General relativity tells us that what we perceive as gravity is curvature of space-time.
On the other hand (as I understand it) gravity can be understood as a force between objects which are exchanging (hypothetical) virtual particles called gravitons, similar to the way electromagnetic forces are due to objects exchanging virtual photons?
At least at first glance, the two concepts seem mutually exclusive. Is there a description of gravity which includes both, or is this contradiction one of the problems in combining GR with quantum mechanics?
Answer
Well, consider this: the same thing happens with electromagnetic forces. We can describe them as particles responding to the presence of electric and magnetic fields, or we can describe them as resulting from the exchange of virtual photons. Those views seem similarly incompatible, but nevertheless both theories (classical electrodynamics and quantum electrodynamics, respectively) give excellent predictions. We can't really say that one is more "right" than another; we just have to accept them both.
The situation with gravity is pretty much a direct analogy to electromagnetism. We can describe gravity as particles responding to the presence of spacetime curvature, or we can describe them as resulting from the exchange of virtual gravitons. As with EM, these views would correspond to classical gravity and quantum gravity, respectively. But the difference is that, although general relativity fills the role of the classical theory, we don't have a good quantum theory of gravity yet.
I wouldn't say that the field/particle duality is one of the problems that impedes the combination of quantum mechanics with GR. After all, we had no problem getting around the dual descriptions of electromagnetism. It's just the peculiar details of quantum gravity that make it a difficult theory to develop.
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