I know this is an old entry, but I wandered across this and I was reminded of something that I theorised recently.

Everyone has their own "personal timeline" so-to-speak. Whenever I try to describe it though I find it comes off like the usual parallel timelines in fiction - of which I think it is not.
Your timeline works like this:
"Past" future - time travel to "change past" - "new" future.
Your timeline is based on your perception rather than the believed arrow of time. It's like two arrows: one is your memories and physical state, and one is for the rest of the world.

This is sort of like time traveller's immunity right? Well... what if you did something that stopped you from having to go back in time in the first place? Like your example - if you succeed in "fixing" your past you won't need to go back and change it. Or if someone else changed history to stop you from going back.

Only "you" would still exist. You would still have gone back in time and done your thing. To this other you, or someone who'd altered your past also, you would have not.

When I think about it, it seems like Solipsism in the context of time travel though. Which I don't really identify with. Maybe its like Solipsism, but also not. If you do something to someone's past it is changed to you, but not to them. You each have your own timeline, separated by the things you have done, yet you're also in each other's timeline.

... man, this doesn't make any sense.