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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

Three-dimensional time and Thomas precession

G. Ziino

Published Aug 1, 1981• 18 citations
Publisher
DOI
10.1007/bf02777968

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Canadian Journal of Physics•May 16, 2014•4 citations
In 1913, É. Borel (1871–1956) considered the relativistic kinematic rotation of a body that arises in the course of its orbital motion. In order to determine the angular velocity of this rotation, Borel introduced the notion of a kinematic space and applied the Gauss-Bonnet formula for a sphere of a unit radius. However, at that time, his results did not find practical applications and, soon, were forgotten. After the discovery of electron spin by S.A. Goudsmit and G.E. Uhlenbeck in 1925, real interest in this phenomenon was rekindled, and it was considered once again by L.H. Thomas in 1926–1927, being termed the Thomas precession. The Thomas precession manifests itself mostly in optical phenomena.
We show that in the derivation of the frequency of Thomas precession, the fact of implementation of rotation-free Lorentz transformations between a laboratory frame, KL, and Lorentz frames K(t) co-moving with a particle with spin at any time moments, t, has principal importance. Choosing for the observation of the particle’s motion any other inertial frame, K, related with KL by the rotation-free transformation, we have to realize that the transformations between K and K(t) at any t are no longer rotation-free. This way we provide a resolution of the known paradox by Bacry (H. Bacry. Nuovo Cimento, 26, 1164 (1962)) and suggest a reinterpretation of the Thomas precession, which is further discussed.