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So hold on. If someone comes from the future to change it, and accomplishes that, those events they did to create that change still have to have happened correct? So that means they have to have come from that shitty future to motivate them to go back in time to change it, which means that shitty future never really disappeared.
Dragon Ball Z honestly took care of this issue best. All altering the past does is create another timeline while leaving yours unaffected.
Then you had Kingdom Hearts' workaround with the whole inability to alter the past thing, but you could collect people from other time periods, and when they die in the future, they'd just be snapped back to where you took them with no memory of what happened.
But the kingdom hearts method is more coming from the past into future events, and the events being tampered with are supposedly “destined to happen” regardless. They aren’t rewriting anything supposedly. I’m more referring to the paradox of changing ones future by going to the past and altering it, but doing so means you’d have no reason to go to the past since the future is now good effectively erasing what you did(which then means since you didn’t go back in time, the future still fucked). The only workaround here is the dragon ball method of split timelines vs one continuous changing one, which then means you aren’t technically going back to your home (and there’s likely a version of you already there when you return since this is a new timeline) “your” home is still that fucked up timeline, which still exists
There’s a concept for this, I think it’s the grandfather paradox or a stable time loop or something. This is where due to someone exiting the flow of time, there is always some version of that person who travels back to the past to fix it. Different properties handle it different. Some of them have it that the traveller exists outside of history and remembers the original timeline, but exists in a stable time loop where someone returns back to do their actions, and then return back to the changed future. Some of them point this out and how much of a danger it is.
Its lampshades hard in Back to the Future, where Doc believes on two different occasions that there’s such a massive time bending paradox that should destroy the planet then and there. For example, in Part 2 - Future Biff travels from a good timeline back to 1955 to give his younger self a book that lets him win races, become rich, and take over Hill Valley.
With all logic considered, this should cause a huge paradox because this means the future wher Biff grew up poor, and put in his place by George McFly now doesn’t exist, and you’d think this makes sense, as there’s a deleted scene when we see him return that shows him fade from time, which you think is meant to be foreshadowing to later when Doc tells Marty it’s only a matter of time before the timeline catches up and erases them as well. However, this isn’t the case as Word of God confirmed Future Biff didn’t fade because of his timeline not existing anymore, but because Lorraine shot him at some point between 1985 and 2015.
So with this in mind, the timeline should snap completely because a humiliated bitter Future Biff now doesn’t exist to go back to the past to deliver the sports book that allow this future to come to pass.
In BTTF The Game, a similar thing happens on a worse scale - Marty accidentally alters Doc’s own timeline, resulting in the version next to him vanishing, and the new Doc being a totalitarian dictator in a police state. While Marty remains unaffected to the changes, the timeline is royally screwed here, because if Doc never grew up into a scientist, the DeLorean is never built, and that means NONE of the time travel could’ve happened, and the worse that happens is that the DeLorean that now shouldn’t exist is deteriorating as the timeline catches up.
On the other hand, the BTTF comics run with an interesting arc where Marty realises that in his present timeline, his life was led by a different Marty from this timeline who went back in time during the events of the movie, and who Marty fears will return for revenge since he stole his life. It’s established into a time loop of sorts where the Marty of this timeline is always destined to do the events of BTTF1 and become the Marty in BTTF2 onwards.
In short, who really knows? Trying to work through rules for time travel is a disaster.