Time travel doesn't necessarily introduce paradox.
Imagine you have a billiard table, on which there's a wormhole. If you roll a billiard ball into the wormhole on the right trajectory, it will emerge three seconds prior to entering the wormhole, hit its earlier self a solid blow, and its earlier self will never enter the wormhole, creating a paradox.
But when you try, it emerges from the wormhole on an altered trajectory, and strikes itself only a glancing blow. And why did it emerge with an altered trajectory? Because it was struck a glancing blow.
This is the Novikov self-consistency principle [1]. Physicists have been unable to find initial conditions that don't allow a consistent solution. On the other hand, nobody has proven that consistent solutions always exist. And sometimes there are lots of consistent solutions. (I wonder whether that's why quantum physics isn't deterministic, but I'm no physicist.)
Imagine you have a billiard table, on which there's a wormhole. If you roll a billiard ball into the wormhole on the right trajectory, it will emerge three seconds prior to entering the wormhole, hit its earlier self a solid blow, and its earlier self will never enter the wormhole, creating a paradox.
But when you try, it emerges from the wormhole on an altered trajectory, and strikes itself only a glancing blow. And why did it emerge with an altered trajectory? Because it was struck a glancing blow.
This is the Novikov self-consistency principle [1]. Physicists have been unable to find initial conditions that don't allow a consistent solution. On the other hand, nobody has proven that consistent solutions always exist. And sometimes there are lots of consistent solutions. (I wonder whether that's why quantum physics isn't deterministic, but I'm no physicist.)
[1] http://en.wikipedia.org/wiki/Novikov_self-consistency_princi...