A Non-Critical String Approach to Black Holes, Time and Quantum Dynamics

We review our approach to time and quantum dynamics based on non-critical string theory, developing its relationship to previous work on non-equilibrium quantum statistical mechanics and the microscopic arrow of time. We exhibit specific non-factorizing contributions to the ${\nd S}$ matrix associated with topological defects on the world sheet, explaining the r\^ole that the leakage of ${W_{\infty}}$ charges plays in the loss of quantum coherence. We stress the analogy with the quantum Hall effect, discuss the violation of $CPT$, and also apply our approach to cosmology.