Quantum Gravity-Which Theory?

[SOXBLOX]

Which theory do you think is likely to be the theory of quantum gravity? Why? I'd love to see some discussion on this topic. 

[K^2]

Both suffer from the same problems of trying to push a mathematical abstraction entirely too far, and running with it despite lack of experimental support. It's in the same category as using Anti-de Sitter geometry to describe some of the properties of quantum chromodynamics. There is clear correspondence, but it's only practical in so far as a tool for studying QCD, not explaining something new. When correspondence is partial, as is the case with String Theory, and it makes predictions that repeatedly fail to be confirmed, it's a good indicator that it won't be a theory to explain things. LQG is younger, and might actually turn out to have a closer correspondence to standard model, but I doubt it will overcome the main problem of non-renormalizable gravity. I'm not an expert in LQG, however, so I might be entirely out of date on what's new there.

The thing to keep in mind, however, is that we do have a non-renormalizable theory of gravity that, other than being entirely useless, is perfectly solid. By useless I mean that lacking renormalization, you can't compute anything. Everything turns into infinities and you can't do math on it. Which, as far as models of the universe go, is somewhat problematic. The good news about our understanding of gravity is that we can take standard model representation of gravity as a gauge force, quantize, it, and then develop a mean field theory on top of it. That mean field theory effectively is General Relativity with QCD thrown over it. And we have practical uses of it. Some branches of astrophysics are making testable predictions on particle dynamics inside neutron stars using this model. Inside the neutron star, gravity is so strong, that we simply can't treat it as flat space-time. At the same time, individual quantum fluctuations make no difference to overall gravity. So if you plug in the expected density as function of distance from the center, you can first compute the space-time metric throughout the core of the neutron star, and then do particle theory in curved space-time as a fixed background, which helped explained such things as why some neutron stars are more massive than we thought was possible, and it has to do with quantum mechanics in extreme gravitational and magnetic fields.

So saying that we don't have a theory of quantum gravity is a bit misleading. We have a base model that we know has to be satisfied based on symmetries but we can't do practical math with, and we have approximate models that we can use that we know are numerically correct under most practical conditions. The only place where this kind of approach fails is at regions of absolutely immense curvature and extreme energy density, and the only known places for that are big bang and event horizon of a black hole. These are places where we would like to have a better description of quantum gravity, one which still works under these extreme conditions, and does not lead to infinities in computation. It's almost certainly not going to be String Theory and probably not Loop Quantum Gravity either. It's not even guaranteed that such a model can exist. But if it can, it's probably going to be something else that we haven't thought of.