The Accelero-Magnetic Field, Thomas Precession and an Equivalence Principle for Spin

Abstract

In the weak field limit of Einstein gravity, there are gravitational analogues of the vector potential and the magnetic field. The equivalence principle guides us to a magnetic-like interaction arising from inertial acceleration. The spin precession due to this accelero-magnetic field is identified as the Thomas precession. Hence the torque that is responsible for the precession of the spin is identified as resulting from a physical interaction with a magnetic-like inertial-field. Once the equivalence principle is assumed to some accuracy, well supported by precision tests, this implies that the average effect of the accelero-magnetic field on a classical or quantum gyroscope is the same as that of the gravito-magnetic field on a gyroscope. Precision spectroscopy of spin-orbit doublets in atoms is hence an indirect high precision test of the existence and properties of the gravito-magnetic field. This also implies that the planned and current experiments will not see any deviations from the predictions of general relativity. This line of thought is extended to a brief discussion on the possibility of formulating an independent equivalence principle for the spin.