Quantum Gravity is non-renormalizable...So what?

Question

It is well known that quantum gravity is non-renormalizable. But why should we care? We successfully use many EFTs, like the Chiral Lagrangian or even Fermi's theory. So, why do we make such a deal in the case of gravity? Why do we care so much about finding the correct UV completion of the theory, if we can't even prove it experimentally? Is there something else fundamentally wrong in this theory, apart from non-renormalizability?

Answer 1

There's nothing wrong with using gravity as an effective field theory within its regime of validity. In fact, people have used it to compute quantum corrections to Newton's potential, for example: https://arxiv.org/abs/gr-qc/9310024

The problem is that effective field theories break down at their cutoff scale. So, if we want to know a fundamental (or at least more fundamental) description of reality, that goes beyond the Planck scale, we need a UV completion.

Of course, from a purely experimental point of view, this isn't a major problem, because no experiments we can do or can conceive of doing will probe energies above the Planck scale. (Except in certain speculative scenarios, like if we had some large extra dimension and the effective Planck scale we observe was much larger than the fundamental Planck scale, but there is no experimental evidence for this scenarios). Indeed, from a purely experimental point of view, we don't even really need the effective field theory of gravity -- given all observations to date, we might as well just treat general relativity purely classically!

So, at least until someone thinks of a clever way to test quantum gravity, the problem is purely theoretical. We know it should be possible to UV complete gravity, so the question is, how?

There are also interesting open problems that a quantum theory of gravity would presumably help us solve -- although, again, the problems and solutions are mostly theoretical, at least with current understanding and technology. These are things like: what happens at the singularity of a black hole, what happened at the Big Bang singularity, what happens on time scales shorter than a Planck time, what resolves the information paradox, what happened before inflation, etc.

Additionally, there are "spin offs." For example, there are phenomena that have come out of thinking about quantum gravity, like holography, that are interesting to explore in their own right, and may challenge some of our assumptions in normal quantum field theories, like the role of locality. These tools and phenomena may help us understand other areas of physics, like developing new tools to compute S-matrix elements, or (speculatively) applying AdS-CFT to particle physics or condensed matter.

Answer 2

It's true that we don't have a correct UV completion of gravity. But we don't have a correct UV completion of the Standard Model either. So why are we complaining about no UV completion for gravity as if it's a more serious issue for gravity than for SM?

The whole hype of "gravity incompatible with quantum theory" is just absurd. If we regard UV completion as THE criteria for quantum compatibility, then both gravity and our cherished Standard Model are incompatible with quantum theory. It's an obviously absurd conclusion.

Note that according to the modern Effective Field Theory (EFT) approach there's nothing fundamentally wrong with quantum gravity within its low-energy regime of validity. Gravity coupling has negative mass dimension, which seems like an issue for the conventional renormalization procedure. However, in the modern EFT/Wilsonian RG point of view, coupling with negative dimension is perfectly allowable. QG is renormalizable as well: you just have to carefully absorb divergences into higher order Lagrangian terms. See e.g. this paper, which gives a very accurate formula (eq. 20) for the quantum corrections to the Newton potential between two masses at low energies. For more details of QG renormalization, see Section 4 of the paper referenced above. And also see a related post for more explanation.

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Based on conversation with @Andrew, I added below notes on why the Standard Model is NOT UV complete:

One might argue that unlike gravity "it's conceivable the Standard Model actually does just make sense to arbitrarily high energies". This point of view is something we can theoretically entertain on the paper. However, Mother Nature has the final say. There are plenty hints that SM is not UV complete at the energy level of See-Saw scale (manifested by the tiny effective mass of neutrinos) or GUT scale. Since these scales are lower than the Planck scale, these sorts of UV incompleteness issues of SM are not necessarily related to unifying with gravity.

Currently at CERN, a slew of experiments are commissioned to detect non-renormalizable mass-dimension 6 or higher non-SM Lagrangian terms based on the widely accepted premise that SM in its current form is not a UV complete theory.

If neither SM nor gravity is UV complete, why do folks in the physics community make a fuss about the lack of UV completion for gravity as if it's a more serious issue than the lack of UV completion for SM?