What if we could travel to the past, but not change the past, due to the Novikov self-consistency principle?
What an odd topic for you to pick, given its extreme mind bending background and complexity.
The answer from the timeline theory, of whether you have a fixed destiny because of a causality chain ever since the big bang, or whether you can navigate the future through the choices you make and therby alter your "fixed" destiny - turns out its a mixture of both.
One way to understand this, is the way EnderX once talked about entropy and configuration spaces (BTW I am not affiliated with EnderX in any way, it's just the timeline theory contains similar concepts as what he talked about)
Treat a configuration space as a single static snapshot of your relativistic referential frame. Instead of calling it that, let's just call it your localized universe.
The snapshot reflects the complexity of a moment in your timeline. Your timeline is made from all possible local universes that can ever be, in a series of static configuration spaces, like the frames of a movie or the cells in a cartoon, "played" through the arrow of time. And, no - because of the expansion of space, you cannot run your film backwards.
To put the projector in reverse, the universe would need to contract. But even then, your actions through your intent to change things will still look like you are moving forward. It's just your localized universe will be shrinking. And, you can visit its previous states along the way. Can you think of other places in the universe where space contracts like this?
Because it takes the least work to manifest the simplest snapshots (project them into physical space more easily), timelines tend to drift to configuration spaces with the lowest complexities, and then osscilate around them.
EnderX proposes a slightly different variation. He says there are so many more similar versions of simple configuration spaces than complex ones, that you have a higher probability of picking a simple one by accident just because of their greater numbers.
Likely neither view is completely correct, and the reality is somewhere inbetween. I favor that the next frame is picked by branching off one that was selected through intentional choice rather than by probalistic randomness.
So, what happens if you make a change in your local universe, and then leave everything alone? Your change will fade overtime, in favor of simpler configurations, and you will return to the path of your fixed destiny.
But, if you went back to a previous configuration space, could you make a change and hold it there?
First, by doing this you will alter all the particles and attributes of the frame just by your presence. If you continually reinforce the change and stay in the timeline from that point going forward in an expanding universe, you will jump to a different timeline with more entropy than the simpler ones.
Subsequent configuration spaces will then be chosen that closely resemble your persisted change. Other events will build around them. And, slowly there will be more configuration spaces with a similar entropy to the new timeline than the plain vanilla configuration spaces.
Maybe that's the wrong way of putting it. There will be more cues in the changed timeline from which to pick the next frame. No, that's wrong too. The new timeline's common entropy will branch off to create configuration spaces similar to it, just like gateway universes do with slight changes to their fixed constants.
So, your original timeline doesn't disappear. But, going back and killing your grandparents changes the configuration space enough to create a different timeline than the one you came from.
In effect, this is the Novikov principle. You don't exist as a native of the new timeline. But, you still exist because you came from somewhere else. The net effect, is you don't get to meet your earlier self.
Had you not killed the grandparents, then you might be able to talk to yourself in a slightly later point in time. And, that's how you change destiny through the choices you make (in my opinion).
There is also an odd consequence of this. Given that the complexity of the new timeline increases over its duration, it's easier to make changes in near future incremental steps than it is to try to change the whole thing at once.
And, then again, you are not really altering the content of timelines. They are made out of static configuration spaces that by definition don't change. What you are really doing is jumping to different localized universes.
en.m.wikipedia.org