Steven Weinberg offers a way to explain inflation

Haelfix

The question of whether or not a blackhole decays to a remnant or something like that is besides the point, why are we even talking about this??? I just read the Bonnano-Reuter paper, and it says nothing about high energy quantum collisions, only that when the mass of the blackhole is very low (after the Hawking radiation evaporates away most of the mass of the hole) that it turns off.. Quite on the contrary, it seems to agree with the relatively pedestrian notion that a black hole forms when the mass M is large enough (and you can arrange for collisions off arbitrarily high energy in this little thought experiment, makign the shock waves as big as you want, even making an astrophysical sized one if you want) and that indeed it remains more or less classical in that regime.

And there the scaling argument comes into play, b/c a local conformal quantum field theory cannot satisfy an area law.

If on the other hand, blackholes do not form in the AS scenario at high energies (which I think none of the AS authors claim), then that indeed makes the point off the paper and you are back to trying to show which of the generic assumptions fail in the AD arguments. For instance, why the 1 graviton exchange eikonal regime ceases to be well described semiclassically and why it doesn't dominate the density of states.

atyy

Yes, I agree. Let me just paraphrase to see if I got what you are saying right: AD is a general argument goimg back to Bekenstein that suggests if AS works, then something interesting is happening maybe with the dimensionality or with asymptotically dS space. The Bonanno and Reuter papers don't address AD and are about something else.

Finbar

Let me try and explain the situation for high energy scattering and black holes in AS.

Classically when I have a energy E>>M_p located in a region of radius R<2GE a black hole will form. Where M_p is the Planck mass G is Newtons constant. But as E>>M_p we also have R_s>>l_p the Planck length where R_s is the radius of the black hole. So here we can neglect quantum gravity effects at the horizon and throughout most of the spacetime apart from at the singularity. So the semi-classical approximation is still valid.

The Black hole will then evaporate and the semi-classical approximation will break down once the energy E of the black hole falls to the Planck scale E~M_p. Here AS predicts that a remnant forms which stops the black hole from evaporating further.

On the other hand if we take if we begin with an energy E~M_p in a region R<2GE, where the curvature will be Planckian, we already cannot trust classical physics and AS predicts a black hole will not form.

I think a key point here is when we have to worry about QG effects. Note that it is not when E>>M_p but when the density~ E/R^3 is high this follows from the Einstein equations that relate the strength of the gravitational field with the energy density. If R~2GE then density ~ 1/E^2 so the smaller the black hole mass the more we need to worry about QG effects.

Another consequence of the density~1/E^2 is that it is indeed very "easy" to create black holes with a large energy who's formation can be described with classical physics.

marcus

The discussion has not been limited to black holes forming remnants. Bonanno's recent paper argues that BH simply do not form below a certain critical mass. This does not have to do with evaporation. But evaporation and remnants are also discussed in the same paper.I'm skeptical when I hear talk of imparting transplanckian energies to two particles and having them collide and form a black hole. It's speculative and has no clear connection with Weinberg's paper.

atyy

Isn't AD limited to the case where E>>M_p? For example, Tong's notes say "Firstly, there is a key difference between Fermi’s theory of the weak interaction and gravity. Fermi’s theory was unable to provide predictions for any scattering process at energies above sqrt(1/GF). In contrast, if we scatter two objects at extremely high energies in gravity — say, at energies E ≫ Mpl — then we know exactly what will happen: we form a big black hole. We don’t need quantum gravity to tell us this. Classical general relativity is sufficient. If we restrict attention to scattering, the crisis of non-renormalizability is not problematic at ultra-high energies. It’s troublesome only within a window of energies around the Planck scale." http://www.damtp.cam.ac.uk/user/tong/string/string.pdf

So it's that case which leads to the information paradox and the suggestion that maybe gravity cannot be a local quantum field theory unless something interesting happens.

Finbar

This is exactly my point "...the crisis of non-renormalizability is not problematic at ultra-energies" when E>>Mpl gravity the black holes are large and described by gravity in the IR. "It's troublesome only within a window of energies around the Planck scale".

AD is the assumption that gravity is not AS and hence gravity is not sufficiently strong to disallow black holes with a radius r<<lpl.


The information paradox is a different problem and AS still needs to deal with it. Personally I don't think the remnant picture is good enough if one assumes all the information is stored in the remnant and doesn't get out some how.

marcus

I strongly agree. If there are any problems that are ready for us to confront they are on the way to Planck scale. This is the perspective that Nicolai adopted at the Planck scale conference. At Planck scale some new physics is expected to take over, his program is, if possible, to get all the way to Planck scale with minimal new machinery and have the theory testable.

And this range E < E_Planck is exactly where Bonanno's assertion applies. It is also where Roy Maartens and Martin Bojowald found, in 2005, that black holes could not form (given the Loop context).

We may in fact not have a problem. The sheer existence of black holes of less than Planck mass is questionable. There is no evidence that they exist, and there are analytical results to the contrary.

I agree strongly again. I'm glad you made these points.

atyy

OK, looks like we all agree on the physics heuristics but maybe not the names of various hypotheses.

atyy

They use a particle physicist thing called the "background field method". You pick a background, but the background is arbitrary. Take a look at http://arxiv.org/abs/0910.5167's discussion beginning before Eq 56 "We can write g=background+h. It is not implied that h is small." up to Eq 59 "Also the cutoff term is written in terms of the background metric ... where is some differential operator constructed with the background metric."

AS is basically not very rigourous (Rivasseau complained about this in a footnote in his GFT renormalization paper) and kinda hopeful, but my impression is that it's often that way in condensed matter. For example in Kardar's exposition at some point he says (I'm doing very free paraphrase) well, how do we know there's not non-perturbative fixed points - we don't, but luckily we can do experiments and they even more luckily match our perturbative calculations! He also says there are several different coarse -graining schemes which actually no one has proven are mathematically equivalent, but they all seem to match experiment, so we live in blissful ignorance! In condensed matter the predictions are "universal", so for example the critical temperature is different for all sorts of materials and the theory cannot predict the temperature - what it gets right is the critical exponent which seems to be independent of material and dependent only on symmetries and dimensionality. So I guess Weinberg and co are hoping for some such generic predictions.

Finbar

Just a note on possible confusion. When one says "high energy" in gravity it can be confused for "low energy" and vice versa. The reason is the following: Newton's constant is dimensionful. It has mass dimension [G]=-2 such that when I write GM this is a length or an inverse mass [GM]=[G]+[M] =-2+1=-1.

One consequence of this is the strange property of black holes that when I increase there mass their temperature drops T=1/(8 pi G M) i.e. they have a negative specific heat.

Other consequences of [G]=-2 are that the entropy of a black hole goes as the S=area/(4G) since G is the Planck area and the infamous power counting non-renormalizability of general relativity.

atyy

Does AS really need a fixed point? Could it live with, say, a limit cycle?

Finbar

If you use the back ground field method rigorously then (slightly paradoxically) you actually ensure background independence. In a sense you quantizing the fields on all backgrounds at the same time. Up until recently however it has not been done rigorously enough though.

The relevant paper is
http://arxiv.org/pdf/0907.2617

Also checkout

Frank Saueressig's talk at perimeter.

Haelfix

I agree with most of what you just said (some technical quibbles aside), which is why i'm now very confused about what we are arguing about. B/c thats exactly what asymptotic darkness says. At transplanckian center of mass energy densities, as you go further and further into the UV you expect larger and larger blackholes to form, which by the above argument implies that you are getting closer and closer to classical GR and QG becomes less and less relevant. Its immaterial what happens at the Planck scale (or say within an order or two thereof). No one knows exactly what goes on there, its only at much smaller energies, or conversely at much larger energies where we enter regimes that we can actually calculate in.

marcus

I think that's a good way to put it. IMO the reason for strong interest in the research community in what physics might be like in the range from say 10⁹ TeV up to 10¹⁶ TeV, is because of interest in high-energy astrophysics and the early universe.

The paradigm of colliding two particles at higher and higher energy, and equating that with physics, has become less interesting. It's a mental rut (almost an obsession) left over from the accelerator era. For example Weinberg was talking about inflation, which is a different business.

Different concepts, and different sources of data, come into play.

You could say that the range 10⁹ TeV up to 10¹⁶ TeV is the range from just over "cosmic ray" energy up to "early universe" energy.

A billion TeV is kind of approximate upper bound on cosmic ray energies. It's quite rare to detect cosmic rays above that level. And 10¹⁶ TeV is the Planck energy.

I would say this is a new erogenous zone for theoretical physics. The putative "GUT" scale, of a trillion-plus TeV, comes in there. But it impressed me that in Nicolai's new model there is no new physics at GUT scale. What Nicolai and Meissner have done is project a model which

*is falsifiable by LHC (once it gets going) and
*is conceptually economical, even minimalistic---based on existing standard model concepts,
*pushes the breakdown/blow-up points out past Planck scale, so it
*delays the need for fundamentally new physics until Planck scale is reached.

Whether Nicolai and Meissner's model is correct is not the issue here. What this example suggests is that this kind of conservative unflamboyant goal, this kind of unBaroque proposed solution, will IMO likely become fashionable among theorists. You could think of it as a reaction to past excesses, or a corrective swing of the pendulum.

This same economical or conservative spirit is the essence of what Weinberg is doing.
The new paper of his that we are discussing simply carries through on what he was talking about in his 6 July CERN lecture, where he said he didn't want to discourage anyone from continuing string research, but string theory might not be needed, might not be how the world is. How the world is, he said, might be described by (asymptotic safe) gravity and "good old" quantum field theory.

I assume that means describing the world pragmatically out to Planck scale (10¹⁶ TeV) so you cover the early universe. An important part of the world! And not worrying about whatever new physics might then kick in, if any does.
It's a modest and practical agenda, just getting that far, compared with worrying about putative seamonsters and dragons out beyond planck energy. But of course that's fun and all to the good as well.

================================
In case anyone new is reading this thread, here is a link to video of Weinberg's 6 July CERN talk:
http://cdsweb.cern.ch/record/1188567/
It gives an intelligent overview of what this paper is about, where it fits into the big picture, and what motivates the Asymptotic Safe QG program (which he describes in the last 12 minutes of the video).

As a leading example of extending known and testable physics out to Planck scale, here is Nicolai's June 2009 talk:
http://www.ift.uni.wroc.pl/~rdurka/p...=1.3%20Nicolai
Here's the index to all the videos from the Planck Scale conference
http://www.ift.uni.wroc.pl/~rdurka/p...ndex-video.php

Finbar

Ok so we're getting somewhere. The problem is exactly the one I was pointing out in my post yesterday...

"Just a note on possible confusion. When one says "high energy" in gravity it can be confused for "low energy" and vice versa. The reason is the following: Newton's constant is dimensionful. It has mass dimension [G]=-2 such that when I write GM this is a length or an inverse mass [GM]=[G]+[M] =-2+1=-1. "

So for the argument about the non-renormalizability of gravity based on its scaling in the UV to be valid the "Asymptotic" in Asymptotic darkness and needs to be the same as the Asymptotic in Asymptotic safety. The reason it is false is because they are not for exactly the reason above.

If I have a large mass black hole M>>Mpl then r=2GM is large r>>lpl. This is what the "Asymptotic" in AD refers to and as you say you get closer and closer to classical GR. But the "Asymptotic" in AS refers to exactly the opposite limit that is when k>>Mpl where k=1/r this is where we are very far from classical GR and hence where we need a full theory of QG to answer any questions appropriately.

This is exactly the point David Tong is making

""Firstly, there is a key difference between Fermi’s theory of the weak interaction and gravity. Fermi’s theory was unable to provide predictions for any scattering process at energies above sqrt(1/GF). In contrast, if we scatter two objects at extremely high energies in gravity — say, at energies E ≫ Mpl — then we know exactly what will happen: we form a big black hole. We don’t need quantum gravity to tell us this. Classical general relativity is sufficient. If we restrict attention to scattering, the crisis of non-renormalizability is not problematic at ultra-high energies. It’s troublesome only within a window of energies around the Planck scale.""

So you see its not the AD scenario that I'm arguing about. Its that AD(an IR property of classical gravity) has any baring on AS/renormalizablity(which is a UV problem of quantum gravity).

marcus

I was surprised anyone would bring up AD in this context. It seems like a red herring. Just distracts from considering the main burden of what Weinberg is doing.

Could it be that some people want to deny or dismiss the significance of AS suddenly coming to the forefront? It seems to me when something like this happens----greatly increased research, first ever AS conference, possible alliance with CDT and even Horava, connection with cosmology revealed---that the appropriate thing to do is to pay attention, and focus on it, not try to dismiss (especially not by handwaving about transplanckian black holes )

Haelfix, could you have been misled by someone with a vested interest that felt threatened by Weinberg's CERN talk, or recent paper, and is grasping at straws? or just blowing smoke? Be careful, maybe a bit more skeptical?

atyy

If AD suggests that gravity cannot be described by a "normal" local quantum field theory even at IR, then it suggests that AS may be wrong - only suggests, since Wilsonian renormalization indicates AS is a logical possibility - but in which case an interesting issue is in what way AS is not a "normal" local quantum field theory, even though the heuristic behind AS is that it is a "normal" local quantum field theory.

One thing I don't understand is that Weinberg's paper (the one being discussed in this thread) starts with the most general generally covariant Lagrangian (http://arxiv.org/abs/0911.3165) - but Krasnov has recently proposed an even more general generally covariant Lagrangian (http://arxiv.org/abs/0910.4028 ) - so presumably Weinberg's is less general - is that because Weinberg admits only local terms, while Krasnov's contains non-local terms? Usually renormalization flows don't generate non-local terms, I think, and naively I would expect the same for AS, but is that true?

Edit: Krasnov says his terms are all local - so what is the difference between his stuff and AS?

Litim's http://arxiv.org/abs/0810.3675 says "A Wilsonian effective action for gravity should contain ... possibly, non-local operators in the metric field." So I guess non-local terms can come about through coarse-graining, which is not intuitive to me - can someone explain? Also what are these terms, and did Weinberg include these?

Edit: As far as I can tell, Weinberg, as well as Codello et al, only included local (or quasilocal) terms. So what are these non-local terms Litim is talking about, and why would they arise?