I have a different theory on time travel and what happens if you travel back in time, based on the "time is a just another dimension" argument. Imagine a universe of only two perceivable dimensions, (two dimensional) people could move about freely in either of these dimensions and interact with anything at the same point in time. Now imagine that this plane is moving through a third dimension which cannot be seen by the beings living in this universe. The entire universe would move at a constant speed and they would have no way of altering that speed. They could only interact with other objects that existed at the same point in space-time (all three dimensions, effectively) but they had no way of altering their movement through the third dimension, which would be equivalent to time travel to them.
Project this into our Universe, everything we can perceive is moving through the Universe at a constant speed (objects moving through time at a different speed would appear to blink in and out of existance instantly as our paths crossed). We cannot alter the rate at which we move through time but we have seen that our movement in the "normal" three dimensions can affect the speed at which time passes relative to a third party.
I know that this is probably full of flawed physics, but it does provide a way of explaining time travel paradoxes. If we could move through time, we would not find the past or the future as we would see it, we would see different Universes that simply moved through time at different positions (for example, if you drive back down on a road, you cannot see yourself drive along it again, you simply see other cars moving at different speeds along the road). So there is in effect, no past. Simply a present that is constantly changing. It could be that we experience time passing because it is impossible to move in space without also moving in time, so if time were to "stop" all movement would also stop. Likewise, we as we approach the speed of light, time passes more slowly relative to our viewpoint because we are moving faster in relation to time.
I realise this is all pretty far fetched, and I don't consider it to be true for a second, but I feel it is an interesting idea (hence its presence in fictional models of time travel).