Hydrodynamic Dual Space Yields a Prediction of the Muon Magnetic Moment Anomaly with Better Accuracy than the Standard Model

Despite their foundations in classical mechanics, hydrodynamic models have experienced a resurgence in modern physics, particularly in the context of electron-phonon interactions. These “tantalizing parallels1” between modern physics and hydrodynamics have not, however, seen a similar resurgence in the context of atomic theory. Here, a hydrodynamic dual space is investigated as a model for electron-photon interactions across orbital transitions. A diffusive equation is derived from dimensional analysis of a solid body of arbitrary shape displacing an unspecified, fluid-like matrix. The frictional energy dissipated across the solid-fluid interface is then treated as an equivalent to electromagnetic energy (i.e., photons). This relationship is shown to correspond to the Planck-Einstein relation and suggests a hidden diffusive variable within the Planck constant with units of m2/s. An experimental value of this apparent constant is determined and the resulting value is used to predict a theoretical value of the muon magnetic moment anomaly. The accuracy of the resulting prediction is within 0.04 sigma of the most recent experimental value and is an improvement over the 5.2 sigma predicted via the standard model of particle physics.