Zitterbewegung as purely classical phenomenon

TL;DR

This paper demonstrates that Zitterbewegung, traditionally considered a quantum phenomenon, can be explained as a purely classical effect arising from internal degrees of freedom in a nonrelativistic framework.

Contribution

It develops a nonrelativistic formalism for systems with internal degrees of freedom, showing classical origins of Zitterbewegung and proposing a new classical perspective on electron spin and charge.

Findings

Center of mass follows helical and complex trajectories due to internal degrees of freedom.

Zitterbewegung can occur in nonrelativistic classical systems with internal structure.

New classical equations for spin and charge are derived.

Abstract

Nonrelativistic formalism is developed, which allows describing systems with internal degrees of freedom in the scalar potential field $U$, which is a function both on relative coordinates and time, and on relative speed and accelerations. The equation for energy, which is an integral of motion when $U$ satisfies to certain differential condition, is derived for the general case. For a free mass point all solutions of the equations of motion in the center-of-inertia reference frame, moving with constant velocity, are found. As a result, the center of mass follows along helical and more complicated trajectories round a direction of motion of the center of inertia. This motion can be interpreted as trembling movement (Zitterbewegung). On this basis a conclusion is done that Zitterbewegung has purely classical origin, arising even in a nonrelativistic case if internal degrees of freedom are taken into account. The general equation of motion for a spin which can be interpreted from positions of a classical mechanics is written down. Application of the obtained results to the electron leads to new conception of electric charge, sign of which corresponds to a sign of spin polarization.