  The Bloch theorem mathematically proves that in a periodic crystal, electrons
can acquire a negative mass. The present work aims to provide a physical
understanding for why this is so. We successively analyze the consequences of
the 3-fold orbital valence state coupling to (i) a non-degenerate orbital level
in the conduction band, (ii) a 3-fold orbital level in the conduction band, and
(iii) spin states through spin-orbit interaction. We show that it is not at all
trivial for valence electrons to acquire a negative mass for whatever their
momentum with respect to the crystal axes: it is necessary to not only have a
coupling to a degenerate orbital conduction level, but also a symmetry breaking
of the 3-fold valence subspace by the spin quantization axis, as induced by
spin-orbit interaction. Due to the relativistic origin of this interaction, the
existence of negative valence masses thus constitutes an unexpected signature
of quantum relativity.
