Under certain conditions, the theory of relativity suggests that closed causal loops can be formed, which seems to allow the causal paradoxes (like killing your grandfather and so). Namely, under certain conditions general relativity allows nontrivial spacetime topologies (like wormholes), while special relativity under certain conditions allows superluminal signaling (e.g. by tachyons). There are basically 3 types of solutions of such paradoxes: 1. Chronology protection: The true laws of physics conspire so that such exotic topologies and superluminal velocities are not really possible. The problem is to explain it with the presently known physical laws. 2. Self-consistency: Only self-consistent solutions are physical. It is related to the block-time view of the universe, in which time does not "lapse", but simply is, just like space. It is very much in spirit with the relativistic view of time. The problem is that it confronts with the subjective experience of time and the notion of "free will". 3. Parallel universes: Seems too speculative and unscientific, but it seems that many people still like it. So, what is your (favored) choice?