I've been noticing a lot of people aren't exactly sure of how the flow of time / time travel mechanics work in this story. Well, if you are one of those people, here's a spoiler-free explanation from a source-reader, elaborating on some of the things that have already been stated so far in the anime (up to episode 14)!
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Every time a decision is made at an event occurrence, the worldline branches off into multiple possible paths.
Say, for instance, I wake up at 6 am every day for work.
Usually I take a shower when I wake up and leave at 6:30 for my commute to work, but today I decide (E1) to skip my shower and leave right when I wake up at 6 am.
My commute is an hour, and I get to work at 7 am.
At 7:01 am, the same road I drive to get to work, halfway between my house and my work, an idiot driver runs a red light and hits a pedestrian, killing them.
I hear about this on the news and realize that had I taken a shower and left at 6:30 like usual, I would have been halfway to work at 7 am and stopped at that very traffic light where the idiot driver hit a pedestrian.
I decide to use my reflector device and go back to the event occurrence: the point where I needed to make a decision about taking a shower.

I then choose to take a shower, leave for work at 6:30, get to the traffic light at 7 am on the dot, and guess what? The idiot driver at 7:01 doesn't blow the red light because I'm stopped at it in front of him when he pulls up. The pedestrian doesn't get hit, and I get to work at 7:30.
The original worldline where the pedestrian got hit and dies must continue to exist because I used my reflector device while I was on that worldline. If that world disappeared from me going back in time, how would have I used the reflector device to go back in time in the first place?
Thus, worldline A continues to exist. By using the reflector device, I have created a path which takes me back to E1 where I make the decision whether or not to take a shower. Notice that worldline B includes the usage of the reflector device - it is a direct result of me having used the reflector device.
This is how time travel in YU-NO works: every time Takuya uses the reflector device, it is sending his consciousness to the point he saved at, in a straight line, which is a direct result of having used the reflector device in the worldline he wanted to leave. Therefore, the worldline he leaves continues to exist with him in it suffering the consequences of it. By using the reflector device, all he does is create another worldline where things may or may not turn out differently.
This means that history can not be overwritten - the past cannot be changed. All you can do with time-travel is create a different worldline that progresses in a different manner. The other worldline that is already predetermined to happen will continue to exist even though you have left it.
With Chaos Correction, Takuya actually physically disappears from the worldline because his existence in that wordline is too much of an irregularity and must be reverted. The wordline does continue to exist after he disappears, only without him.
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At the very beginning of episode 14, Takuya's father more or less explains this. Although his monologue might seem like he's speaking in riddles, it's actually fairly simple:
Takuya's dad's original theory was that it's impossible to rewrite history/change the past, because using the reflector device to 'go back in time' will cause another worldline to branch out and the one you just left will continue existing. Events bound by causality will continue to flow and there is nothing you can do to reverse them from occurring once they've been set off. Therefore you aren't changing the past, you're just creating a different branch whereby the worldline flows differently.
At least that's what he thought until he met them, whoever they are. He met some people that apparently changed his theory about it being impossible to rewrite history.
A question regarding the Tree of Vrinda is.... if you go back to before the VERY FIRST EVENT DIVERGENCE IN HISTORY.... will you then be rewriting history? If you remember episode 13 with Eriko and Abel, this might sound familiar because it sounds like the exact experiment they were trying to carry out.
(TL;DR:
Takuya's dad means that you cannot change the past or what has already happened. You cannot rewrite history, only create different worldlines where history branches off and occurs differently from the branch you once were on.
That's the theory he believed until he met them.)
Perhaps this is where this story is ultimately heading towards: is it possible to rewrite history and events as if they never happened in the first place? Food for thought. |