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Very helpful! But what’s still a bit unclear to me is the status of all possible future states of the multiverse. Are they all already part of the “script”, all the way into an infinite future ?

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Yes, they are. The multiverse as a whole is timeless, meaning the future states of the multiverse don’t have to come into existence -- just as it’s past states don’t vanish from existence.

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I think it’s more likely that the future is computed from the past. This is probably demanding enough that we need a dedicated multiverse to do it. As time moves forward and interactions occur, things pick up more correlations with other things. I think this gives us an arrow of time to work with.

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That's assuming that the universes is a computer, which it isn't. It also runs counter to general relativity, in which spacetime exists in full in and doesn't evolve. It simply exists. It's inside of a spacetime that systems can evolve.

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But time does not flow. Nor does it move forward. hence my question.

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