We review why the Thomas rotation is a crucial facet of special relativity,
that is just as fundamental, and just as "unintuitive" and "paradoxical,"
as such traditional effects as length contraction, time dilation, and the a
mbiguity of simultaneity. We show how this phenomenon can be quite naturall
y introduced and investigated in the context of a typical introductory cour
se on special relativity, in a way that is appropriate for, and completely
accessible to, undergraduate students. We also demonstrate, in a more advan
ced section aimed at the graduate student studying the Dirac equation and r
elativistic quantum field theory, that careful consideration of the Thomas
rotation will become vital as modern experiments in particle physics contin
ue to move from unpolarized to polarized cross sections. (C) 2001 American
Association of Physics Teachers.