Introduction to The Vortex Atom
2. The Fundamental Unit
The invariant
The program identifies the fundamental irreducible element as a finite string that follows a helical trajectory where linear translation and intrinsic rotation are fluidly interchangeable.
Mechanical refraction
This provides a purely mechanical basis for the refractive index n. In dispersive media, linear action is redistributed into rotational action (Sp-1) allowing the photon to slow down while maintaining frequency and action conservation.
Figure 1. A finite string that follows a helical path with a rake angle π/4 at speed √2c on a notional tube. This produces a Sp-1 rotation at speed c and a linear motion at speed c.
See also, Barry R. Clarke, 'Reinterpretation of the Grangier experiment using a multiple-triggering single-photon model'. Modern Physics Letters B, 37(15), 2023.
3. Particle Morphology and Momentum Fields
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Sp-1 (String): Optical SAM. The intrinsic rotation of the string as it takes a helical path.
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Sp-2 (Poloidal): Optical OAM. The rotation of the Sp-1 axis around a notional tube. This defines rest mass and is constrained to an angular momentum ħ. This rotation generates a magnetic momentum field.
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Sp-3: (Toroidal): Rotation of the notional tube axis around the toroidal centre. The electron or proton is the Sp-3 structure. This rotation generates the electric momentum field (charge) and (when aligned with a conductor) the macroscopic magnetic field surrounding the wire. The electron is thus a stationary resonant state of toroidal momentum rather than a point-particle in orbit (for example, in a hydrogen atom).
Matter is modelled as a captured helical string closed into a double-loop vortex. The structure possesses three nested degrees of freedom.
Figure 2. (a) Sp-3 toroidal ring with Sp-2 tube passing around it. The momentum fields p are shown. (b) Sp-1 axis at speed c rotating around notional Sp-2 tube.
Barry R. Clarke, The Quantum Puzzle: Critique of Quantum Theory and Electrodynamics, World Scientific Publishing, 2017.
See also, Barry R. Clarke, A photonic toroidal vortex model of the hydrogen atom fine structure, Quantum Studies Mathematics and Foundations, 12, 19 (2025).
4. Fundamental Departures from Maxwell
It should be kept in mind that Maxwell's equations are only macroscopic laws of association. For example, when a current of a certain magnitude flows in a conductor, it is associated through an equation with a magnetic field of a certain strength circulating around it. Maxwell's equations provide no mechanism for what might be happening on a microscopic level. The PTV substructure renders several Maxwellian devices obsolete.
Intrinsic magnetism
Although the PTV model generates a magnetic momentum field from Sp-2 rotation, the observed magnetic field around a current-carrying conductor arises from the electron's Sp-3 field (electric momentum flow). The field does not require the motion of charge to exist; it only requires common toroidal alignment.
Momentum flow v rotation
Magnetic field lines represent a flow of momentum. There is no intrinsic rotational momentum (curl) around a magnetic field line.
Obsolescence of displacement current
Maxwell's ∂D/∂t represented fictitious ether charges and its only utility was to obtain a wave equation. In PTV theory, the rotating light-string provides the wave-nature inherently.
Local field generation
Induction is an internal redistribution of action between Sp-2 and Sp-3 to preserve the Sp-2 action h. A changing magnetic momentum field around a target Sp-2 circuit results in a decrease or increase in Sp-3 (electric) momentum. No electric field is generated ex nihilo in the vacuum
See also, Barry R. Clarke, The Lorentz force and the nature of charge from a photonic toroidal vortex model, https://www.preprints.org/manuscript/202603.2233
Geometrical interpretation of the hydrogen atom hyperfine structure
For a preprint version of
the paper click below
Barry R. Clarke, The Vortex Atom: A New Paradigm, World Scientific Publishing, 2021.
TUTORIAL 1. WHY THIS MODEL?
The three tables below show how accurately the Photonic Toroidal Vortex (PTV) model reproduces experimental measurements of the hydrogen spectrum. The calculations rest on a set of nested vortices denoted as Sp-1 (optical SAM), Sp-2 (optical OAM), and Sp-3 (toroidal rotation). No quantum mechanical wavefunction, no external potential, and no perturbative expansion series have been employed.
Table 1 shows that sub-MHz accuracy can be produced in the hydrogen fine structure without a Coulomb potential generating the energy levels. Instead an internal potential is defined. The hyperfine energies involve the interaction between the electron and nuclear magnetic moments. These are traditionally based on the centroids of the hyperfine levels. In PTV theory, the target is the hyperfine midpoint frequency as being more appropriate for geometrical symmetry. Table 2 compares the experimental hyperfine midpoint frequencies (calculated from Horbatsch and Hessels) with the PTV prediction. Errors are at or below 0.1 MHz across thirty states. For the lowest state of each set, agreement is essentially exact. Table 3 gives the magnitude of the shift each side of the hyperfine mid-point.
TABLE I. Comparison of a selection of fine-structure energy levels (MHz) of atomic hydrogen as given by the Sommerfeld–Dirac theory, against the new PTV theory without adjustments.
TABLE 2. Comparison of a selection of hyperfine mid-point frequencies (MHz) of atomic hydrogen as given by Horbatsch and Hessels against PTV theory without adjustments.
Source: M. Horbatsch, and E. A. Hessels, Tabulation of the bound-state energies of atomic hydrogen, Physical Review A , 022513 (2016), Tables III, IV, V.
TABLE 3. Results for the magnitude of the hydrogen hyperfine shift from the mid-point hyperfine frequency (MHz) for various states using Eq. (35), Paper C. The same shift occurs each side of the mid-point so this is half the usual quoted value. The experimental value from Horbatsch and Hessels is at the top and the PTV value at the bottom. The deviation from experiment is hf-error.
Source: M. Horbatsch, and E. A. Hessels, Tabulation of the bound-state energies of atomic hydrogen, Physical Review A , 022513 (2016), Table III.
Paper A Paper B Paper C Paper D Paper E
Paper A: Barry R. Clarke, Reinterpretation of the Grangier experiment using a multiple-triggering single-photon model, Modern Physics Letters B , 15, 2350042 (2023).
Paper B: Barry R. Clarke, A photonic toroidal vortex model of the hydrogen atom fine structure, Quantum Studies Mathematics and Foundations, 12, 19 (2025).
Tutorial 2
Physics
Paper C: Barry R. Clarke, Geometrical interpretation of the hydrogen atom hyperfine structure, under peer review.
Paper D: Barry R. Clarke, The Lorentz force and the nature of charge from a Photonic Toroidal Vortex Model, under peer review.
Paper E: Barry R. Clarke, A heuristic model of the Bose-Einstein distribution with distinguishable photons