Why Time Travelers are Free to Change the Past
The standard solution to worries about time travelers' freedom to 'change the past' rests on a distinction between legitimate and illegimitae facts in such considerations. (See e.g. this great paper by Ted Sider.) Assume for simplicity that x is free to do y iff he really would do y should he decide to do y. Now consider Tina the time traveler. Is she free to kill her earlier self? I.e. is it true that
1) She would kill her earlier self if she decided to do so
It seems not, at least not if "killing" implies that the victim doesn't live any more after the killing. For then it is logically impossible that someone is first killed and later enters a time machine. And nobody is free to make contradictions come true.
The standard solution is that (1) contains illegitimate information about the future, viz. the information that Tina survives to become a time traveler, and that nobody is free to do anything given such illegitimate facts about the future.
I believe this is the right thing to say. But I would like to know just why facts about the future are generally illegitimate. Why not facts about the past?
Indeed, sometimes facts about the past should be illegitimate as well. Consider Tina shortly before she traveled back in time. There she sits in her time machine and thinks about what time she would like to travel to. In the end she decides to go to 1927. Thus back in 1927 she emerges with her time machine. Was she free to choose another destination? It seems not. For instance, given that in 1928 no person like Tina ever emerged with a time machine, she couldn't have selected 1928. Similarly for all other years except 1927. Moreover, it seems that she couldn't even have chosen not to time travel at all given that in 1927 she emerged with the time machine.
This time the information that spoils the freedom is information about the past, not about the future.
So I think what kind of information is legitimate in considerations of freedom has little to do with pastness or futurity. At least not directly. Instead, S is illegitimate iff S would not be the case if the subject made the counterfactual decision. The fact that this girl is Tina's earlier self is illegitimate if we ask whether Tina is free to kill the girl. For if she decided to kill her, the girl wouldn't be her earlier self. In the second case, the fact that no person like Tina emerged in 1928 is illegitimate if we ask whether she could have chosen to travel to 1928. For if she had so chosen, a person like Tina would have emerged in 1928.
In general, we are free to 'change the past' iff there are true backwards counterfactuals of the relevant kind linking our decisions with past events. As far as I know, there aren't any. But as far as I know, this is a contingent feature of our world.