  I argue that Deutsch's model for the behavior of systems traveling around
closed timelike curves (CTCs) relies implicitly on a substantive metaphysical
assumption. Deutsch is employing a version of quantum theory with a
significantly supplemented ontology of parallel existent worlds, which differ
in kind from the many worlds of the Everett interpretation. Standard Everett
does not support the existence of multiple identical copies of the world, which
the D-CTC model requires. This has been obscured because he often refers to the
branching structure of Everett as a "multiverse", and describes quantum
interference by reference to parallel interacting definite worlds. But he
admits that this is only an approximation to Everett. The D-CTC model, however,
relies crucially on the existence of a multiverse of parallel interacting
worlds. Since his model is supplemented by structures that go significantly
beyond quantum theory, and play an ineliminable role in its predictions and
explanations, it does not represent a quantum solution to the paradoxes of time
travel.
