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Luke_A_Somers comments on Can infinite quantities exist? A philosophical approach - Less Wrong
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It's not clear to me that MWI has infinite worlds rather than merely 'a mindbogglingly huge number, so large one may reasonably approximate it as infinite for most purposes'.
Worlds aren't fundamental in MWI; they don't show up the equations. It's just a loose, non-technical term you can apply to a subset of the wavefunction. But under most common definitions of a "world", there are "uncountably many" in the same sense that there are "uncountably many" (sub-) line segments within a given line segment.
I'm aware of that. I mean that there are fewer effectively different worlds than that. Like, if you consider a scattering event - a major source of decoherence and thus new world formation.
With which other particle will this particle's next interaction (over some minimal threshold of impulse) occur, cut off by time X in some reference frame (e.g. our frame, right now)? (setting aside the fact that particles don't have individual identities, since that would decrease the world count)
This is a stronger question than that asked by decoherence, but you can already see we've narrowed it down to something that seems like picking out of a list - even if the universe is infinite, the number of particles in a truncated future light cone is finite.
Of course you're doing this a huge number of times, and each one creates a huge number of alternatives, but that's just making an unimaginably huge finite number. See?