waterfall said:
atyy said:
The big problem is gravity which is perturbatively not UV renormalizable. The Wilson-Kadanoff picture of renormalization as a way of seeing how a theory looks like at low energies points to two different approaches. The first is that the theory is incomplete, and new degrees of freedom enter - this is the approach of string theory. The second is that the theory could be UV complete if the renormalization flow is non-perturbatively reversed to high energies - this approach is called Asymptotic Safety.
I'm trying to find the connection between Renormalization Group and the Final Theory that can explain the RG being based on effective field theory. The above doesn't mention about Loop Quantum Gravity, just string theory and Asymptotic Safety. If Loop Quantum Gravity were proven to approximate classical GR. Won't it explain or complete why the Renormalization Group is only an effective field theory.. I wonder why you didn't include LQG above.
Waterfall, I'm glad to see your friend Bill Hobba has joined us. He seems experienced careful and well-informed. Belated welcome, Bill!
I think I see what you are driving at (the unaccustomed use of some technical terms doesn't bother me in this case as long as the intuition comes thru.) I think there is a kernel of insight.
The RG-based approach (Asym. Safety) might be limited in its ability to resolve certain classical singularities and nevertheless it might be nearly right---effectively right within certain limits.
Let's imagine, just for the sake of illustration, that AS works as long as the underlying manifold which it requires is not going to develop singularities or defects---a topological condition. AS requires you to set out some prior metric on the smooth manifold you plan to be working with, for starters, so that scale can be defined in the first place. then it has some key numbers change with scale and run to a happy conclusion. But in its present form AS seems to be having trouble resolving the big bang singularity.
We can't use the word "effective" because that word is owned by people who do conventional perturbation theory--a type of math where you have a long series of numbers describing a blip on a flat background, and stuff like that. Each number is calculated according to its own elaborate formula and a theory is "effective" if you can just consider the low energy terms and it works OK.
We don't want to offend these gentlemen, so we need a new word like, say, "
quasi-excellent"
to describe what Asymptotic Safety might achieve. It might be effectively successful as a basis for quantizing gravity EXCEPT for not resolving the big bang singularity.
Because of the breakdown of conventional topology itself or some damn reason like that, so what's a poor theory supposed to do? if it's defined on a smooth manifold model continuum. It is effectively right except it doesn't quite make it where the basic topological or else smoothness assumption breaks down. So we call it "quasi-excellent"
I'm only half serious here, trying to imagine what you are driving at, by attempting a speculative illustration of what might be.
So then you say (to generalize a bit) suppose SOME quantum theory of geometry, Loop or some other, turns out to reproduce Gen Rel.
Then (I hear you reasoning) since Gen Rel is asymptotically safe, then that QG theory, Loop say, must be asymptotically safe. So it would be not only quasi-excellent, it would also resolve the singularity, so it would be fully excellent. It would complete the picture, geometry-wise.
And then you'd have to see if you could build satisfactory matter-fields on it.
It could be very convenient if Loop or some such QG turned out to underly and complete AS, then one could use AS, which is continuum-based and has a conventional manifold, all the way back in time to very near start of expansion and then seamlessly shift theoretical gears and continue on. But that's just speculation. People are only just getting started implementing RG-type stuff in Loop. Maybe some other related QG (like Oriti GFT or Livine's approach) is farther along. I don't have a complete picture, by far.
One extremely nice thing is the recent Cai Easson paper indicating that AS could give inflation "for free" just by the running of the couplings and without a made-up "inflaton" field having to be added on and finetuned. This is the nicest thing I've seen this year. Maybe someone will tell me why it doesn't work.
To me this makes it seem almost imperative that Loop should embrace and encompass AS, to acquire that yummy feature.
Anyway waterfall, I see sense in your post, rebounding off of the Atyy post you copied. IMO there's a valuable kernel of insight.
.
