  The motion of spinning test particles in general relativity is described by
Mathisson-Papapetrou-Dixon equations, which are undetermined up to a spin
supplementary condition, the latter being today still an open question. The
Mathisson-Pirani (MP) condition is known to lead to rather mysterious helical
motions which have been deemed unphysical, and for this reason discarded. We
show that these assessments are unfounded and originate from a subtle (but
crucial) misconception. We discuss the kinematical explanation of the helical
motions, and dynamically interpret them through the concept of hidden momentum,
which has an electromagnetic analogue. We also show that, contrary to previous
claims, the frequency of the helical motions coincides exactly with the
zitterbewegung frequency of the Dirac equation for the electron.
