Cosmology, with fairly low confidence, predicts that the universe (or multiverse) is infinite in both time and space. While this does not directly follow, it is also predicted that every possible configuration of matter exists somewhere in this universe/multiverse (source 1, source 2, source 3).
If this is the case, then infinitely many people qualitatively identical to us exist. In some views of personal identity, such as psychological continuity, it seems that these people are equally "us." In a way, this is a sort of practical teletransportation. However, we seem to be quite separate from all these other "us's."
Are arguments like these used at all in discussions on personal identity? It seems to be a useful way to empirically determine if a given theory of personal identity makes sense.