The geometry of the de Broglie wavelength

I thought I would no longer post stuff here but I see this site still gets a lot more traffic than the new one, so I will make an exception and cross-post an announcement of a new video on my YouTube channel. Indeed, yesterday I was to talk for about 30 minutes to some students who are looking at classical electron models as part of an attempt to try to model what might be happening to an electron when moving through a magnetic field. Of course, I only had time to discuss the ring current model, and even then it inadvertently turned into a two-hour presentation. Fortunately, they were polite and no one dropped out—although it was an online Google Meet. In fact, they reacted quite enthusiastically, and so we all enjoyed it a lot. So much that I adjusted the presentation a bit the next morning (which added even more time to it unfortunately) and published it online. So this is the link to it, and I hope you enjoy it. If so, please like it—and share it! 🙂

Oh! Forgot to mention: in case you wonder why this video is different than others, see my Tweet on Sean Carroll’s latest series of videos hereunder. That should explain it. 🙂

Post scriptum: I got the usual question from one of the students, of course: if an electron is a ring current, then why doesn’t it radiate its energy away? The easy answer is: an electron is an electron and so it doesn’t—for the same reason that an electron in an atomic orbital or a Cooper pair in a superconducting loop of current does not radiate energy away. The more difficult answer is a bit mysterious: it has got to do with flux quantization and, most importantly, with the Planck-Einstein relation. I will not be too explicit here (it is just a footnote) but the following elements should be noted:

1. The Planck-Einstein law embodies a (stable) wavicle: a wavicle respects the Planck-Einstein relation (E = h·f) as well as Einstein’s mass-energy equivalence relation (E = mc2). A wavicle will, therefore, carry energy but it will also pack one or more units of Planck’s quantum of action. Both the energy as well as this finite amount of physical action (Wirkung in German) will be conserved—cycle after cycle.

2. Hence, equilibrium states should be thought of as electromagnetic oscillations without friction. Indeed, it is the frictional element that explains the radiation of, say, an electron going up and down in an antenna and radiating some electromagnetic signal out. To add to this rather intuitive explanation, I should also remind you that it is the accelerations and decelerations of the electric charge in an antenna that generate the radio wave—not the motion as such. So one should, perhaps, think of a charge going round and round as moving like in a straight line—along some geodesic in its own space. That’s the metaphor, at least.

3. Technically, one needs to think in terms of quantized fluxes and Poynting vectors and energy transfers from kinetic to potential (and back) and from ‘electric’ to ‘magnetic’ (and back). In short, the electron really is an electromagnetic perpetuum mobile ! I know that sounds mystical (too) but then I never said I would take all of the mystery away from quantum physics ! 🙂 If there would be no mystery left, I would not be interested in physics.  On the quantization of flux for superconducting loops: see, for example, http://electron6.phys.utk.edu/qm2/modules/m5-6/flux.htm. There is other stuff you may want to dig into too, like my alternative Principles of Physics, of course ! 🙂

Rutherford’s idea of an electron

Pre-scriptum (dated 27 June 2020): Two illustrations in this post were deleted by the dark force. We will not substitute them. The reference is given and it will help you to look them up yourself. In fact, we think it will greatly advance your understanding if you do so. Mr. Gottlieb may actually have done us a favor by trying to pester us.

Electrons, atoms, elementary particles and wave equations

The New Zealander Ernest Rutherford came to be known as the father of nuclear physics. He was the first to provide a reliable estimate of the order of magnitude of the size of the nucleus. To be precise, in the 1921 paper which we will discuss here, he came up with an estimate of about 15 fm for massive nuclei, which is the current estimate for the size of an uranium nucleus. His experiments also helped to significantly enhance the Bohr model of an atom, culminating – just before WW I started – in the Bohr-Rutherford model of an atom (E. Rutherford, Phil. Mag. 27, 488).

The Bohr-Rutherford model of an atom explained the (gross structure of the) hydrogen spectrum perfectly well, but it could not explain its finer structure—read: the orbital sub-shells which, as we all know now (but not very well then), result from the different states of angular momentum of an electron and the associated magnetic moment.

The issue is probably best illustrated by the two diagrams below, which I copied from Feynman’s Lectures. As you can see, the idea of subshells is not very relevant when looking at the gross structure of the hydrogen spectrum because the energy levels of all subshells are (very nearly) the same. However, the Bohr model of an atom—which is nothing but an exceedingly simple application of the E = h·f equation (see p. 4-6 of my paper on classical quantum physics)—cannot explain the splitting of lines for a lithium atom, which is shown in the diagram on the right. Nor can it explain the splitting of spectral lines when we apply a stronger or weaker magnetic field while exciting the atoms so as to induce emission of electromagnetic radiation.

Schrödinger’s wave equation solves that problem—which is why Feynman and other modern physicists claim this equation is “the most dramatic success in the history of the quantum mechanics” or, more modestly, a “key result in quantum mechanics” at least!

Such dramatic statements are exaggerated. First, an even finer analysis of the emission spectrum (of hydrogen or whatever other atom) reveals that Schrödinger’s wave equation is also incomplete: the hyperfine splitting, the Zeeman splitting (anomalous or not) or the (in)famous Lamb shift are to be explained not only in terms of the magnetic moment of the electron but also in terms of the magnetic moment of the nucleus and its constituents (protons and neutrons)—or of the coupling between those magnetic moments (we may refer to our paper on the Lamb shift here). This cannot be captured in a wave equation: second-order differential equations are – quite simply – not sophisticated enough to capture the complexity of the atomic system here.

Also, as we pointed out previously, the current convention in regard to the use of the imaginary unit (i) in the wavefunction does not capture the spin direction and, therefore, makes abstraction of the direction of the magnetic moment too! The wavefunction therefore models theoretical spin-zero particles, which do not exist. In short, we cannot hope to represent anything real with wave equations and wavefunctions.

More importantly, I would dare to ask this: what use is an ‘explanation’ in terms of a wave equation if we cannot explain what the wave equation actually represents? As Feynman famously writes: “Where did we get it from? Nowhere. It’s not possible to derive it from anything you know. It came out of the mind of Schrödinger, invented in his struggle to find an understanding of the experimental observations of the real world.” Our best guess is that it, somehow, models (the local diffusion of) energy or mass densities as well as non-spherical orbital geometries. We explored such interpretations in our very first paper(s) on quantum mechanics, but the truth is this: we do not think wave equations are suitable mathematical tools to describe simple or complex systems that have some internal structure—atoms (think of Schrödinger’s wave equation here), electrons (think of Dirac’s wave equation), or protons (which is what some others tried to do, but I will let you do some googling here yourself).

We need to get back to the matter at hand here, which is Rutherford’s idea of an electron back in 1921. What can we say about it?

Rutherford’s contributions to the 1921 Solvay Conference

From what you know, and from what I write above, you will understand that Rutherford’s research focus was not on electrons: his prime interest was in explaining the atomic structure and in solving the mysteries of nuclear radiation—most notably the emission of alpha– and beta-particles as well as highly energetic gamma-rays by unstable or radioactive nuclei. In short, the nature of the electron was not his prime interest. However, this intellectual giant was, of course, very much interested in whatever experiment or whatever theory that might contribute to his thinking, and that explains why, in his contribution to the 1921 Solvay Conference—which materialized as an update of his seminal 1914 paper on The Structure of the Atom—he devotes considerable attention to Arthur Compton’s work on the scattering of light from electrons which, at the time (1921), had not even been published yet (Compton’s seminal article on (Compton) scattering was published in 1923 only).

It is also very interesting that, in the very same 1921 paper—whose 30 pages are more than a multiple of his 1914 article and later revisions of it (see, for example, the 1920 version of it, which actually has wider circulation on the Internet)—Rutherford also offers some short reflections on the magnetic properties of electrons while referring to Parson’s ring current model which, in French, he refers to as “l’électron annulaire de Parson.” Again, it is very strange that we should translate Rutherford’s 1921 remarks back in English—as we are sure the original paper must have been translated from English to French rather than the other way around.

However, it is what it is, and so here we do what we have to do: we give you a free translation of Rutherford’s remarks during the 1921 Solvay Conference on the state of research regarding the electron at that time. The reader should note these remarks are buried in a larger piece on the emission of β particles by radioactive nuclei which, as it turns out, are nothing but high-energy electrons (or their anti-matter counterpart—positrons). In fact, we should—before we proceed—draw attention to the fact that the physicists at the time had no clear notion of the concepts of protons and neutrons.

This is, indeed, another remarkable historical contribution of the 1921 Solvay Conference because, as far as I know, this is the first time Rutherford talks about the neutron hypothesis. It is quite remarkable he does not advance the neutron hypothesis to explain the atomic mass of atoms combining what we know think of as protons and neutrons (Rutherford regularly talks of a mix of ‘positive and negative electrons’ in the nucleus—neither the term proton or neutron was in use at the time) but as part of a possible explanation of nuclear fusion reactions in stars or stellar nebulae. This is, indeed, his response to a question during the discussions on Rutherford’s paper on the possibility of nuclear synthesis in stars or nebulae from the French physicist Jean Baptise Perrin who, independently from the American chemist William Draper Harkins, had proposed the possibility of hydrogen fusion just the year before (1919):

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

We may add that, just to make sure he get this right, Rutherford is immediately requested to elaborate his point by the Danish physicist Martin Knudsen: “What’s the difference between a hydrogen atom and this neutron?”—which Rutherford simply answers as follows: “In a neutron, the electron would be very much closer to the nucleus.” In light of the fact that it was only in 1932 that James Chadwick would experimentally prove the existence of neutrons (and positively charged protons), we are, once again, deeply impressed by the the foresight of Rutherford and the other pioneers here: the predictive power of their theories and ideas is, effectively, truly amazing by any standard—including today’s. I should, perhaps, also add that I fully subscribe to Rutherford’s intuition that a neutron should be a composite particle consisting of a proton and an electron—but that’s a different discussion altogether.

We must come back to the topic of this post, which we will do now. Before we proceed, however, we should highlight one other contextual piece of information here: at the time, very little was known about the nature of α and β particles. We now know that beta-particles are electrons, and that alpha-particles combine two protons and two neutrons. That was not known in the 1920s, however: Rutherford and his associates could basically only see positive or negative particles coming out of these radioactive processes. This further underscores how much knowledge they were able to gain from rather limited sets of data.

Rutherford’s idea of an electron in 1921

So here is the translation of some crucial text. Needless to say, the italics, boldface and additions between [brackets] are not Rutherford’s but mine, of course.

“We may think the same laws should apply in regard to the scattering [“diffusion”] of α and β particles. [Note: Rutherford noted, earlier in his paper, that, based on the scattering patterns and other evidence, the force around the nucleus must respect the inverse square law near the nucleus—moreover, it must also do so very near to it.] However, we see marked differences. Anyone who has carefully studied the trajectories [photographs from the Wilson cloud chamber] of beta-particles will note the trajectories show a regular curvature. Such curved trajectories are even more obvious when they are illuminated by X-rays. Indeed, A.H. Compton noted that these trajectories seem to end in a converging helical path turning right or left. To explain this, Compton assumes the electron acts like a magnetic dipole whose axis is more or less fixed, and that the curvature of its path is caused by the magnetic field [from the (paramagnetic) materials that are used].

Further examination would be needed to make sure this curvature is not some coincidence, but the general impression is that the hypothesis may be quite right. We also see similar curvature and helicity with α particles in the last millimeters of their trajectories. [Note: α-particles are, obviously, also charged particles but we think Rutherford’s remark in regard to α particles also following a curved or helical path must be exaggerated: the order of magnitude of the magnetic moment of protons and neutrons is much smaller and, in any case, they tend to cancel each other out. Also, because of the rather enormous mass of α particles (read: helium nuclei) as compared to electrons, the effect would probably not be visible in a Wilson cloud chamber.]

The idea that an electron has magnetic properties is still sketchy and we would need new and more conclusive experiments before accepting it as a scientific fact. However, it would surely be natural to assume its magnetic properties would result from a rotation of the electron. Parson’s ring electron model [“électron annulaire“] was specifically imagined to incorporate such magnetic polarity [“polarité magnétique“].

A very interesting question here would be to wonder whether such rotation would be some intrinsic property of the electron or if it would just result from the rotation of the electron in its atomic orbital around the nucleus. Indeed, James Jeans usefully reminded me any asymmetry in an electron should result in it rotating around its own axis at the same frequency of its orbital rotation. [Note: The reader can easily imagine this: think of an asymmetric object going around in a circle and returning to its original position. In order to return to the same orientation, it must rotate around its own axis one time too!]

We should also wonder if an electron might acquire some rotational motion from being accelerated in an electric field and if such rotation, once acquired, would persist when decelerating in an(other) electric field or when passing through matter. If so, some of the properties of electrons would, to some extent, depend on their past.”

Each and every sentence in these very brief remarks is wonderfully consistent with modern-day modelling of electron behavior. We should add, of course, non-mainstream modeling of electrons but the addition is superfluous because mainstream physicists stubbornly continue to pretend electrons have no internal structure, and nor would they have any physical dimension. In light of the numerous experimental measurements of the effective charge radius as well as of the dimensions of the physical space in which photons effectively interfere with electrons, such mainstream assumptions seem completely ridiculous. However, such is the sad state of physics today.

Thinking backward and forward

We think that it is pretty obvious that Rutherford and others would have been able to adapt their model of an atom to better incorporate the magnetic properties not only of electrons but also of the nucleus and its constituents (protons and neutrons). Unfortunately, scientists at the time seem to have been swept away by the charisma of Bohr, Heisenberg and others, as well as by the mathematical brilliance of the likes of Sommerfeld, Dirac, and Pauli.

The road then was taken then has not led us very far. We concur with Oliver Consa’s scathing but essentially correct appraisal of the current sorry state of physics:

“QED should be the quantized version of Maxwell’s laws, but it is not that at all. QED is a simple addition to quantum mechanics that attempts to justify two experimental discrepancies in the Dirac equation: the Lamb shift and the anomalous magnetic moment of the electron. The reality is that QED is a bunch of fudge factors, numerology, ignored infinities, hocus-pocus, manipulated calculations, illegitimate mathematics, incomprehensible theories, hidden data, biased experiments, miscalculations, suspicious coincidences, lies, arbitrary substitutions of infinite values and budgets of 600 million dollars to continue the game. Maybe it is time to consider alternative proposals. Winter is coming.”

I would suggest we just go back where we went wrong: it may be warmer there, and thinking both backward as well as forward must, in any case, be a much more powerful problem solving technique than relying only on expert guessing on what linear differential equation(s) might give us some S-matrix linking all likely or possible initial and final states of some system or process. 🙂

Post scriptum: The sad state of physics is, of course, not limited to quantum electrodynamics only. We were briefly in touch with the PRad experimenters who put an end to the rather ridiculous ‘proton radius puzzle’ by re-confirming the previously established 0.83-0.84 range for the effective charge radius of a proton: we sent them our own classical back-of-the-envelope calculation of the Compton scattering radius of a proton based on the ring current model (see p. 15-16 of our paper on classical physics), which is in agreement with these measurements and courteously asked what alternative theories they were suggesting. Their spokesman replied equally courteously:

“There is no any theoretical prediction in QCD. Lattice [theorists] are trying to come up [with something] but that will take another decade before any reasonable  number [may come] from them.”

This e-mail exchange goes back to early February 2020. There has been no news since. One wonders if there is actually any real interest in solving puzzles. The physicist who wrote the above may have been nominated for a Nobel Prize in Physics—I surely hope so because, in contrast to some others, he and his team surely deserve one— but I think it is rather incongruous to finally firmly establish the size of a proton while, at the same time, admit that protons should not have any size according to mainstream theory—and we are talking the respected QCD sector of the equally respected Standard Model here!

We understand, of course! As Freddy Mercury famously sang: The Show Must Go On.

Joseph Larmor and the ring current model of an electron

Joseph Larmor is surely not among the more famous participants in the Solvay Conferences. He only joined the 1921 Conference, together with Charles Glover Barkla and others, and his one and only substantial intervention there is limited to some remarks and questions following a presentation by H.A. Lorentz on the Theory of Electrons, during which Lorentz highlights all of the issues in regard to what was then supposed to be the understanding of what an electron actually is (which, in my not-so-humble-view, is still pretty much the state of our current understanding of it).

I find his one intervention (and Lorentz’ reply to it) very interesting though, and so that’s why I am writing about it here. I am not aware of any free online English translations of the proceedings of the Solvay Conferences (nor of any translation of Lorentz’ paper in particular) but you may be luckier than me when googling: if you find it, please do let me know. In the meanwhile, I am happy to freely translate part of Larmor’s rather short intervention after Lorentz’ presentation from French to English:

“I understand that Mr. Lorentz was given the task to give an overview of how electrons behave inside of an atom. That requires an overview of all possible theories of the electron. That is a highly worthwhile endeavor which, in itself, would already justify the holding of this Conference. However, Mr. Lorentz might have paid more attention to the viewpoint that the electron has some structure, and that its representation as a simple distribution of electric charge can only be provisional: electrons explain electricity, but electricity does not explain electrons. However, the description of an electron in terms of a charge distribution is, for the time being, all we can imagine. In the past, we thought of the atom as an indivisible unit – a fundamental building block – and we imagined it as a swirling ring. That idea is gone now, and the electron has now taken the place of the atom as an indestructible unit. All we can know about it, is how it influences other bodies. If this influence is transmitted all across the aether, we need to be able to express the relations between the electron and the aether[1], or its force field in the space that surrounds it. It may have other properties, of course, but physics is the science that should analyze the influence or force of one body upon others.

The question we should raise here is whether or not an electron formed by a perfectly uniform current ring can grab onto the aether in a physical sense, and how it does so if its configuration does not change.” (Joseph Larmor, 1921, boldface and italics added)

Larmor then talks about the (possible) use of the energy-momentum tensor to address the latter question, which is a very technical discussion which is of no concern to us here. Indeed, the question on how to use tensors to model how an electron would interact with other charges or how it would create an electromagnetic field is, effectively, a rather standard textbook topic now and, in case you’d be interested, you can check  my blog on it or, else, (re-)read Chapters 25, 26 and 27 of Feynman’s Lectures on electromagnetism.

What grabbed my attention here was, effectively, not the technicality of the question in regard to the exact machinery of the electromagnetic force or field. It was Larmor’s description of the electron as a perpetual or persistent current ring (the French reference to it is this: un electron formé par un courant annulaire parfaitement uniforme), and his language on it, which indicates he thought of it as a rather obvious and natural idea! Hence, Parson’s 1915 toroidal ring model – the precursor to Schrödinger’s Zitterbewegung model and modern-day ring current models – was apparently pretty well established at the time! In fact, Rutherford’s lecture on the Structure of the Atom at the 1921 Conference further confirms this, as he also talks about Parson’s électron annulaire (ring electron) and the apparent magnetic properties of the electron (I will talk about Rutherford’s 1921 Solvay lecture in my next post).

Larmor’s belief that the electron was not pointlike should, of course, not surprise us in light of his rather famous work on the quantum-mechanical precession of the magnetic moment of an electron, but I actually wasn’t aware of Joseph Larmor’s own views in regard to its possible reality. In fact, I am only guessing here but his rather strong views on its reality may explain why the scientific committee − which became increasingly dominated by scientists in favor of the Bohr-Heisenberg interpretation of physical reality (basically saying we will never be able to understand it)  − did not extend an invitation to Larmor to attend the all-important Solvay conferences that would follow the 1921 Conference and, most notably, the 1927 Conference that split physicists between realists and… Well… Non-realists, I guess. 🙂

Lorentz’ immediate reaction to Larmor mentioning the idea of a swirling ring (in French: un anneau tourbillon), which is part of his reply to Larmor’s remarks, is equally interesting:

“There is a lot to be said for your view that electrons are discontinuities in the aether. […] The energy-momentum formulas that I have developed should apply to all particles, with or without structure. The idea of a rotating ring [in French: anneau tournant] has a great advantage when trying to explain some issues [in the theory of an electron]: it would not emit any electromagnetic radiation. It would only produce a magnetic field in the immediate space that surrounds it. […]” (H.A. Lorentz, 1921, boldface and italics added)

Isn’t that just great? Lorentz’ answer to Larmor’s question surely does not solve all of the problems relating to the interpretation of the electron as a current ring, but it sure answers that very basic question which proponents of modern quantum mechanics usually advance when talking about the so-called failure of classical physics: electrons in some electron orbital in an atom should radiate their energy out, but so they do not. Let me actually quote from Feynman’s Lectures on Quantum Mechanics here: “Classically, the electrons would radiate light and spiral in until they settle down right on top of the nucleus. That cannot be right.”

Surely You’re Joking, Mr. Feynman! Here is the answer of the classical quantum theorists: superconducting rings of electric current do not radiate their energy out either, do they?

[1] Larmor believed an aether should exist. We will re-quote Robert B. Laughlin here: “The word ‘ether’ has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum. […] The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo.”

On the concept of the aether, we can also usefully translate part of Lorentz’ answer to Larmor: “As for the aether, even the physicists who still talk about it have stripped the concept of anything it might have in common with matter. I was a believer in an immobile aether myself but I realize that, because of relativity, we cannot talk about any force acting on the aether. However, I still think of the aether as the seat of electromagnetic energy (in French, le siège de l’énergie électromagnétique). Now, we can all think of the components of the energy-momentum tensor like we want, but if we think of some of them being real in some sense, then all of them should be real in the same sense.”

Post scriptum: I should really stop duplicating posts between this and my other blog site on physics. Hence, I beg the readers who want to keep following me to do so on my ideez.org site. I think I’ll devote it a historical analysis of how useful and not-so-useful ideas in physics have evolved over the past hundred years or so, using the proceedings of the Solvay Conferences as the material for analysis.

The metaphysics of physics

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!

A theory of matter-particles

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.

Text:

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[1], 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[2] 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[3] – moving about at (nearly) the speed of light around the center of its motion.

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[6] 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 + ay2a2·ω4·cos2(ωt) + a2·ω4·sin2(ωt) = a2·ω4ac = 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.[7] 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.[8] 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[9] 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

[1] In this paper, we make abstraction of the anomaly, which is related to the zbw charge having a (tiny) spatial dimension.

[2] 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.

[3] See footnote 1.

[4] See our paper on the proton radius (https://vixra.org/abs/2002.0160).

[5] See reference above.

[6] 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.

[7] 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).

[8] 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/).

[9] 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).

The Mystery Wallahs

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.

JL

The ultimate electron model

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.

JL

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.]

Philosophy and Physics

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