The center of mass and center of charge of the electron

TL;DR

This paper explores the classical and quantum implications of the electron having distinct centers of mass and charge, proposing that this distinction influences its angular momentum, spin, and related phenomena, with potential insights into the proton spin crisis.

Contribution

It introduces the idea that the electron's center of mass and charge are separate points, affecting its angular momentum and spin dynamics, and links this to unresolved issues like the proton spin crisis.

Findings

The center of charge follows a helical path at light speed.

Dirac spin operators relate to classical spin about the charge center.

Implications for proton spin composition and electron-related phenomena.

Abstract

If the assumption that the center of mass(CM) and the center of charge(CC) of the electron are two different points was stated 100 years ago, our conceptual ideas about elementary particles would be different. This assumption is only compatible with a relativistic description. It suggests, from the classical point of view, that the angular momentum of the electron has to have a unique value. In the free motion, the CC follows a helix at the speed of light. The spin with respect to CC and to CM satisfy two different dynamical equations which shows that Dirac spin operator in the quantum case satisfies the same dynamical equation as the classical spin with respect to the CC. This means, among other things, that the addition of the three Dirac's spin operators of the three quarks can never give rise to the spin of the proton, so that the proton spin crisis could be related to this incompleteness in the addition of the quark's angular momenta. Some other effects related to spinning particles like the concept of gyromagnetic ratio, a classical description of tunneling and the formation of bound pairs of electrons, are analized.