The relativistic mechanism of the Thomas–Wigner rotation and Thomas precession

Abstract

We consider the Thomas-Wigner rotation of coordinate systems under successive Lorentz transformations of inertial reference frames and disclose its physical mechanism on the basis of relativistic contraction of moving scale and relativity of simultaneity of events for different inertial observers. This result allows us to understand better the physical meaning of the Thomas precession and to indicate some of the missed points in the physical interpretation of this effect with two particular examples: the circular motion of a classical electron around a heavy nucleus and the motion of a classical electron along an open path, where its initial velocity and acceleration are mutually orthogonal to each other.

Nonlinear effects in Thomas precession due to the interplay of Lorentz contraction and Thomas–Wigner rotation

“…The overall equation for the spin vector, however, is linear, and it is but the Bargmann-Michel-Telegdi equation [9] represented in the lab frame. The presence of a nonlinearity was found out by Stepanov [8] in a particular case, and also by Kholmetskii and Yarman [10]. Furthermore, we shall prove that for a uniform circular motion, for which the linear precession rate (3) is constant, the average contribution of the nonlinear term (4), when added to the linear term yields Eq.…”

“Tracking rule” and generalization of special relativity

“…Recently, we have analyzed some important features of the Thomas-Wigner rotation and Thomas precession [4][5][6][7][8][9][10] and, in particular, emphasized [8] that the known expression for the frequency of Thomas precession  T of the axis of a point-like gyroscope (e.g., the spin of a classical electron), given as…”