The center of mass and center of charge of the electron

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.

💡 Research Summary

The paper revisits the most elementary assumptions about the electron by postulating that its center of mass (CM) and its center of charge (CC) are distinct points in space. This hypothesis, the author argues, can only be made consistent within a fully relativistic framework; in a non‑relativistic picture the two points would collapse into a single location. By introducing two independent world‑lines—one for the massive core (CM) and one for the charge distribution (CC)—the author constructs a classical Lagrangian that yields, after applying Lorentz transformations, two markedly different motions. The CM follows the usual straight‑line inertial trajectory, while the CC moves at the speed of light along a helical (corkscrew) path. This helical motion reproduces the Zitterbewegung originally discovered in the Dirac theory, but here it emerges as a purely kinematic consequence of the CM‑CC separation.

Two spin vectors are defined accordingly. The “CM‑spin” ( \mathbf{S}{\text{CM}} ) is the conventional intrinsic angular momentum associated with the massive core, and together with the orbital angular momentum about the CM it composes the total angular momentum ( \mathbf{J}= \mathbf{L}{\text{CM}}+\mathbf{S}{\text{CM}} ). The “CC‑spin” ( \mathbf{S}{\text{CC}} ) originates from the circulating charge around the CC; it is directly linked to the magnetic moment generated by the light‑speed current loop. By explicit calculation the author shows that ( \mathbf{S}_{\text{CC}} ) obeys the same dynamical equation as the Dirac spin operator: \