Thomas Precession and the Bargmann-Michel-Telegdi Equation

Abstract

A direct method showing the Thomas precession for an evolution of any vector quantity (a spatial part of a four-vector) is proposed. A useful application of this method is a possibility to trace correctly the presence of the Thomas precession in the Bargmann-Michel-Telegdi equation. It is pointed out that the Thomas precession is not incorporated in the kinematical term of the Bargmann-Michel-Telegdi equation, as it is commonly believed. When the Bargmann-Michel-Telegdi equation is interpreted in curved spacetimes, this term is shown to be equivalent to the affine connection term in the covariant derivative of the spin four-vector evolving in a gravitational field. It then contributes to the geodetic precession. The described problem is an interesting and unexpected example showing that approximate methods used in special relativity, in this case to identify the Thomas precession, can distort the true meaning of physical laws. © 2011 The Author(s).