In the movie A prisoner of Azkaban, Harry Potter is saved by a mysterious figure that looks like his father shortly before passing out. After that, he learns that time travel is real. He travels to the past and stops by the event to meet his father but no one comes to save him, so he decides to step up himself - only later realizing that he only saw himself.
Which philosophical theories that acknowledge the existence of free will are compatible with this scenario? In other words - let's imagine that the future is "determined" in the sense of "perfect predictability" but some features of the future are contingent on the influence of some cognitive structures I consider "the self". That is, free will, as conceptualized here, is part of what determines the universe. In this model of the world, can libertarian free will exist? Or is the mere predictability of what some free agent will freely do incompatible with libertarian free will?