  The possible role of decoherence due to space-time foam is discussed within
the context of two models, one based on string/brane theory. and the other
based on properties of black hole horizons in general relativity. It is argued
that the density matrix satisfies a dissipative master equation, primarily from
the study of renormalization group flows in non-critical string theory.This
interpretation of the zero mode of the Liouville field as time leads
necessarily to the CPT operator being ill defined. One striking consequence is
that the quantum mechanical correlations of pair states of neutral mesons
produced in meson factories are changed from the usual EPR state. The magnitude
of this departure from EPR correlations is characterised by a parameter
$\omega$. The predicted value of $\omega$ is very small or zero. However it is
shown explicitly that the the non-vanishing of $\omega$ is only a feature of
the model based on string/brane theory.
