Spin and Statistics from a Classical Vibrational Field

Extending the Yaremenko Hydron Model

Abstract

We extend the recently introduced purely vibrational, classical field model of the hydrogen atom in two essential directions. First, the electron scalar field is replaced by a classical Dirac spinor field, which naturally generates intrinsic spin angular momentum and, in the non-relativistic limit, yields the Pauli equation with the correct spin–orbit coupling and Darwin term; the resulting fine-structure corrections match the standard quantum mechanical formula. Second, we incorporate a classical, Lorentz-invariant zero-point electromagnetic radiation background and show that, when a measurement apparatus is modelled as a resonant detector, the time averaged detection probability for a given stationary vibrational mode is proportional to its energy fraction. The Born rule thus emerges as a statistical consequence of deterministic evolution with zero-point noise, without any fundamental quantum postulate. The combined model reproduces both the full hydrogen spectrum (including fine structure) and the probabilistic predictions of quantum mechanics from purely classical field equations.