Most time travel paradoxes have the single fault that they assume there is only one dimension of time. Given even a mere two dimensions in time, we have an infinite number of linear paths to follow from any one point.
According to some theorists, no events can be "created". thus creating a new timeline in which they exist. These events have already happened, or will happen, or are happening... I'm speaking outside of time here, imagining the whole universe as not just the collection of space that we observe and are not limited by, but also the collection of time that we are limited by.
The theory states that all possible outcomes for every event happen. Everything that can happen, DOES happen. Meaning that there is already a reality in which you have gone back in time and killed your grandfather. You would cease to be a part of the reality in which your father exists. The reality which you are now apart of would eventually, 30 or so years in the future, curve back on itself in spacetime, therefore making this possible.
Yes, it was the Sum Over Histories thoery by Hawkings, proposing that everything that can happen, does happen, and we are observing the most probable outcome of those events. It can be somewhat scientifiacally explained - photons have been observed to exist 50% in one place and 50% in another. Yes, the same matter occupying 2 differnt points in space-time. We only observe the most likely location, just as we only observe the most likely outcome of the event which define our reality. It lends credibilty to alternate realities and touches on the possibility of moving from one to the other.
And since everything possible happens, this means that spacetime is curved back on itself in an infinite number of places to in infinite number of points in time, since all time travel possible has already occured. This would lend credibility to the possibility of time travel, and solve the grandfather paradox. I can go back in time and kill my grandfather, but this will not effect the reality in which I did not, which is the reality I come from, and which has curved back onto a different reality and interected with it.
That is how I understand it currently.
