The Three Magnetic Moments of Hydrogen - Ampère, Liénard, and Lorentz

This preprint develops a mechanistic description of the magnetic moment of the hydrogen atom within a classical–relativistic electron–proton gyroscopic model. Three distinct magnetic moments are derived in different reference frames: the Ampère, Liénard, and Lorentz magnetic moments. The Ampère and Liénard contributions are found to have nearly equal magnitudes and opposite directions, leading to an approximate cancellation, while the much smaller Lorentz magnetic moment remains as the externally observable contribution. Within the proposed model, this Lorentz magnetic moment is identified as the intrinsic magnetic moment of the ground-state hydrogen atom and is expressed entirely in terms of fundamental physical constants. The paper further compares this intrinsic moment with the Bohr magneton using both the standard fine-structure-constant relation and a previously proposed mechanistic expression for the Planck constant, yielding closely related dimensionless ratios. The work aims to provide a physically intuitive framework linking orbital dynamics, relativistic effects, and atomic magnetism.