# Cardinality of the Universes Set

No expert by any means, but sometimes, in different contexts the term multiverse used. In quantum mechanics, some say that it is possible that there are actually many universes where all the possible states are manifested, cf. the many-worlds interpretation. I wondered what is the cardinality of the set of all possible universes? Does the answer to this question has or can have any theoretical consequences?

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Concerning many-worlds versus multiverse, see also physics.stackexchange.com/q/10140/2451 – Qmechanic Mar 23 '13 at 20:03
Thanks @Qmechanic! I didn't know that distinction exists and that it is even oversimplified. I did found this thread though : link, which actually leads nowhere. Ending up with "this is not interesting". I find this assertion problematic as physics and in particular quantum mechanics is based on some non trivial mathematical tools. I mean, if the mathematics of the formulation will collapse or be problematic, wouldn't physics care? At the very least it seams to be worth exploring. – Sonia Mar 23 '13 at 21:00
There are objects in mathematics which are not sets, for example class. It can be detrimental to the analysis. – Sonia Mar 24 '13 at 6:47
There is not one 'interpretation' but several mutually incompatible 'interpretations'. Second, each one of them has been shown to be wrong. Check Against Many-Worlds Interpretations. A physics FAQ for general public is available here. – juanrga Mar 24 '13 at 16:13

One easy way of working out the cardinality of the "multiverse" (which does not have a unique, concrete model behind it) would be to think of how the "universes" within the multiverse are labeled. Suppose that your multiverse is based on different choices for some physical parameter $\Lambda$, and each universe would have its own setting for $\Lambda$. Then, the cardinality of the multiverse would be determined by the cardinality of the set of possible choices for $\Lambda$. Therefore, if you could only have $\Lambda \in \{1,2,7\}$, then there are clearly three possible universes; if you can only have $\Lambda \in \{1,2,3,\dots\}$, then there are countably infinite universes, etc.