Experiments on electron vortices show that they can adopt discrete energy levels in a field-free space. However, quantum mechanics requires an external potential to work. So in a fusion of the latest research on optical OAM and the classical Sommerfeld hydrogen atom fine structure theory, a photonic toridal vortex (PTV) model with an internal potential is developed. This gives accurate fine structure values. Some novel characteristics appear in the theory.

(1) The toroid is constructed by curving the trajectory of optical OAM.

(2) The poloidal rotation generates a magnetic momentum field and the toroidal rotation creates an electric momentum field. These fields result from the rotation of a light ray; the ray is not constructed from these fields.

(3) An electron possesses a magnetic field around it whether or not it is in relative motion.

(4) There is a problem with the concept of a 'rigid rod' in Special Relativity.

(5) Geometrical explanations of attraction and repulsion effects are given.

View paper (Quantum Studies: Mathematics and Foundations, 12 (2025) https://doi.org/10.1007/s40509-025-00364-9 )

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