  For time travel to be consistent with the known laws of physics, the
resulting paradoxes must be resolved. It has been suggested that parallel
timelines (a.k.a. multiple histories) may provide a resolution. However, so
far, a concrete mechanism by which parallel timelines can be created has never
been satisfactorily formulated. In this paper we propose such a mechanism
within the framework of unmodified quantum mechanics, also known as the Everett
or "many-worlds" interpretation. The timelines in our model are emergent, like
the "worlds" of the Everett interpretation; they are created by quantum
entanglement between the time machine and the environment. Therefore, we call
them "entangled timelines" or E-CTCs. As the entanglement gradually spreads out
to additional systems, the timelines spread out as well, providing a local and
well-defined alternative to the naive "branching timelines" picture often
presented in the literature. The E-CTC model is similar to Deutsch's familiar
D-CTC model, but differs from it mainly by making the entanglement explicit,
which allows us to create a clearer practical definition of the resulting
parallel timelines.
