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** = *i***E**). 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 (d*s*)^{2} = (d*x*)^{2} + (d*y*)^{2} + (d*z*)^{2} – (dct)^{2} to the modified Hamilton’s **q** = **a** + *i***b** + *j***c** – *k***d** expression then). Using vector equations throughout and thinking of **h** as a vector when using the E = **hf** and **h** = **p**λ 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/*r*^{n} 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 = n**hf** 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 = 4**hf** 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. 🙂