In the garden-variety time travel story, there is a single, fully logically consistent timeline. Trying to change the past is futile. There can be no change. You can be the proximate cause of whatever actually happens, if that’s your thing.
Of course it is never quite clear why nothing could be changed. It just happens that nothing changes, however mightily the characters strive to change things, as if by coincidence. Or Fate is watching—but why is watching enough? Doesn’t Fate actually have to intervene somehow to make everything line up?
It occurred to me once that there could be a possible physical theory to explain this, using fixed points.
I’m not surprised that someone already thought of this. I’m a little surprised that it was Richard Feynman, in a paper titled “Classical electrodynamics in terms of direct interparticle action,” back in 1949.
The Stanford Encyclopedia of Philosophy’s entry on Time Travel and Modern Physics, section 3, explains all.