  The spin ice materials Ho$_{2}$Ti$_{2}$O$_{7}$ and Dy$_{2}$Ti$_{2}$O$_{7}$
are by now perhaps the best-studied classical frustrated magnets. A crucial
step towards the understanding of their low temperature behaviour -- both
regarding their unusual dynamical properties and the possibility of observing
their quantum coherent time evolution -- is a quantitative understanding of the
spin-flip processes which underpin the hopping of magnetic monopoles. We attack
this problem in the framework of a quantum treatment of a single-ion subject to
the crystal, exchange and dipolar fields from neighbouring ions. By studying
the fundamental quantum mechanical mechanisms, we discover a bimodal
distribution of hopping rates which depends on the local spin configuration, in
broad agreement with rates extracted from experiment. Applying the same
analysis to Pr$_{2}$Sn$_{2}$O$_{7}$ and Pr$_{2}$Zr$_{2}$O$_{7}$, we find an
even more pronounced separation of timescales signalling the likelihood of
coherent many-body dynamics.
