No, there is no quantum theory of gravity & QFT doesn’t include gravity at all. The best you can do is add gravitational effects as an after-thought, but the things you might analyse with the full QFT are generally far too small & short lived for gravitational effects to matter anyway.
The extent to which these are complete, consistent, natural (in the fine-tuning sense), and so forth is debatable but these are certainly existing examples of quantum theories of gravity, and indeed the first is a perfectly reasonable Effective Field Theory that people work in regularly.
> QFT doesn’t include gravity at all
I think you mean "The Standard Model of Particle Physics", which is a quantum field theory (as is e.g. perturbative quantum gravity).
> the things you might analyse with the full QFT
Atoms and molecules have gravitational fields; when you send one through a double slit, which way does their gravitational field go?
A quantum theory of gravity is needed to answer that.
Assemble a huge number of particles in superposition with 1/(sqrt 2) (|M @ a> + |M @ b>), with a & b separated. A quantum theory of gravity is needed to describe the gravitational influence of M on a small test object (General Relativity's answer is just wrong :( ).
I’m not sure I believe that a mathematical formalism that is unable to make useful real world predictions deserves the “theory” moniker. Hence your list of quantum theories of gravity aren’t.
But perhaps that’s me being picky :)
> I think you mean "The Standard Model of Particle Physics", which is a quantum field theory (as is e.g. perturbative quantum gravity).
Sure: I was just quoting the parent comment & using the term informally to stand in for the mouthful that is TSMoPP.
(I’d love to see an experimental setup that was capable of detecting the gravitational field of a single molecule: that would be impressive!)
> I’m not sure I believe that a mathematical formalism that is unable to make useful real world predictions deserves the “theory” moniker. Hence your list of quantum theories of gravity aren’t.
On the contrary, the ones I listed are all completely in accord with General Relativity up to strong gravity and absent superposed sources, which is found from studying the renormalization group flow of perturbative quantum gravity and is four loops of gravitons in a 3+1 dimensional spacetime. Strong gravity can only be found very close to the singularity of black holes (and well inside event horizons, except at the final evaporation), or in the very early universe. So we're good for neutron stars, and have no problems studying things around the event horizons of astrophysical black holes.
The only new mathematical formalism in perturbative quantum gravity is renormalization, and that goes back to the 1980s. Perturbative quantum gravity itself comes from the 1990s.
Sean Carroll has a good explanation of renormalization and effective field theory here:
Asymptotically safe gravity posits an ultraviolet fixed point at which one can take a finite number of measurements, producing a strong gravity completion that perturbative renormalzation cannot; this is prompted by asymptotic safety in QCD. Below that limit, ASG completely matches perturbative quantum gravity, and so in the EFT limit it's the same as General Relativity.
There are five or six of other viable families of quantum theories of gravity, where viability means they accord exactly with perturbatively quantized General Relativity in its effective field limit, and thus agree completely with GR in the classical limit and weak gravity, and additionally are candidates as fundamental theories because they do not rely on perturbative renormalization by power counting and thus are expected to be useful to arbitrarily high energies.
Additionally it is not wildly irresponsible to think that mathematical research (perhaps not driven by physics!) will produce a tractable renormalization that does not require nature to select a convenient effect to suppress the explosion of parameters at high energies.
> I’d love to see an experimental setup that was capable of detecting the gravitational field of a single molecule: that would be impressive!
Everyone would. We're down below milligrams and yoctoNewtons:
I'm not as au fait about how the other side of the tunnel is approaching the ultimate meeting point, but it's not unreasonable to think of nanogram masses in superposition. Experiments were only at thousands of atomic mass units a few years ago, though: https://arxiv.org/abs/1310.8343
Unfortunately General Relativity can only have the whole gravitational influence of these molecules go through one or the other slits. However all of the quantum theories in my previous message have the distribution of the gravitational influence follow distribution of the matter, as one would expect.
which is reasonably accessible and high-level in a way that's hard to find for asymptotically safe gravity (which is unsurprising given that renormalization group flow is a bit abstruse).
If one can extract practical comparisons between a pair of mathematical formalisms, and map those to differences in observables, I think that qualifies both as physical theories. Between ASG and string theory (with some assumptions about how to get the latter out of the AdS box and ignoring the landscape problem) there are noteworthy differences that are likely to manifest in the detailed accounting of accretion disks around astrophysical black holes. QG phenomenologists (who are sadly rare) are professionally interested in extracting such comparisons among various theories with a view to distinguishing them observationally or experimentally.
Annoyingly, experimental evidence can be hard to come by because any viable mathematical formalism has to reproduce the successes of GR, and it is shockingly easy to depart from GR in a serious way even in very weak gravity.
ASG's main anti-features are that it's not in itself a fundamental ToE; what it would accomplish (if it holds up) is getting the gravity part right to Planck scales and avoiding the incompatibility with QFT. Who knows what beyond-the-Standard-Model physics outside the gravitational sector will look like at those scales?
ASG is not alone in this, though.
String theory, on the other hand, would let gravity and matter emerge from something like a field of strings resembling dark energy, where cooling increases the apparent volume of the cosmological frame at a given scale factor. Slow thermalization in turn produces everything else, like dark matter, baryons, light, and so on.
There are other less popular theories from which matter
and spacetime geometry emerge, too.
And of course it goes the other way around too, where matter theories can arise from geometry (Cartan torsion is still viable, and Poplawski still tries to get people to pick up Riemann-Cartan geometry; and quantum geometrodynamics remains viable too).
> We live in amazing times
The amazing thing is that collaboration, simulation, and publication is hugely improved upon even a couple of decades ago. If in the early 1900s people had WWW and message boards, email and message boards, LaTeX, ArXiv, and so forth, who knows what might have been different given the big brains around at the time !
In richer countries we have relative peace, antibiotics and sanitation. Feynman's wife died of TB while he was working on the Manhattan project; that's the trifecta there, just once removed from a theoretical physicist. Henry Moseley was shot through the head on the battlefield at Gallipoli. Many other scientists had their work seriously disrupted during both world wars and during cold war repressions (Sakharov on the one hand, Condon on the other; the former got it much worse of course).
> If one can extract practical comparisons between a pair of mathematical formalisms, and map those to differences in observables, I think that qualifies both as physical theories.
That’s fair. I wasn’t aware that anyone had managed to make any potentially observable predictions at this point, so thanks for updating me on that.
(As an observer from the sidelines of physics I’ve always had a fondness for Loop Quantum Gravity / Spin Foams over String Theory(ies) personally, but not for any particularly deep reason that I can point to as justification.)
