Revisiting the Neutron and Deuteron puzzle

My previous note on the proton model utilized radically simplified semi-classical reasoning to recover empirical metrics without introducing free parameters.

This new paper scales that exact framework up into the multi-body nuclear domain, treating the neutron and deuteron not as static configurations bound by unobservable “glue” forces, but as an elegant, non-linear synchronization problem involving coupled electromagnetic phase clocks.

Oddly enough, by shifting the ontology away from isolated particles toward relational, phase-locked coherence, the math naturally operates within realistic nuclear regimes—generating an internal neutron magnetic radius of 0.81-0.93 fm, a finite spatial interaction boundary of about 2 fm, and a near-field locking energy of about 2 MeV. These values all closely match experimentally observed ranges.

We, therefore, think this is quite significant. If anything, it shows, perhaps, that progress sometimes does not come from adding more parameters to describe some ‘black box’, but from acknowledging that stable matter may correspond to highly constrained, coherent oscillatory organization.

Read the paper here: “Relational Stability and Synchronization Geometry in the Neutron–Deuteron System”

Post Scriptum (23 May 2026):
A subsequent multi‑stage sanity check, involving adversarial cross‑checking between DeepSeek, ChatGPT, and Google Gemini, resulted in three companion pieces that should be read alongside the main paper (click on ‘public files’ on the above‑referenced RG page).

“On the Factor 2 in the Electron’s Ring‑Current Model: A Clarification of Scales” resolves a long‑standing confusion about the electron’s Compton radius and the equipartition of energy, showing that the model is internally consistent.
“On the Binding Energy of the Deuteron: A Correction and Reinterpretation” corrects a numerical error in the static magnetic dipole‑dipole calculation (the correct value is ~15 keV, not 2.2 MeV) and reinterprets the deuteron binding energy as a non‑linear phase‑locking energy.
“The Fine‑Structure Constant and the Deuteron Binding Energy” (with an appended sanity check by Gemini) completes the arc: from the heuristic proposal $η \cdot α \cdot (m_{p} c^{2} / 2) \approx 2.31$ η⋅α⋅(mpc2/2)≈2.31 MeV (4% error) to the logically and numerically superior expression $(1 - η) \cdot α \cdot m_{p} c^{2} \approx 2.22$ (1−η)⋅α⋅mpc2≈2.22 MeV (error <0.3%), using only the incoherent neutron deficit $(1 - η)$ (1−η) and the full proton rest energy. The fine‑structure constant $α$ α enters naturally as the electromagnetic coupling strength.

All notes are available on the ResearchGate page. I thank DeepSeek for its careful analytical assistance and for helping to turn an initial overreach into a refined, honest, and testable hypothesis.

Revisiting the Proton Radius and Magnetic Moment

My previous post discussed a more formal and “mainstream-compatible” paper on structured oscillatory fields, multipole geometry, and emergent interaction scales.

This new note goes in the opposite direction: radically simplified semi-classical reasoning using only rotating charge, Maxwellian current geometry, coupled oscillations, and elementary rotational dynamics.

Oddly enough, both approaches seem to converge toward similar intuitions about oscillatory structure and geometry in physics.

Perhaps progress sometimes comes not from moving in a straight line, but from oscillating between abstraction and simplicity.

Paper:
“A Minimal Rotational Model of the Proton”
https://www.researchgate.net/publication/405058923_A_Minimal_Rotational_Model_of_the_Proton

Concluding remarks

In our previous post, we wrote that we’ve said goodbye to this fascinating field of research. We did: I entered this line of research – fundamental physics – as an amateur 10+ years ago, and now I leave it—as much an amateur now as back then. I wanted to understand the new theories which emerged over the past 50 years or so. Concepts such as the strong force or weak interactions and the new weird charges that come it with: flavors and colors—or all of the new quantum numbers and the associated new conservation laws, which Nature apparently does not respect because of some kind of hidden variables which cause the symmetries that are inherent to conservation laws to break down. […] Apparently, I didn’t get it. 🙂

However, in the process of trying to understand, a whole other mental picture or mindset emerged: we now firmly believe that classical mechanics and electromagnetism – combined with a more creative or realistic explanation of the Planck-Einstein relation – are sufficient to explain most, if not all, of the observations that have been made in this field since Louis de Broglie suggested matter-particles must be similar to light quanta—in the sense that both are energy packets because they incorporate some oscillation of a definite frequency given by the Planck-Einstein relation. They are also different, of course: elementary particles are – in this world view – orbital oscillations of charge (with, of course, an electromagnetic field that is generated by such moving charge), while light-particles (photons and neutrinos) are oscillations of the electromagnetic field—only!

So, then we spend many years trying to contribute to the finer details of this world view. We think we did what we could as part of a part-time and non-professional involvement in this field. So, yes, we’re done. We wrote that some time already. However, we wanted to leave a few thoughts on our proton model: it is not like an electron. In our not-so-humble view, the Zitterbewegung theory applies to it—but in a very different way. Why do we think that? We write that out in our very last paper: concluding remarks on the proton puzzle. Enjoy it !

That brings the number of papers on RG up to 80 now. Too much ! There will be more coming, but in the field that I work in: computer science. Stay tuned !