Why are we trying to fit GR in QFT when there's a chance that GR is incomplete?

Question

GR explains most phenomena in our universe, but not everything.. Dark matter and Dark energy still don't fit in explanation of GR. QFT, on other hand, is almost complete. Shouldn't physicists go for redefining GR for other strange things in universe instead? Even if we succeed to fit GR and QFT in one framework, we still won't have theory of everything, for there would be other unexplained things.

Answer 1

Why are we trying to fit GR in QFT when there's a chance that GR is incomplete?

There's not just a chance that GR is incomplete. It is certainly incomplete: it can't account for quantum phenomena.

That's why physicists are not trying to fit GR in QFT. Instead, they're trying to find something new that reproduces the successful predictions of GR while also accounting for quantum phenomena. Both GR and QFT have made lots of accurate predictions (under different conditions), so whenever somebody proposes a theory of "quantum gravity," the first thing to check is whether or not GR and QFT can each be recovered under those conditions where they are already known to work well. The new theory doesn't need reproduce GR exactly (it can't, because GR isn't compatible with quantum effects), but it should reproduce GR approximately to within the measurement uncertainties of the experiments that have already tested it.

This is analogous to how GR reproduces the successful predictions of Newton's theory of gravity in cases where the latter was already known to work. This is one of the first things that Einstein checked when developing GR. Newton's theory of gravity doesn't fit into GR; instead, Newton's theory is an approximation to GR, and an excellent one for many practical purposes. Similarly, GR won't fit into its quantum replacement, but it should be a good approximation to its replacement under the right conditions, and that's one of the first things we need to check whenever such a theory is proposed.

Dark matter and Dark energy still don't fit in explanation of GR.

That's not quite correct. We don't know what dark matter and dark energy actually are, but accounting for their effects in GR is not the problem. The problem is coming up with a hypothesis for exactly what those things are that is consistent with all of the available evidence (both positive and negative evidence), including evidence from particle physics.

QFT, on other hand, is almost complete. Shouldn't physicists go for redefining GR for other strange things in universe instead?

Yes, that's exactly what they're doing: looking for a quantum-based replacement for GR. String theory is the leading candidate, and something called the AdS/CFT correspondence is currently the most well-developed formulation of string theory — though this particular formulation assumes a universe with a negative cosmological constant, which is not consistent with the real universe. It's a work in progress. Ironically, this formulation of string theory is a QFT, albeit a QFT formulated in a lower-dimensional spacetime. It is currently our most well-developed example of the "holographic principle" that was proposed a long time ago based on thought experiments with black holes, and physicists are still working hard to understand exactly how the AdS/CFT correspondence manages to achieve this. (The math is hard. Really hard. But steady progress is being made.)

Even if we succeed to fit GR and QFT in one framework, we still won't have theory of everything, for there would be other unexplained things.

Of course, having both GR-like and QFT-like properties is only a necessary condition, not a sufficient condition. Even ignoring gravity, there are a countless number of different models that satisfy the general principles of QFT, and most of them are completely unrealistic, so clearly just satisfying those general principles is not enough. A similar comment applies to GR even if we ignore quantum effects; by itself, GR would let us have pretty much any spacetime metric we wanted if we ignored the question of what type of matter it would require, so clearly just satisfying the general principles of GR (even if only approximately) is not enough.