  In December 1924 Wolfgang Pauli proposed the idea of an inner degree of
freedom of the electron, which he insisted should be thought of as genuinely
quantum mechanical in nature. Shortly thereafter Ralph Kronig and,
independently, Samuel Goudsmit and George Uhlenbeck took up a less radical
stance by suggesting that this degree of freedom somehow corresponded to an
inner rotational motion, though it was unclear from the very beginning how
literal one was actually supposed to take this picture, since it was
immediately recognised (already by Goudsmit and Uhlenbeck) that it would very
likely lead to serious problems with Special Relativity if the model were to
reproduce the electron's values for mass, charge, angular momentum, and
magnetic moment. However, probably due to the then overwhelming impression that
classical concepts were generally insufficient for the proper description of
microscopic phenomena, a more detailed reasoning was never given. In this
contribution I shall investigate in some detail what the restrictions on the
physical quantities just mentioned are, if they are to be reproduced by rather
simple classical models of the electron within the framework of Special
Relativity. It turns out that surface stresses play a decisive role and that
the question of whether a classical model for the electron does indeed
contradict Special Relativity can only be answered on the basis of an
\emph{exact} solution, which has hitherto not been given.
