A wealth of different expressions for the frequency of the Thomas precession (TP) can be found in the literature, with the consequence that this issue has been discussed over a long period of time. It is shown that the correct result was obtained in the works of several authors, which were published more than forty years ago but remained unnoticed against the background of numerous erroneous works. Several TP-related physical paradoxes formulated primarily to disprove the special relativity theory are shown to be fallacious. Different techniques for deriving the correct expression are considered and the reasons for the emergence of the main incorrect expressions for the TP frequency are analyzed.

http://iopscience.iop.org/article/10.1070/PU2006v049n08ABEH005870/pdf

Thomas precession: correct and incorrect solutions

The precision of a relativistic magnetic top (a point magnetic moment that executes translational motion as it rotates) in special electromagnetic field configuration is investigated. The directions of the intrinsic torque (spin) and the magnetic moment of the top are assumed to coincide. A novel representation of the classical spin equations is given, and the criterion of free motion is formulated for the magnetic top. General solutions of the spin precession equations is constant and uniform electromagnetic fields are obtained for any direction of motion of the top. Special cases of constant fields are discussed: a uniform magnetic field; mutually orthogonal electric field and magnetic field, both uniform (E<H). It is shown how the solutions in the vector and tensor descriptions of the spin are related to the solution of its precession equation specified in the proper rest frame of the top.

Relativistic magnetic top in electromagnetic fields

Es werden die Hauptthesen der klassischen relativistischen Theorie des Spins eines punktformigen Teilchens formuliert. Ausgehend davon wird die Ableitung der Spinbewegungsgleichungen angegeben und gezeigt, das bei Berucksichtigung des anomalen magnetischen Momentes des Teilchens die BARGMANN-MICHEL-TELEGDI-Gleichungen sowie die Gleichungen von Good, NYBORG und anderen als Spezialfalle in den klassischen Spin-Gleichungen von FRENKEL enthalten sind.



The Spin Problem in Classical Electrodynamics



The main principles of the classical relativistic theory of a spin point-particle are formulated. Proceeding from this, the consequences for the spin motion are derived. Taking into account the anomalous magnetic moment of the particle the classical spin equations of FRENKEL are schown to contain as special cases the equations of BARGMANN-MICHEL-TELEGDI and also those of Good, NYBORG and others.

I. M. Ternov

Papers

Das Spinproblem in der klassischen Elektrodynamik