What Keeps Electrons from Exploding?
High school students, many electrical engineers, even some physicists conveniently think of a single free electron as a charged "point" of zero size. This is a useful picture (model) for our imagination, or for simplifying physics problems, but we all know it's not really possible. "True Zero" never occurs in nature. If the diameter is really truly ZERO, the charge density would be infinite, the mass density infinite, the electric field infinite, the energy infinite, and so on. That's nonsense. In real life the electron must have size bigger than zero.
Background
Dirac's field equations (1928) can be interpreted as describing the electron as a real physical field with a smooth local mass distribution in space and a matching smooth charge distribution. The energy and spin are also distributed in space. Every point in the field has a mass density, a charge density, and spin density. Imagine something like an incompressible charged magnetic fluid. [Rashkovskiy 2016, see abstract below]. This field picture of reality is very different from the statistical quantum mechanics view where wave functions are mathematical "probability amplitudes." That's the probability of finding the electron particle at any given point. Rashkovskiy interprets the fields as real physical things, not probability.
But Why Doesn't it Explode?
If we model the free electron as a ball or blob of charged mass we have a huge problem: What keeps it from exploding? All the electric charge has the same sign and it repels itself. For example the left half would forcefully repel the right half and they would instantly fly apart.
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| Fireworks Explosions [Photo has no copyright] |
Confined Electrons
A confined electron is a different story. We have all seen simulations of the Hydrogen atom with perfectly stable electron orbitals. They don't fly apart because the positively charged protons in the nucleus hold the charged "liquid" in a kind of container, called a potential well. Here is the picture (from computer simulations).
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| Captive electrons in the Hydrogen orbitals [Wikipedia] |
Why Don't Free Protons Explode?
It's a similar question. We know from particle accelerator data that protons are much larger and heavier than electrons and that protons are held together by gluons. The gluon field is opposite the electric field so they somehow hold the proton together. As far as anyone knows protons are stable, they do not decay. So far proton decay has never been observed. But there are no gluons holding the electron together. So what does hold an electron together? What keeps free electrons from exploding?
How about Photons?
Electromagnetic wave bursts (photons) are stable only when they are moving (propagating). The electromagnetic field can not have bumps or lumps that stand still because they instantly dissipate. Maxwell's field equations don't allow peaks or valleys that stand still. When a charged object moves, it radiates EM waves with peaks and valleys that move away at the speed of light. Electromagnetic waves certainly can't stand still.
How about Water Waves?
Everybody has seen water waves move slowly along the surface. We never see a pile of water just standing still because that would be unstable. It would immediately fall apart and dissipate. The left half would repel the right half.
What about Rope Waves?
Waves travel in ropes. But a rope can not have a hill or valley that stands still. Waves exist only when they move. Standing waves (like vibrating guitar strings) are possible if the string is confined. Oscillations are standing waves in a resonant object or "cavity." Rope waves can't stand still.
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| Battle Rope for exercise https://www.hyperwear.com/product/battle-ropes/ |
So What Keeps Free Electrons from Exploding?
I'm still looking for the answer. Maybe free electrons need to keep moving, like every other wave. There must be some mechanism to hold it together as it moves. Some kind of wave motion that keeps it from exploding. I can't visualize it. I think somebody with a supercomputer could simulate Dirac's equation in free space and take some snapshots. I see lots of simulations of captive electrons. I'm still searching. Some people have conjectured that maybe the electron is like a knot in the rope, or some kind of bubble or "raindrop." But I can't find any justification for that.
Reference
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