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Time extending into the future is validated by direct experience.

A continuum of variants of myself is bought.

What is the value of assuming that literally every possible trajectory actually happens, but somehow I am only in one of them, while also being a continuum of other ones? If everything is true, than nothing is true.

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If time did not continue into the future, it would not be observable. Therefore hypothesis that it will continue to do so is not disprovable.

As far as multiverse goes, there isn't any inherit value in assuming that the wavefunction as given actually happens, it's just a simpler explanation than trying to come up with (arguable unprovable) ways to cull the wavefunction.

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