For what it's worth, my knowledge of physics tells me the following:

• If it's possible to transmit information back in time, physical laws probably nevertheless have at least one consistent solution, i.e. paradoxes are impossible. This comes from something I read about how this is the case in a billiard-ball computer (researchers built a NOT gate and put it across a wormhole; the result was that an invalid logic value came out of the wormhole and the NOT gate left this invalid value unaffected), and the fact that quantum computers use only unitary transformations, which... tend to have fixed points, at least.
• It is probably not possible to transmit information back in time.