What are Electrons Made of?
It may sound stupid at first, but can anyone explain electrons?
Electrons that are confined inside an atom can be described pretty well by a wave picture. They are waves acting like a simple harmonic oscillator. They behave like standing waves with discrete energy levels, energy gaps, energy bands. This wave model is reasonable for electrons whether confined in an atom or in a solid crystal. They exhibit wavelength, frequency, spin, mass, charge, momentum, all the usual wave behaviors. Conduction bands, valence bands, spectroscopic emission and absorption. Even superconductivity of electrons can be described very well using wave models (see Carver Mead's book Collective Electrodynamics).
Free electrons are another matter. The Schrodinger wave packet model seems to have
the right behavior (for example the two-slit interference phenomenon) but it is hard for me
to find a reasonable description or model for the charge cloud. If the Schrodinger wave is
REAL (not just a probability wave) then the charge and mass are distributed in space. But then
how can a cloud (or blob) of charge be stable? Free electrons should explode.
Confined electrons don't have that problem because they are always embedded in a net neutral
environment. In atoms, there is always a positive proton charge to hold things together. In a solid
crystal, the lattice positive charge averages out the negative electron wave. But free electrons,
like in an electron beam, are charged and should fly apart violently. The Schroedinger wave packet (low energy)
simulations are beautiful and realistic, but the simulations set the electron charge to zero, as if the electron was neutral.
The Dirac equation for the electron does have a "q" in it, but it only feels the force of the external electric field,
not it's own self field arising from it's own distributed charge "cloud."
S. Rashkovskiy (and others before him like A. O. Barut 1989) have
solved the Dirac equation INCLUDING a self-interaction term,
but nobody else seems to be convinced. I am convinced. There MUST be a self-interaction term, because
I believe point-charge infinities are nonsensical. Nothing in nature has zero size. Zero is very, very, very small!!!
Zero is impossible, just like infinity. If the electron wave has a size, then one half must repel the other half.
Rashkovskiy's solution is adding a new term for a "spin field" that counteracts the repulsive electric force. This
spin field holds the electron together somehow. I can't follow his math. Also his solution is for electrons confined in an atom. He doesn't talk about free electrons.
Another problem is that single free electrons spread out over time. It is clear from the Schroedinger simulations
that the single electron Gaussian wave packet spreads out with time. So after a long time (say, a hundred years) the wave packet
of a single free electron will be very large. If the Schroedinger wave is understood as a real wave (QFT) then mass and charge become spread out very thinly over a very, very large volume of space. Waves can easily be
split into many pieces. Can an electron matter wave be split into many pieces??? Doesn't this violate
charge quantization? Can electron charge be split into pieces? Rashkovskiy says "YES." I would
like to see some actual measurement data. That's why I found the electron bubble article (H. Maris) so interesting. They seemed to show that electrons can be split into many pieces!
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