This post is intended to open speculation about time travel. As far as I’ve seen, there are three main theories of how time travel works, depending on what you’re watching/reading.
1. Time is a slate–anything can be can be changed! Be very careful, you might prevent your own birth. (ala Back to the Future). Paradoxes are a major problem–if you change antyhing you could prevent yourself from going back which would keep you from going back to prevent yourself from going back–and so on.
2. Time is a tree. You can change things, but all you’ll do is create an alternate timeline. That is by making a change you just force yourself down a different branch. You can’t prevent your birth, but you can send yourself down a branch where you were never born. (ala Back to the Future II, which doesn’t seem to use the same concepts as Back to the Future)
3. Time is written in stone. Whatever happens in the past has already happened, observed events are 100% unchangeable. For me to believe in this one, I feel I also need to believe in a higher power (a fate or a god or what-have-you) to make sure everything is neat and tidy. (ala 12 Monkeys)
To me #1 is unlikely. If this were the way time travel worked, the space-time continuum would have ripped a long time ago, or a long time from now, which amount to the same thing when you’re talking about the space-time continuum.
#3 can only work if there’s a higher power, because something needs to decide what events are “allowed” to happen.
#2 is the most likely in my mind, though it opens the door to another discussion–alternate realities. Each branch of possibility creates new realities that may exist only in potentia. Changing events instantiates these realities.