Another World In A Parallel Universe

(i) A man is mysteriously transported from this familiar world to another world where he is a hero.

(ii) Quantum mechanics might entail the coexistence of many parallel universes.

(i) and (ii) are entirely unrelated concepts. However, when (ii) has been formulated, it might then be used to provide a "scientific explanation" for the in fact much older narrative of (i).

Apparently, this is what happened with Poul Anderson's Three Hearts And Three Lions. When Anderson had sold a shorter version to Anthony Boucher, editor of The Magazine of Fantasy and Science Fiction, Boucher persuaded him to include a scientific rationalization which subsequently remained in the longer version, published as a novel.

"Wave mechanics already admits the possibility of one entire cosmos coexisting with ours. The lecturer said it was not hard to write the equations for an infinity of such parallel worlds. By logical necessity the laws of nature would vary from one to another. Therefore, somewhere in the boundlessness of reality, anything you can imagine must actually exist!"
-Poul Anderson, Three Hearts And Three Lions (London, 1977), NOTE, pp. 7-11 AT p. 9.

Slow down there, author, narrator, lecturer or whoever we are hearing in this NOTE.

First, is it logically possible for laws of nature to vary? I can see no logical necessity for water to boil at 100 degrees instead of at 101 degrees. Such laws have to be discovered empirically and cannot be deduced from any logical or mathematical axioms. So, yes, let us accept that the laws could vary.

Secondly, however, this establishes only that it is possible, not that it is necessary, that natural laws vary between universes.

Thirdly, if, by an infinity of parallel worlds, is meant an infinity encompassing every possible alternative world, then, yes, the conclusion follows because it is merely a restatement of the premise.

However, we all know that this is just a rationalization for getting Holger into a world where he can wield a fabulous sword.