Revisiting the Neutron and Deuteron puzzle

Mathematics, Philosophy of science, Physics, quantum mechanics 2 Minutes

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).

  1. “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.
  2. “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.
  3. “The Fine‑Structure Constant and the Deuteron Binding Energy” (with an appended sanity check by Gemini) completes the arc: from the heuristic proposal η⋅α⋅(mpc2/2)≈2.31η⋅α⋅(mp​c2/2)≈2.31 MeV (4% error) to the logically and numerically superior expression (1−η)⋅α⋅mpc2≈2.22(1−η)⋅α⋅mp​c2≈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 αα 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.

Unknown's avatar

Published by Jean Louis Van Belle

Published

8 thoughts on “Revisiting the Neutron and Deuteron puzzle”

  1. I don’t understand Eq. 4 of “On the Factor 2 in the Electron’s Ring-Current Model: A Clarification of Scales”. In my understanding you cannot use a non-relativistic approximation of the kinetic energy for a mass-point that is moving with the speed of light. Can you clarify?

    Reply

      1. I actually don’t explicit use a ‘non-relativistic approximation’ in any of the equations

        I’m reading Eq. 4: E_kin = m_e v^2 / 2 (with v = c) as a non-relativistic approximation of E_kin = m_e c^2 / sqrt(1-v^2/c^2) – m_e c^2 for small v. Am I wrong? Is there another motivation for the way Eq. 4 computes the kinetic energy?

        Can you specify exactly what paper/section you are referring to?

        The title of the paper is “On the Factor 2 in the Electron’s Ring-Current Model: A Clarification of Scales”. It’s the first equation (Eq. 4) in the 3rd section “Where Does the Factor 2 Come From?” on the 2nd page.

      2. Oh, you changed your reply while I was replying to it! Your explanation makes sense to me because I observed a similar distribution of field energy in my modified Born-Infeld electron model. Thanks!

      3. Yes. Apologies. I often react too fast. I do ‘co-create’ with AI and then it’s often hard to remember what I wrote exactly, and where exactly. In any case, your reaction now seems to indicate that you understand how I look at it (this section was actually the result of a rather intensive ‘triangulation’ between ChatGPT, DeepSeek and myself – and I initially thought: ChatGPT is right but… Well… No. I revisited the original intuition and let DeepSeek make the ‘final’ write-up). Science these days is ‘tough’ but ‘pleasant’ with all of these powerful tools at your disposal… But you’re right on the risk for ‘AI slop’ (your other remark). I try to not fall into that trap even if – I admit – sometimes I ask AI to prepare an email to a close friend to make sure I don’t forget any ‘angle’ or ‘viewpoint’. All that is ‘out there’ is, however, my responsibility. By the way, you mentioned the ‘modified Born-Infeld electron model’ now several times, so I will look into that but not tomorrow. Perhaps next week or so: I honestly have had it for a while with quantum physics: after all, I am just an amateur (which means: not paid for this). 🙂

      4. Hi – I sent you an email with an AI-generated paper but DeepSeek ‘shot it down’. I actually ‘like’ it but – as part of my ‘cross-triangulation’ with AI platforms – I don’t publish anything if one of the three big ‘systems’ I use (ChatGPT, Gemini or DeepSeek) doesn’t agree. Perhaps you can have a look at it, and see if it would be worthwhile pursuing? I think you’d be the ideal person in light of your work on ‘modified Born-Infeld electron modeling’ – even if I haven’t looked at your work yet. Can you acknowledge receipt of the email – and no worries if you think it’s not worth pursuing. 🙂 Kindest regards – Jean Louis

Leave a comment