Abstract
The goal of this contribution is to show that the hypothesis that the center of mass (CM) and the center of charge (CC) of a classical electron are two different points is only compatible with a relativistic description. The existence of two separated points is analyzed by the different dynamical behaviour of the angular momenta with respect to both points. It shows, from the classical point of view, that the angular momentum with respect to the CC of the electron satisfies the same dynamical equation as Dirac spin operator in the quantum case. In the free motion, the CC follows a helix at the speed of light, and the CM the axis of the helix. The particle, if its electromagnetic structure is reduced to a total charge e located at CC, has a magnetic moment and also an electric dipole moment with respect to the CM, like in Dirac's theory. The analysis of Dirac spin operator in the quantum case, shows that the electron is a particle where the CM and CC are necessarily different points.
Highlights
If real particles are exactly mathematical points all their mechanical and electromagnetic properties will be defined at that point
The spin with respect to charge of the particle (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
From the electromagnetic point of view, its electromagnetic structure can be reduced to a single point r where we locate the total charge of the particle and the electric and magnetic multipoles
Summary
If real particles are exactly mathematical points all their mechanical and electromagnetic properties will be defined at that point. − Sir, the Lagrangian L0 describes the mechanical properties of the particle and LI its interaction This last part LI suggests that the particle is an object with a complete spherical symmetry as far as the charge distribution and the possible internal currents are concerned. Its complete electromagnetic structure is reduced to a charge e located at a single point r, where the external fields are defined, and no other electric or magnetic multipoles, since there are no multipole couplings in LI. The two subsections are a summary of Marianne’s thesis
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