Pair creation and annihilation

I had been wanting to update my paper on matter-antimatter pair creation and annihilation for a long time, and I finally did it: here is the new version of it. It was one of my early papers on ResearchGate and, somewhat surprising, it got quite a few downloads (all is relative: I am happy with a few thousand). I actually did not know why, but now I understand: it does take down the last defenses of QCD- and QFT-theorists. As such, I now think this paper is at least as groundbreaking as my paper on de Broglie’s matter-wave (which gets the most reads), or my paper on the proton radius (which gets the most recommendations).

My paper on de Broglie’s matter-wave is important because it explains why and how de Broglie’s bright insight (matter having some frequency and wavelength) was correct, but got the wrong interpretation: the frequencies and wavelengths are orbital frequencies, and the wavelengths are are not to be interpreted as linear distances (not like wavelengths of light) but the quantum-mechanical equivalent of the circumferences of orbital radii. The paper also shows why spin (in this or the opposite direction) should be incorporated into any analysis straight from the start: you cannot just ignore spin and plug it in back later. The paper on the proton radius shows how that works to yield short and concise explanations of the measurable properties of elementary particles (the electron and the proton). The two combined provide the framework: an analysis of matter in terms of pointlike particles does not get us anywhere. We must think of matter as charge in motion, and we must analyze the two- or three-dimensional structure of these oscillations, and use it to also explain interactions between matter-particles (elementary or composite) and light-particles (photons and neutrinos, basically). I have explained these mass-without-mass models too many times now, so I will not dwell on it.

So, how that paper on matter-antimatter pair creation and annihilation fit in? The revision resulted in a rather long and verbose thing, so I will refer you to it and just summarize it very briefly. Let me start by copying the abstract: “The phenomenon of matter-antimatter pair creation and annihilation is usually taken as confirmation that, somehow, fields can condense into matter-particles or, conversely, that matter-particles can somehow turn into lightlike particles (photons and/or neutrinos, which are nothing but traveling fields: electromagnetic or, in the case of the neutrino, some strong field, perhaps). However, pair creation usually involves the presence of a nucleus or other charged particles (such as electrons in experiment #E144). We, therefore, wonder whether pair creation and annihilation cannot be analyzed as part of some nuclear process. To be precise, we argue that the usual nuclear reactions involving protons and neutrons can effectively account for the processes of pair creation and annihilation. We therefore argue that the need to invoke some quantum field theory (QFT) to explain these high-energy processes would need to be justified much better than it currently is.”

Needless to say, the last line above is a euphemism: we think our explanation is complete, and that QFT is plain useless. We wrote the following rather scathing appreciation of it in a footnote of the paper: “We think of Aitchison & Hey’s presentation of [matter-antimatter pair creation and annihilation] in their Gauge Theories in Particle Physics (2012) – or presentations (plural), we should say. It is considered to be an advanced but standard textbook on phenomena like this. However, one quickly finds oneself going through the index and scraping together various mathematical treatments – wondering what they explain, and also wondering how all of the unanswered questions or hypotheses (such as, for example, the particularities of flavor mixing, helicity, the Majorana hypothesis, etcetera) contribute to understanding the nature of the matter at hand. I consider it a typical example of how – paraphrasing Sabine Hossenfelder’s judgment on the state of advanced physics research – physicist do indeed tend to get lost in math.”

That says it all. Our thesis is that charge cannot just appear or disappear: it is not being created out of nothing (or out of fields, we should say). The observations (think of pion production and decay from cosmic rays here) and the results of the experiments (the mentioned #E144 experiment or other high-energy experiments) cannot be disputed, but the mainstream interpretation of what actually happens or might be happening in those chain reactions suffers from what, in daily life, we would refer to as ‘very sloppy accounting’. Let me quote or paraphrase a few more lines from my paper to highlight the problem, and to also introduce my interpretation of things which, as usual, are based on a more structural analysis of what matter actually is:

“Pair creation is most often observed in the presence of a nucleus. The role of the nucleus is usually reduced to that of a heavy mass only: it only appears in the explanation to absorb or provide some kinetic energy in the overall reaction. We instinctively feel the role of the nucleus must be far more important than what is usually suggested. To be specific, we suggest pair creation should (also) be analyzed as being part of a larger nuclear process involving neutron-proton interactions. […]”

“Charge does not get ‘lost’ or is ‘created’, but [can] switch its ‘spacetime’ or ‘force’ signature [when interacting with high-energy (anti)photons or (anti)neutrinos].”

“[The #E144 experiment or other high-energy experiments involving electrons] accounts for the result of the experiment in terms of mainstream QED analysis, and effectively thinks of the pair production being the result of the theoretical ‘Breit-Wheeler’ pair production process from photons only. However, this description of the experiment fails to properly account for the incoming beam of electrons. That, then, is the main weakness of the ‘explanation’: it is a bit like making abstraction of the presence of the nucleus in the pair creation processes that take place near them (which, as mentioned above, account for the bulk of those).”

We will say nothing more about it here because we want to keep our blog post(s) short: read the paper! 🙂 To wrap this up for you, the reader(s) of this post, we will only quote or paraphrase some more ontological or philosophical remarks in it:

“The three-layered structure of the electron (the classical, Compton and Bohr radii of the electron) suggest that charge may have some fractal structure and – moreover – that such fractal structure may be infinite. Why do we think so? If the fractal structure would not be infinite, we would have to acknowledge – logically – that some kind of hard core charge is at the center of the oscillations that make up these particles, and it would be very hard to explain how this can actually disappear.” [Note: This is a rather novel new subtlety in our realist interpretation of quantum physics, so you may want to think about it. Indeed, we were initially not very favorable to the idea of a fractal charge structure because such fractal structure is, perhaps, not entirely consistent with the idea of a Zitterbewegung charge with zero rest mass), we think much more favorably of the hypothesis now.]

“The concept of charge is and remains mysterious. However, in philosophical or ontological terms, I do not think of it as a mystery: at some point, we must, perhaps, accept that the essence of the world is charge, and that:

  • There is also an antiworld, and that;
  • It consists of an anticharge that we can fully define in terms of the signature of the force(s) that keep it together, and that;
  • The two worlds can, quite simply, not co-exist or – at least – not interact with each other without annihilating each other.

Such simple view of things must, of course, feed into cosmological theories: how, then, came these two worlds into being? We offered some suggestions on that in a rather simple paper on cosmology (our one and only paper on the topic), but it is not a terrain that we have explored (yet).”

So, I will end this post in pretty much the same way as the old Looney Tunes or Merrie Melodies cartoons used to end, and that’s by saying: “That’s all Folks.” 🙂

Enjoy life and do not worry too much. It is all under control and, if it is not, then that is OK too. 🙂


Dirac’s wave equation and particle models


I had not touched physics since April last year, as I was struggling with cancer, and finally went in for surgery. It solved the problem but physical and psychological recovery was slow, and so I was in no mood to work on mathematical and physical questions. Now I am going through my ResearchGate papers again. I start with those that get a fair amount of downloads and – I am very pleased to see that happen – those are the papers that deal with very fundamental questions, and lay out the core of an intuition that is more widely shared now: physicists are lost in contradictions and will not get out of this fuzzy situation until they solve them.

[Skeptical note here: I note that those physicists who bark loudest about the need for a scientific revolution are, unfortunately, often those who obscure things even more. For example, I quickly went through Hossenfelder’s Lost in Math (and I also emailed her to highlight all that zbw theory can bring) but she did not even bother to reply and, more in general, shows no signs of being willing to go back to the roots, which are the solutions that were presented during the early Solvay conferences but, because of some weird tweak of the history of science, and despite the warnings of intellectual giants such as H.A. Lorentz, Ehrenfest, or Einstein (and also Dirac or Bell in the latter half of their lifes), were discarded. I have come to the conclusion that modern-day scientists cannot be fashionable when admitting all mysteries have actually been solved long time ago.]

The key observation or contradiction is this: the formalism of modern quantum mechanics deals with all particles – stable or unstable – as point objects: they are supposed to have no internal structure. At the same time, a whole new range of what used to be thought of as intermediate mental constructs or temporary classifications – think of quarks here, or of the boson-fermion dichotomy – acquired ontological status. We lamented that in one of very first papers (titled: the difference between a theory, a calculation and an explanation), which has few formulas and is, therefore, a much easier read than the others.

Some of my posts on this blog here were far more scathing and, therefore, not suitable to write out in papers. See, for example, my Smoking Gun Physics post, in which I talk much more loudly (but also more unscientifically) about the ontologicalization of quarks and all these theoretical force-carrying particles that physicists have invented over the past 50 years or so.

My point of view is clear and unambiguous: photons and neutrinos (both of which can be observed and measured) will do. The rest (the analysis of decay and the chain of reactions after high-energy collisions, mainly) can be analyzed using scattering matrices and other classical techniques (on that, I did write a paper highlighting the proposals of more enlightened people than me, like Bombardelli, 2016, even if I think researchers like Bombardelli should push back to basics even more than they do). By the way, I should probably go much further in my photon and neutrino models, but time prevented me from doing so. In any case, I did update and put an older paper of mine online, with some added thoughts on recent experiments that seem to confirm neutrinos have some rest mass. That is only what is to be expected, I would think. Have a look at it.


This is a rather lengthy introduction to the topic I want to write about for my public here, which is people like you and me: (amateur) physicists who want to make sense of all that is out there. So I will make a small summary of an equation I was never interested in: Dirac’s wave equation. Why my lack of interest before, and my renewed interest now?

The reason is this: Feynman clearly never believed Dirac’s equation added anything to Schrödinger’s, because he does not even mention it in his rather Lectures which, I believe, are, today still, truly seminal even if they do not go into all of the stuff mainstream quantum physicists today believe to be true (which is, I repeat, all of the metaphysics around quarks and gluons and force-carrying bosons and all that). So I did not bother to dig into it.

However, when revising my paper on de Broglie’s matter-wave, I realized that I should have analyzed Dirac’s equation too, because I do analyze Schrödinger’s wave equation there (which makes sense), and also comment on the Klein-Gordon wave equation (which, just like Dirac’s, does not make much of an impression on me). Hence, I would say my renewed interest is only there because I wanted to tidy up a little corner in this kitchen of mine. 🙂

I will stop rambling now, and get on with it.

Dirac’s wave equation: concepts and issues

We should start by reminding ourselves what a wave equation actually is: it models how waves – sound waves, or electromagnetic waves, or – in this particular case – a ‘wavicle’ or wave-particle – propagate in space and in time. As such, it is often said they model the properties of the medium (think of properties such as elasticity, density, permittivity or permeability here) but, because we do no longer think of spacetime as an aether, quantum-mechanical wave equations are far more abstract.

I should insert a personal note here. I do have a personal opinion on the presumed reality of spacetime. It is not very solid, perhaps, because I oscillate between (1) Kant’s intuition, thinking that space and time are mental constructs only, which our mind uses to structure its impressions (we are talking science here, so I should say: our measurements) versus (2) the idea that the 2D or 3D oscillations of pointlike charges within, say, an electron, a proton or a muon-electron must involve some kind of elasticity of the ‘medium’ that we commonly refer to as spacetime (I’d say that is more in line with Wittgenstein’s philosophy of reality). I should look it up but I think I do talk about the elasticity of spacetime at one or two occasions in my papers that talk about internal forces in particles, or papers in which I dig deep into the potentials that may or may not drive these oscillations. I am not sure how far I go there. Probably too far. But if properties such as vacuum permittivity or permeability are generally accepted, then why not think of elasticity? However, I did try to remain very cautious when it comes to postulating properties of the so-called spacetime vacuum, as evidenced from what I write in one of the referenced papers above:

“Besides proving that the argument of the wavefunction is relativistically invariant, this [analysis of the argument of the wavefunction] also demonstrates the relativistic invariance of the Planck-Einstein relation when modelling elementary particles.[1] This is why we feel that the argument of the wavefunction (and the wavefunction itself) is more real – in a physical sense – than the various wave equations (Schrödinger, Dirac, or Klein-Gordon) for which it is some solution. In any case, a wave equation usually models the properties of the medium in which a wave propagates. We do not think the medium in which the matter-wave propagates is any different from the medium in which electromagnetic waves propagate. That medium is generally referred to as the vacuum and, whether or not you think of it as true nothingness or some medium, we think Maxwell’s equations – which establishes the speed of light as an absolute constant – model the properties of it sufficiently well! We, therefore, think superluminal phase velocities are not possible, which is why we think de Broglie’s conceptualization of a matter particle as a wavepacket – rather than one single wave – is erroneous.[2]

The basic idea is this: if the vacuum is true nothingness, then it cannot have any properties, right? 🙂 That is why I call the spacetime vacuum, as it is being modelled in modern physics, a so-called vacuum. 🙂

[…] I guess I am rambling again, and so I should get back to the matter at hand, and quite literally so, because we are effectively talking about real-life matter here. To be precise, we are talking about Dirac’s view of an electron moving in free space. Let me add the following clarification, just to make sure we understand exactly what we are talking about: free space is space without any potential in it: no electromagnetic, gravitational or other fields you might think of.

In reality, such free space does not exist: it is just one of those idealizations which we need to model reality. All of real-life space – the Universe we live in, in other words – has potential energy in it: electromagnetic and/or gravitational potential energy (no other potential energy has been convincingly demonstrated so far, so I will not add to the confusion by suggesting there might be more). Hence, there is no such thing as free space.

What am I saying here? I am just saying that it is not bad that we remind ourselves of the fact that Dirac’s construction is theoretical from the outset. To me, it feels like trying to present electromagnetism by making full abstraction of the magnetic side of the electromagnetic force. That is all that I am saying here. Nothing more, nothing less. No offense to the greatness of a mind like Dirac’s.

[…] I may have lost you as a reader just now, so let me try to get you back: Dirac’s wave equation. Right. Dirac develops it in two rather dense sections of his Principles of Quantum Mechanics, which I will not try to summarize here. I want to make it easy for the reader, so I will limit myself to an analysis of the very first principle(s) which Dirac develops in his Nobel Prize Lecture. It is this (relativistically correct) energy equation:

E2 = m02c4 + p2c2

This equation may look unfamiliar to you but, frankly, if you are familiar with the basics of relativity theory, it should not come across as weird or unfathomable. It is one of the many basic ways of expressing relativity theory, as evidenced from the fact that Richard Feynman introduces this equation as part of his very first volume of his Lectures on Physics, and in one of the more basic chapters of it: just click on the link and work yourself through it: you will see it is just another rendering of Einstein’s mass-equivalence relation (E = mc2).

The point is this: it is very easy now to understand Dirac’s basic energy equation: the one he uses to then go from variables to quantum-mechanical operators and all of the other mathematically correct hocus-pocus that result in his wave equation. Just substitute E = mc2 for W, and then divide all by c2:

So here you are. All the rest is the usual hocus-pocus: we substitute classical variables by operators, and then we let them operate on a wavefunction (wave equations may or may not describe the medium, but wavefunctions surely do describe real-life particles), and then we have a complicated differential equation to solve and – as we made abundantly clear in this and other papers (one that you may want to read is my brief history of quantum-mechanical ideas, because I had a lot of fun writing that one, and it is not technical at all) – when you do that, you will find non-sensical solutions, except for the one that Schrödinger pointed out: the Zitterbewegung electron, which we believe corresponds to the real-life electron.

I will wrap this up (although you will say I have not done my job yet) by quoting quotes and comments from my de Broglie paper:

Prof. H. Pleijel, then Chairman of the Nobel Committee for Physics of the Royal Swedish Academy of Sciences, dutifully notes this rather inconvenient property in the ceremonial speech for the 1933 Nobel Prize, which was awarded to Heisenberg for nothing less than “the creation of quantum mechanics[1]:

“Matter is formed or represented by a great number of this kind of waves which have somewhat different velocities of propagation and such phase that they combine at the point in question. Such a system of waves forms a crest which propagates itself with quite a different velocity from that of its component waves, this velocity being the so-called group velocity. Such a wave crest represents a material point which is thus either formed by it or connected with it, and is called a wave packet. […] As a result of this theory, one is forced to the conclusion to conceive of matter as not being durable, or that it can have definite extension in space. The waves, which form the matter, travel, in fact, with different velocity and must, therefore, sooner or later separate. Matter changes form and extent in space. The picture which has been created, of matter being composed of unchangeable particles, must be modified.”

This should sound very familiar to you. However, it is, obviously, not true: real-life particles – electrons or atoms traveling in space – do not dissipate. Matter may change form and extent in space a little bit – such as, for example, when we are forcing them through one or two slits[2] – but not fundamentally so![3]

We repeat again, in very plain language this time: Dirac’s wave equation is essentially useless, except for the fact that it actually models the electron itself. That is why only one of its solutions make sense, and that is the very trivial solution which Schrödinger pointed out: the Zitterbewegung electron, which we believe corresponds to the real-life electron. 🙂 It just goes through space and time like any ordinary particle would do, but its trajectory is not given by Dirac’s wave equation. In contrast, Schrödinger’s wave equation (with or without a potential being present: in free or non-free space, in other words) does the trick and – against mainstream theory – I dare say, after analysis of its origins, that it is relativistically correct. Its only drawback is that it does not incorporate the most essential property of an elementary particle: its spin. That is why it models electron pairs rather than individual electrons.

We can easily generalize to protons or other elementary or non-elementary particles. For a deeper discussion of Dirac’s wave equation (which is what you probably expected), I must refer, once again, to Annex II of my paper on the interpretation of de Broglie’s matter-wave: it is all there, really, and – glancing at it all once again – the math is actually quite basic. In any case, paraphrasing Euclid in his reply to King Ptolemy’s question, I would say that there is no royal road to quantum mechanics. One must go through its formalism and, far more important, its history of thought. 🙂

To conclude, I would like to return to one of the remarks I made in the introduction. What about the properties of the vacuum? I will remain cautious and, hence, not answer that question. I prefer to let you think about this rather primitive classification of what is relative and not, and how the equations in physics mix both of it. 🙂


[1] To be precise, Heisenberg got a postponed prize from 1932. Erwin Schrödinger and Paul A.M. Dirac jointly got the 1933 prize. Prof. Pleijel acknowledges all three in more or less equal terms in the introduction of his speech: “This year’s Nobel Prizes for Physics are dedicated to the new atomic physics. The prizes, which the Academy of Sciences has at its disposal, have namely been awarded to those men, Heisenberg, Schrödinger, and Dirac, who have created and developed the basic ideas of modern atomic physics.”

[2] The wave-particle duality of the ring current model should easily explain single-electron diffraction and interference (the electromagnetic oscillation which keeps the charge swirling would necessarily interfere with itself when being forced through one or two slits), but we have not had the time to engage in detailed research here.

[3] We will slightly nuance this statement later but we will not fundamentally alter it. We think of matter-particles as an electric charge in motion. Hence, as it acts on a charge, the nature of the centripetal force that keeps the particle together must be electromagnetic. Matter-particles, therefore, combine wave-particle duality. Of course, it makes a difference when this electromagnetic oscillation, and the electric charge, move through a slit or in free space. We will come back to this later. The point to note is: matter-particles do not dissipate. Feynman actually notes that at the very beginning of his Lectures on quantum mechanics, when describing the double-slit experiment for electrons: “Electrons always arrive in identical lumps.”

[1] The relativistic invariance of the Planck-Einstein relation emerges from other problems, of course. However, we see the added value of the model here in providing a geometric interpretation: the Planck-Einstein relation effectively models the integrity of a particle here.

[2] See our paper on matter-waves, amplitudes, and signals.

New horizons

Looking back and forward

I want to revive this blog. I have not written anything substantially new since a very long time (OK, all is relative: since one year only), except short posts pointing to a new paper when I put one online on my ResearchGate site. However, I have started to think my blog is still worthwhile. I effectively keep getting a few likes here and there (if only from a handful of some of the followers (only 186 people in total, which is not a whole lot), and the sheer size and history of this blog suggests it can be revived rather easily: when I worked rather intensively on it (second half of 2022 and first half of 2021, basically), the stats did see a significant surge according to the site’s statistical dashboard (below).

Of course, a lot (if not most) of this traffic is semi-automatic because it is driven by hash tags out there on rather arcane topics such as Maxwell-Boltzmann and Bose-Einstein versus Fermi-Dirac statistics (I cannot imagine the top posts that WordPress automatically lists on this site are really top posts), but I will think positively of this and, yes, try to present both simpler as well as more relevant material in the coming years. In short: I feel like going at it again.

The problem with writing blog posts is that the process is rather tedious when it comes to quickly inserting some mathematical formula or argument to make a point (which is what, inevitably, one has to do when writing about physics), but I guess that is also why the readers of this blog turn to a blog rather than to my ResearchGate papers: they do not necessarily want to dig into all of the formulas. Hence, I need to separate out the two. Not to separate the two audiences, because I do believe the two audiences are similar: both are searching for some kind of truth or explanation (as opposed to a calculation), right? I just need to work harder on using the blog to highlight essential points, and then point to the papers for the math behind it.

Before I try my hand at that, let me say a few things about the papers. These papers are and remain working papers: I have academic credentials, but not in this field (quantum physics), which is why I will probably never really break through mainstream academic thought on all of the topics I write about. I gave up on trying to publish in journals or get a book published by a publisher. I tried several scientific publishers but, despite of all the hard work involved in making sure you get copyright on illustrations, and inserting more bibliographic detail, it did not work out. I stick to Einstein’s style: few references, because I believe the logic should speak for itself and, hence, one should only use what is strictly necessary and relevant in this regard, so as to improve readability (I feel that I use too many footnotes in my papers already, so more bibliographic detail would further downgrade the flow of my papers).

Nevertheless, papers like the one on my interpretation on the de Broglie frequencies as orbital rather than linear frequencies get high RI (research interest) scores on that RG site: the score of that particular paper, for example, is higher than 96% of all research items published in 2020). The RI scores of my rather critical papers on the formalism of quantum math and on the boundaries between Maxwell’s equations and the world of the smallest of small field oscillations (both of which I revised recently) are equally impressive in my, yes, not-so-humble (not anymore) view (the RI scores of these two papers are higher than 90% of all research items published in 2020). More relevant, of course, is the CV of the people who download them, most of which have that one PhD (in physics) which I am lacking (I got on ResearchGate because I could demonstrate I had published scientific papers in other fields in a far-gone past – mainly economics, as I once was an assistant professor working on a PhD in econometrics, which I did not finish, as a result of which I only have an old Doctor in Science (Drs) title, which is a rather particular title that is no longer valid).

In fact, I sometimes think I might get censured on RG for that one day, but I do not think so: my overall RI score in the field of quantum physics is now higher than 70% of researchers in the same field, despite me publishing these working papers on RG only since 2020. The quick rise and interest is evidenced by the fact that my overall RG score remains stubbornly higher than 99% of ResearchGate members who first published in 2020. Again, this does not prove much, perhaps, but it should convince both you as well as myself that I am not some kind of Cosmic Stan, although I did have my bad moments while pushing myself very hard on the very questions that drove geniuses like Ehrenfest into depression or, in his particular case, suicide.

Sure, I did have my bad moments too, as evidenced in this 2020 blog post at the occasion of Freeman Dyson’s demise. However, I will keep it there, if only because it mentions Oliver Consa, whose instinct (something is rotten in the state of modern physics) I share, but he was (and probably still is not) in a mood to collaborate on anything. If you read this blog, I recommend you read his article, which suggests the mysteries of quantum physics are there and are being perpetuated because of a weird mix of post-war secrecy around atomic physics and, much more probable now (the second world war is only a distant memory now), manipulation by a select group of academics aimed at keeping research money flowing.

Ten or twenty years ago, I would have dismissed such thinking out of hand, but I have myself been subject to rather weird attempts to take down this very blog of mine. I was surprised because I am quite vocal on social media, such as LinkedIn or Twitter, and I also have other blogs, on other topics that are often quite controversial (on current tensions between the US, Europe, Russia and China, or other questions of war and peace, for example), and I did not experience anything like that there. It may be Sayre’s Law: “Academic politics is much more vicious than real politics, because the stakes are so small.”

In any case, let us get back to the matter at hand: this blog and its future. What do I want to do with it? What can I usefully do with it? One experiment I want to try out is to distill the essence out of my papers as I have started a process of revising them one by one. Yes, unlike what I wrote about in the overall Post Scriptum to all of my 29 papers (that it was too much work to do that, basically), I think I should do that. I am getting older and, hence, I now think of that as a rather nice pastime.

So, I will stop rambling and make a first attempt at elucidating some aspects of my world vision, so to speak, for the intermediate-level hobbyist. To be clear on what I mean with that: I still consider myself to be an intermediate-level hobbyist as well but, looking at those RG stats, I think I might have it easier with some of the mathematical formalism than others, so that is why I am going to try to avoid it.

Let us go for it. In the next section(s) of this blog post, I am going to condense and distill the key conclusions in regard to the essential nature of mass, because that is still the question that intrigues most of us: what is it – not approximately, but exactly? If we know what matter is all about, then we know, pretty much, what reality is all about, right? Maybe. Maybe not. We miss a great deal about the mystery of fields and radiation but, yes, it is an important piece of the whole intellectual puzzle, so let us start here.

The nature of mass

We explained the nature of mass in our papers on elementary physics.[1] However, we did use rather advanced mathematical concepts (if you are not familiar with imaginary units or vector algebra, that is), so let us summarize the very basics here.

At the macro-level, mass appears as inertia to a change in the state of linear motion of an object or particle. That is how it appears in Newton’s first law of motion which – in its relativistically correct form – is written as F = dp/dt = d(m·v)/dt.[2] Now, the idea of a particle is a philosophical or ontological concept and we will, therefore, avoid it – to some extent, at least – and prefer to speak of things we can measure, such as charge and, yes, mass. We will also speak of physical laws because these are based on measurements too.

Now I do have to insert one formula. It is simple (just a formula that says a rather particular ratio is equal to some number). Try to think through it. From the Planck-Einstein and mass-energy equivalence relations (E = h·f and E = m·c2, so h·f = m·c2), we get the following fundamental equation for a frequency per unit mass (f/m or, expressing frequency in radians per second rather than cycles per second, ω/m):

f/m = c2/h = 1.35639248965213×1050

This humongous value[3] is an exact value since the 2019 redefinition of SI units, which fixed the value of ħ, and just like c and ħ, you may think of it as some God-given number but you should not do that: just like the fine-structure constant[4], this is just a number which we derived from a more limited number of fundamental constants of Nature. [Of course, you will note that the number depends on the units, and that both the second and the kg are very large units when talking about small things, but you can recalculate the number using other units, just like you can do that for other constants.]

The point is this: this simple formula, and that enormous number, reflect the true nature of mass at the micro-level. You must appreciate that is quite different from mass being, at the macro-level, a measure of inertia. At the most fundamental level, matter is nothing but charge in motion. Such interpretation may not be mainstream (although it should be, judging from how physicists actually treat matter) but it is consistent with Wheeler’s ‘mass without mass’ ideas and – more importantly, probably – with the 2019 revision of the system of SI units, in which mass also appears as a derived unit from more fundamental constants now, most notably Planck’s constant.

This f/m ratio is, of course, valid for all matter or – let us be precise – for all (stable) elementary particles.[5] However, it is important to note that, while the f/m ratio is the same for both the electron as well as the proton mass, the q/me and q/mp ratios are, obviously, very different. We, therefore, do associate two very different charge oscillations with them: we think of the electron and proton as a two- and three-dimensional ring current, respectively. Hence, while these specific oscillator equations are, theoretically and mathematically, compatible with any mass number, we do not think of the electron and proton energies as variables but as constants of Nature themselves.

In short, we must think of the electron and the proton mass as fundamental constants too because, as far as we know, these are the only two stable constituents of matter, and they also incorporate the negative and positive elementary charge, respectively.[6] The f/m = c2/h formula above holds for both and, combined with Newton’s force law (m = F/a: mass as inertia to change of (a state of) motion), we conclude that the mass idea is one single concept but that we should, at the very minimum, distinguish between electron and proton mass. Of course, Einstein’s mass-energy relation tells us it might be better to just talk about two fundamental energy levels (Ee and Ep), and to re-write the f/m = c2/h expression above as the Planck-Einstein relation applied to two (different) oscillations. We insert the mathematical representation of that idea below too, but do not worry too much about it:

As mentioned above, in the realist interpretation we have been pursuing, we effective think of the two oscillations as a planar and a spherical oscillation, respectively, which is reflected in the wavefunction which we use to represent the electron and proton, respectively. Indeed, the effective radius of a free electron follows directly from the orbital velocity formula v = c = ω´r = ω´a and the Planck-Einstein relation[7]:

The point here is not to burden you with formulas (we said we would not, but we cannot help it here), but to show you how easy it is to get the measurable properties of the electron from the basic equations. Now that we are doing that, we will also quickly introduce the wavefunction of both the electron and the proton, although you can skip through the next paragraphs if you would not like that (we are just doing it for the more academic or advanced reader, to show that we are not afraid of the math and formalism). We write the wavefunction of an electron as:

This notation introduces the imaginary unit, which serves as a rotation operator and, therefore, denotes the plane of oscillation. The sign of the imaginary unit (±) indicates the direction of spin and, interpreting 1 and 1 as complex numbers (cf. the boldface notation), we do not treat ± p as a common phase factor.[8]

As mentioned several times already, we think of the proton oscillation as an orbital oscillation in three rather than just two dimensions. We, therefore, have two (perpendicular) orbital oscillations, with the frequency of each of the oscillators given by ω = E/2ħ = mc2/2ħ (energy equipartition theorem), and with each of the two perpendicular oscillations packing one half-unit of ħ only.[9] Such  spherical view of a proton fits with packing models for nucleons and yields the experimentally measured radius of a proton:

The 4 factor here is the one distinguishing the formula for the surface of a sphere (A = 4πr2) from the surface of a disc (A = πr2).[10] So do we consider the (in)famous proton radius puzzle solved? Yes. We do. Let us – for the more advanced reader again – write the proton wavefunction. We think of it as a combination of two elementary wavefunctions:

While the electron and proton oscillation are very different, the calculations of their magnetic moment based on a ring current model (with a square root correction to take the spherical nature of the proton into account) strongly suggest the nature of both oscillations and, therefore, the nature of all mass, is electromagnetic. However, we may refer to the electron and proton mass as electromagnetic and nuclear mass respectively because protons (and neutrons) make up most of the mass of atomic nuclei[11], while electrons explain the electromagnetic interaction(s) between atoms and, therefore, explain molecular shapes and other physical phenomena.

Finally, the two oscillations may be associated with the two lightlike particles we find in Nature: photons and neutrinos. These lightlike particles carry energy (but no charge) but are traditionally associated with electromagnetic and nuclear reactions respectively (emission and/or absorption of photons/neutrinos, respectively), which also explains why referring to the three-dimensional proton oscillation as a nuclear oscillation makes sense.[12]

Is that it, then? You may have a few immediate reactions and one of them would be this: we reduce mass to charge in motion here. So what is charge, then? And can we reduce charge to something else. It would take me quite a bit of text to reply to that, so I will only be short here.

First, getting rid of one concept in physics is already a great simplification, and we cannot get rid of the concept of charge by reducing it to mass. In contrast, we do have this nice ‘mass without mass’ model here, and so that is great. Second, never forget that mass (and energy) are relative: you will measure them differently in different reference frames. In contrast, charge is absolute: the proton and electron charge are a unit of charge that does not change depending on your frame of reference. It is just like the speed of light, or Planck’s constant: these constants are c and h, respectively. They are absolute. So that is why we can get rid of the mass concept, so to speak. We cannot get rid of (electric) charge.

So, this is it. See you next time (for my next post, that is)?

[1] See our papers in our K-12 level physics series.

[2] The formula is relativistically correct because both m and v are not constant: they are functions varying in time as well and that is why we cannot easily take them out of the d()/dt brackets.

[3] A number with 50 zeros would be referred to as one hundred quindecillion (using the Anglo-Saxon short scale) or one hundred octillions (using the non-English long scale of naming such astronomic numbers).

[4] The fine-structure constant pops up in electromagnetic theory, and is co-defined with the electric and magnetic constants. Their CODATA values are related as follows:

[5] Note that the electron and proton (and their anti-matter counterparts) are stable, but the neutron (as a free particle, i.e., outside of a nucleus) is not, even if its average lifetime (almost 15 minutes) is very large as compared to other non-stable particles.

[6] As mentioned above, the neutron is only stable inside of the nucleus, and we think of it as a combination of a positive and negative charge. It is, therefore, reducible and, as such, not truly elementary. However, such view is, obviously, part of another speculative model of ours and, hence, should not be a concern to the reader here.

[7] We write this as a vector cross-product, and assume an idealized circular orbital when writing the position vector r as a wavefunction r = ψ = a·e±iθ = a·[cos(±θ) + i · sin(±θ)]. The magnitude ½r½is, obviously, equal to ½a·e±iθ ½ = a. This is a variant of Wheeler’s mass-without-mass model because the model assumes a pointlike (but not necessarily infinitesimally small or zero-dimensional) charge, whose rest mass is zero and, therefore, moves at lightspeed and acquires relativistic mass only. As such, it is photon-like, but photons (light-particles) carry no charge. The a = r notation may be somewhat confusing because a is also used to denote acceleration¾an entirely different concept, of course!

[8] See our paper on Euler’s wavefunction and the double life of -1, October 2018. This paper is one of our very early papers – a time during which we developed early intuitions – and we were not publishing on RG then. We basically take Feynman’s argument on base transformations apart. The logic is valid, but we should probably review and rewrite the paper in light of the more precise intuitions and arguments we developed since then, even if – as mentioned – I have no doubt as to the validity of the argument.

[9] Such half-units of ħ for linearly polarized waves also explains the results of Mach-Zehnder one-photon interference experiments. There is no mystery here.

[10] We also have the same 1/4p factor in the formula for the electric constant, and for exactly the same reason (Gauss’ law).

[11] Binding energy – also electromagnetic in nature – makes up for the rest.

[12] See our paper on the nuclear force hypothesis, April 2021.

Post Scriptum (2)

When I wrote my first PS in November last year, I thought it would be my last blog post here – but the stats keep going up. Good enough here on WordPress, and even better on ResearchGate: a 170+ score now and still rising fast: top 1% climber still – despite that I have published nothing since a year now – which got me into the top 25% bracket of RG researchers in less than two years – and, while it is far from going viral, further rise looks a bit inevitable now.

It clearly shows that I am not mad and that you are reading serious physics here – but without the usual hocus-pocus and ‘mystery’ that leaves so many young and-not-so-young people disgusted. I repeat: there is no serious puzzle in physics any more. All that is being done now, is to further work out the consequences of the fundamental laws of physics that were written down about a hundred years ago (de Broglie wrote his thesis in 1924, so this centenary is almost there). For those who are seeking to simplify further by resorting to some kind of ‘meta-symbolism’ or an even more ‘holistic’ perspective (whatever that might mean), I think the exchange below (from my ResearchGate account) might be useful. For the rest, I have nothing to add anymore. It is all there ! 🙂

M (7 days ago): Dear JL – I was amazed to find your piece on the jitter-bugging phenomena [sic] (not hypothesis). I think you may find my more holistic perspective useful in fine-tuning your work. I hope you agree, and I would love to collaborate. After all, as far as I know, your work is the first substantive effort in nearly 60 years+ (in this very fertile direction). Cheers, etc. ~ M


M (7 days ago): Dear JL – Bravo!!! I just saw the abstract of your paper on conserving the enthusiasm of young people afflicted by modern SM-QM nonsense, dogma, etc. I am now even more motivated to have your help reviewing, editing, and developing my next-gen ontology of the cosmos. Cheers ~ M

My rapid-fire answers (yesterday and today):

Txs man ! This developed partly because (1) I had too much time on my hands (a difficult past five years as I came back from abroad and my mom and bro died from cancer – I had to go through cancer surgery myself) and (2) helping my son getting through his exams on quantum physics as part of his engineering studies (he is just as much as a rebel as me and (also) wanted more ‘common-sense’ explanations. The ‘orbital’ or ‘circular’ motion concept for interpreting de Broglie’s wavefunction (orbital frequencies instead of linear ones) is the key to everything. 🙂 No magic. 🙂 Charge and motion are the only concepts that are real. 🙂 There is no copyright to what I produced (a lot is just about building further on strands the ‘Old Great’ (including Schroedinger himself) had in mind) so feel free to use it and further develop. My blog post on Paul Ehrenfest’ s suicide is probably still the most ‘accessible’ introduction to it all. It is also tragic – as tragic (or more, probably) as Dirac’s depression when he sort of ‘turned his back’ on the young wolves he used to support – but still…


I also did some YouTube videos to ‘market’ it all – but there is only so much one can do. It is a weird situation. APS, WSP and even Springer Verlag wanted to do something with me but they all backed off in the end. Fortunately I do not suffer from much ego (one advantage of my experience in war-torn countries such as Afghanistan and in Ukraine (March)) – so I take everything lightly. My “Post Scriptum” to my papers – – is a read of 15 minutes only and guides all of the material. Have fun with it ! Life is short. I know – having come clean out of cancer (unlike my mom and my bro), so every day is a perfect day now. As for day job:


As for the formalism that you are introducing, I would recommend close(r) study of:
(1) : my physics is a ‘mass without mass’ approach – but I do not believe charge can be further reduced (we need the concept to distinguish between matter and anti-matter, for example – geometry does not suffice to explain all degrees of freedom there);
(2) The failure of Wittgenstein’s formalism – as he admitted himself in what is commonly referred to as the ‘Wittgenstein II’ (nothing more than some of his comments in letters on his little booklet). I studied Wittgenstein as part of my philosophy studies and I am not too impressed. I feel we need a bit of ‘common’ language to add nuance and meaning to the mathematical symbols. Without the ambiguity in them, they do not mean all that much to me. Also see:


To add – I also believe step (3) of the geometrodynamics is not possible. We can do without the mass concept (and still it is useful to use in the higher-level physics), but not without charge or fields. Charge and field are not further reducible. The last slide of my ‘philosophy and physics’ presentation on YouTube shows the fundamental ‘categories’ I believe in (categories in an Aristotelian sense). These concepts can be both ‘relative’ or ‘absolute’ (not-relative, in the sense of (special/general) relativity theory).

One more thing, despite my criticism on ‘Wittgenstein-like’ formalism, his first statement in his Tractatus should obviously be the point of departure of any ‘metaphysics’ or epistemology: 1.1 Die Welt ist die Gesamtheit der Tatsachen, nicht der Dinge. Perhaps it is the only thing we can seriously say about ‘the world’ or ‘reality’. It serves as a ‘good enough’ definition to me, in any case. 🙂

Post Scriptum

I made a start with annotating all of my papers. I will arrange them in a paper of itself: working paper no. 30 on ResearchGate. I will date it on 6 December when finished, in honor of one my brothers who died on that day (6 December), from a cancer that visited me too. Jean-Claude was his name. He was a great guy. I miss him, and sometimes feel guilty of having survived. Hereunder follows the first draft – a sort of preview for those who like this blog and have encouraged me to go on.

Post scriptum: The final paper is here and so you can click and download, rather than go through the draft underneath.


The 29 papers which I published on ResearchGate end a long period of personal research, which started in earnest when I sent my very first paper, as a young student in applied economics and philosophy, to the 1995 ‘Einstein meets Magritte’ Conference in Brussels. I do no longer have that paper, but I remember it vehemently defended the point of view that the ‘uncertainty’ as modeled in the Uncertainty Principle must be some kind of statistical determinism: what else can it be? Paraphrasing the words of H.A. Lorentz, at the occasion of the 1927 Solvay Conference, a few months before his death, there is, effectively, no need to elevate indeterminism to a philosophical principle: scientists must keep determinism has to be kept as ‘an object of faith.’ That is what science is all about. All that is needed is to replace our notion of predictability by the notion of statistical determinism: we can no longer predict what is going to happen, because we can or do not know the initial conditions, or because our measurement disturbs the phenomenon we are analyzing, but that is it. There is nothing more to it. That is what Heisenberg’s now rather infamous Uncertainty Principle is all about it: it is just what he originally thought about it himself.

I found the metaphor of a fast-rotating airplane propeller a very apt one[1], and several people who wrote me also said it made them see what it was all about. One cannot say where the blades are, exactly, and if you would shoot bullets through it, those bullets will either hit a blade and be deflected or will, quite simply, just go straight through. There is no third possibility. We can only describe the moving propeller in terms of some density in space. This is why the probabilities in quantum physics are proportional to mass densities or, what amounts to the same because of Einstein’s mass-energy equivalence relation, energy densities.

The propeller metaphor is useful in other contexts too. It explains quantum-mechanical tunneling, for example: if one thinks of matter-particles as pointlike charges in motion – which is what we do[2] – then the fields that surround them will be dynamic and, therefore, be like a propeller too: at one particular point in space and in time, the field will have a magnitude and a direction that will not allow another particle (think of it as a bullet) to get through – as the field acts as a force on the charge – but ‘holes appear in the wall’, so to speak, and they do so in a regular fashion, and then the incoming particle’s kinetic energy – while lower than the average potential energy of the barrier – will carry it through. There is, therefore, nothing weird or mysterious about tunneling.

Many more examples may be mentioned, but then I would be rewriting my papers, and that is not the purpose of this one, which is to conclude my research by revisiting and commenting on the rather vast mass of paper I produced previously: 29 papers in just one year (April 2020 – April 2021). These papers did not bring me fame, but did generate enough of a readership to produce a decent RG score – as evidenced below (sorry if this looks egotistical: it is not meant that way[3]).

I have effectively been ridiculed by family, friends and – sadly – by quite a few fellow searchers for truth. But I have also been encouraged, and I prefer to remember the encouragements. One of my blog posts writes about the suicide of Paul Ehrenfest and other personal tragedies in the history of physics. It notes a remark from a former diplomat-friend of mine, who remarked this: “It is good you are studying physics only as a pastime. Professional physicists are often troubled people—miserable.”

I found it an interesting observation from a highly intelligent outsider who, as a diplomat, meets many people with very different backgrounds. I do understand this strange need to probe things at the deepest level—to be able to explain what might or might not be the case (I am using Wittgenstein’s definition of reality here). I also note all of the founding fathers of quantum mechanics ended up becoming pretty skeptical about the theory they had created. Even John Stewart Bell – one of the more famous figures in what may be referred to as the third generation of quantum physicists – did not like his own ‘No Go Theorem’ and thought that some “radical conceptual renewal”[4] might disprove his conclusions.

It sounds arrogant, but I think my papers are representative of such renewal. It is, as great thinkers in the past would have said, an idea whose time has come. Einstein’s ‘unfinished revolution’ – as Lee Smolin calls it – was finished quite a while ago, but mainstream researchers just refuse to accept that.[5] And those researchers who think quantum physicists are ‘lost in math’ are right but, unfortunately, usually make no effort by speaking up and showing the rather obvious way out. Sabine Hossenfelder uses as much guru-like talk as a Sean Carroll.[6]

So what is this paper about?

In May this year, after finishing what I thought of as my last paper on quantum physics, I went to hospital for surgery. Last year, one of my brothers died from prostate cancer at a rather young age: 56, my age bracket. He had been diagnosed but opted for a more experimental treatment instead of the usual surgery that is done, because the consequences of the surgery are effectively very unpleasant and take a lot of joy out of life. I spent a week in a hospital bed, and then a month in my bed at home. I stopped writing. I gave up other things too: I stopped doing sports, and picked up smoking instead. It is a bad habit: Einstein was a smoker and – like me – did not drink, but smoking is bad for health. I feel it. I will quit smoking too, one day – but not now.

The point is: after a long break (more than six months), I did start to engage again in a few conversations, and I also looked at my 29 papers on my ResearchGate page again, and I realized some of them should really be re-written or re-packaged so as to ensure a good flow. I also note now that some of the approaches were more productive than others (some did not lead anywhere at all, actually), and so I felt like I should point those out. There are some errors in logic here and there too (small ones, I think, but errors nevertheless), and then quite some typos.[7] Hence, I thought I should, perhaps, produce an annotated version of these papers, with comments and corrections as mark-ups. Re-writing or re-structuring all of them would require too much work, so I do not want to go there.

So that is what this paper is about: I printed all of the papers, and I will quickly jot down some remarks so as to guide the reader through the package, and alert them to things I thought of good stuff at the time (otherwise I would not have written about it), but that I do think of as not-so-great now.

Before I do so, I should probably make a few general remarks. Let me separate those out in yet another introductory section of this paper.

General remarks

1. The first remark is that I do repeat a few things quite a lot – across and within these papers. Too much, perhaps. However, there is one thing I just cannot repeat enough: one should not think of the matter-wave as something linear. It is an orbital oscillation. This is really where the Old Great Men went wrong. The paper that has been downloaded the most is, effectively, the one on what I refer to as de Broglie’s mistake: the intuition of the young Louis de Broglie that an electron has a frequency was a stroke of genius (and, fortunately, Einstein immediately saw this, so he could bring this young scientist under the attention of everyone else), but this frequency is an orbital frequency. That, I repeat a lot – because only a few people seem to get that (with ‘a few’, I mean the few thousand people who download that paper).

Having said that, I did not do a good job at pointing out the issues with Dirac’s wave equation: I sort of dismiss it out of hand referring to Oppenheimer and Dirac’s discussion at the occasion of the first post-WW II Solvay Conference in my brief history paper on quantum-mechanical ideas, during which they both agree it does not work but fail to provide a consistent alternative. However, I never elaborated on why the equation does not work, so let me do this now.

The reason that it does not work is, basically, the same as the reason why de Broglie’s wave-packet idea does not work: Dirac’s equation is based on the relativistic energy-momentum relation. Just look at Dirac’s 1933 Nobel Prize lecture, in which he gives us the basic equation he used to derive his (in)famous wave equation:

W2/c2 – pr2 – m2/c2 = 0

Dirac does not bother to tell us but this is, basically, just the relativistic energy-momentum relationship: m02c4 = E2 – p2c2 (see, for example, Feynman-I-16, formula 16.13). Indeed: just divide this formula by c2 and re-arrange and you get Dirac’s equation. That is why Dirac’s wave equation is essentially useless: 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, leads nowhere[8]: one has to incorporate the reality of spin from the start. Spin-zero particles do not exist and any modeling that starts off from modeling spin-zero particles, therefore, fails: you cannot put spin back in through the back door once you are done with the basic model, so to speak. It just does not work. It is what gives us, for example, those nonsensical 720-degree symmetries, which prevent us from understanding what is actually happening.

2. The second remark that I should make is that I did not pay enough attention to the analysis of light-particles: photons and neutrinos and, possibly, their antiforce or antimatter counterparts. Huh? Their anti-force counterparts? Yes. Remember: energy is measured as a force over a distance, and a force acts on a charge. And then Einstein’s energy-mass energy equivalence relation tells us we should think of mass in terms of energy. Hence, if we know the force, we have got everything. Electrons and protons have a very different charge/mass ratio (q/m) and, therefore, involve two very different forces, even if we think of these two very different forces – which we could refer to as ‘weak’ and ‘strong’ respectively, but that would generate too much confusion because these terms have already been used – as acting on the same charge.

I refer to my paper(s) on this: the hypothesis is, basically, that we have two different forces, indeed! One that keeps, say, the electron together, which is nothing but the electromagnetic force, and one that is much stronger and seems to have a somewhat different structure. That is the force that keeps a muon-electron or a proton together. The structure of this much stronger force is the same because it also acts on a charge, and we also have two field vectors: think of the magnetic field vector lagging the electric field by 90 degrees. However, it is also not the same because the form factor differs: orbital oscillations can be either planar or spherical (2D or 3D).

I will not go into the detail here – again, I would be rewriting the papers, which is not what I want to do here – but the point is that antimatter is defined by an antiforce, which sees the magnetic field vector preceding the electric field vector by the same phase difference (90 degrees). It is just an application of Occam’s Razor Principle: the very same principle which made Dirac predict the existence of the positron: if the math shows there is some possibility of something else existing – a positively charged ‘electron’, at the time – then that possibility must be real, and we must find ‘that thing’. The history of science has shown scientists always did.

That is all clear enough (or not), but so the point here is this: the lightlike particles (photons and neutrinos) that carry the electromagnetic and nuclear force respectively (I refer to that strong(er) force as ‘nuclear’ for rather obvious reasons[9]) must have anti-counterparts: antiphotons and antineutrinos. And so I regret that I did not do too much analysis on that. I am pretty sure, for example, that antiphotons must play a role in the creation of electron-positron pairs in experiments such as SLAC’s E144 experiment (pair production out of light-on-light (photonic) interaction).

In short, I regret I did not have enough time and/or inspiration to analyze such things much more in detail than I did in my paper on matter-antimatter pair production/annihilation, especially because that is a paper that gets a lot of downloads too, so I feel I should rework it to present more material and better analysis. It is unfortunate that energy and time is limited in a man’s life. The question is, effectively, very interesting because the ‘world view’ that emerges from my papers is a rather dualistic one: we have the concept of charge on the one hand, and the concept of a field on the other. Matter-antimatter pair creation/annihilation from/into photons suggest that charge may, after all, be reducible to something that is even more fundamental. That is why I bought a rather difficult book on chiral field theory (Lähde and Meißner, Nuclear Lattice Effective Field Theory, 2019), but an analysis of that will probably be a retirement project or something.

3. The remark above directly relates to something else I think I did not do so well, and that is to explain Mach-Zehnder interference by a model in which we think of circularly polarized photons (or elliptically polarized, I should say, to be somewhat more general) as consisting of two linear components, which we may actually split from each other by a beam splitter. That takes the mystery out of Mach-Zehnder interference, but I acknowledge my analysis in a paper like my ‘K-12 level paper’ on quantum behavior (which gives a one-page overview of the logic) may be too short to convince skeptical readers. The Annex to my rather philosophical paper on the difference between a theory, a calculation and an explanation is better, but even there I should have gone much further than I did.[10]

4. I wrote quite a few papers that aim to develop a credible neutron and/or deuteron model. I think of the neutron in very much the same way as Ernest Rutherford, the intellectual giant who first hypothesized the existence of the neutron based on cosmological research, thought about neutrons: a positively charged proton or other nuclear particle attached to some kind of deep electron.[11] It is worth quoting his instinct on this, as expressed at the occasion of the 1921 Solvay Conference, in response to a question during the discussions on Rutherford’s paper on the possibility of nuclear synthesis in stars or nebulae from the French physicist Jean Baptiste Perrin who, independently from the American chemist William Draper Harkins, had proposed the possibility of hydrogen fusion just the year before (1919):

“We can, in fact, think of enormous energies being released from hydrogen nuclei merging to form helium—much larger energies than what can come from the Kelvin-Helmholtz mechanism.[12] I have been thinking that the hydrogen in the nebulae might come from particles which we may refer to as ‘neutrons’: these would consist of a positive nucleus with an electron at an exceedingly small distance (“un noyau positif avec un électron à toute petite distance[13]). These would mediate the assembly of the nuclei of more massive elements. It is, otherwise, difficult to understand how the positively charged particles could come together against the repulsive force that pushes them apart—unless we would envisage they are driven by enormous velocities.”

We may add that, just to make sure he gets this right, Rutherford is immediately requested to elaborate his point by the Danish physicist Martin Knudsen, who asks him this: “What’s the difference between a hydrogen atom and this neutron?” Rutherford simply answers as follows: “In a neutron, the electron would be very much closer to the nucleus.” 

In light of the fact that it was only in 1932 that James Chadwick would experimentally prove the existence of neutrons (and positively charged protons), we should be deeply impressed by the foresightof Rutherford and the other pioneers here: the predictive powerof their theories and ideas is truly amazing by any standard—including today’s. It may have something to do with the fact that the distinction between theoretical and experimental physicists was not so clear then.[14] The point is this: we fully subscribe to Rutherford’s intuition that a neutron should, somehow, be a composite particle consisting of a proton and an electron, but we did not succeed in modeling that convincingly. We explored two ways to go about it:

  1. One is to think of a free neutron which, we should remind ourselves, is a semi-stable particle only (its lifetime is a bit less than 15 minutes, which is an eternity in comparison to other non-stable particles). The challenge is then to build a credible n0 = p+ + e model.
  2. The other option is to try to build a neutron model based on its stability inside of the deuteron nucleus. Such model should probably be based on Schrödinger’s D+ = p+ + e + p+ Platzwechsel model, which thinks of the electron as a sort of glue holding the two positive charges together.

The first model is based on the assumption that we have two forces, very much like the centripetal and centrifugal force inside of a double-star. The difference – with a double-star model, that is – is that the charges have no rest mass.[15] The nature of those two forces is, therefore, very different than (1) the centripetal gravitational force that keeps the two stars together and (2) the centrifugal force that results from their kinetic energy and/or orbital momentum. We assumed the attractive force between the p+ and e is the usual electromagnetic force between two opposite charges (so that keeps them together). However, because the two charges clearly do not just go and sit on top of each other, we also assumed a ‘nuclear’ force acts at very close distances, and we tried to model this by introducing a Yukawa-like nuclear potential.

We will discuss this more in detail when commenting on our papers in the next section, but the truth is that we feel we have not been able to develop a fully consistent model: it is not like our electron or proton model, which yields fully consistent calculations of the experimentally measured mass, radius, magnetic moment and other so-called intrinsic properties (e.g. the anomaly in the magnetic moment of the electron) of these two elementary particles. We could not do for the neutron. However, we hope some smart PhD student will try his or her hand at improving on our models and succeed where we did not.

As for the second model (the deuteron nucleus model), we did not work all that because that is, basically, an even more complicated problem than the math of a classical three-body problem which, as you know, has no analytical solution. So we inevitably have to lump two bodies together – the two protons might make for a nice massive pair, for example – but then you lose the idea of the neutron. In other words, it may give you a deuteron model, but nothing much in terms of a neutron model.  

5. Those were the main frustrations, I think. We will probably point out others too in the more detailed paper-by-paper comments in the next section, but I would like to make one or two more remarks regarding style and conversation culture in physics now.

The main remark is this: I did some research in economics (various sub-disciplines ranging from micro-economics to the history of thought in economics) and I found the conversational style of fellow researchers in those fields much more congenial and friendly than in physics. It may have something to do with the fact such study was done while I was young (so that was almost 30 years ago and people were, quite simply, friendlier then, perhaps), but I also think there might be a different reason. I was (and still am) interested in quantum physics because I wanted to know: this search for truth in modeling (or whatever you want to call it) is rooted in a deep need or desire to understand reality. Personally, I think the Uncertainty Principle got elevated to some kind of metaphysical principle because some of the scientists wanted to reserve a space for God there. I am not religious at all, and if God exists, I am sure he would not to be hiding there but inside of our mind.

In any case, my point here is this: I think there is an emotional or religious aspect to discussions on fundamentals that is absent in the social sciences which, in most cases, turns these discussions quickly personal or even aggressive. As an example, I would refer to all these ‘relativity doubters’ that pop up in the more popular or general ResearchGate discussion threads on the ‘consistency’ of quantum physics, or the pros and cons of modern cosmological theories. I vented my frustration on that on my blog a few times (here is an example of my issues with SRT/GRT doubters), and so then I just stop arguing or contributing to these threads, but I do find it sad because a lot of people like me probably just do the same: they stop engaging, and that probably makes the ignorance even worse and then there is no progress at all, of course!

However, having said this, I also note unfriendliness is inversely proportional to expertise, knowledge and experience. In other words: never be put off by anyone. I did go through the trouble of contacting the PRad Research Lab and people like Dr. Randolf Pohl (Max Planck Institute), and I got curt but useful answers from them: answers that challenged me, but those challenges have helped me to  think through my models and have contributed to solidifying my initial intuitions, which I would sum as follows: there is a logical interpretation of everything. I refer to it as a realist interpretation of quantum physics and, as far as I am concerned, it is pretty much the end of physics as a science. We do know it all now. There is no God throwing dices or tossing coins. Statistical determinism, yes, but it is all rooted in formulas and closed mathematical models representing real stuff in three-dimensional space and one-dimensional time.

Let me now (self-)criticize my own papers one by one. 😊

Note: I briefly tried to hyperlink the titles (of the papers) to the papers themselves, but the blog editor (WordPress) returned an error. I guess this blog post is quite long and has to many links already. In any case, the titles do refer to the papers on my RG site, and the reader can consult them there.

Paper-by-paper remarks

The concepts of charge, elementary ring currents, potential, potential energy, and field oscillations

No comments. We think this paper gives a rather nice overview of what made sense to us. We also like the two annexes because they talk about quantum-mechanical operators and show why and how the argument of the wavefunction incorporates (special) relativity (SRT/GRT naysayers should definitely read this).

There is a remnant of one of the things we tried and did not yield much: a series expansion of kinetic and/or potential energy from Einstein’s energy-mass equivalence relation. That result from a discussion with researchers trying to model other deep electron orbitals (other than the ‘deep’ electron in a neutron or a deuteron nucleus): they were thinking of potentials in terms of first-, second-, third-, etc.-order terms, so as to simplify things. I went along with it for a while because I thought it might yield something. But so it did not. Hence, I would leave that out now, because the reader probably wonders what it is that I am trying to do, and rightly so!

Lectures on Physics Chapter VI : All of Quantum Math

This is one in a series of what I jokingly thought of as a better or more concise version of Feynman’s Lectures on Physics. I wrote six of these. Feynman once selected ten ‘easy pieces’ and ten ‘not-so-easy’ pieces from his own lectures, if I am not mistaken¾but so these should qualify as relatively ‘easy’ pieces (in comparison with other papers, that is).

It downplays the concept of the gyromagnetic ratio in quantum mechanics somewhat by focusing on the very different charge/mass ratio for the electron and a proton (q/m) only. For the rest, there is nothing much to say about it: if you are a student in physics, this is the math you surely need to master!

All of physics

This paper is one of those attempts to be as short as I can be. I guess I wanted it to be some kind of memorandum or something. It still developed into five pages, and it does not add anything to all of the longer papers. Because it is short and has no real purpose besides providing some summary of everything, I know think its value is rather limited. I should probably take it down.

Do we need the nuclear force hypothesis?

This is one of the papers on a neutron or deuteron model. I think the approach is not bad. The use of orbital energy equations to try to model the orbital trajectories of (zero rest-mass) charges instead of the usual massive objects in gravitational models is promising. However, it is difficult to define what the equivalent of the center of mass would be in such models. One might think it should be the center of ‘energy’, but the energy concepts are dynamic (potential and kinetic energy vary all the time). Hence, it is difficult to precisely define the reference point for the velocity vector(s) and all that. We refer to our general remarks for what we think these papers might have yielded, and what not. For the rest, we let the reader go through them and, hopefully, try to do better.

The nuclear force and quaternion math

We like this paper very much because it shows why quaternion math should be used far more often than it is actually done in physics: it captures the geometry of proton and neutron models so nicely. We probably will want to delve into this more as yet another retirement project. We also like this paper because it is short and crispy.

The language of math

Probably not our best paper, and one that should or could be merged with others covering the same topics. However, the philosophical reflections in this paper – on the arrow of time and what is absolute and relative in physics – are nice and can be readily understood. They would probably come first if ever we would want to write a textbook or something. We also recommend the primordial dimensional analysis of basic equations in physics: modern-day papers usually do not bother to check or comment on these.

Nuclear potential and energy conservation

This is one of these papers which shows the shortcomings of our approach to modeling anything ‘nuclear’. The idea of two or three charges holding and pushing each other apart simultaneous – with two opposite forces acting, just like the centripetal and centrifugal force in any gravitational model – is nice, and we think the substitution of mass by some combination of charge and mass in the orbital energy equation is brilliant (sorry if this sounds egotistical again) but, as mentioned above, it is difficult to define what the equivalent of the center of mass would be in such models.

Also, because of the distance functions involved (the ‘nuclear’ force in such a model varies with the square of the distance and is, therefore, non-linear), one does not get any definite solution to the system: we derived a lower limit for a ‘range’ factor for the nuclear force, for example (and its magnitude corresponds more or less to what mainstream physicists – rather randomly – use when using Yukawa-like potentials[17]).

It would be an interesting area for modeling if and when I would have more time and energy for these things, so I do hope others pick up on it and, hopefully, do better.

The language of physics

Same remarks as above: I like this paper because it is short. I also allow myself to blast away at quark-gluon theories (‘smoking gun physics’, as I call it[18]). There are also the explanations of useful derivatives of the wavefunction, which show why and how our geometric interpretation of the wavefunction makes sense.

We also quickly demonstrate the limitations of the scattering matrix approach to modeling unstable particle and particle system processes, despite the fact we do love it: the problem is just that you lose track of directions and that we, therefore, cannot explain even very simple stuff such as scattering angles in Compton scattering processes using that S-matrix approach. Here too, we hope some clever people might ‘augment’ the approach.

The Zitterbewegung hypothesis and the scattering matrix

We like this paper. It deserves a lot more downloads than it gets, we think. It is the proper alternative to all kinds of new ‘conservation laws’ – and the associated new ‘strange’ properties of particles – that were invented to make sense of the growing ‘particle zoo’. The catalogue of the Particle Data Group should be rewritten, we feel. 😊

The Finite Universe

Of course, any physicist should be interested in cosmology – if only because any Big Bang theory uses pair creation/annihilation theories rather extensively. As mentioned in our general remarks, we still struggle with these theories and, yes, definitely on our list as a retirement project.

The main value of the paper is that it offers a consistent explanation of ‘dark matter’ in terms of antimatter, and also that it does not present the apparently accelerating pace of the expansion of the Universe as something that is necessarily incongruent: there may be other Universes around, beyond what we can observe. The paper also offers some other ‘common-sense’ explanations: none of them involves serious doubts on standard theory (we do not doubt anything like SRT and/or GRT). We, therefore, think that this paper shows that I am much more ‘mainstream’ and far less ‘crackpot’ than my ‘enemies’ pretend I am. 😊

Ontology and physics

This is definitely my worst paper in terms of structure. It has no flow and jumps from this to that. Even when I read it myself, I wonder what it is trying to say. I must have been in a rather weird mood when I wrote it, and then it got too long and I probably then suddenly had enough of it.[19] The conclusions do sound like I had gone mad: if my kids or someone else would have read it before I published it, they might have prevented me from doing so. Any case, it is there now. I will probably take it off one day.

Of course, I note the month of writing: my specialist had just confirmed my prostate cancer was very aggressive, and that I had to do the surgery sooner rather than later if I wanted to avoid what had killed my brother just months before: metastasis to kidneys and other organs. And my long-term girlfriend has just broke up – again. And I had just come back from yet another terrible consultancy job in Afghanistan. Looking into my diary of those days, I had probably relapsed into a bit of drinking, and too many parties with the ghosts of Oppenheimer and Ehrenfest. :-/ In short, I should take that paper of the web, but I will leave it there just for the record.

A mass-without-mass model of protons and neutrons

This paper is better than the one mentioned above but – at the same time – suffers from the same defects: no clear flow in the argument, ‘jumpy’, and lots of ‘deus ex machina’-like additions and sidekicks.[20] Its only advantage is that it does offer a rather clear explanation of what works and probably cannot work in Wheeler’s geometrodynamicsprogramme: mass-without-mass models are fine. The way to go: forces act on charges, and energy is force over a distance, and mass relates to energy through Einstein’s mass-energy equivalence relation. No problem. But the concept of charge is difficult to reduce. Chiral field theories may yet prove to do that, but I am rather skeptical. I bought the most recent book(s) on that, but I need to find time and energy to work myself through it.

The nuclear force and the neutron hypothesis

This is a much more focused paper. However, I cannot believe I inserted remarks on the ‘elasticity’ of spacetime there: that stinks of what physicist and Nobel Prize winner Robert B. Laughlin wrote[21]:

“It is ironic that Einstein’s most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed [..] The word ‘ether’ has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum. . . . Relativity actually says nothing about the existence or nonexistence of matter pervading the universe, only that any such matter must have relativistic symmetry. [..] It turns out that such matter exists. About the time relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids. Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness. It is filled with ‘stuff’ that is normally transparent but can be made visible by hitting it sufficiently hard to knock out a part. The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo.”

I was intrigued by that, because I was still struggling somewhat with the meaning of various ratios in my ‘oscillator’ model of elementary particles, but I now think any reference to an ‘aether-like’ quality of space time is not productive. Space and time are, effectively, categories of our mind – as Immanuel Kant had already pointed out about 240 years ago (it is interesting that the Wikipedia article on Einstein notes that Albert Einstein had digested all of Kant’s philosophy at the age of twelve) – and space and time are relativistically related (there is no ‘absolute’ time that ‘pervades’ all of 3D space) – but there is no reason whatsoever to think of relativistic spacetime as being aether-like. It is just the vacuum in which Maxwell’s electromagnetic waves propagate themselves. There is nothing more to it.

An electromagnetic deuteron model

See the general remarks on my attempts to develop a decent model of the neutron and deuteron nucleus. They were triggered by interesting discussions with a Canadian astrophysicist (Andrew Meulenberg), an American retired SLAC researcher (Jerry Va’vra) and a French ‘cold fusion’ researcher (Jean-Luc Paillet). I was originally not very interested because these are aimed at proving a smaller version of the hydrogen (which is usually referred to as the ‘hydrino’) must exist, and that ‘hydrino’ would offer endless possibilities in terms of ‘new energy’ production. The whole enterprise is driven by one of the many crooks that give the field of ‘cold fusion’ a bad name, but managed to get lots of private funding nevertheless: Randell L. Mills, the promotor of the Brilliant Light Power company in New Jersey. The above-mentioned researchers are serious. I do not think as highly of Randell Mills, although I note he impresses people with his books on ‘classical quantum physics’. I note a lot of ‘hocus-pocus’ in these books.

Lectures on Physics Chapter V : Moving charges, EM waves, radiation and near and far fields

This is one of those ‘Feynman-like’ lectures I wrote. I think of all of them as rather nice. I do not go into speculative things, and I take the trouble of writing everything out, so the reader does not have to do all that much thinking and just can ‘digest’ everything rather easily.

Pair production and annihilation as a nuclear process

This is definitely one of the papers I wanted to further develop if ever I would have more time and energy. See my general remarks: SLAC’s E144 experiment (and similar experiments) are very intriguing because they do seem to indicate the quintessential concept of charge may be further reducible to ‘field-like’ oscillations. I must thank André Michaud here for kindly pointing that out to me.

Lectures on Physics Chapter IV : Electron propagation in a lattice

I think of this paper as highly relevant and practical. It points out why the common view that Schrödinger’s wave equation would not be relativistically correct is erroneous: it is based on an erroneous simplification in the ‘heuristic’ derivation of this wave equation in the context of, yes, crystal lattices. Definitely one of the better papers when I look back at it now¾just like the other ‘lecture-like’ papers. The history of these ‘lecture-like’ papers is simple: I realized I needed to write more ‘K-12 level’ papers (although they are obviously not really K-12 level) so as to be able to communicate better on the ‘basics’ of my realist interpretation of quantum physics and the ‘essentials’ of my elementary particle models.

The paper usefully distinguishes concepts that are often used interchangeably, but must be distinguished clearly: waves, fields, oscillations, amplitudes and signals.

The meaning of uncertainty and the geometry of the wavefunction

This is an oft-downloaded paper, and the number of downloads reflects its value: it does offer a rather clear overview of all of my work on ‘interpreting’ the wavefunction, and shows its geometrical meaning. Hence, I will not comment on it: it speaks for itself.

A survivor’s guide to quantum physics

I like this paper. It wanted to present a sort of ‘short-cut’ for people who want to learn about physics fast and, therefore, will want to avoid all of the mistakes I made when trying to understand it.

Lectures on Physics III : The concept of a field

Same remark as for the other ‘lecture-like’ papers: I think of this as a ‘nice’ paper covering all you would want and need to know about the concept of fields.

Feynman’s Time Machine

This paper talks about where Feynman went wrong in his Lectures. Parvus error in principio magnus est in fine (as Aquinas and, before him, Aristotle said so eloquently), and the ‘small mistake at the beginning’ is surely not a ‘happy’ one! :-/ I consider the discovery of this ‘mistake’ to be my greatest personal ‘discovery’ in terms of making sense of it all, and so I do recommend any interested reader to go through the paper.

Lectures on Physics II : Probability amplitudes

This is like the other lectures: a rather straightforward treatment. Of the concept of probability amplitudes, and the related math and physics¾this time.

Lectures on Physics I : Quantum behavior

I appreciate this paper in the same vein: quite straightforward and to the point. It explains the basic ‘mysteries’ which are usually presented in the first course on quantum mechanics at any university in terms that are readily understandable, and shows these are not ‘mysteries’ after all!

Principles of Quantum Physics

For some weird reason, this is a much better ‘summary’ paper than the ones I wrote later (see, for example, my remarks on my Feb 2020 papers).

Matter-waves, amplitudes and signals

This paper further expands on what I consider to be my best paper of all, which is the next one (on de Broglie’s matter-wave). It gets a fair amount of downloads, and so I am happy about that.

De Broglie’s matter-wave: concept and issues

Of all papers, definitely the one I would recommend reading if you have time for only one. See my general remarks on why mainstream QED/QFT does not work. The only thing I should have added are the remarks on Dirac’s equation (this paper has an Annex on wave equations, and so I should have talked about Dirac’s too). But so I did that in the introductory section with general remarks on all of my papers above.

A brief history of quantum-mechanical ideas

I like this paper too. It is not so technical as all of the others, so the ‘lay’ reader may want to go through this. It traces a rather ‘bad’ history of ideas that led nowhere¾but so that is useful to see what should work, and does work, in the field of quantum physics!

The difference between a theory, a calculation, and an explanation

I like this one too. It should probably be read in combination with the above-mentioned paper on the bad ideas in the history of quantum physics.

It is fifty (50!) pages, though. But it has some really interesting things, such as much more consistent presentation of why Mach-Zehnder interference (‘one-photon’ diffraction, or the so-called ‘interference with a photon with itself’) is not so mysterious as it appears to be. It surely should not be explained in terms of nonsensical concepts such as non-locality, entanglement and what have you in modern-day gibberish.

An alternative Theory of Everything: Classical Quantum Physics

This was my very first ‘entry’ on ResearchGate. It is based on the 60-odd papers and the hundreds of blog posts I had published in the decades before, on sites such as that are not considered to be mainstream and, therefore, shunned by most. In fact, in the very beginning, I copied my papers on three sites: ResearchGate, and I stopped doing that when things picked up on RG. I do think of it as the more serious site of the three. 😊


Well… That is it! If you got here, congratulations for your perseverance!

Jean Louis Van Belle, 6 December 2021

[1] I downloaded the image from a website selling Christmas presents long time ago, and I have not been able to trace back from where I have got it. If someone recognizes this as their picture, please let us know and we will acknowledge the source or remove it.

[2] Particles are small – very small – but not infinitesimally small: they have a non-zero spatial dimension, and structure! Only light-like particles – photons and neutrinos – are truly pointlike, but even they do have a structure as they propagate in relativistic spacetime.

[3] I got the label of ‘crackpot theorist’ or the reproach of ‘not understanding the basics’ a bit all too often, and too often from people who do have better academic credentials in the field, but a publication record which is far less impressive¾or in an unrelated field.

[4] See: John Stewart Bell, Speakable and unspeakable in quantum mechanics, pp. 169–172, Cambridge University Press, 1987 (quoted from Wikipedia). J.S. Bell died from a cerebral hemorrhage in 1990 – the year he was nominated for the Nobel Prize in Physics and which he, therefore, did not receive (Nobel Prizes are not awarded posthumously). He was just 62 years old then.

[5] We think the latest revision of SI units (2019) consecrates that: that revision completes physics. It defines a very precise number of constants in Nature, and simplifies the system such that the system is complete without redundancy. It, therefore, respects Occam’s Razor Principle: the number of degrees of freedom in the description matches that which we find in Nature. Besides prof. dr. Pohl’s contributions to solving the proton radius puzzle, his role in the relevant committees on this revision probably also make him one of the truly great scientists of our era.

[6] We contacted both. Ms. Hossenfelder never reacted to our emails. Mr. Carroll quoted some lines from John Baez’ ‘crackpot index’. I had heard such jokes before so I did not find them so amusing anymore.

[7] Sometimes I find an error even in a formula. That is annoying, but then it is also good: it makes readers double-check and look at the material more carefully. It makes them think for themselves, which is what they should do.

[8] Dirac basically expands this basic energy-momentum relation into a series, but the mathematical conditions for which such expansion is valid are, apparently, not there. The first-, second-, third-, fourth-, etc.-order terms do not converge, and one gets those ‘infinities’ which blow it all up¾which is why Dirac, nearing the end of his life, got so critical and annoyed by the very theory his wave equation led to: quantum field theory. Reading between the lines, a number of Nobel Prize winners in physics do seem to reject some of the theories for which they got the award. W.E. Lamb is one of them: he wrote a highly critical paper of the concept of a photon at rather old age, despite the fact that his contributions to this field of study had yielded him a Nobel Prize! Richard Feynman is another example: he got a Nobel Prize for a number of modern contributions, but his analysis of ‘properties’ such as ‘ strangeness’ in his 1963 Lectures on Physics can be read as being highly critical of the ‘ontologizing’ of concepts such as quarks and gluons, which he seems to think of as being mathematical concepts only. I talk a bit about that in my paper on the alternative to modern-day QED and QFT (a new S-matrix programme), so I will not say more about this here.

[9] Protons are ‘nuclear’ particles.

[10] I think I do a much better job at explaining interference and/or diffraction of electrons in the mentioned papers, although the reader may also be hungry for more detail there.

[11] The reader should note that, although the mass of an electron is only about 1/2000 of that of a proton, the radius of a (free) electron is actually much larger than the radius of a proton. That is a strange thing but it is what it is: a proton is very massive because of that very strong (nuclear) force inside. Hence, when trying to visualize these n = p + e models, one should think of something like an electron cloud with a massive positive charge whirling around in it¾rather than the other way around.

[12] The interested reader can google what this is about.

[13] It is a weird coincidence of history that the proceedings of the Solvay Conferences are publicly available in French, even if many papers must have been written in English. The young Louis de Broglie was one of those young secretaries tasked with translations in what was then a very prominent scientific language: French. It got him hooked, obviously.

[14] When reading modern-day articles in journals, one gets the impression a lot of people theorize an awful lot about very little empirical or experimental data.

[15] The idea is that the pointlike charge itself has no inertial mass. It, therefore, goes round and round at the speed of light. However, while doing so, it acquires an effective mass, which is (usually) half of the total mass of the particle as a whole. This ½ factor confuses many, but should not do so. It comes directly out of the energy equipartition principle, and can also be derived from rather straightforward relativistically correct oscillator energy calculations (see p. 9 of our paper on the meaning of the wavefunction).

[17] We get value that is twice as large as the usual 2.8 fm range. By the way, we think of the latter value as being ‘rather random’ because it is just the deuteron radius. Indeed, if, as a nuclear scientist, you do not have any idea about what range to use for a nuclear scale factor (which is pretty much the case), then that is surely a number that would come in handy, because it is empirical rather than theoretical. We honestly think there is nothing more to it, but I think academics will probably cry wolf and say that their models are much more sophisticated than what I suggest here. I will be frank: can you show me why and how, not approximately but exactly?

[18] If you click on the link, you will see my blog post on it, which also thinks of the Higgs particle – a ‘scalar’ particle, really? – as a figment of the mind. My criticism on these theories which can never really be proven goes back years ago, but has not softened. On the contrary.

[19] This is also a paper with a fair amount of types. On page 36, I talk of the prediction of the proton, for example. Of course, I meant to say: the prediction of the existence of the positron. Such typos are bad. I am ashamed.

[20] Some of these ‘sidekicks’ do get more attention in later papers (e.g. this paper has the early thinking on using orbital energy equations to model orbitals of pointlike charges instead of masses), but they come across as rather chaotic and not well thought-through in this paper, because they were chaotic and not well thought-through at that point in time.

[21] We quote from the Wikipedia article on aether theories here.

Extreme views: enthusiasts versus relativity doubters

As mentioned in my previous post, I did pick up a few discussion threads again – on email and on ResearchGate. It led to some more enthusiastic responses and more readings of some of my papers. More substantially, I updated my paper on electron-positron pair production with a discussion on SLAC’s famous 1997 E144 experiment, and my views on it (I do not think matter/antimatter comes out of photons – the experiment does not keep track of the incoming electrons, and what happens to them), and that was an important question which had lingered in my mind and on which I did not have much of an answer (my answer now is not ‘definite’ in any way, but I think it is logical and, therefore, I do not think of the experiment as invalidating the ‘realist’ interpretation of quantum physics that I have been pursuing.

However, the renewed engagement in RG discussions also attracted rather mindboggling interventions of a whole range of new ‘nay-sayers’ who – for some reason I do not understand – doubt relativity theory. I think one can doubt a lot in quantum physics (if you have read any of my papers, you will see I do doubt quite a few things), but not relativity. It pervades each and every equation we use, and those equations have proven to work. Frankly, it is discouraging to see such intelligent people saying such stupid things. I copy one exchange below to highlight the nature of these exchanges, which made me ‘switch off’ again: there are more important things in life than trying to make a blind man see something he just cannot.

I must admit I hate to hear from people who truly seem to doubt that SRT and/or GRT theory is valid that I ‘do not understand the basics’. Pretty incredible, really. It does make one leave the discussion at where it stands – which is at a pretty miserable state. :-/

Deep electron orbitals and the essence of quantum physics

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):

m02c4 = E2 – p2c2 (see, for example, Feynman-I-16, formula 16-3)

Divide the above by c2 and re-arrange and you get Dirac’s equation: W2/c2 – pr2 – m2/c2 = 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 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,


_ _ _

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-vector
potential 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.

We can see the reality of vector potential
in the Aharonov-Bohm effect:
In fact, we can see that vector potential contains more information than E,B fields.
Best regards

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 (, 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,


_ _ _

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

Physical humbug

A good thing and a bad thing today:

1. The good thing is: I expanded my paper which deals with more advanced questions on this realist interpretation of QM (based on mass-without-mass models of elementary particles that I have been pursuing). I think I see everything clearly now: Maxwell’s equations only make sense as soon as the concepts of charge densities (expressed in coulomb per volume or area unit: C/m3 or C/m2) and currents (expressed in C/s) start making sense, which is only above the threshold of Planck’s quantum of action and within the quantization limits set by the Planck-Einstein relation. So, yes, we can, finally, confidently write this:

Quantum Mechanics = All of Physics = Maxwell’s equations + Planck-Einstein relation

2. The bad thing: I had an annoying discussion on ResearchGate on the consistency of quantum physics with one of those people who still seem to doubt both special as well as general relativity theory.

To get my frustration out, I copy the exchange below – as it might be informative when you are confronted with weirdos on some scientific forum too! It starts with a rather non-sensical remark on the reality of infinities, and an equally non-sensical question on how we get quantization from classical equations (Maxwell’s equations and then Gauss and Stokes theorem), to which the answer has to be: we do not, of course! For that, you need to combine them with the Planck-Einstein relation!

Start of the conversation: Jean Louis Van Belle, I found Maxwell quite consistent with, for instance Stokes aether model. Can you explain how he ‘threw it out‘. It was a firm paradigm until Einstein removed it’s power to ‘change‘ light speed, yet said “space without aether is unthinkable.” (Leiden ’21). He then mostly re-instated it in his ’52 paper correcting 1905 interpretations in bounded ‘spaces in motion within spaces) completed in the DFM. ‘QM’ then emerges.

My answer: Dear Peter – As you seem to believe zero-dimensional objects can have properties and, therefore, exist, and also seem to believe infinity is also real (not just a mathematical idealization), then we’re finished talking, because – for example – no sensible interpretation of the Planck-Einstein relation is possible in such circumstances. Also, all of physics revolves around conjugate variables, and these combine in products or product sums that have very small but finite values (think of typical canonic commutator relations, for example): products of infinity and zero are undefined – in mathematics too, by the way! I attach a ‘typically Feynman’ explanation of one of these commutator relations, which talks about the topic rather well. I could also refer to Dirac’s definition of the Dirac function (real probability functions do not collapse into an infinite probability density), or his comments on the infinities appearing in the perturbation theory he himself had developed, and which he then distanced himself from exactly because it generated infinities, which could not be ‘real’ according to him. I’ve got the feeling you’re stuck in 19th century classical physics. Perhaps you missed one or two other points from Einstein as well (apart from the references you give).To relate this discussion to the original question of this thread, I’d say: physicists who mistake mathematical idealizations for reality do obviously not understand quantum mechanics. Cheers – JL

PS: We may, of course, in our private lives believe that God ‘exists’ and that he is infinite and whatever, but that’s personal conviction or opinion: it is not science, nothing empirical that has been verified and can be verified again at any time. Oh – and to answer your specific question on Maxwell’s equations and vector algebra (Gauss and Stokes theorem), they do not incorporate the Planck-Einstein relation. That’s all. Planck-Einstein (quantization of reality) + Maxwell (classical EM) = quantum physics.

Immediate reply: Jean Louis Van Belle , I don’t invoke either zero dimensional objects, infinity or God! Neither the Planck length or Wolframs brilliant 10-93 is ‘zero’. Fermion pair scale is the smallest ‘Condensed Matter‘ but I suggest we must think beyond that to the condensate & ‘vacuum energy’ scales to advance understanding. More 22nd than 19th century! Einstein is easy to ‘cherry pick’ but his search for SR’s ‘physical’ state bore fruit in 1952!

[This Peter actually did refer to infinities and zeroes in math as being more than mathematical idealizations, but then edited out these specific stupidities.]

My answer: Dear Peter – I really cannot understand why you want to disprove SRT. SRT (or, at least, the absoluteness of lightspeed) comes out of Maxwell’s equations. Einstein just provided a rather heuristic argument to ‘prove’ it. Maxwell’s equations are the more ‘real thing’ – so to speak. And then GRT just comes from combining SRT and Mach’s principle. What problem are you trying to solve? I understand that, somehow, QM does NOT come across as ‘consistent’ to you (so I do not suffer from that: all equations look good to me – I just have my own ‘interpretation’ of it, but I do not question their validity). You seem to suspect something is wrong with quantum physics somewhere, but I don’t see exactly where.

Also, can you explain in a few words what you find brilliant about Wolfram’s number? I find the f/m = c2/h = 1.35639248965213E50 number brilliant, because it gives us a frequency per unit mass which is valid for all kinds of mass (electron, proton, or whatever combination of charged and neutral matter you may think of), but so that comes out of the E = mc2 and E = hf, and so it is not some new ‘God-given’ number or something ‘very special’: it is just a straight combination of two fundamental constants of Nature that we already know. I also find the fine-structure constant (and the electric/magnetic constants) ‘brilliant numbers’ but, again, I don’t think they are something mysterious. So what is Wolfram’s number about? What kind of ratio or combination of functions or unexplained explanation or new undiscovered simplification of existing mainstream explanations does it bring? Is it a new proportionality constant – some elasticity of spacetime, perhaps? A combination of Planck-scale units? Does it connect g and the electric constant? An update of (the inverse of) Eddington’s estimate of the number of protons in the Universe based on latest measurements of the cosmological constant? Boltzmann’s number and Avogadro’s constant (or, in light of the negative exponent, their inverse) – through the golden ratio or a whole new ‘holographic’ theory? New numbers are usually easy to explain in terms of existing theory – or in terms of what they propose to change to existing theory, no?

Perhaps an easy start is to give us a physical dimension for Wolfram’s number. My 1.35639248965213E50 number is the (exact) number of oscillations per kg, for example – not oscillations of ‘aether’ or something, but of charge in motion. Except for the fine-structure constant, all numbers in physics have a physical dimension (except if they’re scaling or coupling constants, such as the fine-structure constant), even if it’s only a scalar (plain number), it’s a number describing x units of something) or a density (then it is x per m3 or m2, per J, per kg, per coulomb, per ampere, etcetera – whatever SI unit or combination of SI units you want to choose).

On a very different note, I think that invoking some statement or a late paper of Einstein in an attempt to add ‘authority’ to some kind of disproof of SRT invokes the wrong kind of authority. 🙂 If you would say Heisenberg or Bohr or Dirac or Feynman or Oppenheimer started doubting SRT near the end of their lives, I’d look up and say: what? Now, no. Einstein had the intellectual honesty to speak up, and speak up rather loudly (cf. him persuading the US President to build the bomb).

As for the compatibility between SRT and GRT and quantum mechanics, the relativistically invariant argument of the wavefunction shows no such incompatibility is there (see Annex II and III of The Zitterbewegung hypothesis and the scattering matrix). Cheers – JL


Personal conclusion: I think I’ll just stay away from ResearchGate discussions for a while. They are not always good for one’s peace of mind. :-/

All of physics

This five-pager has it: all you ever wanted to know about the Universe. Electron mass and proton mass are seen as input to the model. To the most famous failed experiment in all of classical physics – the 1887 Michelson-Morley experiment, which disproved aether theories and established the absoluteness of lightspeed – we should add the Kamioka Nucleon Decay Experiment, which firmly established that protons do not decay. All the rest is history. 🙂

Post scriptum (26 April): I added another five-pager on fundamental concepts on ResearchGate, which may or may not help to truly understand what might be the case (I am paraphrasing Wittgenstein’s definition of reality here). It is on potentials, and it explains why thinking in terms of neat 1/r or 1/r2 functions is not all that helpful: reality is fuzzier than that. Even a simple electrostatic potential may be not very simple. The fuzzy concept of near and far fields remains useful.

I am actually very happy with the paper, because it sort of ‘completes’ my thinking on elementary particles in terms of ring currents. It made me feel like it is the first time I truly understand the complementarity/uncertainty principle – and that I invoke it to make an argument.

The nuclear force and gauge

I just wrapped up a discussion with some mainstream physicists, producing what I think of as a final paper on the nuclear force. I was struggling with the apparent non-conservative nature of the nuclear potential, but now I have the solution. It is just like an electric dipole field: not spherically symmetric. Nice and elegant.

I can’t help copying the last exchange with one of the researchers. He works at SLAC and seems to believe hydrinos might really exist. It is funny, and then it is not. :-/

Me: “Dear X – That is why I am an amateur physicist and don’t care about publication. I do not believe in quarks and gluons. 😊 Do not worry: it does not prevent me from being happy. JL”

X: “Dear Jean Louis – The whole physics establishment believes that neutron is composed of three quarks, gluons and a see of quark-antiquark pairs. How does that fit into your picture? Best regards, X”

Me: “I see the neutron as a tight system between positive and negative electric charge – combining electromagnetic and nuclear force. The ‘proton + electron’ idea is vague. The idea of an elementary particle is confusing in discussions and must be defined clearly: stable, not-reducible, etcetera. Neutrons decay (outside of the nucleus), so they are reducible. I do not agree with Heisenberg on many fronts (especially not his ‘turnaround’ on the essence of the Uncertainty Principle) so I don’t care about who said what – except Schroedinger, who fell out with both Dirac and Heisenberg, I feel. His reason to not show up at the Nobel Prize occasion in 1933 (where Heisenberg received the prize of the year before, and Dirac/Schroedinger the prize of the year itself) was not only practical, I think – but that’s Hineininterpretierung which doesn’t matter in questions like this. JL”

X: “Dear Jean Louis – I want to to make doubly sure. Do I understand you correctly that you are saying that neutron is really a tight system of proton and electron ? If that is so, it is interesting that Heisenberg, inventor of the uncertainty principle, believed the same thing until 1935 (I have it from Pais book). Then the idea died because. Pauli’s argument won, that the neutron spin 1/2 follows the Fermi-Dirac statistics and this decided that the neutron is indeed an elementary particle. This would very hard sell, if you now, after so many years, agree with Heisenberg. By the way, I say in my Phys. Lett. B paper, which uses k1/r + k2/r2 potential, that the radius of the small hydrogen is about 5.671 Fermi. But this is very sensitive to what potential one is using. Best regards, X.”

Quaternions and the nuclear wave equation

In this blog, we talked a lot about the Zitterbewegung model of an electron, which is a model which allows us to think of the elementary wavefunction as representing a radius or position vector. We write:

ψ = r = a·e±iθ = a·[cos(±θ) + i · sin(±θ)]

It is just an application of Parson’s ring current or magneton model of an electron. Note we use boldface to denote vectors, and that we think of the sine and cosine here as vectors too! You should note that the sine and cosine are the same function: they differ only because of a 90-degree phase shift: cosθ = sin(θ + π/2). Alternatively, we can use the imaginary unit (i) as a rotation operator and use the vector notation to write: sinθ = i·cosθ.

In one of our introductory papers (on the language of math), we show how and why this all works like a charm: when we take the derivative with respect to time, we get the (orbital or tangential) velocity (dr/dt = v), and the second-order derivative gives us the (centripetal) acceleration vector (d2r/dt2 = a). The plus/minus sign of the argument of the wavefunction gives us the direction of spin, and we may, perhaps, add a plus/minus sign to the wavefunction as a whole to model matter and antimatter, respectively (the latter assertion is very speculative though, so we will not elaborate that here).

One orbital cycle packs Planck’s quantum of (physical) action, which we can write either as the product of the energy (E) and the cycle time (T), or the momentum (p) of the charge times the distance travelled, which is the circumference of the loop λ in the inertial frame of reference (we can always add a classical linear velocity component when considering an electron in motion, and we may want to write Planck’s quantum of action as an angular momentum vector (h or ħ) to explain what the Uncertainty Principle is all about (statistical uncertainty, nothing ontological), but let us keep things simple as for now):

h = E·T = p·λ

It is important to distinguish between the electron and the charge, which we think of being pointlike: the electron is charge in motion. Charge is just charge: it explains everything and its nature is, therefore, quite mysterious: is it really a pointlike thing, or is there some fractal structure? Of these things, we know very little, but the small anomaly in the magnetic moment of an electron suggests its structure might be fractal. Think of the fine-structure constant here, as the factor which distinguishes the classical, Compton and Bohr radii of the electron: we associate the classical electron radius with the radius of the poinlike charge, but perhaps we can drill down further.

We also showed how the physical dimensions work out in Schroedinger’s wave equation. Let us jot it down to appreciate what it might model, and appreciate why complex numbers come in handy:

Schroedinger’s equation in free space

This is, of course, Schroedinger’s equation in free space, which means there are no other charges around and we, therefore, have no potential energy terms here. The rather enigmatic concept of the effective mass (which is half the total mass of the electron) is just the relativistic mass of the pointlike charge as it whizzes around at lightspeed, so that is the motion which Schroedinger referred to as its Zitterbewegung (Dirac confused it with some motion of the electron itself, further compounding what we think of as de Broglie’s mistaken interpretation of the matter-wave as a linear oscillation: think of it as an orbital oscillation). The 1/2 factor is there in Schroedinger’s wave equation for electron orbitals, but he replaced the effective mass rather subtly (or not-so-subtly, I should say) by the total mass of the electron because the wave equation models the orbitals of an electron pair (two electrons with opposite spin). So we might say he was lucky: the two mistakes together (not accounting for spin, and adding the effective mass of two electrons to get a mass factor) make things come out alright. 🙂

However, we will not say more about Schroedinger’s equation for the time being (we will come back to it): just note the imaginary unit, which does operate like a rotation operator here. Schroedinger’s wave equation, therefore, must model (planar) orbitals. Of course, the plane of the orbital itself may be rotating itself, and most probably is because that is what gives us those wonderful shapes of electron orbitals (subshells). Also note the physical dimension of ħ/m: it is a factor which is expressed in m2/s, but when you combine that with the 1/m2 dimension of the ∇2 operator, then you get the 1/s dimension on both sides of Schroedinger’s equation. [The ∇2 operator is just the generalization of the d2r/dx2 but in three dimensions, so x becomes a vector: x, and we apply the operator to the three spatial coordinates and get another vector, which is why we call ∇2 a vector operator. Let us move on, because we cannot explain each and every detail here, of course!]

We need to talk forces and fields now. This ring current model assumes an electromagnetic field which keeps the pointlike charge in its orbit. This centripetal force must be equal to the Lorentz force (F), which we can write in terms of the electric and magnetic field vectors E and B (fields are just forces per unit charge, so the two concepts are very intimately related):

F = q·(E + v×B) = q·(E + c×E/c) = q·(E + 1×E) = q·(E + j·E) = (1+ j)·q·E

We use a different imaginary unit here (j instead of i) because the plane in which the magnetic field vector B is going round and round is orthogonal to the plane in which E is going round and round, so let us call these planes the xy– and xz-planes respectively. Of course, you will ask: why is the B-plane not the yz-plane? We might be mistaken, but the magnetic field vector lags the electric field vector, so it is either of the two, and so now you can check for yourself of what we wrote above is actually correct. Also note that we write 1 as a vector (1) or a complex number: 1 = 1 + i·0. [It is also possible to write this: 1 = 1 + i·0 or 1 = 1 + i·0. As long as we think of these things as vectors – something with a magnitude and a direction – it is OK.]

You may be lost in math already, so we should visualize this. Unfortunately, that is not easy. You may to google for animations of circularly polarized electromagnetic waves, but these usually show the electric field vector only, and animations which show both E and B are usually linearly polarized waves. Let me reproduce the simplest of images: imagine the electric field vector E going round and round. Now imagine the field vector B being orthogonal to it, but also going round and round (because its phase follows the phase of E). So, yes, it must be going around in the xz– or yz-plane (as mentioned above, we let you figure out how the various right-hand rules work together here).

Rotational plane of the electric field vector

You should now appreciate that the E and B vectors – taken together – will also form a plane. This plane is not static: it is not the xy-, yz– or xz-plane, nor is it some static combination of two of these. No! We cannot describe it with reference to our classical Cartesian axes because it changes all the time as a result of the rotation of both the E and B vectors. So how we can describe that plane mathematically?

The Irish mathematician William Rowan Hamilton – who is also known for many other mathematical concepts – found a great way to do just that, and we will use his notation. We could say the plane formed by the E and B vectors is the EB plane but, in line with Hamilton’s quaternion algebra, we will refer to it as the k-plane. How is it related to what we referred to as the i– and j-planes, or the xy– and xz-plane as we used to say? At this point, we should introduce Hamilton’s notation: he did write i and j in boldface (we do not like that, but you may want to think of it as just a minor change in notation because we are using these imaginary units in a new mathematical space: the quaternion number space), and he referred to them as basic quaternions in what you should think of as an extension of the complex number system. More specifically, he wrote this on a now rather famous bridge in Dublin:

i2 = -1

j2 = -1

k2 = -1

i·j = k

j·i= k

The first three rules are the ones you know from complex number math: two successive rotations by 90 degrees will bring you from 1 to -1. The order of multiplication in the other two rules ( i·j = k and j·i = –k ) gives us not only the k-plane but also the spin direction. All other rules in regard to quaternions (we can write, for example, this: i ·j·k = -1), and the other products you will find in the Wikipedia article on quaternions) can be derived from these, but we will not go into them here.

Now, you will say, we do not really need that k, do we? Just distinguishing between i and j should do, right? The answer to that question is: yes, when you are dealing with electromagnetic oscillations only! But it is no when you are trying to model nuclear oscillations! That is, in fact, exactly why we need this quaternion math in quantum physics!

Let us think about this nuclear oscillation. Particle physics experiments – especially high-energy physics experiments – effectively provide evidence for the presence of a nuclear force. To explain the proton radius, one can effectively think of a nuclear oscillation as an orbital oscillation in three rather than just two dimensions. The oscillation is, therefore, driven by two (perpendicular) forces rather than just one, with the frequency of each of the oscillators being equal to ω = E/2ħ = mc2/2ħ.

Each of the two perpendicular oscillations would, therefore, pack one half-unit of ħ only. The ω = E/2ħ formula also incorporates the energy equipartition theorem, according to which each of the two oscillations should pack half of the total energy of the nuclear particle (so that is the proton, in this case). This spherical view of a proton fits nicely with packing models for nucleons and yields the experimentally measured radius of a proton:

Proton radius formula

Of course, you can immediately see that the 4 factor is the same factor 4 as the one appearing in the formula for the surface area of a sphere (A = 4πr2), as opposed to that for the surface of a disc (A = πr2). And now you should be able to appreciate that we should probably represent a proton by a combination of two wavefunctions. Something like this:

Proton wavefunction

What about a wave equation for nuclear oscillations? Do we need one? We sure do. Perhaps we do not need one to model a neutron as some nuclear dance of a negative and a positive charge. Indeed, think of a combination of a proton and what we will refer to as a deep electron here, just to distinguish it from an electron in Schroedinger’s atomic electron orbitals. But we might need it when we are modeling something more complicated, such as the different energy states of, say, a deuteron nucleus, which combines a proton and a neutron and, therefore, two positive charges and one deep electron.

According to some, the deep electron may also appear in other energy states and may, therefore, give rise to a different kind of hydrogen (they are referred to as hydrinos). What do I think of those? I think these things do not exist and, if they do, they cannot be stable. I also think these researchers need to come up with a wave equation for them in order to be credible and, in light of what we wrote about the complications in regard to the various rotational planes, that wave equation will probably have all of Hamilton’s basic quaternions in it. [But so, as mentioned above, I am waiting for them to come up with something that makes sense and matches what we can actually observe in Nature: those hydrinos should have a specific spectrum, and we do not such see such spectrum from, say, the Sun, where there is so much going on so, if hydrinos exist, the Sun should produce them, right? So, yes, I am rather skeptical here: I do think we know everything now and physics, as a science, is sort of complete and, therefore, dead as a science: all that is left now is engineering!]

But, yes, quaternion algebra is a very necessary part of our toolkit. It completes our description of everything! 🙂

The physics of the wave equation

The rather high-brow discussions on deep electron orbitals and hydrinos with a separate set of interlocutors, inspired me to write a paper at the K-12 level on wave equations. Too bad Schroedinger did not seem to have left any notes on how he got his wave equation (which I believe to be correct in every way (relativistically correct, too), unlike Dirac’s or others).

The notes must be somewhere in some unexplored archive. If there are Holy Grails to be found in the history of physics, then these notes are surely one of them. There is a book about a mysterious woman, who might have inspired Schrödinger, but I have not read it, yet: it is on my to-read list. I will prioritize it (read: order it right now). 🙂

Oh – as for the math and physics of the wave equation, you should also check the Annex to the paper: I think the nuclear oscillation can only be captured by a wave equation when using quaternion math (an extension to complex math).

Cold and hot fusion: just hot air?

I just finished a very short paper recapping the basics of my model of the nuclear force. I wrote it a bit as a reaction to a rather disappointing exchange that is still going on between a few researchers who seem to firmly believe some crook who claims he can produce smaller hydrogen atoms (hydrinos) and get energy out of them. I wrote about my disappointment on one of my other blogs (I also write on politics and more general matters). Any case, the thing I want to do here, is to firmly state my position in regard to cold and hot fusion: I do not believe in either. Theoretically, yes. Of course. But, practically speaking, no. And that’s a resounding no!

The illustration below (from Wikimedia Commons) shows how fusion actually happens in our Sun (I wrote more about that in one of my early papers). As you can see, there are several pathways, and all of these pathways are related through critical masses of radiation and feedback loops. So it is not like nuclear fission, which (mainly) relies on cascaded neutron production. No. It is much more complicated, and you would have to create and contain a small star on Earth to recreate the conditions that are prevalent in the Sun. Containing a relatively small amount of hydrogen plasma in incredibly energy-intensive electromagnetic fields will not do the trick. First, the reaction will peter out. Second, the reaction will yield no net energy: the plasma and electromagnetic fields that are needed to contain the plasma will suck everything up, and much more than that. So, yes, The ITER project is a huge waste of taxpayers’ money.

As for cold fusion, I believe the small experiments showing anomalous heat reactions (or low-energy nuclear reactions as these phenomena are also referred to) are real (see my very first blog post on these) but (1) researchers have done a poor job at replicating these experiments consistently, (2) have failed to provide a firm theoretical basis for those reactions, and (3) whatever theory there is, also strongly hints we should not hope to ever get net energy out of it. This explains why public funding for cold fusion is very limited. Furthermore, scientists who continue to support frauds like Dr. Mills will soon erase whatever credibility smaller research labs in this field have painstakingly built up. So, no, it won’t happen. Too bad, because LENR research itself is quite interesting, and may yield more insights than the next mega-project of CERN, SLAC and what have you. :-/

Post scriptum: On the search for hydrinos (hypothetical small hydrogen), following exchange with a scientist working for a major accelerator lab in the US – part of a much longer one – is probably quite revealing. When one asks why it has not been discovered yet, the answer is invariably the same: we need a new accelerator project for that. I’ll hide the name of the researcher by calling him X.

Dear Jean Louis – They cannot be produced in the Sun, as electron has to be very relativistic. According to my present calculation one has to have a total energy of Etotal ~34.945 MeV. Proton of the same velocity has to have total energy Etotal ~64.165 GeV. One can get such energies in very energetic evens in Universe. On Earth, it would take building special modifications of existing accelerators. This is why it has not been discovered so far.

Best regards, [X]

From: Jean Louis Van Belle <>
Date: Wednesday, March 31, 2021 at 9:24 AM
To: [X]
Cc: [Two other LENR/CF researchers]
Subject: Calculations and observations…

Interesting work, but hydrino-like structures should show a spectrum with gross lines, split in finer lines and hyperfine lines (spin coupling between nucleon(s) and (deep) electron. If hydrinos exist, they should be produced en masse in the Sun. Is there any evidence from unusual spectral lines? Until then, I think of the deep electron as the negative charge in the neutron or in the deuteron nucleus. JL

Temperature, RIs, and spectral lines

A sympathetic researcher, Steve Langford, sent me some of his papers, as well as a link to his ResearchGate site, where you will find more. Optical minerology is his field. Fascinating work – or, at the very least, a rather refreshing view on the nitty-gritty of actually measuring stuff by gathering huge amounts of data, and then analyzing it in meaningful ways. I learnt a lot of new things already (e.g. kriging or Gaussian regression analysis, and novel ways of applying GLM modelling).

Dr. Langford wrote me because he wants to connect his work to more theory – quantum math, and all that. That is not so easy. He finds interesting relations between temperature and refractive indices (RIs), as measured from a single rock sample in Hawaii. The equipment he used, is shown below. I should buy that stuff too! I find it amazing one can measure light spectra with nanometer precision with these tools (the dial works with 0.1 nm increments, to be precise). He knows all about Bragg’s Law and crystal structures, toys with statistical and graphical software tools such as JMP, Surfer, and talks about equipping K-12 level students with dirt-cheap modular computer-connected optical devices and open software tools to automate the data gathering process. In short, I am slightly jealous of the practical value of his work, and the peace of mind he must have to do all of this! At the very least, he can say he actually did something in his life! 🙂

Having showered all that praise, I must admit I have no clue about how to connect all of this to quantum effects. All I know about temperature – about what it actually is (vibrational motion of molecules and atoms within molecules, with multiple degrees of freedom (n > 3) in that motion) – is based on Feynman’s Lectures (Chapters 40 to 45 of the first Volume). Would all that linear, orbital and vibrational motion generate discernible shifts of spectral lines? Moreover, would it do so in the visible light spectrum (X-rays are usually used – increases measurement precision – but such equipment is more expensive)? I have no idea.

Or… Well, of course I do have some intuitions. Shifts in frequency spectra are well explained by combining statistics and the Planck-Einstein relation. But can we see quantum physics in the data? In the spectral lines themselves? No. Not really. And so that’s what’s got me hooked. Explaining a general shift of the frequency spectrum and discerning quantum effects in RIs in data sets (analyzing shifts of spectral lines) are two very different things. So how could we go about that?

Energy is surely quantized, and any small difference in energy must probably translate into small shifts of the frequencies of the spectral lines themselves (as opposed to the general shift of the spectrum as such, which, as mentioned above, is well-explained by quantum physics) respecting the Planck-Einstein relation for photons (E = hf). I do not know if anyone tried to come up with some kind of quantum-mechanical definition of the concept of entropy, (but I have not googled anything on that, so I expect there must be valuable resources on that out there), and Boltzmann’s constant was re-defined at the occasion of the 2019 revision of the SI system of units – and a careful examination of the rationale of that revision or re-definition should yield deeper insights in this regard, especially because I think that revision firmly anchors what I refer to as a realist interpretation of quantum physics. Thermal radiation is microwave-range radiation, so a 0.1 nm resolution should be enough to capture a shift in spectral lines – if it is there, that is.

I need to think on this. As for now, I look at Langford’s work as art, and one of his interests is, effectively, to connect art and science. Let me quote one of his commentaries on one of his images: “Light and matter dance at 30°C, upon what is essentially a Calcium-Silicate substrate through which light and various chemicals flow. Swirling Yin-Yang patterns reminiscent of Solar flares and magnetic lines of force also remind me of fractal patterns.” [My italics.]

He does phrase it very beautifully, doesn’t he? Maybe I will find some deeper meaning to it later. Dr. Langford’s suggestion to re-phrase quantum-mechanical models in terms of Poynting vectors is one that strikes a note, and there are other ideas there as well. It must be possible to find quantum-mechanical effects by further analyzing, for example, the relation between temperature and RIs, indeed – and to use the formal (consistent and complete!) language of quantum mechanics to (also) explain Dr. Langford’s findings. This would conclusively relate the micro-level of quantum physics to the macro-level of crystals (isotropic or anisotropic structures), and it would not require supercooled condensates or massive investments in new accelerator facilities.

It would also provide amateur physicists with a way to discover and verify all by themselves. That would be a great result in itself. 🙂

Post scriptum (27 March): Looking at the papers again, I do not see a shift in spectral lines. Spectral lines correspond to differences between quantized energies in electron orbitals. These are either atomic orbitals or molecular orbitals (valence electrons), and shifts between orbitals corresponds to spectral lines in the visible spectrum (Rydberg-scale energies) or, in case of molecular orbitals, microwave photons being absorbed or emitted. Temperature just increases the intensity of photon beams going in and out of the system (the rock sample, in this case), and so it causes a shift of the spectrum, but the lines are what they are: their energy is and remains what it is (E = hf). Of course, the superposition principe tells us the energies of microwave and visual-spectrum energies can combine in what resembles a normal distribution around a mean (which, yes, shifts with temperature alright).

As for the gist of the matter, yes, of course, what Dr. Langford is seeing, are quantum-mechanical effects alright.

Post scriptum (9 April 2021): In the preceding week, I found that Dr. Langford seems to find my math too difficult, and turns to pseudo-scientists such as Nassim Haramein, and contributes to Haramein’s Resonance Science Foundation. I dissociate completely from such references and like associations. Everyone is free to seek inspiration elsewhere, but Haramein’s mystical stories are definitely not my cup of tea.

The Language of Physics

The meaning of life in 15 pages !🙂 [Or… Well… At least a short description of the Universe… Not sure it helps in sense-making.] 🙂

Post scriptum (25 March 2021): Because this post is so extremely short and happy, I want to add a sad anecdote which illustrates what I have come to regard as the sorry state of physics as a science.

A few days ago, an honest researcher put me in cc of an email to a much higher-brow researcher. I won’t reveal names, but the latter – I will call him X – works at a prestigious accelerator lab in the US. The gist of the email was a question on an article of X: “I am still looking at the classical model for the deep orbits. But I have been having trouble trying to determine if the centrifugal and spin-orbit potentials have the same relativistic correction as the Coulomb potential. I have also been having trouble with the Ademko/Vysotski derivation of the Veff = V×E/mc2 – V2/2mc2 formula.”

I was greatly astonished to see X answer this: “Hello – What I know is that this term comes from the Bethe-Salpeter equation, which I am including (#1). The authors say in their book that this equation comes from the Pauli’s theory of spin. Reading from Bethe-Salpeter’s book [Quantum mechanics of one and two electron atoms]: “If we disregard all but the first three members of this equation, we obtain the ordinary Schroedinger equation. The next three terms are peculiar to the relativistic Schroedinger theory”. They say that they derived this equation from covariant Dirac equation, which I am also including (#2). They say that the last term in this equation is characteristic for the Dirac theory of spin ½ particles. I simplified the whole thing by choosing just the spin term, which is already used for hyperfine splitting of normal hydrogen lines. It is obviously approximation, but it gave me a hope to satisfy the virial theorem. Of course, now I know that using your Veff potential does that also. That is all I know.” [I added the italics/bold in the quote.]

So I see this answer while browsing through my emails on my mobile phone, and I am disgusted – thinking: Seriously? You get to publish in high-brow journals, but so you do not understand the equations, and you just drop terms and pick the ones that suit you to make your theory fit what you want to find? And so I immediately reply to all, politely but firmly: “All I can say, is that I would not use equations which I do not fully understand. Dirac’s wave equation itself does not make much sense to me. I think Schroedinger’s original wave equation is relativistically correct. The 1/2 factor in it has nothing to do with the non-relativistic kinetic energy, but with the concept of effective mass and the fact that it models electron pairs (two electrons – neglect of spin). Andre Michaud referred to a variant of Schroedinger’s equation including spin factors.”

Now X replies this, also from his iPhone: “For me the argument was simple. I was desperate trying to satisfy the virial theorem after I realized that ordinary Coulomb potential will not do it. I decided to try the spin potential, which is in every undergraduate quantum mechanical book, starting with Feynman or Tippler, to explain the hyperfine hydrogen splitting. They, however, evaluate it at large radius. I said, what happens if I evaluate it at small radius. And to my surprise, I could satisfy the virial theorem. None of this will be recognized as valid until one finds the small hydrogen experimentally. That is my main aim. To use theory only as a approximate guidance. After it is found, there will be an explosion of “correct” theories.” A few hours later, he makes things even worse by adding: “I forgot to mention another motivation for the spin potential. I was hoping that a spin flip will create an equivalent to the famous “21cm line” for normal hydrogen, which can then be used to detect the small hydrogen in astrophysics. Unfortunately, flipping spin makes it unstable in all potential configurations I tried so far.”

I have never come across a more blatant case of making a theory fit whatever you want to prove (apparently, X believes Mills’ hydrinos (hypothetical small hydrogen) are not a fraud), and it saddens me deeply. Of course, I do understand one will want to fiddle and modify equations when working on something, but you don’t do that when these things are going to get published by serious journals. Just goes to show how physicists effectively got lost in math, and how ‘peer reviews’ actually work: they don’t. :-/

A simple explanation of quantum-mechanical operators

I added an Annex to a paper that talks about all of the fancy stuff quantum physicists like to talk about, like scattering matrices and high-energy particle events. The Annex, however, is probably my simplest and shortest summary of the ordinariness of wavefunction math, including a quick overview of what quantum-mechanical operators actually are. It does not make use of state vector algebra or the usual high-brow talk about Gilbert spaces and what have you: you only need to know what a derivative is, and combine it with our realist interpretation of what the wavefunction actually represents.

I think I should do a paper on the language of physics. To show how (i) rotations (i, j, k), (ii) scalars (constants or just numerical values) and (iii) vectors (real vectors (e.g. position vectors) and pseudovectors (e.g. angular frequency or momentum)), and (iv) operators (derivatives of the wavefunction with respect to time and spatial directions) form ‘words’ (e.g. energy and momentum operators), and how these ‘words’ then combine into meaningful statements (e.g. Schroedinger’s equation).

All of physics can then be summed up in a half-page or so. All the rest is thermodynamics 🙂 JL

PS: You only get collapsing wavefunctions when adding uncertainty to the models (i.e. our own uncertainty about the energy and momentum). The ‘collapse’ of the wavefunction (let us be precise, the collapse of the (dissipating) wavepacket) thus corresponds to the ‘measurement’ operation. 🙂

PS2: Incidentally, the analysis also gives an even more intuitive explanation of Einstein’s mass-energy equivalence relation, which I summarize in a reply to one of the many ‘numerologist’ physicists on ResearchGate (copied below).

The Nature of Antimatter (dark matter)

The electromagnetic force has an asymmetry: the magnetic field lags the electric field. The phase shift is 90 degrees. We can use complex notation to write the E and B vectors as functions of each other. Indeed, the Lorentz force on a charge is equal to: F = qE + q(v×B). Hence, if we know the (electric field) E, then we know the (magnetic field) B: B is perpendicular to E, and its magnitude is 1/c times the magnitude of E. We may, therefore, write:

B = –iE/c

The minus sign in the B = –iE/c expression is there because we need to combine several conventions here. Of course, there is the classical (physical) right-hand rule for E and B, but we also need to combine the right-hand rule for the coordinate system with the convention that multiplication with the imaginary unit amounts to a counterclockwise rotation by 90 degrees. Hence, the minus sign is necessary for the consistency of the description. It ensures that we can associate the aeiEt/ħ and aeiEt/ħ functions with left and right-handed spin (angular momentum), respectively.

Now, we can easily imagine a antiforce: an electromagnetic antiforce would have a magnetic field which precedes the electric field by 90 degrees, and we can do the same for the nuclear force (EM and nuclear oscillations are 2D and 3D oscillations respectively). It is just an application of Occam’s Razor principle: the mathematical possibilities in the description (notations and equations) must correspond to physical realities, and vice versa (one-on-one). Hence, to describe antimatter, all we have to do is to put a minus sign in front of the wavefunction. [Of course, we should also take the opposite of the charge(s) of its antimatter counterpart, and please note we have a possible plural here (charges) because we think of neutral particles (e.g. neutrons, or neutral mesons) as consisting of opposite charges.] This is just the principle which we already applied when working out the equation for the neutral antikaon (see Annex IV and V of the above-referenced paper):

Don’t worry if you do not understand too much of the equations: we just put them there to impress the professionals. 🙂 The point is this: matter and antimatter are each other opposite, literally: the wavefunctions aeiEt/ħ and –aeiEt/ħ add up to zero, and they correspond to opposite forces too! Of course, we also have lightparticles, so we have antiphotons and antineutrinos too.

We think this explains the rather enormous amount of so-called dark matter and dark energy in the Universe (the Wikipedia article on dark matter says it accounts for about 85% of the total mass/energy of the Universe, while the article on the observable Universe puts it at about 95%!). We did not say much about this in our YouTube talk about the Universe, but we think we understand things now. Dark matter is called dark because it does not appear to interact with the electromagnetic field: it does not seem to absorb, reflect or emit electromagnetic radiation, and is, therefore, difficult to detect. That should not be a surprise: antiphotons would not be absorbed or emitted by ordinary matter. Only anti-atoms (i.e. think of a antihydrogen atom as a antiproton and a positron here) would do so.

So did we explain the mystery? We think so. 🙂

We will conclude with a final remark/question. The opposite spacetime signature of antimatter is, obviously, equivalent to a swap of the real and imaginary axes. This begs the question: can we, perhaps, dispense with the concept of charge altogether? Is geometry enough to understand everything? We are not quite sure how to answer this question but we do not think so: a positron is a positron, and an electron is an electron¾the sign of the charge (positive and negative, respectively) is what distinguishes them! We also think charge is conserved, at the level of the charges themselves (see our paper on matter/antimatter pair production and annihilation).

We, therefore, think of charge as the essence of the Universe. But, yes, everything else is sheer geometry! 🙂

The End of Physics?

There are two branches of physics. The nicer branch studies equilibrium states: simple laws, stable particles (electrons and protons, basically), the expanding (oscillating?) Universe, etcetera. This branch includes the study of dynamical systems which we can only describe in terms of probabilities or approximations: think of kinetic gas theory (thermodynamics) or, much simpler, hydrostatics (the flow of water, Feynman, Vol. II, chapters 40 and 41), about which Feynman writes this:

“The simplest form of the problem is to take a pipe that is very long and push water through it at high speed. We ask: to push a given amount of water through that pipe, how much pressure is needed? No one can analyze it from first principles and the properties of water. If the water flows very slowly, or if we use a thick goo like honey, then we can do it nicely. You will find that in your textbook. What we really cannot do is deal with actual, wet water running through a pipe. That is the central problem which we ought to solve some day, and we have not.” (Feynman, I-3-7)

Still, we believe first principles do apply to the flow of water through a pipe. In contrast, the second branch of physics – we think of the study of non-stable particles here: transients (charged kaons and pions, for example) or resonances (very short-lived intermediate energy states). The class of physicists who studies these must be commended, but they resemble econometrists modeling input-output relations: if they are lucky, they will get some kind of mathematical description of what goes in and what goes out, but the math does not tell them how stuff actually happens. It leads one to think about the difference between a theory, a calculation and an explanation. Simplifying somewhat, we can represent such input-output relations by thinking of a process that will be operating on some state |ψ⟩ to produce some other state |ϕ⟩, which we write like this:


A is referred to as a Hermitian matrix if the process is reversible. Reversibility looks like time reversal, which can be represented by taking the complex conjugate ⟨ϕ|A|ψ⟩* = ⟨ψ|A†|ϕ⟩: we put a minus sign in front of the imaginary unit, so we have –i instead of i in the wavefunctions (or i instead of –i with respect to the usual convention for denoting the direction of rotation). Processes may not reversible, in which case we talk about symmetry-breaking: CPT-symmetry is always respected so, if T-symmetry (time) is broken, CP-symmetry is broken as well. There is nothing magical about that.

Physicists found the description of these input-output relations can be simplified greatly by introducing quarks (see Annex II of our paper on ontology and physics). Quarks have partial charge and, more generally, mix physical dimensions (mass/energy, spin or (angular) momentum). They create some order – think of it as some kind of taxonomy – in the vast zoo of (unstable) particles, which is great. However, we do not think there was a need to give them some kind of ontological status: unlike plants or insects, partial charges do not exist.

We also think the association between forces and (virtual) particles is misguided. Of course, one might say forces are being mediated by particles (matter- or light-particles), because particles effectively pack energy and angular momentum (light-particles – photons and neutrinos – differ from matter-particles (electrons, protons) in that they carry no charge, but they do carry electromagnetic and/or nuclear energy) and force and energy are, therefore, being transferred through particle reactions, elastically or non-elastically. However, we think it is important to clearly separate the notion of fields and particles: they are governed by the same laws (conservation of charge, energy, and (linear and angular) momentum, and – last but not least – (physical) action) but their nature is very different.

W.E. Lamb (1995), nearing the end of his very distinguished scientific career, wrote about “a comedy of errors and historical accidents”, but we think the business is rather serious: we have reached the End of Science. We have solved Feynman’s U = 0 equation. All that is left, is engineering: solving practical problems and inventing new stuff. That should be exciting enough. 🙂

Post scriptum: I added an Annex (III) to my paper on ontology and physics, with what we think of as a complete description of the Universe. It is abstruse but fun (we hope!): we basically add a description of events to Feynman’s U = 0 (un)worldliness formula. 🙂