TimeCrystal Model of the Electron Spin
Abstract
The waveparticle duality is one of the most intriguing properties of quantum objects. The duality is rather pervasive in the quantum world in the sense that not only classical particles sometimes behave like waves, but also classical waves may behave as point particles. In this article, motivated by the waveparticle duality, I develop a deterministic timecrystal Lorentzcovariant model for the electron spin. In the proposed timecrystal model an electron is formed by two components: a particletype component that transports the electric charge, and a wave component that moves at the speed of light and whirls around the massive component. Interestingly, the motion of the particlecomponent is completely ruled by the trajectory of the wavecomponent, somewhat analogous to the pilotwave theory of de BroglieBohm. The dynamics of the timecrystal electron is controlled by a generalized least action principle. The model predicts that the electron stationary states have a constant spin angular momentum, predicts the spin vector precession in a magnetic field and gives a possible explanation for the physical origin of the anomalous magnetic moment. Remarkably, the developed model has nonlocal features that prevent the divergence of the selffield interactions. The classical theory of the electron is recovered as an "effective theory" valid on a coarse time scale. The reported results suggest that timecrystal models may be used to describe some features of the quantum world that are inaccessible to the standard classical theory.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.12158
 Bibcode:
 2021arXiv210712158S
 Keywords:

 Physics  Classical Physics;
 Physics  Optics;
 Quantum Physics
 EPrint:
 57 pages