It's certainly intriguing that our best models of the universe seem to
allow for something as paradoxical as time travel. The question is,
is there something wrong with the models, or something wrong with the
universe? :-)
Oops, my prejudice is showing. I can hardly believe that time travel
will be possible because of the paradoxes and contradictions it would
bring.
David Deutsch has suggested that the paradoxes could be resolved if you
combine time travel with parallel universes, so that when you go back into
the past you are moving into a parallel universe. That way you never close
the circle and can't change your past, avoiding contradictions. But I
haven't seen a rigorous explanation of this idea.
Hal