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The many worlds interpretation suggests that the universe (or multiverse, not sure on the terminology) is composed of a superposition of quantum worlds?

It seems like there is a splitting off of worlds whenever a measurement occurs, but don't measurements occur basically infinitely often in quantum mechanics? So if this splitting off during measurements (I mean measurement in the quantum sense) has been occurring since the Big Bang, does that not mean that the number of worlds is infinite, or even impossible to define?

Can the rate at which measurements have been occurring since the Big Bang be quantified statistically to quantify the number of worlds which now co-exist in ''many worlds''? '

Tom
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