Thomas Precession: The Missing Link

Abstract

This first chapter presents the Thomas precession of relativity physics as the motivational approach that led the author to the discovery of the theory of gyrogroups and gyrovector spaces. The theory of gyrogroups and gyrovector spaces provides a most natural generalization of its classical counterparts, the theory of groups and the theory of vector spaces. Readers who wish to start familiarizing themselves with the theory may, therefore, start reading this book from its second chapter and return to the first chapter only if and when their curiosity about the origin of the Thomas precession arises.

THE BIRTH OF THE THOMAS PRECESSION [Tho82]. I, being a reasonably brash young man in the presence of Bohr, said: “Why doesn’t someone work it out relativistically.” Kramers who had known of the earlier work on the motion of the moon by De Sitter said to me: “It would be a very small relativistic correction. You can work it out, I won’t.” Over that weekend I looked at it. I had the advantage of having attended Eddington’s lectures on relativity theory and I knew how to work the mathematics. I found that if you look at the change in the direction of the axis of a rotating electron, there should be a very considerable relativistic effect, in fact, a factor of two. I brought this idea back with a formula to Kramers and Bohr just after that one Christmas weekend [December 25–27, 1925]. Bohr insisted that a letter should be written to Nature, which had this result in it. This letter, which is my second or third original paper, was published in Nature in April 1926[Tho26].

—Llewellyn H. Thomas (1902–1992)