## A Zitterbewegung model of the neutron

As part of my ventures into QCD, I quickly developed a Zitterbewegung model of the neutron, as a complement to my first sketch of a deuteron nucleus. The math of orbitals is interesting. Whatever field you have, one can model is using a coupling constant between the proportionality coefficient of the force, and the charge it acts on. That ties it nicely with my earlier thoughts on the meaning of the fine-structure constant.

My realist interpretation of quantum physics focuses on explanations involving the electromagnetic force only, but the matter-antimatter dichotomy still puzzles me very much. Also, the idea of virtual particles is no longer anathema to me, but I still want to model them as particle-field interactions and the exchange of real (angular or linear) momentum and energy, with a quantization of momentum and energy obeying the Planck-Einstein law.

The proton model will be key. We cannot explain it in the typical ‘mass without mass’ model of zittering charges: we get a 1/4 factor in the explanation of the proton radius, which is impossible to get rid of unless we assume some ‘strong’ force come into play. That is why I prioritize a ‘straight’ attack on the electron and the proton-electron bond in a primitive neutron model.

The calculation of forces inside a muon-electron and a proton (see ) is an interesting exercise: it is the only thing which explains why an electron annihilates a positron but electrons and protons can live together (the ‘anti-matter’ nature of charged particles only shows because of opposite spin directions of the fields – so it is only when the ‘structure’ of matter-antimatter pairs is different that they will not annihilate each other).

[…]

In short, 2021 will be an interesting year for me. The intent of my last two papers (on the deuteron model and the primitive neutron model) was to think of energy values: the energy value of the bond between electron and proton in the neutron, and the energy value of the bond between proton and neutron in a deuteron nucleus. But, yes, the more fundamental work remains to be done !

Cheers – Jean-Louis

## The electromagnetic deuteron model

In my ‘signing off’ post, I wrote I had enough of physics but that my last(?) ambition was to “contribute to an intuitive, realist and mathematically correct model of the deuteron nucleus.” Well… The paper is there. And I am extremely pleased with the result. Thank you, Mr. Meulenberg. You sure have good intuition.

I took the opportunity to revisit Yukawa’s nuclear potential and demolish his modeling of a new nuclear force without a charge to act on. Looking back at the past 100 years of physics history, I now start to think that was the decisive destructive moment in physics: that 1935 paper, which started off all of the hype on virtual particles, quantum field theory, and a nuclear force that could not possibly be electromagnetic plus â totally not done, of course ! â utter disregard for physical dimensions and the physical geometry of fields in 3D space or â taking retardation effects into account â 4D spacetime. Fortunately, we have hope: the 2019 fixing of SI units puts physics firmly back onto the road to reality – or so we hope.

Paolo Di Sia‘s and my paper show one gets very reasonable energy and separation distances for nuclear bonds and inter-nucleon distances when assuming the presence of magnetic and/or electric dipole fields arising from deep electron orbitals. The model shows one of the protons pulling the âelectron blanketâ from another proton (the neutron) towards its own side so as to create an electric dipole moment. So it is just like a valence electron in a chemical bond. So it is like water, then? Water is a polar molecule but we do not necessarily need to start with polar configurations when trying to expand this model so as to inject some dynamics into it (spherically symmetric orbitals are probably easier to model). Hmm… Perhaps I need to look at the thermodynamical equations for dry versus wet water once again… Phew ! Where to start?

I have no experience â I have very little math, actually â with modeling molecular orbitals. So I should, perhaps, contact a friend from a few years ago now â living in Hawaii and pursuing more spiritual matters too â who did just that long time ago: orbitals using Schroedingerâs wave equation (I think Schroedinger’s equation is relativistically correct â just a misinterpretation of the concept of âeffective massâ by the naysayers). What kind of wave equation are we looking at? One that integrates inverse square and inverse cube force field laws arising from charges and the dipole moments they create while moving. [Hey! Perhaps we can relate these inverse square and cube fields to the second- and third-order terms in the binomial development of the relativistic mass formula (see the section on kinetic energy in my paper on one of Feynman’s more original renderings of Maxwell’s equations) but… Well… Probably best to start by seeing how Feynman got those field equations out of Maxwell’s equations. It is a bit buried in his development of the LiĂ©nard and Wiechert equations, which are written in terms of the scalar and vector potentials Ï and A instead of E and B vectors, but it should all work out.]

If the nuclear force is electromagnetic, then these ânuclear orbitalsâ should respect the Planck-Einstein relation. So then we can calculate frequencies and radii of orbitals now, right? The use of natural units and imaginary units to represent rotations/orthogonality in space might make calculations easy (B = iE). Indeed, with the 2019 revision of SI units, I might need to re-evaluate the usefulness of natural units (I always stayed away from it because it âhidesâ the physics in the math as it makes abstraction of their physical dimension).

Hey ! Perhaps we can model everything with quaternions, using imaginary units (i and j) to represent rotations in 3D space so as to ensure consistent application of the appropriate right-hand rules always (special relativity gets added to the mix so we probably need to relate the (ds)2 = (dx)2 + (dy)2 + (dz)2 â (dct)2 to the modified Hamilton’s q = a + ib + jc â kd expression then). Using vector equations throughout and thinking of h as a vector when using the E = hf and h = pÎ» Planck-Einstein relation (something with a magnitude and a direction) should do the trick, right? [In case you wonder how we can write f as a vector: angular frequency is a vector too. The Planck-Einstein relation is valid for both linear as well as circular oscillations: see our paper on the interpretation of de Broglie wavelength.]

Oh – and while special relativity is there because of Maxwell’s equation, gravity (general relativity) should be left out of the picture. Why? Because we would like to explain gravity as a residual very-far-field force. And trying to integrate gravity inevitable leads one to analyze particles as ‘black holes.’ Not nice, philosophically speaking. In fact, any 1/rn field inevitably leads one to think of some kind of black hole at the center, which is why thinking of fundamental particles in terms ring currents and dipole moments makes so much sense! [We need nothingness and infinity as mathematical concepts (limits, really) but they cannot possibly represent anything real, right?]

The consistent use of the Planck-Einstein law to model these nuclear electron orbitals should probably involve multiples of h to explain their size and energy: E = nhf rather than E = hf. For example, when calculating the radius of an orbital of a pointlike charge with the energy of a proton, one gets a radius that is only 1/4 of the proton radius (0.21 fm instead of 0.82 fm, approximately). To make the radius fit that of a proton, one has to use the E = 4hf relation. Indeed, for the time being, we should probably continue to reject the idea of using fractions of h to model deep electron orbitals. I also think we should avoid superluminal velocity concepts.

[…]

This post sounds like madness? Yes. And then, no! To be honest, I think of it as one of the better Aha! moments in my life. đ

Brussels, 30 December 2020

Post scriptum (1 January 2021): Lots of stuff coming together here ! 2021 will definitely see the Grand Unified Theory of Classical Physics becoming somewhat more real. It looks like Mills is going to make a major addition/correction to his electron orbital modeling work and, hopefully, manage to publish the gist of it in the eminent mainstream Nature journal. That makes a lot of sense: to move from an atom to an analysis of nuclei or complex three-particle systems, one should combine singlet and doublet energy states – if only to avoid reduce three-body problems to two-body problems. đ I still do not buy the fractional use of Planck’s quantum of action, though. Especially now that we got rid of the concept of a separate ‘nuclear’ charge (there is only one charge: the electric charge, and it comes in two ‘colors’): if Planck’s quantum of action is electromagnetic, then it comes in wholes or multiples. No fractions. Fractional powers of distance functions in field or potential formulas are OK, however. đ

## The complementarity of wave- and particle-like viewpoints on EM wave propagation

In 1995, W.E. Lamb Jr. wrote the following on the nature of the photon: âThere is no such thing as a photon. Only a comedy of errors and historical accidents led to its popularity among physicists and optical scientists. I admit that the word is short and convenient. Its use is also habit forming. Similarly, one might find it convenient to speak of the âaetherâ or âvacuumâ to stand for empty space, even if no such thing existed. There are very good substitute words for âphotonâ, (e.g., âradiationâ or âlightâ), and for âphotonicsâ (e.g., âopticsâ or âquantum opticsâ). Similar objections are possible to use of the word âphononâ, which dates from 1932. Objects like electrons, neutrinos of finite rest mass, or helium atoms can, under suitable conditions, be considered to be particles, since their theories then have viable non-relativistic and non-quantum limits.â[1]

The opinion of a Nobel Prize laureate carries some weight, of course, but we think the concept of a photon makes sense. As the electron moves from one (potential) energy state to another â from one atomic or molecular orbital to another â it builds an oscillating electromagnetic field which has an integrity of its own and, therefore, is not only wave-like but also particle-like.

We, therefore, dedicated the fifth chapter of our re-write of Feynman’s Lectures to a dual analysis of EM radiation (and, yes, this post is just an announcement of the paper so you are supposed to click the link to read it). It is, basically, an overview of a rather particular expression of Maxwellâs equations which Feynman uses to discuss the laws of radiation. I wonder how to â possibly â âtransformâ or âtransposeâ this framework so it might apply to deep electron orbitals and â possibly â proton-neutron oscillations.

[1] W.E. Lamb Jr., Anti-photon, in: Applied Physics B volume 60, pages 77â84 (1995).

## Signing off…

I have been exploring the weird wonderland of physics for over seven years now. At several occasions, I thought I should just stop. It was rewarding, but terribly exhausting at times as well! I am happy I did not give up, if only because I finally managed to come up with a more realist interpretation of the ‘mystery’ of matter-antimatter pair production/annihilation. So, yes, I think I can confidently state I finally understand physics the way I want to understand it. It was an extraordinary journey, and I am happy I could share it with many fellow searchers (300 posts and 300,000 hits on my first website now, 10,000+ downloads of papers (including the downloads from Phil Gibb’s site and academia.edu) and, better still, lots of interesting conversations.

One of these conversations was with a fine nuclear physicist, Andrew Meulenberg. We were in touch on the idea of a neutron (some kind of combination of a proton and a ‘nuclear’ electronâfollowing up on Rutherford’s original idea, basically). More importantly, we chatted about, perhaps, developing a model for the deuterium nucleus (deuteron)âthe hydrogen isotope which consists of a proton and a neutron. However, I feel I need to let go here, if only because I do not think I have the required mathematical skills for a venture like this. I feel somewhat guilty of letting him down. Hence, just in case someone out there feels he could contribute to this, I am copying my last email to him below. It sort of sums up my basic intuitions in terms of how one could possibly approach this.

Can it be done? Maybe. Maybe not. All I know is that not many have been trying since Bohrâs young wolves hijacked scientific discourse after the 1927 Solvay Conference and elevated a mathematical technique â perturbation theory â to the scientific dogma which is now referred to as quantum field theory.

So, yes, now I am really signing off. Thanks for reading me, now or in the pastâI wrote my first post here about seven years ago! I hope it was not only useful but enjoyable as well. OhâAnd please check out my YouTube channel on Physics ! đ

From: Jean Louis Van Belle
Sent: 14 November 2020 17:59
To: Andrew Meulenberg
Subject: Time and energy…

These things are hardâŠ You are definitely much smarter with these things than I can aspire tooâŠ But I do have ideas. We must analyze the proton in terms of a collection of infinitesimally small charges â just like Feynmanâs failed assembly of the electron (https://www.feynmanlectures.caltech.edu/II_28.html#Ch28-S3): it must be possible to do this and it will give us the equivalent of electromagnetic mass for the strong force. The assembly of the proton out of infinitesimally small charge bits will work because the proton is, effectively, massive. Not like an electron which effectively appears as a âcloudâ of charge and, therefore, has several radii and, yes, can pass through the nucleus and also âenvelopesâ a proton when forming a neutron with it.

I cannot offer much in terms of analytical skills here. All of quantum physics â the new model of a hydrogen atom â grew out of the intuition of a young genius (Louis de Broglie) and a seasoned mathematical physicist (Erwin Schroedinger) finding a mathematical equation for it. That model is valid still â we just need to add spin from the outset (cf. the plus/minus sign of the imaginary unit) and acknowledge the indeterminacy in it is just statistical, but these are minor things.

I have not looked at your analysis of a neutron as an (hyper-)excited state of the hydrogen atom yet but it must be correct: what else can it be? It is what Rutherford said it should be when he first hypothesized the existence of a neutron.

I do not know how much time I want to devote to this (to be honest, I am totally sick of academic physics) but â whatever time I have â I want to contribute to an intuitive, realist and mathematically correct model of the deuteron nucleus.

JL

## Quantum field theory and pair creation/annihilation

The creation and annihilation of matter-antimatter pairs is usually taken as proof that, somehow, fields can condense into matter-particles or, conversely, that matter-particles can somehow turn into light-particles (photons), which are nothing but traveling electromagnetic fields. However, pair creation always requires the presence of another particle and one may, therefore, legitimately wonder whether the electron and positron were not already present, somehow.

Carl Andersonâs original discovery of the positron involved cosmic rays hitting atmospheric molecules, a process which involves the creation of unstable particles including pions. Cosmic rays themselves are, unlike what the name suggests, no rays â not like gamma rays, at least â but highly energetic protons and atomic nuclei. Hence, they consist of matter-particles, not of photons. The creation of electron-positron pairs from cosmic rays also involves pions as intermediate particles:

1. The Ï+ and Ï particles have net positive and negative charge of 1 e+ and 1 e respectively. According to mainstream theory, this is because they combine a u and d quark but â abandoning the quark hypothesis[1] â we may want to think their charge could be explained, perhaps, by the presence of an electron![2]

2. The neutral pion, in turn, might, perhaps, consist of an electron and a positron, which should annihilate but take some time to do so!

Neutral pions have a much shorter lifetime â in the order of 10-18 s only â than Ï+ and Ï particles, whose lifetime is a much more respectable 2.6 times 10-8 s. Something you can effectively measure, in order words.[3] In short, despite similar energies, neutral pions do not seem to have a lot in common with Ï+ and Ï particles. Even the energy difference is quite substantial when measured in terms of the electron mass: the neutral pion has an energy of about 135 MeV, while Ï+ and Ï particles have an energy of almost 140 MeV. To be precise, the difference is about 4.6 MeV. That is quite a lot: the electron rest energy is 0.511 MeV only.[4] So it is not stupid to think that Ï+ and Ï particles might carry an extra positron or electron, somehow. In our not-so-humble view, this is as legitimate as thinking â like Rutherford did â that a neutron should, somehow, combine a proton and an electron.[5]

The whole analysis â both in the QED as well as in the QCD sector of quantum physics â would radically alter when thinking of neutral particles â such as neutrons and Ï0 particles â not as consisting of quarks but of protons/antiprotons and/or electrons/positrons cancelling each otherâs charges out. We have not seen much â if anything â which convinces us this cannot be correct. We, therefore, believe a more realist interpretation of quantum physics should be possible for high-energy phenomena as well. With a more realist theory, we mean one that does not involve quantum field and/or renormalization theory.

Such new theory would not be contradictory to the principle that, in Nature, the number of charged particles is no longer conserved, but that total (net) charge is actually being conserved, always. Hence, charged particles could appear and disappear, but they would be part of neutral particles. All particles in such processes are very short-lived anyway, so what is a particle here? We should probably think of these things as an unstable combination of various bits and bobs, isnât it? đ

So, yes, we did a paper on this. And we like it. Have a look: it’s on ResearchGate, academia.edu, and – as usual – Phil Gibb’s site (which has all of our papers, including our very early ones, which you might want to take with a pinch of salt). đ

[1] You may be so familiar with quarks that you do not want to question this hypothesis anymore. If so, let me ask you: where do the quarks go when a ÏÂ± particle disintegrates into a muon-eÂ±?

[2] They disintegrate into muons (muon-electrons or muon-positrons), which themselves then decay into an electron or a positron respectively.

[3] The point estimate of the lifetime of a neutral pion of the Particle Data Group (PDG) is about 8.5 times 10-17 s. Such short lifetimes cannot measured in a classical sense: such particles are usually referred to as resonances (rather than particles) and the lifetime is calculated from a so-called resonance width. We may discuss this approach in more detail later.

[4] Of course, it is much smaller when compared to the proton (rest) energy, which it is about 938 MeV.

[5] See our short history of quantum-mechanical ideas or our paper on protons and neutrons.