God in Multiple Realities
One of the most interesting philosophical questions I have found is the problem of multiple universes. The conjecture is basically something along these lines: there exist other universes we cannot see or communicate with. A common variant posits that there exist different universes with alternative histories and chronologies to ours.
So, for instance, in another universe, Hitler and Nazi Germany may have triumphed in World War II, or John F. Kennedy may never have been assassinated. (The possibilities of such universes intrigue me for similar reasons as alternative history.)
This may seem like purely theoretical and philosophical conjectures, since we apparently have no way of proving them or disproving them, and as such they do not form a reasonable hypothesis (similarly, God's existence cannot be proven or disproven).
However, advances in physics suggest that there may indeed be multiple universes out there. Contrary to what some have posited, there are probably no more than a handful of other universes (as opposed to the untold numbers there would be if an alternate universe existed for every different possible permutation of atoms/protons/quanta/what have you), and the most interesting about these universes if they exist is that they have different laws of physics.
Nevertheless, it is a real (albeit very insignificant) possibility that alternative universes exist, where perhaps another me is typing this right now on a MacBook instead of an NEC Versa. I have always wondered how our views of religion and God would be altered by the discovery that an alternative universe exists for each and every possible choice life and matter may make.
As a Christian, my views are probably clouded and inclined in certain directions by the monotheistic nature and other such theological aspects of my faith. It is possible that the implications of alternate realities would be different for other religions.
To me, the immediate implication would be that God may have, at the very least, no role in human affairs. After all, what is the point of his intervention, if there must be one universe for every possible permutation of matter? If he prevents me from falling down the stairs in this universe, there must nevertheless surely be another universe where I fall down the stairs, another one where I fall down the stairs and break my leg, another one where I fall down the stairs and break my neck, etc.
This implication troubled me for quite a while, until it occurred to me that there may still be room for God's intervention. After all, God could choose which reality sees which outcome. Although all universes are fated to see all possible states of matter, and thus all outcomes, God can choose which individual universe has people who live happily ever after, and which universe is full of pain and suffering.
But other problems arise. The main one I can think of is that it is demonstrated that God is not omnipotent (unless he has intentionally chosen to play by a certain set of rules). After all, since each universe is doomed to see out a particular and unique course of events, God cannot choose to make certain events off-limits. In an alternative universe, our entire solar system may have just suddenly been destroyed by some cataclysm, God powerless to stop it (although doubtless in other universes the same solar system has survived).
Perhaps most troublingly, the idea that we can influence God to influence us is proven wrong. What is the point of praying? Even if God grants you your prayer, it just means another you in another universe, despite having prayed the same prayer and done the same things, is subjected to the outcome you did not pray for.
I think it is likely non-monotheistic religions would also have to deal with similar problems. In Buddhism, for example, the idea of karma would probably have to be rejected. After all, you may be reincarnated as a higher being in your next life in this universe, but in an alternative universe, despite all other variables being the same (ceteris paribus as the economist might say), you would be reborn as a lower being or a being of the same standing.
These are all very troubling philosophical questions, all arising from the issue of multiple universes and multiple realities. The odds of there being multiple universes and multiple realities which exist in the way I have described (i.e. one universe for every possible state of all matter in the universe) are very small. But if ever it turns out that the laws of nature indicate that this is the state of things, theologians and philosophers will have a lot to ponder.