  We show that when an electron or photon propagates in a cylindrically
symmetric waveguide, its spin angular momentum (SAM) and its orbital angular
momentum (OAM) interact. Remarkably, we find that the dynamics resulting from
this spin-orbit interaction are quantitatively described by a single expression
applying to both electrons and photons. This leads to the prediction of several
novel rotational effects: the spatial or time evolution of either particle's
spin/polarization vector is controlled by the sign of its OAM quantum number,
or conversely, its spatial wavefunction is controlled by its SAM. We show that
the common origin of these effects in electrons and photons is a universal
geometric phase. We demonstrate how these phenomena can be used to reversibly
transfer entanglement between the SAM and OAM degrees of freedom of
two-particle states.
