If you travel in the speed of light, you would not experience any time flow. The beginning and end of universe would be the same timewise. This is called blocktime.
So both past and future exists in the scientific explanation.
According to 'science' the illusion of time is created by our memories.(memories perhaps created outside universe? This cannot be...)
I would say, based on this, that it is very plausible we would be caught in a still frame going back in time. Since we did not travel to a position in space and time continously remembering our previous point in time, since we do not exist in the moment thereafter.
In order to travel back in time with lifelike properties, one would need to rearrange full time space segment. Naturally then, there would be no free will, since we had to stage everything.
(Hmm, this solves the time travel paradox, since a timetravel of this sort would have no effect on the future... interesting)
Edit: Aha! There is a hidden dualism in modern science, we asume that information is free, as in freely distributed in universe although delayed by the speed of light, while matter is not free. We belive that while we would not be allowed to travel back in our own past, our body would be allowed to travel and make information exchange with a parallel past. It is the emerging paradox of mind and soul all over again.