Reexamining the Thomas precession

Abstract

We review the Thomas precession exhibiting the exact form of the Thomas rotation in the axis-angle parameterization. Assuming three inertial frames S, S′, and S″ moving with arbitrary velocities and with S and S″ having their axes parallel to the axes of S′, we focus our attention on the two essential elements of the Thomas precession: (i) there is a rotation between the axes of frames S and S″ and (ii) the combination of two Lorentz transformations from S to S′ and from S′ to S″ fails to produce a pure Lorentz transformation from S to S″. The physical consequence of (i) and (ii) refers to the impossibility of arbitrary frames S, S′, and S″ moving with non-parallel relative velocities having their axes mutually parallel. Then, we reexamine the validity of (i) and (ii) under the conjecture that time depends on the state of motion of the frames and we show that the Thomas precession assumes a different form as formulated in (i) and (ii).