Also, what you say about dollars is true because they have certain properties - effectively they have two different criteria of identity, one economic, the other physical. What is the criterion of identity for universes/branches?

But they are (presumed under this model to be) splitting. You posited a case where two later happen to be identical, but that doesn't mean they merge. You'd just have two of them.

>Also, what you say about dollars is true because they have certain properties - effectively they have two different criteria of identity, one economic, the other physical. What is the criterion of identity for universes/branches?

I'd guess that there is none, like electrons. But though those are even more indistinguishable than dollars, you can still have two of them.

Okay, but what's the actual model here? Let's talk about two different versions of many-worlds:

Version 1: Universes splitting

Version 2: No "splitting" per se ever actually occurs, universes are identical up to time t, different thereafter

Is there any difference between 1 and 2 from a physics perspective–any difference in the maths, or in conceivable results of observation or experiment? Or are they just different ways of wording it? A metaphysical/philosophical difference, but not an empirical/mathematical one?

Also, if the theory is symmetric with respect to time, you'd expect merger as well as splitting, since the former is just the time reversal of the latter – isn't QM supposed to have T-symmetry? Does MWI have T-symmetry?