Time-Crystal Model of the Electron Spin

Abstract: The time-crystal concept was originally introduced by Frank Wilczek [1] and relates to systems with a spontaneously broken time-translational symmetry, such that the ground-state evolves periodically in time, not withstanding the equations of motion are invariant under arbitrary time-translations (i.e., do not depend on the time origin). Thus, the ground state of a time-crystal is some sort of “perpetuum mobile”. The time-crystal idea was originally introduced in the context quantum many-body systems. It is natural to wonder if non-driven classical time-crystals may naturally occur in nature and if they can have a role in the description of physical reality. In this talk, I will show that a hypothetical classical massless particle has forcibly a time-crystal (non-driven) dynamics characterized by a spontaneous time symmetry breaking that originates a spin angular momentum. I will show that a time-crystal particle is formed by two inseparable components: a massive-component that behaves as a classical particle and a wave-component that whirls around the “particle” and generates the spin and an intrinsic angular momentum. The spin vector is parallel to the binormal of the velocity trajectory and is the spatial component of a 4-vector. The trajectory of the particle is fully controlled by the trajectory of the wave, reminiscent of the pilot-wave theory of de Broglie and Bohm. Furthermore, in the proposed framework the “mass” is an emergent property, in the sense that it originates from the fact that the center of mass frame speed is necessarily less than c. The trajectory of a time-crystal particle is controlled by a dynamical least action principle. The massless-component dynamically probes the nearby space and the particle moves on average towards the direction of space that minimizes an action integral. Interestingly, the proposed model predicts the precession of the spin vector about a static magnetic field, and most remarkably it suggests that the mismatch between the spin precession frequency omega_s and the cyclotron frequency omega_c –which is at the origin of the famous anomalous magnetic moment – is a manifestation of the electromagnetic self-energy. The time-crystal model pr edicts that the difference between omega_s and omega_c results in an axial oscillatory motion, which is consistent with the experiment typically used to measure the anomalous magnetic moment.

mathematical physicsgeneral physicsquantum physics

Audience: researchers in the topic

( paper )

---

QM Foundations & Nature of Time seminar

Series comments: Description: Physics foundations discussion seminar

Current access link in th.if.uj.edu.pl/~dudaj/QMFNoT

---