Let’s assume you decide to travel into the future. If there was such a thing as free will, it should be impossible to have any discernable destination. For instance, you decide to travel forward in time to meet your great-great-grandchildren. In order for them to exist in a future that you can travel to, a necessary timeline would have to take place whereupon certain individuals met and had children, etc. etc. This would imply fate as key events must take place for the voyage to occur. Without fate it would be impossible to have any destination as an infinite number of potential outcomes are possible.
Now, if free will does exist and you are able to travel into the future, there is no guarantee that two individuals traveling to the future would necessarily land in the “same future.” This follows the multiple world concept (somewhat akin to the movie “The One” starring Jet Li).
Traveling into the past would seem “logically cleaner” as events have already transpired and you should be able to jump into them. However, the Observer Effect will inevitably alter the outcome of time as it would be impossible to be present in the past without having some influence.
Unless, the world were governed by fate. In that case, you could travel back in time because you were “supposed to” and the past has already compensated for you being there. While you may perceive that you are altering things, the circular loop of time that you are involved in will show that event has always taken place and fate requires that you DO travel back in time to do it. This would allow you to actually return to your own time reference without having created any anomalies, because it has always happened that way.
Free will, throws a monkey wrench into the system because conceivably you could alter the past in such a way as to negate the fact that you ever existed. Or alter the past such that time travel was never discovered which means you never went to the past which means you could never have disrupted things. BLAAAAAAHHHH (runs away with hair on fire waving arms in the air). Or, avoiding the self-negating paradox, free will causes the same problem as traveling into the future – how do you return to your “present” if your existence in the past introduces variables and options that will inevitably create numerous pathways through time?
Thus, it seems to me, that for time travel to exist – it is a requirement that 1) FATE exists and man has no FREE WILL or 2) somehow the multiple world/dimension thing exists and we simply move through those worlds based on choices (which isn’t that far from actually being fate anyway).