I think ObieX touched on this... but here's my take on it.
If there are N universes but we cannot interact with other ones or prove/disprove them - then they are irrelevant. We should not postulate them in theories. This seems to leave us with the statistical interpretation (but my QM is mostly forgotten anyways at this time).
The concept reminds me of some descriptions of reincarnation. My impression from the majority of reincarnation advocates that I've talked to is that it works something like this
-> body is different in next reincarnation
-> you will not remember your past life
-> you will not have the same personality
At which point I say that my reincarnated self would not be me, and is to all intents and purposes irrelevant to my current life. This seems true whether or not they inherit my "spirit" and/or karma.
Back to multiple-universes. Unless there's a way in which this is provable/disprovable or helpful in the model, my view is that they are about as useful as postulating a higher being. It predicts nothing, solves nothing and cannot be checked (though I do recall reading of one possible experiment, it was ~15yrs ago and memory is dim).
Unless the MUs simplify the equations/model/concept, why include them in our thinking. Is it possibly religion or SF that makes this idea so popular?
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