  Spin ice illustrates many unusual magnetic properties, including zero point
entropy, emergent monopoles and a quasi liquid-gas transition. To reveal the
quantum spin dynamics that underpin these phenomena is an experimental
challenge. Here we show how crucial information is contained in the frequency
dependence of the magnetic susceptibility and in its high frequency or
adiabatic limit. These measures indicate that monopole diffusion is strictly
Brownian but is underpinned by spin tunnelling and is influenced by collective
monopole interactions. We also find evidence of driven monopole plasma
oscillations in weak applied field, and unconventional critical behaviour in
strong applied field. Our results resolve contradictions in the present
understanding of spin ice, reveal unexpected physics and establish adiabatic
susceptibility as a revealing characteristic of exotic spin systems.
