I saw that someone posted on my blog a question of this kind and I started thinking about it. In the context of string theory this has already been done and I ask myself: is it possible to go on this track further? Is it really so that quantum gravity effects should never affect our reality and the study of them should forever remain at the level of metaphysical interest only? I really don’t think so. Quantum gravity is a part of reality and it may have some influence through more general principles that may be derived in that way on questions related to our reality that we did not even asked by now. There are many times many misconceptions about physical objects. While things that are outside our labs and our models are certainly real and physical we may figure them out also in a less direct way, not necessarily by having them directly and actually look at them.
Maybe the hardest thing to say is that two ideas, phenomena or results are unrelated. In physics one is used with this when one speaks about timelike and spacelike intervals but in mathematics to simply state that two ideas are unrelated is a extremely powerful and often wrong statement. Are Kahler structures unrelated to Homotopy? Is the Mayer-Vietoris sequence theorem unrelated to Complex manifolds? Is a triangle unrelated to a sphere? well, what means “related”? What kind of relations are we speaking about? The whole discussion starts being extremely vague… and dogmatic and ugly: X doesn’t believe there is a relation between them so it cannot be one… The absence of a “relation” is probably harder to prove than its presence… Physicists don’t bother with this kind of problems (existence, unicity, etc.). Physicists nowadays have a very limited conceptual power. This means they know very few methods of proving or disproving something and in most of the cases these methods are simply put aside by reality.