  We develop a mathematical description of the decoherence caused by "spin
baths", such as nuclear spins or magnetic impurities. In contrast to the usual
oscillator bath models of quantum environments, decoherence in the spin bath
can occur without any dissipation. Given the almost ubiquitous presence of
nuclear spins in nature, our results have important consequences for quantum
measurement theory, particularly as the decoherence mechanisms in spin baths
work very differently from those in oscillator baths.
