An electron is usually assumed to be either a point particle or a Planck length vibrating string which is virtually a point particle. While these models work well for some mathematical analysis, there are also numerous difficulties. For example, renormalization is often required when the electron’s size becomes part of the calculation. This implies that a rigorous extension of the starting assumptions gives infinity – the wrong answer. Also, if an electron has a radius equal to or less than Planck length, the energy in the electron’s electric field would exceed the electron’s measured energy by a factor of at least 1020 times . The small size also makes it impossible to explain spin as physical angular momentum.
Collision experiments have been interpreted as implying the radius of an electron must be less than 10-18 m. On the other hand, the very successful Dirac equation implies that an isolated electron has a radius on the order of its reduced Compton wavelength which is about 10-13 m. I have proposed a wave-based model of an electron (see link below) that has a radius in isolation equal to the electron’s reduced Compton wavelength but reduces its wavelength (radius) in energetic collisions. This is one example of an electron model which permits an isolated electron to have a relatively large radius. In your opinion, are electrons and other fundamental particles virtually point particles or do they have size larger than Planck length? Do they have internal structure that will eventually permit their physical properties to be calculated and conceptually understood?
http://onlyspacetime.com/QM-Foundation.pdf
Whatever we assume the electron radius to be is a pretty much speculative matter; to me once we talk about radius, the only sensible way of looking at it is how we can observe it -- yes, experimentally, or at least using a theory that aims to describe a feasible experiment. The most straightforward kind of experiment would be to observe/measure a scattering and respective cross-section by any other particle (preferably neutral). And the most universal "particles" would be photons.
Now. for low photon energies, hbar omega m_0 c^2, where the cross-section slowly goes down as energy encreases due to generation-annihilations of electron-positron pairs; to the first order in alpha, it is described by a powerful Klein-Nishina theory. In the limit eps >> m_0 c^2, where eps=hbar omega, we have approximately sigma_KN / sigma_0 ~ (3/ (8 eps)) [ln(2 eps) + 1/2]. All this of course have nothing to do with Planck radius...
Hello John,
Nice question , I have explained structure of electron and positron in attached paper and conference link.
Electron radius should be in order of Compton wavelength.
Regards,
Bhushan Poojary
https://www.youtube.com/watch?v=WtA6W7KkEp0
Thesis Fine Structure Decoded
Different definitions of the radius must not be mixed up. The Dirac equation starts from an electron of radius 0. The compton wave length correspond to its radius after renormalization, that is, in quantum field theory. This radius includes the virtual particle-antiparticle pairs in the vicinity of the point electron. It is approximately equal to the so called classical radius.
Spin is correctly described by the Dirac equation. It isn't an orbital angular momentum, but the consequence of the multi-components wave function, that transforms like a spinor.
Whatever we assume the electron radius to be is a pretty much speculative matter; to me once we talk about radius, the only sensible way of looking at it is how we can observe it -- yes, experimentally, or at least using a theory that aims to describe a feasible experiment. The most straightforward kind of experiment would be to observe/measure a scattering and respective cross-section by any other particle (preferably neutral). And the most universal "particles" would be photons.
Now. for low photon energies, hbar omega m_0 c^2, where the cross-section slowly goes down as energy encreases due to generation-annihilations of electron-positron pairs; to the first order in alpha, it is described by a powerful Klein-Nishina theory. In the limit eps >> m_0 c^2, where eps=hbar omega, we have approximately sigma_KN / sigma_0 ~ (3/ (8 eps)) [ln(2 eps) + 1/2]. All this of course have nothing to do with Planck radius...
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