Anomalous magnetic moment, BMT equation, and Mathisson-Papapetrou-Dixon equations
It is my understanding that the Bargmann-Michel-Telegdi (BMT) equation [Phys. Rev. Lett. 2, 435 (1959)] plays a central role in precision experiments measuring the anomalous magnetic moment of the muon or electron in order to look for physics beyond the standard model [e.g., <PERSON>, The Anomalous Magnetic Moment of the Muon (Springer, 2017)]. I believe that the BMT equation is really equivalent to <PERSON>'s old theory on the electrodynamics of the rotating electron [Z. Phys. 37, 243 (1926)]. The equations of motion derived by <PERSON> and BMT involve what is sometimes called the <PERSON> (-Mathisson) condition, that is, the orthogonality of spin angular momentum $S^{\mu\nu}$ and velocity $v_\mu$ of the system, $S^{\mu\nu} v_\mu = 0$ [Eq. (7a) = (18b) in <PERSON>'s paper; Eq. (2) in the BMT paper]. The same condition was used by <PERSON> (and others) in a theory for the dynamics of rotating objects in the framework of general relativity [<PERSON>, Acta Phys. Pol. 6, 163 (1937); also Gen. 346
Relat. Gravit. 42, 1011 (2010)]. Later it was noted that <PERSON>'s and <PERSON>'s equations of motion are problematic because they are third-order differential equations [e.g., <PERSON> and <PERSON>, Acta Phys. Pol. 9, 7 (1947); <PERSON>, Nuovo Cimento 34, 317 (1964)]. Therefore, <PERSON> [Acta Phys. Pol. 18, 393 (1959)] and <PERSON> [loc. cit.; also Nuovo Cimento 38, 1616 (1965)] suggested to replace the <PERSON> condition $S^{\mu\nu} v_\mu = 0$ by what became known as Tulczyjew-Dixon condition $S^{\mu\nu} p_\mu = 0$, where $p_\mu$ is momentum. I believe that these things are well-known in general relativity, where the equations of motion based on the Tulczyjew-Dixon condition are called Mathisson-Papapetrou-Dixon equations, see, e.g., <PERSON> et al., Equations of Motion in Relativistic Gravity (Springer, 2015).
My question is: are these things also relevant for experiments such as those studying the anomalous magnetic moment of the muon or electron? Should the interpretation of these precision experiments possibly use the <PERSON>-Papapetrou-Dixon equations? [It is my understanding that the difference between these models is not a matter of bringing general relativity into the discussion, as in the recent work by <PERSON> and <PERSON>, Class. Quantum Grav. 35, 175003 (2018). But the difference between the <PERSON> condition and the Tulczyjew-Dixon condition becomes relevant already at the level of the special theory of relativity.] 469