I wondering what precisely it was, in terms of predictions of observations, that General Relativity gets right, that QFT cannot explain. And what QFT gets right, that GR cannot explain.
I'm assuming GR cannot predict quantum effects, like wave-particle duality, but is there anything else? Or a more thorough list?
GR is not intended as a model of particle physics, and makes no predictions in that field, and QFT is not intended as a model of spacetime curvature and makes no predictions in that field either. They were formulated to solve completely different classes of problems and it is not particularly surprising that there are problems in one field that can't be solved with the methods of the other.
General Relativity (GR) is a theory of space and time, necessary to model large masses and energies. Quantum Field Theory (QFT) is an extension of quantum mechanics to many particle outputs, and is based on the postulates of quantum mechanics.
Though the gravitational interactions can be predicted using the formulae of GR, gravity has not been quantized, to quantize gravity is the aim of present theorists.
Effective quantizations of gravity exist, and so in these effective theories one might use QFT to solve problems.
GR gets right that spacetime is curved and dynamically responds to the energy-matter density.
QFT gets the particle spectrum and interactions right.
What it gets wrong is that in the usual development, it only works only over a fixed flat spacetime. There are versions of the theory that work over a fixed spacetime which is an improvement. But again, contra gravity, it is not dynamical. And in this, it is most likely wrong.
Another thing that it gets right and which it also inherits from gravity is that the classical description of the fields relies on a geometric formulation just as gravity does. This is the theory of fibre bundles. Here, the field strength is simply the curvature of the field potential.
It's worth noting that in Veltman's Diagramattica he writes out the full Lagrangian for the standard model and this takes around a hundred terms. It turns out that this, including neutrino mixing and the Higgs, can all be written as a spectral action in Connes non-commutative geometry of a spectral Lagrangian which is akin to that of gravity on a spacetime multiplied by a 'fat' point. This is a manifold which is classically 1d and non-classically (in fact, in K-theory) has dimension 6. This is a massive simplification and deserves to be known much more widely. Plus the fact it relies on a spectral action akin to the Hilbert-Einstein action of GR. It's also worth pointing out that the non-classical 6d of the fat point is exactly the size of the extra dimensions in string theory. Further, the geometrical model of Connes-Lott-Barrett-Chamesdine is very nice. It simply looks like a fattened up 4d spacetime where we have spacetime atoms - not points - on which a higher form of gravity is acting on.
In all this, we see another win for gravity
GR is the theory meant to explain the forces meant on a macroscopic scale far larger than even newtonian mechanics. Thus it only explain macroscopic objects, taken from a past answer it is not a particle physics model and cannot explain microscopic particles in the same way QM or QFT would do.
