After a long break (more than six months), I have started to engage again in a few conversations. I also looked at the 29 papers on my ResearchGate page, and I realize some of them would need to be re-written or re-packaged so as to ensure a good flow. Also, some of the approaches were more productive than others (some did not lead anywhere at all, actually), and I would need to point those out. I have been thinking about how to approach this, and I think I am going to produce an annotated version of these papers, with comments and corrections as mark-ups. Re-writing or re-structuring all of them would require to much work.

The mark-up of those papers is probably going to be based on some ‘quick-fire’ remarks (a succession of thoughts triggered by one and the same question) which come out of the conversation below, so I thank these thinkers for having kept me in the loop of a discussion I had followed but not reacted to. It is an interesting one – on the question of ‘deep electron orbitals’ (read: the orbitals of negative charge inside of a nucleus exist and, if so, how one can model them. If one could solve that question, one would have a theoretical basis for what is referred to as low-energy nuclear reactions. That was known formerly as cold fusion, but that got a bit of a bad name because of a number of crooks spoiling the field, unfortunately.

PS: I leave the family names of my correspondents in the exchange below out so they cannot be bothered. One of them, Jerry, is a former American researcher at SLAC. Andrew – the key researcher on DEPs – is a Canadian astrophysicist, and the third one – Jean-Luc – is a rather prominent French scientist in LENR.]

**From:** Jean Louis Van Belle**Sent:** 18 November 2021 22:51**Subject:** Staying engaged (5)

Oh – and needless to say, Dirac’s basic equation can, of course, be expanded using the binomial expansion – just like the relativistic energy-momentum relation, and then one can ‘cut off’ the third-, fourth-, etc-order terms and keep the first and second-order terms only. Perhaps it is equations like that kept you puzzled (I should check your original emails). In any case, this way of going about energy equations for elementary particles is a bit the same as those used in perturbation equations in which – as Dirac complained – one randomly selects terms that seem to make sense and discard others because they do not seem to make sense. Of course, Dirac criticized perturbation theory much more severely than this – and rightly so. 😊 😊 JL

**From:** Jean Louis Van Belle**Sent:** 18 November 2021 22:10**Subject:** Staying engaged (4)

Also – I remember you had some questions on an energy equation – not sure which one – but so I found Dirac’s basic equation (based on which he derives the ‘Dirac’ wave equation) is essentially useless because it incorporates *linear *momentum only. As such, it repeats de Broglie’s mistake, and that is to interpret the ‘de Broglie’ wavelength as something linear. It is not: frequencies, wavelengths are orbital frequencies and orbital circumferences. So anything you would want to do with energy equations that are based on that, lead nowhere – in my not-so-humble opinion, of course. To illustrate the point, compare the relativistic energy-momentum relation and Dirac’s basic equation in his Nobel Prize lecture (I hope the subscripts/superscripts get through your email system so they display correctly):

m_{0}^{2}*c*^{4} = E^{2} – p^{2}*c*^{2} (see, for example, Feynman-I-16, formula 16-3)

Divide the above by *c*^{2} and re-arrange and you get Dirac’s equation: W^{2}/*c*^{2} – p_{r}^{2} – m^{2}/*c*^{2} = 0 (see his 1933 Nobel Prize Lecture)

So that cannot lead anywhere. It’s why I totally discard Dirac’s wave equation (it has never yielded any practical explanation of a real-life phenomenon anyway, if I am not mistaken).

Cheers – JL

**From:** Jean Louis Van Belle**Sent:** 18 November 2021 21:49**Subject:** Staying engaged (3)

Just on ‘retarded sources’ and ‘retarded fields’ – I have actually tried to think of the ‘force mechanism’ inside of an electron or a proton (what keeps the pointlike charge in this geometric orbit around a center of mass?). I thought long and hard about some kind of model in which we have the charge radiate out a sub-Planck field, and that its ‘retarded effects’ might arrive ‘just in time’ to the other side of the orbital (or whatever other point on the orbital) so as to produce the desired ‘course correction’ might explain it. I discarded it completely: I am now just happy that we have ‘reduced’ the mystery to this ‘Planck-scale quantum-mechanical oscillation’ (in 2D or 3D orbitals) without the need for an ‘aether’, or quantized spacetime, or ‘virtual particles’ actually ‘holding the thing together’.

Also, a description in terms of four-vectors (scalar and vector potential) does not immediately call for ‘retarded time’ variables and all that, so that is another reason why I think one should somehow make the jump from E-B fields to scalar and vector potential, even if the math is hard to visualize. If we want to ‘visualize’ things, Feynman’s discussion of the ‘energy’ and ‘momentum’ flow in https://www.feynmanlectures.caltech.edu/II_27.html might make sense, because I think analyses in terms of Poynting vectors are relativistically current, aren’t they? It is just an intuitive idea…

Cheers – JL

**From:** Jean Louis Van Belle**Sent:** 18 November 2021 21:28**Subject:** Staying engaged (2)

But so – in the shorter run – say, the next three-six months, I want to sort out those papers on ResearchGate. The one on the de Broglie’s matter-wave (interpreting the de Broglie wavelength as the circumference of a loop rather than as a linear wavelength) is the one that gets most downloads, and rightly so. The rest is a bit of a mess – mixing all kinds of things I tried, some of which worked, but other things did not. So I want to ‘clean’ that up… 😊 JL

**From:** Jean Louis Van Belle**Sent:** 18 November 2021 21:21**Subject:** Staying engaged…

Please do include me in the exchanges, Andrew – even if I do not react, I do read them because I do need some temptation and distraction. As mentioned, I wanted to focus on building a credible n = p + e model (for free neutrons but probably more focused on a Schrodinger-like D = p + e + p Platzwechsel model, because the deuteron nucleus is stable). But so I will not do that the way I studied the zbw model of the electron and proton (I believe that is sound now) – so that’s with not putting in enough sleep. I want to do it slowly now. I find a lot of satisfaction in the fact that I think there is no need for complicated quantum field theories (fields are quantized, but in a rather obvious way: field oscillations – just like matter-particles – pack Planck’s quantum of (physical) action which – depending on whether you freeze time or positions as a variable, expresses itself as a discrete amount of energy or, alternatively, as a discrete amount of momentum), nor is there any need for this ‘ontologization’ of virtual field interactions (sub-Planck scale) – the quark-gluon nonsense.

Also, it makes sense to distinguish between an electromagnetic and a ‘strong’ or ‘nuclear’ force: the electron and proton have different form factors (2D versus 3D oscillations, but that is a bit of a non-relativistic shorthand for what might be the case) but, in addition, there is clearly a much stronger force at play within the proton – whose strength is the same kind of ‘scale’ as the force that gives the muon-electron its rather enormous mass. So that is my ‘belief’ and the ‘heuristic’ models I build (a bit of ‘numerology’ according to Dr Pohl’s rather off-hand remarks) support it sufficiently for me to make me feel at peace about all these ‘Big Questions’.

I am also happy I figured out these inconsistencies around 720-degree symmetries (just the result of a non-rigorous application of Occam’s Razor: if you use all possible ‘signs’ in the wavefunction, then the wavefunction may represent matter as well as anti-matter particles, and these 720-degree weirdness dissolves). Finally, the kind of ‘renewed’ S-matrix programme for analyzing unstable particles (adding a transient factor to wavefunctions) makes sense to me, but even the easiest set of equations look impossible to solve – so I may want to dig into the math of that if I feel like having endless amounts of time and energy (which I do not – but, after this cancer surgery, I know I will only die on some ‘moral’ or ‘mental’ battlefield twenty or thirty years from now – so I am optimistic).

So, in short, the DEP question does intrigue me – and you should keep me posted, but I will only look at it to see if it can help me on that deuteron model. 😊 That is the only ‘deep electron orbital’ I actually believe in. Sorry for the latter note.

Cheers – JL

**From:** Andrew**Sent:** 16 November 2021 19:05**To:** Jean-Luc; Jerry; Jean Louis**Subject:** Re: retarded potential?

Dear Jean-Louis,

Congratulations on your new position. I understand your present limitations, despite your incredible ability to be productive. They must be even worse than those imposed by my young kids and my age. Do you wish for us to not include you in our exchanges on our topic? Even with no expectation of your contributing at this point, such emails might be an unwanted temptation and distraction.

Dear Jean-Luc,

Thank you for the Wiki-Links. They are useful. I agree that the 4-vector potential should be considered. Since I am now considering the nuclear potentials as well as the deep orbits, it makes sense to consider the nuclear vector potentials to have an origin in the relativistic Coulomb potentials. I am facing this in my attempts to calculate the deep orbits from contributions to the potential energies that have a vector component, which non-rel Coulomb potentials do not have.

For examples: do we include the losses in Vcb (e.g., from the binding energy BE) when we make the relativistic correction to the potential; or, how do we relativistically treat pseudo potentials such as that of centrifugal force? We know that for equilibrium, the average forces must cancel. However, I’m not sure that it is possible to write out a proper expression for “A” to fit such cases.

Best regards to all,

Andrew

_ _ _

On Fri, Nov 12, 2021 at 1:42 PM Jean-Luc wrote:

Dear all,

I totally agree with the sentence of Jean-Louis, which I put in bold in his message, about *vector potential* and *scalar potential,* combined into a *4-vectorpotential A*

**,**for representing EM field in covariant formulation. So EM representation by 4-vector

*A*has been very developed, as wished by JL,

in the framework of QED.

We can note the simplicity of Lorentz gauge written by using

*A.*

https://en.wikipedia.org/wiki/Lorenz_gauge_condition

We can see the reality of vector potential

https://en.wikipedia.org/wiki/Lorenz_gauge_condition

in the Aharonov-Bohm effect:

*https://en.wikipedia.org/wiki/Aharonov-Bohm_effect.*

In fact, we can see that vector potential contains more information than E,B fields.

Best regards

Jean-Luc

Le 12/11/2021 à 05:43, Jean Louis Van Belle a écrit :

Hi All – I’ve been absent in the discussion, and will remain absent for a while. I’ve been juggling a lot of work – my regular job at the Ministry of Interior (I got an internal promotion/transfer, and am working now on police and security sector reform) plus consultancies on upcoming projects in Nepal. In addition, I am still recovering from my surgery – I got a bad flue (not C19, fortunately) and it set back my auto-immune system, I feel. I have a bit of a holiday break now (combining the public holidays of 11 and 15 November in Belgium with some days off to bridge so I have a rather nice super-long weekend – three in one, so to speak).

As for this thread, I feel like it is not ‘phrasing’ the discussion in the right ‘language’. Thinking of E-fields and retarded potential is thinking in terms of 3D potential, separating out space and time variables without using the ‘power’ of four-vectors (four-vector potential, and four-vector space-time). It is important to remind ourselves that we are measuring fields in continuous space and time (but, again, this is relativistic space-time – so us visualizing a 3D potential at some point in space is what it is: we visualize something because our mind needs that – wants that). The fields are discrete, however: a field oscillation packs one unit of Planck – always – and Planck’s quantum of action combines energy and momentum: we should not think of energy and momentum as truly ‘separate’ (discrete) variables, just like we should not think of space and time as truly ‘separate’ (continuous) variables.

I do not quite know what I want to say here – or how I should further work it out. I am going to re-read my papers. I think I should further develop the last one (https://www.researchgate.net/publication/351097421_The_concepts_of_charge_elementary_ring_currents_potential_potential_energy_and_field_oscillations), in which I write that the **vector potential is more real than the electric field and the scalar potential should be further developed, and probably it is the combined scalar and vector potential that are the ’real’ things.** Not the electric and magnetic field. Hence, illustrations like below – in terms of discs and cones in space – do probably not go all that far in terms of ‘understanding’ what it is going on… It’s just an intuition…

Cheers – JL

**From:** Andrew**Sent:** 23 September 2021 17:17**To:** Jean-Luc; Jerry; Jean Louis**Subject:** retarded potential?

Dear Jean-Luc,

Becasue of the claim that gluons are tubal, I have been looking at the disk-shaped **E**-field lines of the highly-relativistic electron and comparing it to the retarded potential, which, based on timing, would seem to give a cone rather than a disk (see figure). This makes a difference when we consider a deep-orbiting electron. It even impacts selection of the model for impact of an electron when considering diffraction and interference.

Even if the field appears to be spreading out as a cone, the direction of the field lines are that of a disk from the retarded source. However, how does it interact with the radial field of a stationary charge?

Do you have any thoughts on the matter.

Best regards,

Andrew

_ _ _

On Thu, Sep 23, 2021 at 5:05 AM Jean-Luc wrote:

Dear Andrew, Thank you for the references. Best regards, Jean-Luc

Le 18/09/2021 à 17:32, Andrew a écrit :

> This might have useful thoughts concerning the question of radiation

> decay to/from EDOs.

>

> Quantum Optics Electrons see the quantum nature of light

> Ian S. Osborne

> We know that light is both a wave and a particle, and this duality

> arises from the classical and quantum nature of electromagnetic

> excitations. Dahan et al. observed that all experiments to date in

> which light interacts with free electrons have been described with

> light considered as a wave (see the Perspective by Carbone). The

> authors present experimental evidence revealing the quantum nature of

> the interaction between photons and free electrons. They combine an

> ultrafast transmission electron microscope with a silicon-photonic

> nanostructure that confines and strengthens the interaction between

> the light and the electrons. The “quantum” statistics of the photons

> are imprints onto the propagating electrons and are seen directly in

> their energy spectrum.

> Science, abj7128, this issue p. 1324; see also abl6366, p. 1309