Nice post by Moshe Rozali about the problems facing physicists trying to unify general relativity and quantum physics:
Alas, there are many indications (which I may get to at some stage) that quantizing the gravitational field is problematic: when going down to length scales for which the quantum mechanics of gravity is important, we simply don’t know what to do. Unfortunately, this distance scale, the Planck length, is tiny. If we are not extremely lucky, we probably cannot probe this length scale directly. Nevertheless, we have now an incomplete story, full of interesting puzzles and paradoxes, and making that story coherent is the problem of quantum gravity.
So, what can happen when we go to such short distances? in other words, what is the quantum structure underlying classical general relativity? There are exactly two possibilities:
1. The description of gravitational physics by a field theory involving the metric tensor holds all the way down to the Planck length. This is similar to what happens in QED: this field theory describes the physics accurately all the way down to distance scales for which quantum mechanics is relevant. In this case, in order to describe quantum gravitational phenomena, one has to quantize the metric tensor, something we don’t really know how to do.
2. The metric field shows some substructure already at distance scales larger than the Planck scale. That substructure is what underlies the physics of classical gravity. In order to describe physics at extremely short distance scales, such as the Planck length, one has to quantize that substructure. This is similar to nuclear physics, when we are interested in very short scales we look at the quantum mechanics of the quark and gluon fields, QCD.
That is the basic dichotomy of quantum gravity (and not background independence, as is often claimed). There are many clues, about which I will write at some point, that it is the second option that is more likely. Among those clues are the myriad of conceptual and practical problems we encounter when we try to follow the first route, and the fact that nearly 80 years of attempts have not resulted in much progress. On the other hand, after countless failed attempts, we do now have in string theory a few working examples of general relativity emerging as long distance approximation to something more fundamental, lending us confidence this is indeed the right scenario.
As a result, most researchers interested in quantum gravity (almost all of whom are labeled string theorists) have abandoned the attempt to quantize the metric tensor directly. There are still a few holdouts, who take at least some features of classical general relativity seriously all the way down to extremely short distances, I hope everyone can join me in wishing them good luck in their quest.