We present a geometric interpretation of elementary particles in which mass, magnetic moment, and characteristic length scales emerge from internally circulating wave structures (toroidal solitons). In this framework, particles are modeled as stable, closed-loop configurations of propagating wave modes (ring–waves), whose internal periodicity is identified with the Compton frequency derived from the Planck–Einstein relation . By imposing a closure condition on the circulating mode, a characteristic radius is obtained, corresponding to the reduced Compton wavelength. For the electron, this yields , consistent with established Compton-scale structure. Using this geometric radius, the magnetic moment follows directly from a circulating current model, recovering the standard expression for the Bohr magneton . Relativistic effects are interpreted geometrically as a deformation of internal trajectories from closed circular paths to helices under external motion, recovering the Lorentz factor of special relativity. Within this interpretation, time corresponds to the internal periodicity of the structure, and time dilation reflects an increase in the effective path length per cycle. The proposed framework is phenomenological and does not replace established theories such as quantum electrodynamics, but offers a complementary geometric perspective in which several physical quantities arise from a unified structural principle.
Dorin Gherlea (Sun,) studied this question.