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 – totally not done, of course ! – utter disregard for physical dimensions and the physical geometry of fields in 3D space or – taking retardation effects into account – 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 ‘electron blanket’ 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 – I have very little math, actually – with modeling molecular orbitals. So I should, perhaps, contact a friend from a few years ago now – living in Hawaii and pursuing more spiritual matters too – who did just that long time ago: orbitals using Schroedinger’s wave equation (I think Schroedinger’s equation is relativistically correct – just a misinterpretation of the concept of ‘effective mass’ 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 Liénard and Wiechert equations, which are written in terms of the scalar and vector potentials φ and A instead of E and B vectors, but it should all work out.]

If the nuclear force is electromagnetic, then these ‘nuclear orbitals’ 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 ‘hides’ 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 – (dct)2 to the modified Hamilton’s q = a + ib + jckd expression then). Using vector equations throughout and thinking of h as a vector when using the E = hf and h = pλ 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. 🙂

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. 🙂 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. 🙂

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: “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 “aether” or “vacuum” to stand for empty space, even if no such thing existed. There are very good substitute words for “photon”, (e.g., “radiation” or “light”), and for “photonics” (e.g., “optics” or “quantum optics”). Similar objections are possible to use of the word “phonon”, 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.”[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 – from one atomic or molecular orbital to another – 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 Maxwell’s equations which Feynman uses to discuss the laws of radiation. I wonder how to – possibly – ‘transform’ or ‘transpose’ this framework so it might apply to deep electron orbitals and – possibly – proton-neutron oscillations.


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

Cold fusion

I thought I should stop worrying about physics, but then I got an impromptu invitation to a symposium on low-energy nuclear reactions (LENR) and I got all excited about it. The field of LENR was, and still is, often referred to as cold fusion which, after initial enthusiasm, got a not-so-good name because of… More than one reason, really. Read the Wikipedia article on it, or just google and read some other blog articles (e.g. Scientific American’s guest blog on the topic is a pretty good one, I think).

The presentations were very good (especially those on the experimental results and the recent involvement of some very respectable institutions in addition to the usual suspects and, sadly, some fly-by-night operators too), and the follow-on conversation with one of the co-organizers convinced me that the researchers are serious, open-minded and – while not quite being able to provide all of the answers we are all seeking – very ready to discuss them seriously. Most, if not all, experiments involve transmutions of nuclei triggered by low-energy inputs such as a low-energy radiation (irradiation and transmutation of palladium by, say, a now-household 5 mW laser beam is just one of the examples). One experiment even triggered a current just by adding plain heat which, as you know, is nothing but very low-energy (infrared) radiation, although I must admit this was one I would like to see replicated en masse before believing it to be real (the equipment was small and simple, and so the experimenters could have shared it easily with other labs).

When looking at these experiments, the comparison that comes to mind is that of an opera singer shattering crystal with his or her voice: some frequency in the sound causes the material to resonate at, yes, its resonant frequency (most probably an enormous but integer multiple of the sound frequency), and then the energy builds up – like when you give a child on a swing an extra push every time when you should – as the amplitude becomes larger and larger – till the breaking point is reached. Another comparison is the failing of a suspension bridge when external vibrations (think of the rather proverbial soldier regiment here) cause similar resonance phenomena. So, yes, it is not unreasonable to believe that one could be able to induce neutron decay and, thereby, release the binding energy between the proton and the electron in the process by some low-energy stimulation provided the frequencies are harmonic.

The problem with the comparison – and for the LENR idea to be truly useful – is this: one cannot see any net production of energy here. The strain or stress that builds up in the crystal glass is a strain induced by the energy in the sound wave (which is why the singing demos usually include amplifiers to attain the required power/amplitude ratio, i.e. the required decibels). In addition, the breaking of crystal or a suspension bridge typically involves a weaker link somewhere, or some directional aspect (so that would be the equivalent of an impurity in a crystal structure, I guess), but that is a minor point, and a point that is probably easier to tackle than the question on the energy equation.

LENR research has probably advanced far enough now (the first series of experiments started in 1989) to slowly start focusing on the whole chain of these successful experiments: what is the equivalent, in these low-energy reactions, of the nuclear fuel in high-energy fission or fusion experiments? And, if it can be clearly identified, the researchers need to show that the energy that goes into the production of this fuel is much less than the energy you get out of it by burning it (and, of course, with ‘burning’ I mean the decay reaction here). [In case you have heard about Randell Mills’ hydrino experiments, he should show the emission spectrum of these hydrinos. Otherwise, one might think he is literally burning hydrogen. Attracting venture capital and providing scientific proof are not mutually exclusive, are they? In the meanwhile, I hope that what he is showing is real, in the way all LENR researchers hope it is real.]

LENR research may also usefully focus on getting the fundamental theory right. The observed anomalous heat and/or transmutation reactions cannot be explained by mainstream quantum physics (I am talking QCD here, so that’s QFT, basically). That should not surprise us: one does not need quarks or gluons to explain high-energy nuclear processes such as fission or fusion, either! My theory is, of course, typically simplistically simple: the energy that is being unlocked is just the binding energy between the nuclear electron and the protons, in the neutron itself or in a composite nucleus, the simplest of which is the deuteron nucleus. I talk about that in my paper on matter-antimatter pair creation/annihilation as a nuclear process but you do not need to be an adept of classical or realist interpretations of quantum mechanics to understand this point. To quote a motivational writer here: it is OK for things to be easy. 🙂

So LENR theorists just need to accept they are not mainstream – yet, that is – and come out with a more clearly articulated theory on why their stuff works the way it does. For some reason I do not quite understand, they come across as somewhat hesitant to do so. Fears of being frozen out even more by the mainstream? Come on guys ! You are coming out of the cold anyway, so why not be bold and go all the way? It is a time of opportunities now, and the field of LENR is one of them, both theoretically as well as practically speaking. I honestly think it is one of those rare moments in the history of physics where experimental research may be well ahead of theoretical physics, so they should feel like proud trailblazers!

Personally, I do not think it will replace big classical nuclear energy plants anytime soon but, in a not-so-distant future, it might yield much very useful small devices: lower energy, and, therefore, lower risk also. I also look forward to LENR research dealing the fatal blow to standard theory by confirming we do not need perturbation and renormalization theories to explain reality. 🙂

Post scriptum: If low-energy nuclear reactions are real, mainstream (astro)physicists will also have to rework their stories on cosmogenesis and the (future) evolution of the Universe. The standard story may well be summed up in the brief commentary of the HyperPhysics entry on the deuteron nucleus:

The stability of the deuteron is an important part of the story of the universe. In the Big Bang model it is presumed that in early stages there were equal numbers of neutrons and protons since the available energies were much higher than the 0.78 MeV required to convert a proton and electron to a neutron. When the temperature dropped to the point where neutrons could no longer be produced from protons, the decay of free neutrons began to diminish their population. Those which combined with protons to form deuterons were protected from further decay. This is fortunate for us because if all the neutrons had decayed, there would be no universe as we know it, and we wouldn’t be here!

If low-energy nuclear reactions are real – and I think they are – then the standard story about the Big Bang is obviously bogus too. I am not necessarily doubting the reality of the Big Bang itself (the ongoing expansion of the Universe is a scientific fact so, yes, the Universe must have been much smaller and (much) more energy-dense long time ago), but the standard calculations on proton-neutron reactions taking place, or not, at cut-off temperatures/energies above/below 0.78 MeV do not make sense anymore. One should, perhaps, think more in terms of how matter-antimatter ratios might or might not have evolved (and, of course, one should keep an eye on the electron-proton ratio, but that should work itself out because of charge conservation) to correctly calculate the early evolution of the Universe, rather than focusing so much on proton-neutron ratios.

Why do I say that? Because neutrons do appear to consist of a proton and an electron – rather than of quarks and gluons – and they continue to decay and then recombine again, so these proton-neutron reactions must not be thoughts of as some historic (discontinuous) process.

[…] Hmm… The more I look at the standard stories, the more holes I see… This one, however, is very serious. If LENR and/or cold fusion is real, then it will also revolutionize the theories on cosmogenesis (the evolution of the Universe). I instinctively like that, of course, because – just like quantization – I had the impression the discontinuities are there, but not quite in the way mainstream physicists – thinking more in terms of quarks and gluons rather than in terms of stuff that we can actually measure – portray the whole show.