Let me briefly offer, if I may, the perspective of one humble Physics undergraduate (me) on the issue of parallel universes.
The idea of parallel universes has its origin in the branch of physics known as quantum mechanics. There are a number of natural processes concerned with elementary particles which have entirely random outcomes. For example we cannot predict whether any given radioactive nucleus will decay within a given time interval; we can only find the probability that it will do so. The idea is that every possible outcome takes place, but in separate, 'parallel', universes.
Let me say that as a Physicist I find this idea wholly useless. Occam's proverbial Razor simply cuts it to ribbons; if our explaination of the world doesn't require us to include a multitude of unreachable universes in addition to our own, then we need not do so. The "theory" (it is not a theory in the scientific sense of the word) makes no testable predictions and mathematically explains no previously unaccounted for phenomena, and is thus, to Physics, utterly useless.
Recently the idea of parallel universes has resurfaced in the context of M-Theory, the controversial successor to String Theory. I am not familiar with M-Theory, but I know of no experiment which could be performed, even in principle, which would either prove or disprove the existence of parallel universes. So at present such ideas reside firmly in the realms of speculation.
The idea of parallel universes, with the added ingredient of the possibility of interaction between them, is certainly attractive in a fictional setting. I have read several excellent books which make use of it to good effect. But, quite frankly, the idea simply does not appeal to me, or seem necessary, as part of a mathematical explaination of the Physical world. Faced with a lack of evidence, or even the possibility of evidence, I have to say I simply don't believe it.
To tie the discussion, very tentatively, back to the original subject of the thread, I do not think that, even if we hypothetically accept the 'existence' of parallel universes, that a Middle Earth-like universe could ever exist. This is because the Physical laws which allow the existence of parallel universes in the first place would surely have to apply within any given parallel universe, and the laws of Physics simply do not apply in Middle Earth.
Back to Tolkien, I hope.
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"If you would be a real seeker after truth, you must at least once in your life doubt, as far as possible, all things." -- René Descartes
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