  At low temperatures, spin dynamics in ideal spin ice is due mainly to dilute,
thermally excited magnetic monopole excitations. I consider how these will
affect the dynamics of a nuclear spin (the same theory applies to muon spin
resonance if implanted muons do not diffuse). Up to the time scale for nearby
monopoles to be rearranged, a stretched-exponential form of the relaxation
functions is expected. I work out the expected exponent in that exponential and
the formulas for the $T_1$ (longitudinal) and $T_2$ (dephasing) relaxations, as
a function of the monopole density. Experimental NMR is incompatible with the
predictions and I suggest is due to magnetic impurities.
