I recommend reading Up the Line by Robert Silverberg. It's a time travel novel where the protagonist, Jud Eliot, is hired as a Time Courier to escort groups of tourists "up the line" (back in time) to witness notable historical events that happened in/around the city of Constantinople. One of the legal issues that becomes very important is what happens if somebody commits "timecrime" - if it's serious enough, the guilty person is executed. Example: on one time tour, a tourist decides to kill Jesus so Christianity never happens. He poisons Jesus at age 11. A Time Courier later escorts a tour group to see the Crucifixion... and Jesus isn't there. So the Time Patrol (the law enforcement side of the Time Service) has to figure out what happened. When they do, they make a video record of the murderer poisoning Jesus (for evidence), and then arrest him. But to make sure that history gets put back together properly, they have to make the murder un-happen. So they arrest the murderer at an earlier time, before he poisons Jesus. It doesn't matter that to that version of the murderer he hasn't done anything; there's a video record bearing witness that he did/would do it. The novel acknowledges a whole plethora of paradoxes and admits that it's a difficult and headache-inducing thing to try to figure out. Therefore, I didn't have a problem with one version of Braxton being arrested for something he hadn't done yet, because the proof existed that another version of him did/would have committed the crime. Also, it's made clear in Up the Line and also in Poul Anderson's excellent Time Patrol series that just because you know you'll succeed at doing something in the future, that doesn't excuse you from going through all the necessary steps in the present to accomplish that goal.