Thomas precession and Thomas-Wigner rotation: Correct solutions and their implications

Abstract

We address the Thomas precession for the hydrogen-like atom and point out that in the derivation of this effect in the semi-classical approach, two different successions of rotation-free Lorentz transformations between the laboratory frame K and the proper electron's frames, K-e(t) and K-e(t + dt), separated by the time interval dt, were used by different authors. We further show that the succession of Lorentz transformations K -> K-e(t) -> K-e(t + dt) leads to relativistically non-adequate results in the frame Ke(t) with respect to the rotational frequency of the electron spin, and thus an alternative succession of transformations K -> K-e(t), K -> K-e( t + dt) must be applied. From the physical viewpoint this means the validity of the introduced "tracking rule", when the rotation-free Lorentz transformation, being realized between the frame of observation K and the frame K(t) co-moving with a tracking object at the time moment t, remains in force at any future time moments, too. We apply this rule to the moving macroscopic objects and analyze its implications with respect to the Thomas-Wigner rotation and its application to astrometry. Copyright (C) EPLA, 2020.