Matter and anti-matter: what’s the difference? The charge, of course: positive versus negative. Yes. Of course! But what’s beyond? Our ring current model offers a geometric explanation, so we thought we might try our hand at offering a geometric explanation of the difference between matter and anti-matter too. Have a look at the paper. It’s kinda primitive, but I need to start somewhere, right? 🙂
I just produced a first draft of the Metaphysics page of my new physics site. It does not only deal with the fundamental concepts we have been developing but – as importantly, if not more – it also offers some thoughts on all of the unanswered questions which, when trying to do science and be logical, are at least as important as the questions we do consider to be solved. Click the link or the tab. Enjoy ! 🙂 As usual, feedback is more than welcome!
In my previous post, I wrote about the End of Physics. Of course, we need to replace the Old Physics by the new. I have structured a new website (ideez.org), and created the very first page for it. It is probably the most fundamental one, as it deals with all of the matter-particles: it uses the ring current model to explain their geometry which – in turn – explains all of their intrinsic properties. No magic here ! Or… Well… Maybe it’s the right kind of magic ! No Bright Shining Lies, in any case ! Enjoy ! JL
I just uploaded an update of my 10-page summary of what—paraphrasing Wittgenstein—I think might be the case. 🙂 So what’s that? It’s a basic description of what I think of as reality—at the most fundamental level, that is—in terms of a concise set of (classical) equations that speak to us (or to me, I should say). Needless to say, that set of classical equations includes an interpretation of the Planck-Einstein relation: E = h·f or E·T = h, in which T is interpreted as the cycle time of a particle.
The reader who hasn’t read me before will probably raise his (or her?) eyebrows here: the cycle time of a particle? Seriously? What do you mean by that?
Well… I won’t try to explain, really. The gist of it is this: think of it as a clock. The frequency of that clock is either on or off—relative to what we may refer to as some fundamental frequency of spacetime. If it’s on (the same frequency), our particle will be stable. If not, it will disintegrate into stable(r) constituents—electrons, protons, photons or neutrinos. Or—if we’re talking much larger conglomerates falling apart—some stable configuration of them: think of a neutron inside a nucleus, a hydrogen atom, a simple naked nucleus, or an actual atom (but here we’re entering the realm of chemistry—as opposed to elementary physics).
As a result, the paper has become a bit longer. Well… More than a bit, perhaps: it’s 20-25 pages now. The point is this: I feel it’s pretty complete, but I am left with the following issues and questions—or ‘clusters of analysis’ as I’d say in my line of business (which is finance and project management—not QM!):
- Is the (electric) charge inside an electron – and a proton—any matter-particle, really – a fractal structure or not?
- What is the nature of the ‘stronger’ force inside of the proton: I vaguely distinguish between the fundamental frequency and one or more higher modes of spacetime – but that needs to be ‘translated’ into a better ‘visual’ image of what might or might not be going on.
- Electron-positron pair creation/annihilation. Or—more generally speaking—the question of the fundamental nature of anti-matter in general.
I have a few preliminary thoughts on that, but I’d like to invite comments—because I am really puzzled by the above and talking about it surely helps! My guts instinct tells me this:
1. The idea of the zbw charge inside matter-particles being some fractal structure is appealing and not. It’s appealing because the radius of the zbw charge inside a proton must be smaller than the classical electron radius – so some fractal structure (to explain the origin of mass) is definitely something to consider.
—But then it’s also not appealing because it keeps that ambiguity: is Nature continuous or not? Is a charge some finite structure or not? Perhaps we should just accept the idea of a charge combines all of our concepts: force, mass—and the idea of (in)definiteness? 🙂
[I am joking and then I am not: I often feel the Uncertainty Principle is where the Pope thinks God might be hiding, so if we abolish that, the Vatican will need something else, right?]
2. The idea of the ‘strong’ (or ‘stronger’) force grabbing onto the same charge (i.e. the electric charge) is great because it greatly simplifies the analysis. The idea of a strong force grabbing onto a strong charge is appealing (we had already invented a unit for the strong charge) but it hugely complicates our thinking of the proton as some unitary particle. Why? Think of this question: what force grabs on what charge, and how exactly, and how do the two charges then relate to each other? – no strong charge needed! I really must thank Giorgio Vassallo here for pointing out I should try to simplify as much as possible when thinking about the QCD sector. [I hope Dr. Vassallo appreciates the compliment—can’t be sure of that coz he’s rather taciturn. :-)]
3. The third of the three questions is the most difficult one. From all of Dirac’s formal or informal remarks on the state of our knowledge, it’s clear he struggled very much with that too. The gist of the matter is this: our world could be an anti-matter world. We may think of that as a mathematical fiction: who cares if we write q or −q in our equations? No one, right? It’s just a convention, and so we can just swap signs, right?
Well… No. Dirac had noticed the mathematical possibility early on—in 1928, to be precise, as soon as he had published his equation for the free electron. He said this about it in his 1933 Nobel Prize Lecture:
“If we accept the view of complete symmetry between positive and negative electric charge so far as concerns the fundamental laws of Nature, we must regard it rather as an accident that the Earth (and presumably the whole solar system), contains a preponderance of negative electrons and positive protons.”
The carefully chosen ‘preponderance’ term shows he actually did imagine some stars could possibly be made of anti-matter, and he said as much in the very same lecture:
“It is quite possible that for some of the stars it is the other way about, these stars being built up mainly of positrons and negative protons. […] The two kinds of stars would both show exactly the same spectra, and there would be no way of distinguishing them by present astronomical methods.”
Strangely enough, he doesn’t mention Carl D. Anderson who – just the previous year (1932) – had actually found the trace of an actual positron on one of his cloud chamber pictures of what happens to cosmic radiation when it enters… Well… Anderson’s cloud chamber. 🙂 Anderson got his own Nobel Prize for it – and one that’s very well deserved (the reader who’s read our previous posts will know we have serious doubts on the merit of some (other) Nobel Prizes).
The point is this: we should not think of matter and anti-matter as being ‘separate worlds’ (theoretical and/or physical). No. Pair creation/annihilation should be part and parcel of our ‘world view’ (read: our classical explanation of quantum physics). So what can/should we do with this?
Nothing at all, perhaps. If we stare at the equations long enough, they all start making sense after a while, don’t they? Especially when enjoying a Belgian beer or a good glass of wine. Feynman quoted an unknown poet in one of his introductory lectures to his Lectures:
“The whole universe is in a glass of wine.”
Again, after having deified Feynman for decades, I regret to say that I now have to think of Richard Feynman as being a very complicated personality defending mainstream thought rather than trying to revolutionize scientific thought. Having said that, I still fully agree with most of his metaphorical statements, and the one above surely tops my list. 🙂
As we are doing stupid stuff anyway – like writing to the Nobel Prize Committee – I thought I should just go all the way, and finally contact the man who must know the truth on whether or not mainstream QM is just a gigantic hoax: a sophisticated mass deception effort—think of it as a PR stunt to keep big tech projects going!
The name of the man is Freeman Dyson. He’s the last man standing of the post-WW II generation which I now refer to as the Mystery Wallahs. He’s 96, I think.
Oh hell ! I just checked: he passed away too. Just 10 days ago, on 28 February 2020. He died, apparently, from the complications from a fall in the cafeteria in Princeton’s Institute for Advanced Studies, from which I got his email address. This is plain eerie: I was writing to a dead man !
I did not receive any error or other message. I guess they haven’t deactivated his email account yet.
Post scriptum—or my obituary, I guess: Despite the rather romantic image of Freeman Dyson as the crazy iconoclastic or ‘heretic’ scientist (he never bothered to get a PhD, for example), I do not associate him with anything good—if only because of his stance on climate change, and I thank the NY Times journalist who wrote his obituary for writing what should be written here:
“He doubted the veracity of the climate models, and he exasperated experts with sanguine predictions they found rooted less in science than in wishfulness: Excess carbon in the air is good for plants, and global warming might forestall another ice age.”
That should generate enough dislike, I’d think. However, I don’t like him because of an entirely different: the reason why I finally wrote him that email he now can’t read. Perhaps it’s better this way: I hope he takes what I now think of as a Bright Shining Lie to the grave.
It’s probably a futile hope: editorial lines of scientific journals will probably not change any time soon. Sayre’s Law: “Academic politics is much more vicious than real politics.” Sayre thought it was “because the stakes are so small.”
I agree with Oliver Consa here: the latter probably isn’t true. US$600 m projects do warrant a decent PR fight, don’t they? I, therefore, suspect the Mystery Wallahs will prevail. As most – if not all of them – also said they do believe in God, I guess that suits everyone then.
From: Jean Louis Van Belle
Sent: Monday, March 9, 2020 7:09 AM
To: ‘firstname.lastname@example.org’ <email@example.com>
Subject: Last man standing…
Dear Professor – I hope this email reaches you. I’ve been thinking of writing you for many years, as you are the ‘last man standing’ of a incredibly smart group of people who basically developed what we now refer to as the Standard Model of physics.
As I am reaching a rather ripe old age myself now – but still trying to establish what, in my world (which is consulting and finance), is referred to as some kind of ‘basic version of truth’ – there are many topics and questions I would want to ask, but I’ll reduce them to one very simple question on the enclosed paper, which was written by a very smart young man: Dr. Oliver Consa (Something is rotten in the state of QED, Feb 2020).
The question is this: what do you think of Dr. Consa’s ‘version of truth’?
Kindest regards – Jean Louis
Jean Louis Van Belle
Phone: +32 (0)471 079 892
Skype ID: jean.louis.van.belle
viXra org: https://vixra.org/author/jean_louis_van_belle
“None of us is as smart as all of us.” (Kenneth Blanchard)
It’s funny, but I feel the scientific atmosphere may resemble that of the end of the 19th century: what was supposed to be the triumph of classical physics (with Maxwell publishing his famous equations of electromagnetism) suddenly turned into a catastrophe: the ultraviolet catastrophe, to be precise. And it required an Einstein to publish a radical theory altering the world view (relativity theory). I feel a similar catastrophe – and a better theory of quantum mechanics as well, of course! – may be in the making. Hence, I couldn’t restrain myself and thought it’s time for some fun. So I wrote the following letter to the Nobel Prize Committee.
Let’s see if they react. I don’t think so, but then one never knows, right? 🙂
Dear Sir/Madam – I am just an amateur physicist but, having followed the popular physics scene for many years now, I feel I must alert you to a growing feeling that the Nobel Prize Committee may have been awarded to some rather ‘non-productive forms of atomic theory’ lately.
The mainstream interpretation of quantum physics has been criticized severely, both by professional as well as amateur physicists (for a very professional critique, see – for example – the latest article by Dr. Consa: https://vixra.org/pdf/2002.0011v1.pdf).
Also, awarding a Nobel Prize because experiments reveal ‘signature signals’ of the hypothesized W/Z bosons, quarks and/or Higgs particles do not confirm these ‘intermediate vector bosons’ or these (virtual and non-virtual) quarks and gluons actually exist. There are also other credible ‘mechanisms’ explaining mass and/or the anomalous magnetic moment (the ring current model of electrons and protons, on which I publish myself (see: https://vixra.org/pdf/2002.0160v1.pdf and https://vixra.org/pdf/2003.0094v1.pdf) is just one example of what I think of as credible alternative explanations).
To many of my colleagues – amateur physicists just like me – it feels like the Nobel Prize Committee has really been in a hurry to ‘consecrate’ the Standard Model asap. If this is to confirm the ‘triumph’ of the mainstream interpretation of physics, then I am afraid the effect is just the opposite.
This is just an opinion, of course – but I just wanted to alert you to it – because the unease with the ‘Standard Model’ seems to be spreading quite rapidly lately and has become very palpable, I would think. In this regard, I refer to books such as Hossenfelder’s ‘Lost in Math?’ and other ‘mainstream researchers challenging other mainstream researchers.’
Kindest regards – Jean Louis
Jean Louis Van Belle
Phone: +32 (0)471 079 892
Skype ID: jean.louis.van.belle
viXra org: https://vixra.org/author/jean_louis_van_belle
“None of us is as smart as all of us.” (Kenneth Blanchard)
Yesterday night, I got this email from a very bright young physicist: Dr. Oliver Consa. He is someone who – unlike me – does have the required Dr and PhD credentials in physics (I have a drs. title in economics) – and the patience that goes with it – to make some more authoritative statements in the weird world of quantum mechanics. I recommend you click the link in the email (copied below) and read the paper. Please do it!
It is just 12 pages, and it is all extremely revealing. Very discomforting, actually, in light of all the other revelations on fake news in other spheres of life.
Many of us – and, here, I just refer to those who are reading my post – all sort of suspected that some ‘inner circle’ in the academic circuit had cooked things up:the Mystery Wallahs, as I refer to them now. Dr. Consa’s paper shows our suspicion is well-founded.
Dear fellow scientist,
I send you this mail because you have been skeptical about Foundations of Physics. I think that this new paper will be of your interest. Feel free to share it with your colleagues or publish it on the web. I consider it important that this paper serves to open a public debate on this subject.
Something is Rotten in the State of QED
“Quantum electrodynamics (QED) is considered the most accurate theory in the history of science. However, this precision is based on a single experimental value: the anomalous magnetic moment of the electron (g-factor). An examination of QED history reveals that this value was obtained using illegitimate mathematical traps, manipulations and tricks. These traps included the fraud of Kroll & Karplus, who acknowledged that they lied in their presentation of the most relevant calculation in QED history. As we will demonstrate in this paper, the Kroll & Karplus scandal was not a unique event. Instead, the scandal represented the fraudulent manner in which physics has been conducted from the creation of QED through today.” (12 pag.)
Pre-scriptum (PS), added on 6 March 2020: The ideas below also naturally lead to a theory about what a neutrino might actually be. As such, it’s a complete ‘alternative’ Theory of Everything. I uploaded the basics of such theory on my academia.edu site. For those who do not want to log on to academia.edu, you can also find the paper on my author’s page on Phil Gibb’s site.
We were rather tame in our last paper on the oscillator model of an electron. We basically took some philosophical distance from it by stating we should probably only think of it as a mathematical equivalent to Hestenes’ concept of the electron as a superconducting loop. However, deep inside, we feel we should not be invoking Maxwell’s laws of electrodynamics to explain what a proton and an electron might actually be. The basics of the ring current model can be summed up in one simple equation:
c = a·ω
This is the formula for the tangential velocity. Einstein’s mass-energy equivalence relation and the Planck-Einstein relation explain everything else, as evidenced by the fact that we can immediately derive the Compton radius of an electron from these three equations, as shown below:The reader might think we are just ‘casually connecting formulas’ here but we feel we have a full-blown theory of the electron here: simple and consistent. The geometry of the model is visualized below. We think of an electron (and a proton) as consisting of a pointlike elementary charge – pointlike but not dimensionless – moving about at (nearly) the speed of light around the center of its motion.
The relation works perfectly well for the electron. However, when applying the a = ħ/mc radius formula to a proton, we get a value which is about 1/4 of the measured proton radius: about 0.21 fm, as opposed to the 0.83-0.84 fm charge radius which was established by Professors Pohl, Gasparan and others over the past decade. In our papers on the proton radius, we motivated the 1/4 factor by referring to the energy equipartition theorem and assuming energy is, somehow, equally split over electromagnetic field energy and the kinetic energy in the motion of the zbw charge. However, the reader must have had the same feeling as we had: these assumptions are rather ad hoc. We, therefore, propose something more radical:
When considering systems (e.g. electron orbitals) and excited states of particles, angular momentum comes in units (nearly) equal to ħ, but when considering the internal structure of elementary particles, (orbital) angular momentum comes in an integer fraction of ħ. This fraction is 1/2 for the electron and 1/4 for the proton.
Let us write this out for the proton radius:What are the implications for the assumed centripetal force keeping the elementary charge in motion? The centripetal acceleration is equal to ac = vt2/a = a·ω2. It is probably useful to remind ourselves how we get this result so as to make sure our calculations are relativistically correct. The position vector r (which describes the position of the zbw charge) has a horizontal and a vertical component: x = a·cos(ωt) and y = a·sin(ωt). We can now calculate the two components of the (tangential) velocity vector v = dr/dt as vx = –a·ω·sin(ωt) and vy y = –a· ω·cos(ωt) and, in the next step, the components of the (centripetal) acceleration vector ac: ax = –a·ω2·cos(ωt) and ay = –a·ω2·sin(ωt). The magnitude of this vector is then calculated as follows:
ac2 = ax2 + ay2 = a2·ω4·cos2(ωt) + a2·ω4·sin2(ωt) = a2·ω4 ⇔ ac = a·ω2 = vt2/a
Now, Newton’s force law tells us that the magnitude of the centripetal force will be equal to:
F = mγ·ac = mγ·a·ω2
As usual, the mγ factor is, once again, the effective mass of the zbw charge as it zitters around the center of its motion at (nearly) the speed of light: it is half the electron mass. If we denote the centripetal force inside the electron as Fe, we can relate it to the electron mass me as follows:Assuming our logic in regard to the effective mass of the zbw charge inside a proton is also valid – and using the 4E = ħω and a = ħ/4mc relations – we get the following equation for the centripetal force inside of a proton:
How should we think of this? In our oscillator model, we think of the centripetal force as a restoring force. This force depends linearly on the displacement from the center and the (linear) proportionality constant is usually written as k. Hence, we can write Fe and Fp as Fe = -kex and Fp = -kpx respectively. Taking the ratio of both so as to have an idea of the respective strength of both forces, we get this:
The ap and ae are acceleration vectors – not the radius. The equation above seems to tell us that the centripetal force inside of a proton gives the zbw charge inside – which is nothing but the elementary charge, of course – an acceleration that is four times that of what might be going on inside the electron.
Nice, but how meaningful are these relations, really? If we would be thinking of the centripetal or restoring force as modeling some elasticity of spacetime – the guts intuition behind far more complicated string theories of matter – then we may think of distinguishing between a fundamental frequency and higher-level harmonics or overtones. We will leave our reflections at that for the time being.
We should add one more note, however. We only talked about the electron and the proton here. What about other particles, such as neutrons or mesons? We do not consider these to be elementary because they are not stable: we think they are not stable because the Planck-Einstein relation is slightly off, which causes them to disintegrate into what we’ve been trying to model here: stable stuff. As for the process of their disintegration, we think the approach that was taken by Gell-Man and others is not productive: inventing new quantities that are supposedly being conserved – such as strangeness – is… Well… As strange as it sounds. We, therefore, think the concept of quarks confuses rather than illuminates the search for a truthful theory of matter.
Jean Louis Van Belle, 6 March 2020
 In this paper, we make abstraction of the anomaly, which is related to the zbw charge having a (tiny) spatial dimension.
 We had a signed contract with the IOP and WSP scientific publishing houses for our manuscript on a realist interpretation of quantum mechanics (https://vixra.org/abs/1901.0105) which was shot down by this simple comment. We have basically stopped tried convincing mainstream academics from that point onwards.
 See footnote 1.
 See reference above.
 The reader may wonder why we did not present the ½ fraction is the first set of equations (calculation of the electron radius). We refer him or her to our previous paper on the effective mass of the zbw charge (https://vixra.org/abs/2003.0094). The 1/2 factor appears when considering orbital angular momentum only.
 The reader may not be familiar with the concept of the effective mass of an electron but it pops up very naturally in the quantum-mechanical analysis of the linear motion of electrons. Feynman, for example, gets the equation out of a quantum-mechanical analysis of how an electron could move along a line of atoms in a crystal lattice. See: Feynman’s Lectures, Vol. III, Chapter 16: The Dependence of Amplitudes on Position (https://www.feynmanlectures.caltech.edu/III_16.html). We think of the effective mass of the electron as the relativistic mass of the zbw charge as it whizzes about at nearly the speed of light. The rest mass of the zbw charge itself is close to – but also not quite equal to – zero. Indeed, based on the measured anomalous magnetic moment, we calculated the rest mass of the zbw charge as being equal to about 3.4% of the electron rest mass (https://vixra.org/abs/2002.0315).
 For a basic introduction, see my blog posts on modes or on music and physics (e.g. https://readingfeynman.org/2015/08/08/modes-and-music/).
 See, for example, the analysis of kaons (K-mesons) in Feynman’s Lectures, Vol. III, Chapter 11, section 5 (https://www.feynmanlectures.caltech.edu/III_11.html#Ch11-S5).
I’ve been looking at chapter 4 of Feynman’s Lectures on Quantum Mechanics (the chapter on identical particles) for at least a dozen times now—probably more. This and the following chapters spell out the mathematical framework and foundations of mainstream quantum mechanics: the grand distinction between fermions and bosons, symmetric and asymmetric wavefunctions, Bose-Einstein versus Maxwell-Boltzmann statistics, and whatever else comes out of that—including the weird idea that (force) fields should also come in lumps (think of quantum field theory here). These ‘field lumps’ are then thought of as ‘virtual’ particles that, somehow, ‘mediate’ the force.
The idea that (kinetic and/or potential) energy and (linear and/or angular) momentum are being continually transferred – somehow, and all over space – by these ‘messenger’ particles sounds like medieval philosophy to me. However, to be fair, Feynman does actually not present these more advanced medieval ideas in his Lectures on Quantum Physics. I have always found that somewhat strange: he was about to receive a Nobel Prize for his path integral formulation of quantum mechanics and other contributions to what has now become the mainstream interpretation of quantum mechanics, so why wouldn’t he talk about it to his students, for which he wrote these lectures? In contrast, he does include a preview of Gell-Mann’s quark theory, although he does say – in a footnote – that “the material of this section is longer and harder than is appropriate at this point” and he, therefore, suggests to skip it and move to the next chapter.
[As for the path integral formulation of QM, I would think the mere fact that we have three alternative formulations of QM (matrix, wave-mechanical and path integral) would be sufficient there’s something wrong with these theories: reality is one, so we should have one unique (mathematical) description of it).]
Any case. I am probably doing too much Hineininterpretierung here. Let us return to the basic stuff that Feynman wanted his students to accept as a truthful description of reality: two kinds of statistics. Two different ways of interaction. Two kinds of particles. That’s what post-WW II gurus such as Feynman – all very much inspired by the ‘Club of Copenhagen’—aka known as the ‘Solvay Conference Club‘ – want us to believe: interactions with ‘Bose particles’ – this is the term Feynman uses in this text of 1963 – involve adding amplitudes with a + (plus) sign. In contrast, interactions between ‘Fermi particles’ involve a minus (−) sign when ‘adding’ the amplitudes.
The confusion starts early on: Feynman makes it clear he actually talks about the amplitude for an event to happen or not. Two possibilities are there: two ‘identical’ particles either get ‘swapped’ after the collision or, else, they don’t. However, in the next sections of this chapter – where he ‘proves’ or ‘explains’ the principle of Bose condensation for bosons and then the Pauli exclusion principle for fermions – it is very clear the amplitudes are actually associated with the particles themselves.
So his argument starts rather messily—conceptually, that is. Feynman also conveniently skips the most basic ontological or epistemological question here: how would a particle ‘know‘ how to choose between this or that kind of statistics? In other words, how does it know it should pick the plus or the minus sign when combining its amplitude with the amplitude of the other particle? It makes one think of Feynman’s story of the Martian in his Lecture on symmetries in Nature: what handshake are we going to do here? Left or right? And who sticks out his hand first? The Martian or the Earthian? A diplomat would ask: who has precedence when the two particles meet?
The question also relates to the nature of the wavefunction: if it doesn’t describe anything real, then where is it? In our mind only? But if it’s in our mind only, how comes we get real-life probabilities out of them, and real-life energy levels, or real-life momenta, etcetera? The core question (physical, epistemological, philosophical, esoterical or whatever you’d want to label it) is this: what’s the connection between these concepts and whatever it is that we are trying to describe? The only answer mainstream physicists can provide here is blabber. That’s why the mainstream interpretation of physics may be acceptable to physicists, but not to the general public. That’s why the debate continues to rage: no one believes the Standard Model. Full stop. The intuition of the masses here is very basic and, therefore, probably correct: if you cannot explain something in clear and unambiguous terms, then you probably do not understand it.
Hence, I suspect mainstream academic physicists probably do not understand whatever it is they are talking about. Feynman, by the way, admitted as much when writing – in the very first lines of the introduction to his Lectures on Quantum Mechanics – that “even the experts do not understand it the way they would like to.”
I am actually appalled by all of this. Worse, I am close to even stop talking or writing about it. I only kept going because a handful of readers send me a message of sympathy from time to time. I then feel I am actually not alone in what often feels like a lonely search in what a friend of mine refers to as ‘a basic version of truth.’ I realize I am getting a bit emotional here – or should I say: upset? – so let us get back to Feynman’s argument again.
Feynman starts by introducing the idea of a ‘particle’—a concept he does not define – not at all, really – but, as the story unfolds, we understand this concept somehow combines the idea of a boson and a fermion. He doesn’t motivate why he feels like he should lump photons and electrons together in some more general category, which he labels as ‘particles’. Personally, I really do not see the need to do that: I am fine with thinking of a photon as an electromagnetic oscillation (a traveling field, that is), and of electrons, protons, neutrons and whatever composite particle out there that is some combination of the latter as matter-particles. Matter-particles carry charge: electric charge and – who knows – perhaps some strong charge too. Photons don’t. So they’re different. Full stop. Why do we want to label everything out there as a ‘particle’?
Indeed, when everything is said and done, there is no definition of fermions and bosons beyond this magical spin-1/2 and spin-1 property. That property is something we cannot measure: we can only measure the magnetic moment of a particle: any assumption on their angular momentum assumes you know the mass (or energy) distribution of the particle. To put it more plainly: do you think of a particle as a sphere, a disk, or what? Mainstream physicists will tell you that you shouldn’t think that way: particles are just pointlike. They have no dimension whatsoever – in their mathematical models, that is – because all what experimentalists is measuring scattering or charge radii, and these show the assumption of an electron or a proton being pointlike is plain nonsensical.
Needless to say, besides the perfect scattering angle, Feynman also assumes his ‘particles’ have no spatial dimension whatsoever: he’s just thinking in terms of mathematical lines and points—in terms of mathematical limits, not in terms of the physicality of the situation.
Hence, Feynman just buries us under a bunch of tautologies here: weird words are used interchangeably without explaining what they actually mean. In everyday language and conversation, we’d think of that as ‘babble’. The only difference between physicists and us commoners is that physicists babble using mathematical language.
I am digressing again. Let us get back to Feynman’s argument. So he tells us we should just accept this theoretical ‘particle’, which he doesn’t define: he just thinks about two of these discrete ‘things’ going into some ‘exchange’ or ‘interaction’ and then coming out of it and going into one of the two detectors. The question he seeks to answer is this: can we still distinguish what is what after the ‘interaction’?
The level of abstraction here is mind-boggling. Sadly, it is actually worse than that: it is also completely random. Indeed, the only property of this mystical ‘particle’ in this equally mystical thought experiment of Mr. Feynman is that it scatters elastically with some other particle. However, that ‘other’ particle is ‘of the same kind’—so it also has no other property than that it scatters equally elastically from the first particle. Hence, I would think the question of whether the two particles are identical or not is philosophically empty.
To be rude, I actually wonder what Mr. Feynman is actually talking about here. Every other line in the argument triggers another question. One should also note, for example, that this elastic scattering happens in a perfect angle: the whole argument of adding or subtracting amplitudes effectively depends on the idea of a perfectly measurable angle here. So where is the Uncertainty Principle here, Mr. Feynman? It all makes me think that Mr. Feynman’s seminal lecture may well be the perfect example of what Prof. Dr. John P. Ralston wrote about his own profession:
“Quantum mechanics is the only subject in physics where teachers traditionally present haywire axioms they don’t really believe, and regularly violate in research.” (1)
Let us continue exposing Mr. Feynman’s argument. After this introduction of this ‘particle’ and the set-up with the detectors and other preconditions, we then get two or three paragraphs of weird abstract reasoning. Please don’t get me wrong: I am not saying the reasoning is difficult (it is not, actually): it is just weird and abstract because it uses complex number logic. Hence, Feynman implicitly requests the reader to believe that complex numbers adequately describes whatever it is that he is thinking of (I hope – but I am not so sure – he was trying to describe reality). In fact, this is the one point I’d agree with him: I do believe Euler’s function adequately describes the reality of both photons and electrons (see our photon and electron models), but then I also think +i and −i are two very different things. Feynman doesn’t, clearly.
It is, in fact, very hard to challenge Feynman’s weird abstract reasoning here because it all appears to be mathematically consistent—and it is, up to the point of the tricky physical meaning of the imaginary unit: Feynman conveniently forgets the imaginary unit represents a rotation of 180 degrees and that we, therefore, need to distinguish between these two directions so as to include the idea of spin. However, that is my interpretation of the wavefunction, of course, and I cannot use it against Mr. Feynman’s interpretation because his and mine are equally subjective. One can, therefore, only credibly challenge Mr. Feynman’s argument by pointing out what I am trying to point out here: the basic concepts don’t make any sense—none at all!
Indeed, if I were a student of Mr. Feynman, I would have asked him questions like this:
“Mr. Feynman, I understand your thought experiment applies to electrons as well as to photons. In fact, the argument is all about the difference between these two very different ‘types’ of ‘particles’. Can you please tell us how you’d imagine two photons scattering off each other elastically? Photons just pile on top of each other, don’t they? In fact, that’s what you prove next. So they don’t scatter off each other, do they? Your thought experiment, therefore, seems to apply to fermions only. Hence, it would seem we should not use it to derive properties for bosons, isn’t it?”
“Mr. Feynman, how should an electron (a fermion – so you say we should ‘add’ amplitudes using a minus sign) ‘think’ about what sign to use for interaction when a photon is going to hit it? A photon is a boson – so its sign for exchange is positive – so should we have an ‘exchange’ or ‘interaction’ with the plus or the minus sign then? More generally, who takes the ‘decisions’ here? Do we expect God – or Maxwell’s demon – to be involved in every single quantum-mechanical event?”
Of course, Mr. Feynman might have had trouble answering the first question, but he’d probably would not hesitate to produce some kind of rubbish answer to the second: “Mr. Van Belle, we are thinking of identical particles here. Particles of the same kind, if you understand what I mean.”
Of course, I obviously don’t understand what he means but so I can’t tell him that. So I’d just ask the next logical question to try to corner him:
“Of course, Mr. Feynman. Identical particles. Yes. So, when thinking of fermion-on-fermion scattering, what mechanism do you have in mind? At the very least, we should be mindful of the difference between Compton versus Thomson scattering, shouldn’t we? How does your ‘elastic’ scattering relate to these two very different types of scattering? What is your theoretical interaction mechanism here?”
I can actually think of some more questions, but I’ll leave it at this. Well… No… Let me add another one:
“Mr. Feynman, this theory of interaction between ‘identical’ or ‘like’ particles (fermions and bosons) looks great but, in reality, we will also have non-identical particles interacting with each other—or, more generally speaking, particles that are not ‘of the same kind’. To be very specific, reality sees many electrons and many photons interacting with each other—not just once, at the occasion of some elastic collision, but all of the time, really. So could we, perhaps, generalize this to some kind of ‘three- or n-particle problem’?”
This sounds like a very weird question, which even Mr. Feynman might not immediately understand. So, if he didn’t shut me up already, he may have asked me to elaborate: “What do you mean, Mr. Van Belle? What kind of three- or n-particle problem are you talking about?” I guess I’d say something like this:
“Well… Already in classical physics, we do not have an analytical solution for the ‘three-body problem’, but at least we have the equations. So we have the underlying mechanism. What are the equations here? I don’t see any. Let us suppose we have three particles colliding or scattering or interacting or whatever it is we are trying to think of. How does any of the three particles know what the other two particles are going to be: a boson or a fermion? And what sign should they then use for the interaction? In fact, I understand you are talking amplitudes of events here. If three particles collide, how many events do you count: one, two, three, or six?”
One, two, three or six? Yes. Do we think of the interaction between three particles as one event, or do we split it up as a triangular thing? Or is it one particle interacting, somehow, with the two other, in which case we’re having two events, taking into account this weird plus or minus sign rule for interaction.
Crazy? Yes. Of course. But the questions are logical, aren’t they? I can think of some more. Here is one that, in my not-so-humble view, shows how empty these discussions on the theoretical properties of theoretical bosons and theoretical fermions actually are:
“Mr. Feynman, you say a photon is a boson—a spin-one particle, so its spin state is either 1, 0 or −1. How comes photons – the only boson that we actually know to exist from real-life experiments – do not have a spin-zero state? Their spin is always up or down. It’s never zero. So why are we actually even talking about spin-one particles, if the only boson we know – the photon – does not behave like it should behave according to your boson-fermion theory?” (2)
Am I joking? I am not. I like to think I am just asking very reasonable questions here—even if all of this may sound like a bit of a rant. In fact, it probably is, but so that’s why I am writing this up in a blog rather than in a paper. Let’s continue.
The subsequent chapters are about the magical spin-1/2 and spin-1 properties of fermions and bosons respectively. I call them magical, because – as mentioned above – all we can measure is the magnetic moment. Any assumption that the angular momentum of a particle – a ‘boson’ or a ‘fermion’, whatever it is – is ±1 or ±1/2, assumes we have knowledge of some form factor, which is determined by the shape of that particle and which tells us how the mass (or the energy) of a particle is distributed in space.
Again, that may sound sacrilegious: according to mainstream physicists, particles are supposed to be pointlike—which they interpret as having no spatial dimension whatsoever. However, as I mentioned above, that sounds like a very obvious oxymoron to me.
Of course, I know I would never have gotten my degree. When I did the online MIT course, the assistants of Prof. Dr. Zwieback also told me I asked too many questions: I should just “shut up and calculate.” You may think I’m joking again but, no: that’s the feedback I got. Needless to say, I went through the course and did all of the stupid exercises, but I didn’t bother doing the exams. I don’t mind calculating. I do a lot of calculations as a finance consultant. However, I do mind mindless calculations. Things need to make sense to me. So, yes, I will always be an ‘amateur physicist’ and a ‘blogger’—read: someone whom you shouldn’t take very seriously. I just hope my jokes are better than Feynman’s.
I’ve actually been thinking that getting a proper advanced degree in physics might impede understanding, so it’s good I don’t have one. I feel these mainstream courses do try to ‘brainwash’ you. They do not encourage you to challenge received wisdom. On the contrary, it all very much resembles rote learning: memorization based on repetition. Indeed, more modern textbooks – I looked at the one of my son, for example – immediately dive into the hocus-pocus—totally shamelessly. They literally start by saying you should not try to understand and that you just get through the math and accept the quantum-mechanical dogmas and axioms! Despite the appalling logic in the introductory chapters, Mr. Feynman, in contrast, at least has the decency to try to come up with some classical arguments here and there (although he also constantly adds that the student should just accept the hocus-pocus approach and the quantum-mechanical dogmas and not think too much about what it might or might not represent).
My son got high marks on his quantum mechanics exam: a 19/20, to be precise, and so I am really proud of him—and I also feel our short discussions on this or that may have helped him to get through it. Fortunately, he was doing it as part of getting a civil engineering degree (Bachelor’s level), and he was (also) relieved he would never have to study the subject-matter again. Indeed, we had a few discussions and, while he (also) thinks I am a bit of a crackpot theorist, he does agree “the math must describe something real” and that “therefore, something doesn’t feel right in all of that math.” I told him that I’ve got this funny feeling that, 10 or 20 years from now, 75% (more?) of post-WW II research in quantum physics – most of the theoretical research, at least (3) – may be dismissed as some kind of collective psychosis or, worse, as ‘a bright shining lie’ (title of a book I warmly recommend – albeit on an entirely different topic). Frankly, I think many academics completely forgot Boltzmann’s motto for the physicist:
“Bring forward what is true. Write it so that it is clear. Defend it to your last breath.”
OK, you’ll say: get real! So what is the difference between bosons and fermions, then? I told you already: I think it’s a useless distinction. Worse, I think it’s not only useless but it’s also untruthful. It has, therefore, hampered rather than promoted creative thinking. I distinguish matter-particles – electrons, protons, neutrons – from photons (and neutrinos). Matter-particles carry charge. Photons (and neutrinos) do not. (4) Needless to say, I obviously don’t believe in ‘messenger particles’ and/or ‘Higgs’ or other ‘mechanisms’ (such as the ‘weak force’ mechanism). That sounds too much like believing in God or some other non-scientific concept. [I don’t mind you believing in God or some other non-scientific concept – I actually do myself – but we should not confuse it with doing physics.]
And as for the question on what would be my theory of interaction? It’s just the classical theory: charges attract or repel, and one can add electromagnetic fields—all in respect of the Planck-Einstein law, of course. Charges have some dimension (and some mass), so they can’t take up the same space. And electrons, protons and neutrons have some structure, and physicists should focus on modeling those structures, so as to explain the so-called intrinsic properties of these matter-particles. As for photons, I think of them as an oscillating electromagnetic field (respecting the Planck-Einstein law, of course), and so we can simply add them. What causes them to lump together? Not sure: the Planck-Einstein law (being in some joint excited state, in other words) or gravity, perhaps. In any case: I am confident it is something real—i.e. not Feynman’s weird addition or subtraction rules for amplitudes.
However, this is not the place to re-summarize all of my papers. I’d just sum them up by saying this: not many physicists seem to understand Planck’s constant or, what amounts to the same, the concept of an elementary cycle. And their unwillingness to even think about the possible structure of photons, electrons and protons is… Well… I’d call it criminal.
I will now conclude my rant with another down-to-earth question: would I recommend reading Feynman’s Lectures? Or recommend youngsters to take up physics as a study subject?
My answer in regard to the first question is ambiguous: yes, and no. When you’d push me on this, I’d say: more yes than no. I do believe Feynman’s Lectures are much better than the modern-day textbook that was imposed on my son during his engineering studies and so, yes, I do recommend the older textbooks. But please be critical as you go through them: do ask yourself the same kind of questions that I’ve been asking myself while building up this blog: think for yourself. Don’t go by ‘authority’. Why not? Because the possibility that a lot of what labels itself as science may be nonsensical. As nonsensical as… Well… All what goes on in national and international politics for the moment, I guess. 🙂
In regard to the second question – should youngsters be encouraged to study physics? – I’d say what my father told me when I was hesitating to pick a subject for study: “Do what earns respect and feeds your family. You can do philosophy and other theoretical things on the side.”
With the benefit of hindsight, I can say he was right. I’ve done the stuff I wanted to do—on the side, indeed. So I told my son to go for engineering – rather than pure math or pure physics. 🙂 And he’s doing great, fortunately !
Jean Louis Van Belle
(1) Dr. Ralston’s How To Understand Quantum Mechanics is fun for the first 10 pages or so, but I would not recommend it. We exchanged some messages, but then concluded that our respective interpretations of quantum mechanics are very different (I feel he replaces hocus-pocus by other hocus-pocus) and, hence, that we should not “waste any electrons” (his expression) on trying to convince each other.
(2) It is really one of the most ridiculous things ever. Feynman spends several chapters on explaining spin-one particles to, then, in some obscure footnote, suddenly write this: “The photon is a spin-one particle which has, however, no “zero” state.” From all of his jokes, I think this is his worst. It just shows how ‘rotten’ or ‘random’ the whole conceptual framework of mainstream QM really is. There is, in fact, another glaring inconsistency in Feynman’s Lectures: in the first three chapters of Volume III, he talks about adding wavefunctions and the basic rules of quantum mechanics, and it all happens with a plus sign. In this chapter, he suddenly says the amplitudes of fermions combine with a minus sign. If you happen to know a physicist who can babble his way of out this inconsistency, please let me know.
(3) There are exceptions, of course. I mentioned very exciting research in various posts, but most of it is non-mainstream. The group around Herman Batalaan at the University of Nebraska and various ‘electron modellers’ are just one of the many examples. I contacted a number of these ‘particle modellers’. They’re all happy I show interest, but puzzled themselves as to why their research doesn’t get all that much attention. If it’s a ‘historical accident’ in mankind’s progress towards truth, then it’s a sad one.
(4) We believe a neutron is neutral because it has both positive and negative charge in it (see our paper on protons and neutrons). as for neutrinos, we have no idea what they are, but our wild guess is that they may be the ‘photons’ of the strong force: if a photon is nothing but an oscillating electromagnetic field traveling in space, then a neutrino might be an oscillating strong field traveling in space, right? To me, it sounds like a reasonable hypothesis, but who am I, right? 🙂 If I’d have to define myself, it would be as one of Feynman’s ideal students: someone who thinks for himself. In fact, perhaps I would have been able to entertain him as much as he entertained me— and so, who knows, I like to think he might actually have given me some kind of degree for joking too ! 🙂
(5) There is no (5) in the text of my blog post, but I just thought I would add one extra note here. 🙂 Herman Batelaan and some other physicists wrote a Letter to the Physical Review Journal back in 1997. I like Batelaan’s research group because – unlike what you might think – most of Feynman’s thought experiments have actually never been done. So Batelaan – and some others – actually did the double-slit experiment with electrons, and they are doing very interesting follow-on research on it.
However, let me come to the point I want to mention here. When I read these lines in that very serious Letter, I didn’t know whether to laugh or to cry:
“Bohr’s assertion (on the impossibility of doing a Stern-Gerlach experiment on electrons or charged particles in general) is thus based on taking the classical limit for ħ going to 0. For this limit not only the blurring, but also the Stern-Gerlach splitting vanishes. However, Dehmelt argues that ħ is a nonzero constant of nature.”
I mean… What do you make of this? Of course, ħ is a nonzero constant, right? If it was zero, the Planck-Einstein relation wouldn’t make any sense, would it? What world were Bohr, Heisenberg, Pauli and others living in? A different one than ours, I guess. But that’s OK. What is not OK, is that these guys were ignoring some very basic physical laws and just dreamt up – I am paraphrasing Ralston here – “haywire axioms they did not really believe in, and regularly violated themselves.” And they didn’t know how to physically interpret the Planck-Einstein relation and/or the mass-energy equivalence relation. Sabine Hossenfelder would say they were completely lost in math. 🙂
I’ve been working across Asia – mainly South Asia – for over 25 years now. You will google the exact meaning but my definition of a wallah is a someone who deals in something: it may be a street vendor, or a handyman, or anyone who brings something new. I remember I was one of the first to bring modern mountain bikes to India, and they called me a gear wallah—because they were absolute fascinated with the number of gears I had. [Mountain bikes are now back to a 2 by 10 or even a 1 by 11 set-up, but I still like those three plateaux in front on my older bikes—and, yes, my collection is becoming way too large but I just can’t do away with it.]
Any case, let me explain the title of this post. I stumbled on the work of the research group around Herman Batelaan in Nebraska. Absolutely fascinating ! Not only did they actually do the electron double-slit experiment, but their ideas on an actual Stern-Gerlach experiment with electrons are quite interesting: https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1031&context=physicsgay
I also want to look at their calculations on momentum exchange between electrons in a beam: https://iopscience.iop.org/article/10.1088/1742-6596/701/1/012007.
Outright fascinating. Brilliant ! […]
It just makes me wonder: why is the outcome of this 100-year old battle between mainstream hocus-pocus and real physics so undecided?
I’ve come to think of mainstream physicists as peddlers in mysteries—whence the title of my post. It’s a tough conclusion. Physics is supposed to be the King of Science, right? Hence, we shouldn’t doubt it. At the same time, it is kinda comforting to know the battle between truth and lies rages everywhere—including inside of the King of Science.
A rather eminent professor in physics – who has contributed significantly to solving the so-called ‘proton radius puzzle’ – advised me to not think of the anomalous magnetic moment of the electron as an anomaly. It led to a breakthrough in my thinking of what an electron might actually be. The fine-structure constant should be part and parcel of the model, indeed. Check out my last paper ! I’d be grateful for comments !
I know the title of this post sounds really arrogant. It is what it is. Whatever brain I have has been thinking about these issues consciously and unconsciously for many years now. It looks good to me. When everything is said and done, the function of our mind is to make sense. What’s sense-making? I’d define sense-making as creating consistency between (1) the structure of our ideas and theories (which I’ll conveniently define as ‘mathematical’ here) and (2) what we think of as the structure of reality (which I’ll define as ‘physical’).
I started this blog reading Penrose (see the About page of this blog). And then I just put his books aside and started reading Feynman. I think I should start re-reading Penrose. His ‘mind-physics-math’ triangle makes a lot more sense to me now.
PS: I agree the title of my post is excruciatingly arrogant but – believe me – I could have chosen an even more arrogant title. Why? Because I think my electron model actually explains mass. And it does so in a much more straightforward manner than Higgs, or Brout–Englert–Higgs, or Englert–Brout–Higgs–Guralnik–Hagen–Kibble, Anderson–Higgs, Anderson–Higgs–Kibble, Higgs–Kibble, or ABEGHHK’t (for Anderson, Brout, Englert, Guralnik, Hagen, Higgs, Kibble, and ‘t Hooft) do. [I am just trying to attribute the theory here using the Wikipedia article on it.]
I took my blog offline 10 days ago because I got an email from Mr. Gottlieb, which I copied below. Mr. Gottlieb and Mr. Pfeiffer did mankind a favor by publishing Feynman’s seminal Lectures on Physics online. While doing so, however, they reclaim copyright on what is basically a very standard textbook which was published almost 60 years ago.
I think I’ve done my utmost to properly attribute material. The e-links go straight to the online edition, and the name and site of this blog (readingfeynman.org) say it all. I also think I’ve done my best to put Mr. Gottlieb and Mr. Pfeiffer in the picture in the ‘About‘ section of this blog, where I actually recommend you do not read this blog but just buy the Lectures (or use their site) and grind through them yourself.
Fortunately, I am one of the lucky people to have an original 1963 print copy and I should, therefore, probably change all references and refer to this original edition. I am sure Richard Feynman would have approved of that.
In fact, I was thinking of fundamentally reviewing all of my blog posts anyway as part of the insights I gained while searching for a realist interpretation of quantum mechanics, which I published on Phil Gibb’s viXra.org site as well as on academia.edu.
Indeed, I now think Feynman was very close to a full and complete realist interpretation of quantum mechanics. In fact, when I re-read his lectures on electromagnetic mass and his classical explanations of the spin and angular momentum of an electron, it makes me think he privately must have had such realist interpretation. But then he probably couldn’t say so as a mainstream academic—and especially not as one who was eager to get a Nobel Prize.
He got one in 1965, together with Schwinger and Tomonaga. He, therefore, had huge stakes in keeping the ‘mystery’ alive and ensuring the survival of gauge and quantum field theories and all of the associated nonsense.
Jean Louis Van Belle
20 February 2020 (20/02/2020)
Post scriptum (dated 23 February 2020): We’ll do our best to make Mr. Gottlieb happy. 🙂 I was planning to review the whole site anyway to add some references here and there to my more recent models of the photon, the electron and the proton. Plus some other corrections so as to incorporate some more recent insights. In the process, I’ll check on the links. I will probably refer to the original 1963 print edition instead of the online edition. Too bad Mr. Gottlieb doesn’t understand it’s people like me who direct (rather than divert) traffic to it.
Post scriptum (dated 17 June 2020): Yesterday, I received an email from WordPress/Automattic confirming some of the illustrations and images will be taken down. It is mainly for older posts. While it will result in some mutilation of the posts and, more importantly, while I find this completely ridiculous, I will let it happen. If this is what Mr. Gottlieb does for a living or for self-entertainment, we should let him do this. I am getting too old to be bothered by such nonsense.
From: Michael A. Gottlieb <firstname.lastname@example.org>
Sent: Monday, February 10, 2020 5:01 PM
To: Support <email@example.com>
Cc: Jean Louis Van Belle <firstname.lastname@example.org>; Adam Cochran <email@example.com>
Subject: Re: [-] DMCA submission from firstname.lastname@example.org
I sent you two DMCA notices because when I sent the first one (detailed below) I did not understand the kinds of links to the material you would accept in your notice. So I sent links to Mr. Van Belle’s posts (below) in which the copyrighted material is infringed. However, after sending that I realized I could be (and should be) more specific, so I sent a second DMCA notice (which you’ve also acknowledged) with links to specific copyrighted material that is being violated, namely, figures and images of equations copied from the online edition of The Feynman Lectures on Physics on which I share copyright with Caltech and Rudolf Pfeiffer.
Mr. Van Belle would like to make “Fair Use” of the figures in The Feynman Lectures on Physics, and Caltech, myself and Rudolf Pfeiffer welcome him to do so. The problem is, that he isn’t doing that, because Fair Use requires proper attribution, which Mr. Van Belle is not giving our material.
Two years ago we contacted Mr. Van Belle about another one of his blogs in which our copyrighted material is similarly infringed. [He did not mention at that time the fact he had another (WordPress) blog (the one I am complaining about now) in which he was similarly infringing.] In our letter Caltech’s Office of the General Counsel provides Mr. Van Belle with instructions on how to attribute our copyrighted material when it is re-published in his blogs for “Fair Use”. I have copied that letter below.
I would like to retract this DMCA notice (but not the other one I sent, concerning images), because, as I wrote above, this one may be too broad. We are specifically concerned about images (figures and images of equations) that Mr. Van Belle has copied from www.feynmanlectures.caltech.edu and is using in his blog without proper attribution. This is addressed in the second DMCA notice I sent you, and which you’ve acknowledged under separate cover.
(We are also concerned about copyrighted text Mr. Van Belle has copied where it is not properly attributed – specifically, the text of exercises in our book, Exercises for The Feynman Lectures on Physics, which is the subject of his WordPress blog – but we prefer to deal with that separately, as it violates a different copyright.)
This email is copied to Caltech’s Office of the General Counsel and to Mr. Van Belle.
I thought I’d stop blogging, but I can’t help it: I think you’d find this topic interesting – and my comments are actually too short for a paper or article, so I thought it would be good to throw it out here.
If you follow the weird world of quantum mechanics with some interest, you will have heard the latest news: the ‘puzzle’ of the charge radius of the proton has been solved. To be precise, a more precise electron-proton scattering experiment by the PRad (proton radius) team using the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab has now measured the root mean square (rms) charge radius of the proton as:
rp = 0.831 ± 0.007stat ± 0.012syst fm
If a proton would, somehow, have a pointlike elementary (electric) charge in it, and if it it is in some kind of circular motion (as we presume in Zitterbewegung models of elementary particles), then we can establish a simple relation between the magnetic moment (μ) and the radius (a) of the circular current.
Indeed, the magnetic moment is the current (I) times the surface area of the loop (πa2), and the current is just the product of the elementary charge (qe) and the frequency (f), which we can calculate as f = c/2πa, i.e. the velocity of the charge divided by the circumference of the loop. We write:Using the Compton radius of an electron (ae = ħ/mec), this yields the correct magnetic moment for the electron:What radius do we get when applying the a = μ/0.24…´10–10 relation to the (experimentally measured) magnetic moment of a proton? I invite the reader to verify the next calculation using CODATA values:When I first calculated this, I thought: that’s not good enough. I only have the order of magnitude right. However, when multiplying this with √2, we get a value which fits into the 0.831 ± 0.007 interval. To be precise, we get this:
Of course, you will wonder: how can we justify the √2 factor? I am not sure. It is a charge radius. Hence, the electrons will bounce off because of the electromagnetic fields. The magnetic field of the current ring will be some envelope to the current ring itself. We would, therefore, expect the measured charge radius to be larger than the radius of the current ring (a). There are also the intricacies related to the definition of a root mean square (rms) radius.
I feel this cannot be a coincidence: the difference between our ‘theoretical’ value (0.83065 fm) and the last precision measurement (0.831 fm) is only 0.00035 fm, which is only 5% of the statistical standard deviation (0.007 fm). Proton radius solved?
Maybe. Maybe not. The concluding comments of Physics Today were this: “The PRad radius result, about 0.83 fm, agrees with the smaller value from muonic and now electronic hydrogen spectroscopy measurements. With that, it seems the puzzle is resolved, and the discrepancy was likely due to measurement errors. Unfortunately, the conclusion requires no new physics.” (my italics)
I wonder what kind of new physics they are talking about.
Jean Louis Van Belle, 24 January 2020
PS: I did make a paper out of this (see my academia.edu or viXra.org publications), and I shared it with the PRad team at JLAB. Prof. Dr. Ashot Gasparian was kind enough to acknowledge my email and thought “the approach and numbers are interesting.” Let us see what comes out of it. I need to get back to my day job. 🙂
 Zitterbewegung models assume an electron consists of a pointlike charge whizzing around some center. The rest mass of the pointlike charge is zero, which is why its velocity is equal to the speed of light. However, because of its motion, it acquires an effective mass – pretty much like a photon, which has mass because of its motion. One can show the effective mass of the pointlike charge – which is a relativistic mass concept – is half the rest mass of the electron: mγ = me/2.
 The calculations do away with the niceties of the + or – sign conventions as they focus on the values only. We also invite the reader to add the SI units so as to make sure all equations are consistent from a dimensional point of view. For the values themselves, see the CODATA values on the NIST website (https://physics.nist.gov/cuu/Constants/index.html).
I had wanted to write this little paper a while ago, but time constraints (read: my day job) had prevented me from doing this so far. It details how photon-electron interference (scattering) might work. Enjoy ! 🙂
A young researcher, Oliver Consa, managed to solve a complicated integral: he gave us an accurate calculation of the anomalous magnetic moment based on a (semi-)classical model. Here is the link to his paper, and this is the link to my first-order approach. I admit: he was first. Truth doesn’t need an author. 🙂
This is a great achievement. We now have an electron model that explains all of the mysterious ‘intrinsic’ properties of the electron. It also explains the interference of an electron with itself. Most importantly, the so-called ‘precision test of QED’ (the theoretical and experimental value of the anomalous magnetic moment) also gets a ‘common-sense’ interpretation now. Bye-bye QFT!
So now it’s time for the next step(s). If you have followed this blog, then you know I have a decent photon model too – and other researchers – most are small names but there are one or two big names as well 🙂 – are working to refine it.
The End of Physics is near. Mankind knows everything now. Sadly, this doesn’t solve any of the major issues mankind is struggling with (think of inequality and climate change here).
Post scriptum: When you check the references, it would seem that Consa borrowed a lot of material from the 1990 article he mentions as a reference: David L. Bergman and J. Paul Wesley, Spinning Charged Ring Model of Electron Yielding Anomalous Magnetic Moment, Galilean Electrodynamics, Vol. 1, Sept-Oct 1990, pp. 63–67). It is strange that David Hestenes hadn’t noted this article, because it goes back to the same era during which he tried to launch the Zitterbewegung interpretation of quantum physics ! I really find it very bizarre to see how all these elements for a realist interpretation of quantum physics have been lying around for many decades now. I guess it’s got to do with what Sean Carroll suggested in his 7 Sept 2019 opinion article in the NY Times: mainstream physicists do not want to understand quantum mechanics.
This is my summary of what I refer to as a common-sense interpretation of quantum physics. It’s a rather abstruse summary of the 40 papers I wrote over the last two years.
1. A force acts on a charge. The electromagnetic force acts on an electric charge (there is no separate magnetic charge) and the strong force acts on a strong charge. A charge is a charge: a pointlike ‘thing’ with zero rest mass. The idea of an electron combines the idea of a charge and its motion (Schrödinger’s Zitterbewegung). The electron’s rest mass is the equivalent mass of the energy in its motion (mass without mass). The elementary wavefunction represents this motion.
2. There is no weak force: a force theory explaining why charges stay together must also explain when and how they separate. A force works through a force field: the idea that forces are mediated by virtual messenger particles resembles 19th century aether theory. The fermion-boson dichotomy does not reflect anything real: we have charged and non-charged wavicles (electrons versus photons, for example).
3. The Planck-Einstein law embodies a (stable) wavicle. A stable wavicle respects the Planck-Einstein relation (E = hf) and Einstein’s mass-energy equivalence relation (E = m·c2). A wavicle will, therefore, carry energy but it will also pack one or more units of Planck’s quantum of action. Planck’s quantum of action represents an elementary cycle in Nature. An elementary particle embodies the idea of an elementary cycle.
4. The ‘particle zoo’ is a collection of unstable wavicles: they disintegrate because their cycle is slightly off (the integral of the force over the distance of the loop and over the cycle time is not exactly equal to h).
5. An electron is a wavicle that carries charge. A photon does not carry charge: it carries energy between wavicle systems (atoms, basically). It can do so because it is an oscillating field.
6. An atom is a wavicle system. A wavicle system has an equilibrium energy state. This equilibrium state packs one unit of h. Higher energy states pack two, three,…, n units of h. When an atom transitions from one energy state to another, it will emit or absorb a photon that (i) carries the energy difference between the two energy states and (ii) packs one unit of h.
7. Nucleons (protons and neutrons) are held together because of a strong force. The strong force acts on a strong charge, for which we need to define a new unit: we choose the dirac but – out of respect for Yukawa, we write one dirac as 1 Y. If Yukawa’s function models the strong force correctly, then the strong force – which we denote as FN – can be calculated from the Yukawa potential:
This function includes a scale parameter a and a nuclear proportionality constant υ0. Besides its function as an (inverse) mathematical proportionality constant, it also ensures the physical dimensions on the left- and the right-hand side of the force equation are the same. We can choose to equate the numerical value of υ0 to one.
8. The nuclear force attracts two positive electric charges. The electrostatic force repels them. These two forces are equal at a distance r = a. The strong charge unit (gN) can, therefore, be calculated. It is equal to:
9. Nucleons (protons or neutrons) carry both electric as well as strong charge (qe and gN). A kinematic model disentangling both has not yet been found. Such model should explain the magnetic moment of protons and neutrons.
10. We think of a nucleus as wavicle system too. When going from one energy state to another, the nucleus emits or absorbs neutrinos. Hence, we think of the neutrino as the photon of the strong force. Such changes in energy states may also involve the emission and/or absorption of an electric charge (an electron or a positron).
Does this make sense? I look forward to your thoughts. 🙂
Because the above is all very serious, I thought it would be good to add something that will make you smile. 🙂
Feyerabend was a rather famous philosopher. He was of the opinion that ‘anything goes’. We disagree. Let me know your views on my latest paper. 🙂 Let me know your views on my latest paper. 🙂 Also check out this one: https://www.academia.edu/40226046/Neutrinos_as_the_photons_of_the_strong_force.
I started to edit and add to the rather useless Wikipedia article on the Zitterbewegung. No mention of Hestenes or more recent electron models (e.g. Burinskii’s Kerr-Newman geometries. No mention that the model only works for electrons or leptons in general – not for non-leptonic fermions. It’s plain useless. But all the edits/changes/additions were erased by some self-appointed ‘censor’. I protested but then I got reported to the administrator ! What can I say? Don’t trust Wikipedia. Don’t trust any ‘authority’. We live in weird times. The mindset of most professional physicists seems to be governed by ego and the Bohr-Heisenberg Diktatur.
For the record, these are the changes and edits I tried to make. You can compare and judge for yourself. Needless to say, I told them I wouldn’t bother to even try to contribute any more. I published my own article on the Vixrapedia e-encyclopedia. Also, as Vixrapedia did not have an entry on realist interpretations of quantum mechanics, I created one: have a look and let me know what you think. 🙂
Zitterbewegung (“trembling” or “shaking” motion in German) – usually abbreviated as zbw – is a hypothetical rapid oscillatory motion of elementary particles that obey relativistic wave equations. The existence of such motion was first proposed by Erwin Schrödinger in 1930 as a result of his analysis of the wave packet solutions of the Dirac equation for relativistic electrons in free space, in which an interference between positive and negative energy states produces what appears to be a fluctuation (up to the speed of light) of the position of an electron around the median, with an angular frequency of ω = 2mc2/ħ, or approximately 1.5527×1021 radians per second. Paul Dirac was initially intrigued by it, as evidenced by his rather prominent mention of it in his 1933 Nobel Prize Lecture (it may be usefully mentioned he shared this Nobel Prize with Schrödinger):
“The variables give rise to some rather unexpected phenomena concerning the motion of the electron. These have been fully worked out by Schrödinger. It is found that an electron which seems to us to be moving slowly, must actually have a very high frequency oscillatory motion of small amplitude superposed on the regular motion which appears to us. As a result of this oscillatory motion, the velocity of the electron at any time equals the velocity of light. This is a prediction which cannot be directly verified by experiment, since the frequency of the oscillatory motion is so high and its amplitude is so small. But one must believe in this consequence of the theory, since other consequences of the theory which are inseparably bound up with this one, such as the law of scattering of light by an electron, are confirmed by experiment.”
In light of Dirac’s later comments on modern quantum theory, it is rather puzzling that he did not pursue the idea of trying to understand charged particles in terms of the motion of a pointlike charge, which is what the Zitterbewegung hypothesis seems to offer. Dirac’s views on non-leptonic fermions – which were then (1950s and 1960s) being analyzed in an effort to explain the ‘particle zoo‘ in terms of decay reactions conserving newly invented or ad hoc quantum numbers such as strangeness – may be summed up by quoting the last paragraph in the last edition of his Principles of Quantum Mechanics:
“Now there are other kinds of interactions, which are revealed in high-energy physics. […] These interactions are not at present sufficiently well understood to be incorporated into a system of equations of motion.”
Indeed, in light of this stated preference for kinematic models, it is somewhat baffling that Dirac did not follow up on this or any of the other implications of the Zitterbewegung hypothesis, especially because it should be noted that a reexamination of Dirac theory shows that interference between positive and negative energy states is not a necessary ingredient of Zitterbewegung theories. The Zitterbewegung hypothesis also seems to offer interesting shortcuts to key results of mainstream quantum theory. For example, one can show that, for the hydrogen atom, the Zitterbewegung produces the Darwin term which plays the role in the fine structure as a small correction of the energy level of the s-orbitals. This is why authors such as Hestenes refers to it as a possible alternative interpretation of mainstream quantum mechanics, which may be an exaggerated claim in light of the fact that the zbw hypothesis results from the study of electron behavior only.
Zitterbewegung models have mushroomed and it is, therefore, increasingly difficult to distinguish between them. The key to understanding and distinguishing the various Zitterbewegung models may well be Wheeler‘s ‘mass without mass’ idea, which implies a distinction between the idea of (i) a pointlike electric charge (i.e. the idea of a charge only, with zero rest mass) and (ii) the idea of an electron as an elementary particle whose equivalent mass is the energy of the zbw oscillation of the pointlike charge. The ‘mass without mass’ concept requires a force to act on a charge – and a charge only – to explain why a force changes the state of motion of an object – its momentum p = mγ·v(with γ referring to the Lorentz factor) – in accordance with the (relativistically correct) F = dp/dt force law.
As mentioned above, the zbw hypothesis goes back to Schrödinger’s and Dirac’s efforts to try to explain what an electron actually is. Unfortunately, both interpreted the electron as a pointlike particle with no ‘internal structure’.David Hestenes is to be credited with reviving the Zitterbewegung hypothesis in the early 1990s. While acknowledging its origin as a (trivial) solution to Dirac’s equation for electrons, Hestenes argues the Zitterbewegung should be related to the intrinsic properties of the electron (charge, spin and magnetic moment). He argues that the Zitterbewegung hypothesis amounts to a physical interpretation of the elementary wavefunction or – more boldly – to a possible physical interpretation of all of quantum mechanics: “Spin and phase [of the wavefunction] are inseparably related — spin is not simply an add-on, but an essential feature of quantum mechanics. […] A standard observable in Dirac theory is the Dirac current, which doubles as a probability current and a charge current. However, this does not account for the magnetic moment of the electron, which many investigators conjecture is due to a circulation of charge. But what is the nature of this circulation? […] Spin and phase must be kinematical features of electron motion. The charge circulation that generates the magnetic moment can then be identified with the Zitterbewegung of Schrödinger “ Hestenes’ interpretation amounts to an kinematic model of an electron which can be described in terms of John Wheeler‘s mass without mass concept. The rest mass of the electron is analyzed as the equivalent energy of an orbital motion of a pointlike charge. This pointlike charge has no rest mass and must, therefore, move at the speed of light (which confirms Dirac’s en Schrödinger’s remarks on the nature of the Zitterbewegung). Hestenes summarizes his interpretation as follows: “The electron is nature’s most fundamental superconducting current loop. Electron spin designates the orientation of the loop in space. The electron loop is a superconducting LC circuit. The mass of the electron is the energy in the electron’s electromagnetic field. Half of it is magnetic potential energy and half is kinetic.”
Hestenes‘ articles and papers on the Zitterbewegung discuss the electron only. The interpretation of an electron as a superconducting ring of current (or as a (two-dimensional) oscillator) also works for the muon electron: its theoretical Compton radius rC = ħ/mμc ≈ 1.87 fm falls within the CODATA confidence interval for the experimentally determined charge radius. Hence, the theory seems to offer a remarkably and intuitive model of leptons. However, the model cannot be generalized to non-leptonic fermions (spin-1/2 particles). Its application to protons or neutrons, for example, is problematic: when inserting the energy of a proton or a neutron into the formula for the Compton radius (the rC = ħ/mc formula follows from the kinematic model), we get a radius of the order of rC = ħ/mpc ≈ 0.21 fm, which is about 1/4 of the measured value (0.84184(67) fm to 0.897(18) fm). A radius of the order of 0.2 fm is also inconsistent with the presumed radius of the pointlike charge itself. Indeed, while the pointlike charge is supposed to be pointlike, pointlike needs to be interpreted as ‘having no internal structure’: it does not imply the pointlike charge has no (small) radius itself. The classical electron radius is a likely candidate for the radius of the pointlike charge because it emerges from low-energy (Thomson) scattering experiments (elastic scattering of photons, as opposed to inelastic Compton scattering). The assumption of a pointlike charge with radius re = α·ħ/mpc) may also offer a geometric explanation of the anomalous magnetic moment.
In any case, the remarks above show that a Zitterbewegung model for non-leptonic fermions is likely to be somewhat problematic: a proton, for example, cannot be explained in terms of the Zitterbewegung of a positron (or a heavier variant of it, such as the muon- or tau-positron). This is why it is generally assumed the large energy (and the small size) of nucleons is to be explained by another force – a strong force which acts on a strong charge instead of an electric charge. One should note that both color and/or flavor in the standard quark–gluon model of the strong force may be thought of as zero-mass charges in ‘mass without mass’ kinematic models and, hence, the acknowledgment of this problem does not generally lead zbw theorists to abandon the quest for an alternative realist interpretation of quantum mechanics.
While Hestenes‘ zbw interpretation (and the geometric calculus approach he developed) is elegant and attractive, he did not seem to have managed to convincingly explain an obvious question of critics of the model: what keeps the pointlike charge in the zbw electron in its circular orbit? To put it simply: one may think of the electron as a superconducting ring but there is no material ring to hold and guide the charge. Of course, one may argue that the electromotive force explains the motion but this raises the fine-tuning problem: the slightest deviation of the pointlike charge from its circular orbit would yield disequilibrium and, therefore, non-stability. [One should note the fine-tuning problem is also present in mainstream quantum mechanics. See, for example, the discussion in Feynman’s Lectures on Physics.] The lack of a convincing answer to these and other questions (e.g. on the distribution of (magnetic) energy within the superconducting ring) led several theorists working on electron models (e.g. Alexander Burinskii) to move on and explore alternative geometric approaches, including Kerr-Newman geometries. Burinskii summarizes his model as follows: “The electron is a superconducting disk defined by an over-rotating black hole geometry. The charge emerges from the Möbius structure of the Kerr geometry.” His advanced modelling of the electron also allows for a conceptual bridge with mainstream quantum mechanics, grand unification theories and string theory: “[…] Compatibility between gravity and quantum theory can be achieved without modifications of Einstein-Maxwell equations, by coupling to a supersymmetric Higgs model of symmetry breaking and forming a nonperturbative super-bag solution, which generates a gravity-free Compton zone necessary for consistent work of quantum theory. Super-bag is naturally upgraded to Wess-Zumino supersymmetric QED model, forming a bridge to perturbative formalism of conventional QED.”
The various geometric approaches (Hestenes’ geometric calculus, Burinskii’s Kerr-Newman model, oscillator models) yield the same results (the intrinsic properties of the electron are derived from what may be referred to as kinematic equations or classical (but relativistically correct) equations) – except for a factor 2 or 1/2 or the inclusion (or not) of variable tuning parameters (Burinskii’s model, for example, allows for a variable geometry) – but the equivalence of the various models that may or may not explain the hypothetical Zitterbewegung still needs to be established.
The continued interest in zbw models may be explained because Zitterbewegung models – in particular Hestenes’ model and the oscillator model – are intuitive and, therefore, attractive. They are intuitive because they combine the Planck-Einstein relation (E = hf) and Einstein’s mass-energy equivalence (E = mc2): each cycle of the Zitterbewegung electron effectively packs (i) the unit of physical action (h) and (ii) the electron’s energy. This allows one to understand Planck’s quantum of action as the product of the electron’s energy and the cycle time: h = E·T = h·f·T = h·f/f = h. In addition, the idea of a centripetal force keeping some zero-mass pointlike charge in a circular orbit also offers a geometric explanation of Einstein’s mass-energy equivalence relation: this equation, therefore, is no longer a rather inexplicable consequence of special relativity theory.
The section below offers a general overview of the original discovery of Schrödinger and Dirac. It is followed by further analysis which may or may not help the reader to judge whether the Zitterbewegung hypothesis might, effectively, amount to what David Hestenes claims it actually is: an alternative interpretation of quantum mechanics.
Theory for a free fermion
[See the article: the author of this section does not seem to know – or does not mention, at least – that the Zitterbewegung hypothesis only applies to leptons (no strong charge).]
The Zitterbewegung may remain theoretical because, as Dirac notes, the frequency may be too high to be observable: it is the same frequency as that of a 0.511 MeV gamma-ray. However, some experiments may offer indirect evidence. Dirac’s reference to electron scattering experiments is also quite relevant because such experiments yield two radii: a radius for elastic scattering (the classical electron radius) and a radius for inelastic scattering (the Compton radius). Zittebewegung theorists think Compton scattering involves electron-photon interference: the energy of the high-energy photon (X- or gamma-ray photons) is briefly absorbed before the electron comes back to its equilibrium situation by emitting another (lower-energy) photon (the difference in the energy of the incoming and the outgoing photon gives the electron some extra momentum). Because of this presumed interference effect, Compton scattering is referred to as inelastic. In contrast, low-energy photons scatter elastically: they seem to bounce off some hard core inside of the electron (no interference).
Some experiments also claim they amount to a simulation of the Zitterbewegung of a free relativistic particle. First, with a trapped ion, by putting it in an environment such that the non-relativistic Schrödinger equation for the ion has the same mathematical form as the Dirac equation (although the physical situation is different). Then, in 2013, it was simulated in a setup with Bose–Einstein condensates.
The effective mass of the electric charge
The 2m factor in the formula for the zbw frequency and the interpretation of the Zitterbewegung in terms of a centripetal force acting on a pointlike charge with zero rest mass leads one to re-explore the concept of the effective mass of an electron. Indeed, if we write the effective mass of the pointlike charge as mγ = γm0 then we can derive its value from the angular momentum of the electron (L = ħ/2) using the general angular momentum formula L = r × p and equating r to the Compton radius:
This explains the 1/2 factor in the frequency formula for the Zitterbewegung. Substituting m for mγ in the ω = 2mc2/ħ yields an equivalence with the Planck-Einstein relation ω = mγc2/ħ. The electron can then be described as an oscillator (in two dimensions) whose natural frequency is given by the Planck-Einstein relation.
Preliminary note: Since writing the post, I developed a more comprehensive paper. You can find it on my academia.edu site (click here). It’s a bit longer – and also more technical – than the post below. Have fun ! 🙂
According to common wisdom, we need to introduce a new charge – and, therefore, a new force – to explain why protons will stick together. But we have neutrons too, right? Can’t they serve as glue? Now that’s an idea. About 99.999866 per cent of helium on this planet consists of two protons and two neutrons: we write this isotope as 4He. The only other stable isotope is 3He, which consists of two protons and one neutron. Let me google this… This is what Wikipedia writes: “Within the nucleus, protons and neutrons are bound together through the nuclear force. Neutrons are required for the stability of nuclei, with the exception of the single-proton hydrogen atom.”
So now we need to examine this glue: what is it? What’s the difference between a neutron and a proton? A proton is stable. Neutrons are only stable inside of a nucleus: free neutrons decay. Their mean lifetime is almost 15 minutes, so that’s almost eternity in atomic physics. Almost, but not quite: free neutrons are transient oscillations. Why are neutrons stable in a nucleus but not in free space? We think it’s the Planck-Einstein relation: two protons, two neutrons and two electrons – a helium atom, in other words – are stable because all of the angular momenta in the oscillation add up to (some multiple of) Planck’s (reduced) quantum of action. The angular momentum of a neutron in free space does not, so it has to fall apart in a (stable) proton and a (stable) electron – and then a neutrino which carries the remainder of the energy. Let’s jot it down:Let’s think about energy first. The neutron’s energy is about 939,565,420 eV. The proton energy is about 938,272,088 eV. The difference is 1,293,332 eV. That’s almost 1.3 MeV. The electron energy gives us close to 0.511 MeV of that difference – so that’s only 40% – but its kinetic energy can make up for a lot of the remainder! We then have the neutrino to provide the change—the nickel-and-dime, so to speak.
Is this decay reversible? It is: a proton can capture an electron and, somehow, become a neutron. It usually happens with proton-rich nuclei absorbing an inner atomic electron, usually from the K or L electron shell, which is why the process is referred to as K- or L-electron capture:Once again, we have a neutrino providing the nickel-and-dime to ensure energy conservation. It is written as the anti-particle of the neutrino in the neutron decay equation. Neutrinos and anti-neutrinos are neutral, so what’s the difference? The specialists in the matter say they have no idea and that a neutrino and an anti-neutrino might well be one and the same thing. Hence, for the time being, we’ll effectively assume they’re one and the same thing: we might write both as νe. No mystery here—not for me, at least. Or not here and not right now, I should say: the neutrino is just a vehicle to ensure conservation of energy and momentum (linear and/or angular).
It is tempting to think of the proton as some kind of atomic system itself, or a positive ion to which we may add an electron so as to get a neutron. You’ll say: that’s the hydrogen atom, right? No. The hydrogen atom is much larger than a neutron: the Bohr radius of a hydrogen atom is about 0.53 picometer (1 pm = 1´10–12 m). In contrast, the radius of a neutron is of the order of 0.8 femtometer (1 fm = 1´10–15 m), so that’s about 660 times smaller. While a neutron is much smaller, its energy (and, therefore, its mass) is significantly higher: the energy difference between a hydrogen atom and a neutron is about 0.78 MeV. That’s about 1.5 times the energy of an electron. The table below shows these interesting numbers.A good model of what a proton and a neutron actually are, will also need to explain why electron-positron pair production only happens when the photon is fired into a nucleus. The mainstream interpretation of this phenomenon is that the surplus kinetic energy needs to be absorbed by some heavy particle – the nucleus itself. My guts instinct tells me something else must be going on. Electron-positron pair production does seem to involve the creation of an electric charge out of energy. It puzzled Dirac (and many other physicists, of course) greatly.Let us think about sizes once more. If we try the mass of a proton (or a neutron—almost the same) in the formula for the Compton radius, we get this:That’s about 1/4 of the actual radius as measured in scattering experiments. We have a good rationale for calculating the Compton radius of a proton (or a neutron). It is based on the Zitterbewegung model for elementary particles: a pointlike charge whizzing around at the speed of light. For the electron, the charge is electric. For the proton or the neutron, we think of some strong charge and we, therefore, get a very different energy and, hence, a very different Compton radius. However, a factor of 1/4 is encouraging but not good enough. If anything, it may indicate that a good model of a proton (and a neutron) should, besides some strong force, also incorporate the classical electric charge. It is difficult to think about this, because we think the pointlike electric charge has a radius itself: the Thomson or classical electron radius, which is equal to:This is about 3.5 times larger than the proton or neutron radius. It is even larger than the measured radius of the deuteron nucleus, which consists of a proton and a neutron bound together. That radius is about 2.1 fm. As mentioned above, this ‘back-of-the-envelope’ calculation of a Compton radius is encouraging, but a good model for a proton (and for a neutron) will need to explain these 1/4 or 3.5 factors.
What happens might be something like this: we fire an enormous amount of electromagnetic energy into a nucleus (the equivalent mass of the photon has to match the mass of the electron and the positron that’s being produced) and, hence, we destabilize the stable nucleus. However, Nature is strong. The strong force is strong. Some intermediate energy state emerges but Nature throws out the spanner in the works. The end result is that all can be analyzed, once again, in terms of the Planck-Einstein relation: we have stable particles, once again. [Of course, the positron finds itself in the anti-Universe and will, therefore, quickly disappear in the reverse process: electron-positron annihilation.]
But so that’s just a story right now. We need to develop it into a proper theory.
Post scriptum: We’ve calculated a Compton radius for the proton. If – in analogy with the electron model – we would (also) have a current inside, then we should be able to calculate that current. Let us limit ourselves to the electric current – because we don’t have much of an idea about what a strong current would represent. The circular electric current creates a magnetic moment. We got the right value for an electron:What do we get if we do a similar calculation for a pointlike charge moving around at the speed of light but in a much smaller loop – a loop measured in femtometer rather than picometer? The calculation below shows we get a similar result in terms of structure but note the result is expressed in terms of the nuclear magneton (mN) which uses the proton mass, as opposed to the Bohr magneton, which uses the electron (rest) mass.Unsurprisingly, the actually measured value is different, and the difference is much larger than Schwinger’s a/2p fraction. To be precise, μp » 2.8·μN, so the measured value of the proton’s magnetic moment is almost three times that of its theoretical value. It should be no surprise to us – because we use a radius that’s 1/4 of what might be the actual radius of the loop. In fact, the measured value of the proton’s magnetic moment suggests the actual radius of the loop should be 2.8 times the theoretical Compton radius:Again, these results are not exact, but they’re encouraging: they encourage us to try to describe the proton in terms of some kind of hybrid model – something that mixes the classical electric charge with some strong charge. No need for QFT or virtual particles. 🙂
 CODATA data gives a standard error in the measurements that is equal to 0.46 eV. Hence, the measurements are pretty precise.
 When you talk money, you need big and small denominations: banknotes versus coins. However, the role of coins could be played by photons too. Gamma-ray photons – produced by radioactive decay – have energies in the MeV order of magnitude, so they should be able to play the role of whatever change we need in an energy equation, right? Yes. You’re right. So there must be more to it. We see neutrinos whenever there is radioactive decay. Hence, we should probably associate them with that, but how exactly is a bit of a mystery. Note that the decay equation conserves linear, angular (spin) momentum and (electric) charge. What about the color charge? We’re not worried about the color charge here. Should we be worried? I don’t think so, but if you’d be worried, note that this rather simple decay equation does respect color conservation – regardless of your definition of what quarks or gluons might actually be.
 See the various articles on neutrinos on Fermi National Accelerator Laboratory (FNAL), such as, for example, this one: https://neutrinos.fnal.gov/mysteries/majorana-or-dirac/. The common explanation is that neutrinos and anti-neutrinos have opposite spin but that’s nonsensical: we can very well imagine one and the same particle with two spin numbers.