photonic toroidal vortex model
George Francis FitzGerald, Oliver Lodge, and James Clerk Maxwell all attempted to construct geometrical models of the electric and magnetic fields but all were left disappointed with their attempts. Carl Anton Bjerknes subsequently saw it as an abandoned problem: "We have theories relating to these [E-M] fields, but we have no idea whatever of what they are intrinsically, nor even the slightest idea of the path to follow in order to discover their true nature" (Bjerknes 1906, 1). Oliver Lodge concurred: "The problem of the constitution of the Ether, and of the way in which portions of it are modified to form the atoms or other constituent units of ordinary matter, has not yet been solved" (Lodge 1909, xix). A satisfactory model of a hydrogen atom that predicts hyperfine energies is also wanting, a problem that Niels Bohr eventually abandoned.
In a new peer reviewed paper, it is pointed out that it is possible to have energy levels in the absence of external fields, a problem that quantum mechanics cannot address. So, a photonic toroidal vortex (PTV) is constructed for an electron and proton, formed by curving the trajectory of optical orbital angular momentum (OAM). ​
Construction of a PTV. In (b), a light ray runs in a helical path around a notional tube at speed c as optical OAM. In (a), the trajectory of the tube in (b) is curved into a toroid.
In (a), a proton PTV (left) and an electron PTV (right) form a hydrogen atom. In (b), the magnetic momentum field p2f results from poloidal rotation and the electric momentum field p3f from toroidal rotation.
ABSTRACT
The calculation of hydrogen energy levels for both the classical Sommerfeld and the quantum mechanical Dirac models relies on the specification of an external potential. However, recent experimental evidence has shown that electrons can adopt quantized orbital states even when there is no external potential. So a revised approach is required and suggested. Using the latest research on optical spin angular momentum (SAM) and optical orbital angular momentum (OAM), a novel reworking of the classical Sommerfeld model is carried out in terms of a photonic toroidal vortex (PTV). A construction for both an electron and proton is presented based on OAM, the difference being only one of scale. When the OAM is curved into a PTV, a self-potential can be defined for the orbiting electron based on the toroidal rotation energy. Using an electron and a proton both in the form of a PTV, a bound state model of the hydrogen atom can be formed. An opportunity presents itself to define concepts such as mass, charge, magnetic momentum, and electric momentum in terms of the poloidal and toroidal rotations of a PTV. A derivation of Coulomb’s law is given using vector line integrals. Fine structure energy states are given for the first six states of each of the following nS1/2, nP1/2, nP3/2, nD3/2, and nD5/2 to an accuracy of less than 2 parts in 10 billion compared with the Sommerfeld model.
References
Bjerknes, V. F. K. (ed.). Fields of Force: A Course of Lectures in Mathematical
Physics Delivered December 1 to 23, 1905. New York: The Columbia
University Press, 1906.
Lodge, Oliver. The Ether of Space. Harper, 1909.
Introduction to The Vortex Atom
Barry R. Clarke, The Quantum Puzzle: Critique of Quantum Theory and Electrodynamics, World Scientific Publishing, 2017.
Barry R. Clarke, A photonic toroidal vortex model of the hydrogen atom fine structure, Quantum Studies Mathematics and Foundations, 12, 19 (2025).
Barry R. Clarke, 'Reinterpretation of the Grangier experiment using a multiple-triggering single-photon model'. Modern Physics Letters B, 37(15), 2023.
Barry R. Clarke, The Vortex Atom: A New Paradigm, World Scientific Publishing, 2021.