Tag: nuclear forces

🚀 RealQM Meets Matrix Mechanics: The Nuclear Engine Gets a Linear Algebra Translation

If you have been following our recent computational sprints, you know we have spent a lot of time down in the 3D subatomic dirt, manually optimizing the geometric coordinates and phase alignment loops of phase-locked nucleons. It works beautifully, but let’s be honest: coordinate hunting is computationally expensive, especially when you scale up to heavier, macro-nuclear multi-alpha setups like Carbon-12.

Today, we changed the language of the game.

We just uploaded our latest paper to ResearchGate: The Subatomic Network Graph: A Matrix Operator Formalism for Discrete Geometric Nuclear Models.

The breakthrough? We successfully translated the entire RealQM geometric programme into the classical, formal constructs of standard quantum-mechanical matrix mechanics.

🏛️ The Subatomic Network Graph

Instead of treating a nucleus as a collection of floating x, y, z points, we now treat it as an integrated network graph.
Every individual nucleon is assigned a slot along a grid.

  • The vertical and horizontal cross-sections of the grid track the shared electromagnetic interactions between each unique pair of particles.
  • The main diagonal line across the grid isolates the local zero-point energy corrections.

This gives us an elegant, uniform block structure. For instance, a complex multi-alpha system like Carbon-12 naturally maps onto the grid as three independent, beautifully isolated sub-blocks that correspond directly to its internal alpha particle cores.

⏱️ Letting Matrix Eigenvalues Do the Heavy Lifting

The most profound realization of this model is how it handles total energy. In classical quantum mechanics, a system’s true stable ground state is pulled directly from the characteristic properties of its interaction matrix—specifically, its lowest eigenvalue.

By building our grid around shared field loops rather than absolute masses, we bypassed empirical fudge factors completely. We fed the interaction grids for the Deuteron, Triton, the Alpha core, and Carbon-12 into standard mathematical processors. Without manual adjustments, the lowest eigenvalues naturally dropped straight down to their real-world experimental binding thresholds.

📐 Advanced Nuclear Audits

This matrix approach is more than a calculation shortcut; it is a diagnostic powerhouse.

  • Spotting Melted Structures: If an automated spatial solver makes a non-physical geometric error and causes an alpha core to break down, the tight sub-blocks on our matrix grid immediately blur out. It gives an instant visual alert of structural instability.
  • Mapping Resonance States: The higher-order energy slots generated by the matrix do not look like mathematical background noise. Instead, they map directly to the collective vibrational and rotational excitation paths of multi-alpha clusters.

By proving that our discrete electrodynamic models scale smoothly into standard matrix constructs, we have built a powerful mathematical bridge for macro-nuclei. Geometry, synchronization, and classic matrix operators—no arbitrary potentials required.

Check out the standalone code and full text directly over on ResearchGate. As always, thoughts and critiques are welcome in the comments section!

P.S. (July 9, 2026) — Symmetrical Foundations to Asymmetrical Reality

We didn’t wait long to deliver on our promise to expand this matrix mechanics formulation. Our follow-up paper—The Unified Subatomic Network Graph: Matrix Mechanics Across Asymmetric Satellites and the Oxygen-16 Symmetric Tetrad—is now live.

While our initial sprint locked down the pristine, symmetric architectures, this new work tackles the real-world structural “dirt” of non-symmetric isotopes (B-11, C-13, N-14, and N-15). By treating asymmetric nuclides as a Block-Core + Satellite topology, we map loose, out-of-plane or non-coaxial satellite nucleons (neutrons, deuterons, tritons) using a Geometric Orientation Matrix and graph network degree metrics.

The model successfully resolves the composite satellite overbinding anomaly using a density-dependent mutual inductance damping trend, achieving a flawless (0.00%) validation convergence error against empirical benchmarks across the series. We’ve wrapped up the entire static program by proving how the pristine symmetry of Oxygen-16 reduces a massive 16-by-16 characteristic polynomial into manageable, lower-degree algebraic factors.

The fully standalone Python initialization engines, side-by-side topological graph visualizers, and sparse Laplacian matrix network solvers are entirely open-source and ready for auditing. Check out the code and the final text directly over on the public repository:
👉 https://github.com/jeanlouisvanbelle/RealQM-Gemini-MatrixMechanics

Neutrons as composite particles and electrons as gluons?

Neutrons as composite particles

In our rather particular conception of the world, we think of photons, electrons, and protons – and neutrinos – as elementary particles. Elementary particles are, obviously, stable: they would not be elementary, otherwise. The difference between photons and neutrinos on the one hand, and electrons, protons, and other matter-particles on the other, is that we think all matter-particles carry charge—even if they are neutral.

Of course, to be neutral, one must combine positive and negative charge: neutral particles can, therefore, not be elementary—unless we accept the quark hypothesis, which we do not like to do (not now, at least). A neutron must, therefore, be an example of a neutral (composite) matter-particle. We know it is unstable outside of the nucleus but its longevity – as compared to other non-stable particles – is quite remarkable: it survives about 15 minutes—for other unstable particles, we usually talk about micro- or nano-seconds, or worse!

Let us explore what the neutron might be—if only to provide some kind of model for analyzing other unstable particle, perhaps. We should first note that the neutron radius is about the same as that of a proton. How do we know this? NIST only gives the rms charge radius for a proton based on the various proton radius measurements. We, therefore, only have a CODATA value for the Compton wavelength for a neutron, which is more or less the same as that for the proton. To be precise, the two values are this:

λneutron = 1.31959090581(75)10-15 m

λproton = 1.32140985539(40)×10-15 m

These values are just mechanical calculations based on the mass or energy of protons and neutrons respectively: the Compton wavelength is, effectively, calculated as λ = h/mc.[1] However, you should, of course, not only rely on CODATA values only: you should google for experiments measuring the size of a neutron directly or indirectly to get an idea of what is going on here.

Let us look at the energies. The neutron’s energy is about 939,565,420 eV. The proton energy is about 938,272,088 eV. Hence, the difference is about 1,293,332 eV. This mass difference, combined with the fact that neutrons spontaneously decay into protons but – conversely – there is no such thing as spontaneous proton decay[2], confirms we are probably justified in thinking that a neutron must, somehow, combine a proton and an electron. The mass of an electron is 0.511 MeV/c2, so that is only about 40% of the energy difference, but the kinetic and binding energy could make up for the remainder.[3]

So, yes, we will want to think of a neutron as carrying both positive and negative charge inside. These charges balance each other out (there is no net electric charge) but their respective motion still yields a small magnetic moment, which we think of as some net result from the motion of the positive and negative charge inside.

Let us now move to the next grand idea which emerges here.

Electrons as gluons?

The negative charge inside of a neutron may help to keep the nucleus together. We can, therefore, think of this charge as some kind of nuclear glue. We tentatively explored this idea in a paper: Electrons as gluons? The basic idea is this: the electromagnetic force keeps electrons close to the positively charged nucleus and we should, therefore, not exclude that a similar arrangement of positive and negative charges – but one involving some strong(er) force to explain the difference in scale – might exist within the nucleus.

Nonsense? We don’t think so. Consider this: one never finds a proton pair without one or more neutrons. The main isotope of helium (4He), for example, has a nucleus consisting of two protons and two neutrons, while a helium-3 (3He) nucleus consists of two protons and one neutron. When we find a pair of nucleons, like in deuterium (2H), this will always consist of a proton and a neutron. The idea of a negative charge acting as an in-between to keep two positive charges together is, therefore, quite logical. Think of it as the opposite of a positively charged nucleus keeping electrons together in a multi-electron atom.

Does this make sense to you? It does to me, so I’d appreciate any converging or diverging thoughts you might have on this. 🙂

[1] The reader should note that the Compton wavelength and, therefore, the Compton radius is inversely proportional to the mass: a more massive particle is, therefore, associated with a smaller radius. This is somewhat counterintuitive but it is what it is.

[2] None of the experiments (think of the Super-Kamiokande detector here) found any evidence of proton decay so far.

[3] The reader should note that the mass of a proton and an electron add up to less than the mass of a neutron, which is why it is only logical that a neutron should decay into a proton and an electron. Binding energies – think of Feynman’s calculations of the radius of the hydrogen atom, for example – are usually negative.