Temporal Paradoxes are paradoxes that are created by the notion we have of time. The most common perception of time is akin to the image of a workman laying a path; once the path is laid, it is immovable, but he can take the unlaid trail in any direction. This notion that an individual's actions determine the course of the future is called Free Will.
The Grandfather ParadoxEdit
Perhaps the best-known temporal paradox is the "Grandfather Paradox", in which you go back in time and kill your maternal grandfather before your mother is conceived. This results in a paradox; if your mother has not not been conceived, you cannot be born. Therefore, you cannot have gone back in time to kill your grandfather. Therefore your mother was conceived. Therefore you were born, and went back in time to kill your grandfather. And so on.
The Grandfather Paradox depends upon the assumption that there is 1) a single timeline, and 2) that no new timelines can be created. One solution to this problem is to argue that every action that changes the past creates a new timeline that results from that action. Time is viewed as a string which may have new strings tied into it or get tangled into loops.
Another solution to the Grandfather Paradox takes this idea even farther, and takes some quantum mechanics into its view. The argument is that since there is a chance for anything to happen, everything does happen. Thus there are near-infinite distinct timelines, each spawned by a different possibility, and that near-infinite new timelines are created with each infinitesimal passing of time. Thus, you killed your grandfather in a parallel universe. In that universe, you were not conceived. Your existence in your own universe is unaltered.
Predetermined Free WillEdit
Yet another view of time is the "predetermined free will" hypothesis; proponents of this assert that the future is already determined, and that we only appear to have free will because we only perceive time in one direction. Thus traveling back in time to kill your grandfather is possible, but you won't kill him- you already haven't.
The Road Less PavedEdit
There is a way, apparently, for one to "change" the past without contradiction. It assumes the finitude of spacetime - spacetime is closed in four dimensions. It is finite and unbounded. And we do not view spacetime as embedded in any higher dimension. Spacetime is more like a ball moving through a garden hose. If we accelerate towards the speed of light, time passes more slowly so we could theoretically reach the end of spacetime where it re-collapses and then re-Bangs and begins again. Then the future is not written and you are free to kill your grandfather.