I'm not an expert at physics, but I think that time flows in only one direction, or at least we can only observe it flowing in one direction, because entropy always increases. So guess it's impossible to travel back in time while being in the system, i.e. the universe. You would have to be able to decrease entropy or something.
Maybe if you could break out of the system and you could exist outside of it, you're existence would perhaps no longer be attached to the universe's "timeline", even though another version of yourself would probably still exist within it.
But I think you just couldn't get out of this (probably closed) system, nor is it likely that you could re-enter it. Assuming you could re-enter at some point in the past and you killed your past-self, your future-self would stop to exist but you, who re-entered the system, would keep existing because your existence would then depend on the period of time from your re-entrance until now (when you just killed your past-self).
That's how I imagine it. Probably doesn't make much sense …
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