Against the point-like nature of the electron

TL;DR

The paper challenges the prevailing view that the electron is strictly point-like by arguing that a stationary electron can have a finite, spherically symmetric density on the order of the classical electron radius $r_ ext{cl}$, a view compatible with QFT's polarization cloud. Using topological soliton models in 1+1 and 3+1 dimensions, it shows that Lorentz contraction in high-energy collisions naturally reduces the effective thickness of extended electrons, explaining cross-section behavior. It derives and interprets classic cross sections, such as Thomson scattering with $\sigma_T=\frac{8}{3}\pi r_ ext{cl}^2$ and high-energy processes with $\sigma_{tot} \propto r_ ext{cl}^2/\gamma^2$, within a finite-size framework, linking experimental data to an extended charge density. The work discusses historical contexts (e.g., Dehmelt's substructure claims) and argues that a finite-size interpretation is not only compatible with, but elucidated by, QFT calculations, potentially prompting reconsideration of fundamental notions like substructure and field quantization.

Abstract

Experts in quantum field theory (QFT) generally answer the question of the ``size of an electron'' with ``point-like''. On the other hand, QFT recognizes quantum effects, shielding by virtual particles, the so-called polarization cloud, which should describe the size of physical electrons. Scattering experiments with electrons, such as those carried out in high-energy experiments at particle accelerators, should be able to clarify whether physical electrons are really point-like, as claimed by experts and in textbooks. In this article, I show that both the formulas of QFT and the corresponding cross sections are consistent with an extent of the electron of the size of the classical electron radius. The assumption that the relativistic energy of electrons in the high-energy limit consists solely of deformation energy from the extended electron density distribution allows for a simple interpretation of the experimental cross sections. For this reason, I refer to classical models in 1+1 and 3+1 dimensions that have precisely this property. The difference between the terms point-like, structureless, and substructureless is highlighted. The usual objections to the claim that the electron radius is finite and has already been measured in electron scattering experiments are discussed.

Figures (3)

• Figure 1: Profiles $\theta(x,t=0)$ for the colliding solitons of Eq. (\ref{['ZweiSolitonTheta']}) at the reversal point for different velocities $\beta$ and corresponding Lorentz factors $\gamma$. Although slow-moving solitons ($\gamma\approx 1$) have a finite size, they can come arbitrarily close to each other when they collide at high relative velocities.
• Figure 2: Rotation angle $\theta(x,t=-1)$ in the kink-antikink system of Eq. (\ref{['SolitonAntisolitonTheta']}) for different values of $\gamma$, if an antikink enters from $x=-\infty$ and a kink from $x=+\infty$.
• Figure 3: Electron-electron scattering is represented in the scattering plane for scattering angles of 45°, 90°, and 135° by a thick green line at the point of closest approach, the periapsis. The density distribution of each electron is distorted by Lorentz contraction $\gamma_\parallel$ in the direction of flight $\vartheta/2$ and by the collision component $\gamma_\perp$ in the orthogonal direction, and is shown as a blue ellipse. The respective position of the collision partners is symbolized by a thin gray line.