecki positive partial transpose criterion.