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Algernoq comments on timeless quantum immortality - Less Wrong Discussion
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Counterexample: I go to sleep (lose consciousness) and wake up again. QI seems to predict that I would never fall asleep, because I stop observing when I'm asleep and so QI would force me into universes in which I don't fall asleep. Timeless QI has no problem with me falling asleep and then observing I'm alive and awake hours later.
I don't think advocates of QI generally mean by it what I think you're taking it to mean.
In terms of conscious experience, dreamless sleep and death feel similar, as far as I know.