The methods of the quantum theory of computation are used to analyze the physics of closed timelike
lines. This is dominated, even at the macroscopic level, by quantum mechanics. In classical physics the
existence of such lines in a spacetime imposes "paradoxical" constraints on the state of matter in their
past and also provides means for knowledge to be created in ways that convict with the principles of the
philosophy of science. In quantum mechanics the first of these pathologies does not occur. The second
is mitigated, and may be avoidable without such spacetimes being ruled out. Several novel and distinctive
(but nonparadoxical) quantum-mechanical effects occur on and near closed timelike lines, including
violations of the correspondence principle and of unitarity. It becomes possible to "clone" quantum systems
and to measure the state of a quantum system. A new experimental test of the Everett interpretation
against all others becomes possible. Consideration of these and other effects sheds light on the nature
of quantum mechanics.