The nature of the matter-wave

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) so as to add it to my YouTube channel. 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.

Sean Carroll

Post scriptum: Of course, I got the usual question from one of the students: 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 long here (I cannot because this is just a footnote to a blog post) 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 oscillation 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 promised 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.

The metaphysics of physics

So if we take all of the scaffolding away, what concepts are we left with? What is substance and what is form? Forget about quarks and bosons: the concepts of a charge and fields are core. A force acts on a charge, and matter-particles carry charge. The charge comes in units: the elementary charge. Anti-matter carries an opposite charge—opposite as defined with respect to the matter-particle of which the antimatter-particle is the counterpart.

Pair creation-annihilation is mysterious but not incomprehensible. It happens when the two particles have the same structure and opposite spacetime signature: ++++ versus +–––. Electrons and positrons annihilate each other, and protons and antiprotons—but not electrons and protons. A neutron disintegrates into a proton and an electron outside of the nucleus. That is why a proton and a antineutron – or a neutron and a antiproton – will also vanish in a flash of energy: a neutron is a composite particle—it consists of an electron and a proton. The exact pattern of the dance between the electron and proton inside of a neutron has not been modeled yet—as opposed to the dance between electrons and the positively charged nucleus in an atom (Rutherford’s contribution to the 1921 Solvay Conference comes to mind here).

The elementary charge itself is mysterious: the charge (and mass) density of an electron is very different from that of a proton. Both elementary particles can be modeled as ring currents, however. The Planck-Einstein relation applies to both but with a different form factor.

Mass is mass without mass: a measure of the inertia of the Zitterbewegung motion of the charge. Einstein’s mass-energy equivalence relations models an oscillation in two dimensions. Euler’s wavefunction represents the same. A proton is very different than an electron: massive and small. The force that keeps the charge inside of a proton together suggests the force may be different: this is the idea of a strong force—strong as compared to the electromagnetic force.

This strong force is not Yukawa’s force, however: inter-nucleon forces – what keeps protons and neutrons together inside of a nucleus – can be explained by the coupling of the magnetic moments of the ring currents.

The Zitterbewegung of the charge explains the magnetic moment of matter-particles. The anomaly in the magnetic moment tells us more about the structure of the charge inside of matter-particles: the charge is pointlike but not dimensionless.

What else can we say? Charge is conservedalways, but we must allow for pair creation-annihilation. Energy and momentum are conserved too. Physical systems are either stable or unstable. Atoms, for example, are stable. They too can be modeled as an oscillation respecting the Planck-Einstein relation. Planck’s quantum of action is like a sum of money: you can spend it very quickly, or you can spend over a longer period of time. Same bang for the buck, but you can bang it fast or slow. 🙂 That is what the E·T = h expression of the Planck-Einstein relation tells us: the same amount of physical action (6.626×1034 N·m·s) can be associated with very different energies and, therefore, very different cycle times.

Photons do no carry charge but they carry energy. They carry energy as electromagnetic fields traveling in space. This begs the question: what is oscillating, exactly? We do not know: the concept of an aether has no use beyond the idea of mediating this oscillation—which is why we can forget about it.

Particle interactions involving the strong force also involve the emission and/or absorption of neutrinos. Neutrinos may, therefore, be thought of as the photons of the strong force: they ensure energy and momentum is being conserved for strong interactions too.

There is no weak force: unstable particles disintegrate because they are in a disequilibrium state: the Planck-Einstein relation does not apply and, hence, the unstable state is a transient oscillation only—or a very short-lived resonance.

The idea of virtual particles going back and forth between non-virtual particles to mediate the electromagnetic or strong force is like the 19th-century aether idea or, worse, a remnant of medieval scholastic thinking: all forces must be contact forces, right? No. Of course not. No force is a contact force: forces work through fields. That’s mysterious too, but it is much simpler than accounting for messenger particles: they must have momentum and energy too, right? It becomes hugely complicated. Just forget about it! No gluons, no W/Z bosons, and no Higgs particle either.


Is that it? Yes. That’s it! I could write some more but then I would exceed the self-allotted one-page for my summary of all of physics. 🙂 Is all of this important? Maybe. If you are reading this, then it is probably important to you. You want to know, right? The most remarkable thing of all of it is the order that emerges from it. Two electrons in the same atomic orbital will align their magnetic moments so as to lower their joint energy: single electrons are valence electrons, and explain why atoms will share them in molecules. Molecules themselves come together in larger and stabler structure. Now it is Darwin’s “survival of the fittest” that comes into play: weaker structures do not survive their environment. At some point in time – very long or not so long ago (depends on your time scale) – some macro-structures became organisms that interacted, in a extremely primitive but real way, with their environment to reproduce themselves. Darwin’s principle tells us that being strong and stable is good, but being able to multiply is even better. So these structures started consuming other structures to multiply. Complexity increased: order and entropy go hand in hand. And so here we are: thinking about where we came from – some raw and uncomplicated state – just before we go back to it. Soon enough. Too soon. As an individual, at least. :-/

That is the true Mystery: your mind—our Mind. Our understanding of things using a very limited number of concepts, equations and elementary constants: the electric charge, Planck’s quantum of action, and the speed of light. Nothing more, nothing less. At larger scales, it is systems interacting with each other and their environment. That’s it. You should think about it. Don’t get lost in math. And surely don’t get lost in amplitude math. It’s not worth it. 🙂

[…] One more thing, perhaps: please do enjoy thinking about this Mystery! A friend of mine once remarked this: “It is good you are studying physics only as a pastime. Professional physicists are often troubled people.” I found the observation strange and sad, but mostly true (think of what Paul Ehrenfest did, for example). There are exceptions, though (H.A. Lorentz and Richard Feynman were happier characters). In any case, if you study physics but you are troubled by it, then study something else: chemistry, biology, or evolutionary psychology, perhaps. Don’t worry about physics: unlike what some are trying to tell you, it all makes sense. 🙂